The polynomial 6x2 + x − 15 has a factor of 2x − 3. What is the other factor?

3x − 5
3x + 5
4x − 5
4x + 5

Answers

Answer 1

Answer:

[tex](3x+5)[/tex]

Step-by-step explanation:

The given polynomial expression is:[tex]6x^2+x-15[/tex]

We compare to [tex]ax^2+bx+c[/tex] and have a=6,b=1,c=-15

The product [tex]ac=6\times -15=-90[/tex]

Two factors of -90 that sums to 1 are -9 and 10

We split the middle term to get:

[tex]6x^2+10x-9x-15[/tex]

[tex]2x(3x+5)-3(3x+5)[/tex]

[tex](3x+5)(2x-3)[/tex]

Therefore the other factor is:

[tex](3x+5)[/tex]

Answer 2

Answer: B

Step-by-step explanation:


Related Questions

In what form is the following linear equation written?
y=9x + 2

A. Standard
B. Rise-run
C. Point-slope
D. Slope-intercept

Answers

Answer:

D

Step-by-step explanation:

ax+by=c is standard form

point slope form is y-y1=m(x-x1)

slope-intercept form is y=mx+b

rise-run is not a form for a linear equation

rise/run equals slope though

So anyways y=9x+2 is comparable to the form y=mx+b

So it is in slope-intercept form

Answer:slope-intercept

Step-by-step explanation:

In general, how does the growth of y = 3x compare to the growth of y = 3x?

Answers

Final answer:

The growth of y = 3x is identical to itself as it's the same function. The growth in y = 3x represents consistent linear growth, with a steady increase of the dependent variable as the independent variable increases. In an exponential function, the growth rate increases over time, unlike the consistent slope of a linear function.

Explanation:

The question seems to contain a typo and asks how the growth of y = 3x compares to the growth of itself, y = 3x. Since this is the same function, their growth rates are identical. To provide a meaningful comparison, let's consider an inverse relationship such as y = k/x versus an exponential relationship such as y = 3x. In the case of the inverse relationship, as x increases, y decreases; the growth rate is negative. In contrast, for the exponential function y = 3x, as the independent variable x increases, the dependent variable y increases exponentially, and the rate at which y grows also increases over time. For example, if x represents time and y represents a population, in exponential growth like that of bacteria under ideal conditions, the population increases significantly with each generation.

Graphs are an essential tool in displaying data and unveiling patterns. In a graph of y = 3x, also referred to as a line graph, you would find that the slope, which describes the growth rate, is consistent along the entire line. Here, the slope of the line is 3, indicating a consistent growth rate, where y increases by 3 units for every 1 unit increase in x. This consistent slope is representative of linear growth, differing from exponential growth where the growth rate increases as the value rises.

Final answer:

The original question likely contains a typo, comparing y = 3x to itself. Assuming the comparison was intended to be between a linear and an exponential function, a linear growth rate is constant as seen in y = 3x, whereas an exponential growth rate increases over time and is proportional to the value of the variable, as would be seen in y = [tex]3^x.[/tex]

Explanation:

The question seems to have a typo since it compares y = 3x to the same expression y = 3x. Assuming the comparison should be between two different types of functions, such as linear and exponential, we can provide a general explanation of how growth rates differ between linear and exponential functions.

For a linear function like y = 3x, the growth is consistent. That means for every unit increase in x, y increases by 3 units. This represents a constant rate of change. In contrast, with an exponential function, such as y =[tex]3^x[/tex], the rate of growth is proportional to the current value. In other words, as x increases, the value of y grows at an ever-increasing rate, which is characteristic of exponential growth.

A good example is in the growth of bacteria which can reproduce at an exponential rate, leading to a much faster increase compared to linear growth, as more bacteria contribute to the population each generation. Similarly, economies can grow exponentially, with the growth applied to an also growing base value, resulting in a curve that steepens over time.

Which of the following is not a solution to the system of linear equations below?
5y = 3x+15
6x = 10y– 30
A. (5,6)
B. (–15, 12)
C. (0,3)
D. (-10,-3)

Answers

Answer:

B. (-15, 12)

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}5y=3x+15&\text{subtract 3x from both sides}\\6x=10y-30&\text{subtract 10y from both sides}\end{array}\right\\\left\{\begin{array}{ccc}-3x+5y=15\\6x-10y=-30&\text{divide both sides by 2}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-3x+5y=15\\3x-5y=-15\end{array}\right}\\.\qquad0=0\qquad\bold{TRUE}\\\\\bold{Infinitely\ many\ solutions}\\\\5y=3x+15\qquad\text{divide both sides by 5}\\\\y=\dfrac{3}{5}x+3\qquad(*)\\\\\text{Put the coordinates of the points to the equation (*)}[/tex]

[tex]A.\ (5,\ 6)\\\\6=\dfrac{3}{5}(5)+3\\\\6=3+3\\\\6=6\qquad\bold{CORRECT}\\\\B.\ (-15,\ 12)\\\\12=\dfrac{3}{5}(-15)+3\\\\12=(3)(-3)+3\\\\12=-9+3\\\\12=-6\qquad\bold{FALSE}\\\\C.\ (0,\ 3)\\\\3=\dfrac{3}{5}(0)+3\\\\3=0+3\\\\3=3\qquad\bold{CORRECT}\\\\D.\ (-10,\ -3)\\\\-3=\dfrac{3}{5}(-10)+3\\\\-3=(3)(-2)+3\\\\-3=-6+3\\\\-3=-3\qquad\bold{CORRECT}[/tex]

What are the solutions of this system of equations?
The first three steps in determining the solution set of the
system of equations algebraically are shown.
y = x2 - x-3
y=-3x + 5
(-2, -1) and (4, 17)
(-2, 11) and (4, -7)
(2, -1) and (-4, 17)
(2, 11) and (-4,-7)
Step
1
2
Equation
x– X-3 = -3x +5
0 = x² + 2x - 8
0 = (x-2)(x+4)
3

Answers

Answer:

Option C is correct.

Step-by-step explanation:

y = x^2-x-3     eq(1)

y = -3x + 5      eq(2)

We can solve by substituting the value of y in eq(2) in the eq(1)

-3x+5 = x^2-x-3

x^2-x+3x-3-5=0

x^2+2x-8=0

Now factorizing the above equation

x^2+4x-2x-8=0

x(x+4)-2(x+4)=0

(x-2)(x+4)=0

(x-2)=0 and (x+4)=0

x=2 and x=-4

Now finding the value of y by placing value of x in the above eq(2)

put x =2

y = -3x + 5

y = -3(2) + 5

y = -6+5

y = -1

Now, put x = -4

y = -3x + 5

y = -3(-4) + 5

y = 12+5

y =17

so, when x=2, y =-1 and x=-4 y=17

(2,-1) and (-4,17) is the solution.

So, Option C is correct.

Answer: Third Option

(2, -1) and (-4, 17)

Step-by-step explanation:

We have the following system of equations:

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

[tex]y=-3x + 5[/tex]

We have the first three steps to solve the system.

[tex]x^2- x-3 = -3x +5[/tex]   equal both equations

[tex]0 = x^2 + 2x - 8[/tex]      Simplify and equalize to zero

[tex]0 = (x-2)(x+4)[/tex]     Factorize

Then note that the equation is equal to zero when [tex]x = 2[/tex] or [tex]x = -4[/tex]

Now substitute the values of x in either of the two situations to obtain the value of the variable y.

[tex]y=-3(2) + 5[/tex]

[tex]y=-6 + 5[/tex]

[tex]y=-1[/tex]

First solution: (2, -1)

[tex]y=-3(-4) + 5[/tex]

[tex]y=12 + 5[/tex]

[tex]y=17[/tex]

Second solution: (-4, 17)

The answer is the third option

2. At a temperature of 20°C the common amoeba reproduces by
splitting in half every 24 hours. If we start with a single amoeba
how many will there be after (a) 8 days, (b) 16 days?​

Answers

Step-by-step explanation:

Each day it splits in half. You wouldn't multiply by 2, for you would have to go, day 1 = 1 amoeba

day 2 = 3 amoebas (because you have the previous amoeba plus the starting one)

You would continue like this until you get day 8 and 16.

Final answer:

Amoebas reproduce by splitting in half every 24 hours. To calculate the number of amoebas after a certain period of time, use the exponential growth formula. After 8 days, there will be 256 amoebas, and after 16 days, there will be 65,536 amoebas.

Explanation:

To determine the number of amoebas after a certain period of time, we need to use the exponential growth formula. In this case, amoebas reproduce by splitting in half every 24 hours. So, if we start with one amoeba, after 24 hours, there will be two amoebae (2¹). After 48 hours, there will be four amoebas (2²) and so on.

For (a) 8 days, we need to calculate the number of 24-hour periods in 8 days. There are 8 days x 24 hours/day = 192 hours. So, we divide 192 by 24 to get the number of 24-hour periods, which is 8. Therefore, after 8 days, there will be 2⁸ = 256 amoebas.

For (b) 16 days, we repeat the same calculations. There are 16 days x 24 hours/day = 384 hours. Dividing 384 by 24 gives us 16 24-hour periods. Therefore, after 16 days, there will be 2¹⁶ = 65,536 amoebas.

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can someone help me please

Answers

For this case we must indicate an expression equivalent to:

[tex]x + 2 + [4x- \frac {x ^ 2 + 6x + 8} {x + 4}][/tex]

If we factor the quadratic expression, we must find two numbers that when multiplied give as result 8, and when summed give as result 6. These numbers are 4 and 2. Then:

[tex]x ^ 2 + 6x + 8 = (x + 2) (x + 4)[/tex]

Rewriting the expression:

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

Simplifying common terms we have:

[tex]x + 2 + [4x- (x + 2)] =[/tex]

Taking into account that:

[tex]- * + = -\\x + 2 + 4x-x-2 =\\x-x + 2-2 + 4x =\\4x[/tex]

ANswer:

4x

What is the following difference?

Answers

Answer:

29 square root 5.

Step-by-step explanation:

You must simplify the surds to subtract them.

ANSWER

[tex]29 \sqrt{5} [/tex]

EXPLANATION

The given radical expression is

[tex]11 \sqrt{45} - 4 \sqrt{5} [/tex]

We remove the perfect squares to get:

[tex]11 \sqrt{9 \times 5} - 4 \sqrt{5} [/tex]

Split the square root sign to obtain:

[tex]11 \sqrt{9} \times \sqrt{5} - 4 \sqrt{5} [/tex]

We simplify further to get:

[tex]11 \times 3 \sqrt{5} - 4 \sqrt{5} [/tex]

[tex]33 \sqrt{5} - 4 \sqrt{5}[/tex]

This simplifies to

[tex]29 \sqrt{5} [/tex]

You have 15 milliliters of a drink that contains 15% milk. How many millimeters of a drink containing 63% milk needs to be added in order to have a final drink that is 45% milk?

Answers

Answer:

4 ml of the 63% milk drink

Step-by-step explanation:

Multiplying 15 ml by 0.15 results in 2.25 ml, the amount of whole milk in the drink.  Let m represent the number of ml of a drink that is 63% milk.

The final amount of milk drink that is to be 45% milk will be 15 ml + m, and the amount of whole milk contained in this drink will be 0.45(15 + m).

Then:

0.15(15 ml) + 0.63(m) = 0.45(15 + m), where m is to be in milliliters.

2.25 + 0.63m = 6.75 + 0.45m

First:  consolidate the m terms on the left.  0.63m less 0.45m yields 18 m; then we have:

2.25 + 18m = 6.75, or

18 m = 4.50, or m = 4 ml.

In conclusion:  adding 4 ml of that 63% milk drink to the initial 15 ml of 15% milk will result in (15 ml + 4 ml) of a 45% milk drink.            

Which of the following equations represents a line that is perpendicular to
y = -2x+4 and passes through the point, (4, 2)?

Answers

Answer:

[tex]\large\boxed{y=\dfrac{1}{2}x}[/tex]

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================[/tex]

[tex]\text{We have the equation:}\ y=-2x+4\to m_1=-2.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-2}=\dfrac{1}{2}.\\\\\text{We have the equation:}\ y=\dfrac{1}{2}x+b.\\\\\text{Put the coordinate of the point (4, 2) to the equation:}\\\\2=\dfrac{1}{2}(4)+b\\\\2=2+b\qquad\text{subtract 2 from both sides}\\\\0=b\to b=0.\\\\\text{Finally:}\\\\y=\dfrac{1}{2}x[/tex]

Which function has an inverse that is also a function?
{(-1, -2), (0, 4), (1,3), (5, 14), (7,4)}
{(-1,2), (0, 4), (1,5), (5, 4), (7, 2)}
{(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}
{(-1, 4), (0, 4), (1, 2), (5,3), (7, 1);

Answers

The third one is correct. A function does not repeat x values. So if it asks the inverse you would have to see if the y values repeat. The third choice is the only one that has non repeating y values.
Final answer:

A function has an inverse that is also a function if each element of the function's range corresponds to exactly one element of the function's domain, a concept known as the horizontal line test. In the given options, the second function (with points {(-1,2), (0, 4), (1,5), (5, 4), (7, 2)}) meets this criterion.

Explanation:

In mathematics, a function has an inverse that is also a function if each element of the function's range corresponds to exactly one element of the function's domain. This concept is also known as the horizontal line test. If any horizontal line intersects the graph of the function exactly once, then the function has an inverse that is also a function.

In this question, you are provided with four sets of points representing four possible functions. Upon examination, you can observe that the second function, represented by points {(-1,2), (0, 4), (1,5), (5, 4), (7, 2)}, meets the criteria of the horizontal line test. Each y-value in this function is unique, meaning that each element of the range corresponds to exactly one element of the domain, making its inverse a function as well.

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Evaluate: 6 x (-2) + 1 - 3

Answers

Answer:

-14

Step-by-step explanation:

Follow PEMDAS, then the left -> right rule.

PEMDAS =

Parenthesis

Exponent (& roots)

Multiplication

Division

Addition

Subtraction

First, multiply 6 with -2:

6 x -2 = -12

Next, add 1, then subtract 3.

-12 + 1 = -11

-11 - 3 = -14

-14 is your answer.

~

Answer:

-14

Step-by-step explanation:

Order of operations

PEMDAS

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

Do parenthesis first.

6*(-2)=-12

-12+1-3

Add and subtract the numbers from left to right to find the answer.

-12+1-3

-12+1=-11

-11-3=-14

-14 is the correct answer.

I hope this helps you, and have a wonderful day!

What is the greatest common factor of 37 and 88

Answers

Answer:

The Greatest Common factor is 1.

Step-by-step explanation:

You can't reduce the numbers anymore.

The greatest common factor of 37 and 88 is 1 .

What is greatest common factor ?

The greatest common factor of two or more integers, which are not all zero, is the largest positive integer that equally divides each of the integers. The greatest common factor of two numbers say x and y is represented as gcf(x,y) .

How to calculate the greatest common factor of the two numbers ?

The two numbers given are 37 and 88 .

There is no common divisors of 37 and 88 except 1 .

Thus the greatest common factor, of numbers -

gcf(37,88) = 1

Therefore, the greatest common factor of 37 and 88 is 1 .

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What is the measure of angle AFE? 79 81 91 99

Answers

Answer:

AFE = 99°

Step-by-step explanation:

Correct on E2020

Answer:  [tex]99^{\circ}[/tex]

Step-by-step explanation:

In the given picture , we have a hexagon having all its exterior angles.

We know that the sum of all exterior angles is [tex]360^{\circ}[/tex].

Let x be measure of [tex]\angle{AFE}[/tex]

Then , the exterior angle to  [tex]\angle{AFE}=180^{\circ}-x[/tex]

Then According to the given figure , we have

[tex]62^{\circ}+44^{\circ}+70^{\circ}+60^{\circ}+43^{\circ}+180^{\circ}-x=360^{\circ}\\\\\Rightarrow\ 459^{\circ}-x=360^{\circ}\\\\\Rightarrow\ x=459^{\circ}-360^{\circ}\\\\\Rightarrow\ x=99^{\circ}[/tex]

Hence, the measure of [tex]\angle{AFE}=99^{\circ}[/tex]

6. When solving an equation like 2x + 10 = 2(x + 5), and, when simplified, you get x = x, 10 = 10, or 0 = 0, what is the solution for X
no solution
any real number
10
zero

HELP PLS THANK U

Answers

Answer:

any real number

Step-by-step explanation:

Answer when simplified gives 0 = 0

This indicates that any real value of x is a solution.

Usually because the equations on both sides are equal.

That is 2x + 10 = 2x + 10 leading to 0 = 0

Nancy sold cosmetics products on a commission if her total sale for the month were 2000 and her rate of commission was 7.5% what was the amount of her commission

Answers

Answer:

The amount of her commission= 150

Step-by-step explanation:

Sale price = 2000

Rate of commission = 7.5%

Amount of commission =?

Formula:

Commission_amount = sale price * commission_percentage / 100

Now put the values in the formula.

Commission_amount=2000*7.5/100

Commission_amount=150.

Thus the amount of her commission is 150....

×=25 but how to get it?​

Answers

The angle at B is 1/2 the angle at O

Angle B = 54

B +C = 54 + 29 = 83

Angle A + B + C = O

A + 54 + 29 = 108

A = 108 - 83

A = 25

X = 25

Which statement best explains ?

Answers

A is the correct answer. Hope this helps. I need brainliest so if you can I really appreciate it!

Need help don’t understand

Answers

Answer:

2 real solutions

Step-by-step explanation:

To determine the nature of the solutions use the discriminant

Δ = b² - 4ac

• If b² - 4ac > 0 then 2 real solutions

• If b² - 4ac = 0 the 2 real and equal solutions

• If b² - 4ac < 0 then no real solutions

Given

x² + 9x + 20 = 0 ← in standard form

with a = 1, b = 9, c = 20, then

b² - 4ac

= 9² - (4 × 1 × 20 ) = 81 - 80 = 1

Since b² - 4ac > 0 then there are 2 real solutions

A 34-m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 37m. Find the length of the shadow. If necessary, round your answer to the nearest tenth.

Answers

Answer:  14.6

Step-by-step explanation:

Draw a right triangle such that the building is perpendicular to the ground (which is where the shadow is cast).

Use Pythagorean Theorem to find the length of the shadow (x):

x² + 34² = 37²

x²          = 37² - 34²

x²          = 213

√x²       = √213

x          = 14.59

Sophie purchased 8 candles at a total cost of $32. The red candles cost $3 each and the silver candles cost $7 each. The equations and graph below can be used to determine the number of each type of candle Sophie purchased, where x represents the number of red candles and y represents the number of silver candles.

A. 7 red candles, 1 silver candle

B. 6 red candles, 2 silver candles

C. 2 red candles, 6 silver candles

D. 3 red candles, 5 silver candles

Answers

Answer:

A. 7 red candles, 1 silver candle

Step-by-step explanation:

6 red candles * $3 each = $18

2 silver candles * $7 each = $14

$18 + $14 = $32 (the total cost)

Answer:

B. 6 red candles, 2 silver candle

Step-by-step explanation:

Tomas is making trail mix using granola and walnuts. He can spend a total of $12 on the ingredients. He buys 3 pounds of granola that costs $2.00 per pound. The walnuts cost $6 per pound. He uses the equation to represent the total cost, where x represents the number of pounds of granola and y represents the number of pounds of walnuts. He solves the equation for y, the number of pounds of walnuts he can buy.

Answer- B Tomas added 6 to both sides of the equation instead of subtracting 6.
just took the test

Answers

Final answer:

Tomas should subtract 2x from both sides of the equation, not add 6.

Explanation:

In the given question, Tomas is buying granola and walnuts and he can spend a total of $12 on the ingredients.

He buys 3 pounds of granola that costs $2.00 per pound, and the walnuts cost $6 per pound.

The equation he uses to represent the total cost is: y = 12 - 2x, where x represents the number of pounds of granola and y represents the number of pounds of walnuts.

To solve the equation for y, Tomas should subtract 2x from both sides, not add.

This will give the correct equation for the number of pounds of walnuts he can buy.

Therefore, the correct equation is: y = 12 - 2x.

Which of the following is an even function?
f(x) = |x|
f(x) = x3 – 1
f(x) = –3x

Answers

Answer:

f(x) = |x|

Step-by-step explanation:

Only f(x) = |x| is an even function.  If you evaluate this function at x = 3, for example, the result is 3; if at x = -3, the result is still 3.  That's a hallmark of even functions.

Answer:

f(x) = |x|

Step-by-step explanation:

If we keep -x in place of x and it does not effect the given function, then it is even function. i.e. f(-x) = f(x).

and, If we put -x in place of x then the resultant function will get negative of the first function, then it is odd function. i.e. f(-x) = -f(x).

1. f(x) = |x|

Put x = -x ,then

f(-x) = |-x| = |x| = f(x)

Hence, f(x) is even function.

2.f(x) = x³ - 1

Put x = -x, then

f(-x) = (-x)³ - 1

      = -x³ - 1 = -f(x)

Hence, this function is odd.

3. f(x) = -3x

Put x = -x

then, f(-x) = -3(-x)

                = 3x = -f(x)

Hence, the given function is odd function.

Thus, only f(x) = |x| is even function.

Find the value of the function sin
7pi/2

Answers

Answer:

The answer is D: -1.00

Step-by-step explanation:

I just took the test on edg 2020 and got it correct

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The required value of the given trigonometric ratio is - 1.

Hence option D is correct.

Use the concept of trigonometric ratio defined as:

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain all trigonometric functions' values.

The trigonometric ratios of an acute angle supplied are the ratios of the sides of a right-angled triangle with respect to that angle.

The given trigonometric ratio is,

[tex]\text{sin}(\dfrac{7\pi}{2})[/tex]

Since we can write the expression of radian as,

[tex]\dfrac{7\pi}{2} = 3\pi + \dfrac{\pi}{2}[/tex]

Then,

[tex]\text{sin}(\dfrac{7\pi}{2}) = \text{sin}(3\pi + \dfrac{\pi}{2})[/tex]

Since we know that,

sin(3π + θ) = -sinθ

Therefore,

[tex]\text{sin}(3\pi + \dfrac{\pi}{2}) = -\text{sin}(\dfrac{\pi}{2})[/tex]

Ans we also know sin(π/2) = 1

So,

[tex]\text{sin}(\dfrac{7\pi}{2}) = -1.00[/tex]

Hence, the required value of the given trigonometric ratio is - 1 which is option D.

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What value of x is in the solution set of 3(x – 4) = 5x + 2?
-10

Answers

Answer:

x = - 7

Step-by-step explanation:

Given

3(x - 4) = 5x + 2 ← distribute left side

3x - 12 = 5x + 2 ( subtract 5x from both sides )

- 2x - 12 = 2 ( add 12 to both sides )

- 2x = 14 ( divide both sides by - 2 )

x = - 7

the matrix below represents the distance in miles between three cities. A row label represents the city traveled from. A column label represents a city traveled to. what is the round trip distance in miles from city 1 to city 3

Answers

Answer:

The round trip distance in miles from city 1 to city 3 is 15. Therefore the correct option is 1.

Step-by-step explanation:

It is given that the matrix below represents the distance in miles between three cities. A row label represents the city traveled from. A column label represents a city traveled to.

[tex]\begin{bmatrix}0 & 5 & 15\\ 5 & 0 & 35\\ 15 & 35 &0 \end{bmatrix}[/tex]

Here first element of first row represents the distance in miles from city 1 to city 1.

[tex]C_1\Rightarrow C_1=0[/tex]

Second element of first row represents the distance in miles from city 1 to city 2.

[tex]C_1\Rightarrow C_2=5[/tex]

Third element of first row represents the distance in miles from city 1 to city 3.

[tex]C_1\Rightarrow C_3=15[/tex]

The round trip distance in miles from city 1 to city 3 is 15. Therefore the correct option is 1.

which is the graph of the inequality? 3y - 9x ≥ 9

Answers

The inequality 3y - 9x ≥ 9, you can start by rearranging it into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Now, you can graph the line y = 3x + 3. When graphing the inequality, you will shade the region above the line, which represents the solutions to the inequality 3y - 9x ≥ 9.

To graph the inequality 3y - 9x ≥ 9, you can start by rearranging it into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

3y - 9x ≥ 9

3y ≥ 9x + 9

y ≥ 3x + 3

Now, you can graph the line y = 3x + 3.

When graphing the inequality, you will shade the region above the line. The shading represents the solutions to the inequality 3y - 9x ≥ 9.

Here's how you can graph it:

Plot the y-intercept at y = 3 on the y-axis.Use the slope m = 3 to find another point. For example, move up 3 units and to the right 1 unit from the y-intercept, and plot another point.Draw a solid line through these two points.

henry recorded the number of miles he biked each day for a week. his miles were 25, 40, 35, 25, 40, 60 and 75. what is the standard deviation of the miles henry biked to the nearest tenth

Answers

Answer:

17.1

Step-by-step explanation:

The standard deviation of the miles Henry hiked is 17.1

The standard deviation of the miles henry biked to the nearest tenth will be 17.08.

What is a standard deviation?

It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in variation.

The standard deviation is given as,

[tex]\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}}[/tex]

Henry recorded the number of miles he biked each day for a week. The data is given below.

25, 40, 35, 25, 40, 60, 75

Then the mean of the data is given as,

μ = (25 + 40 + 35 + 25 + 40 + 60 + 75) / 7

μ = 300/7

μ = 42.857

Then the standard deviation is given as,

[tex]\sigma = \sqrt{\dfrac{(25 - 42.857)^2 + (40- 42.857)^2 + ......+(75- 42.857)^2}{7}}[/tex]

Simplify the equation, then we have

σ = √(2042.857 / 7)

σ = √291.837

σ = 17.08

More about the standard deviation link is given below.

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-5 is a(n)
help please asap

Answers

Answer:

B

Step-by-step explanation:

It is rational because it is terminal (meaning it ends and doesn't go on forever) it is also under 0 because it is negative. It is an integer because it is not a fraction or decimal.

Final answer:

-5 is an integer, a category of whole numbers that includes positive, negative, and zero. Specifically, -5 is a negative integer.

Explanation:

The number -5 in mathematics is classified as an integer. An integer is any whole number found on the number line that can either be positive, negative, or zero. Therefore, the number -5, being a whole number and negative, fits into the category of integers. -5 is also an example of a negative integer.

Learn more about Integers here:

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1/5(x-2)=20 PLZZZZZZZZ HELPPPPP

Answers

Answer:

x=102

Step-by-step explanation:

[tex]\frac{1}{5}[/tex](x-2)=20 (multiply both sides by 5)

x-2=100 (move the -2 to the right)

x=100+2 (add)

x=102

hope this helps :)

Step-by-step explanation:

1/5(x-2) =20

multiply both sides by 5

=> (x-2) = 100

make x the subject of the formula...

x = 100 + 2

x = 102

Determining angle side relationships What are the angle measures in trainable ABC?

Answers

Answer:

m∠A=90°, m∠B=60°, m∠C=30°

Step-by-step explanation:

step 1

Verify if the triangle ABC is a right triangle

Applying the Pythagoras theorem

[tex]12^{2}=6^{2}+(6\sqrt{3})^{2}[/tex]

[tex]144=144[/tex] ----> is true

therefore

Is a right triangle

m∠A=90°

Find the measure of angle C

sin(C)=AB/BC

substitute

sin(C)=6/12=1/2

so

m∠C=30°

Find the measure of angle B

we know that

m∠C+m∠B=90°------> by complementary angles

so

m∠B=90°-30°=60°

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