Rewrite as a single logarithm: 3 log b x+4 log b y​

Answer: 3 inches

Step-by-step explanation:

f(x) = x becomes g(x) = (1/5)x through vertical compression by a factor of 5.

The length of the diagonal brace when Jonathan is building a box in the shape of a rectangular prism is 17 inches.

From the information given, the dimensions are given as 8 inches by 12 inches by 9 inches.

Therefore, the length of the diagonal brace will be:

= ✓12 + ✓8 + ✓9

= ✓289

= 17

In conclusion, the correct option is 17 inches.

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Answer:

The length of the diagonal of Stacy's ceiling was found to be 31 feet using both Pythagorean theorem and trigonometry.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let d represent the length of the diagonal, Usinng Pythagoras:

d² = 22² + 22²

d = 31 feet

Using trigonometric identity:

sin(45) = 22/d

d = 31 feet

The length of the diagonal of Stacy's ceiling was found to be 31 feet using both Pythagorean theorem and trigonometry.

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Step-by-step explanation:

Answer:

Step-by-step explanation:

Jim drank 2 and 4/5 orange juice

2and 4/5=14/5 orange juice

jack drank  1and 1/10 less than Jim= 11/10 less than Jim

I introduce the whole numbers into the fractions

we will convert the number 14/5 into a fraction that has the denominator 10, by multiplying by 2 both numerator and denominator

(14/5 )*2=28/10

Now we can find out how much juine Jack drank

28/10- 11/10= 17/10

so Jack drank 17/10 orange juice , the fraction can be written also as

1 and 7/10

Answer:

C. m=1/2 and b=-4

Step-by-step explanation:

To get the slope-intercept notation, you have to convert Ax+By = C to y = mx + b. We can do that by simply moving y to the left side and the rest to the right, or simply use the formula of m = -A/B, b = C/B

We'll do both, they're the same really.

x-2y=8

x-8=2y

2y=x - 8

y = 1/2*x - 4

Alternatively

x-2y=8

A = 1

B = -2

C = 8

m = -(1/-2) = 1/2

b = 8/-2 = -4

Answer:

D. Industrialization cause of poverty.

Answer:

n=45

Step-by-step explanation:

Sum of interior angles can be calculated using formula: 180(number of sides - 2).

Hexagon has: 720 degrees. we subtract two right angles and get 4x=540. The x is the angle supplement to n. x=135 => 180-x=35 => n=45.

The circle is an illustration of tangent and secant lines, and the length of FE in the circle is 9.3 units

The lengths are given as:

Start calculating the length DF using:

DE * DF = CD²

So, we have:

12 * DF = 16²

Evaluate the exponent

12 * DF = 256

Divide both sides by 12

DF = 21.3

The length FE is then calculated using:

DF = FE + DE

Substitute DE = 12 and DF = 21.3

21.3 = FE + 12

Subtract 12 from both sides

FE = 21.3 - 12

Evaluate the difference

FE = 9.3

Hence, the length of FE in the circle is 9.3 units

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Answer:

x = 10

Step-by-step explanation:

Answer:

[tex]\bf x=10[/tex]

Step-by-step explanation:

[tex]\tt 4x+3(x-1)=67[/tex]

Use the distributive property to multiply 3 by x-1:-

[tex]\tt 4x+3x-3=67[/tex]

Combine 4x and 3x = 7x:-

[tex]\tt 7x-3=67[/tex]

Add 3 to both sides:-

[tex]\tt 7x=70[/tex]

Divide both sides by 7:-

[tex]\tt \cfrac{7x}{7} =\cfrac{70}{7}[/tex]

[tex]\tt x=10[/tex]

Answer:

f(g(x)) = =2(-x^2+5)-3

=-2x^2+10-3

=-2x^2+7

Sorry, I'm not sure about g(f(x)).

Step-by-step explanation:

f(g(x))=f(-x^2+5)=2x-3

=2(-x^2+5)-3

=-2x^2+10-3

=-2x^2+7

Answer:

y = -1/4x + 1

Step-by-step explanation:

Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

The y-intercept of the line is 1, so in slope-intercept form, b will be 1.

Now, the line also intersects the y-axis at (4, 0). We can plug these two points into slope formula to find the slope: (0-1)/(4-0) = -1/4.

Therefore, the equation of the line is y=-1/4x + 1

Answer:

Every third student who enters each homeroom

Step-by-step explanation:

This would produce the least biased results as every third student gives a 3/x for students and there are y homerooms, giving the least biased results.

Answer:

The slope is 6

Step-by-step explanation:

m = y2 - y1/x2 - x1

ΔX = 3 – 2 = 1

ΔY = 7 – 1 = 6

6/1 = 6

Answer:

720, 5040

Step-by-step explanation:

It's always times plus 1. So,
1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

720 x 7 = 5040

Answer:

the answer is C

Step-by-step explanation:

Answer:

c 2.00 in vec ay se the back yard

Answer:

0

Step-by-step explanation:

(x,y)      slope is change in y / change in x⇒  Δy/Δx

(6,2)

(-18,2)

Δy = 2-2 = 0

Δx = 6-(-18) = 24

because the y values are the same, when you subtract you a slope of 0/24 or just 0 a horizontal line (because y is always =2)

We will see that the cube must be 10.23 inches tall.

The volume of the cube must be equal to the volume of the 4 spheres. Remember that the volume of a sphere of radius R is:

V = (4/3)*3.14*R^3

In this case, the radius is 4 inches, so we can write:

V = (4/3)*3.14*(4 in)^3 = 267.95 in^3

Then the volume of the 4 spheres is:

4*267.95 in^3 = 1,071.79 in^3

The volume of a cube of side length S is given by:

V = S^3

Then we must have:

S^3 = 1,071.79 in^3

S = ∛(1,071.79 in^3) = 10.23 in

We conclude that the cube is 10.23 inches tall.

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Answer:

1/2652

Step-by-step explanation:

52 cards    one jack spades      1/52

now 51 cards left   one jack diamonds   1/51

1/52 * 1/51 = 1 / 2652

Answer:

B.

Step-by-step explanation:

Because if you look closely you will be able to tell which answer it is by looking at the way the shape formed andjust breakaprt the shape .

Answer:

75%

Step-by-step explanation:

The probability that the next chew Luis removes from the bag will be a flavour other than strawberry as a fraction in simplest form is (29/37).

The probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

The number of times the experiment was done is 37 (15+14+8). The number of times apple chew came as a result of the experiment is 14, while the number of times peach chew came as a result of the experiment is 15. Therefore, the probability that the next chew Luis removes from the bag will be a flavour other than strawberry as a fraction in simplest form is

[tex]\rm Probability = \dfrac{\text{Number of times apple chew or peach chew was selected}}{\text{Total number of times experiment was performed}}\\\\\\Probability = \dfrac{14+15}{37} = \dfrac{29}{37}[/tex]

Hence, the probability that the next chew Luis removes from the bag will be a flavour other than strawberry as a fraction in simplest form is (29/37).

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Answer:

x=13

Step-by-step explanation:

Side Splitter Theorem states that If a line is parallel to one side of a triangle and intersects the other two sides, it divides both sides proportionally.

21/14 =1.5

6x1.5 = 9

x-4=9

x=13

Using proportions, given the density value, it is found that the ballons contain 9.8 kilograms of helium.

A proportion is a fraction of a total amount.

In this problem, we have that each ballon contain 0.14 kilograms per cubic meter.

You get 5 ballons, each with 14 cubic meters, hence the total volume is given by:

V = 5 x 14 = 70 m³.

Applying the density, we have that the total mass is given by:

M = 0.14 x 70 = 9.8 kilograms.

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Answer:

6,597 cups

Step-by-step explanation:

y=0.9x x=7,330 7,330 x 0.9= 6,597

Answer:

Mean Absolute Deviation: 4

Step-by-step explanation:

A mean absolute deviation is measured how much the values in the data set are likely to differ from the mean.

     [tex]I=\displaystyle \int \dfrac{\sqrt x}{\sqrt x -4} ~dx\\\\\text{Let,}\\\\~~~~u=\sqrt x-4\\\\\implies \dfrac{du}{dx} = \dfrac d{dx} \left( \sqrt x -4 \right)\\\\\implies \dfrac{du}{dx} = \dfrac 1{2 \sqrt x} \\\\\implies dx =2\sqrt x~ du\\\\\\I= \displaystyle \int \dfrac{u+4}{u+4 -4 } 2(u+4) du\\\\\\~~~=2\displaystyle \int \dfrac{(u+4)^2}{u} du\\\\\\~~~=2\displaystyle \int \dfrac{u^2+ 8u+16}{u} du\\\\\\~~~=2\displaystyle \int \left(u+8+\dfrac{16}u\right) du\\\\\\[/tex]

    [tex]~~~=2\left(\displaystyle \int u ~ du + \displaystyle \int 8 ~ du + \displaystyle \int \dfrac{16} u ~ du\right) \\\\\\~~~=2\left( \dfrac {u^2}2 + 8u+16\ln |u| \right) +C\\\\\\~~~~= u^2 + 16u+ 32 \ln |u|+C\\\\\\~~~~=\left( \sqrt x -4 \right)^2 + 16\left( \sqrt x -4 \right) +32 \ln |\sqrt x -4|+C\\\\\\~~~~= x-8\sqrt x+16 +16\sqrt x -64 +32 \ln \left|\sqrt x-4 \right|+C\\\\\\\~~~~=x+8\sqrt x -48 +32\ln|\sqrt x -4| +C[/tex]