Find two numbers whose difference is 5 and sun of whose squares is 100.

(I believe this is the quadratic formula!)

I’m not sure how to go about it. If someone go go through it step by step, that’d be helpful. (Or even give me the values to put into the quadratic formula)

Answers

Answer 1

Answer:

I. x = 14.115 and y = 9.115

II. x = 0.885 and y = -4.115

Step-by-step explanation:

Let the two numbers be x and y respectively.

Translating the word problem, we have;

x - y = 5  ......equation 1

x² + y² = 100  ...... equation 2

x = y + 5  ...... equation 3

Substituting eqn 3 into eqn 2, we have;

(y + 5)² + y² = 100

Simplifying further by opening the bracket, we have;

(y + 5)(y + 5) + y² = 100

y² + 5y + 5y + 25 + y² = 100

y² + 10y + 25 + y² = 100

2y² + 10y + 25 = 100

2y² + 10y + 25 - 100 = 0

2y² + 10y - 75 = 0

To find the roots of the quadratic equation, we would use the quadratic formula;

Note: the standard form of a quadratic equation is ax² + bx + c = 0

a = 2, b = 10 and c = -75

The quadratic equation formula is;

[tex] x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} [/tex]

Substituting into the formula, we have;

[tex] y = \frac {-10 \; \pm \sqrt {10^{2} - 4*2*(-75)}}{2*2} [/tex]

[tex] y = \frac {-10 \pm \sqrt {100 - (-600)}}{4} [/tex]

[tex] y = \frac {10 \pm \sqrt {100 + 600}}{4} [/tex]

[tex] y = \frac {10 \pm \sqrt {700}}{4} [/tex]

[tex] y = \frac {10 \pm 26.46}{4} [/tex]

[tex] y_{1} = \frac {10 + 26.46}{4} [/tex]

[tex] y_{1} = \frac {36.46}{4} [/tex]

[tex] y_{1} = 9.115 [/tex]

Or

[tex] y_{2} = \frac {10 - 26.46}{4} [/tex]

[tex] y_{2} = \frac {-16.46}{4} [/tex]

[tex] y_{2} = -4.115 [/tex]

Next, we would find the value of x;

x = y + 5

When y = 9.115

x = 9.115 + 5

x = 14.115

When y = -4.115

x = -4.115 + 5

x = 0.885

Check:

x - y = 5

14.115 - 9.115 = 5


Related Questions

Cedarburg's zoo has two elephants. The male elephant weighs 3 3/4 tons and the female
elephant weighs 7/12 of a ton. How much more does the male weigh than the female?

Answers

Answer:

the male weigh than the female

Step-by-step explanation:

[tex]\frac{19}{6}[/tex]=[tex]3\frac{1}{6}[/tex]

can somebody help me with this question ​

Answers

Answer:

90 Calories

Step-by-step explanation:

100 g Food contain 300 calories

so,

1 g food contain 3 calories

so 30 gm food = 30 × 3 = 90 calories

hope this helps....

Answer:

A. 90

Step-by-step explanation:

In order to solve this, we first have to write an equation based on the question. In our case, the equation is...

[tex]100g = 300cal[/tex]

(we know that in 100 grams of some food there are 300 calories)

Now we just have to find out how many calories are there in 30 grams of the same food. We do it in the following way...

[tex]100g = 300cal\\100g/3\frac{1}{3} = 300cal/3\frac{1}{3}\\\\30g = 90cal[/tex]

Therefore, there are 90 calories in 30 grams of this food.

A parabola can be represented by the equation x2 = –20y.

What are the coordinates of the focus of the parabola?

(–5,0)
(5,0)
(0,5)
(0,–5)

Answers

Answer:

[tex] {x}^{2} = - 20y \\ y = - \frac{1}{20} {x}^{2} \\ { \tt{y = 4a {x}^{2} }} \\ a = - \frac{1}{5} \\ \\ { \tt{focus = (0, \: - 5)}}[/tex]

The requried coordinates of the focus of the parabola x² = -20y are (0, -2.5), which corresponds to the option (0, -5).

What is a parabola?

A parabola is a cross-section cut out of the cone and represented by an equation y = 4ax².

The standard form of the equation of a parabola is (y - k) = (1 / 4p)(x - h)², where (h, k) is the vertex and p is the distance from the vertex to the focus. We can convert the given equation x² = -20y into this standard form by completing the square:

x² = -20y

x² / (-20) = y

x² / (-20) + 0 = y + 0

(x - 0)² = -20(y - 0)

Comparing this equation to the standard form, we can see that the vertex is at (h, k) = (0, 0), and that 4p = -20, so p = -5/2.

Since the focus is a distance of p below the vertex, the focus is at (h, k - p) = (0, -5/2), which is the same as (0, -2.5).

Therefore, the coordinates of the focus of the parabola x² = -20y are (0, -2.5), which corresponds to the option (0, -5).

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What’s the surface area and the formula for it?

Answers

Answer:

[tex]1440cm^{2}[/tex]

Step-by-step explanation:

SA=2lw+2lh+2wh - Formula

SA=2(12×20)+2(12×15)+2(20×15)

SA=(2×240)+(2×180)+(2×300)

SA=480+360+600

SA=1440

please help me with this!!!!!

Answers

Answer:

C. ΔJKL, in which m∠J = 15° and m∠L = 45°

Step-by-step explanation:

To solve, let's find the missing angle of the triangle:

180 - 120 - 15 = 45°

That means a solution should have at least 2 solutions from the solution set (15 , 45, 120)

C, is the correct choice.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

"C"

Step-by-step explanation:

Similar triangles have all the same corresponding angles, and the total must add to 180 degrees. So the original triangle has angle 1 = 15, 2 = 120, so 3 = 180 - (15 + 120) = 45.

Option C has the same angles.

Công ty A&T có thông tin về hàng tồn kho năm 20X0 như sau: - Giá trị hàng tồn kho: 6.000 triệu đồng (loại 1 là 2.000 triệu đồng, loại 2 là 4.000 triệu đồng). Hai loại hàng tồn kho này không cùng bản chất. Số lượng hàng tồn kho loại 1 dùng cho các hợp đồng bản hàng đã ký lớn hơn số lượng hàng tồn kho loại 1 hiện tại. -Cuối kỳ kế toán công ty đánh giá lại hàng tồn kho với các thông tin đáng tin cậy như sau: + giá bán ước tính của hàng tồn kho loại 1 là 2.000 triệu đồng, loại 2 là 4.300 triệu đồng + chi phi bán hàng, ước tính của loại 1 là 40 triệu đồng, loại 2 là 30 triệu đồng. Yêu cầu: Công ty A ghi nhận các nội dung kinh tế trên như thế nào theo chuẩn mực báo cáo tài chính quốc tế giá trị hàng tồn kho, giá trị thuần có thể thực hiện được hoặc dự phòng)?

Answers

Oh my god why so long

Need help really badly please help .

Answers

Answer:

sin s = 36 / 42 = 18 / 21 = 6/ 7

sin R = 14 / 42 = 7 / 21 = 1 / 3

cos s = 14 / 42 = 1 / 3

cos R = 36 / 42 = 6 / 7

You are 28-year-old healthy male and interested in purchasing life insurance. Using the table, determine what the annual premium for a Whole Life insurance police, given that the face value of the policy is $162,253. If need be, round your answer to the nearest cent.

Answers

the annual premium for a Whole Life insurance police is  $2,881.61. Option A.

How do we calculate the annual premium for a Whole Life insurance police?

For us to solve the annual premium for a Whole Life insurance policy for a 28-year-old male, we need to look at the provided table.

The premium rate for a 28-year-old male for a Whole Life policy is $17.76 per $1,000 of face value.

Annual premium =  $162,253/ 1000 x 17.76

= $2,881.61

The above exercises is from the question provided in the picture;

You are 28-year-old healthy male and interested in purchasing life insurance. Using the table, determine what the annual premium for a Whole Life insurance police, given that the face value of the policy is $162,253. If need be, round your answer to the nearest cent.

                                            Permanent Insurance

Age               Whole Life        20-Payment Life       20-Year Endowment

                     M           F                 M              F                M              F

25              $16.38    $14.38        $28.40    $25.04      $37.02     $34.87

26              $16.91     $14.77          29.11        25.96        37.67       35.30

27              $17.27     15.23           29.97       26.83        38.23      35.96

28              17.76       15.66           30.68      27.54         38.96       36.44

a. $2,881.61

c. $6,321.38

b. $4,977.92

d. $6,438.20

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PLZZZZ I really need help!

Which function rule represents the best line of fit for the data in the plot?

Answers

A function assigns the values. The correct option is C.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The function rule that represents the best line of fit for the data in the plot is option C.

A) f(x)= x+8

Since the line has a positive slope this can not be the appropriate option.

B.) f(x) = -2x+14

Since the y-intercept of the equation is above all the data points, it would not be the best fit for the data in the plot.

D.) f(x) = 10

Since this is a straight horizontal line at y=1. This is not the appropriate option.

Hence, the correct option is C.

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In a class, there are 87 students
in the class, and 38 are boys. What is
the probability that a girl is selected
randomly to represent the class in a
debate?

Answers

Answer:

49/87 = .56 = 56%

Step-by-step explanation:

Answer:

56%

Step-by-step explanation:

Need help, please

Cyndi works in an office. She thinks that she spends 30 minutes in meeting for every 3 hours that she spends working at her desk. One week, she spends 3 hours and 15 minutes in meetings. Using Cyndi's timings above, work out how many hours she would have spent working at her desk?

Answers

Answer:

19.5 hrs

Step-by-step explanation:

30 minutes meeting for every 3 hours of work

10 minutes meeting for every 1 hour of work

15 minutes meeting of every 1 1/2 hour of work

3 hours meeting for every 18 hours of work

She spent 19 1/2 hours

Liz earns a salary of $2,300 per month, plus a commission of 3% of her sales. She wants to earn at least $2,500 this month. Enter an inequality to find amounts of sales that will meet her goal. Identify what your variable represents. Enter the commission rate as a decimal.

Answers

Answer:

she needs 200 more$

Step-by-step explanation:

It's a quartile question.

Answers

Answer:

D. 8

Step-by-step explanation:

the upper quartile = 8

I need points 3+4%34

Answers

Answer:

I do too :(

Step-by-step explanation:

Answer:

4.36

i dont really but uh yea

he perimeter of the figure is given. Find the length of the indicated side.

3x − 3
Perimeter = 14x + 2

The length of the indicated side is .

Answers

Answer:

who's he, is it me, cuz id call that a failed abortion

Answer:

I am also stuck

Step-by-step explanation:

if f(x)=x2+x and g(x)=x-3, find f(g(7))​

Answers

f(g(7)) = 20

Hope it helps you...

Please help.............

Answers

Answer:

...........

2(x + 2) + 2x = 20

Answer:

x(x+2) = 20

Step-by-step explanation:

Perimeter Formulas of rectangle is: Perimeter = 2 × (a + b)

help me please Which of the following graphs shows a negative linear relationship with a
correlation coefficient, r, relatively close to -1?
A
В.
C
D
A. Graph A.
B. Graph B
C. Graph C
D. Graph D

Answers

Answer:

B. Graph B

Step-by-step explanation:

The closer the data points are along the line of best fit, the closer the the correlation coefficient is to -1 or 1.

The data points in graph B are closer to each other along the line of best fits and the increase in variable x leads to a decrease in variable y, which signifies negative linear relationship.

Therefore, the correlation coefficient of graph B will most likely be close to -1.

The radius is of a circle is 7 kilometers what is the area of a sector bounded by a 180 arc

Answers

Answer:

77 square units

Step-by-step explanation:

Taking π as 22/7

=>(180/360)×(22/7)×(7)^2

=>1/2×22×7

=>11×7

=>77  

GRAM is a parallelogram with diagonals RM and GA. If RP = x+7 , PA = 2x+18 , and GP = 8x , find RM

Answers

Answer:

RM =20

Step-by-step explanation:

Find the diagram of the parallelogram attached

From the diagram, GP = PA

8x = 2x+18

8x - 2x = 18

6x = 18

x = 18/6

x = 3

Since RM = 2RP

RM = 2(x+7)

RM = 2(3+7)

RM = 2(10)

RM =20

Hence the length of RM is 20

Reflect A(-2,4), B(3,-5), C(2, 1) over the x-axis.

Answers

Answer:

When you reflect over the x axis, you change all the y values to their opposites (switch the sign)

Step-by-step explanation:

Reflecting on X-axis we get,
i.e P (x,y) P’(x,-y)

A(-2,4). A(-2,-4)
B(3,-5). B(3, 5)
C(2,1). C(2,-1)

?
A sprinter travels a distance of 100 m in a time of 9.67 seconds.
What is the sprinter's average speed rounded to 4 sf?

Answers

Answer:

average speed of sprinter will be 10.42m/s

Step-by-step explanation:

distance covered=s=100m

time taken=t=9.67m/s

average speed=10.42m/s

Which of the following is true about a linear function? (4 points) Select one: a. It may curve in some parts and be horizontal in others. b. It must cross the origin. c. It has a constant rate of change. d. It must contain only positive values.

Answers

Option c: It has a constant rate of change.

please help giving brainly and points :)​

Answers

Answer:

(-7, 8) across the x-axis: (-7, -8)

(-7, 8) across the y-axis: (7, 8)

Step-by-step explanation:

Use any method you like to find the measure of angle A

Answers

A = 71.5 degrees (1 dp)

cos(A) = (21^2 + 16^2 - 22^2) / (2 x 21 x 16)
= 0.31696...
A = cos^-1(0.31696...) = 71.5 degrees

What is the least common denominator of the rational expressions below?
12
x2 - 11x +30
43
x² - 6x
A. x(x-5)
B. x(x-5)(x-6)
C. x(x - 5)(x-6)
D. (X-6)

Answers

Answer:

D. (x-6)

Step-by-step explanation: Just did it

A 16 ft ladder leans against the side of a house the top of the ladder is 15 Ft off the ground find x the angle of elevation of the ladder round your answer to the nearest tenth of a degree

Answers

the answer should be 69.6 :)

Answer:

Step-by-step explanation:

X - 54 + 32x = 53 find the value of x.


a). 23
b). 3 8/33
c). 25
d). 6 2/17

Answers

Answer:

b). 3 8/33

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify

x - 54 + 32x = 53

Step 2: Solve for x

Combine like terms:                                                                                         33x - 54 = 53[Addition Property of Equality] Add 52 on both sides:                                  33x = 107[Division Property of Equality] Divide 33 on both sides:                               x = 107/33Simplify:                                                                                                             x = 3 8/22

Find the measures of a positive angle and a negative angle that are coterminal with each given angle
0=110

Answers

Answer:

Why was Mrs Hallette unhappy when people asked about her son?

Step-by-step explanation:

2. Solve for x and y, Show your work​

Answers

Answer:

use similarity to solve this

so the shape of side x is similar to side

x/6=10/8

8x=10 multiply by 6

8x=60

divide 60 by 8 to get 7.5

so x=7=5

using Pythagorean theorem

side RP=RS squared + SP squared

side RS=7=5

7.5squared =56.25

4.0+8.0=12

12squared=144

56.25+144=200.25

square root of 200.25=14.15

14.15=y+10

y=14.15-10

y=4.15

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