help will give brainliest

Answer:

a) PR = 17 cm, b) QR = 6 cm

Step-by-step explanation:

∠Q=90, so PQ and QR are legs, and PR is hypotenuse.

Pythagorean theorem PQ² + QR² = PR²

a) PQ² + QR² = PR²

    8² + 15² = PR²

PR² = 289

PR = 17 cm

b) PQ² + QR² = PR²

   8² + QR² = 10²

64 + QR² = 100

QR² = 36

QR = 6 cm

Answer:

x = 12

Step-by-step explanation:

Using the Altitude- on- Hypotenuse theorem

The 2 triangles are similar to the outside triangle and to each other, that is

Δ RQT ~ ΔSRT

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{RT}{ST}[/tex] = [tex]\frac{QT}{RT}[/tex], substitute values

[tex]\frac{x}{9}[/tex] = [tex]\frac{16}{x}[/tex] ( cross- multiply )

x² = 144 ( take the square root of both sides )

x = [tex]\sqrt{144}[/tex] = 12

Answer:

x=6

Step-by-step explanation:

x+y=48

x=y-6

substitute "y-6" instead of x

x+y=48

(y+6)+y=48

y+y is equal to y

6+y=48

-6     -6

y= 42

x= 48-y

x=48-42

x=6

I hope this helped

Answer:

Step-by-step explanation:

x  - the small number

x+6  - the big number

x + x + 6 = 48

2x + 6 = 48

  - 6       - 6

  2x  =  42

  ÷2       ÷2

    x = 21

Verifying:

x+6 = 21 + 6 = 27

21 + 27 = 48

Answer:

x= -132

Step-by-step explanation:

Answer:

[tex]x=-132[/tex]

Step-by-step explanation:

[tex]\frac{x}{11}=-12\\ \\x=-12*11\\\\x=-132[/tex]

Answer:

Brainleist!

Step-by-step explanation:

10^x = 0.1

x =log(0.1)

Decimal Form:  x=−1

Answer:

115° and 245°

Step-by-step explanation:

Given

cos x = - 0.4226

Since cos x < 0 then x is an angle in the second / third quadrants, thus

x =  (0.4226) = 65° ← related acute angle , thus

x = 180° - 65° = 115° ← angle in second quadrant

x = 180° + 65° = 245° ← angle in third quadrant

Answer:

[tex]x=\{44\º, 317\º\}[/tex]

Step-by-step explanation:

The interval given is [tex](0, 360\º) \text{ or } (0, 2\pi)[/tex]

In exercises of this kind I usually use

[tex]\cos \left(x\right)=a\quad \Rightarrow \quad \:x=\arccos \left(a\right)+360\º n, n \in \mathbb{Z}[/tex]

[tex]\quad \:x=\arccos \left( 0.7252\right)+360\º n, n \in \mathbb{Z}[/tex]

And [tex]\arccos \left( 0.7252\right) \approx 43.5^{\circ \:}[/tex]

But once we have the solution for cos in two different quadrants, I mean, Quadrant I and Quadrant IV angle.

To the nearest degree, we have

[tex]x=\{44\º, 317\º\}[/tex]

Answer:

2625

Step-by-step explanation:

First let's see all the possible combinations.

(Even=E, Odd= O)

1) EEEO

2) EEOE

3) EOEE

4) OEEE

5) EEEE

Now let's see what E and O possibly could be

E = 0, 2, 4, 5, 6 and 8 (5)

O = 1, 3, 5, 7, 9 (5)

Now we are just simply gonna multiply

1) EEEO = 4*5*5*5

2) EEOE = 4*5*5*5

3) EOEE = 4*5*5*5

4) OEEE = 5*5*5*5

5) EEEE = 4*5*5*5

The even contains a 0, so you can't put 0 in, so (5-1=4), there are only 4 digits for the even.

500 times 4 = 2000

5⁴ = 625

2000+625= 2625

Answer: 29

Step-by-step explanation:

If you set up an equation, it would look like this:

x-13=16

I made "a number" x, and then subtracted 13 from it, making it equal to 16. Then all that is left to do is to add 13 to both sides, so you end up with 29.

