Plot the given parabola on the axes. Plot the roots, the vertex and two other points.
Answers
Solution
Step 1:
The first two points are the roots of the parabola.
To get the roots of the parabola, equate y = 0
[tex]\begin{gathered} \text{y = x}^2\text{ + 2x - 35} \\ x^2\text{ + 2x - 35 = 0} \\ x^2\text{ + 7x - 5x - 35 = 0} \\ x(x\text{ + 7)-5(x + 7) = 0} \\ (x\text{ + 7)(x - 5) = 0} \\ x\text{ = -7 , x = 5} \\ \text{The parabola intercept x-axis at (-7, 0) and (5 , 0)} \end{gathered}[/tex]Step 2:
Find the y-intercept.
To find the y-intercept, plug x = 0
[tex]\begin{gathered} \text{y = x}^2\text{ + 2x - 35} \\ y=0^2\text{ + 2}\times0\text{ - 35} \\ y\text{ = -35} \\ y-\text{intercept is (0 , -35)} \end{gathered}[/tex]Step 3:
Find the vertex
[tex]\begin{gathered} \text{The vertex is (}\frac{-b}{2a}\text{ , y)} \\ b\text{ = 2, a = 1} \\ x\text{ = }\frac{-b}{2a} \\ x\text{ = }\frac{-2}{2\times1} \\ x\text{ = }\frac{-2}{2} \\ x\text{ = -1} \\ y=(-1)^2\text{ + 2(-1) - 35} \\ y\text{ = 1 - 2 - 35} \\ y\text{ = -36} \\ \text{Vertex = (-1, -36)} \end{gathered}[/tex]Final answer
All the five points are:
Roots (x-intercept) = (-7, 0) , (5 , 0)
y-intercept = (0, -35)
vertex = (-1, -36)
Other point = (-5, -20)
Related Questions
I am trying to make a study guide and I need an explanation on this answer please
Answers
Given:
A movies rent for $3.00 except on tuesday, the rent is $0.49.
The cost saved by renting a movie on a Tuesday is,
[tex]\frac{3-0.49}{3}=\frac{2.51}{3}=0.8367[/tex]The percentage is,
[tex]\begin{gathered} 0.8367\times100=83.67\text{ \%}\approx84\text{ \%} \\ \end{gathered}[/tex]Answer: option B)
How do I graph this?
Answers
Select three x values and list them in a table to graph the equation. (Tip: pick values that are simple to calculate, such as 1, 0 and 1). To determine the associated y-coordinate, simplify the equation by substituting each value. Place the sorted pairings on a graph, and then draw a line between each point.
What is an equation graph?
Select three x values and list them in a table to graph the equation. (Tip: pick values that are simple to calculate, such as 1, 0 and 1). To determine the associated y-coordinate, simplify the equation by substituting each value. Place the sorted pairings on a graph, and then draw a line between each point.
example y = 1-1/3x,
x = -3,0,3,6
solution:
given x = -3,0,3,6 to above equation of a graph to get the points
y = 2,0,0,-1
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One integer is 8 less than another integer. The product of the lesser integer and -5 is 28 more than the greater integer. What are the integers?
Answers
Let the lesser integer be "x".
So, the greater integer will be "x + 8".
Given,
Product of lesser and "-5" is 28 MORE THAN greater.
We can write the equation as:
[tex]x\times-5=(x+8)+28[/tex]We can simplify this equation and solve for x. The steps are shown below:
[tex]\begin{gathered} x\times-5=(x+8)+28 \\ -5x=x+36 \\ -5x-x=36 \\ -6x=36 \\ x=\frac{36}{-6} \\ x=-6 \end{gathered}[/tex]Less integer (x) is -6, and
Greater integer (x+8) is -6 + 8 = 2
Answer
-6 and 2
what will the temperature of the juice be 9 minutes after she puts it in the freezer?round off the answer to nearest degree Fahrenheit.
Answers
Let the formula be for time in seconds
Thus, we have:
[tex]T(t)=T_a+(T_0-T_a)e^{-kt}[/tex]T_a would be the freezer temperature, 4
T_0 would be the initial temp, which is 73
t is the time [9 minutes afterwards, t = 9]
k is 0.05
Substituting, we get:
[tex]\begin{gathered} T(t)=T_a+(T_0-T_a)e^{-kt} \\ T(9)=4_{}+(73-4_{})e^{-(0.05)(9)} \\ T(9)=4+69e^{-0.45} \\ T(9)\approx48 \end{gathered}[/tex]To nearest degree Fahrenheight, T = 48 degrees F
Answer: 47 degrees celcius
Step-by-step explanation:
3x – 5 + 6x + 7Step by step please I need help ASAP!!!
Answers
Given the expression
[tex]3x-5+6x+7[/tex]To simplify this expression you have to perform the mathematical operations to all "alike" terms, this is, those who have the unknown value "x" go together and those that do not have the unknown go to another group:
[tex]\begin{gathered} 3x+6x-5+7 \\ 9x+2 \end{gathered}[/tex]What is the value of the expression 8w-5x when w= 4 and x = 2
Answers
The value is 22
Explanation:Given:
[tex]8w\text{ - 5x}[/tex]To find:
the value of the expression when w = 4 and x = 2
To determine the value, we will substitute the values for x respectively and w :
[tex]\begin{gathered} =8(4)\text{ - 5\lparen2\rparen} \\ \\ =\text{ 32 - 10} \\ \\ =\text{ 22} \end{gathered}[/tex]the American Cancer Society do the fundraiser at Allegany State Park that involved a rowing race on Red House Lake . there were 25 boats entered fee in the fundraiser took in 7500 in entry fees.how much was the entry fee for each row
Answers
Given the number of boats = 25
There are 12 rowers in each boat
So, the total number of rowers = 25 x 12 = 300
The total fundraiser = $7500
So, to find the entry fee for each rower, divide 7500 by 300
so, the entry fee =
[tex]\frac{7500}{300}=\frac{75}{3}=25[/tex]so, the answer will be $25
Write and solve an equation to answer the question. A truck rental is $20 plus $.30/mi. Find out how many miles Ken traveled if his bill was $41.30. Ken traveled_____ miles.
Answers
As given by the question
There are given that the truck rent is $20 plus $0.30 per mile.
Now,
The equation of the given statement is shown below:
[tex]20+0.30x=41.30[/tex]Then,
From the given equation, solve for the value of x
So,
[tex]undefined[/tex]36. The histogram shows the ages of the first 45 U.S. presidents on their firstInauguration Day.13TFrequency12111098765432104075Age (years)The ages of 20 of the 45 presidents are shown below.42, 43, 45, 46, 49, 52, 53, 54, 54, 57, 57, 58, 59, 61, 62, 62, 66, 66, 69, 72A certain president's age is in the interval labeled T.What could be the acceptable range for the interval?42 to 4443 to 4945 to 4947 to 54
Answers
Note that the graph shows us that the minimum and maximum value of the ages are 40 and 75, respectively.
We can count the number of bars on the histogram. We see that the are 7 bars in total.
Each bar consider the same age span, so that means that each bar represent an age span of the same amount of years.
To calculate this range, we first find the difference between the maximum and the minimum, that is
[tex]75-40=35[/tex]Now, we divide this number by the total number of bars. That is
[tex]\frac{35}{7}=5[/tex]So, each bar represents a range of 5 years .
Since the minimu is 40, this means that the first bar should represent ages from 40-44. Note that despite the difference between 44 and 40 is only 4, since we are including age 40 in the first bar, we have numbers 40,41,42,43,44 (5 numbers ) associated to the first bar.
This means that for the next one, which is the range T we are looking for, the correspondent age range should be 45-49
help me pleasee!!
thank you <3
Answers
the interval notation is [-7,8] but i have no idea what roster notation is
Find the mean for the amounts: $17,482: $14,987; $13,521: $14,550; $18,570; $14,981
Answers
We have the following data set
17482
14987
13521
14550
18570
14981
there are 6 values, so we can find the mean by adding them all and dividing by 6
[tex]\operatorname{mean}=\frac{17482+14987+13521+14550+18570+14981}{6}=15681.83[/tex]Then, the mean is $15,681.83
Stephanie weighed a gallon of water that measured 8.75 pounds. A gallon of water should weigh 8.33 pounds. What is Stephanie’s percent of error?
Answers
Considering the definition of percent of error, the Stephanie’s percent of error in this case is 5.042%.
Definition of percent of errorPercent of error is a measure of how inaccurate a measurement is, standardized based on the size of the measurement.
In other words, the percent of error allows knowing the differences between the estimated value and the real value. The error may be due to the measurement method (tool or human error) or due to approximations used in the calculation (for example, rounding errors).
To calculate the percent of error you must:
Subtract the real value from the estimated value.Divide the result by the real number.Determines the absolute value of the result. The absolute value of a number is its distance from zero on a number line. Thus, the absolute value of a positive number is the number itself, and the absolute value of a negative number is its opposite.Multiply the result by 100 to get the value in percentage.Therefore, the expression for calculating the percent of error is
percent of error= [|real value - estimated value|÷ real value]×100
Stephanie’s percent of errorIn this case, you know:
Real value= 8.33 poundsEstimated value= 8.75 poundsReplacing in the definition of percent of error:
percent of error= [|8.33 pounds - 8.75 pounds|÷ 8.33 pounds]×100
Solving;
percent of error= [|-0.42 pounds|÷ 8.33 pounds]×100
percent of error= [0.42 pounds÷ 8.33 pounds]×100
percent of error= 0.05042×100
percent of error= 5.042%
Finally, the percent of error in this case is 5.042%.
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3 x ³-8x -x + 4 = x-1 using long division
Answers
Answer:
use followimg steps to your answer
Referring to the figure, segment AB and segment NM are diameters of circle E. Find the angle of arc ACN
Answers
Since the segment MN is the diameter of the circle, the arc MACN has an angle with a measure of 180°, Then by adding the measures of the angles of the arcs MA, AC and CN we should get 180°, like this:
mMA + mAC + mCN = 180
By replacing 55° for mMA and 65° for mCN, we can solve for mAC to get:
55 + mAC + 65 = 180
120 + mAC = 180
120 - 120 + mAC = 180 - 120
mAC = 60
The measure of the arc ACN is calculated by adding the measures of the angles AC and CN, then we get:
mACN = mAC + mCN
mAC = 60 + 65
mAC = 125
Then, the angle of ACN has a measure of 125°
find the real solutions of 9-l2xl=2
Answers
Answer
x = -7/2, 7/2
Step-by-step explanation
Given the equation:
[tex]9-|2x|=2[/tex]Subtracting 9 at both sides of the equation:
[tex]\begin{gathered} 9-9-\lvert2x\rvert=2-9 \\ -\lvert2x\rvert=-7 \end{gathered}[/tex]Dividing by -1 at both sides of the equation:
[tex]\begin{gathered} \frac{-\lvert2x\rvert}{-1}=\frac{-7}{-1} \\ |2x|=7 \end{gathered}[/tex]Now we have two options:
[tex]\begin{gathered} 2x=7 \\ \text{ Or} \\ 2x=-7 \end{gathered}[/tex]Solving the first option:
[tex]\begin{gathered} 2x_1=7 \\ \frac{2x_1}{2}=\frac{7}{2} \\ x_1=\frac{7}{2} \end{gathered}[/tex]Solving the second option:
[tex]\begin{gathered} 2x_2=-7 \\ \frac{2x_2}{2}=\frac{-7}{2} \\ x_2=-\frac{7}{2} \end{gathered}[/tex]The greatest common factor of 60 and 100
Answers
A die is toss three times let X be the sum of three numbers obtainedDetermine whether the random X has a binomial distribution if so take the number of trails N . If it doesn’t explain why
Answers
The given experiment is a die that is tossed three times.
X is the sum of the three numbers obtained.
You need to determine if the random X variable has a binomial distribution.
First, we need to understand what makes a random variable has a binomial distribution. There are 4 conditions to be met:
1. There are a fixed number of trials N
2. Each trial has only two possible outcomes: success or failure
3. The probability of success is equal in each trial
4. The trials are independent.
In this case, condition 1 is met, but condition 2 is not met, since in each trial we can obtain 6 different numbers, then there are not only two possible outcomes, but 6, then the sum of the three numbers has more than two possible outcomes. So, the random X variable doesn't have a binomial distribution.
MATH please solve it now and let it be correct please
Answers
The value of X is ([tex](A-CB)^{-1}[/tex] CD.
Given,
AX[tex](D+BX)^{-1}[/tex] = C
Multiply both sides on the right by (D+BX):
AX[tex](D+BX)^{-1}[/tex] × (D+BX) = C × (D+BX)
AX ([tex](D+BX)^{-1}[/tex] (D+BX)) = C(D+BX)
AX × I = CD + CBX
AX = CD + CBX
Subtract CBX on both sides and factor:
AX – CBX = (CD + CBX) – CBX
AX – CBX = CD + (CBX – CBX)
AX – CBX = CD + 0
(A – CB)X = CD.
Multiply both sides on the left by [tex](A-CB)^{-1}[/tex] :
([tex](A-CB)^{-1}[/tex] × (A – CB)X = ([tex](A-CB)^{-1}[/tex] × CD
([tex](A-CB)^{-1}[/tex] × (A – CB)) X = ([tex](A-CB)^{-1}[/tex] CD
IX = ([tex](A-CB)^{-1}[/tex] CD
X = ([tex](A-CB)^{-1}[/tex] CD.
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The following this gives the number a pet for each of 12 students find the moods of this data set if there is more than one mode right them separated by commas if there is no mold click on low mode
Answers
Explanation
In the question, we are given the number of pets for 12 students below.
[tex]0,3,1,0,4,3,1,3,2,1,4,0[/tex]The mode of a set of values is the number that occurs the most in the data set. Based on this definition, we can go through the data set and pick the number that represents the above concept.
From the above, we can see that three numbers embodies the definition of a mode. Therefore the mode of the data set is
Answer
[tex]\text{Mode = 0,1,3}[/tex]For his phone service Bob pays the monthly fee of $30 and he pays an additional five cents per minute of use. At least he has been charged in a month is $94.70. What are the possible numbers of minutes he has used his phone in a month? Use m for the number of minutes and solve you’re in equality for m.
Answers
We can write an expression for the cost of Bob's phone service as follows:
First, remember that five cents are 0.05 dollars.
[tex]C=30+0.05m[/tex]Where C is the cost and m are the minutes.
We know that at least he has been charged in a month is $94.70.
We can express this as an inequality:
[tex]30+0.05m\ge94.70[/tex]To find the possible number of minutes, we have to solve the previous equation for m. This is:
[tex]\begin{gathered} 0.05m\ge94.70-30 \\ 0.05m\ge64.70 \\ m\ge\frac{64.70}{0.05} \\ m\ge1294 \end{gathered}[/tex]Therefore, the possible numbers of minutes he has used in his phone in a month are:
[tex]m\ge1294[/tex]f(x) = a(x - h)² + k.
f(x) = 3x² + 6x + 2.
Answers
Answer:
f(x) = 3(x + 1)² - 1a = 3, h = - 1, k = - 1
Step-by-step explanation:
It is assumed you need to convert the given function into vertex form.
Converting in below steps:
f(x) = 3x² + 6x + 2 = 3(x² + 2x) + 2 = 3(x² + 2x + 1) - 3 + 2 = 3(x + 1)² - 1We got:
a = 3, h = - 1, k = - 1I dont know how to do this so whatever helps:)
Answers
The function which represents the phone rate is a straight line, which can be gotten by the following formula:
[tex]y=mt+b[/tex]Where m is the slope, and b the point where the y-axis is crossed by the line.
Let's get the slope first:
[tex]m=\frac{27-25}{20-0}=\frac{2}{20}=\frac{1}{10}[/tex]And b = 25 because (0, 25) is where the line has crossed the cost axis.
Therefore:
[tex]y=C(t)=\frac{1}{10}t+25[/tex]2A tennis team bought 8 yards of red fabric to make head bands. If each head band takes į of a yard of fabric, howmany head bands can the team make?You would useto solve this problemThe tennis team can make head bands.
Answers
headbandThe illustration of the question is shown below
Since a length of 8 yards of the fabric is bought
Using j to represent the number of the head band
To determine the number of headbands that can be made from the fabric, we will simply divide 8 by j
=>
[tex]undefined[/tex]what causes an eathquake
Answers
Earthquakes are caused by human activity, like tunnel construction, filling reservoirs that leads to a sudden release of stress along faults in the earth's crust.
What causes an Earthquake?
An earthquake is caused as a result of a sudden slip on a fault in the earths outermost layer.
The genesis of this discussion is that the tectonic plates are usually moving slowly. However, these tectonic plates may get stuck at their edges as a result of undergoing friction. Now, after the stress on the edge overcomes the friction, there would be an earthquake that would release energy in form of waves travelling through the earth's crust that leads to the shaking of the earths surface that humans experience in an earthquake.
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1. Mark earned $8.75 an hour plus an additional
$200 in tips working at a restaurant. He earned
more than $506.25 this week. How many hours
could he have worked this week?
Answers
Solution:17.Graph each system and determine the number of solutions that it has. If it has one solution,name it.A. X +2y=4y= -1/2x+2B. 2x-y=1y=-3
Answers
Systems of Equations
Given the system:
[tex]\begin{gathered} x+2y=4 \\ y=-\frac{1}{2}x+2 \end{gathered}[/tex]It's required to graph and find the solutions of the system.
Solving the first equation for y:
[tex]\begin{gathered} 2y=-x+4 \\ y=-\frac{1}{2}x+2 \end{gathered}[/tex]We can see both equations are exactly the same, so there is only one equation and one line.
Let's give x some values and graph the line.
x = 0:
[tex]\begin{gathered} y=-\frac{1}{2}\cdot0+2 \\ y=2 \end{gathered}[/tex]x = 2
[tex]\begin{gathered} y=-\frac{1}{2}\cdot2+2 \\ y=1 \end{gathered}[/tex]With the points (0, 2) and (2, 1) we graph the line as follows.
Since the number of equations is greater than the number of unknowns, the system has infinitely many solutions. For example, (0, 2) and (2, 1) are solutions for the system.
A house has increased in value by 38% since it was purchased. If the current value is $345,000, what was the value when it was purchased?
Answers
The formula for calculating the percent change over time is:
[tex]\begin{gathered} p=\frac{N-O}{O}\cdot100 \\ \text{ Where} \\ p\text{ is the percent change } \\ N\text{ is the new value } \\ O\text{ is the old value} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} p=38 \\ N=345000 \\ O=x \end{gathered}[/tex][tex]\begin{gathered} p=\frac{N-O}{O}\cdot100 \\ 38=\frac{345000-x}{x}\cdot100 \\ \text{ Multiply by x from both sides} \\ 38x=x\cdot\frac{345000-x}{x}\cdot100 \\ 38x=(345000-x)100 \\ \text{ Divide by 100 from both sides} \\ \frac{38x}{100}=\frac{(345000-x)100}{100} \\ 0.38x=345000-x \\ \text{ Add x from both sides} \\ 0.38x+x=345000-x+x \\ 1.38x=345000 \\ \text{ Divide by 1.38 from both sides} \\ \frac{1.38x}{1.38}=\frac{345000}{1.38} \\ x=250000 \end{gathered}[/tex]AnswerThe value of the house when purchased is 250,000.
What is the slop intercept for (-1,0) and (4,-5)
Answers
The slope intercept form of the line for (-1,0) and (4,-5) is y = -x -1.
We know that,
Slope intercept form of a line is given by:-
y = mx + c
Where,
m is the slope of the line,
c is the y -intercept of the line and,
(x,y) is the ordered pair of each point on the line
We know that,
m = (-5-(-1))/(4 - 0) = (-5 +1)/4 = -4/4 = -1
Putting (-1,0) in the line, we get
0 = (-1)*(-1) + c
0 = 1 + c
c = -1
Hence, the equation of the line is given by:-
y = -1x -1 = -x - 1
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A conical circus tent has a 20 ft central pole that supports it. The slant height of the tent is 26 ft long. Explain how to find the angle the tent pole makes with
the sides of the tent.
26 ft
20 ft
The central pole forms a right triangle with the floor of the tent. The
the length of the side of the tent, which is
Applying
is
V
of the missing angle is the ratio of the length of the central pole to
we find that the angle the tent pole makes with the sides of the tent
Answers
The angle the pole makes with the tent is 39.7°.
What is an angle?
An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle.
Angles formed by two rays are located in the plane containing the rays.
Trigonometric ratio: the trigonometric ratio is used to demonstrate the relationship between the sides and angles of a right-angled triangle.
Let θ represent the angle the pole makes with the tent.
Using trigonometric ratios:
cos(θ) = 20/26
θ = 39.7°
Therefore, the angle the pole makes with the tent is 39.7°.
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67 km 230 m + 11 km 879 m
Answers
Answer:
79.10900 kilometers
Step-by-step explanation:
Answer:
79 kilometers 109 meters
