Answer: B. Function g is the result of f being translated left 2 units and up 4 units. and C. The graph of function f opens upward.
Step-by-step explanation:
It is translated 2 units to the left and 4 units up because in the function of a(x-h)^2k, h represents the function going left of right and k representing the function going up and down. a represents it stretching if it is greater than 1 and compressing if less than 1 and if it is negative it reflects over the x axis however here nothing changed for the a so it did not stretch nor compress nor reflect over the x axis
What is the slope 7y-2x=-16
what is the slope?
what is the y-intercept?
Answer:
slope = 2/7
y-intercept = -16/7
Step-by-step explanation:
We rewrite this equation in slope-intercept form as follows:
[tex] - 2x + 7y = - 16[/tex]
[tex]7y = 2x - 16[/tex]
[tex]y = \frac{2}{7} x - \frac{16}{7} [/tex]
The slope is 2/7, and the y-intercept is -16/7.
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Tom and Sam are running a 40 yard race. The graphs below show both runner’s distance, d, during the time, t, of the race. The horizontal axis represents time (in seconds) and the vertical axis represents the runner’s distance from the starting line.
Use the graph to identify the winner of the race. Explain how you came to your conclusion.
On the graph can see that Tom completes the race in less than 5 hours and Sam in more than 5 hours, so Tom wins.
Who wins the race?
Tom and sam are running a 40-yard race, so, the first one in run 40 yards wins.
Here we have two graphs, both are lines that relate distance and time. With them we can see that:
Tom reaches a distance of 40 miles in a little bit less than 5 hours.Sam reaches 40 miles in a little bit more than 5 hours.Then the one that takes less time to complete the race is Tom, and thus, Tom wins the race.
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the sum of the perimeters of two equilateral triangles is $45$ inches, and the area of the larger one is $16$ times the area of the smaller one. what is the area, in square inches, of the larger triangle? express your answer in the simplest radical form.
The area, in square inches, of the larger triangle is 12.
What is a triangle?A triangle is a type of polygon having three sides and three vertices. In Euclidean geometry, if no three points are collinear, then we determine a unique triangle and a unique plane (that is, two-dimensional Euclidean space). That is, there is only one plane containing this triangle, and all triangles are contained in one plane. If all geometries were just Euclidean planes, there would be only one plane and all triangles would be in it.But this is not the case in high dimensional Euclidean space. This article is about triangles in Euclidean geometry, specifically the Euclidean plane, unless otherwise stated.To learn more about triangle from the given link :
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when a number is added 4 the answer is the same as 19 minus 2. what is the number?
Answer:
.... the number is (13). 13+4=17 , and 19-2=17
Step-by-step explanation:
Write the equation of a circle with its center at the origin and passes through the
point (5,0)
AND ALSO!!
Write the equation of a circle of with the center (2,3) and containing the point (3,2)
please and thank you ! :)
The equation of a circle with its center at the origin and passes through the point (5,0): x2+y2=25
the equation of a circle of with the center (2,3) and containing the point (3,2): x2+y2=2
What is Origin ?Origin is referred to as the first point or the starting point from which we begin our calculations or measurements in mathematics, particularly in the subject of coordinate geometry. The 0 on a ruler is the point at which we begin taking measurements; as a result, it is referred regarded as the scale's origin.
(x-h)^2+(y-k)^2=r2
is the equation for a circle with center (h,k) and radius (r).
This yields the more well-known equation
x2+y2=r2
for a circle centered at the origin.
Since we are aware that the circle's center is at its origin, i.e.
This fact, together with the circle's intersection point (5,0), can be used to determine the radius. The distance formula is used for this.
r=√(x2−x1)^2+(y2−y1)^2
In light of (0,0) and (5,0):
r=√(5−0)^2+(0−0)^2
=√25+0
√25=5
⇒ r=5
Therefore, x^2+y^2=(5)^2
x2+y2=25 is the equation for the circle.
(x-h)^2+(y-k)^2=r2 is the equation for a circle with center (h,k) and radius (r).
