Answer:
Option C is correct.
Step-by-step explanation:
The given function f(x) is:
f(x) = x^2 + 22x + 58
To find the vertex find [tex](\frac{-b}{2a} )^2[/tex] and add and subtract it from both sides of the given function
b= 22, a= 1
Putting values:
[tex](\frac{-b}{2a} )^2 = (\frac{-22}{2(1)})^2\\=(\frac{-22}{2})^2\\= (-11)^2\\=11^2[/tex]
Adding (11)^2 on both sides
f(x) = x^2 + 22x + 58 +(11)^2 -(11)^2
f(x) = x^2+22x+(11)^2 +58-(11)^2
a^2 +2ab+b^2 = (a+b)^2 Using this formula:
f(x)=(x+11)^2+58-121
f(x)=(x+11)^2-63
The vertex of the given function is (-11,-63)
The function is translated 4 units to right and 16 units up
The vertex of new function will be:
(x+4,y+16) => (-11+4,-63+16)
=> (-7,-47)
So, the vertex of new function is (-7,-47)
The function will be
(x+7)^2 -47
So, Option C is correct.
Answer:
C
Step-by-step explanation:
What is the 8th term of this geometric sequence? 6, 48, 384, 3072, . . .
Answer:
a(8)=12582912
Step-by-step explanation:
The 8th term can be determined by the formula:
an = a1 * r^(n-1)
where
n = the term to be found = 8
a1 = 1st number
r = common ratio
Common ratio can be found by dividing the second term by the first term
= 48/6 = 8
Substitute the values in the formula
a(8) = 6 * 8^(8-1)
a(8) = 6 * 8^7
a(8)= 6*8*8*8*8*8*8*8
a(8) = 6 * 2097152
a(8)=12582912 ....
Therefore the 8th term is 12582912 ....
Answer:
12582912
Step-by-step explanation:
You simply need to start by finding the pattern. Divide the second number by the first (the answer is 8), then divide the third number by the second, so on and so on. You will see the answer is always 8 which means each number is getting multiplied by eight to reach the next term. Finally, multiply the last number in the sequence by your answer (8) until you reach the 8th term.
What is the point of intersection when the system of equations below is graphed on the coordinate plane?
x-y=1 and y-x=1
Answer:
not existStep-by-step explanation:
The coordinates of the intersection of the line are the solution of the system of equations.
[tex]\underline{+\left\{\begin{array}{ccc}x-y=1\\y-x=1\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad0=2\qquad\bold{FALSE}[/tex]
The system of equations has no solution. Therefore, the lines are parallel (the intersection does not exist).
What is the circumference of a circle with radius 10cm
Circumference is 62.8
To find the circumference, the formula is 2πr
The radius is half so we must multiply by 2 which is 20.
And finally, you multiply by π (3.14) and you will get 62.8 cm.
In conclusion, the answer is 62.8 cm.
The Circumference of the Circle is 62.8 cm
What is Circumference of Circle?The Circumference (or) perimeter of circle = 2πr
where, r is the radius of the circle. π is the mathematical constant
Given:
Radius- 10 cm
Now, the Circumference of Circle
= 2πr
=2 x 3.14 x 10
= 2 x 31.4
= 62.8 cm
Hence, the Circumference of the Circle is 62.8 cm
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The function gx = x2 - 10x + 24 is graphed on a coordinate plane. Where will the function cross the x axis
Answer:
At (4, 0), (6, 0)
Step-by-step explanation:
[tex]x^2 - 10x + 24 = 0\\(x-6)(x-4) = 0\\x_1 = 6\\x_2 = 4[/tex]
If the cosine value is 40*, the secant value to the hundredths degree is:
A.) 1.30
B.) 1.56
C.) 0.77
D.) 2.13
Answer:
Option A.) 1.30
Step-by-step explanation:
we know that
The secant of x is 1 divided by the cosine of x:
so
sec(40°)=1/cos(40°)
using a calculator
sec(40°)=1.30
Answer:
A.) 1.30
Step-by-step explanation:
If the cosine value is 40*, the secant value to the hundredths degree is 1.30.
sec(40°)=1.30
The area of a rectangle with width x and length 5x is 5x2. What does the coefficient 5 mean in terms of the problem?
Answer:
The length is 5 times the width
Step-by-step explanation:
Let
W ----> the width of the rectangle
L ----> the length of the rectangle
we know that
The area of rectangle is equal to
[tex]A=LW[/tex]
In this problem we have
[tex]L=5x[/tex] ----> equation A
[tex]W=x[/tex] ----> equation B
substitute equation B in equation A
[tex]L=5W[/tex]
therefore
The length is 5 times the width
In ∆ABC, ∠A is a right angle and m∠B = 45°. Find BC.
Step-by-step explanation:
In ∆ABC, if <A is 90° and <B is 45° then hypotenuse is BC.
Now,
Cos B= base/height
Cos B= AB/ BC
BC= AB/cos 45°.
Answer:
17 sqrt 2
Step-by-step explanation:
trust me the length is 24.04163 which equals 17√2
www.calculator.net has a triangle calculator if u think im wrong just look up triangle calculator
PLEASE HELP ASAP WILL MARK BRAINLIEST
Answer:
[tex]\sin \frac{3\pi}{2} = -1[/tex]
[tex]\cos\frac{3\pi}{2} =0[/tex]
Step-by-step explanation:
Please refer to the image attached.
Here we have a circle with unit radius. At some angle Ф the radius = 1 , and it is the hypotenuse (shown by green line in the image attached) of the ΔPQR thus formed. As our angle Ф increases, the hypotenuse gets closer to the positive y axis and at 90°, it overlap the y axis. Hypotenuse (H) and Opposite site (O) becomes same and Adjacent (A) becomes 0.
As our angle move further and reaches 180, the Hypotenuse and adjacent becomes same and overlap negative x axis. As we move further at 270 i.e [tex]\frac{3\pi}{2}[/tex] , the hypotenuse and opposite side overlap on y axis and Adjacent side become 0. However the opposite side becomes negative here .
Our sine ratio says
[tex]\sin \frac{3\pi}{2} =\frac{opposite}{Hypotenuse}[/tex]
[tex]\sin \frac{3\pi}{2} =\frac{-1}{1}[/tex]
[tex]\sin \frac{3\pi}{2} =-1[/tex]
Hence we have our [tex]\sin \frac{3\pi}{2} = -1[/tex]
Now
[tex]\cos\frac{3\pi}{2} =\frac{Adjacent}{Hypotenuse}[/tex]
Adjacent as we discussed is 0 at [tex]\frac{3\pi}{2}[/tex]
[tex]\cos\frac{3\pi}{2} =\frac{0}{1}[/tex]
[tex]\cos\frac{3\pi}{2} =0[/tex]
Help please
3^4 + 4 ⋅ 5 = ____. (Input whole numbers only.) (20 points)
Answer:
101
Step-by-step explanation:
3^4 = 81
4 x 5 20
81 +20 = 101
Answer:
101
Step-by-step explanation:
[tex]3^{4}[/tex] = 81 and 4 x 5 =20, so 20+81= 101.
v= -3i-4sqrt2, find a unit vector that points in the opposite direction as v
Answer:
The unit vector in the opposite direction of u is:
[tex]\vec{u} =-\frac{1}{\sqrt{23}}<-3i-4,\sqrt{2}>[/tex]
Step-by-step explanation:
To find the unit vector suppose u that points in the opposite direction as v
[tex]\vec{v}=<-3i,-4\sqrt{2}>[/tex]
we use the formula:
[tex]\vec{u} =-\frac{1}{||\vec{v}||}\vec{v}[/tex]
Finding [tex]||\vec{v}||[/tex]
[tex]||\vec{v}|| = \sqrt{x^2+y^2}\\||\vec{v}|| = \sqrt{(3i)^2+(4\sqrt{2}^2} \\||\vec{v}|| = \sqrt{9i^2+(16*2)}\\ i^2 = -1\\||\vec{v}|| = \sqrt{9(-1)+32}\\||\vec{v}|| = \sqrt{-9+32}\\||\vec{v}|| = \sqrt{23}[/tex]
[tex]\vec{u} =-\frac{1}{\sqrt{23}}<-3i,-4\sqrt{2}>[/tex]
The unit vector in the opposite direction of u is:
[tex]\vec{u} =-\frac{1}{\sqrt{23}}<-3i,-4\sqrt{2}>[/tex]
Help me with 1 and 2 please
Answer:
C) 2744 cm
Step-by-step explanation:
To find the volume of a cube you have to use this equation:
V = a^3
Now plug in the number:
V = 14^3
14^3 or 14*14*14 = 2,744
The volume is 2,744 cm
Answer:
1) 2744cm^3
2)1176cm^2
Step-by-step explanation:
1)Since it's a square, the sides are all equal length. And volume=base×width×height
thus we can multiply 14×14×14=14^3=2744cm^3
2)for surface area we can find the area of on side and multiply it by 6 because the square has six equal sides. thus, area=base×height so, area=14×14=14^2=196cm^2
Now we multiply it by 6 which is equal to 1176cm^2
a standard number cube is tossed. find p(3 or odd)
Answer:
0.5 or 1/2
Step-by-step explanation:
Let A be the event that the number cube is 3 or odd as 3 is also an odd number. So the event space will be:
{1,3,5}
The total number of outcomes are 6 as in:
{1,2,3,4,5,6}
So the probability of tossing 3 or odd number will be:
P(A) = n(A) / n(S)
= 3/6
=1/2
Hence the probability in fraction form is 1/2 and in decimal form is 0.5 ..
Select the equivalent expression.
(a^5 * 2^3)^3 = ?
1. a^8*2^9
2. a^15*2^6
3. a^8*2^6
3. a^15*2^9
Answer:
a^15 * 2^9
Step-by-step explanation:
(a^5 * 2^3)^3 =
= (a^5)^3 * (2^3)^3
= a^(5 * 3) * 2^(3 * 3)
= a^15 * 2^9
Answer: the second choice 3.
Answer:
3. a^15*2^9
Step-by-step explanation:
We know that (a * b) ^c = a^c * b^c
(a^5 * 2^3)^3
a^5^3 * 2^3^3
And we know that a^b^c = a^(b*c)
a^(5*3) * 2^(3*3)
a^15 * 2^9
#8 Dylan, Mike and Jeremy had $171. Mike had twice as much money as Dylan. Jeremy had three times as much money as Mike. How much money did Jeremy have?
#9 we skipped this one
#10. Maddy had twice as many stamps as Simon. After Maddy sold 60 stamps, Sinom had twice as many stamps as Maddy. How many more stamps did Maddy have than Simon in the beginning?
Answer:
8. $114
10. 60 stamps
Step-by-step explanation:
8.
Let Dylan have d, Mike have m, and Jeremy have j
3 of them have 171, so we can write:
1. [tex]d + m + j = 171[/tex]
Mike has twice as Dylan, so we can write:
2. m = 2d
Jeremy had three times as Mike, so:
3. j = 3m
We can write equation 3 as m = j/3
Also, if we put this into equation 2, we have:
j/3=2d
d=j/6
Now we have d and m in terms of j. We put it into equation 1 and solve for j:
[tex]\frac{j}{6} + \frac{j}{3} + j = 171\\\frac{3j+6j+18j}{18}=171\\\frac{27j}{18}=171\\27j=18*171\\27j=3078\\j=\frac{3078}{27}\\j=114[/tex]
Jaime has $114
10.
amount of stamps Maddy has is m and amount Simon has is s
Maddy had twice as many stamps as Simon:
m = 2s
Also
After Maddy sold 60 stamps, Sinom had twice as many stamps as Maddy:
s+60=2(m-60)
We put the first equation in the second and solve for s:
s+60=2(m-60)
s+60=2(2s-60)
s+60=4s-120
180=3s
s=60
THus, m = 2(60) = 120
So maddy had 120 - 60 = 60 more stamps than Simon
A stained glass window is going to be installed in a semi-circular opening, which is above a 34 inch wide door. If the stained glass window costs $0.95 per square inch, how much will the window cost? Use 3.14 for π
as necessary.
A. $389.10
B. $1,724.17
C. $431.04
D. $494.55
The area of a full circle would be Area = PI x r^2
The diameter would be the width of the dorr, so the radius would be half that. 34/2 = 17 inches.
Area for a full circle would be 3.14 x 17^2 = 907.46 square inches.
A semi circle is a half circle.
