i don't have much time left could someone help me super quickly (trinomials) btw you could get extra 50 points from a previous question on my profile (only if you want) i would really appreciate if i could have help understanding things
Answers
Answer:
(a) [tex](x-2)(x+4)[/tex]
zeros: x = 2, x = -4
vertex: (-1, -9)
(b) [tex]-(x+2)(x+7)[/tex]
zeros: x = -2, x = -7
vertex = (-4.5, 6.25)
Step-by-step explanation:
To factor a quadratic in the form [tex]ax^2+bx+c[/tex]:
Find 2 two numbers (d and e) that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]Rewrite [tex]b[/tex] as the sum of these 2 numbers: [tex]d+e=b[/tex]Factorize the first two terms and the last two terms separately, then factor out the comment term.To find zeros of a factored quadratic in the form [tex](ax+b)(cx+d)[/tex]
Set each of the parentheses to zero and solve for [tex]x[/tex]The midpoint between the two zeros is the x-coordinate of the vertex. To find the y-coordinate of the vertex, substitute this into the given equation.
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Question (a)
Factored
Factor [tex]y=x^2+2x-8[/tex]
[tex]ac=-8[/tex] and [tex]d+e=2[/tex]
[tex]\implies d=4[/tex] and [tex]e=-2[/tex]
Rewrite [tex]2x[/tex] as [tex]+4x-2x[/tex]:
[tex]\implies x^2+4x-2x-8[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies x(x+4)-2(x+4)[/tex]
Factor out common term [tex](x+4)[/tex]:
[tex]\implies (x-2)(x+4)[/tex]
Zeros
[tex]\implies (x-2)=0\implies x=2[/tex]
[tex]\implies (x+4)=0\implies x=-4[/tex]
Vertex
[tex]\sf x-value=\dfrac{2+(-4)}{2}=-1[/tex]
[tex]\sf y-value=(-1)^2+2(-1)-8=-9[/tex]
Vertex = (-1, -9)
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Question (b)
Factor [tex]y=-x^2-9x-14[/tex]
[tex]ac=14[/tex] and [tex]d+e=-9[/tex]
[tex]\implies d=-7[/tex] and [tex]e=-2[/tex]
Rewrite [tex]-9x[/tex] as [tex]-7x-2x[/tex]:
[tex]\implies -x^2-7x-2x-14[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies -x(x+7)-2(x+7)[/tex]
Factor out common term [tex](x+7)[/tex]:
[tex]\implies (-x-2)(x+7)[/tex]
Factor [tex](-x-2):-(x+2)[/tex]
[tex]\implies -(x+2)(x+7)[/tex]
Zeros
[tex]\implies -(x+2)=0\implies -x-2=0 \implies x=-2[/tex]
[tex]\implies (x+7)=0\implies x=-7[/tex]
Vertex
[tex]\sf x-value=\dfrac{-2-7}{2}=-4.5[/tex]
[tex]\sf y-value=-(-4.5)^2-9(-4.5)-14=6.25[/tex]
Vertex = (-4.5, 6.25)
Related Questions
Sophia goes to an icecream shop to get a medium ice cream that costs $4.50, Sophia only has $6.40 and toppings are $0.75 each. Write an inequality to find how many toppings Sophia can get .
Answers
Answer:
x ≤ 2
Step-by-step explanation:
4.5 = medium ice cream
0.75x = toppings, x = amount of toppings
Sophia has $6.4, so 4.5+0.75x has to be less or equal to that.
4.5 + 0.75x ≤ 6.4, solve
0.75x ≤ 1.9
x ≤ 2 8/15
BUT you cannot get half a topping or a fraction of a topping,
so, x ≤ 2 toppings.
Sophia can get 2 or less toppings.
true or false in order to find the surface area of a cube you could find the area of one face and multiply by six
Answers
Answer:
True
Step-by-step explanation:
The surface area of a cube is the total area on each side of the cube. SInce there are 6 sides of a cube, the surface area is equal to six times the area of one of the sides, because they are all the same.
The table below represents the scores of ten students in Ms. Williams’s class on a math and science test.
Answers
Answer: the answer is A or the 1st one
Step-by-step explanation:
Answer:
the answer is the frist one
Step-by-step explanation:
write the inequality from the given number line.
Answers
Answer:
[tex]3 \leqslant - 3[/tex]
(-x^2 -2) + (2x^2 + -1)
Answers
Answer:36
Step-by-step explanation:
x2 - 10x + 25 = 0 2x2 - 2x - 5 = 0 x2 - 16x = 36. This problem has been solved!
Find the volume of the prism.
A drawing of a rectangular prism. It has length 1 foot, width mixed number one and one third feet and height one-half foot.
The volume is
cubic feet.
Answers
Answer:
2 thirds, or 0.666666666667
Step-by-step explanation:
In an arithmetic sequence of numbers a1 = -4 and a6 = 46. Which of the following is the value of a12?
Answers
Answer:
a₁₂ = 106
Step-by-step explanation:
Given
a₁ (first term) = -4a₆ = 46Formula for nth term
aₙ = a₁ + (n - 1)dUsing that to expand a₆ and find d
a₆ = a₁ + (n - 1) d46 = -4 + (6 - 1)d50 = 5dd = 10Finding a₁₂
a₁₂ = a₁ + 11da₁₂ = -4 + 11(10)a₁₂ = 110 - 4a₁₂ = 106Answer:
[tex]a_{12}=106[/tex]
Step-by-step explanation:
Arithmetic sequence
General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termd is the common difference between termsGiven:
[tex]a_1=-4[/tex][tex]a_6=16[/tex]To find the common difference (d), substitute the given values into the general formula and solve:
[tex]\begin{aligned}\implies a_6=(-4)+(6-1)d & =46\\ 5d-4 & =46\\ 5d & = 50\\ d & =10\end{aligned}[/tex]
Therefore, the equation for the nth term is:
[tex]\begin{aligned}a_n &=-4+(n-1)10\\& =10n-14 \end{aligned}[/tex]
To find the 12th term, substitute n = 12 into the equation:
[tex]\implies a_{12}=10(12)-14=106[/tex]
NEED HELP WITH THIS QUESTION QUICK!!!
Answers
Answer:
56 degrees
90-34=56
Right-angle triangle, so the 2 angles should add to 90 to make 180 degrees
Hope this helps!
A tabletop in the shape of a trapezoid has an area of 7,367 square centimeters. Its longer base measures
127 centimeters, and the shorter base is 85 centimeters. What is the height?
The height of the tabletop is
centimeters.
Answers
Answer:
69.5 cm
Step-by-step explanation:
Area trapezoid = 1/2 (b1+b2) * h = 7367
1/2(127+85) h = 7367 h=
fifty million of 94 million households watched the last episode of a popular television show. What percentage of households were not watching the show?
Answers
The percentage of households that were not watching the show were 46.81%.
Step-by-step explanation:In this case, we need to find the percentage of households that don´t watch the show. First, we need to know how much households don´t watch the show, this is:
[tex]94,000,000-50,000,000=44,000,000[/tex]
So, the households that were not watching the show were 44 million.
Now we can calculate the percentage, to find a percentage we use a division and to introduce the percentage units we multiply by 100.
[tex]\frac{44,000,000}{94,000,000}[/tex] × [tex]100=46.81[/tex]The percentage of households that were not watching the show were 46.81%.
The base of a prism are right triangles with leg lengths of 7 inches and 5 inches. the prism height is 12 inches. what is the volume of the prism?
A 105
B 203
C 210
D 420 [but we know for certain d is wrong]
Answers
Answer:
The volume formula is length x width x height. 7x5x12=420 cubic inches
Step-by-step explanation:
A rectangle has one side equal to (2x+4) cm and a perimeter of (6x+4) cm. What is the area of the rectangle in terms of x?
Answers
The area of the rectangle in terms of x is 2x² - 8
A rectangle is a quadrilateral with four right angles in the Euclidean plane.
A region's size on a flat or curved surface is expressed in terms of area, a unit of measurement. A surface region or plane area is the area of an open surface or the boundary of a three-dimensional object, whereas a plane region or area refers to the area of a form or planar lamina.A perimeter is a closed path that surrounds, encircles, or defines a length in one dimension or a shape in two dimensions.Given one side of the rectangle is 2x+4 and the perimeter is 6x+4
Let the other side be y.
We know that:
perimeter = 2 × (sum of two sides)
or, 6x + 4 = 2 (2x+4+y)
or,6x + 4 = 4x + 8 + 2y
or, 2x - 4 = 2 y
or, y = x - 2
Now area of the rectangle = product of sides = (x - 2)(2x+4)
Area = 2x² - 4x + 4x - 8
or, Area = 2x² - 8
Hence the area of the rectangle in terms of x is 2x² - 8
to learn more about area visit:
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The manufacturer of color televisions can sell 1900 sets to his dealers at $575 each. If the price is $470, he can sell 2600 sets. The total cost of producing x television sets is C(x)=3300+608x−0.09x^2. Assuming the demand function is linear, find the price per set that will maximize profit. Round your answer to the nearest cent, if necessary.
Answers
Answer:
$545
Step-by-step explanation:
Finding the price that maximizes profit requires several steps. We need the demand function that tells quantity sold in terms of selling price. With this, we can express the cost and revenue functions in terms of selling price. The profit will be the difference between revenue and cost.
__
demandThe demand (q) is said to be a linear function of price (p). The equation for that can be written ...
q(p) = (q2 -q1)/(p2 -p1)(p -p1) +q1 . . . . . for two points (p1, q1) and (p2, q2)
Using the given demand points, this can be ...
q(p) = (1900 -2600)/(575 -470)(p -470) +2600
q(p) = -20/3(p -470) +2600
q(p) = -20/3p +5733 1/3
__
costThe cost function in terms of selling price can be found by substituting the q(p) equation for x in c(x). For the purpose of finding the maximum profit, we only need the marginal cost function:
c(q(p))' = c'(q(p))·q'(p) = (608 -0.18(q(p)))·(-20/3) = (608 -0.18(-20/3p +5733 1/3))(-20/3)
c'(p) = -8p +2826 2/3
__
revenueAs with cost, the function we need for finding the maximum profit is the marginal revenue function. Revenue is the product of price and demand, so the marginal revenue is ...
r(p) = p·q(p)
r'(p) = q(p) +p·q'(p) = (-20/3p +5733 1/3) +p(-20/3)
r'(p) = -40/3p +5733 1/3
__
maximum profitThe maximum profit is found where the marginal profit is zero. In turn, that is found where the difference between marginal revenue and marginal cost is zero:
P = R -C
P'(p) = 0 = r'(p) -c'(p) = (-40/3p +5733 1/3) -(-8p +2826 2/3)
0 = -16/3p +2906 2/3
16p = 8720 . . . . . multiply by 3, add 16p
p = 545 . . . . . . . price for maximum profit
The price per set that maximizes profit is $545.00.
Natalie Albert deposited checks totaling $1,735,97 into her savings account. She withdrew $100.00 while
depositing some coins. If her total deposit was $1,668.71, how much did Natalie deposit in coins?
Answers
1735.97-100=1635.97
1668.71-1635.97=32.74
Natalie Albert deposited checks totaling $1,735,97 into her savings account, she withdrew $100.00 while depositing some coins. If her total deposit was $1,668.71 then Natalie deposited $32.74 in coins.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let's call the amount Natalie deposited in coins "x".
We know that her total deposit was $1,668.71,
so we can write an equation:
1,735.97 - 100.00 + x = 1,668.71
Simplifying, we get:
1,635.97 + x = 1,668.71
Subtracting 1,635.97 from both sides, we get:
x = 32.74
Therefore, Natalie deposited $32.74 in coins.
To learn more on Equation:
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A researcher is studying the relationship between stress and diet among college students. The researcher recruits students by sending out an e-mail blast, and then includes in the sample the first 100 male and 100 female students who volunteer to participate. What type of sampling did the researcher use
Answers
Using sampling concepts, it is found that convenient sampling was used by the researcher to find the volunteers to participate.
How are samples classified?Samples may be classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.In this problem, the first 100 male and first 100 female students sampled are the ones who volunteer to participate, and volunteering is associated with convenient sampling.
More can be learned about sampling concepts at https://brainly.com/question/25122507
In 3x2 + 1 = 13, what is x called?
A
Coefficient
B
Expression
C
Variable
D
Range
Answers
Answer:
According to this problem, i would say the answer is c
Step-by-step explanation:
a variable examples are letters such as x, y, z, n
PLEASE HELP i realy don’t understand this at all
Answers
Check the picture below, recall that the radius of a circle is always the same length in the circle.
Using substitution, what is the solution for the system of equations below?
Answers
Hey there!
Substitute x = 2 to y = 3x - 1
=> y = 3(2) -1
=> y = 6 - 1
=> y = 5
x = 2,y = 5
Find the volume of the specified cone. Use 3.14 for , and round your answer to the nearest whole numbe
Diameter = 3 cm, Height = 7 cm
a 44 cu, cm
b. 66 cu, cm
c. 99 cu, cm
d 16 cu, cm
Answers
Answer:
Your answer is D 16 cu, cm
Step-by-step explanation:
In which direction does the parabola defined by the equation x = 2y^2 – 4 open?
Answers
Answer:
Upward
Step-by-step explanation:
Upward the graph looks like the above picture.
Base in your answer on exploration, what relationship exist between 30o
and 150o, 45o, and135o, and 60o and 120o?
Answers
Answer:
they all have a factor of 5
Step-by-step explanation:
The sum of two number is −16. One number is 20 less than the other. Find the numbers.
Answers
Answer:
-50 is your answer it is really easy just try to get -50
Help picture below problem 12 will give brainlest
Answers
Answer:
68°
Step-by-step explanation:
triangle ODB is congruent to triangle FIL. Therefore, angle L is equal to angle B. So angle L is 68°
If a kid is 120 cm tall and grows 4 percent taller how tall is he
Answers
im so sorry if im wrong, i hope u have a amazing day:)
Help help help math math
Answers
Answer:
Yes
Step-by-step explanation:
The relation here is we see that the y value is 1 less than the x value.
So, the function can be written as :
y = x - 1And this is clearly a linear functionAldreba 2
Show all work
Answers
Answer:
rewrite f(g(-2))
plug in -2 in g(x)
g(x)=-2-3
g(x)=-5
now plug in -5 into f(x)
f(x)=-5^2
f(x)=25
25 is the answer
Answer:
-2x^3+6x^2
or simplified : -2x^2(x-3)
Step-by-step explanation:
Rewrite the statement as:
[tex]((x^2)(x-3))(-2)\\[/tex]
Distribute:
[tex](x^2*x-3*x^2)(-2)\\(-2)(x^3-3x^2)\\-2x^3+6x^2[/tex]
simplify by taking a common factor out, in this case, -2x^2:
[tex]-2x^2(x-3)[/tex]
50 PTS I WILL MARK BRAINLIEST PLS HELP! A book store manager took several random surveys of customers to determine which book genre they purchased most frequently. This table shows the average of each survey.
Based on the data shown in the table, which conclusions can be made about the frequency that customers purchase a genre?
Select each correct answer.
On average, 1 out of 6 customers purchase fantasy books most frequently.
On average, 24% of the customers purchase autobiographies most frequently.
On average, 22% of the customers purchase romance books most frequently.
On average, 2 out of 10 customers, purchase health and wellness books most frequently.
Book Genre Average of Surveys
Autobiographies 24
Mystery 11
Romance 22
Health and Wellness 18
Fantasy 15
Answers
i need serious help lol
Answers
Answer:
A, C, can't see full answers
Step-by-step explanation:
a. 15/3=5 plus 10 is 15
Subtract. Write the answer as a fraction simplified to lowest terms.
41/40 - 3/8 =
Answers
Hey there!
41/40 - 3/8
= 41/40 - 3 × 5 / 8 × 5
= 41/40 - 15/40
= 41 - 15 / 40 - 0
= 26 / 40
= 26 ÷ 2 / 40 ÷ 2
= 13 / 20
Therefore, your answer is: 13/20
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Assume z is a standard normal random variable. What is the value of z if the area between –z and z is 0.7580?
Answers
to the right is P(z> Z)
so P(z>Z) = 0.9909
P(z< Z) = 1- 0.9909 = 0.0091
Closest values from a z-table
P(z< -2.37) = 0.00889 (-0.00011 away)
p(z< -2.36) = 0.00914 (+0.00014 away)
so the answer must be (c) since it is between -2.36 and -2.37