Therefore , the solution of the given problem of triangle comes out to be and MB or x = √106.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
Here,
Given : A right triangle ,
=> 2√53 = BH
=> MH = √106
∠m / ∠MHB = 45°
Using Pythagoras theorem :
=> ( 2√53)² = (√106)² + x²
=> 4 * 53 - 106 = x²
=> x² = 212 -106
=> x = √106
Therefore , the solution of the given problem of triangle comes out to be
and MB or x = √106.
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A statistician chooses 27 randomly selected dates, and when examining the occupancy records of a particular motel for those dates, finds a standard deviation of 5. 86 rooms rented. If the number of rooms rented is normally distributed, find the 95% confidence interval for the population standard deviation of the number of rooms rented.
The 95% confidence interval for the population standard deviation of the number of rooms rented would be (4.82, 7.90).
1. Calculate sample standard deviation: 5.86 rooms
2. Calculate the degrees of freedom: 26
3. Calculate the t-critical value using the t-distribution table with a 95% confidence level and 26 degrees of freedom: 2.056
4. Calculate the margin of error: t-critical value x sample standard deviation/square root of sample size: 2.056 x 5.86/√27 = 1.08
5. Calculate the confidence interval: sample standard deviation +/- margin of error: 5.86 +/- 1.08 = (4.82, 7.90)
The 95% confidence interval for the population standard deviation of the number of rooms rented would be (4.82, 7.90).
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
1) The radius of the circle is 3 units.
2) The center of the circle lies on the x-axis.
5) The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Step-by-step explanation:
[tex]x^2+y^2-2x-8=0\\x^2-2x-8+y^2=0\\x^2-2x-8+9+y^2=0+9\\x^2-2x+1+y^2=9\\(x-1)^2+y^2=9[/tex]
By completing the square, we can see that the circle has its center at (1,0) and that its radius is 3 units. Thus, the 1st, 2nd, and 5th answers are all true.
a local lighthouse is 170ft tall. During a visit to the lighthouse, Tommy who is 5ft tall, cast a shadow that is 1.8ft long. How long in ft is the lighthouse shadow
The length of the lighthouse shadow is: 61.2 ft
______________________________________
To find the length of the lighthouse shadow given similar triangles, solve a proportion with corresponding sides.
Let's follow these steps:
Draw a diagram to understand the question (see picture).Write the pairs of corresponding sides from similar triangles.Write and solve a proportion.Similar TrianglesIn the diagram, LH is the lighthouse. TY is Tommy. HE is the lighthouse shadow. YE is Tommy's shadow. Notice that the green triangle, ΔTYE, fits onto the larger triangle, ΔLHE.
Using AA similarity, we know that the two triangles in the diagram are similar. To say the triangles are similar, write: ΔLHE ~ ΔTYE
ProportionalitySimilar triangles have proportionate sides. This means that the length of corresponding sides will be longer or shorter by the same multiplication factor, which we can write as K.
Our pairs of corresponding sides are:
LH ~ TYHE ~ YELE ~ TECorresponding sides are related to each other by the multiplication factor, K:
LH ÷ TY = KHE ÷ YE = KLE ÷ TE = KThis makes any pair of corresponding sides written as a fraction equal to each other. Thus, we can write a proportion using these pairs.
Write a proportionWe should choose two pairs of corresponding sides to write a proportion from:
a pair that we know both lengthsa pair that includes 'HE' (the lighthouse shadow)[tex]\displaystyle { \frac{LH}{TY} = \frac{HE}{YE} }[/tex]
Note that this works because: [tex]\displaystyle { K = \frac{LH}{TY} = \frac{HE}{YE} }[/tex]
Solve for the missing side[tex]\displaystyle { \frac{LH}{TY} = \frac{HE}{YE} }[/tex] Write the proportion.
[tex]\displaystyle { \frac{170}{5} = \frac{HE}{1.8} }[/tex] Substitute known lengths.
[tex]\displaystyle { 34= \frac{HE}{1.8} }[/tex] Simplify. Now, isolate HE.
