Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation? {–7, 1} {1, 7}

Answer:

-15

Step-by-step explanation:

the y-intercept would be -15

Answer:

x = - 5, x = 3

Step-by-step explanation:

To find the x- intercepts let y = 0, that is

x² + 2x - 15 = 0

Consider the factors of the constant term (- 15) which sum to give the coefficient of the x- term (+ 2)

The factors are + 5 and - 3, since

5 × - 3 = - 15 and 5 - 3 = + 2, hence

(x + 5)(x - 3) = 0

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 3 = 0 ⇒ x = 3

x- intercepts at (- 5, 0) and (3, 0)

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-interept (0, b)

We have the slope m = -6 and the point (0, 2) → b = 2.

Substitute:

y = -6x + 2

Answer:

x = - [tex]\frac{11}{8}[/tex]

Step-by-step explanation:

Given

(x - 4) - (x + 7 ) = 8x

Distribute parenthesis noting second is distributed by - 1

x - 4 - x - 7 = 8x ← simplify left side

- 11 = 8x ( divide both sides by 8 )

x = - [tex]\frac{11}{8}[/tex]

2

-10 and 10 are 10 units from 0 on the number line

Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 5y + 2x = 12 into this form

Subtract 2x from both sides

5y = - 2x + 12 ( divide all terms by 5 )

y = - [tex]\frac{2}{5}[/tex] + [tex]\frac{12}{5}[/tex] ← in slope- intercept form

with slope m = - [tex]\frac{2}{5}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{5} }[/tex] = [tex]\frac{5}{2}[/tex] → A

Answer:

x= -17

Step-by-step explanation:

When we have 2 points, we can find the slope using

m = (y2-y1)/(x2-x1)

Substituting what we know

1/5 = (0-3)/(x--2)

1/5 = -3/(x+2)

Using cross products

1*(x+2) = 5*(-3)

x+2 = -15

Subtract 2 from each side

x+2-2 = -15-2

x=-17

Answer:

D. 754 m

Step-by-step explanation:

When calculating the circumference of the circle it ends up as 753.98 but rounded it's 754.

Answer: It’s 754!

Explanation: I also got this one on a test lol

Answer:

16 : 25

Step-by-step explanation:

The ratio of girls : boys = 320 : 500

To simplify divide both parts by 10

320 : 500 = 32 : 50 ← now divide both parts by 2

32 : 50 = 16 : 25 ← in simplest form

Final answer:

To calculate the simplified ratio of the number of girls to the number of boys in the school, we divide the numbers 320 (girls) and 500 (boys) by their greatest common divisor, which is 80, resulting in the simplest form of 4:6.25 or 16:25.

Explanation:

The question is asking us to find the ratio of the number of girls to the number of boys in a school, and then to simplify this ratio to its simplest form. There are 320 girls and 500 boys in the school. To find the ratio, we compare the number of girls to the number of boys, which gives us 320 to 500.

To simplify the ratio, we look for the greatest common divisor (GCD) that both numbers share. Both 320 and 500 are divisible by 10 for certain, and further simplification can be found by dividing by the GCD of 80. So, if we divide both numbers by 80, we get 4 to 6.25, which simplifies further to a ratio of 4:6.25 or 16:25 when both sides are multiplied by 4. Therefore, the simplified ratio of the number of girls to the number of boys is 16:25.

Hello There!

Amount Saved = Original Price x Discount % / 100. So,

Amount Saved = 35 x 60 / 100

Amount Saved = 2100 / 100

Amount Saved = $21 (answer)

35 - 21 = 14

60% Off of $35.00 Is $14.00

Answer: Option C

2,400

Step-by-step explanation:

When launching the first 6-sided die there are 6 possible outcomes

When launching the 4-sided die there are 4 possible outcomes

When throwing each die of 10 faces there are 10 possible outcomes

So if all the dice are thrown together, the number of possible combinations that can be obtained is:

[tex]S = 6 * 4 * 10 * 10\\S = 24 * 100[/tex]

[tex]S = 2400[/tex] possible results

Finally the answer is the option C.

Answer:

See below.

Step-by-step explanation:

The triangles are similar because  the angles marked 125 are equal and the sides either side of these angle are in the same ratio:

1.3 / 2.5 = 2.6 /5.

If we are given the length of AE we would find CF from the equation:

1.3 / 2.5 = CF / AE

CF = (1.3 * AE) / 2.5.

Answer:

The sample standard deviation is 14.458

The population standard deviation is 13.967

Step-by-step explanation:

* Lets revise the population standard deviation (σ)

1. Work out the Mean (μ) (average of the numbers)

2. Then for each number subtract the Mean and square

   the result  (xi - μ)²

3. Then work out the mean of those squared differences

    [∑(xi - μ)²/N]

4. Take the square root of that (√[∑(xi - μ)²/N]) and to find σ

* Lets revise the sample standard deviation (s)

1. Work out the Mean (x) (average of the numbers)

2. Then for each number subtract the Mean and square

    the result  (xi - x)²

3. Then work out the mean of those squared differences [∑(xi - x)²/N - 1]

4. Take the square root of that (√[∑(xi - x)²/N - 1]) and to find s

* Now lets solve the problem

- The data are 15 numbers

  17 , 37 , 56 , 16 , 12 , 16 , 19 , 45 , 14 , 37 , 21 , 26 , 43 , 46 , 42

∵ x = μ = sum/number

∴ x = μ = (17+37+56+16+12+16+19+45+14+37+21+26+43+46+42)÷15=29.8

- Subtract the mean from each number and square the result

∵ (17 - 29.8)² = 163.84

∵ (37 - 29.8)² = 51.84

∵ (56 - 29.8)² = 686.44

∵ (16 - 29.8)² = 190.44

∵ (12 - 29.8)² = 316.84

∵ (16 - 29.8)² = 190.44

∵ (19 - 29.8)² = 116.64

∵ (45 - 29.8)² = 231.04

∵ (14 - 29.8)² = 249.64

∵ (37 - 29.8)² = 51.84

∵ (21 - 29.8)² = 77.44

∵ (26 - 29.8)² = 14.44

∵ (43 - 29.8)² = 174.24

∵ (46 - 29.8)² = 262.44

∵ (42 - 29.8)² = 148.84

∴ ∑(xi - μ)² = ∑(xi - x)² = 2926.36

∵ N = 15

∴ The sample standard deviation = √[∑(xi - x)²/(N - 1)]

∴ s = √[2926.36/(15 - 1)] = 14.458

∴ The population standard deviation = √[∑(xi - μ)²/N]

∴ σ = √[2926.36/15] = 13.967

Answer:

B

Step-by-step explanation:

Answer:

8y=-6 or 4y=-3

Step-by-step explanation:

We are given two equations

[tex]x+6y=9\\and\\-x+2y=-15[/tex]

In order to add the equations, the left hand side of one equation will be added to the left hand side of second equation. similarly, the right hand side of first equation will be added to the right hand side of the equation so,

[tex]x+6y+(-x+2y)=9+(-15)\\Combining\ alike\ terms\\x+6y-x+2y=9-15\\6y+2y=-6\\8y=-6\\Can\ also\ be\ written \ as\\4y=-3[/tex]

Answer:

The resultant equation is 8y = -6

Step-by-step explanation:

To get the system of equation that will results from adding the statement, we will follow the steps below;

x+6y=9 -------------------------------------------------------------------------------(1)

-x+2y=-15-------------------------------------------------------------------------------(2)

Adding equation (1) and equation(2), we will have;

(1-1)x + (6+2)y =(9-15)

x variable will go away

8y =-6

The resultant equation is 8y = -6

Answer:

Option A. 20.0 square units

Step-by-step explanation:

Let

[tex]A(2, 5),B(-4, 3),C(-3, 0),D(3, 2)[/tex]

Plot the points

see the attached figure

The area of the rectangle is equal to

[tex]A=AB*AD[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

step 1

Find the distance AB

[tex]A(2, 5),B(-4, 3)[/tex]

substitute in the formula

[tex]AB=\sqrt{(3-5)^{2}+(-4-2)^{2}}[/tex]

[tex]AB=\sqrt{(-2)^{2}+(-6)^{2}}[/tex]

[tex]AB=\sqrt{40}\ units[/tex]

step 2

Find the distance AD

[tex]A(2, 5),D(3, 2)[/tex]

substitute in the formula

[tex]AD=\sqrt{(2-5)^{2}+(3-2)^{2}}[/tex]

[tex]AD=\sqrt{(-3)^{2}+(1)^{2}}[/tex]

[tex]AD=\sqrt{10}\ units[/tex]

step 3

Find the area of rectangle

[tex]A=AB*AD[/tex]

we have

[tex]AB=\sqrt{40}\ units[/tex]

[tex]AD=\sqrt{10}\ units[/tex]

substitute

[tex]A=(\sqrt{40})*(\sqrt{10})[/tex]

[tex]A=20\ units^{2}[/tex]

Answer:

1. y=7.2

2. x=18

Step-by-step explanation:

1. Triangles CMN and CBA are similar triangles (by AAA postulate). Similar triangles have proportional corresponding sides, so

[tex]\dfrac{CM}{CB}=\dfrac{CN}{CA}\\ \\\dfrac{12}{12+y}=\dfrac{10}{10+6}\\ \\12\cdot 16=10\cdot (12+y)\\ \\192=120+10y\\ \\10y=72\\ \\y=7.2[/tex]

2. GK is angle G bisector. Use angle bisector's property:

[tex]\dfrac{GH}{GI}=\dfrac{KH}{KI}\\ \\\dfrac{40}{24}=\dfrac{30}{x}\\ \\40x=24\cdot 30\\ \\4x=24\cdot 3\\ \\x=6\cdot 3=18[/tex]

to get the slope of any line, we can simply use two points off of it, for this one, say (3,12) and (4,16)

[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{12})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{16}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{16-12}{4-3}\implies \cfrac{4}{1}\implies 4[/tex]

Answer: [tex]65.44\ in^3[/tex]

Step-by-step explanation:

To calculate the volume of a cone you can use this formula:

[tex]V_{(cone)}=\frac{1}{3}\pi r^2h[/tex]

Where "r" is the radius and "h" is the height of the cone.

In this case you know that this cone has a height of 2.5 inches and a radius of 5 inches. Then:

[tex]h=2.5\ in\\r=5\ in[/tex]

Finally, you need to substitute these values into the formula. Then you get that the volume of the cone is:

 [tex]V_{(cone)}=\frac{1}{3}\pi (5\ in)^2(2.5\ in)\\\\V_{(cone)}=65.44\ in^3[/tex]

Answer:

138.27 gallons

Step-by-step explanation:

Total cost = snacks + gallons * cost per gallon

387 = 35.80 + g*2.54

Subtract 35.80 from each side

387-35.80 = 35.80-38.50 + g*2.54

351.20=  + g*2.54

Divide by 3.54 on each side

351.20/2.54 = 2.54g/2.54

138.2677165 = g

Rounding to the nearest hundredth

138.27 gallons

Given : Lynn spent 387.00 on gasoline and snacks

Given : Lynn spent 35.80 on snacks for the entire trip

Money spent on gasoline :

Total money spent on gasoline and snacks - Money spent on snacks

[tex]:\implies[/tex]  Money spent on gasoline = 387.00 - 35.80

[tex]:\implies[/tex]  Money spent on gasoline = 351.20

Given : Gasoline costs 2.54 per gallon

[tex]\implies \mathsf{Number\;of\;gallons\;of\;gasoline = \dfrac{Total\;money\;spent\;on\;gasoline}{Cost\;of\;gasoline\;per\;one\;gallon}}[/tex]

[tex]\implies \mathsf{Number\;of\;gallons\;of\;gasoline = \dfrac{351.20}{2.54}}[/tex]

[tex]\implies \mathsf{Number\;of\;gallons\;of\;gasoline = 138.27}[/tex]

Answer: Third Option

[tex]V = 200.96\ in^3[/tex]

Step-by-step explanation:

By definition, the volume of a cone is:

[tex]V = \frac{1}{3}\pi r^2h[/tex]

V is the volume of the cone

h is the height of the cone

r is the radius of the cone

In this case we know that:

[tex]r= 4\ in\\h= 1\ ft[/tex]

We know that in 1 ft there are 12 inches

So

[tex]h=12\ in[/tex]

Now substitute the values of h and r in the formula to obtain the volume of the cone

[tex]V = \frac{1}{3}\pi (4)^2(12)[/tex]

[tex]V = 16*4\pi[/tex]

[tex]V = 200.96\ in^3[/tex]

Answer:

800 people

Step-by-step explanation:

We are given in the question that 2/3 of 2400 people preferred skinless chicken.

We have to find the number of people who prefer skinless chicken

[tex]So,\\= \frac{2}{3} *2400\\=1600[/tex]

1600 people prefer skinless chicken,

So,

The number of people who prefer regular chicken = 2400-1600

= 800 people

Answer: kentucky friend chicken? XD

Step-by-step explanation:

Answer:

ln 3

Step-by-step explanation:

Using the rule of logarithms

log [tex]x^{n}[/tex] ⇔ n log x

Given

3 ln 3 - ln 9

= 3 ln 3 - ln 3²

= 3 ln 3 - 2 ln 3

= ln 3

The given logarithmic expression → {3 ln(3) - ln(9)} can be written as ln(3).

Logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.

Given is the logarithmic expression as -

3 ln(3) - ln(9)

We can solve the expression as -

3 ln(3) - ln(9)

ln(3³) - ln(9)

ln(27) - ln(9)

ln(27/9)

ln (3)

Therefore, the given logarithmic expression → {3 ln(3) - ln(9)} can be written as ln(3).

To solve more questions on logarithmic, visit the link-

https://brainly.com/question/30085872

#SPJ7

The expression that gives the number of shrimp Ariana caught will be 5C - 9.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Ariana and William go shrimping. Ariana caught nine less than five times the number of shrimp that William caught. If C represents the number of shrimp William caught.

Then the expression is given as,

⇒ 5C - 9

The expression that gives the number of shrimp Ariana caught will be 5C - 9.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ2

Answer:

Step-by-step explanation:

[tex](4k^7)^3\ \text{it's equal to}\ 64k^{21}\\\\(4k^7)^3\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=4^3(k^7)^3=64k^{7\cdot3}=64k^{21}\\\\4^3(k^7)^3=4^n(k^7)^3\Rightarrow n=3[/tex]

The value of n in the simplified expression is 3.

To simplify an expression approach write an equivalent expression that includes no comparable terms. This means that we will rewrite the expression with the fewest phrases feasible.

Simplifying means to make it less complicated, clearer, or easier. maths to reduce (an equation, fraction, and many others) to a less difficult form by means of cancellation of commonplace factors, regrouping of phrases in the identical variable, etc.

Learn more about simplifying here: https://brainly.com/question/723406

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Final answer:

The coordinates of the point are (4, 3), where 4 is the x-coordinate (horizontal direction) and 3 is the y-coordinate (vertical direction).

Explanation:

The coordinates of a point on a Cartesian coordinate system are determined by its horizontal position (x-coordinate) and its vertical position (y-coordinate). Given that the point is on the first coordinate axis (x-axis) and in the (1, 2)th coordinate plane, we understand that the x-coordinate is related to the horizontal direction and the y-coordinate is related to the vertical direction.

In the context of this problem, if the figure on the coordinate plane indicates that the point is 4 units to the right of the origin along the x-axis and 3 units above the origin along the y-axis, then the coordinates of the point are ( extbf{4},  extbf{3}). Here, the convention is that moving to the right of the origin increases the x-coordinate and moving upwards increases the y-coordinate.

Answer:

a) Current Interest is $75.8

b) the final payment will be $11,830

Step-by-step explanation:

Principal Amount = $9,100

Interest rate = 10% or 0.1

Time = 36 months = 3 yeras

Balance after 27 payments = $2,526.85

a) What is the CURRENT month's interest?

The formula to find interest is:

Interest = P*r*t

P= Principal

r = Interest rate

t = time in years

Interest = 9100*0.1*3

Total Interest = 2730

As total period is 36 months so, divide total interest by 36

Current Month Interest = 2730/36

Current Month Interest = 75.8

So, current month interest is $75.8

b) What is the final payment?

The formula used will be

A = P(1+r*t)

A = Final amount

r = interest rate

t = time

Putting values:

A = P(1+r*t)

A = 9100*(1+0.1*3)

A = 9100*(1.3)

A = 11,830

So, the final payment will be $11,830

Answer:

[tex]36xy^2 + 8x^2 + 27y^2 + 6x[/tex]

Step-by-step explanation:

Use the FOIL method of multiplying binomials.

First term in each binomial: [tex]-2x * -4x = 8x^2[/tex]

Outside terms: [tex]-2x * -3 = 6x[/tex]

Inside terms: [tex]-9y^2 * -4x = 36xy^2[/tex]

Last term in each binomial: [tex]-9y^2 * -3 = 27y^2[/tex]

Now, rearrange the terms correctly. [tex]36xy^2 + 8x^2 + 27y^2 + 6x[/tex]

This is our final answer, since it can not be simplified any more.

Answer:

C

Step-by-step explanation:

Edge 2020

Answer:

C

Step-by-step explanation:

Total delivery orders is 97

The number of those placed by phone is 28

So you find the percentage of delivery orders placed by phone by doing 28 divided by 97.

.289 approximately so 28.9%  ( I rounded on my answer)

Choice C is the right answer

The answer to this question is option C. 104 °

(Late answer!)

Answer:

The corresponding point is (3,-8)

Step-by-step explanation:

we know that

When you add a constant value (k), to the argument of a function, the graph is shifted  k units to the left.

so

In this problem

The rule of the transformation is equal to

f(x) ------> f(x+2)

(x,y) ------> (x-2,y)

(5,-8) -----> (5-2,-8)

(5,-8) -----> (3,-8)

These are the formulas right?.. I hope so, anyways..

- f(n)= 2^(n-1) -1

- g(n)=3n+6  

f(7)=2^{7-1}-1  -  f(7)=2^{6}-1  -  f(7)=64-1  -  f(7) = 63

g(10)=3\X 10+6  -  g(10)=30+6  -  g(10) = 36

= f(7)>g(10)

I hope that it helped..

Answer:

The one above is right.

Step-by-step explanation: