the table shows the relationship between two variables which selection describes the relationship
Answers
Answer:
C. Decreasing; Linear.
Step-by-step explanation:
We have been given a table that shows the relationship between two variables.
Let us find slope of our given values using slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let us find rate of change for points (1,5) and (2,-1)
[tex]m=\frac{-1-5}{2-1}[/tex]
[tex]m=\frac{-6}{1}=-6[/tex]
Let us find slope for points (3,-7) and (4,-13).
[tex]m=\frac{-13--7}{4-3}[/tex]
[tex]m=\frac{-13+7}{1}[/tex]
[tex]m=\frac{-6}{1}=-6[/tex]
We can see that rate of change is constant (-6), therefore, our function is a linear function. Since slope is negative (-6) and with each increase in x, our y is decreasing, therefore, our function is decreasing.
Related Questions
Can someone pls help me. Find the illegal values of c in the multiplication statement.
Answers
Answer:
c ∈ {-7, -3, 2, 5}
Step-by-step explanation:
"Illegal" values are those values that make the expression undefined—that is, they make the denominator zero.
The denominator of the product factors as (c+7)(c-2)(c-5)(c+3), so the values of c that will make this product zero are ones that make the factors zero:
... c = -7, +2, +5, -3
_____
Comment on factoring
Each of the quadratics is factored by finding two factors of the constant whose sum is the coefficient of the linear term. You want ...
... factors of -14 = -1·14 = -2·7 . . . . that add to give +5. They are -2 and 7, so the quadratic factors as (c-2)(c+7)
... factors of -15 = 1·(-15) = 3·(-5) . . . . that add to give -2. They are 3 and -5, so the quadratic factors as (c+3)(c-5).
Joshua solved this problem. He says the answer is 489 yards. Joshua had 359 yards of his fishing line in the water. Then he reeled in 113 yards of his line from the water. How much of Joshua’s fishing line was still in the water? Solve the problem. Is Joshua’s answer reasonable?
Answers
Joshua’s answer is wrong because he did not add any more fishing line to the water.
The correct answer to the subtraction problem is 246 yards of Joshua's fishing line remaining in the water after reeling in 113 yards out of 359 yards. Joshua's initial answer of 489 yards is incorrect.
The student is asking for verification of Joshua’s solution to a subtraction problem that involves determining how much fishing line remains in the water after some has been reeled in. Joshua initially had 359 yards of line in the water and reeled in 113 yards. To find the remaining length of the line in the water, we subtract the length of the line reeled in from the initial length.
Step-by-Step Explanation
Start with the initial length of the fishing line in the water: 359 yards.
Subtract the length of the line that was reeled in: 113 yards.
Perform the subtraction: 359 yards - 113 yards = 246 yards.
So, the length of the fishing line that remained in the water was 246 yards.
Joshua’s answer of 489 yards is not reasonable because it does not reflect the correct subtraction (359 - 113 = 246). The correct answer is 246 yards still in the water.
Brenda said that the number 2 is prime because it has only two factors. Carla said that the number 2 is composite because it is even, and all even numbers are composite. Who is correct? A) Brenda is correct. B) Carla is correct. C) Both of them are correct. D) Neither of them is correct.
Answers
Answer:
a) brenda is right
Step-by-step explanation:
five prime numbers: 2, 3, 5, 7 and 11. A prime number is an integer, or whole number, that has only two factors — 1 and itself
If ∠A is complementary to ∠B, and ∠C is complementary to ∠B, what can you conclude about ∠A and ∠C?
Answers
∠A ≅ ∠C
Step-by-step explanation:Angles complementary to the same angle are congruent to each other. Angles A and C are both complementary to angle B, hence they are congruent.
If angle A is complementary to angle B, and angle C is also complementary to angle B, then angles A and C must be equal. This is because complementary angles add up to 90 degrees.
Explanation:If ∠A is complementary to ∠B, and ∠C is also complementary to ∠B, then ∠A and ∠C are equal.
Complementary angles add up to 90 degrees. This means that ∠A + ∠B = 90° and ∠C + ∠B = 90°. Therefore, if ∠B is the same in both instances, it can be deducted that ∠A = ∠C because they are both equal to the remaining measure after subtracting ∠B from 90°.
In simpler terms, if you know that two different angles are both complementary to a same angle (∠B in this case), then those two angles must be equal to each other.
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Hey conic section has the equation X+Y^2+ 12X + 8y= 48 determine the following type of conic domain and range axis of symmetry and center?
Answers
Answer:
Axis of symmetry are lines x=-6 and y=-4, center (-6,-4)
Step-by-step explanation:
Consideer the equation [tex]x^2+y^2+12x+8y=48.[/tex]
First, complete perfect squares:
[tex](x^2+12x)+(y^2+8y)=48,\\ \\(x^2+12x+36-36)+(y^2+8y+16-16)=48,\\ \\(x+6)^2+(y+4)^2-36-16=48,\\ \\(x+6)^2+(y+4)^2=100.[/tex]
This equation represents a circle with center at point (-6,-4) and radius r=10.
Axis of symmetry are lines x=-6 and y=-4 (vertical and horizontal lines passing through the center).
Travis spent 20 minutes getting ready for school in the morning. He spent 9/20 of the time eating breakfast. Write this fraction of time as a decimal
Answers
Answer:
0.45
Step-by-step explanation:
9/20=0.45
Travis spent 9/20, which in decimal form is 0.45, of his 20-minute preparation time eating breakfast, which is equivalent to 9 minutes.
Travis spent a total of 20 minutes getting ready for school. Out of this time, he spent 9/20 of it eating breakfast. To express this fraction of time as a decimal, we simply perform division: 9 divided by 20.
9 / 20 = 0.45
Therefore, Travis spent 0.45 of the 20 minutes, or 45% of his preparation time, eating breakfast. When converting this to minutes, 0.45 * 20 minutes equals 9 minutes. Thus, Travis spent 9 minutes eating breakfast.
Derrick and Mark are brothers who live in the same house. Mark is home, and Derrick is 5 mi from home. Both boys begin riding their bikes at the same time. Derrick rides directly home at a constant rate of 15 mph, and Mark rides away from home at a constant rate of 18 mph. Let d represent distance from home, and let t represent time in hours. Which system models this situation? A. d = 5 − 15t d = 18t B. d = 15 − 5t d = 18t C. d = 5 + 15t d = 18t D. d = 5 − 15t d = 5 + 18t
Answers
A. d = 5 − 15t; d = 18t
Step-by-step explanation:Derrick's distance from home is initially 5 miles and is decreasing at the rate of 15 miles per hour. His distance from home can be modeled by ...
... d = 5 - 15t . . . . . . d in miles; t in hours
Mark's distance from home is initially zero and is increasing at the rate of 18 miles per hour. His distance from home can be modeled by ...
... d = 18t . . . . . . . . . d in miles; t in hours
Together, these equations form the pair ...
d = 5 -15td = 18t_____
Comment on the equations
There is nothing in the problem statement or definition of the variables to suggest that one distance is measured in the same direction as the other, or that one value of d has any relationship to the other.
Usually, a "system of equations" expresses relationships among variables that all have the same definition with respect to some problem statement. Here, both values of d are "distance from home", but they don't necessarily have any relationship to each other. Their being the same value doesn't mean the boys have met, for example.
HELP MEEEEEEEEEEE PLEASE!
Answers
Answer:
55,900 cm²
Step-by-step explanation:
The area of a triangle is half the product of its base and height.
... A = (1/2)·b·h
... = (1/2)(430 cm)(260 cm)
... = 55,900 cm²
A painting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. The painting was enlarged by 10%. By what percent is the new frame bigger than the original frame if the width of the frame remains the same?
Answers
Answer:
8.3%
Step-by-step explanation:
4. The exchange rate of U.S. dollars to British pounds (£) is .63. You have $4000 to convert to British pounds. How many British pounds will you receive?
Answers
Answer:
£2,520
Step-by-step explanation:
The exchange rate of U.S. dollars to British pounds is .63. You have $4000 to convert to British pounds (?). 4,000 * .63 = 2,520. Therefore the amount of British pounds you will receive is: £2,520.
HURRYYY 20 PTS
Mrs. Nygaard needs 12 hours to grade all of her students’ projects. She made a chart to show how much time she could spend grading the projects during the week.
How many hours will Mrs. Nygaard need to work over the weekend to finish grading the projects?
Answers
Add all the hours together:
1 3/4 + 1 1/4 = 3 + 1 1/2 = 4 1/2 + 1 1/5
To add fractions with different denominators, find the common denominator and rewrite the fractions
Common denominator of 2 and 5 is 10
1/2 becomes 5/10
1/5 becomes 2/10
now you have 4 5/10 + 1 2/10 = 5 7/10 + 2 = 7 7/10
Now subtract that from 12:
12 - 7 7/10 = 4 3/10 hours
I'll GIVE BRAINLIEST!
y=-( (sqrt(x+2)) /(x/2-3) )^2 + 8
Find the domain and range
Answers
Domain
The argument of the square root function must be non-negative, so ...
... x+2 ≥ 0
... x ≥ -2
The denominator cannot be zero, so there is a disallowed value of x at ...
... x/2 -3 = 0
... x/2 = 3
... x = 6 . . . . . . . . . excluded from the domain
Range
The value of the expression is 8 for x=-2. As x approaches 6, the value of y approaches -∞.
Because the denominator is squared (has an even exponent), the sign does not change as x crosses 6, so function values increase from -∞ toward the horizontal asymptote at y=8.
Thus the range is (-∞, 8].
He daily milk production of guernsey cows is approximately normally distributed with a mean of 35 kg/day and a standard deviation of 6 kg/day. the producer is concerned when the mild production of a cow falls below the 5th percentile because the animal may be ill. the 5th percentile (in kg) of the daily milk production is approximatley:
Answers
Answer:
25.1 kg
Step-by-step explanation:
A suitable probability calculator can tell you the 5th percentile of this distribution.
A rock is pushed out of a six-story window that is 60 feet above the ground. What energy changes occur as the rock falls to the ground?
A)
The potential energy of the rock is destroyed as it falls.
B)
The potential energy of the rock is transformed into kinetic energy.
C)
The kinetic energy of the rock is transformed into potential energy.
Answers
Answer:
B) The potential energy of the rock is transformed into kinetic energy.
Step-by-step explanation:
Our understanding of Physics tells you the potential energy due to the rock's position in the gravitational field is transformed into kinetic energy as the rock gains speed (and loses height).
_____
Comment on the problem
There are additional effects not accounted for by this simplified answer, including thermal effects, radiation effects, and sound effects. (In this new age, there can also be energetic effects in dimensions we're not accustomed to considering, including emotional or other effects on—or due to—consciousness.)
Answer B)it goes from being still to moving
Zoe found a sweatshirt that she wanted at jcpenny when she went shopping the other day. it was 30% off. what was the original cost if the sale price was 21$
Answers
The sale price was 30% off the original price, which means it was on sale for 70% of the original cost ( 100% - 30% = 70%)
To find the original cost, divide the sale price by the percent of the original cost:
21 / 0.70 = 30
The original price was $30
check:
30 x 0.3 = 9 ( amount of discount)
30 - 9 = 21 ( sale price)
Final answer:
To find the original price of the sweatshirt that Zoe found, which was sold at a 30% discount, we use the sale price of $21 to calculate that the original price was $30 by dividing by 0.70. An example with sales tax involves an $85 jacket with 7.5% tax, where sales tax is rounded to $6.38 and added to the original price for a total of $91.38.
Explanation:
To determine the original cost of the sweatshirt that Zoe found, which was discounted by 30%, we need to work backwards from the sale price. The sale price represents 70% of the original cost since the item is 30% off. If the sale price is $21, we can set up the equation 0.70 * original price = $21 to find the original price.
Dividing both sides of the equation by 0.70 gives us the original price. Therefore, original price = $21 / 0.70. After performing this calculation, we find that the original cost of the sweatshirt was $30
Emily bought a jacket for $85. If the sales tax is 7.5%, the amount of sales tax would be calculated as 0.075 * $85, which equals $6.375. To get the total cost, we would round $6.375 to the nearest penny to get $6.38, and then add it to the original price of the jacket. The total cost is $85 + $6.38 = $91.38.
HELP WITH ONE PLEASE!
Amy can ride her bike 4 miles in 30 minutes. Sebastian can ride his bike 3 miles in 24 minutes. At her
24
current rate, what is the distance, in miles, Amy can ride her bike in 12 minutes?
(A) 1.6
(B) 2.5
(C) 3.0
(D) 9.0
Sally drives 66 miles in 3 hours and Molly drives 72 miles in 4 hours. What is the difference between
23
their average speeds, in miles per hour?
(A) 4
(B) 6
(C) 18
(D) 22
Answers
24. (A) 1.6
23. (A) 4
Step-by-step explanation:24.Amy's distance is proportional to the time spent riding, so in 12/30 of the time (12 minutes out of 30 minutes), she will ride 12/30 of the distance:
... (12/30)·(4 mi) = 48/30 mi = 1.6 mi
23.Sally's speed is (66 mi)/(3 h) = 22 mi/h. Molly's speed is (72 mi)/(4 h) = 18 mi/h.
The difference between their speeds is (22 -18) mi/h. = 4 mi/h.
Final answer:
A) 1.6 and A)4
Amy can ride her bike 1.6 miles in 12 minutes, and the difference in average speed between Sally and Molly is 4 mph.
Explanation:
To find the distance Amy can travel in 12 minutes, first determine her speed in miles per minute. Since Amy can ride her bike 4 miles in 30 minutes, her speed is 4 miles / 30 minutes = 0.1333 miles/minute. To find out how far she can go in 12 minutes, multiply her speed by the time: 0.1333 miles/minute x 12 minutes = 1.6 miles. Therefore, Amy can ride 1.6 miles in 12 minutes, which corresponds to answer choice (A).
Calculating the Difference in Average Speed
Sally's average speed is 66 miles / 3 hours = 22 mph, and Molly's average speed is 72 miles / 4 hours = 18 mph. The difference in their average speeds is 22 mph - 18 mph = 4 mph, which corresponds to answer choice (A).
A jacket is on sale for $68.00. There is 5% sales tax on the purchase. What is the total cost, including tax?
Answers
Answer:71.4
Step-by-step explanation:
Cameron is going to the carnival. The price of admission to the carnival is $6.50, and each ride costs an additional 0.75 cents. If Cameron can spend at most $20.00 at the carnival, which inequality represents all the possible values of r rides Cameron can go on? A) 0.75 + 6.50r ≤ 20.00 B) 0.75 + 6.50r ≥ 20.00 C) 6.50 + 0.75r ≤ 20.00 D) 6.50 + 0.75r ≥ 20.00
Answers
r = the number of rides
0.75r + 6.50 ≤ 20.00
[They charge $0.75 per ride (r) plus an admission fee of $6.50, and he can spend at most (maximum) $20. This means that he can spend $20 or less]
Your answer is C
Answer:
Option C is the correct answer.
Step-by-step explanation:
The price of admission to the carnival is $6.50.
Cost per ride = 0.75
Money Cameron having = 20 $
Let the number of rides be r, he cannot spend more than 20 $
That is
6.50 + 0.75 r ≤ 20.00
Option C is the correct answer.
Which of the following expressions are polynomials and which are not (why?)
1/x^3 +x^2
Answers
Answer:
none shown
Step-by-step explanation:
1/x^3 = x^(-3) has a negative exponent. It does not match the requirement that exponents be a non-negative integer. Therefore, any expression containing 1/x^3 will not be a polynomial.
The sum of the digits of a two-digit number is 12. The number with the digits reversed is 15 times the original tens' digit. Find the original number.
I don't need the answer, just the equations! Thanks!
Answers
[tex]a-digit\ of\ tens\\b-digit\ of\ ones\\10a+b-the\ number\\10b+a-the\ number\ with\ reversed\ digits\\\\\left\{\begin{array}{ccc}a+b=12&\to b=12-a\\10b+a=15(10a+b)\end{array}\right\\\\\text{Substitute}\\\\10(12-a)+a=15(10a+12-a)\\10(12-a)+a=15(9a+12)\qquad\text{use distributive property}\\(10)(12)+(10)(-a)+a=(15)(9a)+(15)(12)\\120-10a+a=135a+180\\120-9a=135a+180\qquad\text{subtract 120 from both sides}\\-9a=135a+60\qquad\text{subtract 135a from both sides}\\-144a=60\qquad\text{divide both sides by (-144)}\\\\a=-\dfrac{60}{144}[/tex]
a is negative and it's not a digit.
Conclusion: Such a number does not exist.Donovan eats 2 granola bars and drinks 1 glass of orange juice for breakfast every day. The price of a granola bar is B dollars and the price of a glass of orange juice is J dollars. The expression 7(2B+J) describes how much Donovan spends on breakfast in one week. What does 2B represent in the expression?
Answers
Answer:
# of granola bars and it's cost.
Step-by-step explanation:
It is asking for the meaning of 2B. Note that inside the question, it states that:
"The price of a granola bar is B dollars".
It also states that:
"Donovan eats 2 granola bars".
This means that to solve for the total spent on granola bars, you multiply the price (B) with the amount gotten (2 in this case).
~
Answer:
2B
Step-by-step explanation:
Means the amount Donovan spends on granola bars each day. Since he has 2 granola bars and the price is B dollars.
The Total bill for a dinner, before tax, is $40.00. If you leave a 15% tip, you will leave a tip of $?
Answers
$6.00
Step-by-step explanation:A fairly easy way to do the mental calculation of a 15% tip is to realize that ...
... 15% = 10% + (1/2)·10%
Of course, you can compute 10% by moving the decimal point 1 place left, so ...
... 10% of $40.00 = $4.00
Half that is $2.00, so the 15% tip is $4.00 +2.00 = $6.00.
To calculate the total bill including sales tax and tip, convert the percentages to decimals and multiply by the meal cost. Add the computed sales tax and tip to the original meal cost to get the total payable amount. In the example provided, the total comes to $58.90, including sales tax and tip.
The question involves calculating the total bill for a dinner, which includes the meal cost, sales tax, and tip. To solve this problem, one must perform a series of calculations:
Firstly, figure out the sales tax by converting the percentage to a decimal and multiplying it by the total cost of the meal.
Next, decide on the tip percentage, convert it to a decimal, and again multiply by the cost of the meal.
Add both the sales tax and the tip to the original cost of the meal to get the total amount to be paid at the register.
Using the provided example, if the meal cost is $47.50 and the sales tax is 6%, you would calculate the tax as follows:
0.06 x47.50 = $2.85 (sales tax)
And if they decide to leave an 18% tip:
0.18 x $47.50 = $8.55 (tip)
Finally, you add the meal cost, sales tax, and tip:
$47.50 + $2.85 + $8.55 = $58.90
The total amount to be paid at the register with a credit card is $58.90, which includes the meal cost, sales tax, and tip.
Write an expression as a monomial in a standard form:
−5x^3·y^2·5x^2·y^3
Answers
Answer:
-25x⁵y⁵
Step-by-step explanation:
Coefficients include (-5)(5) = -25
x-factors include (x^3)(x^2) = x^5
y-factors include (y^2)(y^3) = y^5
Then the product is ...
... -25x^5·y^5
Drinking 7 fluid ounces of milk provides 236.25 milligrams of calcium. How many fluid ounce of milk are required tho prove 67.5 milligrams of calcium. Round to the nearest tenth
A.1.7 fluid ounces
B.2.0 fluid ounces
C.2.5 fluid ounces
D.2.3 fluid ounces
Answers
Answer:
Option B is correct.
2.0 fluid ounces of milk are required to provide 67.5 milligrams of calcium
Step-by-step explanation:
Proportion states that the two ratios or fractions are equal.
As per the given statement: Drinking 7 fluid ounces of milk provides 236.25 milligrams of calcium.
Let x be the fluid ounce of milk.
then, by using proportion method we have;
[tex]\frac{7}{236.25} = \frac{x}{67.5}[/tex] ......[1]
Cross multiply states that an equation of fractions when each side consists of a fraction with a single denominator by multiplying the numerator of each side by the denominator of the other side and then, equating the two products obtained.
Apply cross multiply in [1];
[tex]7 \times 67.5 = 236.25 \times x[/tex]
Simplify:
[tex]472.5 = 236.25x[/tex]
Divide 236.25 we get;
[tex]x = \frac{472.5}{236.25}[/tex]
Simplify:
x = 2.0
therefore, 2.0 fluid ounces of milk are required to provide 67.5 milligrams of calcium
m∥n, m∠1 = 50°, m∠2 = 48°, and line s bisects ∠ABC. What is m∠3?
Answers
49°
Step-by-step explanation:∠DEF = ∠1 +∠2 = 50° +48° = 98°
∠ABC = ∠DEF because they are alternate exterior angles, hence congruent.
∠3 = ∠4 because they are vertical angles.
∠3 = (1/2)∠ABC = (1/2)·98° . . . . . ∠4 is half of ∠ABC
∠3 = 49°
The table shows the total distance (d), in kilometers, a bicycle traveled after t hours.
Time in hours (t) Distance in kilometers (d)
(t) (d)
0 0
1 8
2 16
Which equation shows the relationship between d and t?
d=8t
d=16t
d=t+8
d=t+16
Answers
Answer:
d = 8t
Step-by-step explanation:
Neither of the "t + ..." answers work for t=0. The d=16t answer does not work for t ≠ 0. The only choice that works for all of the table values is ...
... d = 8t
find the measure of the missing side. 7.4 3.6
Answers
Check the picture below.
The length of the missing side (the other leg) is approximately 6.47 units.
To find the measure of the missing side of a right triangle when you know the hypotenuse and one of the other sides, you can use the Pythagorean Theorem. The theorem states:
a² + b² = c²
Where:
- a and b are the lengths of the two shorter sides (legs) of the right triangle.
- c is the length of the hypotenuse.
In this case, you know the hypotenuse (c) is 7.4 and one of the legs (height, let's call it 'a') is 3.6. You want to find the length of the other leg (b).
Plug the values into the Pythagorean Theorem:
3.6² + b² = 7.4²
Solve for b:
b² = 7.4² - 3.6²
b² = 54.76 - 12.96
b² = 41.8
To find b, take the square root of both sides:
b = √41.8
b ≈ 6.47 (rounded to two decimal places)
So, the length of the missing side (the other leg) is approximately 6.47 units.
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Solve the equation for the variable. Show each step of your solution process.
Answers
Answer:
x = 12
Step-by-step explanation:
√(x + 4) - 3 = 1 Add 3 to each side
√(x + 4) = 4 Square each side
x + 4 = 16 Subtract 4 from each side
x = 12
=====
Check:
√(12 + 4) – 3 = 1
√16 – 3 = 1
4 – 3 = 1
1 = 1
Answer:
Step-by-step explanation:
We have equation
[tex]\sqrt{x+4} -3=1[/tex]
to solve for x we first add 3 to both side
[tex]\sqrt{x+4}-3+3=1+3\\\sqrt{x+4} =4[/tex]
now we need to remove square root from left side, so we square both sides
[tex]x+4=4^{2}[/tex]
[tex]x+4=16[/tex]
now we subtract 4 from both sides
[tex]x+4-4=16-4\\x=12[/tex]
A quintic polynomial has, at most, how many x-intercepts?
3
4
5
6
Answers
Answer:
5 x-intercepts at most.
Step-by-step explanation:
Polynomial function with degree of 5
End behavior: falls to the left and rises to the right OR falls to the right and rises to the left .
Can have 0,1,2,3 or 4 turning points; can have
0,1,2,3,4 or 5 x-intercepts
A quintic polynomial, which is of degree 5, can have at most 5 x-intercepts as per the Fundamental Theorem of Algebra.
Explanation:A quintic polynomial is a polynomial of degree 5. According to the Fundamental Theorem of Algebra, a polynomial of degree n will have exactly n roots, or solutions. However, not all roots necessarily represent x-intercepts, as some might be complex roots.
On a graph, x-intercepts are points where the polynomial touches or crosses the x-axis, corresponding to the real roots of the polynomial equation. So, in general, a quintic polynomial will have at most 5 x-intercepts. This is because a polynomial of degree n can intersect the x-axis at most n times.
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Someone please help I don’t understand
Answers
Answer:
D 2n+2
Step-by-step explanation:
We can check the slope of the function
m = (y2-y1)/(x2-x1)
= (10-8)/(4-3)
= 2/1
The slope is 2
We can use the point slope form of a line to calculate the equation for a line
y-y1 = m(x-x1)
y-2 = 2(x-2)
Distribute
y-6=2x-4
Add 6 to each side
y-6+6 = 2x-4+6
y = 2x+2