(07.03. 07.04 MC)
Part A: The area of a square is (4x2 + 20x + 25) square units. Determine the length of each side of the square by factoring the area expression completely. Show
your work (5 points)
Part B: The area of a rectangle is (4x2 - 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work
(5 points)

Answer:

B = 70

Step-by-step explanation:

Supplementary angles add to 180

5x+25 + 3x+19 = 180

Combine like terms

8x+ 44 =180

Subtract 44 from each side

8x+44-44 =180-44

8x= 136

Divide by 8

8x/8 = 136/8

x = 17

We want to find B

B = 3x+19 = 3(17)+19 = 51+19 = 70

The line which crosses through L must have an intersect point with L to become perpendicular.

Gien slope is positive 1/2.

            slope(m)=tan∅=y axis/x axis.

Straight line graphs show a linear relationship between the x and y values.

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Answer:

Kevin travels for 2 hours at 60 mph and 3.5 hours at 55 mph

Step-by-step explanation:

Let's say that Kevin spends x hours going 60 mph and y hours going 55 mph. We can say that the sum of the two parts is 5.5, so x+y = 5.5 . Next, he goes 60 miles per hour for the first part of the trip, so for each hour he goes 60 mph, he travels 60 miles. We can then denote 60 * x as the distance traveled during the first part of his trip as he goes 60 mph for x hours. Similarly, 55 * y denotes the distance Kevin travels during the second part of his trip. His total distance is thus 60 * x + 55 * y = 312.5 miles

We have

x + y = 5.5

60 * x + 55 * y = 312.5

One way we can solve this is to solve for y in the first equation and plug that into the second. Subtracting x from both sides in the first equation, we get

y = 5.5 - x

Plugging that into the second equation, we get

60 * x + 55 * (5.5-x) = 312.5

60 * x + 55 * 5.5 - 55x = 312.5

5x  +302.5 = 312.5

subtract 302.5 from both sides to isolate the x and its coefficient

5x = 10

divide both sides by 5 to solve for x

x = 2

y = 5.5 - x = 5.5 - 2 = 3.5

Therefore, Kevin travels for 2 hours at 60 mph and 3.5 hours at 55 mph

The equation of the straight line is [tex]x+y=2[/tex].

Given:

To find: The equation of this line

It is given that a line with intercepts (a,0) and (0,b) has the equation [tex]\frac{x}{a} +\frac{y}{b} =1, a\neq 0, b\neq 0[/tex]

Now, it is given that the referred line has intercepts (a, 0) and (0, a). Then, using the above statement, the equation of this line can be written as,

[tex]\frac{x}{a} +\frac{y}{a}=1[/tex]. It is already given that [tex]a\neq 0[/tex]. So, we need not mention it again.

It is also given that the point (-2, 4) lies on this line. Then, the coordinates of this point must satisfy the equation of the line.

This implies that,

[tex]\frac{-2}{a} +\frac{4}{a} =1[/tex]

[tex]\frac{2}{a} =1[/tex]

[tex]a=2[/tex]

Now, put [tex]a=2[/tex] in the equation of the line, [tex]\frac{x}{a} +\frac{y}{a}=1[/tex] to get,

[tex]\frac{x}{2} +\frac{y}{2} =1[/tex]

[tex]x+y=2[/tex]

So, the equation of the line is [tex]x+y=2[/tex].

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Answer:

volume of shaded region = 112.94 [tex]cm^{3}[/tex]

Step-by-step explanation:

Volume of a cylinder = [tex]\pi r^{2}h[/tex]

volume = 22/7 * [tex]2.5^{2}[/tex] * 14.6

volume = 286.67 [tex]cm^{3}[/tex] approx

volume of sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]

volume = [tex]\frac{4}{3} *\frac{22}{7}*2.4^{3}[/tex]

volume= 57.91 [tex]cm^{3}[/tex] approx

No, of sphere = 3

Volume of 3 sphere = 3 * 57.91

                                 =173.73 [tex]cm^{3}[/tex]

Now , volume of shaded region = volume of cylinder - total volume of sphere

volume of shaded region = 286.67 - 173.73

                                          =112.94 [tex]cm^{3}[/tex]

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

6.22 sec

Step-by-step explanation:

h(t) = 105t-16t^2

For values of t for which height will be 34 feet can be obtained by substituting 34 in place of h(t) and solving for t

34=105t-16t^2, using quadratic formula we have t=1/32*(105±sqrt(8849)) which translates to - 0.34sec and 6.22sec but as time can't be negative, time is 6.22sec

Answer:

The length is 46.05551275 inches, and the width is 26.05551275 inches.

Step-by-step explanation:

We know that the area must be 1200 square inches. Using this information, we can create an equation, where x is length and y is width:

x*y=1200

We know that its length must be 20 inches longer than its width. Therefore, x=y+20. Using this new information, we can replace 'x' in 'x*y=1200' with 'y+20':

(y+20)*y=1200

[tex]y^{2} +20y=1200[/tex]

[tex]y^{2} +20y-1200=0[/tex]

I have decided to use the quadratic formula, but you could also factor this equation into the 'intercept' form to determine the roots, which ultimately provides the same answer.

[tex]y=\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex]

[tex]y=\frac{-(20)+\sqrt{(20)^{2} -4(1)(-1200)} }{2(1)}[/tex]

[tex]y=\frac{-(20)+\sqrt{400+4800} }{2}[/tex]

[tex]y=\frac{-(20)+\sqrt{5200} }{2}[/tex]

[tex]y=\frac{52.11102551 }{2}[/tex]

[tex]y=26.05551275[/tex] inches

[tex]x=y+20[/tex]

[tex]x=(26.05551275)+20[/tex]

[tex]x=46.05551275[/tex] inches

Therefore, the length is 46.05551275 inches, and the width is 26.05551275 inches.

Answer:

3. 100% = 1

3/4 = 0.75

Now, 0.75 is halfway between 0.5 and 1, so Chris is correct.

4. 10% = 10/100 = 0.1

3/5 = 0.6

Now, 0.2 is not halfway between 0.1 and 0.6, so Emily is wrong.

Answer:

3 đúng 4 wrong

Step-by-step explanation:

100%=1

giữa 0, 5 và 1 =(0,5+1)/2=3/4

10%= 0,1

giữa  0,1 và  3/5 =(0,1+3/5)/2=  0,35  #0,2

Answer:

61

Step-by-step explanation:

4 × (8 + 5) + 9

Parentheses first

4 × (13) + 9

Then multiply

52 +9

Then add

61

Answer:

It has 1 term and a degree of 4.

Step-by-step explanation:

3j⁴k-2jk³+jk³-2j⁴k+jk³

= 3j⁴k-2j⁴k-2jk³+jk³+jk³

= j⁴k

So, in this expression, there is 1 term, and it has a degree of 4.

Answer:

Jupiter travels 691200 miles a day

Step-by-step explanation:

I just did 86400 x 8

Plz give brainliest

Answer:

210 miles in 1 hour

Step-by-step explanation:

steps are in picture

Answer:

x = 25

Step-by-step explanation:

x : (x+10) = 5:7

Fractional form

x / x+10 = 5/7

Cross multiply:

x * 7 = (x+10) * 5

7x = 5x + 50

7x - 5x = 5x + 50 - 5x

2x = 50

x = 25

Check:

25 : 25 + 10

25 : 35

25/35 = 5/7

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

2^(1/6) (cos(-pi/12)+i sin(-pi/12))

2^(1/6) (cos(3pi/12)+i sin(3pi/12))

2^(1/6) (cos(7pi/12)+i sin(7pi/12))

2^(1/6) (cos(11pi/12)+i sin(11pi/12))

2^(1/6) (cos(5pi/4)+i sin(5pi/4))

2^(1/6) (cos(19pi/12)+i sin(19pi/12))

Step-by-step explanation:

Let's convert to polar form.

-2i=2(cos(A)+i sin(A) )

There is no real part so cos(A) has to be zero and since we want -2 and we already have 2 then we need sin(A)=-1 so let's choose A=-pi/2.

So z=2(cos(-pi/2)+i sin(-pi/2)).

There are actually infinitely many ways we can write this polar form which we will need.

z=2(cos(-pi/2+2pi k)+i sin(-pi/2+2pi k))

where k is an integer

Now let's find the 6 6th roots or z.

2^(1/6) (cos(-pi/12+2pi k/6)+i sin(-pi/12+2pi k/6))

Reducing

2^(1/6) (cos(-pi/12+pi k/3)+i sin(-pi/12+pi k/3))

Plug in k=0,1,2,3,4,5 to find the 6 6th roots.

k=0:

2^(1/6) (cos(-pi/12+pi (0)/3)+i sin(-pi/12+pi (0)/3))

=2^(1/6) (cos(-pi/12)+i sin(-pi/12))

k=1:

2^(1/6) (cos(-pi/12+pi/3)+i sin(-pi/12+pi/3))

2^(1/6) (cos(3pi/12)+i sin(3pi/12))

k=2:

2^(1/6) (cos(-pi/12+2pi/3)+i sin(-pi/12+2pi/3))

2^(1/6) (cos(7pi/12)+i sin(7pi/12))

k=3:

2^(1/6) (cos(-pi/12+3pi/3)+i sin(-pi/12+3pi/3))

2^(1/6) (cos(11pi/12)+i sin(11pi/12))

k=4:

2^(1/6) (cos(-pi/12+4pi/3)+i sin(-pi/12+4pi/3))

2^(1/6) (cos(15pi/12)+i sin(15pi/12))

2^(1/6) (cos(5pi/4)+i sin(5pi/4))

k=5:

2^(1/6) (cos(-pi/12+5pi/3)+i sin(-pi/12+5pi/3))

2^(1/6) (cos(19pi/12)+i sin(19pi/12))

9514 1404 393

Answer:

Step-by-step explanation:

Their age total is 15+10=25, so Ram will get 15/25 = 0.6 of the total. Kalpana will get the remaining 0.4 of the total.

