Select the correct answer.

What is the range of the function f(x) = 4x + 9, given the domain D = {-4, -2, 0, 2}?

A. R = {-7, -1, 9, 17}

B. R = {-17, -9, -1, 17}

C. R = {1, 7, 9, 17}

D. R = {-7, 1, 9, 17}

In other words,

=====================================================

Explanation:

Factor 63 and 27 such that the GCF 9 is involved.

So,

63 - 27 = 9*7 - 9*3 = 9(7 - 3)

I used the distributive rule.

For a membership to be worth it to Stewart, the number of days he will have to go to the gym would be 20 days

Assuming the number of days that would make the gym membership worth it is x, the formula for finding the total cost of gyming with the membership fee is:

= 50 + 5. 50 x

The number of days as a nonmember would be:

= 8 x

The number of days till the membership is worth it is therefore:

8x = 50 + 5.50 x

8x - 5.50 x = 50

2. 50x = 50

x = 50 / 2. 50

x = 20 days

Stewart has to for for at least 20 days

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The pair of angles 30⁰ and 30⁰ are supplementary angles.

Examples of additional angles

Angles with a supplementary sum are those whose sum is 180 degrees. For instance, the sum of angle 130° and angle 50° is 180°, hence they are supplementary angles. In the same way, complimentary angles sum to 90 degrees.

Supplementary angles may have three angles.

Three angles can't be added together. Two angles whose sum of the measures is exactly 180 degrees are supplementary angles, according to the definition. Even if three angles, such as 60 degrees, 30 degrees, and 90 degrees, sum up to 180 degrees, they would not be referred to as supplementary angles.

Supplementary angles add up to 180 degrees. An angle is supplementary to another angle if the sum of the measures of the two angles is 180 degrees. So, 30 + 30 = 60 which is supplementary.

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Answer:

First option:
1.2076

Step-by-step explanation:

Just use the standard deviation functionality of any scientific/statistical calculator.

The answer is 1.2076 which is the first option

A secant is a straight line that intersects a curve at two points.

For example, consider the curve y = x^2. If we draw a secant line through the points (1,1) and (3,9), the secant line will intersect the curve at those two points.

Secants are often used to approximate the slope of a curve at a particular point. For example, if you want to find the slope of the tangent line to a curve at a point x = a, you can draw a secant line through that point and another point nearby, and use the slope of the secant line to approximate the slope of the tangent line.

To find the slope of the tangent line using a secant line, you can use the following formula:

where (x1, y1) and (x2, y2) are points on the secant line.

By taking the limit of this formula as x2 approaches x1, we can find the slope of the tangent line at the point where x = x1. This is known as the limit definition of the derivative.

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In the 7th year, Marco will get compounded interest greater than $5, so he will have to keep money in the bank without withdrawing for 6 years.

Simple Interest: is the interest based on the principal amount.

Compound Interest: is the interest based on the principal amount and the interest  that accumulates on it every year.

So 5% simple interest on $100 =   *100 =$5

So the compound interest needs to be greater than $5 .

Lets calculate the  compound interest over the years.

1st Year:   *100 =$4

2nd Year: Now to calculate the interest in second year the interest in first year will be accumulated. So interest will be calculated on 100 +4 =$104

4/100*104 =$4.16

3rd Year: Again interest from 2nd year will be added

4/100*108.16 =$4.33

4th Year: Again interest from 3rd year will be added

4/100*112.49 =$4.49

5th Year:

4/400*116.99 =$4.68

6th Year:

*121.67 =$4.87

7th Year:

*126.54 =$5.06

In the 7th year, Marco will get compounded interest greater than $5, so he will have to keep money in the bank without withdrawing for 6 years.

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Answer:

6 (c)

Hope this helps

Answer:

[tex]10a-4[/tex]

Step-by-step explanation:

[tex]2(3a-2)+4a=(6a-4)+4a=10a-4[/tex]

The expression x⁻². x⁻¹.x⁶ can be simplified as x³.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

x⁻². x⁻¹.x⁶

Simplify the expression,

By using multiplying property,

x⁻²⁺⁽⁻¹⁾⁺⁶

x ⁻²⁻¹⁺⁶

x⁻³ ⁺ ⁶

x³

The simplified form of the expression x⁻². x⁻¹.x⁶ is x³.

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If leg ab = 9 cm and leg cd = 12 cm then the perimeter of this trapezoid will be 46cm.

Angle bisector in geometry refers to a line that splits an angle into two equal angles. Bisector means the thing that bisects a shape or an object into two equal parts.  If we draw a ray that bisects an angle into two equal parts of the same measure, then it is called an angle bisector.

Step-by-step explanation:

It is given that the angle bisector AC divides the trapezoid ABCD into two similar triangles Δ ABC and Δ ACD.

Let us first find the corresponding sides of triangles Δ ABC and Δ ACD.

Since AC is the angle bisector of ∠A,

∠DAC = ∠CAB --- (1)

Also, since ∠DAC and ∠ACB are alternate interior angles,

∠DAC = ∠ACB --- (2)

From (1) and (2),

∠CAB = ∠ACB

Therefore, in Δ ABC,

BC = AB (sides opposite to equal angles are equal)

So, BC = 9 cm.

Now, since ∠DAC = ∠ACB and ∠DAC = ∠CAB, we can take either ∠ACB or ∠CAB as the angle corresponding to ∠DAC. Let us take ∠ACB as the corresponding angle of ∠DAC.

So, the side opposite to ∠DAC in Δ ACD is the corresponding side to the side opposite to ∠ACB in Δ ABC.

That is, the side CD in Δ ACD is the corresponding side to the side AB in Δ ABC.

Now, suppose if the side BC in Δ ABC corresponds to side AD of Δ ACD, then the remaining side AC of Δ ABC should correspond to side AC of Δ ACD which is not possible since they are congruent.

So, the side BC in Δ ABC should correspond to side AC of Δ ACD and the remaining side AC of Δ ABC should correspond to side AD of Δ ACD.

Therefore, we have,

[tex]\frac{AB}{CD} =\frac{BC}{AC} =\frac{AC}{AD}[/tex]

But, [tex]\frac{AB}{CD} =\frac{9}{12} =\frac{3}{4}[/tex]

Therefore,[tex]\frac{BC}{AC} =\frac{3}{4}[/tex]

[tex]\frac{9}{AC} =\frac{3}{4}[/tex]

[tex]AC=(\frac{4}{3} )(9)[/tex]

AC = 12 cm

Also,

[tex]\frac{AC}{AD} =\frac{3}{4}[/tex]

[tex]\frac{12}{AD} =\frac{3}{4}\\AD=(\frac{4}{3} )(12)[/tex]

AD = 16 cm

Now, the perimeter of the trapezoid = AB + BC + CD + AD

= 9 + 9 + 12 + 16

= 46 cm

Therefore, the perimeter of this trapezoid will be 46cm.

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The perimeter of this trapezoid will be 46cm.

Now, According to the question:

Angle bisector in geometry refers to a line that splits an angle into two equal angles. Bisector means the thing that bisects a shape or an object into two equal parts.  If we draw a ray that bisects an angle into two equal parts of the same measure, then it is called an angle bisector.

An angle bisector AC divides a trapezoid ABCD into two similar triangles △ABC and △ACD.

The leg AB=9 cm and the leg CD=12 cm.

Given that AC is the angle bisector of angle A, therefore:

∠DAC = ∠CAB     ----- (1)

∠DAC = ∠ ACB      (alternate interior angles)       ---- (2)

From (1) and (2):

Sides opposite to equal angles are equal, therefore:

BC = AB

Hence, BC = 9 cm

Side BC in triangle ABC should correspond to side AC of triangle ACD and the remaining side AC of triangle ABC should correspond to side AD of triangle ACD.

Therefore, we have

[tex]\frac{AB}{CD} = \frac{BC}{AC} =\frac{AC}{AD}[/tex]

[tex]\frac{AB}{CD}[/tex] = [tex]\frac{9}{12}=\frac{3}{4}[/tex]

Therefore, [tex]\frac{BC}{AC}=\frac{3}{4}[/tex]

[tex]\frac{9}{AC}=\frac{3}{4}[/tex]

AC = 4/3 × 9

AC = 12cm

also, [tex]\frac{AC}{AD} =\frac{3}{4}[/tex]

12/AD = 3/4

AD = 4/3 ×12

AD = 16cm

Now, the perimeter of the trapezoid = AB + BC + CD + AD

= 9 + 9 + 12 + 16

= 46 cm

Therefore, the perimeter of this trapezoid will be 46cm.

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The complete question is this:

An angle bisector AC divides a trapezoid ABCD into two similar triangles △ABC and △ACD. Find the perimeter of this trapezoid if the leg AB=9 cm and the leg CD=12 cm.

The provided polygon is a quadrilateral, and by solving it, we discovered that x is, [tex]x = 23.5^\circ[/tex]

Used the concept of angle as a quadrilateral,

The total of the angles on two adjacent sides equals 180° when there are two additional angles on the same side.

Given that,

A polygon is shown in the image.

Now from the property of the quadrilateral, the equation is,

[tex](6x+3)^\circ + (x + 12.5)^\circ = 180^\circ[/tex]

[tex]7x + 15.5 = 180[/tex]

Subtract 15.5 on both sides,

[tex]7x= 164.5[/tex]

Divide 7 on both sides,

[tex]x= 23.5^ \circ[/tex]

Therefore, the value of x is 23.5°.

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In the given situation we have to drive at the speed of 75 miles per hour.

The speed at which an object's location changes in any direction.

The distance traveled in relation to the time it took to travel that distance is how speed is defined.

Since speed simply has a direction and no magnitude, it is a scalar quantity.

The speed of an item, which is a scalar quantity in everyday usage and kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time.

So, we know that:
We must drive the first 25 miles at 40 miles per hour.

We have a time of 20 minutes.

20 minutes = 1/3 hour

Then our speed will be:

25 ÷ (1/3)

25 * 3/1

75 miles per hour

Therefore, in the given situation we have to drive at the speed of 75 miles per hour.

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Considering the figure the height of  the tree is calculated to be 97.7 feet

The height of the tree is calculated using the trigonometry relation having the pneumonic SOH CAH TOA this is a short form for

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The image describes a right angle triangle of

opposite = height of the tree

adjacent = distance from the tree

The bearing is calculated using tan, TOA

tan 60 = h / WX

h = WX tan 60

Also, tan 40 = h / (60 + WX)

h = (60 + WX) tan 40

hence, equating both h

WX tan 60 = (60 + WX) tan 40

WX tan 60 = 60 tan 40 + WX tan 40

make WX the subject of the formula

WX tan 60 - WX tan 40 = 60 tan 40

WX (tan 60 - tan 40) = 60 tan 40

WX = 60 tan 40 / (tan 60 - tan 40)

substituting WX to h = WX tan 60

h = (60 tan 40 / (tan 60 - tan 40) ) * tan 60

h = 97.6557 feet

h = 97.7 feet to the nearest tenth

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Answer:

x = 18

Step-by-step explanation:

Solve for x:

6.2 = x - 11.8

6.2 = x - 11.8 is equivalent to x - 11.8 = 6.2:

x - 11.8 = 6.2

Add 11.8 to both sides:

x + (-11.8 + 11.8) = 11.8 + 6.2

11.8 - 11.8 = 0:

x = 6.2 + 11.8

6.2 + 11.8 = 18:

Answer: x = 18

Answer:

x-11.8=6.2

Step-by-step explanation:

add 11.8 for both sides

then x=11.8+6.2

the result of adding is 18

x=18.0

S.S={18.0}

68.27% of values are within 2 standard deviations of the mean.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Given that, five hundred values are normally distributed with a mean of 125 and a standard deviation of 10 approximately.

Here, X=125 and σ=10

The percent of the values lies between the interval 115-135 is calculated as follows;

P(115<X<135)=P(115-125/10 < X-μ/σ <135-125/10)

= P(-1<Z<1)

= 0.6827 (Obtained from the standard normal distribution table)

Therefore, 68.27% of values are within 2 standard deviations of the mean.

