Answer:
14c^2
Step-by-step explanation:
The greatest common factor is the factor between the 3 expressions that once divided by each expression, 1 becomes the only number common to all 3. Considering all the expressions as follows (broken into all the factors that make up each expression)
14c^3 = 2 × 7 × c × c
70c^4 = 2 × 5 × 7 × c × c × c × c
28c^2 = 2 × 7 × c × c
From the above, the common factors are 2, 7, c and c,the product of these
= 2 × 7 × c × c
= 14c^2
What are the roots of the polynomial equation?
x2−14x−32=0
We are given the quadratic equation :
[tex] x^{2} -14x-32=0 [/tex]
Now let us use AC method to factorise it.
Step 1:
Find product of A and C
A=1 and C =-32
A*C =-32
Step 2:
Find factors of -32 such that they add up to give -14.
Factors of -32 that add up to give -14 are -16 and 2.
Step 3:
Rewrite the equation using factors found in step 2.
[tex] x^{2} -16x +2x -32 =0 [/tex]
Step 4:
Factoring by grouping.
[tex] x(x-16) +2(x -16) =0 [/tex]
[tex] (x-16) (x+2) =0 [/tex]
Step 5:
Find roots.
x-16=0 gives x=16
x+2=0 gives x=-2
Answer : Roots of the given Polynomial equation are 16 and -2.
We are given the quadratic equation :
[tex] x^{2} -14x-32=0 [/tex]
Now let us use AC method to factorise it.
Step 1:
Find product of A and C
A=1 and C =-32
A*C =-32
Step 2:
Find factors of -32 such that they add up to give -14.
Factors of -32 that add up to give -14 are -16 and 2.
Step 3:
Rewrite the equation using factors found in step 2.
[tex] x^{2} -16x +2x -32 =0 [/tex]
Step 4:
Factoring by grouping.
[tex] x(x-16) +2(x -16) =0 [/tex]
[tex] (x-16) (x+2) =0 [/tex]
Step 5:
Find roots.
x-16=0 gives x=16
x+2=0 gives x=-2
Answer : Roots of the given Polynomial equation are 16 and -2.
50 POINTS!
A high school coach wants to buy new shirts for the 25 members of the track team. The coach must spend less than $300 on the shirts and needs to figure out how much he can spend per shirt, s. Which of the following must be true about the inequality and the resulting graph? Check all that apply
A)The inequality should be written as 25s<300.
B)The inequality should be written as 25s>300.
C)The circle is open.
D)The circle is closed.
E)The arrow points left.
F)The arrow points right
Answer:
Step-by-step explanation:
A,C,E
Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation. Y=4.5 when x = 3
Given that (-4,1) is on the graph of f(x), find the corresponding point for the function 4f(x)
Using the completing-the-square method, rewrite f(x) = x2 + 10x + 7 in vertex form.
Using the completing-the-square method the vertex form of the function
f(x) = x² + 10x + 7 is f(x) = (x + 5)² - 18
The given function is:
f(x) = x² + 10x + 7
Comparing f(x) = x² + 10x + 7 with f(x) = ax² + bx + c
a = 1, b = 10, c = 7
(b/2)² = (10/2)² = 5²
Add and subtract 5² to the right hand side of the equation
f(x) = x² + 10x + 5² + 7 - 5²
f(x) = x² + 10x + 5² + 7 - 25
f(x) = x² + 10x + 5² - 18
f(x) = (x + 5)² - 18
f(x) = (x + 5)² - 18 is of the form f(x) = a(x - h)² + k which is the vertex form of a quadratic equation
Therefore, the vertex form of the function f(x) = x² + 10x + 7 is
f(x) = (x + 5)² - 18
Learn more here: https://brainly.com/question/19105786
The measure of Angle E, the angle of elevation from point A to point B, is ( 3 x plus 1 ). The measure of Angle D, the angle of depression from point B to point A, is 2 ( x plus 8 ) Find the measure of each angle.
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The data set represents a bimonthly progression of gasoline prices over the course of several months in an unspecified city. Use a graphing calculator to determine the quadratic regression equation for this data set. x 0 2 4 6 8 y 2.86 2.89 2.93 3.04 3.11 a. c. b. d.
Answer:
y = 0.0027*x^2 + 0.0111*x + 2.8574
Step-by-step explanation:
Using Excel the procedure is:
First, insert x and y values in a table format, as can be seen in the figure
Then, select data
Next, go to insert tab and inside charts options select scatter plot without any lines
Finally, select a point in the plot, right-click, add trend line, polynomial order 2 and check display equation option
think of 2 numbers that subtract to 5 and multiply to 24
Find the range of ƒ(x) = –2x – 5 for the domain {–2, –1, 1, 2}.
By substituting each value of the domain of x in the function and solving it we will get the range of the function for respective domain
The given function is :
f(x) = -2x - 5
For x = -2 , f(x) is:
f(-2) = (-2*-2) - 5 = 4 - 5 = -1
For x = -1, f(x) is :
f(-1) = (-2*-1) - 5 = 2 - 5 = -3
For x = 1 , f(x) is
f(1) = (-2*1) - 5 = -2 -5 = -7
For x = 2, f(x) is
f(2) = (-2*2) - 5 = -4 -5 = -9
The range is -1 , -3 , -7 , -9
Hope this helps ..!!
