Answer:
Step-by-step explanation:
To find the vertex of this parabola, "complete the square:" Rewrite y = 4x2 - 12x + 9 in the form y = 4(x - h)^2 + k:
y = 4x^2 - 12x + 9 => y = 4(x^2 - 3x) + 9.
Now complete the square of x^2 - 3x: Take half of -3 and square the result, obtaining (-3/2)^2, or 9/4. Add 9/4 to x^2 - 3x and then subtract 9/4 from the result: We get x^2 - 3x + 9/4 - 9/4. Substitute this result back into
y = 4(x^2 - 3x) + 9: y = 4(x^2 - 3x + 9/4 - 9/4) + 9
and then rewrite the perfect square x^2 - 3 + 9/4 as the square of a binomial:
y = 4(x - 3/2)^2 - 9/4) + 9. This simplifies to:
y = 4(x - 3/2)^2 + 0.
Thus, the vertex is at (3/2, 0) and the axis of symmetry is x = 3/2. This agrees with Answer B.
If 5x−4y=22 and 3x+6y=30, what is the value of x−5y
Answer:
-4 See Below:
Step-by-step explanation:
When you have a system of equations, you need to solve for one variable, and subsitute that variable into the other equation to solve for the other variables value.
3x +6y = 30 In this case, it would be easier to solve for x.
3x= 30-6y Divide both sides by 3
x= 10-2y
Now we substitute for x in the other equation.
5x- 4y = 22
5(10-2y)-4y=22
50-10y-4y=22
50-14y=22 Add 14y to both sides
50= 14y + 22 Subtract 22 from both sides
28 = 14y Divide by 14 on both sides.
y = 2
Substitute y=2 and solve for x.
x = 10- 2y
x= 10-2*2
x= 10-4
x= 6
Now we know y=2 and x=6, so we can substitute them into x-5y to find its value.
x - 5y
= 6-5*2
=6-10
= -4
What is the y-intercept of the line given by the equation below? y = 4/17x + 5
Answer:
(0,5)
Step-by-step explanation:
Can you please help please and i will give you a Brainiest please
Answer:
5 grams
Step-by-step explanation:
5*9=45
Answer:
I think the answer is 5 grams
Sorry if it is not correct
Step-by-step explanation:
I think that it is 5 grams because 45 ÷ 9= 5
3х - 40 °
30°
х+ 20
whats x?
So the right answer is 42.5
look at the attached picture
Hope it will help you
Good luck on your assignment
Help me if you don't understand 7, leave it. Thanks!
40 PTS!!How many possible outcomes exist when four fair coins are flipped? 2 4 8 16
Answer:
16
Step-by-step explanation:
4 coins 2 out comes each
2 X 2 X 2 X 2 = 16
2^4 = 16
Hope i helped you
Answer:
16
Step-by-step explanation:
A number cube has faces labeled 1–6. What is the probability of rolling a 2 on the number cube, and then landing on a 3 on this spinner? A spinner containing 6 equal regions containing the following numbers as labels: 2, 2, 3, 3, 6, and 6.
A. 2/6
B. 3/6
C. 1/18
D. 3/36
will give brainliest and 50 points.
Answer:
c
Step-by-step explanation:
use multiplication rule.
1/6 for landing a 2 on the cube and 1/3 for landing a 3 on the spinner
Find the solution set of the inequality 52-3x<-14
Answer:
x>22
Step-by-step explanation:
Make me brainliest
RIGHT ANswer trust me
Jessica uses 9.6 pints of blue paint and white paint to paint her bedroom walls 4/5 of this amount is blue paint in the rest as white paint how many pints of white paint did she use to paint her bedroom walls express your answer in fraction form
Answer:
Step-by-step explanation:
9.6/5=1.92
1.92= 1 23/25
or 48/25
algebra 1 : ordered pairs kinda dont get it
Answer:
Option C; 3x - y = -27 and x + 2y = 16
Step-by-step explanation:
1. Let us consider the equation 21x - y = 9. In this case it would be best to keep the equation in this form, in order to find the x and y intercept. Let us first find to y - intercept, for the simplicity ⇒ 21 * ( 0 ) - y = 9 ⇒ y = - 9 when x = 0. Now if we take a look at the first plot of line q, we can see that the x value is -9 rather than the y value, so this equation doesn't match that of line q. This would eliminate the first two options being a possibility.
2. Now let us consider the equation 3x - y = -27. Let us consider the x-intercept in this case. That being said, ⇒ 3x - ( 0 ) = -27 ⇒ 3x = -27 ⇒ x = -9 when y = 0. As we can see, this coordinate matches with one of the coordinates of line q, which might mean that the second equation could match with the equation for line v.
3. To see whether Option 3 is applicable, we must take a look at the 2nd equation x + 2y = 16. Let us calculate the y - intercept here: ( 0 ) + 2y = 16 ⇒ 2y = 16 ⇒ y = 8 when x = 0. Here we can see that this coordinate matches with that of the second coordinate provided as one of the points in line v. That means that ~ Answer: Option C
Select the solutions to this quadratic equation:
x2−6x+8 = 0
X=2
x=4
x=0
x=-2
x=1
Answer:
X=2
Step-by-step explanation:
Write an addition equation or a subtraction equation to describe the diagram
Answer:
add the diagram
Step-by-step explanation:
what is the formula for figuring out the area of a circle?
Answer:
The area of a circle is pi times the radius squared (A = π r²). Learn how to use this formula to find the area of a circle when given the diameter.
Step-by-step explanation:
Answer:i believe it is length times width
Step-by-step explanation:
One and seventy six hundredths in decimal
Answer:
1.76
Step-by-step explanation:
Answer:
1/76
Step-by-step explanation:
A bag contains 19 cards numbered 1 through 19. A card is randomly chosen from the bag. What is the probability that the card has an even number on it? Write your answer as a fraction in simplest form. willllll get brainest
Answer:
[tex]\dfrac{9}{19}[/tex]
Step-by-step explanation:
It is given that there are a total of 19 cards ({1,2,3,4, ...... ,19}).
Let S be the set of total cards.
S ={1,2,3,4, ...... ,19}
Total number of observations, n(S) = 19
Even number of cards is the set {2,4,6,8,10,12,14,16,18}
Total number of cards with even number on it = 9
Let E be the event of selecting a card with even number on it.
n(E) = 9
Probability of an event A can be formulated as:
[tex]P(A) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
In this case, formula of P(E) is:
[tex]P(E) = \dfrac{n(E)}{n(S)}[/tex]
[tex]\Rightarrow \dfrac{9}{19}[/tex]
The probability that the card chosen at random is an even number is:
[tex]\dfrac{9}{19}[/tex]
The probability that the card will have an even number will be 0.4737.
From the information given, we are informed that a bag contains 19 cards numbered 1 through 19. Based on the information, the even numbers will be 2, 4, 6, 8, 10, 12, 14, 16, and 18. Therefore, the probability of having when numbers will be:= 9/19 = 0.4737
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QUICK HELP PLS
Evaluate the questions below and select the statistical ones.
A
What is the mass of earth?
B
What is the mass of Halley's Comet?
C
How massive are asteroids in the asteroid belt?
Answer:
C
Step-by-step explanation:
A only gives one answer.(5.972 × 10^24 kg to be precise)
B It is only one thing so it has one mass, not providing a range of answers
C= There are many asteroids so a range of answers are made
Give your best conclusion to the following statement: "Distance between two points on the coordinate plane is related to the pythagorean theorem because..."
Answer:
the Pythagorean formula is a²+b²=c², which is a and b are the x and y distances between points and c is the hypotenuse, which is the distance.
Step-by-step explanation:
please help with this problem.
What is the length of a radius of the circle represented by the equation
x2 + y2 - 4x - 4y + 4 = 0?
A) 2 units
B) 4 units
C) 8 units
D) 16 units
Answer:
A) 2 units
Step-by-step explanation:
Given;
x² + y² - 4x - 4y + 4 = 0
Consider general circle equation;
(x - h)² + (y - k)² = r²
where;
(h , k ) is the center of the circle
r is the radius of the circle
x² + y² - 4x - 4y + 4 = 0
subtract 4 from both sides of the equation
x² + y² - 4x - 4y = - 4
square half of coefficient of x and y, and add them to both sides of the equation
x² + - 4x + (-2)² + y² - 4y + (-2)² = - 4 + (-2)² + (-2)²
factorize x and y
(x - 2)² + (y - 2)² = - 4 + 4 + 4
(x - 2)² + (y - 2)² = 4
(x - 2)² + (y - 2)² = 2²
Compare this final equation to general equation of a circle
(x - 2)² + (y - 2)² = 2²
(x - h)² + (y - k)² = r²
r = 2
Thus, the length of a radius of the circle is 2 units
Mr. Smith received a phone call from the bank manager. His bank balance had dropped to - $15 (he had overdrawn his account by $15). Mr. Smith rushed to the bank and deposited $25 into his account. What was Mr. Smith’s new balance after making the $25 deposit?
Answer:
$10
Step-by-step explanation:
(-15) + 25 = 10
-2 1/3-(-5) can someone help me
Express the required calculation in terms of it and then round to the nearest tenth.
How much fencing is required to enclose a circular garden whose radius is 20 meters?
There are of fencing required.
(Simplify your answer. Type an exact answer in terms of 7.)
There are approximately
of fencing required.
(Round to the nearest tenth as needed.)
Answer:
126m
Step-by-step explanation:
The circumference of the circle would be the amount of fencing required for the circular garden.
Circumference, C = 2πr
π = [tex]\frac{22}{7}[/tex]
C = 2*20*[tex]\frac{22}{7}[/tex]
C = 125.71 m
We need 125.71 meters to fence the garden.
Events A and B are mutually exclusive. Find the missing probability.
P(A) = 3/10 P(B) = ? P(A or B) = 4/5
1/2
2/3
1/5
3/10
Answer:
1/2
Step-by-step explanation:
As they are mutually exclusive P(A and B) = 0 therefore the probability of P(A or B)= P(A) + P(B). Just do 4/5-3/10= 5/10=1/2
The value for P(B) is 1/2.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
P(A) = 3/10, P(B) = ?, P(A or B) = 4/5.
As they are mutually exclusive P(A and B) = 0
So, P( A or B)
4/5 = P(A) + P(B)
4/5 = 3/10 + P(B)
P(B) = 4/5 - 3/10
P(B) = 5/10
P(B) = 1/2.
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There are y boats on a lake there are 6 people in each boat write an expression in term of y for the total number of people in the boats
Answer:
6y people are in the boats
Step-by-step explanation:
Here, we are interested in writing an expression for the total number of people in the boats.
We have 6 people in each of the boats and there are a total of y boats.
The total number of people in the boats is thus y * 6 = 6y people
rational or irrational?
Answer:
irrational
Step-by-step explanation:
sqrt(8) = sqrt(4) sqrt(2) = 2 sqrt(2)
sqrt(8) /3 = 2 sqrt(2)/3 which is an irrational number
sqrt(16) =4 which is rational
irrational + rational = irrational
"What is the theoretical probability of rolling a prime number on a standard number cube?"
Answer:
There are three prime numbers and 3 even numbers on a number cube, so the probability of each is 3/6 = 1/2
Step-by-step explanation:
Probability of rolling a prime number on a standard number cube is [tex]\frac{1}{2}[/tex] or 0.5.
What is theoretical probability?The theoretical probability is defined as the ratio of the number of favorable outcomes to the number of possible outcomes.
Numbers on a cube are {1, 2, 3, 4, 5, 6}
Total number of favorable outcomes = 6
Number of prime numbers in {1, 2, 3, 4, 5, 6} are {2, 3, 5}.
Number of favorable outcomes = 3
Probability of rolling a prime number on a standard number cube
P = [tex]\frac{Number of favorable outcomes}{Total number of favorable outcomes }[/tex]
P = [tex]\frac{3}{6}[/tex]
P = [tex]\frac{1}{2}[/tex]
Hence, probability of rolling a prime number on a standard number cube is [tex]\frac{1}{2}[/tex] or 0.5.
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Will mark as brainliest if correct
Answer:
X = 1.09
Step-by-step explanation:
6 to the 1.09th power is 7.04993094301076 so when it is rounded it is 7.
Answer:
the answer is 7
Step-by-step explanation:
log10(6x)=log10(7)
x•log10(6)=log10(7)
x = log10(7)/log10(6)
this works because of
logb(x y) = y ∙ logb(x)
I figured this out from the internet!!
source:TigerAlegbra
Daniel borrowed $5000 from the bank for 2 years at 9% simple interest per annum. Calculate how much interest Daniel is charged.
Answer:
Daniel is charged $900
Step-by-step explanation:
This is because 9 percent of 5000 is 450. Multiply 450x2 and get 900.
A sporting goods factory puts out 98 playground balls in each shipment. Each ball costs $2. What is the total cost of playground balls in three shipments? ENTER NUMBERS ONLY
Answer:
$588
Step-by-step explanation:
As each shipment has 98 balls, to determine the total cost of playground balls in three shipments, you have to multiply 98 for 3. Then, after determine the amount of balls in the three shipments, you have to multiply that for the price of each ball:
Total amount= 98*3= 294
Total cost= 294*$2= $588
The total cost of playground balls in three shipments is $588.
square root of 172 ?
Answer:
13.1148770486
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