Mathematics High School

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Answers

Answer 1

Answer:

As the opposite angles of a cyclic quadrilateral, A is supplementary with C and B is supplementary with D.

In the trapezoid, angle A is supplementary with D and angle B is supplementary with C.

It means ∠A ≅ ∠B and ∠D ≅ ∠C

Now, ∠ABD ≅ ∠ACD as both angles intercept same arc AD.

So we have:

m∠B = m∠ABD + m∠DBC = 35° + 72° = 107°andm∠C = 180° - m∠B = 180° - 107° = 73°

So angles B and A are 107° and angles D and C are 73°

PXR is exterior angle of triangle XSR.

Angles Q and S are supplementary as opposite angles of a cyclic quadrilateral QPSR.

m∠PXR = m∠XRS + m∠XSR = 20° + (180° - 80°) = 120°

Related Questions

Find the length of the third side. If necessary, round to the nearest tenth. 6 10

Answers

If you round, it’ll be 7,0

Answer:

Step-by-step explanation:

In a bowl of fruit, there are green grapes and black grapes in the ratio 3 : 4

If there are 24 green grapes, how many black grapes are there?

Answers

Answer:

Step-by-step explanation:

Green : black

3 4

We have 24 green

3+8=24

so multiply each side by 8

Green : black

3*8 4*8

24 32

There are 32 black grapes

Answer:

Step-by-step explanation:

By Question :-

Green grapes: Black grapes= 3:4

Let :-

Number of black grapes = x

Therefore,

GG/ BG = 3/4 24/x = 3/4 x = 24 × 4/3x = 8 × 4x = 32

plzz help will mark brainliest

Answers

Answer:

Step-by-step explanation:

x^2 + 11y + y^2 -3x + 11 = 5x +23 - y

First put it into general form by setting the equation to zero and moving all variables to one side.

x^2 + 11y + y^2 -3x + 11 = 5x +23 - y

+y -5x -11 -11

x^2 + y^2 - 8x + 12y = 12

Then solve by completing the square

x^2 - 8x y^2 + 12y = 12

(x - )^2 + (y + )^2 =

Half of 8 is 4

Then square 4 to get 16

Therefore, we plug the 4 into the first parentheses

x^2 - 8x + 16 + y^2 + 12y =12 +16

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

Half of 12 is 6

Squared, that would be 36

plug this into the second parentheses

x^2 - 8x + 16 + y^2 +12y + 36 = 12 + 16 + 36

(x - 4)^2 + (y + 6)^2 =

12 + 16 = 28 + 36 = 64

Therefore, the equation of the circle is: (x - 4)^2 + (y + 6)^2 = 64

Which is option D

Frank practiced piano for 2 ⅓ hours yesterday. He practiced 1 ⅛ hours today. How long did he practice on both days combined? Convert your answer to hours and minutes.

Answers

Answer: [tex]3 hr and 27 min[/tex]

Step-by-step explanation:

Given

Frank practiced piano for [tex]2\frac{1}{3}\ \text{hours}[/tex] yesterday and [tex]1\frac{1}{8}\ \text{hours}[/tex]

In total frank practiced

[tex]\Rightarrow 2\dfrac{1}{3}+1\dfrac{1}{8}\\\\\Rightarrow \dfrac{7}{3}+\dfrac{9}{8}\\\\\Rightarrow \dfrac{7\times 8}{3\times 8}+\dfrac{9\times 3}{8\times 3}\\\\\Rightarrow \dfrac{56+27}{24}=\dfrac{83}{24}\ \text{hours}\\\Rightarrow \dfrac{83}{24}\ \text{hours}\ or\ 3\ \text{hours and 27 min 30s}[/tex]

How do you write 56 and 64 as a prime of its product of its prime factors in expended form and in exponential form

Answers

Answer:

Expanded=2x2x2x7

Exponential=2^3x7

Expanded=2x2x2x2x2x2

Exponential=2^6

Plesssse help me with this

Answers

i think it’s the fourth one

X^2 - 2x + 6 = 0
Show all work

Answers

Answer:

x= plus or minus 1 plus imaginary root times square root of 5.

Step-by-step explanation:

[tex] {x}^{2} - 2x + 6 = 0[/tex]

Complete the Square.

[tex] {x}^{2} - 2x = - 6[/tex]

[tex] {x}^{2} - 2x + 1 = - 5[/tex]

[tex](x - 1) {}^{2} = - 5[/tex]

[tex]x = + - 1 + i \sqrt{5} [/tex]

please help!! asap need 5 and 6

Answers

Answer:

both substitutions

Step-by-step explanation:

in 5. based on 3 BC is substituted by its equal counterpart AB.

and in 6. we use 1. to substitute AC by its associated absolute value.

0=(x-8)^2-100 Solve the problem using any type of way.

Answers

0 = (x-8)^2 -100

Add 100 to both sides

100 = (x-8)^2

Take the square root of both sides

10 = (x-8)

Remove the parentheses

10 = x-8

Add 8 to both sides

18 = x

Answer: x = 18

PLEASE HELP 30 POINTS

Find the value of x in the triangle below.
804
155
55°
o
75
80°
Ο Ο
85

Answers

Answer:

75°

Step-by-step explanation:

First, we need to know that the interior angle sum of a triangle is always 180°.

Now, to find the missing angle aside from x, we need to complete the sum 180-155=25, seeing 155° lies on a straight line. Remembering the interior angle sum of a triangle is always 180°, it is thus clear that 25+80+x=180. If we complete this equation, x=75.

Hope this helps!

Find the value of x. Round the length to the nearest tenth.

Answers

Answer:

[tex]x=opposite\: side\: of \:22[/tex]

[tex]16=hypotenese[/tex]

[tex]sin22=opp/hyp[/tex]

[tex]sin22=\frac{x}{16}[/tex]

[tex]\Longrightarrow x=16\times sin22[/tex]

[tex]x=5.99[/tex]

[tex]x=6.0[/tex]

[tex]OAmalOHopeO[/tex]

PLEASE HELP !!!!!!!!!!!!!

Answers

Answer:

the 3rd won for sure

Step-by-step explanation:

hope I helped

Answer:

Step-by-step explanation:

The coordinates are all in (x, y) form.

X is how left or right

y is how tall.

If you just look for the individual coordinates given, you will see that all of the Coordinates in C are on the graph.

I hope this helps!

Which of the following function pairs are inverses?

Answers

Answer:

(A)

x= 5y-3

(x+3)/5

Step-by-step explanation:

Answer:

its A

Step-by-step explanation:

i took the test lol

SOMEONE HELP PLEASE I NEED ANSWER

Answers

T=55+6w is the equation

at the end of 8 weeks you do
T=55+6x8
which equals 103$

Answer:

T = 55 + 6w and $103

Step-by-step explanation:

We have already saved $55, so that is our constant. We gain $6 per week, so that will be our w value

T = 55 + 6w

Solving for T when w = 8 weeks

T = 55 + 6(8)

T= 55 + 48

T = $103

Which number is greater than 234,781,114?
A. 3.425 x 10 to the power of 6
B. 3.425 x 10 to the power of 8
C. 3.425 x 10 to the power of 7
D. 3.425 x 10 to the power of 5

Answers

Answer:

I think its B.

Step-by-step explanation:

sorry if i am wrong.

One condition for performing a hypothesis test is that the observations are independent. Mark is going to take a sample from a population of 400 students.How many students will Marta have to sample without replacement to treat the observations as independent?

Answers

Answer:

Step-by-step explanation:

Given :

The number of the observations in the population is N = 400

There is a [tex]10\%[/tex] rule of assuming the independence.

Now, according to the rule, if we sample without replacement then, any sample of sizes less than or equal to [tex]10\%[/tex] of the population is considered independent.

[tex]10\%[/tex] of population = [tex]10\%[/tex] of 400

[tex]$=\frac{10}{100} \times 400$[/tex]

= 40

Any sample of sizes less than or equal to 40 will be independent for the given population if it is sampled without replacement.

So, the answer is 40.

So, Mark have a sample of 40 students without replacement to treat the observations as independent.

Answer: 40

Step-by-step explanation:

find value of the variable

Answers

Answer:

x=10

Step-by-step explanation:

16/24=(x-2)/12

or, 16/2=x-2

or, 8=x-2

or, x-2=8

or, x=10

Answered by GAUTHMATH

Which of the following are exterior angles? Check all that apply.
A. 21
B. 2
C. 25
D. 26
DE 24
E 23

Answers

Answer:

D. <6

E. <4

Step-by-step explanation:

both are exterior angles

∠4 and ∠6 are exterior angles.

Options D and E are the correct answers.

What are exterior angles?

Exterior angles are angles formed by a straight line and a line segment outside of that straight line.

More specifically, an exterior angle is formed when two non-collinear rays originate from a point on one side of a straight line and intersect with the other side of the line.

We have,

From the figure,

∠4 and ∠6 are exterior angles.

∠5 and ∠3 are interior angles.

And,

∠6 is the sum of ∠3 and ∠1.

Thus,

∠4 and ∠6 are exterior angles.

Learn more about exterior angles here:

https://brainly.com/question/28835566

#SPJ7

What is the value of x in theequation 2.5 (6x - 4) = 10 + 4 (1.5 +0.5 x)?

1/3

1/2

2

13

Answers

Answer:

x = 2

Step-by-step explanation:

Let's solve your equation step-by-step.

2.5(6x−4)=10+4(1.5+0.5x)

Step 1: Simplify both sides of the equation.

2.5(6x−4)=10+4(1.5+0.5x)

(2.5)(6x)+(2.5)(−4)=10+(4)(1.5)+(4)(0.5x)(Distribute)

15x+−10=10+6+2x

15x−10=(2x)+(10+6)(Combine Like Terms)

15x−10=2x+16

Step 2: Subtract 2x from both sides.

15x−10−2x=2x+16−2x

13x−10=16

Step 3: Add 10 to both sides.

13x−10+10=16+10

13x=26

Step 4: Divide both sides by 13.

x=2

99999+999=????????????????????????????

Answers

Answer:

100998 is the answer.

I hope this help u.

Answer:

100998

Step-by-step explanation:

₁ ₁ ₁ ₁ ₁

99999

+ 999

100998

you can also think of it as

99999(+1) + 999(-1)

100000+998

100998

see screenshot below

Answers

Answer:

B only

Step-by-step explanation:

well to solve this question we can consider factor theorem which states that if a Polynomial f(x) is divided by a monomial x-a then x-a is a factor of f(x) if and only if f(a)=0

and to figure "a " we can consider the following equation:

[tex] \displaystyle x - a = 0[/tex]

substitute the given value of a:

[tex] \displaystyle x - 2= 0[/tex]

therefore,

[tex] \displaystyle x = 2[/tex]

option-1:

plugin the value of x to the function A(x):

[tex] \displaystyle A(2) = {2}^{3} + {2}^{2} + 4[/tex]

simplify which yields:

[tex] \displaystyle A(2) = 16[/tex]

since A(2)≠0 x-2 is not a factor of A(x)

option-2:

similarly substitute the value of x to the function B(x) which yields:

[tex] \displaystyle B(2) = {2}^{3} - {2}^{} - 6[/tex]

simplify:

[tex] \displaystyle B(2) =0[/tex]

so, B(2)=0 Hence x-2 is a factor of x³-x-6

option-3:

substitute the value of x to the function C(x)

[tex] \displaystyle C(2) = {2}^{4} + 3.{2}^{} - 10[/tex]

simplify:

[tex] \displaystyle C(2) =12[/tex]

as C(2)≠0 x-2 is not a factor of C(x)

option-4:

likewise plugin the value of x to the function D(x):

[tex] \displaystyle D(2) = {2}^{4} - 2.{2}^{3} - 2[/tex]

simplify and that yields:

[tex] \displaystyle D(2) = - 2[/tex]

therefore,D(2)≠0 hence,x-2 isn't a factor of D(-2)

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

The factor

x-2=0x=2

we have find the value of x .

Now,

we have to select all the polynomial which has x-2 As a factor.

According to the question,

option A:-

[tex]A(x)=x^3+x^2+4\\\\A(2)=(2)^3+(2)^2+4\\\\=8+4+4\\\\16≠0[/tex]

so it is not a factor.