[tex]\displaystyle { 34*1.8 = \frac{HE}{1.8}*1.8}[/tex] Multiply both sides by 1.8.
[tex]\displaystyle { 34*1.8= HE}[/tex] 1.8 cancels out on the right side.
[tex]\displaystyle { HE = 34*1.8}[/tex] Keep the missing variable on the left side.
[tex]HE = 61.2[/tex] Solved for HE.
Remember to write the final answer with units.
Therefore, the lighthouse shadow is 61.2 ft long.
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3-
You are given a baseball card as a gift, and over the next 9 years, it
follows the polynomial function of f(x) = x³-13x² + 40x + 15 to
determine its value. Sketch a graph of the function over the range of
the 9 years.
a. What is the card's starting value?
b. When does it reach its maximum value, and what value is that?
c. When does it reach its minimum value, and what value is that?
d. How much is it worth at the end of the 9 year period?
The graph of the given polynomial function representing a baseball card is shown.
What is a polynomial function?A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial and trinomial, etc. ax+b is a polynomial.
here,
Graph of the polynomial function of f(x) = x³-13x² + 40x + 15, is shown,
From the graph,
a.
The card's starting value is 15.
b.
It reaches it maximum value when x is 2 and 9, the value at that point is 51.
c. It reaches it minimum value when x is 6.67, the value at that point is 0.
d.
As shown in the graph at the end worth of the card is 51.
Thus, the graph of the given polynomial function representing a baseball card is shown.
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I need help solving this math problem.
Help me find was X is please
Answer:
40
Step-by-step explanation:
Using the alternate exterior angles theorem,
[tex]4x-30=3x+10 \\ \\ x-30=10 \\ \\ x=40[/tex]
find the equation of the line in slope-intercept form that passes through 4,-7 and is perpendicular to y=1/8x-2
Answer:
y + 11 = -8(x - 9)
y + 11 = -8x + 72
y = -8x + 61
Step-by-step explanation:
Answer:
open document
Ahmed asked 28 friends if they had texted (T) or
emailed (E) that day. The number who had only
texted was the same as the number who had done
both. The number who had only emailed was two
less than the number who had done both. The
number who had neither texted nor emailed was
twice the number who had done both.
Work out P(E' U T).
Work out P(En T').
Answer:
To find P(E' U T), we need to find the probability that a randomly selected person from Ahmed's friends either only texted or did both.
To find P(En T'), we need to find the probability that a randomly selected person from Ahmed's friends neither texted nor emailed.
To solve these problems, we need to know more information about Ahmed's friends, such as how many of them texted, emailed, or did both. Without this information, it is not possible to find P(E' U T) or P(En T').
is it right?
Solve the absolute value equation −|x − 2| + 3 = 0.
Answer:
x = - 1 , x = 5
Step-by-step explanation:
- | x - 2 | + 3 = 0 ( subtract 3 from both sides )
- | x - 2 | = - 3 ( divide both sides by - 1 )
| x - 2 | = 3
the absolute value always gives a positive value, however, the expression inside the bars can be positive or negative, then
x - 2 = 3 or - (x - 2) = 3 ( solve both equations )
x - 2 = 3 ( add 2 to both sides )
x = 5
or
- (x - 2) = 3
- x + 2 = 3 ( subtract 2 from both sides )
- x = 1 ( multiply both sides by - 1 )
x = - 1
As a check
substitute these values into the equation and if both sides are equal then it is a solution.
x = - 1
left side = - | - 1 - 2 | + 3 = - | - 3 | + 3 = - | 3 | + 3 = - 3 + 3 = 0 = right side
x = 5
left side = - | 5 - 2 | + 3 = - | 3 | + 3 = - 3 + 3 = 0 = right side
solutions are x = - 1 , x = 5
To get the next term multiply the previous term by 7 first term =5
The order is 5 (first term), 35 (second term), and 245 (third term), according to the equation get the next term by multiplying the previous term by 7 (first term).
what is sequence ?A collection of numbers, or "terms," is referred to as a sequence. Examples of terms include 2, 5, and 8. Some sequences can be made endlessly long by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the series. There are formulas that demonstrate where to look for words within a sequence. A collection of objects that are in some order is known as a sequence in mathematics (or events). It resembles a set in that it has pieces (also called elements or terms). The total, perhaps infinite number of ordered objects are referred to as the sequence's length. the act of placing two or more objects in a logical order
given
first term = 5
third term = 35 * 7 = 245
the sequence is 5 , 35 , 245 ........
so an = a(n-1) * 7
The order is 5 (first term), 35 (second term), and 245 (third term), according to the equation get the next term by multiplying the previous term by 7 (first term).
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A remote control car costs $60. Its is reduced to $45 in the sale. By what percentage was the price reduced
Help! My teacher never taught me this and gave it to me for what ever reason. Questions 6-11. (Middle school)
Answer:
6. 12cm
7. 11.2 cm
8. 92 degrees
9. 53 degrees
10. 37.5 cm
11. $ 693.12
Step-by-step explanation:
For questions 6-9 the triangle is congurent which means both their angles will be equal.
For the sides you can see that the second triangle is 1.5 times smaller than the first one as taking one of the sides 21/14= 1.5
So for Q. 6 we can multiply side PQ by 1.5.
For Q.7 divide CA by 1.5.
For Q. 10 we can do cross multiplication:
5/4 = x/30
= 150= 4x
= 37.5=x
For Q 11 we can see the size of the paper is 1.9 times bigger than the original one (38/20)
So the shorter side is 30.4 cm.
Then we have to find the area of the paper to multiply the two dimensions and we get 1155.2 square inches.
Then to figure out the money we multiply again and we get $693.12.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The inequalities' solutions are -6x + 15 10 - 5x, and at 5 there is an open circle. A bold line begins at 5 and points to the right.
What are inequality expressions?An algebraic inequality is a mathematical statement that uses the inequality sign to connect an expression to a value, a variable, or another expression.
Given the inequality expression below:
–3(2x – 5) < 5(2 – x)
Expand to have:
-6x + 15 < 10- 5x
-6x + 5x < 10 - 15
-x <-5
x > 5
Hence the solutions to the inequalities are –6x + 15 < 10 – 5x and an open circle is at 5 and a bold line starts at 5 and is pointing to the right.
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Idris, who is 6 feet tall, wants to measure the height of a flagpole. He casts a shadow that is 10
feet long at the same time that the flagpole casts a 85-foot shadow. The flagpole is ___ feet tall.
The height of the flagpole with a shadow cast of 85 feet is 51 feet.
What is the height of the flag pole?Given the data in the question;
Height of Idris = 6 feetLength of Idris's cast shadow = 10 feetLength of the shadow cast of the flag pole = 85 feetHeight of the pole = ?To find the height of the flagpole, we can use the ratio of the flagpole's shadow length to Idris's shadow length, which is equal to the ratio of the flagpole's height to Idris's height.
Hence;
85 feet : 10 feet = flagpole's height : 6 feet
Solve for the flagpole's height by cross-multiplying and simplifying:
Flag pole height × 10 = 85 × 6
Flag pole height × 10 = 510
Flag pole height = 510 / 10
Flag pole height = 51 feet
Therefore, the height of the flagpole is 51 feet.
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You have $4.50. Each piece of candy at the candy store costs $0.15. Write and solve an inequality that represents the number of gum balls you can buy.
Answer:
So in the first case we buy the candy which costs 1 and take candies worth 3 and 4 for free, also you buy candy worth 2 as well. So min cost = 1 + 2 = 3. In the second case we buy the candy which costs 4 and take candies worth 1 and 2 for free, also We buy candy worth 3 as well. So max cost = 3 + 4 = 7.
Step-by-step explanation:
Drag each tile to the correct box.
Using the order of operations, what are the steps for solving this expression?
8 x 3 divided (4 square - 13 ) + 5 square + 4 x 3
Arrange the steps in the order in which they are performed.
