5. Gabi will graph f(x) = x and m(x) = f(x). Mark each statement as true or false. If false,
rewrite as true in the space below.
a. The slope of m(x) will be steeper than f(x).
_b. The y-intercept of m(x) will be units up from f(x).
d. g(x) = f(x − 3)

Explicit formula for this sequence is (C) an= 6+ (n-1)(-4)

Given sequence,

6, 2, -2, -6.....

First term = a = 6

Difference = d = 2 - 6

                        = -4

No. of terms = n

Therefore, an = a + (n-1)d

                       = 6 + (n-1)(-4)

Hence, an= 6+ (n-1)(-4).

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Answer:

{A) X=5} {B) X=2.75}

Step-by-step explanation:

A) (2)4x-1/2=x+7(2) - multiply each side by denominator

4x-1=x+14

-x + 1 -x +1

3x=15

÷3. ÷3

x=5

B) (2)3x+2=2x+13/2(2)

6x+2=2x+13

-2x -2. -2x -2

4x=11

÷4. ÷4

x=2.75

Answer:

x = 7.5 , x = 1

Step-by-step explanation:

(a)

[tex]\frac{4x-1}{2}[/tex] = x + 7 ( multiply both sides by 2 to clear the fraction )

4x - 1 = 2(x + 7)

4x - 1 = 2x + 14 ( subtract 2x from both sides )

2x - 1 = 14 ( add 1 to both sides )

2x = 15 ( divide both sides by 2 )

x = 7.5

(b)

3x + 2 = [tex]\frac{2x+13}{3}[/tex] ( multiply both sides by 3 to clear the fraction )

3(3x + 2) = 2x + 13

9x + 6 = 2x + 13 ( subtract 2x from both sides )

7x + 6 = 13 ( subtract 6 from both sides )

7x = 7 ( divide both sides by 7 )

x = 1

The missing values for the exponential function are y = 16.875 and y = 25.3125

The general form of the exponential function is y = abˣ

From the table, when x = 0, y = 11.25. Substitute the values into the function:

y = abˣ

11.25 = ab⁰             (Note: b⁰ = 1)

11.25 = a(1)

11.25 = a

a = 11.25

Also, from the table, when x = -1, y = 7.5. Substitute the values into the function:

7.5 = 11.25b⁻¹

7.5 = 11.25/b                (Note: b⁻¹ = 1/b)

7.5b = 11.25

b = 11.25/7.5 = 1.5

We can now write the exponential function for this case:

y = abˣ

y = 11.25(1.5)ˣ

We can find the missing values now:

when x = 1:

y = 11.25(1.5)ˣ

y = 11.25(1.5)¹

y = 16.875

when x = 2:

y = 11.25(1.5)ˣ

y = 11.25(1.5)²

y = 25.3125

Therefore, the missing values are 16.875 and 25.3125. Option c is the correct answer

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Answer:

Scale Factor

[tex]k=5[/tex]

Side Congruency

AL ≅ TD

TK ≅ AH

DK ≅ LH

Angle Congruency

∠A ≅ ∠T

∠D ≅ ∠L

∠H ≅ ∠K  or  ∠K ≅ ∠H

Step-by-step explanation:

Scale Factor

First, to determine the scale factor, I will choose two corresponding segments: AL and TD.

By counting on the graph, I can see that they are the following lengths:

[tex]TD=15\\AL=3[/tex]

Therefore the ratio of the large triangle to the small triangle is 15:3. Written as a fraction and simplified, this is:

[tex]\frac{15}{3}=5[/tex]

5 is the scale factor, or k.

Congruency

Each segment on the small triangle corresponds to the same side on the large triangle. Therefore:

AL ≅ TD

TK ≅ AH

DK ≅ LH

The same goes for the angles, except the angles are actually equal as well:

∠A ≅ ∠T

∠D ≅ ∠L

The bottom of your image is cut off, but I assume the question is one of these:

∠H ≅ ∠K

∠K ≅ ∠H

Answer: -1.73 ft

Step-by-step explanation:

(-2.54 - 3.16 - 2.82 + 1.6) / 4 = -1.73

Large sample size gives more accurate information about population.

The main advantages of Large sample size is :

1. Large sample size provide stronger and more reliable information about parent population.

2. It will help researcher to capture outliers and sweeping out in sample.

3. Measuring large sample size allows one to divide the sample into segments .

4. Large sample size helps in obtaining a quality and precise mean .

Some disadvantages of Large sample size is :

1. Large sample size will be time consuming and more expensive to work with

2. It require higher financial involvement to complete the survey.

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B) direction ratio of any two diagonals in vector form is 60°.

C) cos²α+cos²β+cos²γ+cos²δ= [tex]\frac{4}{3}[/tex]

​In Euclidean geometry, a perspective is a parent created by rays, often referred to as the angle's perimeters, sharing a single endpoint known as the perspective's vertex. Angles created by rays are located in the plane that contains the rays. Angles can also be created by intersecting two planes. They are referred to as dihedral angles. Curves that cross may also define an angle, which is the angle formed by rays that are perpendicular to the individual curves at the point of junction.

