Mr. Yi buys vegetables at a market. He purchases 6 pounds of potatoes, p, and 3 pounds of onions, n, for $18. Onions cost twice as much as potatoes. To determine the unit price for each item, his daughter sets up and solves the system of equations shown.

Answer:

-4x^2-6x+6

(third choice)

Step-by-step explanation:

To do f(x)-g(x) we must insert the expression for f(x) and g(x) into this:

This will give us:

(8x^2-2x+3)

-(12x^2+4x-3)

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

-4x^2-6x+6

Horizontally if you prefer:

(8x^2-2x+3)-(12x^2+4x-3)

Distribute and get rid of paranthesis:

8x^2-2x+3-12x^2-4x+3

Pair up like terms:

8x^2-12x^2-2x-4x+3+3

Combine the like terms:

-4x^2-6x+6

Answer:

h(x) =  -4x^2 - 6x + 6

Step-by-step explanation:

f(x) - g(x)

=  8x^2 - 2x + 3 - (12x^2 + 4x - 3)    (Note the parentheses around g(x))

Distributing the negative over the parentheses:

= 8x^2 - 2x + 3 - 12x^2 - 4x + 3

= -4x^2 - 6x + 6 = h(x).

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=\dfrac{3}{4}x-12&(1)\\y=-4x-31&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\\dfrac{3}{4}x-12=-4x-31\qquad\text{multiply both sides by 4}\\\\3x-48=-16x-124\qquad\text{add 48 to both sides}\\\\3x=-16x-76\qquad\text{add}\ 16x\ \text{to both sides}\\\\19x=-76\qquad\text{divide both sides by 19}\\\\x=-4\\\\\text{Put it to (2):}\\\\y=-4(-4)-31\\y=16-31\\y=-15[/tex]

Answer:

$390.

Step-by-step explanation:

first you need to find out hour much the secretary gets paid an hour.  So you will divide $262.50 by 35 hours

262.50 / 35 = 7.50

so we know that she worked over time of 6 hours and that will be time and half

to figure out how much for time and a half.  We are going to divide her hourly rate by 2.  

7.50 / 2 = 3.75

then to find out how much she made for that 6 hours we will add

7.50 + 3.75 = 11.25

to get the amount for over time on Saturday we will multiply

11.25 x 6 = 67.50

Now for the double time we will double her pay so will add

7.50 + 7.50 = 15

so then we are going to multiply to get your pay for the 4 hours overtime

15(4) = $60

Now to find the total amount we are going to add all of our totals together.  

262.50 + 67.50 + 60 = 390.

Her total gross wage for the week is $390.

Answer:

$390.

Step-by-step explanation:first you need to find out hour much the secretary gets paid an hour.  So you will divide $262.50 by 35 hours

262.50 / 35 = 7.50

so we know that she worked over time of 6 hours and that will be time and half

to figure out how much for time and a half.  We are going to divide her hourly rate by 2.  

7.50 / 2 = 3.75

then to find out how much she made for that 6 hours we will add

7.50 + 3.75 = 11.25

to get the amount for over time on Saturday we will multiply

11.25 x 6 = 67.50

Now for the double time we will double her pay so will add

7.50 + 7.50 = 15

so then we are going to multiply to get your pay for the 4 hours overtime

15(4) = $60

Now to find the total amount we are going to add all of our totals together.  

262.50 + 67.50 + 60 = 390.

Her total gross wage for the week is $390

Answer:

No solution.

Step-by-step explanation:

If the linear equations in a system are parallel, that means there is no solution.

Final answer:

The value of the discriminant of the quadratic equation -2x² - 8x + 8 is 128. The positive discriminant suggests that the equation has two distinct real roots.

Explanation:

The discriminant of a quadratic equation can be calculated using the formula D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax² + bx + c = 0.

In the given quadratic equation -2x² - 8x + 8, a = -2, b = -8, and c = 8. Substituting these values into the discriminant formula:

D = (-8)² - 4(-2)(8) = 64 - (-64) = 128.

The value of the discriminant is 128. The discriminant value can provide information about the nature of the roots of the quadratic equation. If the discriminant is positive (greater than 0), then the equation has two distinct real roots. If the discriminant is 0, then the equation has one real root (a repeated root). If the discriminant is negative, then the equation has no real roots.

Step-by-step explanation:

Average=total numbers of songs /registered users

Average= 4*10^9/5*10^7

Average=40*10^8/5*10^7

Average=8*10^(8-7)

Average=8*10^(1)

Average=80 songs downloaded per user

The Average number is 80 songs downloads per user.

The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average.

The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers.

Given:

Total Registered user = 5 x [tex]10^7[/tex]

Downloaded songs = 4 x [tex]10^9[/tex]

So, Average=total numbers of songs /registered users

Average = 4 x [tex]10^9[/tex]/ 5 x [tex]10^7[/tex]

Average= 40 x [tex]10^8[/tex]/ 5 x [tex]10^7[/tex]

Average = 8 x [tex]10^{(8-7)[/tex]

Average= 8 x 10

Average= 80 songs.

Hence, 80 songs downloaded per user.

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Answer:

Step-by-step explanation:

SAS - Side Angle Side

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

the opposite sides have the same lengths.

the angles formed by these sides are right angles

Answer:

1024 cm²

Step-by-step explanation:

There are 16 rods.  A square has 4 equal sides, so each side must consist of 4 rods.  The length of each rod is 8 cm, so the length of each of the square's sides is 32 cm.  Therefore, the area of the square is:

A = s²

A = (32 cm)²

A = 1024 cm²

Answer:

v=26.41 m/s

Step-by-step explanation:

From the Newtons laws of motions, we sew that x= (2v₁²sin∅os∅)/g where x is the horizontal distance v is the initial speed and ∅ is the launch angle.

From trigonometry we see that 2 sin∅cos∅=sin 2∅

Therefore,  x=(v²sin2∅)/g

x=22m

∅=9°

g=9.8m/s²

22m=v²×sin(2×9)/(9.8m/s²)

v²=(22×9.8)/(sin 18)

v²=697.696

v=√697.696

v=26.41 m/s

Answer:

If there are 5 persons and at a time only 3 can be arranged, the total number of arrangements is 60

Option C is correct

Step-by-step explanation:

There are 5 persons and at a time only 3 can be arranged.

The total number of arrangements = nPr = n!/(n-r)!

Here n = 5 and r = 3

nPr = n!/(n-r)!

nPr = 5!(5-3)!

nPr = 5!/2!

nPr = 5*4*3*2!/2!

nPr = 5*4*3

nPr = 60

So, if there are 5 persons and at a time only 3 can be arranged, the total number of arrangements is 60

Option C is correct.

Answer:

Step-by-step explanation:

f(x) + n - shift a graph of f(x) n units up

f(x) - n - shift a graph of f(x) n units down

f(x + n) - shift a graph of f(x) n units to the left

f(x - n) - shift a graph of f(x) n units to the right

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

We have

[tex]f(x)=x^2,\ g(x)=x^2+(-8x)+7[/tex]

Convert the equation of g(x) to the vertex formula:

[tex]y=a(x-h)^2+k[/tex]

[tex]g(x)=x^2+(-8x)+7\\\\g(x0=x^2-2(x)(4)+7\\\\g(x)=\underbrace{x^2-2(x)(4)+4^2}-4^2+7\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\g(x)=(x-4)^2+7=f(x-4)+7\\\\\text{shift the graph of f(x) 4 units to the right and 7 units up}[/tex]

Answer:

p(z<0.42) = 0.6628

Step-by-step explanation:

A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. That is to say:

μ = 0

σ² = 1

Using a calculator, we find that:

p(z<0.42) = 0.6628 (See picture attached)

Answer:

0.66276.

Step-by-step explanation:

We are asked to find the approximate value of p(z<0.42) for a standard normal distribution.

Our given expression means the probability of getting a z-score less than 0.42.

We need to find the probability of getting the area corresponding to a z-score less than 0.42 under normal distribution curve.

We will normal distribution table to solve our given problem.

[tex]p(z<0.42)=0.66276[/tex]

Therefore, the approximate value of our given expression would be 0.66276.

Answer:

95

Step-by-step explanation:

(9.5)(-2)(-5)

First multiply the first two terms:

9.5* -2(-5)

9.5* -2 = -19

= -19(-5)

now multiply the product of solved terms by -5

-19(-5)

Negative signs will change into positive because - * - = +

95....

Thus the answer is 95....

Answer:

your answer is 95

Step-by-step explanation:

you multiply (9.5) (-2)(5) and you get 95

Answer:

D. 77.6

Step-by-step explanation:

We have been given a triangle ZYA in which B, C, and D are the midpoints. We are asked to find the perimeter of triangle ZYA.

We will triangle mid-segment theorem to solve our given problem.

The triangle mid-segment theorem states that the segment joining midpoints of two sides of a triangle is parallel to 3rd side and half the measure of parallel side.

[tex]\text{Measure of side YA}=2\times BD[/tex]

[tex]\text{Measure of side YA}=2\times 11.1[/tex]

[tex]\text{Measure of side YA}=22.2[/tex]

[tex]\text{Measure of side YZ}=2\times CD[/tex]

[tex]\text{Measure of side YZ}=2\times 13.7[/tex]

[tex]\text{Measure of side YZ}=27.4[/tex]

[tex]\text{Measure of side ZA}=2\times CB[/tex]

[tex]\text{Measure of side ZA}=2\times 14[/tex]

[tex]\text{Measure of side ZA}=28[/tex]

[tex]\text{Perimeter of triangle ZYA}=22.2+27.4+28[/tex]

[tex]\text{Perimeter of triangle ZYA}=77.6[/tex]

Therefore, the perimeter of triangle ZYA is 77.6 units.

Think for a minute.

Three points are given.

What geometric shape has three points?

Answer: Triangle

Answer:

your answer is "18"

Step-by-step explanation:

Formula is:

A= 1/2 (A+B) X H

A = 1/2 (CD + CF) X H

A = 1/2 (5+6) X 3

A = 16.5 CM SQUARED

Hope this is right!

Since ABCF is a rectangle, angle AFC is a right angle. Angle CFE is also a right angle. Since angle DCF is also a right angle, then trapezium CDEF has parallel sides CD and EF.

BC + CD = BD

4 cm + CD = 9 cm

CD = 5 cm

EF = 3 cm

Sides CD and EF are the parallel bases of the trapezium. Side CF is the height of the trapezium.

area of trapezium = (base1 + base2)h/2

area = (5 cm + 3 cm)(6 cm)/2

area = (8 cm)(6 cm)/2

area = 24 cm^2

Answer:

The correct answer is A. Aimee's graph is correct because the ratio [tex]\frac{2}{3} :1[/tex] is equal to 2:3, which her graph shows in each point.

Step-by-step explanation:

We are given that Aimee noticed her plant grew 2/3 of an inch every week since it sprouted and a graph is drawn to show the plant growth.

We are to determine whether which of the given statements is correct.

The ratio [tex]\frac{2}{3} :1[/tex] is basically equal to 2:3. Therefore, the graph is correct as it shows the same ratio at each point.

For the points (6, 4) and (3, 2) = [tex]\frac{4-2}{6-3} =\frac{2}{3}[/tex]

Answer:it’s A great got it right on edge

Step-by-step explanation:

Answer:

center ( -5 , 7).

Step-by-step explanation:

Given  : If the equation of a circle is (x + 5)² + (y - 7)² = 36.

To find : Find its center .

Solution : We have given (x + 5)² + (y - 7)² = 36.

Standard equation of circle : (x – h)² + (y – k)² = r².

Where, (h ,k) = center , r =  radius .

On comparing (x + 5)² + (y - 7)² = 36.

h = -5 , k = 7

So, the center ( -5 , 7).

Therefore, center ( -5 , 7).

Answer:

|-5| is the answer.

Step-by-step explanation:

The opposite of 5 is -5. The absolute value of a number is always positive (e.g: |-10| = 10 because the negative sign is inside the absolute value bars).

-|5| and -|-5| both equal -5 because there is a negative sign outside of the bars. Since |-5| has a negative sign inside the bars, it equals 5.

I tried hard to explain this, so I hope it makes sense! :)

Hey there Brainly Student! Your answer is   I-5I !! I hope this helped! Have a great day!!

[tex]\bf \begin{array}{ll} \stackrel{year}{term}&value\\ \cline{1-2} a_1&3\\ a_2&3r\\ a_3&3rr\\ a_4&3rrr\\ a_5&3rrrr\\ &3r^4 \end{array}\qquad \qquad \stackrel{\textit{5th year}}{108}=3r^4\implies \cfrac{108}{3}=r^4\implies 36=r^4 \\\\\\ \sqrt[4]{36}=r\implies \sqrt[4]{6^2}=r\implies 6^{\frac{2}{4}}=r\implies 6^{\frac{1}{2}}=r\implies \sqrt{6}=r[/tex]

[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} r=\sqrt{6}\\ a_1=3\\ n=11 \end{cases}\implies a_{11}=3(\sqrt{6})^{11-1} \\\\\\ a_{11}=3(\sqrt{6})^{10}\implies a_{11}=3\left(6^{\frac{1}{2}} \right)^{10}\implies a_{11}=3\cdot 6^{\frac{10}{2}} \\\\\\ a_{11}=3\cdot 6^5\implies a_{11}=3\cdot 7776\implies a_{11}=23328[/tex]

Answer:

The investment be worth $23328 after 11 years.

Step-by-step explanation:

It is given that the annual growth reflects a geometric sequence.

An initial investment of $3 is worth $108 after 5 years.

It means the initial value of first term of the gp, a₁ = 3

The 5th term of the gp, a₅ = 108

The nth term of a gp is

[tex]a_n=ar^{n-1}[/tex]              .... (1)

where, a is first term and r is common ratio.

The 5th term of the gp is

[tex]a_5=ar^{5-1}[/tex]

From the given information it is clear that the 5th term of the gp is 108. Substitute a₅ = 108 and a=3.

[tex]108=(3)r^{4}[/tex]

Divide both sides by 3.

[tex]\frac{108}{3}=r^{4}[/tex]

[tex]36=r^{4}[/tex]

Taking fourth root on both the sides.

[tex]\sqrt{6}=r[/tex]

Substitute r=√6, a=3 and n=11 to find the investment worth after 11 years.

[tex]a_{11}=(3)(\sqrt{6})^{11-1}[/tex]

[tex]a_{11}=3(\sqrt{6})^{10}[/tex]

[tex]a_{11}=23328[/tex]

Therefore the investment worth $23328 after 11 years.

Answer:

B and E are the correct answer

Step-by-step explanation:

Because (2,23) and (7,48) are linear

Your question is incomplete and lacks the table. Please check below for the full content.

A group of students is collecting books to add to their library. The table shows the number of books in the library after 1, 3, and 5 days. If the relationship between days and books continues to be linear, which ordered pairs could appear in the table? Check all that apply.

(0, 8)

(2, 23)

(4, 32)

(6, 48)

(7, 48)

The missing table is given below.

The correct options are option 2:(2,23) and 5:(7,48) The ordered pair (2,23),(7,48) will appear in the table.

The equation where highest degree of the variable used in the equation is 1 is called linear equation. Foe example ax+by+c=0

Here given the relationship between days and books is linear.

From the table, it clear that In day 1 the book collected is 18.

in day 3 book collected is 28.

x₁=1,y₁=18

x₂=3,y₂=28

The linear equation will be

(y-y₁)/(x-x₁)=(y₂-y₁)/(x₂-x₁)

⇒(y-18)/(x-1)=(28-18)/(3-1)

⇒(y-18)/(x-1)=10/2

⇒(y-18)/(x-1)=5

⇒y-18=5(x-1)

⇒y-18=5x-5

⇒y=5x-5+18

⇒y=5x+13

So the linear equation will be y=5x+13

By ckecking every option,

1. (0, 8)-  y=5*0+13=13≠8  Option 1 is incorrect.

2. (2,23)-  y=5*2+13=23    Option 2 is correct.

3. (4,32)-   y=5*4+13=33≠32   Option 3 is incorrect.

4.(6,48)-   y=5*6+13=43≠48     Option 4 is incorrect.

5. (7,48)    y=5*7+13=48   Option 5 is correct.

Therefore the correct options are option 2 and 5 i.e. The ordered pair (2,23) , (7,48) will appear in the table.

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39

52 divided by 4 is 13. 52 pickles divided into 4 pickles for each meal is 13. 39 patties divided by 3 patties is 13 aswell so. the answer: 39

The number of meat patties that are needed if 52 pickles are used is:

                                     39 meat patties.

It is given that:

The Big Burger recipe calls for 3 meat patties, 2 slices of cheese, and four pickles.

This means that for every 4 pickles there are 3 meat patties.

This means that for every 1 pickles there are: 3/4 meat patties.

Hence, for every 52 pickles there are: 3/4×52 meat patties

                                                            = 39 meat patties.

Answer:Answer:

the figure is parallelogram

Explanation:

enter image source here

As The mutually edges are parallel each other and equal,

the name of figure is parallelogram .

Step-by-step explanation:

Answer with explanation:

The vertices of Quadrilateral ABCD are ,A(−5,7), B(6,−3), C(10,2), and D(−1,12).

Distance formula between two points (a,b) and (c,d), is given by

          [tex]=\sqrt{(a-c)^2+(b-d)^2[/tex]

[tex]AB=\sqrt{[-5-6]^2+[7-(-3)]^2}\\\\AB=\sqrt{121+100}\\\\AB=\sqrt{221}\\\\BC=\sqrt{[10-6]^2+(2+3)^2}\\\\BC=\sqrt{16+25}\\\\BC=\sqrt{41}\\\\CD=\sqrt{[10+1]^2+[2-12]^2}\\\\CD=\sqrt{121+100}\\\\CD=\sqrt{221}\\\\DA=\sqrt{[-1+5]^2+[12-7]^2}\\\\DA=\sqrt{16+25}\\\\DA=\sqrt{41}\\\\AC=\sqrt{[10+5]^2+[2-7]^2}\\\\AC=\sqrt{225+25}\\\\AC=\sqrt{250}\\\\BD=\sqrt{[6+1]^2+[-3-12]^2]}\\\\BD=\sqrt{49+225}\\\\BD=\sqrt{274}[/tex]

Opposite side of Quadrilateral[AB=CD, AD=BC] is equal, but Diagonals are not equal.

So, it is a Parallelogram.

Answer:

y/2

Step-by-step explanation:

x+3=y+2

------  --------

3          2

Using cross products

2(x+3) = 3(y+2)

Distribute

2x+6 = 3y+6

Subtract 6 from each side

2x+6-6 = 3y+6-6

2x= 3y

Divide each side by 2

2x/2 = 3y/2

x = 3/2 y

We want to find x/3

Divide each side by 3

x/3 = 3/2 y * 1/3

x/3 = 1/2 y

To solve the system of equations, we can use the method of substitution. However, when we substitute the expression for x in the second equation, we get an equation that is not true, indicating that the system has no solution.

To solve the system of equations given by 5x - 2y = -6 and 15x - 6y = 6, we can use the method of substitution. First, we can solve one of the equations for either variable, then substitute that expression into the other equation to solve for the other variable. Let's solve the first equation for x:

5x - 2y = -6

5x = 2y - 6

x = (2y - 6)/5

Now, substitute this expression for x in the second equation:

15((2y - 6)/5) - 6y = 6

6y - 18 - 6y = 6

-18 = 6

This leads to the equation -18 = 6, which is not true. Therefore, the system of equations has no solution. So, the correct answer is C. No solution.

Answer: [tex]80\ ft^2[/tex]

Step-by-step explanation:

You know that the model of a rectangular patio at a landscaping business will be enlarged by a scale factor of 2 and the new area will be 160 square feet.

Since you know that the area of the new enlarged patio will be 160 square feet, you need to divide the area  of the new enlarged patio  in order to find the area of the landscaper’s model.

This is:

[tex]Area_(model)=\frac{160\ ft^2}{2}\\\\Area_(model)=80\ ft^2[/tex]

Answer:

I think its 40

Step-by-step explanation:

i come back and see:)

I got it right. good luck

Answer:

Hi there!

The answer to this question is: x=6

Step-by-step explanation:

All the points are being mirrored across the line x=6.

Answer:

The answer is x=6

Step-by-step explanation:

The two shapes are mirror images of each other around x=6

Step-by-step answer:

If x and y both go by equal steps, not necessarily equal steps between x and y, the relation is linear

Here, x goes by steps of 6 (1,7,13,19) and y goes by steps of 3 (4,7,10,13), therefore the relation is linear.

To find the equation passing through all the points, we find first the slope, which is steps in y divided by steps in x, or

slope, m = 3/6 = 1/2

Next, we take any point from the data, say, P0=(x0,y0)=(1,4), and substitute in the point-slope form of the equation

y-y0 = m(x-x0)...........................(1)

since x0=1, y0=4, and m=1/2, we get the equation

y-4 = (1/2)*(x-1) .........................(2)

Simplify (2) to get the slope-intercept form of the linear relation:

y = (1/2)x + 7/2 ........................(3)

Finally, we check the results of the y-values for given values of x, using the relation given in equation (3):

y(1) = 4

y(2)=7

y(3)=10

y(4)=13

all of which correspond exactly to original data, so the equation of the linear relation is correct.

Answer:

Step-by-step explanation:

It's a right triangle.

The formula of an area of a right triangle:

[tex]A=\dfrac{ab}{2}[/tex]

a, b - legs

Find x-intercept and y-intercept of a line 4x + 5y = 20.

x-intercept (y = 0):

4x + 5(0) = 20

4x + 0 = 20

4x = 20     divide both sides by 4

x = 5

y-intercept (x = 0):

4(0) + 5y = 20

0 + 5y = 20

5y = 20      divide both sides by 5

y = 4

Therefore the legs are a = 5, b = 4.

Substitute:

[tex]A=\dfrac{(5)(4)}{2}=\dfrac{20}{2}=10[/tex]

Look at the picture.

Step-by-step explanation:

Hi there!

The best way to approach this problem is Soh Cah Toa.

In this case you can use sine. sine is opposite over hypotenuse.

so sin(17)= b/15

then to solve for b you multiply 15 on both sides to get 4.4

Answer:

Step-by-step explanation:

This question is an application of the sine law

Equation

b/sin(B) = c / Sin(C)

Givens

b = ????

B = 17

c = 15

C = 140

Solution

Keep in mind that this may not work.

b/sin(17) =   15 / sin(140)                          Multiply both sides by sin(17)

b = 15*sin(17)/sin(140)

b = 15*0.2924/0.6428

b = 6.8233