What is the a-value of the function, then determine if the graph opening up or down f(x)=−5(x+7)2+6?
Question 4 options:
a = -5, opens down
a = -5, opens up
a = 7, opens up
a = 7, opens down
Answers
the equation of the vertical parabola in the vertex form is
y=a(x-h)²+k
where
(h,k) is the vertex of the parabola
if a> 0 then
the parabola opens upwards
if a< 0
then the parabola open downwards
in this problem we have
f(x)=−5(x+7)²+6
a=-5
so
a< 0 -------> the parabola open downwards
the vertex is the point (-7,6) is a maximum
the answer is the option
a = -5, opens down
see the attached figure
a = -5, opens down
Explanation:
The general form of the quadratic equation is:
f(x) = a(x-h)² + k where (h,k) is the vertex of the parabola.
The value of the "a" determines whether the parabola is open upwards or downwards:
1- if the value of "a" is positive, this means that parabola opens upwards
2- if the value of "a" is negative, this means that the parabola opens downwards
Now, for the given:
f(x) = -5(x+7)² + 6
By comparison, we can note that:
a = -5
The value of "a" is negative which means that the parabola opens down.
The attached image shows the graph of the given function
Hope this helps :)
Related Questions
Beulah took out a loan for $1225 at an 11.4% APR, compounded monthly, to buuy a foosball table. If she will make monthly payments of $101.75 to pay off tghe loan, how many total payments will she have to make?
Answers
To answer this problem, get first the Future Value (FV) of the loan for a year. Given the APR and the amount of loan, FV is computed as follows: FV = $1225 x (1+.0095)¹² = $1372.18
Note that the APR and period were changed to 0.95% and 12, respectively because it has to be compounded monthly.
Now, divide the FV by the monthly payment of $101.75.
Number of payments = $1372.18/$101.75 = 13.48 ≈ 13
Answer:
13
Step-by-step explanation:
APEX
What is another name for an indirect proof? Picture included
Answers
6200ft is <>= to 1mi 900ft
Answers
Convert 1 mile to feet. This would be 5280 feet. Add this to 900. 5280+900=6180. So 6200 is greater than 1 mile 900 feet, or 6200>1 mile 900 feet.
I hope this helps!
5280 + 900=6180
6200ft < 1 mi 900ft
cx+5c=7c solve for x assume c doesn't equal 0
Answers
[tex]\begin{aligned} x+5=7 \end{aligned}[/tex]
Subtracting [tex]5[/tex] from both sides gives [tex]x = \boxed{2}[/tex].
A sphere has a radius of 9mm. What is the volume of the sphere, rounded to the hundredths place ?
Answers
V=4/3* π(9)^3
V=4/3* π(243)
V= 324 * π
(rounded): V= 1017.88 mm
The volume of the sphere will be 1017.88 cubic mm.
What is the volume of the sphere?The volume is defined as the space occupied by the solid in a three-dimensional plane. `The volume of the sphere is defined as the space occupied by the sphere in a three-dimensional space.
The volume of the sphere is calculated by the formula below:-
Volume = V=4/3 x πr³
Given that a sphere has a radius of 9mm. Use the formula in calculating the volume of the sphere.
Volume of a sphere:
V=4/3 x πr³
V=4/3 x π(9)³
V=4/3 x π(243)
V= 324 x π
Therefore, the volume of the sphere will be 1017.88 cubic mm.
To know more about volume follow
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Simplify 3a • 3b ÷ 3c ÷ 3d. The exponent on 3 is _____.
Answers
The correct answer is 2.
To simplify the expression 3a • 3b ÷ 3c ÷ 3d, we need to apply the laws of exponents and combine the coefficients and variables.
Given expression: [tex]3a \cdot 3b \div 3c \div 3d[/tex]
[tex]\text{Step 1: Rewrite the expression using exponents}[/tex]
[tex](3^1 \cdot a) \cdot (3^1 \cdot b) \div (3^1 \cdot c) \div (3^1 \cdot d)[/tex]
[tex]\text{Step 2: Apply the laws of exponents for multiplication and division}[/tex]
[tex](3^1 \cdot 3^1 \cdot a \cdot b) \div (3^1 \cdot c) \div (3^1 \cdot d)[/tex]
[tex]= (3^{1 + 1} \cdot a \cdot b) \div (3^1 \cdot c) \div (3^1 \cdot d)[/tex]
[tex]= (3^2 \cdot a \cdot b) \div (3^1 \cdot c) \div (3^1 \cdot d)[/tex]
[tex]\text{Step 3: Simplify the expression by combining the exponents and coefficients}[/tex]
[tex](3^2 \cdot a \cdot b) \div (3^1 \cdot c) \div (3^1 \cdot d)[/tex]
[tex]= (3^2 \cdot a \cdot b) \div (3^{1 + 1} \cdot c \cdot d)[/tex]
[tex]= (3^2 \cdot a \cdot b) \div (3^2 \cdot c \cdot d)[/tex]
[tex]= \frac{a \cdot b}{c \cdot d}[/tex]
Therefore, the simplified expression is [tex]\frac{a \cdot b}{c \cdot d}[/tex], and the exponent on 3 is 2.
Part A: What is the group of points labeled P called? What is the point labeled T called? Give a possible reason for the presence of point T.
Part B: Describe the association between students' test scores and the number of hours they exercise.
Answers
Which of the following functions is quadratic? f(x)=3(x-4)(x+3), f(x)=5^2, f(x)=2/x, f(x)=2x^3+3x^2-5
Answers
In C f(x) = 2/x is a function of a reciprocal, not a quadratic.
In D f(x) = 2x^3 + 3x^2 - 5 is a cubic. A cubic is not a quadratic. The highest power of a quadratic is x^2
That leaves A. When you expand the brackets, you get
3(x^2 + 3x- 4x - 12)
2(x^2 - x - 12) when you remove the brackets you get
2x^2 - 2x - 24. The highest power of x is x^2. This is your quadratic.
A<<<< answer.
Final answer:
The function f(x)=3(x-4)(x+3) is the only quadratic function provided in the options, as it can be expanded to a second-order polynomial form.
Explanation:
The student asks which of the given functions is quadratic. A quadratic function is a second-order polynomial with the highest exponent of the variable being 2. Given the options, the function f(x)=3(x-4)(x+3) is quadratic because it can be expanded to the form ax2 + bx + c, where a, b, and c are constants. The given function will simplify to a quadratic equation once we expand it. No other provided functions display the characteristics of a quadratic equation; f(x)=52 is a constant, f(x)=2/x is a rational function, and [tex]f(x)=2x^3+3x^2-5[/tex] is a cubic function.
Juanita is cutting a piece of construction paper in the shape of a parallelogram. Two opposite sides of the parallelogram have lengths (5n − 6) cm and (3n − 2) cm. The third side measures (2n + 3) cm. What are the lengths of two adjacent sides of the parallelogram? 2 cm and 2 cm 4 cm and 7 cm 7 cm and 9 cm 13 cm and 19 cmJuanita is cutting a piece of construction paper in the shape of a parallelogram. Two opposite sides of the parallelogram have lengths (5n − 6) cm and (3n − 2) cm. The third side measures (2n + 3) cm. What are the lengths of two adjacent sides of the parallelogram? 2 cm and 2 cm 4 cm and 7 cm 7 cm and 9 cm 13 cm and 19 cm
Answers
Answer:
Correct option is 2. The lengths of two adjacent sides of the parallelogram are 4 cm and 7 cm.
Step-by-step explanation:
The opposite sides of a parallelogram are equal.
[tex]5n-6=3n-2[/tex]
[tex]2n=4[/tex]
Divide both sides by 2.
[tex]n=2[/tex]
The value of n is 2.
The lengths of two adjacent sides of the parallelogram are
[tex]5n-6=5(2)-6=10-6=4[/tex]
[tex]2n+3=2(2)+3=7[/tex]
Therefore the correct option is 2. The lengths of two adjacent sides of the parallelogram are 4 cm and 7 cm.
Last question pls help!
A rectangle has a side of 12 inches and another side of 6 inches...
whats the perimeter? whats the area? what would be the area and permieter combined?
Answers
Area = 72 in.
Perimeter = 36 in.
Hope this helps :))
To find perimeter, add the sides. . .
12 + 12 = 24
6 + 6 = 12
24 + 12 = 36 <------ The perimeter is 36 inches.
To find area, multiply the two sides. . .
12 x 6 = 76 <------ the area is 76 inches.
To combine the area and perimeter, add the numbers 76 and 36. . .
36 + 76 = 112 <--- the area and perimeter combined is 112 inches.
Hope this helps you.
Have a great day!
number 248682 rounded off to the nearest hundred becomes what
Answers
Carson wants to put her 232 stickers into a book that has 36 Pages if she puts 8 stickers on each page how many pages will be blank
Answers
Movie A took in $142.44 million on it’s first weekend. This topped the previous opening weekend revenue set by movie B by $4.14 million. How much did movie B take in on its opening weekend?
Answers
According to the given statement, revenue of movie A was $4.14 million more than the revenue of movie B in their first weekends.
So, we can write:
Revenue of movie A = Revenue of movie B + $4.14 million
Revenue of movie B = 142.44 million - 4.14 million = $ 138.30 million.
Thus movie B take in $138.30 million on its opening weekend.
subtracting unlike fractions 8/9 - 5/6
Answers
Here is your answer:
The proper answer to your question is "1/18".
Here is how:
8*6=48
9*6=54
-
5*9=45
6*9=54
48-45=3
Which is 3/54!
3/3=1
54/3=18
Which means your answer is 1/18!
If you need anymore help feel free to ask me!
Hope this helps!
lungimea unei gradini de 78 m iar perimetrul este de 256 m.Afla latimea gradinii
Answers
L= 78 si P=256
P=2L+2W w e width(latime)
256=2*78+2w
256=156+2w
256-156=2 w
100=2w
w=50
The equation below shows the total volume (V), in cubic units, of 4 identical boxes with each side equal to s units: V = 4s3 If s = 2.5 units, what is the value of V? (5 points) 25 cubic units 30 cubic units 62.50 cubic units 156.25 cubic units
Plz help
Answers
volume of one box is length * breadth * height
since its a cube all sides are equal
volume of one box = s³ = 2.5³
since there are 4 boxes,
total volume V = 4s³
V = 4 * 2.5³ = 4 * 15.625
= 62.50 cubic units
third response is correct
Answer:
Option 3 - V = 62.50 cubic units.
Step-by-step explanation:
Given : The equation below shows the total volume (V), in cubic units, of 4 identical boxes with each side equal to s units: [tex]V=4s^3[/tex] If s = 2.5 units.
To find : What is the value of V ?
Solution :
The equation of the total volume is
[tex]V=4s^3[/tex]
Substitute, s=2.5 units
[tex]V=4(2.5)^3[/tex]
[tex]V=4\times 15.625[/tex]
[tex]V=62.5[/tex]
Therefore, Option 3 is correct.
The value of V is 62.50 cubic units.
What is the area of the trapezoid? Enter your answer in the box. in2 The figure shows a trapezoid. The parallel bases of the trapezoid are horizontal, and top base is shorter than the bottom base. Vertical line segments are drawn inside the trapezoid from the upper vertices perpendicular to the bottom base. These segments are each 6 inches and divide the trapezoid into two right triangles and a rectangle. The rectangle lies between the two triangles. The bases of the triangles and rectangle make up the bottom base of the trapezoid. The base of each triangle is 4 inches, and the base of the rectangle is 8 inches.
Answers
Answer: [tex]\text{Area}=72\ inches^2[/tex]
Step-by-step explanation:
By the given description of trapezoid we get,
The height of the trapezoid h= 6 inches
The base of triangle = 4 inches
The base of rectangle (a)= 8 inches
The bottom base of the trapezoid (b)= 2×base of triangle +base of rectangle
The bottom base of the trapezoid (b)= [tex]2(4)+8=8+8=16\ inches[/tex]
The area of trapezoid is given by :-
[tex]\text{Area}=\frac{1}{2}(a+b)h\\\\\Rightarrow\text{Area}=\frac{1}{2}(8+16)(6)\\\\\Rightarrow\text{Area}=72\ inches^2[/tex]
Answer:
72
Step-by-step explanation:
need help plz I need this by today because it's due Tomorrow
Answers
.. income = 52*985 = 51,220
Dale's withholding was
.. tax paid = 0.16*51,220 = 8195.20
According to the 3rd row of the table, Dale owes 8,770 in taxes, so must pay an additional
.. $8770 -8195.20 = $574.80
Dale owes $574.80.
Is 90 g less than, greater than, or equal 9kg
Answers
9 kg = 9000 grams since 1 kg is equal to 1000 grams (kilo = thousand)
So comparing "90 g to 9kg" is the same as "90 g to 9000g"
90g is smaller than 9000 g
therefore, 90 g is smaller than 9 kg
meg runs 1 1/2 miles and walks 2 1/4 miles each day of the week. how far does meg run and walk in al each week? explain. remember, you can write an equivalent fraction fir 1 1/2
Answers
Meg walks and runs 3 3/4 in total each week.
We can find this answer by adding the two numbers, 1 1/2 and 2 1/4
Hope this helps :)
To solve this problem, you first add the numbers 1 1/2 and 2 1/4:
1 + 2 = 3
Try finding the Lowest Common Denominator (LCD) of the fractions. . .
1/2 = 2/4
1/4 = 1/4
2/4 + 1/4 = 3/4
1 + 2 = 3
4 = 4
(Since both have the same denominator, the final denominator stays the same.)
3 + 3/4 = 3 3/4
Since there are 7 days in a week, multiply 7 x 3 3/4 . . .
7 = 7/1
3 3/4 = 15/4
7 x 15 = 105
1 x 4 = 4
105/4 = 26 1/4 <------------
Meg runs 26 1/4 miles overall in each week.
Hope this helps you.
Have a great day!
How many lateral faces does a pentagonal prism have? Explain its actually 8 for anyone who needs this in the future
Answers
Explanation:
You can see the attached figure for better understanding.
A pentagonal prism has 2 bases (the bottom and top faces), each pentagonal, and 5 lateral faces.
The pentagon is a figure with 5 sides. Hence, from each side, the prism will have one lateral face that goes from one base to the other.
The figure attached shows a pentagonal prism where you can see what I explained.
A pentagonal prism has five lateral faces.
A pentagonal prism is a three-dimensional geometric figure with two parallel pentagonal bases and rectangular lateral faces. To determine the number of lateral faces:
(1) Visualize the pentagonal bases; a pentagon has five sides.
(2) Each side of the pentagon is perpendicular to a corresponding rectangle, forming a lateral face.
So, a pentagonal prism has five lateral faces, matching the number of sides of its base pentagon.
An octahedron, a completely different shape, has eight triangular faces, not to be confused with the prism.
How many square feet of outdoor carpet will we need for this hole?
Answers
Answer:
44 square feet
Step-by-step explanation:
We are given a rectangle of dimension 12ft×4ft and a square of dimension 2ft×2ft.
Then, the required outdoor carpet will be:
Outdoor carpet required=Area of the outer hole that is the rectangle - Area of the inner hole that is the square
=[tex](length)(breadth)-(side)^{2}[/tex]
=[tex](12)(4)-2^{2}[/tex]
=[tex]48-4[/tex]
=[tex]44[/tex] square feet.
Yesterday, the price of a gallon of gas at five gas stations was $3.64, $3.79, $3.70, $4.01, and $3.91, respectively, but today each gas station raised its price by $0.08. What is today's mean price of a gallon of gas at the five stations?
A. $3.81
B. $3.89
C. $3.73
D. $3.97
PLEASE BE CORRECT.
Answers
0.08 * 5 = 0.40
19.05 + 0.40 = 19.45
19.45 / 5 = 3.89
Answer is B
Option: B is the correct answer.
B. $ 3.89
Step-by-step explanation:The price of a gallon of gas at five gas stations is given by:
$3.64, $3.79, $3.70, $4.01, and $3.91
The mean of these data values is given by:
[tex]Mean=\dfrac{3.64+3.79+3.70+4.01+3.91}{5}\\\\\\Mean=\dfrac{19.05}{5}\\\\\\Mean=3.81[/tex]
We know that if each of the quantity of the data set is increased by a fixed amount then the mean of the data set also increases by that fixed amount.
As we are given that each gas station raised its price by $0.08.
This means that the mean is also increased by $ 0.08
i.e. Today's mean price of a gallon of gas at the five station is given by:
[tex]Mean=3.81+0.08\\\\\\Mean=3.89[/tex]
Hence today's mean is:
$ 3.89
Which is the correct way to write three and one-tenth of a milliliter as an Arabic number?
Answers
three and one-tenth------> 3 1/10--------> (3*10+1)/10--------> 31/10-----> 3.1
the answer is 3.1 ml
You paid $80 for a tennis racket. If you found the racket under a sign stating 1/4 off, what must the original retail price have been?
Answers
1. You have that you paid $80 for a tennis racket which was under a sign stating 1/4 off. Therefore, you can express this with the following equation:
[tex] x-x/4=80 [/tex]
Where [tex]x[/tex]is the original retail price.
2. When you solve for [tex]x[/tex], you obtain:
[tex]3/4x=80 \\ x=106.67[/tex]
The answer is: [tex]106.67 dollars [/tex]
There were 25 melons at the grocery store. The store sold 3/5 of the melons. How many melons were sold?
Answers
Convert 3/5 to a decimal by dividing its numerator by its denominator.
3 ÷ 5 = 0.6
Next, multiply the total amount of melons in the store by the decimal.
25 × 0.6 = 15
ANSWER:
15 melons were sold.
To the model estimated in table 8.1, add the interaction term, e401k · inc. estimate the equation by ols and obtain the usual and robust standard errors. what do you conclude about the statistical significance of the interaction term?
Answers
Signed General Penguin
P - potassium
S - sodium
L - lithium
M - magnesium
C - calcium
A - aluminium
Z - zinc
I - iron
L - lead
H - hydrogen
C - copper
S - silver
G - gold
P - platinum
James gets headaches. the time between one headache and the next is an exponential random variable. he has noticed that, after having a headache, there is a 50% chance of having another headache within the next 4 days. james has not had a headache in 5 days. what is the probability that he will go for at least 5 more days before the next headache?
Answers
For an exponential distribution,
λ=rate of occurrence=mean number of headaches per day.
probability distribution function
=pdf(x, λ ) = λ e^(- λ x)
cumulative probability distribution function,
cdf(x, λ ) = 1 - e^(- λ x)
We are given probability of having no headaches in 4 days is 0.5,
this means x=4 in
cdf(4, λ ) = 0.5, =>
1 - e^(-4 λ )=0.5
Solve for λ
λ = -log(0.5)/4 = 0.1732868 [log(x)=natural log of x]
=>
interpretation: the mean number of headaches is 0.1732868 per day.
Using the cdf, for x=5 days,
cdf(5,0.1732868)=1-e^(-0.173868*5)=0.57955
=>
interpretation: probability of having a headache in 5 days = 0.57955
Therefore
probability of NOT having a headache in 5 days is (1-0.57955)=0.42045
A regular hexagon has a side of 18 cm, find the area of the regular polygon
Answers
This figure consists of a rectangle and semicircle.
What is the perimeter of this figure?
Use 3.14 for pi.
19.42 cm
20.28 cm
23.42 cm
32.84 cm
Answers
1. for the semicircle p₁=πr=3.1415*3≈9.4248 cm., where r=3 radius of the semicircle;
for the rectangle p₂=4*2+6=14 cm.
2. totaly: p=p₁+p₂=14+9.4248≈23.4248 cm.
answer: 23.42 cm.
Answer:
The perimeter of the figure is [tex]23.42\ cm[/tex]
Step-by-step explanation:
we know that
The perimeter of the figure is equal to the perimeter of the rectangle plus the circumference of a semicircle minus the length of [tex]6\ cm[/tex]
Step 1
Find the perimeter of rectangle
The perimeter of rectangle is equal to
[tex]P=2(L+W)[/tex]
In this problem we have
[tex]L=6\ cm[/tex]
[tex]W=4\ cm[/tex]
substitute
[tex]P=2(6+4)=20\ cm[/tex]
Step 2
Find the circumference of a semicircle
The circumference of a semicircle is equal to
[tex]C=\pi r[/tex]
we have
[tex]r=6/2=3\ cm[/tex] -----> the radius is half the diameter
substitute
[tex]C=3\pi\ cm[/tex]
Step 3
Find the perimeter of the figure
[tex]20\ cm+3\pi\ cm-6\ cm=(20+3.14*3-6)=23.42\ cm[/tex]