what is the slope of the line that passes through the points (1, −3) and (3, −5)

Answer:

134.38

This value represents 134.38

Step-by-step explanation:

Find the mean.

950+620+545+810+775+1120+905+775=6500

6500/8=812.5

Subtract the mean of numbers.

950-812.5=137.5

812.5-620=192.5

812.5-545=267.5

812.5-810=2.5

812.5-775=37.5

1120-812.5=307.5

905-812.5=92.5

812.5-775=37.5

Find the mean.

137.5+192.5+267.5+2.5+37.5+307.5+92.5+37.5=1075

1075/8≈134.38

This means that 134.38 is $134.38

MAD

To find the MAD of the data, you must first find the mean. To do this, simply add all the numbers up and divide by the number of data values.

950+620+545+810+775+1120+905+775=812.5

So the mean is 812.5 ($812.5).

The final step to finding the MAD is to difference between each data value and the mean.

|950-812.5| + |620-812.5| + |545-812.5| + |810-812.5| + |775-812.5| + |1120-812.5| + |905-812.5| + |775-812.5|

137.5 + 192.5 + 265.5 + 2.5 + 37.5 + 307.5 + 92.5 + 37.5/8

1073/8=9.625

So, 134.125 is the answer.

BUT... the question said round to the nearest cents. So, it's 13413 cents.

Answer:

14

Step-by-step explanation:

Evaluate exponents, followed by brackets, multiplication and addition

Given

3² + (- 2 + 3) × 5

= 9 + 1 × 5 ← exponents and bracket

= 9 + 5 ← multiplication

= 14 ← addition

Answer:

The correct answer is 14.

Step-by-step explanation:

I'll give you an a hint. You'd need to know about the order of operations is parenthesis, exponent, multiply, divide, add, and subtract.

First, do parenthesis.

(-2+3)=1

3²+1*5

Next, exponent.

3²=3*3=9

9+1*5

Then, multiply.

5*1=5

Finally, add.

9+5=14

So, the correct answer is 14.

I hope this helps!

Answer:

[tex]\large\boxed{\dfrac{6}{5x^{10}}}[/tex]

Step-by-step explanation:

[tex]\sqrt{\dfrac{72x^{16}}{50x^{36}}}\qquad\text{simplify}\\\\=\sqrt{\dfrac{36x^{16}}{25x{^{20+16}}}}\qquad\text{use}\ (a^n)(a^m)=a^{n+m}\\\\=\sqrt{\dfrac{36x^{16}}{25x^{20}x^{16}}}\qquad\text{cancel}\ x^{16}\\\\=\sqrt{\dfrac{36}{25x^{20}}}\qquad\text{use}\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\ \text{and}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{\sqrt{36}}{\sqrt{25}\cdot\sqrt{x^{10\cdot2}}}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\dfrac{6}{5\sqrt{(x^{10})^2}}\qquad\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=\dfrac{6}{5x^{10}}[/tex]

Answer:

y = -2x+1

Step-by-step explanation:

We have a point and a slope, so we can use the point slope form of a line

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

y-3 = -2(x--1)

y-3=-2(x+1)

Distribute the 2

y-3 = -2x-2

Add 3 to each side

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

y = -2x+1

This is in slope intercept form

Answer:

The correct answer option is A. Loss of 9 oz.

Step-by-step explanation:

We are given that a cat's weight change -8 oz. while she was sick. It means that the cat lost 8 ounces of weight.

We are to determine whether which of the given answer options show a greater change in weight.

The correct answer for this is: loss of 9 oz which is a greater loss than 8 oz.

Answer:

420

Step-by-step explanation:

Amount in the 45% solution + amount in the 70% solution = amount in the 45% solution

0.15 × 350 + 0.70 × V = 0.45 × (350 + V)

52.5 + 0.70V = 157.5 + 0.45V

0.25V = 105

V = 420

You need 420 mL of the 70% solution.

After setting up and solving a weighted average equation, the result reveals that you would need 1050 mL of the 70% alcohol solution to achieve the desired 45% alcohol solution.

To solve this problem, we can use the concept of weighted averages. The final volume of alcohol in the 45% solution will be the sum of the alcohol in the 15% solution and the 70% solution. Let's denote the volume of the 70% solution we need to add as X ml. So, the equation will be:

0.15 × 350 + 0.70 × X = 0.45 × (350 + X)

Solving this equation will give us the amount of 70% solution needed. After simplifying, you get:

52.5 + 0.7X = 157.5 + 0.45X

Further simplification gives:

0.7X - 0.45X = 157.5 - 52.5

Therefore, X = 1050 ml. So, you will need 1050 ml of the 70% solution.

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Answer:

729

Step-by-step explanation:

1/3^-2×3^-4×(-1)^2

=3^2×3^4/1

=9×81

=729

For this case we have the following expression:

[tex]\frac {1} {3^ {- 2} * x^{ - 4} * y ^ 2}[/tex]

We must evaluate the expression to:

[tex]x = 3\\y = -1[/tex]

So:

[tex]\frac {1} {3^{- 2} * 3^{ - 4} * (- 1) ^ 2} =[/tex]

[tex]\frac {1} {\frac {1} {3 ^ 2} * \frac {1} {3 ^ 4} * 1} =\\\frac {1} {\frac {1} {3 ^ 2} * \frac {1} {3 ^ 4}} =\\\frac {1} {\frac {1} {9} * \frac {1} {81}} =\\\frac {1} {\frac {1} {729}} =\\\frac {729} {1} =\\729[/tex]

Answer:

Option B

Answer:

It can be B or C (B is closer to being correct); neither are worded perfectly correct. Definitely not A or C.

Step-by-step explanation:

I am a math teacher and whoever created this question didn't cover everything.

The answer is all numbers greater than 10, not just rational (irrational should also be included) and not just whole numbers (fractions and decimals should be included).

Answer:

(B)a rational number infinitely close to 10 but greater than 10, and all other rational numbers greater than 10

Step-by-step explanation:

x> 10 means all numbers greater than 10

(A)10 and every whole number greater than 10

False, does not include 10

(B)a rational number infinitely close to 10 but greater than 10, and all other rational numbers greater than 10

True

(C)11 and every whole number greater than 11

False, it only included integers. 10.5 is a solution but not included here

(D)a rational number infinitely close to 10 but greater than 10, and all other whole numbers greater than 10

False, it only included whole numbers. 10.5 is a solution but not included here

The answer should really be real numbers, not rational numbers.  

Irrational numbers can be solutions.  But given the choices given, B is the best solution.

Answer: not a black marble: 4/5

Red marble: 3/10

Step-by-step explanation: Count the number of marbles.

5+2+3=10

The total number of marbles that aren’t black are 8 out of 10. The fraction is 8/10. It can be simplified to 4/5.

The number of red marbles is 3 out of 10. As a fraction, it’s 3/10.

Answer:

$135

Step-by-step explanation:

Givens:

1) Jenny + Dan = $330

2) Jenny = $60 + Dan

Substitute Jenny's value into equation 1

(Dan = D)

$60 + D + D = $330

2D = $270

D = $135

Hope this helps :)

Answer:

P = -2600/3 t + 25600/3

P = -8200/3

Step-by-step explanation:

t is the time in years since 1990, so two points on the line are (5, 4200) and (8, 1600).

Using the points to find the slope:

m = (y₂ − y₁) / (x₂ − x₁)

m = (1600 − 4200) / (8 − 5)

m = -2600/3

Now writing the equation in point-slope form:

P − 4200 = -2600/3 (t − 5)

Converting to slope-intercept form:

P − 4200 = -2600/3 t + 13000/3

P = -2600/3 t + 25600/3

In 2003, t = 13:

P = -2600/3 (13) + 25600/3

P = -8200/3

The linear formula for the moose population is P = -800t + 8200. The moose population predicted by this model for the year 2003 is 2,400.

In this question, we are given that in 1995 the moose population was 4200 and by 1998 it was 1600. This change in population mimics a linear relationship. We are asked to find the formula for this line and then predict the moose population in 2003.

We know that 1995 corresponds to t = 5 (since t is the years since 1990) and 1998 corresponds to t = 8. Therefore we can find the slope of the line (m) as (4200- 1600) / (5 - 8) = -800 per year. Since we know that the line crosses the point (5,4200), we can find the y-intercept, denoted as (b), using the formula y = mx + b.

Substitute m = -800, x = 5, and y = 4200 into the equation and solve for b

4200 = -800 * 5 + b

This simplifies to b= 4200 + 4000 = 8200

Therefore, the formula is P = -800t + 8200

To predict the moose population in 2003, simply substitute t = 13 into the formula (since 2003 is 13 years since 1990). Therefore,

P = -800 * 13 + 8200 = 2400

Therefore, the model predicts that the moose population in 2003 would be 2400.

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Answer:

m=(-6,6)

Step-by-step explanation:

m^2 -36 = 0

Reorder the terms:

-36 + m^2 = 0

Solving for variable 'm'.

 Add '36' to each side of the equation.

-36 + 36 + m^2 = 0 + 36

Combine like terms: -36 + 36 = 0

0 + m^2 = 0 + 36

m^2 = 0 + 36

Combine like terms: 0 + 36 = 36

m^2 = 36

Simplifying

m^2 = 36

Take the square root of each side:

√m^2=+/-√36

m=(+/-)6

m = {-6, 6}

Answer:

(-7,-3)

Step-by-step explanation:

The rule of 90° clockwise rotation is given below:

If a point (x,y) is rotated 90° clockwise, the new point would be (y, -x)

Since the point M is given as (3,-7), the rotated point will be (-7,-3).

Note: you can graph and check also

Answer:

(-7, -3)

Step-by-step explanation:

Answer:

The two numbers are 5 and 10.

Step-by-step explanation:

We need to solve the following system of equations:

We know that:

A + B = 15

A/B = 2

Solving the system of equations we have:

A/B = 2 ⇒ A = 2B

Then:

2B + B = 15 ⇒ 3B = 15 ⇒ B = 5

Then, we need to find A:

A = 10

Answer:

The two numbers are 5 and 10

Step-by-step explanation:

Let x be one number and y be the other number

Their sum is 15

x+y = 15

The quotient is 2

x/y =2

Rewriting this equation by multiplying by y

x/y * y = 2*y

x = 2y

Substitute this into the first equation

2y+ y = 15

Combine like terms

3y = 15

Divide by 3 on each side

3y/3 =15/3

y=5

Now we can find x

x = 2y

x =2(5)

x=10

Answer:

add up the lengths of all the sides of the ceiling,is there a diagram that comes with this or something?

Step-by-step explanation:

Answer: multiply

Step-by-step explanation: you must multiply length x width

Answer:Y=7

Step-by-step explanation:

-8x-3y = -13    (eq 1)

-3x-2y = -11    (eq 2)

First, multiply equation 1 by 2.

-16x-6y = -26

Second, multiply equation 2 by 3.

-9x-6y = -33

Subtract the system of equations:

-16x-6y = -26

-9x-6y = -33

-7x = 7

x = -1

Substitute this value into one of the original equations to solve for y

-3x-2y = -11

-3(-1)-2y = -11

3-2y = -11

-2y = -14

y = 7

Really hope this helps  :)

Hey There!

We have been given:

[tex]8x + 3y = 13 \\ 3x + 2y = 11[/tex]

Find the lcm of 3 and 2 to eliminate one equation:

3 * 2 = 6

2 * 3 = 6

Multiply each equation to get to 6:

[tex]2(8x + 3y = 13)\\ 16x + 6y = 26[/tex]

[tex]3(3x + 2y = 11)\\ 9x+6y=33[/tex]

Eliminate:

[tex]16x + 6y = 26\\ -(9x+6y=33)\\ -9x - 6y=-33[/tex]

Simplify:

[tex]16x + 6y = 26\\ -9x - 6y=-33 \\ 7x = -7[/tex]

Solve for x by dividing 7 in both sides:

[tex]7x = -7\\ x = -1[/tex]

Solve for y by substituting x in any equation with -1:

[tex]8(-1) + 3y = 13[/tex]

Simplify:

[tex]-8 + 3y = 13[/tex]

Add 8 in both sides:

[tex]3y = 21[/tex]

Solve for y by dividing 3 in both sides:

[tex]y = 7[/tex]

The value of x is -1 and the value of y is 7

Our answers:

x = -1

y = 7

For this case we have to:

[tex]x \leq \frac {5} {4}[/tex]: Represents all values less than or equal to[tex]\frac {5} {4}.[/tex]

[tex]x \geq \frac {5} {2}[/tex]: Represents all values greater than or equal to [tex]\frac {5} {2}.[/tex]

As the inequalities include the sign "=", then the borders of the graphs will be closed.

[tex]\frac {5} {4} = 1.25\\\frac {5} {2} = 2.5[/tex]

The word "or" indicates one solution or the other, so the correct option is graph B

ANswer:

Option B

Answer:

SECOND graph.

Step-by-step explanation:

Given compound inequality,

[tex]x \leq \frac{5}{4}\text{ or }x \geq \frac{5}{2}[/tex]

[tex]\because \frac{5}{4}=1.25\text{ or }\frac{5}{2}=2.5[/tex]

[tex]\implies x \leq 1.25\text{ or }x\geq 2.5[/tex]

If x ≥ 1.25

In the number line closed circle on 1.25 and shaded left side from 1.25,

If x ≤ 2.5

In the number line closed circle on 2.5 and shaded right side from 2.5

Hence, SECOND option is correct.

Answer:

{-0.36, 8.36) to the nearest hundredth.

Step-by-step explanation:

x^2 - 8x = 3

(x - 4)^2 - 16 = 3

(x - 4)^2 = 19

Taking square roots:

x - 4 = +/- √19

x =  4 +/- √19

x = {-0.36, 8.36} to nearest 1/100.

For this case we have the following expression:

[tex]x ^ 2-8x = 3[/tex]

We must complete squares.

So:

We divide the middle term between two and we square it:

[tex](\frac {-8} {2}) ^ 2[/tex], then:

[tex]x ^ 2-8x + (\frac {-8} {2}) ^ 2 = 3 + (\frac {-8} {2}) ^ 2\\x ^ 2-8x + (- 4) ^ 2 = 3 + 16[/tex]

We have to, by definition:

[tex](a-b) ^ 2 = a ^ 2-2ab + b ^ 2[/tex]

Then, rewriting:

([tex](x-4) ^ 2 = 19[/tex]

To find the roots, we apply square root on both sides:

[tex]x-4 = \sqrt {19}[/tex]

We have two solutions:

[tex]x_ {1} = \sqrt {19} +4\\x_ {2} = - \sqrt {19} +4[/tex]

Answer:

([tex](x-4) ^ 2 = 19\\x_ {1} = \sqrt {19} +4\\x_ {2} = - \sqrt {19} +4[/tex]

Answer:

[tex]\large\boxed{234\,\text{students}}[/tex]

Step-by-step explanation:

In this question, we're trying to find how many students are going to the homecoming dance.

To find the answer, we need to use some information that was provided to us from the question.

Important information:

With the information above, we can solve the question.

To make this simple, we're going to need to figure out how much of 325 is 72%, due to the fact that we need to find the 72% of students that are going to the dance (out of 325 students).

To do this, we would multiply 325 by 0.72

[tex]325*0.72=234[/tex]

When you multiply, you should get 234.

This means that 234 students from the school are going to the dance.

Approximately 234 out of 325 students at Wilson High School, which constitutes about 72% of the whole body, are attending the homecoming dance.

The subject of this question is mathematics, specifically a practical application of percentage calculations. In this scenario, we need to determine the number of students from Wilson High School attending the homecoming dance if 72% of the total student body, which comprises 325 students, is attending.

To solve this, we multiply the total number of students (325) by the percentage of students attending the dance in decimal form (0.72). So, 325 * 0.72 will give us the number of students attending the dance.

After calculating, we find that 234 (rounded to the nearest whole number) students are planning to attend the homecoming dance at Wilson High School.

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Answer:

[tex]f(a)=1+5a^2[/tex]

[tex]f(a+h)=1+5a^2+10ah+5h^2[/tex]

[tex]\frac{f(a+h)-f(a)}{h}=10a+5h[/tex]

Step-by-step explanation:

We are given [tex]f(x)=1+5x^2[/tex].

Find [tex]f(a)[/tex].  All this means is replace [tex]x[/tex] in [tex]f(x)=1+5x^2[/tex] with [tex]a[/tex].

[tex]f(x)=1+5x^2[/tex]

[tex]f(a)=1+5a^2[/tex]

Find [tex]f(a+h)[/tex]. All this means is replace [tex](a+h)[/tex] in [tex]f(x)=1+5x^2[/tex] with [tex](a+h)[/tex].

[tex]f(x)=1+5x^2[/tex]

[tex]f(a+h)=1+5(a+h)^2[/tex]

[tex]f(a+h)=1+5(a+h)(a+h)[/tex]

[tex]f(a+h)=1+5(a^2+2ah+h^2)[/tex]

[tex]f(a+h)=1+5a^2+10ah+5h^2[/tex]

Find [tex]\frac{f(a+h)-f(a)}{h}[/tex]. So we got to put some parts together; the parts above:

[tex]\frac{f(a+h)-f(a)}{h}[/tex]

[tex]\frac{(1+5a^2+10ah+5h^2)-(1+5a^2)}{h}[/tex]

Now in the first ( ) I see 1+5a^2 and in the second ( ) I see 1+5a^2, so this means you have (1+5a^2)-(1+5a^2) which equals 0.

[tex]\frac{10ah+5h^2}{h}[/tex]

Now assuming h is not 0. we can divide top and bottom by h.

[tex]\frac{10a+5h}{1}[/tex]

[tex]10a+5h[/tex]

To calculate the values for the quadratic function f(x) = 1 + 5x^2, substitute the necessary values for x. The difference quotient involves a simplification process of the terms after substitution.

The problem is to evaluate the function f(x) = 1 + 5x^2 at a given value a and at a + h, and then to find the difference quotient which is part of the process to find the derivative of the function. First, we calculate f(a), then f(a + h), and lastly the difference quotient f(a + h) - f(a) / h.

To get f(a), we substitute x with a in the function, so we get:

f(a) = 1 + 5a^2

For f(a + h), we substitute x with (a + h):

f(a + h) = 1 + 5(a + h)^2

Now to find the difference quotient (f(a + h) - f(a)) / h:

(f(a + h) - f(a)) / h = (1 + 5(a + h)^2 - (1 + 5a^2)) / h

We can simplify this further by expanding and combining like terms, eventually canceling out the h in the denominator. However, without further expansion and simplification, the expression is already accurate.

Answer:

D. (1, 9)

Step-by-step explanation:

Plug in each ordered pair into both inequalities. If both inequalities are satisfied, then the ordered pair is a solution.

The only ordered pair that works is (1, 9).

Answer:

P=110in

Step-by-step explanation:let me know if it's correct i'm not 100% sure

Answer:

110 inches

Step-by-step explanation:

The perimeter is basically the sum of all sides

In this case, it will be

25+25=50 for 2 opposite sides

30+30= 60 for 2 other opposite sides

hence 50+60= 110 inches

Answer:

38

Step-by-step explanation:

less than 45

Answer:38

Step-by-step explanation:

Answer:

It a delta notation that change in y over change in x

Answer:

C

Step-by-step explanation:

Edge 2021

Answer:

There are several ways to graph a continuous function. I advise you to graph several points that belongs to the function and then join the points.

If the function is linear, two points will be enough to build the graph. If we have functions of higher degree, is better to plot some points, observe the pattern and then join the points.

If the function is extremly difficult to graph by hand, the help of a graphing calculator may be needed.

To graph a continuous function, identify the independent and dependent variables, ensure the values on axes are evenly spaced, plot values as coordinates, and draw a smooth curve connecting the points without lifting the pen. The area under the graph is significant in calculus for representing continuous change, and for continuous probability distributions, it defines the probability as the area under the curve.

To graph a continuous function, first identify your independent and dependent variables. The independent variable is typically placed on the X-axis, while the dependent variable goes on the Y-axis. Ensure the scales for both axes are evenly spaced to accurately represent the continuous values. After setting up the axes, plot the pairs of values that the function defines as x and y coordinates. For a continuous function, you should be able to draw the curve connecting these points without lifting your pen off the paper.

In the context of calculus, the area under the graph represents the aggregation of continuous change over an interval, which differs from discrete sums used for step changes. This is critical when working with functions to determine areas, volumes, or growth over an interval. As such, if you are graphing a function like f(x) = x², you would plot points for x values from the interval and then draw a smooth curve through those points to represent the function continuously.

When considering continuous probability distributions, the graph will depict a curve known as the probability density function (pdf). Probability is calculated as the area under the curve, emphasizing the importance of a continuous, unbroken line in representing these types of distributions.

Answer:

Step-by-step explanation:

y = (x^2 + 4x)      + 2

Take 1/2 of the linear term 4/2 = 2 and square that result. 2^2 = 4.

Put it after 4x

y = (x^2 + 4x + 4)   +2  Subtract what you put inside the brackets on the outside.

y = (x^2 + 4x + 4) + 2 - 4      Combine the right.

y = (x^2 + 4x + 4) - 2            Express the brackets as a square.

y = (x + 2)^2 - 2

That's your answer

a = 1

h = 2

k = -2

Answer:

(x + 2)2 − 2

Step-by-step explanation:

Just took the test and got it right

Answer:

Vertify is an identity

Sin2x=2cotx(sin^2x)  

starting from the right-hand side

2cotx(sin^2x)

=2(cosx/sinx)(sin^2x)

=2(cosx/sinx)(sin^2x)

=2sinxcosx=sin2x

ans:right-hand side=left-hand side

Step-by-step explanation:

Step-by-step explanation:

sin^2x = 2cotx sin^2x

Rewrite right side as fractions:

sin^2x = [tex]\frac{2}{1}[/tex] * [tex]\frac{cosx}{sinx}[/tex] * [tex]\frac{(sinx)(sinx)}{1}[/tex]

Multiply together [tex]\frac{cosx}{sinx}[/tex] and [tex]\frac{(sinx)(sinx)}{1}[/tex] :

sin^2x = [tex]\frac{2}{1}[/tex] * [tex]\frac{(cosx)(sinx)(sinx)}{sinx}[/tex]

Cancel out sinx on top and bottom:

sin^2x = [tex]\frac{2}{1}[/tex] * [tex]\frac{(sinx)(cosx)}{1}[/tex]

Multiply together 2 and (sinx)(cosx):

sin^2x = 2sinxcosx

Substitute sin^2x in for 2sinxcosx:

sin^2x = sin^2x

Answer:

9.093

Step-by-step explanation:

Of means multiply

.7 * 12.99

9.093

Answer:

9,093

Step-by-step explanation:

Yes. You take 70% of 12,99 [multiply].

I am joyous to assist you anytime.

Answer:

u bought 4 9-volt batteries and

the cost of the 3 AA batteries bought is $4.83

To find out how many 9-volt batteries were bought, you first need to subtract the total cost of AA batteries ($4.83) from the total bill ($14.39) to get the total spent on 9-volt batteries. Then, divide this total by the price of each 9-volt battery ($2.39). The result is 4, so you bought 4 9-volt batteries.

To answer this question, let's first determine how much the total purchase of the AA batteries was. Since AA batteries cost $1.61 each and you bought 3, the total cost for the AA batteries is 3 * $1.61 = $4.83.

Now we need to figure out how much was spent on 9-volt batteries. Subtract the cost of the AA batteries from the total bill: $14.39 - $4.83 = $9.56. This is the total cost of the 9-volt batteries.

The price of each 9-volt battery is $2.39, so to find out how many batteries were bought we divide the total cost of 9-volt batteries by the price of each battery: $9.56 / $2.39 ≈ 4. Therefore, you bought 4 9-volt batteries.

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