Answers
7.
We are given:
abcissa(x-coordinate) of given point: -6
let's say the ordinate(y-coordinate) of the given point is y
distance of the given point from (1,3) = √74
we can rewrite the given information as:
the distance between the points (-6,y) and (1,3) is √74
finding y:
we know that in order to find the distance between any two points, we use the distance formula, which goes as follows:
distance = [tex]\sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}[/tex]
from the data we are given, let's say that:
(x₁, y₁) = (-6, y)
(x₂, y₂) = (1, 3)
(you can use them interchangably, there is no restriction on which point gets to be labelled as 1)
plugging this in the distance formula, we get:
distance = [tex]\sqrt{(-6-1)^2 + (y - 3)^2}[/tex]
we are also given that the distance is √74,
√74 = [tex]\sqrt{(-7)^2 + (y - 3)^2}[/tex]
squaring both sides to get rid of the square root
74 = (-7)² + (y - 3)²
74 = 49 + y² + (3)² -2(y)(3) (using the "square of sum" identity)
74 = 49 + y² + 9 - 6y
74 = 58 + y² - 6y
y² - 6y + 58 - 74 = 0 (subtracting 74 from both sides)
y² - 6y - 16 = 0
y² - 8y + 2y - 16 = 0 (splitting the middle term)
y(y - 8) + 2(y - 8) = 0
(y + 2)(y - 8) = 0
which means that:
y + 2 = 0 , y - 8 = 0
y = -2 , y = 8
These are the two possible values of y
8.
We are given:
points A and B
A: (3, y)
B: (6, 2)
distance between A and B = 5 units
finding possible values of y
here, we will use the distance formula again to find the value of y
distance formula: [tex]\sqrt{(x_a-x_b)^2 + (y_a - y_b)^2}[/tex]
plugging the given values, we get:
5 = [tex]\sqrt{(3-6)^2 + (y - 2)^2}[/tex]
25 = (3 - 6)² + (y - 2)² (squaring both sides)
25 = (-3)² + (y - 2)²
25 = 9 + y² + (2)² - 2(y)(2)
25 = 9 + y² + 4 - 4y
y² - 4y + 9 + 4 - 25 = 0 (subtracting 25 from both sides)
y² - 4y - 12 = 0
y² - 6y + 2y - 12 = 0 (splitting the middle term)
y(y - 6) + 2(y - 6) = 0
(y + 2)(y - 6) = 0
y + 2 = 0 , y - 6 = 0
y = - 2 , y = 6
These are the two possible values of y
Related Questions
Matthew can spend up to $75 on supplies for his garden. The flowers will cost $38 and he wants to spend the rest on bags of top soil. Each bag of top soil costs $6.
How many bags of top soil can he buy?
Enter your answer in the box.
bags of top soil
Answers
Answer:
6 r1
Step-by-step explanation:
Stephanie won 53 super bouncy balls playing hoops
at the county fair. At school she gave three to every
student in her math class. She only has 2 remaining.
How many students are in her class?
(Write an equation, solve, and check your solution)
Answers
equation;
53 divided by 3 equals 17r2
1)Find the quadratic equation
3(3x [tex] {}^{2} [/tex]+ 1)=12x
2)Find the quadratic equation
[tex]9y {}^{2} - 12y - 14 = 0[/tex]
Answers
Step-by-step explanation:
See picture above for solution.
Brainliest if correct
Answers
Answer:
x = -4
Step-by-step explanation:
Divide both sides of the equation by the same term
24=-6x
Divide the numbers
Cancel terms that are in both the numerator and denominator
Move the variable to the left
HOPE IT HELPS, BE SAFE :3
Brainliest if correct
Answers
Answer:
w = 9
Step-by-step explanation:
18 + 4w = 6w
6w - 4w = 2w
2w = 18
18/2 = 9
2w/2 = w
w = 9
[tex]\large\textbf{Hey there!}[/tex]
[tex]\large\textbf{18 + 4w = 6w}\\\large\textbf{4w + 18 = 6w}\\\large\text{SUBTRACT 62to BOTH SIDES}\\\large\textbf{4w + 18 - 6w = 6w - 6w}\\\large\text{SIMPLIFY IT!}\\\large\textbf{-2w + 18 = 0}\\\large\text{SUBTRACT 18 to BOTH SIDES}\\\large\textbf{-2w + 18 - 18 = 0 - 18}\\\large\text{CANCEL out: 18 - 18 because it give you 0}\\\large\text{KEEP: 0 - 18 because it help solve for the w-value}\\\large\text{NEW EQUATION: \bf -2w = 0 - 18}\\\large\text{SIMPLIFY IT!}\\\large\textbf{-2w = -18}[/tex]
[tex]\large\text{DIVIDE -2 to BOTH SIDES}\\\mathbf{\dfrac{2w}{-2}= \dfrac{-18}{-2}}\\\large\text{CANCEL out:} \rm\dfrac{-2}{-2}}\large\text{ because it give you 1}\\\large\text{KEEP: }\rm{\dfrac{-18}{-2}}\large\text{ because it gives you the w-value}\\\large\text{NEW EQUATION: \bf w = }\rm{\bf \dfrac{-18}{-2}}\\\large\text{SIMPLIFY IT!}\\\large\textbf{w = 9}\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{w = 9}}}\huge\checkmark[/tex]
[tex]\large\textbf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A candy bar is created with 28 cubic centimeters of chocolate. If the length is 8 cm and the width is 6 cm, what is the height of the candy bar? Round to the nearest hundredth.
Answers
Answer:
0.58cm
Step-by-step explanation:
l×b×h=volume
Given:
Voume=28cm^3
l=8cm
width or breadth=6cm
h=?
applying the above formula
l×b×h=28cm^3
6×8×h=28cm^3
h=28/48=0.58cm
What is the total price of an $18.97 item plus 8% slaes tax?
Answers
Answer:
$20.49
Step-by-step explanation:
8% = 8/100 = 0.08
Therefore, 8% of 18.97 = 0.08 x 18.97 = 1.5176
So the total price = 18.97 + 1.5176 = 20.4878 = $20.49
Alternatively,
108% = 108/100 = 1.08
18.97 x 1.08 = 20.4878
Part A: If (26)X = 1, what is the value of x? Explain your answer. (5 points)
Part B: If (59x = 1, what are the possible values of x? Explain your answer. (5 points)
Answers
Answer: Part A: 1/26 or 0.38
Part B: 1/59 or 0.017
Step-by-step explanation:
PLEASE HELP ME QUICKKK, FIRST CORRECT PERSON GETS BRAINLIEST
Answers
Answer:
all a,d, and e are correct. Use the area of a circle formula to solveFor the following two numbers, find two factors of the first number such that their product is the first number and their sum is the second number.
65,18
Answers
Product of 5 and 13 is 65 and sum of 5 and 13 is 18
Natalie has 412 apples that she must package into bags. Each bag must hold 8 apples. Natalie divides 412 by 8 and gets an answer of 51 R 4. What is the correct interpretation of R 4 for this situation? 1. Natalie can fill 4 more bags after filling 51 bags. 2. Natalie has 4 bags left after filling 51 bags. 3. Natalie has 4 apples left after filling 51 bags. 4. Natalie can fill at most 51 bags with 4 apples each.
Answers
Answer:
3.
Step-by-step explanation:
The answer is 51 R4, meaning that 54 bags HAVE been filled and 4 apples are the remainder. Therefore, there are 4 apples that have not been bagged and Natalie would need another bag to bag all the apples.
Find the volume of the cylinder. Round your answer to the nearest tenth.
Answers
Answer:
245pi(769.7)
Step-by-step explanation:
V=Bh
B=7pi^2=49pi
V=49pi*5
V=769.6902001
V=~ 769.7
in terms of pi=245pi
Write the improper fraction as a mixed number or a whole number.
956
125
Answers
Answer:
956= 9/56
125= 1/25
Step-by-step explanation:
Find the surface area of the cylinder. Use 3.14 for pi. Do not round the answer.
690.8
224.5
364.8
960.8
Answers
Answer:
690.8
Step-by-step explanation:
I've done this one before
Answer:
690.8 sq units
Step-by-step explanation:
Surface Area(cyl) = 2πrh+2πr²
SA = 2(3.14)(5)(17) + 2(3.14)5²
SA = 6.28(85) + 25(6.28)
= 533.8 + 157
= 690.8
HELP ME OUT PLEASE!!!!!
A point on a pre-image is currently located at (1, -3). The pre-image is translated 3 units right and 6 units up.
What are the NEW coordinates for the point after the translation?
Use graph paper to sketch the translation if needed.
O (3, 4)
O (4, 3)
O (7, 0)
O (-2, 2)
Answers
Answer:
(4,3)
Step-by-step explanation:
5 A line passes through the point (-4,-1) and has a slope of 4 Write an equation in point-slope form for this line.
Answers
Answer:
y + 1 = 4(x + 4)
Step-by-step explanation:
When you write an equation in point-slope form, you only need two things: a point and a slope.
Given:
point: (-4, -1)slope (m): 4The standard point-slope equation is
y - y₁ = m(x - x₁)Plug in what you know.
y - (-1) = 4(x - (-4))Simplify.
y + 1 = 4(x + 4)This is your equation.
Hope this helps!
Learn with another example:
https://brainly.com/question/24436844
The linear equation in point-slope form is y + 1= 4(x + 4)
How to determine the equation of the lineA linear equation is calculated using the following equation:
y - y1= m(x - x1)
From the question, we have:
Slope (m) = 4
(x1,y1) = (-4,-1)
So, the equation becomes
y + 1= 4(x + 4)
Hence, the linear equation in point-slope form is y + 1= 4(x + 4)
Read more about linear equations at:
https://brainly.com/question/15602982
A bank account earns 2% interest each year. Giselle uses the expression p +0.02p
to find how much money will be in the account after one year if she deposits p dollars.
Answers
Answer:
1.02 is the simplified answer and 102% is the answer to the next one
Step-by-step explanation:
The expression p+0.02p can also be written as 1p+0.02p.
To combine like terms, add the coefficients.
1+0.02=1.02, so 1p+0.02p=1.02p.
Vishal decided to return to Greenwood Bakery on Liberty Avenue on Tuesday to buy more desserts. This time he bought cookies and cake pops. He needed to buy at least 10 desserts to share with his family. each cake pop was $4 and each cookie was $2 Vishal could not spend more than $30. of each cake pop is x and each cookie is y determine the different amounts of desserts Vishal can purchase though graphing
Answers
The linear equality that shows this relationship is x + y ≥ 10 and 4x + 2y ≤ 30
Equation
An equation is an expression used to show the relationship between two or more variables and numbers.
Let x represent the number of cake pop and y represent the number of cookie. Hence:
x + y ≥ 10 (1)
Also:
4x + 2y ≤ 30 (2)
The linear equality that shows this relationship is x + y ≥ 10 and 4x + 2y ≤ 30
Find out more on equation at: https://brainly.com/question/13763238
Find the volume of a sphere with a diameter of 10 yards
Answers
Answer:
Step-by-step explanation:
diameter = 2 * radius Divide by 2
radius = diameter /2
Formula
Volume_sphere = 4/3 pi r^3
Givens
r = 10 yards
Solution
Volume = 4/3 * 3.14 * 10^3
Volume = 4.1867*10^3
Volume = 4186.7 yards^3
Coach reynolds bought 23 bottles of sports drink. Each bottle contains 25 ounces of sports drink. If he wants to have 700 ounces of sports drink for the football `game on friday night, how many more bottles of sports drinks should Coach reynolds buy.
4th grade.
Answers
Answer:
5 more bottles
Step-by-step explanation:
23 x 25 will give us how many ounces Coach Reynolds have already.
23 x 25 is 575
700 - 575 will give us how many ounces he needs to buy.
700 - 575 is 125
125 divided by 25 will give us how many bottles he needs to buy
125 divided by 25 is 5
So 5 more bottles
Hope this helps! :)
1. Solve the following LPP using a Simplex method: Max Z = 10X1 + 20X2 + 14X3 Subject to 5X1 + 4X2 + 2X3 < 60 X2 < 5 X3 > 10 X1, X2, X3 > 0
Answers
Answer:
878
Step-by-step explanation:
Please help - trig identity
Answers
Answer:
Step-by-step explanation:
[tex]LHS=cosec(x)-cosec(x)cos^{2} (x)\\\\LHS=cosec(x)-cosec(x)(1-sin^{2} (x))\\\\LHS=cosec(x)-cosec(x)+cosec(x)*sin^{2} (x)\\\\LHS=cosec(x)-cosec(x)+cosec(x)\frac{1}{cosec^{2}(x) } \\\\LHS=cosec(x)-cosec(x)+\frac{1}{cosec(x) }\\\\LHS=\frac{cosec^{2}(x)-cosec^{2}(x)+1 }{cosec(x)} \\\\LHS=\frac{1}{cosec(x)} \\\\LHS=sin(x)=RHS[/tex]
Hence,LHS=RHS proved
Your parents invest $10,000 in a college fund when you are born. They find a fund that will return 8% per year for 18 years.
When you are 18 you find a school that charges $12,000 tuition per year. Tuition increases at a rate of 11% per year (so the second year will have a tuition of $13,320) , will this money take care of four years of school? How many years of college will this take care of? Explain your answer fully.
Answers
The interest is compounded in the investment and the fees, the 4 years
school fees is however larger than the future value of the investment.
Response:
The money is less required to take care of four years of schoolTwo yearsHow can the future value of the amount invested be found?First part:
The future value, FV, of the investment after 18 years is given as follows;
[tex]FV = \mathbf{PV \cdot (1 + i)^n}[/tex]Where;
PV = The present value = $10,000
i = The interest rate = 8% = 0.08
n = The number of years = 18
Which gives;
[tex]FV = 10,000 \times (1 + 0.08)^{18} \approx \mathbf{39,960.195}[/tex]
The future value of the investment, FV = $39,960.195
The school fees each year is given as follows;
Fees = First year fees·(1 + r)ⁿ
Where;
First year fees = $12,000
r = Increase rate of the school fees = 11% = 0.11
n = The number of years
The school fees for four years is given as follows;
∑Fees = $12,000 + $12,000·(1 + 0.11) + $12,000·(1.011)² + $12,000·(1.011)³
Which gives;
∑Fees = 12,000 + 12,000·(1 + 0.11) + 12,000·(1 + 0.11)² +12,000·(1 + 0.11)³ = 56,516.772
The total tuition fees for four years = $56,516.772
The future value of the investment after 18 years, $39,960.195 is less
than the amount required as school fees for four years, therefore;
The money is less than the amount to take care of four years of schoolSecond part:
The fees for 3 years of school is given as follows;
[tex]\displaystyle \sum \limits_{n = 1 }^3[/tex] = 12,000 + 12,000·(1 + 0.11) + 12,000·(1 + 0.11)² = 40,105.2 > 39,960.195
The fees for 2 years of school is given as follows;
[tex]\displaystyle \sum \limits_{n = 1 }^2[/tex] = 12,000 + 12,000·(1 + 0.11) = 25,320 < 39,960.195
The number of years of college the value of the investment will take care of is therefore;
Two yearsLearn more about future value here:
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please help me with this
Answers
Answer:
7
Step-by-step explanation:
We can see that x is equal to 7 and that is we use the exponent of 2 it equals 49 if we divide this by 2 we get 24. 5 and add this by the left over 3.5 gives us 28 and divide this by 2 and we get 14. After this you always need to remember to divide your answer by 2 which gives us 7.
Mr. Bray prepares a list of 434343 US presidents, 888 of whom died in office. Then 181818 of his students each select a president at random (there can be repeats) for their creative writing assignments
Answers
Answer:
where is the question bcz u only gave us a storyAnswer:0.98
Step-by-step explanation:got it right on khan
Find the area of the composite figure.
Answers
Answer:
132 square feet
Step-by-step explanation:
The formula for the area of a triangle is 1/2 * b * h. B stands for base and h stands for height. 1/2 multiplied by the base, 10, is 5. We then multiply 5 by 12 which is 60. Let's look at the rectangle now. The area of a rectangle is length by width. The length is 12ft and the width is 6ft. 12 * 6 = 72. 72+60=132 square feet.
An article reports “attendance dropped 6% this year, to 300.” What was the attendance before the drop?
Answers
Answer:
Approximately 319.15
Step-by-step explanation:
300 ÷ (1 - 6%) = 319.14893617021
simplify the expression
4√ 2 + 2√ 32
Answers
Answer:
16.97056
Step-by-step explanation:
Write a sum of three numbers that equal zero
Answers
Answer:
1 + (-3) + 2 = 0
Step-by-step explanation:
21+77 using gcf and distributive property pls
Answers
1
,
11
1
,
11
is
11
11
.