angle 1 is congruent to angle 2 prove p is parallel to q

Answer:

Step-by-step explanation:

The 15 cm by 15 cm piece of cardboard area = 225 cm².

A cube has six congruent faces. If each edge is 5 cm, the surface area is 6×5² = 150 cm². So there is enough cardboard to make a cube, but not by folding. You'd have to do some cutting and taping.

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Answer:

2, 8

Step-by-step explanation:

-1/2x^2 + 5x = 8

-x^2 + 10x = 16 (Multiplying both sides of the equation by 2)

-x^2 + 10x  - 16 = 0

x^2 - 10x + 16 = 0 (changing the signs)

x^2 -2x -8x +16 = 0

x (x-2) -8 (x-2) = 0

(x-2) (x-8)

x-2 = 0

x = 2

or

x -8 = 0

x = 8

Answer from Gauthmath

The values of x are solutions to this equation that is 2, 8

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given that the equation as;

-1/2x² + 5x = 8

-x² + 10x = 16

Now Multiplying both sides of the equation by 2;

-x² + 10x  - 16 = 0

Or

x² - 10x + 16 = 0

x² -2x -8x +16 = 0

x (x-2) -8 (x-2) = 0

(x-2) (x-8)

The solution are;

x-2 = 0

x = 2

or

x -8 = 0

x = 8

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ2

Answer:

The critical value used is [tex]T_c = 2.132[/tex]

The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).

Step-by-step explanation:

Before building the confidence interval, we need to find the sample mean and the sample standard deviation.

Sample mean:

[tex]\overline{x} = \frac{16+21+22+12+22}{5} = 18.6[/tex]

Sample standard deviation:

[tex]s = \sqrt{\frac{(16-18.6)^2+(21-18.6)^2+(22-18.6)^2+(12-18.6)^2+(22-18.6)^2}{4}} = 4.45[/tex]

Confidence interval:

We have the standard deviation for the sample, so the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 5 - 1 = 4

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 4 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.132. The critical value used is [tex]T_c = 2.132[/tex]

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.132\frac{4.45}{\sqrt{5}} = 4.243[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 18.6 - 4.243 = 14.357

The upper end of the interval is the sample mean added to M. So it is 18.6 + 4.243 = 22.843.

The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).

270 degrees is at the bottom of the unit circle, and it splits the 3rd and 4th quadrants.

Its terminal point is (0, -1).

Hope this helps!

Answer:

A. (0, -1)

Step-by-step explanation:

This question requires a chart to answer. The chart is inserted in the answer.

270 degrees is all the way at the bottom, at South which shows that 270 degrees is at (0, -1).

Meaning, the answer is A, (0, -1).

Hope this helped.

Answer:

y = 3x - 5

Step-by-step explanation:

Slope = 3

x-intercept (what the value of y is when its 0) = -5 so y = 3x - 5

Answer:

y = 3x - 5

Step-by-step explanation:

Find the slope of the line between (0,−5)(0,-5) and (3,4)(3,4) using m=y2−y1x2−x1m=y2-y1x2-x1, which is the change of yy over the change of xx.

m=3m=3

Use the slope 33 and a given point (0,−5)(0,-5) to substitute for x1x1 and y1y1 in the point-slope form y−y1=m(x−x1)y-y1=m(x-x1), which is derived from the slope equation m=y2−y1x2−x1m=y2-y1x2-x1.

y−(−5)=3⋅(x−(0))y-(-5)=3⋅(x-(0))

Simplify the equation and keep it in point-slope form.

y+5=3⋅(x+0)

Add xx and 00.

y+5=3xy+5=3x

Subtract 55 from both sides of the equation.

y=3x−5

9514 1404 393

Answer:

Step-by-step explanation:

The 1-year interest is simply the invested amount times the interest rate.

Let r represent the lower interest rate. Then r+0.02 is the higher rate, and the total interest earned is ...

  1400r + 900(r +.02) = 202

  2300r +18 = 202 . . . . . . . . . .simplify

  2300r = 184 . . . . . . . . . .subtract 18

  r = 184/2300 = 0.08 = 8% . . . . . . divide by the coefficient of r

$1400 was invested at 8%.

$900 was invested at 10%.

Answer:

6.43

Step-by-step explanation:

Cosine: cos(θ) = Adjacent / Hypotenuse

cosine of 39 degrees = 5/x

.77714596145 = 5/x

x = 5/.77714596145

x= 6.43379782952

Answer:

4 sqrt(3) cm

Step-by-step explanation:

The area of a square is

A = s^2  where s is the side length

48 = s^2

Take the square root of each side

sqrt(48) = sqrt(s)

sqrt(16*3) = s

4 sqrt(3) =s

Answer:

4√3 cm

Step-by-step explanation:

The area of square = s²

s meaning side. Remember, by definition of a square, all the sides have equal measurements.

Set the equation:

Area of square = 48cm²

48cm² = s²

Isolate the variable, s. Note the equal sign, what you do to one side, you do to the other. Root both sides of the equation:

√48cm² = √s²

s = √48 = √(8 x 6) = √(2 x 2 x 2 x 3 x 2) = (2 x 2)√3 = 4√3

4√3 cm is your length for a side.

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Answer:

y > -1/2 x + 4

Step-by-step explanation:

Equation of a line : (y-y1)/(y2-y1) = (x-x1)/(x2-x1)

(y-4)/(2-4)= (x-0)/(4-0)

(y-4)/-2 = x/4

(-y+4)/2 = x/4

-y+4 = 1/2 x

-y = 1/2 x - 4

y = -1/2 x + 4

the solutions of the inequality are the points above this line, so

y > -1/2 x + 4

9514 1404 393

Answer:

  20th

Step-by-step explanation:

The person will receive all gifts if the are all of a multiple of 2, a multiple of 4, and a multiple of 5. Since 4 is already a multiple of 2, the person who will receive all is the one who is a multiple of 4 and 5.

20 is 4×5, so is a multiple of both numbers. There is no smaller number that is a multiple of both 4 and 5.

The 20th person will receive all gifts.

_____

The value we have determined here is called the "least common multiple" (LCM). It is the product of the unique prime factors of the numbers of interest, raised to the highest power that appears in any of the numbers.

  2 = 2¹

  4 = 2²

  5 = 5¹

LCM(2, 4 5) = 2² × 5¹ = 20

Answer:

50

Step-by-step explanation:

So we know that 42/3=14.

3 years before was:

14-3=11

42-3=39

The sum of 11+39 is 50

Step-by-step explanation:

x^2+2x+7y=15

7y=15-x^2-2x

y=15/7-1/7x^2-2/7x , x ∈ all real numbers

Answer:

12x - 28° = 116°

7x + 32° = 116°

Step-by-step explanation:

12x - 28° and 7x + 32° are vertical angles. Vertical angles are congruent.

Therefore, to find the measure of each angle, we have to set each equation equal to each other as follows:

12x - 28° = 7x + 32°

Collect like terms

12x - 7x = 28 + 32

5x = 60

Divide both sides by 5

5x/5 = 60/5

x = 12

✔️12x - 28°

Plug in the value of x

12(12) - 28

= 144 - 28

= 116°

✔️7x + 32°

7(12) + 32

= 84 + 32

= 116°

Answer:

[tex]{ \sf{ {x}^{2} + {y}^{2} = {(x + y)}^{2} - 2xy }}[/tex]

Step-by-step explanation:

[tex]{ \tt{ {(x + y)}^{2} = (x + y)(x + y) }} \\ { \tt{ {(x + y)}^{2} = ( {x}^{2} + 2xy + {y}^{2}) }} \\ { \tt{( {x}^{2} + {y}^{2} ) = {(x + y)}^{2} - 2xy}}[/tex]

Answer:

B

Step-by-step explanation:

Answer:

the answer is 3.162

Step-by-step explanation:

Answer:

x = 45

Step-by-step explanation:

5 (2x - 5) = 1/2 (18x + 40)​

10x - 25 = 9x + 20

10x = 9x + 45

x = 45

please mark this answer as brainlist

Answer:

90 ml of the 25 percent mixture and 585 of pure alcohol

Step-by-step explanation:

Firstly, you should find the quantity of alcohol in the desired mixture.

675:100*90= 675*0.9= 607.5

Firstly,  define all the 25 percents mixure as x, the pure alcohol weight is y.

1. x+y= 675 (because the first and the second liquid form a desired liquid).

