4. From ThursdaySimplify the e2 (p + 4) + 6p

The measurement of ∠STU is 20°.

Define Angle

When two rays are connected at their endpoints, they form an angle in geometry. We refer to these rays as the angle's sides or arms.

Components of an Angle

An angle is composed of the arms and the vertex as its two basic components:

Given, ∠STU = [tex](\frac {1}{4} x+8)[/tex]°

∠UTV = x+2°

Given, that the line TV bisects ∠STU,

∠STV = ∠UTV

Substitute their values,

[tex](\frac {1}{4} x+8)[/tex]° = x+2°

Calculating,

[tex]\frac{1}{4}x-x[/tex] = 2-8

[tex]-\frac{3}{4}x[/tex] = -6

x = [tex]-6*(-\frac{4}{3})[/tex]

x = 8

So, we know that:

∠STU = ∠STV + ∠UTV

          =  [tex](\frac {1}{4} x+8)[/tex]° +( x+2°)

          =  [tex](\frac {5}{4} x+10)[/tex]

Now, substitute the value of x,

∠STU =  [tex](\frac {5}{4} )*8[/tex]°+10°

          = 10° + 10°

          = 20°

Therefore, the measure of ∠STU is 20°.

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Answer:

perpendicular slope = 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

x + y = 9 ( subtract x from both sides )

y = - x + 9 ← in slope- intercept form

with slope m = - 1

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-1}[/tex] = 1

$145.60 ---> 74%

x -------------> 100%

answer: $196.76 is the orginal price

Answer:

  28(3 +1)

Step-by-step explanation:

You want the expression 84+28 to be factored using the GCF.

The Greatest Common Factor (GCF) of 84 and 28 can be found by looking at the remainder from division of 84 by 28.

  84 ÷ 28 = 3 r 0

The remainder is 0, so 28 is a factor of 84. Since it is also the largest factor of itself, it is the GCF of the two numbers.

Factoring out 28, we have ...

  84 +28 = 28·3 +28·1 = 28(3 +1)

The factored expression is 28(3 +1).

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Given: The weights of Water melon displayed using a histogram as shown in the figure

To Determine: The weight of the fourth bin

From the histogram, it can be seen that the x-axis represents the weight of the watermelons, while the y-axis represents the quantity

It can observed that the fourth been has 4 watermelons as shown below:

From the above, 4 watermelons marked with red circle on the y-axis, and their weights marked red on the x-axis

Hence, the weight of 4 watermelons is at least 12pounds but no more than 16pounds, the second option

We are given the following information

Carlos works a total of 86 hours in four weeks.

He works 18.5 hours each week for three weeks.

To determine how many hours Carlos work in the fourth week, we can set up the equation

We can make x the subject of the formula

Simplifying further

Therefore in the fourth week, Carlos will work 30.5 hours

the inequality for this situation is

T >= -2

The width of the rectangular frame is 3 1/8 inches.

It should be noted that the area of a rectangular picture frame is 4 3/8 square inches and the length of the frame is 1 2/5 inches.

The area of a rectangle is:

= Length * Width

Therefore, the width will be:

= Area / Length

= 4 3/8 ÷ 1 2/5.

= 4.375 / 1.4

= 3.125 or 3 1/8.

The width is 3 1/8 feet.

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Answer:

x = 8 for f(x) and x = 3 for h(x)

Step-by-step explanation:

the axis of symmetry is a vertical line which passes through the vertex of the graph with equation

x = c ( c is the value of the x- coordinate of the vertex )

the equation of a parabola in vertex form is

f(x) = a(x - h )² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

f(x) = - 4(x - 8)² + 3 ← is in vertex form

with vertex (h, k ) = (8, 3 )

equation of axis of symmetry of f(x) is x = 8

given the graph of h(x) with vertex = (3, 2 ) , then

equation of axis of symmetry of h(x) is x = 3

Given data:

The diameter of the cut sphere, D=14 in.

The radius of the cut sphere is,

The cut sphere is called a hemisphere.

The surface area of a sphere is

So, the lateral surface area of a hemisphere is half the surface area of sphere. Therefore, the lateral surface area of a hemisphere is,

The hemisphere has a lateral surface and a circular surface. The area of the circular surface is,

Therefore, the total area of the hemisphere is,

The total surface area of a hemisphere is,

Therefore, the total surface area of the cut sphere is 461.8 square inches.

Step 1: For solving this exercise, we need to know the speed of sound. We will calculate it this way:

Speed = Distance/Time

Replacing with the values Josh has.

Speed = 5 miles/12 seconds

Speed = 0.417 miles per second

Step 2: Now, let's calculate the distance after 7 seconds:

Using the same formula, we can find the distance, as follows:

Distance = Speed * Time

Distance = 0.417 * 7

Distance = 2.919

Distance = 3 miles (Rounding to the nearest whole number)

Step 3: Interpretation of the answer, as follows:

The lightning was 3 miles away when Josh counted 7 seconds between the next flash of lightning and thunder.

Independent varible are variable that dosent depend on any factor that afftect the scenarios.

the scenarios that identify the independent variable.

A. Charlie gets paid by the hour. The number of hours he works is the independent variable.

B. Oscar likes to go for drives in the car. The cost of the trip increases as the distance he travels increases. The distance is the independent variable.

D. The more Mark practices his golf swing, the better he becomes at hitting the ball. The amount of time he practices is the independent variable.

Answer:

$48

no idea how working out would go

Answer: $48

Step-by-step explanation: First convert 20% to a decimal which is 0.2 or 0.20.

Then multiply 60 x 0.20 which equals 12.

Because it is a markdown then you must subtract 12 from 60 which gives you the answer $48.

I hope this helps!! Good Luck!

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

9/16 + 1/16 * (2/3)^(-1)

Step 02:

we must apply the algebraic rules to find the solution

The answer is:

21 / 32

Answer:

3x=6

Step-by-step explanation:

27/9=3, 54/9=6 so answer is 3x = 6

Answer:

False

Step-by-step explanation:

Answer:

The correct answer is B

Step-by-step explanation:

Given:

The cardboard costs 0.05 per square inch

And the surface area = 286

So, the total cost is the product of the surface area and the cost per square in.

Total cost =

So, the answer will be Total cost = $14.30

The focus of a parabola does not lie on it. Hence, the equation of parabola is given as y² = 2y - x².

The parabola can be defined as a conic section curve, all of whose points are equidistant from a fixed point called as focus and a fixed line called as directrix.

Given that,

The focus of parabola is (0, 1).

The vertex of parabola is (0, 0).

Suppose, there is one more point on parabola as (x, y).

Since focus of a parabola is equidistant from all the points on parabola.

Use distance formula to find the distance between two points (x₁, y₁) and (x₂, y₂) as √((x₂ - x₁)² + (y₂ - y₁)²) to find the equation of parabola as,

√((x - 0)² + (y - 1)²) = √((0- 0)² + (0 - 1)²)

=> x² + (y - 1)² = 1

=>  (y - 1)² = 1 - x²

=> y² - 2y + 1 = 1 - x²

=> y² = 2y - x²

Hence, the equation of the parabola having vertex at origin and focus at  (0, 1) is  y² = 2y - x².

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Function:

A function is a relation in which each input (x) has only one output (y).

If any one input (x) has more than one output (y) then it is not a function.

As you can see from the given table, the value of (a) must be anything other than (2)

So we can set a value of 4 for (a)

Now if you notice, each input will have exactly one output value so the criteria of a function is satisfied.

So, the answer is 4

The percent increase on the price of the home is 20.37%.

What is percent increase?

A percent increase refers to how much a percentage has gone up over time. In order to reach this number, you would need to find the difference between the original value and the final value, subtracting to find the exact total of the decrease.

Formula is given by

New number (value) – original number (value) = increase

Increase / original number (value) x 100 = percent increase

Given ,

initial value of home = $265,000

After few years, the value = $319,000

Increase = $319,000 - 265,000

=54000

Percent increase = 54000/265000× 100

= 20.37%

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The cost of Goods Sold will be $93.5

What is Addition?

A process of combining two or more numbers is called addition.

Given that;

The Cost of Goods Sold for one Holiday Basket:

1 basket = $24.00 per dozen

2 lbs. Cheddar cheese = $1.50 per pound

1 canned ham = $60.00 per dozen

3 jars of jelly = $1.00 each

6 oranges = $2.00 per dozen

1 box crackers = 2.00 per box

Cellophane wrap = $.50 each

Now,

Since, Each basket has only one of each item in it.

So, The total cost = $24 + $1.50 x 2 + $60 + $1 x 3 + $1 + $2 + $0.50

                           = $93.5

Thus, The cost of Goods Sold will be $93.5

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Solution

- 40% of peole would vote for the mMath teacher out f the 750 people. This implies that the number of people tahat would vote for him is

- We are also told that there is a margin of error of 4%. This implies that the number of people that vote for the math teacher is either 4% more or 4% less than the 300 people

- 4% margin of error can be gotten as follows:

- Thus, the number of people that vote for him is 300 give or take 30 people

The  equation of line in point slope form created is

[tex]y - 3 = 1(x - 2)\\[/tex]

What is equation of line in point slope form?

The most general form of equation of line in point slope  form is given by

[tex]y - y_1 = m(x - x_1)[/tex]

Where m is the slope of the line and ([tex]x_1, y_1[/tex]) is the coordinate of the point through which the line passes

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

Here

Let the line passes through ( 2, 3) and (4, 5)

Slope = [tex]\frac{5-3}{4-2}[/tex]

          = [tex]\frac{2}{2}[/tex]

          = [tex]1[/tex]

Equation of line in point slope form

[tex]y - 3 = 1(x - 2)\\[/tex]

This is equation of line in point slope form.

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The possible length of segment AB is 27 < AB < 81

From the question, we have

In triangle ABC

AC = 27

CB = 54

Using Pythagoras theorem,

AC² = AB² + CB²

54² = AB² + 27²

AB = 47

The possible length of segment AB is 27 < AB < 81

Multiplication:

To determine the sum of two or more numbers, mathematicians multiply the numbers. It is a basic mathematical procedure that is widely used in daily life. Multiplication is used when we need to mix groups of like sizes. Multiplication is a representation of the underlying idea of adding the same number repeatedly. The outcome of multiplying two or more numbers is referred to as the product of those numbers, and the factors are the quantities that are multiplied. Multiplying the numbers makes it simpler to add the same number repeatedly.

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The values of the area of the shaded region are;

1. Area = 36, perimeter = 28

2. Area = 16, perimeter = 16

3. Area = 22, perimeter = 30

4. Area = 29, perimeter = 28

6. Area = 53.9

The area of a figure is the area bounded by the line that serves as the boundary of the figure.

The areas and perimeters of the figures are found as follows;

1. The figure consists of two rectangles

The dimension of the small rectangle at the top are;

Length = 4, Width = 3

Area = 3 × 4 = 12

Dimensions of the larger rectangle are;

Width = 4, Length = 6

Area = 4 × 6 = 12

The area of the composite figure is therefore; A = 3 × 4 + 6 × 4 = 36

The sum of the length of the sides, which is the perimeter, P = 8 + 3 + 4 + 3 + 4 + 6 = 28

2. The figure consists of a right triangle at the top rectangle;

The leg lengths of the right triangle are; 3 and 4

The area of the right triangle = 0.5 × 3 × 4 = 6

The dimension of the rectangle are; Length = 5, width = 2

Area of the rectangle = 5 × 2 = 10

Area of the composite figure is therefore, A = 0.5 × 4 × 3 + 2 × 5 = 16

The perimeter of the composite figure, P = 4 + 3 + 2 + 5 + 2 = 16

3. The figure is a composite figure that is found by subtracting the area of a rectangle from the area of a right triangle as follows;

The dimensions of the triangle are;

Leg lengths; (8 + 4) = 12 and (3 + 2) = 5

Area of the right triangle = 0.5 × (8 + 4) × (3 + 2) = 30

Dimensions of the rectangle left blank are;

Length = 4, width = 2

Area of the rectangle = 4 × 2 = 8

Therefore;

Area of the composite figure = 0.5 × (8 + 4) × (3 + 2) - 4 × 2 = 22

Length of the hypotenuse side = √((8 + 4)² + (3 + 2)²) = 13

The perimeter of the composite figure = 3 + 13 + 8 + 2 + 4 = 30

4. The figure is a composite figure that consist a large rectangle and small rectangle.

Dimensions of the large rectangle are;

Length = 2 + 2 + 3 = 7

Width = 5

Area of the large rectangle = 7 × 5 = 35

Dimensions of small rectangle are;

Length = 3, width = 2

Area of the small rectangle = 3 × 2 = 6

Area of the composite figure = 35 - 6 = 29

The perimeter = 2 × (2 × 2 + 3) + 2 × 5 + 2 × 2 = 28

6. Area of the circle = π × 14²/4

Area of the square = 10 × 10 = 100

The area of the shaded region = π × 14²/4 - 100 ≈ 53.9

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From the figure, the total number of students is

The number 15 is common in spanish, chemistry and math.

Hence, the number of students studying spanish, chemistry and math, n=15.

Therefore, the probability of surveying a student that is in math Spanish and chemistry is,

Therefore, the

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

I believe your question is:

For what value of [tex]x[/tex] does [tex]3^{2x}=9^{3x-4}[/tex]?

—

First, rewrite [tex]9[/tex] as [tex]3^2[/tex]:

[tex]3^{2x}=(3^2)^{3x-4}[/tex]

Then, use exponentiation to apply the [tex](a^b)^c=a^{bc}[/tex] rule:

[tex]3^{2x}=3^{2(3x-4)}[/tex]

Rewrite the expression as a non-exponential one since the bases ([tex]3[/tex]) are equal on both sides:

[tex]2x=2(3x-4)[/tex]

Distribute the [tex]2[/tex]:

[tex]2x=6x-8[/tex]

Subtract [tex]6x[/tex] from both sides:

[tex]-4x=-8[/tex]

Divide both sides by [tex]-4[/tex]:

[tex]x=2[/tex]