Answer:
[tex]3(x - 1)^2 - 11= 0[/tex]
Step-by-step explanation:
Given
[tex]3x^2 - 6x = 8[/tex]
Required
Rewrite in form of [tex]3(x - p)^2 + q = 0[/tex]
[tex]3x^2 - 6x = 8[/tex]
Subtract 8 from both sides
[tex]3x^2 - 6x - 8 = 8 - 8[/tex]
[tex]3x^2 - 6x - 8 = 0[/tex]
Express -8 as 3 - 11;
So, we have:
[tex]3x^2 - 6x + 3 - 11= 0[/tex]
Expand [tex]3x^2 - 6x + 3[/tex]
[tex]3(x^2 - 2x + 1) - 11= 0[/tex]
Factorize the expression in the bracket;
[tex]3(x^2 - x -x + 1) - 11= 0[/tex]
[tex]3(x(x - 1) -1(x - 1)) - 11= 0[/tex]
[tex]3((x - 1)^2) - 11= 0[/tex]
[tex]3(x - 1)^2 - 11= 0[/tex]
By comparison: [tex]3(x - p)^2 + q = 0[/tex]
[tex]p= 1[/tex]
[tex]q = -11[/tex]
Write the equation of the parabola in vertex form.
Vertex: (−4,6); Point: (−2,−2)
Answer:
y = - 2(x + 4)² + 6
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k ) = (- 4, 6 ) , thus
y = a(x - (- 4) )² + 6 , that is
y = a(x + 4)² + 6
To find a substitute (- 2, - 2) into the equation
- 2 = a(- 2 + 4)² + 6 ( subtract 6 from both sides )
- 8 = a(2)² = 4a ( divide both sides by 4 )
- 2 = a , thus
y = - 2(x + 4)² + 6 ← equation in vertex form
3.What is the area of a Square with sides measuring 9 inches?
Answer:
81
Step-by-step explanation:
length times width = area
Answer:
81 inches.
Because 9
Step-by-step explanation:
MULTIPLE CHOICE Determine which statement follows
logically from statements (1) and (2).
(1) If a triangle is equilateral, then it has three congruent sides.
(2) If all the sides of a triangle are congruent, then each of its
angles measures 60.
A If a triangle is not equilateral, then it cannot have congruent angles.
B A figure with three congruent sides is always an equilateral triangle.
C If a triangle is not equilateral, then none of the angles equals 60.
D If a triangle is equilateral, then each of its angles measures 60.
If a triangle is equilateral, then each of its angles measures 60°. Therefore, option D is the correct answer.
What is an equilateral triangle?An Equilateral triangle is a triangle in which all three sides are equal and angles are also equal. The value of each angle of an equilateral triangle is 60° therefore, it is also known as an equiangular triangle.
The given statements are
(1) If a triangle is equilateral, then it has three congruent sides.
(2) If all the sides of a triangle are congruent, then each of its
Here, if a triangle is equilateral, then each of its angles measures 60°.
Therefore, option D is the correct answer.
To learn more about an equilateral triangle visit:
https://brainly.com/question/17824549.
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What is the cost of juice in dollars per fluid ounce?
Ratios and Rates
Express each ratio as a fraction in the simplest form
1) 30 miles out of 30 miles
2) B blue cars out of 12 cars
3) 7 quarts to 84 quarto
4) 25 cups to 35 cups
5) 9 gallons to 36 gallons
6) 54 bootles out of 60 insects
7) 10 pennlos to 45 pennies
B) 28 dimes to 48 dimos
Express each phrase as a rate and unit rate
(Round your answer to the nearest hundredth)
Rate
Unit Rate
9) 130 miles on 4 gallons of gas
10) 9 inches of sno
w in 7 hours
11) 6 calculators cost $150.00
12) 8 pencils for 16 dollars
13) 10 chocolate bars cost 17 dollars
14) 7 dollars for 3 cans of tuna
15) 9 batteries cost 13 dollars
16) 14 dollars for 8 books
Math-Ads.com
Answer:
1) 1
2) 12/B
3) 12
4) 1 2/5
5) 4
6) 1 1/10
7) 4 1/2
8) 1 7/10
9) 32 1/2
10) 9
PLEASE ANSWER FAST.
The question is in the picture.
(question 24)
Answer:
As the values of x increase both function decrease in value.
Step-by-step explanation:
PLZ ANSWER THIS QUICK! THANK YOU!
Answer:
a) 14:56
simplest form:- 14:56
=>2:8
=>1:4
b)Total necklaces that are sold each month:-240
No. of necklaces that were sold via the shop's website:-180
No. of necklaces that were sold in a high street shop:-(240-180)=>60.
Ratio:- 180:60
simplest ratio:- 3:1.
Fill in the blanks by creating the line parallel to y= -1/2x+7 that goes through (-2,3) in slope intercept form.
Answer:
y = [tex]-\frac{1}{2}[/tex] x + 2
Step-by-step explanation:
Two parallel lines share the same slope, so the slope of this parallel line will also be [tex]-\frac{1}{2}[/tex].
Now, you'll have to find the y-intercept. But, to make sure your line also goes through the point (-2, 3), plug them into the x and y values:
y = mx + b
3 = (-1/2) (-2) + b
3 = 1 + b
b = 2
Now you can plug the y-intercept and slope into the slope-intercept formula:
y = [tex]-\frac{1}{2}[/tex] x + 2
PLEASE IM BEGGING U I NEED THIS PLEASE!!! THANK U FOR HELPING cries!!
What is the equation of the line, in standard form, if the slope is = - 1/4 and it passes through point (-3,4) ?
THANK U SO MUCH!!
Answer:
x+4y=13
Step-by-step explanation:
slope m= -1/4
(-3,4)
Slope intercept form: y=mx+c. plug in values of x,y,m, find c
4=(-1/4)*(-3)+c
c=4-3/4=(16-3)/4=13/4
Equation of line is:
y=(-1/4)x+13/4
To bring it to standard form, 4y=-x+13
x+4y=13
A band is playing at an auditorium with floor seats and balcony seats. The band wants to sell the floor tickets for$15 each and balcony tickets for$12 each. They want to make at least $3,000 in ticket sales.
Write an inequality whose solutions are the number of floor and balcony tickets sold if they make at least $3,000 in ticket sales.
Answer:
15x + 12y ≥ 3000
Step-by-step explanation:
Let
Number of floor seats tickets sold = x
Number of balcony seats tickets sold = y
Cost of floor tickets = $15
Cost of balcony tickets = $12
They want to make at least $3,000 in ticket sales.
At least in inequality means ≥
The inequality that represent the situation is
15x + 12y ≥ 3000
Answer:
:)
Step-by-step explanation:
15x + 12y ≥ 3000
Number of floor seats tickets sold = x
Number of balcony seats tickets sold = y
Cost of floor tickets = $15
Cost of balcony tickets = $12
They want to make at least $3,000 in ticket sales.
At least in inequality means ≥
The inequality that represent the situation is 15x + 12y ≥ 3000
8x0.3= pls help now 82 points
Answer:
2.4 8 times 3 is 24 so 8 times 0.3 is 2.4
how many triangles in the figure?
26
25
24
27
OMG Help Me !Select all the correct answers. Which tables represent constant functions? Pick 2 and show your work. No guessing.
x y
2 -1
2 0
2 1
x y
2 -3
4 -7
6 -11
x y
2 3
4 3
6 3
x y
1 3
2 12
3 27
x y
1 -1
2 -1
3 -1
Tables 1 and 2 because they move at a constant rate of change and they are linear functions with a slope.
Table 3 is not a function because there is more than one input for each output.
Table 4 is an exponential equation with the equation y = 4x^2
Table 5 is not a function for the same reason as table 3.
Answer:
Yes! The answer is A and B. Or the 1st and 2nd ones.
Step-by-step explanation:
I need someone ti help me with ny homework tmr at 7:30 plzzzz
Answer:
what do you need help with?
1.What is the slope of the function shown on the graph?
A line is graphed on a four quadrant coordinate plane. The x-axis and the y-axis go from negative 10 to 10 in increments of 1. The line passes through (0, 7) and (4, 2).
A−56
B−54
C−65
D−45
2.A quarry runs a delivery service for crushed stone. The cost to deliver the crushed stone is a flat fee for the delivery and the cost of the crushed stone in terms of weight. The graph of the total cost, C, in dollars as a function of the weight, x, in pounds of the crushed stone is shown. What is the meaning of the y-intercept?
A line is graphed on a first quadrant coordinate plane. The horizontal x-axis is labeled Weight in pounds and goes from 0 to 6000 in increments of 200, and the vertical C of x-axis goes from 0 to 500 in increments of 20. The line passes approximately through (0, 120) and (400, 134).
A.The cost of the delivery is $120.
B.The cost of stone dust is $0.035 per pound.
C.The cost of the delivery is $70.
D.The cost of stone dust is $70 per ton.
3.What is the x-intercept of the function f(x) graphed on the coordinate plane?
A line is graphed on a four quadrant coordinate plane. The horizontal axis goes from negative 7 to 7 in increments of 1, and the vertical axis goes from negative 7 to 7 in increments of 1. From left to right, a straight line passes through (0, 1) and (2, 0).
A−2
B−1
C2
D1
Answer:
1) B - 5/4
2) A. The cost of delivery is $120
3) C 2
Step-by-step explanation:
1) The given parameters are;
The demarcations on the x-axis = -10 to 10
The demarcations on the y-axis = -10 to 10
The coordinates of two points on the graph are (0. 7), and (4, 2)
The slope, m, of a graph is given by the following equation;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Given that (x₁, y₁) = (0. 7) and (x₂, y₂) = (4, 2), we have;
[tex]Slope, \, m =\dfrac{2-7}{4-0} = -\dfrac{5}{4}[/tex]
The slope, m = -5/4
Taking B. as = -5/4
2. The given information are;
The nature of the cost of delivery of crushed stone = Cost of delivery, A
The function, f, for the cost of crushed stone of mass, x is the cost C, f(x) = C = m × x + A
Whereby the the graph of the total cost of the crushed stone is a straight line graph, we have;
C = m × x + A
At the y-intercept, x = 0, we have;
C[tex]_{(y-intercept)}[/tex] = m × 0 + A
C[tex]_{(y-intercept)}[/tex] = A = Cost of delivery
The points on the line are;
(0, 120) and (400, 134), therefore, the slope, m, is given as follows;
[tex]Slope, \, m =\dfrac{134-120}{400-0} = \dfrac{14}{400} = 0.035[/tex]
We have;
(C - 134) = 0.035×(x - 400)
C = 0.035·x - 14 + 134 = 0.035·x + 120
C = 0.035·x + 120
At the y-intercept, x = 0, we have;
C[tex]_{(y-intercept)}[/tex] = 0.035 × 0 + 120
C[tex]_{(y-intercept)}[/tex] = 120 = Cost of delivery
Therefore, the cost at the y-intercept = The cost of delivery = $120
3. The coordinates of points on the graph are;
(0, 1) and (2, 0)
The slope, m = (0 - 1)/(2 - 0) = -1/2
The equation of the line in point slope form is given as follows;
(y - 0) = -1/2 × (x - 2)
y = -x/2 + 1
The x-intercept occurs at the point y = 0, which is presented as follows;
0 = -x/2 + 1
-x/2 = -1
x = -1 × (-2) = 2
x = 2
Therefore, the y-intercept occurs at x = 2.
The correct option is
C 2
Before beginning voice lessons, Bryan already knew how to sing 146 pieces, and he expects to learn 2 new pieces during each week of lessons. How many weeks of lessons will Bryan need before he will be able to sing a total of 300 pieces? Write and Solve an equation to find the answer.
Answer:
77 weeks
Step-by-step explanation:
Let the number of weeks be represented as x
The equation for the above question is given as:
146 + 2(x) = 300 pieces
146 + 2x = 300
2x = 300 - 146
2x = 154
x = 154/2
x = 77
Bryan would be needing 77 weeks of lessons
The Wholesome Bakery baked 4 loaves of bread on Thursday, 12 loaves of bread on Friday, 36 loaves of bread on Saturday, 108 loaves of bread on Sunday, and 324 loaves of bread on Monday. If this pattern continues, how many loaves of bread will they bake on Tuesday?
Answer:
once again, the pattern is multiply by 3
Answer:
972
Step-by-step explanation:
the pattern is multiplied by 3
What vocabulary term describes symbols that represent numbers whose quantity we don't know?
Answer:
variable
Step-by-step explanation:
please answer these honestly and take as much time as you need. ty.
Answer:
1) 17/20 2)24 and 1/2 3)terminating 4) 0.8 5)1.8
Step-by-step explanation:
4) 4/5 times both sides by 2 then you get 8/10= 0.8
Answer:
first is 17/20, second is 24 1/2 , third is a terminating decimal, fourth is 0.8, and the fifth is 8.1.
Step-by-step explanation:
hope this helps :)
PLS PLS PLS PLEASEEE HURRY UP
Answer:
Step-by-step explanation:
d
If a diameter of a circle has endpoints (-3, 5) and (5, 7), then the center of the circle is
Answer:
The midpoint formula is ( (x1 + x2)/2, (y + y2)/2 ) The answer will be an ordered pair.
(-7 + 5)/2, (3 + 1)/2
(-2/2, 4/2)
(-1, 2)
The center of the circle is at (-1,2)
What is 3/4 plus 1 1/4?
Answer: 2
Step-by-step explanation:
you add the 3/4 to the 1/4 and get 4/4 which equals 1 next you add that to the 1 from the problem and get 2
if you need it in an improper fraction you can just say 8/4
Wanda the Witch knows Halloween is coming up soon so she
has started increasing the amount of carbs she eats every
day so she can build up some stamina for all the work
that Halloween brings. (Scaring little kids is a lot of work)
Wanda increased her Carbohydrate intake
from 250 grams a day to 415 grams a day.
By what percentage did Wanda increase the amount of
carbs she eats daily?
Answer:
mathematics ba talaga po ba ito?
please help me out!!!
Which statement about the graph is true?
•The period of the graph is 2pi/3
•The amplitude of the graph is 2 units •The domain of the graph is from –3 to 3 and is inclusive.
•The graph represents a reflection over the x-axis of the function y = 3sin(2x)
Answer:
D. The graph represents a reflection over the x-axis of the function y = 3sin(2x).
Step-by-step explanation:
The statement fourth the graph represents a reflection over the x-axis of the function y = 3sin(2x) is true option (D) is correct.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have shown a trigonometric graph in the picture.
The maximum value graph achieve is 3
The minimum value graph achieve is -3
The midline y = 0
The parent function will be f(x) = sinx
Transformed function:
y = 3sin(2x)
Thus, the statement fourth the graph represents a reflection over the x-axis of the function y = 3sin(2x) is true option (D) is correct.
Learn more about trigonometry here:
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Maya is working two summer jobs, making $7 per hour babysitting and $11 per hour landscaping. Last week Maya earned a total of $96 and worked 3 times as many hours babysitting as she worked hours landscaping. Determine the number of hours Maya worked babysitting last week and the number of hours she worked landscaping last week.
Answer:
3 hours for landscaping and 9 hr for babysitting
Step-by-step explanation:
So take x to be babysitting and y to be landscaping
The equation will be 7x+11y=96
$7 for the baby sitting and $11 for the landscaping and 96 for the total
So then it says 3 times as many hours than landscaping so x equation will look like this x=3*y
So replace the terms - 7*(3y)+11y=96
Simplify (7*3)y+11y=96
Simplify more 21y+11y=96
You get 32y=96
Divide both sides by 32 to have y only 32y/32=96/32
You will get y=3
So landscaping will be 3 hours and it says that babysitting is 3 times so multiply 3 you get 9
So landscaping is 3 hours and babysitting is 9 hours
Hope this help
(It may be wrong so if it is im sorry :( )
Answer:3 hours for landscaping and 9 hr for babysitting
Step-by-step explanation:
Someone answer this for brainliest.
Answer:
x < 3
Step-by-step explanation:
4x - 7 < 5
Add 7 to both sides.
4x < -2
Divide by 4 to both sides to get x alone.
x < 3
To check the answer if it's right or not, you can just plug in the 3 for x and multiply it by 4 which would equal 12 and subtract 12 - 7 which would equal 5.
Hope this helps and pls do mark me brainliest:)
Answer:
x < 3
Step-by-step explanation:
4x-7<5
4x<5+7
4x<12(divide both sides by 4)
4. 4
x<3
y = 4x2 - 5X-10
vertex
Tara has 3/4 cup of ice cream. How many 1/5 -cup servings are in 3/4 cup of ice cream?
Answer:
4/15
Step-by-step explanation:
because 1/5÷3/4=4/15
ASAP ASAP ASAP
HELP ME PLEASE
Answer:
D i'm pretty sure
Step-by-step explanation:
Answer: $2.19
Step-by-step explanation: you have to find the surface area. Add 10*7*2 and 7*1.25*2 and 1.25*10*2 and then multiply by 0.012! Then you can get your answer. (17.5 + 140 + 25)*0.012. I think this is right. Sorry if itś not.