Consider this system of equations. Which equation represents the first equation written in slope-intercept form? 5 x minus 2 y = 10. Y = one-fourth x + 1.

Answer:

Step-by-step explanation:

[tex]x^2+\frac bax+\frac ca=0\\\\ ax^2+bx+c=0\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\qquad\quad x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\\\x_1+x_2=\dfrac{-b-\sqrt{b^2-4ac}}{2a}+\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-2b}{2a}=\dfrac{-b}a\\\\\\x_1\cdot x_2=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\cdot\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\\\\{}\ \ =\dfrac{b^2-b\sqrt{b^2-4ac}+b\sqrt{b^2-4ac}-(\sqrt{b^2-4ac})^2}{2a}=\dfrac{b^2-(b^2-4ac)}{4a^2}=\\\\{}\ \ =\dfrac{b^2-b^2+4ac}{4a^2}=\dfrac{4ac}{4a^2}=\dfrac{c}{a}[/tex]

[tex]x_1-x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}-\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-2\sqrt{b^2-4ac}}{2a}=\frac{-\sqrt{b^2-4ac}}{a}\\\\\\x_1\div x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}\div\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-b-\sqrt{b^2-4ac}}{2a}\,\cdot\,\frac{2a}{-b+\sqrt{b^2-4ac}}=\\\\=\frac{-b-\sqrt{b^2-4ac}}{-b+\sqrt{b^2-4ac}}=\frac{b+\sqrt{b^2-4ac}}{b-\sqrt{b^2-4ac}}=\frac{b^2+2\sqrt{b^2-4ac}+b^2-4ac}{b^2-b^2+4ac}=\frac{2b^2+2\sqrt{b^2-4ac}-4ac}{4ac}=[/tex]

[tex]=\frac{b^2+\sqrt{b^2-4ac}-2ac}{2ac}[/tex]

Answer:

a = 26°

b = 48°

c = 26°

d = 106°

Answer:

Both have the same period which is 2π

Step-by-step explanation:

Answer:

f(x) = 5x^2

Step-by-step explanation:

A vertical stretch is in the y direction

y = Cf(x)  C > 1 stretches it in the y-direction

f(x) = 5x^2

Answer:

D. 4z^3

Step-by-step explanation:

First, you see what cubed is 64, which is 4, so you know it is either A or D, but it can not be A because it is not z to the power 5 but x to the power of 3

Hope this helps, if you want me to explain more, feel free to ask questions.

Have a good day! :)

Answer:

4 z^3

Step-by-step explanation:

( 64 z^9) ^ 1/3

Rewriting 64 as 4^3

( 4^3 z^9) ^ 1/3

We know that ( ab) ^c = a^c  * b^c

4^3 ^ 1/3 z^9  ^ 1/3

We know that a^ b^c = a^ ( b*c)

4^(3 * 1/3) z^ (9  * 1/3)

4 ^ ( 1)  z^ ( 3)

4 z^3

Answer:

69242/3 or 23080.666667

Step-by-step explanation:

2345 is multiplied by 2. Then the result is divided by 6. Then 22299 is added to the final result.

2345 × 2

= 4690

4690/6

= 2345/3

2345/3 + 22299

= 69242/3

Answer:

78

Step-by-step explanation:

Let x be the score on the next test

We are averaging 6 tests and want an average of 75

( 82+91+38+78+83+x) /6 = 75

Multiply each side by 6

( 82+91+38+78+83+x) = 75*6

( 82+91+38+78+83+x)  =450

Combine like terms

x+372 = 450

Subtract 372 from each side

x+372-372 = 450-372

x =78

Answer:

100= Initial Amount

1/4= decay factor for each week

w= number of weeks

1/4w= decay factor after w weeks

1 - 0.4= decay factor for each week

w= number of weeks

0.4= percent decrease

Step-by-step explanation:

Answer:

0.0617

Step-by-step explanation:

so the formula is 1.96[tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

P is the proportion (.45) and n is the sample size (250). Inserting these into the problem, we get 1.96[tex]\sqrt{\frac{.45(1-.45)}{250} }[/tex]. Solving this out, you should solve the inside of the square root to get .00099. Take the square root of this, and multiply by 1.96 to get your answer!

This method applies to any problems with the same basic format. Good luck!

Answer:

45

Step-by-step explanation:

There are 3 cones and 15 flavors

Multiply the number of cones by the number of flavors

3*15

45

There are 45 possible combinations

Answer:

-7 is no, -2 is no, 7 is no, and 10 is yes

Step-by-step explanation:

-5+9*(-7)>58

-5+-63>58

-68>58

-5+9*(-2)>58

-5+-18>58

-23>58

-5+9*(7)>58

-5+63>58

58>58

-5+9*(10)>58

-5+90>58

85>58

so the only one that is a solution is v=10, hope this helps

Answer: No, No, No, Yes

Step-by-step explanation:

Solve the equation for "v":

-5 + 9v > 58

      9v > 63

        v > 7

Check the options to see if they make a true statement:

-7 > 7    False

-2 > 7    False

7 > 7     False

10 > 7   TRUE!

Answer:

28

Step-by-step explanation:

We divide the shape covenientely, like this, and area 1 is 4*4=16

area 2=4*4/2=8

area 3= 2*4/2=4

Area total = Area 1 + Area 2 + Area 3=16+8+4=28

Answer:

The answer is below

Step-by-step explanation:

Given that:

The mean (μ) one-way commute to work in Chowchilla is 7 minutes. The standard deviation (σ) is 2.4 minutes.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

a) For x < 2:

[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]

From normal distribution table,  P(x < 2) = P(z < -2.08) = 0.0188 = 1.88%

b) For x = 2:

[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]

For x = 11:

[tex]z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67[/tex]

From normal distribution table, P(2 < x < 11) = P(-2.08 < z < 1.67 ) = P(z < 1.67) - P(z < -2.08) = 0.9525 - 0.0188 = 0.9337  

c) For x = 11:

[tex]z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67[/tex]

From normal distribution table,  P(x < 11) = P(z < 1.67) = 0.9525

d) For x = 2:

[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]

For x = 5:

[tex]z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83[/tex]

From normal distribution table, P(2 < x < 5) = P(-2.08 < z < -0.83 ) = P(z < -0.83) - P(z < -2.08) =  0.2033- 0.0188 = 0.1845  

e) For x = 5:

[tex]z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83[/tex]

From normal distribution table,  P(x < 5) = P(z < -0.83) = 0.2033

Answer:

The expected value for the insurance company is $392.20.

Step-by-step explanation:

The expected value of a random variable, X is:

[tex]E(X)=x\cdot P(X)[/tex]

It is provided that a life insurance company sells a $100,000 one year term life insurance policy to a 30-year old male for $475.

The probability that the male survives the year is, P(S) = 0.999172.

Then the probability that the male does not survives the year is:

P (S') = 1 - P (S)

        = 1 - 0.999172

P (S') = 0.000828

The amount the company owes the male if he survives is, S = $475.

The amount the company owes the male if he does not survives is,

S' = $475 - $100,000 = -$99525.

Compute the expected value for the insurance company as follows:

[tex]E(\text{Insurance Company})=S\cdot P(S)+S'\cdot P(S')[/tex]

                                     [tex]=(475\times 0.999172)+(-99525\times 0.000828)\\=474.6067-82.4067\\=392.20[/tex]

Thus, the expected value for the insurance company is $392.20.

Answer:

Below

Step-by-step explanation:

r us the radius of the base and h is the heigth of the cylinder.

The volume of a cylinder is given by the formula:

V = Pi*r^2*h

V/Pi*r^2 = h

We can write a function that relates h and r

Answer:

One of the cylinders is short and wide, while the other is tall and thin.

Step-by-step explanation:

sample answer given on edmentum

Answer:

greater than

Step-by-step explanation:

An exponential growth function has a base that is__greater than__one.

If the base is less than one, it will be a decay function.

Note: the above assumes an exponent greater than one as well.

Answer:

Step-by-step explanation:

Discount =$7000-$4900

Discount% =

[tex] \frac{2100}{7000} \times 100 \\ = \frac{210000}{7000 } \\ = \frac{210}{7} = 30[/tex]

Answer:

[tex]3x^2+2x+1[/tex]

Step-by-step explanation:

Sum means to add and second power means that the exponent is "2". So, the expression is:

=> [tex]3x^2+2x+1[/tex]

It cannot be simplified further.

Answer:

6

Step-by-step explanation:

From the table given defining a function, the values of "x" on the table represents the input of the function, which gives us an output, f(x), which can be labelled as "y" in some instances.

Thus, the value of f(0), is simply the output value we would get, given an input value of "0".

So therefore, f(0) = 6. That is, at x = 0, f(x) = 6.

Answer: 6

Step-by-step explanation:

Answer: it is =4176000000000000

Step-by-step explanation:

(2.9)(100000)(7.2)(10^2)

5(10^−8)

=

(290000)(7.2)(10^2)

5(10^−8)

=

2088000(10^2)

5(10^−8)

=

(2088000)(100)

5(10^−8)

=

208800000

5(10^−8)

=

208800000

5(1/100000000)=

208800000/1

20000000

=4176000000000000

hope i helped

-lvr

Greetings from Brasil...

Here we don't have much to go

∛Y = A.(C + 1/X)

∛Y = (AC + A/X)

raising both members to the cube.....

(∛Y)³ = (AC + A/X)³

from Notable Products: (a + b)³ = a³ + 3a²b + 3ab² + b³

Y = (AC)³ + 3(AC)².(A/X) + 3AC(A/X)² + (A/X)³

Y = A³[C³ + (3C²/X) + (3C/X²) + (1/X³)]

Answer:

$2,500 was invested in the first account while $7,500 was invested in the second account

Step-by-step explanation:

Here in this question, we want to find the amount which was invested in each of the accounts, given their individual interest rates and the total amount that was accorded as interest from the two investments

Now, since we do not know the amount invested , we shall be representing them with variables.

Let the amount invested in the first account be $x and the amount invested in the second account be $y

Since the total amount invested is $10,000, this means that the summation of both gives $10,000

Mathematically;

x + y = 10,000 ••••••(i)

now for the $x, we have an interest rate of 5%

This mathematically translates to an interest value of 5/100 * x = 5x/100

For the $y, we have an interest rate of 6% and this mathematically translates to a value of 6/100 * y= 6y/100

The addition of both interests, gives 575

Thus mathematically;

5x/100 + 6y/100 = 575

Multiplying through by 100, we have

5x + 6y = 57500 •••••••••(ii)

From 1, we can have x = 10,000-y

let’s substitute this into equation ii

5(10,000-y) + 6y = 57500

50,000-5y + 6y = 57500

50,000 + y = 57500

y = 57500-50,000

y = 7,500

Recall;

x = 10,000-y

so we have;

x = 10,000-7500 = 2,500

Answer:

The correct option is;

[tex]h(x) = \sqrt[3]{x + 2}[/tex]

Step-by-step explanation:

Given that h(x) is a translation of f(x) = ∛x

From the points on the graph, given that the function goes through (-1, 1) and (-3, -1) we have;

When x = -1, h(x) = 1

When x = -3, h(x) = -1

h''(x) = (-2, 0)

Which gives  

d²(∛(x + a))/dx²= [tex]-\left ( \dfrac{2}{9} \cdot \left (x + a \right )^{\dfrac{-5}{3}}\right )[/tex], have coordinates (-2, 0)

When h(x) = 0, x = -2 which gives;

[tex]-\left ( \dfrac{2}{9} \cdot \left (-2 + a \right )^{\dfrac{-5}{3}}\right ) = 0[/tex]

Therefore, a = (0/(-2/9))^(-3/5) + 2

a = 2

The translation is h(x) = [tex]\sqrt[3]{x + 2}[/tex]

We check, that when, x = -1, y = 1 which gives;

h(x) = [tex]\sqrt[3]{-1 + 2} = \sqrt[3]{1} = 1[/tex] which satisfies the condition that h(x) passes through the point (-1, 1)

For the point (-3, -1), we have;

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

Therefore, the equation, h(x) = [tex]\sqrt[3]{x + 2}[/tex] passes through the points (-1, 1) and (-3, -1) and has an inflection point at (-2, 0).

Answer: B

Step-by-step explanation:

Answer:

350 meters cubed.

Step-by-step explanation:

If you visualize it, there are two rectangular prisms: one flat one on the top, and one large one on the bottom.

The width of the top one is 5 meters. The length is 7 meters. The height is 8 - 5 = 3 meters. So, one prism has a volume of 5m x 7m x 3m.

The width of the bottom one is 7 meters. The length is 7 meters. The height is 5 meters. So, the bottom prism has a volume of 7m x 7m x 5m.

(5 * 7 * 3) + (7 * 7 * 5)

= (35 * 3) + (49 * 5)

= 105 + 245

= 350

So, the volume of the figure is 350 meters cubed.

Hope this helps!

Answer:

V = 15 pi m^3

Step-by-step explanation:

The volume of a cone is

V = 1/3 pi r^2 h

The radius is 3 and the height is 5

V = 1/3 pi ( 3)^2 *5

V = 15 pi m^3

Answer:

15 pi m3

Step-by-step explanation:

Answer: -2

Step-by-step explanation:

When x = 1, y = -2.

Hope it helps <3

Answer:

The percentage by which the booster club fell short is 33% as shown on the chart

Step-by-step explanation:

To represent the given data pictorially, a pie chart is suitable

The circumference of the pie chart will represent the amount to be raised by the booster club and a sector of the circle which is two-thirds of the circumference represents the amount raised

Given that the amount raised = 2/3×Goal = $15,000, we have;

We represent the amount raised as a sector of the circle as follows;

Sector angle = 2/3×360° = 240°

Total sector of goal amount = Entire circle = 360°

Amount club fell short = 360° - 240° = 120°

The goal amount = 3/2 × $15,000

Percentage by which the club fell short = 120/360×100 = 1/3×100 = 33.33%

Answer:

The additional information required to prove ΔDEF ~ ΔPQR is the value of the ratio DE/PQ which has to be equal to three-halves for ΔDEF to be similar to ΔPQR

Step-by-step explanation:

Given DF/PR = FE/RQ = 3/2

The Side Side Side,  SSS, similarity theorem states that where there are two triangles that have corresponding sides that are proportional to each other, the two triangles are said to be similar

Given ΔDEF and ΔPQR, have sides DF/PR = FE/RQ, to prove that ΔDEF and ΔPQR, then the additional information required is the ratio of the third sides of the triangles which is DE/PQ.

If DE/PQ = Three-halves, the two triangles ΔDEF and ΔPQR are similar, if not, that is DE/PQ ≠ Three-halves, then the two triangles ΔDEF and ΔPQR are not similar.

Answer:

D: DE/PQ = 3/2

Step-by-step explanation:

Did it on edge 2020

Answer:

A graphing calculator is more accurate than graphing by hand. If the slope and/or y-intercept is a fraction or decimal, it is more difficult to accurately graph by hand.

Step-by-step explanation:

Answer:

WHEN U GRAPH WITH A CALCULATOR  IT IS MUCH MORE ACCURATE

ESPECIALLY IF THERE R FRACTIONS AND DECIMALS AND THE GRAPHING CALCULATOR GOES ON FOREVER WHERE AS THE GRAPHING PAPER  ENDS

Step-by-step explanation:

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

          ✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                         PEACE!