Which are the solutions of the quadratic equation?
x2 = 7x + 4

Answer:

4,444097208657794

Step-by-step explanation:

c = 20ft

b = 19.5ft

just use the pythagorean theeorem

Answer:

there isn't a direct answer for that because it depends on the shape.

but it has rotational symmetry if it can be rotated by an angle between 0° and 360°

Answer:

72 campers.

Step-by-step explanation:

You can do this with a simple equation. 180% = 1.8 as a decimal fraction. Let x be this  year's attendance. Then:

x = 1.8* 40

x = 72 campers.

Answer:

72 Campers

Step-by-step explanation:

Hope this helps:)

Answer:

I can't see Mathieu's work but I will show the right steps and maybe you can find where Mathieu went wrong.

f(x)=x^2+4x+3

f(x)=(x+3)(x+1)       Since 3*1=3 and 3+1=4

The x-intercepts can be found by setting y to 0 and solving for x

(in other words replace that f(x) thing with 0 and solve for x)

0=(x+3)(x+1)

Now set both factors equal to 0

x+3=0       or      x+1=0

x   =-3                    x=-1

The x-intercepts are at (-3,0) and (-1,0)

A function assigns the value of each element of one set to the other specific element of another set. The correct option is C.

A function assigns the value of each element of one set to the other specific element of another set.

The x-intercepts of the function f(x) = x² + 4x + 3 can be found as shown below.

f(x) = x² + 4x + 3

0 = x² + 4x + 3

0 = (x+3)(x+1)

x = -3, -1

Now, it can be seen that Mathieu has actually set the factored expressions equal to each other, which was wrong.

Hence, the correct option is C.

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Answer:

c. When a > 0 and b > 1, the function models exponential growth.

Step-by-step explanation:

You have exponential decay when a > 0 and 0 < b < 1.

The statement that is always true about the function y=a•b^xc is this: C. When a > 0 and b > 1, the function models exponential growth.

Exponential growth is a type of growth that occurs as there is an addition of numbers. This is reflected in the upward movement of the graph if such growth is represented in a graph.

So, the statement that best reflects this meaning of exponential growth is that when in a function, a > 0 and b > 1, then exponential growth is modeled. Thus, the correct option number is C. "When a > 0 and b > 1, the function models exponential growth."

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49 ___ 3 + 32 ÷ 23

49 ___ 3 + 1.39

49 ___ 4.39

49 > 4.39 is the only possible answer. 49 is greater than 4.39.

To determine the correct symbol for the expression 49 ___ 3 + 32 ÷ 23, first calculate the right side following PEMDAS, resulting in 7. Then compare it with the left side (49), which shows that 49 is greater than 7, so the correct symbol is '>'.

The question asks which symbol makes the mathematical statement true for the expression 49 ___ 3 + 32 ÷ 23. We need to solve the right side of the equation first before we can determine the correct symbol to use.

To solve 3 + 32 ÷ 23, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division as they appear from left to right, Addition and Subtraction as they appear from left to right). First, we solve the exponent 23, which equals 8. Then, we perform the division: 32 ÷ 8 = 4. Finally, we add 3 to the result: 3 + 4 = 7. So, our expression on the right side of the equation is equal to 7.

Now we compare the left side of the equation (49) with the result we calculated (7). It is evident that 49 is greater than 7, so the correct symbol to use would be '>'. Therefore, the complete and true mathematical statement would be: 49 > 3 + 32 ÷ 23 or 49 > 7.

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Base x height

To find the base, do pi r squared.

Answer:

(a) 15/3 = 100/x

(b) There are 20 toddlers in the class.

Step-by-step explanation:

(a)

The total number of students is 100% of the students.

Let the total number of students be x.

15% of students is to 3 as 100% of students is to x.

15/3 = 100/x

(b)

15/3 = 100/x

Cross multiply the equation.

15x = 3 * 100

15x = 300

Divide both sides by 15.

x = 20

Answer: There are 20 toddlers in the class.

Answer:

Step-by-step explanation:

You use latex very well. Nice work.

sqrt(17) = 4.123

sqrt(5) = 2.236

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

pi + 7

=====

5

3.14 + 7

======

5

10.14/5 = 2.028

Answer

B. \frac{\pi +7 }{5}   2.028

C. \sqrt{5}               2.236

A. \sqrt{17}              4.123

Answer:

Option  A.)−4

Step-by-step explanation:

we have

4x+5y=-12 -----> equation A

-2x+3y=-16 -----> equation B

Solve the system of equations by elimination

Multiply the equation B by 2

2*(-2x+3y)=-16*2

-4x+6y=-32 -----> equation C

Adds equation A and equation C

4x+5y=-12

-4x+6y=-32

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

5y+6y=-12-32

11y=-44

y=-4

Answer with Step-by-step explanation:

We are given a system of linear equations:

4x + 5y = −12

-2x + 3y = −16

Multiply second equation by 2 and add it to first equation.

4x+5y-4x+6y= -12-32

⇒ 11y= -44

Dividing both sides by 11

⇒ y= -4

Hence, the y-value in the solution to the system of linear equations

4x + 5y = −12

-2x + 3y = −16    is:

A.)−4

Answer:

1.48 m

Step-by-step explanation:

mean height of 14 boys is 1.56 m, so their total height is 14 * 1.56 = 21.84 m

mean height of 32 students is 1.515 m, so their total height is 48.48

48.48 - 21.84 = 26.64 (total height of the girls)

mean height of the girls is 26.64/18 = 1.48 m

Answer:

1.48 m.

Step-by-step explanation:

There are 32 - 14 = 18 girls in the class.

Total height of the whole class = 1.515 * 32

= 48.48 m..

Total height of all the boys = 14 * 1.56 =  21.84 m.

So the total height of the 18 girls = 48.48 - 21.84

= 26.64 m.

Therefore the mean height of the girls

= 26.64 / 18

= 1.48 m.

[tex]\bf \textit{lateral area of a cylinder}\\\\ LA=2\pi rh~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=5 \end{cases}\implies LA=2\pi (4)(5)\implies V=40\pi[/tex]

Answer:

3BC

Step-by-step explanation:

8BC - 9BC + 10BC - 6BC = BC(8 - 9 + 10 - 6) = BC(3) = 3BC

There you go in the attached.

Answer:

Step-by-step explanation:

Rewrite X^2+22x=31, leaving space after the "22x:"

X^2+22x                          = 31

The coefficient of x is 22.  Take half of that, obtaining 11.  

Square this result:  11^2 = 121.

Write in "+121      -121" after the x term:

X^2+22x  + 121 - 121 = 31

Rewrite X^2+22x + 121 as

          (x + 11)^2  -121 =  31

Add 121 to both sides:

           (x + 11)^2 = 152

Take the square root of both sides:

            x + 11 = ±√152 = ±2√38

Finally, x = -11 ±2√38.

This is "solution by completing the square"

Answer: OPTION A

Step-by-step explanation:

We have this quadratic equation: [tex]x^2+22x=31[/tex]

In order to complete the square the first step is to pick the coefficient of the x term, divide it by 2 and square it. Then:

[tex](\frac{22}{2})^2=11^2[/tex]

Now we must add 11² to both sides of the equation:

[tex]x^2+22x+11^2=31+11^2[/tex]

Therefore, after complete the square and factor, we get:

[tex](x+11)^2=152[/tex]

This matches with the option A.

To cover the distance of 14 miles at a speed of 14 miles per hour Brian will take 1 hour means 60 minutes.

The speed is the rate of distance covered by a person or a vehicle in a particular time.

We have been given the distance=14 miles

Speed=14 miles per hour

We have also been given the formula of distance which is

d=rt

we have to rearrange it to calculate time

t=d/r

so the time will be calculated as t=14/14

t=1 hour because the speed is of per hour.

Hence Brian will take 60 minutes to cover the required distance.

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Answer: $17.80

Step-by-step explanation:

2.80 + 3(5) = x

2.80 + 15 = x

17.80 = x

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The total amount paid by Jacob is $17.8.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Jacob bought a magazine for $2.80. Also, three candy bars for $5 each. Therefore, the amount paid by Jacob is,

Amount paid by Jacob = $2.80 + (3 × $5)

                                      = $17.8

Hence, the total amount paid by Jacob is $17.8.

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Answer:

B = 65

C = 115

Step-by-step explanation:

Givens

ABCD is a parallelogram

It is lettered in such a way that B is opposite D

B = 3n+20

D = 6n-25

Solution

<B = <D                      Property of Parallelogram

3n + 20 = 6n - 25      Add 25 to both sides

3n + 20 + 25 = 6n      Combine

3n +45 = 6n                Subtract 3n from both sides

3n +45 = 6n-3n           Combine

45 = 3n                        Divide by 3

45/3=3n/3                    

n = 15                            Value of n    

B = 3n + 20                  Find B. Let n = 15

B= 3*15+20                   Combine

B = 45 + 20                 Combine

B = 65                                

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

B and C are supplementary. They add up to 180

B + C = 180

65 + C = 180

C = 180-65

C = 115

Answer:

Rule is (x, y+k)

New point is (-3,9)

Step-by-step explanation:

A point translated vertically k units up means the x coordinate remains the same in the translation but the y coordinate is increased by k units

This can be represented mathematically as;

Let;s assume the point to be A with coordinates (x,y) then to get the image of the point under  a vertical translation k units up you add k to the y coordinate value.

Given ;

[tex]A=(\frac{x}{y} )\\\\T=(0,k)\\\\A'=(\frac{x}{y} )+(\frac{0}{k} )=(\frac{0+x}{y+k} )\\\\A'=\frac{x}{y+k} =(x,y+k)[/tex]

where T is the translation

In the question

Given (-3,-6) and T is (0,5) the new coordinate will be

[tex]=(\frac{-3}{4}) +(\frac{0}{5} )=\frac{-3}{9} =(-3,9)[/tex]

Answer:

409.86

Step-by-step explanation:

First find the mark up

230 *65%

230 * .65 = 149.50

The new cost of the tent is the original cost plus the mark up

230 + 149.50

379.50

Now we need to find the tax

379.50 * 8%

379.50 *.08

30.36

The total cost is the cost of the tent plus the tax

379.50 + 30.36

409.86

Answer:

409.86

is the correct answe rfor this question

Answer:

B???

Step-by-step explanation:

Answer:

The correct option is A. Figure B repeats in the tessellation shown below.

Step-by-step explanation:

Tessellation can be defined as the arrangement of geographical patterns that are closely attached together to form a particular pattern.

The given figure is formed by the arrangement off figure B.

This large pattern is formed by the repetition of this smaller pattern,

Figure B repeats in the tessellation shown below. Therefore, the correct option is A.

[tex]\bf [cot(\theta )+csc(\theta )]^2=\cfrac{1+cos(\theta )}{1-cos(\theta )} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doing the left-hand side}}{[cot(\theta )+csc(\theta )]^2}\implies cot^2(\theta )+2cot(\theta )csc(\theta )+csc^2(\theta ) \\\\\\ \cfrac{cos^2(\theta )}{sin^2(\theta )}+2\cdot \cfrac{cos(\theta )}{sin(\theta )}\cdot \cfrac{1}{sin(\theta )}+\cfrac{1}{sin^2(\theta )}\implies \cfrac{cos^2(\theta )}{sin^2(\theta )}+\cfrac{2cos(\theta )}{sin^2(\theta )}+\cfrac{1}{sin^2(\theta )}[/tex]

[tex]\bf \cfrac{\stackrel{\textit{perfect square trinomial}}{cos^2(\theta )+2cos(\theta )+1}}{sin^2(\theta )}\implies \boxed{\cfrac{[cos(\theta )+1]^2}{sin^2(\theta )}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doing the right-hand-side}}{\cfrac{1+cos(\theta )}{1-cos(\theta )}}\implies \stackrel{\textit{multiplying by the denominator's conjugate}}{\cfrac{1+cos(\theta )}{1-cos(\theta )}\cdot \cfrac{1+cos(\theta )}{1+cos(\theta )}}[/tex]

[tex]\bf \cfrac{[1+cos(\theta )]^2}{\underset{\textit{difference of squares}}{[1-cos(\theta )][1+cos(\theta )]}}\implies \cfrac{[cos(\theta )+1]^2}{1^2-cos^2(\theta )} \\\\\\ \cfrac{[cos(\theta )+1]^2}{1-cos^2(\theta )}\implies \boxed{\cfrac{[cos(\theta )+1]^2}{sin^2(\theta )}}[/tex]

recall that sin²(θ) + cos²(θ) = 1, thus sin²(θ) = 1 - cos²(θ).

Answer:

The slope of A'B' = -1.2 ⇒ answer A

Step-by-step explanation:

* Lets talk about dilation

- A dilation is a transformation that changes the size of a figure.  

- It can become larger or smaller, but the shape of the

 figure does not change.  

- The scale factor, measures how much larger or smaller  

  the image will be

- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

- If the center of the dilation is the origin then multiply each coordinate

 by the scale factor

* In the problem

∵ Δ ABC is dilated by a scale factor of 3 with the origin as the center

  of dilation

- Let point A is (a , b) and point B is (c , d)

∵ The slope of the line which passes through points (x1 , y1) and (x2 , y2)

  is m = (y2 - y1)/(x2 - x1)

∴ The slope of AB = (d - b)/(c - a) = -1.2

∵ Point A' is (3a , 3b) and point B' is (3c , 3d)

∴ The slope of A'B' = (3d - 3b)/(3c - 3a)

- Take 3 as a common factor from up and down

∴ The slope of A'B' = 3(d - b)/3(c - a) ⇒ cancel 3 up with 3 down

∴ The slope of A'B' = (d - b)/(c - a) = the slope of AB

∵ The slope of AB = -1.2

∴ The slope of A'B' = -1.2

* The slope of A'B' = -1.2

Answer:

x = 2, x = -3

Step-by-step explanation:

We are given the following quadratic equation and we are to solve it for x:

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

We need to find such factors of -6 that when added give a result of 1 and when multiplied, give a product of -6.

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

[tex] x ^ 2 - 2x + 3x - 6 = 0 [/tex]

[tex] x ( x - 2 ) + 3 ( x - 2 ) = 0 [/tex]

[tex](x-2) = 0, (x+3)=0[/tex]

x = 2, x = -3

Answer:

733 inches

Step-by-step explanation:

V= 3.14*5^2*28/3

Order of Operations (PEMDAS)

5^2=25

25*3.14= 78.5

78.5*28= 2198

2198/3=732.66

Round to nearest cubic inch

733 inches

Answer:

see explanation

Step-by-step explanation:

The perimeter (P) is the length of all 3 sides of the triangle

The triangle is isosceles with 2 equal sides 20 - 7xy

P = 20 - 7xy + 20 - 7xy + 12 = 52 - 14xy

When x = 2, y = 1, then

P = 52 - 14(2)(1) = 52 - 28 = 24

Answer:

$17.10

Step-by-step explanation:

Bracelet cost  $15

4% sales tax:  0.04($15) = $0.60

10% Fed tax:  0.10($15) = $1.50

Summing these three amounts, we get a total cost of $17.10.

Answer:

3/8

Step-by-step explanation:

We must first find the LCD in order to add up the amounts taken from the basket.

The Least Common Denominator of 4 and 8 is 8.

We convert 1/4 so that it is a fraction over 8, which is 2/8

2/8+1/8=3/8

Answer:

3/8

Step-by-step explanation:

We want to find the total amount of cherries that Robin and Jim took

1/4 + 1/8

The common denominator is 8

1/4 *2/2 = 2/8

Replacing 1/4 with 2/8

2/8 + 1/8 = 3/8

The fraction that they took is 3/8

Answer:

3

Step-by-step explanation:

Say Jill picks the number x.

She multiplies it by 2 giving 2x.

It says add 5 to that product giving 2x+5.

She multiplies this sum by -3 giving -3(2x+5).

She then subtracts 7 from that product giving -3(2x+5)-7.

Her number after doing all of this is -40 so we hae -3(2x+5)-7=-40

To solve:

First: I would add 7 on both sides:  -3(2x+5)=-33

Second: I would divide boht sides by -3:  2x+5=11

Third: I would subtract 5 on both sides: 2x=6

Last: I would divide both sides by 2:  x=3

Answer:

y = 5x - 4

see attached for graph