Write an equation that represents the line.
Use exact numbers.

Answer: Let the length of the hypotenuse be x

Applying the Pythagorean theorem we have :

x²=20²+48²

⇒x²=2704

⇒x=52( ∀ x >= 0 )

Step-by-step explanation:

Let assume the hypotenuse(longest side of right triangle) be x

By Pythagoras theorem

[tex] \bf \large \longrightarrow \: {c}^{2} \: = \: {a}^{2} \: + \: {b}^{2} [/tex]

Applying Pythagoras theorem

[tex] \bf \large \implies \: {x}^{2} \: = \: {20}^{2} \: + \: {48}^{2} [/tex]

[tex]\bf \large \implies \: {x}^{2} \: = \:400 \: + \: 2304[/tex]

[tex]\bf \large \implies \: {x}^{2} \: = \:2704[/tex]

[tex]\bf \large \implies \: \sqrt{x} \: = \: \sqrt{2704} [/tex]

[tex]\bf \large \implies \: \: x \: = \: 52[/tex]

Hence , the length of hypotenuse is 52.

Answer:

The area is 19.63.

Step-by-step explanation:

Step-by-step explanation:

Area of a circle is

[tex]area = \pi \: r ^{2} [/tex]

area=3.14(2.5)²

19.63in²

Answer:

98 meters

Step-by-step explanation:

Simplify each side of the equation:

318 = 2(61+x)

318= (2)(61) + (2)(x)

318= 122 + 2x

Flip the equation:

2x + 122 = 318

Subtract 122 from each side:

2x + 122 − 122 = 318 − 122

2x = 196

Divide both sides by 2:

2x/2 = 196/2

x = 98

We need not consider a whole triangle but just point B.

Before reflection we know that [tex]B(5,9)[/tex].

Reflecting B over [tex]y=1[/tex] is relatively easy. First because its a reflection over the horizontal line the only coordinates that will change are y coordinates, while x coordinate will not change so half of the reflection is already done for us,

[tex]B(5,a)[/tex]

Now to what has changed, well currently the distance between 9 and 1 on the y axis is 8 up. But because we are reflecting the a must now be 8 down from 1 which means [tex]1 - 8 = -7[/tex] so our point is now [tex]\boxed{B(5,-7)}[/tex].

Hope this helps :)

9514 1404 393

Answer:

  (5, -7)

Step-by-step explanation:

Reflection across the line y = c is accomplished by the transformation ...

  (x, y) ⇒ (x, 2c -y)

For c=1 and point B, we have ...

  B(5, 9) ⇒ B'(5, 2·1 -9) = B'(5, -7)

The image of point B is (5, -7).

Mean:

[tex]E(X) = \displaystyle \sum_{x\in\{1,2,3,4\}}x\,P(X=x) = 1\times0.4 + 2\times0.1 + 3\times0.3 + 4\times0.2 = \boxed{2.3}[/tex]

Variance:

[tex]\displaystyle V(X) = E\left((X-E(X))^2\right) = E(X^2) - E(X)^2 \\\\ E(X^2) = \sum_{x\in\{1,2,3,4\}}x^2\,P(X=x) = 1^2\times0.4 + 2^2\times0.1 + 3^2\times0.3 + 4^2\times0.2 = 6.7 \\\\ \implies V(X) = 6.7 - 2.3^2 = \boxed{1.41}[/tex]

Standard deviation:

[tex]\sigma_X = \sqrt{V(X)} = \sqrt{1.41} \approx \boxed{1.19}[/tex]

Correct options are -10 and 10

-7 + (-10² - 19)³/⁴ = 20

-7 + (100 - 19)^3/4 = 20

-7 + (81)^3/4 = 20

-7 + 27 = 20

20 = 20

RHS = LHS

-7 + (10² - 19)^3/4 = 20

-7 + (100 - 19)^3/4 = 20

-7 + (81)^3/4 = 20

-7 + 27 = 20

20 = 20

RHS = LHS

Rest options are incorrect

Answered by Gauthmath must click thanks and mark brainliest

Answer:

B and C, so 10 and -10

Step-by-step explanation:

Answer:

Z = (42-20)/4 = 5.5

Z = X-μ / σ

Step-by-step explanation:

The z-score for the data value of 42 is 5.5.

A z-score is defined as the fractional representation of data point to the mean using standard deviations.

Formula of z-score = (X - μ) / σ

Given,

μ = 20

σ = 4

X = 42

z-score = (X - μ) / σ

Substitute the values,

z-score =  (42-20)/4

z-score = 22/4

z-score =  5.5

Hence, the z-score for the data value of 42 is 5.5.

Learn more about z-score here:

brainly.com/question/13793746

#SPJ5

Step-by-step explanation:

Hey there!

From the given figure;

Angle FVT = 43°

VT = 53

Taking Angle FVT as reference angle we get;

Perpendicular (p) = FT = ?

Base (b) = VT = 53

Taking the of tan;

[tex] \tan( \alpha ) = \frac{p}{b} [/tex]

Keep all values and simplify it;

[tex] \tan(43) = \frac{ft}{53} [/tex]

0.932515*53 = FT

Therefore, FT= 49.423.

Hope it helps!

Answer:

A. 49.42

Step-by-step explanation:

tan 43 = FT ÷ VT

0.932515086 = FT ÷ 53

49.42 = FT

Question: -4 + 5x -7 = 10 + 3x -2x

⇒ 5x -11 = 10 + x

⇒ 5x - x = 10+11

⇒ 4x = 21

⇒ x = 21/4

Answer is Option D

x = 21/4

Must click thanks and mark brainliest

Answer:

0

Step-by-step explanation:

Arc sec(1)=0, tan(0)=0

Answer:

y = 4

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is

1 : √3 : 2

The sides in this triangle are in the order:

y : 4√3 : x

y/1 = 4√3/√3

y = 4

Answer:

The only limitation is x≠0

The interval notation is (-∞,0)∪(0,∞)

Step-by-step explanation:

Set up the expression.

[tex](x+7)*(\frac{1}{x}-13)[/tex]

Multiply using FOIL.

[tex](x*\frac{1}{x})+(x*-13)+(7*\frac{1}{x})+(7*-13)[/tex]

[tex]1-13x+\frac{7}{x}-91[/tex]

[tex]-13x+\frac{7}{x}-91[/tex]

Find the Domain.

The only limitation is x≠0

The interval notation is (-∞,0)∪(0,∞)

Answer: 3/8

Step-by-step explanation:

A=3

B=5

3/3+5=3/8

Answer:

50

Step-by-step explanation:

19-7=12

6+6+7+19+12

Step-by-step explanation:

=The difference between a number and 6

the term difference is used in mathmatics as subtraction

let x = a number

x - 6 = the difference between that unknown number and 6

Answer:

Step-by-step explanation:

difference means subtract. Difference is always worded the same way. What you have written means that you start with an algebraic letter and then comes the minus sign and then the number

Let the number = x

x - 6

If it was worded as difference between 6 and a number, you would write it this way

6 - x

Answer:

The slope is -2 and a point on the line is (8,9)

Step-by-step explanation:

The equation is in point slope form

y -y1 = m(x-x1) where (x1,y1) is a point on the line and m is the slope

y-9 = -2(x-8)

The slope is -2 and a point on the line is (8,9)

I think it's (2,0).

Because u use the slope of line AB to go down from point C until one of the answers are met.

The point on the x-axis that will make the line that passes through point C parallel to line AB is: D. (2, 0).

Slope of AB = -(3/6)

Slope of AB = -1/2

Slope of from point (2, 0) to point C(-2, 2):

Slope = (2 - 0)/(-2 - 2) = 2/-4

Slope = -1/2

Therefore, the point on the x-axis that will make the line that passes through point C parallel to line AB is: D. (2, 0).

Learn more about slope of parallel lines on:

https://brainly.com/question/10790818

Answer:

x = 1

y = 2

Step-by-step explanation:

5x + 2y = 9

-5x + 4y = 3

==> 6y = 12 ==> y = 12/6 ==> y = 2.

we replace y by its value in the first or the second equation, so will have:

5x + 2×2 = 9

5x + 4 = 9

5x = 5

x = 1

Step-by-step explanation:

14a. One method is two solve for x. Edit: I accidentally press sent. Repost the question and I'll answer it.

Answer:

22 weeks

Step-by-step explanation:

Let Suppose if weeks is x

So if we count it:

$40 + $15x = $370

$15x = $330

x = 22 weeks

So, Alan needs 22 weeks to have enough money to buy the new bicycle

Answer:

d the median if the data is 55

Answer:

18

Step-by-step explanation:

7-5=2

2x9=18

Answer:

c.

Step-by-step explanation:

90/-10

= 9/-1

= -9

So, -9 is the quotient.

9514 1404 393

Answer:

  A.  $11 per week

Step-by-step explanation:

  $187 = (17)(weekly allowance) . . . . . Pete's savings after 17 weeks

  weekly allowance = $187/17 = $11 . . . . . divide by 17

Pete gets $11 each week.

Answer:11 per week

Step-by-step explanation:I did the test

Answer:

In a bag of balls, 1/4th are green, 1/8th are blue, 1/12th are yellow and the remaining 26 are white. How many balls are blue?

There are 4 colours of balls - green, blue, yellow and white.

Add (1/4)+(1/8)+(1/12) = (6/24)+(3/24)+(2/24) = 11/24 so the balance or (24–11)/24 = 13/24 = 26 white. Hence the total number of balls are 2*24 = 48.

Of the 48 balls, green are (1/4)*48 = 12, blue are (1/8)*48 = 6, yellow are (1/12)*48 = 4 and the rest, white are 26.

Check: Total number of balls = 12+6+4+26 = 48

Answer: 6 balls are blue....