A basis for the subspace of R4 defined by the equation−2x1−7x2+2x3−4x4=0 is the set of vectors {(-7/2, 1, 0, 0), (1, 0, 1, 0), (-2, 0, 0, 1)}.
A basis for the subspace of −2x1−7x2+2x3−4x4=0 can be found by solving for one of the variables in terms of the others and then finding the general solution.
First, solve for x1 in terms of the other variables:
-2x1 = 7x2 - 2x3 + 4x4
x1 = (-7/2)x2 + x3 - 2x4
Now, the general solution can be written as:
(x1, x2, x3, x4) = (-7/2)x2 + x3 - 2x4, x2, x3, x4
This can be rewritten in terms of the free variables x2, x3, and x4:
(x1, x2, x3, x4) = x2(-7/2, 1, 0, 0) + x3(1, 0, 1, 0) + x4(-2, 0, 0, 1)
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Three friends, Jessa, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned
food collection goal is represented by the expression 7x? - 4xy + 6. The friends have already collected
the following number of cans:
Jessa: 2x2
Tyree: 3x2 - 4
Ben: 3xy + 6
Part A: Write an expression to represent the amount of canned food collected so far by the three
friends. Show all your work. (5 points)
Part B: Write an expression that represents the number of cans the friends still need to collect to meet
their goal. Show all your work. (5 points)
Answer: Your welcome!
Step-by-step explanation:
Part A: 2x^2 + 3x^2 - 4 + 3xy + 6 + 6 = 7x^2 - 4xy + 6
Part B: 0 = 7x^2 - 4xy + 6 - (2x^2 + 3x^2 - 4 + 3xy + 6 + 6)
= 0 = 5x^2 - 4xy
A) The expression that represents the amount of canned food collected by the three friends is [tex]5x^2 + 3xy + 2[/tex].
B) The expression that represents the number of cans the friends still need to collect to meet their goal is [tex]2x^2 - 7xy + 4[/tex].
Given: Number of cans collected
Jessa: 2x²
Tyree: 3x² - 4
Ben: 3xy + 6
Goal : [tex](7x^2 - 4xy + 6)[/tex]
A) The total amount collected:
Total = Jessa + Tyree + Ben
= [tex]2x^2 + (3x^2 - 4) + (3xy + 6)[/tex]
= [tex]2x^2 + 3x^2 - 4 + 3xy + 6[/tex]
= [tex](2x^2 + 3x^2 + 3xy) + (-4 + 6)[/tex]
= [tex]5x^2 + 3xy + 2[/tex]
Therefore, the expression is [tex]5x^2 + 3xy + 2[/tex].
B) The number of cans the friends still need to collect to meet their goal is
Cans still needed = Goal - Total
[tex]= (7x^2 - 4xy + 6) - (5x^2 + 3xy + 2)[/tex]
[tex]= 7x^2 - 4xy + 6 - 5x^2 - 3xy - 2[/tex]
[tex]= (7x^2 - 5x^2) + (-4xy - 3xy) + (6 - 2)[/tex]
[tex]= 2x^2 - 7xy + 4[/tex]
Therefore, the expression is [tex]2x^2 - 7xy + 4[/tex].
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Find the HCF. 6. ( 26, 32 )=2 7. (32, 58 )= 8. (25, 37 )= 9. (158, 200 ) = 10. (49, 98 )=
The Answers are:
6. HCF is equal to 2
7. HCF is equal to 2
8. HCF is equal to 1
9. HCF is equal to 2
10. HCF is equal to 49
What is HCF?Highest Common Factor is the full form for this term. The highest factor that may divide two integers evenly is known as the HCF of two numbers. HCF can be assessed using two or more numbers.
To find the HCF of the following:
HCF of (26, 32):
2 | 26, 32
| 13, 16
HCF is equal to 2.
HCF of (32, 58)
2 | 32, 58
| 16, 29
HCF is equal to 2.
HCF of (25, 37)
No common divisor except 1.
HCF is equal to 1.
HCF of (158, 200)
2 | 158, 200
| 79, 100
HCF is equal to 2.
HCF of (49, 98)
49 | 49, 98
| 1, 2
HCF is equal to 49.
Hence, 6. HCF is equal to 2
7. HCF is equal to 2
8. HCF is equal to 1
9. HCF is equal to 2
10. HCF is equal to 49
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Ms. Smith wants to buy a home theater system. which is on sale for 35% off the original price of $2299. The sales tax is 6.25%
Answer:
$948.34
Step-by-step explanation:
35% = .35
.35 x $2299
= $804.65
That is the total before the sales tax and after the sale.
