The sum of two integers is 9 their difference is 5 what are the two integers

Answers

Answer 1

x+y=9 x=9-y
solve for x
x-y=5 so substitute x by 9-y
9-y-y=5
9-2y=5 isolate
9-2y-9=5-9
-2y=-4 divide both sides by -2
-2y/-2=-4/-2
y=2 and x=9-2=7
check for x+y=9
7+2=9
check for x-y=5
7-2=5 so x=7 and y=2

Answer 2

The values of the two integers are 7 and 2 respectively.

Let the two integers be a and b respectively.

In this exercise, you're required to determine two integers from the given word problem.

Thus, we would write a mathematical (algebraic expression) for the sentence.

Translating the word problem into an algebraic expression, we have;

The sum of two integers is 9;

[tex]a + b =9[/tex] ....equation 1.

The difference between the two integers is 5;

[tex]a - b = 5[/tex] equation 2.

Solving the systems of linear equations by using the elimination method, we have:

[tex]2a = 14[/tex]

Dividing both sides by 2, we have:

[tex]a = \frac{14}{2}[/tex]

a = 7

To find the value of y:

[tex]a + b =9\\\\7 +b=9\\\\b =9-7[/tex]

b = 2

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Related Questions

Can you help me solve this proof please?

Answers

Okay, so I haven't done proofs in a bit, so when it comes to proving that lines are congruent (or angles), you can try to prove that the triangles are congruent (CPCTC- Corresponding Parts of Congruent Triangles are Congruent). To prove that triangles are congruent, use SSS (Side side side- meaning all sides are congruent), ASA (angle side angle- meaning corresponding angle, then side, then angle are congruent), SSA (2 corresponding sides are congruent and an angle is also congruent) or SAS (you get it). We should use ASA, since obviously it says that ABD and CBD are congruent and obviously BD and BD are congruent and ADB aND CDB are congruent (both are 90degrees). So, we have proven that these traingles are congruent. Now use CPCTC as the last step, since AD and CD are corresponding parts of the triangles.

For the given function, find the vertical and horizontal asymptote(s) (if there are any). f(x) = the quantity x squared plus three divided by the quantity x squared minus nine

Answers

The vertical asymptotes are: "x = 3" and "x = -3" .
__________________________________________
The horizontal asymptote is: "y = 2" .
___________________________________________
Explanation:
___________________________________________

f(x) = [tex] \frac{x^{2}+ 3}{ x^{2} - 9}[/tex] ;

We know that "(x² − 9) ≠ 0 ; since we cannot divide by "0" ; so the "denominator" in the fraction cannot be "0" ;

since: 9 − 9 = 0 ; "x² " cannot equal 9.

So, what values for "x" exist when "x = 9" ?

x² = 9 ;

Take the square root of EACH SIDE of the equation ; to isolate "x" on one side of the equation ; and to solve for "x" ;

√(x²) = √9 ;

x = ± 3
__________________________________________
So; the vertical asymptotes are: "x = 3" and "x = -3" .
__________________________________________
The horizontal asymptote is: "y = 2" .
__________________________________________
(since: We have: f(x) = [tex] \frac{x^{2}+ 3}{ x^{2} - 9}[/tex] ;

The "x² / x² " as the highest degree polymonials; both with "implied" coefficients of "1" ; and both raised to the same exponential power of "2".

A can of paint is 15 centimeters high and has a ddiameter of 13.6 cm. what is the volue of the can? Round to the nearest tenth.

Answers

Hello! A can is the shape of a cylinder. The formula for the volume of a cylinder is this: pi * r^2 * h. The radius is 1/2 of the diameter. Half of 13.6 is 6.8. 6.8^2 is 46.24. 46.24 * 15 is 693.6. Now, we can multiply by pi as 3.14. 693.6 * 3.14 is 2,177.904 or 2,177.9 when rounded to the nearest tenth. The volume of the cam is approximately 2,177.9 cubed centimeters.

Answer:

V=πr2h=π·6.8^2·15≈2179.00866

2179 cm^3

Step-by-step explanation:

In isosceles triangle the length of the base is twice shorter than the length of a leg. The perimeter of this triangle is 50cm. Find the lengths of all sides.

Answers

Perimeter is sum of all 3 sides. Isosceles triangle has two same sides and one short side.
If the short side is X, the other two sides would be 2X and 2X (since the short side is twice shorter)
P = x + 2x + 2x
50 = 5X
10 = X
Short side is 10, other two sides are 2(10) or 20.

The coordinates of the vertices of quadrilateral JKLM are J(-3,2), K(4,-1), L(2,-5) and M(-5,-2).

Find the slope of each side of the quadrilateral and determine if the quadrilateral is a parallelogram.

Answers

Slope of JK=((-1)-2)/(4-(-3)=-3/7 Slope of KL=((-5)-(-1)/(2-4=2 Slope of LM=((-2)-(-5))/(-5-2)=-3/7 Slope of MJ=(2-(-2))/((-3)-(-5))= 2 JK is parallel to LM and KL is parallel to MJ. Therefore JKLM is a parallelogram.

What is the measure of an angle if the measure of its supplement is 39 degrees more than twice the measure of its complement?

Answers

angle is x. sup - adds up to 180. comp adds up to 90

180-x = 2(90-x)+39
180-x = 180-2x+39
180-x = 219-2x
180+x = 219
x = 39

Measure of angle is equals to 39degrees as per given conditions of supplement and complement angles.

What is angle?

" Angle is defined as when two rays meet at one endpoint known as vertex."

According to the question,

'x' represents the measure of an angle

Measure of its supplement angle = 180 - x

Measure of its complement angle= 90 - x

As per given condition of angle we get,

[tex]180 - x = 2(90 - x) +39\\\\\implies 180-x= 180 -2x +39\\\\\implies 2x-x = 39\\\\\implies x=39degrees[/tex]

Hence, measure of angle is equals to 39degrees as per given conditions of supplement and complement angles.

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What do they call the guy who invented the first blue jeans

Answers

Answer:

Levi Strauss!

Step-by-step explanation:

By the 1860s, Levi Strauss's blue pants were daily wear for miners and farmers and cattlemen throughout the West. In 1873 he bought, for $69—the price of the patent application — an idea from a Russian immigrant tailor in Reno for making miner's pants stronger by riveting the critical seams.

Hope this helped!

A stop sign is a regular octagon formed by cutting triangles off the corners of a square. if we have a square with sides of length square root 2, what is the side length of the resulting octagon

Answers

the answer is 3.5147 inches

Final answer:

The side length of the resulting octagon is 2√2.

Explanation:

A stop sign is a regular octagon formed by cutting triangles off the corners of a square. To find the side length of the resulting octagon, we can use the Pythagorean theorem. Since the square has sides of length √2, its diagonal can be found by multiplying its side length by √2. This gives us a diagonal length of 2√2. The diagonal of each triangle cut off the corners of the square will be the side length of the resulting octagon. So, the side length of the octagon is 2√2.

The sum of two numbers is 35 . the smaller number is 19 less than the larger number. what are the numbers?

Answers

let the smaller number be x and the larger be (x+19)
x+x+19=35
2x=16
x=8
x+19=27

the numbers are 8 and 27.

Help please
Solve for r.

s=2πrh

Answers

s/2πh=r

hope this helps u

Here it is
I hope that will help you

Nathan and Steven stacked boxes on a shelf. Nathan lifted 13 boxes and Steven lifted 15 boxes. The boxes that Nathan lifted each weighed 12 lb more than the boxes Steven lifted.

Let s represent the weight of the boxes that Steven lifted.

Which expression represents the total number of pounds Nathan lifted?

s + 12

12(s+13)

15(s+12)

13(s+12)

Answers

13(s+12) is your answer
13 boxes that each weigh 12 more pounds than steven's boxes.

Answer:

13(s+12) is your answer

Step-by-step explanation:

Tape diagram to subtract 33-19

Answers

well 33 - 19 = 14 and what do u mean tape diagram?

To subtract 19 from 33 using a tape diagram, draw a rectangle labeled 33, mark off a section labeled 19, and the unshaded difference represents the result, which is 14.

To create a tape diagram to show the subtraction of 33-19, we start by drawing a long rectangle to represent the number 33. We then mark off the length that represents the number 19 on the same tape, indicating the part we want to subtract. Lastly, the remaining part of the tape diagram represents the difference between the two numbers.

Draw a rectangle and label it 33.Mark a section of the rectangle and label it 19.Shade in or distinguish the remaining part of the rectangle; this is the result of 33 minus 19.See the unshaded part, which represents the difference, and count if necessary to find that it equals 14.

The final result is the length of the unshaded part of the tape diagram, which shows the difference when you subtract 19 from 33.

A one celled organism measures 32 millimeters in a length in a photograph. If the photo has been enlarged by a factor of 100, what is the actual length of the organism? Show your work

Answers

Final answer:

The actual length of the organism is 0.32 millimeters, which is obtained by dividing the photograph length (32 mm) by the magnification factor (100).

Explanation:

To determine the actual length of the one-celled organism when the photograph has been enlarged by a factor of 100, we use the formula:

Actual length = Photograph length ÷ Magnification factor

Substituting the given values:

Actual length = 32 mm ÷ 100

Actual length = 0.32 mm

This calculation shows that the actual length of the organism is 0.32 millimeters, which is equivalent to 320 micrometers (320 µm). It's interesting to note that this is well within the size range for many microorganisms, which may require magnification to be seen clearly, such as with a microscope.

If 5(x+7)=-3, then 5x+35=-3

Answers

5(x+7)=-3
1st step: Distributive Property
5x+35=-3
So, yes this is true.

is it possible to draw three lines in two planes such that all three lines are skew?

Answers

Answer with explanation:

→Two lines in three dimensional plane are said to be Skew if they are neither parallel nor Intersecting.

→Skew lines can be drawn in three dimensional plane only.

→Drawn two skew lines in a Plane , and then drawn another line in a plane and found that , they are skew.

⇒Yes, it is possible to draw three lines in two planes such that all three lines are skew.

Skew lines are non-coplanar lines that are not parallel, and they do not intersect.

In a 2D plane, it is not possible to draw three skew linesIn a 3D plane, it is possible to draw three skew lines

The question does not state the type of plane. So, I will answer this question in 2 ways.

(a) 2D plane

Lines in 2D planes can only be drawn in a flat direction.

This means that, when three lines are drawn in the two planes, one of the following would happen.

The three lines would intersectTwo lines would intersect

See attachment for illustration

So, 3 lines in a 2D plane cannot be skewed lines

(b) 3D plane

Lines in 3D planes can only be drawn in several directions.

The above statement imply that:

Several lines can be drawn where none of the lines would be parallel and none of the lines would intersect.

This means that, when three lines are drawn in the two planes, one of the following would happen.

The three lines would intersectTwo lines would intersectNone of the lines would intersect

The third highlight means that:

It is possible to have skew lines in a 3D plane

Answers

9/15, it can be simplified to 3/5

9/15
9 / 3 = 3
15 / 3 = 5

Question 25 the sum of three numbers is 79 . the second number is 9 less than the first. the third number is 2 times the first. what are the numbers?

Answers

I believe the numbers are 22, 13, and 44.

He length of a rectangle is six times its width. if the perimeter of the rectangle is 70 in , find its area.

Answers

The width is 150 inches squared

Julie needs 3 lengths of string that are each 6 inches long. Marlene needs 7 lengths of string that are each 8 inches long.

How much string do the girls need altogether?

in.

Answers

seventy four because 6*3 is 18 and 7*8 is 56, add them to get 74

please help. !!!!!!!!

Answers

Basically you find the data points and fill in the values. For Point J it is (2,4). They want you to do this: (2-4,4-6)...it then becomes (-2,-2).
So
J: (-2,-2)
K: (-1, -4)
I: (-2, -5)
Those are your new points. I hope this helps love! :)

Terrance bought 3 markers. his sister bought 5 markers. terrance and his sister spent a total of $16 on the markers. what was the price of each marker?

Answers

each marker will cost $2

find the difference without using a calculator 201-72.35

Answers

the answer is 128.65

Here is your answer:

Since its decimal ma!e your equation look like this:

201.00
72.35-
Its going to make 99 because its zeros but add the 1
10-5=5
Then make another 9:
And another use the 2
10-3=7
10-2=8

Which will equals:

201-72.35=128.65
(Since there's 100. Decimal)

F. determine if (x + 3) is a factor of (x) = 2x3 + x2 –8x + 21 by using synthetic division. if so, find the other factors.

Answers

since its x + 3 we use -3

-3| 2 1 -8 21 (these are the # without the x)
___________________

-6 15 -21
-------------------------------
2 -5 7 0

Drag the 2 down, multiple it by -3 to get -6
1+(-6) = -5. -5 * -3 =15 . 15+(-8) = 7
7*-3 = -21. -21 +21 = 0
Since last # is 0 we have a factor.

factor is 2x^2 -5x -7 (we start with a power 1 less the original.)

When constructing parallel and perpendicular lines, how are the steps similar

Answers

The construction of parallel lines includes copying an angle by creating arcs with a compass.
When constructing parallel and perpendicular lines the steps are similar because they both include creating and connecting intersecting arcs.

HOW many times can times 6 go into 59

Answers

6 can go into 59, nine times. Therefore 9 times 6 equals 54

All you have to do is divide 59/6, you get 9.83 hopefully this helps

Find the lengths of the missing sides if side a is opposite angle a, side b is opposite angle b, and side c is the hypotenuse.

Answers

Hello Melissamv9321, find the lengths of the missing sides if side a is opposite angle a, side b is opposite angle b, and side c is the hypotenuse In this right triangle, you are given the measurements for the hypotenuse, c, and one leg, b. The hypotenuse is always opposite the right angle and it is always the longest side of the triangle. To find the length of leg a, substitute the known values into the Pythagorean Theorem. Solve for a2.

Solve 12g=12(2/3g-1)+11

Answers

Solve for g:12 g = 12 ((2 g)/3 - 1) + 11
Put each term in (2 g)/3 - 1 over the common denominator 3: (2 g)/3 - 1 = (2 g)/3 - (3)/3:12 g = 12 (2 g)/3 - (3)/3 + 11
(2 g)/3 - (3)/3 = (2 g - 3)/3:12 g = 12 (2 g - 3)/3 + 11
12/3 = (3×4)/3 = 4:12 g = 4 (2 g - 3) + 11
4 (2 g - 3) = 8 g - 12:12 g = 8 g - 12 + 11
Grouping like terms, 8 g - 12 + 11 = 8 g + (11 - 12):12 g = 8 g + (11 - 12)
11 - 12 = -1:12 g = 8 g + -1
Subtract 8 g from both sides:12 g - 8 g = (8 g - 8 g) - 1
12 g - 8 g = 4 g:4 g = (8 g - 8 g) - 1
8 g - 8 g = 0:4 g = -1
Divide both sides of 4 g = -1 by 4:(4 g)/4 = (-1)/4
4/4 = 1:Answer: g = (-1)/4

Ruchi measured the area of her kitchen as

Answers

Ruchi measured the area of her kitchen as,

Answer:

She is incorrect because 2.81 × 10^4 is around 30,000 so the units must be smaller than feet. She most likely measured in inches.

Hurry When solving a system of equations, Jared found y = x 10 for one equation and substituted x 10 for y in the other equation. Nicole found x = y – 10 for the same equation and substituted y – 10 for x in the other equation. Who is correct? Explain.

Answers

I can say that Jared and Nicole are correct because they manipulated the equation right. They can either write the equation as y as a function of x then substitute it to the y in the other equation and solve for x. They can also write the equation as x as a function of y and substitute it to x in the other equation and solve for y. For both solution, they will still obtain the same answers.

Jared and Nicole both have found the correct value and will get the same solution to the system of equations.

Given information:

Jared found that [tex]y = \dfrac{x} {10}[/tex] for one equation and substituted [tex]\dfrac{x}{10}[/tex] for y in the other equation.

Nicole found [tex]x = y -10[/tex] for the one equation and substituted [tex]y -10[/tex] for x in the other equation.

So, there are two equations. Based on the question, the equation should be,

[tex]x=10y[/tex] and [tex]y-x=10[/tex].

Now, Jared and Nicole have found the value of one variable from one equation and have put it in the other equation.

This method is the substitution method which is used to find the solution of the system of equations.

Therefore, Jared and Nicole both have found the correct value and will get the same solution to the system of equations.

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https://brainly.com/question/14619835

For a craft project, two equilateral triangles are taped together to create a quadrilateral

Answers

The quadrilateral that is made is a rhombus. The triangle lines cause the quadrilateral to look like an uneven square or diamond which is also known as a rhombus.

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