Answer:
The answer is :
DDStep-by-step explanation:
Axis of symmetry is the equation where it cuts the middle of the quadratic graph.
For quadratic equation in the form of (x+a)² + b, the axis of symmetry will be (x+a) = 0 which is x = -a :
Question 1,
[tex](x + 3) = 0[/tex]
[tex]x = - 3[/tex]
Question 2,
[tex](y - 4 )= 0[/tex]
[tex]y = 4[/tex]
Answer:
[tex]\boxed{x=-3} \\ \boxed{y=4}[/tex]
Step-by-step explanation:
Axis of symmetry is a line that cuts the parabola in half touching the vertex.
Quadratic forms ⇒ y = ax² + bx + c or x = ay² + by + c
Axis of symmetry ⇒ x = [tex]\frac{-b}{2a}[/tex] or y = [tex]\frac{-b}{2a}[/tex]
First problem:
y = -3(x+3)²-2
Write in quadratic form ⇒ y = ax² + bx + c
y = -3(x² + 6x + 9) - 2
y = -3x² -18x - 27 - 2
y = -3x² -18x - 29
a = -3, b = -18
Find axis of symmetry.
[tex]x= \frac{-b}{2a}[/tex]
[tex]x=\frac{--18}{2(-3)}[/tex]
[tex]x=\frac{18}{-6}=-3[/tex]
Second problem:
x = -4(y -4)² +6
Write in quadratic form ⇒ x = ay² + by + c
x = -4(y² - 18y + 16) + 6
x = -4y² + 32y - 64 + 6
x = -4y² + 32y - 58
a = -4, b = 32
Find axis of symmetry.
[tex]y= \frac{-b}{2a}[/tex]
[tex]y=\frac{-32}{2(-4)}[/tex]
[tex]y=\frac{-32}{-8}=4[/tex]
What is the quotient in polynomial form?
Answer:
Step-by-step explanation:
We are given the polynomial [tex]x^3+2^2-2x+3[/tex] and we are dividing by (x+3). So by performing one step of synthetic division we get
1 2 -2 3|-3
-3 3 -3
1 -1 1 0
So the quotient in polynomial form is [tex]x^2-x+1[/tex]
Evaluate the expression 23^0-15^1+18^0+(43-12)
Answer:
18
Step-by-step explanation:
23^0 - 15^1 + 18^0 + (43 - 12) =
= 1 - 15 + 1 + 31
= -14 + 1 + 31
= -13 + 31
= 18
here is the picture pls answer another for my lil friend lol
Answer:
Hey there!
The perimeter can be expressed as 140+140+68[tex]\pi[/tex]
This is equal to 493.52 m
Hope this helps :)
A small company that manufactures snowboards uses the relation below to model its profit. In the model,
represents the number of snowboards in thousands, and P represents the profit in ten thousands of dollars.
What is the maximum profit the company can earn? How many snowboards must it produce to earn this
maximum profit?
a. Factor P =
4x2 + 32x + 336 to find the roots.
b. Find the axis of symmetry then use it to find the vertex.
c. Therefore, we need to see snowboards to make a maximum profit of
Answer:
a) x₁ = 14
x₂ = - 6
b) x = 4
c) P(max ) = 4000000 $
Step-by-step explanation:
To find the axis of symmetry we solve the equation
a) -4x² + 32x + 336 = 0
4x² - 32x - 336 = 0 or x² - 8x - 84 = 0
x₁,₂ = [ -b ± √b² -4ac ]/2a
x₁,₂ = [ 8 ±√(64) + 336 ]/2
x₁,₂ = [ 8 ± √400 ]/2
x₁,₂ =( 8 ± 20 )/2
x₁ = 14
x₂ = -6
a) Axis of symmetry must go through the middle point between the roots
x = 4 is the axis of symmetry
c) P = -4x² + 32x + 336
Taking derivatives on both sides of the equation we get
P´(x) = - 8x + 32 ⇒ P´(x) = 0 - 8x + 32
x = 32/8
x = 4 Company has to sell 4 ( 4000 snowboard)
to get a profit :
P = - 4*(4)² + 32*(4) + 336
P(max) = -64 + 128 + 336
P(max) = 400 or 400* 10000 = 4000000
i need help emergrncy shots fire shots fire we neeed all back ups
Answer:
a = 9h + bn
Step-by-step explanation:
total = $9 an hour + (bonus x number of items repaired)
Country X (a developed country) currently has a per capita ecological footprint of 3.2 hectares, while country Y (a developing country) has a per capita ecological footprint of 0.6 hectare. If everybody in the world has an ecological footprint the size of the average footprint between these two countries and there are ~7 billion people on Earth, how many total hectares would be needed
Answer:
Total hectares needed = 13.3 billion hectares of ecological footprint.
Step-by-step explanation:
Country X's per capita ecological footprint = 3.2 hectares
Country Y's per capita ecological footprint = 0.6 hectares
Earth's population = 7 billion
Average footprint between the two nations = 1.9 (3.2 + 0.6) hectares
If everybody in the world (i.e. the earth's population) has an ecological footprint the size of the average footprint between these two countries, i.e. = 1.9 per capita of earth's population,
Therefore, the total hectares of ecological footprint needed will be equal to 7 billion x 1.9
= 13.3 billion hectares of ecological footprint.
In a sequence, the 40th term is 70, the 41st term is 72 and the 42nd term is 74.
a) State the term-to-term rule
b) Work out the first term
c) Work out the 80th term
Answer:
term to term rule is +2
The first term is -8
80th term is 150
Step-by-step explanation:
70 to 72 is adding 2
72 to 74 is adding 2
term to term rule is +2
The equation for a sequence like this is
xn = a + d(n−1)
where n is the term number a is the first term and d is the term to term rule
Using the 40th term is 70
70 = a + 2( 40-1)
70 = a + 2( 39)
70 = a + 78
Subtract 78 from each side
-8 = a
The first term is -8
80th term
xn = a + d(n−1)
x80 = -8 +2 (80-1)
= -8+2(79)
= -8+158
= 150
need help with this question
Answer:
[tex] - 2 {x}^{5} {y}^{7} [/tex]Last option is correct.
Step-by-step explanation:
[tex] - 2 {x}^{3} {y}^{4} {x}^{2} {y}^{3} [/tex]
Multiply the terms with the same base by adding their exponents
[tex] - 2 {x}^{3 + 2} {y}^{4 + 3} [/tex]
Add the numbers
[tex] - 2 {x}^{5} {y}^{7} [/tex]
Hope this helps..
Best regards!
[tex] - 2 {x}^{5} {y}^{7} [/tex]
Solution:
[tex] - 2 {x}^{3} {y}^{4} {x}^{2} {y}^{3} [/tex]
[tex] = 2 {x}^{(3 + 2)} {y}^{(4 + 3)} [/tex]
[tex] = - 2 {x}^{5} {y}^{7} [/tex]
[tex]{\boxed{\blue{\textsf{Some Important Laws of Indices}}}}[/tex]
[tex]{a}^{n}.{a}^{m}={a}^{(n + m)} [/tex]
[tex]{a}^{-1}=\dfrac{1}{a}[/tex]
[tex]\dfrac{{a}^{n}}{ {a}^{m}}={a}^{(n-m)}[/tex]
[tex]{({a}^{c})}^{b}={a}^{b\times c}={a}^{bc}[/tex]
[tex] {a}^{\frac{1}{x}}=\sqrt[x]{a}[/tex]
[tex]a^0 = 1[/tex]
[tex][\text{Where all variables are real and greater than 0}][/tex]
What is the average rate of change of f(x)=-2/x^2 when the interval is 1 to 2
Answer:
1.5
Step-by-step explanation:
average rate of change = (f(x2) - f(x1))/(x2 - x1)
f(x) = -2/x^2
f(x2) = f(2) = -2/(-2)^2 = -2/4 = -0.5
f(x1) = f(1) = -2/1^2 = -2
average rate of change = (-0.5 - (-2))/(2 - 1)
average rate of change = (-0.5 + 2)/1
average rate of change = 1.5
Write the equation of the function of a parabola with vertex at (–1,–2) and a point (1,–6) that lies on the curve.
Answer:
f(x) = -(x + 1)² - 2
Step-by-step explanation:
f(x) = a(x - h)² + k
-6 = a(1 - -1)² + -2
-6 = a(4) -2
-4 = 4a
a = -1
f(x) = -(x + 1)² - 2
PLEASE ANSWER FAST PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! The point (1, −1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.
Answer:
sin = -√2 / 2
cos = √2 / 2
tan = -1
Step-by-step explanation:
Θ is in quad IV
sin = -√2 / 2
cos = √2 / 2
tan = -1
Solve the inequality. –10d ≥ –70
Answer:
d≤7
Step-by-step explanation:
-10d≥-70
d≤7
the sum of two numbers is -26. One number is 148 less than the other. Find the numbers
Answer:
61 and -87
Step-by-step explanation:
If the numbers are x and x - 148, we can write the following equation:
x + x - 148 = -26
2x - 148 = -26
2x = 122
x = 61 so x - 148 = 61 - 148 = -87
A spinner has 4 equal sectors with tour options Dubai, Seoul, Switzerland, and Paris. What is the probability of landing on Seoul or Paris after spinning spinner
The probability of landing on Seoul or Paris after spinning spinner is 1/2 .
What is Probability ?Probability is the measure of likeliness of an event to happen.
It is given that
Total Outcomes = 4 ( Dubai, Seoul, Switzerland, and Paris)
the probability of landing on Seoul or Paris after spinning spinner = ?
The probability of Landing on Seoul P(S) is 1 /4
The probability of Landing on Paris P(P) is 1 /4
The probability of landing on Seoul or Paris after spinning spinner is
P( S∪P) = P(S) + P(P)
= (1/4) + (1/4)
= 1/2
Therefore , The probability of landing on Seoul or Paris after spinning spinner is 1/2 .
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Planes A and B intersect.
Which describes the intersection of line m and line n?
P
point W
point X
m
2
n
2
point y
X
w
Y
point Z
V
Answer:
Point W
Step-by-step explanation:
Planes A and B intersect at an angle. Intersection of lines is when two lines meets at a particular point and cuts each other at the same point. Its a measure of perpendicularity for right angles and greater or lesser for others.
At any point W, line m and line n cuts each other at point W to form an angle as shown from the diagram.
Which linear function represents the line given by the point-slope equation y-8 = {(x - 4)?
O f(x)=x+4
Of(x)= x+6
O fx) = x-10
O f(x) = {x-12
Answer:
[tex]f(x) = x + 4[/tex]
Step-by-step explanation:
[tex]y - 8 = x - 4[/tex]
Add 8 to both sides to isolate the y
[tex]y = x - 4 + 8[/tex]
then you're left with y = x + 4
Solve for X. Pls help asap
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{12}}}}}[/tex]
Step-by-step explanation:
hypotenuse ( h ) = x
Peendicular ( p ) = 10
base ( b ) = 22
Using the Pythagoras theorem
[tex] \boxed{ \sf{ {h}^{2} = {p}^{2} + {b}^{2} }}[/tex]
[tex] \dashrightarrow{ \sf{ {x}^{2} = {10 }^{2} + {22}^{2} }}[/tex]
[tex] \dashrightarrow{ \sf{ {x}^{2} = 100 + 44}}[/tex]
[tex] \dashrightarrow{ \sf{ {x}^{2} = 144}}[/tex]
[tex] \dashrightarrow{ \sf{ \sqrt{ {x}^{2} } = \sqrt{144}}} [/tex]
[tex] \dashrightarrow{ \sf{x = 12}}[/tex]
Hope I helped!
Best regards! :D
What is the solution, if any, to the inequality |3x|≥0?
Answer:
Infinitely many solutions
Step-by-step explanation:
Any value of x will make this inequality true, hence there are infinitely many solutions. Another way to say this is True for all x on the interval [-infinite,+infinite]
The reason this is true, is because all values of an absolute value will be greater than or equal to 0.
Cheers.
That's weird !
X is ANY NUMBER !
-∞ ≤ X ≤ ∞
Solve the equation for X. 2(2x-4)=3(x+4) A -4 B 4 C 20 D 6
Answer:
X=20
Step-by-step explanation:
The answer is C
Find the first four terms of the sequence given a1=31 and an+1=an−3
Step-by-step explanation:
Given the formula
a(n+1)=an−3
The first term a(1) = 31
For the second term
a(2)
We have
a( 1 + 1) = a(1) - 3
a(2) = 31 - 3
a(2) = 28
For the third term
a(3)
We have
a(2+1) = a(2) - 3
a(3) = 28 - 3
a(3) = 25
For the fourth term
a(4)
That's
a(3+1) = a(3) - 3
a(4) = 25 - 3
a(4) = 22
Hope this helps you
Helen has 48 cubic inches of clay to make a solid
square right pyramid with a base edge measuring 6
inches.
Which is the slant height of the pyramid if Helen uses all
the clay?
O 3 inches
O4 inches
O 5 inches
O 6 inches
6 in
Save and Exit
Next
Submit
Mark this and return
Answer:
4 inches.
Step-by-step explanation:
The formula for the volume of a pyramid is v=1/3bh.
V is the volume of the shape
1/3 is just a rational number or fraction.
b is the area of the base shape of the 3d shape
h is the height of the shape (slant height).
The general formula for the volume of all shapes is V=Bh
V is the volume
B is the area of the base
h is the height of the prism.
In this case, we have a pyramid, so let's use the formula V=1/3Bh.
We know what the volume so 48=?
We can put 1/3 so 48=1/2 times ? times ?.
The base shape of this pyramid is a square, and it has an edge of 6 inches. We need to find the area of that square because it is the area of our base. the formula for finding the area of a square is A=S squared.
A is the area of the shape
S is the side length.
The reason why it is squared is because all sides of a square are equal to each other. Since the base edge is 6 inches, the other edges are 6 inches as well. There are 4 edges in a square.
A= 6 times 6.
A=36.
We have the area of the base, so we can put 48=1/3 times 36 times ?.
We are finding what the slant height is, so let's put the letter "h" to represent the slant height.
Now, 48=1/3 times 36 times h.
All we have to do is solve for h.
First we have to simplify one side of the equation.
To simplify, we have to do 1/3 times 36, or you can do 36 divided by 3. It is your choice. 36 divided by 3 is 12.
Now we have 12h=48.
Isolate h by dividing both sides by 12. 12h divided 12 is h. 48 divided by 12 is 4.
Therefore h=4 inches. The reason we divide both sides is because we have to do the inverse operation of the original equation. For instance 12h=48. To get to 48, you do 12 times h. We take the inverse (opposite) operation of multiplication (division). That will isolate for h.
The slant height of this square pyramid is 4 inches.
Hope this helps. Have a good rest of your day!
The slant height of the pyramid is 4 inches. Therefore, the option B is the correct answer.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, volume of square right pyramid = 48 cubic inches and base edge measuring 6 inches.
We know that, the volume of square based pyramid =a²h/3.
Here, a=6 inches and h=slant height
Now, 48= (6²×h)/3
48=36h/3
48=12h
h=4 inches
Therefore, the option B is the correct answer.
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Write an equation and then solve each word problem: My computer can download a movie in 5 hours. If I install an extra processor it can download the movie in 4 hours. How long, working alone, would it have taken the new extra processor to download the movie? Pls help me within 10 minutes
Answer:
The new extra processor would take 20 hours to download the movie.
Step-by-step explanation:
This word problem presents two variables: [tex]n[/tex] - Processing capacity, dimensionless; [tex]t[/tex] - Download time, measured in hours. Both variables exhibit a relationship of inverse proportionality, that is:
[tex]t \propto \frac{1}{n}[/tex]
[tex]t = \frac{k}{n}[/tex]
Where [tex]k[/tex] is the proportionality constant.
Now, let suppose that original processor has a capacity of 1 ([tex]n = 1[/tex]), the proportionality constant is: ([tex]t = 5\,h[/tex])
[tex]k = n\cdot t[/tex]
[tex]k = (1)\cdot (5\,h)[/tex]
[tex]k = 5\,h[/tex]
The equation is [tex]t = \frac{5}{n}[/tex] and if time is reduced to 4 hours by adding an extra processor, the processing capacity associated with this operation is: ([tex]t = 4\,h[/tex])
[tex]n = \frac{5}{t}[/tex]
[tex]n = \frac{5\,h}{4\,h}[/tex]
[tex]n = 1.25[/tex]
Then, the extra processor has a capacity of 0.25. The time required for the new extra processor to download the movie is: ([tex]n = 0.25[/tex])
[tex]t = \frac{5\,h}{0.25}[/tex]
[tex]t = 20\,h[/tex]
The new extra processor would take 20 hours to download the movie.
20x^3+8x^2-30x-12 Rewrite the expression as the product of two binomials.
Answer:
see below
Step-by-step explanation:
20x^3+8x^2-30x-12
Factor out the greatest common factor 2
2 (10x^3+4x^2-15x-6)
Then factor by grouping
2 ( 10x^3+4x^2 -15x-6)
Factor out 2 x^2 from the first group and -3 from the second group
2 ( 2x^2( 5x+2) -3( 5x+2))
Factor out ( 5x+2)
2 ( 5x+2) (2x^2-3)
The 2 can go in either term to get binomials
( 10x +4) (2x^2-3)
or ( 5x+2) ( 4x^2 -6)
Answer:
[tex](10x+4)(2x^2 -3)[/tex]
Step-by-step explanation:
[tex]20x^3+8x^2-30x-12[/tex]
Rewrite expression (grouping them).
[tex]20x^3-30x+8x^2-12[/tex]
Factor the two groups.
[tex]10x(2x^2 -3)+4(2x^2 -3)[/tex]
Take the common factor from both groups.
[tex](10x+4)(2x^2 -3)[/tex]
a) John is 3 years older than his brother Brian, the product of their ages is 54 i) Express this information in equation form ii) Show this information as a quadratic equation iii) Hence, solve the equation to find their individual ages.
Answer:
John is 9, Brian is 6.
Step-by-step explanation:
I)
Let [tex]J[/tex] represent John's age and [tex]B[/tex] represent Brian's age.
John is three years older than Brian. In other words:
[tex]J=B+3[/tex]
The product of their ages is 54. Or:
[tex]JB=54[/tex]
II)
Write this as a quadratic by substituting:
[tex]JB=54\\(B+3)B=54\\B^2+3B-54=0[/tex]
III)
Solve the quadratic:
[tex]B^2+3B-54=0\\B^2-6B+9B-54=0\\B(B-6)+9(B-6)=0\\(B+9)(B-6)=0\\B=-9, 6[/tex]
Since age cannot be negative, Brian must be 6 years old right now.
John is three year older, so John is 9.
Strontium 90 is a radioactive material that decays according to the function Upper A (t )equals Upper A 0 e Superscript negative 0.0244 t Baseline commaA(t)=A0e−0.0244t, where Upper A 0A0 is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 500500 grams of strontium 90. (a) What is the decay rate of strontium 90?
Answer:
Decay rate K = -2.44%
Step-by-step explanation:
From the question, we want to know the decay rate of strontium 90
Mathematically, this is accessible from its decay equation
From the decay equation, we can see that that ;
At = Ao e^-0.0244t
Generally, the decay equation of a radioactive sample can be written as
At = Ao e^-kt
where K represents the decay constant
From the equation, we can see that;
k = 0.0244 which when represented as a percentage is 2.44%
Since it’s a decay we can say that the decay rate is -2.44%
The answer is : -2.44%
A certain variety of pine tree has a mean trunk diameter of y = 150 cm and a
standard deviation of o = 30 cm.
A certain section of a forest has 500 of these trees.
Approximately how many of these trees have a diameter smaller than 120 cm?
Answer:
80 trees have a diameter smaller than 120cm
Step-by-step explanation:
Step 1
To solve this question, we would make use of the Z score formula.
z = x - μ/σ
Where
z = z score
x = Raw score = 120cm
μ = Population mean = 150cm
σ = Population standard deviation = 30cm
Hence,
z =120 - 150/30
z = -1
The z score = -1
Step 2
We find the Probability of the calculated z score using the z score table.
P(z) = P(z = -1) = P(x<120) = 0.15866
Approximately to the nearest hundredth = 0.16
Converting to percentage = 0.16 × 100 = 16%
The percentage of trees with a diameter smaller than 120cm = 16%
Therefore, the number of trees with a diameter smaller than 120cm
= 16% × 500 trees = 80trees
The charge to rent a trailer is $2525 for up to 2 hours plus $99 per additional hour or portion of an hour. Find the cost to rent a trailer for 2.82.8 hours, 33 hours, and 8.78.7 hours. Then graph all ordered pairs, (hours, cost), for the function.
The question is not written properly! Complete question along with answer and step by step explanation is provided below.
Question:
The charge to rent a trailer is $25 for up to 2 hours plus $9 per additional hour or portion of an hour.
Find the cost to rent a trailer for 2.8 hours, 3 hours, and 8.7 hours.
Then graph all ordered pairs, (hours, cost), for the function.
Answer:
ordered pair = (2.8, 34)
ordered pair = (3, 34)
ordered pair = (8.7, 88)
Step-by-step explanation:
Charge for 2.8 hours:
$25 for 2 hours
$9 for 0.8 hour
Total = $25 + $9
Total = $34
ordered pair = (2.8, 34)
Charge for 3 hours:
$25 for 2 hours
$9 for 1 hour
Total = $25 + $9
Total = $34
ordered pair = (3, 34)
Charge for 8.7 hours:
$25 for 2 hours
$9 for 1 hour
$9 for 1 hour
$9 for 1 hour
$9 for 1 hour
$9 for 1 hour
$9 for 1 hour
$9 for 0.7 hour
Total = $25 + $9 + $9 + $9 + $9 + $9 + $9 + $9
Total = $88
ordered pair = (8.7, 88)
The obtained ordered pairs are graphed, please refer to the attached graph.
7987.1569 to the nearest thousandth
Answer:
7987.1569 to the nearest thousandths is 7987.157
Step-by-step explanation:
Choose the correct equation for the parabola based on the given information. Given: Focus:(4,-3) Vertex: (-2,-3) a. 24(y+3) = (x+2)^2 b. 24(x+2)=(y+3)^2 c. 6(x-4)= (y+3)^2 d. 6(y+3)=(x-4)^2
Answer: b. 24(x + 2) = (y + 3)²
Step-by-step explanation:
Vertex: (-2, -3)
Focus: (4, -3)
↓
same y-value so equation will be y²
Equation: a(x - h) = (y - k)²
a = 4p where p is the distance from Vertex to Focush is the x-coordinate of the Vertexk is the y-coordinate of the VertexGiven: h = -2, k = -3, a = 4[4 - (-2)] --> a = 24
Input those values into the equation: 24(x + 2) = (y + 3)²
What is closest to the area of this section of the garden?
Answer:
117.984ft^2
Step-by-step explanation:
To find the area of a circle the formula is PiR^2 so the area for the full 360 degree circle is. 530.929 ft^2.
Now that we know this we can use a ratio.
530.929/360=x/80
u divide out the left side and multiply it by 80.
so that shows that the area of this circle is
117.984ft^2