What are the X intercepts of a parabola with vertex (6,27) and y intercept of (0,-81)?

Answers

Answer 1
so hmm let's see if we can get the parabola's equation

if we assume a vertical parabola, "y" in x-terms.... then

[tex]\bf \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\[/tex]

[tex]\bf \textit{we know that } \begin{cases} h=6\\ k=27 \end{cases}\implies y=a(x-6)^2+27 \\\\\\ \textit{we also know the y-intercept } \begin{cases} x=-81\\ y=0 \end{cases}\implies 0=a(-81-6)^2+27 \\\\\\ -27=a(-87)^2\implies \cfrac{-27}{(-87)^2}=a\implies -\cfrac{3}{841}=a\\\\ -------------------------------\\\\ \boxed{y=-\cfrac{3}{841}(x-6)^2+27}[/tex]

now, to get the x-intercepts, we simply set y = 0

[tex]\bf 0=-\cfrac{3}{841}(x-6)^2+27\implies -27=-\cfrac{3}{841}(x-6)^2 \\\\\\ \cfrac{-27\cdot 841}{-3}=(x-6)^2\implies 7569=(x-6)^2\implies \pm\sqrt{7569}=x-6 \\\\\\ \pm 87=x-6\implies \pm 87+6=x\implies x= \begin{cases} 93\\ -81 \end{cases}[/tex]

and... since the y = 0, then (93, 0) and (-81, 0)

Related Questions

14 1/6-10 11/24= what fraction

Answers

The answer is 3 17/24.
14 1/6-10 11/24
= 14 4/24 - 10 11/24
= 13 28/24 - 10 11/24
= 3 17/24

hope that helps

Write and solve an equation to answer the question.

What number a is 24% of 25?

Answers

a = .42 x 25 = 6

the number 6 is 24% 0f 25.

Just write 24% as a decimal .24 or 0.24


Final answer:

To find the number that is 24% of 25, you multiply 0.24 by 25, which equals 6.

Explanation:

To find what number a is 24% of 25, we can set up an equation using the concept that a percent is a way of expressing a fractional amount of something.

We know that 24% means 24 out of 100, which can be written as the fraction 24/100 or 0.24 in decimal form.

To translate the question into an equation, we write:

a = 0.24 × 25

Next, we calculate the value of a by multiplying 0.24 (the decimal form of 24%) by 25. This gives us:

a = 6

Therefore, the number a, i.e., 24% of 25 is 6.

Donna rented a movie. She started the movie at 10:36 pm, and it was 2 hours 46. minutes long. When did the movie end?

Answers

The answer should be 1:22 am because 2 hours from 10:36 pm is 12:36 am. After adding 46 minutes, the time would be 1:22 am.
The movie ended at 1:22

BE is the midsegment of triangle ACD. The value of x is:


5.
20.
35.
40.

Answers

The midsegment theorem says that the midsegment is half the third side and parallel as well. 20*2 is 40 so x = 35

Explain how to use the standard normal table to find the probability associated with the shaded area under the curve.

Answers

Answer:

The standard normal table gives areas under the curve to the left of z-scores.

Find the probability in the standard normal table that a value is to the left of 1.9.

Find the probability in the standard normal table that a value is to the left of 0.4.

Subtract the probability of a value being to the left of 0.4 from the probability of a value being to the left of 1.9.

Step-by-step explanation:

edge2020

In order to find the probability associated with the shaded area under the curve using the standard normal table, you should subtract the probability of a value left of 0.4 from the probability of a value left of 1.9.

How do you find the probability associated with the shaded area?

We are trying to find the probability of the area between 1.9 and 0.4 so the first thing to do is to find the probability that a value is to the left of 1.9 from the Standard normal table.

After this is done, you then find the probability that the value is left of 0.4.

To find the probability of the middle area, subtract the value to the left of 0.4 from that of the value left of 1.9

Find out more on the standard normal table at https://brainly.com/question/7001627.

3y^2-16y+16

could someone help me walk through this?

Answers

Slip and slide method
3y^2-16y+16
Multiply a by c value and replace as shown below
y^2-16y+48
Factor normally
(y-12)(y-4)
Divide both numbers by the previous a value
(y-12/3)(y-4/3)
(y-4)(y-4/3)
Because -4/3 does not become a whole number change the three to become the coefficient of y
(y-4)(3y-4)
Check by foiling
Final answer: (3y-4)(y-4)

..Simplify √x^100y^16

Answers

√(x^100y^16)  look for perfect squares to move out from under the radical

√(x^50*x^50*y^8*y^8)

x^50*y^8  (third one down :P)

Which of the following is the proper notation used to express a point in the three-dimensional coordinate plane?
A. (x)
B. (x, y, z)
C. (x, y)
D. (w, x, y, z)

Answers

The answer is : B. (x, y, z)


Hope this helps ✌️

Answer:  Option 'B' is correct.

Step-by-step explanation:

Since we have given that

We need to express a point in the three-dimensional coordinate plane.

As we know that In 3- dimensional plane, there are 3 axes;

One for x-axis (say  length)

One for y- axis (say breadth)

One for z-axis (say height)

So, the proper notation would be (x,y,z).

Hence, Option 'B' is correct.

If CD is the perpendicular bisector of AB, then the value of x is:

10.
5.
22.
11.

Answers

In ΔCAD and ΔCBD,

CD = CD [ Common side ]

AD = BD [ CD is the perpendicular "bisector" of AB ]

∠CDA = ∠CDB [ CD is the "perpendicular" bisector of AB ]

Thus, ΔCAD and ΔCBD are congruent triangles. [ SAS congruency ]

If these triangles are congruent, then AC = BC.

2x = 3x -10

x = 10.
value of x=10 G

brainliest + thanks if were safe:)))))

In triangle FE = 5 and angle D=43 . Find DE to the nearest tenth

Answers

sin(43) sin(47) ------ = ------- 5 DE

Answer:

5.4? I don't really know I'm just going off other answers but clearing it up,,,hope it help :')

Step-by-step explanation:

An acorn falls from the branch of a tree to the ground 25 feet below. The distance, S, that the acorn is from the ground as it falls is represented by the equation S(t) = –16t2 + 25, where t is the number of seconds. For which interval of time is the acorn moving through the air?

Answers

The end of its travel is when S(t)=0 or when it has hit the ground...

-16t^2+25=0  divide equation by -1

16t^2-25, this is a difference of squares which always factors:

(a^2+b^2)=(a+b)(a-b), in this case:

(4t+5)(4t-5)=0, since t>0

t=5/4=1.25, and since it started falling at t=0, its time moving in the air is:

1.25-0=1.25 seconds.

Answer: B or 0 < t < 5/4

Step-by-step explanation:

I got it wrong from the other answers and found out that this was the right one.

To determine whether the pipe welds in a nuclear power plant meet specifications, a random sample of welds is selected, and tests are conducted on each weld in the sample. weld strength is measured as the force required to break the weld. suppose the specifications state

Answers

Transmutation is the process of changing the substance, tangible or not, from one form to the other. It means the transformation of one element in the periodic table into another by one or a series of nuclear decays or reactions. One type of transmutation is nuclear transmutation. Nuclear transmutation is the conversion of one chemical element or isotope into another though nuclear reactions or nuclear decay. Second type of transmutation is artificial transmutation. Artificial transmutation occur in machinery that uses nough energy to cause changes in the nuclear structure of the elements.

Engineers test the weld strength of pipe welds in nuclear power plants to ensure they meet safety specifications. Tensile strength and pressure tolerance are key factors tested to maintain plant safety and functionality. Regulatory standards, like those from the NRC, guide acceptable performance levels for power plant components.

To ensure the safety and functionality of the nuclear power plant's infrastructure, engineers conduct tests on components such as pipe welds. These tests involve assessing weld strength, which is the force required to break a weld, and must meet specific specifications for the plant to operate safely. If not, the structural integrity of the power plant could be compromised, potentially leading to failures in electrical generation or even safety hazards.

The tensile strength of a material is a critical factor in this scenario. It is defined as the force per unit area (measured in Newtons per square meter or Pascals) needed to cause failure of the material by pulling it apart. This strength needs to be tested to prevent issues like the SS Schenectady ship's cracking under stress, which can have catastrophic consequences.

Regulatory standards, such as those set by the Nuclear Regulatory Commission (NRC), often determine the acceptable levels of component performance, including valves and tubing, within a power plant. These standards may change over time in response to new findings or incidents, reflecting the evolving understanding of material properties and failure risks under operational conditions.

In statistical terms, such tests might involve a hypothesis test to determine if the pressure tolerances of two valve types differ significantly, or if the structural components meet the required strength, safety, and operational standards.

how to prove a polygon is a rectangle?

Answers

If 2 pairs of sides are parallel and the angles are congruent then the polygon is a rectangle.

Convert 85°to radians

Answers

1 degree = 0.0174533 radians

85* 0.0174533 = 1.4835305 radians

Round answer as needed

Answer:

17pi/36 (PLATO answer)

Step-by-step explanation:

Four students did a survey to find the soda flavor sixth-grade students prefer. The table below shows the method each student used to conduct the survey: Student Method Trey Asked 100 students at random from his seventh-grade class what their favorite soda flavor is Jesse Asked 100 sixth-grade students at random what their favorite soda flavor is Nita Asked 100 eighth-grade students at random what their favorite soda flavor is Ruben Asked 100 third-grade students at random what their favorite soda flavor is Which student's survey not biased?

Answers

Jesse is the only one who surveyed sixth grades, which is what the point of the survey was. They are all biased because they each asked a certain grade. But in the case of this problem, Jesse is the most probable answer.

Answer:

The answer is B

Step-by-step explanation:

Ann is grouping 38 rocks. She can put them into groups of 10 rocks or as single rocks.what are different ways Ann can group the rocks?

Answers

Answer: 4 ways

To answer this question, you need to make a list based on how much "10 group" of rock can be made.
The possible way to group it should be:
0 pcs of 10 group + 38 pcs of 1 group
1 pcs of 10 group + 28 pcs of 1 group
2 pcs of 10 group + 18 pcs of 1 group
3 pcs of 10 group + 8 pcs of 1 group

Assume you have an infinite supply of these candy pieces from which to draw. if you draw two pieces one right after the​ other, are the events of getting a greena green on the first and a greena green on the second​ disjoint, independent, or​ neither?

Answers

First let us define what probability is. Probability is the measure of chance on getting a success or successful event out of all the total possible events. This can be expressed mathematically as:

Probability = Number of successful events / Total events

Which in this case can be written as:

Probability = Number of green candies / Total candies

So if we draw 1 candy in the 1st trial, therefore the value of the numerator and denominator would vary in the 2nd trial (since there is reduction of green candy & total candy). However the problem specifically states that there is an INFINITE supply of candies. Which means that the value do not change in the next trial.

Therefore the probability in the 2nd trial is not affected by the event of the 1st trial. So they are independent events. They cannot be disjoint since they are not mutually exclusive, both can occur at the same time (green and green).

 

Answer:

Independent

Use the zeros of the following quadratic to find the x-value of the vertex.
y = x^2 + 2x -8
A. 2
B. 1
C. -1
D. -8
PLEASE HELP ASAP

Answers

Just use the following formula:
[tex]v= (\frac{-b}{2a}, f( \frac{-b}{2a})) [/tex]

In this problem, b=2 and a=1

Substitute the values into the formula.

v=(-(2)/2(1), f(-(2)/2(1)))
v=(-1,f(-1))
v=(-1,(-1)²+2(-1)-8)
v=(-1,(1-2-8))
v=(-1,-9)

Therefore, the vertex is (-1,-9).

However, you only wanted the x-value which is in fact -1.

Therefore, the correct answer is "C. -1."


To use the zeroes, just solve the quadratic and find the mean of the two zeroes.

So,
[tex] m=\frac{x_{1}+x_{2} }{2} [/tex].


Hope this helps!

A company wants to save for a new piece of equipment that will cost 17,500. They have 15,000 to invest today in an account that earns 4.75% annual simple interest. How long must they invest the money in order to purchase the new equipment? Round to the tenth

Answers

The additional amount of $ needed is $17,500-$15,000, or $2,500.  This is the necessary increase to the $15,000 principal.

So this question boils down to how long it will take for the original $15,000 to earn $2,500 at 4.75% annual simple interest.

We thus must solve the following for n, the # of years:

i = p r t

$2,500 = $15,000 (0.0475) n

Solving for n (the number of years), n = $2,500 / [$15,000*0.0475]

Please finish this arithmetic.  Note that n is measured in years, so include "years" as part of your final answer.

if the area of triangle ABC= 25 square feet, then the area of the rectangle ABCD is:

25 square feet.
35 square feet.
40 square feet.
50 square feet.

Answers

A rectangle has 2 triangle
∴ 25 feet² × 2 = 50 feet²
Should be 50 square feet. Area of triangle is base x height / 2 and area of rectangle is side1 x side2. In this case, base x height = 25 x 2 = 50, and base =side1 and height=side2.

A person wishes to mix coffee worth nine dollars per pound with coffee worth three dollars per pound to get 240 pounds of a mixture worth five dollars per pound how many pounds of the nine dollars and the three dollar coffee will be needed

Answers

[tex]\bf \begin{array}{lccclll} &amount&price&priced\ amount\\ &-----&-----&--------\\ \textit{9 bucks/lb}&x&9&9x\\ \textit{3 bucks/lb}&y&3&3y\\ -----&-----&-----&-------\\ mixture&240&5&1200 \end{array} \\\\\\ \begin{cases} x+y=240\implies \boxed{y}=240-x\\ 9x+3y=1200\\ ----------\\ 9x+3\left( \boxed{240-x} \right)=1200 \end{cases}[/tex]

solve for "x".

what about "y"? well, y = 240 - x

Mitch planted cabbage,squash and carrots on his 150 acre-farm. He planted half the farm with squash and 22% with carrots. How many acres did he plant with cabbagge?

Answers

150 total acres...
he planted half the farm with squash.....150/2 = 75 acres squash
he planted 22% with carrots...0.22(150) = 33 acres carrots

150 - (75 + 33) = 150 - 108 = 42 acres cabbage <==

Answer:

42 acres

Step-by-step explanation:

Mitch planted cabbage,squash and carrots on his 150 acre-farm.

He planted half the farm with squash. The acres planted with squash are:

1/2 × 150 acre = 75 acre

He planted 22% with carrots. The acres planted with carrots are:

22% × 150 acre = 33 acre

The sum of the acres planted with cabbage, squash and carrots is equal to the total number of acres.

cabbage + squash + carrots = 150 acre

cabbage = 150 acre - squash - carrots

cabbage = 150 acre - 75 acre - 33 acre = 42 acre

Sam used his calculator to find the answer and wrote down cos 1.75 = 0.999. Does this seem like a reasonable answer to you? What might he have done wrong on his calculator?

Answers

 

Since pi is equivalent to 3.14 and means 180°, therefore 1.75 which is about half of pi should be at almost 90°. The cos of a 90° angle which is located on the y axis should be zero, therefore cos 1.75 must be near zero. However in this case it is near one, clearly his calculator is in degree mode that is why he got an erroneous answer.

What Sam can do to get the correct answer would be to convert his calculator into radian mode or convert the given 1.75 rad into degrees:

θ = 1.75 rad (180° / π rad)

θ = 100.2676

cos 100.2676 = -0.1782   which is now correct since it is nearer to zero

Ocean currents influence all of the following except
temperature
climate
radiation from the sun
weather

Answers

radiation from the sun. That depends on the sun.
I'm sure it would be weather. :)

Pentagon RSTUV is circumscribed about a circle. What is the value of x if RS = 6, ST = 9, TU = 7, UV = 15, and VR = 14?

Answers

Starting at vertex V going until vertex S, we make our calculations.

VR = 14

Rx = x

therefore, xS = VR – Rx

xS = 14 – x                           ---> 1

 

Now starting at vertex V going left to vertex S, we make our next set of calculations. Assuming x is on VR but nearer R

VR  = 14 - x

at UV = 15 – (14 – x)

at UV = 1 + x

at TU = 7 – (1 + x)

at TU = 6 – x

at ST = 9 – (6 – x)

at ST = 3 + x                        ---> 2


Equate 1 and 2:

14 – x = 3 + x

2 x = 11

x = 5.5

To find the value of x in the circumscribed pentagon RSTUV with given sides, we set up an equation based on the sum of the lengths of the opposite sides. After solving the equation, we determined that x is 25.

Pentagon RSTUV and the Value of x

Given that pentagon RSTUV is circumscribed about a circle, we need to find the value of x,

where RS = 6, ST = 9, TU = 7, UV = 15, and VR = 14.

For a polygon circumscribed about a circle, the sum of the lengths of the pairs of opposite sides must be equal. Therefore, we can set up the equation:

RS + TU + x = ST + UV + VR

Substituting the given values:

6 + 7 + x = 9 + 15 + 14

Simplifying the right-hand side:

6 + 7 + x = 3813 + x = 38x = 38 - 13x = 25

Thus, the value of x is 25.

In a first aid kit the ratio of large bandages to small is 3 to 2 based on this ratio how many large bandages are in the kit if there are a total of 80 bandages

Answers

The ratio of large to small to total is 3:2:5
If the total is 80, we know we need to multiply each number in the ratio by 16 tp get 48 large and 32 small.
Final answer: 48 large bandages.

EASY 5 POINTS!!! Choose the equation that correctly uses the Pythagorean Theorem for the given right triangle.

Answers

The correct answer is g^2 + 2.5^2 = 4.5^2 because the formula for the pythagorean theorem is a^2+b^2 = c^2 . Since the hypotnuse is the longest side of a triangle and c is the hypotnuse that is the correct answer trust me. 

^2 = squared

Answer:

Option C

Step-by-step explanation:

In the given right angle triangle

Hypotenuse = 4.5 cm

Height = 2.5 cm

and base = g cm.

Pythagoras theorem says

(hypotenuse)² = (base)² + (height)²

So by putting the values in the formula

(4.5)² + (2.5)² + g²

Option C is the answer.

simplify the expression the square root of 169

Answers

The square root of 169 is 13.

An employee earned $3,300 working for an employer in the current year. the current rate for fica social security is 6.2% payable on earnings up to $117,000 maximum per year and the rate for fica medicare 1.45%. the employer's total fica payroll tax for this employee is:

Answers

Employer's Total FICA Tax = $3,300 * (0.062 + 0.0145) = $252.45

solve, explain why the algorithm works
3892
-2567

Answers

Unfortunately, you don't share enough info here for the question to make sense.

If I assume that you want to subtract 2567 from 3892, I'd write the problem in a slightly different manner:

 3892
-2567
--------

Now subtract.  Borrow 1 from 9 to obtain a 12, and then subtract 7 from 12, obtaining 5.  Result:  1825.  Is this correct?  You could check by adding 1825 to 2567.  You are correct if their sum is 3892.
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