Can someone please help solve the attached :) it's on simultaneous equations combined with congruent triangles

Can Someone Please Help Solve The Attached :) It's On Simultaneous Equations Combined With Congruent

Answers

Answer 1

Answer:

2a + b = 180
 a + b = 118

a = 64, b = 56

Step-by-step explanation:

If you look at the triangle on the top right of the diagonal, there are 3 angles a, a and b. Since the 3 angles of a triangle add up to 180°

      a + a + b = 180

=>   2a + b = 180.......(1)

We are given that the largest angle is 118°

The largest angle of the parallelogram is a + b. Remember that opposite angles of a parallelogram are equal and the sum of the angles add up to 360

Therefore a + b = 118 ....(2)

Given equations (1) and (2), subtract (1) from (2):

Eq (1) - Eq(2) :

2a + b - (a + b) = 180 - 118

a = 62

Substitute for a in equation (2) to get

a + b = 118

62 + b = 118

b = 118 - 62 = 56

So the two angles are a = 64° and b = 56°

Answer 2

Answer:

a = 62, b = 56

Step-by-step explanation:

given the largest angle is 118° , then

a + b = 118 ( subtract b from both sides )

a = 118 - b → (1)

the sum of the interior angles of a quadrilateral = 360°

the angle adjacent to a is b ( alternate angles ) , then

a + b + a + a + b + a = 360

4a + 2b = 360 → (2)

substitute a = 118 - b into (2)

4(118 - b) + 2b = 360

472 - 4b + 2b = 360

472 - 2b = 360 ( subtract 472 from both sides )

- 2b = - 112 ( divide both sides by - 2 )

b = 56

substitute b = 56 into (1)

a = 118 - 56 = 62

a = 62 and b = 56


Related Questions

at an ice cream store with five flavors of ice cream (peppermint, hoarhound, chocolate malt, gingerbread, and squirrel), ice cream scoops are stored inside the ice cream containers. what is the smallest number of ice cream scoops that would need to be in use so that two of the scoops would have to be stored in the same flavor ice cream container? how many ice cream scoops must be in use if 3 of them have to be stored in the same flavor ice cream container?

Answers

ANSWER: 10 ICE-CREAM SCOOPS

There are 5 icecream flavors

For each we need 2 scoops so = 2*5 = 10 scoops

therefore ther must be 10 icecream scoops in use for five flavors.

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Find an equation for the line that passes through the points (3, -4) and (-3, -1).

Answers

This is the correct answer

Answer:

That is my own idea and I hope it is very helpful

3y=x-6 in standard form

Answers

Answer: x-3y=6

Step-by-step explanation:

so first subtract x to get -x+3y = -6 because standford is ax+by = c

and then multiply by -1 since x has to be positive

x-3y = 6 That is your answer

Please solve with an explanation

Answers

Answer:

10.8

Step-by-step explanation:

Hello!

Once, graphed, a right triangle forms, with PQ as the hypotenuse. The other two lengths are 6 and 9.

We can use the Pythagorean theorem: [tex]a^2 + b^2 = c^2[/tex]

a and b are lengthsc is the hypotenuse

Solve for PQ[tex]a^2 + b^2 = c^2[/tex][tex]6^2 + 9^2 = PQ^2[/tex][tex]36 + 81 = PQ^2[/tex][tex]117 = PQ^2[/tex][tex]\sqrt117 = PQ\\[/tex]10.8 = PQ

The length of PQ is 10.8.

5.What is the area of the triangle?Include the unit of measurein your answer.:::::

Answers

Answer: Area = 126 square inches

Explanation:

The formula for calculating the area of a triangle is expressed as

Area = 1/2 x base x height

From the information in the diagram,

base = 18

height = 14

Thus,

Area = 1/2 x 18 x 14

Area = 1/2 x 252 = 252/2

Area = 126 square inches

What is the slope of the line that passes through the points (-2, 2) and (-4, -1)?
Write your answer in simplest form.

Answers

The slope of the line that passes through the points (-2, 2) and (-4, -1) is 3/2 i.e. 1.5 .

How can we define the slope for a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is provided by the formula m = change in y/change in x = Δy/Δx, where "m" is the slope of a line.
Mathematically, slope of a line = m = (y₂ - y₁)/(x₂ - x₁)

Given, the line passes through the points (-2, 2) and (-4, -1)
Now, using the formula established in the literature, we get:
slope = m = (y₂ - y₁)/(x₂ - x₁) = (-1 - 2)/(-4 - (-2)) = -3/-2 = 3/2 = 1.5
Therefore, the slope of the line that passes through the points (-2, 2) and (-4, -1) is 3/2 i.e. 1.5 .

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What is the equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3? Responses y−1=3(x+2) y plus 1 equals 3 open parenthesis x minus 2 close parenthesis y−2=3(x+1) y minus 2 equals 3 open parenthesis x plus 1 close parenthesis y+1=3(x−2) y plus 1 equals 3 open parenthesis x minus 2 close parenthesis y+2=3(x−1)

Answers

The equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3 is y = 3x - 5

We need to find the equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3

The point slope form of a equation of a line is

y - y₁ = m(x - x₁)

y - (-2) = 3 (x - 1)

y + 2 = 3x - 3

y = 3x - 3 - 2

y = 3x - 5

Therefore the equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3 is y = 3x - 5.

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Which relation is a function?
Responses

(1, 0), (3, 0), (1, 1), (3, 1), (1, 3)
(1, 0), (3, 0), (1, 1), (3, 1), (1, 3)

(1, 1), (2, 2), (3, 3), (4, 4), (5, 8)
(1, 1), (2, 2), (3, 3), (4, 4), (5, 8)

(2, 7), (6, 5), (4, 4), (3, 3), (2, 1)
(2, 7), (6, 5), (4, 4), (3, 3), (2, 1)

(9, -3), (9, 3), (4, -2), (4, 2), (0, 0)

Answers

Answer:{(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}

Step-by-step explanation: hope this helps

PLEASE HELP I WILL GIVE BRAINLIEST TO RIGHT ANSWER!!!!
1 3/5% of what number is 0.64?

Answers

Answer:

0.64 is 1 3/5% of 40

Step-by-step explanation:

Given the slope of a line is -2 and it passes through the point (4,-5), write the equationof the line in standard form.

Answers

Answer:

The equation of the line is;

[tex]y=-2x+3[/tex]

Explanation:

Given that

the slope of a line is -2 and it passes through the point (4,-5).

Applying the slope-intercept form of equation;

[tex]y-y_1=m(x-x_1)[/tex]

Substituting the values of the slope and coordinates;

[tex]\begin{gathered} y-(-5)=-2(x-4) \\ y+5=-2x+8 \\ y=-2x+8-5 \\ y=-2x+3 \end{gathered}[/tex]

Therefore, the equation of the line is;

[tex]y=-2x+3[/tex]

Answer:

2x + y = 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (4, - 5 ) into the partial equation

- 5 = - 8 + c ⇒ c = - 5 + 8 = 3

y = - 2x + 3 ← in slope- intercept form

add 2x to both sides

2x + y = 3 ← equation in standard form

What is x in this equation
2(x-7)=-4

Answers

x = 5

2x - 14 = -4

2x = -10

x = 5

Answer: 5

Step-by-step explanation: First I took away the 2 on the left which was multiplying the brackets.  Then because I did this I had to do the opposite to the other side. -4÷2

Then I just filled in the gaps 5-7=-2

Complete the following statement. Round your answer to the nearest percent
% of $700 = $1,400

Answers

Answer:

50

Step-by-step explanation:

Solution for 700 is what percent of 1400:

700:1400*100 =

(700*100):1400 =

70000:1400 = 50

Now we have: 700 is what percent of 1400 = 50

Meow meow please help me

Answers

Answer:

area of trapezium → 1/2 × Sum of parallel sides × Distance between them.

Area → 15in² {given}

B1 → 4in

B2 → 6in

15 = 1/2 × ( 4+6 ) × h

h = 15 × 2 ÷ 10

h = 3in

I hope it's helpful

Answer:

i wouldd but likee

Step-by-step explanation:

i didnt pay a single second of attention in math

The boxplot displays the arm spans for 44 students.
Which of the following is not a true statement?

There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.

Answers

Answer:

A) there are no outliers in this distribution.

Answer:

Step-by-step explanation:

Answer there are no outlier

the teacher wants to select 6 students from this class. the first selected student will be a media helper, the second one will be a pledge/flag helper, the third one will be a pencil sharpener, the fourth one will be attendance taker, the fifth one will be a board eraser and the sixth one will be a calendar helper. from this class of 13 students, how many different ways can this selection be done?

Answers

From this class, the teacher wishes to selected six students. 2,2,2,2,2,3 different ways are there to selected from this class of 13 students.

Given that,

From this class, the teacher wishes to selected six students. The first chosen student will assist with media, the second will assist with pledges and flags, the third will sharpen pencils, the fourth will take attendance, the fifth will wipe the board, and the sixth will assist with the calendar.

We have to find how many different ways are there to selected from this class of 13 students.

For 13 students,

We divide like 2,2,2,2,2,3.

The first 2 student will be a media helper,

The second 2 students will be a pledge/flag helper,

The third 2 students will be a pencil sharpener,

The fourth 3 students will be attendance taker,

The fifth 2 students will be a board eraser and

The sixth 2 students will be a calendar helper.

Therefore, This many ways we can selected the students.

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Periodic Deposit: $? at the end of each monthRate: 7.5% compounded monthlyTime: 3 yearsFinancial Goal: $35,000O A. $2,628; $31,536 from deposits and $3,464 from interestB. $776; $27,936 from deposits and $7,064 from interestO c. $933; $33,588 from deposits and $1,412 from interestOD. $870; $31,320 from deposits and $3,680 from interest

Answers

Answer:

D. $870; $31,320 from deposits and $3,680 from interest

Explanation:

In order to calculate the monthly payment, we use the formula below:

[tex]P=\frac{A\mleft(\frac{r}{n}\mright)}{\mleft[\mleft(1+\frac{r}{n}\mright)^{nt}-1\mright]}[/tex]

Given:

• The Financial Goal, A= $35,000

,

• Rate = 7.5% = 0.075

,

• Number of compounding period = 12 (Monthly)

,

• Time, t = 3 years

Substitute into the given formula:

[tex]\begin{gathered} P=\frac{35000\mleft(\frac{0.075}{12}\mright)}{\mleft[\mleft(1+\frac{0.075}{12}\mright)^{12\times3}-1\mright]} \\ P\approx\$870 \end{gathered}[/tex]

The monthly payment is $870.

[tex]\begin{gathered} \text{Total deposit}=870\times36=31,320 \\ \text{Interests}=35,000-31,320=3680 \end{gathered}[/tex]

Option D is correct.

For f(x) = 4x + 1 and g(x) = x² - 5 find (g/f)(x)
I need help with this one :/

Answers

Answer:

always go with C- trust me its helped me alot

Step-by-step explanation:

(f+g)(x) = x2+4x−4

Explanation: add them together

f(x)+g(x)(4x+1)+(x2−5)4x+1+x2−5x2+4x−4(f+g)(x) = x2+4x−4

2. The height (cm) of a plant during a period can be described with a function where time is 24 hours after planting. y=3+34x
How tall is the plant after 4 days?
What does the value y=3 mean?

Answers

The height of plant after 4 days  =  139cm .Here y = 3 means , corresponding function when y is 3 .

What is a function?A function is an expression, rule, or law in mathematics that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are commonly represented as y = f(x), which expresses y's dependence on x, or that y is a function of x. Function formulas define the mathematical rules for connecting one set of elements to another.

Here given ,

   y = 3 + 34x

 We have to find height of plant after 4 days,

 so, x = 4,

by substituting x,

y = 3 + 34 x 4

   = 3 + 136

   = 139 cm

here y = 3 means,

The corresponding function when the value of y =3 .

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What is the slope of y = -5x - 11

Answers

Answer:

0

Step-by-step explanation:

What is the distance between 3 and 15?

Answers

The most appropriate choice for distance between numbers will be given by -

Distance between 3 and 15 is 12 units

What is distance between two numbers?

At first it is important to know about number line.

A pictorial representation of real numbers has been done along a horizontal straight line. That horizontal straight line is called number line. On a number line, all the integers has been placed at equal distance apart. In between integers, fractions, decimal numbers, rational numbers and irrational numbers can be marked. Number line can be used for addition or subtraction.

Distance between two numbers indicates how far one number is situated from other number on the number line.

Here,

Distance between 3 and 15 = 15 - 3

                                              = 12 units

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The width of a rectangle is 5 feet, and the diagonal length of the rectangle is 12 feet. Which measurement is closest to the length of this rectangle in feet?

Answers

The measurement is closest to the length of the rectangle is √119 ft.

What is the measure of the length of the given rectangle?

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c = √( a² + b² )

Where c is the diagonal that divides the rectangle into two equal triangle, a and b are the other legs of the triangle.

Given the data in the question;

With ( First leg ) a = 5ftDiagonal c = 12ftSecond leg b = ?

Plug the values into the formula and solve for b.

12ft = √( (5ft)² + b² )

Take the square of both sides

( 12ft )²  = (5ft)² + b²

144ft²  = 25ft² + b²

b² = 144ft² - 25ft²

b² = 119ft²

b = √( 119ft² )

b = √119 ft

Therefore, the measure of the length is √119 ft.

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Select the correct answer.
Which graph shows a function and its inverse?
A. The first graph
B. The second graph
C. The third graph
D. The last graph

Answers

Answer:

B

Step-by-step explanation:

It is asking which graph show (x,y) for one line and (y,x) for the other line.

For example, the blue line shows (0,2) as a point and the red line shows ( 2,0) and so on and so on.

Nancy spent 2 1/2 hours working on her homework on the weekend. she spent 4/5 of her time working her ela homework. how much time did nancy spend working on her ela homework?

Answers

The time Nancy spent working on her ela homework is equal to 2 hours.

The time Nancy spent working on her ela homework can be calculated by multiplication.

We can calculate it by multiplying the fraction of time spent by her on ela homework by the total time she spent on her homework.

As the total time spent by her on homework is 2 1/2 hours we can covert it into decimals as;

2 1/2 = 5/2 = 2.5 hours

Now multiplying it by the fraction of her time spent on ela homework,

Time spent on ela homework = 4/5 × 2.5

Time spent on ela homework = 10/5

Time spent on ela homework = 2 hours.

Hence Nancy spent 2 hours working on her ela homework.

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I need to know what system of inequalities is graphed below

Answers

SOLUTION:

For inequalities, the solution to is usually where the two regions meet.

The graphs here are:

[tex]\begin{gathered} x-3y\leq6\text{ (thick lines)} \\ \text{Here, checks the graph testing points (3,-1) and (0,-2)} \\ 2x\text{ }+\text{ y }>2.\text{ (broken lines)} \\ \text{Here, the checks the graph testing points (}0,2)\text{ and (1,0)} \end{gathered}[/tex]

Final answer:

The final answer here is Option (B)

1. Given the function g(x)=(x-4)² + 3
I’ve been asked to graph the function but they gave me no reference points to be able to find my corresponding points how do I find them with just the function?

Answers

There is no need of reference points to plot the graph of this function and we can select our reference range by ourselves as discussed above. The graph is attached in the end.

What is a function?

A function is a relation between a independent variable and a dependent variable such that the value of dependent variable depends upon the independent one. For example -

f(x) = 2x + 5

g(x) = 4x + 9

Given is function g(x) = (x - 4)² + 3

There is no need of any reference points to graph this function. You can take the reference points in a specific range. For example, you can plot the graph for the values of [x] from x = -5 to x = 5. It can be noticed that we have taken 5 - 5 points on both sides of the [x] axis. Make sure that you ensure this symmetry. Range could be any, for example from x = - 7 to 7, x = - 10 to 10 etc. The given function is -

g(x) = (x - 4)² + 3

We will plot the graph for x = -3 to x = 3

g(-3) = 52

g(-2) = 39

g(-1) = 28

g(0) = 19

g(1) = 12

g(2) = 7

g(3) = 4

Now, we will plot these coordinates on the graph. The plotted graph is attached with the answer.

Therefore, we can conclude that, there is no need of reference points to plot the graph of this function and we can select our reference range by ourselves as discussed above.

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help please ill give brainlest !!

Answers

Answer:

-31, 9, 1, 5, 37

Step-by-step explanation:

f(x) = -2(-2)^2 + 1

f(x) = 4^2 + 1

f(x) = 8+1

f(x) = 9

f(x) = -2(0)^2 +1

f(x) = 0^2 + 1

f(x) = 0 + 1

f(x) = 1

f(x) = -2(1)^2 + 1

f(x) = -2^2 + 1

f(x) = 4+1

f(x) = 5

f(x) = -2(3)^2 + 1

f(x) = -6^2 + 1

f(x) = 36+1

f(x) = 37

Find the distance between the ordered pairs.
(w + 2, m) and (2t, c - 3) when w = 6, m = 3, t = 4
and c = 10.

Answers

The distance between the ordered pairs is 4 units

What is distance formula?

Distance formula calculates the distance between two coordinates. it calculates the straight line distance between two points. The formula can be given as [tex]distance=\sqrt{(c-a)^{2}+(d-b)^{2} }[/tex] for the coordinates (a, b) (c, d)

We are given the ordered pair (w+2,m) and (2t,c-3)

We are given the value w = 6, m = 3, t = 4 and c = 10.

Substituting the values in the pairs

We get,

(6+2,3),(2(4),10-3)

(8,3),(8,7)

We use distance formula to find the distance

[tex]d=\sqrt{(8-8)^{2} +(7-3)^{2} }\\ d=\sqrt{4^{2} }\\ d=4[/tex]

Hence the distance between the ordered pairs is 4 units.

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Kyle just graduated from college and got his first job, he has $45,000 in student loan debt, wants to buya new car, and is considering opening up a retirement account. He has a disposable income of$300/month, what would you recommend he do with this money? Why?

Answers

Problem

Kyle just graduated from college and got his first job, he has $45,000 in student loan debt, wants to buy a new car, and is considering opening up a retirement account. He has a disposable income of $300/month, what would you recommend he do with this money? Why?

Solution

For this case the best option would be put the $45000 in a bank with a compound interest

And with the earnings each month of 300$ he can put the half of this into the account and the remain to spend on other things

Which of the following is used to identify outliers in a set of data?

1.5(IQR)
1.5(range)
2(mean)
2(median)

Answers

A) 1.5 (IQR) is used to identify outliers in a set of data.

What is the Interquartile range (IQR)?

The interquartile range is a measure of statistical dispersion, or the spread of the data, in descriptive statistics.

The middle 50%, fourth spread, or H-spread are additional names for the IQR.

It is described as the discrepancy between the data's 75th and 25th percentiles.

The interquartile range is the best tool to use to find all of your outliers (IQR).

Knowing the IQR makes it simple to identify outliers because it represents the middle portion of your data.

Find the median (middle value) of the lower half and upper half of the data before calculating the interquartile range (IQR).

Quartile 1 (Q1) and Quartile 3 are these values (Q3).

The IQR represents the variation between Q3 and Q1.

As it is given in the description itself, the interquartile range is the best tool to use to find all of your outliers (IQR).

Therefore, (A) 1.5 (IQR) is used to identify outliers in a set of data.

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The correct question is given below:

Which of the following is used to identify outliers in a set of data?

(A) 1.5(IQR)

(B) 1.5(range)

(C) 2(mean)

(D) 2(median)

P.s hopes this helps

48/8 6/w

1=?



Help me please helpp

Answers

Answer:

w = 1

Step-by-step explanation:

You have to divide 48 by 8 to get 6, so you have to divide 8 by 8 to find w.

8/8 = 1

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