Solve for x. Round to the nearest tenth, if necessary.

Answer:

2 ( Option A )

Step-by-step explanation:

The given integral to us is ,

[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]

Here 5 is a constant so it can come out . So that,

[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]

Now we can write √x as ,

[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]

Simplify ,

[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]

On simplifying we will get ,

[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]

Step-by-step explanation:

[tex]thank \: you[/tex]

Answer:

x = 15, y = 4

Step-by-step explanation:

To solve this, we have to define the triangles first. Since the triangles are congruent by HL, it means that the hypotenuse and the leg of the triangle are defined to be equal. By flipping one of the triangles upsidedown, we can visualize the hypotenuse of the triangles and the leg of the triangles (which are equal).

The two equations are the following:

[tex]x + 1 = 4y[/tex]

[tex]x = y + 11[/tex]

If I add 1 to both sides of the second equation, I get the following equation:

[tex]x + 1 = y + 11 + 1 = y + 12[/tex]

By comparing this new equation with the first one, we will get:

[tex]x + 1 = 4y = y + 12[/tex]

We can ignore x+1 for now since y can not be solved.

[tex]4y = y + 12[/tex]

By subtracting both sides of this equation by y, we will get.

[tex]3y = 12[/tex]

This solves for y, where

[tex]y = 4[/tex]

Now, we can re-use one of the equations, which is

[tex]x = y + 11[/tex]

Now that we know y is 4, we can plug it into this equation.

[tex]x = 4 + 11 = 15[/tex]

Answer:Steve age will be 15 y.o

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

the whole area is the sum of the area of the rectangle in the middle and the 2 triangles on either side of the rectangle.

sBC = distance between (0,3) and (4,-1)

and that is the Pythagoras calculation with the coordinate differences

sBC² = (4-0)² + (-1 - 3)² = 16 + 16 = 32

sBC = sqrt(32) = sFE

to get the area of the rectangle we need also FB (or CE).

sFB² = (0 - -2)² + (3-1)² = 4 + 4 = 8

sFB = sqrt(8) = sCE

area of rectangle is

sBC×sFB = sqrt(32)×sqrt(8) = sqrt(32×8) = sqrt(256) = 16

the area of a right-angled triangle is

a×b/2

we have sFB and need sAF

sAF² = (-5 - -2)² + (4-1)² = 9 + 9 = 18

sAF = sqrt(18)

the area of the left triangle is

sFB×sAF/2 = sqrt(8)×sqrt(18)/2 = sqrt(8×18)/2 = sqrt(144)/2 = 12/2 = 6

for the right triangle we have sCE and need sED.

sED² = (2 - 4)² + (-3 - -5)² = 4 + 4 = 8

sED = sqrt(8)

the area of the right triangle is

sCE×sED/2 = sqrt(8)×sqrt(8)/2 = 8/2 = 4

so in total we have for the area

16 + 6 + 4 = 26

Area = length x width

Fill in the given information

20 = 2 x width

Solve for width by dividing both sides by 2

Width =20/2

Width = 10 feet

Answer:

It is 10 feet wide

Step-by-step explanation:

The area of a rectangle is:

A = Length x width

So if we have the area, finding the width means diving the area by the given length.

In this case, the area of the rectangle is 20 square feet and the length is 2 feet:

20/2 = 10

Therefore the missing width is 10 feet

Answer:

50.265

Step-by-step explanation:

Area is radius square times pi. Radius is half of diameter .Diameter is 8 inches. Radius is 4 inches. 4 squared is 16. 16 times pi is 50.265

Answer:

x = his sister's height = 19 inches

Step-by-step explanation:

Let

x = his sister's height

Jahlil's height is given by the equation:

4x - 6 = 70

4x = 70 + 6

4x = 76

x = 76/4

x = 19 inches

x = his sister's height = 19 inches

Check:

4x - 6 = 70

4(19) - 6 = 70

76 - 6 = 70

70 = 70

Answer:

Step-by-step explanation:

A: true. Her graph goes 4 units up.

B: False. His graph goes 4 units to the left. Be sure you check this answer out.

C: True. It moved from (0,0) to (0,4)

D: Victor's graph move left in the minus direction. False.

E. True. See C.

The correct statements are true regarding the two graphs are as follows;

Ava’s graph is a vertical translation of f(x) = x^2.

Ava’s graph moved 4 units from f(x) = x^2 in a positive direction.

Ava’s graph has a y-intercept of 4.

A function relates an input to an output. It is like a machine that has an input and an output. And the output is related somehow to the input.

Ava graphs the function h(x) = x^2 + 4.

Victor graphs the function g(x) = (x + 4)^2.

To find the y-intercept we plug in 0 for x;

[tex]\rm h(x) = x^2 + 4\\\\h(0)=(0)^2+4\\\\h(0)=4[/tex]

Ava’s graph has a y-intercept of 4.

Ava graphs the function h(x) = x^2 + 4.

If any number is added at the end then the graph will be shifted up. 4 is added at the end so there will be vertical translation.

Hence , Ava’s graph is a vertical translation of f(x) = x^2.

Also Ava moved 4 units up from f(x) = x^2 in a positive y- direction.

Victor graphs the function g(x) = (x + 4)^2.

If any number is added with x then the graph will be shifted left. the graph will be shifted in the negative x-direction.

Learn more about function here;

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Answer:

[tex]g(-2)=20[/tex]

Step-by-step explanation:

Given [tex]g(x)=2x^2-2x+8[/tex], substitute what is in the parentheses for [tex]x[/tex] to find an output.

For [tex]g(-2)[/tex], the term [tex]-2[/tex] is in the parentheses. Thus, substitute [tex]x=-2[/tex] into [tex]2x^2-2x+8[/tex] to find [tex]g(-2)[/tex]:

[tex]g(-2)=2(-2)^2-2(-2)+8,\\g(-2)=2\cdot 4+4+8,\\g(-2)=8+4+8,\\g(-2)=\boxed{20}[/tex]

Answer:

a) 8

b) 20

c) 20

Step-by-step explanation:

a) Insert X=0 from g(0) to the equation: 2(0) power of 2 - 2x0 +8.

b) Insert X=(-2) from g(-2) to the equation: 2(-2) power of 2 - 2x(-2) +8.

c) Insert X=3 from g(3) to the question 2(3) power of 2 - 2x3 +8.

Answer:

(12, 48 )

Step-by-step explanation:

Given the 2 equations

y = 5x - 12 → (1)

y = 3x + 12 → (2)

Substitute y = 5x - 12 into (2)

5x - 12 = 3x + 12 ( subtract 3x from both sides )

2x - 12 = 12 ( add 12 to both sides )

2x = 24 ( divide both sides by 2 )

x = 12

Substitute x = 12 into either of the 2 equations and evaluate for y

Substituting into (2)

y = 3(12) + 12 = 36 + 12 = 48

solution is (12, 48 )

Answer:

The value of P(AUB) = 0.438

Step-by-step explanation:

Given:

P(A) = 0.36

P(B) = 0.2

P(A∩B) = 0.122

Find:

The value of P(AUB)

Computation:

P(AUB) = P(A) + P(B) - P(A∩B)

The value of P(AUB) = 0.36 + 0.2 - 0.122

The value of P(AUB) = 0.56 - 0.122

The value of P(AUB) = 0.438

Answer:

[tex]\left(3x+4\right)\left(x-8\right)[/tex]

[tex]a=3x,\:b=4,\:c=x,\:d=-8[/tex]

[tex]=3xx-3\cdot \:8x+4x-4\cdot \:8[/tex]

[tex]=3x^2-20x-32[/tex]

--------------------------

hope it helps...

have a great day!!

Answer:

D=22-90+22d/7

Step-by-step explanation:

D=22/7×d-90

D=-90+22d/7

Answer:

Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.

Ice Cubes 4 2 3 5 5 3 1

Juice (milliliters) 177 234 202 140 155 210 265

She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:

y = -29.202x + 293.5.

Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice

Step-by-step explanation:

Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice.

Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.

Ice Cubes             4        2      3        5       5      3        1

Juice (milliliters)  177    234   202   140   155   210   265

She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:

y = -29.202x + 293.5.

A line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points. Statisticians typically use the least-squares method to arrive at the geometric equation for the line, either through manual calculations or regression analysis software.

Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice.

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Answer:

Step-by-step explanation:

This is because the triangle has exactly two sides that are the same length.

If all three sides were the same length, then it would be equilateral.

If neither of those cases, then we consider the triangle scalene.

Answer:

A. Similar - AA

Step-by-step explanation:

The given parameters of ΔPQR and ΔXYZ are;

In ΔPQR, we have; PQ = 3, PR = 5, and ∠PQR = 80°

In ΔXYZ, we have; XY = 6, XZ = 10, and ∠XYZ = 80°

In ΔPQR, by sine rule, we have;

3/(sin(∠PRQ)) = 5/(sin(80°))

sin(∠PRQ) = (3/5) × sin(80°)

∴ ∠PRQ = arc sin((3/5) × sin(80°))

In ΔXYZ, by sine rule, we have;

6/(sin(∠XZY)) = 10/(sin(80°))

sin(∠XZY) = (6/10) × sin(80°) = (3/5) × sin(80°)

∴ ∠XZY = arc sin((3/5) × sin(80°))

∠PRQ = ∠XZY by transitive property of equality

Therefore in ΔPQR and ΔXYZ, we have;

∠PRQ = ∠XZY and ∠PQR = ∠XYZ

Therefore, ΔPQR is similar to ΔXYZ by Angle Angle, AA, similarity postulate.

Step-by-step explanation:

The answer is B 24:15,divide both by 3 and check out the answers

Answer:

5/12

Step-by-step explanation:

1/2 x 5/6 = 5/12

Answer:

All numbers have an equal chance of being landed on.

Answer:

40 degrees

Step-by-step explanation:

Answer:

4

Explanation:

Answer:

22

Step-by-step explanation:

1.) -2²-9(-2)

2.) -2(-2)+18

3.) 4+18

4.) 22

Answer:

a. 42

b. -12x-5

c. -60

d. -75

e. 66

f. -90

g. 144

h. -135

Answer:

-1

Step-by-step explanation:

we match the input to the output to find that f(3) points towards -1

Answer:

The vertical line test can be used to determine whether a graph represents a function.

If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value.

Answer: D. between 4.79 and 4.8

Step-by-step explanation:

The square root of 23 (√23) is 4.79583152331. We can obviously eliminate A and B. C and D is left. C is wrong because if we approximate the square root of 23, which is 4.79583152331, we get 4.79. 4.79 > 4.78, so it can't be C. Hope this helps :)

i'm on the same test-

Given,

d = 2t

here, t = 25

Therefore,

d = 2*25

= 50m

Answer:

120 * 0.90 = 108 km

Step-by-step explanation:

Answer:

108km

Step-by-step explanation: