solve these absolute value equations step by step ​

Answer:

The solutions are 3 and -8

Step-by-step explanation:

2x² + 10x - 48 = 0

Divide both sides by 2:

x² + 5x - 24 = 0

Factor using AM method (What two numbers add to 5 and multiply to -24?):

(x - 3)(x + 8) = 0

Set both expressions equal to 0:

x - 3 = 0   x + 8 = 0

Solve both equations for x:

x = 3   x = -8

The solutions to the quadratic equation 2x² + 10x - 48 = 0 are x = 3 and x = -8.

To find the solutions to the quadratic equation 2x2 + 10x - 48 = 0, we can use the quadratic formula: x = (-b ± √(b2 - 4ac)) / (2a), where a, b, and c are the coefficients from the equation. In this case, a = 2, b = 10, and c = -48. Plugging these values into the formula, we have: x = (-10 ± √(102 - 4(2)(-48))) / (2(2)). Simplifying further, x = (-10 ± √(100 + 384)) / 4. Continuing to simplify, x = (-10 ± √484) / 4, which becomes x = (-10 ± 22) / 4. Finally, we have x = (-10 + 22) / 4 and x = (-10 - 22) / 4, giving us x = 3 and x = -8 as the two solutions to the quadratic equation.

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Answer:

27 vests

Step-by-step explanation:

       1 vest --------- 2/3 yard

       x vest -------- 18 yards

Final answer:

Mrs. Smith's class can make 27 vests out of 18 yards of fabric by dividing the total yards of fabric by the fabric needed for one vest, i.e., dividing 54 thirds of fabric by 2 thirds per vest.

Explanation:

The student's question involves a practical application of division in mathematics, specifically the division of fractions. To determine how many vests can be made from 18 yards of fabric, we need to divide the total yards of fabric by the amount of fabric needed for each vest.

Since each vest uses 2/3 of a yard of fabric, and Mrs. Smith has 18 yards of fabric, we can set up the following equation to find the number of vests:

Convert 18 yards to thirds to match the unit in the vest requirement. (18 yards * 3 thirds) = 54 thirds.

Divide the total thirds of fabric by the thirds needed for one vest. (54 thirds ÷ 2 thirds per vest) = 27 vests.

Therefore, Mrs. Smith's class can make 27 vests out of 18 yards of fabric.

1. 64 - 7c

2. 4x-3

3. p< -28

Step-by-step explanation:

6. -6 -7(c+10)

[tex]-6-7c+70\\-7c+64\\64-7c[/tex]

64 - 7c

7. 3x+4(x-6)-3(x-7)

[tex]3x+4x-24-3x+21\\4x-3[/tex]

4x-3

8. p+4 < -24

Subtracting 4 from both sides

[tex]p+4-4<-24-4\\p<-28[/tex]

p< -28

Keywords: linear equations, subtraction

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Answer:

Since the independent variable x is not the exponent, [tex]y = - 7 x^{8}[/tex] does not represent an exponential function.

Step-by-step explanation:

The general expression of an exponential function is [tex]f(x) = a^{x}[/tex], where a > 0 and a ≠ 1

Now the given function is [tex]y = - 7 x^{8}[/tex] ..... (1)

So, we can say that the function f(x) = y is not an exponential function as x is not in power of any constant.

Therefore, since the independent variable x is not the exponent, [tex]y = - 7 x^{8}[/tex] does not represent an exponential function. (Answer)

Answer:

1/2

Step-by-step explanation:

p(-2) = 2 | -1/2(-2) |

= 2 | -1/-4|

= 2 |1/4|

= 1/2

Answer:

Your answer is C.

Step-by-step explanation:

When multiplying matrices, if they are the same number of rows and columns, you multiply.

The answer is C.

[ -9  -8]

[2      0]

Step-by-step explanation:

You multiply -3 by 3, 4 by -2, 2 by 1, and -5 by 0

which gives you:

-3 x 3= -9

4 x -2= -8

2 x 1 = 2

-5 x 0= 0

Answer:

-11 x + 19 thus c.) is your answer

Step-by-step explanation:

Simplify the following:

-5 + 4 (6 - 2 x) - 3 x

4 (6 - 2 x) = 24 - 8 x:

-3 x + 24 - 8 x - 5

Add like terms. 24 - 5 = 19:

-3 x - 8 x + 19

-8 x - 3 x = -11 x:

Answer:  -11 x + 19

Answer:

31

Step-by-step explanation:

50 x .62= 31

(games played) x the percentage won.

You could muliply 50 by 62% if your calculator has the % symbol if not you have to turn it into a decimal. To go from percent to decimal just take your percentage and move the decimal to the left twice. 62% = .62

Answer:

45 cm

Step-by-step explanation:

Find LCM(15,9). First factor both numbers:

[tex]15=3\cdot 5\\ \\9=3\cdot 3[/tex]

So,

[tex]LCM(15,9)=3\cdot 5\cdot 3=45[/tex]

This means that the length of the side of the smallest square area that can be covered by these tiles is 45 cm.

Practically, you can put 3 tiles in a row (to make 3 lenghts of 15 cm each that add up to 45 cm) and put such 5 rows (to make 5 lengths of 9 cm that add up to 45 cm).

Answer:

The expressions that are equivalent are A, D, and E.

Step-by-step explanation:

Given:

-7z+ ( - 6.5) + 3.5z + 6y - 1.5.

On solving the equation:

[tex]-7z+ ( - 6.5) + 3.5z + 6y - 1.5[/tex]

[tex]-7z - 6.5+ 3.5z + 6y - 1.5[/tex]

[tex]-7z  + 3.5z + 6y - 1.5-6.5[/tex]

[tex]-3.5z+6y-8[/tex]

So, on solving the equation we get the expression:

[tex]-3.5z+6y-8[/tex]

According to question:

We see that expressions:

A. [tex]-8+6y+(-3.5z)[/tex]

   [tex]=-8+6y-3.5z = 3.5z+6y-8[/tex]

So, this expression is equivalent.

D. [tex]6y-8-3.5z[/tex]

   [tex]=3.5z+6y-8[/tex]

So, this expression is also equivalent.

E. [tex]-3.5z+6y-8[/tex]

So, this expression is also equivalent.  

Therefore, the expressions that are equivalent are A, D, and E.

Discriminant = 16

As 16>0, The roots will be real and unequal.

Step-by-step explanation:

The standard form of a quadratic equation is:

[tex]ax^2+bx+c = 0[/tex]

The discriminant is calculated as:

[tex]D=b^2-4ac[/tex]

Given equation is:

[tex]Y=-4x^2+2x+1[/tex]

Here

a = -4

b = 2

c = 1

Putting the values

[tex]D =(2)^2 - 4(-4)(1)\\=4+16\\=20[/tex]

The discriminant is 16 which is greater than zero so the roots of the equation will be real and unequal.

Keywords: Discriminant, Quadratic equation

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Answer:

780 and 800

Step-by-step explanation:

hdvevdbsbsvbsbsbsbd

Answer:

40 single tickets were sold.

Step-by-step explanation:

12x+8y=1580

2x+y=250

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

y=250-2x

12x+8(250-2x)=1580

12x+2000-16x=1580

-4x+2000=1580

-4x=1580-2000

-4x=-420

4x=420

x=420/4=105

y=250-2(105)=250-210=40

The requried number of singles tickets sold is 40. Option B is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
As mentioned in the quesiton, Tickets are $12 for couples and $8 for singles. Let x be the number of couples and y be the number of singles. This system of equations represents the situation in which ticket sales totaled $1,580 and a total of 250 students attended the dance.

12x + 8y = 1,580 - - - - -(1)

2x + y = 250 - - - - - -(2)

From equation 2
y = 250 - 2x - - - - -(3)

Put y from 3 in equation 1
12x + 8(250 - 2x) = 1580
12x + 2000 - 16x = 1580
-4x = 1580 - 2000
x = -420/-4
x = 105

Now,
y = 250 - 2(105)
y = 250 - 210
y = 40

Thus, the requried number of singles tickets sold is 40. Option B is correct.

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Answer:

[tex]18 ≥ \displaystyle \frac{c}{5}[/tex]

Step-by-step explanation:

You can either write what I did in the above answer, or you could have done this:

[tex]\displaystyle \frac{c}{5} ≤ 18[/tex]

The keyphrase is at most, so you would give the inequality a less than or equal to.

I am joyous to assist you anytime.

Answer:

i believe it is a and b

Step-by-step explanation:

Answer:

make it general to include a career goal and qualifying skills.

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

which of the following is important to remember when writing a job objective select all that apply  :

My answer:

We need to understand what is a career objective?

It is a short introduction about your resume or CV to prove recruiters why they should hire you. It should be short and attractive with no more than five lines. Declaration career goals should be realistic and specific roles (SMART goal) In this case, a joint statement with career goals and skills your eligibility can serve as a good job goals

Only the first choice is the best answer for this question.

Hope it will find you well.

Answer: B. 26

Step-by-step explanation:

(21+9)-(8-4)=p

30-4=p

26=p

Answer:

You have a total of 2.25 cups of liquid each time you add 2 cups of water with .25 cups of concentrate.

You want to know how many times 2.25 cup "units" there are in 18 cups.

(18)/(2.25) = 8, so you have 8 "units" of water and concentrate

In each of those 8 "units" you have .25 cups concentrate, so (8)(.25) = 2 cups of concentrate.

In each of the "units" you have 2 cups of water, so (8)(2) = 16 cups water.

Please let me know if you have any questions.

Step-by-step explanation:

To make 18 cups of juice, you'll need approximately 2 cups of concentrate and 16 cups of water given the ratio of the recipe.

To answer your question, we need to solve a proportion problem.

The recipe's ratio is 0.25 cups of juice concentrate to 2 cups of water. This means for every 0.25 cups of concentrate, you add 2 cups of water to get 2.25 cups of juice.

Since you want to make 18 cups of juice, you can set up a proportion:

Therefore, to make 18 cups of juice, you'll need approximately 2 cups of concentrate and 16 cups of water.

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Final answer:

To find the 8th term of the geometric sequence with a first term of 7 and a common ratio of 1/3, we apply the geometric sequence formula to get ≈ 0.0032.

Explanation:

To find the 8th term of a geometric sequence, you can use the formula for the nth term of a geometric sequence, which is an = a1 × [tex]r^{(n-1)}[/tex], where a1 is the first term, r is the common ratio, and n is the term number. In this case, the first term a1 is 7 and the common ratio r is 1/3. Applying the formula gives us the 8th term as a8 = 7 × [tex](\frac{1}{3} )^{7}[/tex].

First, we need to calculate the power of the common ratio: [tex](\frac{1}{3} )^{7}[/tex]

The 8th term of the sequence can be simplified to a8 = 7 × 1/2187, which calculates to approximately 0.0032.

The 8th term of the geometric sequence with a first term of 7 and a common ratio of 1/3 is approximately 0.0032.

We will use the formula for the nth term of a geometric sequence, which is given by:

[tex]a_n = a(r)^{(n-1)[/tex]

For this sequence:

Plugging in the values, the 8th term is found as follows:

a₈ = 7(1/3)⁽⁸⁻¹⁾

= 7(1/3)⁷

Calculating the powered fraction:

(1/3)⁷ = 1/(3⁷) = 1/2187

So:

a₈ = 7 × 1/2187

= 7/2187

≈ 0.0032

Answer:

12.5%

Step-by-step explanation:

Step1. Determine the points Matthew had during playoff by subtracting points made during regular season from total points in season.

   168 points this season

-   147 points regular season

    21 points scored in playoff

Step 2. Get the percentage, by dividing playoff points over total points in season

21 ÷ 168 = 0.125

Step 3. Multiply it by 100 to get the percentage equivalent from decimal.

0.125 x 100% = 12.5%

Answer:

[tex]\large\boxed{6\dfrac{3}{4}\ meters=675\ centimeters}[/tex]

Step-by-step explanation:

[tex]PREFIXES\\\\mega\ (M)=10^6\\\\kilo\ (k)=10^3\\\\hecto\ (h)=10^2\\\\deko\ (da)=10\\\\decy\ (d)=10^{-1}=0.01\\\\centi\ (c)=10^{-2}=0.01\\\\mili\ (m)=10^{-3}=0.001\\\\mikro\ (\mu)=10^{-6}=0.000001[/tex]

[tex]1\ m=100\ cm\qquad(1\ meter=100\ centimeters)\\\\\text{Therefore}\\\\6\dfrac{3}{4}\ m=\dfrac{6\cdot4+3}{4}\ m=\dfrac{27}{4}\ m=\dfrac{27}{4}\cdot100\ cm=\dfrac{2700}{4}\ cm=675\ cm[/tex]

The missing figure of the given line is attached

The equation in the point-slope form of the line is  [tex]y+3=\frac{1}{4}(x+4)[/tex] ⇒ 3rd answer

Step-by-step explanation:

The relation between the perpendicular lines

The formula of the slope of a line is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

The point-slope form of the equation of a line is [tex]y-y_{1}=m(x-x_{1})[/tex] , where [tex](x_{1},y_{1})[/tex] is a point on the line

From the attached figure

The given line passes through points (-1 , 1) and (0 , -3), use them to find the slope of the line

∵ [tex]x_{1}[/tex] = -1 and [tex]x_{2}[/tex] = 0

∵ [tex]y_{1}[/tex] = 1 and [tex]y_{2}[/tex] = -3

∴ The slope of the given point = [tex]\frac{-3-1}{0-(-1)}=\frac{-4}{1}=-4[/tex]

∵ The product of the slopes of the perpendicular lines is -1

∵ The slope of the given line = -4

- Reciprocal the number and change its sign

∴ The slope of the perpendicular line = [tex]\frac{1}{4}[/tex]

∵ The slope-form of the equation is [tex]y-y_{1}=m(x-x_{1})[/tex]

∵ [tex]m=\frac{1}{4}[/tex]

∵ The line passes through point (-4 , -3)

∴ [tex]x_{1}[/tex] = -4 and [tex]y_{1}[/tex] = -3

- Substitute these values in the form of the equation

∴ [tex]y-(-3)=\frac{1}{4}(x-(-4))[/tex]

∴ [tex]y+3=\frac{1}{4}(x+4)[/tex]

The equation in the point-slope form of the line is [tex]y+3=\frac{1}{4}(x+4)[/tex]

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The equation in point-slope form of the line that is perpendicular to the given line and passes through the point (−4, −3) is; y + 3 = 1/4(x + 4)

The slope of the given straight line graph is; -4.

The slope of the perpendicular line is therefore; -1/-4 = 1/4

In essence, the point-slope form of the equation of a straight line takes the form;

I'm this case; a = -3 , b= -4 and m = 1/4

The equation is therefore; y + 3 = 1/4(x + 4)

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Answer:

x = 7

Step-by-step explanation:

Since the segment is an angle bisector, the sides are in the ratio

[tex]\frac{14}{21}[/tex] = [tex]\frac{6}{3x-12}[/tex] ( cross- multiply )

14(3x - 12) = 126 ( divide both sides by 14 )

3x - 12 = 9 ( add 12 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

Answer:

Step-by-step explanation:

Line LP = Line ON

Line MP =  Line MN

Line ML = Line MO

__       __

LP  =   ON

Final answer:

According to the recipe, 3.5 cups of flour will be needed when using 4 and 2/3 cups of milk.

Explanation:

To determine the quantity of flour needed according to the recipe, we can set up a proportion using the given ratios. The recipe states that 1 and 1/3 cups of milk is needed for 1 cup of flour. So, we can set up the proportion:

Next, process is to cross-multiply and find x:

Therefore, according to the recipe, 3.5 cups of flour will be needed when using 4 and 2/3 cups of milk.

Answer:

Step-by-step explanation:

Solve for the quantity of flour using a proportion.

let x be the missing quantity of flour

Recipe ratio is        1  1/3   to  1

Needed ratio is      4 2/3  to x

Write each milk to flour ratio as a fraction. Equate them, and they become a proportion:

[tex]\dfrac{1\dfrac{1}{3} }{1} = \dfrac{4 \dfrac{2}{3} }{x}[/tex]

Find the scale factor for the increase of milk by dividing the needed quantity by the recipe quantity .

Divide 4 2/3 by 1  1/3:

[tex]4\dfrac{2}{3} \div 1\dfrac{1}{3}[/tex]

[tex]=\dfrac{14}{3} \div \dfrac{4}{3} = \dfrac{14}{3} * \dfrac{3}{4}[/tex]

[tex]= \dfrac{42}{12} = \dfrac{7}{2} = 3.5[/tex]

The scale factor is 3.5.

The scale factor for increasing milk is the same for flour. Multiply the recipe quantity of flour by the scale factor to get the needed quantity of flour.

Multiply  1  by 3.5:

1 * 3.5 = 3.5

We will write this in word form, just as it is in the question.

Therefore, we need three and a half cups of flour when there are four and two-thirds cup of milk.

Answer:

its B

Step-by-step explanation:

He should calmly leave and then report the threat.

Grant can respond in this situation by calmly leaving and then report the threat.

Violence threat can be risky if not properply managed. Some of the ways to handle violence threat in school include the following;

Thus, Grant can respond in this situation by calmly leaving and then report the threat.

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Answer:

Step-by-step explanation:

In each triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle.

Calculate a measure of an angle A.

We know: The sum of the angle measures in a triangle is 180°.

Therefore:

m∠A = 180° - (46° + 62°) = 180° - 108° = 72°

m∠B = 62°

LB is opposite ∠A, LA is opposite ∠B.

m∠A > m∠B → LB > LA.

Therefore Ship B is further away.

6 • (2p + 1) Is the correct answer.

Answer:

12.56x^2+452.16

Step-by-step explanation:

A=pie r^2

(4x-24)/2= 2x-12 which is your radius

(2x-12)^2=4x^2+144

Pie=3.14ish

3.14(4x^2+144)

12.56x^2+452.16

Answer:

Step-by-step explanation:

The formula for the area of a circle is

A = πr².  We need the radius, r, to calculate the circle.

If the diameter of the circle is 4x - 24, then the radius is half that, or

2x - 12.

Then the area of the circle in question is  A = πr², or

A = π(2x -12)²

If desired, this could be expanded:

A = π(4)(x - 6)² = 4π(x^2 -12x + 36)

Answer:

$1.50

Step-by-step explanation:

To get the answer, simply divide the cost of 10 watermelon by the total number of watermelon, to get the cost of one watermelon.

So:

$15/10=1.50

one watermelon costs $1.50