Final answer:
To find (g - f)(3) with given functions f(x) and g(x), subtract f(x) from g(x) to get the new function, then evaluate this function at x = 3. The result is 23.
Explanation:
The student is asking to find the result of the operation (g - f)(3) where f(x) = 4 - x2 and g(x) = 6x. (g - f)(x) means we subtract the function f from the function g, and then evaluate the resulting function at x = 3.
To solve this:
First, find the function g(x) - f(x):g(x) is 6x, and f(x) is 4 - x2, so g(x) - f(x) is 6x - (4 - x2) = 6x - 4 + x2.Next, evaluate this new function at x = 3: (6*3) - 4 + (32) = 18 - 4 + 9 = 23.So (g - f)(3) is 23.
Kyle ran for 27 minutes on Tuesday. On Wednesday, Kyle ran for n fewer minutes than he ran on Tuesday. On Friday, Lee ran for 3 times longer than Kyle ran on Wednesday. Kyle wrote this expression to show how long Lee ran.
Answer:
(27 - n) times 3 is the expression Kyle should use.
Step-by-step explanation:
If Lee ran for 3 times longer than Kyle ran on Wednesday, then we have to figure out how long Kyle ran on Wednesday. If Kyle ran n fewer minutes than he ran on Tuesday, then we need to figure out how long he ran on Tuesday. If Kyle ran 27 minutes on Tuesday, the we need to subtract n from that to get how long Kyle ran on Wednesday. We can't figure that out with an undefined variable, therefore, that will just have to be 27 - n in the equation. If Lee ran for 3 times that, we need to multiply that by 3. 27 - n would have to be done first, so we will put that in parenthesis. We put all of that together to get (27 - n) times 3. Hope this helps!
Factor completely 2x^2 - 98
Answer:
Step-by-step explanation:
2x^2 - 98 = 2 * ( x^2 - 49)
= 2 * (x^2 - 7^2)
= 2 * (x+7) * (x-7) {a²-b² = (a+b)(a-b)}
What is the cube of 27x18
Answer:
114791256
Step-by-step explanation:
27*17=486
486^3=114791256
Answer:
114791256
Step-by-step explanation:
27*17=486
486^3=114791256
GIVING BRAINLIEST!!! STATEMENT REASONING NEEDED!!! 100 POINTS!!!
Answer:
See explanation
Step-by-step explanation:
a1) Given
[tex]\angle A\cong \angle C\\ \\\angle ABD\cong \angle CDB[/tex]
Statement Reason
1. [tex]\angle A\cong \angle C[/tex] - Given
2. [tex]\angle ABD\cong \angle CDB[/tex] - Given
3. [tex]\overline{BD}\cong \overline{DB}[/tex] - Reflexive property
4. [tex]\triangle ABD\cong \triangle CDB[/tex] - AAS postulate
5. [tex]\overline {AB}\cong \overline{CD}[/tex] - Congruent triangles have congruent corresponding parts
6. [tex]AB=CD[/tex] - Definition of congruent segments
a2) Given
[tex]\overline{H O}\parallel \overline{E N}\\ \\H W=N W[/tex]
Statement Reason
1. [tex]H W=W N[/tex] - Given
2. [tex]\overline{H O}\parallel \overline{E N}[/tex] - Given
3. [tex]\angle O H W\cong \angle E N W[/tex] - Alternate interior angles theorem (two parallel lines H O and E N are cut by transversal H N)
4. [tex]\angle H W O\cong \angle N W E[/tex] - Vertical angles theorem
5. [tex]\triangle H O W\cong \triangle N E W[/tex] - ASA postulate
b) Given
[tex]PO=PR\\ \\OS=RS\\ \\\angle O\cong \angle R\\ \\m\angle P=90^{\circ}[/tex]
Statement Reason
1. [tex]m\angle P=90^{\circ}[/tex] - Given
2. [tex]\triangle OPE, \triangle RPN[/tex] are right triangles - Definition of right triangles
3. [tex]\angle O\cong \angle R[/tex] - Given
4. [tex]PO=PR[/tex] - Given
5. [tex]\triangle POE\cong \triangle PRN[/tex] - HA postulate
6. [tex]OS=RS[/tex] - Given
7. [tex]\angle O\cong \angle R[/tex] - Given
8. [tex]\angle OSN\cong \angle SRE[/tex] - Vertical angles theorem
9. [tex]\triangle SON\cong \triangle SRE[/tex] - ASA postulate
c1) Given
[tex]\overline{SA}\parallel \overline{NE}\\ \\\overline{SE}\parallel \overline{NA}[/tex]
Statement Reason
1. [tex]\overline{SA}\parallel \overline{NE}[/tex] - Given
2. [tex]\angle ENS\cong \angle ASN[/tex] - Alternate interior angles theorem (two parallel lines SA and NE are cut by transversal SN)
3. [tex]\overline{SE}\parallel \overline{NA}[/tex] - Given
4. [tex]\angle ESN\cong \angle ANS[/tex] - Alternate interior angles theorem (two parallel lines SE and NA are cut by transversal SN)
5. [tex]\overline{SN}\cong \overline{NS}[/tex] - Reflexive property
6. [tex]SN=NS[/tex] - Definition of congruent segments
7. [tex]\triangle ENS\cong \triangle ASN[/tex] - ASA postulate
8. [tex]\overline{SA}\cong \overline {NE}[/tex] - Congruent triangles have congruent corresponding parts
9. [tex]SA=NE[/tex] - Definition of congruent segments
c2) Given
[tex]\angle BTO\cong \angle IWE\\ \\\overline{WI}\cong \overline{BT}\\ \\\overline{OW}\cong \overline{ET}[/tex]
Statement Reason
1. [tex]\angle BTO\cong \angle IWE[/tex] - Given
2. [tex]\overline{WI}\cong \overline{BT}[/tex] - Given
3. [tex]\overline{OW}\cong \overline{ET}[/tex] - Given
4. [tex]\overline{WT}\cong \overline{TW}[/tex] - Reflexive property
5. [tex]WI=BT[/tex] - Definition of congruent segments
6. [tex]OW=ET[/tex] - Definition of congruent segments
7. [tex]WT=TW[/tex] - Definition of congruent segments
8. [tex]OT=OW+WT[/tex] - Segment addition postulate
9. [tex]WE=WT+TE[/tex] - Segment addition postulate
10. [tex]OW+WT=ET+WT[/tex] - Substitution property
11. [tex]OT=WE[/tex] - Substitution property
12. [tex]\triangle BOT\cong \triangle IEW[/tex] - SAS postulate
Answer:
What he said
Step-by-step explanation:
help pls will give brainliest
Answer:
9 * 10^7.
Step-by-step explanation:
(3 * 10^5) * (3 * 10^2)
= 3 * 3 * 10^5 * 10^2
= 9 * 10^(5+2)
= 9 * 10^7.
sin^-1 0.42 find the nearest degree
Answer:
[tex]25^o[/tex]
Step-by-step explanation:
Let
x ----> the angle in degrees
we know that
[tex]sin(x)=0.42[/tex]
Find the measure of angle x
Using a calculator
[tex]x=sin^{-1}(0.42)=24.83^o[/tex]
Round to the nearest degree
[tex]x=25^o[/tex]
Mrs. Burke wants to get family portraits taken and is comparing prices between two different photography studios. Cameron Photography charges $33 per portrait sheet, plus $51 for the session fee. Lasting Memories Company charges $99 for the session fee and $29 per portrait sheet. If Mrs. Burke plans to purchase a certain number of portrait sheets, the cost will be the same at either studio. How many portrait sheets would that be? What would the total cost be? If Mrs. Burke orders portrait sheets, the portrait session will cost $ at either studio.
Answer:
12 portrait sheets with total cost of $447
Step-by-step explanation:
x sheets ordered
Cameron: 33x + 51 = Lasting Memory : 29x + 99
33x + 51 = 29x + 99
33x - 29x = 99 -51
4x = 48
x = 12 sheets ordered
Total cost: 33 * 12 + 51 = 447
check: 29 * 12 + 99 = 447
Final answer:
Mrs. Burke needs to purchase 12 portrait sheets for the cost to be the same at either studio, and the total cost would be $495.
Explanation:
Mrs. Burke is comparing the costs of family portraits between Cameron Photography and Lasting Memories Company to find out how many portrait sheets will result in the same total cost at either studio. To solve this, we can set up an equation where the total cost at Cameron Photography equals the total cost at Lasting Memories.
Let x be the number of portrait sheets. The total cost at Cameron Photography is given by the expression 33x + 51 (where 33 is the cost per portrait sheet and 51 is the session fee). The total cost at Lasting Memories is expressed as 29x + 99 (with 29 being the cost per portrait sheet and 99 is the session fee).
To find the number of portrait sheets that results in equal costs, we set the two expressions equal to each other:
33x + 51 = 29x + 99
Subtracting 29x from both sides, we get:
4x + 51 = 99
Subtracting 51 from both sides, we get:
4x = 48
Dividing by 4, we find that x = 12. So, Mrs. Burke would need to purchase 12 portrait sheets for the cost to be the same at either studio. Plugging x back into either original cost equation, we find that the total cost at either studio will be 33(12) + 51 = 99(12) + 99 = $495.
why would 3/2 be a rational number?
Explanation: All fractions positive or negative are rational numbers so 3/2 must be rational. Another way to think about rational numbers is that if you can turn the number into a fraction, it's rational. Since 3/2 is already in fraction form, it's a rational number.
domain of the function f(x)=3x3 is 2,5 what is the function range?
Domain of the function f(x)=3x^3 is 2,5 what is the function range?
Answer:
The range of given function is {24, 375}
Solution:
Domain of the function is possible input of the function that is "x" and range of the function is possible output of the function that is f(x)
So we can substitute the given domain values of "x" in f(x) and find the range of function
As per the given question:
The domain of the function [tex]f(x) = 3x^3[/tex] is, [2, 5]
We have to find the range of the function
At x = 2:Substitute x = 2 in f(x)
[tex]f(x) = 3x^3[/tex]
[tex]f(2) = 3 (2)^3 = 3(8) = 24[/tex]
At x = 5:Substitute x = 5 in f(x)
[tex]f(5) = 3(5)^3 = 3 \times 125 = 375[/tex]
Therefore range of given function is {24, 375}
Which equation relates f(x) with g(x)?
A. g(x) = f(x) + 5
B. g(x) = f(x + 5)
c. g(x) = f(x) - 5
D. g(x) = f(x - 5)
Answer:
g(x)=f(x-5)
Step-by-step explanation:
I did this question for my EOC & got it correct.
The equation that relates f(x) with g(x) is g(x) = f(x - 5).
Explanation:The equation that relates f(x) with g(x) is option D. g(x) = f(x - 5).
Option D represents a translation of the function f(x) in the positive x-direction by a distance of 5 units. This means that every y-value of f(x) at x will now be the y-value of g(x) at (x + 5). The equation g(x) = f(x - 5) precisely captures this relationship between f(x) and g(x).
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The measure of an exterior angle of a regular polygon is 2x, and the measure of an interior angle is 4x. Using the relationship between interior and exterior angles, find the value of x.
The value of x is 30
Solution:
Given that measure of exterior angle of regular polygon is 2x
The measure of interior angle is 4x
To find: value of x
The sum of an interior angle plus an exterior angle must be equal to 180 degrees (supplementary angles)
measure of exterior angle + measure of interior angle = 180
2x + 4x = 180
6x = 180
x = 30
Finding the measure of an exterior angle
measure of exterior angle = 2x = 2(30) = 60 degrees
Finding the measure of interior angle
measure of interior angle = 4x = 4(30) = 120 degrees
Emily participates in a trivia quiz show. In each round, 20 points are awarded for a correct answer and 10 points are deducted for an incorrect answer. Emily answered 7 questions correctly and 8 incorrectly in the first round. What was her first-round score? Emily answered 4 questions correctly and 11 incorrectly in the second round. What was her score in the second round? The final score is the average of the two rounds, what is Emily's final score?
Answer:
1. Emily scored 60 points in the first round
2. Emily scored minus 30 points in the second round
3. Emily's final score is 15 points.
Step-by-step explanation:
1. Let's review all the information given to us to answer the questions correctly:
Points awarded for a correct answer = 20
Points deducted for a incorrect answer = 10
2. Let's calculate the score of Emily in the first round:
Score = 7 * 20 - 8 * 10
Score = 140 - 80
Score = 60
Emily scored 60 points in the first round
3. Let's calculate the score of Emily in the second round:
Score = 4 * 20 - 11 * 10
Score = 80 - 110
Score = - 30
Emily scored minus 30 points in the second round
4. Let's calculate the final score of Emily:
Final score = (Score 1st round + Score 2nd round)/2
Final score = (60 + - 30)/2
Final score = (60 - 30)/2 = 30/2 = 15
Emily's final score is 15 points.
