Answer:
D
Step-by-step explanation:
To find the standard function, open the bracket
f(x) = (x-2)^2 + 6
(x-2)^2 becomes
x(x-2) -2(x-2)
= x^2 -2x -2x + 4
= x^2 -4x + 4
Now add 6 and it becomes x^2 -4x + 4 + 6
= x^2 -4x + 10
6. Suppose you bought supplies for a party. Three rolls of streamers and 15 balloons
cost $30. Later, you bought 2 rolls of streamers and 4 balloons for $11. How much did
each roll of streamers cost? How much did each balloon cost?
Answer:
Streamers are $2.50 each
Balloons are $1.50 each
Step-by-step explanation:
Make a system of equations
3s + 15b = 30
2s + 4b = 11
Solve by elimination: multiply the top equation by 2 and the bottom equation by -3.
6s + 30b = 60
-6s -12b = -33
18b = 27
b = 1.5
Plug in 1.5 as b to find s
3s + 15(1.5) = 30
3s +22.5 = 30
3s = 7.5
s = 2.5
The streamers are $2.50 and the balloons are $1.50
0.3y-0.3=0.4-0.4y
A=7
B=-1
C=-7
D=1
Answer: The answer is D: 1 (Vote me brainliest)
Answer:
y=1
Step-by-step explanation:
0.3y-0.3=0.4-0.4y
+0.4y
0.7y-0.3=0.4
+0.3
0.7y=0.7
-----
0.7
y=1
Which of the following linear equations corresponds to the table above?
The linear equation of the corresponding table is y = 4x+3 which is correct option(D).
What is the slope of a linear function?The slope of a linear function is defined as the angle of the line. It is denoted by m.
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a linear function —Point 1 and Point 2. Point 1 has coordinates (x₁, y₁) and Point 2 has coordinates (x₂, y₂)
We need two of those points to come up with the equation of the corresponding line.
Solution in y-intercept form y = mx+b
We can calculate the slope of the line using any 2 of the given points: I pick (0,3) and (3,15).
The formula for determining the slope of the line through 2 points (x₁,y₁) and (x₂,y₂) as m=(y₂-y₁)/(x₂-x₁)
By plugging in the corresponding values,
m = (15-3)/(3-0) = 12/3 = 4
Since the value of y when x is zero, i.e. the point (0,3) of the table, then the value of b is 3.
Now, Substitute the values in y = mx+b,
y = 4x+3
Hence, the linear equation of the corresponding table is y = 4x+3.
Learn more about linear function here:
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What effect will 4 have on the graph of y = sin(x)?
Answer:
The effect of 4 on the graph of y = sin(x) + 4 is that it shifts the graph by 4 units up.
The effect of 4 on the graph of y = sin(4x) is that its period would be 1/4th of 2π, i.e it completes one oscillation every π/2 units.
Step-by-step explanation:
The graph of y = sin(x) is a wave that keeps oscillating between -1 and 1, and repeats its shape every 2π units. The maximum value of the graph is 1 unit with a range of [-1, 1]
The graph of y = sin(x) is referred to as a periodic function because it repeats itself infinitely.
The effect of 4 on the graph of y = sin(x) + 4 is that it shifts the graph by 4 units up.
The effect of 4 on the graph of y = sin(4x) is that its period would be 1/4th of 2π, i.e it completes one oscillation every π/2 units.
Use FOIL and the distributive property to derive (a-b)^3
Answer:
(a-b)^3 = [tex]\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3[/tex]
Step-by-step explanation:
(a-b)^3 = (a-b)(a-b)(a-b)
According to the perfect cube formula (a-b)^3 = [tex]\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3[/tex]
And there you have it! The perfect cube formula already solved your equation!
Finn's pool leaked a total of 3.5 liters in 4 days. What rational number represents the average change in water volume each day?
Answer:
The rational number representing the average change in the volume of water each day is:
[tex]\frac{0.875 liters}{1 day}[/tex]
Step-by-step explanation:
Rational numbers are those that can be represented as the quotient of two integers. That is, rational numbers can be represented by a fraction [tex]\frac{a}{b}[/tex], where a is the numerator and b is the denominator that must be other than zero. To express the set of these numbers, mathematicians use a capital Q.
In this case we know that Finn's pool leaked a total 3.5 L in 4 days, so the rate can be written as:
[tex]\frac{3.5 liters}{4 days}[/tex]
Now you must make this division or quotient, where the denominator will be 1 because you must know the number of liters drained per day:
[tex]\frac{3.5 liters}{4 days}=\frac{0.875 liters}{1 day}[/tex]
So the rational number representing the average change in the volume of water each day is:
[tex]\frac{0.875 liters}{1 day}[/tex]
HELP ASAP!!1 Write the phrase as a rate in simplest form. 320 miles on 34 gallons a. 160miles/ 17 gallons b. 160miles/ 34 gallons c. 320gallons/ 34 miles d. 320miles/ 34 gallons e. 160gallons/17 gallons
Answer: c( 320 gallons/34 miles or d( 320 miles/34 gallons
hope it helps..
in a Gallup youth survey done in 2000, 501 randomly selected American teenagers were asked how well they get along with their parents. A survey result was that of 270 teenagers said they get along "very well" with their parents. Use this to estimate the proportion who would say they got along "very well" with their parents, including a margin of error.
The margin of error would be 1 / √n, where n is the number of students asked.
Margin of error = 1/√501 = 0.0446
Multiply by 100 to change to a percent:
0.446 x 100 = 4.46%
Rounding may be off slighly, so it looks like b would be the correct answer.
WHOEVER IS THE FIRST ANSWER I'LL MARK THE BRAINIEST ANSWER!!!
Find the arc length of the partial circle.
Either enter an exact answer in terms of
π
πpi or use
3.14
3.143, point, 14 for
π
πpi and enter your answer as a decimal.
Answer:
4π
Step-by-step explanation:
find the circumference first
2π r
2π 8=16π
then find the arc length
16π * 1/4
4π
What is the solution to log (10x-1)= logs(9x+ 7)?
6
O X=
6
19
O X=
19
X= 7
X= 8
Answer:
[tex]x=8[/tex]
Step-by-step explanation:
[tex]\log _{10}\left(10x-1\right)=\log _{10}\left(9x+7\right)\\\mathrm{Apply\:log\:rule:\:\:If}\:\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\:\mathrm{then}\:f\left(x\right)=g\left(x\right)\\10x-1=9x+7\\\mathrm{Add\:}1\mathrm{\:to\:both\:sides}\\10x-1+1=9x+7+1\\\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\10x-9x=9x+8-9x\\\mathrm{Simplify}\\x=8\\[/tex]
The solution of the equation ㏒₅(10x - 1) = ㏒₅(9x + 7) is x = 8.
What are Logarithms?A logarithm is simply the opposite function of the exponentiation.
It is the exponent to which a number or value is raised to get some other number.
That is, if c = aˣ, then we can write it as x =logₐ c.
Given that,
㏒₅(10x - 1) = ㏒₅(9x + 7)
Let the value of both be n.
So, ㏒₅(10x - 1) = n and ㏒₅(9x + 7) = n
By the definition of logarithms,
10x - 1 = 5ⁿ and 9x + 7 = 5ⁿ
So,
10x - 1 = 9x + 7
10x - 9x = 7 + 1
x = 8
Hence the value of x is 8.
Learn more about Logarithms here :
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Find M a
A.
49
B.
35
C.
95
D.
275
Answer:
85
Step-by-step explanation:
The sum of the angles of a triangle are 180 degrees
A + B+ C = 180
A +72+ 23 = 180
Combine like terms
A + 95 = 180
Subtract 95 from each side
A +95-95 = 180-95
A =85
Find the surface area.
please help me i really need help i dont understand
write an inequality for the folowing statement :
The sum of triple a number x and eight is atleast a number y.
Inequality : ___________
Cupcakes cost $2.00 each. Ballons cost $1.25 each. Her bill was no less than $25.00.Write an inequality that could be used to find n, the greatest possible number of cupcakes, and m, the greatest possible number of ballons , she bought. Inequality:____________
Answer:
Step-by-step explanation:
First problem: 3x + 8 ≥ y
Second problem: Represent the number of cupcakes with n and that of balloons by m. Then ($2/cupcake)(n) + ($1.25/balloon)(m) ≥ $25
< Salir
Topic 14 Online Assessment
Esperado 06/10/20 11:59 pm
00:00
Kurt and Drew walk the same distance to school. Their start and end times are different.
Who got to school faster, and by how many minutes?
Kurt
Answer:
Option C.
Step-by-step explanation:
Kurt started for the school at 07:35 and ends at 08:25.
Time taken by Kurt to reach the school
= 08:25 - 07:35
= (07 hours + 85 minutes) - (07 hours + 35 minutes) [Since 08 hours + 25 minutes = 07 hours + (60 + 25)minutes]
= 85 minutes - 35 minutes
= 50 minutes
Time taken by Drew to reach the school
= 08:30 - 07:55
= (07 hours + 90 minutes) - (07 hours + 55 minutes) [Since 08 hours + 30 minutes = 07 hours + (60 + 30)minutes]
= 90 minutes - 55 minutes
= 35 minutes
Difference in the time taken by Kurt and Drew = 50 - 35 = 15 minutes.
Therefore, Drew is 15 minutes faster than Kurt.
Option C. is the answer.
The largest of the great pyramids in Egypt was built with a square base having edges measured 754 feet and a height of 418 feet. To the nearest cubic foot, what was the volume of the original structure
Answer:
[tex]79213229.3 ft^3[/tex]
Step-by-step explanation:
The great pyramids pf Egypt are square based pyramids.
The volume of a square based pyramid is:
[tex]V = a^2h/3[/tex]
where a = length of square base
h = height of pyramid
The pyramid has a square base measured as 754 feet and a height of 418 feet. Its volume is:
[tex]V = 754^2 * 418 / 3\\\\V = 79213229.3 ft^3[/tex]
The ordered pair (a, b) gives the location of point P on the coordinate plane. The value of aaa is 0, but b is not zero. Where could point P be located on the coordinate plane?
Answer:
On the y-axis line
Step-by-step explanation:
Given the location (a,b) of the point P on the coordinated plane.
If a=0
Then the location of P on the x-axis is at x=0
Since b is not equal to zero, b could be positive or negative.
Therefore, the point P could be located on the positive y-axis or the negative y-axis,
It must be exactly on the line.
What is the value of x in the equation 4(2x + 14) = 0? a 9 b 7 c −7 d −9
Answer:
x = -7
Step-by-step explanation:
4(2x + 14) = 0
Divide each side by 4
2x+14 = 0
Subtract 14 from each side
2x+14-14 = 0-14
2x= -14
Divide each side by 2
2x/2 = -14/2
x = -7
Answer:
C, -7
Step-by-step explanation:
Use distributive property to get: 8x +56 = 0
Isolate x to get: 8x = -56
Then divide each side by 8: x= -7
The answer is C
4y+3x =25 is the tangent to the circle x^2+ y^2 = 25 at the point P(3,4). The equation of the radius of the circle that passes through P is
PLEASE SHOW SOLUTION!
Answer:
4x - 3y = 0
Step-by-step explanation:
The angle between the radius and the tangent at P is right
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 4y + 3x = 25 into this form
Subtract 3x from both sides
4y = - 3x + 25 ( divide all terms by 4 )
y = - [tex]\frac{3}{4}[/tex] x + [tex]\frac{25}{4}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{3}{4}[/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{3}{4} }[/tex] = [tex]\frac{4}{3}[/tex] , thus
y = [tex]\frac{4}{3}[/tex] x + c ← is the partial equation
To find c substitute P(3, 4) into the partial equation
4 = 4 + c ⇒ c = 4 - 4 = 0
y = [tex]\frac{4}{3}[/tex] x ← equation of radius in slope- intercept form
Multiply through by 3
3y = 4x ( subtract 3y from both sides )
4x - 3y = 0 ← equation of radius in standard form
Which of the following is not a case of direct variation?a Number of sheets of some kind and increased when their total weight its inceased. b More quantity of petrol is required to travel more distance with a fixed speed. c More fees would be collected if number of students increased in a class. d Time taken will be less if number of workors are increased to complete the same work.
Answer:
Step-by-step explanation:
If two variables, x and y have a direct variation, it means that an increase in x would lead to a corresponding increase in y. A decrease on x would lead to a corresponding decrease in y.
Therefore, we would compare the scenarios to determine which is not a direct variation. The correct option is
d) Time taken will be less if number of workers are increased to complete the same work.
The rest are direct variation scenarios
Enzo drew Triangle K L N. In Enzo's triangle, Measure of angle K is represented as x degrees. The measure of Angle L is 5 times Measure of angle K. The measure of Angle N is 16 degrees less than 8 times Measure of angle K. Which statements must be true about the angle measures of Enzo's triangle? Check all that apply. Measure of angle K = x degrees Measure of angle L = (5 x) degrees Measure of angle N = (16 minus 8 x) degrees Measure of angle K + measure of angle L = measure of angle N Measure of angle K + measure of angle L + measure of angle N = 180 degrees
Answer: (1) Measure of angle K = x degrees
(12) Measure of angle L = (5x) degrees
(3) Measure of angle k + Measure of angle L + Measure of angle N = 180 degrees
Step-by-step explanation: First of all, what we have is a triangle, and one of the properties of a triangle is all three angles add up to 180 degrees. This simply means that the addition of angles K and L and N would be equal to 180 degrees.
The question states that angle K is represented as x degrees, and angle L is 5 times the measure of angle K. Therefore, if K is x degrees, then L is 5 times x, which becomes 5x degrees. Also, angle N is given as 16 degrees less than 8 times the measure of angle K (x degrees). Eight times the measure of angle K is given as 8x. Sixteen degrees less than 8x would now become, 8x - 16 (degrees). Therefore, the angles have been derived as;
Angle K = x degrees
Angle L = 5x degrees
Angle N = 8x - 16 degrees
Having known that one of the properties of any triangle is all angles adding up to 180 degrees, we can now derive the following equation;
x + 5x + 8x - 16 = 180
14 x - 16 = 180
Add 16 to both sides of the equation
14x = 196
Divide both sides of the equation by 14
x = 14
Therefore, angle K = 14 degrees (x), angle L = 70 degrees (5x) and angle N = 96 degrees (8x - 16)
*14 + 70 + 96 = 180*
Answer:
145
Step-by-step explanation:
Which of the following is an x-intercept of the function, f() = x3-5x2 - 8x +48
Answer:
Step-by-step explanation:
x^3 - 5x2 - 8x + 48 = 0
You haven't supplied a list . To confirm which value is the correct one substitute the values for x and see if the result is 0.
Since the last term is 48 you could try some of the factors of 48 : 1, -1, 2, -2, 3 -3 and so on.
HELP ANYONE PLEASE RIGHT ANSER ?!
Answer:
B.
Step-by-step explanation:
They all are alternating interior angles so they'll be congruent.
Answer:
B. Alternating interior angles are congruent
Step-by-step explanation:
The angles that are in the statements are all interior angles. When compared to each other, they lie on opposite sides of the transversal.
The diagram below is a scale drawing of a building and the parking lot outside of it. A scale factor of 1cm= 6ft was used to make the drawing
What is the area of the parking lot
Plz help this makes no sense to me
Answer:
8,181 ft^2
Step-by-step explanation:
Area of the parking lot = Area of the whole structure - Area of the building
The building is a square of 12cm by 12cm
which is 72ft by 72ft since 1 cm is 6 ft
its area is thus 72 * 72 = 5,184 ft^2
The structure measures 16.5 cm by 22.5 cm
Multiplying the sides by 6, we have 99 ft by 135 ft
So its area is 99 * 135 = 13,365 ft^2
The area of the parking lot = 13,365 - 5,184 =
8,181 ft^2
at an ice cream parlor a sundae is $1.25 more than the cost of a cone. if three cones and two sundaes cost $8.00. find the cost of a sundae and the cost of a cone.
I need help please!! Identify the solution for the system of equations graphed here.
A. (1,1)
B. (-1,1)
C. (1,-1)
D. (-1,-1)
Answer:
C. (1,-1)
Step-by-step explanation:
Lines are intersecting each other at point (1, - 1).
Hence, the system of equations graphed here would be (1, - 1)
PLEEEASE HELP!!! EXPLAIN ALL PARTS!!!
A candle burns down at the rate of 0.5 inches per hour. The original height of the candle was 8 inches.
Part A: Write a list of 6 ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) from the first hour after it started burning. For example, the point (0, 8) would represent a height of 8 inches after 0 hours. Explain how you obtained the ordered pairs. (5 points)
Part B: Is this relation a function? Justify your answer using the list of ordered pairs you created in Part A. (2 points)
Part C: If the rate at which the candle burned was 0.4 inches per hour instead of 0.5 inches per hour, would the relation be a function? Explain your answer using input and output values. (3 points)
Answer:
see below
Step-by-step explanation:
A: Some points could be (1, 7.5), (2, 7), (3, 6.5), (4, 6), (5, 5.5) and (6, 5) because the y-coordinates all represent the heights of the candle after the x hours.
B: This is a function because no input has multiple outputs.
C: It would still be a function because no input would have multiple outputs.
Answer:
Have a great day!!
Step-by-step explanation:
Part A: my rate of change was first y= - 5x + 8 the reason i put a negative sign beforehand is that when the candle melts its height it's decreasing
(0,8),(1,7.5)(2,7)(3,6.5)(4,6)(5, 5.5)
Part B: This is a function because there is one different output for each different input
Part C: yes, it still would be a function because the numbers haven't changed and are exactly the same and it still has one input for each output.
(0,8), (1,75), (2,7), (3,6.5), (4,6), (5,5.5)
write 47 and 1000 as a decimal
Answer:
47=4.7
1000= 100.0
In right triangle ABC, ∠C is a right angle and sin A = sin B. What is m∠A?
Answer:
If sinA = sinB, that means that ∠A = ∠B. Because this is a right triangle, ∠A = 45°.
The line AB had midpoint (2, 5).
A has coordinates (1, 2).
Find the coordinates of B.
Answer:
The line AB, with A(Ax, Ay), B(Bx, By) and midpoint M(Mx, My) satisfying:
Ax + Bx = 2Mx
Ay + By = 2My
=>
2 + Bx = 2*1
5 + By = 2*2
=> Bx = 0
=> By = -1
=> B(0, -1)
Hope this helps!
:)
Answer:
B(3, 8 )
Step-by-step explanation:
Using the midpoint formula
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then midpoint is
[ [tex]\frac{1}{2}[/tex](x₁ + x₂ ), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]
let the coordinates of B = (x, y ), then
[tex]\frac{1}{2}[/tex](1 + x) = 2 ( multiply both sides by 2 )
1 + x = 4 ( subtract 1 from both sides )
x = 3
and
[tex]\frac{1}{2}[/tex] (2 + y) = 5 ( multiply both sides by 2 )
2 + y = 10 ( subtract 2 from both sides )
y = 8
Thus
coordinates of B = (3, 8 )
1
The table shows the cost y (in dollars) of x cold drinks.
Drinks, x 0 2 4
6
0
Cost y
6
3
9
Graph the data
Answer: Attached graph in the explanation.
Step-by-step explanation:
Hi, to answer this question we have to graph points in a Cartesian coordinate graph.
The horizontal axis is called the x-axis, and the vertical axis is the y-axis.
To graph a point, first we have to locate its position on the x-axis, and then find its location on the y-axis, and finally plot where these meet.
For example, to plot the point (2, 3), we have to find the positive 2 on the x-axis and the positive 3 on the y-axis.
Finally when we have plotted all the points, we simply link all the points to form a line.
