Final answer:
The missing length of the hypotenuse (c) in the right triangle with legs a=6 and b=8 is found using the Pythagorean theorem. By squaring both a and b, adding those squares together, and then taking the square root, we determine that c equals 10 units.
Explanation:
To find the missing length of the hypotenuse (c) of the right triangle when given the lengths of the other two sides (a and b), we can use the Pythagorean theorem. The theorem states that for a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In mathematical terms, this is represented as a² + b² = c².
Given that side a is 6 and side b is 8, we can substitute these values into the theorem's formula:
Calculate the square of a: 6² = 36.Calculate the square of b: 8² = 64.Add the squares of a and b: 36 + 64 = 100.Take the square root of the sum to find c: √100.c = 10.Therefore, the length of the hypotenuse (c) is 10 units.
The graph of f(x) is shown below has the same shape as the graph of g(x)= x^4 but is shifted 3 units to the left. What is the equation
A. Any horizontal transformations or reflections you make to y = x^4 must be contained within the parentheses.
Find the difference between (15,-17) and (-20,-5)
Answer:
37 units
Step-by-step explanation:
The horizontal distance between these two points is 35 and the vertical is 12.
Treat these distances as the lengths of the legs of a right triangle whose hypotenuse we want to determine:
d^2 = 35^2 + 12^2 = 1369, so d = the distance between these two points = d = sqrt(1369) = 37 units
The difference between the points (15,-17) and (-20,-5) is calculated by subtracting the coordinates, resulting in a difference of (35, -12).
To find the difference between the two points (15,-17) and (-20,-5), we need to subtract the coordinates of the second point from the coordinates of the first point.
For the x-coordinates: 15 - (-20) = 15 + 20 = 35
For the y-coordinates: -17 - (-5) = -17 + 5 = -12
Therefore, the difference between the two points is (35, -12).
Three 3/10 converted into a decimal
Answer:
3.3
Step-by-step explanation:
3 3/10 = 3 + 3/10 = 3 + 0.3 = 3.3
What is M
A.
42°
B.
50°
C.
58°
D.
100°
Answer:
C. 58°
Step-by-step explanation:
m∠ACB=(180-138)°
m∠B + m∠A +∠mACB =180
80+ m∠A + (180 -138) =180
80 + m∠A - 138 = 0
m∠A = 58
Answer:
C
Step-by-step explanation:
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ACD is an exterior angle of the triangle and
∠A and ∠B are the 2 opposite interior angles, hence
∠A + ∠B = 138, that is
∠A + 80 = 138 ( subtract 80 from both sides )
∠A = 58° → C
Two quadratic functions are shown.
Function 1:
f(x) = 2x2 - 8x + 1
Function 2:
x g(x)
-2 2
-1 -3
0 2
1 17
Which function has the least minimum value and what are its coordinates? (5 points)
Function 1 has the least minimum value and its coordinates are (0, 1).
Function 1 has the least minimum value and its coordinates are (2, -7).
Function 2 has the least minimum value and its coordinates are (0, 2).
Function 2 has the least minimum value and its coordinates are (-1, -3).
Answer:
Function 1 has the least minimum value and its coordinates are (2, -7).
Step-by-step explanation:
Two quadratic functions are shown.
Function 1:
[tex]f(x) = 2x^2 - 8x + 1[/tex]
Function 2:
x g(x)
-2 2
-1 -3
0 2
1 17
LEts find the vertex to get the minimum value
to get the minimum value for function 1 we use formula [tex]x=\frac{-b}{2a}[/tex]
[tex]f(x) = 2x^2 - 8x + 1[/tex], a=2, b=-8
[tex]x=\frac{-b}{2a}=\frac{8}{2(2)}=2[/tex]
when x=2, the value of [tex]f(2) = 2(2)^2 - 8(2) + 1=-7[/tex]
minimum point of function 1 is (2,-7)
For function 2, we find the minimum point using the table
minimum point of function 2 is (-1,-3)
Function 1 has the least minimum -7.
Function 1 has the least minimum value and its coordinates are (2, -7).
The true statement is (b) function 1 has the least minimum value and its coordinates are (2, -7).
The first quadratic function is given as:
[tex]f(x)= 2x^2 - 8x +1[/tex]Factor out 2 in the above equation
[tex]f(x)= 2(x^2 - 4x) +1[/tex]
Rewrite the expression in the bracket, as follows:
[tex]f(x)= 2(x^2 - 4x + 4 - 4) +1[/tex]
This gives
[tex]f(x)= 2(x^2 - 4x + 4 ) -8+1[/tex]
[tex]f(x)= 2(x^2 - 4x + 4 ) -7[/tex]
Express x^2 - 4x + 4 as a perfect square
[tex]f(x)= 2(x - 2)^2 -7[/tex]
A quadratic function is represented as:
[tex]f(x)= a(x - h)^2 +k[/tex]
Where
[tex]Vertex = (h,k)[/tex]
By comparison, we have:
[tex]Vertex = (2,-7)[/tex] --- this represents the minimum of function 1From the graph, the minimum of function 2 is:
[tex]Vertex = (-1,-3)[/tex](2,-7) is lesser than (-1,-3).
Hence, the function 1 has the least minimum value at a coordinate of (2,-7)
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Solve for x.
A.
x = 4
B.
x = 3
C.
x = 12
D.
x = 1v
Answer:
the answer is a
Step-by-step explanation:
Order the following measures from least to greatest: 0.5 m, 30 in, 1.25 ft, 17cm
Answer:
30 in, 0.5 m, 1.25 ft, 17 cm
30in, 0.5m, 1.25, 17cm
To investigate a community’s reading habits, a magazine invites readers to complete and mail in a survey. What is the sampling method?
A. Convenience Sampling
B. Systematic Sampling
C. Self-Selected Sampling
D. Random Sampling
Does the sampling method have any bias?
A. Yes, because the survey is leading. It suggests that a certain answer is wanted.
B. Yes, because the people who respond to the survey may underrepresent the number of readers in the community.
C. No, the sampling method has no bias because part of the population equally represents the entire population.
D. Yes, because the people who respond to the survey may overrepresent the number of readers in the community.
The sampling method used in this case is Self-Selected Sampling (C) and it has bias because those who respond to the survey may overrepresent the number of readers in the community.
Explanation:The sampling method used in this case is Self-Selected Sampling (C). The magazine invites readers to complete and mail in a survey, therefore the readers themselves choose whether or not to participate. There is no random selection involved in this sampling method.
The sampling method used in this case does have bias. (D) Yes, because the people who respond to the survey may overrepresent the number of readers in the community.
This is because only those who choose to respond will be included in the sample, and those who are more interested in the magazine or have strong opinions about reading may be more likely to respond.
Final answer:
The sampling method used in this situation is Convenience Sampling, and it does have bias because it may underrepresent the number of readers in the community.
Explanation:
The sampling method used in this situation is Convenience Sampling. This is because the magazine invites readers to complete and mail in a survey based on their convenience, rather than using a random or systematic method to select the sample.
The sampling method used in this situation does have bias. The correct answer is B. Yes, because the people who respond to the survey may underrepresent the number of readers in the community. This is because the sample is based on self-selection, meaning that only those who choose to respond to the survey are included. This can result in a biased sample that may not accurately represent the entire community's reading habits.
Shawn bought 8 boxes of erasers. Each of the erasers is either pink or blue. Each box has x pink erasers and y blue erasers in it. The expression shown below represents the total number of erasers Shawn bought.
8(x + y)
Which expression also represents the total number of erasers Shawn bought?
Question 7 options:
a 8x + 8y
b 8x + y
c 8xy
d 8 + x + y
Answer:
A
Step-by-step explanation:
You need to distribute the 8 to everything in the equation. You need to keep the sign in the middle. So in the end you would get 8x+8y.
Final answer:
Option a), 8x + 8y, accurately represents the total number of erasers Shawn bought since it's obtained by distributing the number of boxes, 8, to both x and y inside the parentheses.
Explanation:
The expression 8(x + y) represents the total number of erasers Shawn bought, where x is the number of pink erasers in each box and y is the number of blue erasers in each box. Since Shawn bought 8 boxes, and each box contains x pink erasers and y blue erasers, we need to multiply the sum of pink and blue erasers in one box by the number of boxes to get the total. Hence, the correct expression that also represents the total number of erasers Shawn bought is option a), 8x + 8y which is obtained by distributing the 8 to both x and y inside the parentheses.
sweet t has 1,258 staples that he will use to create art canvases. Each canvas requires 24 staples. How many canvases can he make AND how many staples will he have remaining
Answer:
He can make 52 canvases and will have 10 remaining staples
Step-by-step explanation:
1258/24=52 10/24
Answer:
52 canvases can be prepared and 10 staples will be remaining
Step-by-step explanation:
Sweet t has number of staples to create art canvases = 1258
Each canvas requires number of staples = 24
Let n canvases can be prepared by these staples.
Number of staples used in n canvases = 24n
The expression representing this process will be
24n = 1258
n = [tex]\frac{1258}{24}[/tex]
= 52.42 canvases
Staples used to prepare 52 canvases = 52 × 24
= 1248
Remaining staples = 1258 - 1248
= 10 staples
Therefore, 52 canvases can be prepared and 10 staples will be remaining.
a shopper gives a cashier $60 to pay for a $49 how much does the cashier of the shopper
Answer:
$11.00
Explanation:
$60 given - $49 order = $11 change
Answer:
It's 11 because 60-49 equals 11.
Step-by-step explanation:
One number is 5 times another number. The product of the two numbers is 245. Find the two numbers.
Let's assume the unknown number is x and as another one is 5 times the number then second number is 5x
》x × 5x = 245
》5x square =245
》x square =245÷5
》x square =49
》x=7
So 5x = 5×7=35
42x^3+35×^2-36x-30 factor
Answer:
(6x + 5)(7x² - 6)
Step-by-step explanation:
Factor the first/second and third/fourth term
42x³ + 35x² - 36x - 30
= 7x²(6x + 5) - 6(6x + 5) ← factor out (6x + 5) from each term
= (6x + 5)(7x² - 6)
Answer:
(6x+5)(7x2−6)
Step-by-step explanation:
Factor 42x3+35x2−36x−30
42x3+35x2−36x−30
=(6x+5)(7x2−6)
what is the midpoint between (-8,5) and (2,-2)
Answer:
the midpoint between (8,5) and (2,-2) is P(5,1.5)
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{2-8}{2}~~,~~\cfrac{-2+5}{2} \right)\implies \left( \cfrac{-6}{2}~,~\cfrac{3}{2} \right)\implies \left(-3~~,~~1\frac{1}{2} \right)[/tex]
Find the values for a and b that would make the equality true. 4(ax^2 -5x+3)=8x^2 +bx+12
Answer:
a 2 and b -20
Step-by-step explanation:
Answer:
a = 2 and b = -20
Step-by-step explanation:
4(ax^2 -5x+3)=8x^2 +bx+12 should be multiplied out. Next, we equate the coefficients of the several powers of x:
4ax² - 20x + 12 = 8x² + bx + 12
Then 4a = 8, so a = 2
and -20 = b
a large rectangular swimming pool is 1,000 feet long 100 feet wide and 10 feet deep how much water does the pool hold?
ANSWER
The swimming pool can hold 1,000,000 cubic feet of water.
EXPLANATION
The capacity of water the pool holds is the volume of water in the swimming pool.
The swimming pool is rectangular, therefore its volume can be calculated using the formula,
[tex]V = l \times w \times h[/tex]
where l=1000ft is the length, w=100ft is the width and h=10ft is the height of the pool.
We substitute all these values into the formula to get:
[tex]V = 1000 \times 100 \times 10 = 1000000 {ft}^{3} [/tex]
The swimming pool can hold 1,000,000 cubic feet of water.
The amount of water the pool can hold is 1,000,000 ft³.
What is the amount of water the pool can hold?In order to determine the amount of water the pool can hold, we have to determine the volume of the rectangular swimming pool. Since the swimming pool has the shape of a cuboid, the formula for the volume of a cuboid would be used.
Volume = length x width x height
1000 x 100 x 10 = 1,000,000 ft³
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The measures of three angles of a triangle are given by 4x-1,2x+1 and 6x. What is the measure of the largest angle
Answer:
The largest angle is 6x,and 6x=90
So, the measure of the largest angle is 90
Step-by-step explanation:
First, you create an equation by adding the three angles together and equal to 180,because a triangle has 180 degrees.
The result will be 15.If x=15 ,you need to plug it in.
the largest angle is 6x,So, 6.15=90
90 degrees
The problem states the measures of three angles of a triangle as 4x-1, 2x+1, and 6x. According to the basic theorem that the sum of the angles in a triangle is 180 degrees, if we add these angles together, and equate them to 180, we get the equation 4x - 1 + 2x + 1 + 6x = 180. Adding like terms simplifies this to 12x = 180, and dividing each side by 12 gives us x = 15. Therefore, the largest angle is 6x, which would be 6 * 15 = 90 degrees.
A store had 800 T-shirts in stock for a weekend sale.T-shirts are sold in packs of 4 each.During the sale,20 packs of T-shirts were sold on Saturday, and 70 more packs were sold on Sunday.
During the weekend sale, a total of 360 T-shirts were sold from the initial stock of 800 T-shirts in packs of 4. This resulted in 440 T-shirts leftover in stock after the sale.
Explanation:In the context of the store scenario, we have an initial stock of 800 T-shirts, which are sold in packs of 4 each. On Saturday, 20 packs are sold, resulting in a reduction of 20 packs times 4 shirts per pack, which equals 80 shirts. On Sunday, 70 more packs are sold, which corresponds to 70 packs times 4 shirts per pack, totaling 280 shirts sold on Sunday. Adding up the shirts sold on both days, we get 80 + 280, which equals 360 shirts sold in total during the weekend. To find the remaining stock, we subtract the total shirts sold from the initial stock: 800 shirts - 360 shirts = 440 shirts remaining after the sale.
Scott went snowboarding down a mountain. The trail was 2 miles long and took him 5 minutes to complete. If Tom snowboards three times as fast, how long would it take him to get down the mountain?
Answer:
1 minute and 40 seconds or 1 2/3 minute
Step-by-step explanation:
If it took Scott 2 miles for 5 minutes, than it took him 2.5 minutes to do 1 mile. For 3 times as fast, we need to divide by 3. 2.5/3= 5/2*1/3=5/6. It is 2 miles, so 5/6*2=10/6=5/3=1 2/3 minute. 2/3 minute=40 seconds. So, the answer is 1 minute and 40 seconds or 1 2/3 minute.
Answer:
1 minute and 40 seconds or 1 2/3 minute(s)
Step-by-step explanation:
find the length of the missing side. if necessary, round to the nearest tenth.
A. 44
B. 22
C. 15.6
D. 484
the answer to this question would be c- 15.6
Which is the approximate measure of this angle?
Answer:
120 degrees aka answer D
Step-by-step explanation:
Answer:
D. 120°.
Step-by-step explanation:
Since the angle is obtuse (greater than 90), it cannot be 30°, since 30° is an acute angle.
The angle cannot be 90° since the angle is obtuse, and red curved line is not a square.
The line would be straight if the angle was 180°, so the most reasonable answer would be D. 120°.
Choose all of the rectangular prisms that have a volume of 24
Answer:
pictures 1, 2, 4, and 6
Step-by-step explanation:
Order numbers to least to greatest 0.8,8%,18%,1/8,8/18
Answer 8%, 1/8, 18%, 8/18, 0.8
Step-by-step explanation:
0.8 = 80%
1/8 = 12.5%
8/18 = 44.4%
8% < 12.5% < 18% < 44.4% < 80%
Bob sold small and large beach umbrellas. Small ones cost $10 each and large ones cost $25 each. One afternoon Bob sold 10 umbrellas and made $190. How many of each size umbrella did he sell?
Answer:
4 Small, 6 Large
Step-by-step explanation:
We can start by finding values that would help add our two prices together.
We know that each large umbrella is $25, so if we keep adding until we can add up the umbrellas to 10, then we'll get our answer.
1 Large: $25
2 Larges: $50
3 Larges: $75
4 Larges: $100
5 Larges: $125
6 Larges: $150
Now don't forget, we need 10 umbrellas in total, and we know that we need 4 more umbrellas to get to 10, and we need 40 more dollars to get to 190.
40/10 = 4
6 Larges, 1 Small = $160
6 Larges, 2 Small = $170
6 Larges, 3 Small = $180
6 Larges, 4 Small = $190
Line AB is parallel to Line CD. Line AC and Line BD are perpendicular to Line AB and Line CD. What is the relationship between AC and BD?
Line AC and Line BD are perpendicular to each other.
Explanation:In this scenario, we have Line AB parallel to Line CD, and both Line AC and Line BD are perpendicular to Line AB and Line CD. Since two perpendicular lines intersect at a 90-degree angle, we can say that Line AC and Line BD are also perpendicular to each other. This means that Line AC forms a 90-degree angle with Line BD.
Samantha threw an apple out of a window from the tenth floor of her apartment building. The equation y = -16t2 + 120 can be used to represent the fruit's height above the ground, where t represents time, after she thew the apple. How long did it take the apple to hit the ground? Round your answer to the nearest hundredth.
Answer:
2.74
Step-by-step explanation:
The height of the apple when it hits the ground is zero
Equate to zero and solve for t
- 16t² + 120 = 0 ( subtract 120 from both sides )
- 16t² = - 120 ( divide both sides by - 16 )
t² = 7.5 ( take the square root of both sides )
t = [tex]\sqrt{7.5}[/tex] ≈ 2.74
(a-b)^2/(1/a-1/b) simplify
The solution of the expression (a-b)²/{(1/a)-(1/b)} is ab² - a²b.
What is factorization?Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.
Given:
An expression,
(a-b)²/{(1/a)-(1/b)}.
Simplifying,
(a-b)²/{(1/a)-(1/b)},
= (a-b)²/{(b-a)/ab},
= -(a-b)² (ab)/(a-b)
= -(a-b)(ab)
= ab² - a²b.
Therefore, ab² - a²b is the solution.
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Final answer:
The expression (a-b)²/(1/a-1/b) simplifies by first finding a common denominator, then multiplying to remove the fraction, resulting in the simplified form -ab(a-b).
Explanation:
To simplify the expression (a-b)²/(1/a-1/b), we can start by finding a common denominator for the terms in the denominator 1/a and 1/b. The common denominator is a × b, so we rewrite the expression as:
((a-b)²) / ((b - a) / (ab))
Now, we can simplify by multiplying both the numerator and the denominator by ab to eliminate the fraction in the denominator:
(a-b)² × (ab) / (b - a)
Note that (a - b) is equal to -(b - a), so:
(a-b)² × (ab) / -(a - b)
Because (a - b)² is (a - b) × (a - b), one (a - b) in the numerator cancels with the (a - b) in the denominator, leaving us with:
-(a - b) × (ab)
Which simplifies to:
-ab(a - b)
The total cost of 5 boxes of pasta is $13. There are 12 ounces of pasta in each box. Each box of pasta cost the same amount. What is the cost in dollars of the maximum number of boxes needed to total 48 ounces of pasta?
Answer: $10.40
Explanation:
First, find the cost of 1 box of pasta. 13/5 = 2.6, so $2.60 a box.
Next, find how many boxes there are. 48/12 = 4, so 4 boxes of pasta.
Finally, multiply 4*2.6 to get the final cost.
Angles T and U are a linear pair. Angle U measure (9x+6) and Angle T measures(6x+9). What is the value of x, in degrees?
Answer:
11 degrees.
Step-by-step explanation:
"Angles T and U are a linear pair. Angle U measure (9x+6) and Angle T measures(6x+9). What is the value of x, in degrees?"
We know that a linear pair MUST add up to 180 degrees, therefore (9x+6)+(6x+9)= 180
Now for some algebra-
(9x+6)+(6x+9)= 180
6 and nine can both be divided by 3, so we will do that for simplicity:
((9x+6)+(6x+9)= 180)/3=
(3x+2)+(2x+3)=60
We will now separate the parenthesis, as they serve no purpose anymore.
(3x+2)+(2x+3)=60
3x+2+2x+3=60
Combine terms
5x+5=60
Take away the 5 to isolate the variables
5x+5=60
-5
5x=55
Divide by 5
5x=55
/5
x=11
The value of x is 11 degrees.
The chart shows the marginal revenue of producing apple pies.
According to the chart, the marginal revenue
decreases by ten dollars as production increases.
increases by ten dollars as production increases.
falls to zero dollars as production increases.
remains the same as production increases.
Answer:
(d) remains the same as production increases
Step-by-step explanation:
All of the numbers in the Marginal Revenue column are the same. That means we can conclude marginal revenue ...
remains the same as production increases.
Answer:
(d) remains the same as production increases
Step-by-step explanation: