The enrollment of students in evening classes at a local university decreased by 8% between two recent years. If the total number of students attending
evening classes in both years was 13,876, find how many students enrolled in evening classes in each of the years.

Answer:

D(- 1) = 2

Step-by-step explanation:

To evaluate D(- 1), substitute x = - 1 into D(x) , that is

D(- 1) = (- 1)² - 2(- 1) - 1 = 1 + 2 - 1 = 2

Answer:

25 and 18

Step-by-step explanation:

Let's say that the first number is x and the second one is y.

First, the difference between them is 7, so x-y=7

Next, the sum of their squares is 949, so x²+y² = 949

We have

x-y=7

x²+y²=949

One thing we can do to solve this problem is to solve for x in the first equation, plug that into the second equation, and go from there

Adding y to both sides in the first equation, we have

x = 7 + y

Plugging that into the second equation for x, we have

(7+y)²+ y² = 949

expand

(7+y)(7+y) + y² = 949

49 + y² + 7y + 7y + y² = 949

combine like terms

2y² +14y + 49 = 949

subtract 949 from both sides to put this in the form of a quadratic equation

2y² + 14y - 900 = 0

divide both sides by 2

y² + 7y - 450 = 0

To factor this, we want to find 2 numbers that add up to 7 and multiply to -450.

The factors of 450 are as follows:

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.

Note that we want to find two numbers with a difference of 7, as one will have to be negative for the multiplication to end up at -450. Two numbers that stand out are 18 and 25. To make them add up to 7, 18 can be negative. We therefore have

y² + 25y - 18y - 450 = 0

y(y+25) - 18(y+25) = 0

(y-18)(y+25) = 0

Solving for 0,

y-18 = 0

add 18 to both sides

y=18

y+25 = 0

subtract 25 from both sides

y= -25

As the question states "two positive integers", this means that y must be positive, so y = 18. We know x-y=7, so

x-18 = 7

add 18 to both sides to isolate x

x = 25

The value of x in the figure is 125°

 And the right option is (D) 125°

To solve the problem, we use the formular for the sum of the interior angle of a polygon.

(n-2)180°

         [tex](5-2)180 = 540[/tex]

     ∠P+∠T+∠R+∠Q+∠S = 540°

       [tex]35+200+x+90+90 = 540[/tex]

        [tex]415+x = 540[/tex]

         [tex]x = 540-415[/tex]

         [tex]x = 125[/tex]

Hence the value of x in the figure is 125°

And the right option is (D) 125°

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Answer:

18 feet

Step-by-step explanation:

The distance of the center of the fountain from the enter edge is equal to the radius of the circular fountain.

Use the circumference formula, c = 2[tex]\pi[/tex]r, to find the radius.

c = 2[tex]\pi[/tex]r

112 = 2[tex]\pi[/tex]r

18 = r

So, to the nearest whole number, the distance between the center of the fountain and outer edge is 18 feet.

Answer:

Base is 3 centimeter and hight is 12 cent.

Answer:

three

Step-by-step explanation:

The three countries expect to have an increase in population. Then the correct option is C.

A diagram is made up of rectangles whose size is related to a variable's frequency and whose width is comparable to the training sample.

The bar chart of the countries is shown.

From the bar chart, the population from 1950 to 2000 and from 2000 to 2050 of Australia increased.

From the bar chart, the population from 1950 to 2000 and from 2000 to 2050 of Hungary first increases then decreases.

And from the bar chart, the population from 1950 to 2000 and from 2000 to 2050 of Canada increased.

From the bar chart, the population from 1950 to 2000 and from 2000 to 2050 in South Korea first increases then decreases.

From the bar chart, the population from 1950 to 2000 and from 2000 to 2050 of Egypt increased.

The three countries expect to have an increase in population.

Then the correct option is C.

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Answer:

0.254

Step-by-step explanation:

Table A-6 will be shown below for reference. Since none of the answer choices contain the critical value for 61, we can just round that number to 60. We will see that the critical value is 0.254. If you're having trouble reading the table below, look at the columns to find the corresponding significance level you are working with then find the sample value.

Best of Luck!

Answer:

Step-by-step explanation:

Amplitude 2

wave height 4

trough 5

crest 3

wave length 1

Answer:

-2 from both sides

Step-by-step explanation:

32=5x+2

-2        -2

________

30=5x

__=__

5      5

6=x

The first step to solve for X is to use subtraction property of equality to subtract 2 from both sides.