Thank you :)
A jar contains 17 orange,7 pink, and 4 black marbles. A marble is drawn at random.What is the probability that the marble is pink or orange
Mrs. Rodriguez has 18 packages of pens in stock at her store on monday. On tuesday, she has 5/6 the number of pens she had on monday. On Wednesday, she has 2/5 of the number of pens she had on tuesday. How many packages of pens does she hve on Wednesday?
Mrs. Rodriguez has 18 packages of pens in stock at her store on Monday.
[tex] Number \; of\; packages\; of \; Pens\; on\; Monday=18\\ \\ [/tex]
On Tuesday, she has 5/6 the number of pens she had on Monday, which means...
[tex] Number \; of\; packages\; of \; Pens\; on\; Tuesday=\frac{5}{6} \; of \ 18 = \frac{5}{6} \times 18=\frac{90}{6}=15\\ [/tex]
On Wednesday, she has 2/5 of the number of pens she had on Tuesday, which means...
\\ Number \; of\; packages\; of \; Pens\; on\; Wednesday = \frac{2}{5} \; of \ 15=\frac{2}{5} \times 15=\frac{30}{5}=6
Conclusion:
Number of packages of pens does she have on Wednesday is 6 Packages
Choose the option that correctly completes the statement.
A triangle must have _____ one acute angle.
at most
at least
can someone help me with this?
What is the area of this polygon?
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Sylvia is going to pick out a souvenir hat while she is on vacation. She knows the price of the hat will increase by 5% when she pays sales tax. She writes the expression h + 0.05h to find the total amount she will pay for the hat if it costs h dollars. Jin correctly writes another expression, 1.05h, that will also find the the total amount Sylvia will pay for the hat if it costs h dollars. Use the drop-down menus to explain what each part of Sylvia's and Jin's expressions mean.
Answer:
Step-by-step explanation:
Sylvia's expression
H: Price of hat
0.05: percent sales tax
0.05 h: amount of sales tax Sylvia will pay
h+0.5 h: total amount Sylvia will pay
Jin's Expression
1.05: One whole plus percent sales tax
H: price of hat
1.05 h: total amount Sylvia will pay
How to find two consecutive positive even integers such that their sum is 48?
Zach uses his car for business and must keep accurate driving records so that his company will reimburse him for car expenses. When he started his trip, the odometer read 26.645, When he returned home, the odometer read 28,017. Zach's car gets about 48 miles per gallon. If the tank was full at the beginning of the trip and it cost $62.28 to fill the tank at the end of the trip, what price did Zach pay per gallon?
.help please and thank you
Choose the graph which represents the solution to the inequality.
Rachel earned $34 dollar sign, 34 in 4 hours at her job today. She wants to know how much she could earn (e)left parenthesis, e, right parenthesis tomorrow if she works 10 hours at the same hourly rate
Answer: Hence, She earned $85 in 10 hours at her job.
Step-by-step explanation:
Since we have given that
In 4 hours at her job, amount she earned = $34
We need to find the amount she earned in 10 hours.
We will use unitary method, to find this.
In 4 hours, amount = $34
In 1 hour, amount is given by
[tex]\dfrac{34}{4}[/tex]
In 10 hours, amount is given by
[tex]\dfrac{34}{4}\times 10\\\\=\dfrac{340}{4}\\\\=\$85[/tex]
Hence, She earned $85 in 10 hours at her job.
Whereas < is called a relational operator, x < y is called a(n) _______?
Graph the following inequality and then select the correct graph below.
y ≤ x - 2
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y\leq x-2[/tex]
The solution of the inequality is the shaded area below the solid line
The equation of the line is [tex]y= x-2[/tex]
The slope of the line is positive [tex]m=1[/tex]
The y-intercept of the line is the point [tex](0,-2)[/tex]
The x-intercept of the line is the point [tex](2,0)[/tex]
therefore
the graph in the attached figure
Picture included!
What is the slope of the line shown in the graph?
A.) -1
B.) -2
C.) 1/2
D.) 2
You work at an ice-cream shop. One of your jobs is to order new ice-cream cones. You pick the cone that is 5 inches high and has a diameter of 3.5 inches. What is the volume of each cone? Use 3.14 to approximate pi. Round your answer to the nearest whole number.
Answer:
The answer is about 16
Step-by-step explanation:
PLEASE HELP
8.04b
1. Eliminate the parameter.
x = 5t, y = t + 8
A) y = 5x + 8
B) y = x divided by five + 8
C) y = 5x - 8
D) y = x divided by five - 8
2. Eliminate the parameter.
x = square root of x , y = 3t + 7
A) y = 3x2 + 7
B) y = 3 square root of x + 7, x ≥0
C) y = 3 square root of x - 7, x ≥0
D) y = 3x2 - 7
3. Eliminate the parameter.
x = t2 + 2, y = t2 - 4
A) y = x - 6, x ≥ 1
B) y = x + 6, x ≥ 1
C) y = x2 - 6, x ≥1
D) y = x2 + 6, x ≥1
4. Eliminate the parameter.
x = 4 cos t, y = 4 sin t
Eugene knows the circumference of a circle is 125.6 meters. Does he have enough information to find the area?
Answer:
the answer is aStep-by-step explanation:
i did the test
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A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function =S+0.60M18.95, where M is the number of miles driven.
The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function =I+0.15M3.70
.
Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.