The sum of two numbers is 6 and the sum of their squares is 90. Find the numbers.

Answers

Answer 1

Let's set up the variables for the two numbers --> 'a' , 'b'

Now let's set up some equations based on the given information:

sum of two numbers is 6 --> a + b = 6sum of their squares is 90 --> a^2 + b^2 = 90

Equations:

a + b = 6 -- equation 1a^2 + b^2 = 90 -- equation 2

   Solve (equation 1) for b in terms of a

     b = a - 6 -- equation 3

 

    (equation 3) into (equation 2)

     a^2 + (a - 6)^2 = 90

     a^2 + a^2 - 12a + 36 = 90

     2a^2 - 12a - 54 = 0

     (2a + 6)(a - 9) = 0

       a = -3 -- equation 4

       a = 9 -- equation 5

    (equation 4) into (equation 1)

      -3 + b = 6

       b = 9  - ---   a = -3, b= 9

    (equation 5) into ( equation 1)

     9 + b = 6

     b = -3 - ---     a = 9, b= -3

Since the numbers are interchangeable, the two numbers are -3 and 9.

Hope it helps!

     

   

   


Related Questions

Pls answer i will mark u brainlist

Answers

Answer:

0%

Step-by-step explanation:

125/100x375

=468.75

75/100x375

= 281.25

gain= 468.75-375

=93.75

loss=375-281.25

=93.75

375x2=750

468.75+281.25

=750

750/750x100

=100%

100%-100%

=0%

its neither a gain nor a loss

Select the correct statements

Answers

∠G , ∠H , ∠K

∠G and ∠H are congruent as they have same shape and size. Their angle measure and length is same. Either of the shape is reflected over the x-axis. ∠K is congruent with the shape, due to same angle measure and is enlarged over the y-axis.

∠M is not congruent, it does not have similar shape. Their angle differs.

Answer:

H, G, K

Step-by-step explanation:

G and H are congruent. Their angle measure and length is same. K is congruent with the shape.

M is not similar it does not have the same shape. It's angle differs.

Find the area of the triangle.
14 m
24 m
The area of the triangle is
(Type a whole number.)
а
m3.
m.
m?

Answers

168 m^2

area of a triangle = 1/2 (L • W)

[1/2 (24m • 14m] = 168 m^2 (meters squared)

Which shows the expression below simplified? 0.000024 ÷ (4 × 10-3)
6 × 10-1
B.
6 × 10-2
C.
6 × 10-4
D.
6 × 10-3

Answers

Answer:

  D.  6×10^-3

Step-by-step explanation:

When powers of the same base are divided, the power of the denominator is subtracted from the power of the numerator.

  [tex]\dfrac{0.000024}{4\times10^{-3}}=\dfrac{24\times10^{-6}}{4\times10^{-3}}=\dfrac{24}{4}\times10^{-6-(-3)}=\boxed{6\times10^{-3}}[/tex]

__

A calculator or spreadsheet can help you with these.

algebra tile grid (x+2)(x-3)

Answers

We basically use the foil method

2
X -X - 6

Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

$300

Step-by-step explanation:

multiply that 6000 in 0.05

h31p m3 pl3as3 1 d0nt know th!s

Answers

Answer:B

5x-8/12y

Step-by-step explanation:

Choose the net for the figure.

Answers

The answer is definitely the first one

The required net figure is shown in A. Option A is correct.

What is 3d geometry?

3D geometry is the study of shapes in 3D space using three coordinates: x-coordinate, y-coordinate, and z-coordinate. To discover the exact location of a point in 3D space, three criteria are required.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
As the given figure is shaded on the square faces,
When it unfolds there will be three shaded squares, 2 unshaded pentagons, and two unshaded squares.

Thus, The required net figure is shown in A. Option A is correct.

Learn more about 3d -geometry here:

https://brainly.com/question/15451289
#SPJ2

In 153.72, which digit is in the hundredths place?

Answers

Answer:

2 is in the hundredths place

What is the area of the flag shown below? 2 3/4. 1 3/4

Answers

Answer:

the answer must be 7/4

I hope it helps you

The diameter of a circle is 22 millimeters. What is the circle's area?

Use 3.14 for PI

please answer i will give brainliest

Answers

Solution:

We know that:

Radius: Diameter/2Area of circle: (π)(r²)

Step-1: Find the radius:

Diameter = 22 mm=> Radius: 22 mm/2=> Radius: 11 mm

Step-2: Find the area of the circle:

Area of circle = (π)(r²)=> Area of circle = (3.14)(11²)=> Area of circle = (3.14)(121)=> Area of circle = 3.14 x 121 = 379.94 mm²
Diameter=22mmRadius=11mm

[tex]\\ \rm\Rrightarrow Area=\pi r^2[/tex]

[tex]\\ \rm\Rrightarrow Area=(3.14)11^2[/tex]

[tex]\\ \rm\Rrightarrow Area=121(3.14)[/tex]

[tex]\\ \rm\Rrightarrow Area=379.9mm^2[/tex]

1) Which BEST describes the arrangement of the categories on the Pareto graph?
es
A) The categories are arranged in order of their frequencies from the least frequent to the most frequent on the Pareto graph.
B) The categories are arranged in order of their frequencies from the most frequent to the least frequent on the Pareto graph.
The categories are arranged in alphabetical order on the Pareto graph.
D) The categories are arranged in no specific order on the Pareto graph.

Answers

The arrangement of categories on the Pareto graph is such that B) The categories are arranged in order of their frequencies from the most frequent to the least frequent.

How is data organized on the Pareto graph?

A pareto graph is such that the category which has the highest frequency will be shown first. The next highest is second and this goes on till the least.

The attached pareto graph does this by showing traffic as the first because it has the highest frequency.

In conclusion, option B is correct.

Find out more on pareto graphs at https://brainly.com/textbook-solutions/q-22-state-graph-pareto-chart-time-series-6#q-22-state-graph-pareto-chart-time-series-2.

good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.

Answers

Answer:

[tex]P=236000(1+0.04)^t[/tex]

Step-by-step explanation:

Exponential equation:  [tex]y=a(1+r)^x[/tex]

where:

[tex]a[/tex] is the initial value[tex]r[/tex] is the growth rate (in decimal form)[tex]x[/tex] is the independent variable[tex]y[/tex] is the dependent variable

Given:

Population is increasing at a rate of 4% each yearPopulation in 2000 was 236000Let t = number of years since 2000Let P = population

Therefore,

[tex]a[/tex] = 236000[tex]r[/tex] = 4% = 4/100 = 0.04[tex]t[/tex] is the independent variable[tex]P[/tex] is the dependent variable

[tex]\implies P=236000(1+0.04)^t[/tex]

Note the rule

[tex]\\ \rm\rightarrowtail y=P(1+\dfrac{r}{100})^t[/tex]

Now

P=236000Rate of change=r=4%

Put it

[tex]\\ \rm\rightarrowtail y=236000(1+4/100)^t[/tex]

[tex]\\ \rm\rightarrowtail y=236000(1+0.04)^t[/tex]

State the period, midline, amplitude, and range of the given graph. (I will mark brainliest, my answers were wrong!)

Answers

Answer:

Period:  [tex]4\pi[/tex]

Midline:  y = 2

Amplitude:  3

Range:   [-1, 5]

Step-by-step explanation:

Period - from one peak to the next (or from one trough to the next)

⇒ Period:  [tex]2\pi - (-2\pi )=4\pi[/tex]

Midline - center line

Range = -1 ≤ f(x) ≤ 5

[tex]\implies \sf midline =\dfrac{5-(-1)}{2}+(-1)=2[/tex]

⇒ Midline:  y = 2

Amplitude - height from the center line to the peak (or to the trough)

Maximum height:  y = 5

center line:  y = 2

Therefore, amplitude = 5 - 2 = 3

Range - the set of all values that the function takes

-1 ≤ f(x) ≤ 5  →  [-1, 5]

Period:-

Only one peak is shown so we take distance between troughs

Period=2π+2π=4π

#Midline

The mean of pitch

[-1,5]

Midline::

[tex]\\ \tt\Rrightarrow \dfrac{5+1}{2}-1=3-1=2[/tex]

y=2

#Amplitude

Distance between trough and midline

2-(-1)=2+1=3

#Range:

The pitch

[-1,5]

The speed that a tsunami can travel is modeled by the equation s = 356 StartRoot d EndRoot , where S is the speed in kilometers per hour and d is the average depth of the water in kilometers. What is the approximate depth of water for a tsunami traveling at 200 kilometers per hour?

Answers

Answer:

0.32km

Step-by-step explanation:

The speed that a tsunami can travel is modeled by the equation s = 356 StartRoot d EndRoot , where S is the speed in kilometers per hour and d is the average depth of the water in kilometers.

This is written mathematically as:

S = 356√d

What is the approximate depth of water for a tsunami traveling at 200 kilometers per hour?

S = 200km/hr

Hence:

200km/hr = 356√d

Divide both sides by 356

200/356 = 356√d/356

√d = 200/356

Square both sides

(√d)² = (200/356)²

d =(0.5617977528)²

d = 0.3156167151km

Approximately = 0.32km

Answer:

0.32 kilometers

Step-by-step explanation:

edge 2020

hope this helps!

you get an 4% commission on a $300 T.V.How much commission you earned?​

Answers

Answer:

I'm pretty sure it's 12. hope it helps.

p is inversely proportional to v when v=8 p=5 given that p=40/v calculate the value of p when v is 2

Answers

Answer:

p = 20

Step-by-step explanation:

Given that the equation of variation is

p = [tex]\frac{40}{v}[/tex]

When v = 2 , then

p = [tex]\frac{40}{2}[/tex] = 20

What is the value of B in terms of π?

____π in.2

Answers

Answer:

Step-by-step explanation:

B is base area of cone  and h is the height.

[tex]V =\dfrac{1}{3}Bh\\\\\\96\pi =\dfrac{1}{3}B*18\\\\\\96\pi =B *6\\\\\\Now, \ divide \ the \ entire \ equation \ by \ 6 \\\\\dfrac{96\pi }{6}=\dfrac{B*6}{6}\\\\\\16\pi = B[/tex]

Answer:  B = 16 π in²

Ty is right inches taller than his brother Reece if ty is 42 inches tall how tall is Reece. Write an equation using a variable r?

Answers

Mi llamos Bryson y tu ¿

Somebody help please ASAP!

Answers

Answer: 4th box

Step-by-step explanation:

Number 4 fourth box. That’s the answer

What is the potential energy of a 3 kg ball that is on a shelf 2 meters high?

Answers

Step-by-step explanation:

mass(m)= 3kg

height(h)= 2m

gravity(g)= 9.8 m/s^2

P.E.= mgh

=3*2*9.8

=58.8 Joule

Answer:

58.84 Joules

Step-by-step explanation:

3(Mass)*2(Height)*9.8=58.84J

-650 ÷ (-26)
with solutions ​

Answers

Answer:

The answer is 25

Step-by-step explanation:

I used a calculator. if this is for a quiz for other people do

A. 25

B. 34

C. -5

D. -65

How would u model 3(2x - 4)?

Answers

3(2x-4)

= 3*2x-3*4

= 6x-12

What is 4.75 as a mixed number and improper fraction

Answers

Answer:

improper fraction- 475/100

mixed fraction- 4 75/ 100

improper fraction 475/100
mixed number 4 3/4

Which student correctly translated the phrase ""twice the sum of a number cubed and nine"" and evaluated it for r = 3? Antonio's work. 2 (r cubed 9) = 2 (3 cubed 9) = 2 (9 9) = 2 (18) = 36. Jessica's work. 2 (r cubed 9) = 2 (3 cubed 9) = 2 (27 9) = 2 (36) = 72. Maria's work. 2 r cubed 9 = 2 3 cubed 9 = 2 27 9 = 29 9 = 38. Mark's work. 2 3 r 9 = 2 3 (3) 9 = 2 9 9 = 11 9 = 20.

Answers

By simplifying given phrase "twice the sum of a number cubed and nine" and  evaluating it for r = 3 we got that Jessica done it correctly

What is cube of any number ?

Cube of any number means multiplying that number with itself 3 times.

For example [tex]3^3=3\times3\times3=27[/tex]

Here given phrase is

twice the sum of a number cubed and nine

let number be r

We can write it as

[tex]2(r^3+9)[/tex]

Now evaluating it for r=3

[tex]2(3^3+9)[/tex]

Now we can simplify it as

[tex]2(27+9)\\\\=(36)\\\\=72[/tex]

By simplifying given phrase "twice the sum of a number cubed and nine" and  evaluating it for r = 3 we got that Jessica done it correctly

To learn more about cube visit : https://brainly.com/question/107100

Answer:

B

Step-by-step explanation:

sorry if I'm late<3

Calculate the amount of property tax Alice Brown owes on her home, which has an assessed value of $90,000. The tax rate in her community is $31. 00 per $1,000 of assessed value.

Answers

Answer:

$2,790

Step-by-step explanation:

This is the concept of commercial arithmetic, the amount of tax calculated from $90,000 will be:

Rate*value

=31/1000*90000

=$2,790

the answer is $2,790

A oil company has a large tank that holds the oil before it is distributed. Which of the following amounts of oil would fit in the tank properly?
A: 21,000
B: 30,000
C: 20,000
D: 22,000

Answers

It would be D cause a truck would not be able to hold over 25k in with this case there’s on 22k

(5x + k)2 = mx2 + 70x + 49
Find m
Find k

Answers

Answer:

10x+2k=(2m+70) x + 49

10= 2m+70

2m=-60

m = -30

2k=49

k= 49/2

I NEED HELP ASAP Im not understanding and its due

Answers

Answer:

y = x/2 means that it's whatever x is and that divided by 2

Step-by-step explanation:

For example for 8 it would be y=8/2 which is 4

14 would be 7

3 would be y= 3 x 2 your multiplying because the value is y so it's 6

Answers (from top to bottom)

y = 4y = 7x = 6

Reasoning:

The rule says if you know what x is, divide by 2 to get y

In the first row, if x = 8, then y = x/2 = 8/2 = 4.

In the second row, x = 14 leads to y = 7 since 14/2 = 7.

The third row has us go in reverse. We multiply the y value by 2 to find x

This is because y = x/2 solves to x = 2y. So if y = 3, then x = 2y = 2*3 = 6.

We can then check this to get y = x/2 = 6/2 = 3.

The parabola y=x^2 is shifted down by 6 units and to the right by 5 units. What is the equation of the new parabola

Answers

Answer:

y = (x - 5)^2 - 6

Step-by-step explanation:

If you slide a parabola up or down, that translation will show up in the equation just tacked on to the end of the equation. Down 6 will be a MINUS 6.

A horizontal shift will show up in the equation tucked in close to the x in a set of parenthesis. BUT it will look less intuitive...a right shift will be a MINUS.

Untransformed:

y = x^2

Shift down 6:

y = x^2 - 6

Shift right 5:

y = (x - 5)^2

Down6 AND Right5:

y = (x - 5)^2 - 6

Other Questions
Given that a = 24 and b = 70.Work out x , explaining each stage of your working in the comment box. The Europeans believed they helped their African and Asian colonies modernize and civilize for the benefit of the native population. Imagine you are a native in Africa, India, or China Would you agree with this view? Why or why not How did the repeal of the Missouri Compromise affect Kansas? (5 points) The distinguishing feature of a coronavirus is its? Which issue was debated during the 1925 Scopes trial?A.Distributing anarchist literature.B.Granting women the right to vote.C.Teaching evolution in public schools.D.Banning the consumption of alcohol. A scientist has 50 grams of a radioactive element. The amount of radioactive element remaining after t days can bedetermined using the equationf(0) - 50(3)After two days the scientist receives a second shipment of 50 grams of thesame element. The equation used to represent the amount of shipment 2 remaining after t days is R8) - 5050l. Whichof the following is an equivalent form of the expression for the amount remaining in shipment 2? Did social media mess up people mindset? Why did Americans believe that the Compromise of 1850 resolved divisions over enslavement?It allowed Congress to interfere in the domestic slave trade.It made the majority of people happy.It removed the Fugitive Slave Law that caused so many divisions.It allowed new states to determine if they permitted enslavement. A cone has a radius of 5.1 inches and a height of 5 inches.What is the volume of the cone?Use 3.14 for pi. Round to the nearest tenth What is the central idea of paragraph 4?The Dust Belt is a strip of dry land that covers many continents.Droughts happen when there are long periods of time during which there is very little rainfall.Dust storms are a problem not only in Africa and China but also in Australia and the United States.A large part of Earths population is harmed when droughts cause farmable land to become unusable. compltez complete each statement based on the reading According to the key above, which characteristics are necessary to identify a female aedes mosquito.1. Antennea, palps, and proboscis2. palps, abdomen tip, and scales and legs3. eyes, scales on legs and abdomen tip4. pals, abdomen tip and wings URGENT!! 50 Points Please Help!! Will mark brainliest!! Assignment due in 30 minutes.2.) Round off each of the answers correctly.a.) 8.7g + 15.43g + 19g = 43.13gb.) 4.32cm 1.7cm = 7.3444[tex]cm^{2}[/tex]c.) 853.2L - 627.443L = 225.757Ld.) 38.732[tex]m^{2}[/tex] 0.421m = 92.02375me.) 5.40m 3.21m 1.871m = 32.431914[tex]m^{3}[/tex]f.) 5.47[tex]m^{3}[/tex] + 11[tex]m^{3}[/tex] + 87.300[tex]m^{3}[/tex] = 103.770[tex]m^{3}[/tex]3.) Make the following conversions:a.) 157cs to secondsb.) 42.7L to millilitersc.) 261nm to millimetersd.) 0.065km to decimeterse.) 642cg to kilogramsf.) 8.25 [tex]10^{2}[/tex]cg to nanograms Which maps give you a more detailed picture of the terrain?Road mapsPhysical mapsPolitical mapsRelief maps Is 3/4 less then or greater than 1 whole A rapid reaction between oxygen and fuel that results in fire. The cell membrane is described as being fluid because:A. the phosphate groups move between fatty acids.B. the membrane lets materials pass through it.C. the fatty acid chains are inside it.D. the phospholipids move from side to side. F is directly proportional to a.If F = 42 when a 7 finda when F = 18 what practices do the religion buddhism do? Precisez la nature de l'information logique ou analogique pour chaque exaple ci dessous