Option B:-

[tex]B(x)=x^3-x-6\\\\=B(2)=(2)^2-2-6\\\\0=0[/tex]

so it is a factor

Option C:-

[tex]C(x)=x^4+3x-10\\\\=C(2)=(2)^4+3(2)-10\\\\=16+6-10\\\\12≠0[/tex]

so it is not a factor

option D:-

[tex]D(x)=x^4-2x^3-2\\\\D(2)=(2)^4-2(2)^3-2\\\\=16-16-2\\\\-2≠0[/tex]

so it is not a factor

therefore:-

The option B is correct.

88 POINTS PLS HELP!!!

Answers

Answer:

aw no me la seee lo.sientooo no puedooo

Preston's Bakery sold one customer 4 dozen chocolate cookies and 9 dozen oatmeal cookies for $126. The bakery also sold another customer 8 dozen chocolate cookies and 5 dozen oatmeal cookies for $122. How much do the cookies cost?

Answers

Let's refer to the chocolate cookies using the variable c, and the oatmeal cookies using the variable o.

Using the information we have, we can set up two equations for the two different transactions.

4c + 9o = 126

8c + 5o = 122

Now, we need to solve for one of the variables in the first equation. I will solve for o.

4c + 9o = 126

9o = 126 - 4c

o = 14 - 4/9c

Next, we'll take this value for o and plug it into the second equation for the variable o. Then we can solve for c.

8c + 5(14 - 4/9c) = 122

8c + 70 - 2 2/9c = 122

5 7/9c + 70 = 122

5 7/9c = 52

c = 9

Finally, we can use the value of c and plug it back into the first equation to solve for o.

o = 14 - 4/9(9)

o = 14 - 4

o = 10

1 dozen chocolate cookies costs $9

1 dozen oatmeal cookies costs $10

Hope this helps!

[tex]\text{Solve for x:}\\\\3x - 5 = 5x + 3[/tex]

Answers

Hi there!

»»————-　★　————-««

I believe your answer is:

[tex]\boxed{x = -4}[/tex]

»»————-　★　————-««

Here’s why:

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x'...}}\\\\3x - 5 = 5x + 3\\-----------\\\rightarrow 3x - 5 + 5 = 5x + 3 + 5\\\\\rightarrow 3x = 5x + 8\\\\\rightarrow 3x - 5x = 5x - 5x +8\\\\\rightarrow -2x = 8\\\\\rightarrow \frac{-2x=8}{-2}\\\\\rightarrow \boxed{x = -4}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««

Hope this helps you. I apologize if it’s incorrect.

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex] [tex]\sf{ 3x-5=5x+3 }[/tex]

[tex]\sf{5x-3x=-5-3 }[/tex]

[tex]\sf{ 2x=-8 }[/tex]

[tex]\sf{ x=\dfrac{-8}{2} }[/tex]

[tex]\bold{ x=-4 }[/tex]

Please help urgent all info is in screenshot

Answers

IT IS A DIRECT VARIATION...BECAUSE WHEN X COMPONENT IS INCREASED THEN Y COMPONENT ATE ALSO INCREASING.....

In triangle ABC, AC=13, BC=84, and AB=85. Find the measure of angle C

Answers

Given:

In triangle [tex]ABC, AC=13, BC=84, AB=85[/tex].

To find:

The measure of angle C.

Solution:

Law of Cosines:

[tex]\cos C=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

[tex]\cos C=\dfrac{BC^2+AC^2-AB^2}{2(BC)(AC)}[/tex]

Substituting the given values, we get

[tex]\cos C=\dfrac{(84)^2+(13)^2-(85)^2}{2(84)(13)}[/tex]

[tex]\cos C=\dfrac{7056+169-7225}{2184}[/tex]

[tex]\cos C=\dfrac{0}{2184}[/tex]

[tex]\cos C=0[/tex]

Taking cos inverse on both sides, we get

[tex]C=\cos^{-1}(0)[/tex]

[tex]C=90^\circ[/tex]

Therefore, the measure of angle C is 90 degrees.

Answer:

eason

Step-by-step explanation:

boy

why did u read this