6.25% = .0625
.0625 x $2299
= $143.69, and because that is 6.25% of the total, it must be added onto that as tax.
That means the total is $804.65 + $143.69
= $948.34
The Parks Commision hired a landscape architect to design and construct a
quadrilateral trail that connects the four sides of an isosceles trapezoid-shaped park,
with all sides of the trail the same length. The landscape architect conjectured that if
she designs the trail in the shape of a rhombus that connects the midpoint of the
adjacent sides, the trail will satisfy the Park Commission's condition for the trail's
design. Use the information on the figure below to prove the landscape architect's
conjecture.
Since the park is isosceles trapezoid-shaped, the two sides, AB and CD, that make up the parallel sides of the trapezoid are of equal length.
What is isosceles?An isosceles triangle is a type of triangle with two sides of equal length. It has two equal angles opposite of the two equal sides, and the third angle is usually different. Isosceles triangles are named after the Greek term isoskelēs, which means “equal legs”. They are very common in geometry and are used in many applications, including architecture and engineering.
We can then use the midpoints of the adjacent sides of the trapezoid, E and F, to form a rhombus. Since the rhombus is formed from the midpoints of the two parallel sides, we know that the two sides AE and CF of the rhombus are of equal length. Similarly, the two sides BE and FD of the rhombus are also equal in length. This means that the trail, if constructed in the shape of the rhombus, will have all sides of equal length, satisfying the criteria set by the Parks Commission.
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(1 point) If the 100th term of an arithmetic sequence is 783, and its common difference is 8, then its first term a = 9 its second term Q2 = its third term az = (1 point) Express the following sum i
The first term is 9, the second term is 17, and the third term is 25.
The 100th term of an arithmetic sequence is given by the formula:
Tn = a + (n-1)d
Where Tn is the nth term, a is the first term, n is the number of terms, and d is the common difference.
In this case, the 100th term is 783, the common difference is 8, and the first term is 9.
Plugging in the values into the formula, we get:
783 = 9 + (100-1)8
Solving for the first term, we get:
783 = 9 + 792
783 = 801
a = 9
The second term, Q2, can be found by adding the common difference to the first term:
Q2 = a + d
Q2 = 9 + 8
Q2 = 17
The third term, az, can be found by adding the common difference to the second term:
az = Q2 + d
az = 17 + 8
az = 25
the first term is 9, the second term is 17, and the third term is 25.
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Write an equivalent expression to m-(8-3m) without parentheses
m - (8 - 3m)
m - 8 + 3m
m + 3m - 8
4m - 8
Answer:
Step-by-step explanation:
m-(8-3m)
m-8 + 3m
=m+3m-8
=4m-8
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The radius of this circle corresponds to the radius of the circle whose answer is x2 + y2 = 9, where the circle's centre is on the x-axis.
what is circle ?In mathematics, a circle is a geometric figure made up of all the points in a sphere that are equally spaced from the circle's centre. The radius of the circle is the distance measured from any location on the circle to its centre. The width of a circle is the distance across the circle that passes through its centre, and the circumference of a circle is the distance around the circle. The equations of circles in the coordinate plane can be used to characterise them. The equation for a circle with centre (h,k) and radius r has the following conventional form:
(x - h)² + (y - k) (y - k)² = r² where (x,y) are any location on the circle's coordinates.
given
We can begin by completing the cube to rewrite the equation in standard form:
x2 - 2x + y2 = 8
(x - 1)2 + y2 = 9
We can see from this standard shape that the circle's centre is (1, 0), which is located on the x-axis. This circular has a radius of √9 units, or 3 units. Thus, the following assertions are true:
The circular has a radius of three units.
The x-axis is where the circle's middle is located.
The radius of this circle corresponds to the radius of the circle whose answer is x2 + y2 = 9, where the circle's centre is on the x-axis.
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Joe's Plumbing Service sold 2,390 feet of 5/8-inch galvanized pipe in August. If 2,558 feet were sold in September, what is the percent increase in pipe footage sales?
7%
6.5%
14.22%
None of the above
The percent increase in pipe footage sales is approximately 7%.
To find the percent increase in pipe footage sales, use the formula:
[(New Value - Old Value)/Old Value] × 100.
In this case, the new value is the amount of pipe sold in September (2,558 feet) and the old value is the amount of pipe sold in August (2,390 feet). Plugging these values into the formula, we get:
[(2,558 - 2,390)/2,390] × 100 = [168/2,390] × 100 = 0.0703 × 100 = 7.03%
Therefore, the correct answer is 7%, which is option A. The percent increase in pipe footage sales from August to September is 7%.
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4(5x+3y) need help or get f
After factoring out, 4(5x+3y) simplifies to 20x + 12y.
What is simplification?The act of replacing a complex mathematical expression with a simpler equivalent is known as simplification (usually shorter).
An equivalent fraction is one in which the numerator and denominator are both divisible by the same non-zero number. If a fraction's numerator and denominator are both divisible by a number greater than 1, the fraction can be reduced to an equivalent fraction by reducing both its numerator and its denominator.
To simplify 4(5x+3y), we can use the distributive property of multiplication over addition:
4(5x + 3y) = 4(5x) + 4(3y)
Simplifying the multiplication:
4(5x + 3y) = 20x + 12y
Therefore, 4(5x+3y) simplifies to 20x + 12y.
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what is an equilvalent expression to 15x + 10
Answer:
5 (3x+2)
Step-by-step explanation:
Hope this helps! :)
If you have a 65 and you turn in a grade for 40% what would that grade turn into?
Please someone help I really need help
Answer: 26
Step-by-step explanation:
65x40%
calculate 65x0.4
Please give me brainliest
From the plots of porosity and permeability vs depth given in Question 2,what can you say about variability of porosity and permeability? Calculate the coefficient of variation for both porosity and permeability, For comparison, the Vdp for the plug permeability is given as 0.46 -3834 -3835 -3836 Core depth (m) -3837 -3838 -3839 -3840 10 15 25 30 20 Porosity (%) -3834 -3835 -3836 Core depth (m) -3837 -3838 -3839 -3840 0 600 100 200 300 400 500 Horizontal Permeability (mD) 4. From the plots of porosity and permeability vs depth given in Question 2,what can you say about variability of porosity and permeability? Calculate the coefficient of variation for both porosity and permeability, For comparison, the Vdp for the plug permeability is given as 0.46
The Vdp for the plug permeability is given as 0.46, which indicates that the variability of permeability in the plug is lower than that of the porosity and permeability in the core samples.
From the plots of porosity and permeability vs depth given in Question 2, we can say that both porosity and permeability have a certain degree of variability as they change with depth. However, the variability of permeability appears to be greater than that of porosity as the values of permeability change more drastically with depth compared to the values of porosity.
To calculate the coefficient of variation for both porosity and permeability, we can use the formula:
Coefficient of Variation (CV) = (Standard Deviation / Mean) * 100
For porosity:
Mean = (10 + 15 + 25 + 30 + 20) / 5 = 20
Standard Deviation = √[(10 - 20)² + (15 - 20)² + (25 - 20)² + (30 - 20)² + (20 - 20)²] / 5 = 7.07
CV = (7.07 / 20) * 100 = 35.35%
For permeability
Mean = (0 + 600 + 100 + 200 + 300 + 400 + 500) / 7 = 300
Standard Deviation = √[(0 - 300)² + (600 - 300)² + (100 - 300)² + (200 - 300)² + (300 - 300)² + (400 - 300)² + (500 - 300)²] / 7 = 200
CV = (200 / 300) * 100 = 66.67%
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You are given that the columns of A are linearly independent. Compute the least squared error solution to \( A x=b \), \[ A=\left[\begin{array}{ll} 4 & 1 \\ 5 & 1 \\ 6 & 1 \end{array}\right], x=\left[
$$x = \frac{1}{21} \begin{bmatrix} 4b_1 + 2b_2 \\ 5b_1 - b_2 \end{bmatrix}.$$
To compute the least squared error solution to \( A x=b \), we will use the formula \(x = (A^T A)^{-1} A^T b\).
In this case, \(A = \begin{bmatrix} 4 & 1 \\ 5 & 1 \\ 6 & 1 \end{bmatrix}\), so \(A^T = \begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix}\). Therefore, we have that
$$(A^T A)^{-1} A^T b = \left(\begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix} \begin{bmatrix} 4 & 1 \\ 5 & 1 \\ 6 & 1 \end{bmatrix}\right)^{-1} \begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix} b$$
From here, we can compute the inverse of the matrix \(A^T A\) to get
$$(A^T A)^{-1} = \frac{1}{21}\begin{bmatrix} -1 & 2 \\ 2 & -1 \end{bmatrix}$$
Substituting this into the equation above and multiplying through, we get
$$x = \frac{1}{21}\begin{bmatrix} -1 & 2 \\ 2 & -1 \end{bmatrix} \begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix} b = \frac{1}{21} \begin{bmatrix} 4b_1 + 2b_2 \\ 5b_1 - b_2 \end{bmatrix}$$
Therefore, the least squared error solution to \( A x=b \) is $$x = \frac{1}{21} \begin{bmatrix} 4b_1 + 2b_2 \\ 5b_1 - b_2 \end{bmatrix}.$$
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Write a general form of an explicit function for what the nth term of any arithmetic sequence would be in terms of a and d. Use the form below to write your function. Type the correct answer in the box.
The general form of an explicit function for what the nth term of any arithmetic sequence would bean = a + (n-1)*d
What is explicit function?An explicit function is a mathematical function containing only the independent variable or variables —opposed to an implicit function which is written in terms of both dependent and independent variables
The general arithmetic progression can be written as:
T₁ , T₂, T₃, T₄, ......, Tn.
Where n is any term
Now since a = 1 and d = common difference, The general arithmetic progression can be written as:
a, a+d, a+2d, a+3d, a+4d, a+(n-1)*d
Thus, the explicit function becomes a+(n-1)*d
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Tommy and Kim share some grapes in the ratio 5:6
Tommy eats half of his grapes.
Kim eats 4 more than Tommy.
They now have the same number of grapes.
How many grapes did they share to begin with?
Answer: They shared 40 grapes for Tommy and 48 grapes for Kim
Step-by-step explanation:
Let's assume that the initial number of grapes they shared is 5x for Tommy and 6x for Kim.
After Tommy eats half of his grapes, he will have 5x/2 grapes left.
Kim eats 4 more grapes than Tommy, so she will have 5x/2 + 4 grapes.
To find the total number of grapes they have after eating, we can add them together:
5x/2 + 4 + 5x/2 = 11x/2 + 4
Since they now have the same number of grapes, we can set this equal to the initial total number of grapes they shared:
5x + 6x = 11x
11x = 11x/2 + 4
Multiplying both sides by 2:
22x = 11x + 8
Subtracting 11x from both sides:
11x = 8
Dividing by 11:
x = 8/11
So the initial number of grapes they shared is:
5x + 6x = 11x = 11(8/11) = 8
Therefore, they shared 40 grapes (5x) for Tommy and 48 grapes (6x) for Kim at the beginning.
Find (fo) (fog )(x) and (gof )(x) and the domain of each. f(x)=x+1,g(x)=7x^(2)-6x-1
(fo)(fog)(x) = 7x^(2)-6x+1
(gof)(x) = 7x^(2)+8x
Domain is a real number.
The first step in finding (fo)(fog)(x) and (gof)(x) is to substitute the functions into each other. For (fo)(fog)(x), we will substitute g(x) into f(x) for x:
(fog)(x) = f(g(x))
= f(7x^(2)-6x-1)
= (7x^(2)-6x-1) + 1
= 7x^(2)-6x
Now we will substitute (fog)(x) into f(x) for x:
(fo)(fog)(x) = f((fog)(x))
= f(7x^(2)-6x)
= (7x^(2)-6x) + 1
= 7x^(2)-6x+1
For (gof)(x), we will substitute f(x) into g(x) for x:
(gof)(x) = g(f(x))
= g(x+1) = 7(x+1)^(2)-6(x+1)-1
= 7x^(2)+14x+7-6x-6-1
= 7x^(2)+8x
The domain of each function is the set of all real numbers, since there are no restrictions on the values of x. Therefore, the domain of (fo)(fog)(x) and (gof)(x) is all real numbers.
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1. The two graphs show models characterized by exponential decay representing the
area covered by two different algae blooms, in square yards, w weeks after different
chemicals were applied.
The algae bloom that is covered a larger area when the chemicals were applied is the red arrow.
The algae population that is decreasing more rapidly is the blue dot.
What is a population?A population in statistics is a group of comparable objects or occurrences that are relevant to a particular topic or experiment.
A statistical population can be a collection of real things or a hypothetical, possibly limitless collection of objects derived from experience.
It should be noted that the red arrow represents a larger area that is covered by algae.
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I need help on this asap!!
If Bici expects to produce more than 500 bikes, then they should follow the second plan, and if they expect to produce fewer than 500 bikes, then they should follow the first plan.
How to analyze the plans ?Under the first plan, the total cost to design and build a prototype bicycle is $125,000, and the combined materials and labor costs for each bike made under this plan will be $225. This means that for each bike produced, the total cost will be $125,000 + $225 = $125,225.
Under the second plan, the total cost to design and build a prototype bicycle is $100,000, and the combined materials and labor costs for each bike made under this plan will be $275. This means that for each bike produced, the total cost will be $100,000 + $275 = $100,275.
To determine which plan is more cost-effective, we need to consider the breakeven point where the costs of both plans intersect:
125, 000 + 225x = 100, 000 + 275x
50x = 25, 000
x = 500 bicylces
If Bici Bicycle Company plans to produce more than 500 bikes, then the second plan would be more cost-effective. However, if Bici plans to produce fewer than 500 bikes, then the first plan would be more cost-effective.
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100 points hurry and mark brainly
Jennifer bought three of the same shirt and paid $63 after the 30% discount. What was the original price of each shirt? Show your work or explain in words how did you get the answer.
Step-by-step explanation:
The price is $30.
please make me brainalist and keep smiling dude
Exam 1S22: Problem 5 Previous Problem Problem List Next Problem (8 points) Solve the following inequality. Write the answer in interval notation. x(x-7) x2 - 5x – 50 SO - Answer: Preview My Answers
In interval notation, the solution of the inequality is (25, ∞).
To solve the inequality x(x-7) < x^2 - 5x - 50, we can rearrange the terms and factor the quadratic expression:
x^2 - 7x < x^2 - 5x - 50
-2x < -50
x > 25
In interval notation, the solution is (25, ∞).
So, the answer is (25, ∞).
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Pls help :(
where are the vertical asymptotes for y = 7tan(0. 4x)?
Answer:
x = 3.92699081 + 7.85398163n where n is an integer
One kilogram is how many times one nanogram?
Answer:
1 trillion times larger
Step-by-step explanation:
One kilogram (kg) is equal to 1,000,000,000,000 (1 trillion) nanograms (ng).
Therefore, one kilogram is 1 trillion times larger than one nanogram.
In ΔWXY, WY is extended through point Y to point Z, m∠YWX=(3x+17) , m
Angle, when two straight lines or rays intersect at a single endpoint, then an angle is created.
What is Exterior angle?The exterior angle of a triangle equals the sum of opposite interior angles. The angle between any side of a shape and a line that extends from the next side is known as the exterior angle.
∠XYZ = ∠YWX + ∠WXY
10x - 5 = 3x + 17 + 3x + 2
10x - 5 = 6x + 19
10x - 6x = 24
4x = 24
x = 6
∠WXY = 3x + 2
= 3*6 + 2
= 20°
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What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
The area of the triangle is approximately 6.696 square feet.
What is Area of Triangle?
The area of a triangle is the amount of space enclosed by the three sides of the triangle
To find the area of a triangle with two sides and the included angle, we can use the following formula:
Area = (1/2) x a x b x sin(C)
where "a" and "b" are the lengths of the two sides and "C" is the angle between them.
Substituting the given values, we get:
Area = (1/2) x 3.2 ft x 4.7 ft x sin(62 degrees)
Using a calculator, we can evaluate sin(62 degrees) to be approximately 0.88.
So, Area = (1/2) x 3.2 ft x 4.7 ft x 0.88
= 6.696 ft²
Therefore, the area of the triangle is approximately 6.696 square feet.
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Answer:
The answer is 6.64 ft^2
Step-by-step explanation:
A biologist is trying to find the optimal salt concentration for the growth of a certain species of mollusk. She begins with a brine solution that has 10 g/L of salt and increases the concentration by 14% every day. Let C0 denote the initial concentration and Cn the concentration after n days.
Find a recursive formula for Cn. Write your answer in terms of Cn-1. You will need to use an underscore to make the subscript and parentheses to write the n-1 in the subscript.
Find the salt concentration after 11 days.
After 11 days, the concentration is __________ g/L.
After 11 days, the concentration is 42.4 g/L.
The recursive formula for Cn can be written as Cn = Cn-1 + 0.14Cn-1. This formula shows that the concentration after n days is equal to the concentration after n-1 days plus 14% of the concentration after n-1 days.
To find the salt concentration after 11 days, we can use the recursive formula and plug in the values for C0 and n.
C0 = 10 g/L
C1 = C0 + 0.14C0 = 10 + 0.14(10) = 11.4 g/L
C2 = C1 + 0.14C1 = 11.4 + 0.14(11.4) = 13 g/L
C3 = C2 + 0.14C2 = 13 + 0.14(13) = 14.8 g/L
C4 = C3 + 0.14C3 = 14.8 + 0.14(14.8) = 16.9 g/L
C5 = C4 + 0.14C4 = 16.9 + 0.14(16.9) = 19.3 g/L
C6 = C5 + 0.14C5 = 19.3 + 0.14(19.3) = 22 g/L
C7 = C6 + 0.14C6 = 22 + 0.14(22) = 25.1 g/L
C8 = C7 + 0.14C7 = 25.1 + 0.14(25.1) = 28.6 g/L
C9 = C8 + 0.14C8 = 28.6 + 0.14(28.6) = 32.6 g/L
C10 = C9 + 0.14C9 = 32.6 + 0.14(32.6) = 37.2 g/L
C11 = C10 + 0.14C10 = 37.2 + 0.14(37.2) = 42.4 g/L
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In order to solve the inequality 100 - 3x>= -50, Makayla solves the equation 100 - 3x = -50 and gets x = 50. What is the solution to the inequality?
The solution to the inequality is x <= 50. This means that any value of x less than or equal to 50 will satisfy the inequality.
To solve the inequality 100 - 3x >= -50, we want to find the values of x that satisfy this inequality.
Makayla solved the equation 100 - 3x = -50 and got x = 50. This equation is not the same as the inequality we want to solve, but we can check whether Makayla's solution is a valid solution to the inequality.
Substituting x = 50 into the inequality, we get:
100 - 3x >= -50
100 - 3(50) >= -50
100 - 150 >= -50
-50 >= -50
This is a true statement, so x = 50 is a valid solution to the inequality.
However, we also need to check whether there are any other values of x that satisfy the inequality. We can do this by rearranging the inequality to isolate x:
100 - 3x >= -50
100 + 50 >= 3x
150 >= 3x
50 >= x
Therefore, the solution to the inequality is calculated to x <= 50.
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The following figure is made of
1
11 triangle and
1
11 rectangle.
Find the area of each part of the figure and the whole figure.
Figure Area (square units)
Triangle A
Rectangle B
Whole figure
Answer:
Step-by-step explanation:
3. Find the slope of each of the lines.
4. Find the slope of the line that passes through the points: a. (−2, 3) and (0, 0) b. (2, 5) and (−2, 2)
5. Find the equation of the line parallel to the x-axis passing through the point (2, 3).
The line passes through the point (2, 3), the equation of the line is y = 3.
3. To find the slope of a line, you can use the formula slope = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
4. a. The slope of the line that passes through the points (−2, 3) and (0, 0) is (0 - 3)/(0 - (-2)) = -3/2 = -1.5.
b. The slope of the line that passes through the points (2, 5) and (−2, 2) is (2 - 5)/(-2 - 2) = -3/-4 = 0.75.
5. The equation of a line parallel to the x-axis is y = b, where b is the y-coordinate of any point on the line. Since the line passes through the point (2, 3), the equation of the line is y = 3.
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Gina buys 7 tacos for $4.20 how much does each taco cost
Answer: $29.4
Step-by-step explanation: one taco cost 4.20 so multiply the price of the tacos times the amount of tacos gina buys and you should get your answer which is 29.4
Please help! :>
Jason works at least 16 hours but not more than 24. He earns $15.00 per hour. The function f(t)=15t represents the money he earns for working t hours. What is the practical domain? What is the practical range? Show all your work!
Thanks!!
The practical range is: $76.50 ≤ f(t) ≤ $153
How to solve thisThe minimum number of hours is 5 hours, so the minimum money earned is:
minimum money = 15.30 * 5 = $76.50
The maximum number of hours is 10 hours, so the maximum money earned is:
maximum money = 15.30 * 10 = $153
2. Since the words “at least” and “not more than” are used, hence this is inclusive.
3. The practical range is: $76.50 ≤ f(t) ≤ $153
The domain is the number of hours he worked. It says that he works at least 16 hours, but not more than 24.
This means that the number of hours he worked can be any number between 16 and 24, including 16 and 24 as a possible number of hours.
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