Comparing to the standard equation, the parabola with a vertex at (-2,0) is given by:
y = (x + 2)²
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, we have that h = -2 and k = 0, and all the options have leading coefficient a = 1, hence the equation is:
y = (x + 2)²
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Answer:
B. y = (x + 2)2The diameter of a circle is 8 inches. What is the and
with area 24 square inches?
8 inches
to find:the area
solution:If the diameter is 8 inches, the radius is 4 inches.
a= Pi* r^2
= 16 Pi square inches.
pi= 3.14159 》 16pi
= 15.2655 sq inch
The center of the circle is located at (-4,-3). What is the area? Use 3.14 as an approximation for pi.
Answer:
78.5 units²
Step-by-step explanation:
First, we need to plot the center point of the circle. (Shown in image). Once we plotted the center point, we need to count how many units is the radius away from the boundary.
Note: I have marked each unit by a "red point". Simply, count the number of "red points" to determine the radius.
⇒ Radius according to graph: 5 unitsWe can substitute the radius in the "area of circle" formula to determine the area. Keep in mind that pie is represented as 3.14.
⇒ Area of circle = πr²⇒ Area of circle = π(5)²Now, let's evaluate the area by simplifying the expression. Keep in mind that pie is represented as 3.14.
⇒ Area of circle = π × (5)²⇒ Area of circle = π × 5 × 5⇒ Area of circle = π × 25⇒ Area of circle ≈ 3.14 × 25 [π = 3.14]⇒ Area of circle ≈ 78.5 units²Give me full working and explanation and I give you stars and mark you as brainliest.
PLSS HELPP
I NEED TO FIND THE 2 SIDE LENGTHS
You are building a play pen for your pet pig. You know that you want one side to be 7 feet longer than 3 times the other
side. The area of the play pen that you want is 48 square feet. What are the dimensions of the play pen?
Check the picture below.
[tex]\textit{area of a rectangle}\\\\ A=Lw~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ w=3L+7\\ A=48 \end{cases}\implies 48=L(3L+7)\implies 48=3L^2+7L \\\\\\ 0=3L^2+7L-48\implies 0=(3L+16)(L-3) \\\\[-0.35em] ~\dotfill\\\\ 0=3L+16\implies -16=3L\implies -\cfrac{16}{3}=L \\\\[-0.35em] ~\dotfill\\\\ 0=L-3\implies 3=L~~\textit{\Large \checkmark} \\\\[-0.35em] ~\dotfill\\\\ w=3L+7\implies w=3(3)+7\implies w=16[/tex]
notice, we didn't use the negative value of "L", because the length can't be negative.
PLEASE ANSWER THIS QUICKLY!
Consider the circle shown.
1. What is the length of the minor arc DE? (EXPRESS YOUR ANSWER AS A SIMPLIFIED FRACTION IN TERMS OF PI).
2. What is the length of the major arc DGE? (EXPRESS YOUR ANSWER AS A SIMPLIFIED FRACTION IN TERMS OF PI).
Answer:
minor arc DE: (23/9)π
Major arc DGE:(49/9)π
Step-by-step explanation:
This is a simple problem.
First solve the circumference of the circle: 2π (4).
then use the length formula
L=(x*c)/360
and then plug in, so first we use 115 as x(which is degrees) to find de
so
L = (115* 2π (4))/360
and you will get (23/9)π
To get the major arc you have to get the outside angle, so 360-115, and you do the same thing but with 245 as x.
Hope this helps and im correct!
At his schools book fair, Henry brings $10.00. He purchases a book for $8.50, plus a 6% sales tax. How much money in change will Henry receive?
Answer:
$0.99 in change
Explanation:
To apply the sales tax, you have to multiply:
8.50*1.06=9.01
This means that, with tax, the book will cost $9.01. If he gave them $10, he would get 99 cents back because 10-9.01 is 0.99.
The length of a rectangle is 4/5 of the width. The length of the rectangle is 3/5 meter. Which equation can be used to find w, the width of the rectangle in meters?
A 3/5w = 4/5
B 4/5w = 3/5
C 3/5 + w = 4/5
D 4/5 + w = 3/5
Answer:
B: 4/5w = 3/5
Step-by-step explanation:
The length of the rectangle is stated as being 4/5 of the w. (4/5 * w)
The length is also stated specifically as being 3/5m so that will equal 4/5w on the other side of the equation.
