A line crosses the y-axis at (0,4) and has a slope of -2. Find an equation for this line. A) y = 2x + 4 Eliminate B) y = -2x + 4 C) y = -2x - 4 D) y = -4x + 2

Add up the expressions. Combine like terms wherever possible.

(f+g)(x) = f(x) + g(x)

(f+g)(x) = (x^2+10) + (x-3)

(f+g)(x) = x^2 + x + (10-3)

(f+g)(x) = x^2 + x + 7

Answer: Choice A

Answer: 173

Step-by-step explanation: 173 x 3 = 519. 520-173 = 347

Answer:

1 cm^2 = 100 mm^2

9 cm^2 = 900 mm^2

5.2 cm^2 = 520 mm^2

1 dm^2 = 100 cm^2

17 dm^2 = 1700 cm^2

4.3 dm^2 = 430 cm^2

1 m^2 = 10000 cm^2

7 m^2 = 70000 cm^2

2.5 m^2 = 25000 cm^2

1 km^2 = 1000000 m^2

50 km^2 = 50000000 m^2

8.5 km^2 = 8500000 m^2

Step-by-step explanation:

1 cm = 10 mm

1 [tex]cm^{2}[/tex] = 10×10 [tex]mm^{2}[/tex] = 100 [tex]mm^{2}[/tex]

9 [tex]cm^{2}[/tex] = 9×100 [tex]mm^{2}[/tex] = 900 [tex]mm^{2}[/tex]

5.2  [tex]cm^{2}[/tex] = 5.20×100 [tex]mm^{2}[/tex] = 520 [tex]mm^{2}[/tex]

1 dm = 10 cm

1 [tex]dm^{2}[/tex] = 10×10 [tex]cm^{2}[/tex] = 100 [tex]cm^{2}[/tex]

17 [tex]dm^{2}[/tex] = 17× 100 [tex]cm^{2}[/tex] = 1700 [tex]cm^{2}[/tex]

4.3 [tex]dm^{2}[/tex] = 4.3 × 100 [tex]cm^{2}[/tex] = 430 [tex]cm^{2}[/tex]

1 m = 100 cm

1 [tex]m^{2}[/tex] = 100×100 [tex]cm^{2}[/tex] = 10000 [tex]cm^{2}[/tex]

7 [tex]m^{2}[/tex] = 7×10000  [tex]cm^{2}[/tex] = 70000 [tex]cm^{2}[/tex]

2.5 [tex]m^{2}[/tex] = 2.5×10000 [tex]cm^{2}[/tex] = 25000 [tex]cm^{2}[/tex]

1 km = 1000 m

1 [tex]km^{2}[/tex] = 1000×1000 [tex]m^{2}[/tex] = 1000000 [tex]m^{2}[/tex]

50 [tex]km^{2}[/tex] = 50×1000000 [tex]m^{2}[/tex] = 50000000 [tex]m^{2}[/tex]

8.5 [tex]km^{2}[/tex] = 8.5×1000000 [tex]m^{2}[/tex] = 8500000 [tex]m^{2}[/tex]

Answer:

Approx. 48 cm

Step-by-step explanation:

The two horizontal sides of this parallelogram have length 12 cm each.

The length of one slanting side can be estimated by (eye:  the base of the triangle partially outlined with a dashed line is approx. 3 cm.  Then, using the Pyth. Thm., we estimate the hypotenuse of this triangle to be

sqrt(3^2 + 10^2), or sqrt(109), which is approx. 10.45.

Thus, the estimated perimeter is

P = 2L + 2W, which, here, is

P = 2(12 cm) + 2(10.45 cm), or 44.9 cm.

The fourth answer, 48 cm, is the one closest to this estimated 44.9 cm.

Answer: (13, 47)

The expression t = 4 means that 4 units of time have come off the clock (possibly 4 seconds). Plug this value into each equation given for x and y

x = 2*t + 5 = 2*4 + 5 = 8 + 5 = 13

y = 3*t^2 - 1 = 3*4^2 - 1 = 3*16 - 1 = 48 - 1 = 47

In short, if t = 4 then it leads to x = 13 and y = 47 at the same time. These x and y values pair up to get the final answer (13,47)

--------------

Here's an update:

If t = 2, then,

In short, if t = 2, then x = 9 and y = 11

The point on the graph at time [tex]\(t = 4\) is \((13, 47)\)[/tex].

To find the point on the graph at time [tex]\(t = 4\)[/tex] given the parametric equations [tex]\(x = 2t + 5\)[/tex] and [tex]\(y = 3t^2 - 1\)[/tex], substitute [tex]\(t = 4\)[/tex] into both equations.

1. For [tex]\(x\)[/tex]:

[tex]x = 2t + 5[/tex]

[tex]x = 2(4) + 5[/tex]

[tex]x = 8 + 5[/tex]

[tex]x = 13[/tex]

So, at [tex]\(t = 4\), \(x = 13\)[/tex].

2. For [tex]\(y\)[/tex]:

[tex]y = 3t^2 - 1[/tex]

[tex]y = 3(4)^2 - 1[/tex]

[tex]y = 3(16) - 1[/tex]

[tex]y = 48 - 1[/tex]

[tex]y = 47[/tex]

So, at [tex]\(t = 4\), \(y = 47\)[/tex].

Therefore, the point on the graph at time [tex]\(t = 4\) is \((13, 47)\)[/tex].

Answer:

-1  1/9 degrees Celsius

Step-by-step explanation:

Assuming we have 30 Fahrenheit, we need to plug it into the formula to find the degrees Celsius.

c=5/9 (f-32)

Substitute  f=30

c = 5/9 (30-32)

c = 5/9 (-2)

c = -10/9

c = -1 1/9 degrees Celsius

Answer:

25

Step-by-step explanation:

There are 100 capsules and she can only buy 1/4

Multiply 100 * 1/4

100 * 1/4 =

100/4

25

We can check  by  calculating how many she leaves at the store

100 * 3/4 =

300 /4 = 75

The ones she bought , plus the ones she left behind should be 100 capsules

25+ 75 = 100

100 = 100

Check

Answer:

False

Step-by-step explanation:

To determine whether the statemaent "If [tex]a\Rightarrow b[/tex] is true, then [tex]\neg a\Rightarrow b[/tex] is also true" holds, you can form the truth table:

[tex]\begin{array}{ccccc}a&b&a\Rightarrow b&\neg a&\neg a\Rightarrow b\\1&1&1&0&1\\1&0&0&0&1\\0&1&1&1&1\\0&0&1&1&0\end{array}[/tex]

When the result of the column [tex]a\Rightarrow b[/tex] takes value 1 (true), the result of the column  [tex]\neg a\Rightarrow b[/tex] is not always 1, then the statement is false.

Answer:i cant see it good

Step-by-step explanation:

Answer:B is the answer I think but I’m not sure sorry

Step-by-step explanation:

Answer:

46 boxes

Step-by-step explanation:

So for a total of 20 boxes, the cost is [tex]75+55=130[/tex]

We have remaining [tex]221-130=91[/tex]

Each additional box costs 3.5, so for 91 dollars, we can get:

[tex]\frac{91}{3.5}=26[/tex] boxes

So, total [tex]10+10+26=46[/tex] boxes can be bought for $221.00

Given the budget of $221 and the stipulated price rates, the company can buy a total of 46 boxes of paper clips.

To solve this problem, we first need to calculate how many boxes the company can buy with $221 considering the different rates. The first 10 boxes cost $7.50 each, so ten boxes would cost $75. The next 10 boxes cost $5.50 each, so these together would cost $55. This means that 20 boxes cost $130. Subtract this amount from the total budget, which leaves $91.

Since each additional box over 20 boxes costs $3.50, we divide our remaining fund, $91, by $3.50 to determine how many more boxes can be purchased. This comes out to roughly 26 boxes.

So, adding up all the boxes, the company can buy 10 boxes (at $7.50) + 10 boxes (at $5.50) + 26 boxes (at $3.50) = 46 boxes with $221.

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Answer:

The Answer is a Prime polynomial, it cannot be further factorized.

Step-by-step explanation:

QUESTION 34

We want to find the variance of [tex]82,44,67,52,120[/tex].

The variance can be calculated using the formula,

[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]

where

[tex]\bar X =\frac{82+44+67+52+120}{5}[/tex]

[tex]\bar X =\frac{365}{5}[/tex]

[tex]\Rightarrow \bar X =73[/tex]

This means that,

[tex]\sigma^2=\frac{(82-73)^2+(44-73)^2+(67-73)^2+(52-73)^2+(52-73)^2+(120-73)^2}{5}[/tex]

This gives us,

[tex]\sigma^2=\frac{(9)^2+(-29)^2+(-6)^2+(-21)^2+(47)^2}{5}[/tex]

[tex]\sigma^2=\frac{81+841+36+441+2209}{5}[/tex]

[tex]\sigma^2=\frac{3608}{5}[/tex]

[tex]\sigma^2=721.6[/tex]

QUESTION 35

We want to find the variance of [tex]10,12,15,18,11,13,14,16,19,20[/tex].

The variance can be calculated using the formula,

[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]

where

[tex]\bar X =\frac{10+12+15+18+11+13+14+16+19+20}{10}[/tex]

[tex]\bar X =\frac{148}{10}[/tex]

[tex]\fRightarrow \bar X =14.8[/tex]

This means that,

[tex]\sigma^2 =\frac{(10-14.8)^2+(12-14.8)^2+(15-14.8)^2+(18-14.8)^2+(11-14.8)^2+(13-14.8)^2+(14-14.8)^2+(16-14.8)^2+(19-14.8)^2+(20-14.8)^2}{10}[/tex]

This gives us,

[tex]\sigma^2=\frac{(-4.8)^2+(-2.8)^2+(0.2)^2+(3.2)^2+(-3.8)^2+(-1.8)^2+(-0.8)^2+(1.2)^2+(4.2)^2+(5.2)^2}{10}[/tex]

[tex]\sigma^2=\frac{23.04+7.84+0.04+10.24+14.44+3.24+0.64+1.44+17.64+27.04}{10}[/tex]

[tex]\sigma^2=\frac{105.6}{10}[/tex]

[tex]\sigma^2=10.56[/tex]

QUESTION 36

We want to find the variance of [tex]100,140,130,180,80,160[/tex].

The variance can be calculated using the formula,

[tex]\sigma^2=\frac{\sum(x-\bar X)^2}{n}[/tex]

where

[tex]\bar X =\frac{100+140+130+180+80+160}{6}[/tex]

[tex]\bar X =\frac{790}{6}[/tex]

[tex]\Rightarrow \bar X =131.67[/tex]

This means that,

[tex]\sigma^2=\frac{(100-131.6667)^2+(140-131.6667)^2+(130-131.6667)^2+(180-131.6667)^2+(80-131.6667)^2+(160-131.6667)^2}{6}[/tex]

This gives us,

[tex]\sigma^2=\frac{(-31.6667)^2+(8.3333)^2+(-0.6667)^2+(48.3333)^2+(-51.6667)^2+(28.3333)^2}{6}[/tex]

[tex]\sigma^2=\frac{10325}{9}[/tex]

[tex]\sigma^2=1147.22[/tex]

To find the variance of a set of data, find the mean, subtract the mean from each data point, square the differences, and find the average of the squared differences. The standard deviation is the square root of the variance.

To find the variance of a set of data, follow these steps:

For the data set 82, 44, 67, 52, 120 (Question 34), the mean is 73, the squared differences are 81, 841, 36, 441, and 1849, and the average of the squared differences is 631.20, rounding to two decimal places.

For the data set 10, 12, 15, 18, 11, 13, 14, 16, 19, 20 (Question 35), the mean is 14.8, the squared differences are 23.04, 4.84, 0.64, 8.84, 12.96, 3.24, 1.44, 2.56, 19.36, and 29.16, and the average of the squared differences is 10.10, rounding to two decimal places.

To find the standard deviation of a set of data, take the square root of the variance. For the data set 100, 140, 130, 180, 80, 160 (Question 36), the variance is 9300, and the standard deviation is 96.49, rounding to two decimal places.

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Answer:

g(x) = 4 sin(x - 3)

Step-by-step explanation:

* Lets revise some transformation

- If the function f(x) translated horizontally to the right by h units, then

 the new function g(x) = f(x - h)  

- If the function f(x) translated horizontally to the left by h units, then

 the new function g(x) = f(x + h)  

- If the function f(x) translated vertically up by k units, then the new

 function g(x) = f(x) + k  

- If the function f(x) translated vertically down by k units, then the

 new function g(x) = f(x) – k  

- A vertical stretching is the stretching of the graph away from the

 x-axis  

- If k > 1, the graph of y = k • f(x) is the graph of f(x) vertically  

 stretched by multiplying each of its y-coordinates by k.  

- A vertical compression is the squeezing of the graph toward  

 the x-axis.  

- If 0 < k < 1 (a fraction), the graph of y = k • f(x) is the graph of f(x)

 vertically compressed by multiplying each of its y-coordinates by k.  

* Lets solve the problem

∵ f(x) = sin(x)

∵ f(x) is stretching vertically by a factor of 4

∴ f(x) multiplied by 4

∵ f(x) is shifting 3 units to the right

∴ We will change x to (x - 3)

∵ The new function is g(x)

∴ g(x) = 4 sin(x - 3)

- The attached graph for more understand

f(x) is the red graph

g(x) is the blue graph

Answer:

g(x) = 4 sin(x - 3)

Step-by-step explanation:

The given function is:

f(x) = sin(x)

Stretching by a factor of 4:

A vertical stretch or compression of f(x) can be expressed as:

cf(x), where c is any constant

if c > 1, it indicates a stretch in vertical direction and if 0 < c < 1, it indicates a compression by a factor of c in vertical direction.

Since, given function is being stretched by a factor of 4, the transformed function will become:

4f(x)

Shifting by 3 units right:

A shift of f(x) to right can be obtained by subtracting c from every occurrence of x in f(x) , where c is the number of units f(x) is being shifted in right direction. Since in this case f(x) is shifted 3 units to right, the transformed function will be:

f(x - 3)

Applying both the transformations to f(x), we get g(x) as:

g(x) = 4 f(x - 3)

g(x) = 4 sin(x - 3)

4. -3

5. 3

4. For x > -2, the value of a is the slope of the line. The line goes down 3 units for each 1 to the right, so the slope is -3/1 = -3. Then a = -3.

___

5. The ordered pair (h, k) is typically used to name the point to which a function is translated. The vertex of the function f(x) = |x| is (0, 0). When it is translated to (h, k), the function becomes ...

... q(x) = |x -h| +k

If the new vertex is (3, 0), then h = 3 and k = 0. This is consistent with the equation shown. (k = 0 means q(x) = |x -h|.)

Answer:

x = 8

y = 1

Step-by-step explanation:

Slope = difference in y values / corresponding difference in x values

Slope =  (9 - 5) / (x - 10) = -2

-2x + 20 = 4

x = -16 / -2 = 8  (answer)

Question 4

(y - 6) /(1 - 2) = 5

y - 6 = -5

y = 1  (answer).

Answer:

(1,0)  (-2,-1)

Step-by-step explanation:

We need to find the midpoint of Segment BD

(-3,1) and (-1,-3)

the midpoint is (x1+x2)/2, (y1+y2)/2

                         (-3+-1)/2 , (1+-3)/2

                             -4/2  , -2/2

                                -2, -1

We need to find the midpoint of Segment cD

(3,3) and (-1,-3)

the midpoint is (x1+x2)/2, (y1+y2)/2

                         (3+-1)/2 , (3+-3)/2

                             2/2  , 0/2

                                1, 0

Answer:

Given two events A and B of a sample set :-

P[A] = 0.20  

P[not B]=0.40

[tex]P[B/A]=0.25[/tex]

To find P[A or B]:

[tex]P[A or B] = P[A] + P[B] - P[A \cap B][/tex]                ......[1]

Calculate for [tex]P[B][/tex] and [tex]P[A \cap B][/tex]

P[B] = 1- P[not B]

Substitute the value P[not B] we get;

P[B] = 1-0.40 = 0.60      

[tex]P[A \cap B] = P[B/A] \cdot P[A][/tex]

Substitute the given values we get;

[tex]P[A \cap B] = 0.25 \cdot 0.20 = 0.05[/tex]

Then;

[tex]P[A or B] = 0.20+0.60-0.05 = 0.80-0.05 =0.75[/tex]

Therefore, the value of P[A or B] is, 0.75.

The probability of P(A∪B) is 0.35.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Given

     P(A) = 0.20

     P(B) = 0.40

P(A∩B) = 0.25

The probability of P(A∪B).

We know the formula

P(A∪B) = P(A) + P(B) - (A∩B)

P(A∪B) = 0.20 + 0.40 - 0.25

P(A∪B) = 0.60 - 0.25

P(A∪B) = 0.35

Thus the probability of P(A∪B) is 0.35.

More about the probability link is given below.

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Answer:

48/8=6 bags of chocolate chip cookies.

And 64/8=8 bags of vanilla wafer cookies.

8 bags.

Step-by-step explanation:

Linda is having a bake sale:

48 chocolate chip cookies and 64 vanilla wafer cookies to put in bags

She can fill the bag with same number of cookies and the same number of wafers in each bag

And condition is no wafers or cookies left over.

So, we will find the greatest common factor of 48 and 64  which is 8

Hence, she can fill 8 bags

And 48/8=6 bags of chocolate chip cookies.

And 64/8=8 bags of vanilla wafer cookies.

Answer: D

Step-by-step explanation:

The x-intercepts of the graph are: x = -2 , x = -1, and x = 3

-->                                                 x + 2 = 0, x + 1 = 0, and x - 3 = 0

-->                                                           (x + 2) (x + 1) (x - 3)

Answer:

Sorry if this isnt helpful: Im just going off stuff i learned to see if this will help you at all. Im only in 7th so.. Sorry in advance!!

Step-by-step explanation:

To find the rate, you need to create a unit rate table thing, like this:

5/3 = ?/1 To do this, you would need to divide 5 by 3 and 3 by 3 to get y and x. You get: 1.666 continued. Rounded, about 1.7 . so your unit rate for part A is 1.7/1. You would do the same thing. 2/3 = ?/1. I will let you solve that :)))

Finished A! Now B:

To compare, we use the butterfly method! so 1.7/1 o ?1. cross multiply, and whichever number is bigger comes on top. Then you would explain why that number is bigger. BAM

Answer:

You didn't input the function, but the cosine of 90 degrees is zero.

Cosine values of zero also occur when an angle equals

270 degrees 450 degrees 630 degrees and 810 degrees.

Step-by-step explanation:

Answer:

That would be 0, 180, 360, 540, and 720.

Step-by-step explanation:

If the value of sine is 0. Add 180 five times and we get the five numbers for the answer.

Answer:

32 houses will have a pool

Step-by-step explanation:

40% of 80 is 32

Answer:

$3.08

Step-by-step explanation:

Answer:

[tex]12\frac{1}{2}[/tex] hours.  

Step-by-step explanation:

We have been given that Phyllis Doran worked at Symmes Medical Center for 7 1/2 hours on Monday and from 8:00 a.M. Until 1:00 p.M.

Let us find the number of hours between 8:00 am to 1:00 pm.

There are 4 hours between 8:00 am to 12 noon and 1 hour from noon to 1:00 pm. So the total number of hours between 8:00 am to 1:00 pm is 5 hours.

Now let us find total number of hours worked by Phyllis Doran by adding 7 1/2 and 5.

[tex]\text{The total number of hours Doran worked}=7\frac{1}{2}+5[/tex]

[tex]\text{The total number of hours Doran worked}=12\frac{1}{2}[/tex]

Therefore, the total number of hours worked by Phyllis Doran is [tex]12\frac{1}{2}[/tex] hours.

Answer:

1. [tex]\dfrac{3}{8}[/tex]

2. 240 km

Step-by-step explanation:

Anna drives [tex]\dfrac{1}{8},[/tex] Irina drives [tex]\dfrac{3}{8},[/tex] Vlad drives [tex]\dfrac{1}{8},[/tex] then Avel drives

[tex]1-\dfrac{1}{8}-\dfrac{3}{8}-\dfrac{1}{8}=\dfrac{8}{8}-\dfrac{1}{8}-\dfrac{3}{8}-\dfrac{1}{8}=\dfrac{8-1-3-1}{8}=\dfrac{3}{8}.[/tex]

If the road trip involves 640 km of driving, then Avel drives

[tex]640\cdot \dfrac{3}{8}=80\cdot 3=240\ km.[/tex]