The sum of two numbers is 78. Their difference is 32. Write a system of equations that describes this situation. Solve by elimination to find the two numbers. x + y = 32 y – x = 78 50 and 24 x – y = 78 x + y = 32 54 and 24 x + y = 78 x – y = 32 55 and 23

Answers

Answer 1

Answer:

55, 23, x+y =78; x-y =32

Step-by-step explanation:

-the system of equation

x+y = 78

x-y = 32

-solve by elimination

x-y = 32, add y to both sides

x= y+32

x +y =78, substitute x= y+32

y+32+y = 78, subtract 32 from both sides

y+y = 78-32, combine like terms

2y = 46, divide both sides by 2

y = 23

x +y =78, substitute y = 23

x+ 23 =78, subtract 23 from both sides

x = 78-23, combine like terms

x = 55

Answer 2

Answer:

The equation:

x + y = 78

x - y = 32

The answers:

x= 55

y = 23

Step-by-step explanation:

Call the first number (x) and the second number (y). Take is as a given that (x) is larger than (y). One is given the following information:

"The sum of two numbers is 78"

"Their difference is 32"

Rewrite this in numerical terms:

x + y = 78

x - y = 32

The process of elimination is a way of solving a system of equations. First one manipulates one of the equations such that one variable has an inverse coefficient of its like term in the other equation. This step one does not need to be performed, as the coefficients of the term (y) are inverses in the equations. Next, one adds the equations. Then one uses inverse operations to solve for the remaining variable. Finally, one back solves for the value of the eliminated variable by substituting the value of the solved variable into one of the equations, and simplifying.

Add the equations,

x + y = 78

x - y = 32

____________

2x = 110

Inverse operations,

2x = 110

x = 55

Back solve,

x + y = 78

x = 55

55 + y = 78

y = 23


Related Questions

Olympia ate lunch at a restaurant. The amount of her check was $6.89. She left $8.00 on the table, which included the amount she owed plus a tip for the waiter. Which equation shows t, the amount of her tip, in dollars?
6.89 + t = 8.00
6.89 - t = 8.00
6.89t = 8.00
6.89 = 8.00 Divided by t

Answers

Answer:

not sure if the answer is obvious but I'd say $6.89 + t = $8.00

Step-by-step explanation:

so to make it more understandable you have to first go over the question and ask your self is the tip included in the totally amount owed or is it apart

after you figure out that its apart all you have to do is plug in the numbers you could verify this by checking every equation like this

$6.89 + t = $8.00 (t) in this case is the tip which would be $1.11 all you do to arrive at that answer is subtract the amout owed from the amount given like this $8.00 - $6.89 = $1.11 which will be your tip

now continue checking your answer next is , $6.89 - t = $8.00

which would be $6.89- $1.11 = $5.78 not quite right because now she is short on the pay , on to the next its $6.89t= $8.00 which would be $6.89 x $1.11= $7.65 rounded to neartest tenth which would included the amount but not all the tip given meaning tip would be short 0.35 cents and finally $6.89= $8.00 divided by t , now this takes the amount give which is $8.00 and divides by t which is $1.11 doing this $6.89 = $8.00/$1.11 which it is trying to imply that $6.89 is equal to $7.21 which would be incorrect making the only reasonable equation $6.89 + t = $8.00 reaveling that the tip given was $1.11

hopefully that help maybe i can get brainlist?!

Answer:

6.89 + t = 8.00

Step-by-step explanation:

it's A

Edge 2021

When 4x + 4x + 1 = 33 is solved, the result is:

Answers

Answer:

x = 4

Step-by-step explanation:

1. 8x+1 = 33 and the 4x together

2. 8x = 32 subtract 1 from each side

3. x = 4 Divide both sides by 8

Answer:

x=4

Step-by-step explanation:

4x+4x+1=33

Combine like (similar) terms:

8x+1=33

Rearrange terms to solve for x:

8x=33-1

8x=32

[tex]\frac{8x}{8} =\frac{32}{8}[/tex]

x=4

Therefore, x=4.

The length of a rectangle is 2 Inches less than three times its width, and its perimeter is 36 Inches. Find the width of the
rectangle

Answers

Answer: Width = 5 inches

Concept:

Here, we need to know the idea of the perimeter.

A perimeter is a path that encompasses/surrounds/outlines a shape.

Perimeter of rectangle = 2 (w + l)

w = width

l = length

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

w = w

l = 3w - 2

P = 36 inches

Given formula

P = 2 (w + l)

Substitute the value into the formula

36 = 2 (w + 3w - 2)

Simplify values in the parentheses

36 = 2 (4w -2)

Divide 2 on both sides

36 / 2 = 2 (4w - 2) / 2

18 = 4w - 2

Add 2 on both sides

18 + 2 = 4w - 2 + 2

20 = 4w

Divide 4 on both sides

20 / 4 = 4w / 4

w = 5

Hope this helps!! :)

Please let me know if you have any questions

Unit Rates
Assignment Active
Completing a Rate Table
Miles
Hours
Margie can walk 3.5 miles in 1 hour.
Find the values of a, b, c, and that complete the table
showing this relationship
3.5
a=
7
v
a
5
3
d=
14
e
5

Answers

Answer:

its c

Step-by-step explanation:

i did it on ed

Answer:

Heres the answer!

Step-by-step explanation:

Find the slope of the line that passes through (7, 2) and (9, 9).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Answer:

the slope is m=7/2

Step-by-step explanation:

Answer:

7/2

Step-by-step explanation:

please help! :)

Answer question B.

Thank you!​

Answers

Answer:

t f dis say mane ion speak italian

Step-by-step explanation:

ion think anyone can read that

Hellllpppppp please?????

Answers

Answer:

∠ 1 = 65°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

5x - 10 is an exterior angle of the triangle, then

5x - 10 = 3x + 40 ( subtract 3x from both sides )

2x - 10 = 40 ( add 10 to both sides )

2x = 50 ( divide both sides by 2 )

x = 25

The sum of the 3 angles in a triangle = 180° , so

∠ 1 + 40 + 3x = 180°

∠ 1 + 40° + 3(25) = 180°

∠ 1 + 40° + 75° = 180°

∠ 1 + 115° = 180° ( subtract 115° from both sides )

∠ 1 = 65°

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 46 feet. Use your graphing calculator to answer the following questions. Write your answers in percent form. Round your answers to the nearest tenth of a percent. a) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 210 feet

Answers

Answer:

On the graphing calculator, use the function normCdf, where

lower bound = -9999upper bound = 210mean = 250standard deviation = 46

It will result in normCdf(-9999,210,250,46) ≈ 0.192269 or 19.2269%

which choice is equivalent to the expression below when x > 0?
√50x³ - √25x³ + 5√x³ - √2x³
A. 4√x
B. 28√x³³
C. 5√2x
D. 4x√2x

Answers

Answer:

D

Step-by-step explanation:

5[tex]\sqrt{2x^3}[/tex] -5[tex]\sqrt{x^3}[/tex] + 5√x³ -√2x³ = 4[tex]\sqrt{2x^3}[/tex] = 4x√2x

the base of a right prism is an equilateral triangle each of whose sides measures 4cm. The altitude of the prism measures 5cm. Find the volume of the prism

Answers

Volume = (√3/4)a^2 × h

= (√3/4)4^2×5

=(√3/4)16×5

=√3×4×5

=20√3

Ans Volume is 20√3cm^2

Answered by GauthMath if you like please click thanks and comment thanks

which of the following is a tinomial

Answers

B! There are three parts of the equation, hence "tri-"nomial :)
Good luck.

Which of the following sets represent D ∪ E?
{2, 4, 5, 6, 8, 15}
{2, 4, 5, 6, 8, 10, 15, 20}
{10, 20}
{3, 7, 9, 11}

Answers

Answer:

{2,4,5,6,8,10,15,20}

Answer:

{ 2,4,5,6,8,10,15,20}

Step-by-step explanation:

D ∪ E

This means the union of the two sets or what is in both circles with no duplicates

{ 2,4,5,6,8,10,15,20}


1) What is the common difference of the arithmetic sequence 5, 8, 11, 14?

Answers

Answer:

The common difference of the sequence 5,8,11,14 is 3.

Answer:

the answer is 3

Step-by-step explanation:

5 + 3 = 8

8 + 3 = 11

11 + 3 = 14, therefore the common difference of the arithmetic sequence is three.

Suppose that 65% of the people who inquire about investments at a certain brokerage firm end up investing in stocks, 38% end up investing in bonds, and 36% end up investing in both stocks and bonds. What is the probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both)?

Answers

Answer:

0.67 = 67% probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both).

Step-by-step explanation:

This question is solved treating these probabilities as Venn events.

I am going to say that:

Event A: Person invests in stocks.

Event B: Person invests in bonds.

65% of the people who inquire about investments at a certain brokerage firm end up investing in stocks

This means that [tex]P(A) = 0.65[/tex]

38% end up investing in bonds

This means that [tex]P(B) = 0.38[/tex]

36% end up investing in both stocks and bonds.

This means that [tex]P(A \cap B) = 0.36[/tex]

What is the probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both)?

This is [tex]P(A \cup B)[/tex], given by the following equation:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

Considering the values we have for this problem:

[tex]P(A \cup B) = 0.65 + 0.38 - 0.36 = 0.67[/tex]

0.67 = 67% probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both).

solve the problem below

Answers

Answer:  207 degrees

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

Explanation:

Refer to the diagram below.

There's a lot of info given to us that we don't need (and won't use).

The only key piece of info we'll really use is the fact that angle XZY is 27 degrees.

Draw in segments RU and RT to form quadrilateral TRUZ

Focusing solely on this quadrilateral, we see that the angles T and U are 90 degrees each (since the tangents are perpendicular to the radii at the point of tangency). Furthermore, we see that angle Z is 27 while angle R is x

For any quadrilateral, the four angles always add to 360 degrees

T+R+U+Z = 360

90+x+90+27 = 360

x+207 = 360

x = 360-207

x = 153

That means angle R of quadrilateral TRUZ is 153 degrees.

Furthermore, it means angle TRU is 153 degrees.

By extension, it indicates that minor arc TU is 153 degrees.

That makes arc TSU = 360 - (minor arc TU) = 360 - 153 = 207 degrees

By Joining TR and UR we got 2 right angles and a Quadrilateral

now

In a Quadrilateral sum of angles=360°

[tex]\\ \large\sf\longmapsto x+90+90+27=360[/tex]

[tex]\\ \large\sf\longmapsto x+180+27=360[/tex]

[tex]\\ \large\sf\longmapsto x+207=360[/tex]

[tex]\\ \large\sf\longmapsto x=360-207[/tex]

[tex]\\ \large\sf\longmapsto x=153°[/tex]

<TSU =360-153=207°

write a linear equation in standard form for the line that goes through(2.-3) and (4 -2)

Answers

Answer:

y =1/2x -4

Step-by-step explanation:

x1 y1  x2 y2

2 -3  4 -2

   

(Y2-Y1) (-2)-(-3)=   1  ΔY 1

(X2-X1) (4)-(2)=    2  ΔX 2

   

slope=   1/2    

B= -4          

   

Y =0.5X -4    

Nuclear Power is a perfect example of exponential relations. Canada produces over half of its electricity using nuclear reactors. One of the major problems associated with nuclear power generation is the radioactive waste. Currently all nuclear waste is stored on site at the power plant and there is no solution for the long term waste.

A) What would you do with the long term waste?

B) How would you take care of Canada’s energy needs for the future?

Answers

Nuclear waste is a long term waste and is a major problem the world is facing regarding its disposal.

Answer :

Nuclear fission is exponential. This is known as chain reaction and a number of uranium atoms are fission together to increase exponentially.

Canada, for example produces electricity using the process of fission process in its nuclear reactors.

The nuclear waste includes :

used reactor fuel,  uranium mill tailings and other radioactive wastes.

These wastes remain radioactive and are dangerous for the human health.

A).

The long term nuclear waste are stored in deep excavations and covered with rocks and mud. They are also stored in some high density and thick cylinders and remained isolated in the dump yard from the people and nature.

B).

Most of the energy requirement of Canada can be taken care off by using wind energy. Canada is planning to set up wind energy mills in most of its part and generate electricity from it.Canada has also installed several solar power projects which is clean and can help the people to use this solar energy to produce electricity.

Learn More :

https://brainly.com/question/1013815  

Find the area of a parallelogram with a base of 9m and a height of 5​

Answers

Answer:

A=45m²

Step-by-step explanation:

A=bh=9·5=45m²

Using the graph, determine the equation of the axis of symmetry.​

Answers

Answer:

x = 6

Step-by-step explanation:

The axis of symmetry passes through the vertex of the graph

It is a vertical line with equation

x = c ( c is the x- coordinate of the vertex )

vertex = (6, 1 ) with x- coordinate 6 , then

equation of axis of symmetry is x = 6

WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!!

2 questions

Answers

Answer:

Confidence Interval - "P" values  

(0.4433 , 0.5444 )

~~~~~~~~~~~~~~~~~~~~~~~

[tex]\mathrm{Expand\:}\left(x+4y\right)^3:\quad x^3+12x^2y+48xy^2+64y^3[/tex]

in you image it is the last on "D"

Step-by-step explanation:

Confidence Level - "P" values  

99% 2.58

Confidence Interval - "P" values  

(0.4433 , 0.5444 )  

2 cos(3x+40°)-1=0
Thanks for your question

Answers

Step-by-step explanation:

gjfjdjjfu from Florida for Christmas and technology center and technology and technology

HELP ASAP LIKE PLEASE

Answers

Answer: (3b+2)(b+2)

Step-by-step explanation:

PLz, Help fast! 100 points
A line is drawn on a scatter plot, as shown below:

A graph shows values till 10 on both x- and y axis with increments of 1.Dots are shown at 0.5, 7.5 and 1.8, 6.5 and 3, 6 and 4.4, 5 and 4.8, 4 and 5.9, 3.2 and 6.6, 2 and 7.5, 2.5 and 8, 1 and 8.8, 0. A straight line joins the ordered pairs 0, 7.9 and 10, 0.

Which statement best describes the line?

Answers

Answer:

It can be the line of best fit because it closely fits the data points.

Step-by-step explanation:

The line is near the data points and goes down from left to right just like the data points.  It is just above or just below the data points.

Answer:

guy above is right

Step-by-step explanation:

Reflect triangle ABC across the line x = 2. Then the reflect (image) A', B' and C' across the line x = -3.

Answers

Answer:

The first reflection makes the points (1,1), (-1,1) and (1,4) and the second reflection changes THOSE to (-7,1) (-5,1) and (-7,4).  Just connect the dots to make the triangle.

Let me know if anything did not make sense.  

Step-by-step explanation:

Reflect just means how far away is each point to the line of reflection?  then ake a new point the sae distance, but in the opposite direction.  You always want to use a line that makes a right angle to the line of reflection too, so since x=2 and x=-3 are verticallines you are going to use horizontal lines to measure where A, B and C are.

So the three points are A:(3,1), B:(5,1) and C:(3,4)

Now use a horizontal line to measure how far A, B and C are from x=2.

A is 1 spance to the right of x=2, so A' (what A turns into) is 1 space to the left.  so (3,1) becomes (1,1)  The y value does not change since you are only using the horizontal direction for reflection.  B changes fro (5,1) to (-1,1) and finally C changes from (3,4) to (1,4)

Now the second reflection is the exact same process, but witht he new points reflected across x = -3.  So the new points are (-7,1) (-5,1) and (-7,4).

What is the numerical Absolute values of -16

Answers

Answer:

16

Step-by-step explanation:

The absolute value always gives a positive value , that is

| - a | = | a | = a , then

| - 16 | = | 16 | = 16

I NEED HELP

THERE ARE TWO OTHER QUESTIONS AS WELL

Answers

Answer:

Please find attached the drawing of ABCD, A'B'C'D', and A''B''C''D'', created with MS Excel

Step-by-step explanation:

The given composition of transformation is [tex]r_{y-axis} \ \circ \ r_{x = - 4}[/tex]

