Graph the equation y = x2 + 6x + 5 on the accompanying set of axes. You must
plot 5 points including the roots and the vertex.
Answers
Answer:
Please check the graph below.
Step-by-step explanation:
Given the function
[tex]y\:=\:x^2\:+\:6x\:+\:5[/tex]
Axis interception points of the function
x-axis interception points can be computed by setting y=0
[tex]x^2+6x+5=0[/tex]
[tex]\left(x+1\right)\left(x+5\right)=0[/tex]
Using the zero factor principle
if [tex]\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]
[tex]x+1=0\quad \mathrm{or}\quad \:x+5=0[/tex]
[tex]x=-1,\:x=-5[/tex]
Hence,
x-axis interception points are: (-1, 0), (-5, 0)
y-axis interception points can be computed by setting x=0
[tex]x^2+6x+5=0[/tex]
[tex]y\:=\:\left(0\right)^2\:+\:6\left(0\right)\:+\:5[/tex]
[tex]y=0+0+5[/tex]
[tex]y=5[/tex]
Hence,
y-axis interception points are: (0, 5)
From the graph, it is clear that at (-3, -4) the parabola changes direction, hence (-3, -4) it the "vertex".
Also at the point x=-2, then y is = -3
So, all the points are labeled and the graph is attached below.
Related Questions
Use long division to find the quotient below.
(8x3 + 4x2 + 100) = (2x + 5)
A. 4x2 + 12x + 20
B. 4x2 + 8x+ 20
C. 4x2 - 12x+ 20
D. 4x2 - 8x + 20
Answers
Answer:
D
Step-by-step explanation:
D 4x2-8x+20
The equation of line L is y=5x+1
The equation of line L is 2y-10x+3=0
Show that these two lines are parallel.
Please help, will award brainliest.
Answers
Answer:
see explanation
Step-by-step explanation:
Parallel lines have equal slopes.
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
L₁ is y = 5x + 1 ← in slope- intercept form
with slope m = 5
L₂ is 2y - 10x + 3 = 0 ( subtract - 10x + 3 from both sides )
2y = 10x - 3 ( divide all terms by 2 )
y = 5x - [tex]\frac{3}{2}[/tex] ← in slope- intercept form
with slope m = 5
Since L₁ and L₂ have equal slopes then they are parallel lines
The product of 3 and a number decreased by 10
Answers
Answer:
5
Step-by-step explanation:
1.A study was created to test the effects of jazz on people's sleep patterns. The hypothesis of the experiment was
that if people listened to jazz music as they fall asleep, they will sleep for longer periods of time. For the experiment,
2 groups of people were created. Group I was placed in a quiet room where they went to sleep and they were timed
on how long they slept. The Group 2 was placed in a room where jazz music played softly as they began to sleep and
played throughout the night. As each group awoke, their sleep times were monitored.
Independent Variable:
Dependent Variable:
Experimental Group:
Control Group:
3 constants:
?
Answers
Answer:
Independent Variable: Jazz music
Dependent Variable: Sleeping Time
Experimental Group: people sleeping with jazz music
Control Group: people sleeping without jazz music
3 constants:
No of people in group
Jazz music
Sleep
Step-by-step explanation:
The independent variable is the one which is not altered by any outer influence. For example the jazz music will not be interrupted by the sleeping habits of people.
The dependent variable is the one which is affected by external changes such as sleeping time is afffected by external music or noises.
Experimental group on which experiment is being carried out.
Control group is which determines the changes in experimental group.
Constants which do not change for the number of experiment, could be number of people, type of jazz music, volume of jazz music also sleep is a constant .
1. What is the relationship of angles 1 and 2?
2. What is the measure of angles 1 and 2?
3. What is the measure of angle 3?
4. Each of these triangles would classify by angles to
be:
PLS HELP
Answers
Answer:
Question 1 answer: the two angles are the same.
Question 2 answer: The value of the angles is 76.
Question 3 answer: The value of the angle is 36.
Question 4 answer: all angles in the figures are classified as acute angles
Step-by-step explanation:
First all of, using one of the triangle rules, both the angles are congruent. Then, because both 1 and 2 are the same and the triangle in 1 already have the other two angles, use 180 - 85 - 19 and get 76. Lastly moving on to the other triangle, same method, 180 - 76 -68 and get 36. Because all these angles are less than 90 degrees and anything less than 90 is considered to be acute.
I hope this helped
I need help On This !!!!!!!!
Answers
Answer:
Step-by-step explanation:
L'= 3, -3 M'= -3, -6 N'= -3, 3
line with a slope of 2 and passes through point (3, 5)
Answers
Answer:
i dont get what you are trying to say is their a graph u can show
Step-by-step explanation:
Answer:
y = 2x - 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 )
Here m = 2, thus
y = 2x + c ← is the partial equation
To find c substitute (3, 5) into the partial equation
5 = 6 + c ⇒ c = 5 - 6 = - 1
y = 2x - 1 ← equation of line
Travis would like to buy some toys to donate to charity. The expression 9d + 2c +3t
represents the total that Travis spent on toy trains, c cars, and d dolls in dollars. How much
did each car cost?
*ANSWER FAST PLEASE*
Answers
Answer:
Step-by-step explanation:
D. $14
Can someone pls gave me an idea for a business letter.
U get brainliest if i like it!
Answers
Answer:
Try writing to your teacher, why students should have game time on Fridays.
Step-by-step explanation:
Children at school are getting worried about recent events, but letting kids play Video games will keep their minds more focus on the game, instead of their worries. Plus this can give teachers extra time to plan lessons or just take a relaxing break, teachers deserve it anyways.
The lower quartile of a set of data is calculated by __________.
A.
averaging the lower half of the data set
B.
finding the median of the lower half of the data set
C.
finding the mean of the data set remaining after removing the lower half
D.
subtracting the smallest value of the lower half of the data set from the biggest value of the lowest half of the data set
Answers
Step-by-step explanation:
D.
subtracting the smallest value of the lower half of the data set from the biggest value of the lowest half of the data set
The lower quartile of a set of data is calculated by subtracting the smallest value of the lower half of the data set from the biggest value of the lowest half of the data set.
What is a quartile ?"A quartile is a statistical term that describes a division of observations into four defined intervals based on the values of the data and how they compare to the entire set of observations.
Just like the median divides the data into half so that 50% of the measurement lies below the median and 50% lies above it, the quartile breaks down the data into quarters so that 25% of the measurements are less than the lower quartile, 50% are less than the median, and 75% are less than the upper quartile."
From the definition it is clear that,
lower quartile of a set of data is calculated by :
subtracting the smallest value of the lower half of the data set from the biggest value of the lowest half of the data set.
Hence, D is the correct option.
To know more about quartile here
https://brainly.com/question/7039036
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Joe opened a bank account with $80. He then withdrew $35 and deposited $115. What is his account balance after these transactions?
Answers
Answer:
160 dollars
Step-by-step explanation:
80-35=45
45+115=160 dollars
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The amount after the transaction.
= Amount in account - Amount withdrawn + Amount deposited
The account balance after the transaction is $160.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example:
2 + 3x + 4y = 7 is an expression.
3 + 4 + 4 - 3 is an expression.
3x + 4 = 5 - 3 is an expression.
We have,
Amount at the account when open = $80
Amount withdrawn = $35
Amount deposited = $115
The amount after the transaction.
= Amount in account - Amount withdrawn + Amount deposited
= 80 - 35 + 115
= $160
Thus,
The account balance after the transaction is $160.
Learn more about expressions here:
https://brainly.com/question/3118662
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In Joey's neighborhood the ratio of families with dogs to families with cats is 5 to 2. There are 15 more families with dogs than families with cats. How many families have cats, and how many families have dogs?
Answers
Answer:
10 families have cats
25 families have dogs
Step-by-step explanation:
The difference of ratio units is 5-2 = 3. The difference in pet counts is 15, so we can see that each ratio unit stands for 15/3 = 5 pets. Then ...
dogs : cats = 5 : 2 = (5·5) : (2·5) = 25 : 10
There are 10 families with cats and 25 families with dogs.
Answer:
B D and E.
Step-by-step explanation:
2. At a restaurant, Mike and his three friends decided to divide the bill evenly. If each person paid $13.25
then what was the total bill?
Variable:
Equation:
Answer:
Answers
Step-by-step explanation:
39.75 is your answer for this question
Variable = 13.25
Equation = 13.25+13.25+13.25
Answer = 39.75
PLZ PLZ PLZ BRAINLIEST AND 20 POINTSJack and Jillian sell apples at a produce stand. Jillian earns $2 for each bag of apples she sells. At the end of the week, Jack has earned $8 less than Jillian. The following expression shows Jack's earnings:
2x − 8
In the expression, what does the first term represent?
Jack's earnings at the end of the week
The number of bags of apples Jillian sold
Jillian's earnings at the end of the week
The number of bags of apples Jack sold
Answers
Answer:
.
Step-by-step explanation:
.
We are given that Jack and Jillian sell apples at a produce stand .
We are given that an expression which shows Jack's earning=2x-8
We have to find that first term what represent in the given expression
Jillian earns for each bag of apples she sells=$2
Let Jillian sold number of bags of apples =x
Then ,Jillian earn total at the end of the week =
Jack has earned $ 8 less than Jillian earn
Therefore, total earning of jack=
In the given expression the first term 2x represent the earning of Jillian.
What are two consecutive integers that their product, minus 147, is equal to -75?
Answers
Answer:
8 and 9 or -8 and -9Step-by-step explanation:
x - first integer
x+1 - the next consecutive integer
x(x+1) - their product
x(x + 1) - 147 = -75
x² + x - 72 = 0
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-1\pm\sqrt{1-4(-72)}}{2}=\dfrac{-1\pm\sqrt{289}}{2}\\\\\\x_1=\dfrac{-1+17}2=8\,,\qquad x_2\dfrac{-1-17}2=-9\\\\x_1+1=9\,,\qquad\qquad\qquad x_2+1=-8[/tex]
can you help me with sas and sss congruent criteria please?
Answers
What is the perimeter of the
figure below?
2 in
9 in
2 in
11 in
Answers
Which expression is a perfect cube?
Answers
Can you guys help me please
Answers
Answer:
No it's not a function
Step-by-step explanation:
Every point line up evenly when it's vertical. just take your pencil and put it on the circle vertically and you will see that the points will line up
So it's not. function
pls mark brainiest because i didn't waste your time lol
Answer:
no
Step-by-step explanation:
the answer is no because each value in the domain is associated with exactly one point in the codomain, but a line passing though the circle generally intersects the circle at two points
f(x) = 3x + 1. Solve for x if f(x) = 19
Answers
3x+1=19
Start by subtracting 1 from each side to start isolating the x.
3x+1=19
-1 -1
————-
3x=18
Next, divide both sides by 3 to completely isolate the x.
3x=18
—- ——
3 3
x=6
Therefore, x for f(x)= 19 is 6
You can check by inserting into the equation 3(6)+1=18+1=19.
Hope this helps!!
Answer:
Step-by-step explanation:
f(x) = 3x + 1
First, we substitute 19 for x :
f(x) = 3(19) + 1
Next we re write the problem and solve for 3 times 19 :
f(x) = 57 + 1
So, the answer should be :
f(x) = 58
The speed of an object can be found by taking the distance it travels and dividing it by the time it takes to travel that distance. An object travels 100 feet in 2.5 seconds. Let the speed, , be measured in feet per second.
Write an equation to represent the relationship between the three quantities (speed, distance, and time).
Answers
speed = [tex]\frac{distance}{time}[/tex]
speed = [tex]\frac{100}{2.5}[/tex]
speed = 40 feet per second
In 1980 the social security tax was 5.83% up to a maximum of 25,900 if Nina earned $34,200 in 1989,how much did she pay in social security taxes?
Answers
Answer:
1882
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What is the domain and range please?
Answers
Answer:
Both infinate.
Step-by-step explanation:
what does 28-8 represent?
Answers
Step-by-step explanation:
subtraction if that wut u askim
what’s the value of x?
Answers
Answer:
X=85
Step-by-step explanation:
the sum of the angels in a triangle adds to 180 so do
180-43-52=85
Step-by-step explanation:
Answer is 85,because x+52+43=180
John is planning a trip that he needs to rent a car. The rental car company charges $50 per day plus $0.25 per mile. How many miles will John travel if his bill is $125.
Answers
Answer:
300 mile
Step-by-step explanation:
($125–$50)÷$0.25
=$75÷$0.25
=300 miles
I WILL GIVE BRAINLIEST Identify the coefficients in the following expression.
3x – 5y – z + 13
A. 3, -5, -1
B. 3, -5
C. 3, 5, 13
D. 3, 5, 1, 14
SHOW YOUR WORK PLZSSSSSSS
Answers
Step-by-step explanation:
the coefficients are the whole numbers accompanied by the variable. would be: 3, 5, 1, 13
When the equation 16/x = 4 is simplified, the value of x is??
Answers
Answer: x=4
Step-by-step explanation:
multiply each side by the denominator to cancel out the fraction so the new equation is 16=4x then divide by 4 to eliminate the x and 16 divided by 4 is 4 which is the anwser.
Rewrite the number in STANDARD NOTATION
Answers
The one with 5 zeros
Tommy Thomas’s tankard holds 480ml when it is one quarter empty. How much does it hold when it is one quarter full?
Answers
Answer:
Tommy Thomas's tankard holds 160ml when it is one-quarter full.
Step-by-step explanation:
When Tommy's tankard holds 480ml when it's one-quarter empty. There are three other quarters in the tankard. So, you would divide 480 by 3 to see how much is in each of the other 3 quarters. The answer comes down to 160ml per quarter, which equals one-quarter full.