the solution set for the inequality h < 8 is {h | h ∈ ℤ and h < 8}, which includes all whole numbers less than 8. The solution set differs from the solution on the number line in that it only includes discrete values and does not have a graphical representation.
How to solve the question?
The number line shows the solution for the inequality h < 8, where h represents the number of hats that Max can buy with the money he has saved. The solution set for this inequality is all the possible values of h that satisfy the inequality. In this case, the solution set consists of all integers less than 8, which can be represented as {h | h ∈ ℤ and h < 8}.
The solution set differs from the solution on the number line in that the solution set is a set of discrete values, while the number line is continuous. The number line represents all the possible values of h, including fractions and decimals, but the solution set only includes whole numbers. For example, the number line would include values like 7.5 or 7.9, but the solution set would only include 7.
Additionally, the number line shows the inequality graphically, with an open circle at 8 to indicate that 8 is not included in the solution set, and an arrow pointing to the left to indicate that the values of h are less than 8. The solution set does not have any graphical representation and is simply a list of values.
In conclusion, the solution set for the inequality h < 8 is {h | h ∈ ℤ and h < 8}, which includes all whole numbers less than 8. The solution set differs from the solution on the number line in that it only includes discrete values and does not have a graphical representation.
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x=10 3x+5y=20 in the system of equations, what is the value of x
In the coordinate plane, a square has vertices (4, 3), (-3, 3), (-3, - 4). What is the location of the fourth vertex?
The two possible locations for the fourth vertex are (4, -4) and (-3, -1).
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.
To find the location of the fourth vertex of the square, we need to use the fact that a square has four equal sides and four right angles.
The first two vertices given are (4, 3) and (-3, 3), which lie on a horizontal line segment of length 7.
The third vertex is (-3, -4), which is 7 units away from the first two vertices and lies on a vertical line segment.
Since the square has four equal sides, the distance between the third vertex and the fourth vertex must also be 7 units.
And since the square has four right angles, the fourth vertex must be located on a vertical line passing through the first two vertices or on a horizontal line passing through the third vertex.
So, there are two possible locations for the fourth vertex:
(4, -4): This point is located 7 units below the first vertex (4, 3) on the vertical line passing through it.
(-3, -1): This point is located 7 units to the right of the third vertex (-3, -4) on the horizontal line passing through it.
Therefore, the two possible locations for the fourth vertex are (4, -4) and (-3, -1).
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Triangle ABC with vertices at A(−4, −4), B(8, 8), C(2, 6) is dilated to create triangle A′B′C′ with vertices at A′(−2, −2), B′(4, 4), C′(1, 3). Determine the scale factor used.
2
one half
4
one fourth
Answer: there all divided by 2
so it's 2
plsssssssss 2/7=4/5+9q
Answer: q= -2/35
Step-by-step explanation:
Rearrange terms 2 Subtract from both sides 3.Simplify the expression Subtract the numbers Subtract the numbers 4 Divide both sides by the same factor 5 Simplify the expression Divide the numbers Cancel terms that are in both the numerator and denominator Move the variable to the left
Answer:
q = -2/35
Step-by-step explanation:
2/7 = 4/5 + 9q
(2/7) - (4/5) = 9q
(10/35) - (28/35) = 9q
-18/35 = 9q
(-18/35) / 9 = q
(-18/(35*9)) = q
-18/315 = q
q = -2/35
Check:
2/7 = 4/5 - 9*2/35
2/7 = 4/5 - 18/35
10/35 = 28/35 -18/35
10 = 28 -18
what is the answer to this equation?
7/10 divided by 1/3
Answer:
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction.
So, 7/10 divided by 1/3 can be written as:
(7/10) ÷ (1/3) = (7/10) x (3/1)
Multiplying the numerators and denominators, we get:
(7 x 3) / (10 x 1) = 21/10
Therefore, the answer is 21/10, which is an improper fraction. We can simplify it to a mixed number by dividing the denominator into the numerator.
21 ÷ 10 = 2 with a remainder of 1, so the mixed number is:
= 1 1/10
Hence, the answer is 1 1/10 or 11/10.
Step-by-step explanation:
7/10 / (1/3) is equal to 7/10 * 3/1 = (7*3) / (10*1) = 21/10 = 2 1/10
What am i supposed to do?
The histogram that displays the data in the table correctly is C. Histogram C.
How to find the histogram ?Look at the data in the table and look for the number of photocopies that are located between 800 and 899. There are 3 of these.
The number located between 900 and 999 are 5 in number including 915, 919, 923, 950, and 989. The number located between 1,000 and 1, 099 is 8 photocopies.
The histogram that shows this is Histogram C.
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If P = 3x² - x + 2 and Q = x² + 5x - 6, then P+ Q =
Answer:
Step-by-step explanation:
If P = 3x² - x + 2 and Q = x² + 5x - 6, then P+ Q = 3x² - x + 2 + x² + 5x - 6 =
4x^2 +4x - 4
D = 16 + 64 = 80
x12 = [tex]\frac{-4+-\sqrt{80} }{8}[/tex]
write a quadratic function in standard form that models the data (8,-2),(0,-1),(-4,0),(-4,1),(0,2)
To write a quadratic function in standard form that models the given data points, we can use the standard form of a quadratic equation:
y = ax^2 + bx + c
where a, b, and c are constants to be determined.
To determine these constants, we can substitute the given data points into the equation and solve for a, b, and c.
Substituting the point (8, -2):
-2 = a(8)^2 + b(8) + c
64a + 8b + c = -2
Substituting the point (0, -1):
-1 = a(0)^2 + b(0) + c
c = -1
Substituting the point (-4, 0):
0 = a(-4)^2 + b(-4) - 1
16a - 4b = 1
Substituting the point (-4, 1):
1 = a(-4)^2 + b(-4) - 1
16a - 4b = 2
Substituting the point (0, 2):
2 = a(0)^2 + b(0) - 1
-1 = a
What is the quadratic function in standard form that models the data (8,-2),(0,-1),(-4,0),(-4,1),(0,2)?Now we can substitute the value of a into the equation we obtained from the point (-4, 0):
16(-1) - 4b = 1
-16 - 4b = 1
b = -17/4
Therefore, the quadratic function in standard form that models the given data points is:
y = -x^2 - (17/4)x - 1
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Suppose that the function h is defined as follows.
if
-2
-1
h(x)= 0
1
2
Graph the function h.
-3.5
if-2.5
if-1.5
if -0.5
if 0.5 ≤x≤1.5
+
X
Ś
The required graph of the function given; h (x) has been attached.
Define a graph?In mathematics, graph theory is the study of graphs, which are mathematical structures used to represent pairwise interactions between objects. In this definition, a network is made up of nodes or points called vertices that are connected by edges, also called links or lines. In contrast to directed graphs, which have edges that connect two vertices asymmetrically, undirected graphs have edges that connect two vertices symmetrically. Graphs are one of the primary areas of study in discrete mathematics.
Here as per the question the graph of the function, h (x) has been attached.
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An investment opportunity is offering an annual interest rate of 12% compounded continuously.
How much should you invest initially if you want to have fifteen thousand dollars after nine years?
Do not include a dollar sign in your answer. Round your answer to the nearest cent.
I
Answer:
data given
interest rate 12%
amount to be received 15ooo
time9years
Step-by-step explanation:
from
A=p[1+r/100]^n
where
A is amount
p is principal
r is rate interest
n number of interist period
now,
15000=p[1+12/100]^8
15000/1.12^8 =p×1.12^8/1.12^8
p=6058.24
p=6058)
: .you should invest 6,058
The amount to be invested initially if you want to have fifteen thousand dollars after nine years is $3947.18.
How to find the compound interest?If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
We are given that:
A=15000
r=0.12
t=9
We need to find P. You can do this by rearranging the formula:
P=ertA
Then plug in the given values and use a calculator:
P=e0.12×915000
P≈3947.18
Therefore, by the given interest rate the answer will be $3947.18.
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A retail manager constructs a 95% confidence interval to estimate the mean amount of money each customer spends per visit to the retail store. Assume that all conditions have been met. The one-sample t-interval is ($10.53, $31.89). The owner of the retail store will issue the manager a bonus if the customers spend $35, on average, per visit. Is it reasonable to believe this manager will receive a bonus? No. Because a different sample might give different results, no conclusion can be drawn. No. Because the interval does not contain $35, the manager would not be issued the bonus. Yes. Because the interval representing the mean amount customers spend per visit is entirely below $35, it is reasonable to believe the manager will be issued a bonus. Yes. Because the interval representing the mean amount customers spend per visit does not contain $35, it is reasonable to believe the manager will be issued a bonus.
The correct option is: No. Because the interval does not contain $35, the manager would not be issued the bonus.
What is an interval?An interval refers to a range of values between two points on a numerical scale. It can be represented by two numbers, called endpoints, and includes all the values that lie between these endpoints.
The two common types of intervals are closed intervals and open intervals.
According to the given information:
In a confidence interval, the range of values within which the true population parameter (in this case, the mean amount of money each customer spends per visit) is likely to fall is estimated. A 95% confidence interval means that there is a 95% probability that the true population parameter falls within the interval.
In this case, the confidence interval is ($10.53, $31.89), which means that we are 95% confident that the true mean amount customers spend per visit falls between $10.53 and $31.89. Since the interval does not contain $35, it is not reasonable to believe that the manager will receive a bonus, as the estimated mean amount spent per visit is below $35 according to the confidence interval.
The correct answer is: No. Because the interval does not contain $35, the manager would not be issued the bonus.
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What is the approximate distance from the origin to the point (-2, -7, -4)? Round to the nearest tenth
O 3.6 units
O 7.6 units
O 8.3 units
O 9.4 units
The approximate distance from the origin to the point (-2, -7, -4) is 8.3 units.
Distance between two points formula:In three-dimensional space, the distance formula is used to calculate the distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in a three-dimensional coordinate system.
The formula is given by:
d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]
Here we have
The point (-2, -7, -4)
We need to find the distance between the origin to the point
Let (x₁, y₁, z₁) = (-2, -7, -4) and (x₂, y₂, z₂) = (0, 0, 0)
Using the distance formula,
d = √ [(x₂ - x₁)² + (y₂ - y₁)²+ (z₂ - z₁)² ]
d = √ [(0 - (-2))² + (0 - (-7))²+ (0 - (-4))² ]
d = √ [(2)² + (7)²+ (4)² ]
d = √ [4 + 49 + 16 ]
d = √69 = 8.3066
d = 8.3
Therefore,
The approximate distance from the origin to the point (-2, -7, -4) is 8.3 units.
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Find the area and perimeter of the parallelogram. (Hint: Don't forget your units!)
7 cm
8 cm
4 cm
The area and perimeter of the parallelogram are: 56 square units and 30 units respectively
What is a parallelogram?In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The parameters that will help us do the math are
base = 7
height = 8
Area = 8*7 = 56 square units
perimeter 2b + 2h
perimeter = 2*7 + 2*8
= 14 +16
P = 30 units
Therefore, the perimeter of the parallelogram and area are 30 units and 56 square units
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Can you help me please
The half-life of Radium-226 is 1590 years. If a sample contains 300 mg, how many mg will remain after 2000 years? ---------
the united states has approximate population of 3.3 x 108 people. Each person in the united states consumes an average of about 14,000 grams of rice per year. how much rice in grams, does the population of the U.S consume each year?
the population of the U.S consumes approximately [tex]4.62 * 10^{12}[/tex] grams of rice each year.
What is marginal utility?
The additional pleasure a consumer has from owning one extra unit of an item or service is known as marginal utility.
We can calculate the total amount of rice consumed in the U.S per year by multiplying the population by the amount of rice consumed per person per year:
Total amount of rice consumed = (Population of the U.S) x (Amount of rice consumed per person per year)
Total amount of rice consumed = [tex](3.3* 10^8) * (14,000)[/tex]
Total amount of rice consumed = [tex]4.62* 10^{12} grams[/tex]
Therefore, the population of the U.S consumes approximately [tex]4.62 * 10^{12}[/tex] grams of rice each year.
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The Chicago white Sox had a home record of 53-28 in the 2021 season. How would you interpret this?
The interpretation of the Chicago white sox data is shown below
Interpreting the Chicago dataThe record 53-28 for the Chicago White Sox in the 2021 season means that they won 53 games and lost 28 games in the home games they played during the season.
This record indicates that the White Sox were a strong team at home, winning more games than they lost.
It also suggests that they had a good advantage playing in their home stadium, as winning a high percentage of home games is generally seen as a positive factor in sports.
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Please help now!!!
give <1 = <2
prove p l l q
p l l q, { < 2 and <3 } are corresponding angles and they are equal Hence , proved p l l q.
What are parallel lines ?In a Two-dimensional plane, parallel lines are those that, no matter how far they are extended, never cross.
In other words, two or more lines that have the same slope and never intersect are said to be parallel.
It is crucial to understand parallel lines in geometry since they are useful in many areas of mathematics, including trigonometry, calculus, and linear algebra.
Examining the slopes of two lines might help you decide if they are parallel. Two lines are parallel if they have the same slope.
Examining the equations of two lines is another method for figuring out if they are parallel.
If the slopes are the same and the equations for the two lines are of the form y = mx + b (where m is the slope and b is the y-intercept),
then the lines are parallel.
What is Two-dimensional plane ?A flat surface that extends infinitely in two directions is referred to as a two-dimensional (2D) plane and is sometimes depicted as a flat sheet of paper.
A two-dimensional plane is frequently referred to as a coordinate plane, Cartesian plane, or just a plane in mathematics.
The x-axis and y-axis, also known as the x and y axes, respectively, intersect at the origin to form the two-dimensional (2D) plane.
The horizontal direction is represented by the x-axis, while the vertical direction is represented by the y-axis.
An ordered pair of coordinates (x, y), where x is the value along the x-axis and y is the value along the y-axis, uniquely identify each point on the plane.
Prove :-
From the graph , we can get
∠1 ≅ ∠3 ------------ (1) {vertical angles are equal.}
Given what we know,
∠1 ≅ ∠2 -------------(2)
According (1) and (2)
We can get
∠2 ≅ ∠3
According to the theorem.
if corresponding angles are equal,
then two lines are
parallel. we can get ,
p l l q
{ < 2 and <3 }
are corresponding angles and they are equal
Hence , proved p l l q.
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He makes 8.50 an hour plus 3 every oil change that he performs last week he worked 36hours n performed 17 oil changes how much money did he make
Answer:
$357
Step-by-step explanation:
Hours = h
Oil changes = o
Money = m
m = 8.5h + 3o
Now we can substitute:
m = 8.5(36) + 3(17)
m = 306 + 51
m = 357
what is the percent of decrease from 8 to 6
The calculated value of the percent of decrease from 8 to 6 is 25%.
What is the percent of decrease from 8 to 6To find the percent of decrease from 8 to 6, we need to find the difference between the two numbers and express it as a percentage of the original number (8).
The difference between 8 and 6 is 8 - 6 = 2.
To express this difference as a percentage of 8, we can use the formula:
percent decrease = (difference / original number) x 100%
Substituting the values we get:
percent decrease = (2 / 8) x 100% = 0.25 x 100% = 25%
Therefore, the percent of decrease from 8 to 6 is 25%.
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7. A group of students wants to demonstrate that sunlight provides the energy for plants to grow. What is
the control group for the experiment?
A. Some plants will receive less water
B. Some plants will receive fertilizer
C. Some plants will receive no sunlight
D. Some plants will receive no water
I
The control group for the experiment would be option C: some plants will receive no sunlight.
What is control group for experiment ?The control group in an experiment is the group that does not receive the treatment or intervention being tested, so that the effects of the treatment can be compared to a baseline or reference point. In this experiment, the treatment being tested is the provision of sunlight as an energy source for plant growth.
Therefore, the control group should not receive sunlight, so that the effects of sunlight can be compared to the baseline of plant growth without sunlight.
Therefore, the control group for the experiment would be option C: some plants will receive no sunlight.
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
y² -5y = 750750 -y(y -5) = 0(y +25)(y -30) = 0Step-by-step explanation:
You want three equations that can be used to solve for the length (y) of a room that is whose width is 5 feet less than its length and whose area is 750 square feet.
AreaThe area of the room is the product of its length and width. We are given that the length is y, so the width is (y-5) and that product is ...
A = LW
750 = y(y -5)
This equation can be rearranged into several different forms:
y² -5y = 750 . . . . . . . multiply it out
750 -y(y -5) = 0 . . . . . subtract the right side expression
(y +25)(y -30) = 0 . . . . factor it
A survey asked 10 boys and 10 girls how many text messages they sent the previous day. The number of texts are given in the line plots.
Select from the drop-down menus to complete each statement.
The data set with the greater range is
Choose...
. The median
Choose...
.
The data set with the greater range is greater for girls. The median is greater for girls.
What is the range of a dataset?
The range of a dataset is the difference between the maximum and minimum values in the set. The median is the middle value in a sorted dataset, or the average of the two middle values if the set has an even number of elements.
To determine which dataset has a greater range, you need to compare the difference between the highest and lowest values of the two datasets.
To determine which dataset has a larger median, you need to sort the datasets and find the middle value(s).
The range for boys is 60 as for girls the range is 80. The median for boys is 90 and for girl 110.
Hence, The data set with the greater range is greater for girls. The median is greater for girls.
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Complete question:
A survey asked 10 boys and 10 girls how many text messages they sent the previous day. The number of texts is given in the line plots.
Select from the drop-down menus to complete each statement.
The data set with the greater range is __________The median________
Boys Greater for Boys
Girls Greater for Girls
Neither Same
The number line is in the attached image.
Marlo uses 252
lb of gravel to cover a garden plot of 36 ft2
How many pounds of gravel does it take to cover one square foot?
Marlo will need 7 pounds of gravel to cover one square foot if he uses 252 lb of gravel to cover a garden plot of 36 ft²
What does a pound mean?In general, a pound (lb) is a unit of measurement for weight, which is commonly used in the United States and other countries that follow the imperial system of units. 1 pound is equal to 16 ounces or approximately 0.45 kilograms. The pound is derived from the Latin word "libra," which means balance or scales, and has been used as a unit of weight since ancient Roman times.
To find out how many pounds of gravel it takes to cover one square foot, we need to divide the total amount of gravel used by the area of the garden plot:
pounds per square foot = total pounds / area
In this case, Marlo used 252 lb of gravel to cover a garden plot of 36 ft², so:
pounds per square foot = 252 lb / 36 ft²
Simplifying this expression, we get:
pounds per square foot = 7 lb/ft²
Therefore, it takes 7 pounds of gravel to cover one square foot.
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50 Points! Multiple choice algebra question. If r(x)=x^3-2x+1, find r(2a^3). Photo attached. Thank you!
Answer:
D
Step-by-step explanation:
Answer:
D. [tex]8a^{9} -4a^{3} +1[/tex]
Step-by-step explanation:
Given [tex]r(x)=x^{3} -2x+1[/tex] and find [tex]r(2a^{3} )[/tex] :
[tex]r(2a^{3} )[/tex] is the same as saying [tex]x=2a^{3}[/tex]So, we have [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1[/tex]Solve for [tex]r(2a^{3} )[/tex] :
1. [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1[/tex]
Start with simplifying [tex](2a^{3})^{3}[/tex][tex](2a^{3})^{3}=2^{3}*(a^{3})^{3}=8*a^{3*3}=8a^{9}[/tex]When you have a quantity raised to a power, or an exponent, you have to distribute the exponent to each term multiplied.When you multiply two terms that are raised to a power, you add the powers.When you divide two terms that are raised to a power, you subtract the power in the numerator from the power in the denominator.When you have a power raised to a power, you multiply the powers.2. [tex]r(2a^{3} )=8a^{9} -2(2a^{3})+1[/tex]
Simplify [tex]2(2a^{3})[/tex]Multiply two times the quantity[tex]2(2a^{3})=4a^{3}[/tex]3. [tex]r(2a^{3} )=8a^{9} -4a^{3}+1[/tex]
Answer:
So, if [tex]r(x)=x^{3} -2x+1[/tex], then [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1=8a^{9} -4a^{3}+1[/tex].
Then the answer is D. [tex]r(2a^{3} )=8a^{9} -4a^{3}+1[/tex]
4. The elevation at ground level is 0 feet. An elevator starts 80 feet below ground level. After
traveling for 20 seconds, the elevator is 30 feet below ground level. Which statement describes
the elevator's rate of change in elevation during this 20-second interval?
A. The elevator traveled upward at a rate
1 rate of 2½ feet per second.
B. The elevator traveled downward at a rate of 2 feet per second.
C. The elevator traveled upward at a rate of 4 feet per second.
D. The elevator traveled downward at a rate of 4 feet per second.
a
Answer:
[tex]m = \frac{ - 30 - ( - 80)}{20 - 0} = \frac{50}{20} = 2 \frac{1}{2} [/tex]
A. The elevator traveled upward at a rate of 2 1/2 feet per second. -30 > -80.
f(x) = 4(1+ 0.1/0.5)^0.5x is
Answer:
f(x) = 4(1.095)^x.
Step-by-step explanation:
The function f(x) = 4(1+0.1/0.5)^0.5x can be simplified using the order of operations, which is PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction).
First, we can simplify 0.1/0.5 to get 0.2.
Next, we can simplify (1 + 0.2) to get 1.2.
Then, we can simplify (1.2)^0.5 to get approximately 1.095.
Finally, we can multiply 4 by 1.095^x to get the simplified function:
What does a residual value of –0.8 mean in reference to the line of best fit?
The given point is 0.8 units above the line of best fit.
The given point is 0.8 units below the line of best fit.
The line of best fit is not appropriate to the data.
The line of best fit has a slope of 0.8.
Which equation represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page?
y = –55x + 407
y = –41x + 814
y = –38x + 922
y = –26x + 723
Answer: A residual value of –0.8 means that the given point is 0.8 units above the line of best fit.
The equation that represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page is:
y = –38x + 922.
Therefore, the answer is y = –38x + 922.
Step-by-step explanation:
Find the slope of the line tangent to the graph of the function at the given value of x.
y = x4 + 2x3 + 2x + 2 at x = -3
Answer:
To find the slope of the line tangent to the graph of the function at x = -3, we need to find the derivative of the function and evaluate it at x = -3.
First, let's find the derivative of the function y = x^4 + 2x^3 + 2x + 2:
y' = 4x^3 + 6x^2 + 2
Now, let's evaluate y' at x = -3:
y'(-3) = 4(-3)^3 + 6(-3)^2 + 2
= -108 + 54 + 2
= -52
Therefore, the slope of the line tangent to the graph of the function y = x^4 + 2x^3 + 2x + 2 at x = -3 is -52.
The equation shown is used to find the force of gravity, , between two objects, where
G is the gravitational constant,
m1 and m2 are the masses of the two objects, and
r is the distance between the two objects.
Which equation correctly shows the distance between the two objects?
Answer:
the right answer is option D
Please help with the answer!
Answer:
Step-by-step explanation:
2.1 so a
