A family recycled 66 cans in February, 94 cans in March, 122 cans in April, and 150 cans in May. If this pattern went from January through May, how many cans did the family recycle in January?

Given line: y =3x - 7

Slope-intercept form is y = mx + b where m is slope and b is the y intercept

To find m you must take the slope of the line given, which would be 3, and take its opposite reciprocal (switch its sign to negative/positive if it was originally positive/negative and flip the numerator and denominator)

the opposite of 3 is -3 and the reciprocal of -3 is [tex]\frac{-1}{3}[/tex]

This means that the slope of a line perpendicular to y = 3x - 7 is [tex]\frac{-1}{3}[/tex]

This is the current formula you found:

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

To find the y-intercept (b) in the point that this line goes through (2, -1) into the x and y of the equation and solve for b

-1 = [tex]\frac{-1}{3}[/tex](2) + b

-1 = [tex]\frac{-2}{3}[/tex] + b

[tex]\frac{-1}{3}[/tex] = b

That means that the equation perpendicular to y = 3x - 7 is...

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

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

y =3x - 7

Step-by-step explanation:

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.

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

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.

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.            

Answer:

6 units²

Step-by-step explanation:

The area (A) of a triangle is

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 3 and h = 4, hence

A = 0.5 × 3 × 4 = 0.5 × 12 = 6

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!

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 .

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) .

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 .

To learn more about greatest common factor , refer -

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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]

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

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

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

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.

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.

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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Answer:

x<11

Step-by-step explanation:

To solve this inequality, we must isolate the x. To do that, we divide both sides by 5. This gives us x<11. So all numbers less than eleven belong to the solution set of the inequality.

Answer:

All number less than 11.

Step-by-step explanation:

5x < 55

We just isolate x by dividing both sides by 5:

5x / 5 < 55/5

x < 11.

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

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

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]

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.

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.

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

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°

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

Answer:

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]

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:

Answer:

x=20

Step-by-step explanation:

Since this is a right angle, it is equal to 90 degrees

x + 3x+10 = 90

Combine like terms

4x+10 = 90

Subtract 10 from each side

4x+10-10 =90-10

4x=80

Divide by 4

4x/4=80/4

x = 20

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]

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.

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

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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.

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

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.

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Answer:

g(4) = 12

Step-by-step explanation:

We need to find the value the function g(x) when x = 4, that is;

g(4)

In the first definition of the function, the value of x is strictly less than 4. Consequently, we shall use the second definition of the function to evaluate g(4)

In the second definition, g(x) is given as;

Q(x) = 0.5x + 10

plug in x = 4 and simplify;

Q(4) = 0.5(4) + 10

Q(4) = 12

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.

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: