13. What is the missing mumber in the input-output table below?
Input
3
5
?
17
Output
16
22
31
58
A. 8
C. 11
B. 9
D. 14

Answer:

100%_$40.80

? × _$38.76

Step-by-step explanation:

100%×$38.76÷$40.80=95%

Answer:

40.80

Step-by-step explanation:

x + y = 32 (1)

3x + 4y = 120 (2)

x = 8; y = 24

Step-by-step explanation:

Total students = 120

Number of groups = 32

If the number of three person groups = x

Number of four person groups = y

write a system of equations that models this situation

x + y = 32 (1)

3x + 4y = 120 (2)

From (1)

x = 32 - y

Substitute x = 32 - y into (2)

3(32 - y) + 4y = 120

96 - 3y + 4y = 120

- 3y + 4y = 120 - 96

y = 24

Substitute y = 24 into (1)

x + y = 32

x + 24 = 32

x = 32 - 24

x = 8

x = 8; y = 24

Answer: 4 Shirts

Step-by-step explanation:

Given

Person has [tex]\$80[/tex]

Pant costs [tex]\$29[/tex] and shirt costs [tex]\$12[/tex]

Suppose [tex]x\ \text{and}\ y[/tex] as number of pant and shirts

Spent money must be equal or less than the total money. The inequality becomes

[tex]\Rightarrow 80\geq29x+12y[/tex]

For 1 pair of pants that is, 1 pants

[tex]\Rightarrow 80\geq 29+12y\\\Rightarrow 51\geq 12y\\\Rightarrow 4.25\geq y[/tex]

That is maximum number of shirts that can be bought are 4.

Given:

The expression is:

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}[/tex]

To find:

The correct form of the partial fraction decomposition for the given expression.

Solution:

We have,

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}[/tex]

By partial fraction decomposition, it can be written as:

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{A}{x+1}+\dfrac{B}{(x+1)^2}+\dfrac{Cx+D}{x^2+7}[/tex]           ...(i)

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{(x+1)^2(Cx+D)+(x+1)(x^2+7)A+(x^2+7)B}{(x+1)^2(x^2+7)}[/tex]

[tex]4x^3+3x^2=(x+1)^2(Cx+D)+(x+1)(x^2+7)A+(x^2+7)B[/tex]

[tex]4x^3+3x^2=x^3A+x^3C+x^2A+x^2B+2x^2C+x^2D+7xA+xC+2xD+7A+7B+D[/tex]

[tex]4x^3+3x^2=x^3(A+C)+x^2(A+B+2C+D)+x(7A+C+2D)+7A+7B+D[/tex]

On comparing both sides, we get

[tex]A+C=4[/tex]

[tex]A+B+2C+D=3[/tex]

[tex]7A+C+2D=0[/tex]

[tex]7A+7B+D=0[/tex]

On solving these equations, we get

[tex]A=\dfrac{23}{32},B=-\dfrac{1}{8},C=\dfrac{105}{32},D=-\dfrac{133}{32}[/tex]

Substituting these values in (i), we get

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{\dfrac{23}{32}}{x+1}+\dfrac{-\dfrac{1}{8}}{(x+1)^2}+\dfrac{\dfrac{105}{32}x-\dfrac{133}{32}}{x^2+7}[/tex]

Therefore, the required partial fraction decomposition is:

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{\dfrac{23}{32}}{x+1}+\dfrac{-\dfrac{1}{8}}{(x+1)^2}+\dfrac{\dfrac{105}{32}x-\dfrac{133}{32}}{x^2+7}[/tex]

Answer:

A on Edg

Step-by-step explanation:

got it right

b) ( 7, 21)

Step-by-step explanation:

5(7)=2(21)-7

35=42-7

35=35

Answer:

None of them

Step-by-step explanation:

a: 5*0=2*6-7 False

b: 5*21=2*7-7 False

c: 5*18=2*8-7 False

d: 5*4=2*-3-7 False

Answer:

32 cars

Step-by-step explanation:

we know that 14 and 30 lie on opposite sides of the ferris wheel, so we need to calculate how many cars are inbetween car number 14 and carn number 30. since each car is numbered starting from 1, we know that the cars do not skip any numbers. after counting, we know that there are 16 cars inbetween car number 14 and car number 30. since there are 2 sides of a circle we have to double our number by 2. so 16×2 is 32

Math step-by-step:

30-14=16

16×2=32

Answer:

19:1

Step-by-step explanation:

There are 10000 headlights. If 5% are defective, then 500 are defective. Since we took that 500 out, we get 9500 good headlights. The ratio is 9500:500 or 19:1

The ratio of defective headlights to non-defective headlights will be 19:1.

The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.

There are 10000 headlights. If 5% are defective, then 500 are defective. Since we took that 500 out, we get 9500 good headlights.

The ratio will be calculated as below:-

Ratio = 9500:500

Ratio = 19:1

Therefore, the ratio of defective headlights to non-defective headlights will be 19:1.

To know more about percentages follow

https://brainly.com/question/24304697

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Answer:

( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2

Step-by-step explanation:

x^2 = - 7x - 8

x^2 + 7x + 8 = 0

Here,

a = 1

b = 7

c = 8

D = b^2 - 4ac

= 7^2 - 4 ( 1 ) ( 8 )

= 49 - 32

D = 17

x = - b ± √D / 2a

= - 7 ± √17 / 2 ( 1 )

x = ( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2

Answer: No

Step-by-step explanation:

Add 2 sides together. If the sum of greater than the length of the 3rd side for all 3 options it can form a right triangle if it doesn’t than it can’t:

9 + 12 = 21 which is not greater than the 3rd side length of 21 so this cannot form a right triangle.

Answer:

70 degrees

Step-by-step explanation:

there are multiple ways, as all the trigonometric functions are related.

let's try it this way :

consider the missing side to be the radius of a circle.

then 41 would be the cos value of the angle (multiplied by that radius, of course).

so, let's calculate the missing side per Pythagoras

c² = a² + b² = 113² + 41² = 12769 + 1681 = 14450

c = 120.21

and now

41 = cos(?) × 120.21

cos(?) = 41/120.21 = 0.341...

? = 70.0576... ≈ 70 degrees

Answer:

70°

Step-by-step explanation:

tangent θ = (opposite side / adjacent side)

tangent θ = (113 / 41)

θ = arctan (113 / 41)

θ = 70.0576°

*Note: "arctan" is the same as "inverse tangent"

**Note: "soh-cah-toa" (and "cho-sha-cao" for sec, csc, & cot) is an easy mnemonic device to remember the trig functions (sin, cos, & tan) and their relations to the sides of a given angle.

(x-h)²+(y-k)²=r²

(3-h)²+(3-0)²=5²

h²-6h+9+9=25

h²-6h-7=0 —> (h-7)(h+1)=0

h=7 , h=-1

h=7 —> (x-h)²+y²=r² —> (x-7)²+y²=25 —>

x²-14x+49+y²=25 —> x²+y²-14x+24=0

h=–1 —> (x-h)²+y²=r² —> (x+1)²+y²=25 —>

x²+2x+1+y²=25 —> x²+y²+2x–24=0

I hope it helped you ^_^

Answer:

B.

Step-by-step explanation:

Other equations don't have any value of x.

Answer:

Because if you see.. The component of x will get canceled in each of the other 3 options.. ( 2x - 2x) which means no solution.. In option B.. 2x + 2x will give 4x..= 31-31 = 0..

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

Hope it helps...

Have a great day!!

Answer:

[tex]2x + 3 = 13 \\ 2 \times 5 + 3 = 15 \\ 10 + 13 = 15 \\ 23 = 15 \\ 23 - 15 = 8 \\ \\ 3x + 2 = 13 \\ 3 \times 5 + 2 = 13 \\ 15 + 2 = 13 \\ 17 - 13 \\ = 4 \\ \\ x - 5 = 0 \\ 5 - 5 = 0 \\ 0 = 0 \\ \\ 4x - 9 = 21 \\ 4 \times 5 - 9 = 21 \\ 20 - 9 = 21 \\ 21 - 11 \\ = 10[/tex]

Answer:

x=6

pqs=82

sqr=59

Step-by-step explanation:

13x + 4 + 10x - 1 = 141

23x + 3= 141

23x = 136

x = 136/23 = 6

~~~~~~~~~~~~~~~

pqs = 13x + 4  = 13(6) + 4 = 78+4 = 82

sqr =  10x - 1 = 10(6)-1 = 60 - 1 = 59

Answer:

x = 6

Angle PQS is 82

Angle SQR is 59

Step-by-step explanation:

13x + 4 + 10x - 1 = 141

Group like terms : 23x + 3 = 141

Subtract 3 from both sides to get 23x = 138

Divide both sides by 23 to get x = 6

Angle PQS: Plug 6 into x  for 13x + 4 = 13 (6) + 4 = 82

Angle SQR: Plug 6 into x for 10x - 1 = 10 (6) -1 = 59

tienees que fijartelos extrreemos

Answer:

The last answer

Step-by-step explanation:

We can check

For example,

a5=-6×a4

a5=-6×(-216)

a5=1296

Answer:

60

Step-by-step explanation:

To get the value of x;

3x:90

(90/3) = 30

x = 30

To get the value of 2x;

(2×X);

2 × 30

=60

Answer:

Let the inverse of f(x) be h(x):

[tex]{ \tt{h(x) = \frac{1}{4x} }}[/tex]

Answer:

(0,-9)

Step-by-step explanation:

To find the y-intercept, substitute x=0

y=(0)^2+4(0)-9

=-9

Here's a tip to help you find the y-intercept faster, it is usually the constant of the graph equation

Answer:

see explanation

Step-by-step explanation:

Given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

The equation of the axis of symmetry which is also the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = x² + 4x - 9 ← is in standard form

with a = 1, b = 4 , then

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

x = - 2 is the equation of the axis of symmetry

Substitute x = - 2 into the equation for corresponding y- coordinate of vertex

y = (- 2)² + 4(- 2) - 9 = 4 - 8 - 9 = - 13

vertex = (- 2, - 13 )

To find the y- intercept let x = 0 and solve for y

y = 0² + 4(0) - 9 = 0 + 0 - 9 = - 9

y- intercept = (0, - 9)

From the standard form of the parabola

• If a > 0 then vertex is a minimum

• If a < 0 then vertex is a maximum

Here a = 1 , that is > 0

vertex (- 2, - 13 ) is a minimum

Answer:

A & D

First and last

Step-by-step explanation:

Answer:

Step-by-step explanation:

If we are looking for how long it will take the level to be less than or equal to 64 cups, we are solving an inequality as opposed to an equation. It would look like this:

-.414t + 129.549 ≤ 64  We subtract 129.549 from both sides to get

-.414t ≤ -65.549 and then divide by -.414. But because we are dividing by a negative number we need to change the way the inequality is pointing:

t ≥ 158.3 minutes which is about 2.6 hours

Answer:

t ≥ 158.33, or rounded, t ≥ 160.

Explanation:

The equation we're given is

W = -0.414t + 129.549, which an be written as

-0.414t + 129.549 = W.

We are asked to find the amount of time it would take for the water level to be less than or equal to 64 cups.  Plugging this information in, we have:

-0.414t + 129.549 ≤ 64

To solve this, we first cancel 129.549 by subtracting from both sides:

-0.414t + 129.549 - 129.549 ≤ 64 - 129.549

-0.414t ≤ -65.549

Now divide both sides by -0.414:

-0.414t/-0.414 ≤ -65.549/-0.414

t ≥ 158.33

(When we multiply or divide both sides of an inequality by a negative number, we must flip the inequality symbol)

Answer:

1. Multiply by 3

2. Multiply by 1/3

Step-by-step explanation:

6x - 3y = 3

-2x + y = -14

1. In order to eliminate the x-terms, they would both have to equal the same number with opposite signs (positive and negative). Since we are only touching the second equation, how can we get from 2 to 6? We can multiply 2 by 3 to get to 6 (negative 6 in the end.) This would result as follows:

6x - 3y = 3

-6x + 3y = 42

2. In order to eliminate the y-terns through multiplying with the first equation, we have to figure out how to make 3y into 1y. We can do this by adding its reciprocal, 1/3. 1/3 × 3 = 1. This would result as follows:

2x - y = 1

Answer:

83 spins

Step-by-step explanation:

Number of red spins = n

Number of orange spins = 8n

Number of yellow spins = 3n

Total number of trials = 240

Total number of spins :

(n + 8n + 3n) = 240

12n = 240

n = 240 / 12

n = 20

Number of red spins = 20

(1000/240) * n

4.1666666 * 20

= 83.333

= 83 spins

Answer:

D

Step-by-step explanation:

Pythagorean

[tex]x^{2} + 9^{2} = 15^{2}[/tex] (x>0)

=> [tex]x=\sqrt{15^{2}-9^{2} }[/tex] [tex]=12[/tex]

Answer:

157 miles

Step-by-step explanation:

total cost = flat fee + cost per mile * miles

133.17 = 16.99 + .74 * m

Subtract 16.99 from each side

116.18 = .74m

Divide each side by .74

116.18 / .74 = .74m/.74

157 = m