The difference between two positive integers is 7 and the sum of their squares is 949. What are the numbers?

Answers

Answer 1

Answer:

25 and 18

Step-by-step explanation:

Let's say that the first number is x and the second one is y.

First, the difference between them is 7, so x-y=7

Next, the sum of their squares is 949, so x²+y² = 949

We have

x-y=7

x²+y²=949

One thing we can do to solve this problem is to solve for x in the first equation, plug that into the second equation, and go from there

Adding y to both sides in the first equation, we have

x = 7 + y

Plugging that into the second equation for x, we have

(7+y)²+ y² = 949

expand

(7+y)(7+y) + y² = 949

49 + y² + 7y + 7y + y² = 949

combine like terms

2y² +14y + 49 = 949

subtract 949 from both sides to put this in the form of a quadratic equation

2y² + 14y - 900 = 0

divide both sides by 2

y² + 7y - 450 = 0

To factor this, we want to find 2 numbers that add up to 7 and multiply to -450.

The factors of 450 are as follows:

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.

Note that we want to find two numbers with a difference of 7, as one will have to be negative for the multiplication to end up at -450. Two numbers that stand out are 18 and 25. To make them add up to 7, 18 can be negative. We therefore have

y² + 25y - 18y - 450 = 0

y(y+25) - 18(y+25) = 0

(y-18)(y+25) = 0

Solving for 0,

y-18 = 0

add 18 to both sides

y=18

y+25 = 0

subtract 25 from both sides

y= -25

As the question states "two positive integers", this means that y must be positive, so y = 18. We know x-y=7, so

x-18 = 7

add 18 to both sides to isolate x

x = 25


Related Questions

Find the minimum and maximum value of the function on the given interval by comparing values at the critical points and endpoints.

y= √1+x^2 −2x, [0, 1]

Answers

Answer:

maximum: y = 1

minimum: y = 0.

Step-by-step explanation:

Here we have the function:

y = f(x) =  √(1 + x^2 - 2x)

we want to find the minimum and maximum in the segment [0, 1]

First, we evaluate in the endpoints, which are 0 and 1.

f(0)  =√(1 + 0^2 - 2*0) = 1

f(1) = √(1 + 1^2 - 2*1) = 0

Now let's look at the critical points (the zeros of the first derivate)

To derivate our function, we can use the chain rule:

f(x) = h(g(x))

then

f'(x) = h'(g(x))*g(x)

Here we can define:

h(x) = √x

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

Then:

f(x) = h(g(x))

f'(x)  =  1/2*( 1 + x^2 - 2x)*(2x - 2)

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

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

this function does not have any zero in the segment [0, 1] (you can look it in the image below)

Thus, the function does not have critical points in the segment.

Then the maximum and minimum are given by the endpoints.

The maximum is 1 (when x = 0)

the minimum is 0 (when x = 1)

What is the difference between the temperature - 7 Celsius and - 12 Celsius on a scatter diagram

Answers

Answer:

Sự khác biệt giữa nhiệt độ - 7 độ C và - 12 độ C trên biểu đồ phân tán là gì

Step-by-step explanation:

PLz help!!

What is the degree of the polynomial

Answers

Answer:

3 maybe I'm just guessing.

now thats room for an answer again: yeah, 3 is right. its the x³ that defines the degree, its just the biggest power.

Need help! Thank you :)

Answers

Answer:

The value of [tex]x[/tex] is 10.

Step-by-step explanation:

Both angles ABC and CBD are complementary, that is, the sum of the measures of both angles equals 90°, that is:

[tex]\angle ABC + \angle CBD = 90^{\circ}[/tex] (1)

If we know that [tex]\angle ABC = 5\cdot x[/tex] and [tex]\angle CBD = 4\cdot x[/tex], then the value of [tex]x[/tex] is:

[tex]5\cdot x + 4\cdot x = 90^{\circ}[/tex]

[tex]9\cdot x = 90^{\circ}[/tex]

[tex]x = 10[/tex]

The value of [tex]x[/tex] is 10.

The length of a rectangle is 2 centimeters less than three times its width. Its area is 21 square centimeters. Find the dimensions of the rectangle. Use the​ formula, area=length*width.

Answers

Area = length x width

Area = 21 square cm

Width = x

Length = 3x + 2

21 = 3x+ 2 * x

21 = 3x ^2 + 2x

Subtract 21 from both sides:

3x^2 + 2x -21 = 0

Use the quadratic formula to solve for x:

-2 +/- sqrt(2^2-4*3(-21))/(2*3)

X = 7/3 and -3

A dimension can’t be a negative value so x needs to be 7/3

Width = x = 7/3 = 2 1/3 cm

Length = 3(7/3) + 2 = 9 cm

Check: 9 x 2 1/3 = 21

Dimensions: width 2 1/3 cm length 9 cm

Answer:

The dimensions of the rectangle are 7 by 3 centimeters.

Step-by-step explanation:

We are given that the length of a rectangle is two centimeters less than three times its width. In other words:

[tex]\displaystyle \ell = 3w-2[/tex]

Given that the area of the rectangle is 21 square centimeters, we want to determine the dimensions of the rectangle.

Recall that the area of a rectangle is given by:

[tex]A= w\ell[/tex]

Substitute:

[tex](21)=w(3w-2)[/tex]

Solve foro the width. Distribute:

[tex]3w^2-2w=21[/tex]

Isolate the equation:

[tex]3w^2-2w-21=0[/tex]

Factor. Find two numbers that multiply to 3(-21) = -63 and add to -2.

-9 and 7 suffice. Hence:

[tex]3w^2-9w+7w-21=0 \\ \\ 3w(w-3)+7(w-3) = 0 \\ \\ (3w+7)(w-3)=0[/tex]

Zero Product Property:

[tex]3w+7=0\text{ or } w-3=0[/tex]

Solve for each case. Hence:

[tex]\displaystyle w = -\frac{7}{3}\text{ or } w=3[/tex]

Since width cannot be negative, we can ignore the first solution.

Therefore, our width is three centimeters.

And since the length is two less than three times the width, the length is:

[tex]\ell = 3(3) - 2 = 7[/tex]

The dimensions of the rectangle are 7 by 3 centimeters.

HELP ASAP PLEASE!!!!!!!!

Answers

Answer:

1

Step-by-step explanation:

1 : 1 :sqrt(2)

The legs are  in the ratio of 1 to 1

tan 45 = opp side / adj side

tan 45 = 1/1

tan 45 =1

Answer:

Step-by-step explanation:

Find the y-intercept from the line passing through (1, 3) and having slope m=2.

Answers

Answer:

The y intercept is 1

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = 2x+b

Substitute the point into the equation and solve for y

3 = 2(1)+b

3 =2+b

1 = b

The y intercept is 1

Y-intercept is (0,1)

Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.

Explain how you could find the shortest distance from A(6, 5) to the line y = 5x – 10. (Use a diagram, be specific, and list all your steps.

Answers

Step-by-step explanation:

I cannot draw a diagram here.

but I can explain what to do in general.

the shortest distance from a point to a line is always via a connecting line that is perpendicular to the given line and his through the given point.

and then the distance from the given point to the intersection point is calculated.

every line is defined in the form like

y = ax + b

where a is the slope of the line, and b is the intersection point on the y-axis (the offset from point 0).

the slope of a line is the ratio y/x defining how many units y changes when x changes a certain amount of units.

in our example,

y = 5x - 10

5 (or rather 5/1) is the slope of the line.

it means that y grows by 5 units every time x grows by 1 unit.

a perpendicular line (cuts the original line with a 90 degree angle) has a related slope : it reverts x and y and flips the sign :

5/1 turns into -1/5

that means at the perpendicular line whenever x grows by 5 units, y goes down by 1 unit.

so, the first approach for the perpendicular line is

y = -1/5 x + b

to get b we use the given point (6, 5) that has to be in the perpendicular line.

5 = -1/5 × 6 + b

25/5 = -6/5 + b

31/5 = b

=> y = -1/5 x + 31/5

the intersecting point is now where both lines are equal

5x - 10 = -1/5 x + 31/5

25x - 50 = -x + 31

26x = 81

x = 81/26

y = 5×(81/26) - 10 = 405/26 - 260/26 = 145/26

the distance of the given point (6, 5) to the line intersection point (81/26, 145/26) is the calculated as

distance² = (6 - 81/26)² + (5 - 145/26)²

distance = sqrt((6-81/26)² + (5-145/26)²)

since the result was not requested here, I save us the calculation.

What value of x makes the equation 3x +7=22

Answers

Answer:

x = 5

Step-by-step explanation:

Your goal is to isolate x

3x + 7 = 22

Subtract 7 from both sides and you are left with

3x = 15

In order to isolate x divide both sides by 3

x = 5

if one half of a number is 5 more than 6, what is the value when the number is tripled

Answers

Answer:

66

Step-by-step explanation:

let's use x to represent the unknown number

1/2x is 5 more than 6:

1/2x=5+6

solve to find x

1/2x=11

x=22

next, it asks us what is the value of the number when the number is tripled

since we already found what x is equal to, we can multiply that by 3 to figure out its value when it's tripled

3(22)=66

Using mathematical equation to model the scenario, the value of the number when tripled is 66

Let the number = n

0.5n = 5 + 6

0.5n = 11

Divide both sides by 0.5

n = 22

When n is tripled :

n = 22 × 3

n = 66

Hence, the value of the number when tripled is 66

Learn more : https://brainly.com/question/25480062

Pls if anyone knows the answer that will be greatly appreciated :)

Answers

Answer:

I think the area is 60 but i couldn't figure out the perimeter, sorry.

Step-by-step explanation:

Answer:

perimeter = 36 m

area = 60 m²

Step-by-step explanation:

there is some missing information. for example about the types of the shapes. e.g. if the triangle on the top is an isosceles triangle (2 equal sides). or if the rectangle at the bottom is actually a square with 6 m on all sides. in order to make the sloped side of the top triangle a round, whole number, i assume that the bottom part is a square.

so, the area of this combined shape is the area of the bottom square plus the area of the top triangle.

area square As = 6×6 = 36 m²

so, one side of the triangle is also 6 m, the other is 14-6 = 8 m.

the area of such a right-angled triangle is half of the full rectangle of 6×8.

area triangle At = 6×8/2 = 48/2 = 24 m²

total area = As + At = 36 + 24 = 60 m²

the perimeter of the total shape is the sum of all sides.

so, 14, 6, 6 and ... the baseline/ Hypotenuse of the top triangle.

for that r need the mentioned Pythagoras :

c² = a² + b²

where a and b are the sides, and c is the Hypotenuse (the side opposite of the 90 degree angle).

so, in our case of an isosceles triangle with a 90 degree angle :

c² = 8² + 6² = 64 + 36 = 100

c = 10 m

so, the perimeter is

14+6+6+10 = 36 m

what is 4 9/6 as a mixed number

Answers

Answer:

33

Step-by-step explanation:

6x4+9= 33

33 would be ur answer i think :)

Annie bought a 2 3/4 pound roast for the family dinner. A total of 9 people will be at dinner. How many pound of roast will each person get if the roast is divided up equally?

Answers

Answer:

11 /36 of a pound

Step-by-step explanation:

Take the pounds and divide by the number of people

2 3/4 ÷ 9

Change the mixed number to an improper fraction

(4*2+3)/4 ÷9

11/4 ÷9

Copy dot flip

11/4 * 1/9

11/36

Add 2/5, 3/10 and 1/2. Give your answer as a mixed number

Answers

Answer:

I hope this will help you

What is the scale factor of the dilation?

PLEASE BE CORRECT

Answers

2
Because
Notice the horizontal side of the red triangle is 2 times that of the blue triangle. Therefore the dilation factor is 2
Scale factor is 2
I could be wrong

The FDA regulates that fish that is consumed is allowed to contain 1.0 mg/kg of mercury. In Florida, bass fish were collected in 53 different lakes to measure the amount of mercury in the fish. The data for the average amount of mercury in each lake is in the given table ("Multi-disciplinary niser activity," 2013). Do the data provide enough evidence to show that the fish in Florida lakes has more mercury than the allowable amount? Test at the 10% level. Use the framework below to guide your work. Hypotheses:
H0 : u = 1.0 mg/kg
HA: ul > 1.0 mg/kg
Test statistic = -10.09 p-value is approximately 1, would report 0.9999. Since this is not less than or equal to 0.10, we do not favor Ha. We would conclude that there is not enough evidence to show that the mean amount of mercury in fish in Florida lakes is more than the allowable amount Why is the p-value so high when the test statistic seems extreme?
A. The alternative is > so the p-value matches the area to the left. Since the TS is negative, this results in shading most of the curve.
B. The TS is negative so the p-value matches the area to the left and results in a very small area. This p-value reported is not correct.
C. The alternative is > so the p-value matches the area to the right. Since the TS is negative, this results in shading most of the curve.
D. The TS should be positive so the p-value matches the area to the left and results in shading most of the curve.

Answers

Answer:

Step-by-step explanation:

H0 : u = 1.0 mg/kg

HA: u > 1.0 mg/kg

Test statistic = -10.09

p-value is approximately 1, would report 0.9999

α = 10% ; 0.1

Using the Pvalue, we can make a decision pattern ;

Recall ; H0 is rejected If Pvalue < α

Here,

Pvalue Given is ' 0.99999 α = 0.1

Pvalue > α ; Hence, we fail to reject the Null ;

The actual Pvalue calculated using the test statistic will be :

Pvalue(-10.09) with test statistic value using a Pvalue calculator

Pvalue < 0.00001

Write expression with two terms that is equivalent to the expression shown. 4(2x + 11 - x)

Answers

Answer:

4x + 44

Step-by-step explanation:

4(2x + 11 - x) =

8x + 44 - 4x =

4x + 44

Find the distance from point A (0,5) to the line y = -3x - 5. Round to the nearest tenth

Answers

Answer:

3.2

Step-by-step explanation:

Substitute in the equation:

|(mx1-y1+b)| / √(m2 + (1)2) =

= |(0+-5+-5)| / √(9 + 1)

Sum and operate:

|-10| / √10 = 10 / √10

Exact solution is:

√10

Approximate solution is:

3.2

Answered by GAUTHMATH

Identify the two types of incorrect decisions in a hypothesis test. For each incorrect​ decision, what symbol is used to represent the probability of making that type of​ error?

Answers

Answer:

Type I error and Type II error

Explanation:

Type I and Type II errors are statistical errors made in hypothesis testing where an accepted hypothesis is actually the false hypothesis and the other true.

Type I error occurs when the chosen hypothesis is the alternative hypothesis which is false since the null hypothesis is true. We reject the null hypothesis which is actually true.

Type II error occurs when we accept or fail to reject the null hypothesis which is false and reject the alternative hypothesis which is true.

The probability of making a Type I error is represented by your alpha level (α)(we reject when below p-value)

The probability of a type-II error is represented by β which is beta.

A number is chosen at random from 1 to 50. What is the probability of selecting
multiples of 10.

Answers

Answer: 25

Step-by-step explanation:

What is the quadratic regression equation that fits these data?

Answers

9514 1404 393

Answer:

  D.  y = -0.32x² -1.26x +15.81

Step-by-step explanation:

This is one of those multiple-choice questions where you only need a vague idea of what the answer is supposed to look like.

In this case the answer must be a quadratic equation with a negative leading coefficient. (The parabola opens downward.)

The only answer choice that is a 2nd degree polynomial with a negative leading coefficient is choice D.

__

A: linear equation

B: exponential equation

C: quadratic that opens upward (positive leading coefficient)

D: quadratic that opens downward -- the answer you're looking for

If 3^2x+1 =3^x+5, what is the value of x?

Answers

Answer:

x = 4

Step-by-step explanation:

[tex]3^{2x+1} = 3^{x+5}[/tex]

if the bases are equal then the powers must be equal as well

2x+ 1 = x+5 export like terms to same side of equation

2x - x = 5 - 1 add/subtract like terms

x = 4


Part A
What is the relationship between squaring and taking the square root? Because of this relationship, what happens when you square a square
root?

Answers

Squaring a number is the inverse of taking its square root. These two operations cancel each other out.

Evaluate f(x) = X - 8 for x = -8

Answers

Answer:-16

Step-by-step explanation:

I put 22.5 but it won’t work is there any other way for this to work??

Answers

Try rounding off your answer

Find a fraction equivalent to
that has a denominator of 10.

Answers

Answer:

1/10

Step-by-step explanation:

any number (1-9) as the number above the fraction line (numerator) with the number 10 below the fraction line is a fraction with a denominator of 10.

if it was 10/10, it will = 1

Based on experience, the Ball Corporation’s aluminum can manufacturing facility in Ft. Atkinson, Wisconsin, knows that the metal thickness of incoming shipments has a mean of 0.2935 mm with a standard deviation of 0.000924 mm.

(a) A certain shipment has a diameter of 0.2963. Find the standardized z-score for this shipment.

Answers

Answer:

Step-by-step explanation:

the formula attached

This function is _____over the interval
[tex]x < - 1[/tex]


This function is_____ over the interval l
[tex] - 1 < x < 1[/tex]



Select all of the possible degrees of this polynomial function
2
3
4
5​

Answers

Answer:

the answer to this question is 1

Step-by-step explanation:

the reason to that is because when the line goes over 2 and -2.

Answer:

first part is decreasing and increasing

second part is 3 and 5

Step-by-step explanation:

edg 2021

I really need help
Dz,2 of X is
(0-4)
(2,-2)
(6,2)

Answers

9514 1404 393

Answer:

  (6,2)

Step-by-step explanation:

As is often the case with multiple-choice problems, you don't actually need to know the detailed working. You just need to know what the answer looks like.

When point X is dilated by a factor of 2 with point Z as the center of dilation, it will move to a location twice as far from Z. You can tell by looking at the graph that X' will be in the first quadrant, above and to the right of the location of X. The only sensible answer choice is ...

  X' = (6, 2)

_____

Additional comment

X is a distance of X-Z = (4, 0) -(2, -2) = (2, 2) from Z Doubling that will put the image point a distance of 2(2, 2) = (4, 4) from Z. When this is added to Z, we find ...

  X' = Z + (4, 4) = (2+4, -2+4) = (6, 2)

Yanni read 24 pages of
a book. One third of the book is
still left to read. How many
pages are there in the
whole book?

Answers

Answer:

36 pages

Step-by-step explanation:

If one third of the book is left to read until completion, then Yanni has read two thirds of the book so far.

24 pages is equal to two thirds, so one third will be half of this; 12 pages.

The whole book is three thirds, so 12 * 3, which is 36 pages

Answer:

di gun0ifulgwuytid5

Step-by-step explanation:

DJ e57

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