Answer:
4
Step-by-step explanation:
Let x be the unknown number.
[tex]\begin{aligned}&\textsf{A number is raised to the third power}: & x^3&\\&\textsf{Subtracted from 15}: & 15-x^3&\\&\textsf{To get 7}: & 15-x^3&=7\end{aligned}[/tex]
Solve the found equation for x:
[tex]\begin{aligned}&\textsf{Given}: & 15-x^3&=7\\&\textsf{Subtract $15$ from both sides}: & -x^3&=-8\\&\textsf{Divide both sides by $-1$}: & x^3&=8\\&\textsf{Rewrite $8$ as $2^3$}: &x^3&=2^3\\&\textsf{Cube root both sides}: & x&=2\end{aligned}[/tex]
Therefore, the number squared is:
[tex]\implies x^2=2^2=4[/tex]
(Please help quick!)
Which rectangle has the same area as the triangle
shown?
The rectangle with the sides 4 and 3 is the required rectangle.
The correct option is third shape.
What is area?Area is the amount of area occupied by an object's flat (2-D) surface or shape.
The area of the triangle,
= 1/2 x base x height
= 1/2 x 6 x 4
= 12 square millimeters.
And rectangle has the same area as the triangle.
The rectangle with the sides 4 and 3 is the required.
Therefore, the rectangle with the sides 4 and 3 is the required rectangle.
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3) a² + 3a - 10 = 0
I don’t know how to do this and I need to solve it by quadratic formula
A quadratic equation in one unknown;
[tex]ax^2+bx+c=0[/tex]has two roots. In order to determine these roots, we need to apply certain operations. We can get information about the existence of these roots by discrimination. Below is the discrimination formula.
[tex]D=b^2-4ac[/tex]If we apply discriminant for the above equation, we obtain the following expression;
[tex]D=(3)^2-4(1)(-10)[/tex][tex]D=9+40[/tex][tex]D=49[/tex]If the discriminant number is greater than [tex]0[/tex], the equation has two real and distinct roots.
[tex]D > 0,[/tex] [tex]x_{1}\neq x_{2}[/tex][tex]D=0,[/tex] [tex]x_{1}=x_{2}[/tex][tex]D < 0,[/tex] [tex]No[/tex] [tex]Root[/tex] [tex]in[/tex] [tex]Real[/tex] [tex]Numbers.[/tex]Now let's remember our formula for finding the roots and solve the problem using the discriminant value.
[tex]x_{1}=\frac{-b-\sqrt{D} }{2a},[/tex] [tex]x_{2}=\frac{-b+\sqrt{D} }{2a}.[/tex]Therefore;
[tex]x_{1}=\frac{-3-\sqrt{49} }{2}[/tex][tex]x_{1}=-5[/tex]Other root is;
[tex]x_{2}=\frac{-3+\sqrt{49} }{2}[/tex][tex]x_{2}=2[/tex]
Find the critical value t g corresponding to a 99% confidence level, given that the sample has size n = 12
The critical value is 2.65
Given,
The confidence interval = 99%
Sample size, n = 12
We have to find the critical value;-
Critical value;-
A critical value is the test statistic's value that establishes a confidence interval's upper and lower boundaries or the level of statistical significance for a given test.
Here,
The sample size n = 12,
Then, the degrees of freedom is n - 1 = 12 - 1 = 11
The critical value= t₀.₀₀₁/2 = t₀.₀₀₅
Using the t-table and selecting df =12 and since it’s a 2 tail the corresponding t-score is 2.65
Therefore, the critical value is 2.65
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What is the solution to the following system?
The solution to the system is x = 0, y =2, z = 5
How to find the solution to the system?Given the following system:
x+ 2y+z=9 -------- (1)
x- y+3z = 13 -------- (2)
2z = 10 -------- (3)
From (3):
2z = 10
z = 10/2 = 5
Put z = 5 into (1) and (2):
x+ 2y+z=9
x+ 2y+5 = 9
x +2y = 9-5
x +2y = 4 -------- (4)
x- y+3z = 13
x -y + 3(5) = 13
x-y + 15 = 13
x-y = 13 -15
x-y = -2 -------- (5)
Using elimination method on (4) and (5):
Subtracting (5) from (4):
x +2y = 4
x-y = -2
3y = 6
y = 6/3 = 2
Put y = 2 into (4):
x +2y = 4
x + 2(2) = 4
x + 4 = 4
x = 4-4 = 0
Therefore, the solution is x = 0, y =2, z = 5. The 3rd option is the answer.
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Neal buy a board game. He pay for the board game and pay 1.54 in ale tax. The ale tax rate i 5.5% what i the original price of the board game before tax
Answer:
$28
Step-by-step explanation:
5.5%=0.055
1.54/0.055=28
what is the best solution to this equation 2log2x-log2(2x)=3
The best solution for the given equation is x=4
What are logarithmic functions?
The inverse function to exponentiation in mathematics is called the logarithm. Accordingly, the exponent to which b must be raised in order to obtain a number x is determined by its logarithm to the base b.
Use Property:
logb(xy)=logbx+logby and logby = x ⇔ x^b = y
log2(x(x−2))=3
2^3 =x^2 −2x
8=x^2−2x
0=x^2−2x−8
0=(x−4)(x+2)
x−4=0
or
x+2=0
x=4
or
x=−2
Hence, x=4
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Answer: X=16
Step-by-step explanation:
trust,, also good luck to plato 2b algebra people
There are 10 squares and 2 circles. What is the simplest ratio of circles to squares?
Answer: 5:1
Step-by-step explanation: 10:2 can be simplified by dividing both by 2, making it 5:1
a recent survey of 6 social networking sites has a mean of 9.05 million visitors for a specific month. the standard deviation was 5 million. find the 98% confidence interval of the true mean. assume the variable is normally distributed. round your answers to at least two decimal places.
The 98% confidence interval of the true mean is 43.02 million < true mean < 13.80
Given,
Number of social networking sites being surveyed = 6
Sample mean = 9.05 million visitors per month
Standard deviation = 5 million
We have to find the 98% confidence interval of the true mean;
Here,
Sample mean, x = 9.05 million
Standard deviation, σ = 5 million
Sample size, n = 6
z score of 98% is 2.326
Now,
9.05 million - 2.326 × (5 million / √6) < true mean < 9.05 million + 2.326 × (5 million / √6)
43.02 million < true mean < 13.80
Therefore,
The 98% confidence interval of the true mean is 43.02 million < true mean < 13.80
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Using the completing-the-square method, find the vertex of the function f(x)=-2x^2+12x+5 and indicate whether it is a minimum or a maximum and at what point.
Using the completing-the-square method, find the vertex of the function f(x)=-2x^2+12x+5 and indicate whether it is a minimum or a maximum and at what point.
Given function is: [tex]f(x) = -2x^{2}+12x+5[/tex]
[tex]f(x) = a(x-h)^{2} +k[/tex] , where (h,k) is the vertex
Apply completing the square method to find vertex
[tex]f(x) = -2x^{2}+12x+5\\\\f(x) = -2(x^{2}-6x)+5[/tex]
Lets take half of coefficient of x is -6
divide by 2 that is -3
square it [tex](-3)^{2}[/tex] that is 9
Add and subtract 9
[tex]f(x) = -2(x^{2}-6x+9-9)+5[/tex]
Take out -9 and multiply by -2
[tex]f(x) = -2(x^{2}-6x+9)+18+5\\\\f(x) = -2(x^{2}-6x+9)+23[/tex]
Now factor the parenthesis part
[tex]f(x) = -2(x-3)^{2} +23[/tex]
The value of h=3 and k=23
So vertex is (3,23)
The value of 'a' is -2, it means the parabola is upside down. so vertex is maximum
Hence the answer is the vertex is maximum at (3,23)
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Help!! I need this ASAP!
The given expression rewritten in simplified exponential form is [tex]5x^{\frac{3}{2}}[/tex]
Simplifying an expressionFrom the question, we are to rewrite the given expression is simplified exponential form.
The given expression is
[tex]\sqrt{\sqrt{25^{2} x^{6} } }[/tex]
First, we will evaluate the inner square root
[tex]\sqrt{25^{\frac{2}{2} } x^{\frac{6}{2} } }[/tex]
[tex]\sqrt{25 x^{3 } }[/tex]
Simplifying further
[tex]\sqrt{25 } \times \sqrt{x^{3}}[/tex]
[tex]5\times x^{\frac{3}{2}}[/tex]
= [tex]5x^{\frac{3}{2}}[/tex]
Hence, the expression in simplified form is [tex]5 x^{\frac{3}{2}}[/tex]
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HELP WHATS IS A multi step equation that has a variable on both side that equals 10
Answer:
Step-by-step explanation:
an equation that takes two or more steps to solve is called a multi-step equation. let's take a multi-step equation that will satisfy the given condition:
4x - 8 = 22 + x
4x -x = 22 + 8
3x = 30
x = 10
Sharon spent #13.60 on baseball Cards. She bought 16 packs How much did each pack cost?
Answer:
#0.85
Step by step:
13.60/16 = #0.85
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A cheetah can run 18.75 miles in 1/4 hours. What is its speed in miles per hour?
Answer: miles per hour = mi/hr = 17.5mi/0.25hr = 17.5*4mi/0.25*4hr = 70mi/hr
Step-by-step explanation:miles per hour = mi/hr = 17.5mi/0.25hr = 17.5*4mi/0.25*4hr = 70mi/hr
Step-by-step explanation:
18.75 miles in 1/4 hour.
that is the ratio 18.75 / 1/4
but we want the miles in an hour.
so, how many 1/4 are in a whole ?
well, 4.
so we need to multiply the ratio by 4/4 (so that on one hand we multiply the denominator by 4 to make it a whole, and on the other hand we are not changing the value of the ratio) :
18.75 × 4 / (1/4 × 4) = 75 miles / 1 hour = 75 mph.
Solve the equation -4(x - 1) + 6x =34 for x
Answer:
Step-by-step explanation:
-4(x - 1) + 6x =34
-4x + 4 + 6x = 34
-4x + 6x + 4 = 34
2x + 4 = 34
2x + (4-4) = (34-4)
2x = 30
2x/2 = 30/2
x = 15
Find an
for a line parallel to
4x + 5y + 2 = 0, with an
an x-intercept of 3
The equation of the parallel line is 4x + 5y - 12 = 0
How to determine the line equation?The equation is given as
4x + 5y + 2 = 0
The x-intercept is also given as
x-intercept = 3
We have
4x + 5y + 2 = 0
Make y the subject
5y = -4x - 2
Divide through by 5
y = -4x/5 - 2/5
The equation of a line can be represented as
y = mx + c
Where
slope = m
By comparing the equations, we have:
m = -4/5
This means that the slope of 4x + 5y + 2 = 0 is =4/5
The slopes of parallel lines are equal
This means that the slope of the other line is -4/5
The equation of the parallel line is then calculated as
y = m(x - x₁) +y₁
Where
m = -4/5
(x₁, y₁) = (3, 0) i.e. the x-intercept
So, we have
y = -4/5(x - 3) + 0
Multiply through by 5
5y = -4(x - 3)
Open the brackets and evaluate
5y = -4x + 12
This gives
4x + 5y - 12 = 0
Hence, the parallel line has an equation of 4x + 5y - 12 = 0
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Find the Area of the figure below, composed of a rectangle with a semicircle removed from it. Round to the nearest tenths place.
4
6
Two number have a product of 7. One of the number i 4 2/3, what i the other number?
Answer:
1 1/2
Step-by-step explanation:
You want the other number when one of the two numbers that have a product of 7 is 4 2/3.
SolutionLet x represent the unknown factor. Then we have ...
(4 2/3)x = 7
(14/3)x = 7 . . . . . . write as improper fraction
x = (3/14)(7) . . . . . multiply by the inverse of the coefficient of x
x = 3/2 = 1 1/2
The other number is 1 1/2.
Find the rectangular coordinates of the point whose spherical coordinates are given. (a) (1,0,0) (x, y, z) =( (b) (18, 1/3, 1/4) (X, Y, z)
The rectangular coordinates are
a. (1,0,0) ⇒ (x,y,z) = (0,0,1)
b. (18,1/3,1/4) ⇒ (x,y,z) = (11.022,11.022,9)
Let us take ( x, y, z ) as cartesian or rectangular coordinates and ( r, Θ, ∅ ) are the spherical coordinates, then
x = r.sinΘ.cos∅ → 1
y = r.sinΘ.sin∅ → 2
z = r.cosΘ → 3
According to the given problem,
a.) ( 1, 0, 0 ) = ( r, Θ, ∅ )
Substitute the values r = 1, Θ = 0 and ∅ = 0 in 1, 2, 3.
1 ⇒ x = r.sinΘ.cos∅
= 1.sin0.cos0
= 1.0.1
x = 0
2 ⇒ y = r.sinΘ.sin∅
= 1.sin0.sin0
= 1.0.0
y = 0
3 ⇒ z = r.cosΘ
= 1.cos0
= 1.1
z = 1
∴ ( x, y, z ) = ( 0, 0, 1 )
b.) ( 18, π/3, π/4 ) = ( r, Θ, ∅ )
Substitute the values r = 18, Θ = π/3 and ∅ = π/4 in 1, 2, 3.
1 ⇒ x = r.sinΘ.cos∅
= 18.sinπ/3.cosπ/4
= 18.√3/2.1/√2
x = 11.022
2 ⇒ y = r.sinΘ.sin∅
= 18.sinπ/3.sinπ/4
= 18.√3/2.1/√2
y = 11.022
3 ⇒ z = r.cosΘ
= 18.cosπ/3
= 18.1/2
z = 9
∴ ( x, y, z ) = ( 11.022, 11.022, 9 )
Therefore the rectangular coordinates for the spherical coordinates of
a. ( 1, 0, 0 ) is ( 0, 0, 1 )
b. ( 18, 1/3, 1/4 ) is ( 11.022, 11.022, 9 )
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The graph of a linear function passes through (−8,−4) and (4, 5). What is the equation of the function? Please help.
Answer: y=(3/4)x+2
Step-by-step explanation:
1. Find the slope (change of y/change of x)
(5-(-4))/(4-(-8)
9/12
SLOPE: 3/4
2. Find the y-intercept. Insert the points into an equation and find b.
5=(9/12)(4)+b
5=3+b
b=2
Y-INTERCEPT=2
An artist creates a cone shaped sculpture for an art exhibit. If the sculpture is 15 feet tall and has total volume 235.5 cubic feet, what is the radius of the sculpture? Use 3.14 for pi
Answer: r = 19.35 ft
Step-by-step explanation:
[tex]Volume = V = \pi r^{2} \frac{h}{3} \\235.5 = \pi r^{2} 15/3\\r^{2} = \frac{235.5}{\pi} 5\\r = \sqrt{374.8} = 19.35[/tex]
Please help (Algebra 1)
The average rate of change of the function is 0.2 inches per day
How to determine the average rate of change of the function?
A rate of change describes how one quantity changes in relation to another quantity. Mathematically, it is defined as the change in one divided by the change in the other quantity.
In this case, the average rate of change of the function g(n) from n=1 to n=5 will be:
Given the function, g(n) = 10(1.02)ⁿ
average rate of change = g(5)-g(1) / n₅-n₁
g(5) = 10(1.02)⁵ = 11.0
g(1) = 10(1.02)¹ = 10.2
average rate of change = 11.0-10.2 / 5-1
= 0.8/4
= 0.2 inches per day
Therefore, the average rate of change from n=1 to n=5 is 0.2 inches per day
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a construction worker is pouring concrete stairs. the first step requires 1.8 cubic feet of concrete, and the first 5 steps require a total of 27 cubic feet. if the steps follow an arithmetic series, how much concrete is required for the first 12 steps?
If the steps follow an arithmetic series, the concrete required for the first 12 steps is 140.4.
Given, the first term of the arithmetic series, a=1.8 and the sum of first five terms that is s5=27, we have to find the sum of first 12 steps.
The formula to calculate the sum of the terms in AP is
Sn = n/2 {2a + (n - 1) d}
S5=5/2(2(1.8) +(5-1)d)
27=2.5(3.6+ 4d)
27=9+10d
27-9=10d
18=10d
d=18/10
d=1.8
The common difference d is 1.8.
Now we have to find S12,
S12=12/2(2(1.8) +(12-1)1.8)
= 6(3.6+19.8)
=6(23.4)
=140.4
S12=140.4
Therefore, the concrete required for the first 12 steps is 140.4.
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Find the value of X
(Triangle Congruence)
Answer:
x = 139°
Step-by-step explanation:
The sum of the internal angles of a triangles is 180°
a + 59 + 80 = 180
a = 180 - 139
a = 41°
a and x are supplementary angles. Supplementary angles sum 180°.
Then:
a + x = 180
41 + x = 180
x = 180 - 41
x = 139°
3[tex]3 divided by 19.5[/tex]
Answer:
1.38461538462
Step-by-step explanation:
The scale of a map is 1.5 centimeters =
120 kilometers. If two cities are
4.75 centimeters apart on the map,
what is their actual distance?
A. 420 km
B. 390 km
C.
380 km
D. 360 km
f(x)=-x^2-7x please answer
Answer:
[tex]f( x) = x2 - 7 x[/tex]
What is the slope of the line passing through the following two points.
P1 (4,6) and P2 (5, 9)
Enter your answer in the box.
you need to plug the coordinates into the slope formula, which is m=(y2-y1)/(x2-x1).
m=(9-6)/(5-4)
m=(3)/(1)
m=3
The two-way frequency table contains data about how students access courses.
Traditional Online Row totals
Computer 28 62 90
Mobile device 46 64 110
Column totals 74 126 200
What is the joint relative frequency of students who use a computer in a traditional class?
45%
37%
28%
14%
The joint relative frequency of students who use a computer in a traditional class is of:
37%.
How to obtain a relative frequency?The relative frequency of an event in an experiment is calculated as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.
In this problem, we want the joint relative frequency of students who use a computer in a traditional class, hence the total and desired outcomes are given as follows:
Total outcomes: 74 students in a traditional class.Desired outcomes: 28 students using a computer in a traditional class.Hence the joint relative frequency of students who use a computer in a traditional class is calculated as follows:
28/74 = 37%. (rounded down).
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Answer:
14%
Step-by-step explanation:
1. I took the test
2.Likes running and swimming=28
Total=200
28/200=.14
.14 in percent form is 14%
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Which transformation can be applied to the blue figure to create the red figure?
The sequence of transformations that we should apply is the one that appears on the top left option:
Reflection across the y-axis followed by a rotation of 90° counterclockwise.
Which sequence of transformations map the blue figure into the red one?We can see that the blue figure is on the third quadrant, and the "spiral" part is pointing upwards.
First, we would want to apply a rotation of 90° clockwise, this will move the blue figure to the second quadrant, and now the "spiral" part will point thowards the right.
Now you can see that the red figure is a reflection along the y-axis of the blue figure, so we need to apply that transformation.
Concluding, the sequence of transformations is:
rotation of 90° clockwise.reflection across the y-axis.Notice that this is equivalent to:
Reflection across the y-axis.rotation of 90° counterclockwise.Then the correct option is the one in the top left corner.
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The first container of milk contains twice as much milk as the second contamer After John uses 2 galions of milk from the second container and 3 gallons of milk from the first container, the first container has 45 times as much milk as the second, How many gallons of milk were in each container originally?
The gallons of milk were in each container originally is 2.4 and 4.8 gallons respectively.
How to calculate the gallons?Let us say that:
V₁ = initial gallons in the first container
V₂ = initial gallons in the second container.
From the problem statement, we can create the expression:
V₁ = 2 V₂
V₁ – 3 = 45 (V₂ – 2)
Combining the two expressions:
2 V₂ – 3 = 45 (V₂ – 2)
2 V₂ – 3 = 45 V₂ – 9
2.5 V₂ = 6
Divide
V₂ = 6 / 2.5
V₂ = 2.4 gallons
V₁ = 2 V₂:
= 2 × 2.4
= 4.8 gallons
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Complete question
The first container of milk contains twice as much milk as the second contamer After John uses 2 galions of milk from the second container and 3 gallons of milk from the first container, the first container has 4.5 times as much milk as the second, How many gallons of milk were in each container originally?