A quadrilateral has two angles that measure 222° and 81°. The other two angles are in a ratio of 6:13. What are the measures of those two angles?

Answers

Answer 1

[tex]\sf\huge\underline{\star Solution:-}[/tex]

[tex]\rightarrow[/tex] Ratio of two angles are 6:13.

So, let the one angle be [tex]\sf{6x}[/tex] and another be [tex]\sf{13x.}[/tex]

As we know that,

Sum of all interior angles of a quadrilateral = [tex]\sf\pink{360°.}[/tex]

So let's sum up the given angles,

[tex]\rightarrow[/tex] [tex]\sf{222°+81°+6x+13x \:=\: 360°}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{303+19x \:=\: 360°}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{19x \:=\: 360-303}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{19x \:=\: 57}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{x \:=\: \frac{19}{57}}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{x \:=\: 3}[/tex]

Hence, [tex]\sf{x \:=\: 3}[/tex]

So, First angle [tex]\sf{= \:6x\: = \:6×3 \:=}[/tex] [tex]\sf\purple{18°.}[/tex]

Second angle [tex]\sf{= \:13x\: = \:13×3 \:=}[/tex] [tex]\sf\purple{39°.}[/tex]

_________________________________

Hope it helps you:)


Related Questions

PLS I really need this a have 40 questions due tomorrow :( (please help anyone) 16 points

Answers

15. 20,5,4
You can use division to solve each of these,
60/3= 20,
60/12= 5
60/15=4

16. 3/10 + 5/100 = 7/20 or 0.35

x2 +9 x- 22,
Which graph shows the solution set of
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Answers

Answer...

Ok done. Thank to me >:3

what is x if 1/4x = 9?

Answers

Answer:

x is 36

Step-by-step explanation:

the way to find out is 1/4 multiplied by what gives you 9. 9 divided by 1/4 is 36. 36 1/4's gives you 9.

Answer: 2

Step-by-step explanation:first u subtract 1-9=8then u divide 4/8=2 tell me if wrong

Point P is located at (4, 6) on a coordinate plane. Point P will be reflected over the x-
axis. What will be the coordinates of the image of point P? What transformation was
performed on the given figure
1. (8,4)
2. (4-6)
3. (4,28)
4. (24,4)

Answers

Answer:

2.

Step-by-step explanation:

it's the reciprocal

so it's gonna reflect

(WILL MARK BRAINLIST)
Write an inequality to represent the graph.
у
-5
4
3
(0, 2)
2 1
x
x
-5 -4 -3 -2 -1 0
-1
2
4 5 6 7 8 9 10
(4,-1)
-2
-3
-4
-51
-6
-7
-8
-9
-Previous Question
Question 1 (Answered)

Answers

i believe the answer is the second one

How to solve 3x - 1/2 = 8 1/2 please no links and do it step by step

Answers

Answer:

[tex]x=\frac{3}{2}[/tex]

Step-by-step explanation:

Step 1.  Put each term in [tex]3x-\frac{1}{2}[/tex] over the common denominator 2.

[tex]\frac{6x}{2}-\frac{1}{2}[/tex]

Therefore we have [tex](\frac{6x}{2}-\frac{1}{2})=4[/tex]

Step 2.

Combine [tex]\frac{6x}{2}-\frac{1}{2}[/tex] into a single fraction.

[tex]\frac{6x-1}{2}[/tex]  

Therefore we have [tex](\frac{1}{2}(6x-1))=4[/tex]  or [tex]\frac{6x-1}{2}=4[/tex]

Step 3.

Multiply both sides by a constant to simplify the equation.

Multiply both sides of [tex]\frac{6x-1}{2}=4[/tex]  by 2:

[tex]\frac{2*(6x-1)}{2}=4*2[/tex]

Step 4.

Cancel the common terms in the numerator and denominator of   [tex]\frac{2*(6x-1)}{2}[/tex]

Then we get [tex]\frac{2}{2}*(6x-1)[/tex]  which simplifies to [tex](6x-1)[/tex]

So all together we have [tex](6x-1)=2*4[/tex]

Step 5.

Multiply 2 and 4 together and remove the parenthesis.

[tex]6x-1=8[/tex]

Step 6.

Isolate terms with the variable x to the left hand side.

So add 1 to both sides:

[tex]6x+(1-1)=8+1[/tex]

Evaluate   [tex]1-1=0[/tex]  which cancels out

Step 7.

Add the like terms on the right side:

[tex]6x=9[/tex]

Step 8.

Divide both sides by a constant to simplify the equation.

Divide both sides of [tex]6x=9[/tex]  by 6.

[tex]\frac{6x}{6} =\frac{9}{6}[/tex]

Any non-zero number divided by itself is 1.

[tex]x=\frac{9}{6}[/tex]  which simplifies to [tex]x=\frac{3}{2}[/tex]

If the percent of discount of an item is 25 percent and the sale price is $40 what is the original price

Answers

Answer:

$53.33

Step-by-step explanation:

40/1 - .25

40/.75 = $53.33

Using the tree diagram below, what is the probability of getting tails and an even number?

Answers

hi the awnser us defiantly going to be that I 56

Step-by-step explanation:

edge

Need help with khan geometry no link pls just answer

Answers

Angles ABC and CBD are complementary - they add up to 90°. This means

(4x + 52°) + (8x - 10°) = 90°

Solve for x :

12x + 42° = 90°

12x = 48°

x = 4°

It follows that angle CBD has measure

4 • 4° + 52° = 16° + 52° = 68°

Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
y= 22 + 3
y = -3.2 + 3
2=
y =
y

Answers

Answer:

Step-by-step explanation:

y=2x+3

y=-3x+3

**This is what's on the image.**


You need to aline the two together.

2x+3 = -3x+3


Add 3x both sides

3x+2x+3=3

5x+3=3

Now subtract 3 from both sides

5x=3-3

x= 0

This should be a vertical line from (0,0) to above since there is no slope you should have a straight line that is vertical.

Jean estimates that her friend completes a new level of a video game on the first try 20% of the time. She conducts a simulation to predict how many times out of 80 her friend would complete a new level on the first try. Jean uses a random number generator. Every digit that is 8 or 9 represents completing the level. Examine the table. ​

Answers

The probability of the friend completing the new level in her first try is 22.5%

What is probability?

This is a concept that is used to talk about the likelihood or the chances of an event occuring.

For the digit 8, the frequency is 7

For the digit 9, the frequency is 11

The total number of frequencies is given as

10 + 9 + 6+ 7 + 8 + 12 + 4 + 6 + 7 + 11 = 80

7 + 11 = 18

Probability = 18/80

= 0.225 x 100

= 22.5%

Read more on probability here: https://brainly.com/question/251701

WILL GIVE BRAINLIEST!!!
Solve 3(2x - 3) = 15. Explain ALL steps.

Answers

Answer:

x=4

Step-by-step explanation:

distributive property goes first.

you get 6x-9=15

add 9 on both sides so 9 cancells out on the left side.

you get 6x=24

divide by 6 and you get x=4

3 x 2x = 6x
3 x -3 = -9

6x - 9 = 15
Add nine to both sides of the equal sign
15+9= 24

Divide both sides by 6

24/6= 4

X=4

Tell me if this helps
Please mark me as brainliest

What’s the area of the circle?
r= 4m

Answers

Answer:

50.3

Set A to the value of pi times the radius squared.

[tex]4^2 = 4 * 4 = 16\\\\A = \pi *r^2(4^2) = 50.26548245...[/tex]

The sum of 5 times a number and 7 equals 8

Answers

Answer:

0.2

Step-by-step explanation:

the sum of 5 times 0.2 and 7 equals 8

A right triangle has leg lengths of 9 units and 12 units. Write an equation that can be
used to determine the length of the hypotenuse, c .

Answers

The Pythagorean Theorem

The Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]

a and b are the two legs in a right trianglec is the hypotenuse (the longest side of a right triangle; opposite the 90° angle*keep in mind that this theorem applies only to right triangles

Solving the Question

We're given:

Legs = 9 units and 12 unitsHypotenuse = c

Plug these measurements into the Pythagorean theorem:

[tex]a^2+b^2=c^2\\9^2+12^2=c^2[/tex]

⇒ Combine like terms:

[tex]81+144=c^2\\c^2=225[/tex]

Answer

[tex]c^2=225[/tex]

Super Sandwiches offers 4 kinds of breads, 3 kinds of meats, 5 cheeses, and 7 dressings for a sandwich. How many possible combinations would there be for making a sandwich

Answers

Answer:

19

Step-by-step explanation:

Answer:

420

Step-by-step explanation:

From first principle, find the derivative of y=2x^3+x²+4x with respect to X​

Answers

Answer:

[tex]derivative \: of \: y = 6 {x}^{2} + 2x + 4[/tex]

Step-by-step explanation:

we know that

[tex] \frac{d}{dx} {x}^{n} = n {x}^{n - 1} [/tex]

Now the derivative of y=2x³+x²+4x

[tex] \frac{dy}{dx} = \frac{d}{dx} (2 {x}^{3} + {x}^{2} + 4x)[/tex]

[tex] \frac{dy}{dx} = \frac{d}{dx} (2 {x}^{3} ) + \frac{d}{dx}( {x}^{2} ) + \frac{d}{dx} (4x)[/tex]

[tex]\frac{dy}{dx} = 2(\frac{d}{dx} {x}^{3} ) + \frac{d}{dx} {x}^{2} + 4(\frac{d}{dx} x)[/tex]

here

[tex]\frac{d}{dx} {x}^{3} = 3 {x}^{2} [/tex]

[tex]\frac{d}{dx} {x}^{2} = 2x[/tex]

[tex]\frac{d}{dx} x = 1[/tex]

Now

[tex]\frac{dy}{dx} = 2(3 {x}^{2} ) + 2x + 4(1)[/tex]

[tex]\frac{dy}{dx} = 6 {x}^{2} + 2x + 4[/tex]

I hope it helped you

Help asap!!! NO LINKS PLS!!

Answers

Answer:

18

Solution:First, evaluate 2^3, which equals 8.Next, evaluate 4^2, which equals 16.This is the simplified expression:3/4(8+16)3/4(24)Multiply:18

Hope it helps.

Do comment if you have any query.

Helpppp I will mark brainliest

Answers

Problem 25

Point P has the x coordinate x = -5, while point Z has the x coordinate x = 5. This is a distance of 10 units on the number line. Segment PZ is 10 units long which is the base of the triangle.

The height of the triangle is 8 units because it's the vertical distance from R to segment PZ. Notice we go from x = 4 to x = -4. The base and height are always perpendicular to one another.

Area = (base*height)/2

Area = (10*8)/2

Area = 80/2

Area = 40

Answer:  40 square units

==========================================================

Problem 26

I'm not sure about this one because the instructions mention a grid, but I don't see any grid lines here. I'm not sure if the grid lines are just really faint or if your teacher forgot to put them in.

Given the following graph, define a) the vertex, b) the intercepts, c) the axis of symmetry, and the sign of the lead coefficient.

Answers

Answer:

Option D is correct

[tex]Slope[/tex] [tex]of[/tex] [tex]AC=Slope[/tex] [tex]of[/tex] [tex]DF[/tex]

Step-by-step explanation:

Given:

1.

ΔABC and ΔDEF are similar

Property of similar states that corresponding sides are in proportion.

2.

[tex]\frac{BC}{EF}=\frac{AB}{DE}[/tex] [By property of similar triangles]

Property of proportions allows you to cross multiply the equation.

then;

3.

[tex]\frac{AB}{BC}=\frac{DE}{EF}[/tex]   [Property of proportion]

Definition of slope: Slope is described as the steepness and direction of line.

then by definition of slope;

4.

[tex]Slope[/tex] [tex]of[/tex] [tex]AC=\frac{BC}{AB}[/tex]

5.

[tex]Slope[/tex] [tex]of[/tex] [tex]DF=\frac{EF}{DE}[/tex]

6.

Substitution property of equality states that:

If a = b then a can be substituted in place of b in any equation or vice-versa.

then;

[tex]Slope[/tex] [tex]of[/tex] [tex]AC= Slope[/tex] [tex]of[/tex] [tex]DF[/tex]

Therefore, the missing step in 6 we get,

[tex]Slope[/tex] [tex]of[/tex] [tex]AC= Slope[/tex] [tex]of[/tex] [tex]DF[/tex]

The equation y = 8x 12, where x is the number of hours and y is the total cost, represents what the surf instructor charges for lessons. use this information to describe how to draw the line on a graph.

Answers

Answer:

Use points (0,12) and (1,20) on graphing paper or a program to find final answer.

Step-by-step explanation:

In the problem, I was unable to understand the equation so I am presuming the equation actually means y=8x+12

Whenever you graph a Linear Function you always need two points. The first point is always easy to acquire.

You can plug in any value for x, which will be your x cordinate and the output (solution) of the equation will be you y cordinate.

I'm plugging in 0 for X first.

y=8x+12

y=8(0) +12

y=12

We have our first point as (0,12)

Now you can plug in any other number for X other then Zero.

I choose 1 this time for X.

y=8x+12

y=8(1)+12

y=8+12

y=20

We now have our second point (1,20). Two points will be enough to graph this graph, you can graph these two points and then draw a line if on paper or use an application and get the line that way.

Answer:

Use the rise/run strategy to draw the line. Start at the y-intercept (0, 12), and count 8 up and 1 to the right to the point (1, 20). Then, draw a line through the points. Test the point (3,36) in the equation y = 8x + 12 to verify that the line is correct.

Step-by-step explanation:

got it right

what is the name of the shape

Answers

Answer:

triangular prism

Step-by-step explanation:

Have a great day!

The sum of two numbers is 122. The difference of the first number and twice the second number is 23. Find the two numbers.

Answers

Answer:

One is 89 , the other is 33.

Step-by-step explanation:

Set up a system of 2 equations:

x + y = 122

x - 2y = 23        Subtracting:

0 + 3y = 99

y = 33.

So:

x + 33 = 122

x = 122 -33 = 89.

Answer:

first number= 89 and second number= 33

Step-by-step explanation:

here, let the first number be X and the second number be y,then

From the question,

x + y = 122 ---- eq i

x -2y = 23 ----- eq ii

From substitution method,

From eq i,

x + y = 122

or, x =122 - y

Now, putting the vale of x in eq ii,we get,

122 -y -2y = 23

or, -3y = 23-122

or, -3y = -99 (cut minus sign in both sides)

or, y=99/3

or, y = 33

Again, putting the value of y in eq i,we get,

x + 33 = 122

or, x= 122-33

or, x=89

A square pyramid is 6.3 in by 4 in by 4 in what is the surface area of the pyramid

Answers

Answer:

32.2 square feet

Twelve identical cylindrical pop cans are placed in a box. If sand fills the space between the pop cans and the cans and the sides of the box, what volume of sand is needed?

Answers

Answer:

Step-by-step explanation:

I don't see any information on dimensions of the cans or box, so I'll assume the question wants a general solution.

Three steps will result in the volume of sand required to fill the remaining space in the box.

1.  Calculate the volume of a can using the equation for the volume of a cylinder:  Vol = πr²h

2.  Multiply the can volume by 12.  This will give the total volume of the 12 cans in the box.

3.  Calculate the volume of the box:  Volume = (Base)(Width)(Height)

[Make sure the units are the same as those used in calculating the can volume.  E.g., if the can is calculated with cm as the measue, the box dimensions must also be cm]

4.  Subtract the volume of the12 cans (from step 2) from the volume of the box.

The result from 4 will be the volume of sand required to fill the box containing 12 cans.  

I'm not clear why filling the box with sand is important, but perhaps it will absorb any soda released from cans broken when the heavy box is dropped by the person shocked that 12 cans of pop could be so heavy.

At the beginning of the year, Mrs. Wilkinson's class had 19 packages of colored paper. So far, the class has used 401 pieces of colored paper.
If each package of colored paper contained 75 pieces, how many pieces of colored paper does the class have left?