Hope this helps you! Feel free to ask me any further questions!

Answer:

29-13=16

I just took the test and got it right.

Answer:

Slope = 32+5/-21+55

= 37 / 34

Hope this helps

Answer:

the square root of 91 lies between 9 and 10

The value of the square root of 91 is 9.54 thus the two consecutive whole numbers 9.54 lie in between will be 9 and 10.

The number system is a way to represent or express numbers.

A decimal number is a widespread number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

As per the given square roots,√91

The value of √91 is 9.539

The whole number less than 9.539 is 9 and greater than 9.539 is 10.

Thus, 9 < 9.539 < 10

Hence "The value of the square root of 91 is 9.54 thus the two consecutive whole numbers 9.54 lie in between will be 9 and 10".

For more about the number system,

https://brainly.com/question/22046046

#SPJ5

Answer:

B) Acute triangle

Step-by-step explanation:

In acute triangles, all of the angles are less than 90°. This is true for this triangle :)

I hope this helps!!

Answer:

B) Acute triangle

Step-by-step explanation:

All the angles are less than 90 degrees so all the angles are acute

Answer:

[tex]3y + x = -6[/tex]

Step-by-step explanation:

Given

y = 3x + 1

Required

Equation of line that passes through (12,-6) and is perpendicular to y = 3x + 1

First, the slope of the line has to be calculated;

Th slope of a line is the coefficient of x in its linear equation;

This implies that the slope of y = 3x + 1 is 3

Having calculated the slope of the first line;

The relationship between both lines are perpendicularity; this implies that [tex]m_1 * m_2 = -1[/tex]

Where m_1 = 3 and m_2 is the slope of the secodnd line

[tex]m_1 * m_2 = -1[/tex] becomes

[tex]3 * m_2 = -1[/tex]

Divide both sides by 3

[tex]\frac{3 *m_2}{m_2} = \frac{-1}{3}[/tex]

[tex]m_2 = \frac{-1}{3}[/tex]

The equation of the line can be calculated using the folloing formula

[tex]m = \frac{y - y_1}{x - x_1}[/tex]

Where [tex](x_1, y_1) = (12,-6)[/tex] and [tex]m_2 = \frac{-1}{3}[/tex]

The equation becomes

[tex]\frac{-1}{3} = \frac{y -- 6}{x - 12}[/tex]

[tex]\frac{-1}{3} = \frac{y + 6}{x - 12}[/tex]

Cross multiply

[tex]-(x - 12)= 3(y + 6)[/tex]

[tex]-x + 12=3y + 18[/tex]

Collect like terms

[tex]12 - 18 = 3y +x[/tex]

[tex]-6 = 3y + x[/tex]

[tex]3y + x = -6[/tex]

Answer:

e/4 = 2.5

e/ 4 × 4 = 2.5 × 4

e = 10

His mistake was in step 2 since

2.5 × 4 = 10

Hope this helps

Answer:

Option D is true. ( graph of a vertical line through the point (negative 4,0)

Step-by-step explanation:

Answer:

The answer would be just about 61% or 9/14

Step-by-step explanation:

So, it would be a 71% chance to get 1 green out of the bag, but then you have to keep that green out, which then lowers the chances of getting another green out of the bag, then you have to combine the percentages, and then that is the final percentage.

The probability of getting 2 greens is 5/31

Probability is the likelihood or chance that an event will occur. It is expressed as:

Probability = Expected outcome/Total outcome

Given that a bag is filled with 4 blue, 3 red and 5 green marbles, the total outcome is expressed as:

If green is picked at first, the probability of selecting a green is  5/12

The probability of getting 2 greens = 5/12 × 4/11

The probability of getting 2 greens = 20/132

The probability of getting 2 greens = 5/31

Hence the probability of getting 2 greens is 5/31

Learn more here: https://brainly.com/question/13604758

The rational expression that has a value of 1 when x =-1 would be; D 2x²/ (x + 3).

