What is the average rate of change of f(x) = −2x + 1 from x = −5 to x = 1?
Answer:-2
Step-by-step explanation:
Maxine bought items costing $5.25, $18.99, $2.99, and $17.50. She used a coupon worth $5.50. If Maxine had $60.00 before she went into the store, how much did she have when she left?
The price of a calculator has decreased from $200 to $150. What is the percent of decrease?
1.A system of two linear equations is graphed on a coordinate plane. If the system of equations has infinitely many solutions, which statement must be true?
A.On the graph, there is exactly one point (x,y) that satisfies both equations.
B.On the graph, any point (x,y) that satisfies one of the equations cannot satisfy the other equation.
C.On the graph, there are no points (x,y) that satisfy both equations.
D.On the graph, any point (x,y) that satisfies one of the equations must also satisfy the other equation.
2.Mark drank a total of 10 glasses of water and iced tea yesterday.
Each glass of water contained 8 ounces. Each glass of iced tea contained 12 ounces.
All together, he drank 96 ounces. The system of equations below models this situation.
x + y = 10
8 x + 12 y = 96
How many glasses of water did Mark drink yesterday?
A.3 glasses
B.4 glasses
C.5 glasses
D.6 glasses
Mark drank 6 classes of water. :) im probably late on answering this, sorry
peter walks 40 meters in 1 minute what is his walking rate in meters per second
there is a 20% markup on a tv if the tv is $450 before the markup what is the cost after the markup
write an equation of the line given its slope,m=3,and it's y-intercept b=10
Rachel and Sabrina belong to different local gyms. Rachel pays $35 per month and a one-time registration fee of $15. Sabrina pays only $25 a month with a one-time registration fee of $75. Write an equation to represent Rachel's total cost, T, as a function of the number of months, m.
The radius of a circle can be found by dividing the circumference of the circle by 6.28. What is the radius of a circle that has a circumference of 17.27 feet?
Answer:
23.55 feet
Step-by-step explanation:
You are standing above the point (5,4)(5,4) on the surface z=15−(2x2+3y2)z=15−(2x2+3y2). (a) in which direction should you walk to descend fastest? (give your answer as a unit 2-vector.)
To descend fastest from the point (5,4) on the surface z=15-(2x^2+3y^2), you should walk in the direction of the negative gradient vector, normalized to be a unit vector, which is approximately <0.640, 0.768>.
Explanation:To determine the direction in which you should walk to descend fastest from the point (5,4) on the surface z=15-(2x^2+3y^2), we can find the gradient of the surface at that point. The gradient vector will point in the direction of the steepest ascent, so the direction of the steepest descent is the opposite direction of the gradient vector.
First, calculate the partial derivatives of z with respect to x and y:
∂z/∂x = -4x
∂z/∂y = -6y
Next, evaluate these derivatives at the point (5,4):
∂z/∂x(5,4) = -4(5) = -20
∂z/∂y(5,4) = -6(4) = -24
The gradient vector at (5,4) is <-20, -24>. To get the direction of steepest descent, we take the negative of the gradient vector, which is <20, 24>.
Finally, normalize this vector to make it a unit vector (so it has a length of 1):
Length of gradient vector = √(20^2 + 24^2) = √(400 + 576) = √976 ≈ 31.24
The unit vector in the direction of steepest descent is <20/31.24, 24/31.24> ≈ <0.640, 0.768>.
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Name the property the equation illustrates.
8.2 + (–8.2) = 0
Answer:
The name of the property the equation illustrates is the Inverse Property of Addition.
Step-by-step explanation:
The Inverse Property of Addition says that if you add a number to the negative version of itself, the numbers will cancel out and the result will be 0. In other words, if you add 8.2 + (–8.2), the answer will always be 0.
he average distance between Jupiter and the sun is 7.8 × 108 kilometers, and the average distance between the sun and Neptune is 4.51 × 109 kilometers. What is the approximate difference between these average distances?
Final answer:
The approximate difference between the average distances from the Sun to Jupiter and from the Sun to Neptune is approximately [tex]-3.71 * 10^9 km.[/tex]
Explanation:
The approximate difference between the average distances from the Sun to Jupiter and from the Sun to Neptune can be found by subtracting the average distance to Neptune from the average distance to Jupiter.
Average distance to Jupiter: 7.8 × 108 km
Average distance to Neptune: 4.51 × 109 km
Subtract the average distance to Neptune from the average distance to Jupiter:
[tex]= 7.8 * 10^8 km - 4.51 * 10^9 km[/tex]
= [tex]-3.71 * 10^9[/tex]
The approximate difference between the average distances is [tex]-3.71 * 10^9 km.[/tex]
A hollow ball is made of rubber that is 1 centimeter thick. The ball has a radius of 5 centimeters at the outside surface.
What is the approximate volume of rubber used to make the ball?
Answer: I got the same answer. It's 255.4 cm3
Step-by-step explanation:
What's the radius of a circle with an area of 123 square feet? A. 6.26 ft. B. 39.17 ft. C. 26.32 ft. D. 3.14 ft.
The number of Adult tickets is the same as the number of Child (age 5-12) tickets. A total of 38 tickets was purchased. What is the total cost of the tickets? Explain.
Data: Adult Tickets $23
Child Tickets $17
Under 5 $8
What is the measure of the smallest angle?
52°
61°
67°
69°
Answer:
52° is ur answer
Step-by-step explanation:
I just did the quiz so i know
What is the factored form of 6x2 + 11x – 10? (2x + )( x – )
Answer:
[tex]6x^2+11x-10=(2x+5)(3x-2)[/tex]
Step-by-step explanation:
we are given
[tex]6x^2+11x-10[/tex]
We can factor it
[tex]6x^2+11x-10=6x^2+15x-4x-10[/tex]
we can use grouping method
[tex]6x^2+11x-10=(6x^2+15x)-(4x+10)[/tex]
now, we can take out common terms
[tex]6x^2+11x-10=3x(2x+5)-2(2x+5)[/tex]
we can take 2x+5 from both terms
[tex]6x^2+11x-10=(2x+5)(3x-2)[/tex]
so, we get factor terms as
[tex]6x^2+11x-10=(2x+5)(3x-2)[/tex]
The factored form of 6x² + 11x - 10 is: (2x + 5)(3x - 2)
Factorization of Algebraic ExpressionsGiven the algebraic expression, 6x² + 11x - 10, it can be factorized as shown in the steps below:
6x² + 11x - 10
6x² + 15x - 4x - 10
(6x² + 15x) - (4x - 10)
3x(2x + 5) - 2(2x + 5)
6x² + 11x - 10 = (2x + 5)(3x - 2)
Therefore, the factored form of 6x² + 11x - 10 is: (2x + 5)(3x - 2).
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callie spent 3/4 hour on a science report and 1/3 hour on a social studies report. What fraction of an hour longer did she spend on the science report ?
Which equation can be used to find the number of wolves in the state on January 1? A zoologist is recording the loss of wolves in her state. She notes the number of wolves, w, in the state on January 1. One year later, there were 84 wolves in the state, which is 23 fewer wolves than were in the state a year earlier. What is the number of wolves in the state on January 1? w−84=−23 w−23=84 23−w=84 w + 23 = 84
Answer: w - 23 = 84
Step-by-step explanation:
Triangle CAT is translated using the rule (x,y)→(x−3, y+4) to create triangle C'A'T'. If a line segment is drawn from point C to point C' and from point A to point A', which statement would best describe the line segments drawn?
The answer is: Parallel and congruent.
What are the answers for both drop downs the first one is asking for 3.113 and the second is asking for 1.2795
Increasing W-4 allowances will ________ the net pay in your paycheck and ______ your total tax burden.
A spherical balloon with radius r inches has volume defined by the function below. find a function that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r + 3 inches. (give the answer in terms of π and r.) v(r) = 4/3 pi r^3
Subtract 9 from z. 9-Z, Or Z-9
What value of n makes the equation true?
0.7n+0.8n=2.1
n=3.60
n=3.15
n=1.40
n=0.60
A Pitcher of fruit punch holds 2 gallons , If 9 people share the entire pitcher equally how much punch does ecah person get
A high school basketball team scores 85 points in a playoff game. The team leaders are Greg and Tremaine who scored a total of 38 points. If Tremaine scored 8 more points than Greg, how many points did Greg and Tremaine score individually?
Answer:
Total Points scored by team leaders are Greg and Tremaine=38 points
Let Points scored by Greg =x points
Then , Points scored by Tremaine =(x+8) points
So, writing the condition in equality form
x +x+8=38
2 x =38-8
2 x=30
Dividing both sides by ,2
x=15
Points scored by Greg =15 points
Then , Points scored by Tremaine =(15+8)=23 points
what is 4 1/2 divided by 3
PLEASE HELP WILL GIVE BRAINLIEST
Find the measure of SMK
A) 36°
B) 48°
C) 56°
D) 66°
The required measure of ∠SMK is 66° for the given figure.
What are supplementary angles?The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.
The figure is given in the question, as shown.
According to the given figure, we have
In triangle ΔAMS,
∠ASM + ∠SAM + ∠AMS = 180° (sum of the interior angle)
36° + 30° + ∠AMS = 180°
∠AMS = 180° - 66°
∠AMS = 114°
∠SMK + ∠AMS = 180° (Supplementary angles)
∠SMK + 114° = 180°
∠SMK = 180° - 114°
∠SMK = 66°
Thus, the measure of ∠SMK is 66°.
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On st. Patrick's day, 3/5 of the students in Ms. pikes band class are wearing green . If there are 60 students in her class , how many of them are wearing green?