To determine how the surface area of a rectangular prism changes when all dimensions are quadrupled, we need to compare the original surface area to the new surface area.
The original surface area of the rectangular prism is given by:
SA_original = 2lw + 2lh + 2wh
where l, w, and h represent the length, width, and height of the prism, respectively.
In this case, the dimensions of the original box are:
Length (l) = 3 ft
Width (w) = 6 ft
Height (h) = 5 ft
Substituting these values into the formula, we have:
SA_original = 2(3)(6) + 2(3)(5) + 2(6)(5)
= 36 + 30 + 60
= 126 square feet
Now, if we quadruple all the dimensions of the box, the new dimensions would be:
Length (l_new) = 4(3) = 12 ft
Width (w_new) = 4(6) = 24 ft
Height (h_new) = 4(5) = 20 ft
The new surface area of the enlarged box is given by:
SA_new = 2(l_new)(w_new) + 2(l_new)(h_new) + 2(w_new)(h_new)
= 2(12)(24) + 2(12)(20) + 2(24)(20)
= 576 + 480 + 960
= 2016 square feet
Comparing the original surface area (SA_original = 126 sq ft) to the new surface area (SA_new = 2016 sq ft), we can see that SA_new is 16 times greater than SA_original.
Therefore, the correct answer is:
1. The new surface area would be 16 times the original surface area.
Change 0.12 to a ratio.
Answer:
3:25
Step-by-step explanation:
The photo shows how it's solved.
Answer: 3:25
Step-by-step explanation:
Step 1) Convert the decimal number to a fraction by making 0.12 the numerator and 1 the denominator
0.12 = 0.12/1
Step 2) Multiply the numerator and denominator by 100 to eliminate the decimal point.
0.12 x 100
------------ = 12/100
1 x 100
Step 3) Simplify the fraction in the previous step by dividing the numerator and the denominator by the greatest common factor (GCF) of 12 and 100. (The GCF of 12 and 100 is 4.)
12 ÷ 4
--------- = 3/25
100 ÷ 4
Step 4) Convert the fraction in the previous step to a ratio by replacing the divider line with a colon like this:
3
25 = 3:25
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The length of the radius of the circle of equation (x + 3)² + (y - 7)² = 289 is given as follows:
b) 17.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by the equation presented as follows:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The equation for the circle in this problem is given as follows:
(x + 3)² + (y - 7)² = 289.
Hence the center and the radius are obtained as follows:
Center (-3, 7).Radius of r = 17, as 17² = 289.Hence option B is the correct option for this problem.
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Fill in the y-intercept to complete the function equation.
Answer:
y=3x+5
Step-by-step explanation:
you do 4 times 3 then subtract that from 17
What is the value of x?.
4
B
24
Q
R
15
40
C
X
1 2
The value of x would be,
⇒ x = 15
We have to given that;
A figure with QC is parallel to BR
Now, We can formulate that,
Triangle BDR and triangle CDQ are similar.
Hence, By using proportionality we get;
⇒ BD / DR = QD / CD
Substitute all the values we get;
⇒ (24 + 40) / (15 + x) = 40 / x
Solve for x,
⇒ 64 / (15 + x) = 40 / x
⇒ 64x = 40 (15 + x)
⇒ 8x = 5 (15 + x)
⇒ 8x = 45 + 5x
⇒ 8x - 5x = 45
⇒ 3x = 45
⇒ x = 15
Thus, The value of x would be,
⇒ x = 15
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100 Points! Geometry question. Photo attached. Use the Pythagorean Theorem to find x. Please show as much work as possible. Thank you!
The value of x is,
⇒ x = 21.65
We have to given that,
A right triangle is shown in image.
Since, The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Hence, We get;
⇒ 25² = 12.5² + x²
⇒ 625 = 156.25 + x²
⇒ x² = 625 - 156.25
⇒ x² = 468.75
⇒ x = 21.65
Thus, The value of x is,
⇒ x = 21.65
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a pyramid and a cone are both 10 centimeters tall and have the same volume what statement
Answer: "The pyramid and the cone have the same volume despite their different shapes."
Step-by-step explanation: If a pyramid and a cone are both 10 centimeters tall and have the same volume, then the statement that can be made is:
"The pyramid and the cone have the same volume despite their different shapes."
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Taylor recorded Weekly grocery expense for the past 16 weeks and determine the mean weekly expense was $83.20 later she discovers that one week expense of $90 was incorrectly recorded at $38. What is the mean
The mean weekly expense, after correcting the incorrectly recorded week, is $81.25.
How to solveGiven that Taylor recorded the past 16 weeks' expenses, excluding the incorrect recording of $90 as $38, we have 15 correct expense values.
Sum of correct expenses = $83.20 * 15 = $1248
Now we need to include the corrected expense of $90 instead of $38.
New sum of expenses = $1248 - $38 (incorrectly recorded) + $90 (corrected) = $1300
Finally, we calculate the mean by dividing the new sum by the total number of weeks, which is 16.
Mean weekly expense = $1300 / 16 = $81.25
Therefore, the mean weekly expense, after correcting the incorrect recording, is $81.25.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
8 feet
Step-by-step explanation:
Let b be the length of the base. Then the height is b+6 ft.
The area of the parallelogram is given by:
Area = b(b + 6) = 160
Solving for b, we get,
[tex]b^2 + 6b - 160 = 0[/tex]
Factoring the expression, we get:
(b - 8)(b + 20) = 0
Therefore, b = 8 or b = -20.
Since the base cannot be negative, b = 8.
Therefore, the length of the base of the parallelogram is 8 feet.
Given the number pattern:
20; 18: 14; 8;
a) Determine the nth term of this number pattern.
b) Determine the value of T12 in this number pattern.
c) Which term in this number pattern will have a value of - 36?
A quadratic number pattern has a second term equal to 1, a third term equal to -6 and a fifth term equal to - 14.
a) Calculate the second difference of this quadratic number pattern.
b) Hence, or otherwise, calculate the first term of this number pattern.
Answer:
[tex]\textsf{a)} \quad T_n=-n^2+n+20[/tex]
[tex]\textsf{b)} \quad T_{12}=-112[/tex]
[tex]\textsf{c)} \quad \sf 8th\;term[/tex]
a) Second difference is 2.
b) First term is 10.
Step-by-step explanation:
The given number pattern is:
20, 18, 14, 8, ...To determine the type of sequence, begin by calculating the first differences between consecutive terms:
[tex]20 \underset{-2}{\longrightarrow} 18 \underset{-4}{\longrightarrow} 14 \underset{-6}{\longrightarrow}8[/tex]
As the first differences are not the same, we need to calculate the second differences (the differences between the first differences):
[tex]-2 \underset{-2}{\longrightarrow} -4 \underset{-2}{\longrightarrow} -6[/tex]
As the second differences are the same, the sequence is quadratic and will contain an n² term.
The coefficient of the n² term is half of the second difference.
As the second difference is -2, the coefficient of the n² term is -1.
Now we need to compare -n² with the given sequence (where n is the position of the term in the sequence).
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5}n&1&2&3&4\\\cline{1-5}-n^2&-1&-4&-9&-16\\\cline{1-5}\sf operation&+21&+22&+23&+24\\\cline{1-5}\sf sequence&20&18&14&8\\\cline{1-5}\end{array}[/tex]
We can see that the algebraic operation that takes -n² to the terms of the sequence is to add (n + 20).
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5}n&1&2&3&4\\\cline{1-5}-n^2&-1&-4&-9&-16\\\cline{1-5}+n&0&-2&-6&-12\\\cline{1-5}+20&20&18&14&8\\\cline{1-5}\sf sequence&20&18&14&8\\\cline{1-5}\end{array}[/tex]
Therefore, the expression to find the the nth term of the given quadratic sequence is:
[tex]\boxed{T_n=-n^2+n+20}[/tex]
To find the value of T₁₂, substitute n = 12 into the nth term equation:
[tex]\begin{aligned}T_{12}&=-(12)^2+(12)+20\\&=-144+12+20\\&=-132+20\\&=-112\end{aligned}[/tex]
Therefore, the 12th term of the number pattern is -112.
To find the position of the term that has a value of -36, substitute Tₙ = -36 into the nth term equation and solve for n:
[tex]\begin{aligned}T_n&=-36\\-n^2+n+20&=-36\\-n^2+n+56&=0\\n^2-n-56&=0\\n^2-8n+7n-56&=0\\n(n-8)+7(n-8)&=0\\(n+7)(n-8)&=0\\\\\implies n&=-7\\\implies n&=8\end{aligned}[/tex]
As the position of the term cannot be negative, the term that has a value of -36 is the 8th term.
[tex]\hrulefill[/tex]
Given terms of a quadratic number pattern:
T₂ = 1T₃ = -6T₅ = -14We know the first differences are negative, since the difference between the second and third terms is -7. Label the unknown differences as -a, -b and -c:
[tex]T_1 \underset{-a}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-b}{\longrightarrow}T_4 \underset{-c}{\longrightarrow} -14[/tex]
From this we can create three equations:
[tex]T_1-a=1[/tex]
[tex]-6-b=T_4[/tex]
[tex]T_4-c=-14[/tex]
The second differences are the same in a quadratic sequence. Let the second difference be x. (As we don't know the sign of the second difference, keep it as positive for now).
[tex]-a \underset{+x}{\longrightarrow} -7\underset{+x}{\longrightarrow} -b \underset{+x}{\longrightarrow}-c[/tex]
From this we can create three equations:
[tex]-a+x=-7[/tex]
[tex]-7+x=-b[/tex]
[tex]-b+x=-c[/tex]
Substitute the equation for -b into the equation for -c to create an equation for -c in terms of x:
[tex]-c=(-7+x)+x[/tex]
[tex]-c=2x-7[/tex]
Substitute the equations for -b and -c (in terms of x) into the second two equations created from the first differences to create two equations for T₄ in terms of x:
[tex]\begin{aligned}-6-b&=T_4\\-6-7+x&=T_4\\T_4&=x-13\end{aligned}[/tex]
[tex]\begin{aligned}T_4-c&=-14\\T_4+2x-7&=-14\\T_4&=-2x-7\\\end{aligned}[/tex]
Solve for x by equating the two equations for T₄:
[tex]\begin{aligned}T_4&=T_4\\x-13&=-2x-7\\3x&=6\\x&=2\end{aligned}[/tex]
Therefore, the second difference is 2.
Substitute the found value of x into the equations for -a, -b and -c to find the first differences:
[tex]-a+2=-7 \implies -a=-9[/tex]
[tex]-7+2=-b \implies -b=-5[/tex]
[tex]-5+2=-c \implies -c=-3[/tex]
Therefore, the first differences are:
[tex]T_1 \underset{-9}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-5}{\longrightarrow}T_4 \underset{-3}{\longrightarrow} -14[/tex]
Finally, calculate the first term:
[tex]\begin{aligned}T_1-9&=1\\T_1&=1+9\\T_1&=10\end{aligned}[/tex]
Therefore, the first term in the number pattern is 10.
[tex]10 \underset{-9}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-5}{\longrightarrow}-11 \underset{-3}{\longrightarrow} -14[/tex]
Note: The equation for the nth term is:
[tex]\boxed{T_n=n^2-12n+21}[/tex]
(02.02 MC)
If trapezoid ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A′′′ lie?
Trapezoid formed by ordered pairs A at negative 4, 1, B at negative 3, 2, C at negative 1, 2, D at 0, 1.
(1, −1)
(−4, 1)
(1, 1)
(−4, −1)
The location of point A''' after the three transformations would be (-4, 1).
To determine the location of point A''', we need to apply the three transformations (reflection over the y-axis, reflection over the x-axis, and rotation of 180°) to point A.
When a point is reflected over the y-axis, the x-coordinate is negated while the y-coordinate remains the same.
So, the reflection of point A (-4, 1) over the y-axis would be (4, 1).
When a point is reflected over the x-axis, the y-coordinate is negated while the x-coordinate remains the same. So, the reflection of point (4, 1) over the x-axis would be (4, -1).
When a point is rotated 180°, the x-coordinate and y-coordinate are both negated. So, the rotation of point (4, -1) by 180° would be (-4, 1).
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For what value of x is the rational expression below undefined?
x-3
3+x
A. 3
OB. -1
O C. 0
OD. -3
Answer:
x= -3
Step-by-step explanation:
x-3
-----------
x+3
This expression is undefined when the denominator is zero.
x+3 =0
x= -3
Multiply the following binomials (2x - 3y)(8x - y)
Answer:
16x + [tex]3y^{2}[/tex] - 26xy
Step-by-step explanation:
PEMDAS
(2x - 3y)(8x - y)
= 16x - 2xy - 24xy + [tex]3y^{2}[/tex]
= 16x + [tex]3y^{2}[/tex] - 26xy
Please help (easy economics question)!!!
The dollar value of total revenue at each price is $[tex]0[/tex], $[tex]10[/tex], $[tex]12[/tex], $[tex]12[/tex], $[tex]10[/tex], and $[tex]6[/tex]. Total revenue will be the greatest at a price of $[tex]4[/tex], with [tex]3[/tex] units sold.
To find the dollar value of total revenue at each price, we can multiply the price by the corresponding quantity in the demand schedule:
Price: $[tex]6[/tex]
Quantity: [tex]0[/tex]
Total Revenue: $[tex]6 \times 0[/tex] = $[tex]0[/tex]
Price: $[tex]5[/tex]
Quantity: [tex]2[/tex]
Total Revenue: $[tex]5 \times 2[/tex] = $[tex]10[/tex]
Price: $[tex]4[/tex]
Quantity: [tex]3[/tex]
Total Revenue: $[tex]4 \times 3[/tex] = $[tex]12[/tex]
Price: $[tex]3[/tex]
Quantity: [tex]4[/tex]
Total Revenue: $[tex]3 \times 4[/tex] = $[tex]12[/tex]
Price: $[tex]2[/tex]
Quantity: [tex]5[/tex]
Total Revenue: $[tex]2 \times 5[/tex] = $[tex]10[/tex]
Price: $[tex]1[/tex]
Quantity: [tex]6[/tex]
Total Revenue: $[tex]1 \times 6[/tex] = $[tex]6[/tex]
To determine at which price the total revenue will be the greatest, we observe that the highest total revenue occurs at the price with the highest quantity sold. In this case, the price with the highest quantity is $[tex]3[/tex], and the corresponding quantity sold is [tex]4[/tex] units.
Therefore, at a price of $[tex]3[/tex], the total revenue will be the greatest, with [tex]4[/tex] units sold.
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For Exercises 24-29, find each value.
24. Sin x
25 cos x
26 tan x
27. Sin y
28. Cos y
29. Tan y
All the values of expressions are,
24. Sin x = 1/√17
25 cos x = 4/√17
26 tan x = 1/4
27. Sin y = 4/√17
28. Cos y = 1/√17
29. Tan y = 4
We have to given that,
A right triangle is shown in figure.
Now, We can simplify all the values,
24. Sin x = Opposite / Hypotenuse
sin x = 2 / 2√17
sin x = 1/√17
25) cos x = Base / Hypotenuse
cos x = 8 / 2√17
cos x = 4/√17
26) tan x = Opposite / Base
tan x = 2 / 8
tan x = 1/4
27. Sin y = Opposite / Hypotenuse
sin y = 8 / 2√17
sin y = 4/√17
28. Cos y = Base / Hypotenuse
cos y = 2 / 2√17
cos y = 1/√17
29. Tan y = Opposite / Base
tan y = 8 / 2
tan y = 4
Thus, All the values of expressions are,
24. Sin x = 1/√17
25. cos x = 4/√17
26. tan x = 1/4
27. Sin y = 4/√17
28. Cos y = 1/√17
29. Tan y = 4
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Graph the equation shown below by transforming the given graph of the parent
function.
Answer:
Step-by-step explanation:
it is only moving 3 to the right, so shift the green dot to (3,0)
I used desmos . com for the graph
Which of the following answers to the question below is correct (multiple answers can be chosen)?
Question: Let s(t) be the position of a moving particle at time t. Choose ALL that represent the average speed of the particle over the time interval [0,4]?
1. s(4)/4
2. s(4)-s(0)/4
3. The slope of the secant line from (0, s(0)) to (4, s(4))
4. The slope of the tangent line at (0, s(0))
Answer:
The average speed of a particle over a time interval is defined as the total distance traveled divided by the time elapsed. In this case, the average speed of the particle over the time interval [0,4] is represented by options 2 and 3. Option 2 represents the change in position over the time interval [0,4] divided by the time elapsed. Option 3 represents the slope of the secant line connecting the points (0,s(0)) and (4,s(4)), which is equivalent to the average rate of change of position over the time interval [0,4].
the correct answers are, 2 and 3
Multiplying polynomials 4n2(n2 + 5n - 8)
Answer:
4n^4 + 20n^3 - 32n^2
Step-by-step explanation:
We have to distribute 4n2 to each term.
4n2 x n2. We can multiply the two n2 together resulting in 4n^4.
Now we do 4n2 x 5n. Here we multiply 4 x 5 which equals 20. Then, we multiply the n2 and n. Which results in n^3. Now we put them together; 20n^3.
Finally, we multiply 4n2 by -8. Since 8 doesn't have any variables, we just multiply the 4 and -8. Which equals to -32, now we just combine -32 and the variable; -32n2.
Now we combine these terms together. Our final answer is, 4n^4 + 20n^3 -32n^2.
^ represents an exponent.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
B. 108 ft³
Step-by-step explanation:
solution given:
We have Volume of solid = Area of base * length
over here
base : 9ft
height : 6 ft
length : 4ft
Now
Area of base : Area of traingle:½*base*height=½*9*6=27 ft²
Now
Volume : Area of base*length
Volume: 27ft²*4ft
Therefore Volume of the solid=108 ft³
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
Step-by-step explanation:
32 60 68
What is B^2+8b+7??
Can someone explain it step by step please?
Step-by-step explanation:
B^2+8b+7 is a quadratic expression. It can be factored as (b+7)(b+1).
To factor a quadratic expression, you can use the following steps:
1. Find two numbers that add up to the coefficient of the middle term (8) and multiply to the constant term (7).
2. Write the quadratic expression as a product of two binomials, with the two numbers you found in step 1 as the coefficients of the terms in each binomial.
In this case, the two numbers that add up to 8 and multiply to 7 are 7 and 1. So, we can factor B^2+8b+7 as follows:
(b+7)(b+1)
This means that B^2+8b+7 is equal to the product of (b+7) and (b+1).
Here is a step-by-step explanation of how to factor B^2+8b+7:
1. The coefficient of the middle term is 8.
2. The constant term is 7.
3. The two numbers that add up to 8 and multiply to 7 are 7 and 1.
4. Therefore, B^2+8b+7 can be factored as (b+7)(b+1).
Two cars leave towns 850 kilometers apart at the same time and travel toward each other. One car's rate is 16 kilometers per hour less than the other's. If they meet in 5 hours, what is the rate of the slower car? Do not do any rounding.
Answer:9.5
Step-by-step explanation:
geometry worksheet find the measure of the arc or angle indicated
The value of the measure of the arc or angle indicated are,
⇒ m ∠DCE = 54°
⇒ m ∠MON = 53°
Now, We can simplify as,
4) As shown in figure,
m arc DE = 360° - (121° + 131°)
m arc DE = 360° - 252°
m arc DE = 108°
So, We get;
⇒ m ∠DCE = m DE / 2
⇒ m ∠DCE = 108 / 2
⇒ m ∠DCE = 54°
4) As shown in figure,
m arc MN = 360° - (109° + 145°)
m arc MN = 360° - 254°
m arc MN = 106°
So, We get;
⇒ m ∠MON = m MN / 2
⇒ m ∠MON = 106 / 2
⇒ m ∠MON = 53°
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which table does not show y as a function of x?
Answer:
I am confident the answer is H.
Descrive in words the rule that is used to determine the term value from its position in the sequence
The rule used to determine the term value from its position in the sequence is often referred to as the "nth term" rule.
What is the nth-term rule?The nth-term rule involves identifying a pattern or relationship between the position (n) of a term in the sequence and the value of that term.
By analyzing the pattern, such as the common difference or common ratio, the nth-term rule allows us to express the value of any term in the sequence based on its position.
This rule provides a formula or equation that relates the position of a term to its corresponding value in the sequence.
Mathematically, the rule is:
T(n) = a + (n - 1) * d
where:
T(n) represents the value of the term at position n.a represents the first term in the sequence.n represents the position or index of the term in the sequence.d represents the common difference (for arithmetic sequences) or the common ratio (for geometric sequences) between consecutive terms.More on sequence and series can be found here: https://brainly.com/question/15583579
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The length of the arc LM is 8.72 cm.
We have,
The length of an arc is the distance that runs through the curved line of the circle making up the arc.
The length of an arc is expressed as;
l = tetha/360 × 2πr
tetha = R
R = 100°
and, radius = 5 units
so, we get,
l = 100/360 × 2 × 3.14 × 5
l = 8.72 cm (1.dp)
therefore the length of the arc LM is 8.72 cm
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The centre of a circle is the point with coordinates (-1, 2)
The point A with coordinates (5, 9) lies on the circle.
Find an equation of the tangent to the circle at A.
Give your answer in the form ax + by + c = 0 where a, b and c are integers.
The equation of the tangent to the circle at point A is 6x + 7y - 93 = 0
How do we solve for the equation of the tangent to the circle?The equation of a circle in standard form is (x-h)² + (y-k)² = r²,
(h,k) is the center of the circle
r is the radius.
The radius formula ⇒ √((x₂ - x₁)² + (y₂ - y₁)²).
Here,
x₁ = -1, y₁ = 2 (center of the circle),
x₂ = 5, y₂ = 9 (point A on the circle).
∴
r = √((5 - (-1))² + (9 - 2)²) = √(36 + 49) = √85.
Now, we have the equation of the circle: (x - (-1))² + (y - 2)² = 85, or (x + 1)² + (y - 2)² = 85.
The slope of the radius from the center of the circle to point A ⇒ (y₂ - y₁) / (x₂ - x₁)
= (9 - 2) / (5 - (-1)) = 7/6.
tangent line is the negative reciprocal of the slope of the radius, ∴ -6/7.
The equation of a line in point-slope form is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.
The slope of the tangent line (m) is -6/7 and it passes through point A(5,9). Substituting these values in, it becomes
y - 9 = -6/7 (x - 5).
Multiplying every term by 7 to clear out the fraction and to have the equation in the ax + by + c = 0 form, we get:
7y - 63 = -6x + 30,
or
6x + 7y - 93 = 0.
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pedro walks at a rate of 4 miles per hour and runs at a rate of 8 miles per hour. Each Week, his exercise program requires him to cover a total fist of 20 miles with some combination of walking and/or running.
A. write an equation that represents the different amounts of time pedro can walk, x, and run, y, each week.
B. graph the equation
C. what is the y- intercept? what does this tell you?
The equation showing the problem is: 4x + 8y = 20
The graph is attached and the y intercept is (0, 2.5)
How to model the equationAssuming that:
Time spent walking x hoursTime spent running y hoursSince Pedro walks at a rate of 4 miles per hour, the distance he covers by walking would be
4x milesAlso Pedro runs at a rate of 8 miles per hour, the distance he covers by running would be
8y milesAccording to the given information, the total distance Pedro covers each week is 20 miles. Therefore, we can write the equation:
4x + 8y = 20
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What is the meaning of "The set of all functions from X to Y"?
"The set of all functions from X to Y" refers to the collection of all possible functions that can be defined from a set X to a set Y. This set is denoted as Y^X or X→Y.
Each element of the set Y^X is a function that maps each element of set X to a unique element of set Y. The notation for such a function f is f: X → Y.
Given,
f is a function from X to Y .
Note:
The cardinality (size) of the set Y^X is given by |Y^X| = |Y|^|X|. In other words, if the set X has m elements and the set Y has n elements, then the set of all functions from X to Y has n^m elements.
It is often used to describe the space of all possible solutions to a given problem or equation.
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Find the x-intercept and the y-intercept of the line below. Click on "None" if applicable.
6543/2
-24
1-3-
Answer:
x intercept at( -2)
y intercept at (4)
The x-intercept and the y-intercept are -2 and 4 respectively.
The X-intercept is the point where the line of an equation intersects the X-axis. While y-intercept is the point where the line of an equation intersects the Y-axis. Here, the X-axis is the horizontal axis, and the Y-axis is the vertical axis.
Since the given graph shows the line intersecting the X-axis i.e. the horizontal axis at -2, the x-intercept of the line would be -2. Whereas, since the line intersects the Y-axis at 4, the y-intercept is 4. The points that show these intercepts are (-2,0) for the x-intercept and (0,4) for the y-intercept.
∴ The intercepts are -2,4 respectively.
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Phil spends no more than 12 hours per week knitting. It takes him 2 hours to knit a hat and
3 hours to knit a scarf. He uses 150 yards of yarn for each hat and 400 yards of yarn for each
scarf. Which combinations of complete hats and scarves can Phil knit if he has 900 yards of yarn?
Select all of the correct answers.
A. 1 hat, 1 scarf
B. 3 hats, 2 scarves
C. 6 hats, 0 scarves
D. 4 hats, 1 scarf
E. 0 hats, 4 scarves
F. 2 hats, 1 scarf
The correct options regarding the inequality are:
A. 1 hat, 1 scarf
D. 4 hats, 1 scarf
F. 2 hats, 1 scarf
How to explain the inequalityBased on the time constraint, Phil can spend a maximum of 12 hours knitting, so we can set up the following inequality:
2h + 3s ≤ 12,
Phil can knit at most 6 hats per week, because 6 hats * 2 hours/hat = 12 hours.
Phil can knit at most 4 scarves per week, because 4 scarves * 3 hours/scarf = 12 hours.
Phil can use at most 900 yards of yarn, because he has 900 yards of yarn.
Phil can knit 1 hat and 1 scarf, because 1 hat * 150 yards/hat + 1 scarf * 400 yards/scarf = 550 yards < 900 yards.
Phil can knit 4 hats and 1 scarf, because 4 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 900 yards.
Phil can knit 2 hats and 1 scarf, because 2 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 700 yards < 900 yards.
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