The zero of the quadratic function is therefore x = 1. Since both factors give the same zero, we have a repeated zero and f(x) only touches the x-axis at one point, x = 1.
The zeros of the quadratic function f(x) = 4x^2 - 12x + 8 are the values of x that make f(x) = 0. In this function, we can factor by finding two numbers that multiply to give the constant term (8 times 4, the coefficient of x^2) and add to give the coefficient of x (-12). Here, those numbers are -4 and -4, so we rewrite the middle term -12x as -4x - 4x, and factor by grouping:
4x^2 - 4x - 4x + 8 = 0
4x(x - 1) - 4(x - 1) = 0
(4x - 4)(x - 1) = 0
Now we have two factors equal to zero, which gives us two equations to solve:
4x - 4 = 0 or x - 1 = 0
x = 1
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A regression line was calculated as ŷ = 1.7x + 2.1. What is the slope of the regression line. is _____. Type a numerical answer in the space provided.
ASAP What is the lateral area of this regular octagonal pyramid?? Explain your answer if you can plz thanks
Answer:
Hello! The correct answer is 298.7 [tex]cm^{2}[/tex]
Step-by-step explanation:
I am just confirming!
Need to find the formula for:
Car problem: Julie wants to borrow her parent's car to drive to a tournament. Her parents tell her she has to pay for the gas she uses. The car gets 26 mpg. Julie wonders how much gas she will need to purchase to get to the tournament and back.
Kevin is 2 times as old as Gabriela. 12 years, Kevin was 6 times as old as Gabriela.How old is Gabriela now
Final answer:
Gabriela's current age is found by setting up algebraic equations based on the information that Kevin is twice as old as Gabriela now, and was six times as old 12 years ago. Solving the equations, we find that Gabriela is 15 years old.
Explanation:
Finding Gabriela's Current Age:
The problem statement tells us that Kevin is currently 2 times as old as Gabriela and that 12 years ago, Kevin was 6 times as old as Gabriela. To solve for Gabriela's current age, let us use algebra. Let's denote Gabriela's current age as G and Kevin's current age as K. The given information can be translated into the following two equations:
K = 2G (Kevin is 2 times as old as Gabriela now)K - 12 = 6(G - 12) (12 years ago, Kevin was 6 times as old as Gabriela)Substituting the first equation into the second, we get:
2G - 12 = 6(G - 12)
Expanding both sides:
2G - 12 = 6G - 72
Moving all terms involving G to one side and constant terms to the other side, we get:
2G - 6G = -72 + 12
-4G = -60
Dividing both sides by -4 to solve for G:
G = 15
So, Gabriela is currently 15 years old.
HOW would I go about figuring this out? I need explanation not just answer
A box contains 24 light bulbs of which 4 are defective
which scale factor would produce a contraction?
A.) 5/2
B.) 1.2
C.) 2.3
D.) 3/4
You made 1/2 quart of lemonade. How many 1/4 quart-sized glasses will you be able to fill with lemonade?
The solution is 2 glasses
The number of 1/4 quart-sized glasses to fill the lemonade is given by the equation A = 2 glasses
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of 1/4 quart-sized glasses to fill the lemonade be A
Now , the equation will be
The amount of lemonades = 1/2 quart of lemonade
The size of the glasses = 1/4 quart-sized glasses
So , the equation will be
A x 1/4 quart-sized glasses = 1/2 quart of lemonade
On simplifying the equation , we get
A / 4 = 1/2
Multiply by 4 on both sides of the equation , we get
A = ( 1/2 ) x 4
A = 2 glasses
Therefore , the value of A is 2 glasses
Hence , the number of glasses is 2
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Colin was thinking of a number. Colin adds 18 to it, then doubles it and gets an answer of 65.5. What was the original number?
Answer:
14.75
Step-by-step explanation:
65.5/2 = 32.75.