I need help

Answers

Answer:

1024 pages left

Step-by-step explanation:

19 pack  * 75 page/pack - 401 page =

Two angles are supplementary. The larger angle is 15 more than 10 times the smaller angle. FInd the measure of each angle.

Answers

[tex]\text{Larger angle} =x\\\\\text{Smaller angle} =y\\ \\\text{According to the condition,}\\\\x=10y+15\\\\\text{The two angles are supplementary, so their sum is}~ 180^{\circ} \\\\x+y=180\\\\\implies 10y+15 +y = 180\\\\\implies 11y = 180-15\\\\\implies 11y=165\\\\\implies y = \dfrac{165}{11}\\\\\implies y = 15\\\\\text{So,} ~x =180-15 = 165\\\\\text{Hence the larger angle is}~ 165^{\circ}~ \text{and the smaller angle is }15^{\circ}[/tex]

The shorter leg of a right triangle has a measure of x + 5. The longer leg is one less than three times the length of the shorter leg. The hypotenuse is thirteen more than two times the shorter leg. The area of the triangle, A, is 2.5 times the magnitude of the perimeter.
Create a system of equations to model the situation above. Determine if there are any solutions, and, if possible, whether or not they are viable.

How many total possible solutions of the form (x, A) are there for this situation?

How many total viable solutions of the form (x, A) are there for this situation?

Answers

Answer:

Given:

[tex]\textsf{Shorter leg}=(x+5)[/tex][tex]\textsf{Longer leg}=3(x+5)-1[/tex][tex]\textsf{Hypotenuse}=2(x+5)+13[/tex][tex]\sf A=2.5P\quad \textsf{(where A is area and P is perimeter)}[/tex]

[tex]\begin{aligned} \textsf{Perimeter} & =\textsf{shorter leg + longer leg + hypotenuse}\\ & = (x+5)+[3(x+5)-1]+[2(x+5)+13]\\ & = x+5+3x+15-1+2x+10+13\\ & = 6x+42\end{aligned}[/tex]

[tex]\begin{aligned} \textsf{Area} & =\dfrac12\textsf{(shorter leg)(longer leg)}\\ & =\dfrac12(x+5)[3(x+5)-1]}\\ & =\dfrac12(x+5)(3x+14)\\ & = \dfrac12(3x^2+29x+70)\\ & = \dfrac32x^2+\dfrac{29}{2}x+35 \end{aligned}[/tex]

[tex]\begin{aligned} \textsf{Area} & =2.5 \sf (Perimeter)\\ \implies \dfrac32x^2+\dfrac{29}{2}x+35 & =\dfrac52(6x+42)\\ 3x^2+29x+70 & =5(6x+42)\\ 3x^2+29x+70 & =30x+210\\ 3x^2 -x-140 & =0\\ 3x^2-21x+20x-140 & =0\\ 3x(x-7)+20(x-7) &=0\\ (x-7)(3x+20)& =0\end{aligned}[/tex]

Therefore:

[tex](x-7)=0 \implies x=7[/tex]

[tex](3x+20)=0 \implies x=-\dfrac{20}{3}[/tex]

[tex]x=-\dfrac{20}{3}[/tex] is not a viable solution as when inputting this into the formula for the shorter leg, it gives a negative value:

[tex]\textsf{Shorter leg}=-\dfrac{20}{3}+5=-\dfrac53[/tex]

As distance cannot be negative, this is not a viable solution.

When x = 7:

[tex]\textsf{Shorter leg}=7+5=12[/tex]

[tex]\textsf{Longer leg}=3(7+5)-1=35[/tex]

[tex]\textsf{Hypotenuse}=2(x+5)+13=37[/tex]

[tex]\textsf{Perimeter}=6(7)+42=84[/tex]

[tex]\textsf{Area} & =\dfrac32(7)^2+\dfrac{29}{2}(7)+35=210[/tex]

Therefore, there is one viable solution.  This solution in the form (x, A) is  (7, 210)

Manuel works out at the gym 2 days each week for 3/4 hour each day


how many hours does manuel work out each week?