We are given the algebraic equation;

32 = 5X + 2

The first step to solve for X is to use subtraction property of equality to subtract 2 from both sides to get;

32 - 2 = 5X + 2 - 2

30 = 5X

Divide both sides by 5 using division property of equality to get;

X = 6

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Step-by-step explanation:

Here you go;

49.49

19.88

25.93

14.2

Set up a ratio:

1/50 = x/480

Cross multiply:

50x = 480

Divide both sides by 50:

X = 9.6

The distance on the map is 9.6 cm

Answer:

2.5

Step-by-step explanation:

8x + 2 = 7 + 5x + 15

Combine like terms:

8x + 2 = 7 + 5x + 15

8x + 2 = 22

      -2     -2

-----------------

8x = 20

----    ----

8       8

x = 2.5

Hope this helped.

Answer: D

Step-by-step explanation:

Answer:

Let the number of courses that are worth 3 credits each be x and those worth 4 credits be y. With the given information, you can write the following equations:  

x + y = 48

3x + 4y = 155

You can solve the above equations by method of elimination/substitution

x + y = 48 ⇒ x = 48 - y (Now, substitution this equation into 3x + 4y = 155)

3(48 - y) + 4y = 155

144 -3y + 4y = 155

y + 144 = 155

y = 11

Now plug this solution back into x = 48 - y  

x = 48 - 11 = 37  

Check work (by plugging the solutions back into the 3x + 4y and see if it's equal to 155):

3(37) + 4(11) = 155

Answer: There are 37 of the 3-credit course and 11 of the 4-credit course

Answer:

2

+

3

2

Step-by-step explanation:

First simplify the expression into polynomial form,

[tex](x-1)(x-3)(x+5)(x+7)=297[/tex]

[tex]x^4+8x^3-10x^2-104x+105=297[/tex]

[tex]x^4+8x^3-10x^2-104x-192=0[/tex]

Now factor into,

[tex](x-4)(x+8)(x^2+4x+6)=0[/tex]

Which means the solutions are,

[tex]x-4=0\implies\boxed{x_1=4}[/tex]

[tex]x+8=0\implies\boxed{x_2=-8}[/tex]

and then two complex solutions because determinant of the third factor [tex]D\lt0[/tex],

[tex]x^2+4x+6=0[/tex]

[tex]x^2+4x+4=-2[/tex]

[tex](x+2)^2=-2\implies\boxed{x_3=i\sqrt{2}-2},\boxed{x_4=-i\sqrt{2}-2}[/tex]

Hope this helps :)

Answer:

x=4

Step-by-step explanation:

(4-1)(4-3)(4+5)(4+7)=297

Answer:

Step-by-step explanation:

Assuming the gravel reaches the top of the walls and no higher, the volume is 7×4×16 = 448 m³

Answer:

hello thereee

now vol of truck = l b h = 7 * 4 * 16 = 448 m^3

( 448m^3 is final ans...

glad for brainliest.... hope that helps <3

Answer:

=4-7

=5

:same will be 5 years older than Sabrina

Answer:

its d      47

Step-by-step explanation:

yep yep

Answer:

D: 47

Step-by-step explanation:

Edge 2022

Kurt Blixen must invest $85,2296.94.

Given the following data;

To find how much money Kurt Blixen must invest;

Mathematically, simple interest is given by the formula;

[tex]S.I = \frac{PRT}{100}[/tex]

Where:

First of all, we would convert the time in days to years.

Conversion:

365 days = 1 year

90 days = x year

Cross-multiplying, we have;

[tex]365 * x = 90\\\\x = \frac{90}{365}[/tex]

x = 0.247 year

Making P the subject of formula;

[tex]P = \frac{S.I(100)}{RT}[/tex]

Substituting the values into the formula, we have;

[tex]P = \frac{10000(100)}{4.75*0.247}\\\\P = \frac{1000000}{1.1733}[/tex]

P = $85,2296.94

Therefore, Kurt Blixen must invest $85,2296.94.

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Answer:

{-3, 1, 5, 6}

Step-by-step explanation:

The domain of a relation is the x-values represented in that function. In a coordinate pair, the x-value comes first, so all of the first numbers in each of the pairs are part of the domain. When writing domain, it should always be in the least to greatest order. Therefore, the domain is {-3, 1, 5, 6}. Since this relation is a function, none of the x-values will repeat.

hi

9x750 = 630 +450= 1080 ml

so 1.08 liter.

Answer:

x = 5/2

Step-by-step explanation:

4x-1=9

Add 1 to each side

4x-1+1=9+1

4x = 10

Divide by 4

4x/4 = 10/4

x = 5/2

Answer:

72 degrees

Step-by-step explanation:

Area of a sector=(pi*r^2)*(Theta/360)

125*pi=pi*(625)*(theta/360)

(125*360)/625=theta

Theta=72 degrees

The angle theta of the sector of the given circle is 72 degrees.

We have given that,

In the diagram below, the circle has a radius of 25 inches.

The area of the shaded sector is 125π in^2.

[tex]Area \ of \ a \ sector=(pi*r^2)*(\Theta/360)[/tex]

Therefore we get,

[tex]125*pi=pi*(625)*(\theta/360)[/tex]

[tex](125*360)/625=\theta[/tex]

[tex]\theta=72 degrees[/tex]

Therefore we get the angle of the sector of the given circle is 72 degrees.

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[tex]\\ \sf\longmapsto \dfrac{2}{3}x=10[/tex]

[tex]\\ \sf\longmapsto \dfrac{2x}{3}=10[/tex]

[tex]\\ \sf\longmapsto 2x=3(10)[/tex]

[tex]\\ \sf\longmapsto 2x=30[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{30}{2}[/tex]

[tex]\\ \sf\longmapsto x=15[/tex]

[tex] \begin{cases}\large\bf{\red{ \implies}} \tt \frac{2}{3} x \: = \: 10 \\ \\ \large\bf{\red{ \implies}} \tt \frac{2x}{3} \: = \: 10 \\ \\ \large\bf{\red{ \implies}} \tt 2x \: = \: 3 \: \times \: 10 \\ \\ \large\bf{\red{ \implies}} \tt 2x \: = \: 30 \\ \\ \large\bf{\red{ \implies}} \tt \: x \: = \:\frac{ \cancel{30} \: \: ^{15} }{ \cancel{2}} \\ \\ \large\bf{\red{ \implies}} \tt \: x \: = \: 15 \end{cases}[/tex]

Answer:

2x^3+5x^2+2x

Step-by-step explanation:

x+2 x and 2x+1

The volume of a rectangular prism is solved by multiplying the height, width, and base. So to solve for the volume, it is (x^2+2x)*(2x+1) [just multiplies x+2 and x] 2x^3+5x^2+2x

Step-by-step explanation:

[tex]thank \: you[/tex]

Answer:

how did not orderstan that

Answer:

Step-by-step explanation:

Out of 12 consecutive integers:

Sum of 3 integers will be divisible by 4 if the remainders are:

So total number of combinations is:

Answer:

y = 54/25 when x = 4.

Step-by-step explanation:

y is given by the equation:

[tex]\displaystyle y = p\times q^{x-1}[/tex]

Where p and q are numbers.

We are also given that when x = 1, y = 10 and when x = 6, y = 0.7776.

And we want to determine the value of y when x = 4.

Since y = 10 when x = 1:

[tex]\displaystyle (10) = p\times q^{(1)-1}[/tex]

Simplify:

[tex]10 = p \times q^0[/tex]

Any number (except for zero) to the zeroth power is one. Hence:

[tex]p=10[/tex]

Thus, our equation is now:

[tex]y = 10\times q^{x-1}[/tex]

When x = 6, y = 0.7776. Thus:

[tex](0.7776) = 10\times q^{(6)-1}[/tex]

Simplify and divide both sides by ten:

[tex]\displaystyle 0.07776 = q^5[/tex]

Take the fifth root of both sides:

[tex]\displaystyle q = \sqrt[5]{0.07776}[/tex]

Use a calculator. Hence:

[tex]\displaystyle q = \frac{3}{5} = 0.6[/tex]

Our completed equation is:

[tex]\displaystyle y = 10\times \left(\frac{3}{5}\right)^{x-1}[/tex]

Then when x = 4, y equals:

[tex]\displaystyle \begin{aligned} y &= 10\times \left(\frac{3}{5}\right)^{(4)-1} \\ \\ &= 10\times \left(\frac{3}{5}\right)^3 \\ \\ &= 10\times \left(\frac{27}{125}\right) \\ \\ &= \frac{54}{25}\end{aligned}[/tex]

Step-by-step explanation:

What is the equation of the parabola that has a vertex at

(

−

4

,

2

)

and passes through point

(

−

7

,

−

34

)

?

To solve this you need to use the vertex form of the equation of a parabola which is

y

=

a

(

x

−

h

)

2

+

k

, where

(

h

,

k

)

are the coordinates of the vertex.

Explanation:

The first step is to define your variables

h

=

−

4

k

=

2

And we know one set of points on the graph, so

x

=

−

7

y

=

−

34

Next solve the formula for

a

y

=

a

(

x

−

h

)

2

+

k

−

34

=

a

(

−

7

+

4

)

2

+

2

−

34

=

a

(

−

3

)

2

+

2

−

34

=

9

a

+

2

−

36

=

9

a

−

4

=

a

To create a general formula for the parabola you would put in the values for

a

,

h

, and

k

and then simplify.

y

=

a

(

x

−

h

)

2

+

k

y

=

−

4

(

x

+

4

)

2

+

2

y

=

−

4

(

x

2

+

8

x

+

16

)

+

2

y

=

−

4

x

2

−

32

x

−

64

+

2

So the equation of a parabola that has a vertex at

(

−

4

,

2

)

and passes through point

(

−

7

,

−

34

)

is:

y

=

−

4

x

2

−

32

x

−

62