↓
↓
↓
↓
↓
↓
↓
The solution to the expression 8 * 3 / (4² - 13) + 5² + 4 * 3 is 45.
How to solve an equationAn equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
8 * 3 / (4² - 13) + 5² + 4 * 3
To solve this question we use PEDMAS. That is parenthesis, then exponents, division, multiplication, addition and subtraction.
First solving the exponents to get:
= 8 * 3 / (16 - 13) + 25 + 4 * 3
Then solving the bracket:
= 8 * 3 / 3 + 25 + 4 * 3
Performing the division:
= 8 * 1 + 25 + 4 * 3
Performing the multiplication:
= 8 + 25 + 12
Performing the addition:
= 45
The solution to the expression is 45.
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When writing a regression equation, which of the following is not a name for the x-variable? Choose the correct answer below. O Independent variable O Explanatory variable Dependent variable
The x-variable is not referred to as the dependent variable when formulating a regression equation.
There are dependent and independent variables in statistical modeling, experimental sciences, and mathematical modeling. Dependent variables are so-called because, during an experiment, their values are assessed under the presumption or requirement that they are dependent on the values of other variables as a result of a certain law or rule (for example, a mathematical function). Independent variables are ones that are not seen as being reliant on any other variables in the context of the experiment in question.
Common independent variables that can be used to forecast include time, space, density, mass, fluid flow rate, and previous values of some observed value of interest (such the size of the human population).
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Tran is making fasnachts (deep-fried German doughnuts) to sell the
Tuesday before Ash Wednesday, her bakery's biggest fasnacht day of
the calendar year. She has 8 pounds of butter and her recipe calls for
1
cup of butter per 2 dozen fasnachts. If 1 pound of butter is 2 cups,
then how many individual fasnacht doughnuts will Tran be able to
make?
Equation A = 384, where Tran has 8 pounds of butter, yields the total number of fasnacht doughnuts.
What is an Equation?Equations are statements in mathematics containing the equals (=) sign flanked on either side by two algebraic expressions. An equation's constituent parts include coefficients, variables, operators, constants, terms, expressions, and the equal to sign. An equation must always begin with the "=" sign and have terms on both sides.
given the data,
Let A represent the total number of fasnacht doughnuts.
The equation will now be
8 pounds of butter are in Tran's possession.
2 cups of butter from 1 pound
8 pounds of butter therefore equal 8 x 2 cups.
16 cups of butter from 8 pounds
Additionally, the recipe calls for 2 dozen fasnachts and 1 cup of butter.
Consequently, 16 cups of butter equal 16 dozen fasnachts.
16 cups of butter equal 32 dozens of fasnachts when the equation is simplified.
Additionally, there are 32 dozens of fasnacht doughnuts in all.
A = 32 x 12 = the total number of fasnacht doughnuts.
A total of 384 fasnacht doughnuts make up the entire batch.
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A trapezoid has an area of 27.5
cm². What is the measure of the
height if the bases measure 7 cm
and 4 cm?
Answer:
The height is 5 cm.
Step-by-step explanation:
a = 1/2([tex]base_{1}[/tex] + [tex]base_{2}[/tex])h
27.5 = 1/2(7+ 4) h
27.5 = 1/2 (11) h
27.5 = 5.5 h Divide both sides by 5.5
5 = h
Answer:
5cm
Step-by-step explanation:
Given ,
A trapezoid has an area of 27.5cm²bases measure 7 cm and 4 cmTo Find : The height of the Trapezoid
In order to find the height of the trapezoid we
[tex]27.5 = \frac{1}{2} X ( 7+4)h[/tex]
[tex]27.5X2 = 11 X h[/tex]
[tex]55 = 11h\\\frac{55}{11}= h\\ 5 = h[/tex]
Hence, the height of the trapezoid is 5cm
A sequence of transformations maps triangle ABC to triangle A’B’C’. The sequence of transformations that maps triangle ABC to triangle A’B’C’ is a reflection across the - y-axis
- x-axis
- line y=x
OR - line y=-x
...followed by a translation
- 4 units to the right and 10 units up
- 8 units to the right and 10 units up
- 10 units to the right and 2 units up
OR - 10 units to the right and 4 units up.
