Write an equation in which the quadratic expression 4x^2-26x+42 equals 0. Must show all work to receive credit.
Show the expression in factored form
Explain what your solutions mean for the equation in complete sentences.
HIGH POINT AND BRAIN LIST
Answers
Answer:
(a) (x + 3)(2x + 7) = 0
(b) These solutions mean that for these two x values, f(x) is equal to 0. It's also where the graph of f(x) crosses the x-axis.
Step-by-step explanation:
(a) We set 4x² -26x + 42 equal to 0:
4x² -26x + 42 = 0
Let's divide both sides by 2 to simplify this a bit:
2x² - 13x + 21 = 0
Now, we need factors a and b of 2 and c and d of 21 such that ac + bd = -13. The factors of 2 are: 1 and 2, so let's say a = 1 and b = 2. The factors of 21 are: (1, 21), (3, 7), (-1, -21), and (-3, -7). We see that if c = -7 and d = -3, this works:
ac + bd = 1 * (-7) + 2 * (-3) = -7 - 6 = -13
So, the factored form is:
(x - (-3))(2x - (-7)) = 0
(x + 3)(2x + 7) = 0
(b) So now we need to solve this. Set each of the two parenthetical expressions equal to 0:
x + 3 = 0
x = -3
AND
2x + 7 = 0
x = -7/2
These solutions mean that for these two x values, f(x) is equal to 0. It's also where the graph of f(x) crosses the x-axis.
Answer:
a) 2(x - 3)(2x - 7) = 0
b) function is 0 when x = 3 or 7/2
Step-by-step explanation:
4x² - 26x + 42 = 0
2(2x² - 13x + 21) = 0
2[2x² - 6x - 7x + 21] = 0
2[2x(x - 3) - 7(x - 3)] = 0
2(x - 3)(2x - 7) = 0
Solutions:.
x = 3, 7/2
Related Questions
Enter the trigonometric equation you would use to solve for x in the following right triangle. Do not solve the equation.
Answers
Answer:
Step-by-step explanation:
You need to use the Tangent
tan = opposite / adjacent
Rearrange formula to solve for opposite.
opposite = tan(angle) x adjacent
Which graph represents the equation y = --3x – 1?
Answers
Answer:
Step-by-step explanation:
The equation y = -3x - 1 represents a straight line with a slope of -3 and y-intercept of -1. The graph will be a line falling to the right and crossing the y-axis at -1.
Explanation:The question asks which graph represents the equation y = -3x - 1. This is a linear equation, where the coefficient of 'x', -3 here, gives us the slope of the line, and the constant, -1 here, gives us the y-intercept. A slope of -3 means for each step of 1 increase in x, the value of y decreases by 3. The y-intercept is the point where the line intersects with the y-axis, in this case at y = -1.
A graph representing this equation will be a straight line with a slope of -3 (indicating the line falls as we move along the positive x-axis) and will cut the y-axis at y = -1.
Learn more about Linear Equations here:https://brainly.com/question/32634451
#SPJ11
What is the slope of the line through (-1, 4) and (1, -2)?
Answers
Answer:
slope = - 3
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (1, - 2)
m = [tex]\frac{-2-4}{1+1}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3
Answer
Slope = -3
Step-by-step explanation:
do you need an explanation
Can someone please help me with this question??
Answers
Answer:
0.01 or 1%
Step-by-step explanation:
Find the original value of the stock by adding the amount lost to the end value.
$67.32 + $0.68 = $68.00
You would then divide the end value by the original value.
$67.32 / $68.00 = 0.99
To find what percentage the stock declined by, you would subtract.
1.00 - 0.99 = 0.01
To convert 0.01 to a percentage, you would multiply it · 100 to get 1%.
h(t) = (t + 3) ^ 2 + 5
Answers
Answer:
If you are looking for the vertex then the answer is (-3, 5)
Step-by-step explanation:
Hope this works
4. If a student is chosen at random from
those who participated in the survey,
what is the probability that the student
participates in school sports, given that
the student is a male?
Answer choices:
0.379
0.476
0.524
0.621
Answers
Answer:
0.524
Step-by-step explanation:
To find the probability that a student participates in school sports given that the student is a male, we use conditional probability. The probability is approximately 0.624.
Explanation:To find the probability that a student participates in school sports given that the student is a male, we need to use conditional probability. Conditional probability is calculated by dividing the probability of two events happening together by the probability of the given condition.
Let's denote the event of a student participating in school sports as A and the event of a student being a male as B.
The probability of a student participating in school sports and being a male is given as 0.409. The probability of a student being a male is given as 0.654. Therefore, the conditional probability of a student participating in school sports given that the student is a male can be calculated as:
P(A|B) = P(A and B) / P(B)
P(A|B) = 0.409 / 0.654 ≈ 0.624
So, the probability that a student participating in the survey participates in school sports, given that the student is a male, is approximately 0.624.
Learn more about Conditional probability here:https://brainly.com/question/10567654
#SPJ5
A jar contains 11 brown and 18 blue marbles. A marble is drawn at random. What is the probability that the marble is not blue?
A. 18⁄29
B. 1⁄11
C. 11⁄18
D. 1⁄18
E.11⁄29
Answers
Answer:
E
Step-by-step explanation:
A punch bowl has a capacity of
8 quarts. How many cups can the
punch bowl hold?
A 16 cups
B 24 cups
C 32 cups
D 48 cups
Answers
Answer:
The answer is C
Step-by-step explanation:
There are 32 oz in a quart, 8 oz in a cup, and therefore 4 cups
in a quart. 4 cups(quart) X 8 quarts (Punch bowl)= 32 cups
You should know 4 cups are in one quart so if you multiply 4 times 8 you get 32 so you know 32 cups is the answer
Hope that helps
the probabiltiy for snow today is 0.6 the probabiltiy foe anow tomorrrw of 0.4. the pr ability for snow both days is 0.1. fins the probability that it will snow at least one if the two days
Answers
Answer:
Step-by-step explanation:
1%
Answer:
1% I think. I used a calculator but sometime my calculator doesn’t work.
Mrs. Henson's rectangular afghan is 2 feet
longer than it is wide. If the afghan has an
area of 24 square feet, what is its width?
(Remember, the area of a rectangle is its
length times its width.)
Answers
Answer:
The width is 4
Step-by-step explanation:
If the length is 6 feet, minus 2 will be 4. Six times 4 is 24, which is the area of the afghan rug. We are multiplying 6 and 4 because it is length times width in rectangle area.
Mrs. Henson's rectangular afghan width will be 4 feet
Area of a rectangleIt is the product of its length and width
How to solve this problem?
Let, x be width of rectangular afghanGiven,Length of afghan is 2 feet more than its width
∴ l = x+2
Area of rectangular afghan = 24 square feet
Now,Area of rectangular afghan = lw
[tex]24=x(x+2)\\24=x^{2} +2x\\x^{2} +2x-24=0\\x^{2} -4x+6x-24=0\\(x-4)(x+6)=0\\x=4 or -6[/tex]
Since width can not be in negative[tex]x=4feet[/tex]
So the width of rectangular afghan will be 4 feet
Learn more about area of a rectangle here:
https://brainly.com/question/25292087
#SPJ2
please help me solve this quadratic equation
Answers
x = - 26.53197
The sum of three numbers is -39.22. One of the numbers is 22.8. The other two numbers are equal to each other. What is the value of the other two numbers?
Answers
Answer:
The value of the other two numbers is 31.01
Step-by-step explanation:
Let the two numbers equal to each other be x
One of the numbers is 22.8
The sum of three numbers is -39.22.
So, x+x+22.8=-39.22
2x+22.8=-39.22
2x=-39.22-22.8
2x=-62.02
[tex]x=\frac{-62.02}{2}[/tex]
x=-31.01
Hence the value of the other two numbers is 31.01
Quinn mailed four postcards that each cost $0.25, five letters that each cost $0.44, two large envelopes that each cost $0.80, and one small package for $5.10. Which cost on the list of mailing fees on Quinn’s receipt would skew the mean?
the cost of a postcard
the cost of a letter
the cost of a large envelope
the cost of the small package
Answers
Answer:
the cost of the small package
Step-by-step explanation:
I hope this is correct. I'm sorry if it's not...
Select three expressions that are equivalent to 2x(4x+8y) Please include explanation.
Will choose brainliest
Answers
Answer:
Its f,e,c
Step-by-step explanation:
Its correct because when u solve one side is 8x and the other is 16y
Consider the equation, 3x+4y=12.
Write the equation in slope-intercept form.
Identify the y-intercept.
Identify the slope.
Answers
The equation in slope-intercept form is y = -3x/4 + 3.
The y-intercept is 3.
The slope is -3/4.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m is the slope or rate of change.x and y are the points.b is the y-intercept or initial value.Based on the information provided about this line, a linear equation that models it is given by;
y = mx + b
3x + 4y = 12
By making y the subject of formula, we have the following:
4y = -3x + 12
4y/4 = -3x/4 + 12/4
y = -3x/4 + 3
Therefore, the y-intercept is 3 and the slope is -3/4.
Read more on slope-intercept here: brainly.com/question/7889446
#SPJ6
What is the value of the expression 6x (2.2+12.8)-4
Answers
Which statements are true about the locations of points A and B? Select all that apply.
1 Point A is at (0, –2).
2 Point A is at (0, –4).
3 Point A is at (–4, 0).
4 Point B is at (–4, –3).
5 Point B is at (–8, –6).
6 Point B is at (–8, –7).
Answers
Answer:
the answers would be 2 and 6
Step-by-step explanation:when plotting points on a graph to wright where the point is you would use (x,y) x being the horizontal line on the graph and y being the vertical. In this case point A is located at (0,-4) because it is ) on the x-axis and -4 on the y-axis. point B is located at (-8,-7) because it is -8 on the x-axis and -7 on the y-axis.
John was given a math equation. He completed it in 5 seconds. Is his answer correct? If it is, show how he got the answer. Show your work. See picture down below.
Answers
Answer:
His work is correct, easiest question in the world!LOL
Step-by-step explanation:
1+1= 2
1 bag in addition to 1 bag is 2 bags
Which graph best represents the cost to mail a package based on weight categories?
Plz help
Answers
Answer:
IV
Step-by-step explanation:
Since the cost is the same for weights in one interval, it will form a step function
can someone help me really please
Answers
Answer:
A) .1
B) .5
C) .7
D) .7
E) 1.2
F) 1.9
G) 3.2
H) 3.6
I) 4.4
Step-by-step explanation:
There are 10 dashes between each number so when you reach a whole number and have to go beyond that point, just count the dashes which will give you your whole number, if you have one, and your decimal.
Which number is an irrational number?
Answers
Answer:
0.6
Step-by-step explanation:
(07.01)Amanda created a table to help her represent the sample space of spinning a spinner and flipping a coin
Result of spin
Result of coin tossRed Green
Yellow Blue
Heads
Red, heads Green, heads Yellow, heads Blue, heads
Tails
Red, tails Green, tails Yellow, tails Blue tails
What is the probability that the result of the spin is blue and the coin lands heads up?
2
8
3
8
1
8
4
8
Answers
Answer:
1/8
Step-by-step explanation:
i got it right
Of the 24,400 working hours logged at a beauty salon last year, Beatrice worked 976 hours. What percentage of the total hours did Beatrice work?
Answers
Answer: 4% (or 4.1% when rounded to the nearest tenth or 4.08 % when rounded to the nearest hundredth)
Step-by-step explanation:
First, you would need to put it into a fraction.
You have [tex]\frac{996}{24400}[/tex].
When you divided it, you would get:
0.04081....
Then you have to multiply times 100 to get it into percent form. This gives you:
4.081%
Then, round as you please!
This is your answer!
which box plot represents a data set with a lower quartile or 24 and an upper quartile of 42
Answers
The box plot that represents a data set with a lower quartile of 24 and an upper quartile of 42 from the given option is D(The bottom option on the right end).
What are quartiles?When we get data that can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.
Quartiles are then selected as 3 points such that they create four groups in the data, each group approximately possessing 25% of the data.
The lower quartile, also called the first quartile has approx 25% in its left partition, and on its right lies approx 75% of the data.Similarly, the second quartile (also called median) is approximately in mid of the data.The third quartile (also called the upper quartile) has approx 75% in its left partition, and on its right lies approx 25% of the data.Left to right is said in the assumption that data were arranged increasingly from left to right
Since we need to find the box plot that has a lower quartile of 24 and an upper quartile of 42, therefore, we need to find a box plot whose rectangle starts at 24 and ends at 42, from left to right.
Hence, the box plot that represents a data set with a lower quartile of 24 and an upper quartile of 42 from the given option is D(The bottom option on the right end).
Learn more about quartiles here:
brainly.com/question/9260741
#SPJ2
Which is a solution of x^2- x - 3/4= 0?
-1/4
1/2
3/2
3/4
Answers
Answer:
its B
Step-by-step explanation:
Rewrite the equation by completing the square.
x² + 4x = 0
Answers
Answer:
(x+2)^2 = 4
Step-by-step explanation:
x² + 4x = 0
Take the coefficient of the x term
4
Divide by 2
4/2 =2
Square it
2^2 =4
Add this to each side
x^2+4x+4 = 0+4
(x+4/2)^2 = 4
(x+2)^2 = 4
-7-4x=18
What does x stand for?
PLEASE!!
Answers
This is what x equals
Help! I need help please!
Answers
Answer:
[tex] \sin A = \frac{3}{5} [/tex]
The figure below has one base
and eight lateral faces. Find its surface
area to the nearest whole number.
Answers
Answer: B
Total surface area = 320 m^2
Step-by-step explanation:
The figure is a combination of a cuboid and pyramid.
The Surface Area of a Pyramid When all side faces are the same:
[Base Area] + 1/2 × Perimeter × [Slant Length]
Let us use pythagorean theorem to calculate the slant length
Slant length = root(6^2 + 4^2)
Slant length = 7.2 m
Base area = 8 × 8 = 64 m^2
Perimeter = 8+8+8+8 = 32 m
Surface area of the pyramid will be
= 64 + ( 1/2 × 32 ) × 7.2
= 64 + 16 × 7.2
= 64 + 115.4
= 179.4 m^2
The surface area of the cuboid will be
LB + LH + BH = 8×8 + 8×5 + 8×5
= 64 + 40 + 40
= 144 m^2
Total surface area = 179.4 + 144
Total surface area = 323.4 m^2
= 320 m^2 to the nearest whole number.
How many 4-digit numbers are multiples of at least one of these two numbers: 2; 5.
How many 4-digit numbers are multiples of both 2 and 5?
How many 4-digit numbers are neither multiples of 2 nor multiples of 5?
Answers
Answer:
I believe that there is 3087 multiples of 5
Step-by-step explanation:
Answer:
5400
Step-by-step explanation: