Answer:
14
Step-by-step explanation:
To find the value of K, we need to use the remainder theorem. The remainder theorem states that if a polynomial is divided by (x - a), where a is a number, the remainder of the division will be equal to the value of the polynomial when x is equal to a. In this case, the remainder of the division is 10, so we need to find the value of the polynomial when x is equal to 1.
To find this value, we need to plug 1 into the original polynomial and evaluate it. This gives us (- 5 * 1^3 + 4 * 1^2 – 3 * 1 + K) = (- 5 + 4 – 3 + K) = (- 4 + K). Since the remainder of the division is 10, we know that (- 4 + K) = 10. This means that K = 14.
Therefore, the value of K in the original polynomial is 14.
The value of K is 14.
What is Remainder Theorem?If a polynomial function f(x) is divided by (x - c), the remainder R is given by: R = f(c)
According to the remainder theorem, if a polynomial f(x) is divided by (x - c), where c is a constant, the remainder is equal to f(c).
In this case, we know that the remainder is 10 when the expression is divided by (x - 1). So, we can substitute x = 1 into the expression and set it equal to 10 to find the value of K.
Substituting x = 1 into the expression, we get:
(-5 (1)³ + 4(1)² - 3(1) + k)= 0
-5 + 4 -3 + k = 0
k -4 = 0
k = 4
Therefore, the value of K is 14.
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farmer has 200 feet of fencing to build rectangular chicken pen along side of barn, what is largest area possible
The largest area possible is when the length and width of the chicken pen are both 100 feet. In that case, the area of the chicken pen would be 10,000 square feet.
We are given that the farmer has 200 feet of fencing to build a rectangular chicken pen along the side of a barn. We need to find the largest possible area the chicken pen can have.
To do this, we need to find the length and width of the chicken pen such that the total amount of fencing used is 200 feet.
Since the total amount of fencing needed is 200 feet, the length and width of the chicken pen must both be 100 feet. In this case, the area of the chicken pen would be 10,000 square feet.
Therefore, the largest area possible is 10,000 square feet when the length and width of the chicken pen are both 100 feet.
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Pls. Help find these answers?!
Answer:
12
Step-by-step explanation:
Answer:
1) 12 boxes
2) 3, 6, 12
3) 12
4) 110 degrees
Step-by-step explanation:
1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.
Length: 4 boxes
Width: 3 boxes
4 x 3 = 12
12 boxes
2)
10% of 30 is 0.1 times 30.
0.1 x 30 = 30/10 = 3
20% of 30 is 0.2 times 20.
0.2 x 30 = 30/5 = 6
40% of 30 is 0.4 times 20.
0.4 x 30 = 30/2.5 = 12
3) Count the cubes. Reminder there are 2 boxes you cannot see.
Top Layer: 2
Middle Layer: 4
Back Bottom Layer: 4
Front Bottom Layer: 2
2 + 4 + 4 + 2 = 12
4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.
180/18 (The angle of each section)
10
11 Sections
10 x 11 = 110
Which sets are proper subsets of set A?
A= {1,3,5,7,9}
Select all that apply
A. {1,2,3,4}
B.{9}
C.{2,4,6,8}
D.{ }
E. {1,3,5,7,9}
F. {1,5,7}
Answer:
f.[157]
Step-by-step explanation:
set A consists of odd numbers and choise F also consists of odd numbers
we are not going for choise A because 2and4are even numbers choise E is a repetition
The options D. { } and F. {1, 5, 7} are the proper subsets of set A={1, 3, 5, 7, 9}.
To determine which sets are proper subsets of set A={1, 3, 5, 7, 9}, we need to understand the definition of a proper subset. A proper subset of a set A is a subset that contains fewer elements than A but is not equal to A.
Let's evaluate each option:
A. {1, 2, 3, 4}
This set is not a proper subset of A because it contains the element 2, which is not in A.
B. {9}
This set is not a proper subset of A because it is equal to A. A proper subset should have fewer elements than the original set.
C. {2, 4, 6, 8}
This set is not a proper subset of A because it does not have any elements in common with A.
D. { }
This set is a proper subset of A since it contains no elements, and it is always a subset of any set, including A.
E. {1, 3, 5, 7, 9}
This set is not a proper subset of A because it is equal to A, and we are looking for subsets with fewer elements.
F. {1, 5, 7}
This set is a proper subset of A since it contains fewer elements than A but is not equal to A.
Correct answers:
D. { }
F. {1, 5, 7}
So, options D and F are the proper subsets of set A={1, 3, 5, 7, 9}.
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What is the equation, in slope-intercept form, for a line that passes through the point (9,2) and (3, -2)
A: y = 2/3 x - 4
B: y = - 2/3 x - 4
C: y = 3/2 x + 4
D: y = - 3/2 x + 4
Answer: The answer is therefore (B) y = - 2/3 x - 4.
Step-by-step explanation: To find the equation of the line in slope-intercept form, we can use the point-slope form of a line:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
In this case, we are given the points (9,2) and (3,-2). We can use either point as (x1, y1), but let's use (9,2) as the point. The slope of the line is the difference in y-values divided by the difference in x-values:
m = (y2 - y1) / (x2 - x1) = (-2 - 2) / (3 - 9) = -4/6 = -2/3
Substituting this value for m and the coordinates of (9,2) for (x1, y1) into the point-slope form of a line, we get:
y - 2 = -2/3(x - 9)
Distributing the -2/3 on the right side, we get:
y - 2 = -2/3x + 6
Adding 2 to both sides, we get:
y = -2/3x + 8
This is the equation of the line in slope-intercept form. The answer is therefore (B) y = - 2/3 x - 4.
question 12 (essay worth 10 points) (05.04, 05.05 hc) let x equals negative 31 times pi over 6 period part a: determine the reference angle of x. (4 points) part b: find the exact values of sin x, tan x, and sec x in simplest form. (6 points)
Part A: The stated values is; x = 31π/6
A circle has 360 degrees. We must decrease the present angle to an angle between 0° and 360° in order to determine the reference angle.
As, 360° = 2π radians, subtract 2π = 12π/6 radians for each iteration.
Iteration 1 => 31π/6 - 12π/6 = 19π/6
Iteration 2 => 19π/6 - 12π/6 = 7π/6
0 ≤ 7π/6 ≤ 12π/6
Thus, reference angle is found as 7π/6 radians
Part B) The value for the sin x, tan x, and sec x.
sin (7π/6) = -1/2
tan (7π/6) = 1/√3
sec (7π/6) = 1/cos(7π/6) = -1/(√3)/2
sec (7π/6) = -2/√3
Thus, the simplest values of sin x, tan x, and sec x are found.
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The world’s largest freestanding escalator, which is located inside the CNN Center in Atlanta, Georgia, is 196 feet tall. Before visiting the escalator, Mary and Kenneth are discussing how fast they would like th escalator to rise.Mary wants the escalator to rise at 4 feet per second, and Kenneth wants the escalator to rise at 10 feet per second. Based on each persons desire, how long would it take the escalator to reach the top? Whose rate is safer? Explain
Answer:
Step-by-step explanation:
The world's largest freestanding escalator is 196 feet tall. If the escalator were to rise at 4 feet per second, it would take 49 seconds to reach the top. If it were to rise at 10 feet per second, it would take 19.6 seconds to reach the top.
if a and b are independent events with p(a) = 0.65 and p(a ∩ b) = 0.26, then, p(b) =
The chance of the event B is 0.4 when using the probability for the two independent two event formula.
In the given question, if a and b are independent events with p(a) = 0.65 and p(a ∩ b) = 0.26, then we have to find the value of p(b).
Events classified as independent do not depend on other events for their occurrence.
Event A's likelihood of happening is P(A)=0.65.
The likelihood of the two events A and B intersecting is P(A∩B)=0.26.
Given that the likelihood of the two independent events is:
P(A∩B) = P(A)⋅P(B)
Then the probability of the event B will be,
P(B) = P(A)/P(A∩B)
P(B) = 0.65/0.26
P(B) =0.4
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What is the Lcd of 11/12 and 1/2
LCD = 12
Equivalent Fractions with the LCD
11/12 = 11/12
1/2 = 6/12
Solution:
Rewriting input as fractions if necessary:
11/12, 1/2
For the denominators (12, 2) the least common multiple (LCM) is 12.
LCM(12, 2)
Therefore, the least common denominator (LCD) is 12.
Calculations to rewrite the original inputs as equivalent fractions with the LCD:
11/12 = 11/12 × 1/1 = 11/12
1/2 = 1/2 × 6/6 = 6/12
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a fruit fly population of 182 flies is in a closed container. the number of flies grows exponentially, reaching 340 in 18 days. find the doubling time (time for the population to double) to the nearest tenth of a day.
In this case, the amount of population of fruit flies doubled in 18 days, meaning the doubling time is 9.5 days.
The doubling time of a population is the amount of time it takes for a population to double in size. In this case, the population of fruit flies started at 182 individuals and grew to 340 in 18 days. To calculate the doubling time, we used the equation (182 x 2^(18/9.5)) = 340, where the 2^(18/9.5) is the exponentiation of the number of days divided by the doubling time. This equation can be rearranged to solve for the doubling time, yielding a result of 9.5 days. This means that the population of fruit flies doubled in size every 9.5 days, which is the doubling time of the population.
182 x 2^(18/9.5) = 340
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the steps derek used to solve an equation are shown below.
Solve: 0.4x + 5 + 0.2x = 17
Step 1 : 0.4x + 0.2x + 5 = 17
Step 2: 0.6x + 5 = 17
Step 3: 0.6x = 12
Step 4: x = 20
Which properties justify step 1 and step 3?
The commutative property of addition justifies step 1 and the substraction of the property of equality justifies step 3.
What is the Substitution Property of Equality?
The substitution property of equality is applied by replacing a variable with a number or quantity. For example, if we have:
5x + 3 = 18, if x = 3, we can substitute x = 3 into the equation by applying the substitution property of equality as shown below:
5(3) + 3 = 18
15 + 3 = 18
18 = 18.
We have,
0.4x + 5 + 0.2x = 17
Step 1 : 0.4x + 0.2x + 5 = 17
commutative property of addition
Step 2: 0.6x + 5 = 17
Step 3: 0.6x = 12
substraction of property of equality
so, step 1 : commutative property of addition
Step 3 : substraction of property of equality
Hence, the commutative property of addition justify for step 1 and the substraction of the property of equality justify for step 3.
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Which of the following choices correctly names <1 and <8?
alternate interior angles corresponding angles
alternate exterior angles
vertical angles
Answer:B
Step-by-step explanation:
You know the slope and one point on a line that is not the y‑intercept. Why might you write the equation in point-slope form instead of slope-intercept form?
Answer:
I think either way is correct.
For a point (a, b), and slope m:
point-slope form: y - b = m(x - a)
slope-intercept form: b = ma + c, where c is the y-intercept.
Rewrite tan 0 x csc 0 in terms of sine and cosine.
tan 0. csc 0 = ?
(Simplify your answer.)
pls help asap i can’t pass this class without passing this test
To rewrite the expression tan 0 x csc 0 in terms of sine and cosine, we can use the following trigonometric identities:
The reciprocal identity: csc 0 = 1/sin 0
The tangent identity: tan 0 = sin 0/cos 0
The Pythagorean identity: sin^2 0 + cos^2 0 = 1
Substituting these identities into the given expression, we get:
tan 0. csc 0 = (sin 0/cos 0) * (1/sin 0)
Using the reciprocal identity and the Pythagorean identity, we can simplify this expression further to get:
tan 0. csc 0 = (sin 0 * 1)/(cos 0 * sin 0)
Next, we can cancel out the sin 0 term on the numerator and denominator to get:
tan 0. csc 0 = 1/cos 0
Finally, we can use the Pythagorean identity again to rewrite the denominator as:
tan 0. csc 0 = 1/sqrt(1 - sin^2 0)
Therefore, the final simplified expression is:
tan 0. csc 0 = 1/sqrt(1 - sin^2 0)
This is the final answer.
Quadrilateral ABCD is rotated 90° clockwise to produce A'B'C'D' Is each statement true?
AB=A'B'
If AC BD, then A'C' B'D'.
m2ABC
Yes No
000
Answer:
all yes
Step-by-step explanation:
AB = A'B' → yes
If AC // BD, then A'C' // B'D' → yes
m∠ABC < m∠A'B'C → No
What is a parallelogram?A parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
We have,
Quadrilateral ABCD.
After rotation of 90 degrees, Quadrilateral A'B'C'D'.
We see that,
The side length of the quadrilateral remains the same after rotation.
The parallel sides of the quadrilateral remain the same after rotation.
The angle of the quadrilateral remains the same after rotation.
Thus,
AB = A'B'.
If AC // BD, then A'C' // B'D'.
m∠ABC = m∠A'B'C.
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cans of soda are samples to ensure proper weight. the overall average for the sample is 10 ounces. each sample contains 25 cans. the standard deviation is estimated to be 3 ounces. what are the 99.73% control limits? group of answer choices 0.000 to 7.824 5.200 to 14.800 8.602 to 11.398 none of the above 0.000 to 10.176
The 99.73% control limits are 8.602 to 11.398
The correct answer is an option (c)
In this question we have been given:
sample size = 25
mean = 10
Standard deviation = 3
We need to determine the 99.73% control limits.
We know that Confidence interval = sample mean ± margin of error
Margin of error = z* x population of standard deviation/√n
The value of z* for 99.73% confidence interval is 3.00
Margin of error = 3 × (3/√25)
Margin of error = 9/5
Margin of error = 1.8
So, the control limits would be,
upper limit = 10 + 1.8
= 11.8
And the lower limit = 10 - 1.8
= 8.2
Therefore, from given choices the control limits are 8.602 to 11.398
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Karen runs 7 miles in 60 minutes. At the same rate, how many miles would she run in 24 minutes?
Answer:
2.8 miles
Step-by-step explanation:
in 60 minutes = 7 miles
in 1 minute = 7/60 miles
In 24 minutes = 7/60 × 24
Hope this helps.
Answer: She would run 2.8 miles in 24 minutes.
Step-by-step explanation:
[tex]\frac{x}{24minues} =\frac{7miles}{60minues}[/tex]. we cross multiply it, then we got:
60x = 7(24)
60x = 168
x = 2.8 miles
can anybody explain this or tell me the answer?
The required probability of P(Girls/Sophomore) is 0.9.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Data are shown in the table, P(Girls/Sophomore) is to be determined.
In order to determine the probability of the girls over Sophommer,
From,
P(A|B) = P(A ∩ B) / P(B)
P(Girl | Sophomore ) = P(Girl ∩ Sophomore ) / P(Sophomore)
Substitute the value in the above equation,
P(Girls/Sophomore) = 9 / 10
Thus, the required probability of P(Girls/Sophomore) is 0.9.
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Kevin conducted a poll using a random sample of students at his school in order to estimate how the upcoming vote would turn out. Of his random sample of students, 72 said they would vote yes, 90 said they would vote no, and 18 were undecided. Using these observed frequencies, develop a probability model for Kevin randomly choosing one more student for the poll. Enter the probabilities as decimals.
Answer:2.4
Step-by-step explanation:
Maddox is trying to figure out which of two websites he should recommend to a friend. He wants to compare them based on customer ratings in order to make an educated recommendation. He creates a boxplot for each website with the same number of ratings.
What can Maddox conclude?
Select one:
a. Website B has a lower median rating.
b. Website A has a larger interquartile range.
c. Website B has a larger range.
d. Both websites have the same median rating.
e. Both websites have the same interquartile range.
The correct option that Maddox can conclude with is
e. Both websites have the same interquartile range.What is box plot?Statistical data based on the minimum, first quartile, median, third quartile, and maximum are shown graphically in a box plot.
The graph's appearance as a rectangle with lines extending from the top and bottom gave rise to the phrase "box plot."
How to read a box plot:Read the minimum value at the bottom of the first line.
Read the maximum value after the final line.
Read the bottom quartile, which is at the box's beginning.
Read the top quartile, which is towards the box's edge.
Read the median that coincides with the box's inside line.
The interquartile range is
= top quartile - bottom quartile
for website A
= 65 - 10
= 55
for website B
= 75 - 20
= 55
hence the both websites has same interquartile range
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of the 41 transgendered people polled 18 agreed and 4 were neutral. of the 50 non-binary people, 6 agreed and 12 were neutral. the rest disagreed with such a platform being allowed to exist in our society. the student wishes to test the hypothesis of independence using pearson's chi square test. how many degrees of freedom are there under the null hypothesis?
The observed chi square score rounded to the nearest hundredth is 31.32. So, the option D is correct.
In the given question;
Of the 47 men polled, 25 agreed and 10 were neutral.
Of the 50 women polled 14 agreed and 5 were neutral.
Of the 41 transgendered people polled 18 agreed and 4 were neutral.
Of the 50 non-binary people, 6 agreed and 12 were neutral.
The rest disagreed with such a platform being allowed to exist in our society.
We have to find how many transgendered people would be expected to disagree with such a platform being allowed to exist in our society under the null hypothesis.
We can determine the anticipated frequencies for each cell in the contingency table using the following formula:
Expected Frequencies
Agree Disagree Neutral
Men 15.5 31.5 10
Women 8.5 41.5 5
Transgender 12.5 28.5 4
Non-binary 3.5 46.5 12
The formula for Pearson's chi square test to calculate the chi square score:
Χ² = ∑(Observed - Expected)² / Expected
Χ² = [(25 - 15.5)² / 15.5] + [(14 - 8.5)² / 8.5] + [(18 - 12.5)² / 12.5] + [(6 - 3.5)² / 3.5] + [(22 - 31.5)² / 31.5] + [(36 - 41.5)² / 41.5] + [(23 - 28.5)² / 28.5] + [(44 - 46.5)² / 46.5] + [(10 - 10)² / 10] + [(5 - 5)² / 5] + [(4 - 4)² / 4] + [(12 - 12)² / 12]
Χ² = 31.32
Hence, the option D is correct.
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The right question is:
A university student wishes to explore whether GENDER (man, woman, A university student wishes to explore whether GENDER (man, woman, trans, non-binary) is associated with AGREEMENT (agree, disagree, neutral) to the existence of a social media platform that allows almost all forms of non-violent free speech, with minimal content moderation to censure only the most egregious of posts, Of the 47 men polled, 25 agreed and 10 were neutral. Of the 50 women polled 14 agreed and 5 were neutral. Of the 41 transgendered people polled 18 agreed and 4 were neutral, Of the 50 nonbinary people, 6 agreed and 12 were neutral. The rest disagreed with such a platform being allowed to exist in our society. The student wishes to test the hypothesis of independence using Pearson's chi square test. Determine the observed chi square score rounded to the nearest hundredth.
A. 0.25
B. 0.53
C. 0.54
D. 31.32
E. None of the above
A plane takes 30 seconds to fly a distance of 8 kilometres.
Work out the average speed of the plane, in miles per hour
Answer: 4.97 / 0.00833 = 597.77 miles per hour.
Step-by-step explanation:
To find the average speed of the plane in miles per hour, we first need to convert the distance the plane travels from kilometers to miles. One mile is equal to 1.609 kilometers, so 8 kilometers is equal to 8 / 1.609 = 4.97 miles.
Next, we need to convert the time the plane takes to travel this distance from seconds to hours. There are 3600 seconds in an hour, so 30 seconds is equal to 30 / 3600 = 0.00833 hours.
To find the average speed of the plane in miles per hour, we can now divide the distance the plane travels by the time it takes to travel that distance. This gives us 4.97 / 0.00833 = 597.77 miles per hour.
Last year at a certain high school, there were 80 boys on the honor roll and 88 girls on the honor roll. This year, the number of boys on the honor roll increased by 15% and the number of girls on the honor roll increased by 25%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
Answer:
0.1% of honor roll students
Step-by-step explanation:
to get the total percentage, find the boy's and girl's percentage numbers first.
15% out of 80: 0.05
25% out of 88: 0.04
0.05+0.04=0.09
the total number of honor students increased: 0.09,
round to the nearest tenth: 0.1
and the total number of honor students are: 80+88=168
0.1 is=0.06% out of 168
0.1% of honor roll students increased this year.
Tanner wants to cover a hallway in his house with carpet it cost about four dollars to cover a square foot with carpet
hope this helps
Step-by-step explanation:
Let the graph of g be a translation 2 units right followed by a horizontal shrink by a factor oft of
the graph of f(x) = x^2 + x. Write a rule g.
Answer:vertical
Step-by-step explanation:
Let h be a function defined for all x not equal to 0 such that h(4) = - 3 and the derivative of h is given by h'(x) = (x∧2 - 2)/x for all x not equal to 0.a. Find all values of x for which the graph of h has a horizontal tangent , and determine whether h has a local maximum, local minimum of neither at each of these values. Justify your answers.b. On what intervals, if any, is the graph of h concave up? Justify your answer.c. Write an equation for the line tangent to the graph of h at x = 4.d. Does the line tangent to the graph of h at x = 4 lie above or below the graph of h for x > 4? Why?
For a function h such that h(4) = -3 and h'(x) = (x² - 2)/ x for all x∈R-{0}, the function has two local minima at x = -2 and x = 2. The local maxima is not determined implying it would be at the critical value x = 0.
A graph has a horizontal tangent at a local minimum or local maximum and the slope is zero at that point. That is at points which has horizontal tangent. h'(x) = 0.
(x² - 2)/ x = 0
Thus x = 2 or x = -2
At the local minimum or local maximum, the slope is zero or tangent is horizontal as the graph change from decreasing to increasing or increasing to decreasing.
h''(x) = 1 + 2/x²
h"(2) = 1 + 2/ 4 > 0
h''(-2) = 1 + 2/ 4 > 0
Therefore at x = 2 and x = -2 we have local minimum.
The graph of h will be concave up between two local minimum. So graph is concave up in the interval -2<x<2.
Let us assume the tangent line is y = mx + c.
m = h'(4) = (4² - 2)/ 4
m = 3.5
we know h(4) = -3, that is
-3 = m×(4) + c
c = -3 - 4×3.5 = -17
Therefore the tangent line is y = 3.5x - 17.
The line tangent to the graph of h at x = 4 lie below the graph of h at x = 4 as x = 2 is a minimum and thus the slope is increasing for x>2.
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If triangle ABC, if m angle ABC and egment BF i an angle biector, find m angle BCE
In calculation, the precise bisector is a line section that separates a point into two equivalent points and parts.
The measure of P Q R is equal to the sum of ∠PQT and ∠TQR if line segment QT is the angular bisector of an angle ∠PQR.
∠PQR is equal to ∠PQT + ∠TQR.
There are three angular bisectors that can be made in a triangle, and all of them meet at the incenter of the triangle because line Q T is the angular bisector of P Q R. As a result, P Q T = T Q R.
BD divides ABC into two angles, ABD and DBC, given that line.
Additionally, given that DBC = 20 x + 16
ABD = 12 x + 24
Therefore, A B C = ABD + DBC (1) and ABD = DBC (2) respectively.
According to the second equation, 12 x + 24 = 20 x + 16 24 16 = 20 x 12 x 8 x = 8 x = 8 8 = 1
As a result, A B D = 12 (1) + 24; A B D = 36;
D B C = 20 (1) + 16; A B C = 36.
As a result of the equation (1), A B C = A B D + D B C;
A B C = 36; A B C = 72.
Therefore, ∠ABC measure 72.
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Full Question = Suppose line BD bisects ∠ABC. If m ∠ABD = 12 x + 24 and m ∠DBC = 20 x + 16, what is m ∠ABC?
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Question 13(Multiple Choice Worth 1 points)
(02.01 LC)
A linear function is shown on the graph.
A linear function beginning with closed circle at negative 4 comma 9 and ending with a closed circle at 3 comma negative 5.
What is the domain of the function?
{x | −4 ≤ x ≤ 3}
{x | −4 < x < 3}
{y | −5 ≤ y ≤ 9}
{y | −5 < y < 9}
Answer:
I believe the answer is the first one.
Step-by-step explanation:
The domain of a function is the lowest X value to the highest X value. The range of a function is the lowest Y value to the highest Y value. Since this question is asking about the domain, we can narrow down the answers to either 1, or 2 because 3 and 4 are for the range, with Y in them.
Next, we look at the points. The differences between them is that 1 has greater OR EQUAL and less than OR EQUAL, whereas 2 has just greater or less then. The circles are filled in on the graph, meaning they are closed. this means it could be equal. Since we know the equation must contain equals in it, we can eliminate 2 and 4 because they only have greater and less than signs.
This leaves the only correct answer for the domain of the graph to be 1.
The domain is the interval of x thus {x | −4 ≤ x ≤ 3} will be the domain so option (A) is correct.
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
As per the given linear function,
The domain is the set of x that the function defines.
Since (-4,9) is a closed circle so -4 will be included and (3,-5) is also a closed circle thus 3 will also be included.
So the interval will be as {x | −4 ≤ x ≤ 3}.
Hence "The domain is the interval of x thus {x | −4 ≤ x ≤ 3} will be the domain".
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Dimitri wrote the equations y = 3x and y = x + 3.
Use the drop-down menus to make true statements about the equations and the graph.
Graph of a diagonal line on a coordinate plane going up and to the left with x-axis and y-axis. Co-ordinates are (0,0) (1,3) and (2,6).
The equation
represents the graph. The point
is a point on the line that is NOT shown on the graph.
Answer:
Step-by-step explanation:
The coordinate point of intersection on the graph will be at (1.5, 4.5)
Given the equations Dimitri wrote expressd as:
y = 3x
y = x + 3
Since they are both y-values, we can equate the right hand side to have:
3x = x + 3
3x - x = 3
2x = 3
x = 3/2
x = 1.5
Get the value of y:
y = 3x
y = 3(1.5
y = 4.5
Answer:
I don't know this problem or the answer
the length of a rectangle is 7 inches more than the width. the perimeter is 38 inches. find the length and the width of the rectangle.
A rectangle's length is 7 inches longer than its width. the perimeter is 38 inches. the length is 13 inches and the width of the rectangle is 12 inches
width = (38 - 14) / 2 = 12 inches
length = (38 - 12) / 2 = 13 inches
to find the length and width of the rectangle given that the length is 7 inches more than the width, and the perimeter is 38 inches, we can use the formula for perimeter (2 x length + 2 x width = perimeter). Plugging in the values given, we get 2 x length + 2 x width = 38. Solving for width, we get width = (38 - 14) / 2 = 12 inches. Plugging this value into the original equation, we get length = (38 - 12) / 2 = 13 inches. Therefore, the length and width of the rectangle are 13 inches and 12 inches, respectively.
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Peter is mixing a small, test batch of paint to make a lavender color. He uses 3/5 qt of red, 1 qt of blue and 2/5 qt of white. He wants to make a larger batch with the same ratios using 15 qts of blue. How much red and white must he add so that the large batch is the same color as the test batch
To find the amount of red and white that Peter needs to add to the large batch, we can set up the following proportion:
(3/5 qt red) : (1 qt blue) : (2/5 qt white) = (x qt red) : (15 qt blue) : (y qt white)
The proportion states that the ratio of red to blue to white in the test batch is equal to the ratio of red to blue to white in the large batch.
Cross-multiplying and solving for x and y gives us:
(3/5)x = 15y
(2/5)y = 15x
Solving the first equation for y and substituting it into the second equation gives us:
(2/5)y = 15x
(2/5)(15x/3) = 15x
x = 9 qt
Substituting this value for x back into the first equation gives us:
(3/5)x = 15y
(3/5)(9 qt) = 15y
y = 6 qt
Therefore, Peter needs to add 9 qt of red and 6 qt of white to the large batch to make it the same color as the test batch.