The transformation that maps triangle ABC to A'B'C' is given by :
1. Reflection across is given by option c. y = x line.
2. Translation of triangle ABC is done by option D. 10 units to the right and 4 units to the up.
Figure is attached.
As given in the question,
Transformation of the triangle ABC maps to the triangle A'B'C' is given by:
Reflection of the triangle ABC across the line y = x is given byCoordinate of point C is ( -4 , 2 ) after reflection across the line y = x coordinate changes to ( 2, -4 ).
In translation to C' it changes to ( 12,0) as it translate to 10 units right and 4 units up.Change in x-coordinate is of 10 units right and change in y-coordinates in 4 units up.2 + 10 = 12 x-coordinates, and -4 + 4 = 0 y-coordinate after translation.Therefore, the reflection and translation of the triangle ABC to A'B'C' after transformation is given by :
1. reflection across option C. line y = x.
2. Translation option D. 10 units to the right and 4 units to the up.
The above question is incomplete, the complete question is :
A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC to ∆A′B′C′ is a reflection across the (1.)_____ followed by a translation (2.)_____ .
Answers for (1.)
* y-axis
* x-axis
* Line y = x
* Line y = -x
Answers for (2.)
* 4 units to the right and 10 units up
* 8 units to the right and 4 units up
* 10 unit to the right and 2 units up
* 10 units to the right and 4 unit s up
Required Figure is attached.
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I need the simplified form
6 to the -1st power is 1/6
6 to the -2nd power is 1/36
6 to the -3rd power is 1/216
and 6 to the -4th power is 1/1296
(b) Algebraically show that this product has a
constant value (seen in (a)) regardless of the
value of x.
(x+2)(x-2)-(x+4)(x-4)
The constant value in the polynomial expression is 12
What are the roots of a polynomial expression?The roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero. If a is the root of the polynomial p(x), then p(a) = 0.
Given here, the expression as (x+2)(x-2)-(x+4)(x-4) now using the identity a²-b²=(a+b) (a-b) we get
(x+2)(x-2)-(x+4)(x-4) = x²-4-x²+16
=12
Hence, The constant value in the polynomial expression is 12
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Use elimination to solve each system of equations.
1. x - y = 1
x + y = 3
2. x + y = 1
x + y = 11
3. x + 4y = 11
x - 6y = 11
4. -3 + 3y = 6
x + 3y = 18
The solutions to the systems of linear equations by elimination method are listed below:
Point (x, y) = (2, 1) is a solution of the system of equations. The system of linear equations has no solution. Point (x, y) = (0, 11) is a solution of the system of equations. Point (x, y) = (3, 5) is a solution of the system of equations.How to solve a system of linear of equations by eliminationIn this problem we find four cases of two linear equations with two variables. There are different methods to solve the system, herein we must use elimination method to find the solution to each system of linear equations, which takes advantage of adding / subtracting linear equations and multiplying linear equations by scalars in order to get every solution set.
Case 1
x - y = 1
x + y = 3
First, add the two equations:
(x - y) + (x + y) = 1 + 3
2 · x = 4
x = 2
Second, determine the variable y:
y = 3 - x
y = 3 - 2
y = 1
Point (x, y) = (2, 1) is a solution of the system of equations.
Case 2
x + y = 1
x + y = 11
Subtract the second equation from the first one:
(x + y) - (x + y) = 1 - 11
0 = - 10 (CRASH!)
The system of linear equations has no solution.
Case 3
x + 4 · y = 11
x - 6 · y = 11
First, subtract the second equation from the first equation:
(x + 4 · y) - (x - 6 · y) = 11 - 11
10 · y = 0
y = 0
Second, determine the variable y:
x = 11 + 6 · y
x = 11 + 6 · 0
x = 11 + 0
x = 11
Point (x, y) = (0, 11) is a solution of the system of equations.
