The hypotenuse of this triangle is equal to 16√5 cm.
What is Pythagorean theorem?In Euclidean geometry, Pythagorean's theorem is given by this mathematical expression:
a² + b² = c²
Where:
c represents the hypotenuse of a right-angled triangle.a represents the adjacent side (shorter leg) of a right-angled triangle.b represents the opposite side (longer leg) of a right-angled triangle.Note: c = 4a
Substituting the given parameters into the Pythagorean's theorem formula, we have the following;
a² + b² = c²
a² + (4√15)² = 4a²
4a² - a² = (4√15)²
3a² = 240
a² = 80
a = 4√5 cm.
For the hypotenuse, we have:
Hypotenuse, c = 4a
Hypotenuse, c = 4(4√5)
Hypotenuse, c = 16√5 cm.
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Answer:
Hypotenuse : 16cm
Shorter leg of triangle: 4cm
Step-by-step explanation:
So, we are told [tex]4\sqrt{15}[/tex] is the longer leg, let's say this is a.
[tex]4\sqrt{15} = \sqrt{240}[/tex], the Pythagorean is [tex]a^2+b^2=c^2[/tex], we'll say b = shortest leg, which is what we're solving for.
Since the hypotenuse (c), is 4 times b I changed it to 4b in my equation.
[tex]\sqrt{240} + b = 4b[/tex], square this to get [tex]240 + b^2 = 16b^2[/tex], -b^2 on both sides
[tex]240=15b^2[/tex], then divide by 15. [tex]16=b^2[/tex], use square root and you get [tex]4 = b[/tex]
hope this helps. btw since hypotenuse is 4 times b, just do 16cm, but your answer is 4 cm
how do i solve this equation with addition and subtraction? please help
Graph the line with slope 1 passing through the point (5, 3)
The line with slope 1 passing through the point (5, 3) is y = x - 2.
What is slope of a line?A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.
The letter m is frequently used to represent slope; the reason for this is unclear, but it is first used in English by O'Brien in 1844, who wrote the equation for a straight line as "y = mx + b," and by Todhunter in 1888,
who wrote it as
y = mx + c
To Graph the line with slope 1 passing through the point (5, 3) we need to find the slope intercept form
The slope formula = y - y₁ = m(x -x₁)
⇒ y - 3 = 1(x -5)
⇒ y = x -5 + 3
⇒ y = x - 2
Now putting the value on graph we get [See attachment]
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David baked two kinds of pasta in pans. Each pan was the same size. One pan was sliced into 8 equal pieces and the other was sliced into 6 equal pieces. If he wanted to have the same number of pieces in each pan, how many pieces would there be in each pan?
Answer: LCM(6,8)
Step-by-step explanation: Each of six slices of the first pasta has the area 1%2F6 of the entire pan.
Each of eight slices of the second pasta has the area 1%2F8 of the original pan.
David will cut each 1%2F6 in 4 equal pieces to get 1%2F24.
he also will cut each 1%2F8 in 3 equal pieces to get 1%2F24.
Then he will meet his goal.
Notice that the number 24 is the Less Common Multiple of the numbers 6 and 8: 24 = LCM(6,8).
Answer:
There would be six pieces in each pan.
Step-by-step explanation:
1. To make the number of pieces in each pan equal, the total number must be the same.
2. 8 pieces from the first pan + 6 pieces from the second pan = 14 pieces.
3. Divide 14 by 2 to get the same number of pieces in each pan:
14/2 = 7
4. Round down 7 to get six pieces in each pan.
A small ring of mass 0.2 kg is threaded on a fixed vertical rod. The end A of a light inextensible string is attached to the ring. The other end C of the string is attached to a fixed point of the rod above A. A horizontal force of magnitude 8 N is applied to the point B of the string, where AB = 1.5 m and BC = 2m. The system is in equilibrium with the string taut and AB at right angles to BC (see diagram). The equilibrium is limiting with the ring on the point of sliding up the rod. (ii) Find the coefficient of friction between the ring and the rod.
