Answers
Average rate of change of [tex]y = x^2 + 4x - 1\\[/tex] over the interval [tex]-4 \leq x \leq 1[/tex] is 1
What is average rate of change of a curve?
Average rate of change of a curve is equal to the slope of the curve and is obtained by dividing the change in functional value by the change in the value of the domain.
Here,
[tex]y = x^2 + 4x - 1\\[/tex]
At x = -4,
[tex]y = (-4)^2+ 4(-4)-1\\y = -1[/tex]
At x = 1
[tex]y = (1)^2 + 4(1) -1\\y = 4[/tex]
Average rate of change of [tex]y = x^2 + 4x - 1\\[/tex] over the interval [tex]-4 \leq x \leq 1[/tex]
= [tex]\frac{4 - (-1)}{1- (-4)}\\\\\\\frac{5}{5}\\\\1[/tex]
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Related Questions
Which plane in the rectangular prism is parallel to plane ABC?
plane ABH
plane EFG
plane CDF
plane BCE
Answers
The plane EFG in the rectangular prism is parallel to plane ABC.
In this question, we have been given the rectangular prism ABCDEFGH
We need to find the plane which is parallel to plane ABC.
We can observe that in given rectangular prism,
plane ABH is parallel to the plane CDF
plane BCE is parallel to the plane AGF
plane EFG is parallel to plane ABC.
Therefore, the plane EFG in the rectangular prism is parallel to plane ABC.
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Translate the numerical expression: Five times as large as the product of 3 and 6
Answers
Five times as large= multply by 5
As large as five times
Then
X =5x 3x6 =
X = 90
GeometryQuestion 5•For what values of the variables must ABCD be a parallelogram?
Answers
SOLUTION:
For parallelograms; opposite sides are congruent;
Thus;
[tex]\begin{gathered} 2y-12=y-2 \\ solving\text{ for y} \\ 2y-y=12-2 \\ y=10 \end{gathered}[/tex]The shorter opposite sides must be equal too, thus;
[tex]\begin{gathered} 2x+1=y+3 \\ substitute\text{ in y = 10} \\ 2x+1=10+3 \\ 2x+1=13 \\ 2x=12 \\ x=6 \end{gathered}[/tex]Thus, for the figure to be a parallelogram, x = 6 and y = 10
estimate the answer the cost of 5 items at a grocery store if the items cost $6.93, $5.99, $15.73, $3,78 and $18.29
Answers
the total cost is:
[tex]6.93+5.99+15.73+3.78+18.29=50.72[/tex]$50.72
What value of p satisfies the inequality shown below?
Answers
Answer:
7
Step-by-step explanation:
-8(7+2)<-56
-56-16<-56
-72<56
-72 is less than -56
A tile pattern is represented by the equation "y = 6x + 4".A) what does the six represent in the patternB) what does the four represent in the patternC) how many times will there be in the 75th figure.
Answers
A tile pattern is represented by the equation "y = 6x + 4".
A) what does the six represent in the pattern
B) what does the four represent in the pattern
C) how many times will there be in the 75th figure.
_______________________
if x represents the figure number and y represents the number of tiles.
A) what does the six represent in the pattern
The six represent
B) what does the four represent in the pattern
C) how many times will there be in the 75th figure.
A plane traveled 1160 kilometers each way to Havana and back. The trip there was with the
wind. It took 10 hours, The trip back was into the wind: The trip back took 20 hours. Find the
speed of the plane in still air and the speed of the wind.
Answers
The speed of the plane in still air is 87 kilometers, and the speed of the wind is 87 kilometers.
A plane traveled 1160 kilometers to Havana and back.
The trip there was with the wind. It took 10 hours.
The trip back was into the wind. The trip back took 20 hours.
What is speed, distance, and time?
The formula speed distance time is used to explain the relationship between speed, distance, and time. That is speed = time/distance. To put it another way, distance divided by speed equals time. You can figure out the third input if you know the first two.
Consider,
s = plane speed in still air
w = speed of the wind
then
(s+w) = ground speed with the wind
and
(s-w) = ground speed against the wind:
A dist equation for each way (dist = speed * time)
10(s+w) = 1160
20(s-w) = 1160
Simplify divide the 1st equation by 13, and the 2nd equation by 26, and you have:
s + w = 116
s - w = 58
Using adding s & eliminates w,
2s = 174
s = 174/2
s = 87 km plane speed in still air
The wind speed
87 + w = 96
w = 9 km is the wind speed
Hence, the speed of the plane in still air is 87 kilometers, and the speed of the wind is 87 kilometers.
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In triangle ABC, angle C is a right angle. If cos A = 58, what is the value of cos B?
Answers
Question:
Solution:
The diagram of a triangle ABC, where C is the right angle is:
Now, by definition and according to the data of the problem, we get that:
[tex]\cos (A)=\frac{5}{8}=\frac{adjacent\text{ side to the angle A}}{hypotenuse}[/tex]that is:
now, to find the cos(B), first, we must find the missing side of the triangle. To do that, we can apply the Pythagorean theorem:
[tex]BC\text{ =}\sqrt[]{8^2-5^2}\text{ = }\sqrt[]{39}[/tex]now, with respect to angle B, we obtain that:
[tex]\cos (B)=\frac{adjacent\text{ side to the angle B}}{hypotenuse}=\frac{\sqrt[]{39}}{8}[/tex]So that, we can conclude that the correct answer is:
[tex]\frac{\sqrt[]{39}}{8}[/tex]Kevin borrowed some money from his friend in order to help buy a new video game system. Kevin agreed to pay back his friend $5 per week and originally borrowed $90. Make a table of values and then write an equation for L, in terms of t, representing the amount Kevin owes his friend after t weeks.
Answers
1. The table of values showing the amount Kevin owes his friend after t weeks is as follows:
Table of Values:Week Amount Owed
0 $90
1 $85
2 $80
3 $75
4 $70
...
18 $0 ($5 - $5)
2. The equation representing the amount (L) Kelvin owes his friend after t weeks is L = 90 - 5t.
What is an equation?An equation is a mathematical statement showing that two mathematical expressions using the equation symbol (=) are equal or equivalent.
Equations establish the numerical relationship existing between two or more mathematical expressions, numbers, values, or variables.
Week Amount Owed
0 $90
1 $85 ($90 - $5)
2 $80 ($85 - $5)
3 $75 ($80 - $5)
4 $70 ($75 - $5)
The total amount borrowed = $90
The amount of repayment = $5
The repayment period = weekly
Equation:Let the balance after t weeks of payment = L
L = 90 - 5t
In eighteen weeks, Kevin will complete the repayment of the loan.
Check:
If t = 18
L = 90 - 5t
L = 90 - 5(18)
L = 90 - 90
L = 0
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A researcher weighed watermelons grown across a certain region. the data are rounded to the nearest pound and displayed in this histogram.
Answers
Given: The weights of Water melon displayed using a histogram as shown in the figure
To Determine: The weight of the fourth bin
From the histogram, it can be seen that the x-axis represents the weight of the watermelons, while the y-axis represents the quantity
It can observed that the fourth been has 4 watermelons as shown below:
From the above, 4 watermelons marked with red circle on the y-axis, and their weights marked red on the x-axis
Hence, the weight of 4 watermelons is at least 12pounds but no more than 16pounds, the second option
let p represenst "angke A is an obtuse angle" and q represent " the measure of angle A = 75 degrees. convert the symbolic statement to a sentence.
Answers
In this scenario, we are considering if-then statements. Looking at the given statement,
p = angle A is an obtuse angle
q = the measure of angle A = 75 degrees
A statement of if q, then p would be
q - p
where - is an arrow pointing to the right
Looking at the picture, the symbol before p represents negation. It tells us that
if q, then not p. By translation, the correct answer would be
If the measure of angle A = 75 degrees, then angle A is not an obtuse angle
ASAP PLEASE
Show how we can use the factors method to find the value of 53 × 20
Write it Step by step.
Answers
Answer:
1060
Step-by-step explanation:
I am assuming the factors method is the distributive property:
We can break 53x20 into 50x20+3x20
50x20=1000 and 3x20 is 60
1000+60=1060
Please give me brainiest.
What is the slope of the line passing through the points (0, - 5) and (4, 2)?
Answers
Step-by-step explanation:
What is the slope of the line passing through the points (0, - 5) and (4, 2)?
slope = change in rise/change in run
OR:
slope = change in y/change in x
your point format is: (x , y)
SO:
slope = (-5 - 2) / (0 - 4)
slope = -7/-4
slope = 7/4
Answer:
[tex]\sf \dfrac{7}{4}[/tex]
Step-by-step explanation:
Slope:(0 , -5) ⇒ x₁ = 0 & y₁ = -5
( 4 ,2) ⇒ x₂ = 4 & y₂ = 2
[tex]\sf \boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}\\\\[/tex]
[tex]\sf = \dfrac{2-[-5]}{4-0}\\\\\\\=\dfrac{2+5}{4}\\\\\\=\dfrac{7}{4}[/tex]
juan has fewer than ten $10 bills. he has more tahn three $1 bills. he has twice as many tens as ones. how much money does he have?
Answers
Answer:
$64.00
Step-by-step explanation:
I graphed a parallelogram. Now I need to show that the diagonals bisect each other, or have the same midpoint. What does this mean?
Answers
A biscetor is a line that curs another one exactrly at its midpoint. If the diagonals of the paallelogram bisect each other, this means that both cut the other in exact halves.
For example
For the square ABCD, its diagonals BD and AC cut each other in point M.
M is their midpoint, which means that the haves of each diagonal are the same:
For diagonal AC you get that AM=MC
For diagonal BD you get that BM=MD
This means that the diagonals bisect each other and have the same midpoint M
pls help me out I really need to sleep
Answers
Answer:
4
Step-by-step explanation:
Point 1: (-2, 0)
Point 2: (3, 4)
(4-0) ÷ (3-2) = 4 ÷ 1 = 4
on the 1st of January a student puts N10 in a box. on the 2nd she puts N20 in the box. putting the same number of 10 naira notes as the day of the month. how much money will be in the box if she keeps doing this for the first 10 days of January and the whole of January
Answers
Answer:
N550
N4960
Step-by-step explanation:
10 days
First day: N10
Second day: N20
Third day: N30
...
Tenth day: N100
Sum of sequence: 10 + 20 + 30 + 40 + ... + 80 + 90 + 100
sum = (n/2)[2a+(n−1)d]
a = 10; n = 10; d = 10
sum = (10/2) × [2(10) + (10 - 1)(10)]
sum = 5[20 + 9(10)]
sum = 5[110]
sum = 550
Answer: N550
31 days
First day: N10
Second day: N20
Third day: N30
...
Thirty-first day: N100
Sum of sequence: 10 + 20 + 30 + 40 + ... + 290 + 300 + 310
sum = (n/2)[2a+(n−1)d]
a = 10; n = 31; d = 10
sum = (31/2) × [2(10) + (31 - 1)(10)]
sum = 15.5[20 + 30(10)]
sum = 15.5[320]
sum = 4960
Answer: N4960
I have one more question
Answers
Answer: 19
Step-by-step explanation:
[tex]49-6(5)=19[/tex]
Answer:
19
Step-by-step explanation:
a=49,b=5
a-6b
we will just substitute for the values
=49 – 6(5)
= 49 – 30
= 19
Write a simplified expression for the right half of the equation that can be used to find the nth term in the sequence The sequence is 7,9,11,13,15
Answers
7,9,11,13,15
First, find the common difference (d)
9-7 = 11-9 = 13-11 = 15-13 = 2
d= 11
a1 = first term = 7
apply the formula:
an = a1 + (n-1) d
an = 7 + (n-1) 2
an = 7 + 2n-2
an = 2n + 5
The price of gas at the pump recently rose from $2.95 to $3.04 in one week. This represents what percent increase?
Answers
Answer:
Step-by-step explanation:
(3.00 - 2.40)/2.40 = p/100;
Then. 0.60/2.40 = p/100;
1/40 = p/100;
p = 100/40;
p = 2.5;
The percentage increase was 2.5%;
The ratio of second graders to third graders at the spelling bee was 2 to 7. If there were 204 second graders, how many third graders were there?
Answers
There are 714 third-graders.
What is ratio?A ratio is a way to show a relationship or compare two numbers of the same kind.
Given that, the ratio of second-graders to third-graders at the spelling bee was 2 to 7 and there are 204 second-graders
Let the number of third-graders be x, then,
2/7 = 204/x
x = 714
Hence, There are 714 third-graders.
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help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: 2.5, 5.4
Step-by-step explanation:
[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]
Question
Solve for x.
5(x−225)=−5.2
Enter your answer as a decimal or simplified mixed number in the box.
x =
Answers
Answer:
x=223.96
Step-by-step explanation:
Answer as a decimal: x=223.96
Answer as a fraction: x= 223 24/25
Let's solve this equation step-by-step!
5(x−225)=−5.2
Step 1: Simplify both sides of the equation.
5(x−225)=−5.2
(5)(x)+(5)(−225)=−5.2 (Distribute)
5x+−1125=−5.2
5x−1125=−5.2
Step 2: Add 1125 to both sides.
5x−1125+1125=−5.2+1125
5x=1119.8
Step 3: Divide both sides by 5.
5x/5=1119.8/5
x=223.96
A wheel on Amanda's bicycle is 0.3 m in diameter. Amanda rides the bicycle in a race, and the wheel turns 50 times during the course of the race. How long is the race?Use the value 3.14 for pie. Round your answer to the nearest tenth. Do not round any intermediate steps.
Answers
To be able to determine how long the race that Amanda took, let's multiply the circumference of Amanda's bicycle wheel by 50 times since it turns 50 times during the course of the race.
The formula of the circumference of a circle is,
[tex]\text{Circumference = }\pi d[/tex]Where,
pi = 3.14
d = diameter = 0.30 m
Let's determine the Circumference of Amanda's bicycle wheel,
[tex]\text{ Circumference = }\pi d\text{ = (3.14)(0.30)}[/tex][tex]\text{ Circumference = 0.942 m}[/tex]Let's now determine how long the race is,
[tex]\text{ Distance}_{Race}\text{ = (Circumference)(50) = (0.942)(50)}[/tex][tex]\text{ Distance}_{Race}\text{ = 47.10 m}[/tex]Therefore, the bicycle race that Amanda took is 47.10 m long.
complementary angles. If m/A= (5x - 11)° and
ZA and ZB are
m/B = (6x + 2)°, then find the measure of ZA.
PLEASE ANSWER ASAP !!!!
Answers
Answer:
∠ A = 34°
Step-by-step explanation:
complementary angles sum to 90° , then
5x - 11 + 6x + 2 = 90
11x - 9 = 90 ( add 9 to both sides )
11x = 99 ( divide both sides by 11 )
x = 9
Then
∠ A = 5x - 11 = 5(9) - 11 = 45 - 11 = 34°
4+( ) Rewrite the expression 4-11 as the sum of two numbers
Answers
Answer:
4+(-11)
Step-by-step explanation:
you need to put the negative 11 in ()
Enter the equation of the line in slope-intercept formSlope is -4, and (6,1) is on the line.The equation of the line is
Answers
Equation of a line in slope-intercept form:
[tex]y=mx+b[/tex]m is the slope
b is the y-intercept
As you have the slope (m= -4) and a point (6,1) you use it in the equation above to find the y-intercept, as follow:
(6,1) x=6 y=1
m= -4
[tex]1=-4(6)+b[/tex]Solve b:
[tex]\begin{gathered} 1=-24+b \\ \\ 1+24=-24+24+b \\ 25=b \end{gathered}[/tex]Then, the equation of the given line in slope-intercept form is:[tex]y=-4x+25[/tex]The area of a triangle is 50
the length is x+10 and the width is x
solve for x.
Answers
In a rectangle of area 50 the value of x is 5
How to solve for xArea of a rectangle is given by multiplication of the length and the width
Area was given as 50
length = x + 10
width = x
Area = L * w
50 = (x + 10) * x
50 = x^2 + 10x
rearranging the equation
x^2 + 10x - 50
factorizing gives
x - 5x + 10x - 50
x(x- 5) + 10(x - 5)
(x - 5)(x + 10)
therefore
x = 5 or x = -10
taking the positive value
x = 5
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Question
The area of a rectangle is 50 the length is x+10 and the width is x
solve for x.
Solve forj: -16 = j/2 + -19
Answers
Given:
[tex]-16=\frac{j}{2}+(-19)[/tex]To solve for j :
Explanation:
Multiplying by 2 on both sides,
[tex]-32=j-38[/tex]Adding 38 on both sides, we get
[tex]\begin{gathered} -32+38=j-38+38 \\ 6=j \end{gathered}[/tex]Final answer:
The value of j is 6.
Can someone give me a clear answer? I'll give or try to give 100 points... The crown is yours after.
Part A: Given the function g(x) = |x + 3|, describe the graph of the function, including the vertex, domain, and range. (5 points)
Part B: If the parent function f(x) = |x| is transformed to h(x) = |x| − 2, what transformation occurs from f(x) to h(x)? How are the vertex and range of h(x) affected?
Answers
The required solutions are as follows,
(a) Vertex, domain, and range of the given function is (0,3), the domain is all real numbers and the range is all real value greater than +3 respectively.
(b) The trasformation shifts the f(x) two units below and vertex and range are (0, -2) and all real values greater and equal to -2 respectively.
here,
(A)
f(x) = |x - 3|
put x= 0
f(x) = 3
So the vertex is (0, 3)
Absolute functions has a domain of all real numbers, while the range of the given function is from positive 3 to infinity because the minimum value of the function is 3.
Similarly
(b)
f(x) = |x|
Vertex = (0, 0)
For the trasformation,
f(x) = |x|-2
Vertex = {0, -2}
Range = f(x) > -2
Thus, The required solutions are as mentioned above,
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