Case 4
- 3 · x + 3 · y = 6
x + 3 · y = 18
First, subtract the second equation from the first equation:
(- 3 · x + 3 · y) - (x + 3 · y) = 6 - 18
- 4 · x = - 12
x = 3
Second, determine the variable y:
3 · y = 18 - x
3 · y = 18 - 3
3 · y = 15
y = 5
Point (x, y) = (3, 5) is a solution of the system of equations.
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Round 18.7347 to two decimal places
The value upto two decimal is 18.73.
What is Decimal?A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.
Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number.
Given digit 18.7347
to round off to two decimals
for rounding off we need to check the next digit of digit upto we round
the digit after 3 is 4 which is less than 5 then there is no change in digit,
so 18.73447 = 18.73
Hence the round 18.7347 is 18.73.
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If the original quantity is 12 and the new quantity is 15, what is the percent increase?
The percent increase is 25%.
To calculate the percent increase from an original quantity to a new quantity, we can use the following formula:
percent increase = [(new quantity - original quantity) / original quantity] * 100
In this case, the original quantity is 12 and the new quantity is 15, so the percent increase would be:
percent increase = (15 - 12) / 12 * 100 = 3 / 12 * 100 = 25%.
This means that the new quantity is 25% larger than the original quantity.
Find a given that: a P(2, 3) and Q(a, -1) are 4 units apart b P(-1, 1) and Q(a, -2) are 5 units apart c X(a, a) is √√8 units from the origin d A(0, a) is equidistant from P(3, -3) and Q(-2, 2).
Answer:
To solve this problem, we can use the Pythagorean Theorem to solve for a.
For part (a), we know that P(2, 3) and Q(a, -1) are 4 units apart, so we can use the Pythagorean Theorem to calculate a:
(a - 2)² + (-1 - 3)² = 4²
Solving for a, we get:
a = 7
For part (b), we know that P(-1, 1) and Q(a, -2) are 5 units apart, so we can use the Pythagorean Theorem to calculate a:
(a + 1)² + (-2 - 1)² = 5²
Solving for a, we get:
a = 4
For part (c), we know that X(a, a) is √√8 units from the origin, so we can use the Pythagorean Theorem to calculate a:
a² + a² = 8
Solving for a, we get:
a = 2√2
For part (d), we know that A(0, a) is equidistant from P(3, -3) and Q(-2, 2), so we can use the Pythagorean Theorem to calculate a:
(3 - 0)² + (-3 - a)² = (-2 - 0)² + (2 - a)²
Solving for a, we get:
a = -1
Therefore, the value of a that satisfies all conditions is a = -1.
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Zhiyuan and his family are planning to attend a football game. The time it takes Zhiyuan to get from his house to the football stadium is dependent upon the traffic. If traffic is heavy, he will only average 30 mi/h and he will arrive right on time. If traffic is light, he will average 55 mi/h and arrive 1 hour and 15 minutes early. In miles, what is the distance from Zhiyuan's house to the football stadium? Express your answer as a decimal to the nearest tenth.
The distance from Zhiyuan's house to the football stadium is given by the equation A = 82.5 miles
What is Speed?Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude
Speed = Distance / Time
Given data ,
Let the time taken for Zhiyuan to get from house to stadium be = t hours
Now , the equation will be
Let the total distance from Zhiyuan's house to the football stadium be = D
The speed of Zhiyuan to get from house to stadium without traffic = 30mph
So , Speed s₁ = 30 miles/hour
Speed = Distance / Time
Time t₁ = t hours
So , the distance d₁ = 30t mile
Now , when the traffic is light ,
Speed s₂ = 55 miles/hour
Time t₂ = ( t - 1 1/4 ) hours
On simplifying the equation , we get
Time t₂ = ( t - 5/4 ) hours
Speed = Distance / Time
And , distance d₂ = 55 ( t - 5/4 ) miles
Now , the distance from house to stadium remains constant , so
distance d₁ = distance d₂
Substituting the values in the equation , we get
30t = 55 ( t - 5/4 )
On simplifying the equation , we get
30t = 55t - 55 ( 5/4 )
Subtracting 30t on both sides of the equation , we get
25t - 68.75 = 0
Adding 68.75 on both sides of the equation , we get
25t = 68.75
Divide by 25 on both sides of the equation , we get
t = 2.75 hours
So ,
The distance D = Speed x time
Distance D = 30t
Distance D = 30 x 2.75
Distance D = 82.5 miles
Hence , the distance is 82.5 miles
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3500 dollars is placed in an account with an annual interest rate of 8.75%. to the nearest tenth of a year, how long will it take for the account value to reach 36700 dollars?