This yields the more well-known equation x2+y2=r2 for a circle centered at the (2,3).
Since we are aware that the circle's center is at (2,3), i.e.
This fact, together with the circle's intersection point (3,2), can be used to determine the radius. The distance formula is used for this.
r=√(x^2−x1)^2+(y2−y1)^2
In light of (2,3) and (3,2):
r=√(3−2)^2+(2−3)^2
r = √(1)^2+(-1)^2
= √1+1
=√2
⇒ r=√2
Therefore, x2+y2=(√2)^2
x2+y2=2 is the equation for the circle.
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If three consecutive term of an AP are x+4,2x+8 and 12. Find the value of x
Since the series is an Arithmetic progression, the difference between the consecutive terms is constant,
Therefore,
(2x+8) - (x+4) = 12 - (2x+8)
⇒ 2x + 8 - x - 4 = 12 - 2x - 8
⇒x + 4 = 4 - 2x
⇒ 3x = 0
⇒ x = 0
The value of x is 0,
So, the Arithmetic Progression is 4, 8, 12.......
What is an Arithmetic Progression?A numerical series in which the difference between the succeeding terms is constant is known as an arithmetic progression (AP). The number sequence 5, 7, 9, 11, 13, 15... is an example of an arithmetic progression with a common difference of 2.The term "finite arithmetic progression" or "arithmetic progression" refers to a finite segment of an arithmetic progression. An arithmetic series is the total of a finite arithmetic progression.There is a chance to come up with a formula for the nth term in an arithmetic progression. As an illustration, the number sequence 2, 6, 10, 14... is an example of an arithmetic progression (AP) since it follows a pattern in which each number is created by adding 4 to its preceding term. The nth word in this progression equals 4n-2.To learn more about Arithmetic Progression, refer to:
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pushing a car 15 m using a force of 500 N
When pushing a car using a force of 500 N. The work done is 7500 Joule.
What is force?Force is a power that results in the motion of an object. It is calculated by newton. Distance is the measurement of two entities from one side to another side. It is calculated in meters and kilometers.
By multiplying the total force used, and the total distance traveled, the total work done may be calculated.
Given, the force is 500 N
Distance is 15 m
Total work done = force × distance
500 × 15 N = 7500 Joule
Hence, 7500 Joule work is done.
Therefore, the total work done is 7500 Joule.
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The question is incomplete. Your most probably complete question is given below:
Pushing a car 15 m using a force of 500 N. How much work was done?
where would i plot 1.25 on a number line
Answer:
Quarter of a way through 1 and 2
Step-by-step explanation:
Quarter of a way through 1 and 2
please answer the question below .
The length of side EC of the △ECD is 12 meters if the length of AB of △ABC is 9 meters using the concept of similarity of triangles.
As per the question statement, we are given an image depicted as a lattice bridge where △ABC ∼ △ECD and the ratio of lengths of corresponding sides in △ABC and △ECD is 3:4
Length of AB is 9 meters and we are supposed to find the length of side EC of the △ECD.
As ratio of corresponding sides is 3:4 and △ABC ∼ △ECD (given)
AB : EC = 3 : 4
But AB = 9 meters (given)
9 /EC = 3/4
EC = 4*9/3
EC = 12 meters.
Hence, The length of side EC of the △ECD is 12 meters if the length of AB of △ABC is 9 meters using the concept of similarity of triangles.
Similar triangles: If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are items that feature more than two figures that are the same form but different sizes.
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Ella has a cake cut intoeighths. If each personeats 1/4 of the cake. HOWmany people can eatcake?
If each person eat one quarte (1/4) of the cake, this means that only 4 people can eat from one cake, as:
[tex]\begin{gathered} n\cdot\frac{1}{4}=1 \\ n=1\cdot\frac{4}{1} \\ n=4 \end{gathered}[/tex]Each person eats 2 pieces of 1/8 of the cake, as 2*1/8=2/8=1/4.
Answer: 4 people can eat cake.
It takes 120 minutes to drive home at 60kmh
how long it will take to drive home at 120kmh
Answer: 240 mins
Step-by-step explanation:
Given that
5
x
−
4
y
=
34
Find
y
when
x
=
−
3
Give your answer as an improper fraction in its simplest form.
Help me please i don’t know what to do
Quadratic applications include: Horizontal Motion Issues For a moving object, one uses the formula h = -16t2 + vt+s. The following is represented by the variables: h is a symbol for the object's height when it is moving.
How can one calculate h in a projectile motion?h = v 0 y 2 2 g This equation, which only depends on the vertical component of the initial velocity, specifies the maximum height of a projectile above its launch site.
If v is the starting speed, g is the gravitational acceleration, and H is the highest point that may be reached in meters, then is the initial speed's angle from the horizontal plane (radians or degrees). The equation H = v 0 2 s I n 2 2 g yields the projectile's greatest height
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If you had a single deck of cards (52 cards). What is the probability of pulling a king card from the deck?
Answer:
Hence for drawing a card from a deck, each outcome has probability 1/52. The probability of an event is the sum of the probabilities of the outcomes in the event, hence the probability of drawing a spade is 13/52 = 1/4, and the probability of drawing a king is 4/52 = 1/13.
Step-by-step explanation:
Scott purchases food for his dog in large bags and feeds the dog the same amount of dog food each
day. The amount of dog food left in the bag at the end of each day can be modeled by an arithmetic
sequence. On a particular day, Scott opened a new bag of dog food and fed his dog. By the end of the third day there were 115.5 cups of dog food remaining in the bag and at the end of the eighth day
there were 108 cups of dog food remaining in the bag.
a) Find the number of cups of dog food
i) fed to the dog per day. Show your work.
The number of cups of dog food fed to the dog per day is 1.5 cups.
What is the number of cups of dog food fed to the dog per day?Since the same quantity of dog food is fed to the dog per day, the decrease in the cups of dog food can be modelled with a linear equation. A linear equation is an equation that has one variable that is raised to the power of one.
Number of cups of dog food fed to the dog per day = (cups left after the 8th day - cups left after the 3rd day) / change in the number of days
(108 - 115.5) / (8 - 5)
4.5 / 3 = 1.5 cups
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If someone could please help me on the first three that would be great!
( please only answer if you know the answer! )
Substitution Property of Equality - (2) You replace one expression with another equivalent expression.
Segment Addition Postulate - (10) Parts of line segment combine to form longer segments.
Triangle Sum Theorem - (4)The measure of three interior angles in a triangle have a sum of 180 degrees.
Reflexive Property - (8) An expression is equal to itself
Angle Addition Postulate - (6)The measure of an angle formed by two adjacent angles is the sum of the measures of the two angles.
Symmetric Property - (9) You switch expressions from one side of the equals symbol to the other.
Angle Congruence Postulate - (1) If two angles are congruent their measures are equal.
Segment Congruence Postulate - (7)Two segments are congruent so they have the same length.
Definition of Right Angle - (5) An angle is a right angle so its measure is 90 degrees.
Transitive Property - (3) a = c because a = b and b = c.
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Discussion Topic
The equation y = kx represents a proportional relationship between x and y, where k is
the constant of proportionality. For a moving object, the equation d = st represents a
proportional relationship between distance (d) and speed (s) or between distance (a)
and time (1). Explain the different ways that you can define the constant of
proportionality for this equation. Then describe some other equations that represent
proportional relationships in the real world and explain why they're useful. Research on
the internet, if needed.
Proportional relationships in real world settings are given as follows:
Distance and time: d = st, velocity is the constant.Time and distance: one divided by the velocity is the constant.Velocity and distance: one divided by the time is the constant.What is a proportional relationship?A direct proportional relationship is modeled as follows:
y = kx.
In which:
y is the output variable.k is the constant of proportionality.x is the input variable.One example is the relation between distance, velocity and time, given as follows:
d = st.
In which the velocity is the constant.
This relationship can also be interpreted as proportional between distance and velocity, with time as constant.
Another format of this relationship is:
t = d/s
Which means that time and distance are proportional, which one divided by the velocity as the constant.
Velocity and distance can also be proportional, as follows:
s = d/t.
With one divided by the time as constant.
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The ratio of the number of tomato plants in Inessa’s garden
to the number of tomato plants in Ralph’s garden was 5 : 6. After 1
2
of the tomato plants from Inessa’s garden were replanted into Ralph’s
garden, Ralph’s garden had 850 tomato plants. How many tomato plants
did Ralph’s garden have in the first place?
So in the first place, the 5:6 ratio of 12 tomato plants would be 2 tomato plants left over making ralph's plant # 840 in the first place.
-5(4x-3y-1) distributive property remove all parentheses
Distribute -5 to all terms inside the parenthesis.
-5(4x - 3y - 1)
-5(4x) + -5(-3y) + -5(-1)
-20x + -5(-3y) + -5(-1)
-20x + 15y + -5(-1)
-20x + 15y + 5
F is a point on segment EG. If EF = 19, FG = x + 13, and EG = 6x + 14, what is EG?Simplify your answer and write it as a proper fraction, mixed number, or integer.
You have the segment EG and point F in it.
Point F separates the segment in two smaller ones EF and FG.
You can say that
EG= EF + FG
You have to replace the name of the segments with their values to get the equation:
[tex]6x+14=19+(x+13)[/tex]Now that you have a one unknown equation you can clear X
[tex]\begin{gathered} 6x=19+x+13-14 \\ 6x-x=\text{ 18} \\ 5x=18 \\ x=\frac{18}{5}=\text{ 3.6} \end{gathered}[/tex]The value of x is 3.6
Find the distance between the points(5, 7) and (5, -4) . Pelas Help
Answer: 11
Step-by-step explanation:
Use distance formula: [tex]\sqrt{(x_1 - x_2)^2 + (y_2 - y_1)^2\\}[/tex]
5 - 5 = 0
7 - - 4 = 7 + 4 = 11
[tex]\sqrt{11^2} = 11[/tex]
Find the standard deviation of this sample of times. ROUND YOUR ANSWER TO DECIMAL PLACES
The formula for calculating standard deviation of a sample is expressed as
Standard deviation = √Σ(x - mean)^2/(n - 1)
where
n = the number of samples = 5
Mean = (17 + 20 + 44 + 39 + 40)/5
Mean = 32
Σ(x - mean)^2 = (17 - 32)^2 + (20 - 32)^2 + (44 - 32)^2 + (39 - 32)^2 + (40 - 32)^2 = 626
n - 1 = 5 - 1 = 4
Standard deviation = √(626/4)
Standard deviation = 12.51
The width of a rectangle is 4 units less than the length. The area of the rectangle is 12 units. What is the width, in units, of the rectangle?
The width of a rectangle is 4 units less than the length. The width, in units, of the rectangle is 2 units.
Represent the length and width by L and W.
Then W = L - 4.
The area of the rectangle is 12 units
= Length x width
= L x W
= L(L - 4)
=L^2 - 4L = 12
L^2 -4L - 12 = 0
Now on solving this quadratic equation we get
L^2 -4L - 12 = 0
L^2 - 6L + 2L -12 = 0
L(L - 6 ) -2(L - 6) = 0
(L-6)(L-2) = 0
This factors easily into
(L - 2)(L - 6) = 0
so L must be 2,6.
When L = 2
The width of the rectangle is W = L - 4 = 2 - 4 = -2 units.
We ignore the negative values.
when L= 6
The width of the rectangle is W = L - 4 = 6 - 4 = 2 units.
The width of a rectangle is 4 units less than the length. The width, in units, of the rectangle is 2 units.
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6) Hamal has a part-time job bagging groceries after school.
The equation y = 10x + 50 shows the relationship between
his hours of work (x) and the amount of money in his bank
account (y). How much is Hamal earning per hour? Explain how
you know.
The number of hours Hamal works is represented as x.
Since we need to find the amount Hamal is earning per hour (or in an hour), we replace x as 1 (for 1 hour)
Now, we get the equation : y = 10 x 1 + 50.
Since y represents the amount of money he earns, we need to find y when x = 1, or the equation above.
-> y = 60.
Therefore, Hamal earns 60 (dollars?) per hour.
This is due tomorrow!! A creek is 3 feet deep. During a flood last month, it rose to 20 feet deep. The weather man said it rained 0.5 feet an hour. How many hours did it rain?
The number of hours of rain is 34.
The depth of the creek before the rain was 3 feet. There was a flood last month. The depth of the creek rose to 20 feet after the flood. The weather man said that it rained for 0.5 feet every hour.
The rise in the depth of the creek is the difference between the final and initial depths.
D = 20 - 3 = 17 feet
The number of hours for which it rained is the result of the division of the rise in the depth by the rate of rain.
N = 17/0.5
N = 34 hours
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For what values of x is x² + 2x = 24 true?
-6 and -4
-4 and 6
4 and -6
6 and 4
The most appropriate choice for Quadratic equation will be given by -
Third option is correct
What is Quadratic equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A two degree equation is known as Quadratic equation.
Here,
[tex]x^2 +2x=24\\x^2+2x-24=0\\x^2+6x-4x-24=0\\x(x+6)-4(x+6)=0\\(x+6)(x-4)=0\\[/tex]
[tex]x+ 6 = 0[/tex] or [tex]x - 4 = 0[/tex]
x = -6 or x = 4
Third option is correct
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Alang runs a farm stand that sells blueberries and grapes. Each pound of blueberries sells for $1 and each pound of grapes sells for $3.50. Alang sold 20 more pounds of grapes than pounds of blueberries and made $182.50 altogether. Write a system of equations that could be used to determine the number of pounds of blueberries sold and the number of pounds of grapes sold. Define the variables that you use to write the system.
By solving a system of equations we can see that Alang sold 25 pounds of blueberries and 45 pounds of grapes.
How to write and solve the system of equations?
Here we need to define the variables:
g = pounds of grapes bought.
b = pounds of blueberries bought.
We know that:
"Alang sold 20 more pounds of grapes than pounds of blueberries and made $182.50 altogether."
then we can write the system of equations:
g = b + 20
g*3.5 + b*1 = 182.50
To solve this, we can replace the first equation into the second one, so we get:
(b + 20)*3.5 + b*1 = 182.50
b*4.5 + 70 = 182.50
b*4.5 = 182.50 - 70
b*4.5 = 112.50
b = 112.50/4.5 = 25
And we know that:
g = b + 20 = 25 + 20 = 45
So he sold 25 pounds of blueberries and 45 pounds of grapes.
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did you hear the story about the piece of butter? 3.2 puzzle
Answer:Never mind I don't want to spread it around
Step-by-step explanation:
lol
Determine the instantaneous rate of change without using derivatives please
we have the function
[tex]f(x)=\frac{x}{x-2}[/tex]To find out the instantaneous rate of change without using derivatives, we need two points
For x=0
[tex]f(0)=\frac{0}{0-2}=0[/tex]The first point is (0,0)
For x=-1
[tex]f(-1)=\frac{-1}{-1-2}=\frac{1}{3}[/tex]The second point is (-1,1/3)
Find out the slope
[tex]\begin{gathered} m=\frac{\frac{1}{3}-0}{-1-0} \\ \\ m=-\frac{1}{3} \end{gathered}[/tex]therefore
The instantaneous rate of change is -0.33Verify the answer with the exact answer (with derivative)
Please help identify the equation
And the answer
Two more than 4 times a number is -18
Answer:
x = -5
Step-by-step explanation:
4x + 2 = -18
or
2 + 4x = -18
(Subtract 2 from both sides) -20 = 4x
(Then you divide by 4) so you get... x = -5
Answer:
2 + 4x = -18
Step-by-step explanation:
Two more than: +2
4 times a number: 4x
is -18: = -18