The area would be 907.46 / 2 = 453.73 square inches.
Multiply the area by the cost:
453.73 x 0.95 = 431.04
The answer is C.
Final answer:
To find the cost of the stained glass window, calculate the area of a 34-inch diameter semi-circular window, and then multiply that by the cost per square inch ($0.95). The total cost is approximately $431.17.
Explanation:
To calculate the cost of the stained glass window, we must first find the area of the semi-circular window above the door. Since the width of the door is 34 inches, the diameter of the semi-circle is also 34 inches, which means the radius (r) is half of that, or 17 inches.
Step 1: Calculate the area of the semi-circle
The formula for the area of a circle is A = πr². For a semi-circle, it would be half of that area, so the formula changes to A = (πr²) / 2.
Plugging in the radius, we get A = (3.14 * (17²)) / 2 = (3.14 * 289) / 2 = 453.86 square inches.
Step 2: Calculate the cost of the stained glass
The cost per square inch is $0.95. Multiplying the area by the cost per square inch, we get Total Cost = 453.86 * $0.95 = $431.167, which rounds to $431.17.
The closest cost option given is C. $431.04.
Find the height of a pyramid whose volume is 500 cubic inches and whose area base is 50 square inches.
Answer:
30 inches
Step-by-step explanation:
By definition,
volume of a pyramid = (Base Area x height ) / 3
or
500 = (50 x h ) / 3
50h = (500) (3)
h = (500)(3) / (50) = 30 inches
Answer:
h=30in
Step-by-step explanation:
The height of a pyramid whose volume is 500 cubic inches and whose area base is 50 square inches is 30inches.
Formula: V = Ab h/3
h=3 V/Ab = 3 ⋅ 500/50 = 30 inches
Use the function y=0.0875x^2 - `10.5x + 436.25 calculate the number of accidents that occur at 60 km/h? Select the right answer.
Answer:
About 121.25
Step-by-step explanation:
Step 1: Interpret x and y
y is the number of accidents that occur = ?
x is the speed = 60 km/h
Step 2: Substitute value of x in the equation
y=0.0875x² - 10.5x + 436.25
y=0.0875(60)² - `10.5(60) + 436.25
Step 3: Find the value of y
y=0.0875(60)² - `10.5(60) + 436.25
y = 121.25
Therefore, the right answer is the last option which is 'about 121.25.'
!!
What is the answer help me
One kilogram is approximately equal to 2.21 pounds. Find the number of pounds in 165 kilograms. Round to the nearest tenth of a pound, if needed.
Answer: 364.7 pounds
Step-by-step explanation: Multiply the number of kilograms, 165, by the number of pounds per kilogram, 2.21.
165 x 2.21 = 364.65
Round to the nearest tenth.
364.7 pounds in 165 kilograms.
The number of pounds in 165 kilograms is approximately 363.2 pounds. Rounding to the nearest tenth, the number of pounds in 165 kilograms is approximately 363.2 pounds.
Explanation:To find the number of pounds in 165 kilograms, we can use the conversion rate of 1 kilogram is approximately equal to 2.21 pounds. We can set this up as a proportion: 1 kilogram / 2.21 pounds = 165 kilograms / x pounds. Cross-multiplying, we get x pounds = (165 kilograms * 2.21 pounds) / 1 kilogram. Simplifying, x pounds = 363.15 pounds. Rounding to the nearest tenth, the number of pounds in 165 kilograms is approximately 363.2 pounds.
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Terry is skiing down a steep hill. Terry's elevation, E(t), in feet after t seconds is given by E(t)=2600−50t.
Answer:
Part 1) The equation tells us that Terry started at an elevation of 2,600 ft
Part 2) The elevation is decreasing by 50 feet each second
Step-by-step explanation:
we have
[tex]E(t)=2,600-50t[/tex]
where
E(t) is Terry's elevation in feet
t is the time in seconds
Part 1) Find the E intercept of the equation
The E-intercept is the value of E when the value of t is equal to zero
so
For t=0
substitute
[tex]E(0)=2,600-50(0)[/tex]
[tex]E(0)=2,600\ ft[/tex]
therefore
The equation tells us that Terry started at an elevation of 2,600 ft
Part 2) Find the slope of the equation
we have
[tex]E(t)=2,600-50t[/tex]
This is the equation of the line into slope intercept form
The slope m is equal to
[tex]m=-50\ ft/sec[/tex]
The slope is negative, because is decreasing
therefore
The elevation is decreasing by 50 feet each second
The subject of this question is Physics. The given equation represents Terry's elevation while skiing down a steep hill.
Explanation:The subject of this question is Physics. The given equation E(t) = 2600 - 50t represents Terry's elevation in feet after t seconds while skiing down a steep hill.
To better understand the equation, let's break it down step-by-step:
- The constant term 2600 represents Terry's initial elevation at t = 0 seconds.
- The coefficient of t, -50, represents the rate at which Terry's elevation decreases as time passes. This means that Terry's elevation decreases by 50 feet for every second that goes by.
Based on this equation, Terry's elevation will progressively decrease as time passes.
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the delivery ramp at the corner cafe id a right triangle. The hypotenuse is 4 meters long. One leg is 3 meters long. What is the length of the other leg
f. sqrt 7 meters
g. sqrt 12 meters
h. 3.5 meters
j. 5 meters
Answer:
f. sqrt 7 meters
Step-by-step explanation:
we use Pythagoras' theorem here,
let the unknown side be x,
therefore,
=> 3² + x² = 4²
=> x² = 16 - 9
=> x = √7 m
Answer:
f. sqrt 7 meters
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem to solve. We know the hypotenuse is 4 and one leg is 3. We want to solve for the other leg.
a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse.
Substituting into the equation
3^2 + b^2 = 4^2
9+b^2 = 16
Subtracting 9 from each side
9-9+b^2 = 16-9
b^2 =7
Taking the square root of each side
sqrt(b^2) = sqrt(7)
b = sqrt(7) meters
Which angle in
ABC has the largest measure?
Answer:
angle B
Step-by-step explanation:
A machine cuts a strip of carpet into two pieces. The length of the smaller piece is 5 meters greater than the length of the larger piece. If the length of the smaller piece is 12 meters, the length of the bigger piece is meters and the total length of the carpet is meters.
Answer:
Length of larger piece: 7 m
Total length of carpet is: 19 m
Step-by-step explanation:
Let the smaller piece have length x.
Let the larger piece have length y.
"The length of the smaller piece is 5 meters greater than the length of the larger piece."
x = y + 5
"If the length of the smaller piece is 12 meters"
x = 12
x = y + 5
12 = y + 5
7 = y
y = 7
The larger piece has length 7 meters.
The total length of the carpet is x + y = 12 m + 7 m = 19 m
To find the length of the larger piece of carpet, use the equation x + 5 = 12, and solve for x. Substitute the total length of the carpet for x in the formula to find the length of the larger piece.
Explanation:The problem involves finding the length of the larger piece of carpet when the length of the smaller piece and the total length of the carpet are known. Let's assume the length of the larger piece is x meters. According to the problem, the length of the smaller piece is 5 meters greater than the length of the larger piece, so the length of the smaller piece can be represented as x + 5 meters. The total length of the carpet is the sum of the lengths of the smaller and larger pieces, so we can create the equation: x + (x + 5) = total length. Given that the length of the smaller piece is 12 meters, we can substitute x + 5 with 12 in the equation and solve for x:
x + (x + 5) = total length
x + x + 5 = total length
2x + 5 = total length
2x = total length - 5
x = (total length - 5) / 2
Now we have the formula to calculate the length of the larger piece. Simply substitute the total length of the carpet into the formula to find the length of the larger piece.
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Where does f(x) = 3x2 – 11x - 4 intersect the x-axis?
Answer:
The x-intercepts are (4,0) and (-1/3,0).
Step-by-step explanation:
f or any relation/function will intersect the x-axis when y is 0.
Set that's what we will do is set y to 0 and solve for x.
0=3x^2-11x-4
I'm going to attempt to factor.
a=3
b=-11
c=-4
We need to find two numbers that multiply to be ac and add up to be b.
ac=-12=-12(1)
b=-11=-12+1
Let's factor 3x^2-11x-4 by grouping.
3x^2-11x-4
3x^2-12x+1x-4 ; I replaced -11x with -12x+1x
Group the first 2 pairs and group the last two pairs like so:
(3x^2-12x)+(1x-4)
Now factor what you can from each pair:
3x(x-4)+1(x-4)
Now you have two terms, both with the common factor (x-4) so factor it out:
(x-4)(3x+1)
Now let's go back to solving:
3x^2-11x-4=0
This is the same as solving:
(x-4)(3x+1)=0 (because this is just the factored form of the original equation.)
Now this means either x-4=0 or 3x+1=0.
We need to solve both.
x-4=0 can be solved by adding 4 on both sides resulting in x=4.
3x+1=0 requires two steps.
3x+1=0
Subtract 1 on both sides:
3x=-1
Divide both sides by 3:
x=-1/3
The x-intercepts are (4,0) and (-1/3,0).
Answer:
The negative x-intercept is at (-1/3 , 0).
The positive x-intercept is at (4 , 0).
Explanation:
Where does f(x) = 3x2 – 11x – 4 intersect the x-axis?
The negative x-intercept is at (-1/3 , 0).
The positive x-intercept is at (4 , 0).
Set f(x) equal to zero so
3x2 – 11x – 4 = 0
Plug in a. b, and c into the quadratic formula
and get 2 solutions:
1/3 and -4
take the opposite signs and put it in the x intercepts
a piece of paper, graph y> 2x.Then determine which answer matches the graph you drew.
To graph the equation y > 2x, start by graphing the line y = 2x and shading the region above it.
Explanation:To graph the equation y > 2x, we start by graphing the line y = 2x. This line has a positive slope (b > 0) and passes through the origin (0, 0). Since we want to graph y > 2x, we need to shade the region above the line.
Draw the line y = 2x as a solid line. Then, shade the region above the line to indicate that y is greater than 2x.
Answer: Graph (a) matches the given inequality y > 2x.
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A breakfast restaurant sold 889 orders of scrambled eggs, 313 orders of poached eggs, 594 orders of fried eggs, and 41 orders of hard-boiled eggs. How many orders of eggs did the restaurant sell in all?
Answer:
1873
Step-by-step explanation:
just add them up
The restaurant sold a total of 1837 orders of eggs.
To calculate the total number of orders of eggs sold by the breakfast restaurant, we need to add up all the individual orders for each type of eggs.
Scrambled eggs: 889 orders
Poached eggs: 313 orders
Fried eggs: 594 orders
Hard-boiled eggs: 41 orders
Now, let's add these numbers together:
889 + 313 + 594 + 41 = 1837 orders
Therefore, the restaurant sold a total of 1837 orders of eggs.
Find each sum.
(-7)+9
Find the product of (4x + 3y)(4x − 3y). (2 points)
(4x+3y)(4x-3y)
Multiply the two brackets together
4x(4x)(4x-3y)(-3y)(4x)(3y)(-3y)
16x^2-12xy+12xy-9y^2
16x^2-9y^2
Answer is 16x^2-9y^2
[tex]\huge{\boxed{16x^2-9y^2}}[/tex]
Use the FOIL method.
First term in each binomial: [tex]4x*4x=16x^2[/tex]
Outside terms: [tex]4x*-3y=-12xy[/tex]
Inside terms: [tex]3y*4x=12xy[/tex]
Last term in each binomial: [tex]3y*-3y=-9y^2[/tex]
Add these all together. [tex]12xy-12xy+16x^2-9y^2=\boxed{16x^2-9y^2}[/tex]
Alex originally paid $5200 for her car 1 year ago. The value of her car now is $4,420. What is
the percent of decrease in the value of her car?
Answer:
15%
Step-by-step explanation:
87 is 15% of what number
Answer:
580
Step-by-step explanation:
Let's translate this word for word.
87 is 15% of what number
87 = 15% times x
87=.15 times x
[tex]87=.15 \cdot x[/tex]
Divide both sides by .15
[tex]\frac{87}{.15}=\frac{.15x}{.15}[/tex]
Cancel out the common factor of .15 on the right; that is .15/.15=1.
[tex]580=x[/tex]
580 is the number
Answer:
580
Step-by-step explanation:
Alright. Translate that into math, and you get:
87=15/100x
multiply both sides by x
8700/15=x
x=8700/15
x=580
Check:
580*15/100
58*15/10
870/10
87
BINGO!