Answer:
75 = 4w
Step-by-step explanation:
Let w = width
Let w + 5 = length
Let p = perimeter ( Perimeter is given: 70 ft. )
Write the formula to find the perimeter of a rectangle
p = 2 ( l + w )
Sub the numbers in
70 = 2 [(w+5) + (w)]
Simplify the equation
70 = 2 (2w + 5)
70 = 4w + 5
75 = 4w
Find the average rate of change of the function
f
(
x
)
=
−
1
x
2
−
2
x
+
2
, on the interval
x
∈
[3,5].
Answer:
The average rate of change is −10.
Step-by-step explanation:
The average rate of change of f(x) on the interval [a,b] is f(b) − f(a) / b−a.
We have, a=3, b=5, f(x) = -1x^2 − 2x + 2.
Thus, f(b) − f(a) = −(5)^2 −2(5) + 2 − [−(3)^2 −2(3) + 2]
= -25 - 10 + 2 - ( -9 - 6 + 2 )
= -33 - 13
= - 20
Then, b−a = 5 - 3 = 2
f(b) − f(a) / b−a = - 20 / 2 = −10
Answer: the average rate of change is −10.
Write an equation of the line that passes through the given points.
(-2,8) and (1,0)
The equation is ______. (Type your answer in slope-intercept form.)
Answer:
y = -8/3x + 8/3
Step-by-step explanation:
(-2, 8) and (1, 0)
m = 0-8/1+2
m = -8/3
y = -8/3x + b
0 = -8/3(1) + b
0 = -8/3 + b
b = 8/3
y = -8/3x + 8/3
1. What is the range of the quadratic function?
72 boxes is 5% of how many boxes?
Answer:
1440
Step-by-step explanation:
"Percent" means "out of 100"
5 "percent" means 5 out of 100
[tex]\frac{5}{100} =\frac{72}{x}[/tex]
We need to find the number that when multiplied by 5, equals 72.
72 / 5 = 14.4
Now, we need to multiply 100 by 14.4 to "scale" proportionately.
100 * 14.4 = 1440
We can check our work:
1440 * (0.05) = 72
What is the slope of the line that contains the points (2, −8) and (−4, 4)? 2 one half negative one half −2
Answer;
-2
Step-by-step explanation;
Well take the last numbers in these points and subtract them
4 - (-8)
4+8
12
You've got the upper part of the slope fraction now subtract the first two numbers.
-4-2
-6
Put this fun together, 12/-6 = -2
hence, slope=-2 .
Answer:
Step-by-step explanation:
-2
A 2-quart carton of yogurt costs $5.36. What is the price per cup?
need correct answer.
The price per cup when a 2-quart carton of yogurt costs $5.36 is $0.67.
How to illustrate the word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real.life scenario given.
In this case, a 2-quart carton of yogurt costs $5.36. It should be noted that 1 quart = 4 cups.
Therefore, 2 quarts will be:
= 2 × 4.
= 8 cups
Therefore, the price per cup will be:
= $5.36 / 8
= $0.67
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For a company picnic, Dale ordered a box of fresh-baked gingerbread cookies and sugar cookies. He got 49 gingerbread cookies and 1 sugar cookie. What percentage of the cookies were gingerbread
The percentage of the cookies were gingerbread is 60%.
Given that, the total number of gingerbread cookies and sugar cookies= 55 and the number of gingerbread =22.
Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%"
Here, Difference =55-22
=3
Percentage =33/55 ×100
= 0.6 ×10
= 60%
Therefore, the percentage of the cookies were gingerbread is 60%.
Answer:
Step-by-step explanation:
cccccc
Solve negative 4 times y plus five halves times y equals negative 4 minus three halves times y minus 3 for y.
y = −7
y = 0
Infinite solutions
No solution
Answer:
No solution
Step-by-step explanation:
When you solve it, it ends up as 0=-7 which isn't true.
Answer:
No solution!
Step-by-step explanation:
7518 [tex]7518 divided by 3[/tex] 3
Answer:
2,506
Step-by-step explanation:
1/5/2023
7:37PM
Practice using graphs to solve systems of linear equations. Which graph represents the solution set to this system of equations? y = –1 2 x + 3 and y = 1 2 x - 1 On a coordinate plane, a line goes through (negative 4, 1) and (0, 3) and another line goes through (negative 2, negative 2) and (0, negative 1). On a coordinate plane, a line goes through (negative 2, 2) and (0, 3) and another line goes through (negative 2, 0) and (0, negative 1). On a coordinate plane, a line goes through (negative 2, 0) and (0, negative 1). On a coordinate plane, a line goes through (0, 3) and (2, 2) and another line goes through (0, negative 1) and (2, 0).
On a coordinate plane, a line goes through (0, 3) and (2, 2) and another line goes through (0, negative 1) and (2, 0).
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
given that,
y = –1 2 x + 3 and y = 1 2 x - 1, the systems of linear equations.
from the graph , we have,
the solution set to this system of equations is,
On a coordinate plane, a line goes through (0, 3) and (2, 2) and another line goes through (0, negative 1) and (2, 0).
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Answer: D
Step-by-step explanation:
The dollar value vt of a certain car model that is t years old is given by the following exponential function.
v(t)= 25,900(0.90)^2
Find the initial value of the car and the value after 11 years.
Round your answers to the nearest dollar as necessary.
Initial Value:
Value after 11 years:
Answer:
$25,900 initially
$8,128 after 11 years
Step-by-step explanation:
One thing to note, is I'm assuming you meant: [tex]v(t)=25,900(0.90)^t[/tex] and not [tex]v(t)=25,900(0.90)^2[/tex], otherwise that would just be a constant function and not an exponential function.
Exponential Function Key Features:There are a couple key features of exponential functions we can derive from simply analyzing the equation.
For now I will be using the form: [tex]y=a(b)^x\text{ where b} > 0, \text{b}\ne 1[/tex]
y-intercept:The y-intercept, is just the "a" value, which is because the y-intercept is simply when x=0, and if we raise a number to the power of zero, we get one (excluding zero as a base), so we get the form: [tex]y=a[/tex], so "a" is our y-intercept.
Rate of Change:there's actually two type of exponential functions: exponential growth and exponential decay.
Exponential Decay:
Exponential decay, as the name implies, is when a function is decaying or decreasing. This occurs when [tex]0 < b < 1[/tex].
The decay rate can be represented as "r" in decimal form, where: [tex]b=1-r[/tex].
The reason for this is because "1" can be thought of as 100% and "r" is r%, so you're taking away r% or decaying the value by r%, also known as a decay rate.
Exponential Growth:
Exponential growth as the name implies, is when a function is growing or increasing. This occurs when b > 1
The growth rate can be represented as "r" in decimal form where: [tex]b=1+r[/tex]
The reason for this is similar to decay rate except instead of taking away r% or decaying, it's "giving r%" or growing.
Solving the Question:The question doesn't actually require finding exponential growth or decay, but it's still an important key feature.
In this case, we really just need to find the y-intercept and plug in t=11.
The y-intercept in many graphs, not just exponential graphs, represents some sort of initial value, which in this case, is the initial value of the car. As stated above, this y-intercept is just the value in front, which is 25,900.
As for the value after 11 years, we simply need to plug in t=11 to get the following: [tex]v(11)=25,900(0.90)^{11}[/tex], from here we can use a calculator to simplify this: [tex]v(11)\approx25,900(0.31381059609)\approx 8,127.694438731[/tex], which rounds to 8,128
Question content area top
Part 1
A car with a full tank that holds 11.6 gallons of gasoline is using 1.45 gallons per hour. Is the tank more than half full of gasoline after 3.5 hours? Explain your answer.
Answer:
Yes, the tank is more than half full of gasoline after 3.5 hours.
Step-by-step explanation:
To calculate the amount of gasoline left in the tank after 3.5 hours, we need to subtract the amount used (1.45 gallons per hour) from the total capacity (11.6 gallons). So 11.6 - (1.45 x 3.5) = 9.3 gallons, which is more than half the tank's capacity of 11.6 gallons. Hope this helps!
how do the perimeters of the rectangles compare original 30 in 36 in scaled 6 in 5 in
Answer:
Step-by-step explanation:
ur mom
AXY Z is translated left 4 units to form the image AX'Y'Z'.
What are the coordinates of the vertices of AX'Y'Z' ?
Enter your answer by filling in the boxes.
X'=(
Y' = (0)
Z' = (00)
On solving the provided question we can say that - Pythagorean Theorem triangle [tex]5^2+x^2=10^2 = > x²=100−25=75[/tex]x=√75=√3×25=5√3
What is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
On solving the provided question, we can say that the value of x = 5√3
values of x and y
Pythagorean theorem,
The trigonometric ratio: soh-cah-toa, and
According to the given question:
Using the table of trig values, we find that
sin30°=1/2
So, this gives us:
[tex]1/2 = sin 30° = 5/y\\1/2 = 5/y\\(1xy)/2 = 5\\y= 2×5 =10\\[/tex]
Pythagorean Theorem
[tex]5²+x²=10²\\x²=100−25=75\\[/tex]
x=√75=√3×25=5√3
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division homework need help
Answer:
8296/17 = 488
4590/34 = 135
4550/26 = 175
8132/38 = 214
5265/15 = 351
8760/24 = 365
5643/33 = 171
4403/37 = 119
2400/48 = 50
Find the line that contains the error, explain the error and how you would find the correct solution. Include the correct solution in your answer.
Pls help
The final answer of the corrected expression is (-22, -26).
What is the solution to the linear equation?
The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
We have given:
y = x - 4
-2x + y = 18
---------------------
-2x + (x - 4) = 18
-x - 4 = 18
x = 22
y = 22 - 4
y = 18
Solution: (22, 18)
The error is in lines 3, 4, and 5.
It should have,
y = x - 4
-2x + y = 18
---------------------
-2x + (x - 4) = 18
-x - 4 = 18
-x = 22
x = -22
y = -22 - 4
y = -26
Solution: (-22, -26)
Hence, the final answer of the corrected expression is (-22, -26).
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Please help me. I have been trying to figure out this assignment forever! Can you please show your work
1. The length of the sides of the two smaller squares are 3 and 4
2. Area of 4 triangles and middles square = 25
3. Area of the big square = 5
How to find the area of the 4 triangles and and the squareThe dimensions of the the triangle and the square are
length of square = 1
base = 3
height = 4
Area of the triangle
= 1/2 base * height
= 0.5 * 3 * 4
= 6
For four triangles
= 4 * 6
= 24
Area of small square
= 1 * 1
= 1
summation of the areas
= 24 + 1
= 25
Solving for side of the big square from the area
= √25
= 5
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Which description does NOT guarantee that a quadrilateral is a rectangle?
a quadrilateral with four right angles
a quadrilateral with all congruent angles
a quadrilateral with diagonals that are congruent and bisect each other
a parallelogram with congruent sides
The description does NOT guarantee that a quadrilateral is a rectangle is option C. a quadrilateral with diagonals that are congruent and bisect each other
What is a quadrilateral?A quadrilateral is a four-sided polygon. It is a closed geometric figure with four straight sides and four angles and A rectangle is a four-sided shape with two pairs of parallel, perpendicular sides. Its opposite sides are equal in length and also opposite angles are equal in measurement.
Therefore, the correct answer is as identified. It can be concluded that the one that does not guarantee that a quadrilateral is a rectangle is option C. a quadrilateral with diagonals that are congruent and bisect each other
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O LINEAR EQUATIONS AND INEQUALITIES
Graphing a compound inequality o...
Graph the compound inequality on the number line.
x>-8 and x≤-3
The compound inequality on the number line is shown below.
We have been given a compound inequality. We are asked to graph the given inequality on number line.
x>8 and x≤3
The solution for the inequality is all values of x less than or equal to 3 and greater than or equal to 8.
We will have solid dots at x>-8 and x≤-3 .
One arrow of the number line would be from 3 to left of the number line (towards negative infinity). The other arrow will be from 8 to right side of number line towards positive infinity.
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1. Peter and John went shopping and spent money in the ratio 2 : 3 .
(a) If Peter spent 500 dollars, how much did John spend?
(b) If John spent 600 dollars, how much did they spend altogether?
(c) If both boys spent 2000 dollars altogether, how much did they spend?
(d) If John spent 100 dollars more than Peter, how much did both boys spend?
The ratio of the amount Peter spent to that of John is 2:3, so:
(a) If Peter spent 500 dollars, then John spent 75p dollars
(b) If John spent 600 dollars, then they spend altogether 1000 dollars.
(c) If both boys spent 2000 dollars altogether, then John spent 1200 dollars and Peter spent 800 dollars.
(d) If John spent 100 dollars more than Peter, then they both spent 500 dollars as Peter will spend 200 dollars while John spends 300 dollars.
How to evaluate for the amount spent using their ratio.Let us represent the amount of money spent for Peter and John with P and J respectively.
Using the ratio 2:3 for the amount Peter spent to that of John;
If Peter spent 500 dollars, then;
2/3 = $500/J {cross multiply}
J = (3 × $500)/2
J = $1500/2
J = $750
If John spent 600 dollars, then;
2/3 = P/$600 {cross multiply}
P = (2 × $600)/3
P = $1200/3
P = $ 400
Peter and John spent altogether = $1000
If both boys spent 2000 dollars altogether, then;
their total ratio = 5
unit amount = $2000/5
unit amount = $400
Peter spent = 2 × $400 = $800
John spent = 3 × $400 = $1200
If John spent 100 dollars more than Peter, then;
2/3 = P/(P + $100) {cross multiply}
3P = 2(P + $100)
3P = 2P + $200 {collect like terms}
3P - 2P = $200
P = $200.
Peter spent = $200
John spent = $300.
In conclusion, using the ratio 2:3 for the amount of money spent by Peter and John respectively, we have the answers: $750, $1000, $800 for Peter and $1200 for John, and $200 for Peter and $300 for John for the questions lettered (a), (b), (c), and (d) respectively.
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Hellllllpppp I Neeeeeeedddddd Heeeeellllllllpppp
Answer: 5
Step-by-step explanation:
A triangle's area is half of a squares, so we can treat this as a square for now. It says the area is 20 units squared, and if we convert this to the area of the square, it is 40 units. 40/8 is 5, and so 5 is the length of x
A company is expanding its building area from 18,000 square feet to 25,380 square feet. What is the percentage increase of the area of the building space?
Answer:
Below
Step-by-step explanation:
(25380 - 18000) / 18000 * 100% =
7380/18000 * 100 = 41 % increase
Find the measure of
The measure of ∠A is 123 degrees.
How to find the measure of angles?The angle made between the radius and the tangent at the point of contact on a circle is 90°.
Therefore,
∠D = 90 degrees
∠E = 90 degrees
The diagram ACDE forms a quadrilateral. The sum of angles in a quadrilateral is 360 degrees. Therefore, we have to equate the sum of the quadrilateral angles to 360 degrees.
Hence,
90 + 90 + 2x + 7 + 5x - 2 = 360
180 + 7x + 5 = 360
7x = 360 - 180 - 5
7x = 180 - 5
7x = 175
x = 175 / 7
x = 25
Therefore,
∠A = 5(25) - 2 = 125 - 2 = 123 degrees.
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If 2 melons cost Php190.50, then 4 melons cost __.
If 1 kg of Bangus costs Php167.35, then 3.5 kgs of Bangus cost __.
Answer: If 2 melons cost Php190.50, then 4 melons cost 381 .
If 1 kg of Bangus costs Php167.35, then 3.5 kgs of Bangus cost 585.725
Step-by-step explanation:
2x2=4
190.50x2=381
1x3.5=3.5
167.35x3.5=585.725
What number is 10 times greater than 318.625
Answer:
3186.25
Step-by-step explanation:
318,625*10 = 3186.25
assume that ryan does save 10% for retirment. if he alloctes the remainder of his take home pay to entertainment, then what percent of his total budget wil entertainment comprise?
Consider the following two circles.
Segment d1 is a diameter of ⨀A, and segment d2 is a diameter of ⨀B.
If d1=1 and d2=2r, and if CB denotes the circumference of ⨀B, which equation is true?
1/2r = CB/2π
1/2r = π/CB
1/2r = CB/π
The equation 1/2r = π/CB is true. Choose the second option
How to determine which equation is true?The circumference of a circle is the distance around the circle, or the length of the perimeter of the circle. It is given by the formula:
circumference = 2πr = πd
where r is the radius and d is the diameter
Note: d = 2r
Given: d2 = 2r and CB denotes the circumference of ⨀B
CB = πd2
CB = 2πr (d2 = 2r)
Divide both sides by CB:
CB/CB = 2πr/CB
1 = 2πr/CB
Divide both sides by 2r:
1/2r = 2πr/2rCB
1/2r = π/CB
Thus, the second equation is true
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prove that change of basis matrix is always invertible
Answer:
The only way for this to happen is if BA=In is the identity. The same argument, now interpreting ei as [wi]β2, shows that AB is also the identity. So A and B are both invertible. So every change-of-basis matrix is necessarily invertible if you think about it carefully.There are 3400 students at Central High School and 3/8 of these students are freshmen. If 3/5 of the freshmen are in favor of the school forming a track team and 1/5 of the remaining students (not freshmen) are also in favor of forming a track team, how many students are opposed to this idea?
First, we need to find the number of students that are freshmen: 3400 students x 3/8 = 1050 students
Next, we need to find the number of students that are in favor of forming a track team: 3/5 of the freshmen are in favor = 3/5 * 1050 = 630 students
To find the number of non-freshmen students: 3400 students - 1050 students = 2350 students
Now we need to find the number of non-freshmen students in favor of forming a track team: 1/5 of the non-freshmen students are in favor = 1/5 * 2350 = 470 students
Finally, to find the number of students opposed to the idea we need to subtract the number of students in favor from the total number of students: 3400 students - (630 students + 470 students) = 3400 - 1100 = 2300 students
So there are 2300 students at Central High School that are opposed to the idea of forming a track team.
divied 3.64× 10^8 by 3.3×10^4
3.64 x [tex]10^8[/tex] divided by 3.3 x [tex]10^4[/tex] is equal to 110.12121212121212.
What is division?The division is an arithmetic operation that is the inverse of multiplication. It involves splitting a quantity into a number of equal parts. The symbol for division is typically a forward slash (/) or a horizontal line. For example, if you have 10 apples and you want to divide them equally among 5 people, each person would receive 2 apples (10 ÷ 5 = 2). The result of division is called the quotient.
Here is one way to divide 3.64 x 10^8 by 3.3 x 10^4 step by step:
Write the numbers as decimal numbers: 3.64 x 10^8 is equal to 364000000 and 3.3 x 10^4 is equal to 33000.
Divide the decimal numbers: 364000000 ÷ 33000 = 11006.06
The result is 11006.06.
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