The transformation on the right, [tex]r_{x = - 4}[/tex], is carried out first as follows;

The point A with coordinate (-7, 7) reflected across the line x = -4, gives;

A(-7, 7) [tex]r_{x = - 4}[/tex] → A'(-1, 7)

Similarly, we have;

B(-5, 7) [tex]r_{x = - 4}[/tex] → B'(-3, 7)

C(-5, 1) [tex]r_{x = - 4}[/tex] → C'(-3, 1)

D(-7, 1) [tex]r_{x = - 4}[/tex] → D'(-1, 1)

Therefore, the image of the given rectangle after reflection across the lie, x = -4, is A'(-1, 7), B'(-3, 7), C'(-3, 1), and D'(-1, 1)

The second transformation, [tex]r_{y-axis}[/tex], is found as follows;

(x, y) [tex]r_{y-axis}[/tex] → (x, -y)

Therefore, we have;

A'(-1, 7) [tex]r_{y-axis}[/tex] → A''(-1, -7)

B'(-3, 7) [tex]r_{y-axis}[/tex] → B''(-3, -7)

C'(-3, 1) [tex]r_{y-axis}[/tex] → C''(-3, -1)

D'(-1, 1) [tex]r_{y-axis}[/tex] → D''(-1, -1)

The points ABCD, A'B'C'D', and A''B''C''D'' are plotted on MS Excel and the points joined with straight lines to form the drawing of the triangles as shown in the attached figure.

PLEASE HELP 25 MINUTES LEFT
38
Marlene wrote an arithmetic sequence where al
=
8 and the common difference is -3.
What is a rule for the nth term of this sequence?

Answers

Answer:

D

Step-by-step explanation:

The nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 8 and d = - 3 , then

[tex]a_{n}[/tex] = 8 - 3(n - 1) = 8 - 3n + 3 = - 3n + 11 → D

Can someone help me please

Answers

Answer:

=2⁵it's option B 2⁵(B) 2⁵ is the right option

Create a triangle ABC of your choice. Using GeoGebra tools, construct the angle bisectors of ∠A and ∠B. Mark the intersection point of the angle bisectors, and label it point D.
Create a line through point D perpendicular to .
Find the intersection of line segment and the perpendicular line, and label it point E. With point D as the center, create a circle passing through point E.
Measure and label the radius of the inscribed circle of ΔABC on the diagram.
Take a screenshot of your result, and paste it below.

Answers

The steps to create attached screenshot of the inscribed circle of triangle ΔABC using GeoGebra tools includes;

1) Clicking on the Geometry link, under Powerful Math Apps group

2) On the opened Geometry page click on the Polygon icon and follow the instructions that come up, which is Select all vertices and then the first vertex (selected) again (a second time)

3) Once the triangle is created, select the Angle Bisector icon, under the Construct group; A message will appear, asking to Select three points or two lines, select three vertex, of the triangle created with a mouse click, with the vertex A in the center, such as BAC, or CAB a straight line representing the angle bisector of angle ∠A is created

4) Repeat the above to create the angle bisector of angle ∠B

5) Click on the Point button under the Basic Tools group, then click on the intersection of the two angle bisectors created above, the point will be automatically labelled point D

6) Click on the Perpendicular Line, icon under the Construct group, then click on point D, and then the line AB to draw the perpendicular from D to AB

7) Click on the point Point icon and then the intersection point of the perpendicular from D and AB to label the point E

8) Click on the Circle with Center basic tool and then points D and E above, to create the inscribed circle of triangle ΔABC

9) Select the Segment tool, then select the center of the circle and a point

on the circumference. Click on the label, from the pop up options, select

the label option AA then change the label of the segment created to Radius

and select Show Label and Show Value. The inscribed circle of ΔABC created with GeoGebra tools is attached

Learn more about GeoGebra hear;

https://brainly.com/question/10400398

Answer:

Step-by-step explanation: from edmentum

Please help me factorise these and expand these brackets

Answers

Answer:

-9xy+16x

Step-by-step explanation:

x(y-2)+3x(6-y)-7xy

xy-2x+18x-3xy-7xy

xy-3xy-7xy-2x+18x

-9xy+16x

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