The degree of an angle or rotation is also expressed in terms of perspective. This metric represents the relationship between a circular arc's length and radius.

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Step-by-step explanation:

Great Meadow Loop and Jordan Pond Path

The correct interpretation of the expression "minus, 7, minus, left parenthesis, minus, 11, right parenthesis" is 8.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We have to write the correct interpretation of the expression "minus, 7, minus, left parenthesis, minus, 11, right parenthesis".

We have to subtract when two different signs appear next to each other (-+ or +-)

Similalry We have to add when two of the same signs appear next to each other (++ or --)

So:

-7 - (-11)−7−(−11)

-7 + 11 - 7 + 11

-14 + 22

8

Therefore, the correct interpretation of the expression "minus, 7, minus, left parenthesis, minus, 11, right parenthesis" is 8.

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Answer:

50.6 ft

Step-by-step explanation:

We can use the pythagoreas theorem to solve this problem.

If the service drop is 20 ft from the ground and the insulator is 35 ft, that means that the insulator is 15 ft higher than the service drop.

a² + b² = c²

15² + 48² = c²

255 + 2304 = c²

2559 = c²

√2559 = c

50.6 ≈ c

Answer: He is incorrect.

Step-by-step explanation:

        Since we are talking about -8.0, we can "ignore" the .0 because 0 has no value. An integer is a whole negative number, whole positive number, or zero. -8 is a whole negative number, since .0 means "nothing" here, so it is an integer.

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Answer: 18.75%

Step-by-step explanation:

To find the percentage decrease, the formula is shown below.

Plug in the values and calculate:

[tex]\frac{8-6.5}{8} *100=18.75%[/tex]

So, the chunk of meat lost 18.75% of its initial weight.

Answer:

2 pound bottle

Step-by-step explanation:

convert ounce to pounds:

37/16=2.3125

find price of 1 pound of bbq sauce:

35.15/2.3125=$15.2

23.36/2=$11.68

$11.68 is more cheaper so 2 pound bottle is better to buy

Answer:

False

Step-by-step explanation:

[tex]10^{-2}[/tex] id not a negative number it means

[tex]\frac{1}{10^{2} }[/tex] or [tex]\frac{1}{100}[/tex]  Which is a number with a lesser value than 1, but it is not a negative number.

Answer:

  12.1 hours

Step-by-step explanation:

You want to know the mowing time for 5 acres if Hannah can mow 1000 square yards in 1/2 hour.

We can convert the acreage to square yards to facilitate the calculation:

  5 ac × (4840 yd²)/(1 ac) = 24,200 yd²

Hannah mows her lawn at the rate of ...

  (1000 yd²)/(0.5 h) = 2000 yd²/h

At this rate, the time it takes for 24200 yd² will be ...

  (24,200 yd²)/(2000 yd²/h) = 12.1 h

It would take Hannah 12.1 hours to mow 5 acres.

Using trigonometric ratio, the horizontal distance from A to B is 314 feet

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios. The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively.

To calculate the distance from point A to point B, we can use trigonometric ratio here.

Note: We are going to add the two angles and then use the vertical distance as the adjacent side of the triangle.

Data;

Using tangent of the angle;

Tanθ = opposite / adjacent

tan 66 = AB / 140

AB = 140 tan66

AB = 314ft

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Answer:5,149 pounds of sawdust for $1,132.78

Step-by-step explanation:

Step 1 is to convert 4 tons into pounds is:

4 tons * 2000 pounds per ton = 8000 pounds

Step 2 is to find the cost of saw dust per pound in each scenario:

Scenario 1: $1132.78 / 5149 = .22 dollars per pound

Scenario 2: $2800 / 8000 = .35 dollars per pound

Step 3 is just comparing which one is the cheapest per pound based on step 2:

.22 per pound is less than .35 per pound. So the answer is scenario 1 (5149 pounds for 1132.78) is the better buy

Answer:

70 dogs

Step-by-step explanation:

total animal is 98

total ratio is 5+2 = 7

calculate how much each ratio has

98/7 = 14

5 ratio are dogs, so multiply 14 with 5 to get 70 dogs

you can also do:

5/7 × 98 = 70

The area of the smaller triangle is 18 squared units which is determined by the property of similar triangles.

The area of the larger triangle is 36.

The two triangles are similar which is given in the question

We know that the corresponding sides of similar triangles are being in the same ratio.

As per the property of similar triangles,

A₁ : S₁ = A₂ : S₂

Here A₁ is area of the larger triangle,  A₂ is area of the smaller triangle

S₁ is side of the larger triangle, and S₂ is side of the smaller triangle,

⇒ A₁ / S₁ = A₂ / S₂

⇒ 36 / 12 = A₂ / 6

⇒ 3 = A₂ / 6

⇒ A₂ = 18

Therefore, the area of the smaller triangle is 18 squared units.

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The order of T is 82.

Let n and e be the order and number of edges of T respectively.

Also, let a, b, c and d be the number of vertices of degree 2, 3, 4 and 5 respectively.

Then, 50+a+b+c+d = n

And by the Handshake Lemma,  the sum of the degrees of all the vertices of T is twice the number of edges, so we have

50+2a+3b+4c+5d = 2e

Since a=b=c=d then we have the following two equations,

50+4a = n

50+14a = 2e

But, T is a tree so e=n=1, then the two equations become,

50+4a = n ...............(1)

50+14a = 2(n-1) .............(2)

Solving for a in (1) we get,

a = [tex]\frac{n-50}{4}[/tex]

Plugging a into (2) we get,

50+14([tex]\frac{n-50}{4}[/tex]) = 2(n-1)

50+3.5n-175 = 2n-2

3.5n-2n = 175-50-2

1.5n = 123

n = [tex]\frac{123}{1.5}[/tex] = 82

Therefore, the order of T is 82.

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Answer:

28.3

Step-by-step explanation:

To solve this problem, we must follow PEMDAS, which must be used in solving all mathematical equations and expressions.

PEMDAS is the order you solve the equation/expression in. It is an acronym for:

P: Parenthesis

E: Exponents

M: Multiplication

D: Division

A: Addition

S: Subtraction

Keep in mind that multiplication and division are too be done left and right. You do not do multiplication first and division last, read left to right. Same goes with addition and subtraction.

This is the less confusing notation of PEMDAS.

P: Parenthesis

E: Exponents

M: Multiplication D: Division

A: Addition S: Subtraction

Now, lets solve the problem.

92.3 - (3.2 ÷ 0.4) × 2³

What do we do first? Well since parenthesis is first according to PEMDAS, we must solve the division in side of the parenthesis first.

3.2/0.4 = 8

Now we have:

92.3 - (8) × 2³

Remove the parenthesis as there is only one term inside and therefore not needed.

92.3 - 8 × 2³

What do we do next?

We have:

Subtraction: 92.3 - 8

Multiplication: -8 × 2³

Exponent: 2³

Because PEMDAS states exponents is to be solved in front of multiplication/division and addition/subtraction, we must do that.

What is an exponent?

2³

2 is the base, 3 is the exponent.

2³

Means multiplying 2 by itself 3 times:

2 × 2 × 2

8

Now we have:

92.3 - 8 × 8

Because PEMDAS states solving multiplication/division is prioritized over addition/ subtraction, we must solve 8 × 8

8 × 8 = 64

Now we have: 92.3 - 64

Solve.

28.3

The goal of a hypothesis test is to determine if the data can refuse an assumption a parameter or a population.

Statistical hypothesis test:

A statistical hypothesis test is a technique for determining whether the available data are sufficient to support a specific hypothesis. We can make probabilistic claims about population parameters through hypothesis testing.

The purpose of a hypothesis test is to ascertain whether the data can refute a parameter or population assumption.

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After the multiplication of (3+√16) (6-√64), the resultant answer is -14.

Multiplying in math is the same as adding equal groups.

The number of items in the group grows as we multiply.

Parts of a multiplication issue include the product, the two factors, and the product.

The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.

So, the multiplication of:

(3+√16) (6-√64)

Now, multiply as follows:

(3+√16) (6-√64)

We know that: 3+√16 = 7

7(6-√64)

We know that: 6-√64 = -2

7(-2)

-14

Therefore, after the multiplication of (3+√16) (6-√64), the resultant answer is -14.

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According to the given standard deviation, the true mean number of chocolate chips per cookie to within 2 chocolate chips with 99% confidence is 10.6

Standard deviation:

Basically, the standard deviation refers a quantity expressing by how much the members of a group differ from the mean value for the group.

Given,

It is desired to estimate the mean number of chocolate chips in a chocolate chip cookie.

Here we need to find how many cookies need to be sampled to estimate the true mean number of chocolate chips per cookie to within 2 chocolate chips with 99% confidence and assume that the population standard deviation is 3.7 chocolate chips.

From the given question we have identified the following details,

Confidence interval = 99%

Standard deviation = 3.7

So, the critical value is calculated as,

=> 1 - 0.99

=> 0.01

So, the z scores is 2.576.

Now, the formula to confidence interval is given by : -

=> 10.6 ± 2.576 (0.01)/ √3.7

=> 10.6

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The number of problem that can she grade in hour is 60 problems

The number of problems that math teacher graded in 3/4 of an hour = 45 problem

Here we have to use the unitary method

The unitary method is defined as the method of finding the value of the single unit.

The number of problem that can math teacher grade in 1 hour = The number of problems that math teacher graded in 3/4 of an hour ÷ 3/4

Substitute the value in the equation

The number of problem that can math teacher grade in 1 hour = 45 ÷ (3/4)

= 45 × (4/3)

= 60 problem

Hence, the number of problem that can she grade in hour is 60 problems

The complete question is:

A math teacher graded 45 problems in 3/4 of an hour. At that rate, how many problems can she grade in 1 hour?

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