In the diagram shown, altitude AC is drawn from a right angle to BD in such a way that BC: DC = 4:1 Find the length of DC algebraically. Show your work below.​

Answer:x=125

Step-by-step explanation:

180-55=125

Answer:

Step-by-step explanation:

x+55=180[Sum of linear pair]

x=180-55

x=125

Answer:

D: PQ is congruent to QR

Step-by-step explanation:

In a rectangle, there are a few statements that are always true. Opposite sides are congruent and parallel and all angles meet at 90 degrees. However, adjacent sides (sides that are touching/share a vertex) are not necessarily congruent. They can be; if they are then that rectangle is a square. Nevertheless, if adjacent sides are not congruent, then it is still a rectangle, so long as they meet at a right angle.

Answer: D

Step-by-step explanation:

Answer:187

Step-by-explanation: width multiply by height

=11 times 17

=187

Step-by-step explanation:

5(y+52) = -13

5y + 260 = -13

5y = -13 -260

y = -273 ÷ 5

y = -54.6

Answer:

83.33 or 83.3 feet per second

Step-by-step explanation:

250 feet/3 seconds = 83.33 ft per second

Answer:

$31950

Step-by-step explanation:

We multiply 30,000 by .065 to get 1950. We ad them together to get $31,950. :)

Answer:

$31,950 dollars

Step-by-step explanation:

Given the following question:
Initial price of the car is $30,000...
The car has an increase tax of 6.5% (which means 6.5% of the initial price of the car is the sales tax.)

In order to find the total cost of the car, we need to find 6.5% of $30,000 and then add that number to the initial price to have the answer.

[tex]\frac{6.5\times30000}{100} =6.5\times30000=19500\div100=1950[/tex]
[tex]30000+1950=31950[/tex]
[tex]t=31950[/tex]

Therefore, the car has the total cost (including tax) of "$31,950 dollars."

Hope this helps.

Answer:

Leonard’s balance is −$8.00.

Step-by-step explanation:

Answer:

8.23 cm

Step-by-step explanation:

A circle is given to us and we need to find out the length of the bolded arc . The arc subtends an angle of 118° at the centre . And the radius of the circle is 4cm .As we know that , length of the arc is given by ,

[tex]\longrightarrow Length_{arc}= \dfrac{\theta}{360}\times 2\pi r [/tex]

Here ,

On substituting the respective values,

[tex]\longrightarrow Length_{arc}=\dfrac{118^o}{360^o}\times 2(3.14)(4cm) [/tex]

Simplify ,

[tex]\longrightarrow Length_{arc}= 0.3277 \times 25.18 \ cm [/tex]

Multiply ,

[tex]\longrightarrow \underline{\underline{Length _{arc}= 8.23 \ cm}} [/tex]

This is the required answer!

Answer:

Step-by-step explanation:

To convert this mixed numbers;  mixed numbers are converted by multiplying the denominator with the whole number and add answer gotten to the numerator.  you then place final answer over the denominator.

1.  21 /3  x  9 2/3  = 21/3 x 29/ 3

7 x 9.67  = 67.66

2.  5 3/7 x 2 2/5  =  38 / 3   x   12 /5  =

                             12.67   x  2.4 =  30.43

3.  2 6/13  x  2 1/4  =  32 / 14   x  9 /4

                                     2.28  x  2.25  = 9.13

4.  2 11/12 x 3 7/9   =  35 / 12  x  34 /9

                                  2.916  x 3.77   =  11.016

5.  5 3/5 x 5 1/7  =  28/5  x 31 / 7

                              5.6   x 4.428  = 24.8

6.   2 2/3 x 2 11/14   =  8/3  x  39/14

                                    2.66      x  2.78 =  7.413

7.   7 1/4  x 2 1/2  = 29/4   x  5 /2

                              7.25   x 2.5   = 18.125

8.  1 12/3  x 2 2/3 =  15 /3   x  8/3

                               5  x 2.66   =  13.33

9. 2 3/4  x 1 1/6 =   11/4  x 7/6

                                2.75 x  1.166  = 3.20

10.  10 1/3  x 2 1/5 =  31/3 x 11/5

                                  10.33  x  2.2  =  22.726

Answer:

Step-by-step explanation:

We know that sine and cosine are equal when angles are complementary.

sin and cos are equal when their sum is 90°

So

The principal of a loan is the amount of money they took out as a loan.

Principal = $35,000

Answer:

11. It will take about 26 minutes to install a singular tile.

12. It will take about 10 more minutes to install a light than it does to install a cable.

Step-by-step explanation:

11. Since installing 15 new tiles took a total of 390 minutes and each tile took the same amount of time, you can divide the total amount of time by the number of tiles.

390/15= 26 minutes

It will take about 26 minutes to install a single tile.

12. By looking at the chart it can be assumed that installing a light takes about 22 minutes since it is in the middle of 20 and 24 minutes. Installing a cable only takes 12 minutes.

22-12= 10 minutes

It takes about 10 minutes longer to install a light than it does a cable.

It took about 26 minutes to install a single tile and 10 minutes longer to install a light than it does a cable.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

Installing 15 new tiles took a total of 390 minutes and each tile took the same amount of time,

We have to divide the total amount of time by the number of tiles.

390/15= 26 minutes

It will take about 26 minutes to install a single tile.

By observing the chart, it can be assumed that installing a light takes about 22 minutes since it is in the middle of 20 and 24 minutes. Installing a cable only takes 12 minutes.

22-12= 10 minutes

It takes about 10 minutes longer to install a light than it does a cable.

Hence, it took about 26 minutes to install a single tile and 10 minutes longer to install a light than it does a cable.

To learn more on Graph click:

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Answer:

7.7.7.7 and 7^4 and seven to the fourth power

Step-by-step explanation:

They all equal 2401.

They are all the same but in different forms:

(7.7.7.7- expression)

(7^4 - exponential form)

(seven to the fourth power-word form of exponent)

Answer:

Step-by-step explanation:

a)

i)

Time taken at the first part:

ii)

Time taken at the second part:

b)

If time is 3 hours and 15 minutes = 3 1/4 hours = 13/4 hours, the equation is:

c)

Solve the equation:

d)

Answer:

see below

Step-by-step explanation:

Let t = time (in hours)

a) i)  First 105 km of journey

[tex]\mathsf{speed=\dfrac{distance}{time}}[/tex]

[tex]\implies x=\dfrac{105}{t_1}[/tex]

[tex]\implies t_1=\dfrac{105}{x}[/tex]

ii) Rest of journey

distance = 190 - 105 = 85 km

speed = [tex]x+12[/tex] km/h

[tex]\mathsf{speed=\dfrac{distance}{time}}[/tex]

[tex]\implies x+12=\dfrac{85}{t_2}[/tex]

[tex]\implies t_2=\dfrac{85}{x+12}[/tex]

b)  3 hours 15 minutes = 3.25 hours

[tex]\implies[/tex]  total time = [tex]t_1+t_2=3.25[/tex]

[tex]\implies \dfrac{105}{x}+\dfrac{85}{x+12} =3.25[/tex]

[tex]\implies \dfrac{105(x+12)+85x}{x(x+12)} =3.25[/tex]

[tex]\implies 105(x+12)+85x =3.25x(x+12)[/tex]

[tex]\implies 105x+1260+85x =3.25x^2 +39x[/tex]

[tex]\implies 3.25x^2-151x-1260=0[/tex]

multiply by 4:

[tex]\implies 13x^2-604x-5040=0[/tex]

c)

[tex]\textsf{quadratic formula} \ x=\dfrac{-b \pm\sqrt{b^2-4ac} }{2a}}[/tex]

[tex]\implies x=\dfrac{604 \pm\sqrt{(-604)^2-4(13)(-5040)} }{2(13)}}[/tex]

[tex]\implies x=\dfrac{604 \pm\sqrt{626896} }{26}}[/tex]

[tex]\implies x = 53.68, x=-7.22[/tex]

(to 2 decimal places)

d) time ≥ 0, therefore, x = 53.68 only

Substitute x = 53.68 into the expression for [tex]t_1[/tex] and solve for [tex]x[/tex]:

[tex]\implies t_1=\dfrac{105}{53.68}=1.955912... \textsf{hours}=\textsf{1 hr 57 min}[/tex]

Answer:

Yes

Step-by-step explanation:

Yes; Dividing by 2 is the same as multiplying by [tex]\frac{1}{2}[/tex].

Answer:

4x+2

and 22

Step-by-step explanation:

2x-5+6+2x-5+6=4x+2

if x=5, so perimeter 4(5)+2=20+2=22

Answer:

24

Step-by-step explanation:

(4 times 2 to the third power) - (64 divided by 8) = 4*(2^3) - 64/8

= 4*8 - 8 = 32 - 8 = 24

The answer is 24

Hope this helps :)

Have a great day!

Answer:

x=13.243568

Step-by-step explanation:

1000=58.3x+227.9

Step 1: Flip the equation.

58.3x+227.9=1000

Step 2: Subtract 227.9 from both sides.

58.3x+227.9=1000

         −227.9   −227.9

58.3x=772.1

Step 3: Divide both sides by 58.3

58.3x/58.3 = 772.1/58.3

x=13.243568

Answer:

12

Step-by-step explanation:

30% of 40=12

The expected number of female children in a family with three children is 1.5.

The correct option is B.

We have to determine

What is the expected number of female children in a family with three children?

Probability is defined as the sum of all observations and the number of observations.

The expected value of female children= Probability of female children x Total number of children.

A child can be male or female, so there are 2 combinations, the favorable outcome is female.

The probability of female children = 1/2.

Therefore,

The expected number of female children in a family with three children is;

[tex]= \dfrac{1}{2}\times 3\\\\=1.5[/tex]

Hence, The expected number of female children in a family with three children is 1.5.

To know more about probability click the link given below.

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Answer:

-21

Step-by-step explanation:

the y intercept is when x=0.

you can see that this is a linear equation where each increase in x results in  an increase of 4 onto the y value.

so if when x=1, y=-17, subtract 4 to find what y equals when x is 0.

-17 -4=-21

good luck :)

Answer:

In y = kx, where k is the constant of proportionality.

Answer:

k is the constant

Step-by-step explanation:

Direct variation is simply explained as when a number is directly proportional to another number. For example, when 8 is directly proportional to 4 then it will result to

=> 8= k4, where k is the constant

=> divide both sides by 4 to get k

=> k= 2

Answer:

x² + 6x + 9

Step-by-step explanation:

(x + 3)² = (x + 3)(x + 3)

Each term in the second factor is multiplied by each term in the first factor , that is

x(x + 3) + 3(x + 3) ← distribute parenthesis

= x² + 3x + 3x + 9 ← collect like terms

= x² + 6x + 9

Answer:

what event there is no picture or words to tell me please explain

Step-by-step explanation:

I think you mean the circles

x² + y² = 4

(x - 2)² + (y - 2)² = 4

Notice that both have radius 2, but the first one is centered at the origin (0, 0) while the second one is centered at (2, 2). The two circles intersect at the points (2, 0) and (0, 2), which means the bounded region between them is contained entirely in the first quadrant.

If we solve both equations above for y, we would find two solutions in each case:

x² + y² = 4   ⇒   y = ± √(4 - x²)

(x - 2)² + (y - 2)² = 4   ⇒   y = 2 ± √(4 - (x - 2)²)

The positive/negative root corresponds to the upper/lower semicircle the make up the full circle. The semicircles we're interested in are

y = + √(4 - x²)

y = 2 - √(4 - (x - 2)²)

that is, the upper half of the circle centered at the origin, and the lower half of the circle centered at (2, 2).

So, in standard Cartesian coordinates, the bounded region (call it R) is the set

[tex]R = \left\{(x, y) : 0 \le x \le 2 \text{ and } 2-\sqrt{4-(x-2)^2} \le y \le \sqrt{4-x^2} \right\}[/tex]

and the area is given by the double integral

[tex]\displaystyle \iint_R dA = \boxed{\int_0^2 \int_{2-\sqrt{4-(x-2)^2}}^{\sqrt{4-x^2}} dy \, dx}[/tex]

Answer: a minute and a half

Step-by-step explanation:

3/4 +3/4 is 6/4 which is 1 1/2 or 1 2/4

Total pounds=1lbs

Total mins:-