Cindy wants to paint a border around her circular picture frame. The
distance around the frame was 18 inches. What is the approximate
diameter of the picture frame?
O 12 in
5 in
6 in
13 in

Answer: y=4.5, z=6.7, x=6

Step-by-step explanation:

The value which shows the true solution to the logarithmic equation solved below is 1.

Domain of a function is the set of all the possible input values which are valid for that function.

Range of a function is the set of all the possible output values which are valid for that function.

The given logarithmic equation is,

[tex]\log_2x+\log_2(x+7)=3[/tex]

Use the addition property of log in above expression.

[tex]\log_2[x\times(x+7)]=3[/tex]

Use the power rule property of log in above expression.

[tex][x\times(x+7)]=2^3\\x\times(x+7)=8\\x^2+7x-8=0[/tex]

Solve the quadratic equation with the help of split the middle term method,

[tex]x^2+8x-1x-8=0\\x(x+8)-1(x+8)=0\\(x+8)(x-1)=0\\x=-8,1[/tex]

Here, the two values of variable we get. One is positive and another is negative. As the logarithmic function is defined only for positive real number as its input.

Thus, the value which shows the true solution to the logarithmic equation solved above is 1.

Learn more about the domain and range of the function here;

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Answer:

1

Step-by-step explanation:

edge 2022

Consider the missing lines of question are "Due to the Enhanced Community Quarantine, Grand Royal Spa temporarily stopped its operation and to help the employees, the owner decided to split evenly its total revenue of 65,000.00".

Given:

Total revenue = 65000

Number of employees = x

To find:

The function which represents the  amount each received.

Solution:

We know that,

[tex]\text{Amount each received}=\dfrac{\text{Total revenue}}{\text{Number of employees}}[/tex]

Substitute the given values in the above formula.

[tex]\text{Amount each received}=\dfrac{65000}{x}[/tex]

So, the function which represents the  amount each received is

[tex]f(x)=\dfrac{65000}{x}[/tex]

Therefore, the required function is [tex]f(x)=\dfrac{65000}{x}[/tex].

Note: Given options are not correct and option C is incomplete.

This question was not properly written

Complete Question

Select all the pairs of equivalent expressions.

a. (4³)³ and 4³ ⋅ 4³

b. (3⁴)⁴ and 3⁸ ⋅ 3⁸

c. 6⁴ ⋅ 3⁴ and 18⁸

d. 4³ ⋅ 5³and 20³

e. (4³)³ and 4³ ⋅ 4³ ⋅ 4³

2. Choose an equivalent expression for 12³ • 12⁹• 12⁴ • 12².

a. 12^4

b. 12^18

c. 12^35

d. 12^216

3. Choose an equivalent expression for 10⁶ ÷ 10⁴.

a. 10^2

b. 10^3

c. 10^10

d. 10^24

4. Select all the expressions that are equivalent to 7⁸ • 7.

a. 7³• 7³

b. 7^18/7^9

c. (7³)³

d. 7⁴ + 7⁵

e. 7⁴ • 7⁵

5. Is this equation correct?

6³⋅ 7³= 42³

A. Yes; 6³• 7³ is equal to (6 • 7)³ or 42³.

B. Yes; 6³ • 7³is equal to (6 • 7 • 3) or (42 • 3).

C. No; 6³ • 7³ is equal to (6 • 7 • 3) or (42 • 3).

D. No; 6³ • 7³ is equal to (6 • 7)³+ 3 or 42⁶.

Answer:

1 The correct answer is

d. 4³ ⋅ 5³ and 20³

e. (4³)³ and 4³ ⋅ 4³ ⋅ 4³

2b. 12^18

3 a = 10²

4a. 7³ • 7³

c. (7³)³

e. 7⁴ • 7⁵

5 A. Yes; 6³• 7³ is equal to (6 • 7)³ or 42³.

Step-by-step explanation:

1) Select all the pairs of equivalent expressions.

These are the correct options

d. 4³ ⋅ 5³and 20³

4³ × 5³ = 8000

20³ = 8000

e. (43)3 and 43 ⋅ 43 ⋅ 43

2. Choose an equivalent expression for 12³ • 12⁹• 12⁴• 12².

For an Algebraic Expressions,

We have the rule

x^a × x^b = x ^a+ b

Hence: 12³ • 12⁹• 12⁴ • 12².

= 12^3+9+4+2 = 12^18

Hence, b. 12^18

3. Choose an equivalent expression for

10⁶ ÷ 10⁴.

For an Algebraic expressions

x^a ÷ x^b = x ^a - b

Therefore

10⁶÷ 10⁴ = 10²

a. 10^2 Is the correct option

4. Select all the expressions that are equivalent to 7⁸ • 7.

7⁸ . 7= 7^8+1

= 7^9 or 7⁹

The equivalent expressions are:

a. 7³ • 7³ = 7⁹

b. 7^18/7^9 = 7⁹

c. (7³)³ = 7⁹

e. 7⁴ • 7⁵ = 7⁹

5. Is this equation correct?

6³ ⋅ 7³ = 42³

A. Yes; 6³• 7³ is equal to (6 • 7)³ or 42³

Answer:

8 pizzas

Step-by-step explanation:

If each of the 20 people eats 3/8 of pizza, to calculate the total number of pizzas needed, multiply 20 by 3/8 and round up to the nearest whole number.

[tex]\sf total \ number \ of \ pizzas=20 \times\dfrac38[/tex]

                                  [tex]=\dfrac{20 \times3}8[/tex]

                                  [tex]=\dfrac{60}8[/tex]

                                  [tex]=\dfrac{15}2[/tex]

                                  [tex]=7.5[/tex]

Therefore, he should buy 8 pizzas for the party.

Answer:

[tex]x=6[/tex]

Step-by-step explanation:

Using the given measurements of the angles and the lengths of the sides, we can determine that this figure must be a rectangle.

Diagonals of a rectangle are always equivalent/congruent.

We can use this information to set up an equation:

[tex]DF=EG\\7x-3=5x+9[/tex]

Add 3 to both sides:

[tex]7x-3+3=5x+9+3\\7x=5x+12[/tex]

Subtract 5x from both sides:

[tex]7x-5x=5x-5x+12\\2x=12[/tex]

Divide both sides by 2

[tex]\frac{2x}{2}=\frac{12}{2}\\x=6[/tex]

Answer:

[tex] \: [/tex]

Step-by-step explanation:

A rectangle is a parallelogram with equal angles and the diagonals of a rectangle are of equal length.

[tex] \: [/tex]

Therefore,

[tex] \\ { \longrightarrow \qquad{ \sf{ \pmb {DF = EG}}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ \sf{ \pmb {7x - 3 = 5x + 9}}}} \: \: \\ \\[/tex]

Subtracting 5x from both sides we get :

[tex] \\ { \longrightarrow \qquad{ \sf{ \pmb {7x - 5x - 3 = 5x - 5x + 9}}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ \sf{ \pmb {2x - 3 = 9}}}} \: \: \\ \\[/tex]

Adding 3 to both sides we get :

[tex] \\ { \longrightarrow \qquad{ \sf{ \pmb {2x - 3 + 3 = 9 + 3}}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ \sf{ \pmb {2x = 12}}}} \: \: \\ \\[/tex]

Dividing 2 from both sides we get :

[tex] \\ { \longrightarrow \qquad{ \sf{ \pmb { \frac{2x}{2} = \frac{12}{2} }}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ \frak{ \pmb {x = 6}}}} \: \: \\ \\[/tex]

Therefore,

Answer:

polyester, orange

polyester, blue

polyester, yellow

cotton, orange

cotton, blue

cotton, yellow

Step-by-step explanation:

Answer:25

Step-by-step explanation:

Answer:

The new points after a rotation of 180 degrees is;

M’ = (-3, 1)

N’ = (-8,4)

O’ = (-6,6)

P’ = (-1 , 7)

Step-by-step explanation:

Given a point (x , y) and we rotate by 180 degrees , the new point will be (-x , -y)

So to the question;

M’ = (-3, 1)

N’ = (-8,4)

O’ = (-6,6)

P’ = (-1 , 7)

Answer:

Length of the rectangle = 14.5 inches

Width of the rectangle = 37.5 inches

Step-by-step explanation:

Let the length of a rectangle = a inches

Since, width of the rectangle is 6 inches less than 3 times the length,

w = 3a - 6

Perimeter of the rectangle = 104 inches

Formula to calculate the perimeter of a rectangle = 2(length + width)

104 = 2[a + (3a - 6)]

2a + 2(3a - 6) = 104 → [Starting equation]

8a - 12 = 104 → [Distributive property]

8a - 12 + 12 = 104 + 12 → [Addition property of equality]

a = [tex]\frac{116}{8}=14.5[/tex] → [Division property of equality]

a). width of the rectangle = (3a - 6) = 37.5 inches

b). length of the rectangle = 14.5 inches

The width of the rectangle is 37.5 inches and the length of the rectangle is 14.5 inches.

The perimeter of a rectangle is represented as follows:

perimeter = 2l + 2w

where

w = width

l = length

Therefore,

perimeter = 104 inches

let

the length = a

Therefore,

width = 3a - 6

Therefore,

104 = 2a + 2(3a - 6)

104 = 2a + 6a - 12

116  = 8a

a = 116 / 8

a = 14.5  inches

width = 3(14.5 ) - 6 = 37.5  inches

Therefore, the width of the rectangle is 37.5 inches and the length of the rectangle is 14.5 inches.

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Answer:

give me a sec........I need to analyze somethings

The equation for the first and second model will be y = - (x + 3)³ and y = 2(√x) + 1, respectively.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The equation for a cubic function that has been reflected over the x-axis and shifted left 3 units. Then add 3 in the function and multiply the function by negative 1.

y = - (x + 3)³

The equation for a square root function has been stretched by a factor of 2 and shifted 1 unit up. Then multiply the function by 2 and add 1 to the function.

y = 2(√x) + 1

More about the function link is given below.

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The expression which is equivalent to Start Fraction 5 y cubed Over (5 y) Superscript negative 2 Baseline End Fraction is

[tex]125y^5[/tex]

Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.

To find the equivalent expression, simplify the provided function using the mathematical operations.

The given algebraic expression is,

[tex]\dfrac{5y^3}{(5y^{-2})}[/tex]

Suppose the equivalent expression of this fraction is n. Thus,

[tex]n=\dfrac{5y^3}{(5y^{-2})}\\\\n=\dfrac{5y^3}{((5)^{-2}y^{-2})}\\[/tex]

In the division the power of the same number is subtracted. Therefore,

[tex]n=(5)^{1-(-2)}(y)^{3-(-2)}\\n=5^3\times y^5\\n=125y^5[/tex]

Hence, the expression which is equivalent to StartFraction 5 y cubed Over (5 y) Superscript negative 2 Baseline EndFraction is

[tex]125y^5[/tex]

Learn more about the equivalent expression here;

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Answer:

The answer is D.

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

I think it's 31

Step-by-step explanation:

Answer:

x = 31°

Step-by-step explanation:

The two triangles seem to be identical.

All angles of a triangle must add up to 180° to make a triangle.

So, 53° + 96° = 149°

Subtract 149° from 180°

180° - 149° = 31°

So x = 31°

Hope I helped :)

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Answer:

The true solution to the logarithmic equation log(x)+log(x+5)=log(6x+12) is 4 option second is correct.

It is given the logarithmic equation [tex]\rm logx+log(x+5)=log(6x+12)[/tex].

It is required to find the true solution to the above logarithmic equation.

It is another way to represent the power of numbers and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

[tex]\rm a^b=c\\[/tex]

[tex]\rm log_ac=b[/tex]

We have:

[tex]\rm logx+log(x+5)=log(6x+12)[/tex]

By using log property:

[tex]\rm logx + logy= log(xy)[/tex]

[tex]\rm log((x)(x+5))=log(6x+12)[/tex]

Taking [tex]\rm log_1_0[/tex] base and removing the log from the sides we get:

[tex]\rm x(x+5)= 6x+12\\\\\rm x^2+5x=6x+12\\\\\rm x^2-x-12=0[/tex]

It is quadratic equation solving by factorization method:

[tex]\rm x^2-x-12=0\\\\\rm x^2+3x-4x-12=0\\\\\rm x(x+3)-4(x+3)=0\\\\\rm (x+3)(x-4)=0\\\\\rm x+3=0 \ or \ x-4=0\\\\ \rm x=-3 \ or \ x=4\\\\[/tex]

A negative Logarithm value does not exist.

Hence, the true solution to the logarithmic equation log(x)+log(x+5)=log(6x+12) is x = 4

Learn more about the logarithm here:

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So, when you look at a graph. Where the line passes over the X-Axis, that is the X intercept. Where the line passes over the Y-Axis, that is the y intercept.

Step-by-step explanation:

I am not sure I understand the question with all the typos and potentially missing parts.

as I understand it, it will take her 4 hours to reach her destination when going 15 mph.

and the question is how long the trip will take, if she travels at 12 mph.

4 h × 15 m/h = 4 × 15 m = 60 miles

that is the distance of her trip.

when going slower, the distance is of course still the same, only the needed time changes :

x h × 12 m/h = 60 m

x × 12 m = 60 m

x = 60/12 = 5 hours

the trip would take her 5 hours to complete (instead of 4).

Answer:

∠x = 50°

Step-by-step explanation:

All external angles of a polygon add up to 360°.

Therefore,

Answer:

The answer is "Option c"

Step-by-step explanation:

In the given question, in choice c the numerice value is missing, that is "0.05".

The null hypothesis can only be rejected whether there is enough statistical data than that of the critical values.

Answer:

13 hours

Step-by-step explanation:

567/9= 63 mile per hour

819/63 = 13

13 hours

Answer:

13 hours

Step-by-step explanation:

how long does she drive in one hour?

567/9=63

she drives 63mph

819/63=13

it will take her 13 hours to drive 819 miless

Answer:

C.) mAngleGLI = 2mAngleGLH

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

x-14=42

Step-by-step explanation:

let x be Julies age x= the difference between julies unknown age and 14

Solution,

The population of a city is 2,549,786.

We can convert it into nearest million as follows :

Million = 10 lakhs

Rounding off to the nearest million

2,549,786 = 3,000,000

There are 6 zeroes after 3. We can express as the product of a single digit and a power of 10 as follows :

[tex]3,000,000=3\times 10^6[/tex]

Hence, the population of the city is 2,549,786 or [tex]3\times 10^6[/tex].

Answer:x=y-bm

Step-by-step explanation:

Answer:

x = y-b/m

Step-by-step explanation:

Step 1:  y = mx + b

Step 2: Bring b to the left side of the equation

Step 3: y - b = mx

Step 4: To isolate for x, we must get rid of m. Therefore, divide m on both sides of the equation

Step 5: y-b/m = mx/m

Step 6: On the right side of the equation, m and m crosses out.

Step 7: All we have left is: y-b/m = x

(Or you can write it as x = y-b/m)

Hope this helps.

Answer:

  12 c

Step-by-step explanation:

You can add up the hourly changes, or you can use multiplication to do the repeated addition. The increase in temperature over 6 hours is ...

  2c +2c +2c +2c +2c +2c

  = 6 × 2c

  = 12c

The total change in temperature was an increase of 12c over the 6-hour time period.

Answer:

No, the correct answer is 32cm.

Step-by-step explanation:

First of all, lets cut the shape into two. A rectangle and a triangle. This will help us find the slanted side of the shape.

We will use the pythagorean theorem to find the length of the slanted line.

The pythagorean theorem is [tex]a^{2} +b^{2} =c^{2}[/tex].

Input the given information of the triangle lengths that we know; that is the length= 6 and the base=3.

[tex]c= \sqrt{a^{2}+b^{2} } =\sqrt{6^{2}+\ 3^{2} } = 6.7082[/tex]

Now, we round.

6.7082≈ 6.7

We have found the length of the slanted line of the shape.

Now, let's add all the lengths together.

8+6+6.7+11= 31.7

Now, lets round.

31.7 ≈ 32cm

Hope this helps!

Answer: C, D

Step-by-step explanation: