Write the equation of the line in fully simplified slope-intercept form.

Answer:

(fog)(x) =  4x^2 -12x +10

(gof)(x) = 2x^2 -1

Step-by-step explanation:

(fog)(x) = (2x-3)^2 + 1

= 4x^2 + 9 -12x +1

= 4x^2 -12x +10

(gof)(x) = 2(x^2+1)-3

= 2x^2 +2 -3

= 2x^2 -1

The exterior angle to ∠X is 104.25°

The exterior angle theorem states that when a triangle's side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle. The theorem can be used to find the measure of an unknown angle in a triangle.

from the above definition , if ∠Y = 62.45° and ∠Z = 41.8°

It means from exterior angle theorem that

exterior ∠X = ∠Y + ∠Z

exterior ∠X  = 62.45° + 41.8°

exterior ∠X  = 104.25°

In conclusion the exterior angle X is 104.25°

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Answer:

x=d

Step-by-step explanation:

He has a total of $90 in his cafeteria wallet, thus the most lunches he may purchase is 20.

A number is divided in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of objects being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that can be made. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

Here,

Amount added=$50

Amount already in wallet=$40

Total amount in wallet=50+40

=$90

Cost of each lunch=$4.5

Number of lunch he can buy,

=90/4.5

=20

The maximum number of lunch he can buy is 20 lunch as he has a total of $90 in his cafeteria wallet.

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Answer:

18x^2 + 9x - 20

18x^2 + 24x - 15x - 20

6x(3x+4) - 5(3x+4)

Therefore, (6x-5)(3x+4)

Answer:

(1/2x+3)(1/2x+3)

         OR

[tex](1/2x+3)^{2}[/tex]

Answer: 15

Step-by-step explanation:

15+3=18

The lines C and D are parallel.

What is a line?

In pure mathematics, a line is an infinitely long object with no dimension, depth, or curvature. Thus, lines ar one-dimensional objects, although they'll exist in 2, three, or higher dimension areas

Main body:

As Line LM cuts the line at C the angle made by both line is 48°

and line NP cuts the line at D , the angle made by line is 132°

we know that to make a line parallel , the sum of angle on one side of the line should be 180°

∠C +∠D = 48° +132°

             = 180°

Hence , the lines C and D are parallel.

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Answer:

1. This study uses blocking to reduce variability from known factors.

2. This study uses random sampling.

Step-by-step explanation:

Hope it helps!

Answer: Number of small boxes = 7, Number of large boxes =3

Step-by-step explanation:

Let x= Number of small boxes , y = Number of large boxes.

As per given , 30x+55y=375  (i)

x+y=10   (ii)

Multiply (ii) by 30, we get

30x+30y=300    (iii)

Eliminate (iii) from (i), we get

25y=75

⇒ y= 3   [Divide both sides by 25]

Put y=3 in (ii), we get

x+3=10 ⇒ x=7

Hence,  Number of small boxes = 7, Number of large boxes =3

Hope this helps!!! :)

Answer:

g(x)=3^x+7

Step-by-step explanation:

f(0)=3^0

that is the y-intercept

now we can take the known y-intercept of g(x) which is 8 and then we can get our b in the y=mx+b equation.

The percent increase in the total number of students on the honor roll is   9.4% .

In the question,

it is given that ,

last year , the number of boys in the honor roll is = 60 boys ,

the number of girls in the honor roll is = 100 girls ,

total number of students last year = 160

percent increase in the number of boys in the honor roll is = 20% ,

so , number of boys become = 60 + (0.20*60) = 72 boys ,

percent increase in the number of girls in the honor roll is = 3% ,

so , number of girls become = 100 + (0.03*100) = 103 girls ,

total number of students this year = 103 + 72 = 175 .

increase in number of students = 175 - 160 = 15

So , percent increase is = (15/160) × 100

= 0.09375 × 100

= 9.375 %

≈ 9.4%

Therefore , the percent increase is 9.4% .

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You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval.

We can be 90% certain that the interval contains the population mean,, if the level of confidence is 90%. The associated z-scores are 1.645. We can be 95% certain that the interval contains the population mean, if the level of confidence is 95%.

In other words, the difference in effect estimates between the two subgroups is deemed to be statistically unimportant if the confidence intervals overlap.

You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval.

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Answer:

B: 3(x-6) = 3x-18

Step-by-step explanation:

The left and right sides of this equation are actually equal! We can see this by dividing the 3 on the left through the parentheses. This gives us [tex]3x-18[/tex], which is equal to the right-hand side of the equation!

To solidify this, we add 18 to both sides, and subtract 3x from both sides, which gives us that 0=0, so there are infinitely many solutions for x(since no matter what x is, it will result in 0=0 which is always true).

I hope this helps!

Answer:

2.4.6.8.10

Step-by-step explanation:

that's the answer

Answer:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Step-by-step explanation:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, multiply all numbers frmo 1 to 10

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

1 pound = $1.38

175 pounds = $241.50

The number of pounds for the strawberries order of $241.50 is

175 pounds.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Cost of strawberries per pound = $1.38

The cost of a strawberry order = $241.50

The number of pounds for the order of $241.50.

1 pound = $1.38

Multiply 241.50/1.38 on both sides.

241.50/1.38 x 1 pound = $241.50

175 pounds = $241.50

Thus,

The number of pounds for the strawberries order of $241.50 is

175 pounds.

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The complete question is:

A grocer can buy strawberries for $1.38 per pound.

Write an equation relating c, the cost, and p, the pounds of strawberries.

A strawberry order cost $241.50.

How many pounds did the grocer order?

The lengths of AN=2.5cm and MN=3.5cm

What is similar triangle?

Similar triangles are triangles that have a similar form, however their sizes might vary.

Main body:

IN ΔAMN ≈ΔABC

Since MN∣∣BC

∠AMN=∠ABC (Corresponding angles)

∠ANM=∠ACB (Corresponding angles)

∴ΔAMN∼ΔABC(By $$AA similarity criterion)

⇒AM/AB =AN/AC=MN/BC (CPCT)

since , M is the mid point of AB.

AM = 1/2 AB  , OR

AM/AB = 1/2

AM/AB =AN/AC = 1/2

AN/AC = 1/2

AN/5= 1/2

AN = 2.5 cm

AM/AB =MN/BC = 1/2

​ [∵BC=7cm]

MN/7 = 1/2

MN= 7/2 =3.5

Hence , the lengths of AN=2.5cm and MN=3.5cm

the complete question is :

In triangle ABC, M is mid-point of AB and a straight line through M and parallel to BC cuts AC at N. Find the lenghts of AN and MN, if BC=7cm and AC=5cm.

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The equation of the parabola that passes through (0, -5) and has a vertex at (-1, 4) will be y = -9(x + 1)² + 4.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The vertex of the parabola is at (-1, 4). Then the equation is given as,

y = a(x + 1)² + 4

The equation passes through (0, -5), then we have

y = a(x + 1)² + 4

-5 = a(0 + 1)² + 4

-5 = a + 4

a = -9

Then the equation of the parabola that passes through (0, -5) and has a vertex at (-1, 4) will be y = -9(x + 1)² + 4

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Answer:

No

Step-by-step explanation:

5+10=15, which cannot be less than 17

Answer:

Step-by-step explanation:

y = 1/6x + 5/6

-5x + 6(1/6x + 5/6) = -11

-5x + x + 5 = -11

-4x + 5 = -11

-4x = -16

x = 4

y = 2/3 + 5/6

y = 7/6 or 1 1/6

(4, 7/6)

Answer:

Step-by-step explanation:

y = 6x + 42

6x + 42 = y

6x = y - 42

x = (y - 42)/6

The probability that both hats are different colors is; 0.7425  

We are given;

Total number of hats = 30 hats

Number of green hats = 5 hats

Number of blue hats = 7 hats

Number of red hats = 12 hats

Number of brown hats = 6 hats

Now, if Mary selects two hats at random, then the probability that they are different colors is;

P(they are different colors) = 1 - P(both are the same color)

P(both are the same color) = (⁵/₃₀ * ⁴/₂₉) + (⁷/₃₀ * ⁶/₂₉) + (¹²/₃₀ * ¹¹/₂₉) + ( ⁶/₃₀ * ⁵/₂₉)

= (20 + 42 + 132 + 30)/(30*29)

=  224/(30*29)

= 0.2575

Thus;

P(they are different colors) = 1 - 0.2575

P(they are different colors) = 0.7425  

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By solving the linear matrices we got the values X = 1000000  , Y = 800000 ,  Z = 200000

According to algebra, an equation is a statement that shows the equality of two mathematical expressions. For instance, the equation 4x + 5 = 15 consists of the two equations 4x + 5 and 15, which are separated by the 'equal' sign.

According to the given information

X + Y + Z  =  2000000

0.07X + 0.085Y + 0.095Z = 157000

Y = 4Z

Y = 4Z is substituted into the first and second equations as follows:

X + 5Z = 2000000

0.07X + 0.085 (4Z) + 0.095Z = 157000

X = 2000000 - 5Z

0.07X + 0.435Z = 157000

0.07 (2000000 - 5Z) + 0.435Z = 157000

140000 - 0.35Z + 0.435Z = 157000

0.085Z + 140000 = 157000

0.085Z = 17000

Z = 200000

Y = 800000

X = 1000000

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The inequality which represents is 2x + 3y ≤ 12 where x is the number of daisies and y is the number of tulips.

A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

Suppose the cost of one daisy is x while the cost of one tulip is y.

2x + 3y will be totally spent and it can be almost $12.

2x + 3y ≤ 12

Hence "The inequality which represents is 2x + 3y ≤ 12 where x is the number of daisies and y is the number of tulips.".

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When solving a system of linear equations by substitution, normally, we want to try to solve for the easiest one to get to or we choose a variable with unit coefficient.

A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem. Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.

A constant component of a word as opposed to a variable. a measurement of some property or characteristic using a number (as of a substance, device, or process)

There are many factors, it is all a matter of preference, normally, we want to try to solve for the easiest one to get to

example;

if we have

(x-3)^2+y=9

we would solve for y because it is less tricky or we choose a variable with unit coefficient.

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Answer:

5 tables

Step-by-step explanation:

Let x be the number of tables the school needs to rent, and c be the total cost of renting the tables.

We can use the following equation to represent the cost of renting from the first company:

c = 20 + 12x

And we can use the following equation to represent the cost of renting from the second company:

c = 30 + 10x

As c is the same constant in both equations, we can say the following:

20 + 12x = 30 + 10x

Now we can solve this equation by simplifying:

20 + 12x = 30 + 10x

20 + 2x = 30

2x = 10

x = 5

Therefore, the school will need to rent 5 tables for the cost to be the same from both renting companies.

Answer: 5 tables

Step-by-step explanation:

The first rental company will charge $32 for one table.

The second rental company will charge $40 for one table.

So if we make a table, and keep adding $12 to the first company and $10 to the second it will look like this.

First company                          Second company                   Table

 $32                                                  $40                                     1

 $44                                                  $50                                     2

 $56                                                  $60                                     3

 $68                                                  $70                                     4

 $80                                                  $80                                     5

Therefore, the school can rent 5 tables for the same price in both companies.

The Assessment Triangle and the Domains and Dimensions of the Assessment Framework.

Perimeter of A/perimeter of B = a/b

Given that triangles ABC and DEF are similar triangles, we have the following:

Perimeter of triangle ABC = x

One side length of triangle ABC = 4 cm

Perimeter of triangle DEF = 12 + 6 + 9 = 27 cm

One side length of triangle DEF = 6 cm

Therefore:

x/27 = 4/6

Cross multiply

6x = (27)(4)

6x = 108

6x/6 = 108/6

x = 18

Thus, the perimeter of tr8angle DEF that is similar to triangle ABC is: 18 cm.

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Answer:

39.05 miles

Step-by-step explanation:

0.05+0.1+38

Answer:

1 : 16

Step-by-step explanation:

6 hours : 4 days

6 hours : 96 hours

1 hour : 16 hours