The coefficient of friction between the ring and the rod is approximately 0.408.
STEPS TO FIND THE COEFFICIENTTo find the coefficient of friction between the ring and the rod, we can use the equation:friction = (force parallel to the surface) ÷ (force perpendicular to the surface)
In this case, the force parallel to the surface is the force of friction between the ring and the rod, and the force perpendicular to the surface is the weight of the ring. We can call this coefficient of friction as "µ"In order for the ring to be in equilibrium, the horizontal force applied at B must be balanced by the force of friction between the ring and the rod. So:F_horizontal = friction
F_horizontal = µ × F_perpendicular
8 N = µ × m × g
where m is the mass of the ring and g is the acceleration due to gravity.
Substituting the values, we have8 N = µ × 0.2 kg × 9.8 m/s²
µ = 8 N ÷ (0.2 kg * 9.8 m/s²)
µ = 0.408
So the coefficient of friction between the ring and the rod is approximately 0.408.
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The vertices of pentagon JKLMN are listed below.
What is the approximate perimeter of the pentagon?
The perimeter of the triangle would be -
{P} = {JK} + {KL} + {LM} + {MN} + {NJ}
Given is a pentagon JKLMN .
The perimeter of a figure is the sum of the length of its sides. So, we can write the perimeter of the pentagon as -
{P} = {JK} + {KL} + {LM} + {MN} + {NJ}
Therefore, the perimeter of the triangle would be -
{P} = {JK} + {KL} + {LM} + {MN} + {NJ}
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blank divided by twenty four equals one third
Answer: 8
Step-by-step explanation: make it x = 1/3 times 24.
Also, try inserting 8 in the blank.
Thanks for the help whoever helps me!
Answer:
B
Step-by-step explanation:
What is the leading coefficient of. Y=2x³ +5
Answer:
2
Step-by-step explanation:
the leading coefficient is the number in front of the variable with the largest exponent.
here, the largest exponent is 3 in 2x³ and the corresponding coefficient for that is 2
Can you solve it to me?
Therefore , When the side lengths are (2x-1) and (4x + 5), the smartboard's perimeter is expression is as 12x2 - 8.
what is expression ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.
Here,
Given :
smartboard of side length is ( 2x-1) and ( 4x + 5 )
perimeter of small board = 2( l+ b)
2( 2x-1 + 4x + 5 )
2( 6x - 4)
When the side lengths are (2x-1) and (4x + 5), the smartboard's perimeter is expressed as 12x2 - 8.
The diagram can be imagined as a big whiteboard of shape of rectangle.
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4x+10+x=2.5(2x-4)
WITH SOLUTION PLEASEE AND I RLLY NEED IT RN thank u
Answer:
no solution
Step-by-step explanation:
4x + 10 + x = 2.5(2x - 4) ← distribute parenthesis
5x + 10 = 5x - 10 ( subtract 10 from both sides )
5x = 5x - 20 ( subtract 5x from both sides )
0 = - 20 ← not possible
this indicates the equation has no solution
A label is placed around the juice box, not including the bases: Determine the surface area of the label. 2 in 4 in 1.5 in
The surface area of the label would be 30.48 square centimeters.
What is surface?Surface is the outermost layer of a body, such as the skin, the crust of a planet, or the outermost layer of a liquid. Surface can also refer to the top of an object, such as the surface of a table or a lake. The term can also be used to describe a general area, such as the surface of the moon. In terms of physics, surface is any area where two materials meet.
The surface area of the label can be determined by multiplying the three
Measurements of the box together. In this case, the label is 2 inches in length, 4 inches in width, and 1.5 inches in height. Multiplying these three numbers together results in a surface area of 12 square inches. To find the surface area in a different unit of measurement, such as centimeters, the measurements must first be converted to the appropriate unit. For example, if the measurements were converted to centimeters, the surface area of the label would be 30.48 square centimeters.
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PLEASE HELP!!!
State the congruence that is needed to prove A ABC A DEF
using the given postulate or theorem.