It will take approximately 4.3 years for the account value to reach $36,700 with an 8.75% annual interest rate.
1. Calculate the interest rate per period (year):
8.75%
= 0.0875
2. Calculate the number of periods (years) required to reach the desired total:
(36700-3500)/3500
= 10.2857
3. Calculate the final number of years to the nearest tenth of a year: 10.2857/0.0875
= 117.1429 or 4.3 years
To calculate the time it will take for the account value to reach $36,700, we need to first calculate the interest rate per period. In this case, the interest rate is 8.75% per year. This can be converted to a decimal by dividing 8.75 by 100 to get 0.0875. Next, we need to calculate the number of periods (years) required to reach the desired total. To do this, we subtract the initial account value of $3,500 from the desired account value of $36,700 and then divide this difference by the initial account value of $3,500. This gives us 10.2857. Finally, we need to calculate the final number of years to the nearest tenth of a year, which can be done by dividing 10.2857 by 0.0875. This gives us a result of 117.1429, which is equivalent to 4.3 years.
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2 divided by 5 x 4 divided by 3 x 3 - 2 x 20
Answer:
-8
Step-by-step explanation:
in the binomial expansion of ((2/x^2) -5x^5)^n the sixth term contains x^25. Solve for n.
The value of n that makes the sixth term in the expansion contains x²⁵ is n = 5.
What is binomial expansion?
The binomial theorem (or binomial expansion) is a result of expanding the powers of binomials or sums of two terms. The coefficients of the terms in the expansion are the binomial coefficients (kn).
The general term in the binomial expansion of (a + b)ⁿ is given by:
[tex]T(r+1) = (n \, choose \, r) * a^{(n-r)} * b^r[/tex]
where "n choose r" represents the binomial coefficient, which is given by:
(n choose r) = n! / (r! * (n-r)!)
In this case, a = 2/x² and b = -5x⁵. We want to find the value of n such that the sixth term in the expansion contains x²⁵.
To find the term that contains x²⁵, we need to set the exponent of x in the general term equal to 25 and solve for r:
(n-r) = 25
n = r + 25
The exponent of x in the general term is given by:
[tex](2/x^2)^{(n-r)} * (-5x^5)^r = 2^{(n-r)} * (-5)^r * x^{(5r - 2(n-r))}[/tex]
Setting 5r - 2(n-r) = 25, we get:
7r - 2n = 25
We know that the sixth term has r = 5, so we can substitute this into the equation:
7(5) - 2n = 25
35 - 2n = 25
2n = 10
n = 5
Therefore, the value of n that makes the sixth term in the expansion contains x²⁵ is n = 5.
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3(2x+1)+2(x+4) can you pls tell me what the answer is
Answer:
8x+11
Step-by-step explanation:
3(2x+1)+2(x+4)
distribute
3(2x)+3(1)+2(x)+2(4)
6x+3+2x+8
combine like terms
6x+2x+3+8
8x+11
this can't be simplified anymore
hopes this helps
Answer:
[tex] \sf \: 8x + 11 [/tex]
Step-by-step explanation:
Given expression,
→ 3(2x + 1) + 2(x + 4)
Let's simplify the expression,
→ 3(2x + 1) + 2(x + 4)
→ 6x + 3 + 2x + 8
→ (6x + 2x) + (3 + 8)
→ (8x) + (11)
→ 8x + 11
Hence, the answer is 8x + 11.