2 x 3/4 =

Answers

Answer:

1.5, so an hour and thirty minutes

Step-by-step explanation:

Simplify 3/4 as 0.75. 0.75 times 2 is 1.5.

a fishing tackle box is 13 inches long 6 inches wide and 2 1/2 inches high. what is the volume of the tackle box

Answers

Answer:

195 cubic inches

Step-by-step explanation:

A fishing tackle box is 13 inches long, 6 inches wide, and inches high. What is the volume of the tackle box? SOLUTION: The volume of the tackle box is 195 cubic inches.

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When an element is removed from the queue, it is removed from the Mr. Ledger buys a box of 24 donuts for a lesson in his math class about circumference.Write an equation for the number of donuts y that are left at the end of the day when x donuts are used during the lesson.Last year, Mr. Ledger used 18 donuts during the lesson. This year, he used 22 donuts.Place points on the graph to show how many donuts are left at the end of last year's lesson and this year's lesson. The Sausage Hut is looking at a new sausage system with an installed cost of $330,000. This cost will be depreciated straight-line to zero over the project's three-year life, at the end of which the sausage system is estimated to have zero value. The project has no impact on net working capital. 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What was the short-term effect of this change for African Americans in the 1920s?C) Growing isolationism Question 11Which economic policy of the 1920s resulted in lower taxes?A)The Revenue Act of 1924 Question 12How did the Harding and Coolidge presidential administrations' policies compare and contrast with each other?A)Both were pro-business, but only Harding's presidency is famous for scandals Question 13 What impact did Henry Ford's assembly line have on the automotive industry? B)It helped lower the cost of automobiles through a more efficient manufacturing process. Question 14How did new consumer products and advertising impact the economy during the 1920s?c)The economy did very well as consumers had new found wealth and credit to buy new products Question 15What issues in American society were highlighted by the case of Sacco and Vanzetti?B)A growing sense of fear and anxiety over rising immigration Question 16Which two of the issues below were directly linked to the Scopes trial? Select the two correct answers.A)The revival of Protestant fundamentalism C)The conflict between urban and rural values Question 17Germany built up its supply of Warships and other armaments as a matter of international Prestige. This is an example of what factor that led to World War 1?D)MilitarismQuestion 18President Woodrow Wilson, in his Declaration of Neutrality, stated," the people of the United States are drawn from many nations, and chiefly from the nation's now at war." Why did President Wilson want to keep the United States out of World War 1? A)He worried that entering the war would cause conflict and disloyalty among Americans because many had cultural ties to the countries at war. Question 19During World War I, which already existing weapon was made significantly more effective with new technology?D) machine gunQuestion 20During World War 1, labor unions worked for which of the following concessions for workers? Select the two correct answers.B)Workers were paid a living wage D)8-hour work day become standard Question 21What was the role of the War Industries Board during World War I?A)To ensure adequate military supplies Question 22What was the major goal of this American propaganda poster from World War 1?A)To encourage people to help finance the war effort Question 23Why did President Wilson's "Fourteen Points" speech call for freedom of the Seas and the reduction of armaments?A)Wilson wanted to reduce the amount of violence caused by deadly weapons and unrestricted submarine warfare Question 24Why did the Klu Klux Klan decline towards the end of the 1920s? Select the two correct answers.A)Legislation from opposition groups E)Public scandals the rest is up to you, sorry. Identify details in Mandela's argument supportinghis claim that " with freedom comes responsibility.Explain why this idea applies not only to SouthAfricans but to people all over the world. Describe the overall trends you see in the employment graph. give your answer in the form of at least two complete sentences. Create 5 sentences using the liaisons (z and n sounds.)Part B:Create another 5 sentences using the silent -ent sound A trader sold a bag of sugar at kshs. 4000. The buyer was allowed a trade discount of 10%. If he pays the debt in two weeks and a cash discount of 3% if payment is made within one month. Calculate the amount the trader received if the buyer paid within 15days 3x^2=4x+3 Solve using quadratic formula will give brainliest if your answer is CORRECT what is the slope for 10 and 11? Which of the following is evaluating to 3(y+4)-7?