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol.

We need to determine the expression that has a value of 1 when x =-1

Let's consider the rational expression of the option D;

2x²/ (x + 3)

Now substitute the value x = -1 in the given expression

2x²/ (x + 3)

2(-1)²/ (-1 + 3)

= 2/ 2

= 1

Hence, the required rational expression is D 2x²/ (x + 3).

To know more about an expression follow;

brainly.com/question/19876186

#SPJ6

Answer:

The probability that 6 out of the next 8 individuals in his community are in favor of the president.

P( X=6) = 0.070 or 7 percentage

Step-by-step explanation:

Step(i):-

Given data the researcher has obtained data that states that 45% of citizens are in favor of the president

probability of success  'p' = 45% or 0.45

                                       q = 1-0.45 = 0.55

Given random sample size 'n' = 8

Let 'X' be the random variable

let 'X' = 6

[tex]P(X=r) = n_{C_{r} } (p)^{r} (q)^{n-r}[/tex]

The probability that 6 out of the next 8 individuals in his community are in favor of the president.

[tex]P(X=6) = 8_{C_{6} } (0.45)^{6} (0.55)^{8-6}[/tex]

[tex]8_{C_{6} } = \frac{8!}{(8-6)!6!} = \frac{8 X 7 X 6!}{2 X 1 X 6!} =\frac{8 X 7}{2 x1} = 28[/tex]

P( X=6) = 28 × 0.00830 ×0.3025

P( X=6) = 0.070

Conclusion:-

The probability that 6 out of the next 8 individuals in his community are in favor of the president.

P( X=6) = 0.070 or 7 percentage

Answer:

28

Step-by-step explanation:

Answer:

y° = 110°

z° = 26°

Step-by-step explanation:

Looking at the above geometry, we have two parallel lines , m and m

We have been asked to solve for y° and z°

Step 1

We solve for y°

On line n , we have can see that 70° and y° are CONSECUTIVE INTERIOR ANGLES

It is important to note that THE SUM OF TWO CONSECUTIVE INTERIOR ANGLES = 180°

Hence,

70° + y° = 180°

y° = 180° - 70°

y° = 110°

Step 2

Solve for z°

Looking at the geometric diagram we can see that

y° and (6z - 46) ° are ALTERNATE INTERIOR ANGLES

This means

y° = (6z - 46) °

In step 1 , we have already solved for y°

y° = 110°

Hence,

110° = (6z - 46) °

110° = 6z° - 46°

collect like terms

110° + 46° = 6z°

156° = 6z°

Divide both sides by 6

156°/6 = z°

z° = 26°

Therefore, the value y = 110° and the value of z = 26°

Answer:

Choice D

Step-by-step explanation:

After writing the data down seperate the values according to the x-axis on the graphs. You will find that 6 people chose between 0 to 3, 4 people chose between 4 to 7, 3 people chose between 8 to 11 and 2 people chose between 12 to 15.

Answer:

y = -1/2x + 1

Step-by-step explanation:

Step 1: Find slope

m = (2-4)/(-2+6) = 1/2

Step 2: Find y-intercept

y = -1/2x + b

2 = -1/2(-2) + b

2 = 1 + b

b = 1

Step 3: Write it all together

y = -1/2x + 1

And we have our final answer!

Answer:

18

Step-by-step explanation:

The required height of the green bar is 18. Option A is correct.

Number of sample = 50
Height of the green bar is = 9

The statistic is the study of mathematics which deal with relations between static data.

Here,
Percentage of green bar on vertical axis = 9/50 x 100
                                                                     =  9 x 2
                                                                     =   18%

Thus. the required height of the green bar is 18.

Learn more about Statistics here:
https://brainly.com/question/23091366

#SPJ2

Answer:

C 2:1

Step-by-step explanation:

10 is double 5

and 2 is double 1

Answer:

C 2:1

Step-by-step explanation:

this is the answer

Answer:

[tex]\frac{3(\sqrt{3} -\sqrt{x})}{3-x}[/tex] or [tex]\frac{3\sqrt{3}-3\sqrt{x} }{3-x}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt{9} }{\sqrt{3} +\sqrt{x} }[/tex]

[tex]\frac{3}{\sqrt{3}+\sqrt{x} }[/tex]

Multiply by the opposite by using the difference of squares converse formula.

[tex]\frac{3}{\sqrt{3} +\sqrt{x} } *\frac{\sqrt{3} -\sqrt{x}}{\sqrt{3} -\sqrt{x}}[/tex]

[tex]\frac{3(\sqrt{3} -\sqrt{x})}{3-x}[/tex]

[tex]\frac{3\sqrt{3}-3\sqrt{x} }{3-x}[/tex]

Answer:

3 sqrt(3) - 3 sqrt(x)

---------------------------

3  - x

Step-by-step explanation:

sqrt(9) = 3

so writing the expression as

3

--------------------

sqrt(3) + sqrt(x)

Multiply by the conjugate, sqrt(3) - sqrt(x) in the numerator and denominator

3                            sqrt(3) - sqrt(x)

-------------------- * ------------------

sqrt(3) + sqrt(x)    sqrt(3) - sqrt(x)

Foil the denominator

3 sqrt(3) - 3 sqrt(x)

---------------------------

sqrt(3) sqrt(3) + sqrt(3x) - sqrt(3x) - sqrt(x^2)

Simplify

3 sqrt(3) - 3 sqrt(x)

---------------------------

3  - x

Answer:

Step-by-step explanation:

[tex]a_{n}=1+(n-1)(4)[/tex]

Answer:

[tex](x-2)^2+(y+4)^2=34[/tex]

Step-by-step explanation:

The standard form for the equation of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex], where h is the x coordinate of the center of the circle, k is the y coordinate, and r is the radius. Since you already know the coordinates of the center of the circle, all you need to do is find the radius. Using the distance formula:

[tex]r=\sqrt{(7-2)^2+(-1-(-4))^2}=\sqrt{5^2+3^2}=\sqrt{25+9}=\sqrt{34}[/tex]

The equation of the circle is therefore:

[tex](x-2)^2+(y+4)^2=34[/tex]

Hope this helps!

Answer:

Volume of cuboid = length × width × height

length = 20cm

width = 8cm

height = 15cm

Volume = 20cm × 8cm × 15cm

= 2400cm³

Volume of the cuboid is 2400cm²

Hope this helps.

Answer:

2,400cm³

Step-by-step explanation:

FORMULA FOR VOLUME OF A CUBOID= L×B×H

WHERE L IS LENGTH = 20cm

B IS BREADTH = 15cm

H IS HEIGHT=8cm

:• VOLUME= 20cm ×15cm × 8cm

= 2,400cm³

Hey there! :)

Answer:

C(-1) = -5.

Step-by-step explanation:

C(x) = -4x² + 4x + 3

Plug in -1 for x to solve for C(-1):

C(-1) = -4(-1)² + 4(-1) + 3

Simplify:

C(-1) = -4 + (-4) + 3

C(-1) = -5

Answer:

C(-1)= -5

Step-by-step explanation:

This question asks us to find C(-1). We know what C(x) is, it is:

[tex]C(x)=-4x^{2} +4x+3[/tex]

Therefore, we must substitute -1 in for every x to find C(-1).

[tex]C(-1)=-4(-1)^{2} +4(-1)+3[/tex]

Now, solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

First, evaluate the exponent.

-1^2=-1*-1=1

[tex]C(-1)=-4(1) +4(-1)+3[/tex]

Next, multiply -4 and 1.

[tex]C(-1)=-4+4(-1)+3[/tex]

Multiply 4 and -1 again.

[tex]C(-1)=-4+ -4 + 3[/tex]

Add the numbers together.

[tex]C(-1)=-8+3[/tex]

[tex]C(-1)=-5[/tex]