solve and show working:- log(x^2 + 7) base 4 = 2​

7 + 7 + 7 + 7 + 7​ means 7 is added 5 times

It could be written as

5(7)

7 x 5 and

7 . 5

But it can not be written as 7^5 because 7^5 means 7 x 7 x 7 x 7 x 7

Hence, 7^5 does not represent the expression 7 + 7 + 7 + 7 + 7​

This makes the correct option to be the third option. That is 7^5

Answer:

  $16.90 per hour

Step-by-step explanation:

You want the hourly wage Taylor earned when she worked 20 hours for $338.00.

To find dollars per hour, divide dollars by hours:

  $338.00/(20 h) = $16.90/h

Taylor earned $16.90 per hour.

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Answer:

6.75 miles

Step-by-step explanation:

27/2 = 13.5

27/4 = 6.75

27 miles in 2 hours

13.5 in 1 hour

6.75 in half an hour :)

Answer: 6.75 miles

Step-by-step explanation:27/4=6.75, I divided by 4 to get the half hour

Average rate of change is calculated using the slope of the line linking the interval's ends on the graph of the function. The average rate of change, in simplest form, is -1/6.

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

The formula for calculating the gradient of a function exists expressed as:

[tex]$m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}[/tex]

Using the coordinate points from the table (6, 53) and (24, 50).

Substitute the coordinate into the expression:

[tex]$m=\frac{50-53}{24-6} \\[/tex]

[tex]$&m=\frac{-1}{6} \\[/tex]

Therefore, the average rate of change, in simplest form is -1/6.

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The minutes will it be until they complete a lap at the same time is 2.4 minutes

From the information, Lana can walk around the track in 4 minutes and Raul can walk around the track in 6 minutes.

Lana will cover a distance of 1/4 while Raul will be represented as 1/6.

This will be illustrated as:

1/4 + 1/6 = 1

3/12 + 2/12 = 1

5x/12 = 1

Cross multiply

5x = 12

x = 12/5

x = 2.4 minutes

Note that x = number of minutes

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Answer:

you wmekekd

Step-by-step explanation:

Ramones’s Chemistry test was much better as it has higher Z-Score than history

For History test, Test score (x) = 40

Mean (μₓ) = 30, Standard deviation (σₓ) = 10

For Chemistry test, Test score (Y) = 40

Mean (μ) =30, Standard deviation (σ) =5

Ramones’s Z-score for History test is given by,

Z-Score = (x-μₓ)/σₓ =(40-30)/10 = 1

Ramones’s Z-score for chemistry test is given by,

Z-Score = (y-μ)/σ =(40-30)/5 = 2

Thus, Ramones’s Chemistry test was much better, because Chemistry test has higher z-score.

Difference in the mean score (α) =μₓ -μ =0

Difference in Z-Score= Z- Zₓ =1

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The multiplication model represented by the image is given as follows:

12(4 x 10) + (3 x 10) + (6 x 10) + 18.

A multiplication operation is equivalent to consecutive additions.

For the green squares, the following addition is obtained:

10 + 10 + 10 + 10 + 6.

(which is the number of squares painted green).

Considering a multiplication with consecutive additions, it is written as follows:

4 x 10 + 6.

For the red squares, the expression is:

4 + 4 x 10 + 2 = 4 x 10 + 6.

For the blue squares, the expression is:

8 + 3 x 10 + 8

3 x 10 + 16

For the white squares, the expression is:

2 + 6 x 10

Hence the total model is calculated as follows:

4 x 10 + 6 + 4 x 10 + 6 + 3 x 10 + 16 + 2 + 6 x 10

(4 x 10)(6 + 6) + (3 x 10) + (6 x 10) + 18.

12(4 x 10) + (3 x 10) + (6 x 10) + 18.

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We have to solve this linear equation for x:

The answer is x=19/6

Answer: A z=9

Step-by-step explanation:

Answer:

z = 12

Step-by-step explanation:

To understand the equation, you must first know that m∠a = 108°. It equals that because a regular five-sided polygon has an interior angle of 108° each.

Next, you would want to group all constants to the right side of the equation. By doing so, you want to subtract 72 from both sides.

(3z + 72) - 72 = 108 - 72

3z = 36

Lastly, you want to isolate the z by dividing 36 by 3.

z = 36 ÷ 3

z = 12

Answer:

I'll do #17 as an example of how to do the others. #15 doesn't make sense.  What is "= ≤⁄x?"

Step-by-step explanation:

17. (-3, 2); y=-4

y=4 is a horizontal line, where all values of y are 4, regardless of x.  A horizontal line has a slope of 0.  [Y does not depend on x].

That leaves us with y =0x + b

For this line to go through point (-3,2), it would have to have a y-intercept (b) of 2 [b is the value of y when x=0].  Since y=0 regardless of x, b must be 2.

The parallel line that goes through (-3,2) is:

y = 0*x + 2, or

y = 2

Answer:

10.736

Step-by-step explanation:

11 1/9 - 3/8 =10/53/72

= 10.736

The baker has 13/3 pounds of sugar.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

We have been given two fractions.

The three containers have 3/4 pounds of sugar and fourth one have 1/2 pounds of sugar.

To find the total sugar, we have to add both the fractions

Total pounds of sugar = Sugar in three containers + sugar in fourth container

= 3/4 + 1/3

= (9 + 4)/3

= 13/3 pounds

So, the total sugar the baker has is 13/3 pounds.

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The ratio of r-32 to r-125 is 3:2

A ratio in math displays how many times one number is contained in another. Comparing two numbers by dividing them is how ratios work. Your formula would be A/B if you were contrasting one data point (A) with another data point (B). When both sides of a ratio are whole numbers and cannot be divided by a whole number, the ratio is in its simplest form.

Given,

Refrigerant r-32 and r-125 are the two main constituents of refrigerant r-410.

60 pounds of r-32 and 40 pounds of  r-125 make up to 100 pounds of r-410.

The ratio of r-32 to r-125 = 60/40 =3/2.

Hence, the required ratio of r-32 to r-125 is 3:2

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The decimal number 1.025 is 41/40 in fractions.

A number system is defined as a system of writing to express numbers.

A fraction is a part of a whole

The decimal number one point zero two five should be converted to fraction.

The conversion of 1.025 to fraction is 41/40.

If we calculate  41/40 we get the value 1.025.

Hence 1.025 is 41/40 in fractions.

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Recall that the opposite of 2 is

Therefore, the opposite of the opposite of 2 is

Now, recall that a horizontal number line is of the form:

Therefore, 2 is to the right of zero.

Answer:

On a horizontal number line, the opposite of the opposite of 2 is to the right of zero and is written as 2.

       The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Below is a scale illustration of the Colombian flag that ranges from 1 cm to 2 ft.

         It is already stated that all measurements would be done using a fixed scale for a given scale drawing. Let the scale, for illustration, be K feet to s inches.

1ft ; s/k in

Thus, all foot measures will be multiplied by s/k to obtain the relevant lengths in the drawing.

Since the ratio is 2:1, there are 1 centimeter for every 2 feet.

This indicates that to reach 33, we must divide 66 by 2.

66/2 = 3

As a result, the scale drawing of the Colombian flag is attached below and has a scale of 1 cm to 2 ft.

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The equation of the quadratic function f(x) is f(x) = (x + 4)(x - 2)

From the question, we have the following parameters:

Roots = -4 and 2

Point = (1, -5)

Rewrite the given parameters as

Roots: x = -4 and x = 2

Point: (x, y) = (1, -5)

Recall that:

x = -4 and x = 2

This gives

x + 4 = 0 and x - 2 = 0

Multiply the equations

So, we have

y = a(x + 4)(x - 2)

When (x, y) = (1, -5), we have

-5 = a(1 + 4)(1 - 2)

This gives

a = 1

Substitute a = 1 in y = a(x + 4)(x - 2)

y = (x + 4)(x - 2)

Hence, the equation of f(x) = (x + 4)(x - 2)

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Answer:

f(x) = (x − 2)(x + 4)

Hope this helps you

To answer this question, we need to apply the rules of "PEMDAS".

Thus:

- we first deal with the numbers in the "Parentheses" or brackets

- then we perform the "Multiplication" operation

- and then we perform the "Subtraction" operation

This is done as follows:

- by dealing with the numbers in the parentheses, we get:

- now, by dealing with the multiplication, we have:

- finally, we deal with the subtraction, as follows:

Answer:

4:8

Step-by-step explanation:

Equivalent ratios have the same simplified ratio.

The simplified ratio of 3:6 is 1:2. We can get it by dividing both sides of the ratio by a common factor of 3.

18:9 is incorrect because its simplified ratio is 2:1. Equivalent ratios have the same order.

4:8 is correct because dividing both sides of the ratio by 4 gives us 1:2.

11:12 is incorrect because it can not be simplified to give 1:2.

Answer:

The answer for the question is = -18.6y - 64.8

33,800,000 are total distinct six characters license plates possible such that the two letters must appear next to each other. We can solve it by using combination formula ( ⁿCr ) .

Total number of digits are 10 i.e., 0,1,2,3,4,5,6,7,8,9. We have given the option to select any four digits out of 10 with repetition. So, we use combination formula

ⁿ C r = n!/(r! ×(n-r)! )

For 1ˢᵗ digit, the number ways to choose the 1ˢᵗ digit is ¹⁰C ₁= 10

For 1ˢᵗ letter, the number of ways to choose the 1ˢᵗ letter is ²⁶C ₁= 26

There are 10×10×10×10 = 10⁴ ways to choose four digits . In a similar way, the total number of letters for choice is 26 ; i.e., from A to Z. We were given the task of choosing two letters from a list of 26 , which were not necessarily distinct .

There are 26×26 = 26²ways to choose the two letters . For the letters to be next to each other, they can be the 1ˢᵗ and 2ⁿᵈ, 2ⁿᵈand 3ʳᵈ, 3ʳᵈand 4ᵗʰ, 4ᵗʰand 5ᵗʰ, 5ᵗʰ and 6ᵗʰ characters . So, there are 6-1 = 5 are choices for the positions of the letters .

Therefore, numbers of distinct license plates is 5×10⁴× 26² = 33,800,000

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Let the rectangle with side as x and y.

Determine the area of the rectangle.

The sides of the rectangle is increased by twice means that new sides are 2x and 2y.

Determine the area of new rectangle.

So new area is four times the previous rectangle.

Thus correct answer is option A quadruples.

In order to get the volume of the irregular figure, let's cut it into two regular figures. See the cut below.

First, let's calculate the volume of the upper part.

The dimensions of the upper part are 7cm by 3 cm by 3 cm. Since the shape is a rectangular prism, let's multiply 7, 3, and 3.

Hence, the volume of the upper figure is 63 cm³.

Let's now calculate the volume of the lower figure.

The dimensions of the lower figure are 5cm by 4 cm by 3 cm. Since this is a rectangular prism too, let's multiply the dimensions.

The volume of the lower figure is 60 cm³.

Let's add the volume of the two figures to get the volume of the entire irregular figure.

Therefore, the entire volume of the given irregular figure is 123 cm³.

Answer:

2^9

Step-by-step explanation:

8 is [tex]2^3\\[/tex], so we can replace [tex]8^3[/tex] for [tex](2^3)^3[/tex]

Exponents separated by parenthesis, multiply.

So [tex](2^3)^3=2^9[/tex]

The coordinates of the dresser

i.e A(-1,-1), B(2,-1), C(2,1), D(-1,1)

after rotating the dresser 180 degrees about the origin, translating 2 units left and 3 units up becomes

A(3, 2), B(0, 2), C(0,0), D(3, 0)

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

The coordinates of the vertices of the dresser.

A(-1,-1), B(2,-1), C(2,1), D(-1,1).

Now,

Rotating 180 degrees the coordinates become,

A(2, 1), B(-1, 1), C(-1, -1), D(2, -1)

Translating 2 units left.

The coordinates become:

A(2-2, 1-2), B(-1-2, 1-2), C(-1-2, -1-2), D(2-2, -1-2)

A(0, -1), B(-3, -1), C(-3, -3), D(0, -3)

Translating 3 units up.

The coordinates become:

A(0+3, -1+3), B(-3+3, -1+3), C(-3+3, -3+3), D(0+3, -3+3)

A(3, 2), B(0, 2), C(0,0), D(3, 0)

Thus,

The coordinates of the dresser

i.e A(-1,-1), B(2,-1), C(2,1), D(-1,1)

after rotating the dresser 180 degrees about the origin, translating 2 units left and 3 units up becomes

A(3, 2), B(0, 2), C(0,0), D(3, 0)

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Answer:

65

Step-by-step explanation:

First find the area of the triangles

a*b/2 is the equation for triangles

5*6/2 is 15

multiply 15*2 because there are two triangles

15*2=30

Now find the area of the rectangle

5*7=35

Then add.

30+35=65

:)

Answer: 198

Step-by-step explanation:

9 * 36 = 324

9 * 14 = 126

324 - 126 = 198

Hope this helps!

Both Sheila and Bob together can wash the car in 10 minutes

Calculating work :

The formulas to find work and time is given by

Time Taken = 1 / Rate of Work

Rate of Work = 1 / Time Taken

If a work can be done in x number of days, then the work can be done in one day = 1/x

Total Work done = Number of Days × Efficiency ( of the person or machine )

Given that,    

Sheila can wash her car in 15 minutes

Let us consider washing the car is 1 unit of work

Then the work can done by Sheila in 1 minute = 1/15  

Bob take twice as long as Sheila to wash the same

Bob can wash the same car in 30 minutes

Then the work can done by Bob  in 1 minute = 1/30  

From above calculation,

The work can be done by Sheila and Bob = (1/15 + 1/30)

= (2+1) /30 = 3/30 = 1/10  

So the efficiency of Both Sheila and Bob per minute = 1/10

Let Both can complete the work in x minutes

As we know Total Work done = time × Efficiency

⇒ 1 = x × 1/10

⇒ x = 1 × 10

⇒ x = 10 minutes

Therefore,

Both Sheila and Bob together can wash the car in 10 minutes

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