Then find the equation for spirit

The first mixture contains 25 percents. It is x/100*25= 0.25x

When the second one consists of pure alcohol, it contains 100 percents of spirit,  so it is x.

2. 0.25x+y=607.5

Then you have a system of equations ( 1.x+y= 675 and 2. 0.25x+y= 607.5)

try 2-1 to get rid of y

x+y- (0.25x+y)= 675-607.5

0.75x= 67.5

x= 90

y= 675-x= 675-90= 585

It means that you need90 ml of the 25percents mixture and 585 0f pure alcohol

we can use this equation to solve:

[tex]a = p(1 + \frac{r}{n} ) ^{nt} [/tex]

a = final amount

p = initial amount

r = percentage increment (in decimal form)

n = amount of time interest is compounded

t= time (in years)

Since the guy w withdrew $300 and saw that his account still has $2021 left, he must have had $2321 in total.

5% interest is .05 in decimal form

since the account is compounded monthly, n=12

Because the account has been collecting interest for 3 months and t is supposed to be in years, dividing 3 by 12 will yield 1/4, or . 25

[tex]\\ \sf\longmapsto \left\{x|x \epsilon I,x\leqslant 3\right\}[/tex]

In listing

[tex]\\ \sf\longmapsto \left\{\dots,0,1,2,3\right\}[/tex]

Jane is given a $100 gift to start and saves $35 a month from her allowance.

   After 1 month, Jane has saved

   After 2 months, Jane has saved

   After three months, Jane has saved

   and so on

In general, after x months Jane has saved

This means that it makes sense to represent the relationship between the amount saved and the number of months with one constant rate (in this case the constant rate is 35). It makes sense because the amount of money increases by $35 each month. Since the amount of increase is constant, we get constant rate. Also the initial amount is known ($100), so there is a possibility to write the equation of linear function representing this situation.

Step-by-step explanation:

Answer:

The answer is s = d/t

Step-by-step explanation:

For question 12, I think this is called a literal equation, I might be wrong but I believe so it is a literal equation. They are asking you to get s on one side. And they are asking you what s is in terms of d and t. So what you do is, d = s x t. You multiply the t with the s and get d = st. Then you will divide t from both sides so, d/t = s/t, this will eliminate t from the s, and add it on to the d (distance). Which will leave you s on one side and d and t on the other. The answer is s = d/t.

Section 3

12) a) Here, as we need that s or speed is the subject so speed should be in place of distance. So, we get

s = d/t

Here, s is speed, d is distance and t is the time

12) b) We know that :

Average Speed = Total Distance/Total Time

Here, total distance is given 748 km

total time 11.5 hrs

Avg. Speed = 748/11.5

Avg. Speed = 65.04 km/h

Hence, the answer is 65.04 km/h

13) a) We know that volume of a rabbit hutch is

Volume of rabbit hutch = ½ × b × h × l

Here,

b is the breadth, h is the height and l is the length

Volume= ½ × 50 cm × 50 cm × 2.5 m

Now, here Length is in metre so we need to convert to cm

1 m = 100 cm

2.5 m = 2.5 × 100 = 250 cm

So, now

Volume= ½ × 50 cm × 50 cm × 250 cm

Volume = 50 cm × 50 cm × 125 cm

Volume = 312,500 cm³

Hence, the volume of this hutch is 312,500 cm³

13) b) Let us assume that the orange be a sphere

So, volume of orange = 4/3πr³

Here, r is the radius and π is pi

radius is 4 cm

Volume = 4/3π(4)³

Volume = 4/3 × 64π

Volume = 85.33π cm³

Volume of the orange is 85.33π cm³

Answer:

Hello,

Are you still alive ?

Step-by-step explanation:

a)

c=k*b (c varies directly as b)

6=k*2 ==> k=3 ( c = 6 when b = 2.)

[tex]\boxed{c=3*b }\\[/tex]

b)

b=14 ==> c=3*14=42

c)

c=39

[tex]b=\dfrac{c}{3} =\dfrac{39}{3} =13\\[/tex]

Answer:

[tex]-\frac{x^{2} }{4}[/tex]  -2x - 7

Step-by-step explanation:

Never seen a phone with 3 cameras before or something but ok.

Took a while to use brainly's insert character thingie since fractions and the exponent kinda threw me off.

Because the account is compounded continuously, Euler number is required

e = 2.7182818