Answer:
Step-by-step explanation:
C. 878 and D. 1 are the only whole numbers. The rest are either mixed numbers or fractions.
Derive the equation of the parabola with a focus at (0, −4) and a directrix of y = 4. f(x) = −16x2 f(x) = 16x2 f(x) = − x2 f(x) = x2
Answer:
[tex]f(x)=-\frac{1}{16} x^2[/tex]
Step-by-step explanation:
We are to derive the equation of the parabola with a focus at [tex](0, -4)[/tex] and a directrix of y = 4.
We know that a parabola is the locus of all the points as long as the distance from the fixed point on the parabola to the fixed line directrix is kept same.
This parabola is facing downwards. So assuming any point on the parabola to be [tex](x,y)[/tex].
Distance from focus [tex](0,-4)[/tex] to [tex](x,y)[/tex] = [tex]\sqrt{(x-0)^{2} +(y+4) ^{2}}=\sqrt{x^{2}+ (y+4)^{2}}[/tex]
Distance from [tex](x,y)[/tex] to directrix [tex](y=4)[/tex] = [tex]\left | y-4 \right |[/tex]
Equating these distances as they are equal:
[tex]\sqrt{x^{2}+ (y+4)^{2}}=\left | y-4 \right |[/tex]
[tex]{x^{2}+ (y+4)^{2}=(y-4)^{2}[/tex]
[tex]x^2+y^2+8 y +16 = y^2 - 8 y+16[/tex]
[tex]x^2 = -8 y - 8 y= -16 y[/tex]
[tex]x^2= - 16 y[/tex]
So the equation of the parabola is [tex]f(x)=-\frac{1}{16} x^2[/tex].
Answer:
The equation of the parabola is y = -1/16 x²
Step-by-step explanation:
* Lets revise some facts about the parabola
- Standard form equation for a parabola of vertex at (0 , 0)
- If the equation is in the form x² = 4py, then
- The axis of symmetry is the y-axis, x = 0
- 4p equal to the coefficient of y in the given equation to
solve for p
- If p > 0, the parabola opens up.
- If p < 0, the parabola opens down.
- Use p to find the coordinates of the focus, (0 , p)
- Use p to find equation of the directrix , y = - p
* Lets solve the problem
∵ The focus at (0 , -4)
∵ The coordinates of the focus are (0 , p)
∴ p = -4
∵ The directrix is y = 4
∵ The equation of the directrix , y = - p
∴ -p = 4 ⇒ p = -4
∵ the equation is in the form x² = 4py
∵ p = -4
∴ x² = 4(-4)y
∴ x² = -16y ⇒ divide both sides by -16
∴ y = -1/16 x²
* The equation of the parabola is y = -1/16 x²
convert 9.25% to fraction form
Answer:
[tex]\frac{37}{400}[/tex]
Step-by-step explanation:
9.25% as a fraction would be [tex]\frac{9.25}{100}[/tex], since a percentage is always out of 100.
Multiply the fraction by 100 to convert the decimal into fraction form
[tex]\frac{9.25}{100} \rightarrow\frac{925}{10000}[/tex]
Reduce to the simplest terms
[tex]925\div25=37\\\\ 10000\div25=400\\\\ \frac{37}{400}[/tex]
Simplify the expression –3(x + 3)2 – 3 + 3x. What is the simplified expression in standard form?
–3x2 – 18x – 27
–3x2 – 15x – 30
–3x2 + 3x + 6
–3x2 + 3x – 30
Answer:
[tex]-3x^2-15x-30[/tex]
Step-by-step explanation:
The given expression is [tex]-3(x+3)^2-3+3x[/tex].
We expand to obtain:
[tex]-3(x^2+6x+9)-3+3x[/tex].
We apply the distributive property to get:
[tex]-3x^2-18x-27-3+3x[/tex].
Group and combine the like terms;
[tex]-3x^2-18x+3x-27-3[/tex].
[tex]-3x^2-15x-30[/tex].
This polynomial expression is in standard form because it is descending powers of x.
The simplification of the algebraic expression in standard form is -3x² - 15x - 30
What is an algebraic expression?An algebraic expression is the expression of mathematical variables with their coefficients(numbers), integers, and arithmetic operations. The simplification of algebraic expression usually follows a pattern such as;
opening the bracketstaking like terms and solving the like terms separately.From the given algebraic expression, we have:
= -3(x + 3)² - 3 + 3x
Let's expand the above terms in the bracket, we have:
= -3(x² +6x + 9) - 3 + 3x
= -3x² - 1x - 27 - 3 + 3x
By rearrangement, we have:
= -3x² - 18x + 3x - 27 - 3
= -3x² - 15x - 30
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In an '80% off' sale, an oven was £112. Work out the original price.
Answer:520
Step-by-step explanation:
Suppose the original prize is=x
If the discount is of 80%,the selling prize is of 20%
20% of x=112
20x/100=112
X=520
Its the original prize...
Answer:
£560
Step-by-step explanation:
80% off means that the sale price is 20% of the original price.
The original price is represented by 100%
Divide the sale price by 20 to find 1% then multiply by 100 to obtain the original price
original price = [tex]\frac{112}{20}[/tex] × 100 = £560
How do you solve this?
Answer:
x =[tex]\frac{1}{8}[/tex]
Step-by-step explanation:
[tex]\frac{3}{8}-x=[tex]\frac{1}{4}[/tex]
⇒ Minus [tex]\frac{3}{8}[/tex] from both sides
- x =[tex]-\frac{1}{8}[/tex]
⇒ Multiply both sides by -1 to get rid of negative
x =[tex]\frac{1}{8}[/tex]
Answer:
x = 1/8.
Step-by-step explanation:
3/8 - x = 1/4
Subtract 3/8 from both sides:
- x = 1/4 - 3/8
-x = 2/8 - 3/8
-x = -1/8
Divide both sides by -1:
x = 1/8.
C is the center of the circle. Find the length of QPR
Answer:
30
Step-by-step explanation:
The length from one point on the edge of a circle to the middle will always be the same otherwise it isn't a circle. If QC is the same as CR than 15 and 15 would get you 30.
Answer:
70.686
Step-by-step explanation:
In order to know the length of QPR, we have to notice that QR=1/4 of the perimeter of the circle (circumference), then QPR= 3/4 of the perimeter of the circle.
Remember:
Circumference of a circle= 2[tex]\pi[/tex]*radius
Where:
[tex]\pi[/tex]= 3.1416 (its a constant value)
radius=15
Circumference of a circle=2*3.1416*15=94.248
Then:
QPR= 3/4 of the circumference of the circle
QPR= 3/4*94.248
QPR= 70.686
While driving from his house to the beach, Cameron passed a sign the read “beach 21 miles.” If the distance from Cameron’s house to the beach is 46 miles, how many miles had Cameron already traveled?
Answer:
Step-by-step explanation:
46-21=25
Answer: 25 miles
Step-by-step explanation:
Given : The distance is remaining to travel to reach the beach from the sign = 21 miles
The distance between the beach and his house = 46 miles
Now, the distance Cameron traveled already is given by :-
[tex]\text{Total distance-Remaining distance}\\\\=46-21=25\text{ miles}[/tex]
Hence, Cameron already traveled 25 miles.
What value of x is in the solution set of 3(x-4)>5x+2?
3(x - 4) > 5x + 2
First you must distribute the 3 to the numbers inside the parentheses
(3 * x) + (3 * (-4)) > 5x + 2
3x + (-12) > 5x + 2
3x - 12 > 5x + 2
Now you must combine like terms
3x goes with 5x
^^^To do this subtract 3x to both sides of the equation
(3x - 3x) - 12 > (5x - 3x) + 2
0 - 12 > 2x + 2
-12 > 2x + 2
-12 goes with 2
^^^To do this subtract 2 to both sides
-12 - 2 > 2x + (2 - 2)
-14 > 2x + 0
-14 > 2x
Isolate x by dividing 2 to both sides
-14/2 > 2x/2
-7 > x
Hope this helped!
~Just a girl in love with Shawn Mendes
The rate (gallons per day) at which a pond loses water due to evaporation from one day after observation has started is give by w(t)=1/T2 (squared).
where t is the number of days after the first day. suppose we want to find out what the trend is for the total change in gallons in the pond. (Fill in the following table)
t is the number of days after the first day, and w is the number of gallons.
T: 1 2 10 50 100 200 500 1000
w(t): ? ? ? ? ? ? ? ?
Answer: see table below
Step-by-step explanation:
[tex]\left\begin{array}{c|l}T&\qquad w(t)\\1&\dfrac{1}{1^2}=1\implies 1.00\\\\2&\dfrac{1}{2^2}=\dfrac{1}{4}\implies 0.25\\\\10&\dfrac{1}{10^2}=\dfrac{1}{100}\implies 0.01\\\\50&\dfrac{1}{50^2}=\dfrac{1}{2500}\implies 0.0004\\\\100&\dfrac{1}{100^2}=\dfrac{1}{10000}\implies 0.0001\\\\200&\dfrac{1}{200^2}=\dfrac{1}{40000}\implies 0.000025\\\\500&\dfrac{1}{500^2}=\dfrac{1}{250000}\implies 0.000004\\\\1000&\dfrac{1}{1000^2}=\dfrac{1}{100000}\implies 0.000001\\\end{array}\right[/tex]
It is about a 425-mile drive from San Jose to
Los Angeles down CA-1, and about a 320-
mile drive from San Jose to Santa Barbara
along the same route.
If you stop in Santa Barbara, you can take a
walk along the water front, or visit the Santa
Barbara Zoo.
How far is the drive from
Santa Barbara to Los Angeles?
Answer:
105
Step-by-step explanation:
425 - 320 = 105 miles
Final answer:
The drive from Santa Barbara to Los Angeles is 105 miles, which is the difference between San Jose to Los Angeles (425 miles) and San Jose to Santa Barbara (320 miles).
Explanation:
The question asks how far it is to drive from Santa Barbara to Los Angeles. To determine this distance, we utilize the total distance from San Jose to Los Angeles and subtract the distance from San Jose to Santa Barbara. Starting with the overall distance of San Jose to Los Angeles, which is 425 miles, we deduct the San Jose to Santa Barbara distance of 320 miles. This calculation will provide us with the distance from Santa Barbara to Los Angeles.
By subtracting 320 miles from 425 miles, we find that the distance from Santa Barbara to Los Angeles is 105 miles.
Charles is on a 8 1/2 mile bike ride. He stops for a rest after he’s gone 5 2/5 miles. How much farther does he still have to go?
Answer:
31/10 or 3 1/10 more miles.
Step-by-step explanation:
=
(17 × 5) - (27 × 2)
2 × 5
Answer:
[tex]3\frac{1}{10}[/tex] miles
Step-by-step explanation:
The total distance of Charles bike ride is = [tex]8\frac{1}{2}[/tex] miles
He has covered the distance = [tex]5\frac{2}{5}[/tex] miles
We will subtract his covered distance from total distance.
He still have to go = [tex]8\frac{1}{2}[/tex] - [tex]5\frac{2}{5}[/tex]
= [tex]\frac{17}{2}[/tex] - [tex]\frac{27}{5}[/tex]
= [tex]\frac{85-54}{10}[/tex]
= [tex]\frac{31}{10}[/tex]
= [tex]3\frac{1}{10}[/tex] miles
He still have to go [tex]3\frac{1}{10}[/tex] miles
What is the approximate probability of choosing an orange marble and a green marble
Answer:
Step-by-step explanation:
It depends on how many green and orange marbles their are...If their is 30 marbles in a bag and 10 of them are orange and green it would be 10/30 divide both of them by 10 and you would get 1/3 But that is just an example.
Hope my answer has helped you in any way!
Answer:0.04444
Step-by-step explanation:
Number of red balls = 5
Number of orange balls = 2
Number of yellow balls = 1
Number of green balls = 2
Therefore total number of balls = 10.
Probability of getting a ball =
P(choosing orange ball) =
After picking an orange ball, we are left with 9 balls
P ( choosing a green ball) =
P(choosing an orange marble and a green marble) =
0.04444 is the approximate probability of choosing an orange marble and a green marble.
On Monday Sarah had homework in 7/10 of her classes Tuesday 3/5 Wednesday 9/11 Thursday 1/2 which day she had the most
wednesday (9/11) has the most homework for Sarah. because it is equivalent to 90/110 which is greater than every other fraction answer given.
--mark brainliest please! thank you and i hope this helps
Sarah had the most homework on Wednesday.
What is least common multiple?The acronym LCM stands for the least common multiple or factor of any two or more specified integers. The least common multiple for the numbers 16 and 20 is 80, hence the LCM of those two numbers will be, for instance, 2 x 2 x 2 x 2 x 5 = 80.
Given
Sarah had the most homework on Wednesday. Least common multiple for 10, 5, 11 and 2 is 110.
Monday: 7/10 = (7*11)/(10*11) = 77/110
Tuesday: 3/5 = (3*22)/(5*22) = 66/110
Wednesday: 9/11 = (9*10)/(11*10) = 90/110
Thursday: 1/2 = (1*55)/(2*55) = 55/110
Since 90 > 77 > 66 > 55 it is clear that Sarah had the most homework on Wednesday.
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Somebody help this is algebra
Answer:
2 is your answer
Step-by-step explanation:
If h(x)= 5 then 5= 2x +1
so 5 = 2x + 1
-1 -1 on both sides
then 2x = 4
2 2 divide by 2
which x = 2
Hope my answer has helped you!
What equation has the steepest graph ?
Answer:
B
Step-by-step explanation:
for a linear equation y = mx + b,
the steepness of the graph is denoted by the slope, m
The larger the absolute number of the slope, the steeper it is
in this case it is quite clear that B has the largest absolute number for m.
i.e abs (-10) = 10
In a basketball match a team average 67 points over 10 games. After the next game the average is 68 points.
How many points did they score in the game?
Answer:
78 points
Step-by-step explanation:
Let x = sum of the 10 scores
x/10 = 67
x /10 *10 = 67* 10 = 670
The sum of the 10 scores is 670
Now we play 1 more game and score g
We want to find the average for the 11 games
The average is 68
(670 + g)/11 = 68
Multiply each side by 11
(670+g)/11 *11 = 68*11
670+g =748
Subtract 670 from each side
670+g-670 = 748-670
g =78
write an expression to find the area and perimeter of the rectangle:
L=
[tex] {2x}^{2} - x + 3[/tex]
W=
[tex] {4x}^{2} + 2x - 1[/tex]
Answer:
Step-by-step explanation:
the area is :A= L×W
A= (2x²-x+3)(4x²+2x-1).....calculate
the perimeter is : P= 2(L+W)
P= 2(2x²-x+3)+(4x²+2x-1))....calculate
10. One number is 5 times another number, and
their sum is -60. What is the lesser of the two
numbers?
F. -5
G. -10
H. -12
1 -48
Answer:
G. -10
Step-by-step explanation:
Let one number = x
Let the second one = y
Equations
y = 5x
x + y = -60
Solution.
Put 5x in for y in the second equation.
x + 5x = -60 Combine like terms on the left
6x = -60 Divide by 6
6x/6 = -60/6 Do the division
x = -10
So one of the numbers is minus 10
Determine the best method to solve the system of equations. Then solve the system.
7x-2y=8
5x+2y=4
Answer:
x=1 y = -1/2
(1,-1/2)
Step-by-step explanation:
7x-2y=8
5x+2y=4
I would use elimination since we have 2y in one equation and -2y in the other
7x-2y=8
5x+2y=4
--------------------
12x = 12
Divide each side by 12
12x/12 = 12/12
x =1
The substitute back into equation 2
5(1) +2y = 4
5 +2y = 4
Subtract 5
5-5+2y = 4-5
2y = -1
Divide by 2
2y/2 = -1/2
y = -1/2
Answer:
The best method is the elimination method. The solution is (1, -1/2).
Step-by-step explanation:
7x - 2y = 8
5x + 2y = 4
12x = 12
x = 1
7(1) - 2y = 8
7 - 2y = 8
-2y = 1
y = -1/2
Make sure to write the answer in the form of an ordered pair.
Note: Alternative methods are graphing and the substitution method.
if the diameter of a circle is 7/8 of an inch what is its radius
Answer:
r = 7/16 inch
Step-by-step explanation:
The radius is 1/2 of the diameter
r = 1/2 d
r =1/2 (7/8)
r = 7/16 inch
Serena counts her calories over several days. What is her total caloric intake given these values: 1,405; 1,219; 1,119; 1,353.
For this case we add the quantities of calories consumed per day, that is:
[tex]1,405 + 1,219 + 1,119 + 1,353 = 5,096[/tex]
So Serena consumed 5,096 calories in 4 days. If we want to know the average calorie content per day, we divide the amount obtained by 4:
[tex]\frac {5,096} {4} = 1,274[/tex]
ANswer:
5,096 total calories
Consumes on average 1,274 calories per day.
what is 123,456,789 times 2 divided by 4
Answer:
61728394.5
Step-by-step explanation:
Using order of operations, you can either perform the multiplication first or the division first.
123,456,789 × 2 / 4 =
123,456,789 / 2 =
61728394.5
Answer:
61,728,394.5
Step-by-step explanation:
Remember to follow PEMDAS & left->right rule.
In this case, they are multiply & divide, so you can solve through left - > right rule:
123,456,789 x 2 = 246,913,578
246,913,578/4 = 61,728,394.5
61,728,394.5 is your answer.
~
7(y + 2) – (4y – 10) = 44 – 2y + 5
Answer:
y = 5
Step-by-step explanation:
7(y + 2) – (4y – 10) = 44 – 2y + 5
(7y+14) - (4y - 10) = 49 -2y
3y +24 = 49 -2y
5y +24 = 49
5y = 25
y = 5
To solve the equation 7(y + 2) – (4y – 10) = 44 – 2y + 5, distribute and combine like terms to simplify both sides of the equation. Isolate the variable y on one side of the equation by performing inverse operations. The solution to the equation is y = 3.
Explanation:To solve the equation 7(y + 2) – (4y – 10) = 44 – 2y + 5, we need to simplify both sides by distributing and combining like terms. Starting with the left side, we distribute 7 to both y and 2 to get 7y + 14. Then, distribute -1 to both 4y and -10 to get -4y + 10. Combining like terms, we have 7y + 14 - 4y + 10 = 44 - 2y + 5. Simplifying further gives us 3y + 24 = 39 - 2y. To isolate the variable y, we need to get all the y terms on one side. Adding 2y to both sides gives us 5y + 24 = 39. Finally, subtracting 24 from both sides yields 5y = 15. Dividing both sides by 5 gives us y = 3. Therefore, the solution to the equation is y = 3.
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Which of the points are solutions to the inequality?
Check all that apply.
y > 2x - 4
(-2,-5)
(0,4)
(1,1)
(3,5)
(5,5)
Answer: First option, Second option, Third option and Fourth option.
Step-by-step explanation:
You need to substitute each point into the inequality:
1) Point (-2,-5):
[tex]y > 2x - 4\\\\-5 > 2(-2) - 4\\\\-5>-8\ (This\ is\ true)[/tex]
2) Point (0,4):
[tex]y > 2x - 4\\\\4 > 2(0) - 4\\\\4>-4\ (This\ is\ true)[/tex]
3) Point (1,1):
[tex]y > 2x - 4\\\\1 > 2(1) - 4\\\\1>-2\ (This\ is\ true)[/tex]
4) Point (3,5):
[tex]y > 2x - 4\\\\5 > 2(3) - 4\\\\5>2\ (This\ is\ true)[/tex]
5) Point (5,5):
[tex]y > 2x - 4\\\\5 > 2(5) - 4\\\\5>6\ (This\ is\ not\ true)[/tex]
Answer:1st 3rd and 4th
Step-by-step explanation:
Hope I helped
Ying Zyiyu covered the first 300 miles of a trip going at 60 mph and the last hundred going at 40 mph. What was his average speed for the entire trip?
Answer:
53 1/3 mph
Step-by-step explanation:
Speed equals distance over time.
She covered 300 miles in 60mph, which took 5 hours.
(300/60=5 )
She also covered 100 miles in 40mph, which means she took 2.5 hours.
(100/40=2.5)
So the total distance is 400miles and the total time is 7.5 hours.
s=d/t substitute values which gives you 400/7.5 which equals 53 1/3 mph
Which table of ordered pairs represents a proportional relationship?
Answer:
The correct option is 3.
Step-by-step explanation:
We need to find a table of ordered pairs that represents a proportional relationship.
Proportional relationship: It means y-values are proportional to x-values.
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
where, k is constant of proportionality.
For table 1,
[tex]\frac{y_1}{x_1}=\frac{8}{4}=\frac{2}{1}[/tex]
[tex]\frac{y_2}{x_2}=\frac{11}{7}[/tex]
[tex]\frac{2}{1}\neq \frac{11}{7}[/tex]
Table 1 does not represents a proportional relationship.
Similarly,
For table 2,
[tex]\frac{25}{5}\neq \frac{49}{7}[/tex]
Table 2 does not represents a proportional relationship.
For table 3,
[tex]\frac{3}{6}=\frac{5}{10}=\frac{7}{14}=\frac{1}{2}[/tex]
Table 3 represents a proportional relationship.
For table 4,
[tex]\frac{6}{3}\neq \frac{11}{8}[/tex]
Table 4 does not represents a proportional relationship.
Only table 3 represents a proportional relationship. Therefore the correct option is 3.
Solve the system of equations.
3x+3y+6z=6
3x+2y+4z=5
7x+3y+3z=7
Answer:
answer : c ( x = 1 , y = -1 , z = 1)
Step-by-step explanation:
put x = 1 , y = -1 , z = 1
in this equations :
3(1)+3(-1)+6(1)=6 ........ 6=6 right
3(1)+2(-1)+4(1)=5 .....5=5 right
7(1)+3(-1)+3(1)=7......7=7 right
12b−17b−b how solve this?
Answer:
-6b
Step-by-step explanation:
In this question, its simple math,how?
All the terms are alike, so just apply subtraction method;
[tex]=12b-17b-b\\\\\\\\=12b-18b\\\\=-6b[/tex]
For this case we have the following expression:
[tex]12b-17b-b=[/tex]
We have that by definition of Law of the Signs of the Sum that: Equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the greater is placed. So:
[tex]-5b-b =\\-6b[/tex]
Answer:
-6b
A hamburger bun merchant can ship 8 large boxes or 10 small boxes of hamburger buns into a carton for shipping. In one shipment, he sent a total of 96 boxes of hamburger buns. If there are more large boxes than small boxes, how many cartoons did he ship?
56 large boxes and 40 small boxes.
Step-by-step explanation:To solve this problem, we need to use the concept of multiples. By definition, a multiple of a number is that number multiplied by an integer. For instance, 3, 6, 9, 12 are multiples of 3. So let's do a chart and list the multiples of large and small boxes:
[tex]\begin{array}{cccccccccc}Number\,of\,boxes & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\\Large & 8 & 16 & 24 & 32 & 40 & 48 & 56 & 64 & 72\\Small & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 & 90\end{array}[/tex]
From this, our goal is to select the number of small and large boxes such that the sum is 96 boxes of hamburger burns and the number of large boxes is greater than the number of small boxes. From the table, the correct solution is:
56 large boxes and 40 small boxes, and this meets our requirement, because 56 + 40 = 96 and 56 > 40
The surface area (SA) of a cube with a as the length of each of its sides is given by the formula . If the surface area is known, how can you rewrite the formula to find its side?
Answer:
Step-by-step explanation:
1 surface area of the cube is s*s.
There are 6 faces on such a cube.
Area = 6*s^2 Divide by 6
Area/6 = 6s^2 / 6 Do the divsion
Area/6 = s^2
s = sqrt(area/6)