The sum of two numbers is 50 and the difference is 22 . what are the numbers?

Answers

Answer 1

set this up as an algebra problem with two equations x+y=22 also written as x=22-y x-y=10

substitute the first x into the second equation (22-y)-y=10 22-2y=10 22-10=2y 12=2y y=6

now plug in the known y into the first equation x+6=22 x=22-6 x=16

now, let's check this sum is 22=16+6 checks difference is 10=16-6 checks

16 is the larger number
6 is the smaller number.

hope this helps.

Related Questions

Write the equation of the circle with center (0, 0) and (5, 2) a point on the circle.

Answers

we know that
the equation of the circle with center (0, 0) is ---------> x²+y²=r²

Step 1
find the radius
the radius is simply the distance from the center to the point (5,2)
d=√[(5²+2²)]-------> d=√29
r=√29
the equation of the circle is
x²+y²=29

the answer is x²+y²=29

1. You have that:

r²=(x-h)²+(y-k)²

2. The center of this circle is (0,0), then:

h=0
k=0

3. When you substitute the values of h and k into the equation, you have:

r²=(x-h)²+(y-k)²
r²=(x-0)²+(y-0)²
r²=x²+y²

3. Now, you must find the radius "r".

4. You know that the point is (5,2), so:

r²=x²+y²

5. Finally:

√29=x²+y²

What is the value of b in the equation (yb) 4= 1/y24

Answers

Answer:

The value of b is [tex]\frac{1}{y^7}[/tex].

Step-by-step explanation:

Here the given expression is,

[tex](yb)^4=\frac{1}{y^{24}}[/tex]

[tex]y^4b^4=\frac{1}{y^{24}}[/tex] ( Using [tex](ab)^m=a^mb^m[/tex] on left side )

[tex]y^4b^4y^24 = 1[/tex] ( By cross multiplication )

[tex]y^{4+24}b^4=1[/tex] ( Using [tex]a^ma^n=a^{m+n}[/tex] on left side )

[tex]y^{28}b^4=1[/tex]

[tex]b^4=\frac{1}{y^{28}}[/tex]

[tex]b=(\frac{1}{y^{28}})^{\frac{1}{4}}[/tex] ( [tex]a^m=b^n\implies a=b^\frac{n}{m}[/tex] )

[tex]b=\frac{1^{\frac{1}{4}}}{(y^{28})^\frac{1}{4}}[/tex] ( [tex](\frac{a}{b})^m=\frac{a^m}{b^m}[/tex] )

[tex]b=\frac{1}{y^{28\times \frac{1}{4}}}[/tex] ( [tex](a^m)^n=a^{m\times n}[/tex] )

[tex]b=\frac{1}{y^7}[/tex]

Answer:

It is -6

Step-by-step explanation:

Which of the following forms of bonds has the least risk

Municipal bonds

Below investment grade bonds

Corporate bonds

Treasury bonds

Answers

Treasury bonds have the lowest risk as they are backed by the federal government. The more security and guarantee you have to be paid back, the least the risk there is.

Treasury Bonds is the correct answer.

Treasury Bonds has the least risk as these bonds are issued and backed by the United States federal government. They are credit-risk free as they have practically no default risk and thus the safest bonds to buy. These are issued by the government to finance its budget deficits.

Write the equation in slope-intercept form of the line that has a slope of -5 and a y-intercept of 2.

Answers

Hi!

Slope intercept form is in the form y=mx+b
m is the slope, and that is given so we can plug that into the equation

y = -5x + b

We are also given the y-intercept (0,2) and we can plug that into the equation as well, to find b

2 = 5(0) + b
2 = b

So now that we know both m and b, plug only those two into the equation.
y = -5x + 2

That is your equation

helppppppppppppppppppppppppp

Answers

Answer:
x = 10

Explanation:
Note the following rules before we begin:
2 ln(a) = ln (a²)
ln (a) + ln (b) = ln (ab)

Now, for the given:
ln(20) + ln(5) = 2 ln(x)
ln(20*5) = ln(x²)
ln(100) = ln(x²)

This means that:
100 = x²
Therefore:
either x = 10 .........> acceped
or x = -10 .........> rejected as no negatives are allowed within ln functions

Hope this helps :)

What does the 80 inches represent in an 80" TV

Answers

It represents the distance diagonally between two opposite corners of a Television. (i.e. the distance between the bottom-left corner and the top-right corner)

The 80 inches on an 80" TV refers to the diagonal measurement of the screen, which determines the size of the TV. This measurement is essential for potential buyers to know to match the TV to their space and optimal viewing distance. Other factors like screen resolution and whether to choose plasma or LCD also influence the viewing experience and cost.

When we refer to an 80" TV, the 80 inches represents the diagonal measurement of the screen. This measurement is taken from one corner to the opposite corner of the screen, not horizontally or vertically, which is the standard for sizing televisions and monitors. The importance of considering screen size arises from the need to match the viewer's space and viewing distance to optimize the viewing experience. With larger screens, such as an 80-inch TV, viewers can enjoy a more immersive viewing experience, especially when watching sports, movies, or DVDs. However, depending on the resolution, like 1080p for full HD or 768p for a lower resolution, the quality of the image may affect the perceived difference in quality, especially on smaller screens in which it might not be distinguishable to the nak.ed eye.

The number of animals in a population is 775, and it increases by of 51% each year.
a. Model the situation with an exponential function.

b. Find how many animals there will be in 10 years.

c. How many years will it take for the population to become 1150.

Show all work!

Answers

Answer(a):

Exponential growth formula is given by

[tex]A=P(1+r)^t[/tex]

Where preset population = P= 775

Rate of increase = r = 51% = 0.51

t= number of years

A= Future value.

Plug these values into above formula:

[tex]A=775(1+0.51)^t[/tex]

[tex]A=775(1.51)^t[/tex]

Hence required exponential function is [tex]A=775(1.51)^t[/tex]

Answer(b):

plug t=10 years

[tex]A=775(1.51)^t=775(1.51)^{10}=775(61.6267795034)=47760.7541151[/tex]

which is approx 47761.

Answer(c):

Plug A=1150

[tex]1150=775(1.51)^t[/tex]

[tex]\frac{1150}{775}=(1.51)^t[/tex]

[tex]\ln(\frac{1150}{775})=t*\ln(1.51)[/tex]

[tex]0.394654192004=t*0.412109650827[/tex]

0.957643654334=t

Which is approx 1 year.

What are MODE,MEDIAN
EXPLAIN pls.

Answers

To find the mean, add up the values in the data set and then divide by the number of values that you added.
To find the median, list the values of the data set in numerical order and identify which value appears in the middle of the list.
To find the mode, identify which value in the data set occurs most often.

mode- is the number that is repeated the most, and median is the middle number when u list the numbers from least to greatest. hope this helps....

which pair of triangles is congruent by AAS?

Answers

pqt rqt are congruent by aas i think

Answer:

Triangles PQT and RQT are congruent (option D)

Step-by-step explanation:

The AAS or Angle- Angle- Side Theorem says that if two angles and any side of one triangle are congruent to two angles and any side of another triangle, then the triangles are congruent.

So, triangles PQT and RQT are congruent.

Both triangles have angle Q as right angle and angle P and R are also equal. And both have side QT common.

So, these are congruent via AAS.

what is 85% of 2500 meters

Answers

2500*0.85=2125 meters

What is the quotient (2x3 − 13x2 + 16x − 5) ÷ (x − 5)?

2x2 − 3x + 1

2x2 + 3x − 1

2x2 − 3x − 1

2x2 + 3x + 1

Answers

Answer:

Correct choice is A

Step-by-step explanation:

1 step. Multiply [tex]x-5[/tex] by [tex]2x^2[/tex] to get [tex]2x^3-10x^2[/tex] and subtract this polynomial from the polynomial [tex]2x^3-13x^2+16x-5:[/tex]

[tex]2x^3-13x^2+16x-5-(2x^3-10x^2)=2x^2-13x^2+16x-5-2x^3+10x^2=-3x^2+16x-5.[/tex]

2 step. Multiply [tex]x-5[/tex] by [tex]-3x[/tex] to get [tex]-3x^2+15x[/tex] and subtract this polynomial from the polynomial [tex]-3x^2+16x-5:[/tex]

[tex]-3x^2+16x-5-(-3x^2+15x)=-3x^2+16x-5+3x^2-15x=x-5.[/tex]

3 step. Multiply [tex]x-5[/tex] by [tex]1[/tex] to get [tex]1[/tex] and subtract this polynomial from the polynomial [tex]x-5:[/tex]

[tex]x-5-(x-5)=x-5-x+5=0.[/tex]

Then

[tex]2x^3-13x^2+16x-5=(x-5)(2x^2-3x+1).[/tex]

Answer:

Correct answer is 2x2 − 3x + 1

Step-by-step explanation:

Solve the system algebraically. Check your work.

4x + 2y = 10
3x + 2y = 6

ANSWER: {(
a0)}

Answers

Hey there! :D

We can subtract the equations from each other.

4x-3x=x

2y-2y=0

10-6=4

x=4 <== that's all we have left of the equation

Now plug that in to solve.

3(4)+2y=6

12+2y=6

2y=-6

y=-3

Solution: (4,-3)

I hope this helps!
~kaikers

Answer:

x = 4 and y = -3.

Step-by-step explanation:

Given : 4x + 2y = 10 and 3x + 2y = 6.

To find : Solve the system algebraically. Check your work.

Solution : We have given that

4x + 2y = 10 ----(1)

3x + 2y = 6.------(2)

Subtracting equation 2 from 1

4x + 2y = 10

(-)3x + (-)2y =(-) 6.

_____________

x + 0 = 4

x =4

Plug x = 4 in equation 1

4 (4) + 2y = 10.

16 + 2y = 10.

2y = 10 -16.

2y = -6.

On dividing by 2 both sides

y = -3.

Check:

Plug the values x =4 , y =-3 in equation 1

4 (4) + 2 ( -3) = 10

16 -6 = 10

10 =10

Verify,

Therefore, x = 4 and y = -3.

What is the probability of drawing a diamond from a standard deck of cards on a second draw, given that a diamond was drawn on the first draw and not replaced?

twelve over fifty one

one over fifty two

one over fifty one

thirteen over fifty two,

Answers

Since you have removed one diamond out of thirteen and not replaced it, the answer is twelve over 51. There are four suits of thirteen cards, so when the first card was drawn, the odds were 13/52 or 1/4 simplified. However, previous events are not a predictor of the future, and so the odds are 12/51.

Simplify using the distributive property.

8(y + 12)

8y + 12
20y
20 + y
8y + 96

Answers

8(y + 12)
= 8y + 96 (Answer D)

The expression 8(y + 12) simplifies to 8y + 96 using the distributive property, which involves multiplying 8 by both y and 12.

The question asks us to simplify the expression using the distributive property. The expression given is 8(y + 12). To simplify, we apply the distributive property by multiplying 8 with both y and 12.

So, we have:

8(y) + 8(12) = 8y + 96.

Therefore, the simplified form of the expression 8(y + 12) is 8y + 96.

Which rational number represents a decrease in water level from 8 feet to 6 feet?

Answers

-6/8...I guess so
Tell me if it is right or not

find the difference 6x^2-14x+4/x(x-2) - 6x-1/x+1

Answers

Final answer:

To find the difference between two expressions in the given question, you need to simplify each expression first and then subtract them. The steps involve simplifying each expression separately and then performing the subtraction.

Explanation:

To find the difference 6x² - 14x + 4 / x(x - 2) - 6x - 1 / x + 1, you need to first simplify each expression and then subtract them from each other.

Step 1: Simplify each expression separately.

6x² - 14x + 4 / x(x - 2) = (3x - 2)(2x - 1) / x(x - 2) = 3(2x - 1) / x

- 6x - 1 / x + 1 = -6 - 1 / x + 1 = -7 / (x + 1)

Step 2: Subtract the two simplified expressions: 3(2x - 1) / x - 7 / (x + 1).

Then, the dot ran from −34 to −66. What distance did it cover? If this run took the dot 5 minutes, what was its average speed?

Answers

The distance between -66 and -34 is 32 units. To find the speed in 5 minutes, you will divide the distance of 32 units by the time it took to travel that distance (5 minutes). You can write it as a rate 32 units/5 mins. The speed is 6.4 units per minutes when you divide it out.

Final answer:

The dot covered a distance of 32 units when it ran from -34 to -66. Assuming the distance is measured in meters, and the dot took 5 minutes (300 seconds) to cover this distance, the average speed would be 0.1067 m/s.

Explanation:

To determine the distance the dot covered when it ran from -34 to -66, we need to calculate the absolute value of the difference between the two points. The formula for distance in this case is |final position - initial position|, so the distance covered = |-66 - (-34)| = |-66 + 34| = | -32 | = 32 units.

Now, to determine the average speed of the dot, we divide the total distance traveled by the time it took to cover that distance. Given that it took the dot 5 minutes to cover the distance, we convert minutes to seconds because speed is typically measured in meters per second (m/s) in physics. There are 60 seconds in a minute, so 5 minutes is 300 seconds. Therefore, the average speed is distance/time = 32 units / 300 seconds.

The exact units of measurement for distance have not been specified in the question, but assuming the distance is in meters (m), the average speed would be calculated as 32 m / 300 s = 0.1067 m/s.

HELP FAST - given that ig= x-4 , ik = 9x-19 and jk = 5x+12 find ij, jk and ik

Answers

Answer:

THIS IS WRONG I TOOK THE TEST... DONT KNOW THE ANSWER STILL.

Step-by-step explanation:

What are the zeros of the quadratic function f(x) = 2x2 + 8x – 3? x = –2 – and x = –2 + x = –2 – and x = –2 + x = 2 – and x = 2 + x = 2 – and x = 2 +

Answers

The given quadratic function is:

[tex]f(x)=2 x^{2} +8x-3[/tex]

The zeros of the quadratic functions also known as its roots can be found using the quadratic formula.

According to the quadratic formula:

[tex]x= \frac{-b+- \sqrt{ b^{2}-4ac } }{2a} [/tex]
here,
b = coefficient of x-term
a = coefficient of x²-term
c = costant term

For given function:
a = 2
b = 8
c = - 3

Using these values in the formula, we get:

[tex]x= \frac{-8+- \sqrt{64-4(2)(-3)} }{2(2)} \\ \\ x= \frac{-8+- \sqrt{88} }{4} \\ \\ x= \frac{-8+-2 \sqrt{22}}{4} \\ \\ x= \frac{-4+- \sqrt{22} }{2} \\ \\ x= \frac{-4+ \sqrt{22} }{2}, x= \frac{-4- \sqrt{22} }{2} [/tex]

Thus, these values of x are the zeros of the given quadratic function f(x)=2x²+8x-3

The answer is A for anyone that doesn't understand the other answer.

after examining the figure shown here, Daniel determines that FG/TU= EF/ST wich theorem or collary allowed him to draw that conclusion?
A. Side-splitting theorem
B. two- transversal proportionality corollary
C.Proportional Altitudes theorem
D. Proportional Medians Theorem

Answers

C. Proportional Altitudes theorem :)

The Proportional Medians Theorem states:If two triangles are similar, then the ratio of the lengths of two corresponding medians is the same as the ratio of the lengths of two corresponding sides.

A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.

It is given the two triangles are similar.FG and TU are the medians of the triangle .

By Proportional Medians Theorem ratio of the lengths of two corresponding medians is the same as the ratio of the lengths of two corresponding sides.

So [tex] \frac{FG}{TU} =\frac{EF}{ST} [/tex]

Option D. Proportional Medians Theorem is the right answer.

Find the first four terms of the given sequence tn = (-1)n(n).

A.
-1, -2, -3, -4

B.
-1, 2, -3, 4

C.
1, ½, 2/3, ¾

D.
1, 2, 3, 4

Answers

First we rewrite the expression correctly:
tn = ((-1) ^ n) * (n)
We now look for each of the terms:
t1 = ((-1) ^ 1) * (1) = - 1
t2 = ((-1) ^ 2) * (2) = 2
t3 = ((-1) ^ 3) * (3) = - 3
t4 = ((-1) ^ 4) * (4) = 4
The first four terms of the sequence are then:
-1, 2, -3, 4
Answer:
B.
-1, 2, -3, 4

The number 64 is a perfect

A.square and cube
B.square
C.cube

Answers

The answer to this question is A.

The prime factorization of 64 is [tex]2^6[/tex]

This can be written in two ways.

[tex]64=2^6=2^3 \times 2^3 = 8 \times 8 = 8^2[/tex]
[tex]64=2^6=2^2 \times 2^2 \times 2^2=4 \times 4 \times 4=4^3[/tex]

Thus, 64 is both a perfect square and perfect cube. Hope this helps! :)

The distance formula is d = rt. A trip of 92 miles traveled at 65 mph will take 1.35 hours.
A. True
B. False

Answers

65 * 1.35 = 87.75

87.75 does not equal 92
so this is False

PART A: All but two of the pyramids built by the ancient Egyptians have faces inclined at 52 degree angles. Suppose an archaeologist discovers the ruins of a pyramid. Most of the pyramid has eroded, but the length of a side of the square base is 82 meters. How tall was the pyramid, assuming its faces were inclined at 52 degrees? Round your answer to the nearest meter.

25 m
32 m
52 m
105 m,

Answers

The height is 52m.

The height forms a right triangle with the slant height of the pyramid and half of the length of the square base. Half of the length of the square base would be 41m. The angle is 52°. The sides we have are the height, which is opposite the angle, and half of the base, which is adjacent to the angle. The ratio opposite/adjacent is used for the tangent. Our equation would be:

tan 52=h/41

We multiply both sides by 41:
41*tan 52 = (h/41)*41
41*tan 52 = h

Evaluating this we get 52m.

In the problem, we were asked to compute for the height of the pyramid. Given are the base of the pyramid which is 82 m and the angle of 52°.

If given an illustration, the height is opposite to the angle and the adjacent side is given by half the base.

Based on the mnemonics of trigonometry (SOH CAH TOA), the function to be used is tangent.

The computation is as follows:

Let h = height of pyramid (m)

tan52 = h/41

h = 41tan52

h ≈ 52.5 m

Hence, the height of the pyramid is approximately 52.5.

However, the closest answer based on the choices you provided is 52 m.

Katie decides to sell lemonade to make some money. Katie’s mom said she will double the amount of money she makes. If Katie sells 66 cups of lemonade at $0.75 each, how much money does she make?

Answers

First take 66(.75) to get the number she makes. then tripple that answer to get the number she makes total, as her mom is doubling it. think that if she makes $10, her mom would pay her $20, so she would have $30. just apply it to this problem set.

The answer is $99! :)

By what factor does the y-value change for y = 4x?

Answers

picture is complex answer!

Simple answer: y increases by four every time x increases by one.

Answer:

the answer is 4

Step-by-step explanation:

13 Pts

PLEASE SOMEONE HELP ME WITH THIS QUESTION
PLZ EXPLAIN

THANK U

Answers

It's the third one and the last one are the only ones that make immediate sense.

The answer is 3n+2

She starts off with 2 in the first hour

And then every additional hour ( represented with n) she designs 3

Type 3xxyyy using exponents.

Answers

Nsnnsnsnsbsbbsbsbsbbs s s. Ssbsb

Hello there!

The answer to your question is simple.

3xxyyy

Count how many xs there are. This is the exponent on the x.

3x²yyy

Count how many ys there are. This is the exponent on the y.

3x²y³

I really hope this helps!
Best wishes :)

Sketch the following to help answer the question. Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P. Side QR = 5 m and diagonal QS = 6 m. Find the length of segment RP.
3 m
4 m
5 m
6 m

Answers

The length of RP is 4 m.

Since a kite is symmetric about one of its diagonals, then the other diagonal bisects that one. Additionally, the diagonals are perpendicular to each other. This forms two right triangles inside of the kite.

The bottom leg of the right triangle will be 3 (half of the diagonal) and the hypotenuse will be 5. We will use the Pythagorean theorem to answer this:

3²+b²=5²
9+b²=25

Subtract 9 from both sides:
9+b²-9=25-9
b²=16

Take the square root of both sides:
√(b²) = √16
b=4

Answer:

Given: Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P. Side QR = 5m and diagonal QS = 6m.

Since, diagonals of kite bisect each other, thus QP=6m

Now, in ΔPQR, we have

(QR)²= (RP)²+(QP)²

(5)²= (3)²+(RP) ²

25=9+(RP)²

25-9= (RP)²16= (RP)²

RP= 4m

Therefore, the length of segment RP is 4m.

Step-by-step explanation:

Parallelogram DEFG has been rotated. Which statements are correct? Check all that apply.

Answers

The statements that are correct are:

point F ⇒ point F'
Point D of the pre-image corresponds to pint D' of the image
Parallelogram DEFG maps to parallelogram D'E'F'G'

In geometry, rotation involves turning of an object about a center. The statements that are correct are:

point F [tex]\to[/tex] point F'point D of the preimage corresponds to point D' of the imageparallelogram DEFG maps to parallelogram D'E'F'G

When rotation is applied to a shape, the orientation of the shape will change; however the corresponding points will be unchanged.

This means that:

DEFG will be mapped to D'E'F'GPoints D, E, F and G will correspond to points D', E', F' and G'.

Hence, the true statements are: (a), (c) and (e)