Answer:
Step-by-step explanation:
You have to know some basics of parabolas to get this far in your math class, so hopefully you do, and what I'm about to do and say is not new or surprising to you.
If you plot the center (0, 0) which is your h and k, and then plot the focus, you should know that, since the parabola wraps itself around the focus, this parabola opens to the left. There is a work form and a standard form for a left-opening parabola. The work form will be
[tex]x=-a(y-k)^2+h[/tex] and the standard form will be
[tex]-(y-k)^2=4p(x-h)[/tex]
We will figure out what we need and will fill in both of these forms.
In general, the value of p is a distance; namely, it is the distance from the center to either the focus or the directrix (which is the same for both since the focus and the directrix are the same distance from the center, one on either side of it). From this we can determine that, since the focus is one unit away from the center, p = 1. Now that we know p we can find |a|:
[tex]|a|=\frac{1}{4p}[/tex]
Since p = 1, then [tex]|a|=\frac{1}{4}[/tex]
Now we can write the work form:
[tex]x=-\frac{1}{4}(y-0)^2+0[/tex] which of course simplifies to
[tex]x=-\frac{1}{4}y^2[/tex]
And remember we have the p value for the standard form:
[tex]-(y-0)^2=4(1)(x-0)[/tex] which simplifies a bit to
[tex]-y^2=4x[/tex] and when we solve for x:
[tex]x=-\frac{1}{4}y^2[/tex] which is the exact same as the work form!!! Look at that! : )
A scientist counts 35 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y = 35 • 3x models the number of bacteria after x hours. Estimate when there will be about 550 bacteria in the culture.
Answer: About 5.2 Hours
Step-by-step explanation:
550= 35 x 3x
183.33= 35x
5.2 = x
The slope of a line is 2. The y-intercept of the line is –6. Which statements accurately describe how to graph the function?
Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
Locate the ordered pair (0, –6). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.
Locate the ordered pair (–6, 0). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
Locate the ordered pair (–6, 0). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.
Answer:
Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
Step-by-step explanation:
The answer is the first one because the slope is technically [tex]\frac{2}{1}[/tex]
Up 2 over 1
Since the slope is positive, the graph goes to the right.
(0, -6) is the y intercept because it intersects the y - axis.
Then you draw those two points and connect them.
Answer:
its A OwO
Step-by-step explanation:
State the variable term(s) in the equation 2p + 4 = -5 - P.
Answer:
p=−3
Step-by-step explanation:
Let's solve your equation step-by-step.
2p+4=−5−p
Step 1: Simplify both sides of the equation.
2p+4=−5−p
2p+4=−5+−p
2p+4=−p−5
Step 2: Add p to both sides.
2p+4+p=−p−5+p
3p+4=−5
Step 3: Subtract 4 from both sides.
3p+4−4=−5−4
3p=−9
Step 4: Divide both sides by 3.
3p/3 = −9 /3
p=−3
Answer:
p=−3
please mark me brainliest!
Answer:
p=-3
Step-by-step explanation:
move the 5 to the left to get 2p + 9 = -p. Then move the 2p to the right to get 9 = -3p. Divide both sides with -3 and p = -3
2/xy^2
Give the equivalent numerator if the denominator is x3y2.
a) x²y
b) 2x^2
c) 2x^3y^2
What is the slope of the line through (-4,2)(−4,2)left parenthesis, minus, 4, comma, 2, right parenthesis and (3,-3)(3,−3)left parenthesis, 3, comma, minus, 3, right parenthesis?
Answer:
The slope of the line through the points is -5/7
Step-by-step explanation:
Here, we want to calculate the value of the slope through the lines
Mathematically;
m = y2-y1/(x2-x1)
Where (x1,y1) = (-4,2)
and (x2,y2) = (3,-3)
Substituting these values, we have;
m = (-3-2)/(3-(-4)) = -5/7 = -5/7
The slope of the line through (-4, 2) and (3, -3) is; -5/7
According to the question;
We are required to determine the slope of the line through the points given.The slope, m of the line is given mathematically as;
m = (y2 -y1)/(x2 - x1)Therefore, in this case;
Slope, m = (-3 - 2)/(3 -(-4))Slope, m = -5/7
Read more:
https://brainly.com/question/16949303
If matrix Ais a 6 x 5 matrix, which order of matrix can be multiplied by matrix A?
Answer:
A matrix that is a 5 × (any #)
Step-by-step explanation:
CAN SOMEONE HELP :) IF YOU CAN TYSM!
Answer:
i. x = -0.5 and 1.5; ii. x = 1.5
Step-by-step explanation:
For part i, we can take a look at the x-intercepts of the parabola. When a quadratic equation equals 0, this means that we are taking a look at its roots, or solutions.
The parabola intersects the x-axis at approximately -0.5 and 1.5. We can say this is an estimate to the solutions.
For part ii, the question is asking the x value that makes the function equal 2. We just look at the point where y = 2, which happens to be 1.5. So when x = 1.5, y = 2, which is what we want.
I hope this helps!
Please do 69 and 70 quick please
I just have the answer of the 70.
it is 10560
Answer:
69 is 1/3 and 70 is 10560
Step-by-step explanation:
Find the value of x round to the nearest tenth. Enter the number that belongs in the green box. 20 points!!!! And marking brainlist!
Answer:
80.4 =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opposite/ adjacent
tan 15 = x / 300
Multiply each side by 300
300 tan 15 = x
80.38475773=x
To the nearest tenth
80.4 =x
Answer:
80.4
Step-by-step explanation:
use tan x = opp/adj
tan 15° = x/300 multiply by 300 on both sides
tan 15° * 300 = x
x = 80 .38 ≈80.4
Solve for n.
9n − 7 = 3 + 8n − 2
n =
Answer:
[tex] \boxed{n = 8} [/tex]
Step-by-step explanation:
[tex] = > 9n - 7 = 3 + 8n - 2 \\ \\ = > 9n - 7 = 8n + 3 - 2 \\ \\ = > 9n - 8n = 1 + 7 \\ \\ = > n = 8[/tex]
Answer:
8
Step-by-step explanation:
9n - 7 = 3 + 8n - 2
Combine like factors.
9n - 7 = 8n + 1
Subtract 8n from both sides
n - 7 = 1
Add 7 to both sides.
n = 8
how to solve 56 x 12 using a area model
Answer:
well your answer is 778 but I forgot how to use an area model
Step-by-step explanation:
A group of students was asked, "How many hours did you watch television last week?" Here are their responses.
16, 11, 7, 18, 19, 5
Find the mean number of hours for these students.
If necessary, round your answer to the nearest tenth.
Step-by-step explanation:
Mean = 16 + 11 + 7 + 18 + 19 + 5 / 6
Mean = 76 / 6
Mean = 12.66
m∠ABD is a straight angle m∠CBD=8x+16 m∠ABC=6x−60
Answer:[tex]36^{\circ}[/tex]
Step-by-step explanation:
A straight angle means that the angle has a measure of 180 degrees. Therefore:
[tex]CBD+ABC=180 \\\\(8x+16)+(6x-60)=180 \\\\14x-44=180\\\\14x=224\\\\x=16\\\\6x-60=6(16)-60=96-60=36[/tex]
Hope this helps!
Answer:
m∠ABC = 36 degrees
Step-by-step explanation:
8x + 16 + 6x - 60 = 180 Add both angles to equal 180
14x - 44 = 180
+ 44 + 44 Add 44 to both sides
14x = 224 Divide both sides by 14
x = 16
Plug this into the equation for angle ABC
6(16) - 60 Multiply
96 - 60 Subtract
m∠ABC = 36
write the equation for a paraloba with a focus at (7,2) and a directrix at y=-2
Answer:
y = (x-7)^2 / 8
Step-by-step explanation:
The focus to vertex distance is (2-(-2))/2 = 2 and the parabola open's upwards.
Thus: a = 1/(4·2) = 8, vertex at (7,0).
This means that:
y = (x-7)2/8
The function fox) = x + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new
function?
x (x - 11)2 + 58
(r+ 22)2 – 121
(x + 7)2 - 47
(x-15)2 + 94
Intro
7
Done
Answer:
Step-by-stfffffffffffffffffffffffffffffffffffffffffffffffffffffep explanation:
POSSIBLE POINTS 100
A bank pays 3% annual simple interest on CDs (certificates of deposit) of $25,000. The Branson family
invests in 3 of the $25,000 CDs. How much interest does the family make in one year?
O A $22.50
OB $22,500.00
OC $2,250.00
OD $225.00
Answer:
Total interest in 1 year = $2,250
Step-by-step explanation:
Given:
Rate of simple interest = 3% = 0.03
Amount of investment = $25,000
Number of investment = 3
Find:
Total interest in 1 year .
Computation:
Simple interest = Amount of investment × Rate of simple interest
Simple interest = $25,000 × 0.03
Simple interest = $750
Total interest in 1 year = Simple interest × Number of investment
Total interest in 1 year = $750 × 3
Total interest in 1 year = $2,250
39) Natural numbers that have 1 as the common number between them are called?
Answer:
I think they're called The Prime numbers.
Tell me if it's correct
Answer:
odd numbers
1,3,5,7,9,11.......
Step-by-step explanation:
I've ordered this shed. It is 2 meters wide, 3.25 meters long and 2 meters tall to the roof line. From the roof line to the peak is 0.8 meters high. I would like a 2nd floor or loft to increase the storage space. Please calculate the total amount of storage.
Answer:
18.2 cubic meters.
Step-by-step explanation:
From the measurements they give us, we assume that the shed has the shape of a rectangular prism, however, to calculate the amount of storage, we must calculate the volume.
The volume would be:
V = height * width * length
According to the statement height = 2, width = 2 and length = 3.25
V = 2 * 2 * 3.25
V = 13
That is, the volume of the shed is 13 cubic meters, but then they mention that the roof line to the peak is 0.8 meters high, which means that the volume can increase, the new volume would be changing the height = 2 + 0.8 = 2.8, the other values remain the same:
V = 2.8 * 2 * 3.25
V = 18.2
That is to say that when adding that part, the volume that is to say total amount of storage is 18.2 cubic meters.
Which relation is a function of x?
Answer:
it is the last one. because it passes the verticle line test, and the first one repeats the same number two times.
Randy makes two slices through a three-dimensional object. One plane is parallel to the base; the other plane is perpendicular to the base. The two cross-sections are the same size and shape. What three dimensional shapes Might randy have cut
Answer:
cubeStep-by-step explanation:
I would have said circle, but it has no base, so it has to be a hedron
Randy might have probably cut a cube, since only it has congruent perpendicular/parallel to the base cross sections
Please help me. I already have the systems of linear equations which is y=87x+2129
Y=171x
I had solved using substitution method and got y=4334.85 and x=25.35
I attached the question that I need help with.
Step-by-step explanation:
that's it hope u understood
Answer:
Step-by-step explanation:
Your answer for x = 25.35 is correct.
Since the night must be an integer, you need to take 26 as your final answer. b) for y = 1500, you solve for x to consider which one is better.
for plan A, y = 87 x + 2129, you have to pay $2129 before starting the trip, hence $1500 is NOT enough to pay.
for plan B, y = 171x and y = 1500, hence x = 8.77. So, with $1500 you can travel for 8 nights.
What is the common difference of 4, 10, 16, 20
Answer:
6 and 4
Step-by-step explanation:
4, 10, 16, 20
common difference:
10-4= 16-10= 6, 20-16 = 4
Since common difference is not equal this is not AP
PLEASE HELP!!!!! Chloe stops for lunch in a town that has no meal tax. She has $20 and tips 15%. Select all the prices of meals she could buy. $18.50 $16.25 $15.75 $17.45 $15.95
Answer:
$16.25 $15.95 $15.75
Step-by-step explanation:
because a 15% tip is $3.00
Jess found that 10% of the students surveyed like to clean their rooms. Which
does not represent 10%?
The probability of a chance event is 0.5, it is
to happen
when compared to a chance event with a probability of 1.
Select one:
Answer:
75%
Step-by-step explanation: i know the answer
Use the fraction bar interactive tool to find the lowest common denominator before subtracting 2 3 from 5 6 . What is the lowest common denominator? Rewrite the difference as a sum of the fractions using the lowest common denominator. What is the answer?
Answer:
What is the lowest common denominator?
✔ 6
Rewrite the difference as a sum of the fractions using the lowest common denominator.
✔ 5/6 + (–4/6)
What is the answer?
✔ 1/6
Step-by-step explanation:
Fractions can be combined by taking their LCMs
The lowest common denominator is 6The new expression is [tex]\mathbf{-\frac{4}{6} + \frac{5}{6}}[/tex]The numbers are given as:
[tex]\mathbf{\frac{2}{3}\ and\ \frac{5}{6}}[/tex]
The denominators are 3 and 6.
Factor both numbers;
[tex]\mathbf{3 = 1\times 3}[/tex]
[tex]\mathbf{6 = 1 \times 2 \times 3}[/tex]
So, the LCM is:
[tex]\mathbf{LCM = 1 \times 2 \times 3}[/tex]
[tex]\mathbf{LCM = 6}[/tex]
The lowest common denominator is 6
The expression is represented as:
[tex]\mathbf{ - \frac{2}{3}\ + \ \frac{5}{6}}[/tex]
Rewrite as:
[tex]\mathbf{ - \frac{2}{3}\ + \ \frac{5}{6} = -\frac{4}{6} + \frac{5}{6}}[/tex]
Hence, the new expression is [tex]\mathbf{-\frac{4}{6} + \frac{5}{6}}[/tex]
Read more about fractions at:
https://brainly.com/question/6201432
The parallelograms with opposite sides equal and diagonals
equal are _________ and _____________
Answer:
It is also a rhombus and a square!
Step-by-step explanation:
Henry invested $59,000 in an account paying an interest rate of 2% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 20 years?
9514 1404 393
Answer:
$87,929.98
Step-by-step explanation:
The future value formula can be used for this:
FV = P(1 +r/n)^(nt)
where principal P is invested at annual rate r for t years, compounded n times per year. With your numbers, we have ...
FV = $59,000(1 +.02/4)^(4·20) ≈ $87,929.98
Henry will have $87,929.98 after 20 years.
Answer:
A≈87929.98
Step-by-step explanation:
Sofi is competing in a long jump competition. His first jump is 5.25 m. Your best jump is 8% more than this. However, his best jump is 10% lower than the winning jump. Calculate the length of the winning jump.
Answer: 6.3 m
Step-by-step explanation:
"8% more" = 1.08 (which is 1+0.08). "10% less" = 0.90 (which is 1-0.10).
first = 5.25
her_best = 1.08*first
her_best = 0.90*winning
Substitute to determine the winning jump's length.
winning = 1.08*5.25/0.90 = 6.3
So, the winning jump was 6.3 meters.
A number is selected from the set {1, 2, 3, 5, 15, 21, 29, 38, 500}. If equal elemental probabilities are assigned, what is the probability that the number chosen is either less than 29 or odd? 6/9 7/9 8/9
Answer:
The required probability is [tex]\frac{7}{9}[/tex].
Step-by-step explanation:
Set given is:
S = {1, 2, 3, 5, 15, 21, 29, 38, 500}
Total number of elements in set, [tex]n(S)[/tex] = 9
Let A be the event that the number is less than 29 ({1, 2, 3, 5, 15, 21}).
Number of items in the event A, [tex]n(A)[/tex] = 6
Probability of event A,
[tex]P(A) = \dfrac{n(A)}{n(S)}}=\dfrac{6}{9} \Rightarrow \dfrac{2}{3}[/tex]
Formula for probability of any event E:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Let B be the event that the number is odd (either of {1,3,5,15,21,29}).
Number of items in the event B, [tex]n(B)[/tex] = 6
Probability of event B,
[tex]P(B) = \dfrac{n(B)}{n(S)}}=\dfrac{6}{9} \Rightarrow \dfrac{2}{3}[/tex]
The event A and B have a few elements in common, i.e. numbers less than 29 which are odd as well.
The common elements are represented as:
[tex]A \cap B = \{1, 3, 5, 15, 21\}[/tex]
[tex]n(A\cap B) = 5[/tex]
[tex]P(A \cap B ) = \dfrac{n(A \cap B)}{n(s)}\\\Rightarrow P(A \cap B) = \dfrac{5}{9}[/tex]
To find probability of selecting a number which is either less than 29 (event A) or odd (event B),
We have to find [tex]P(A\ or \ B)[/tex] which is represented as [tex]P(A \cup B)[/tex] and the formula is:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)\\\Rightarrow \dfrac{2}{3} + \dfrac{2}{3} - \dfrac{5}{9}\\\Rightarrow \dfrac{12-5}{9}\\\Rightarrow \dfrac{7}{9}[/tex]
The required probability is [tex]\frac{7}{9}[/tex].