Solve for X. Thanks for the help!!!!
Check the picture below.
what is 9 out of 100 as a percent ?
Answer:
9%
Step-by-step explanation:
9/100 = 0.09
To convert to a percent, multiply by 100 and add a percent sign:
0.09 * 100 = 9%
Answer: 9%
Step-by-step explanation:
I Looked it up online.
A construction crew has just finished building a road. The road is 10 kilometers long. If the crew worked for 4 2/3 days, how many kilometers of road did they build each day? (Assume they built the same amount each day.)
2.14 kilometers of road is built each day
Solution:
Given that road is 10 kilometers long
The crew worked for [tex]4\frac{2}{3}[/tex] days
To find: Kilometers of road build each day
Assume they built the same amount each day
Length of road = 10 km
number of days worked = [tex]4\frac{2}{3} = \frac{3 \times 4 + 2}{3} = \frac{14}{3}[/tex]
Kilometers of road build each day is given as:
Kilometers of road build each day = total length of road divided by number of days the crew worked
[tex]\rightarrow \frac{10}{\frac{14}{3}}=\frac{10}{1} \times \frac{3}{14}=2.14[/tex]
Thus 2.14 kilometers of road is built each day
Write an equation in point-slope form of the line that passes through the point (4,−9) and has a slope of 6. The equation is y− = (x− )
Answer:
y + 9 = 6(x - 4)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 6 and (a, b) = (4, - 9), thus
y - (- 9) = 6(x - 4), that is
y + 9 = 6(x - 4)
What is a equation of a line that passes threw the points (3,1) and (-2,4)
Answer:
y-1=-3/5(x-3)
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-1)/(-2-3)
m=3/-5
m=-3/5
y-y1=m(x-x1)
y-1=-3/5(x-3)
Last year, Goran biked 384 miles. This year he biked c miles, using c write an expression for the total number of miles he biked
Answer:
384 + c = m.
Step-by-step explanation:
You can use another variable such as t to represent "total." I used m to represent total "miles." The variable you use to represent the total shouldn't matter but these two variables make the most sense. 384 for last year's miles plus c, which is this year's miles, equals the total miles. A very simple, straight forward and easy equation to write.
if r equals 35 and s equals to 5t t=2u and u≠0 what is the value of rst/u³
2. before last nights game a basketball player has scored an average ( arithmetic mean) of 20 points per game . she scored 25 points in last nights game raising her average go 21 points per game. how many games did she play before last night's game
@3 (b)4(c)5(d)6(e)7
Question:
before last nights game a basketball player has scored an average ( arithmetic mean) of 20 points per game . she scored 25 points in last nights game raising her average go 21 points per game. how many games did she play before last night's game
Answer:
She played 4 games before last night's game
Step-by-step explanation:
Given:
Average of last night basketball games = 20
Points scored in last night game = 25
Rise in average after last night game = 21
To Find:
The number of games played last night = ?
Solution:
Let the number of games played before last night's game be x
Then
The average of x games =20
That is
[tex]\frac{\text{ Total points scored in x games}}{x}= 20[/tex]
Total points scored in x games = 20x
In last night game she scored 25 points
So now the total score will be = 20x+25 and
the number of games will be x+1
Now the
The average of x+1 games = 21
[tex]\frac{20x+25}{x+1}[/tex] =21
[tex]20x+25 =21 \times (x+1) [/tex]
[tex]20x+25 =21x+ 21[/tex]
[tex]25-21 =21x-20x[/tex]
x=4
A store sells two different packages of glue sticks as described below. Package A : 18 glue sticks. Package B : 12 glue sticks.
Answer:
Package A: [tex]g=18p[/tex] and Package B: [tex]g=12p[/tex]
Step-by-step explanation:
Here is the complete question: A store sells two different packages of glue sticks as described below. Package A : 18 glue sticks. Package B : 12 glue sticks. Write an equation for package A and B that represents the total number of glue sticks is "g" in "p" package.
Given: There are 2 packages .
Package A has 18 glue sticks
Package B has 12 glue sticks
As given let "g" be the total number of glue sticks in "p" packages.
Package A:
Total number of glue sticks in "P" packages= [tex]Total\ number\ of\ glue\times p[/tex]
∴ [tex]g=18\times p= 18p[/tex]
∴ [tex]g=18p[/tex]
Package B:
Total number of glue sticks in "P" packages= [tex]Total\ number\ of\ glue\times p[/tex]
∴ [tex]g=12\times p= 12p[/tex]
∴ [tex]g=12p[/tex]
Solve the system by elimination. 4x+6y=10 6x=9y−3
Answer:
x=1, y=1. (1, 1).
Step-by-step explanation:
4x+6y=10
6x=9y-3
-----------------
4x+6y=10
9y-6x=3
-----------------
4x+6y=10
-6x+9y=3
---------------
simplify -6x+9y=3 into -2x+3y=1
------------------------
4x+6y=10
-2x+3y=1
---------------
4x+6y=10
2(-2x+3y)=2(1)
-----------------------
4x+6y=10
-4x+6y=2
---------------
12y=12
y=12/12
y=1
4x+6(1)=10
4x+6=10
4x=10-6
4x=4
x=4/4=1
To solve the system of equations by elimination, multiply one equation by a constant that will create opposite coefficients for one of the variables. Then, combine the equations and solve for the remaining variable.
Explanation:To solve the system of equations by elimination, we need to eliminate one of the variables by adding or subtracting the equations.
In this case, let's eliminate y. We can do this by multiplying the first equation by 3 and the second equation by 6, so that the coefficients of y will be the same but opposite in sign. This gives us:
12x + 18y = 30
36x = 54y - 18
Now subtract the second equation from the first equation:
(12x + 18y) - (36x) = (30) - (54y - 18)
12x + 18y - 36x = -54y + 48
-24x + 18y = -54y + 48
Collect like terms:
-24x - 18y = -54y + 48
Rearrange the equation:
-24x + 54y = 48
The resulting equation is -24x + 54y = 48.
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A study will investigate the effectiveness of a new early reading program on
Prekindergarten students' reading abilities. The samples (n = 30 and
n =40) included in the study are taught by two preschool teachers.
Which of the
following are possible limitations of the study? Select all that apply.
A. The sample size is too small.
B. The teachers may differ in number of years teaching.
C. The teachers may differ in early childhood experience.
D. The teachers may differ in number of years teaching reading.
Answer:
B, C, D
Step-by-step explanation:
The information given about the teachers is limited to the fact they teach preschool.
B and D. If a teacher has more experience teaching, they are probably better at teaching. Even if the subject is not reading, they gain transferable teaching skills with experience.
C. Although both teachers teach preschool, one may have many more years of experience or other qualifications, which will likely help them to teach better in generally.
A. The samples 30 and 40 students in a typical class are enough to show different students' various learning styles and strengths. The sample size is big enough.
(SAT Prep) Find the value of x in each of the following exercises:
Answer:
[tex]x=115^o[/tex]
Step-by-step explanation:
Angles Inside a Polygon
A polygon of n sides must have the sum of its internal angles
[tex]S=180^o(n-2)[/tex]
The polygon shown in the figure has n=5 sides, so the sum of its internal angles is
[tex]S=180^o(5-2)=540^o[/tex]
The construction of the internal angles of the polygon is shown in the image below. The sum of them is
[tex]50+180-x+180-x+360-x+x=540[/tex]
Reducing
[tex]-2x+770=540[/tex]
Solving
[tex]\displaystyle x=\frac{770-540}{2}[/tex]
[tex]\boxed{x=115^o}[/tex]
Answer:
x is 115 degrees
Step-by-step explanation:
Please help!!!
Given: △ABC is isosceles; 1 ≅ 3
Prove: AB || CD
Answer:
Step-by-step explanation:
△ABC is isosceles. So ∠3 = ∠4
given 1 ≅ 3.
therefore, 1 ≅ 4
alternate interior angles are equal if only AB//CD
What is the perimeter of the parallelogram?
(2, 2), (5,2), (4,4), (1,4)
Answer:
10.5 units (3 s.f.)
Step-by-step explanation:
Please see attached picture for full solution.
Note that AB and CD are horizontal lines because A and B have the same y coordinate, and C and D have the same y coordinate. As a result, I can simply subtract their x coordinate values to find length of AB and CD.
Problem Set
1. Use the set of ordered pairs below to answer each question.
{(4,20), (8,4),(2,3), (15,3), (6,15),(6,30), (1,5),(6,18),(0,3)}
a. Write the ordered pair(s) whose first and second coordinate have a greatest common factor of 3.
b. Write the ordered pair(s) whose first coordinate is a factor of its second coordinate.
c. Write the ordered pair(s) whose second coordinate is a prime number.
a) (15, 3) and (6, 15) and (0, 3) are the ordered pairs whose first and second coordinate have a greatest common factor of 3
b) The ordered pair(s) whose first coordinate is a factor of its second coordinate are (4, 20) and (6, 30) and (1, 5) and (6, 18)
c) (2 , 3) and (15, 3) and (1, 5) and (0, 3) are ordered pair(s) whose second coordinate is a prime numbers
Solution:
Given that,
Use the set of ordered pairs below to answer each question.
{(4, 20), (8, 4), (2, 3), (15, 3), (6, 15), (6, 30), (1, 5), (6, 18), (0, 3)}
a. Write the ordered pair(s) whose first and second coordinate have a greatest common factor of 3So we must find GCF of the ordered pairs
GCF of 4 and 20:
The factors of 4 are: 1, 2, 4
The factors of 20 are: 1, 2, 4, 5, 10, 20
Then the greatest common factor is 4
GCF of 8 and 4:
The factors of 4 are: 1, 2, 4
The factors of 8 are: 1, 2, 4, 8
Then the greatest common factor is 4
GCF of 2 and 3:
The factors of 2 are: 1, 2
The factors of 3 are: 1, 3
Then the greatest common factor is 1
GCF of 15 and 3:
The factors of 3 are: 1, 3
The factors of 15 are: 1, 3, 5, 15
Then the greatest common factor is 3
GCF of 6 and 15:
The factors of 6 are: 1, 2, 3, 6
The factors of 15 are: 1, 3, 5, 15
Then the greatest common factor is 3
GCF of 6 and 30:
The factors of 6 are: 1, 2, 3, 6
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
Then the greatest common factor is 6
GCF of 1 and 5:
The factors of 1 are: 1
The factors of 5 are: 1, 5
Then the greatest common factor is 1
GCF of 6 and 18:
The factors of 6 are: 1, 2, 3, 6
The factors of 18 are: 1, 2, 3, 6, 9, 18
Then the greatest common factor is 6
GCF of 0 and 3:
The factors of 0 are: All Whole Numbers
The factors of 3 are: 1, 3
Then the greatest common factor is 3
Summarizing the results:
(15, 3) and (6, 15) and (0, 3) are the ordered pairs whose first and second coordinate have a greatest common factor of 3
b. Write the ordered pair(s) whose first coordinate is a factor of its second coordinate.So let us find the factors of second cordinate and check
For (4, 20) , the factors of 20 are 1, 2, 4, 5, 10, 20
Thus first coordinate 4 is factor of second cordinate
For (8, 4) the factors of 4 are 1, 2, 4
Thus first coordinate is not a factor of second cordinate
For (2, 3), the factors of 3 are 1, 3
Thus first coordinate is not a factor of second cordinate
For (15, 3), the factors of 3 are 1 and 3
Thus first coordinate is not a factor of second cordinate
For (6, 15) , the factors of 15 are 1, 3, 5, 15
Thus first coordinate is not a factor of second cordinate
For (6, 30), the factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
Thus first coordinate 6 is factor of second cordinate
For (1, 5) , the factors of 5 are 1 and 5
Thus first coordinate 1 is a factor of second cordinate
For (6, 18) , the factors of 18 are 1, 2, 3, 6, 9, 18
Thus first coordinate 6 is factor of second cordinate
For (0, 3) , the factors of 3 are 1 and 3
Thus first coordinate is not a factor of second cordinate
Summarizing the results:
The ordered pair(s) whose first coordinate is a factor of its second coordinate are (4, 20) and (6, 30) and (1, 5) and (6, 18)
c. Write the ordered pair(s) whose second coordinate is a prime number.A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole numbers that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.
Therefore,
(2 , 3) and (15, 3) and (1, 5) and (0, 3) are ordered pair(s) whose second coordinate is a prime numbers
To find the ordered pairs with a GCF of 3, divide the second coordinate by the first to find pairs where the first is a factor of the second, and check the second coordinate for prime numbers.
Explanation:To find the ordered pairs whose first and second coordinates have a greatest common factor of 3, we can go through each pair and check the GCF. The pairs that have a GCF of 3 are (6, 15), (6, 30), and (0, 3).
To find the ordered pairs whose first coordinate is a factor of its second coordinate, we need to divide the second coordinate by the first coordinate and check if the result is a whole number. The pairs that meet this condition are (2, 3), (15, 3), and (0, 3).
To find the ordered pairs whose second coordinate is a prime number, we need to check if the second coordinate is divisible only by 1 and itself. The pair that meets this condition is (2, 3).
h=-16t^2+96t+4
solve by factoring
Answer:
6 plus or minus square root of 37/2
Step-by-step explanation:
Is the quadratic formula allowed or no?
Answer:
t = 3 ± ½√37
Step-by-step explanation:
0 = -16t² + 96t + 4
This isn't factorable, so complete the square or use quadratic formula. Completing the square:
16t² − 96t = 4
t² − 6t = 1/4
t² − 6t + 9 = 1/4 + 9
(t − 3)² = 37/4
t − 3 = ±½√37
t = 3 ± ½√37
solve 9 is subtracted from 2 times the sum of 7 and 4
2×11+9
22+9
31
This the the way to solve this answer
Answer:77
Step-bystep explanation:
[9-2] * [7+4]
[7] * [11]
7*11=77
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Which equation represents the line that passes through the points (-1,-2)and(3,10)
Answer:
y= 3x +1
Step-by-step explanation:
Let's write the equation of the line in slope-intercept form. That is, y= mx +c, where m is the slope and c is the y-intercept.
Start by finding the slope with the formula below:
[tex]\boxed{\text{slope}=\frac{y_1-y_2}{x_1-x_2} }[/tex]
Slope
[tex]=\frac{10-(-2)}{3-(-1)}[/tex]
[tex]=\frac{10+2}{3+1}[/tex]
[tex]=\frac{12}{4}[/tex]
= 3
Substitute m= 3 into the equation:
y= 3x +c
To find the value of c, substitute a pair of coordinates into the equation.
When x= -1, y= -2,
-2= 3(-1) +c
-2= -3 +c
c= -2 +3
c= 1
Thus, the equation of the line is y= 3x +1.
_______
Alternatively, we can write the equation in the point-slope form.
[tex]\boxed{y-y_1=m(x-x_1)}[/tex]
Substitute m= 3 and a pair of coordinates into [tex](x_1,y_1)[/tex]:
y -10= 3(x -3)
Additional:
For more questions on writing equations of line, check out:
https://brainly.com/question/25549430The equation which passes through the points (-1,-2)and(3,10) will be y= 3x +1
What is an equation?An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Let's write the equation of the line in slope-intercept form. That is, y= mx+c, where m is the slope and c is the y-intercept.
Start by finding the slope with the formula below:
[tex]\rm Slope =\dfrac{y_1-y_2}{x_1-x_2}[/tex]
Slope
[tex]\rm Slope =\dfrac{10-(-2)}{3-(-1)}[/tex]
[tex]\rm Slope=\dfrac{12}{4}[/tex]
Slope = 3
Substitute m= 3 into the equation:
y = 3x + c
To find the value of c, substitute a pair of coordinates into the equation.
When x= -1, y= -2,
-2 = 3(-1) + c
-2= -3 + c
c = -2 + 3
c = 1
Thus, the equation of the line is y = 3x + 1.
Alternatively, we can write the equation in the point-slope form.
y - y₁ = m ( x - x₁ )
Substitute m= 3 and a pair of coordinates into :
y - 10 = 3 ( x - 3 )
Therefore the equation which passes through the points (-1,-2)and(3,10) will be y= 3x +1
To know more about equations follow
https://brainly.com/question/2972832
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What is -4x+y=-8 equal to
Answer:
y=4x+8
Step-by-step explanation:
I assume you want this rewritten in slope intercept form. That means we need to isolate the y.
-4x+y=-8
Add 4x to both sides
y=-8+4x
Now let's rewrite it in slope intercept form. Recall slope intercept form is y=mx+b. That means our 'b' (8) must be on the end of the equation.
y=4x+8