Answers
Answer:
the turning point is (-2,-1)
i dont know the turning point but i hope this helps
Step-by-step explanation:
Answer:
a) (-2 , -1)
b) (-1 , 0) and (-3 , 0)
Step-by-step explanation:
For part a)
We can find the coordinates of the turning point by seeing at the graph where it turns the other way or in simpler words the axis of symmetry so if see the graph the axis of symmetry is the line x = -2 so that means the turning point is (-2 , -1).
For finding the turning point mathematically we compare the equation to its standard form which is:
[tex]x^2+4x+3=a(x-h)^2+k[/tex]
where h is the x coordinate and k is the y coordinate of the turning point of the equation (h , k) = (x , y).
so just solve the left side,
[tex]a(x-h)^2+k\\a((x)^2-2(x)(h)+(h)^2)+k\\a(x^2-2xh+h^2)+k\\\\ax^2-2ahx+ah^2+k=x^2+4x+3\\[/tex]
and so we compare the coefficients of x^2 on the right and left side we get
[tex]a=1[/tex]
if we compare the coefficients of x on the right and left side we get
[tex]-2ah=4\\-2(1)h=4\\-2h=4\\h=\frac{4}{-2}\\\\h=-2[/tex]
now we compare the constants on the right and left side we get
[tex]ah^2+k=3\\(1)(-2)^2+k=3\\(1)(4)+k=3\\4+k=3\\k=3-4\\k=-1[/tex]
so the turning point is (-2 , -1) proven mathematically and graphically as well
For part b)
Roots of the equation are also called as x-intercepts which means where the graph intersects/cuts the x-axis so if see the graph it cuts the x-axis at 2 points firstly at -3 and then at -1 so the roots of the equation would be (-1 , 0) and
(-3 , 0) the y coordinate is zero when the points lies on the x-axis.
for mathematically solving the equation we would equate the equation to zero
[tex]y=x^2+4x+3\\x^2+4x+3=0[/tex]
Now solve it by either factorizing or by using the quadratic formula we would get two values for x those are the roots of the equation
we solve it by factoring
[tex]x^2+4x+3=0\\x^2+3x+x+3=0\\x(x+3)+1(x+3)=0\\(x+3)(x+1)=0\\x=-3\ ,\ x=-1\\[/tex]
proven mathematically as well as graphically.
Related Questions
HELPPP PLS
What is the vertex form of the equation?
y = x² – 2x+8
Answers
90% of the workers are men. If 590 people work for the company who aren't men, how many workers are there in all?
Answers
Step-by-step explanation:
do 590 divided by 90 if that doesn't work multiply it
please help i cant figure this out
Tyson has a collection of 60 sports ribbons. Of these ribbons, 30% are first place ribbons, 45% are second place ribbons, and the rest are third place ribbons. How many third place ribbons are in Tyson’s sports ribbon collection?
answers:
27
32
15
18
Answers
Answer:
15
Step-by-step explanation:
First do, 30% + 45% = 75%. Then do, 100-75=25.
Lastly,
proportions:
x/60 = 25/100
So your answer is, 15.
I need help doing this equation
Answers
Answer:
Candy = $ 0.5
Soda = $ 4.0
Step-by-step explanation:
x + 2y = 5
x + 4y = 6
2y = 1
y = 1/2
= two candies were added and the price increased by 1 dollar, meaning that the a single candy is 0.5 dollar
1 candy = 0.5
x + 2(0.5) = 5
x + 1 = 5
x = 4
Ellen writes 2 pages in a hour. Determine the equation that represents the function and state it graphically.
Answers
Answer:
1 page every 0.5hours, or 1 page every 30 minutes. The equation is
2x = y
a small pool can hold 42.8 gallons of water it is currently 5/8 full how many gallons are in the pool
Answers
Answer:
There are 26.75 gallons in the pool.
Step-by-step explanation:
Divide 42.8 by 8, multiply the quotient by 5.
Answer:
26.75
Step-by-step explanation:
42.8 * 5/8 = 26.75
Which situation could be represented by 5x > 15? Jakiera makes $5 per hour working at her father's repair shop. She needs to make more than $15 to buy the calendar that she wants for next year. How many hours can she work to achieve this goal? Thomas brought 5 cans for the campus food drive. How many more cans does he need to have at least 15 cans for the food drive? Clarice collects comic books. Her brother, Samuel, has 15 comic books. How many comic books does Clarice need to have more comics than Samuel? Elizabeth is five times older than her grandchild, who is 15. How old is Elizabeth?
Answers
Answer:
First situation
More than 3 hours
At least 10
15
75
Step-by-step explanation:
Let x be the number of hours
The equation will be
[tex]5x>15\\\Rightarrow x>\dfrac{15}{5}\\\Rightarrow x>3[/tex]
So, she needs to work more than 3 hours in order to make more than $15.
The situation that represents [tex]5x>15[/tex] is the first one.
Let x be the additional number of cans
The inequality will be
[tex]x+5\geq15\\\Rightarrow x\geq 15-5\\\Rightarrow x\geq 10[/tex]
So, the additional number of cans to be bought is at least 10.
Let x be the number of comic books Clarice has.
[tex]x>15[/tex]
So, Clarice needs to have more than 15 comic books.
Let x be age of Elizabeth
The equation will be
[tex]x=5\times 15\\\Rightarrow x=75[/tex]
So, Elizabeth is 75 years old.
Given FGH with vertices F(-1, 3), G(-5, 1), and H(-3, 5) reflected by Rx-axis
Find the coordinate of vertices F'G'H the image of FGH
1, F(-1, 3), G(-5, 1), and H(-3, 5)
2, F(-1, -3), G(-5, -1), and H(-3, -5)
3, F(1, 3), G(5, 1), and H(3, 5)
4, F(-1, 3), G(-5, 1), and H(-3, -5)
Answers
Answer:
Option F is true.
Step-by-step explanation:
The rule of reflection across the x-axis
P(x, y) → P'(x, -y)
For example, when a point P with coordinates (1, 2) is reflected across the x-axis, the coordinates of the image of point P will be: P'(1,-2).
i.e.
P(x, y) → P'(x, -y)
P(1, 2) → P'(1, -2)
Now, given FGH with vertices F(-1, 3), G(-5, 1), and H(-3, 5) reflected by Rx-axis.
Using the rule of reflection across the x-axis
P(x, y) → P'(x, -y)Thus, the coordinate of vertices F'G'H the image of FGH will be:
F(-1, 3) → F'(-1, -3)
G(-5, 1) → G'(-5, -1)
H(-3, 5) → H'(-3, -5)
Hence, option F is true.
How many solutions does the following equation have?
3x + 7 + 2x = 5x + 7
One. Many. None
Answers
Answer:
Infinite/many
Step-by-step explanation:
3x + 7 + 2x = 5x + 7
3x + 2x + 7 = 5x + 7
5x + 7 = 5x + 7
5x - 5x + 7 = 7
7 = 7
Infinite solutions
Answer: many (all real numbers)
Step-by-step explanation:
1) add 2x and 3x to give you 5x
You now have 5x+7=5x+7
2) you can simplify this by subtracting 7 on both sides and dividing by 5
3) you are then left with x=x
not prime number in 12n- 5
Answers
Answer:
55
Step-by-step explanation:
12 x 5 = 60
60-5 = 55
55 is not prime
write 1.054 in words
Answers
Answer:
one and fifty-four thousandths
Step-by-step explanation:
The 1 is easy.
The 4 is in the thousandths place, so the decimal part is 54/1000.
Answer: one and fifty-four thousandths
My friend Dubble got 10 rews and corazs for about $32. Rews for $2 each and some corazs for $8 each
Answers
Answer:
"Dubble" bought 10 rews for $2.00 each and 1 corazs for $8.00 each
-I put quotation marks on Dubble bc i didnt know if it was a boy or girl name sorryyy its.. um.. unique :) -
Step-by-step explanation:
The price for the rews is 10x 2 because the price of each is $2 and he got 10 so he spent $20 on rews.
Then you subtract the total amount of money "Dubble" used buying these things and the amount of money "Dubble" used on the rews which is 32-20=8
The last step is that you divide 8 by the pice of each corazs which is 8 divided by 8 so the answer is 1.
Hope this helped you sorry im a little late bubs.<3
Am I doing this right? The question is... At the first store Arlene visited, she spent 40% of her money plus $4. At the second store she spent 50% of her remaining money plus $5. At the third store Arlene spent 60% of her remaining money plus $6. When Arlene finished shopping at the three stores, she had $2 left over. How many dollars did she have when she started shopping?
My equation was x - 2 = ((0.4x+4)0.5+5)0.6+6. Both sides of the equation were to find how much she spent. I got 13.86363...
Answers
9514 1404 393
Answer:
$90
Step-by-step explanation:
Let's consider the remaining money. If x represents the amount Arlene started with, then the remaining amounts are ...
after first store: x -(0.4x +4) = 0.60x -4
After spending 50% of her money, the amount remaining will be 1-50% = 50%. Then spending 5 more dollars reduces the amount remaining by another 5.
after second store: (0.60x -4)(0.50) -5 = 0.30x -2 -7 = 0.30x -7
After spending 60% of her money, the amount remaining will be 1-60% = 40%. Then spending 6 more dollars reduces the amount remaining by another 6.
after third store: (0.30x -7)(0.40) -6 = 0.12x -2.80 -6 = 0.12x -8.80
This is reported to be $2, so we have ...
0.12x -8.80 = 2
0.12x = 10.80
x = 90
Arlene started shopping with $90.
_____
Check
At the first store, Arlene spent 0.40×$90 +$4 = $40, so she had $90-40=$50 remaining.
At the second store, Arlene spent 0.50×$50 +$5 = $30, so she had $50-30=$20 remaining.
At the third store, Arlene spent 0.60×$20+$6 = $18, so she had $20-18 =$2 remaining.
Madelyn has a total of 15 dimes and quartets in her piggy bank. The total amount of money in her piggie bank is $2.85. Write and solve a system of equations to determine the number of dimes and the number of quarters in madelyn’s piggie bank.
Answers
(d + q = 15)0.10
0.10d + 0.25q = 2.85
0.10d + 0.10q = 1.50
Subtract both equation
0.15q = 1.35, q = 9
15 - 9 = 6
Solution: 9 quarters and 6 dimes
The system of equations is x + y = 15 and 0.10x + 0.25y = 2.85. Then the number of dimes and quarters will be 6 and 9, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Madelyn has a total of 15 dimes and quartets in her piggy bank. The total amount of money in her piggy bank is $2.85.
Let 'x' be the number of dimes and 'y' be the number of quarters. Then the equations are given as,
0.10x + 0.25y = 2.85 ....1
x + y = 15 ....2
From equations 1 and 2, then we have
0.10(15 - y) + 0.25y = 2.85
1.5 - 0.10y + 0.25y = 2.85
0.15y = 1.35
y = 9
Then the value of the variable 'x' is given as,
x + 9 = 15
x = 6
The system of equations is x + y = 15 and 0.10x + 0.25y = 2.85. Then the number of dimes and quarters will be 6 and 9, respectively.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ5
OH MY GOSH PLEASE IM ABOUT TO CRY HELP ASAPP
Answers
Answer:
All systems have 2 real solutions.
Explanation: there are X and Y unknowns.
In 1 hour the employee dropped 635 chocolates. If this represents 25% of the days chocolate molds, how many chocolates were planned to be
produced
Answers
Answer:
2540
Step-by-step explanation:
25% is a quarter of 100% so if 635 is 25% you multiple 635 x 4 to get your final answer concluding in 2540. if i'm wrong let someone else correct me :b
A person standing close to the edge on top of a 32-foot building throws a ball vertically upward. The quadratic function h(t)=−16t^2+124t+32 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown. a) What is the maximum height of the ball? __feet b) How many seconds does it take until the ball hits the ground? ____ seconds
Answers
Answer:
a) The maximum height of the ball is 272.25 feet
b) The balls take 8 seconds to hit the ground.
Step-by-step explanation:
a) You know that the quadratic function h(t)=−16*t²+124*t+32 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown.
Being a quadratic function of the form:
f (x) = a*x² + b*x + c
The vertex of a quadratic or parabola equation is the highest or lowest point on the graph corresponding to that function. When a> 0, the vertex of the parabola is at the bottom of it and indicates the minimum of the function. When a <0 the vertex is at the top and indicates the maximum of the function.
The value of x at the vertex is calculated by the expression:
[tex]x=\frac{-b}{2*a}[/tex]
The value of y at the vertex is calculated by substituting the value of x at the vertex into the quadratic function.
In this case, being a=-16, b=124 and c=32 you get that the maximum time is:
[tex]x=\frac{-124}{2*(-16)}=3.875[/tex]
Then a maximum height of:
h(3.875)=−16*(3.875)²+124*3.875+32
h(3.875)= 272.25
The maximum height of the ball is 272.25 feet
b) When the ball hits the ground the height is zero. So h (t) = 0:
0=−16*t²+124*t+32
Applying the resolvent:
[tex]\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a} =\frac{-124+-\sqrt{124^{2} -4*(-16)*32} }{2*(-16)}[/tex]
you get:
[tex]\frac{-124+\sqrt{124^{2} -4*(-16)*32} }{2*(-16)} =-0.25[/tex]
[tex]\frac{-124-\sqrt{124^{2} -4*(-16)*32} }{2*(-16)} =8[/tex]
Since the time cannot be negative, the balls take 8 seconds to hit the ground.
My question is in the picture
Answers
1. Geneva has 24 points. Then her spin lands on blue. What is her score now? Explain.
Blue = + 4. This means that you will need to add 4 to 24, causing Geneva's new amount of points to be 28. You could put down,
Geneva now has 28 points. Blue is equal to +4, so I added 24 + 4 to get 28.
2. Geneva and Juan start a new game. Each player has 0 points.
a. Geneva's first two spins are yellow and red. What is her score now? Explain.
Geneva's score is now -2. Yellow is equal to -4, red is equal to +2. -4 + 2 = -2.
b. Juan's first two spins are red and green. What is his score now? Explain.
Red is equal to +2 and green is equal to -1. That means that Juan has 1 point because 2 + -1 = 1.
c. Which player has a greater score now? Explain.
Juan has a greater score. He has a greater score because 1 is greater than -2.
1.3181818...... as fraction units lowest term
Answers
Answer:
29/22
Step-by-step explanation:
Let x = 1.31818181818....
Then, 10x = 13.18181818..., and 1000x = 1318.18181818..... Subtracting the first equation from the second, we get that 990x = 1305. This means that x = 1305/990. In lowest terms, this is 29/22.
cotA . cos(30°-A) - sin ( 30°- A) = ✓3÷2
Answers
Answer:
cotA. cos(30° - A) - sin(30° - A) = √3/2
⇔
Step-by-step explanation:
I got this question on a math homework and I don't understand it, 5 5/8 cups of water fill 4 1/2 identical water bottles. How many cups fill each bottle?
Answers
Answer:
1-1/4 cups (1 and 1/4 cups) or 1.25 cups
Step-by-step explanation:
To find the answer you need to take the total volume (5-5/8 cups) and divide it by the number of bottles you have:
5-5/8 divided by 4-1/2
There are two easy ways to do this: you can convert the mixed fractions into decimal form (A) or into improper fractions (B).
A)
First, convert to decimal form:
5-5/8 = 5.625 and 4-1/2 = 4.5
Then, you divide them:
5.625 / 4.5 = 1.25 (converted back to fraction form, if thats what you need, is 1-1/4)
B)
First, convert to mixed numbers:
5-5/8 = 45/8 and 4-1/2 =9/2
Then, you divide them:
45/8 / 9/2
When you divide fractions, you multiply by the inverse of the number you're dividing by (that means swapping the numerator and denominator):
45/8 * 2/9 = 90/72 (converted back to a mixed fraction, this equals 1-1/4)
Which arrangement shows 275, 5.36, 535, and 336 in order from least to greatest?
275, 5.36, 336, 535
535, 5.36, 275,336
5.36, 275,336, 535
5.36, 275, 535, 336
Answers
Answer:
I have a feeling it's 5.36, 275, 336, 535.
Sorry if I'm wrong.
Step-by-step explanation:
Answer:
C is the answer........
Hey guys help me with this question plzzzzzz
Answers
Answer:
625 cm³ and 64000 cm³
Step-by-step explanation:
Given
x = [tex]\sqrt[3]{V}[/tex] ( cube both sides )
x³ = V
(a)
x = 25 cm , then
V = 25³ = 625 cm³
(b)
x = 40 cm , then
V = 40³ = 64 000 cm³
Which of the two elements below have similar properties?
Chlorine (CI) and Zinc (Zn)
Sodium (Na) and Fluorine (F)
Potassium (K) and Francium (Fr)
Magnesium (Mg) and Helium (He)
Answers
Answer:
C
Step-by-step explanation:
A truck and a car go at the same time against each other from two cities, which are at a distance of 400 km from each other. If the vehicles are moving at a constant speed of 68 km / h and 82 km / h, respectively, find after how long they have met?
Answers
Answer: after about 96 Minutes
Step-by-step explanation:
1+2+3+...98+99+100 what's the total and how many pairs will there be?
Answers
Answer:
5050 and 100 pairs
Step-by-step explanation:
Mike bulit a sand casitle that mersured 54 inches by 77 inches and dug a moat aorund it afterward, he decided to change the size, making it 112 inches by 38 inches how much longer wil the new moat be than the old one?
Answers
Step-by-step explanation:
Initial dimension of a sand castle is 54 inches by 77 inches. Mike decided to change the size, making it 112 inches by 38 inches.
He wanted to dug a moat around it.
The perimeter of moat with initial dimensions,
P = 2(54+77)
= 262 inches
The perimeter of moat with new dimensions,
P = 2(112+38)
= 300 inches
Difference in perimeter = 300 - 262
= 38 inches
Hence, the new dimension is 38 inches longer than the initial dimensions.
Use the formula a^2-b^2= (a+b)(a-b) to factor completely. What are the factors of 36x^8-49 ?
Answers
Answer:
(6x^4-7)(6x^4+7)
Step-by-step explanation:
36x^8-49
1. look for a gcf. since there isn't one, you move on to the next step.
2. what multiplies to what you need. you can do box method or diamond method.
3. (6x^4-7)(6x^4+7)
Answer:
C
Step-by-step explanation:
Which equation is equivalent to 9x+4y=16
y=9/4x+4
y=-9/4x+4
y=4/9x+16/9
y=-4/9x+4/7
Answers
Answer:
The answer is 4/9x+16/9
Step-by-step explanation:
Find the least whole number that can replace blank 80 to make the statement true. ÷ 18 > 86
Answers
Answer:
649
Step-by-step explanation:
Given the expression :
__ ÷ 18 > 86
Let blank = y
y ÷ 18 > 36
y / 18 > 36
Multiply both sides by 18
(y / 18) * 18 > 36 * 18
y > 648
Hence, the least whole number which can make the statement true is (648 + 1) = 649