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The point that is a solution to the inequality 2x - у < 10 is (2, -5)

From the question, we have the following parameters that can be used in our computation:

2x - y < 10

Next, we make the variable y the subject of the formula

Using the above as a guide, we have the following:

-y < 10 - 2x

Divide both sides by -1

y > 2x - 10

Assume a value for x

y > 2 * 2 - 10

So, we have

y > -6

This means that the possible y value at x = 2 is -5

Hence, the point is (2, -5)

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Let's consider what the question asks for:

 --> find the value of 'x'

The function gives us a quadrilateral

  --> separated into two triangles

In the triangle that has one angle with measure 65 degrees

 -->it is an isosceles triangle thus the top most angle in that triangle is also

     65 degrees

      --> the other unknown angle is, therefore:

                [tex]\text{unknown angle} + 65 + 65 = 180\\\text{unknown angle}+130=180\\\text{unknown angle}=180-130=50\\\text{unknown angle}=50[/tex]

Now that unknown angle forms a complementary relationship with the angle of the other triangle.

   [tex]50 + \text{bottom most angle of other triangle}=90\\\text{bottom most angle of other triangle}=90-50\\\text{bottom most angle of other triangle}=40[/tex]

Now that the bottom triangle

  --> has an angle with measure 'x'

    --> that triangle is also an isosceles

      --> meaning that our triangle's angle looks like this

              [tex]40 + x+x+180\\2x+40=180\\2x=140\\x=70[/tex]

Answer: 70

The coordinate (x, y) of the midpoint is (2, 15)

The midpoint of a line is a point halfway between the two endpoints of the line, such that the line is divided into two equal segments. The coordinates of the midpoint can be found by taking the average of the x-coordinates of the endpoints and the average of the y-coordinates of the endpoints.

The formula of midpoint of a line is given as;

M = [(x₂ + x₁) / 2], [(y₂ + y₁) / 2]

The coordinates given are;

M = [(-9 + 3) / 2], [(11 + 19) / 2]

M = (6/3) , (30/2)

M = 2, 15

The midpoint is (2, 15)

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Answer: 181.61

Step-by-step explanation:

130 x 139.7

----------------    =181.61

100

Answer:

Step-by-step explanation:

Teaching angles to 5th graders can be a fun and engaging process.

Here are a few strategies that you can use to help students understand angles:

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Answer:

  d.  5% decrease

Step-by-step explanation:

You want the change in price of coins bought for x dollars and sold for 0.95x dollars.

The percent change in price is given by ...

  % change = ((new price)/(old price) -1) × 100%

  % change = (0.95x/x -1) × 100% = (0.95 -1) × 100%

  % change = -0.05 × 100% = -5%

The change in the price of the coins is described as a 5% decrease.

<95141404393>

The range of the function represented by the graph is 1 ≤ y ≤4. The correct option is c.

These visual representations include tables and graphs. They are employed to arrange data in order to highlight patterns and correlations. This information is displayed as a shape on a graph.

To present the results of their research, scientists and researchers frequently employ tables and graphs. Graphs present information to you as a picture or visual representation. This knowledge is referred to as "data." When you put data into a picture, it can appear lean or bulky, lengthy or short.

Therefore, the correct option is c, 1 ≤ y ≤4.

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Answer:

  y = 2x +4

Step-by-step explanation:

You want an equation of the line through point P(0, 4) parallel to y = 2x.

The parallel line will have the same slope, so can be written in the form ...

  y = 2x +b

where 'b' is the y-intercept.

The point (0, 4) is the y-intercept, telling you b=4.

An equation for the line is y = 2x +4.

__

Additional comment

"An equation" covers a lot of territory. The equation we found can be written several other ways, including ...

<95141404393>

The total number of questions is 10 + 15 = 25.

Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points. The total number of points can be calculated by the following formula: x*5 + y*2.

For example, if there are 10 questions worth 5 points and 15 questions worth 2 points, the total number of points is calculated by 10*5 + 15*2 = 100.

In order to calculate the average points per question, we divide the total number of points by the total number of questions. This can be formulated as (x*5 + y*2) / (x + y).

For the example above, the average points per question can be calculated as (10*5 + 15*2) / (10 + 15) = 100 / 25 = 4. This means that the average points per question is 4 points.

Finally, if we want to calculate the total number of questions, we can use the formula x + y. Continuing with the example, the total number of questions is 10 + 15 = 25.

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14 questions worth 5 points and 15 questions worth 2 points

In this question we have been given that Mr. Martin’s math test worth 100 points, has 29 questions and each problem is worth either 5 points or 2 points.

We have been given a system of equations:

x + y = 29                                ................(1)

5x + 2y = 100                          ................(2)

Assuming x be the number of questions worth 5 points and let y be the number of questions worth 2 points, we need to find the number of questions of each point value.

i.e., we need to find the value of x and y

From equation (1),

x = 29 - y                      ..............(3)

Subatitute above value of x in equation (2)

5(29 - y) + 2y = 100  

145 - 5y + 2y = 100

-3y = 100 - 145

-3y = -45

y = 15

Subatitute above value of y in equation (3)

x = 29 - 15

x = 14

Therefore, there are 14 and 15 questions worth 5 and  2, respectively.

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The data set that could be represented by the box plot would be = 32,36,27,30,35,39,28,34. That is option D.

The box plot is defined as the type of data representation that is used in descriptive statistics to show the distribution of numerical data such as the number of hours Judy takes to complete a quilt.

The characteristics of the box plot is that is shows the outliers, the median, and the mode of the given numerical data.

Therefore, the data set that could be represented by the box plot would be = 32,36,27,30,35,39,28,34.

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The ratio of the given conversion units is; 24:5

Conversion of units is defined as the conversion between different units of measurement for the same quantity, and this is typically done through multiplicative conversion factors that change the measured quantity value without changing its effects.

Now, we are given a ratio of yards to inches but to get an effective ratio without units, we need to convert them to the same units.

Now, from conversion of units, we know that;

1 yard = 36 inches

Thus;

4 yards = 4 * 36 = 144 inches.

Thus;

The ratio = 144:30

This can be simplified to 24:5

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The product of  [tex]$ (5 \times 10^6)(8.2 \times10^{-9})[/tex] is  [tex]$ 4.1 \times 10^{-2}[/tex]  in scientific notation.

Numbers that are either too large or too small to be conveniently written in decimal form can be expressed using scientific notation. It is also known as "scientific form" in Britain, and it is frequently used by scientists, mathematicians, and engineers for difficult calculations involving large numbers. It is commonly referred to as "SCI" display mode on scientific calculators.

Scientific notation is a way to express numbers in terms of a decimal number between 1 and 10, but not 10 itself multiplied by a power of 10.

The standard for scientific notation is N × 10ᵃ

Given to find product of

⇒ [tex]$ (5 \times 10^6)(8.2 \times10^{-9})[/tex]

⇒ [tex]$ (5 \times 8.2 )10^{6 +(-9)}[/tex]

⇒ [tex]$ (5 \times 8.2 )10^{-3}[/tex]

⇒ [tex]$ (41 )10^{-3}[/tex]

⇒ [tex]$ 4.1 \times 10^{-2}[/tex]

Thus, The product of  [tex]$ (5 \times 10^6)(8.2 \times10^{-9})[/tex] is  [tex]$ 4.1 \times 10^{-2}[/tex]  in scientific notation.

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Answer:

[tex]\dfrac{a-4\sqrt{a+1}+5}{a-3}[/tex]

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{\sqrt{a+1}-2}{\sqrt{a+1}+2}[/tex]

To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator.

The conjugate of a binomial is where we change the sign between the two terms of the binomial.  So the conjugate of √(a+1)+2​ is √(a+1)-2​.

Therefore:

[tex]\implies \dfrac{\sqrt{a+1}-2}{\sqrt{a+1}+2} \cdot \dfrac{\sqrt{a+1}-2}{\sqrt{a+1}-2}[/tex]

[tex]\implies \dfrac{(\sqrt{a+1}-2)(\sqrt{a+1}-2)}{(\sqrt{a+1}+2)(\sqrt{a+1}-2)}[/tex]

[tex]\implies \dfrac{(a+1)-4\sqrt{a+1}+4}{(a+1)-4}[/tex]

[tex]\implies \dfrac{a-4\sqrt{a+1}+5}{a-3}[/tex]

The number of pre-sale tickets must she sell to make her goal is (c) 200

From the question, we have the following parameters that can be used in our computation:

These parameters can be represented using the following system of equations

10x + 15y = 3500

x + y = 300

The graph that completes the question is added as an attachment

From the graph, we have

(x, y) = (200, 100)

The variable y represents the number of pre-sale ticket

So, we have

x = 200

Hence, the number of pre-sale ticket is (c) 200

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Answer:

C, 200

Step-by-step explanation:

An easier way to get the answer in this case would be to see where the 2 lines meet, which is at 200 pre-sale tickets :))