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
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
Answer:
Step-by-step explanation:
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 .
Answer:
who's he, is it me, cuz id call that a failed abortion
Answer:
I am also stuck
Step-by-step explanation:
?
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?
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
if f(x)=x2+x and g(x)=x-3, find f(g(7))
f(g(7)) = 20
Hope it helps you...
please help giving brainly and points :)
Answer:
(-7, 8) across the x-axis: (-7, -8)
(-7, 8) across the y-axis: (7, 8)
Step-by-step explanation:
GRAM is a parallelogram with diagonals RM and GA. If RP = x+7 , PA = 2x+18 , and GP = 8x , find RM
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
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?
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
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?
Answer:
49/87 = .56 = 56%
Step-by-step explanation:
Answer:
56%
Step-by-step explanation:
The radius is of a circle is 7 kilometers what is the area of a sector bounded by a 180 arc
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
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)
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).
Learn more about parabola here:
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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.
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
Find more useful exercises on calculating annual premium;
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Reflect A(-2,4), B(3,-5), C(2, 1) over the x-axis.
Answer:
When you reflect over the x axis, you change all the y values to their opposites (switch the sign)
Step-by-step explanation:
PLZZZZ I really need help!
Which function rule represents the best line of fit for the data in the plot?
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.
Learn more about Function:
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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?
Answer:
the male weigh than the female
Step-by-step explanation:
[tex]\frac{19}{6}[/tex]=[tex]3\frac{1}{6}[/tex]
please help me with this!!!!!
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.
X - 54 + 32x = 53 find the value of x.
a). 23
b). 3 8/33
c). 25
d). 6 2/17
Answer:
b). 3 8/33
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-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 8/22help 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
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.
Need help really badly please help .
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
2. Solve for x and y, Show your work
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
Use any method you like to find the measure of angle A
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.
Option c: It has a constant rate of change.
Find the measures of a positive angle and a negative angle that are coterminal with each given angle
0=110
Answer:
Why was Mrs Hallette unhappy when people asked about her son?
Step-by-step explanation:
What’s the surface area and the formula for it?
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
It's a quartile question.
Answer:
D. 8
Step-by-step explanation:
the upper quartile = 8
Please help.............
Answer:
...........
2(x + 2) + 2x = 20
Answer:
x(x+2) = 20
Step-by-step explanation:
Perimeter Formulas of rectangle is: Perimeter = 2 × (a + b)
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)
Answer:
D. (x-6)
Step-by-step explanation: Just did it
can somebody help me with this question
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.
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)?
I need points 3+4%34
Answer:
I do too :(
Step-by-step explanation:
Answer:
4.36
i dont really but uh yea
Liz earns a salary of $2,300 per month, plus a commission of 3% of her sales. She wants to earn at least $2,500 this month. Enter an inequality to find amounts of sales that will meet her goal. Identify what your variable represents. Enter the commission rate as a decimal.
Answer:
she needs 200 more$
Step-by-step explanation: