The parabolic equation that passes through the points is y = 29/7x^2 + -27/7x - 342/7
What are parabolic equations?Parabolic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the equation of the parabola?The given parameters are
x-intercepts (-3,0) and (4,0)
Point = (2,-40)
From the definition above, we have the form to be
y = ax^2 + bx + c
Substitute (-3,0) and (4,0) in the above equation
So, we have
0 = a(-3)^2 + b(-3) + c
0 = a(4)^2 + b(4) + c
This gives
9a -3b + c = 0
16a + 4b + c = 0
Substitute (2,-40) in the above equation y = ax^2 + bx + c
a(2)^2 + b(2) + c = -40
So, we have
4a + 2b + c = -40
The equations become
9a -3b + c = 0
16a + 4b + c = 0
4a + 2b + c = -40
Using a graphing tool, we have
a = 29/7, b = -27/7 and c = -342/7
So, we have
y = ax^2 + bx + c
This gives
y = 29/7x^2 + -27/7x - 342/7
Hence, the equation is y = 29/7x^2 + -27/7x - 342/7
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A spinner with 10 equally sized slices has 5 red slices , and 3 yellow slices, and 2 blue slices. The dial 500 times and got the following results. What is the probability that the dial stops on a red or yellow slice?
Part a
The experimental probability that landing on red is equal to
P=277/500
P=0.554
Part b
The theoretical probability that landing on red is equal to
P=5/10
P=0.5
Part c
the answer is the first option
please answer preferably with steps, but not necessary
Answer:
Step-by-step explanation:
(5n - 3)/2=n-0.3
Then we solve for n.
Multiply the whole thing by 2.
5n-3=2n-0.6
Add 0.6
5n-2.4=2n
Add 2.4
5n=2n+2.4
Subtract 2n
3n=2.4
Divide by 3
n=0.8
A large group is ordering shirts for a company outing. The order will be based on how many employees sign up for a shirt.
The independent variable in this situation is the size of the order.
True
OR
False
Answer:
False
Step-by-step explanation:
The dependent variable changes, the size of the order will change depending on how many employes want a shirt.
Day 6: Textbook Page 321 Problem 9 When Esteban looks at the puddle, he sees a reflection of the top of the cactus. How tall is the cactus? use 10 m, 2.5 m, 1.5 m
The given figure can be drawn as,
From the figure,
[tex]\tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}}[/tex][tex]\begin{gathered} \tan \theta=\frac{DE}{EC} \\ \tan \theta=\frac{1.5}{2.5} \\ \tan \theta=0.6 \end{gathered}[/tex]Since angle of incidence will be equal to angle of reflection, [tex]\begin{gathered} \text{tan}<\text{ACB}=\frac{h}{10\text{ m}} \\ \text{tan}\theta=\frac{h}{10\text{ m}} \\ 0.6=\frac{h}{10\text{ m}} \\ 6\text{ m=h} \end{gathered}[/tex]Therefore, the height of cactus is 6 m.
The fuel economies in miles per gallon (mpg) for nine vehicles are listed below. If one more vehicle is added to the list with a rate of 40 mpg, how will this affect the mean and median?
A. The mean and median will both increase.
B. The mean will increase and the median will decrease.
C. The mean will increase and the median will not change.
D. The mean will decrease and the median will not change.
Option C. The way that the change would affect the mean and the median is that The mean will increase and the median will not change.
How to solve for the mean and the medianWe will find the mean and the median before the 40 was added and after it was added
Before it was added
Mean = 16 + 18 + 20 + 24 + 24 + 24 + 24 + 31 + 32 / 9
= 213 / 9
= 23.67
The median is 24
After we have added 40 the mean would be
16 + 18 + 20 + 24 + 24 + 24 + 24 + 31 + 32 + 40 / 10
= 253 / 10
= 25.3
The median would be 24 + 24 / 2
= 48 / 2
= 24
Hence we can see that the mean got to be higher while the median still remained as 24.
The solution is C.
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Kendall read 1 1/3 books in a 1/2day. At that rate how many books will she read in
1 day?
Answer:
Step-by-step explanation:
1/2 to 1 day is 2 1/2
11/3 x 11/3 = 121/9
13.4 books
Slope intercept form for points through (0,4) and (-3,3)
Answer:
y = (1/3)x + 4
Step-by-step explanation:
(0, 4) and (-3, 3)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 3 - 4 -1 1
m = ------------- = ------------ = --------- = --------
x₂ - x₁ -3 - 0 -3 3
y - y₁ = m(x - x₁)
y - 4 = (1/3)(x - 0)
y - 4 = (1/3)x - 0
+4 +4
----------------------------
y = (1/3)x + 4
I hope this helps!
Can someone help me with this please and thank you!
Answer: b
Step-by-step explanation:
Can someone help me with this please and thank you
all the statements prove that a line is parallel to b.
WHAT ARE PARALLEL LINES ?If two non-vertical lines in the same plane have the same slope, they are said to be parallel. Never will two parallel lines cross. If two non-vertical lines in the same plane cross at a right angle, they are said to be perpendicular.
CALCULATIONSLines can either be parallel or intersecting. When two lines meet at a point in a plane, they are known as intersecting lines. If a line intersects two or more lines at distinct points then it is known as a transversal line.
line intersects lines a and b at points P and Q respectively. The line l is the transversal here.
∠1,∠2,∠7 and ∠8 are the exterior angles and ∠3,∠4,∠5 and ∠6 denote the interior angles.
The angle pairs formed due to intersection by a transversal are named as follows:
Corresponding Angles: ∠1 and ∠6; ∠4 and ∠8; ∠2 and ∠5; ∠3 and ∠7 are the corresponding pair of angles.
Alternate Interior Angles: ∠4 and ∠5 ; ∠3 and ∠6 denote the pair of alternate interior angles.
Alternate Exterior Angles: ∠1 and ∠7; ∠2 and ∠8 are the alternate exterior angles.
Same side Interior Angles: ∠3 and ∠5; ∠4 and ∠6 denote the interior angles on the same side of the transversal or co-interior or consecutive interior angles.
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A constant force is applied to an object, causing the object to accelerate at 12.50 m/s/s. What will the acceleration be if both the force and the
mass are doubled? Round to two decimal places and use SI units.
Answer:
a₂ = 12.5 m/s²
Step-by-step explanation:
Applying the 2º Newton's Law:
∑F = m * a
F₁ = m₁ * a₁
F₁ = m₁ * 12.5
F₁ = 12.5m₁
F₂ = m₂ * a₂
2F₁ = 2m₁ * a₂
a₂ = F₁ / m₁
So:
a₂ = 12.5m₁ / m₁
a₂ = 12.5 m/s²
3x-1/5=x+1/3 pls help me
Answer:
x=4/15
Step-by-step explanation:
first you need to make common denominators for 1/5 and 1/3
the common denominator is 15
5*3=15, 3*5=15. 1*3=3, 1*5=5
new equation:3x-3/15=x+5/15
now subtract x from both sides: 3x-3/15=x+5/15
-x -x
2x-3/15=5/15
now you can add 3/15 to 5/15
2x=8/15
now for the last step, divide by 2 because there are 2 x's
2x/2=x 8/15 /2=4/15
x=4/15
Answer:
4/15
Step-by-step explanation:
3x-1/5 = x+1/3
make a common denominator
3x -3/15 = x + 5/15
next you can take away one x from both sides
2x - 3/15 = 5/15
then we want to have x alone on one side and everything else on the other
2x = 5/15 + 3/15
2x = 8/15
1x = 8/15 ÷ 2
1x = 8/30
simplify that
x = 4/15
solution a is 2% alcohol and solution b is 5% alcohol. she uses 800 milliliters of solution A how many milliliters of solution b does she use if the resulting mixture is a 3% alcohol situation
She uses 800 mL of solution A; that is, 2% of those 800 mL is alcohol
Alcohol on a:
2% of 800 = 2*800/100 = 16mL
If we use x mL of b, the amount of alcohol is:
5% of x = 5*x/100 = x / 20
Total amount of alcohol: 16 + x/20
Total amount of solution mixture: 800 + x
The ratio:
(16 + x/20) / (800 + x) = 3%
(16 + x/20) / (800 + x) = 3/100
1600 + 5x = 2400 + 3x
Solving for x:
5x - 3x = 2400 - 1600
2x = 800
x = 400 mL
She used 400 mL of solution b
what are the domain and range of the function?
Answer:
B
Step-by-step explanation:
If we look at the x-axis, the function increases and decreases. Therefore, the domain is all real numbers.
If we look at the y-axis, the same is occurring. Therefore the range is also all real numbers.
BenchenIf these two lines were graphed, where would they intersect? Drag the point to theirintersection's coordinates.y = x - 3y = -X- 1
y = x - 3
y = - x -1
They intersect at
Describe the transformation that maps the pre-image A to the image A.translated 8 units up and then reflected across the y-axisB)translated 8 units down and then reflected across the y-axisC)translated 1 unit to left and then rotated 180° counterclockwise about theoriginD)translated 1 unit to right and then rotated 180° counterclockwise about theorigin
Answer:
C. translated 1 unit to left and then rotated 180° counterclockwise about the
origin
Explanation:
In the graph:
• The vertices of Figure A are: (0,4), (-9,3) and (-9,6)
,• The vertices of Figure A' are: (1,-4), (10,-3) and (10,-6)
If Figure A is translated 1 unit to the left, the vertices are:
[tex](-1,4),(-10,3),(-10,6)[/tex]Next, a rotation of 180° counterclockwise about the origin gives:
[tex](1,-4),(10,-3),(10,-6)[/tex]These are the vertices of Figure A'.
Thus, the correct transformation is: translated 1 unit to left and then rotated 180° counterclockwise about the origin.
The correct choice is C.
A passenger car will go 310 miles on 15.5 gallons of gasoline in city driving. What is the rate in miles per gallon?
The rate is
mpg.
(Simplify your answer.)
Answer:
20 mpg
Step-by-step explanation:
Given:
A passenger car will go 310 miles on 15.5 gallons of gasoline in city driving. What is the rate in miles per gallon?
Solve:
To find the rate in miles per gallon we have to divide.
Knowing that "Per" means "Each/One"
Hence, to find miles per gallon we divide :
Miles by Gallons
⇒ 310/15.5
Solving using long division format: ( Multiply both by 10 first)
[tex]155\overline{|\smallspace3100}\:\:\:\:[/tex]
Divide 310 by 155 to get 2:
[tex]\begin{matrix}\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace2\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ 155\overline{|\smallspace3100}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\underline{\emptyspace3\emptyspace1\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\emptyspace0\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]
Divide 0 by 15.5 to get 0.
[tex]\begin{matrix}\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace2\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\\ 155\overline{|\smallspace3100}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\underline{\emptyspace3\emptyspace1\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\emptyspace0\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\:\:\underline{\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]
Hence, the rate is 20 mpg.
~kavinsky
Rewrite the expression 26 + 8 as the product of the GCF (greatest common factor) and a sum. Then, simplify the expression. Show all of your steps.
HELP ITS DUE TODAY
Answer:
34
Step-by-step explanation:
[tex]26+8 \\ \\ =2(13+4) \\ \\ =2(17) \\ \\ =34[/tex]
how do I solve this
1/9 = z/23
Answer: z=23/9
Step-by-step explanation:
I will use cross multiplication
[tex]\frac{1}{9} =\frac{z}{23} \\23(1)=9(z)\\23=9z\\\frac{23}{9} =\frac{9z}{9} \\z=\frac{23}{9}[/tex]
I hope this helps.
25×10 to the power of -3 to standard form
The number 25×10 to the power of -3 written in the standard form is 2.5×10⁻⁴.
What is meant by the term scientific notations?Scientific notation is a way of displaying very large or extremely small numbers in a more simplified format. We know that whole numbers could be extended indefinitely, but such large numbers cannot be written on a sheet of paper. The scientific notation allows us to represent very large or very small numbers by multiplying single-digit numbers by 10 raised to a power of a respective exponent. If the number is so very large, the exponent is positive; otherwise, it is negative. For a better understanding, learn power and exponents.The given number is;
25×10 to the power of -3
This can be written as;
= 25×10⁻³
Now, as per the standard form, the number should contain only one digit to the left of decimal.
Thus, shifting one decimal to the left of the 5 and converting the power by adding one to the current power,.
The number becomes;
= 2.5×10⁻⁴.
Thus, the number written in the standard form is 2.5×10⁻⁴.
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Write the equation of the line passing through
(−2, −5)
that is parallel to
3x + 5y = 11.
Answer:
y = (-3/5)x - (31/5)
Step-by-step explanation:
3x + 5y = 11
-3x -3x
------------------------------
5y = -3x + 11
÷5 ÷5 ÷5
-----------------------
y = (-3/5)x + (11/5)
y - y₁ = m(x - x₁)
y - (-5) = (-3/5)(x -(-2))
y + 5 = (-3/5)(x + 2)
y + 5 = (-3/5)x - (6/5)
-5 -5
-----------------------------------
y = (-3/5)x - (31/5)
I hope this helps!
Olivia and Camille went clothes shopping. Camille spent $14 less than three
times what Olivia spent. In total, they spent $54. How much did each girl
spend?
By solving a system of equations we can see that Olivia spent $14 and Camiller spent $37.
How much did each girl spend?Let's define two variables:
x = Amount that Olivia spends.y = Amount that Camille spendsWe know that " Camille spent $14 less than three times what Olivia spent" so we can write:
y = 3*x - 14
And "In total, they spent $54"
x + y = 54
Then we have a system of equations:
y = 3*x - 14
x + y = 54
Replacing the first equation into the second one, we get:
x + 3x- 14 = 54
4x - 14 = 54
4x = 54 + 14
4x = 68
x = 68/4 = 17
Now that we know the value of x, we can try to find the value of y.
y = 3x - 14 = 3*17 - 14 = 37
So Olivia spent $14 and Camiller spent $37.
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Select the correct equation and correct answer to solve for X using the triangle below.
The correct equation to solve for x is 2(2x-15)=2x-8 , and the value of x is 11 .
in the question ,
from the given figure , we can see that RL=LQ and PK=KQ which means
that L and K are the mid points of sides RQ and PQ respectively .
The Mid Point Theorem states that
If the line segment adjoining the mid points of any of the sides of the triangle then the line segment is said to be parallel to the third side and is half of the length of third side .
which means LK parallel to RP and RP/2=LK ( ... by mid point theorem)
Substituting the values of LK = 2x-15 and RP = 2x-8 .
(2x-8)/2=2x-15
Multiplying both sides by 2
2x-8 = 2(2x-15)
So, the equation to solve for x is 2(2x-15)=2x-8
Simplifying further
2x-8 = 4x-30
4x-2x= 30-8
2x = 22
x = 11
Therefore , the correct equation to solve for x is 2(2x-15)=2x-8 , and the value of x is 11 .
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Find the y intercept (if there is one) put your answer as a ordered pair.
(-2,6) (1,6)
The y-intercept of the line that passes through points (-2,6) and (1,6) in an ordered pair is ( 0,6 ).
What is the y-intercept of the line that passes through the given points?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
The slope of a line is expressed as change in y over change in x.
Slope m = (y₂-y₁)/(x₂-x₁)
Given the data in the question;
Point A ( -2,6 )
x₁ = -2y₁ = 6Point B ( 1, 6 )
x₂ = 1y₂ = 6First, we determine the slope of the line.
Slope m = (y₂-y₁)/(x₂-x₁)
Slope m = ( 6 - 6 )/( 1 - ( -2) )
Slope m = ( 0 )/( 1 + 2) )
Slope m = ( 0 )/3
Slope m = 0
Now, we can determine the y-intercept b, using the slope and coordinates of 1 point.
y = mx + b
6 = (0)(1) + b
Solve for b
6 = 0 + b
b = 6
Therefore, the coordinates of the y-intercept is ( 0,6 ).
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Find the x-intercept of the line that passes through (-3,4) and is perpendicular to the graph of x-2y=7
Answer:
x - intercept = - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
x - 2y = 7 ( subtract x from both sides )
- 2y = - x + 7 ( divide through by - 2 )
y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{7}{2}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2 , then
y = - 2x + c ← is the partial equation of the perpendicular line\to find c substitute (- 3, 4 ) into the partial equation
4 = 6 + c ⇒ c = 4 - 6 = - 2
y = - 2x - 2 ← equation of perpendicular line
to find the x- intercept let y = 0 into the equation and solve for x
- 2x - 2 = 0 ( add 2 to both sides )
- 2x = 2 ( divide both sides by - 2 )
x = - 1
the x- intercept of the perpendicular line is - 1 or (- 1, 0 )
Help me answer this.
iven:
here are givren the expression:
[tex](2z-y)^{20}[/tex]xplanation:
o find the coefficient of the given expression, we need to use the binomial expansion formula:
So,
From the formula of binomial expansion:
[tex](x+y)^n=\sum_{k\mathop{=}0}^n(n,k)x^ky^{n-k}[/tex]then,
After using the above formula in the given binomial, the expansion will be:
[tex](2z-y)^{20}=y^{20}-40y^{19}z+760y^{18}z^2-9120y^{17}z^3+77520y^{16}z^4-496128y^{15}z^5+...[/tex]inal answer:
ence , the coefficient of the given term is shown below:
[tex]77520[/tex]Simplify (4 ^4) ^−1.
4 ^3
−4 ^4
one over four raised to the fourth power
one over four raised to the power of negative four
The simplified expression of (4⁴)⁻¹ is one over four raised to the fourth power
How to simplify an expression?The expression can be simplified as follows:
(4⁴)⁻¹
Therefore, the expression can be simplified using laws of indices.
[tex](a^{c} )^{b} = a^{cb}[/tex]
and
[tex](a^{-b} )^{c} = \frac{1}{a^{bc} }[/tex]
Therefore, using the laws of indices, the expression can be simplified below:
(4⁴)⁻¹ = 4⁻⁴
Hence,
4⁻⁴ = 1 / 4⁴ = (1 / 4)⁴
Hence,
(4⁴)⁻¹ = 1 / 4⁴ = (1 / 4)⁴
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use the picture shown solve for m
Answer: Provided the geometric diagram, we have to find the unknown angle DCF.
Assuming, that the line segments AC and EF are parallel and the same is true for the line segments DE and CB.
[tex]\begin{gathered} AC\text{ }||\text{ EF} \\ \\ \text{ and} \\ \\ DE\text{ \mid\mid }CB \end{gathered}[/tex]The new diagram is:
Therefore the answer is:
[tex]m\angle DCF=61^{\circ}[/tex]or 61 degrees.
The table shows the number of insects in each group. What is the combined population of the four insect groups?
Insect Population
Honeybees
7
.
3498
×
10
4
Ants
6
.
822
×
10
3
Termites
9
.
8
×
10
5
Aphids
2
.
9502
×
10
4
1089822 is the combined population of the four insect groups.
What is exponents?The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 2³) signifies 2 x 2 x 2 = 8. 2³ and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the power of 1.
Given Data
Insect population
Population of honeybees = 7.3498(10⁴)
Population of honeybees = 73498
Population of ants = 6.822(10³)
Population of ants = 6822
Population of termites = 9.8(10⁵)
Population of termites = 980000
Population of aphids = 2.9502(10⁴)
Population of aphids = 29502
Combined population = 73498 + 6822+980000+29502
Combined population = 1089822
1089822 is the combined population of the four insect groups.
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please help im begging ill give brainliest
Answer:
t=44 hrs.
Step-by-step explanation:
1. a. you are asked to find the total hours the 2 girls work in a week.
b. it needs to be a greater number than 26
2. variables: h= hours per week
t= total hrs.
3. h= hrs. per week
t= total hrs.
4. 44=26+h
-26 -26
18=h
5. 44=26+18
44=44
6. The total hours the two work in a week is 44 hours.
Anyone know how to find the frequency for this?
The frequency of specific five classes (67, 68, 69, 70, and 71) will occur a total of 19 times.
What do we mean by frequency?The frequency of a given data value is the number of times it occurs.The frequency of a data value is represented by f.For instance, if five students received As in science, the frequency of grade A is said to be five.So, the frequency for the particular 5 classes is as follows:
4 times in 67.6 times in 68.4 times in 69.4 times in 70. 1 time in 71.The following five classes will appear most frequently overall:
4 + 6 + 4 + 4 + 1 = 19Therefore, the frequency of specific five classes (67, 68, 69, 70, and 71) will occur a total of 19 times.
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