Answer:
The equation of the parabola in standard is [tex]y=x^{2}+5x-1[/tex]
Step-by-step explanation:
The standard form equation of the parabola is:
[tex]y=ax^{2}+bx+c[/tex]
Using the three points we can find a, b and c.
Let's put the first point (0,-1)into the standard form equation.
[tex]-1=a(0)^{2}+b(0)+c[/tex]
[tex]c=-1[/tex]
Using the second point (1,5) and the value of c found above.
[tex]5=a(1)^{2}+b(1)+c[/tex]
[tex]5=a+b-1[/tex]
[tex]6=a+b[/tex] (1)
Finally using the las point (-1,-5)
[tex]-5=a(-1)^{2}+b(-1)+c[/tex]
[tex]-5=a-b-1[/tex]
[tex]-4=a-b[/tex] (2)
Solving the system of equations (1) and (2) we can find a and b.
[tex]6=a+b[/tex]
[tex]-4=a-b[/tex]
Adding both of them we have:
[tex]2=2a[/tex]
[tex]a=1[/tex]
And b = 5.
Therefore, the equation of the parabola in standard form will be.
[tex]y=x^{2}+5x-1[/tex]
I hope it helps you!
Use the linear equations to answer the question.
y=2/3x-3
y=-3/2x+2
Which statement about the lines is true?
Answer:
c. the lines are perpendicular.
Step-by-step explanation:
Which fractions are equivalent to 1/8+5/8? Check all that apply.
Answer:
3/4 and 12/16
Step-by-step explanation:
[tex]\frac{1}{8} +\frac{5}{8} =\frac{1+5}{8} =\frac{6}{8} =\frac{3}{4} \\\\\frac{12}{16} =\frac{3}{4}[/tex]
Need answer asap pls..............
Answer:
These go up by 1.
Step-by-step explanation:
10 20 30 40 50 60 70 80 90
1 + 1 = 2
2 + 1 = 3
3 + 1 = 4, and so forth.
Answer:
A (they go up by one )
Step-by-step explanation:
10, 20 , 30 ,40,50 The tens place goes up by 1 each time
how much is left from 50 after buying 3 books at $
12.65 each
Answer:$12.05
Step-by-step explanation:
12.65*3=$37.95
$50-$37.95=$12.05
The midpoint of \overline{\text{AB}}AB is M(-6, -4)M(−6,−4). If the coordinates of AA are (-4, -3)(−4,−3), what are the coordinates of BB?
Answer:
The coordinates of B is (-8,-5).
Step-by-step explanation:
The midpoint of line AB is M. The coordinate of M is (-6,-4).
The coordinates of A is (-4,-3)
We need to find the mid point of B.
If M(x,y) is the midpoint of the coordinates (x₁,y₁) and (x₂,y₂). The mid point theorem is used as follows :
[tex]M(x,y)=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]
Let the mid point of B is (x₂,y₂). Put (x,y) = (-6,-4), (x₁,y₁) = (-4,-3).
[tex](-6,-4)=(\dfrac{-4+x_2}{2},\dfrac{-3+y_2}{2})\\\\\dfrac{-4+x_2}{2}=-6\ \text{and}\ \dfrac{-3+y_2}{2}=-4\\\\-4+x_2=-12\ \text{and}\ -3+y_2=-8\\\\x_2=-12+4\ \text{and}\ y_2=-8+3\\\\x_2=-8\ \text{and}\ y_2=-5[/tex]
So, the coordinates of B is (-8,-5).
The coordinates of B are (-8, -5).
Given that,
The midpoint of AB is M(-6, -4). If the coordinates of A is (4,-2),
We have to determine,
The coordinates of B.
According to the question,
The midpoint of line AB is M. The coordinate of M is (-6,-4).
And the coordinates of A is (-4,-3)
If M(x, y) is the midpoint of the coordinates (x₁, y₁) and (x₂, y₂). The midpoint theorem is used as follows :
[tex]M(x, y) = ( \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]
Let the midpoint of B be (x₂, y₂).
M (x, y) = (-6,-4), and (x₁, y₁) = (-4,-3).
[tex]M(-6, -4) = ( \dfrac{-4+x_2}{2}, \dfrac{-3+y_2}{2})\\\\[/tex]
Solving the equation for the co-ordinate B.
[tex]\dfrac{-4+x_2}{2} = -6\\\\-4 + x_2 = -6 \times 2\\\\-4 + x_2 = -12\\\\x_2 = -12+4\\\\x_2 = -8[/tex]
And,
[tex]\dfrac{-3+y_2}{2} = -4\\\\-3 + y_2 = -4 \times 2\\\\-3 + y_2 = -8\\\\y_2 = -8 + 3\\\\y_2 = -5[/tex]
Hence, The required coordinates of B are (-8, -5).
To know more about Geometry click the link given below.
https://brainly.com/question/20261153
volcano Puu Puai in Hawaii was formed in 1959 when a massive “lava fountain” erupted. The lava shot from the ground with an initial velocity of 350 feet per second.
a. For how long was the lava in the air until it returned to the ground?
b. What was the maximum height of the lava?
c. After how many seconds did the maximum height occur?
Answer:
a)Tt = 21,41 s
b) y(max) = 1873 ft
c) t = 10,70 s
Step-by-step explanation:
We assume that this is a case of vertical shooting then:
a) Vf = V₀ - g*t
Vf = 0 -g*t = -V₀
t = V₀ /g t = 350 ft/s / 32,7 ft/s²
t = 10,70 s time for lava to reach y maximum
a) Then Tt = 2*10,7 Tt = 21,41 s
Lava was in the air for Tt = 21,41 s
b) y = y₀ + v₀*t - (1/2 )*g*t²
for y = ymax we get:
y(max) = 0 + 350*10,70 - 0,5* 32,7* ( 10,70)²
y(max) = 3745 - 1872
y(max) = 1873 ft
c) t = 10,70 s
I desperately need the answers to this, it’s about compound interests
Answer:
quarterly is n = 4semiannually is n = 2monthly is n = 12annually is n = 1Step-by-step explanation:
n is the number of times the interest is compounded, so just figure out stuff like monthly and annually mean. (ex. since annually means once a year, n = 1)
If b= 3, then b-2 is equivalent to
Answer:
1
Step-by-step explanation:
son
Use the substitution method.
b-2
3-2
= 1
Answer :
1
If Arron's boat travels 9 mph and the river runs 4 miles mph in still water.how long will it take to travel 18 miles upstream
Answer: It will take Aaron's boat 3³/₅ hours to travel 18 miles upstream.
That is 3.6 hours or 3 hours and 36 minutes.
Step-by-step explanation:
Traveling upstream, the boat's speed will be reduced by the speed of the river current.
9 - 4 = 5mph
18mi/5mph = 3.6 hours 0r 3³/₅ hours
A biology student wants to determine if using a fertilizer would help promote the growth of new babies in spider plants. The student has access to 90 baby spider plants of three varieties: green, variegated, and curly. There are 30 plants of each variety. They all are potted in the same amount and type of soil, given the same amount of water, and exposed to the same amount of light. The numbers 1–30 are written on slips of paper, placed in a hat, and mixed thoroughly. A plant is selected and a slip of paper is drawn. If the slip has the numbers 1–15, then the plant will receive fertilizer. If the slip has the numbers 16–30, the plant will not receive fertilizer. A green spider plant is selected and a slip of paper is drawn. This plant is placed in the treatment group indicated by the number, and the slip is not put back in the bag. The slips are mixed again, the next green spider plant is selected, and a slip is drawn. The plant is placed in the treatment group indicated by the number. This procedure is repeated until all 30 green spider plants are assigned to treatments. The numbered slips are placed back in the bag and this procedure is repeated for the remaining types of spider plants. After one year, the shoots will be counted for each plant.
Which of the following best describes the design for this experiment?
observational study
matched pairs design
randomized block design
completely randomized design
Answer:
Randomized block design
Step-by-step explanation:
From the question, we can see the following:
- There are 30 plants of each variety. This means that they are divided into variety subgroups which we will call blocks.
- Now, we are told each plant in each block all are potted in the same amount and type of soil, given the same amount of water, and exposed to the same amount of light. This means that each plant in each block is assigned a treatment condition.
- The procedure is repeated by subjecting each plant one after the other in teach Block to different treatments and this will reduce variability.
Looking at all the statements above, it is clear that this is a randomized block design because a randomized block design is when the experimenter/researcher divides members/participants into subgroups called blocks in a manner that the variability within the blocks is less than the variability between the blocks. Thereafter, the participants within each block will now be randomly assigned to treatment conditions.
The best describe about the design for this experiment is random block design.
A randomized block design is an experimental design where the experimental units are in groups called blocks. The treatments are randomly allocated to the experimental units inside each block.
When all treatments appear at least once in each block, we have a completely randomized block design.
There are 30 plants of each variety. This means that they are divided into variety subgroups which we will call blocks.
Each plant in each block all are potted in the same amount and type of soil, given the same amount of water, and exposed to the same amount of light.
This means that each plant in each block is assigned a treatment condition.
The procedure is repeated by subjecting each plant one after the other in teach Block to different treatments and this will reduce variability.
The statements above, it is clear that this is a randomized block design because a randomized block design is when the experimenter/researcher divides members/participants into subgroups called blocks.
In a manner that the variability within the blocks is less than the variability between the blocks. Thereafter, the participants within each block will now be randomly assigned to treatment conditions.
Hence, The best describe about the design for this experiment is random block design.
To know more about Random block design click the link given below.
https://brainly.com/question/20165310
I dont know how to dis um can yalls help me yalls are so nice for helping me thx
Answer:
5 gallons
Step-by-step explanation:
please help with right answers
Answer:
25
Step-by-step explanation:
the ratio is 4:5
20/4=5
so multiply 5 by 5 and you will get 25
on the number line jump to where it shows the very end where 20 is and at the bottom it is 25
hope that helps
The two-way table shows the number of books of each type in Eliza’s home.
A 5-column table has 3 rows. The first column has entries hardcover, paperback, total. The second column is labeled Fiction with entries 28, 4, 32. The third column is labeled biographies with entries 2, 1, 3. The fourth column is labeled Reference with entries 10, 15, 25. The fifth column is labeled Total with entries 40, 20, 60.
What is the probability that a randomly selected reference book is hardcover?
0.25
0.4
0.6
0.75
The probability that a randomly selected reference book is hardcover is 0.4.
The two-way table depicts the distribution of books in Eliza's home by type (hardcover, paperback, biographies, fiction, and reference), as well as the number of books in each category (32 fiction books, 3 biographies, and 25 reference books).
There are a total of 25 reference books, of which 10 are hardcover.
So the probability that a randomly selected reference book is hardcover is:
10/25 = 0.4
Therefore, the probability is: 0.4.
For more details regarding probability, visit:
https://brainly.com/question/30034780
#SPJ7
Which graph represents the function y=-(x-2)²+3?
Answer:
Graph D
Step-by-step explanation:
the bottom right graph represents the function y=-(x-2)²+3. I put it in a graphing calculator soo
What is the slope of a line going through these 2 points? Point 1: (12,16) Point 2: (34 , 49)
Answer:
1.5
Step-by-step explanation:
Determine if each function is linear or non linear.
y = x/2 - 19,
3y = x^2,
13y = 1/3x + 5,
y = x + 25/5
y^3 = x
Answer:1)Linear 2)Non linear 3)Linear 4)Linear 5)Non linear
Step-by-step explanation:
If x is alone with no degree, it’s linear.
urgent answer please!!! :)
Answer:
a and b are relative on maxima interval x =-4,x=0
Please help I have ten minutes
Answer:
$10 per hour
Step-by-step explanation:
As you can see, at (2, 20) the employee earns 20 dollars for 2 hours and at (4, 40) we can see the employee earn $40 per 4 hours. So we can find the slope of these two points to get the answer.
Slope formula y1-y2/x1-x2
so plug it in
40-20/4-2 and we get 20/2 =10
PLEASE HELP ME WITH THIS. 5 POINTS
Answer:
I think b is not proportional
-2/7x - 11 + 4/7x - 7
Answer:
2/7x - 18
Step-by-step explanation:
-2/7x - 11 + 4/7x - 7
rearrange the expression so it's easier to add, optional
-2/7x + 4/7x - 11 - 7
2/7x - 18
Answer this please thanks
Answer:
D. 182.4
Step-by-step explanation:
0.48 x 380 = 182.4
g E. (i). An oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil. What is the probability that the first strike comes on the third well drilled
Answer:
0.128
Step-by-step explanation:
Given that :
Probability of striking oil = p = 20% = 0.2
Striking occurs on the 3rd well drilled : x = 3
Hence ;
P(x = 3) =?
Using a geometric probability function :
p(x = x) = (1 - p)^(x - 1) * p
P(x = 3) = (1 - 0.2)^(3 - 1) * (0.2)
P(x = 3) = 0.8^2 * 0.2
P(x = 3) = 0.64 * 0.2
P(x = 3) = 0.128
What is the magnitude of the vector shown?
5
13
radical 5
radical 13
Answer:
D on edge
Step-by-step explanation:
radical 13
Solve the system:
x=49-5y
x=16-2y
Write down the solution.
40% of x is 35 Write an equation that shows the relationship of 40%, X, and 35.
Use your equation to find x. Show your reasoning
Answer:
87.5
Step-by-step explanation:
James has 165 centimeters of yarn left. How many inches does he have left?
(1 inch = 2.54 centimeters).
Answer:
64.96 inches
Step-by-step explanation:
this is because calculations excuse length value by dividing by 2.54
Why are whole numbers rational numbers? Use 15 as an example.
Answer:
Every whole number n can be written as a fraction of integers.
Step-by-step explanation:
Every whole number n can be written as a fraction of integers: x=x/1.
If we use 15 as an example, it would be 15 = 15/1. 15/1 is 15.
So whole numbers are rational
Whole numbers are rational numbers because all whole numbers can be expressed in the form a/b. Hence, 15 can be expressed as a rational fraction thus 15/1
When a number can be expressed in the form a/b ; such that the value of the denominator, b ≠ 0 ; then the number is said to be rational. Whole numbers are positive integer values and as such, they are not decimals. Every whole number can be expressed such that the denominator is 1 ; hence, they can be expressed in the form a/b.15 as a whole number can be rewritten as 15/1. Hence, all whole numbers are rational.
Learn more : https://brainly.com/question/18109354
The point R(-3,a,-1) is the midpoint of the line segment jointing the points P(1,2,b)
and Q(c,-7,4)
Find the values of:
a=
b=
C=
Answer:
The values are:
a = -5/2
b = -6
c = -7
Step-by-step explanation:
Given
P = (x₁, y₁, z₁) = (1, 2, b)
Q = (x₂, y₂, z₂) = (c, -7, 4)
As the point R(-3, a, -1) is the midpoint of the line segment jointing the points P(1,2,b) and Q(c,-7,4), so
m = R = (x, y, z) = (-3, a, -1)
Using the mid-point formula
[tex]m\:=\:\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2},\:\frac{z_1+z_2}{2}\right)[/tex]
given
(x₁, y₁, z₁) = (1, 2, b) = P
(x₂, y₂, z₂) = (c, -7, 4) = Q
m = (x, y, z) = (-3, a, -1) = R
substituting the values in the mid-point formula
[tex]m\:=\:\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2},\:\frac{z_1+z_2}{2}\right)[/tex]
[tex]\left(x,\:y,\:z\right)\:=\:\left(\frac{1+c}{2},\:\frac{2+\left(-7\right)}{2},\:\frac{b+4}{2}\right)[/tex]
as (x, y, z) = (-3, a, -1), so
[tex]\left(-3,\:a,\:-1\right)\:=\:\left(\frac{1+c}{2},\:\frac{2+\left(-7\right)}{2},\:\frac{b+4}{2}\right)[/tex]
so solving 'c'
-3 = (1+c) / (2)
-3 × 2 = 1+c
1+c = -6
c = -6 - 1
c = -7
solving 'a'
a = (2+(-7)) / 2
2a = 2-7
2a = -5
a = -5/2
solving b
-1 = (b+4) / 2
-2 = b+4
b+4 = -2
b = -2-4
b = -6
Thus, the values are:
a = -5/2
b = -6
c = -7
Verification:
[tex]\left(x,\:y,\:z\right)\:=\:\left(\frac{1+c}{2},\:\frac{2+\left(-7\right)}{2},\:\frac{b+4}{2}\right)[/tex]
[tex]\left(-3,\:a,\:-1\right)\:=\:\left(\frac{1+c}{2},\:\frac{2+\left(-7\right)}{2},\:\frac{b+4}{2}\right)[/tex]
put a = -5/2, b = -6, c = -7
[tex]\left(-3,\:-\frac{5}{2},\:-1\right)\:=\:\left(\frac{1+\left(-7\right)}{2},\:-\frac{5}{2},\:\frac{\left(-6\right)+4}{2}\right)[/tex]
[tex]\left(-3,\:-\frac{5}{2},\:-1\right)\:=\:\left(\frac{-6}{2},\:-\frac{5}{2},\:\frac{-2}{2}\right)[/tex]
[tex]\left(-3,\:-\frac{5}{2},\:-1\right)\:=\:\left(-3,\:-\frac{5}{2},\:-1\right)[/tex]
Mike is 5 years old and Randy is 8 years old. Select the proportional relationship that has the same ratio to that of Mike and Randy's age.
Simplify:
7r + 10 - 2(2r + 3s - 5t) + 2(4s - t) + 5 *
Answer:
3r+2s+8t+15
Step-by-step explanation:
After simplifying 7r+10-2(2r+3s-5t)+2(4s-t)+ 5, you will have 3r+2s+8t+15.