Answer:
Option C:Vertex = (–2,–25), y-intercept = (0,–21), x-intercepts = (–7,0) and (3,0), axis of symmetry is x = –2
Step-by-step explanation:
We are given the function;
f(x) = (x - 3)(x + 7)
The axis of symmetry in a quadratic equation is given by the formula;
x = -b/2a
Expanding the function given, we have;
f(x) = x² + 4x - 21
a = 1
b = 4
c = - 21
Thus;
Axis of symmetry is:
x = -(4)/(2 × 1)
x = -2
Now, y-intercept is when x = 0
Thus;
f(0) = (0 - 3)(0 + 7)
f(0) = - 3 × 7 = - 21
y - intercept is (0, - 21)
x-intercept is when f(x) = 0
Thus;
(x - 3)(x + 7) = 0
Thus;
x - 3 = 0 or x + 7 = 0
x = 3 or x = - 7
x - intercept is (-7, 0) and (3,0)
The y-coordinate of vertex will be at the line of axis of symmetry.
Thus, we will put x = -2 into the function to get;
y = (-2 - 3)(-2 + 7)
y = -5 × 5 = - 25
Vertex is at (-2, -25)
Correct Answer is option C
Answer:
Vertex = (–2,–25), y-intercept = (0,–21), x-intercepts = (–7,0) and (3,0), axis of symmetry is x = –2
Step-by-step explanation:
Which two numbers have a product of −18 and a sum of −7?
Answer:
2 and -9
Step-by-step explanation:
2 times -9 is -18
2 plus -9 is -7
Hope this helped!
Janet and Jack are walking in a two-day event to raise money for charity. Janet asks a friend for a $7.50 donation, plus $0.10 for each mile she walks. Jack asks a friend for a $5.50 donation, plus $0.15 for each mile he walks. At how many miles of walking would Janet and Jack collect the same amount of money?
Answer:
Step-by-step explanation:
A. 40
B. 28
C. 44
D. 25
The yield in bushels from a grove of orange trees is given by Y = x(600 − x), where x is the number of orange trees per acre. How many trees will maximize the yield?
Answer:
90000
Step-by-step explanation:
Y = x(600 - x)
Let's rearrange the equation so that we have
Y = x(-x + 600)
Y = -x² + 600
When you take a look at parabolas, we know that their maximum or minimum values are usually on the axis of symmetry. This axis of symmetry has an equation of
x = -b/2a,
In this question, the axis of symmetry is
x = -600 / -2
x = 300
This means that planting 300 trees will maximize your yield. If you substitute for x = 300 into the equation, the maximum yield will be
y = 300 (600 - 300)
y = 90000.
Answer: 300
Step-by-step explanation:
use the formula X=-b/2a
x=-600/-2
x=300
Given: angle EGF = 60° and Angle AGF = 90°. Prove: AGB = 30
I need two column proof btw
Step-by-step explanation:
you you can state that angles in a triangle add up to 180° and 180 degrees - 90 + 60 is equals to 30 degrees
Which of these steps will eliminate a variable in this system? 4x-9y=8 2x+3y=24
For eliminate a variables we need addition method or elimination method.
Define the term Variable?In an equation or formula, a variable is a symbol or letter that stands in for an unknowable or varying quantity or value.
We can multiply the second equation by -2, so that the coefficient of x in both equations will be the same but with opposite signs:
⇒ 4x - 9y = 8
⇒ -4x - 6y = -48
Add the two equations together: ⇒ -15y = -40
⇒ y = 8/3
Substitute this value of y back into either equation to solve for x.
⇒ 4x - 9(8/3) = 8
⇒ 4x - 24 = 8
⇒ x = 8
Therefore, the steps to eliminate a variable in this system using the addition method are to multiply the second equation by -2, add the two equations together to eliminate the x variable, solve for y, and then substitute that value back into either equation to solve for x.
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What is the image of (2,8) after a reflection over the line y = x?
PLS ANSWER FAST
Ended up getting the answer wrong because the other person this is the correct answer.
(8,2)
Enjoy and Happy Holidays :)
The image of (2,8) after a reflection over the line y = x is (8, 2).
The given coordinate is (2, 8).
What is a reflection over the line y=x?Reflect over the y = x: When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places.
When we reflect (2, 8) over the line y=x, we get the coordinate as (8, 2). Because the x-coordinate and y-coordinate changed places.
Therefore, the image of (2,8) after a reflection over the line y = x is (8, 2).
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A triangle has a base length of 10 inches and a height of 4 inches.
What is the area of the triangle?
Answer:
No, The answer is 20. Remember area of triangle equals 1/2bh (or half of base and height multiplied.)
The area of triangle that has a base length of 10 inches and a height of 4 inches is 20 square inches.
What is area of a triangle?
The area of a triangle is one half the product of its base multiplied by height. Mathematically -
Area [Δ] = 1/2 x base x height
Given is a triangle (Δ) has a base length of 10 inches and a height of 4 inches.
We can write -
Base Length [B] = 10 inches
Height of triangle [H] = 4 inches
Area of triangle (Δ) = 1/2 x B x H
A(Δ) = 1/2 x B x H
A(Δ) = 1/2 x 10 x 4
A(Δ) = 20 square inches
Therefore, the area of triangle that has a base length of 10 inches and a height of 4 inches is 20 square inches.
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Oxygen makes up about 20% of the volume of air. Which of these expresses the amount of air made up of oxygen?
PLZ I GIVE BRAILIEST
Answer:
Step-by-step explanation:
in decimal it is 20.00, in fraction it is 1/5.
I need help on math
he sum of two numbers is 60. The greater number is 6 more than the smaller number. Which equation can be used to solve for the smaller number?
x + (x + 6) = 60
x − (x + 6) = 60
x(x + 6) = 60
x(x− 6) = 60
Answer:
x+(x+6)=60
Since the greater number is six more than the smaller number, the variable value will be of the smaller number. And since the bigger number is six more than the smaller number, it needs to be in parantheses as x plus six. But, since the value of both the numbers is sixty, the equation will finally become x+(x+6)=60
solve for g when g=1/6(w+40)
9514 1404 393
Answer:
g = 1/6(w+40)
Step-by-step explanation:
The given equation is already solved for g. Nothing need be done.
g = 1/6(w+40)
A thermometer read -17° F at 1:00 a.m. By 2:30 a.m., the temperature had dropped 9.1° F. What was the temperature at 2:30
a.m.?
Answer:
-26.1°
Step-by-step explanation:
So when the temperature decreases, you want to get more negative. So -17°-9.1°=-26.1°
please help me with this i need help with it+ send the answers not the explnation please
Answer: the picture is blocked
Step-by-step explanation:
Need help with number 6 I’ll mark you as the brainliest please help.
Answer:
Formula
Step-by-step explanation:
[tex]Equation (y-y1) = m(x-x1)[/tex]
Plug in 8 for x1 and -1 for y1 and 3/4 for m
Solve for y
Use basic math skills
What number is represented by a point 6 units to the left of 5 on the number ling
shown
Answer:
-1
Step-by-step explanation:
5-6=-1
scientists are studying a population of 20 bugs and tracking the population, y, as it grows over time, t, in weeks. If the population grows by at least 6.1% each week, which system of inequalities represents the scenario?
Answer:
I am pretty sure it is
y >_ 20(0.061)^t
t >_ 0
Step-by-step explanation:
The photo below is the reduced form of a 16-by-20-inch print. What is the scale factor being used to reduce te
4 in
5 in
Answer:
Option (B)
Step-by-step explanation:
Photo given in the picture has dimensions as,
Length = 4 in.
Width = 5 in.
This photo is the reduced form of a photo having dimension 16 by 20 inch print.
Since scale factor of an image is given by,
Scale factor = [tex]\frac{\text{Dimension of the image}}{\text{Dimension of the original picture}}[/tex]
= [tex]\frac{4}{16}[/tex]
= [tex]\frac{1}{4}[/tex]
Therefore, scale factor used to reduce the picture is [tex]\frac{1}{4}[/tex].
Option (B). will be the correct option.
Answer:
it's 4
Step-by-step explanation:
it's 1:4 cause 16/4 is 4 so the scale factor is 4
Please help me solve this
Answer: number 11 is 12.3 or 12.30
Step-by-step explanation:
HELP!!!!!!!! I LOVE YOU AND ILL EVEN GIVE BRAIN
How will you write 4x + 23y into a statement
Answer:
Tom wants to go to disneyland this weekend with 23 adults including himself and 4 children Ashley 3, Leslie 1, Brit 4, Victor 2. Children under the age of 6 pay "x" amount while anyone older pay "y" amount. What equation can tom use to find out how much the tickets in total will be.
Step-by-step explanation:
Y = Adults pay y amount - There are 23 adults
X =kids under 6 pay x amount - there are 4 children
4x+23y
4 (kids under 6 ticket cost)+ 23 (Adults ticket cost)
i cant figure this out
Answer:
(xy) ^ (-1)
Step-by-step explanation:
Good luck!!
Tim and Tom are trying to earn money to buy a new game system over a 3-month period. Tim saved $45.69 each month. If they need a total of $214.53 to buy the game system, how much does Tom need to earn each of the 3 months in order to buy the game system?
A.25.82
B.103.07
C.77.46
D.168.84
Answer:
A. 25.82
Step-by-step explanation:
(3*Tim)+(3*tom)=214.53
(3*45.69)+(3*tom)=214.53
137.07+(3*tom)=214.53
-137.07+(3*tom)=214.53-137.07
3*tom=77.46
tom/3=77.46/3
tom=25.82
ryans tennis club Membership Which is 11$ is deducted each month which expression shows the total deductions for the year?
Answer:
(-$11)x12
Step-by-step explanation:
hope this helps if its right can i get brainliest
Help Mr. North can read 3/4 of a novel and 1/5 of a week. How much of the novel can Mr. North read in one entire week?
Al changes saved
4. Ten students in your class put their names on slips of paper inside a box. Out of the ten students, four
are girls, and six are boys. Five names are chosen.
What is the probability that three girls and two boys are chosen?
O 7.14%
350%
O 1.90%
O 23.81%
Answer:
1.90 percent
Step-by-step explanation:
Pls Help :( 15 points
108 students went on a field trip. Three buses were filled and 27 students traveled in cars. How many students were in each bus?
Please include algebraic equation please.
Answer:
(108-27)/3 =27
Each bus has 27 students, because 108-27=81, 81/3=27
Step-by-step explanation:
Hope this helps! <3
The volume of a cube is 27 in.. How long is each side? Each side of the cube is____in. long.
Answer:
the volume is 27 and to get a volume of a cube it will be side cubed meaningit will be side x side x side so to get the length of one side we will look for the cube root of 27 by using factor tree and the cube root will be 3
help me with this please i’ll give u a cookie
Answer:
B
Step-by-step explanation:
The flat rate is 30, and the changing value is 45 extra for every hour, h. The equation should be C=45h+30
Answer:
B
Step-by-step explanation:
The flat rate is 30, and the changing value is 45 extra for every hour, h. The equation should be C=45h+30
Helppppp plsss?!?!?!?!?!
Answer:
153.86
Step-by-step explanation:
3.14 x 7 x 7=153.86
What is the scale factor of ABC to DEF?
A. 1/2
B. 2
C. 10
D. 10/7