32.75 - 18 = 14.75
thats your answer. hope it helps
When solving the equation 10x + 2 = 22, what is the first thing you're going to do?
Simplify.
2x5 - 6x2 + 4x4y
-------------------------
2x
1.01 an rational number
A car salesman earns 2% commission on all of his sales. If he needs to make $3,000 a month for his living expenses, what total dollar amount must he sell to make that in commission each month?
The total dollar amount he must sell to make that in commission each month is $150000.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".Given is that a car salesman earns 2% commission on all of his sales. He needs to make $3,000 a month for his living expenses,
Assume that the total dollar amount he must sell to make that in commission each month is ${x}. Then, we can write -
3000 = 2% of {x}
3000 = (2/100) × {x}
{x} = (3000 x 100)/2
{x] = 300000/2
{x} = 150000
Therefore, the total dollar amount he must sell to make that in commission each month is $150000.
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When triangle ABC is rotated about side AB, what figure is formed?
cylinder
prism
pyramid
cone
Answer:
Cone
Step-by-step explanation:
We are given that a triangle ABC .
We have to find that what shape is formed when a triangle ABC is rotated about side AB.
A given triangle ABC is a right triangle.
When we rotate the figure about side AB then the figure will be cone .The side AB will be height of cone and side AC will be radius of cone.
Hence, when a triangle ABC is rotated about side AB, the cone is formed.
Answer: Cone
What is the value of x? The figure shows 2 right triangles, triangle K L J with right angle J and triangle L J M with right angle M. The measure of angle L K J is 30 degrees. The measure of angle L J M is 45 degrees. The length of side K L is 8 square root 2. The length of side L M is x. Enter your answer in the box. x =
A bakery supplier receives an order for 2 Tons of sudar from a bakery chain. The sugar is shipped in crates. Each crate holds eight 10-pound bags of sugar. How many crates does the supplier need to ship to fulfill the order?
Modern Appliances offers a one-year monthly installment plan for a refrigerator. The payment for the first month is $75, and then it increases by 6% each month for the rest of the year. Which expression can be used to find the total paid in the first 12 months?
Expression used represents the given paid installment for [tex]12[/tex] months is equal to [tex]S_{12} =\frac{ 75(1-1.06^{12}) }{1-1.06}[/tex].
What is expression?" Expression is defined as the equation representing the relation between the numbers or the variables using mathematical operation."
Formula used
Geometric progression,
[tex]S_{n} = \frac{a(1-r^{n}) }{1-r}[/tex]
[tex]a=[/tex] first term
[tex]r=[/tex] common ratio
[tex]n=[/tex] number of terms
According to the question,
Given,
Amount to be paid first month [tex]'a' = \$75[/tex]
Increases by [tex]6\%[/tex] each month
Therefore,
Common ratio [tex]'r' = 1 + \frac{6}{100}[/tex]
[tex]= 1.06[/tex]
Number of months [tex]'n'= 12[/tex]
Substitute the value in the formula to get the expression for the given condition,
Required expression,
[tex]S_{12} =\frac{ 75(1-1.06^{12}) }{1-1.06}[/tex]
Hence, expression used represents the given paid installment for [tex]12[/tex] months is equal to [tex]S_{12} =\frac{ 75(1-1.06^{12}) }{1-1.06}[/tex].
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Jonathan bought a new computer for $1,716, using the electronics store's finance plan. He will pay $143 a month for 12 months. Which equation can Jonathan use to find out how much money he still owes after each month of the plan?
Answer:
y = 1716 -143x
Step-by-step explanation:
You want an equation for the amount owed after x months on a purchase of $1716 paid at the rate of $143 per month.
PaidAfter x months, the amount paid will be 143·x. The amount owed is the difference between the original purchase price and the amount paid:
owed = $1716 - paid
y = 1716 -143x . . . . . . . . . the amount Jonathan still owes after x months
please help asap!!!!!! lots of points
2. Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.
Answer:
m < C =
m < B =
m < A =
m < D =
The length of a rectangle is 7mm longer than its width. It’s perimeter is more than 62mm. Let W equal the width of the rectangle, write an inequality and solve it
What’s the value of x in 46+(7x+9)
Express the given integral as the limit of a riemann sum but do not evaluate: the integral from 0 to 3 of the quantity x cubed minus 6 times x, dx.
To express the integral from 0 to 3 of the function as the limit of a Riemann sum, divide the interval into [tex]f(x) = x^3 - 6x[/tex] subintervals of equal width, find a Riemann sum, and then take the limit as n approaches infinity.
Explanation:To express the given integral as the limit of a Riemann sum without evaluating, we represent the integral of the function [tex]f(x) = x^3 - 6x[/tex]split the interval [0,3] into n equal subintervals, each of width Δx = 3/n. Then we choose sample points x_i in each subinterval [x_{i-1}, x_i]. The Riemann sum is thus [tex]R = Σ(x_i^3 - 6x_i)Δx[/tex]en from i=1 to n and x_i is any point in the ith subinterval.
As n approaches infinity, which is equivalent to Δx approaching zero, the Riemann sums converge to the integral. The limit of the Riemann sum is then represented as lim_{n to ∞} R, which gives the exact area under the curve f(x) between 0 and 3, but we are not evaluating this limit.
Find an ordered pair (x,y) that is a solution to the equation.
3x-y=3
Answer: The required ordered pair is (1, 0).
Step-by-step explanation: We are given to find an ordered pair (x, y) that is a solution to the following equation:
[tex]3x-y=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find an ordered pair, we should either take a value of x and find the corresponding value of y,
or,
we should take a value of y and find the corresponding value of x.
Let us consider that
x = 1.
Then, from equation (i), we get
[tex]3\times 1-y=3\\\\\Rightarrow 3-y=3\\\\\Rightarrow y=3-3\\\\\Rightarrow y=0.[/tex]
Thus, the required ordered pair is (1, 0).
Factor. 25m^100−121n^16
(5m10−11n4)(5m10+11n4)(5m50−11n8)2(5m50−11n8)(5m50+11n8)(5m10−11n4)2
PLEASE HELP
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PLEASE ASSIST ME N TRY TO HELP ME
What is the definition of a circle? A circle is a plane figure with no straight sides. A circle is a point and all the points in a plane that are the same distance from it. A circle is the set of all points in a plane that are a given distance from a given line segment. A circle is the set of all points in a plane that are the same distance from a fixed point called the center.
Answer:
I believe the answer is "A circle is a set of all points in a plane that are the same distance from a fixed point called the center." I am 95% sure but please correct me if I am wrong. Hope this possibly helps someone!
Step-by-step explanation:
You have a bag of bubble gum containing six grape, nine sour apple and five regular flavored pieces. You randomly pick one piece , give it to your friend, and then randomly pick another piece for yourself. What is the probability that both pieces are grape?
The probability that both pieces of bubble gum picked are grape flavored is 3/38, calculated by multiplying the probability of picking a grape piece first (6/20) and then another after the first is given away (5/19).
Explanation:The question asks us to calculate the probability that both pieces of bubble gum picked from the bag are grape flavored. The bag contains six grape, nine sour apple, and five regular flavored pieces. To find the probability that both pieces are grape, we calculate the probability of picking one grape piece and then another grape piece after the first has been given away.
The total number of pieces initially is 6 (grape) + 9 (sour apple) + 5 (regular) = 20 pieces. The probability of picking a grape piece first is 6/20. After giving it away, there are 5 grape pieces left and the total number of pieces in the bag is now 19. The probability of then picking another grape piece is 5/19. To find the overall probability of both events occurring, we multiply the individual probabilities: (6/20) * (5/19) = 30/380 = 3/38.
Therefore, the probability that both pieces are grape is 3/38.
what is the value of x to the nearest tenth?