If the area of the trapezoid below is 75 square units, what is the value of x?
A. 12 units
B. 6 units
C. 1.5 units
D 3 units

Answer:

solution,

<3+<4=180°( linear pair)----> equation (i)

<4+<5=180°( linear pair)------>equation (ii)

From equation (i) and (ii)

<3+<4=<4+<5

<3=<5 (vertically opposite angles)

hope this helps...

Good luck on your assignment

Answer:

6.1 square units

Step-by-step explanation:

Since the triangle was translated from one position to another position, the dimensions of the triangle have not changed. The pre-image and image are congruent.

area = base * height/2

The two sides forming a right angle can be used as the base and the height in the area formula.

BC = base = 2

AB = A'B' = height = 6.1

area = 2 * 6.1/2

area = 6.1 square units

Answer:

y = 3/2x + 3.

Step-by-step explanation:

With these two points, we can find the equation of line L.

y = mx + b

Slope: (5 --1) / (4 - 0) = 5 + 1 / 4 = 6 // 4 = 3/2

Intercept: [stated by the first pair of coordinates] (0, -1)

y = 3/2x - 1

Since the line is parallel to L, the slope is the same as line L.

y = 3/2x + b

The line passes through (-2, 0), so we can substitute the points into the equation and solve for b.

0 = 3/2 * -2 + b

b - 3 = 0

b = 3

So, the equation of the line which is parallel to L and passes through the point (-2, 0), is y = 3/2x + 3.

Hope this helps!

Answer:

Similarity:

In Both cosine and sine graphs, a positive and negative number vertically flips the graph and tells whether the graph starts at maximum (positive) or minimum (negative).

Difference:

The difference between the sine and the cosine graph is the point where they start.

The graph of positive cosine starts at the maximum while that of the negative cosine starts at the minimum.

The graph of a positive sine starts at the middle, goes up and then down while that of the negative sine starts at the middle goes down and then up.

Answer:

5 and 29

Step-by-step explanation:

If k= -2, l = 3, m = 4.

Then to solve

k + l + m and K^2 + l^2 + m^2 , we have to substitute the value of k, l and m with the respective values.

So for k + l + m :

k + l + m = -2 + 3 + 4 = -2 + 7 = 5

And for K^2 + l^2 + m^2:

K^2 + l^2 + m^2 = -2^2 + 3^2 + 4^2 = 4 + 9 + 16 = 29

Hope this helps

Hey there! :)

Answer:

arc AB = 2.5π in (in terms of pi) or ≈7.85 in. (pi = 3.14)

Step-by-step explanation:

Begin by finding the circumference of the circle. Use the formula:

C = 2rπ

C = 2(9)π

C = 18π.

Since ∠AQB equals 50°, set up a ratio to find the length of arc AB:

[tex]\frac{50}{360} = \frac{x}{18\pi }[/tex]

Cross multiply:

50 · 18π = 360x

900π = 360x

Divide both sides by 360:

x = 2.5π in, or ≈7.85 in.

Answer:

3^x + 12x -4

Step-by-step explanation:

f(x) = 3^x + 10x

g(x) = 2x - 4,

(f + g)(x) = 3^x + 10x +  2x - 4

Combine like terms

             = 3^x + 12x -4

Answer:

(f + g)(x)= 3^x +12x -4

Step-by-step explanation:

To find (f+g)(x), we must add f(x) and g(x).

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

We know that f(x)= 3^x + 10x and g(x)= 2x-4

Therefore, we can substitute these into the equation.

(f + g)(x)= (3^x+10x) + (2x-4)

Combine like terms. Add all the terms with an x.

(f + g)(x)= 3^x + (10x+2x) -4

(f + g)(x)= 3^x +12x -4

(f + g)(x) is 3^x +12x -4

Answer:

by game 3(at 1:00 p.m.)

temperature increases to 5 degrees at 1:00 p.m

Answer:

T1=0

T2=2

T3=6

T4=12

T50=2450

59 is not a term in the sequence

Step-by-step explanation:

Tn=n(n-1)

182=n2 - n

0=n2 - n - 182

0=n2-14n+13n-182

0=n(n-14)+13(n-14)

0=(n-14) (n+13)

Since n cannot be negative n is not equal to -13

Therefore,

n=14

Answer:

3x= 2x+18

3x-2×=2×-2×+18

×=18

Answer:

18

Step-by-step explanation:

3x = 2x + 18

3x - 2x = 18

x = 18

Answer:

Children = 200

Adults = 190

Step-by-step explanation:

Children = x

Adults = y

x + y = 390

x = 390 - y..............(1)

20x + 35y = 10650

Substituting

20(390-y) + 35y = 10650

y = 190

x = 390 - 190 = 200

Answer:

Step-by-step explanation:

Number of children = c

Number of adults = a

Total people = 390

a + c = 390 ------------------ (I)

Admission fee for 'c' children = 20 * c = 20c

Admission fee for 'a' adult = 35 * a = 35a

Total amount = $ 10650

35a + 20c = 10650 -------------(II)

Multiply equation (I) by (-20)

(I)*(-20)  -20a - 20c = - 7800

(II)           35a + 20c = 10650    { Now add and so 'c' will be eliminated}

              15a            = 2850

a = 2850/15

a =  190

Plug in a = 190 in equation (I)

190 + c = 390

          c =  390 - 190

c = 200

Number of children = 200

Number of adults = 190

Answer:

[tex]\mathrm{D.} \: (\frac{5}{4} )^{\frac{7}{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{(\frac{5}{4})^7 }[/tex]

Apply rule : [tex]\sqrt{a} =a^{\frac{1}{2} }[/tex]

[tex]((\frac{5}{4})^7 )^{\frac{1}{2} }[/tex]

Apply rule : [tex](a^b)^c=a^{bc}[/tex]

[tex](\frac{5}{4} )^{7 \times \frac{1}{2} }[/tex]

[tex](\frac{5}{4} )^{\frac{7}{2}[/tex]

Answer:

Clean price is $3,977.22

Dirty price = $4110.99

Step-by-step explanation:

We proceed as follows;

Semiannual coupon payments = $3000* 12%/2 = 6% * 3,000 = 6/100 * 3,000 = $180

Coupons are paid on 1st June and 1st December every year(semi-annually means twice a year, every 6 months)

No. of payments remaining = 11 (1 payment in 2020 on 1st December,2020 and 2 in each of the following 5 years)

Semiannual Yield = 6%/2 =3%

The clean price of the bond is given by

P = 180/1.03+ 180/1.03^2+.....+180/1.03^11+ 3200/1.03^11

=180/0.03*(1-1/1.03^11)+3200/1.03^11

=$3977.22

Dirty price = clean price +accrued interest

Accrued Interest = Interest from 1st June , 2020 to 1st December,2020

= no of days from 1st June to 15th October/no of days from 1st June to 1st December * $180

= 136/183*$180

=$133.77

So, Dirty price = $3977.22+$133.22 = $4110.99

Answer:

Step-by-step explanation:

At maximum height, the velocity of the flare will be zero.

If the flare height above the ground is modeled by the equation

h = -16t²+64t+4

Velocity = dh/dt = 0

-32t + 64 = 0

-32t = -64

t = -64/-32

t = 2secs

This shows that the flare reaches its maximum height after 2secs.

To get the maximum height of the flare, we will substitute t = 2s into the equation h = -16t²+64t+4

h = -16(2)² + 64(2)+4

h = -64+128+4

h = 64+4

h = 68 feet

The maximum height of the flare is 64 feet.

Answer:

=

Step-by-step explanation:

1.42 is equal to 1.420. The 0 adds no value since it is after the decimal point so 1.420 is just 1.42, which is equal to itself, 1.42.

Answer:

=

Step-by-step explanation:

When you are looking at decimals, specifically on the right side of the decimal point, the amount of 0's after the last given non-0 digit can be disregarded.

1.420 is the same as 1.42

With this given information:

1.42 ____ 1.420

1.42 ____ 1.42

1.42 = 1.42

= would be your sign.

~

Answer: perpendicular

Answer:

perpendicular

Step-by-step explanation:

If two lines meet at a right angle they are said to be perpendicular to each other.

Two lines are perpendicular when they intersect at a right angle.

Answer:

first tower needs 4

second needs 3

third needs 2

and the fourth needs 1

Total needed triangles for all is 10

Step-by-step explanation:

Answer:

0.08

Step-by-step explanation:

The probability that the bus is late on any day is 0.2

The probability that it rains tomorrow is 0.4

The probability that it will rain tomorrow and the bus is late is the product of both individuals probabilities.

Therefore:

P(late & rains) = 0.2 * 0.4 = 0.08

Answer:

The probability that it rains and the bus is late is 1/7

Step-by-step explanation:

Practically, we can apply the Bayes’ theorem to solve this.

Mathematically, we use the Bayes’ problem as follows;

P( rain| late) = P(rain ^ late)/P(late) = P( late|rain) • P(rain)/[P(late|rain)P(rain) + P(not late|no rain)P(no rain)]

Where P(no rain) = 1-P(rain) = 1-0.4 = 0.6

P(on time) = 1-P(late) = 1-0.2 = 0.8

Kindly recall that P of raining = 0.4 and the probability that the bus is late is 0.2

Substituting these values into the Bayes’ equation above, we have;

P( rain| late) = (0.2)(0.4)/(0.2)(0.4) + (0.8)(0.6)

= 0.08/(0.08 + 0.48) = 0.08/0.56 = 1/7

Answer:

c

Step-by-step explanation:

Answer:the answer is 90

Step-by-step explanation:

Answer & Step-by-step explanation:

[tex]\frac{-t-5}{3}=\frac{t-3}{5}[/tex]

Cross multiply.

[tex]-5t-25=3t-9[/tex]

Subtract -3 on both sides.

[tex]-8t-25=-9[/tex]

Add 25 on both sides.

[tex]-8t=16[/tex]

Divide -8 on both sides.

[tex]t=-2[/tex]

Answer:

b

Step-by-step explanation:

-141 is larger than -143 and -145

Answer:

-$0.67

Step-by-step explanation:

If you buy one ticket, the possible outcomes are:

100% chance of spending $1 (buying the ticket)

1 in 5,000 chance of winning $500

3 in 5,000 chance of winning $300

5 in 5,000 chance of winning $30

20 in 5,000 chance of winning $5.

The expected value of the raffle is determined by:

[tex]E(X)=-1+\frac{1}{5,000}*500+\frac{3}{5,000}*300+\frac{5}{5,000}*30+\frac{20}{5,000}*5\\E(X)=-\$0.67[/tex]

The expected value of this raffle if you buy 1 ticket is -$0.67.

Answer:

ssa

Step-by-step explanation:

Answer: SSA

SSA typically applies when there are two triangles

Answer:

The probability that he doesn’t win is 6/(n + 6)

Step-by-step explanation:

Mathematically, the probability that an event occur is 1 minus the probability that the event doe not occur.

Thus, what we are saying here is that the sum of the probabilities that Paul wins the raffle draw and he doesn’t win the raffle draw is 1

This can be mathematically expressed as;

probability that he doesn’t win = 1 - probability that he wins

Thus we have;

1- n/(n+ 6)

= [(n+ 6) -(n)]/(n+6) = 6/n+ 6

Answer:

9/4

Step-by-step explanation:

Using the slope formula

m = (y2-y1)/(x2-x1)

    = (1--8)/( 4-0)

    = (1+8)/4

    = 9/4

Answer:

1) x = 71°, 2) x = 27°, 3) x= 32°

Step-by-step explanation:

1) Rectangle ABCD.

∠D = 90°

From ΔABE.

∠EAB +∠ABE + ∠BEA = 180°

45 + 90 +∠BEA = 180

∠BEA = 45

∠BEA + ∠AED +∠DEC = 180 °, because ∠BEC is a straight angle

45 + x + 64 = 180

x = 71°

2) Δ XYZ  is equilateral, all angles = 60°.

∠YZX = 60°.

∠YZW = 180°, because it is a straight angle.

∠YZX + ∠XZW= 180

60 +  ∠XZW= 180

∠XZW = 120.

From ΔXZW

∠ZXW + ∠XWZ + WZX = 180

x + 33 + 120 = 180

x = 27°

3) In ΔPQR,

PQ =  PR, so ∠PQR = ∠PRQ = 69°

∠PRQ + ∠PRS = 180, because ∠QRS = 180° as straight angle.

∠PRQ + ∠PRS = 180

69 + ∠PRS = 180

∠PRS  = 111°.

From ΔPRS

∠PRS  + ∠RSP + ∠SPR = 180

111 + 37 + ∠SPR = 180

111 + 37 + x= 180

x = 32

Answer:

$2388.95

Step-by-step explanation:

The worth of a compound deposit after a period of n years is calculated using the formula:

[tex]A(n)=P(1+\frac{r}{k})^{nk}[/tex]

[tex]A(2)=2250(1+\frac{0.03}{12})^{12 \times 2}\\\\=2250(1+0.0025)^{24}\\=2250(1.0025)^{24}\\=\$2388.95[/tex]

At maturity, the deposit will be worth $2388.95.

Answer:

picture is attached

Step-by-step explanation:

there are many options but this is one

I think the answer is D.