D
C
E
9. Given: BC = EF, Use the Hypotenuse-Leg Congruence Theorem.
10. Given: AB = DE, AC DF, Use the SSS Congruence Postulate.
11. Given: ZA ZD, ZB = LE; Use the AAS Congruence Theorem.
12. Given: ZA = ZD, 2C= LF Use the ASA Congruence Postulate.
B
F
According to this postulate, two triangles are congruent if their two angles and included sides are congruent with each other.
What do you meant by Congruence Postulate?If the sides and angles of one triangle are the same as the sides and angles of another triangle, then two or more triangles are said to be congruent. Three postulates—ASA (angle-side-angle), SAS (side-angle-side), and SSS—that are demonstrated in the lesson can also be used to assess for congruency.
If, for example, triangle ABC has a hypotenuse of 5 cm and a leg of 4 cm and triangle PQR has a hypotenuse of 5 cm and a leg of 4 cm, then these two triangles have the same dimensions and, according to the HL theorem, are congruent to one another.
Triangle congruence can be implied in some situations by SSA, but not always. It differs from the other triangle congruence postulates/criteria because of this.
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Given the line Y equals 3X -5 what is the same line given? Is it 3X minus Y equals five or 3X minus Y equals -5 or 3X plus Y equals 15 or 3XY equals -5 or X plus 3Y equals -15.
The line 5 = 3X - Y or3X minus Y equals five is the same line of Y equals 3X -5. The correct option is A.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given line:
Y equals 3X -5
Simplifying,
Y = 3X - 5
This is a linear equation.
To find the same line:
Y = 3X - 5
Taking constant to one side and variable to one side,
That means,
5 = 3X - Y
3X minus Y equals five
Therefore, 3X minus Y equals five or 5 = 3X - Y is the required line.
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i need helppppppppppp
Answer:
3π/2 radians
Step-by-step explanation:
Its 3 quadrants. That's 3/4 of 2π radians, or 3π/2 radians.
Question 14
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Brad needs to rent scaffolding to paint a 2 -story room. Handy Rentals charges $15 plus $12.50 per hour. The EZ Rental Company charges $7.50 plus $13.75 per hour. For how many hours would Brad need to rent the scaffolding for the cost to be the same from each rental company?
Let h represent the number of hours. Select the correct values to write an equation to represent the situation.
Brad needs to rent the scaffolding for 6 hours for the cost to be the same from each rental company.
What is a linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
Handy Rentals
C = $15 + $12.50h ---------- 1
EZ Rental Company
$7.50 + $13.75h ------------ 2
where h is number of hours
Equating both equations
$15 + $12.50h = $7.50 + $13.75h
$15 - $7.50 = $13.75h - $12.50h
$7.5 = $1.25h
h = $7.5/$1.25
h = 6 hours
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He Want to save money to purchase a car he buys in a annuity with quarterly payments that are in 2.5 % interest compounded quarterly payment will be made at the end of each quarter find the total value of annuity in 3 years if each quarterly payment is $ 1508
98,329.16 is the Growing Ordinary Annuity's Future Value (FV). Given a predetermined rate of return or discount rate, the present value of an annuity is the entire cash worth of all of your future annuity payments.
What is annuity and how it is calculated?A sequence of equal-spaced payments constitutes an annuity. There are a lot of real-world examples of financial transactions involving annuities, including. • an automobile loan with a set repayment schedule of equal monthly payments.
Calculating the present value of an annuity is done by multiplying the dollar amount of each payment by the following formula:[tex]P = PMT \times [1- [ (1 / 1+r)^n] / r][/tex] where P is the present value of your annuity stream. PMT is short for payment method type.
A set of periodic payments that will be received in the future at the start of each period or at its conclusion is referred to as a "annuity." The formula used to determine annuity payments and annuities due is based on the PV of annuities due, the effective interest rate, and the number of periods.
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The temperature in Abu Dhabi is 28°C. The temperature in Moscow is 16°C colder. What is the temperature in Moscow?
Plsssss help me I need this
Explain how to determine the zeros of the polynomial f(x)= x³ + (b-a)x² - abx
for the positive real numbers a and b.
The zeros of the polynomial f(x)= x³ + (b-a)x² - abx for the positive real numbers a and b are 0, a, and -b.
What is polynomial?A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and positive-integer powers of variables. It is made up of indeterminate (also known as variables) and coefficients.
Given:
f(x) = x³ + (b-a)x² - abx
Take x common on the right side as shown below,
f(x) = x [x² + (b - a)x - ab]
Factorize the term as shown below,
f(x) = x (x - a)(x + b)
Plug the zero on the left side to find the zeros,
0 = x (x - a)(x + b)
x = 0,
x - a = 0,
x = a
x + b = 0,
x = -b
Thus, the zeros are 0, a, and -b.
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Suppose tortilla chips cost 29.5 cents per ounce. If a bag cost $3.91, how many ounces are in the bag of chips?
There are approximately 13.38 ounces of chips in the bag.
What is division?
Division is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and multiplication. It is the inverse operation of multiplication, and it is used to find out how many times one number is contained within another number.
To find out how many ounces of chips are in the bag, you can use the formula:
cost of bag / cost per ounce = number of ounces
In this case, you know that the cost of the bag is $3.91 and the cost per ounce of chips is 29.5 cents per ounce.
First, you need to convert the cost per ounce from cents to dollars. 29.5 cents is equal to 0.295 dollars (29.5 cents / 100 cents = 0.295 dollars)
So, you can substitute these values into the formula:
3.91 / 0.295 = 13.38
Hence, there are approximately 13.38 ounces of chips in the bag.
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A ream of paper is 500 sheets. Mr. Perez puts 1/4 of the ream in his printer. He stores 2/3 of the remaining ream and divides the rest of the paper equally among his 25 students. How many sheets of paper does each student get?
Answer:
Each student would get 25 sheets of paper.
Step-by-step explanation:
Mr. Perez starts out with 500 sheet. He puts 1/4 in the printer. That leaves 3/4 that he did not put in the printer.
3/4 x 500 = 375.
He take 2/3 of the 375 sheets and stores them. This leaves 1/3 of 375 sheet to hand out to students.
1/3 x 375 = 125
He has 125 sheets to share among 25 students.
125/5 = 25
An investment portfolio is shown below.
Investment Amount Invested ROR
Savings Account $2,700 3.6%
Municipal Bond $3,600 1.8%
Preferred Stock $765 13.6%
Common Stock A $1,155 −1.2%
Using technology, calculate the weighted dollar amount of the savings account.
$64.80
$97.20
$104.04
$108.96
Answer:
Sure, here is a more casual and friendly way to explain how to calculate the weighted dollar amount of the savings account:
"Hey there! To find out the weighted dollar amount of the savings account, you just need to do a little math. First, multiply the amount invested in the savings account by the return on investment (ROR). Then, divide that number by the total ROR for all investments.
So, if you have $2,700 invested in the savings account and it has an ROR of 3.6%, the weighted dollar amount of the savings account would be:
($2,700 * 3.6%) / (3.6% + 1.8% + 13.6% - 1.2%) = $104.04
Easy peasy! Let me know if you have any other questions!
Please help! Thank you!
Answer:
The answer is D, y=0.25t + 9.5
Step-by-step explanation:
Since the crew has been painting at a rate of 0.25 per hour continuosly, it will be 0.25 times the number of hours (t), plus the already completed road, which is 9.5.
Use function composition to determine if f(x) and g(x) are inverse functions.
f(x)=\sqrt[3]{x-1} and g(x)=x^3+1
By function composition, f(x) and g(x) are inverse functions
How to use function composition to determine if functions are inverse functions?A function is a relationship between inputs where each input is related to exactly one output.
f(x)= ∛(x-1) and g(x)=x³+1
To confirm the inverse relationship using composition.
If f(g(x)) = g(f(x)) then they are inverse functions
Let's confirm:
f(g(x)) = f(∛(x³+1))
= ( ∛((x³+1)-1 )
= ∛(x³)
= x
g(x)=x³+1
g(f(x)) = g(∛(x-1) )
= (∛(x-1))³ + 1
= x-1+1
= x
Since f(g(x)) = g(f(x)) then they are inverse functions
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What’s the correct answer asap for brainlist
Answer:
(A)
Step-by-step explanation:
SOS: Here is The correct answer, Brainly would not allow me to type it, so I took a screenshot instead. Hope this helps!! :D
rewrite 3 to the power of -7 using a positive exponant
Answer: 1/7^3
Step-by-step explanation:
When dealing with negative integers, you divide instead of multiplying and you write it as a fraction. Therefore, 1/7 to the 3rd power is the same as 3 to the power of -7. Hope this helps!
which of the following graphs shows the solution set to t > 4 or t < -1
The graph that shows the solution set of the inequality t > 4 or t < -1 is given by the image presented at the end of the answer.
How to graph the solution set of the inequality?The inequality for this problem is defined as follows:
t > 4 or t < -1.
It is a compound inequality, as it has two conditions.
The first condition is given as follows:
t > 4.
Which means that numbers to the right of t = 4 are graphed, with an open circle representing an open interval.
The second condition is given as follows:
t < -1.
Which means that numbers to the left of t = -1 are graphed, with an open circle also representing an open interval.
The open intervals are because none of the conditions contain the equal symbol.
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explicit formula of the arithmetic sequence
2,-2,-6,-10,
The formula for the arithmetic sequence is aₙ = 2 + (n - 1)(-4)
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The arithmetic sequence is a sequence in which the difference between successive numbers is constant. It is given by:
aₙ = a₁ + (n - 1)d
where a₁ is the first term and d is the common difference
Given the sequence:
2,-2,-6,-10
The first term (a₁) = 2, the common difference (d) = -2 - 2 = -4
The formula is:
aₙ = 2 + (n - 1)(-4)
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A company makes Poppy Lapel pins.
Answer:
the percentage profit of the company is 63.9%.
Step-by-step explanation:
Cost of making pins= £1.10
Number of pins= 1000
Total cost for making the pins
= Cost of each pin × Number of pins
= £1.10 × 1000
= £1110
Percentage of pins sold in charities
= 35% of 1000 pins
= (35/100) × 1000
= 350 pins
Left pins= 1000-350 = 650 pins
Number of pins sold at £3.00:
= 60% of 650
= (60/100) × 650
= 390
Selling price of these 390 pins
= 390 × £3.00
= £1170
Number of pins sold at £5.00 for 2:
= 40% of 650
= (40/100) × 650
= 260
These 260 pins were sold in pairs for £5.
Therefore, number of pairs sold
= 260/2
= 130 pairs
Selling price of these 130 pairs of pins
= 130 × £5.00
= £650
Therefore, total selling price
= £1170 + £650
= £1820
Profit by company
= Selling price - Cost price
= £1820 - £1110
= £710
Profit percentage
= Profit × 100 / Total cost price
= 710 × 100 / 1110
= 71000/1110
= 63.9%
Translate each sentence into a formula.
The area A of a squarc is the length of a side e squared.
[tex]A=e^2[/tex], where e is the side length of the square and A is the area of the square.
Polygon Q is a scaled copy of Polygon P using a scale factor of 1/2. Polygon Q's area is what fraction of Polygon P's area?
The fraction of Polygon P's area, that is Polygon Q's area, given the scale factor, is 1 / 4.
How to find the fraction ?The fact that Polygon Q is a scaled copy of Polygon P using 1 / 2 as a scale factor means that Polygon Q is half the size of Polygon P.
This means that in terms of area, Polygon Q in relation to Polygon P would be :
= 1 /2 x 1 / 2
= 1 / 4
For example, a square with sides 6 would have an area of :
= 6 x 6
= 36 units ²
The scaled shape would have sides of 3 because of the scale factor of 1 / 2 :
= 3 x 3
= 9 units ²
The fraction of the smaller shape's area is:
= 9 / 36
= 1 / 4
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