Bonus:
You could work out the equation as
4/5w = 3/5m
multiply by 5
4w = 3m
divide by 4
w = 0.75m (or 3/4m)
Does anybody know this ?
Answer:
0, 1, 2, 3, 4
Step-by-step explanation:
Multiply each x value by 1/3 then add 2. Since the numerator is 1, you would multipy by one and divide by the denominator of 3, so you really need to divide each x value by 3 then add 2.
-6:
-6/3 = -2
-2 + 2 = 0
-3:
-3/3 = -1
-1 + 2 = 1
0:
0/3 = 0
0 + 2 = 2
3:
3/3 = 1
1 +2 = 3
6:
6/3 = 2
2 + 2 =4
5.000g rounded to the nearest whole gram
Answer:
5 g hope this helps
Given circle E with diameter \overline{CD} CD and radius \overline{EA} EA . \overline{AB} AB is tangent to E at A. If EA=18 and DB=12, solve for AB. Round your answer to the nearest tenth if necessary.
The line AB from the diagrammatic expression of the tangent of the circle shows that line AB is 24.0
What is the tangent of a circle?A tangent of a circle is a line that intersects the circle at a single point. The site at which the tangent intersects the circle is referred to as the site of tangency.
From the given information:
Line |CD| = Diameter Line |EA| = radius = 18Line |DB| = 12Then, we can infer that line EA = DE since they are both (radii of the circle.)
Line |DE| = |EA| = 18By using the formula for Pythagoras theorem, we can find line |EA|.
hyp² = opp² + adj²where;
Line |BE| = hypotenuse = DB + BE = 12 + 18 = 30Line |AB| = opposite (x) = ???Line |EA| = adjacent = 18Thus;
30² = x² + 18²
900 = x² + 324
-x² = -900 + 324
x = √576
x = 24.0
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A substance requires 310 J of heat to raise the temperature from 19
°C to 42 °C.. If the mass of the substance is 20 g, what is the specific
heat of the substance?
Answer:
.674 j / (g-C)
Step-by-step explanation:
Spec heat = heat required to raise 1 gram of substance 1 degree celsius
Spec heat units : j / (gm-C)
soooo 310 j / (20g * (42-19)C = .674
Pedro was working on a report on swiss and austrian psychiatrists. he decided to find a 90 percent confidence interval for the difference in mean age at the time of significant psychiatric discoveries for swiss versus austrian psychiatrists. he found the ages at the time of psychological discovery of all the members of both groups and found the 90 percent confidence interval based on a t-distribution using a calculator. the procedure he used is not appropriate in this context because
a
the sample sizes for the two groups are not equal.
b
the entire population is measured in both cases, so the actual difference in means can be computed and a confidence interval should not be used.
c
age at the time of psychological discovery occurs at different intervals in the two countries, so the distribution of ages cannot be the same.
d
age at the time of psychological discovery is likely to be skewed rather than bell shaped, so the assumptions for using this confidence interval formula are not valid.
e
age at the time of psychological discovery is likely to have a few large outliers, so the assumption for using this confidence interval formula is not valid
Answer:
B) the entire population is measured in both cases, so the actual difference in means can be computed and a confidence interval should not be used.
Step-by-step explanation:
Age at the time of psychological discovery is likely to be skewed rather than bell shaped, so the assumptions for using this confidence interval formula are not valid. Therefore, option D is the correct answer.
What is a confidence interval?The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.
A confidence interval is used to estimate an unknown population parameter, such as the mean, from a sample. It does this by providing a range of values within which the true population parameter is likely to lie. To use a confidence interval, the assumptions of the underlying distribution must be valid. In this case, the distribution of the ages of the Swiss and Austrian psychiatrists is likely to be skewed, meaning that it does not follow a bell shaped distribution. This makes the assumptions for using the confidence interval formula invalid and thus the procedure is not appropriate in this context.
Therefore, option D is the correct answer.
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Which probability describes an event that is “very likely”?
A. 0.125
B. 0.9
C. 1
D. 0.50
The probability that describes an event as "very likely" is option B, 0.9.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain.
A probability of 0.9 means that there is a 90% chance that the event will occur, which is a high likelihood of the event happening. In general, probabilities between 0.7 and 1 are often considered to be "likely" or "very likely".
Therefore, the correct option is B.
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solve 650(1+.045) with an exponent of 3
Answer:
741.75798\dots
Step-by-step explanation:
\mathrm{Add\:the\:numbers:}\:1+0.045=1.045
1.045^3=1.141166125
\mathrm{Multiply\:the\:numbers:}\:650\cdot \:1.141166125=741.75798\dots
Ashley arranged the following list of numbers below: 5,2,7,8,2,5,3. Find the mean and median.
Mary sells fruit with four of her friends. If the earnings are divided evenly, how
much must the business make in order for each person to earn $30?
What is the variable for this problem?
A. friends
ООО
B. profit ratio
C. expenditures
D. total earnings
E, fruit
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let the total money earned be x
since each of them get equal share, therefore :
[tex]\qquad \tt \dashrightarrow \:5 \times 30 = x[/tex]
[tex]\qquad \tt \dashrightarrow \:x = \$150[/tex]
And here, we used Total earning as the variable in the problem ~
So, correct choice is D
Total persons including Mary=4+1=5
Earnings per person =$30
Total earnings
5(30)150$Option D
Felipe is ordering new carpet for his bedroom floor. (The floor is represented in the picture below as rectangle JKLM). He knows the base edge, ML, measures 18 ft. And the distance of diagonal KM measures 25 ft. What is the area of Felipe’s bedroom floor? Show all work and round your answer to the nearest tenth.
will mark brainlist
Answer: 312.3 square feet
Step-by-step explanation:
The area of Felipe’s bedroom floor is 312.3 square ft.
What is Pythagoras theorem:If we have a right-angled triangle then we can write the following equation,
(Hypotenuse)² = (Base)² + (Height)²
Properties of a rectangle:In the given figure attached below the properties are as follows:
ML = JKKL = JMarea = (Base × Width) = KL × MLIn the given question and in the figure attached below the given values are:
ML = 18 ft.KM = 25 ft.By applying Pythagoras theorem in ΔKML we get,
(KM)² = (KL)² + (ML)²
Putting all the values in the above equation,
(25)² = (KL)² + (18)²
By rearranging,
(KL)² = (25)² - (18)²
Applying the formula, a² - b² = (a + b)(a - b) we get,
(KL)² = (25 + 18)(25 - 18)
(KL)² = 43 × 7
KL = √301 ft.
Now the area is,
area = KL × ML
= (√301 × 18) square ft.
= 312.3 square ft.
Therefore, the area of Felipe’s bedroom floor is 312.3 square ft.
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LMNO is a kite. LO is 5 less than two times NO. The perimeter is 32 cm. Let x represent the length of side NO.
Answer: 7 cm
Step-by-step explanation:
Consider the system of equations.
x − 4y = 11,
3x + 5y = −1
Which number should you multiply the first equation by to eliminate the x-variable term?
1
–1
3
–3
Answer:
-3
Step-by-step explanation:
since if you multiply by -3 the sum of both equations will not have an x variable.
Answer:
D
Step-by-step explanation:
=
In the accompanying diagram of isosceles triangle ABC,
AB = BC, mZBAC = x, and mLABC = x + 30.
What is the value of x?
B
(x + 30)
A
The value of x is
The measure of the vertex angle is
degrees.
Answer:
x = 50
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180
Since triangle ABC is an isosceles triangle the measure of <c is also = x
x + x + x + 30 = 180 add like terms
3x + 30 = 180 subtract 30 from both sides
3x = 150 divide both sides by 3
x = 50
Ramona is counting the posts between mile makers on the highway. In 1 mile, she counts 33 posts. If the posts are evenly spaced, how many feet apart are they? (1 mile = 5,280 feet)
Answer:
160feet
Step-by-step explanation:
5280 divided by the number of posts
count in mile= 33 posts.
to find:the distance between the posts.
solution:1 mile= 5280ft
distance= 5280/33
=160ft
so the distance between the posts are 160ft.
Describing the Graph of a Polynomial Function 2.) Use the function: f(x) = (x + 2)(x - 1)(x - 2) a) Find the zeros of the function. b) Find the y-intercept of the function. c) Describe the end behavior of the graph.
Answer:
The end behavoir is no solution
Step-by-step explanation:
The reason for this is because if you solve the graph the graph will show no end point
Is the quotient of 3 and 1/4 greater than or less than 3?
Answer:
Greater than
Step-by-step explanation:
The quotient of 3 and 1/4 would be 3/(1/4).
You could then multiply by the inverse of 1/4 to simplify the expression. This would give you [tex]3*\frac{4}{1}[/tex] or just 3 times 4. 3 * 4 = 12.
Since 12 is greater than 3, the quotient of 4 and 1/4 is greater than 3.
The tile pattern below is made up of trapezoids and rhombuses. What is the area of each figure in the pattern?
The trapezoids have a height of 2 inches and bases that measure 2 inches and 3 inches.
The rhombuses have diagonals that measure 1 inch and 4 inches.
The area of the rhombus and trapezoid from the figure are 2 square in and 5 square in respectively
How to find the area of a trapezoid and rhombus?The given pattern consists of rhombus and trapezoids
The formula for calculating the area of rhombus is expressed as:
A = pq/2
Area of trapezoid = 0.5(a+b)h
Given the following
height = 2in
a = 2in
b = 3in
Ara of rhombus = 1(4)/2 = 2 square inches
Area of the trapezoid = 0.5(2+3) * 2
Area of the trapezoid = 5 square inches
Hence the area of the rhombus and trapezoid from the figure are 2 square in and 5 square in respectively
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Choose the correct definition of volume.
the amount of space a 3-dimensional object takes up
distance from one point to another
the amount of space a 2-dimensional object takes up
the distance from the bottom to the top of an object
Answer:
the amount of space a 3-dimensional object takes up
Step-by-step explanation:
Of the four definition options, the first is the only only that incorporates a three dimension explanation. The others only describe a two dimension object. Units for the first would be unit^3. The other three would only be one-dimensional "units."
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A high school basketball coach was searching through records and found that the average height of high school basketball players is 73 inches with a standard deviation of 2.1 inches. The distribution of heights is an approximately normal distribution.
a. The typical basketball team usually has around 16 players. Describe the sampling distribution for samples of size n = 16.
b. Is it surprising to find a random sample of size n = 4 to have an average height over 75 inches? Give appropriate statistical evidence
c. Suppose the population described in the problem was clearly NOT normal. Could the question in part (b) still be answered? Explain why it could still be answered. If not, explain why.
Answer:
The heights of basketball players have an approximate normal distribution with mean, μ = 79 inches and a standard deviation, σ = 3.89 inches.
Step-by-step explanation:
A committee is to consist of two members. If there are seven people available to serve on the committee, how many different committees can be formed?
25(q-954)=775 what is q?
Answer:
The value of q = 985
Step-by-step explanation:
==> 25(q-954)=775
=> q-954 = 775/25
=> q-954 = 31
=> q = 31+ 954
=> q = 985
Answer:
q = 985
Step-by-step explanation:
25 (q-954) = 775
q-954 = 775/25
q = 31 + 954
q = 985
A wheel with the 31 in. diameter has 651 rotations. Reflect on how different wheel sizes would change your answer. What would happen to the number of rotations if the circumference of the wheels were increased by 20%? For the wheel with 31 in. diameter, multiply its circumference 97.4 in. by 1.2 =________.
The number of rotations is reduced to 542.501 when the diameter of wheel is increased by 20 %.
How to compare rotations between two wheels of different diameter
The quantity of rotations (n), no unit, done by a wheel is equal by total traveled distance (s), in inches, divided by its circumference (p), in inches:
[tex]n = \frac{s}{p}[/tex]
[tex]n = \frac{s}{\pi\cdot D}[/tex] (1)
Where D is the diameter of the wheel, in inches.
If we know that n = 651 and D = 31 in, then the travelled distance is:
s = (651) · π · (31 in) (2)
s ≈ 63400.481 in
The travelled distance of the 31-in diameter wheel with 651 rotations is approximately 63400.481 inches.
By (2) we understand that the travelled distance is directly proportional to the diameter. Hence, if the diameter of the wheel is increased by 20 %, then we must multiply the diameter by 1.2 and divide the travelled distance by this result:
s ≈ 1.2 · π · (31 in)
s ≈ 116.867 in
[tex]n = \frac{63400.481\,in}{116.867\,in}[/tex]
[tex]n = 542.501[/tex]
The number of rotations is reduced to 542.501 when the diameter of wheel is increased by 20 %. [tex]\blacksquare[/tex]
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what is the range of the data set 95,86,78,80,91
Answer:
17
Step-by-step explanation:
Range = Highest Value - Smallest Value
95 - 78 = 17
Answer:
17
Step-by-step explanation:
Subtract the minimum data value from the maximum data value to find the data range.
95 - 78 = 17
