Answer:
The circle has radius = 9 units, and its equation is:
[tex]x^2+y^2=81[/tex]
The parabola has equation of the form:
[tex]y=a\,x^2+9[/tex]
with [tex]a[/tex] being a positive number
Step-by-step explanation:
Given the characteristics of the two figures (circle and parabola) as described,
since the parabola intersects the circle at a single point (it vertex) then the radius of the circle centered at the origin must be 9. that makes the equation of the circle to have the following standard form;
[tex]x^2+y^2=9^2\\x^2+y^2=81[/tex]
Since there is no other info regarding the parabola, the most one can say about the equation of the parabola, is that in vertex form, the parabola's equation must be of the form:
[tex]y=a\,(x-x_{vertex})^2+y_{vertex}\\y=a\,(x-0)^2+9\\y=a\,x^2+9[/tex]
with [tex]a[/tex] being a positive number.
A grocery store recently sold a bag of peanuts for $0.76 and a bag of Pikachu's for $3.68 at the end of the day 50 bags of peanuts and Pikachu's were sold for a total of 128 point 52 how many bags of each were sold
Answer:
31 Pikachu bags were sold.
19 peanut bags were sold.
Step-by-step explanation:
Let's set up an equation of the total revenue of the day, where x is the number of Pikachu's sold.
We know that the number of Peanuts sold is 50-x (as the total needs to be 50)
We know that the total revenue is:
Number of Pikachus * Cost per Pikachus + Number of Peanuts * Cost per Peanuts
Using our definitions above:
Total Revenue = x * $3.68 + (50-x) * $0.76
We know that the revenue needs to be $128.52.
$128.52 = x * $3.68 + (50-x) * $0.76
Let's remove the $ signs.
128.52 = x * 3.68 + (50-x) * 0.76
Multiplying both 50 and -x with 0.76, "expanding" the parenthesis.
128.52 = x*3.68 + 50*0.76 - x*0.76
128.52 = x*3.68 + 38 - 0.76*x
Subtracting 38 from both sides
90.52 = 3.68*x - 0.76*x
We can simplify the right side.
90.52 = 2.92*x
We can divide both sides by 2.92:
31 = x
And flip it:
x = 31
So 31 Pikachus were sold (remember we claled that x), and as we know, the number of peanut bags sold is
50-x = 50-31 = 19
31 Pikachu bags were sold.
19 peanut bags were sold.
[tex] \LARGE{ \boxed{ \rm{ \pink{Solution:}}}}[/tex]
Let the number of peanut bags be x
Then, Number of pikachu bags = 50 - x
Given,
Cost of each peanut bag = $0.76Cost of each pikachu bag = $3.68Then,
⇛ Total cost he gets from peanut bag = $0.76 × x
⇛ Total cost he gets from pikachu bag = $3.68(50 - x)
According to question,
⇛ $0.76x+ $3.68(50 - x) = $128.52
Solving this equation,
⇛ 0.76x + 184 - 3.68x = 128.52 (Removed $ symbol)
⇛ 184 - 2.92x = 128.52
⇛ 184 - 128.52 = 2.92x
⇛ 55.48 = 2.92x
Flipping the equation,
⇛ 2.92x = 55.48
⇛ x = 55.48 / 2.92
⇛ x = 19
Then,
⇛ 50 - x = 50 - 19 = 31
[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: peanut \: bags = 19}}}}}[/tex]
[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: pikachu \: bags = 31}}}}}[/tex]
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What are the solutions of the equation x4 – 5x2 – 14 = 0? Use factoring to solve.
Answer:
[tex]x=\pm 7\text{ or } x=\pm i\sqrt{2}[/tex]
Step-by-step explanation:
We have the equation:
[tex]x^4-5x^2-14=0[/tex]
Since this is in quadratic form, we can consider using u-substitution. Thus, we will let:
[tex]u=x^2[/tex]
Then by substitution:
[tex]u^2-5x-14=0[/tex]
Now we can solve normally. Factor:
[tex](u-7)(u+2)=0[/tex]
Zero Product Property:
[tex]u=7\text{ or } u=-2[/tex]
Back-substitute:
[tex]x^2=7\text{ and } x^2=-2[/tex]
Take the square root of both sides. Since we are taking an even-root, we will need to add plus-minus:
[tex]x=\pm 7\text{ and }x=\sqrt{-2}[/tex]
Therefore, our solutions are:
[tex]x=\pm7\text{ and } x=\pm i\sqrt{2}[/tex]
pls help this is from khan academy
Answer:
[tex]y=-3x+7[/tex]
Step-by-step explanation:
This is asking you to provide the equation is slope-intercept form:
[tex]y=mx+b[/tex]
In this equation, m is the slope of the line and b is the y-intercept (where the x value is 0).
By looking at the graph, we can find the y-intercept:
[tex]y-intercept=7\\\\m=7[/tex]
To find the slope of the line, you can count how many spaces it takes to go from one point to another. To do this, it's best to find an even point (1,4) and make your way to (0,7).
The slope is represented by [tex]\frac{rise}{run}[/tex] , where the rise is the change in the y-axis and the run is the change in the x-axis.
From (1,4) , move up (rise) as many spaces as it takes to get to the y-axis level of "7", which is 3 spaces. From here, move to the left (run) as many spaces as it takes to get to the x-axis level of "0", which is 1 space. Since you moved to the left, however, this means that the number will be a negative:
[tex]\frac{rise}{run}=\frac{3}{-1}=-\frac{3}{1}=-3[/tex]
The slope is -3.
Insert the information into the equation:
[tex]y=-3x+7[/tex]
:Done
Answer:
the desired equation is y = -3x + 7
Step-by-step explanation:
The y-intercept can be read directly from the graph: (0, 7).
Another point on the graph is (2, 1).
As we move from (0, 7) to (2, 1), we see x (the run) increasing by 2 and y (the rise) decreasing by 6. Thus the slope of this line is m = rise/run = -6/2, or -3.
Start with the slope-intercept form of the equation of a straight line, which is y = mx + b.
Then 1 = (-3)(2) + b; find b:
1 = -6 + b, or b = 7
Then the desired equation is y = -3x + 7.
Find the volume. Show work plz
Answer:
196π or 615.75 m^3 to the nearest hundredth.
Step-by-step explanation:
This is a cone, so:
Volume = 1/3 π r^2 h
= 1/3 * π * 14^2 * 3
= 196π m^3.
If two 6-sided dice are rolled, what is the
probability of rolling double 2s?
16.7%
There are 6 ways we can roll doubles out of a possible 36 rolls (6 x 6), for a probability of 6/36, or 1/6, on any roll of two fair dice. So you have a 16.7% probability of rolling doubles with 2 fair six-sided dice.
Answer:
The answer is 16.7%
Step-by-step explanation:
There are 6 ways we can roll doubles out of a possible 36 rolls (6 x 6), for a probability of 6/36, or 1/6, on any roll of two fair dice. So you have a 16.7% probability of rolling doubles with 2 fair six-sided dice. hope this helped
the standard form: four and sixty-eight hundredths
Answer:
4 17/25
Step-by-step explanation:
68
four and sixty-eight hundredths => 4 ------- or 4 34/50 or 4 17/25
100
Answer:
you would need to use decimals
Step-by-step explanation:
can somewon help me plz i want help
Answer:
5 * 10^10.
Step-by-step explanation:
(9 * 10^10) - (4 * 10^10) = (9 - 4) * 10^10 = 5 * 10^10.
Hope this helps!
Answer:
5*10^10
Step-by-step explanation:
9 times ten is 9^10, and 4 Times 10^10 is 4^10 so 9^10 minus 4^10 is 50000000000 which is also called 5^10 which is also 5 x 10^10 I think. pls correct me if im wrong
Jerome currently has an account balance of $1,859.55. His initial deposit on the account was $825 and it earned 5.7% simple interest. How long has Jerome held the
account?
Answer:
22 years
Step-by-step explanation:
Well we know the formula for simple interest is
I = PRT
I = interest earned
P = initial balance
R = rate
T = time
We want to solve for time here....so rearrange for T
T= I/(PR )
We have
P = 825
R = .057
And I = current balance - initial balance = 1859.55 - 825 = 1034.55
So plugging all those in we have
T = 1034.55/(825×.057 )
T = 1034.55/47.025
T = 22
It was held for 22 years.
colleen's family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and Colleen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?
Answer: 24
Step-by-step explanation:
Colleen painted 7 windows, some of which were her mother's.
Her dad painted 7+1 (8) windows, and that is twice as much as what her mother was supposed to do. Her mother was supposed to do 4 windows. That means Colleen's share was 3 windows.
If all the kids had to do an equal amount of windows, than each kid had to do 3 windows.
8+7+3+3+3=24
The total windows in the house are 21.
What is an algebraic expression?It is an expression contains a relation between different parameters (variables). It contains variable and constant values, along with algebraic operations.
In our given problem, the algebraic relation between different members work output and total windows can be expressed as:
Windows painted by colleen and her mother = 7
Windows painted by father = (Windows painted by colleen and her mother + 1)
= (7 + 1) = 8
∴ Windows painted by father = 8
Now, as given,
2 Windows painted by mother = Windows painted by father
∴ Windows painted by mother = [tex]\frac{8}{2}[/tex] = 4
and Windows painted by colleen = 7 - 4 = 3
Colleen and her 2 brothers paint equal windows;
∴ They painted 3 windows each.
The total windows in the house is equal to total painted windows by mother, father, colleen and her two brothers:
⇒ 4 + 8 + 3 x 3 = 12 + 9 = 21
Hence the total windows in the house are 21.
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Veronica wants to buy a house that costs $249,900. She is going to make a 20% down payment. How
much is her down payment in dollars?
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▹ Answer
$49,980
▹ Step-by-Step Explanation
[tex]\frac{20}{100} * $249,900 \\\\= $49,980[/tex]
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
- The water rate for Columbus Ohio
is $1.98 per 750 gallons of water.
What is the water bill for a resident
who used 27,000 gallons?
Divide total amount used by the amount in the rate:
27,000 / 750 = 36
Multiply that number by the rate:
36 x 1.98 = 71.28
The bill is $71.28
hello can plzz help me with this question wil mark u brainlest and its for 18 points the file is down below thank u :)
Answer:
a rectangular prism
Step-by-step explanation:
consists of 6 faces which are rectangles
Which property is shown by -6 + 0 = -6? A. Commutative Property of Addition B. Identity Property of Addition C. Distributive Property D. Associative Property of Addition
Answer:
C
Step-by-step explanation:
It is c because you are adding. the 6 and o.
Answer:
Would be C.
Step-by-step explanation:
Just adding the 6 and the 0 basically.
PLEASE HELP PLEASE WILL MARK BRAINLY
Answer:
15, 5, 45, 10
Step-by-step explanation:
2 minutes for 10 photos
1 minute for 5 photos
now:
2×5=10
3×5=15
25÷5=5
9×5=45
50÷5=10
Alexander bought a box of crackers at the store. He ate half of the crackers in the box on Monday, and he ate 1/2 of what was left on Tuesday. On Wednesday, he ate 1/3 of what was left after he was finished eating the crackers on Tuesday.
1) What fractional part of the total crackers originally in the box did Alexander
eat on Wednesday?
2) what fractional part of the total crackers originally in the box are left. 3) if there are 4 crackers left in the box after Alexander finished eating crackers on wensday, how many crackers were in the box before it was opened. (Please help!)
Answer:
Given the equivocal nature of this question, I will need to draw an assumption: I will assume that Ali ate from the cake and so did Jason — not Ali ate from the cake and Jason ate from Ali’s slice.
With that being said, the first approach is make both of these fractions have a common denominator, so that we can find how much each respective person ate from the total amount of slices. Intuitively, the common denominator is 12
12
, so this must be true:
Ali ate 4/12
4
/
12
of the cake;
Jason ate 3/12
3
/
12
of the cake
Adding these two fractions will give us 7/12
7
/
12
— the total amount eaten. Now, to find the amount left, we need only subtract 7/12
7
/
12
from 12/12
12
/
12
(the total amount of the cake). Doing so will give us
Step-by-step explanation:
Solve x*2+5x+6=5x+10
Answer:
x = -2, 2.
Step-by-step explanation:
x*2 + 5x + 6 = 5x + 10
x^2 + 5x - 5x + 6 - 10 = 0
x^2 - 4 = 0
x^2 = 4
x = -2, 2 ( 2 solutions).
-15 POINTS PLS HURRY- Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 4.5 cm to 4 cm
Hi there! :)
Answer:
[tex]\huge\boxed{\frac{9cm}{8cm}}[/tex]
We can disregard the units temporarily to create a ratio for 4.5 to 4:
4.5 is not a whole number- we can convert this number in the ratio to a whole number by multiplying both numbers by 2:
2 · (4.5 : 4) = 9 : 8
Express as a fraction:
[tex]9cm : 8cm = \frac{9cm}{8cm}[/tex]
Vertex Form y=a(x-h)^2+k what does each variable represent if they were in a problem.
What is the distance between points A and B on the grid? (the grid is shown in the image). A. 3 units B. 4.5 units C. 5 units D. 5.5 units
=================================================
Explanation:
Since the x coordinates are the same, we can subtract the y coordinates to get
1.5 - (-3.5) = 1.5 + 3.5 = 5
Note how subtracting a negative is the same as adding.
-------
We can subtract in the other order
-3.5 - 1.5 = -5
but we need to make this result positive. A negative distance is not allowed. Absolute value is applied to make the result positive
|-5| = 5
5.4(m-2)= -2(3m+3) please help asap
Answer:
m = 0.421
Step-by-step explanation:
5.4(m-2)= -2(3m+3) (expand parentheses by distributive property)
m(5.4) -2(5.4) = 3m(-2) + 3(-2)
5.4m - 10.8 = -6m - 6 (add 6m to both sides)
5.4m - 10.8 + 6m = - 6
11.4m - 10.8 = - 6 (add 10.8 to both sides)
11.4m = -6 + 10.8
11.4m = 4.8 (divide both sides by 11.4)
m = 4.8 / 11.4
m = 0.421
Answer:
m = 8/19
Step-by-step explanation :
5.4 (m-2) = -2 (3m +3)
54/10 (m-2) = (3m +3) as n = 1
2.3^3 / 2.5 (m-2) = (3m + 3)
4.868 (m-2) = (3m +3)
4.868 + 3 = (3m^2 * m-2)
8 / 9.5 * 2
m = 8 / 19
help me find VW and YZ
Answer:
VW=35
YZ=50
Step-by-step explanation:
As they are similar triangles with a ratio of 1:2 and we know VW:XZ=1:2, we can make the equation:
2(4y+7)=12y-14
8y+14=12y-14
4y=28
y=7
So, VW=4(7)+7=35.
Similarly, you can find YZ through VT:
2(7x-17)=8x+2
14x-34=8x+2
6x=36
x=6
Therefore, YZ=8(6)+2=50.
Please help me with this geometry question:((
Answer:
a.ans=(1,3)
b.ans=(1,2,3,4,5,6,7,9,11,12)
c.ans=(1,3,5,7,9,11)
Step-by-step explanation:
Between A and C (1,3) are common.So it is the intersection.
(1,2,3,4,5,6,7,9,11,12) are all the number belongs to set A and set C.So it is called the union of both sets.
C denotes the complement and the number except set b belong to the complement.
Mathematics, probability and chance Can somebody help me, I always thank and vote
Answer:
A. 0
Step-by-step explanation:
In order for there to be a 1 in 3 chance, there would have to be an equal number of the three chalices. Since four is the smallest number, the other two must have four left as well. That means Donavan drank 1 spoiled milk and 2 flat sodas. Therefore, he drank 0 purified water.
Plz help I’ll mark brainliest
Answer:
Step-by-step explanation:
Using Pythagoras Theorem, hypotenuse = 5
[tex]h = \sqrt{a^{2}+ b^{2}[/tex]
[tex]h = \sqrt{9+16 }\ = \sqrt{25}\ = 5[/tex]
sin x = height / hypotenuse = 3 / 5
cos y = base / hypotenuse = 3 / 5
sin x = cos y = 3 / 5
The Greenbaum family agreed to pay for 3 months of an online TV service in exchange for a $5 credit on the bill each month. If the Greenbaums spend a total of $11.85 on the service over the 3 months, what is the normal price of one month of online TV service?
$5.00
$6.85
$8.95
$30.55
PLS HELP ME I NEED THIS FOR HOMEWORK!!!!
Answer:
36 degrees
Step-by-step explanation:
Because it's a right angle, AOB and BOC are complementary, meaning they add up to 90 degrees.
(3x+30)+(6x-12)=90
9x+18=90
9x=72
x=8
AOB = 6x-12, so substituting
8 in for x gives us 48-12=36
Directions: Calculate the percent increase or decrease between the starting and ending
quantities below. Round your answer to one decimal place.
1. Start: 3
End: 10
Answer:233.333%
Step-by-step explanation:
1. 10-3=7 subtract end by start
2.7/3=2.333 divide difference by absolute value of start
32.333x100=233.333% multiply by 100 if negative its decreasing if positive it increasing
hoped this helped
According to Newton's Second Law of Motion, the sum of the forces that act on an object with a mass m
that moves in an acceleration a is equal to m . a
An object whose mass in 80 grams has an acceleration of 20 meters per seconds square.
What calculation will give us the sum of the forces that act on the object, in Newtons (which are
kg.m/s2)?
Choose 1 answer.
A 80 . 20
B 80 . 1000 . 20
C 80/1000 . 20
D 80/602. 20
Answer: 80/1000 • 20
Answer:
Screenshots attached! Hope it helps :)
What is the solution of the inequality shown
below?
y+7<-1
Answer:
y<-8
Step-by-step explanation:
y<-1 - 7
y<-8
Answer:
y < -8
Step-by-step explanation:
To solve an inequality, we must get the variable, y, isolated on one side of the inequality.
[tex]y+7 < -1[/tex]
7 is being added to the variable, y. The inverse of addition is subtraction. Subtract 7 from both sides of the inequality.
[tex]y+7-7< -1-7[/tex]
[tex]y < -1-7[/tex]
[tex]y < -8[/tex]
The solution to the inequality is: y< -8
Clare has 150$ in her bank account. She buys a bike for 200$. What is Clares account balance now?
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The amount left in the bank account is -$50.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Amount in the bank account = $150
Cost of the bike = $200
The amount left in the bank account.
= 150 - 200
= -$50
Thus,
The amount left in the bank account is -$50.
Learn more about expressions here:
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