What is the solution to the system of equations
below?
y=2x+8
3(-2x + y) = 12
1) no solution
2) infinite solutions
3) (-1,6)
4) (1/2,9)

Answer:

Step-by-step explanation:

x=2and y=−1

Hope this helps

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Answer:

x=2, y = -1

Step-by-step explanation:

Given the system of equation;

5x + y = 9 ... (1)

3x + 2y = 4 ...(2)

We will solve it simultaneously to get variables x and y.

Using substitution method,

From equation 1, y = 9-5x ...(3)

Substituting equation 3 into 2 we will have;

3x + 2(9-5x) = 4

3x + (18-10x) = 4

3x + 18 -10x = 4

3x-10x+18 = 4

-7x+18 = 4

-7x = 4-18

-7x =-14

Dividing both sides by -7, we will have;

-7x/-7 = -14/-7

x = 2

Substituting x = 2 into equation 1 to get y we will have;

5x+y= 9

5(2) + y = 9

10+y = 9

y = 9-10

y = -1

Therefore x = 2 and y = -1 is the solution to the simultaneous equation.

Answer: B. on e2020

Step-by-step explanation:

The transformation of parent function to h(x) = - ∛x + 3 is such that it is reflected over the horizontal axis, and then translated up 3 units.

The correct option is B.

Transformations are changes done in the shapes on a coordinate plane by rotation or reflection or translation.

Given function,

h(x) = - ∛x + 3

To find the transformation, compare the equation to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis

Parent Function: f(x) = ∛x

Horizontal Shift: None

Vertical Shift: Up 3 Units

Reflection about the x-axis:

f(x) → -f(x)

∛x → - ∛x  

Reflection of the function is over x - axis.

Hence, the transformation from the parent equation to given function can be found  by reflecting over X- axis and translate up 3 units.

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Answer:

A. 90.5 cubic meters pet second.

B. 3.77 square meters per second.

C.  [tex]\frac{dV}{dS} = \frac{r}{2}[/tex]

Step-by-step explanation:

The radius of a sphere is increasing at a constant rate of 0.05 meters per second.

Therefore, [tex]\frac{dr}{dt} = 0.05[/tex] ......... (1)

A. Now, volume of the sphere is given by  

[tex]V = \frac{4}{3}\pi  r^{3}[/tex]

Now, differentiating both sides with respect to t we get,

[tex]\frac{dV}{dt} = \frac{4}{3}\pi (3r^{2}) \frac{dr}{dt} = 4\pi r^{2} \frac{dr}{dt}[/tex]

Then at r = 12 meters, the rate of increase in volume will be

[tex]\frac{dV}{dt} = 4 \times (\frac{22}{7}) \times 12^{2} \times 0.05 = 90.5[/tex] cubic meters pet second. {From equation (1)}

B. When the volume of the sphere is 36π cubic meters, then  

[tex]\frac{4}{3}\pi r^{3} = 36\pi[/tex]

⇒ [tex]r^{3} = 27[/tex]

⇒ r = 3 meters.

Now, surface area of a sphere is given by  

S = 4πr² .......... (2)

Differentiating both sides with respect to time (t) we get,

[tex]\frac{dS}{dt} = 8\pi r\frac{dr}{dt} = 8 \times (\frac{22}{7}) \times 3 \times 0.05 = 3.77[/tex] square meters per second. {From equation (1)}

C. Now, [tex]V = \frac{4}{3}\pi  r^{3}[/tex] and S = 4πr²

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

Now, differentiating with respect to S both sides we get,

[tex]\frac{dV}{dS} = \frac{r}{3} + \frac{S}{3} \frac{dr}{dS}[/tex] ......... (3)

Now, we have, S = 4πr²

Differentiating with respect to S both sides, we get

[tex]1 = 8\pi r\frac{dr}{dS}[/tex]

⇒ [tex]\frac{dr}{dS} = \frac{1}{8\pi r }[/tex] ......... (4)

Now, from equations (2), (3) and (4) we get,

[tex]\frac{dV}{dS} = \frac{r}{3} + \frac{4\pi r^{2} }{3} \times \frac{1}{8\pi r }[/tex]

⇒ [tex]\frac{dV}{dS} = \frac{r}{3} + \frac{r}{6}[/tex]

⇒ [tex]\frac{dV}{dS} = \frac{r}{2}[/tex] (Answer)

Question:

C. Express the rate at which the volume of the sphere changes with respect to the surface are of the sphere (as a function of r)

Step-by-step explanation:

Here's how you solve part C of this question.

Start with what you know:

dV/dt = 4pir^2 x (dr/dt)

(dr/dt) = 0.05

S(r) = (Surface Area) = 4pir^2

So, since S(r) is equal to 4pir^2, we replace 4pir^2 with S(r). We also know that (dr/dt) = 0.05, so we replace (dr/dt) with 0.05.

Now the equation should look like this:

dV/dt = 0.05 x S(r) <----- (your answer).

Hope this helped!! :)

when rounding up, decimals tend to lose accuracy, thus the rounding, due to that, fractions will always be the most accurate to represent the value, but let's go ahead

3/5 = 0.6 <- rounded up to one decimal

3/4 = 0.75

      = 0.8 <- rouned up to one decimal as well

if we add them up 0.6 + 0.8 = 1.4.

[tex]\bf \cfrac{3}{5}+\implies \cfrac{3}{4}\implies \stackrel{\textit{using an LCD of 20}}{\cfrac{(4)3+(5)3}{20}}\implies \cfrac{12+15}{20}\implies \cfrac{27}{20} \\\\\\ 1.35\implies \stackrel{\textit{rounded up}}{1.4}[/tex]

in this case, rounding up each result to 1 decimal, we end up with the same value, mind you that the instructions never said to round it to a certain amount of decimal places, if we do round it to two decimal places, the value will be 1.35 for both cases, and accurate on each.

Answer:

The scale factor is 2.

Step-by-step explanation:

Take the vertical sides of the 2 triangles.

Their length is 3 and 6 so the scale factor is 6/3 = 2.

Also we see than the horizontal lines are in the same ratio 4 : 2  = 2:1.

Answer:

53.33%

Step-by-step explanation:

(16/30)*100=0.5333333333*100=53.33%

Answer:53.3%

Step-by-step explanation:

√12x^3÷√6x

Factor 6 out of both the numerator and denominator:

√2x^3÷√x

Cancel out common factors to get:

√2x^2

Pull the terms out from under the radical to get:

D. x√2

Answer:

altitude

Step-by-step explanation:

Answer:

Draw a line on you paper, go to the start of the line and place your Protractor. Look for the 40 degree mark and place a little slash there. Take away the protractor and draw a line going through the slash. (Use a ruler too)

Step-by-step explanation:

For this you need a protractor

Joanie used a protractor to draw the angle 40° that Joanie will use on her map​ can follow the steps provided here.

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

Steps of Construction:

1. Draw ∠BAC=40° using protractor. By taking A as Centre draw an arc which cuts AB and AC at P and Q.

2. Now take O as centre on another line segment EF and taking the same radius PQ draw an arc which cuts OF at R. Now again take R as Centre and draw the arc which cut at S.

3. Join O to S which is the required ∠ROS=40°.

Therefore, Joanie used a protractor to draw the angle 40° that Joanie will use on her map​ can follow the steps provided here.

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There are triangles ΔABC, ΔFDE, and ΔGIH must be congruent. The correct answer is option A.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

In the given information, we can see that AB is congruent to both DF and GI, and BC is congruent to HI. Also, we know that ∠B is congruent to both ∠D and ∠G.

Using these properties, we can conclude that triangles ABC and FDE are congruent by the Side-Angle-Side (SAS) congruence theorem, since AB is congruent to DF, BC is congruent to DE, and ∠B is congruent to ∠D.

Similarly, we can conclude that triangles ABC and GIH are congruent by the Side-Side-Side (SSS) congruence theorem since AB is congruent to GI, BC is congruent to HI, and AC is congruent to GH.

Therefore,  ΔABC, ΔFDE, and ΔGIH must be congruent.

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Answer: 301

Step-by-step explanation:

the least amount one of the wrestlers could weigh is 301.

The term standard deviation refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Given that,

Mean μ = 265,

Standard deviation σ = 28 lbs.

Let the least amount one of the wrestlers could weigh is x.

To find x such that P(X≥x) = 0.10

1 - P(X<x) = 0.10

P(X<x) = 1 - 0.10

P(X<x) = 0.90

z for area = 0.90 in equal to 1.28 in statistical table,

z = 1.28

Use  formula, to find the value of x,

x = μ + z × σ

x = 265 + 1.28 × 28

x = 265 + 35.84

x = 300.84

x = 301(Rounded to the nearest integer)

The required value of x is 301.

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Answer:

$1.40

Step-by-step explanation:

40 times 30% = 28 because 30% of 40 is 12 so 40-12 =28

28 times .05= 1.40 which  is the tax of  the final total

Answer:140

Step-by-step explanation:

Answer:2³*3²

Step-by-step explanation:

Answer:

d.) 81

Step-by-step explanation:

f(2) would be 27 and 27x3 is 81.

81/3=27

27/3=9

Answer:

81

Step-by-step explanation:

For the recursive function, f(n+1) = one-half(n)

Thus, when n = 2,

f(3) = 9

If n = 1,

f(2) = 9×3

f(2) = 27

If n = 0,

f(1) = 27 ×3

f(1) = 81

The shoot would last eight hours, and the cost would be $699 whether the photographer hires Craig or Kaya.

This question can be solved using algebra, particularly the concept of system of equations, where we set two linear cost equations equal to each other to find out when they cost the same. Given: Craig's cost is $195 + $63p, and Kaya's cost is $171 + $66p, we form an equation $195 + $63p = $171 + $66p. Subtracting $171 and $63p from both sides leaves us with $24 = $3p. So, dividing both sides by $3, we get p = 8.

This means the photo shoot would last 8 hours, and the cost would be either Craig's or Kaya's cost for 8 hours, which is $195 + $63*8 = $699 or  $171 + $66*8 = $699.

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The cost for the photo shoot would be $699, and the duration of the shoot would be 8 hours.

Let's denote:

- [tex]\( C_C \)[/tex]: Total cost if the photographer hires Craig.

- [tex]\( C_K \)[/tex]: Total cost if the photographer hires Kaya.

- [tex]\( h \)[/tex]: Number of hours of the photo shoot.

Given the charges:

- Craig charges $195 for showing up, plus $63 per hour.

- Kaya charges $171 for showing up, plus $66 per hour.

The equations for the total cost [tex]\( C_C \)[/tex] and [tex]\( C_K \)[/tex] are:

[tex]\[ C_C = 195 + 63h \][/tex]

[tex]\[ C_K = 171 + 66h \][/tex]

The photographer realizes that the costs are the same, so:

[tex]\[ C_C = C_K \][/tex]

Substitute the expressions:

[tex]\[ 195 + 63h = 171 + 66h \][/tex]

Now, solve for [tex]\( h \)[/tex]:

[tex]\[ 195 - 171 = 66h - 63h \][/tex]

[tex]\[ 24 = 3h \][/tex]

[tex]\[ h = \frac{24}{3} \][/tex]

[tex]\[ h = 8 \][/tex]

So, the duration of the photo shoot is 8 hours.

Now, substitute [tex]\( h = 8 \)[/tex] back into either equation to find the cost:

Using [tex]\( C_C \)[/tex]:

[tex]\[ C_C = 195 + 63 \cdot 8 \][/tex]

[tex]\[ C_C = 195 + 504 \][/tex]

[tex]\[ C_C = 699 \][/tex]

Using [tex]\( C_K \)[/tex]:

[tex]\[ C_K = 171 + 66 \cdot 8 \][/tex]

[tex]\[ C_K = 171 + 528 \][/tex]

[tex]\[ C_K = 699 \][/tex]

Each student worked on 115 math problems.

Step-by-step explanation:

Given,

Problems solved in 4 hours = 8970

Number of students in competition = 78

As each student solved same number of problems, we will divide the total problems solved by number of students to find the amount of problems solved by one student.

Problems solved by one student = [tex]\frac{8970}{78}[/tex]

Problems solved by one student = 115

Each student worked on 115 math problems.

Keywords: division

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Each student works 115 problems.

Explanation:

I'm going to copy and paste the question here, and bold important info.

"Rayville Elementary sponsors a math competition for 78 students. During the competition, the students work a total of 8,970 math problems in 4 hours. Each student works the same number of problems. How many problems does each student work?"

Now everything not bolded? Forget about it. All you need to know is that there are 78 students. They all do 8,970 # of problems. And all the students do the same amount. Now you just have to divide the # of probs. by the amount of students in the competition, and you have your answer.

8970÷78=115

Hope that helped!

Answer:

Let's find out!

Step-by-step explanation:

15 ounces / 2.49 dollars

≈ 6.024 ounces per dollar

20 ounces / 3.32 dollars

≈ 6.024 ounces per dollar

Your answer is:

C) The unit rates are equal

The amount of ounces per dollar is the same, so your answer MUST be C).

Answer:

C) The unit rates are equal.

Step-by-step explanation:

Answer:

There will be no pieces of paper left over. Each student will receive 15 pieces of paper.

Step-by-step explanation:

If you divide the 345 pieces of paper between the 23 classmates, you will end up with 15. There is no remainder or decimal, just 15, a whole number. That means that there will be no pieces of paper left over.

Answer:

48 units cubed

Step-by-step explanation:

length × height × width

4 × 6 × 2 = 48

Answer:

1/3

Step-by-step explanation:

Answer:

3x ≥ 2 + 2x

Step-by-step explanation:

Given:

[tex]x\geq 2[/tex]

Solution:

Now, we have to write an inequality with x on both sides whose solution is x is greater than or equal to 2.

[tex]x\geq 2[/tex]

Now we add 2x on both side.

[tex]x + 2x\geq 2 + 2x[/tex]

[tex]3x\geq 2 + 2x[/tex]

Therefore, the inequality which has a solution x ≥ 2 is:

3x ≥ 2 + 2x

Answer:

[tex]\large \boxed{\math{8\frac{1}{4}}\text{ km}}}[/tex]

Step-by-step explanation:

[tex]\begin{array}{lcll}2\frac{1}{5} \times 3\frac{3}{4} & = & \dfrac{11}{5} \times \dfrac{15}{4} & \text{Converted the mixed numbers to improper fractions}\\\\& = & 11 \times\dfrac{3}{4}& \text{Cancelled the 5s}\\\\& = & \dfrac{33}{4}& \text{Multiplied numerators and denominators}\\\\& = &\mathbf{8\frac{1}{4}} & \text{Converted the mixed number to a fraction}\\\end{array}\\\text{The length of the road is }\large \boxed{\mathbf{8\frac{1}{4}}\textbf{ km}}}[/tex]

Answer:

Total price of the glass is = $904.78

Step-by-step explanation:

Let's start by finding what is the surface area (in square meters) of the circular piece of glass. The information we have is that the radius of it is 8.0 meters. So we recall the formula for the area of the circle in terms of its radius (the product of the number [tex]\pi[/tex] times the square of the circle's radius):

Area of circle = [tex]\pi \,r^2[/tex]

Therefore, since the circle we need to investigate has radius 8 meters, the formula now becomes:

Area of circle = [tex]\pi \,r^2=\pi\,\,(8\,m)^2=201.062\,m^2[/tex]

Now, since they charge the glass per square meter ($4.50 per square meter), we just multiply the number of square meters we found for the glass' surface times the price per square meters, and get:

Total price = $4.50 * 201.062 = $904.78

Final answer:

The given equation has no solution because it leads to a contradiction.

Explanation:

To determine whether the given equation has one solution, no solution, or infinitely many solutions, we need to simplify the equation and see if it leads to a contradiction or identity. Simplifying the equation:

2/3x = 9 - 2(-1/3x + 3)

We can start by distributing the -2 to (-1/3x + 3):

2/3x = 9 + 2/3x - 6

Combining like terms:

2/3x - 2/3x = 9 - 6

0 = 3

Since we have a contradiction (0 cannot equal 3), there is no solution to the equation. Therefore, the correct answer is no solution.

Answer:

[tex]\displaystyle x - 3y = 6\:OR\:y = \frac{1}{3}x - 2[/tex]

Step-by-step explanation:

First, find the rate of change [slope]:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{3 + 2}{3 + 12} = \frac{5}{15} = \frac{1}{3}[/tex]

Then plug these coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula since you get it swiftly that way. It does not matter which ordered pair you choose:

2 = ⅓[12] + b

4

[tex]\displaystyle -2 = b \\ \\ y = \frac{1}{3}x - 2[/tex]

If you want it in Standard Form:

y = ⅓x - 2

- ⅓x - ⅓x

_________

−⅓x + y = −2 [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]

−3[−⅓x + y = −2]

[tex]\displaystyle x - 3y = 6[/tex]

_______________________________________________

−3 = ⅓[−3] + b

−1

[tex]\displaystyle -2 = b \\ \\ y = \frac{1}{3}x - 2[/tex]

If you want it in Standard Form:

y = ⅓x - 2

- ⅓x - ⅓x

_________

−⅓x + y = −2 [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]

−3[−⅓x + y = −2]

[tex]\displaystyle x - 3y = 6[/tex]

** You see? I told you it did not matter which ordered pair you choose because you will always get the exact same result.

I am joyous to assist you anytime.

Answer:

P = -[tex]\frac{41}{4}[/tex] or -10 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

"What is p? 4 1/2 + p = -5 3/4" was the question you have asked

So basically, in this equation we are looking for what the variable, P, is.

We already know that P plus 4[tex]\frac{1}{2}[/tex] equals -5[tex]\frac{3}{4}[/tex].

Now here's how you solve it:

So when trying to find the value a variable has, you should use inverse operations. What are inverse operations? Well let's look at this example:

453-T=56

How you would solve this is that you would subtract 56 from 453, removing 56 on the other side by subtracting it from the other side. *When performing inverse operations you always do it on BOTH sides*

We subtracted because 56 is positive and when performing operations on both sides of an equation, you do the inverse operation in both which in this case is to subtract.

453-T=56

-56      -56

↓

397-T=0

Now you may wonder 'What now? The other side is just 0! That didn't solve for T.' This is true. We have not solved for T just yet. But after this we will

397-T=0

     +T  +T

        ↓

397 = T

Tada! T is solved! We added T to both sides as T was negative and the opposite of negative is positive.

There are a few other ways to solve this equation like for example you could of subtracted 453 from both sides instead and have made it look like this:

453-T=56

-453    -453

↓

-T = -397

(Multiply both sides by negative 1 to make the -T and the -397 positive)

-1 (-T) = (-397) -1

↓

T = 397

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

Now that we've explained the basics of how that works let's now *actually* solve the problem:

4 1/2 + p = -5 3/4  

-4 1/2          -4 1/2

↓

P = -41/4

(4 1/2 is positive so the inverse operation was to subtract)

(A negative number subtracted by a negative number is a negative number that is even more negative than before)

--

ITS DONE!

Anyways let's check the equation to make sure it is right!

This is not needed but it is helpful to know how to check when you doubt that the value you got for a variable is correct.

You check by simply just pluging in the number you got into the variable and solving the equation to see if makes sense.

Here is how you would check this:

4 1/2 + p = -5 3/4

becomes

4 1/2 -[tex]\frac{41}{4}[/tex] = -5 3/4

subtract 41 fourths from 4 1/2

[tex]\frac{18}{4}[/tex]-[tex]\frac{41}{4}[/tex]= -[tex]\frac{23}{4}[/tex]

↓

-[tex]\frac{23}{4}[/tex] = -[tex]\frac{23}{4}[/tex]

Because the sides are equal, it is correct!

So, P = -[tex]\frac{41}{4}[/tex] or -10 [tex]\frac{1}{4}[/tex]

The value of p in the given algebraic equation 4 1/2 + p = -5 3/4 is -10.25. This is found by isolating p.

To resolve this algebraic equation, you need to subtract 4 1/2 (which is 4.5 in decimal form) from each side of the equation, in order to isolate p. Hence, the equation then becomes p = -5 3/4 - 4 1/2.

First, convert -5 3/4 and 4 1/2 to decimal form. -5 3/4 becomes -5.75 and 4 1/2 becomes 4.5.

Secondly, subtract 4.5 from -5.75. Therefore, p is equal to -5.75 - 4.5 = -10.25.

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The coordinates of the image of ∆CDE after the translation are:

C' (–5, 0)

D' (–6, -2)

E' (–1.5, -1)

To find the image of ∆CDE for a glide reflection, we must first perform a translation. The translation is (x, y) → (x, y – 3). This means that each point of ∆CDE will be moved 3 units down.

Therefore, the coordinates of the image of ∆CDE after the translation are:

C' (–5, 0)

D' (–6, -2)

E' (–1.5, -1)

Next, we need to reflect ∆CDE across the line x = 0. This me The vertices of ∆CDE are C(–5, 3), D(–6, 1), and E(–1.5, 2). Which figure shows the image of ∆CDE for a glide reflection where the translation is (x, y) → (x, y – 3) and the line of reflection is x = 0?

To find the image of ∆CDE for a glide reflection, we must first perform a translation. The translation is (x, y) → (x, y – 3). This means that each point of ∆CDE will be moved 3 units down.

Therefore, the coordinates of the image of ∆CDE after the translation are:

C' (–5, 0)

D' (–6, -2)

E' (–1.5, -1)

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Step-by-step explanation:

equation -

(X+7) (x-1) =0

equation = x2 -x -7x -7 = x2 -8x -7

standard form = x2 -8x -7

factor form = (x+7) (x-1)

Answer:

You may or may not need to include the units.

A = 18x - 18

P = 6x + 6

Graph is attached below. (2, 18)

Step-by-step explanation:

Substitute the information we need, "l" and "w", into the formulas.

l is for length, 6cm.

w is for width, (3x - 3)cm.

Use the formula for area of a rectangle.

A = lw

A = (6)(3x-3)cm²

A = (18x - 18)cm²  or 18x - 18

Use the formula for perimeter of a rectangle.

P = 2(l + w)

P = 2(6 + (3x - 3))cm

P = 2(3x + 3)cm

P = (6x + 6)cm  or 6x + 6

Linear equations are written in the form y = mx + b, so we do not need to factor or further simplify the formulas.

To graph, first turn the "m" value into a fraction form.

8 -> 8/1

6 -> 6/1

You need two points to graph each line.

For each equation, the first point is on the y-axis at the "b" value. Then use the "m" in the equation to count the number of units up (numerator) and to the right (denominator).

The solution is (2,18)

Answer:

4.94

Step-by-step explanation:

Subtract

9.03 - 4.09 = 4.94

Hope this helps :)

Answer:

4.94

Step-by-step

9.03 - 4.09= 4.94