Write a quadratic function whose zeros are -12 and -2.
Answers
Answer:
(x+12) (x+2)
x(x+12)+2(x+12)
x^2+12x+2x+24
x^2+14x+24
Step-by-step explanation:
Answer:
f(x) = x² + 14x + 24
Step-by-step explanation:
Given the zeros of -12 and -2, then it means that:
x + 12 = 0 and x + 2 = 0
As a proof, if you isolate x, you'll end up with the given values:
x + 12 - 12 = 0 - 12
x = -12
x + 2 - 2 = 0 - 2
x = -2
In terms of using these values into the quadratic function:
(x + 12) (x + 2)
Perform the FOIL method in order to find the quadratic function:
(x + 12) (x + 2)
f(x) = x² + 2x + 12x + 24
f(x) = x² + 14x + 24 ⇒ This is the quadratic function, given the zeros as x = -12, and x = -2.
Related Questions
Which number sentence can be used to find the difference between five times three and two times six?
x= 5x3-2x6
x = 5x2+3x6
x = 5(3+2x6)
x = 5x3+2x6
Answers
Which number sentence can be used to find the difference between five times three and two times six?
x= 5x3-2x6
x = 5x2+3x6
x = 5(3+2x6)
x = 5x3+2x6
Tom used the following steps to find the inverse of f(x), but he thinks he made an error.
Answers
Answer:
4
Step-by-step explanation:
He made the mistake in step 4
The correct step should be x +2 as two had the sign "-" when it was on the other side
Tom made a mistake in step 4, and to correct the mistake he should add 2 on both sides in step 4.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
Step 1: f(x) = 4x - 2
Step 2: y = 4x - 2
Step 3: x = 4y - 2
Step 4: x + 2 = 4y (add 2 on both sides)
Thus, Tom made a mistake in step 4, and to correct the mistake he should add 2 on both sides in step 4.
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Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours how far did Simon drive in all
Answers
Answer:
415 miles
Step-by-step explanation:
Start with the speed equation:
speed = distance/time
Now solve the speed equation for distance:
distance = speed × time
Apply the speed equation solved for distance to the two parts of the trip.
4 hours at 55 mph:
distance = 55 mph × 4 hours = 220 miles
3 hours at 65 mph:
distance = 65 mph × 3 hours = 195 miles
Add the two distances to find the total distance:
total distance = 220 miles + 195 miles = 415 miles
Answer: 415 miles
Answer:
415 miles
Step-by-step explanation:
Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours.
How far did he drive?
d=rt
For the first part of the trip:
d = 55 * 4 = 220 miles
For the second part of the trip:
d = 65*3 =195 miles
Add the miles together
220+195 = 415 miles
A school chess club played 35 games ,they won 15 games tied 15 and lost the rest. What percentage of the game did they lose ,win and tie.
Answers
Answer:
3/7 tied
3/7 Won
1/7 lost
Step-by-step explanation:
A total of 96 pints of blood were collected at the blood drive. How many quarts were collected?
Answers
Answer: 48 qt
Step-by-step explanation:
The conversion factor between pints and quarts is two which means there are 2 pints in every quart. divide the number of pints by two to find the number of quarts.
96/2 = 48
EX: 24 pints = 12 quarts
24/2 =12
EX 8 quarts = 16 pints
The same rule works in reverse but instead of dividing you multiply.
8x2 = 16
A certain triathlon consists of a 2.6 mile swim, a 110 mile bicycle ride, and a 26.2mile run. At one point, a participant had completed as many miles as the number of miles left to complete. How many miles had he completed at that mark?
Answers
Answer:
Let x be the number of miles completed by the participant before the mark. Then, the total distance of the triathlon is:
2.6 + 110 + 26.2 = 138.8 miles
At the mark, the participant has completed x miles and has the remaining distance to complete, which is:
138.8 - x
According to the problem, x is equal to the remaining distance:
x = 138.8 - x
Solving for x, we get:
2x = 138.8
x = 69.4
Therefore, the participant had completed 69.4 miles at the mark.
This Venn diagram shows sports played by 10 students.PLAYSBASKETBALLMaiPLAYSSOCCERMickeyMarcusFranEllalanKarlJadaGabbyJuanLet event A = The student plays basketball.Let event B = The student plays soccer.What is PAB)?O A.A. «0.17B. 1=0.1010
Answers
ANSWER
\(P(A|B)=\frac{1}{3}\approx0.333\)EXPLANATION
We want to find the probability P(A|B).
This is a conditional probability and its formula is:
\(P(A|B)=\frac{P(A\cap B)}{P(B)}\)where P(A n B) is the probability that the student plays basketball and soccer and P(B) is the probability that the student plays soccer.
We have that:
\(P(A\cap B)=\frac{1}{10}\)and
\(P(B)=\frac{3}{10}\)Therefore, we have that:
\(\begin{gathered} P(A|B)=\frac{1}{10}\div\frac{3}{10} \\ P(A|B)=\frac{1}{10}\cdot\frac{10}{3} \\ P(A|B)=\frac{1}{3}\approx0.333 \end{gathered}\)That is the answer.
Find the complete factored form of the
polynomial :
-8m²n-7m² nª
Enter the correct answer.
Answers
The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).
To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:
-8m²n - 7m²n = (-m²n) (8 + 7a)
Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.
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Lillian is comparing the amount of water in her bathtub and her sink. Her bathtub is 0.65 full of water. Her sink is 0.9 full of water.
Which statement is true about comparing the amount of water Lillian has in her bathtub and sink? (MGSE4.NF.7)
There is more water in the bathtub because 65 > 9
These amounts cannot be compared because decimals can only be compared if they have the same-sized whole.
These amounts cannot be compared because decimals can only be compared if the have the same place value
There is more water in the sink because 65/100 < 90/100
Answers
Answer:
Step-by-step explanation:
There is more water in the bathtub because 65 > 9
These amounts cannot be compared because decimals can only be compared if they have the same-sized whole.
These amounts cannot be compared because decimals can only be compared if the have the same place value
There is more water in the sink because 65/100 < 90/100
Which data set could be represented by the box plot shown below? A horizontal boxplot is plotted along a horizontal axis marked from 10 to 26, in increments of 1. A left whisker extends from 12 to 15. The box extends from 15 to 21 and is divided into 2 parts by a vertical line segment at 19. The right whisker extends from 21 to 24. All values estimated. Choose 1 answer: Choose 1 answer: (Choice A) 13 1313, 15 1515, 15 1515, 17 1717, 19 1919, 19 1919, 20 2020, 22 2222, 24 2424 A 13 1313, 15 1515, 15 1515, 17 1717, 19 1919, 19 1919, 20 2020, 22 2222, 24 2424 (Choice B) 12 1212, 15 1515, 15 1515, 17 1717, 19 1919, 19 1919, 20 2020, 22 2222, 24 2424 B 12 1212, 15 1515, 15 1515, 17 1717, 19 1919, 19 1919, 20 2020, 22 2222, 24 2424 (Choice C) 12 1212, 15 1515, 15 1515, 17 1717, 20 2020, 20 2020, 20 2020, 22 2222, 24 2424 C 12 1212, 15 1515, 15 1515, 17 1717, 20 2020, 20 2020, 20 2020, 22 2222, 24 2424 (Choice D) 12 1212, 15 1515, 17 1717, 17 1717, 19 1919, 19 1919, 22 2222, 22 2222, 24 2424 D 12 1212, 15 1515, 17 1717, 17 1717, 19 1919, 19 1919, 22 2222, 22 2222, 24 2424
Answers
The dataset represented by the given box plot is 12, 15, 15, 17, 19, 19, 20, 22, 24 option B.
What is box plot?A box plot, sometimes called a box whisker plot, shows the distribution of a dataset graphically. The minimum value, the first quartile (25th percentile), the median (50th percentile), the third quartile (75th percentile), and the maximum value are the five main values used to standardise this method of displaying the distribution of data.
Two whiskers that extend from a rectangular box make up a box plot. The range of values between the first and third quartiles is represented by the box, which is known as the interquartile range (IQR).
From the given box plot we observe that the minimum value is 12 and the maximum value is 24.
Here, the median is 19.
From the information the two data set that have the corresponding values are:
12, 15, 15, 17, 19, 19, 20, 22, 24
12, 15, 17, 17, 19, 19, 22, 22, 24
The lower quartile is 15.
The upper quartile is 21.
Calculating the lower quartile for the data sets:
12, 15, 15, 17, 19, 19, 20, 22, 24
Lower quartile = 15
Hence, the dataset represented by the given box plot is 12, 15, 15, 17, 19, 19, 20, 22, 24 option B.
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An oblique cone has a height equal to the diameter of the base. The volume of the cone is equal to 18π cubic units. An oblique cone has a diameter of 2 x and a height of 2 x. The volume of the cone is 18 pi cubic units. What is the radius of the cone? 2 units 3 units 6 units 9 units
Answers
Answer:
3 units
Step-by-step explanation:
The formula for the volume of the cone is given by
\(V=\frac{1}{3} \pi r^{2}h\)
\(V=18\pi\ unit^{3} \\\\ r=\frac{2x}{2} =x\ units \\ \\ h=2x\ units\)
Substituting in above formula
\(18\pi=\frac{1}{3} \pi*x^{2}*2x\\ \\ 54=2x^{3} \\ \\ x^{3} =27\\ \\ x=\sqrt[3]{27} \\ \\ x=3\ units\)
Thus, the radius of the cone is 3 units.
Question
Marc is building a gazebo and wants to brace each
corner by placing a 8-inch wooden bracket
diagonally as shown. How far below the corner
should he fasten the bracket if he wants the
distances from the corner to each end of the
bracket to be equal?
(Round to the nearest tenth of an inch.)
Answers
The required distance from the corner to each end of the bracket is 5.7 inches.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
Since the distance from the corner to each end is equal.
So ABC make an isosceles right triangle, where
AB = x inches
AC = x inches
BC = 8 inches
According to the Pythagoras theorem, we have
AB² + AC² = BC²
x² + x² = 8²
2x² = 64
x² = 64/2
x² = 32
x = √32
x = 5.668
Round to the nearest tenth, and we get
x = 5.7
Thus, the distance from the corner to each end is 5.7 inches.
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Find the domain and range of the relation. Also determine whether the relation is a function.
{(6,3), (8,5), (-4,-4), (5,5)}
Answers
The domain is:
D: {-4, 5, 6, 8}
The range is:
R: {-4, 3, 5}
And yes, the relation is a function.
How to determine the domain and range?
For a relation that maps elements x into elements y (in the form (x, y)), we define the domain as the set of the inputs (values of x) and the range as the set of the outputs (values of y).
Here our relation is defined by: {(6,3), (8,5), (-4,-4), (5,5)}
The domain is the set of the first values of each pair, so we have:
D: {-4, 5, 6, 8}
The range is the set of the second values of each pair:
R: {-4, 3, 5}
Now, is this a function?
Yes, it is a function, because each input is mapped into only one output.
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The product of two numbers is 1536.
If the HCF of the two numbers is 16.
find the LCM of these two numbers.
Answers
Work Shown:
LCM = (product of two numbers)/(HCF of the two numbers)
LCM = 1536/16
LCM = 96
5. Given the right triangle JKL, identify the locations of sides j, k, and I in relation to angle L
in terms of opposite, adjacent, and hypotenuse.
HELP
Answers
In relation to the angle L of the right triangle the sides are as follows:
l = opposite sidek = hypotenusej = adjacentHow to name the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sides of a right angle triangle can be named according to the position of the angles in the right angle triangle.
The sides of a right triangle can also be solved by using Pythagoras's theorem or trigonometric ratios.
Let's identify the sides j, k, and I in relation to angle L in terms of opposite, adjacent, and hypotenuse.
Therefore,
l = opposite sidek = hypotenusej = adjacentThe hypotenuse side is the longest side of a right triangle.
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The lengths of the sides of the triangle XYZ are written in the terms of the variable M, where m 7
Answers
We know that the shortest side always opposite to the smallest interior angle.
longest side always opposite to the largest interior angle.
for the given triangle the shortest side is XZ=m-2 hence
\(m\angle Y\)is the smallest angle.
ZY=2m+3 is the longest side hence
\(m\angle X\)is the largest angle.
Hence 2nd option is correct which is
\(undefined\)Suppose a shipment of 400 components contains 68 defective and 332 non-defective computer components . From the shipment you take a random sample of 25. When sampling with replacement (so that the p = probability of success does not change), note that a success in this case is selecting a defective part. The standard deviation of this situation is?
Answers
Answer:
The standard deviation for the number of defective parts in the sample is 1.88.
Step-by-step explanation:
The sample is with replacement, which means that the trials are independent, and thus, the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value of the binomial distribution is:
\(E(X) = np\)
The standard deviation of the binomial distribution is:
\(\sqrt{V(X)} = \sqrt{np(1-p)}\)
68 defective out of 400:
This means that \(p = \frac{68}{400} = 0.17\)
From the shipment you take a random sample of 25.
This means that \(n = 25\)
Standard deviation for the number of defective parts in the sample:
\(\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{25*0.17*0.83} = 1.88\)
The standard deviation for the number of defective parts in the sample is 1.88.
The standard deviation of the situation is 1.88
The proportion of success is calculated as:
\(p = \frac xn\)
So, we have:
\(p = \frac {68}{68 + 332}\)
\(p = 0.17\)
The standard deviation is then calculated as:
\(\sigma= \sqrt{np(1-p)}\)
For a shipment of a random sample of 25, we have:
\(\sigma= \sqrt{25 * 0.17 * (1-0.17)}\)
Evaluate the product
\(\sigma= \sqrt{3.5275}\)
Evaluate the root
\(\sigma= 1.88\)
Hence, the standard deviation of the situation is 1.88
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2. The box and whisker plot below shows the starting salaries for 120 graduates of a small college.
a) What is the range of the starting salaries?
b) About 30 graduates make below what amount?
c) How many graduates have a salary above $33,000 ?
d) $25 of the graduates make above what amount?
Answers
The range of the starting salaries is 53,000
Given,
The box and whisker plot below shows the starting salaries
The number of graduates in a small college = 120
We have to find the range of the starting salaries;
Range of a data;
The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation.
Here,
Lowest value = 19,000
Highest value = 72,000
Then,
Range of the set = 72,000 - 19,000 = 53,000
That is,
The range of the given data set is 53,000
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If the store receives a new shipment of 20 car batteries, (we don't know this, but) 5 of them are faulty, and we selected 2 car batteries at random, then what is the probability that;
A. both of them are good batteries?
B. one battery is good while one battery is bad?
c. both batteries are bad?
Answers
a. The probability that both of them are good is 9/16
b. Probability that one battery is good while one 3/16
c. probability that both batteries are bad is 1/16
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1.
Probability = sample space / total outcome
the sample space for bad batteries = 5
the sample space for good batteries = 15
Therefore
a. probability that both are good = 15/20 × 15/20 = 3/4 × 3/4 = 9/16
b. probability that a battery is good and the other is bad = 15/20 × 5/20
= 3/4 × 1/4 = 3/16
c. The probability that both are bad
= 5/20 × 5/20 = 1/4 × 1/4 = 1/16
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Please help it’s 5 times 5 times 5 times 5 times5
Answers
Answer:
625
Step-by-step explanation:
have a great day <3
Answer:
5x5x5x5=625
5x5x5x5= \(5^{4}\)
Step-by-step explanation:
A PAIR OF SHOES IS DISCOUNTED BY 25%. THE DISCOUNTED PRICE WAS $93.75. WHAT WAS THE ORIGINAL PRICE AHHH SOMEONE ANSWER
Answers
Answer:
$70.31
Step-by-step explanation:
Hope this helps
Answer:
$117.19
Step-by-step explanation:
93.75 * .25 =23.4375
23.4375+93.75 = $117.1875
(rounded:$117.19)
Given the function f(a) = 5a + 14, solve for f(a) = 0.
Give an exact answer; do not round.
Answers
Answer:
a = 14
Step-by-step explanation:
Step 1: Write out your problem
f (a) = 5a + 14 | f (a) = 0
Step 2: Solve
f (a) = 5 (0) + 14 , Input a.
f (a) = 0 + 14 , 5 x 0 = 0
(a) = 14 , 0 + 14
a = 14
f(a)=5a+14
so basically y=5x+14 and x=0
plug in 0 for your x
y=0
A. Common Factor
B. Factoring Trinomials by product-sum method
Answers
Answer:
B. factoring Trinomials by product-dum method
Are the points U, H, and L collinear?
U
E
S
H
Answers
Answer:
Yes
Step-by-step explanation:
Collinear means points are lying on the same straight line. U, H, and L are all lying on the line l.
On Saturday, Ms. Rivera went to the store with $50. She needed to get clothes for the gym. She bought 5 pairs of socks for $3 dollars each, then paid $25 for shorts. Thankfully, Ms. Rivera had a coupon for half off everything! How much money did Ms. Rivera go home with?
Answers
Answer:
20
Step-by-step explanation:
She bought 5 pairs of socks which are 3 dollars each
(5 times 3 = 15 )
With the 25 dollar shorts
( 25 + 15 = 40 )
with a coupon of half off
( 40 divided by 2 = 20)
show that if a and b both have linearly independent column vectors, then the column vectors of c will also be linearly independent.
Answers
To show that if the column vectors of matrix A and B are linearly independent, then the column vectors of matrix C = A*B will also be linearly independent, we can use the following proof:
Assume that the column vectors of matrix A and B are linearly independent. Let's assume that the column vectors of matrix C = A*B are linearly dependent.
This means that there exists a non-trivial linear combination of the column vectors of C that results in the zero vector.
C = AB => c_1 = Ab_1, c_2 = Ab_2, ... c_n = Ab_n
Let's assume that a linear combination of c1, c2, ..., cn results in the zero vector.
a_1c_1 + a_2c_2 + ... + a_n*c_n = 0
Now, we can substitute the matrix multiplication for ci:
a_1Ab_1 + a_2Ab_2 + ... + a_nAb_n = 0
Since matrix A is non-singular, we can left multiply by A^-1
A^-1*(a_1Ab_1 + a_2Ab_2 + ... + a_nAb_n) = A^-1*0
This simplifies to
a_1b_1 + a_2b_2 + ... + a_n*b_n = 0
This is a non-trivial linear combination of the column vectors of matrix B that results in the zero vector, which contradicts the assumption that the column vectors of matrix B are linearly independent. Therefore, the column vectors of matrix C = A*B must also be linearly independent.
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PLEASE HELP ASAP
solve -1/6[3-15(1/3)2]
![PLEASE HELP ASAP solve -1/6[3-15(1/3)2]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/C0Nx4ldjSdyeTD1pu34mYu8d7IAOliwi.png)
Answers
Answer:
C) -2/9
Step-by-step explanation:
\(\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}\)
Answer:
Hence, Option (C) - 2/9 is the Answer:
Step-by-step explanation:
-1/6 [3 -15(1/3)^2]
-1/6(3 -15)(1/9))
-1/6(3 - 5/3)
-1/6 (4/3)
Hence, Option (C) - 2/9 is the Answer:
I hope it helps!
sanjana wrote the cross multiplication property for her proportion: xt=uy
Answers
Answer:
what does this mean. oh wAit iM dematerializinG mvxhkgd
hdgxmgxmgxkgzkgsktxktdktdktdktdtdkgd
10 Which of these transformations make the pre-image
and image congruent?
a) Reflection
b) Dilation
c) Translation
d) Rotation
Answers
Answer:
reflection and rotation
Step-by-step explanation:
2. Find the value of x. 3x-9