Write g(x) = 40x 4x2 in vertex form. Write the function in standard form. Factor a out of the first two terms. Form a perfect square trinomial. Write the trinomial as a binomial squared. G(x) = 4x2 40x g(x) = 4(x2 10x) (ten-halves) squared = 25 g(x) = 4(x2 10x 25) – 4(25) g(x) = (x )2 –.
The specified function's vertex form is [tex]g(x) = 4(x+5)^2 - 100[/tex]
What is vertex form of a quadratic equation?If a quadratic equation is written in the form
[tex]y=a(x-h)^2 + k[/tex]
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
What is a perfect square polynomial?If a polynomial p(x) can be written as:
[tex]p(x) = [f(x)]^2[/tex]
where f(x) is also a polynomial, then p(x) is called as perfect square polynomial
For the considered case, the polynomial specified is;
[tex]g(x) = 40x + 4x^2[/tex]
Case 1: Converting to vertex form[tex]g(x) = 40x + 4x^2\\g(x) = 4(x^2 + 10) = 4(x^2 + 10 + 25 -25)\\g(x) = 4(x^2 + 10 + 25) - 100 = 4(x+5)^2 - 100\\[/tex]
Thus, the vertex form of the considered polynomial is [tex]g(x) = 4(x+5)^2 - 100[/tex]
Case 2: Converting to standard formStandard form of a quadratic polynomial is [tex]ax^2 + bx + c[/tex]
Thus, we get: the considered polynomial in standard form as:
[tex]g(x) = 4x^2 +40x[/tex]
Case 3: Factoring the first two terms of polynomial[tex]g(x) = 40x + 4x^2 \\g(x) = 4x(10 + x)[/tex]
Case 4: Forming a perfect square trinomialThe considered polynomial has only two terms, therefore, its not a trinomial.
Thus, the specified function's vertex form is [tex]g(x) = 4(x+5)^2 - 100[/tex]
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Answer:
g(x)=4(x+5)^2-100
Step-by-step explanation:
Have the day you deserve :)
Give two(2)example of the system of linear inequalities in two variables.
Answer: A linear system of two equations with two variables is any system that can be written in the form. ... A solution to a system of equations is a value of x and a value of y that, when substituted into the equations, satisfies both equations at the same time. For the example above x=2 and y=−1 is a solution to the system
Step-by-step explanation:
Write a equation: Two thirds of a number decreased by the product of a number and two, squared, is 43 (PLEASE ANSWER ASAP )
We can transform the mathematical sentence into the equation:
(2/3)*x - (2*y)^2 = 43
How to write the equation?
Here we have the sentence:
" Two thirds of a number decreased by the product of a number and two, squared, is 43"
First, we can define x as "the number"
Then:
" Two thirds of a number..." is:
(2/3)*x
Now we add the next part:
"... decreased by the product of a number and two, squared, is 43"
Assuming that this is another number, let's call it y, we have:
(2/3)*x - (2*y)^2 = 43
This is our two-variable equation.
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point d is the interior of angleABE and point E is the interior of angleDBC....(press on the picture please) (also i scratched out where i tried to work it out)
Answer:
c)41
Step-by-step explanation:
∠DBE = (∠ABE +∠DBC) -∠ABC
= (74 + 103) -136
= 177 - 136
= 41
Two joggers set out at the same time from their homes 21 miles apart. They agree to meet at a point somewhere in
between in an hour and a half. If the rate of one is 2 mph faster than the rate of the other, find the rate of each
The two joggers who are 21 miles apart travel at a speed 8 mph and 6 mph respectively and would meet after one and half hours.
What is an equation?An equation is an expression used to show the relationship between two or more variables and numbers.
Let a represent the speed of the faster jogger and represent the speed of the other jogger. Hence:
a = b + 2 (1)
Also:
In one and half hour (1.5 h):
a = d₁/1.5
d₁ = 1.5a
b = d₂/1.5
d₂ = 1.5b
d₁+ d₂ = 21
1.5a + 1.5b = 21 (2)
From both equation 1 and 2:
a = 8, b = 6
The speed of the joggers is 8 mph and 6 mph respectively.
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does anybody know how
Nina’s sister has 386 stickers that she wants to put in a book. Each page can hold 42 stickers. How many pages will she need? Explain your reasoning.
Answer:
10 pages
Step-by-step explanation:
386/42=9.1 pages
but you can not have .1 of a page so you add another page.
Find the coordinate point for A that would make ABDC a rhombus
(2,3)
O (1,3)
O (3,0)
O(4,0)
1,3 is right correct right answer
The coordinate point for A is (1,3) Therefore, option B is the correct answer.
WE know that rhombus can be defined as a special parallelogram as it fulfills the requirements of a parallelogram, i.e. a quadrilateral with two pairs of parallel sides.
Since a rhombus has all four sides equal just like a square.
Given that, Point C (2, 1), Point B (3,4) and Point D (4,2)
The coordinate point for A that would make ABDC a rhombus.
So, the coordinate point for A is (1,3).
Therefore, option B is the correct answer.
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The original price of a T-Shirt is $15. The T-Shirt is on sale for 35% off. What is the sale price?
Answer:
9.75$
Step-by-step explanation:
Answer:
9.75$
Step-by-step explanation:
The original price of the shirt is $15, and it's on sale for 35% off. What is the item's sale price?
First, convert the 35% to a real mathematical number. For percents, this is always done by dividing the 35% by 100%, or 35% / 100% = 0.350.
Second, find out what 35% of $15 is. This is the amount of the sale discount. This is always found by multiplying 0.350 by the item's cost $15, like this:
0.350 x $15 = $ 5.25.
So for this sale, you'll save $ 5.25 on this item.
This means, the cost of the item to you is
$15 - $ 5.25 = $ 9.75.
PLSSS HELPPP!!! GIVING BRANILLYYYY!!!!
Answer:
very last one
Step-by-step explanation:
hope it helps
Congruent , connected , or in response ?
Answer:
The answer is congruent
The admission fee to the Michigan State Fair is $6 for children and $4 for adults. On the first day $1250 was collected. A total of 220 children and adults attended the fair the first day. How many children and how many adults attended the fair the first day?
Write and solve a system of equations to answer the question.
Show your work here:
Question 2
Answer:
children and
adults attended the fair the first day.
Answer:
185 children and 35 adults
Step-by-step explanation:
first equation: 6x+4y=1250
second equation: x+y=220
work:
6x+4y=1250 (-1)
x+y=220 (6) we eliminate x, that's why I multiply each term by 6 and -1
-6x-4y=-1250
6x+6y=1320
2y=70
2y/2=70/2
y=35 (I used y for adults)
x+35=220
x=220-35
x=185 (and I used x for children)
hope this helps you^^
Using the fundamental theorem of algebra how many solutions will the function have, f (x) = 82x^3+ 216
Answer:
The number of solutions is equal to the highest power exponent.
That is a cubic equation, so it has 3 solutions.
Step-by-step explanation:
PLEASE help me with #2 i’m struggling DUE TODAY
Help with substitution please.
a water bottle has a capacity of 25oz.. How many cups of water will the water bottle hold.
Answer:
3.125 U.S. cups
take how many cups are in one ounce and multiply it.
A line is an undefined term because it
A.)contains an infinite number of points
B.)can be used to create other geometric shapes
C.)describes something that does not have width or depth
D.)is a term that does not have a formal definition
Answer:
C
Step-by-step explanation:
The correct option is C because lines can extend its length in both side infinitely. It contains arrowheads indicating it can extend.
Pls rate.........
A line is an undefined term because it describes something that does not have width or depth. thus, option C is correct answer.
Which ray can be said as belonging to a line segment?If the ray lies onto the considered line segment(overlapping), then it can be said belonging to the considered line segment.
(line segment has 2 fixed ends, whereas a ray has one end only, other end is not fixed)
A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
A lines can extend its length in both side infinitely. It contains arrowheads indicating it can extend.
A line is an undefined term because it describes something that does not have width or depth. thus, option C is correct answer.
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what is the line of symmetry of the parabola y=x2+6×-9
x=6
x=-9
×=-3
Answer:
x = - 3
Step-by-step explanation:
given a parabola in standard form y = ax² + bx + c (a ≠ 0 )
then the equation of the axis of symmetry is
x = - [tex]\frac{b}{2a}[/tex]
y = x² + 6x - 9 ← is in standard form
with a = 1, b = 6 , then the equation of the axis of symmetry is
x = - [tex]\frac{6}{2}[/tex] = - 3 , that is x = - 3
Hello people ~
factorise: x^2 + 3 √3 x + 6
[tex]\\ \rm\rightarrowtail x^2+3\sqrt{3}x+6[/tex]
[tex]\\ \rm\rightarrowtail x^2+\sqrt{3}x+2\sqrt{3}x+6[/tex]
[tex]\\ \rm\rightarrowtail x(x+\sqrt{3})+2\sqrt{3}(x+\sqrt{3})[/tex]
[tex]\\ \rm\rightarrowtail (x+2)(x+2\sqrt{3})[/tex]
Using the quadratic formula,
∆=b²-4ac∆=(3√3)²-4(1)(6)∆=(9×3)-4(6)∆=27-24∆=3[tex]x1 = \frac{ - b - \sqrt{3} }{2a} = \frac{ - 3 \sqrt{3} - \sqrt{3} }{2} = \frac{ - 4 \sqrt[]{3} }{2} [/tex]
[tex]x1 = - 2 \sqrt{3} [/tex]
Similarly,[tex]x 2 = \frac{ - b + \sqrt{3} }{2a} = \frac{ - 3 \sqrt{3} + \sqrt[]{3} }{2} = \frac{ - 2 \sqrt{3} }{2} [/tex]
[tex]x2 = - \sqrt{3} [/tex]
Method 2:x²-Sx+P=0where S is the sum of the roots & P is the product of the roots.x¹+x²= -3√3 x¹x²=6Solving the system you get the same answers.Your factored equation can be written in the form of:
(x-x¹)(x-x²)
(x+2√3)(x+√3)
Tasha earns $75,000 per year. Her payroll deductions are 28% of her gross income. She saves 5% of her net
income each month in case of an emergency. How much will she budget for her emergency savings for the month
of March?
O $3,750
$312.50
O $87.50
O $225.00
Answer:
87.50
Step-by-step explanation:
75,000 x 28% ÷ 12
She will budget $225 for her emergency savings for the month of March
How to determine the amount saved for emergency?We have:
Gross = $75,000 per year.
Payroll deductions = 28%
So, the net pay is:
Net = (1 - 28%) * $75,000
Evaluate
Net = $54000
The net income per month is:
Monthly = $54000/12
Evaluate
Monthly = $4500
5% of her net income goes to emergency.
So, we have:
Emergency = 5% * $4500
Evaluate
Emergency = $225
Hence, she will budget $225 for her emergency savings for the month of March
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Max wants to rent a bicycle. The cost to rent a bike is a $5 insurance fee plus $3 per hour. Max has at most $20 to spend. Write an inequality to represent this scenario. Give a value that satisfies the inequality.
Answer: 5 + 3x ≤ 20; 5
Step-by-step explanation:
at most means not more than(less or equal to),which use the symbol ≤. Let x be the hour that Max rent.
5 + 3x ≤ 20
3x ≤ 15 [Subtract 5 from both sides.]
x ≤ 5 [Divide 3 from both sides.]
Any value less than or equal to 5 will be satisfies the inequality.
The leading brand of lipstick in the US had about 20% of the total sales in the industry. The total sales were $200,000 What was the leading brands sales? Show your work
Answer:
200*20
÷100 ,=100+56
29+63
Step-by-step explanation:
200×20 =40000
40000÷100 =
100
2. A businessman starts
with $10 million and
loses $5 million an
hour. How much
money does he have
after eight hours
Answer:
0
Step-by-step explanation:
He loses it all in 2 hours
Answer:
-25 million
Step-by-step explanation:
Because after 2 hours you will lose all of your money and continue to go down into the negatives.
What is 3(x-1)+4=12 ?
Answer:
3.66666. . . = 11/3 = 3 2/3
Step-by-step explanation:
Use distributive property.
3 ⋅ x = 3x
3 ⋅ (-1) = -3
3x - 3 + 4 = 12
Add -3 to 4
1
3x + 1 = 12
Subtract 1 from both sides.
3x = 11
Divide both sides by 3
3.666666. . .
This can also be written as 11/3
11/3 can be simplified to 3 2/3
Hope I helped :)
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What is the slope of the line shown?
Answers
A: 3
B:2
C:1/2
D:-3
Help me pleaseeee the weekends almost over and it’s due like tomorrow :(
What is the value of the expression 3x-8y when x=10 and y=2?
Answer:
14
Step-by-step explanation:
3x-8y
(3*10)-(8*2)
30-16
14
Answer:
30-16
Step-by-step explanation:
Create a data set that contains 10 values such that the mean is greater than the median.
Answer:
Go with anything, and I mean ANYTHING that is in a numerical order with an outlier
LITERALLY 1,2,3,4,5,6,7,8,9,100
you will get a median of 5.5 but with the high outlier, you will get a mean of 14.5
Need help asap giving 20 points for right answer!!
Answer:
I think it's 600 I think it might be wrong
What civilization found the first known value of pi?.
Answer: The Egyptians, Babylonians, and Archimedes.
Step-by-step explanation: The Egyptians and Babylonians were the first known civilizations to use pi. At the time, Egyptians devised the approximated value of pi as 3.1605. Archimedes, however, did the first calculation of pi, with its approximate value of 3.141592 or 3.14 to make it shorter.
Hopefully, this helps you!