  Ram receives 0.6 × ₹2000 = ₹1200

  Kalpana receives 0.4 × ₹2000 = ₹800

Answer:

A

Step-by-step explanation:

f(x) = 1/(x-3)+7

f(x)-7=1/(x-3)

x=1/(f(x)-7)+3

f^-1(x)=1/(x-7)+3, where x≠7

The correct answer is option (a)  [tex]f^{-1}(x)= \frac{1}{x-7} +3[/tex] where [tex]x\neq 7[/tex].

The domain of a function is the complete set of possible values of the independent variable

Given [tex]f^{}(x)= \frac{1}{x-3} +7[/tex]

Let

[tex]y= \frac{1}{x-3} +7[/tex]

⇒y-7= 1/x-3

⇒x-3 =1/y- 7

⇒ [tex]x= \frac{1}{y-7} +3[/tex]

hence option a is correct

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Answer:

C and E

Step-by-step explanation:

C and E are the correct answer

Juice in a juice box is usually measured in ounces.

Answer:

351.86

Step-by-step explanation:

the formula is

surface area=2πrh+2πr²

r= radius

h=height

Answer: There are 32 dogs and 1 Parrot

Step-by-step explanation: I had a question like this in a math class. What you first do is to recognize that- parrots have 2 legs and dogs have 4. We can do 130/2 = 65 and 130/4= 32.5. Now we know that if there was only one animal, there would be 65 parrots, and 32 dogs- one with half of the legs. Since there is a .5 for the dogs, if we put in one parrot, it would mean that there is exactly 130.

(32 x 4)+(2x1) = 130.  There are 32 dogs and 1 Parrot. I hope this answer is ✅ and helps, i just joined the community and this is the first person I answered. Good Luck!!

Answer:

Step-by-step explanation:

To solve this, we need to list some equations. Letting variable d stand for dogs and p stand for parrots, we have:

d+p=40 (The number of dogs plus the number of parrots equals 40)

4d+2p=130 (Each dog has 4 legs and each parrot has 2 legs and they have 130 legs in total)

With this system of equations, we can quickly solve it for d and p.

Subtract:

 4d+2p=130

- d+p=40

_________

3d+p=90,

p=90-3d

Substitution:

d+(90-3d)=40

90-2d=40

-2d=-50

d=25

Substitution to get p:

p+25=40

p=15

There you have it! There are 25 dogs and 15 parrots. To check our work,

25+15=40

4(25)+2(15)=100+30=130

I hope this helped! :)

Answer:

noent einda  pergnta poudsesrmaesspeeciicofl

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

Use the following formula:

slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Let:

[tex](x_1 , y_1) = (-2 , -8)\\(x_2 , y_2) = (6 , -4)[/tex]

Plug in the corresponding numbers to the corresponding variables:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - (-8)}{6 - (-2)} = \frac{-4 + 8}{6 + 2} = \frac{4}{8}[/tex]

Simplify the slope:

[tex](\frac{4}{8} )/(\frac{4}{4}) = \frac{1}{2}[/tex]

[tex]\frac{1}{2}[/tex] is your answer.

Answer:

c.145.3 to 154.7.

Step-by-step explanation:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.645\frac{20}{\sqrt{50}} = 4.7[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 150 - 4.7 = 145.3.

The upper end of the interval is the sample mean added to M. So it is 150 + 4.7 = 154.7.

Thus the correct answer is given by option c.

Answer:

The required length of AB is 7.28 units.

Let numbers be a and b

Adding both

[tex]\\ \qquad\quad\sf\longmapsto 2a=24[/tex]

[tex]\\ \qquad\quad\sf\longmapsto a=\dfrac{24}{2}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto a=12[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 12-b=9[/tex]

[tex]\\ \qquad\quad\sf\longmapsto b=12-9[/tex]

[tex]\\ \qquad\quad\sf\longmapsto b=3[/tex]

Answer:

26, 42, 68

Step-by-step explanation:

In the Fibonacci sequence, each number is equal to the sum of the two previous numbers. Denoting the sequence as a, we can say that

a₁=2

a₂=4

a₃=6

a₄=10

a₅=16

What we can see here is that each number a₃ or above is equal to the sum of its two previous numbers. For example, a₃ = a₁+a₂ = 2 +4 = 6

Therefore,

a₆ = a₄+a₅ = 10+16 = 26

a₇ = a₅+a₆ = 16 + 26 = 42

a₈ = a₆+a₇ = 26 + 42 = 68

9514 1404 393

Answer:

  [[3, 6, 3] [3, -3, -3]]

Step-by-step explanation:

Reflecting over the x-axis changes the sign of the y-coordinate. The reflected coordinates are ...

  [tex]\left[\begin{array}{ccc}3&6&3\\3&-3&-3\end{array}\right][/tex]

Answer:

48,000,000

Step-by-step explanation:

47,709,982

Look at the millions place and then see if the number after that is a greater number than 4. If it isn't, round down but if it is, round up