What is the solution to the system of equations below?

y = 1/2x - 4 and y = -2x - 9

1. (-2, -5)
2. (-2, -3)
3. (2, -3)
4. (2, -13)

Answer:

[tex]28\frac{1}{2}\ papers[/tex]

Step-by-step explanation:

step 1

Convert mixed numbers to an improper fractions

[tex]4\frac{1}{2}=\frac{4*2+1}{2}=\frac{9}{2}[/tex]

[tex]6\frac{1}{3}=\frac{6*3+1}{3}=\frac{19}{3}[/tex]

step 2

we know that

A teacher reviews 9/2 papers per hour

using proportion

Find how many papers will the teacher review in 19/3 hours

Let

x-----> the number of papers

[tex](9/2)/1=x/(19/3)[/tex]

[tex]x=(19/3)(9/2)[/tex]

[tex]x=28.5\ papers[/tex]

Convert to mixed numbers

[tex]28.5=28\frac{1}{2}\ papers[/tex]

A teacher that reviews 4.5 papers an hour would be able to review approximately 28 papers in 6-1/3 hours, rounding down to the nearest whole paper.

To solve this math problem, you'll need to multiply the amount of papers that the teacher can review in one hour by the total amount of hours they worked. The teacher reviews 4.5 papers per hour, and they will be working for 6.33 hours (which is the decimal equivalent of 6-1/3 hours). Let's do the math:

4.5 papers/hour * 6.33 hours = 28.485 papers

Therefore, the teacher would be able to review approximately 28 papers in 6-1/3 hours. Please note that the number of papers reviewed has been rounded down in this scenario to remain realistic - a paper can either be reviewed or not reviewed and we cannot count half-reviewed papers.

https://brainly.com/question/5992872

#SPJ11

Answer:

B

Step-by-step explanation:

The recommended sample size n for point estimates is:

n = NX / (N + X - 1)

where N is the population size, and X is defined as:

X = Z² p (1 - p) / E²

where Z is the critical value, p is the sample proportion, and E is the margin of error.

Assume a confidence level of level of 95% and a margin of error of 5%.

α = 0.05, Z(α/2) = 1.96

E = 0.05

Of the 40 units tested, 2 had lifespans less than 26 days.  So the proportion is:

p = 2/40 = 0.05

Therefore:

X = (1.96)² (0.05) (1 - 0.05) / (0.05)²

X = 73

Given N = 2000:

n = (2000) (73) / (2000 + 73 - 1)

n = 70.45

Rounding, the recommended sample size is 70.

Answer:

B

Step-by-step explanation:

Answer:

A. 44°

Step-by-step explanation:

180° (straight line) - 88°

= 92

180° - 92°

= 88°

2y = 88°

y = 44°

Answer:

A 44

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

88 = y+y

88 =2y

Divide by 2

88/2 = 2y/2

44 = y

Answer:

5x^7 + 4x^4  - 2x^2 - 4x  - 10

Step-by-step explanation:

(x^4-9x+5x^7)+(5x-10+3x^4-2x^2) = 4x^4 - 9x + 5x^7  + 5x - 10 - 2x^2

                               = 4x^4 - 9x + 5x^7  + 5x - 10 - 2x^2

                                = 4x^4 - 4x + 5x^7  - 10 - 2x^2

                                = 5x^7 + 4x^4  - 2x^2 - 4x  - 10

Answer: first option.

Step-by-step explanation:

You know that the height of the smaller cylinder is 6 cm and the height of the larger cylinder is 18 cm, then you can find the volume ratio. This  is:

[tex]Volume\ ratio=(\frac{6cm}{18cm})^3\\\\Volume\ ratio=\frac{1}{27}[/tex]

Knowing that the volume of the larger cylinder is 40,635 cubic centimeters, you need to multiply it  by the volume ratio to find the volume of the smaller cylinder.

Therefore:

[tex]V_{smaller}=\frac{1}{27}(40,635\ cm^3)\\\\V_{smaller}=1,505\ cm^3[/tex]

Answer:

Step-by-step explanation:

Before we can determine which measure of central tendency is the best we need to determined whether data set is skewed or not.

We can determine the skewness, if we know at least the median and the mean.

The array of the above data set is,

16,18,28,29,35,36,37,38,40,41,44,66,68,72

The Median of the above array is  

\frac{37 + 38}{2} = \frac{75}{2} = 37.5  

The mean is

\frac{16 + 18 + 28 + 29 + 35 + 36 + 37 + 38 + 40 + 41 + 44 + 66 + 68 + 72}{14} = \frac{532}{14} = 38

Since the mean and the median are not the same, the distribution is skewed.

<b>For a skewed distribution, the best measure of central tendency is the median.</b>

To one decimal place, the median is;

37.5

NB: If the distribution is not skewed then it is normal. In a normal distribution the median is equal to the mean. The mode is considered the best measure of center in this case.

Step-by-step explanation:

The median of a data set is the measure of center that is the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude

Answer:

The answer is [4,3] Hope this helps.

Step-by-step explanation:

The solution to the both system of equations A and B are (3.875, 2.375) for system A and (4.133, 2.289) for system B.

Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.

System of linear equations involve two or more linear equations.

Consider system A.

x + 3y = 11

15x − 3y = 51

Adding both equations,

16x = 62

x = 3.875

3y = 7.125

y = 2.375

Consider system B.

x + 3y = 11

15x = 62 ⇒ x = 4.133

3y = 6.867

y = 2.289

Hence the solutions are (3.875, 2.375) for system A and (4.133, 2.289) for system B.

Learn more about System of Equations here :

https://brainly.com/question/24065247

#SPJ7

Answer:

B + 281d

Step-by-step explanation:

I think that's the answer the "is" is throwing me off "is" is either = or (x)

Hope my answer has helped you and if not i'm sorry.

Answer:

b C = 25m + 75

Step-by-step explanation:

The total cost for m months is the one time fee plus the cost per month times the number of months

C = fee + cost per month * m

C = 75 + 25m

Rearranging the equation

C = 25m + 75

Answer:

Step-by-step explanation:

I wonder if it is the minus that is causing the problem?

Let x = - 5

3*(-5) - 9

-15 - 9

This is a money question. If you are 15 dollars in debt and you spend another 9, where are you? (In the company of the American government. They do this all the time).

- 15 - 9 = - 24

Answer:

2/3

Step-by-step explanation:

Y varies directly as x

Y =kx

Y=6 when x = 72

First find the relationship between y and x.

i.e find the value of k

Substitute the value of x and y

6 = k *72

Make k the subject of the formula

K = 6/72

K= 1/12

:. The rlationship between x and y is

Y = 1/12x

When x is 8

Y = 1/12 * 8

Y = 8/12

Y = 2/3 and that is the answer

Hope it helped you

Answer:

The answer is : 2/3

Step-by-step explanation:

Given is that y varies directly as x.

Means as y increases or decreases, x also increases or decreases.

When y is 6 when x is 72,

So, when x = 8, we have to find y.

We can write the relation as follows:

[tex]\frac{6}{y}= \frac{72}{8}[/tex]

[tex]72y=48[/tex]

[tex]y=\frac{48}{72}[/tex] = [tex]\frac{2}{3}[/tex]

Answer:

y = -5 (x+2)

Step-by-step explanation:

We can use the point slope form of a line

y-y1 = m(x-x1) where (x1,y1) is the point and m is the slope

y-0 = -5(x--2)

y = -5 (x+2)

Answer:

Step-by-step explanation:

[tex]4^x=\left(\dfrac{1}{8}\right)^{x+5}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\4^x=(8^{-1})^{x+5}\\\\(2^2)^x=\bigg((2^3)^{-1}\bigg)^{x+5}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2x}=2^{-3(x+5)}\iff2x=-3(x+5)\qquad\text{use the distributive property}\\\\2x=-3x-15\qquad\text{add}\ 3x\ \text{to both sides}\\\\5x=-15\qquad\text{divide both sides by 5}\\\\x=-3[/tex]

Answer:

B, -3

Step-by-step explanation:

Answer:

4x^4

Hope this helps

For this case we must find an expression equivalent to:

[tex](256x^{16}) ^ {\frac {1} {4}[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

Then, rewriting the expression:

[tex](256 ^ {\frac {1} {4}} * x ^ {\frac {16} {4}}) =[/tex]

We have by definition:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]\sqrt [4] {256} * x ^ 4 =\\\sqrt [4] {4 ^ 4} * x ^ 4 =\\4x ^ 4[/tex]

ANswer:

Option B

Answer:

y=68(1.5)^(x-1)

Step-by-step explanation:

Answer:

The function is:

[tex]y = 68 (1.5) ^ x[/tex]

Step-by-step explanation:

Note that the number of people increases by a factor of 1.5 per hour, and the initial number of people is 68.

So:

 After an hour the number of people is:

[tex]y = 68 (1.5)[/tex]

After two hours the number of people is:

[tex]y = 68 (1.5) (1.5) = 68 (1.5) ^ 2[/tex]

After x hours the number of people is:

[tex]y = 68 (1.5) ^ x[/tex]

Therefore, the exponential growth function that models the number of people y at the fair after x hours is:

[tex]y = 68 (1.5) ^ x[/tex]

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2y=-x+9\\3x-6=-15&\text{add 6 to both sides}\end{array}\right\\\left\{\begin{array}{ccc}2y=-x+9\\3x=-9&\text{divide both sides by 3}\end{array}\right\\\left\{\begin{array}{ccc}2y=-x+9\\x=-3\end{array}\right\qquad\text{put the value of x to the first equation}\\\left\{\begin{array}{ccc}2y=-(-3)+9\\x=-3\end{array}\right\\\left\{\begin{array}{ccc}2y=3+9\\x=-3\end{array}\right\\\left\{\begin{array}{ccc}2y=12&\text{divide both sides by 2}\\x=-3\end{array}\right\\\left\{\begin{array}{ccc}y=6\\x=-3\end{array}\right[/tex]

Answer:

option D) (x,y,z)

Step-by-step explanation:

we know that

The three-dimensional Cartesian coordinate is defined by three axes at right angles to each other, forming a three dimensional space.

The three axes are labeled x ,y and z.

The x-axis is called abscissa

The  y-axis is called ordinate

The z-axis is called applicate

therefore

A point in a three-dimensional Cartesian coordinate is represented by (x,y,z)

Answer:

$12

Step-by-step explanation:

If x is the price that George pays for a student ticket, then:

19 = ⅓ x + 15

To solve for x, first subtract 15 from both sides:

19 - 15 = ⅓ x

4 = ⅓ x

Then multiply both sides by 3:

4 × 3 = x

12 = x

Answer:

1/3x + 15 = 19

Step-by-step explanation:

Well this is a simple equation where you write it out EXCACTLY like the question says, the 1/3 is the 1/3 the price of a student ticket and add the x to represent the unknown amount (student ticket), the 15 represents the plus $15.00 which equals 19

Hope this helps,

(btw dont >EVER TRUST< the -->"TRUSTED ANSWERS"<-- because all it means is that they are expirienced NOT that the answer is right)

Final answer:

The number closest to zero on the number line from the given options is 0.3, making the correct answer C) 0.3.

Explanation:

The question asks which number is closest to zero on the number line from the given options: A) -3/8, B) 3/4, C) 0.3, D) 0.50. To find out which is closest to zero, compare the absolute values of these numbers (since we are interested in the distance from zero, not the direction).

Absolute value of A) -3/8 is 0.375

Absolute value of B) 3/4 is 0.75

Absolute value of C) 0.3 is 0.3

Absolute value of D) 0.50 is 0.5

Comparing these values, 0.3 is the smallest absolute value, which means it is the closest to zero. Therefore, the correct answer is C) 0.3.

Answer:

The value of CD is 2√5

Step-by-step explanation:

* Lets describe the figure to know its name

- ABCD is a quadrilateral

∵ BC parallel to AD

∵ BC = 6 units and AD = 8 units

- The quadrilateral which has two parallel sides not equal in length is a

 trapezoid

∴ ABCD is a trapezoid, where BC and AD are its bases

∵ BA perpendicular to AD

∴ BA is the height of the trapezoid

- The area of the trapezoid = 1/2 (base 1 + base 2) × its height

∵ The bases of the trapezoid are BC and AD

∵ BC = 6 and AD = 8

∵ Its area = 28 units²

∴ 1/2 (6 + 8) × height = 28

∴ 1/2 (14) × height = 28

∴ 7 × height = 28 ⇒ divide both sides by 7

∴ height = 4

∵ The height is BA

∴ BA = 4 unit

- To find the length of CD draw a perpendicular line from C to AD and

 meet it at E

∵ BA and CE are perpendicular to AD

∴ BA // CE

∵ BC // AD

- Perpendicular lines between parallel lines are equal in lengths

∴ BA = CE and BC = AE

∵ BA = 4 and BC = 6

∴ CE = 4 and AE = 6

∵ AD = 8 units

∵ AD = AE + ED

∴ 8 = 6 + ED ⇒ subtract 6 from both sides

∴ ED = 2 units

- In ΔCED

∵ m∠CED = 90°

∴ CD = √[(CE)² + (ED)²] ⇒ Pythagoras theorem

∵ CE = 4 and ED = 2

∴ CD = √[(4)² + (2)²] = √[16 + 4] = √20 = 2√5

* The value of CD is 2√5

Final answer:

The value of the unknown side CD in quadrilateral ABCD can be found using the area of a trapezoid formula and the Pythagorean theorem. Given the area, and the lengths of BC and AD, we calculated that CD equals 8 units.

Explanation:

The student has asked to find the value of CD in a quadrilateral ABCD, where BC is parallel to AD, BA is perpendicular to AD, the area of quadrilateral ABCD is 28 square units, BC is 6 units, and AD is 8 units.

Since BA is perpendicular to AD and BC is parallel to AD, we can determine that ABCD is a trapezoid with AB and CD as the non-parallel sides. The area of a trapezoid is given by the formula Area = ½ × (sum of parallel sides) × height. So we have:

½ × (AD + BC) × height = 28
½ × (8 + 6) × height = 28
½ × 14 × height = 28
7 × height = 28
height = 4 units

Since BA is perpendicular to AD, and given BA is the height of the trapezoid, this means that AB = 4 units. Now, because ABCD has right angles at A and B, triangles ABD and ABC are right triangles and we can use the Pythagorean theorem to calculate CD.

In triangle ABD:

Since CD is the hypotenuse of triangle ABD:

Therefore, the correct answer is CD = 8 units.

22.7

They are opposites because they are both the same distance from 0 and are on different sides of 0 on a number line.

They are also opposites because when either of them is multiplied by -1, you get the other one.

[tex]22.7*-1=-22.7[/tex]

[tex]-22.7*-1=22.7[/tex]

Answer:

22.7 because it's the same number but different

Answer:

f^-1(x) = (x+1)/5

Step-by-step explanation:

f(x)=5x-1

y = 5x-1

Exchange x and y

x = 5y-1

Solve for y

Add 1 to each side

x+1 = 5y-1+1

x+1 = 5y

Divide by 5

(x+1)/5 = 5y/5

(x+1)/5 = y

The inverse is (x+1)/5

f^-1(x) = (x+1)/5

Answer: 60/2

Step-by-step explanation:

When you multiply 60 and 1/2 you get 30 which is the same as 60/2

ANSWER

[tex] \sqrt{60} [/tex]

EXPLANATION

The given exponentiial expression is

[tex] {60}^{ \frac{1}{2} } [/tex]

Recall that

[tex] {a}^{ \frac{1}{n} } = \sqrt[n]{a} [/tex]

A special case of this rule is when n=2.

Then,

[tex] {a}^{ \frac{1}{n} } = \sqrt{a} [/tex]

This implies that

[tex]{60}^{ \frac{1}{2} } = \sqrt{60} [/tex]

The correct answer is B.

Answer:

13

Step-by-step explanation:

(3-2i)(3+2i) = 9  + 6i - 6i - 4i^2

9 - 4i^2

9 + 4 = 13

Answer:

1/25

Step-by-step explanation:

The probability of guessing the first question correct is 1/5

The probability of guessing the second question correct is 1/5

Since they are independent

P(correct, correct) = P(1st correct) * P(2nd correct)

                               = 1/5 * 1/5

                               = 1/25

Answer: Slope = 3

Step-by-step explanation:

On a 2D-Plane, any two lines with the same slope and a different y-intercept will be parallel

Knowing this, any line with the same slope as our given line and a different y-intercept will be parallel to it

Therefore, any line with a slope of 3 and a y-intercept other than 5 will be parallel to y = 3x + 5

The answer you are looking for is a slope of 3.

Parallel lines have the same slope (M value in Y = MX + B), but different y-intercepts (B value in Y = MX + B) For example, y = 3x + 7 would be parallel to the line given above, since they slope is the same, but the y-intercept is different.

I hope this helps!

Answer:

1 : 2

Step-by-step explanation:

Since the quadrilaterals are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{HP}{TP}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

Thus the ratio of perimeters is also 1 : 2

Answer:

1:2.

Step-by-step explanation:

HP and TP are corresponding sides and their lengths are  2 and 4.

Thats a ratio of 1 :2.

The perimeter is also one dimensional so the ratio of the perimeters is also 1:2.

Answer:

Filling in the blanks: (rectangular prism) (cylinder) (rectangular prism)

The cylinder has the greater volume because the cylinder fits within the rectangular prism with extra space between the two figures.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

We can see this by comparing the formulas for the volumes of the two shapes.

The volume V of a rectangular prism with length L, width W, and height H is given by:

V = L x W x H

The volume V of a cylinder with radius r and height H is given by:

V = πr²H

Now,

We are told that the length of each side of the prism base is equal to the diameter of the cylinder.

Since the diameter is twice the radius, this means that the width and length of the prism base are both equal to twice the radius of the cylinder.

So we can write:

L = 2r

W = 2r

Substituting these values into the formula for the volume of the rectangular prism, we get:

V prism = L x W x H

V prism = 2r x 2r x H

V prism = 4r²H

Substituting the radius and height of the cylinder into the formula for its volume, we get:

V cylinder = πr^2H

To compare the volumes,

We can divide the volume of the cylinder by the volume of the prism:

V cylinder / V prism = (πr²H) / (4r²H)

V cylinder / V prism = π/4

π/4 is greater than 1/1,

Thus,

The cylinder has a greater volume.

The cylinder fits within the rectangular prism with extra space between the two figures because the cylinder is inscribed within the prism, meaning that it is enclosed within the prism but does not fill it completely.

Learn more about prism here:

https://brainly.com/question/12649592

#SPJ3

Step-by-step explanation:

A=P(1+R)

A/P=1+R

(A/P)-1=r

(3000000/20000)-1=r

149=r

[tex]\textbf{Answer:}[/tex]

[tex]r\approx 0.13345[/tex]

[tex]\textbf{Step-by-step explanation:}[/tex]

[tex]\text{Your formula is missing something: t}[/tex]

[tex]\text{It should read }A=P(1+r)^t[/tex] [tex]\text{Where A is the final amount, P is the principal, r is rate in decimal, and t is time in years}[/tex]

[tex]\text{Given that A=3000000, P=20000, and t=40, we can subsitute and solve}[/tex]

[tex]A=P(1+r)^t[/tex]

[tex]\text{subsitute}[/tex]

[tex]3000000=20000(1+r)^{40}[/tex][tex]\text{ now solve for r}[/tex]

[tex]\text{Divide both sides by 20000}[/tex]

[tex]150=(1+r)^{40}[/tex]

[tex]\text{Take the 40th root of both sides }(\sqrt[40]{})[/tex]

[tex]\sqrt[40]{150}=1+r[/tex]

[tex]\text{subtract 1 from both sides}[/tex]

[tex]\sqrt[40]{150}-1=r[/tex] [tex]\text{ or in approximate form, }[/tex][/tex]r\approx 0.13345[/tex]