Answers
Answer:
C
Step-by-step explanation:
The diagonal of the square creates 2 right triangles with the diagonal as the hypotenuse.
Using Pythagoras' identity in either of the right triangles.
The square on the hypotenuse is equal to the sum of the squares of the other 2 sides.
Let x be the side of the square, then
x² + x² = 40², that is
2x² = 1600 ( divide both sides by 2 )
x² = 800 ( take the square root of both sides )
x = [tex]\sqrt{800}[/tex]
= [tex]\sqrt{100(8)}[/tex]
= = 10[tex]\sqrt{8}[/tex]
= 10 × [tex]\sqrt{4(2)}[/tex]
= 10 × 2[tex]\sqrt{2}[/tex] = 20[tex]\sqrt{2}[/tex] → C
Related Questions
A car salesman had $65,100 in sales. He earned $1,953 in commission. What percent commission did he earn. Explain your answer.
How long was the loan
Interest earned = $299
Principal = $1300
Interest rate = 7%
Answers
Answer:
1. The percent commission earned is 3%.
2. The loan period is 3.29 years.
Step-by-step explanation:
1. Salesman has $65,100 in sales. He earned $1,953 in commission.
Let the percent commission earn be x%
Therefore, x% of the sales equals $1,953
[tex]\frac{x}{100} of $65,100 = $1,953[/tex]
[tex]\frac{x}{100} * 65100 = 1953\\\frac{65100x}{100} = 1953[/tex]
We cross multiply
[tex]\frac{65100x}{100} = 1953\\65100x = 1953 * 100\\65100x = 195300[/tex]
Divide both side by the coefficient of 'x' (65100)
[tex]\frac{65100x}{65100} = \frac{195300}{65100} \\x = 3[/tex]
Therefore, the percent commission earned is 3%
2. Interest (I) = $299 Principal (P) = $1300 Rate (R) = 7%
The formula for finding interest is given as: [tex]I = \frac{PRT}{100}[/tex]
Therefore, substituting into the formula, we have:
[tex]299 = \frac{1300 * 7 * T}{100}[/tex]
We are finding the time it takes the loan to earn an interest of $299
[tex]299 = \frac{1300 * 7 * T}{100} \\299 = \frac{9100T}{100}[/tex]
We cross-multiply:
[tex]299 * 100 = 9100T\\29900 = 9100T[/tex]
Divide both side by the coefficient of T (9100)
[tex]\frac{29900}{9100} = \frac{9100T}{9100}\\T = 3.29[/tex]
Therefore, the time taken for the loan to earn such interest is approximately 3.29 years
What expression is equivalent to 2x^2+2x-4/2x^2-4x+2
Answers
You need to factor the numerator and denominator...
(2x^2+4x-2x-4)/(2x^2-2x-2x+2)
(2x(x+2)-2(x+2))/(2x(x-1)-2(x-1))
((2x-2)(x+2))/((2x-2)(x-1)) so the (2x-2)s cancel out leaving
(x+2)/(x-1)
Answer:
[tex]\large\boxed{\dfrac{2x^2+2x-4}{2x^2-4x+2}=\dfrac{x+2}{x-1}}[/tex]
Step-by-step explanation:
[tex]\dfrac{2x^2+2x-4}{2x^2-4x+2}=\dfrac{2(x^2+x-2)}{2(x^2-2x+1)}=\dfrac{x^2+x-2}{x^2-2x+1}\\\\=\dfrac{x^2+2x-x-2}{x^2-x-x+1}=\dfrac{x(x+2)-1(x+2)}{x(x-1)-1(x-1)}\\\\=\dfrac{(x+2)(x-1)}{(x-1)(x-1)}\qquad\text{cancel}\ (x-1)\\\\=\dfrac{x+2}{x-1}[/tex]
This scatter plot for a fund-raiser shows the time spent raising money for 9 student events. Noting the trend in the scatter plot, which is the most reasonable approximation of the money raised in the 11-hour fund-raiser?
Answers
Answer:
About $90, because the trend line shows that value for $11.
Step-by-step explanation:
It is the only one that shows a constant rate of change.
Answer:
the first one ( the line closest to 90)
Step-by-step explanation:
solve the system of equations below.
2 x 4 y = 10
2 x 4y = -10
A. X=3, Y=1
B. X=6, Y= -4
C. No solution
D. Infinitely many solutions
Answers
Let’s solve this. First we need to put the first equation into y=mx+b form. Let’s do this now.
First equation-
2•4y=10
*subtract 2*
4y=8
*divide 4*
y=2
Now that we know the value of y, let’s substitute that into the second equation.
2•4y= -10
2•4(2)= -10
2•8= -10
16= -10
When solved, these equations produce a result where both sides do not equal each other. 16 does not equal -10, making this have no solution.
This is your answer! Hope this helps comment below for more questions :)
The circumference of a circle is 8.97cm. Find the length of the diameter. Give your answer rounded to 2 DP. PLEASE HELP ME
Answers
Length of diameter is 2.86 cm
Solution:
Given that circumference of a circle is 8.97 cm
To find: length of diameter
We can use the formula for circumference of circle to find radius and then we can find diameter
The circumference of circle is given as:
[tex]C = 2 \pi r[/tex]
Where "r" is the radius of circle and [tex]\pi[/tex] is a constant equals to 3.14
Substituting c = 8.97 and [tex]\pi = 3.14[/tex]
[tex]8.97 = 2 \times 3.14 \times r\\\\8.97 = 6.28 \times r\\\\r = \frac{8.97}{6.28}\\\\r = 1.4283[/tex]
Thus radius of circle is 1.4283 cm
Finding diameter of circle
diameter = 2(radius)
diameter = 2(1.4283) = 2.8566
On rounding to two decimal point we get, 2.86
Thus length of diameter is 2.86 cm
What is the equation of the graph below?
y = cos(x/0.4)
y = cos(5x)
y = cos(0.4x)
Answers
Answer:
The answer is C. y=cos(0.4x)
Step-by-step explanation:
took the test
Answer: c
Step-by-step explanation:
y=cos(0.4x)
Today Robbie is carrying his history textbook and his lunch in his backpack. If the history textbook weighs 2 5/6 pounds and his lunch weighs 1 2/3 pounds, how much weight is in Robbie's backpack?
Answers
Final answer:
To find the total weight in Robbie's backpack, the weights of the history textbook (2 5/6 pounds) and lunch (1 2/3 pounds) are added, resulting in a total of 4 1/2 pounds.
Explanation:
The question involves finding the total weight of items in Robbie's backpack: a history textbook and his lunch. The history textbook weighs 2 5/6 pounds and his lunch weighs 1 2/3 pounds.
To find the total weight, we first convert the mixed numbers into improper fractions for easier addition. The history textbook's weight as an improper fraction is (2×6)+5 = 17/6 pounds. The lunch's weight is (1×3)+2 = 5/3 pounds.
Adding these two fractions gives us:
17/6 + 5/3 = 17/6 + 10/6 = 27/6 pounds
Since 27/6 simplifies to 4 1/2 pounds, the total weight in Robbie's backpack is 4 1/2 pounds.
A clothing store uses the step function f(x) to recommend jeans sizes as a function of x, a child’s height in inches. f(x) = StartLayout Enlarged left-brace 1st row 1st column 1 2nd column 40 less-than-or-equal-to x less-than 42 2nd row 1st column 2 2nd column 42 less-than-or-equal-to x less-than 44 3rd row 1st column 3 2nd column 44 less-than-or-equal-to x less-than 46 4th row 1st column 4 2nd column 46 less-than-or-equal-to x less-than 48 EndLayout According to the function, which is the height of a child who should wear size 2 jeans? 41.9 inches 42 inches 44 inches 44.1 inches
Answers
Answer: B. 42 inches
Step-by-step explanation:
Answer:
42 inches
Step-by-step explanation:
The function states in its second row that for size 2, the range of x (a child’s height in inches) is 42 ≤ x < 44. Then, the option 41.9 is incorrect because is less than 42 and x is greater-or-equal-to 42; option 44 inches is incorrect because it is equal to 44 and the equality sign is not included; option 44.1 inches is greater than 44 and x is less than 44; and option 42 inches is correct because x is greater-than-or-equal to 42, that is, the equal sign is included.
The width of a rectangle is seven meters less than the length. The perimeter is 58 meters. Find the length and width.
Answers
Width = x - 7
Perimeter = 2* length + 2* width
58 = 2x + 2(x - 7)
58 = 2x + 2x - 14
4x = 58 + 14
4x = 72
x = 18
Length = 18 inches
Width = 11 inches.
Hope this helps.
:)
The length of rectangle will be 18 meters and width of rectangle will be 11 meters.
It is given that width of a rectangle is seven meters less than the length.
If perimeter of rectangle is 58 meters then find the value of length and width.
What are the area and perimeter of a rectangle ?
The area of rectangle is A = L × B and the perimeter is 2 ( L + B ) , where ; L = length and B = width.
Let's assume the length of the rectangle is x.
The width of the rectangle will be ;
= x - 7
Also ; the perimeter of triangle is given which is equal to 58 meters.
We know that ; the perimeter of triangle is given by ;
Perimeter = 2 × ( length + width )
So ;
58 = 2 [ x + (x - 7)]
58 = 2 ( 2x - 7 )
58 = 4x - 14
or
4x = 58 + 14
4x = 72
x = 72 ÷ 4
x = 18 meters
So ;
Length = 18 meters
and
Width = 18 -7 = 11 meters
Thus , the length of rectangle will be 18 meters and width of rectangle will be 11 meters.
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A tile pattern has 5 tiles in Figure 0 and adds 7 tiles in each new figure. Write the equation of the line that represents the growth of this pattern
Answers
y = 5 + 7x
where y is the number of tiles and x is the number of the figure.
List ways to show 46 as tens and ones
Answers
Answer:
4 tens 6 ones
Step-by-step explanation:
those are the only way
The number 46 can be expressed as 4 tens and 6 ones, representing the value 40 plus 6, utilizing the powers of ten place value system.
Explanation:When expressing the number 46 in terms of tens and ones, we use the place value system which is based on powers of ten.
In this system, each place in the number represents a power of 10.
To represent 46 as tens and ones, we look for the highest power of ten that fits into the number without exceeding it.
In the case of 46, that value is 40, because 4 tens (4 x 10) equal 40, and there are 6 ones left over.
Therefore, we can say that 46 consists of 4 tens and 6 ones. This can be shown visually as:
The leader board at the Lakeside Golf Tournament shows that Mei's score is 3 and Noah's score is -6. How many more strokes did Mei take than Noah?
A. 3
B. 9
C. 10
D. 8
Part B.
Find the total score made by Mei and Noah together.
Answers
Mai take 9 more strokes than Noah.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
We have to given that;
The leader board at the Lakeside Golf Tournament shows that,
Mei's score is 3 and Noah's score is -6.
Now,
Since, Mei's score is 3 and Noah's score is -6.
Hence, The number of more scores of Mei's than Noah is,
⇒ 3 - (-6)
⇒ 3 + 6
⇒ 9
Thus, Mei take 9 strokes more than Noah.
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For all values of x, which expression is equivalent to 2x + 5 − x + 3x + x − 2?
Answers
Answer:
5x + 3
Step-by-step explanation:
1) Collect like terms.
(2x − x + 3x + x) + (5 − 2)
2) Simplify
5 x + 3
Answer:
D.) hope this help if i don´t then o well
Step-by-step explanation:
A teacher gave a math test to 48 students. The five-number summary of the test scores is shown.
Answers
Answer:
Its 24 and 12
Step-by-step explanation:
Answer:
He's right
Step-by-step explanation:
What is the reason for the last step in the argument?
A) division
B) addition
C) subtraction
D) symmetric property
Answers
Answer:
A) division
Step-by-step explanation:
4x=-4
4x/4=-4/4 (dividing by 4 on both sides)
x=-1
Use the following figure to answer the question
∠ 1 and ∠ 3 are vertical angles.
True
False
Answers
Answer:
True
Step-by-step explanation:
1 and 3 are vertical angles
Answer: False
<1 and <3 are Supplementary Angles
Step-by-step explanation:
what is the area of a 70 mm circle
Answers
Answer:
The area of the circle is 3,8550 mm
Step-by-step explanation:
Diameter (d) = 70 mm
Radius (r) = (70/2) mm = 35mm
Π = 22/7
Area of circle x = πr^2
= 22/7 x 35^2
= 22/7 x 1225
= 26,950/7
= 3,850 mm
May someone please help me?
Answers
Answer:
grapes cost $1.25 per pound
blueberries cost $4 per pound
Step-by-step explanation:
We have two unknowns, the cost of grapes and the cost of blueberries.
I'll call grape g and blueberries b.
since 21lb grapes and 44lb of blueberry cost $202.25, we can set up our first equation.
21g + 44b = 202.25
and the question also said 30lb grape and 22lb blueberries cost $125.50, we can set up our second equation.
30g + 22b = 125.5
now that we have two equations, you can use any methods you want to solve for the variable. I'm gonna use elimination.
21g + 44b = 202.25
-2(30g + 22b = 125.50)
━━━━━━━━━━
-39g = -48.75
g = 48.75/39
g = 1.25, grapes cost $1.25 per pound
now use substitution to find the cost of blueberries. you know the value of g now so plug it back in to one of the equation.
21g + 44b = 202.25
21(1.25) + 44b = 202.25
26.25 + 44b = 202.25
44b = 176
b = 4 , blueberries cost $4 per pound
Round 1.143 to the nearest hundredth
Answers
Answer:
1.14
Step-by-step explanation:
hundreth = 0.01
so we ignore the 3 because it is in teh thousandths
hope this helps :)
1.14
(02.03) The table below shows two equations: Equation 1 |3x − 1| + 7 = 2 Equation 2 |2x + 1| + 4 = 3 Which statement is true about the solution to the two equations? Equation 1 and equation 2 have no solutions.
Answers
Answer:
We can say that equations 1 and 2 have no solutions.
Step-by-step explanation:
The equation 1 is |3x − 1| + 7 = 2 ........ (1)
⇒ |3x − 1| = - 5
This equation is invalid as the absolute value of (3x - 1) will always be positive and here it is - 5.
Therefore, this above equation has no solution.
The equation 2 is |2x + 1| + 4 = 3 ........ (2)
⇒ |2x + 1| = - 1
This equation is invalid as the absolute value of (2x + 1) will always be positive and here it is - 1.
Therefore, this above equation has no solution.
Hence, we can say that equations 1 and 2 have no solutions. (Answer)
The theoretical probability of an event occurring is Two-fifths. Which best describes the experimental probability associated with this event? Out of every 5 trials, the desired outcome will occur exactly 2 times. Out of every 5 trials, the desired outcome will occur approximately 2 times. Out of every 7 trials, there will be 2 desired outcomes and 5 undesired outcomes. Out of every 7 trials, there will be 5 desired outcomes and 2 undesired outcomes.
Answers
Answer:
Out of every 5 trials, the desired outcome will occur approximately 2 times
Step-by-step explanation:
The first statements states that it will happen exactly two times, but probability never guarantee the outcome
The third and fourth statement states out of 7 which cannot be true as 2-5 basically means out of 5
Answer:
B: Out of every 5 trials, the desired outcome will occur approximately 2 times.
Step-by-step explanation:
Kenny wants to place a picture frame in the center of a wall that is 17 3/4 feet wide. The picture is 2 3/4 feet wide. How many feet from each side of the wall must the frame be so that it is centered?
Answers
Answer:
The distance of frame from each side of the wall so that it is at centered is 7.5 feet
Step-by-step explanation:
Given as :
The measure of the wall = 17[tex]\dfrac{3}{4}[/tex] feet
i.e The measure of the wall =[tex]\dfrac{71}{4}[/tex] feet
The measure of the picture = 2[tex]\dfrac{3}{4}[/tex] feet
i.e The measure of the picture =[tex]\dfrac{11}{4}[/tex] feet
Let The distance from each side of wall so that frame at centered = x feet
Now, According to question
x = The measure of the wall - measure of the picture
Or, x = [tex]\dfrac{71}{4}[/tex] feet - [tex]\dfrac{11}{4}[/tex] feet
Or, x = [tex]\dfrac{71 - 11}{4}[/tex] feet
Or, x = [tex]\dfrac{60}{4}[/tex] feet
∴ x = 15 feet
Now, For each side so that frame st centered = [tex]\dfrac{15}{2}[/tex] feet
Or, For each side so that frame st centered = 7.5 feet
Hence,The distance of frame from each side of the wall so that it is at centered is 7.5 feet Answer
Y/4-9=-3please explain how you got the answer in detail if what you did to get the answer you got.
Answers
Answer:
24
Step-by-step explanation:
y/4-9=-3
y/4=-3+9
y/4=6
y=6*4
y=24
find the slope of the line that is horizontal and passes through the point (3,-4). m= ?
Answers
Answer: [tex]m=0[/tex]
Step-by-step explanation:
The slope can be calculated with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Notice that the formula shows the change in "y" for a unit change in "x" on the line.
In order to solve this exercise, it is important to remember that:
1. If a line is increasing, then its slope is positive.
2. If a line is decreasing, then its slope is negative.
3. If the line is horizontal, its slope is zero.
4. If the line is vertical, it has no slope.
Therefore, since the given line that passes through the point [tex](3,-4)[/tex], is horizontal, its slope is:
[tex]m=0[/tex]
HELP ASAP PLEASE
Which types of dilation are the given scale factors?
Select Expansion or Contraction to correctly describe the type of dilation for each given scale factor.
Answers
-4= Contraction
2.5=Expansion
2/3= Contraction
-3/4= Contraction
Best way to solve this, if the scale factor is less than one, is a contraction. If it is greater than one, than it is an expansion.
The average growth of human hair is 0.5 inch
per month. Find how long it takes a human to
grow 3 inches of hair.
Equation:
Solution:
Answers
Answer:6
Step-by-step explanation:
Answer:
6 months
Step-by-step explanation:
3 divided .5 = 6
2 months = 1 inch
1 inch x 3 = 3 inches
2 months x 3 = 6 months
Complete the inequality statement.
14 ft ____ 4 1/2 yd.
<
>
=
Answers
14 ft > [tex]4\frac{1}{2}[/tex] yards
Step-by-step explanation:
Given,
14 ft ____ 4 1/2 yd.
We will convert yards into feet to determine the inequality.
1 yard = 3 feet
[tex]4\frac{1}{2}[/tex] yards = [tex]3*4\frac{1}{2}[/tex]
[tex]4\frac{1}{2}[/tex] yards = [tex]3*\frac{9}{2}[/tex]
[tex]4\frac{1}{2}[/tex] yards = 3*4.5 = 13.5 feet
which is less than 14 feet, making 14 feet greater, therefore, we will use 'greater than' inequality.
14 ft > [tex]4\frac{1}{2}[/tex] yards
Keywords: inequality, conversion
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Answer:
>
Step-by-step explanation:
A right cylinder has a radius of 3 and a height of 12. What is its surface area?
A. 457 pi units squared
B. 90 pi units squared
c. 108 pi units squared
D. 72 pi units squared
Answers
Answer:
90π units²
Step-by-step explanation:
(refer to attached)
Total Surface are off a right cylinder = area of its ends + area of curved surface
Given radius, r = 3 units and height, h = 12 units
Area of 2 ends,
= Area of 2 circles
= 2 x πr²
= 2π (3²)
= 2π (9)
=18π units²
Area of curved surface,
= 2πrh
= 2π(3)(12)
= 72π units²
Hence,
Surface area = 18π + 72π = 90π units²
The solution is, 90π units² is its surface area.
What is area ?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
here, we have,
given that,
A right cylinder has a radius of 3 and a height of 12.
we know that,
Total Surface are off a right cylinder = area of its ends + area of curved surface
Given radius,
r = 3 units and height, h = 12 units
Area of 2 ends,
= Area of 2 circles
= 2 x πr²
= 2π (3²)
= 2π (9)
=18π units²
Area of curved surface,
= 2πrh
= 2π(3)(12)
= 72π units²
Hence,
Surface area = 18π + 72π = 90π units²
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How many ounces does a 2-ton rhinoceros weigh?
Answers
Answer:
64,000 ounces
Step-by-step explanation:
1 ton = 32,000 ounces
2 tons x 32,000 ounces (which is equal to one ton)
=64,000 ounces
2 tons = 64,000 ounces
A 2-ton rhinoceros weighs 64,000 ounces, which is calculated by converting tons to pounds and then pounds to ounces.
Explanation:The weight of a rhinoceros weighing 2 tons can be calculated in ounces by first converting the weight to pounds. As we know from previous examples, 1 ton = 2,000 pounds. So, a 2-ton rhinoceros weighs 2 × 2,000 = 4,000 pounds. Now, to convert pounds to ounces, we use the conversion factor that 1 pound = 16 ounces. Therefore, a 2-ton rhinoceros weighs 4,000 × 16 = 64,000 ounces.
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4. A case of eggs contains 15 dozen eggs. What is the AP unit cos
egg if a case of eggs costs $34.20?
Answers
Answer:
.19 cent per egg
Step-by-step explanation:
15*12=180
34.20/180= .19
The unit cost per egg is $0.60 when a case of eggs costs $34.20.
Explanation:The unit cost per egg is $0.60.
To find the cost per egg when a case contains 15 dozen eggs costing $34.20, you first calculate the cost per dozen by dividing the total cost by the number of dozens (15). Then, you divide the cost per dozen by 12 to find the cost per egg. In this case, $34.20 divided by 15 gives $2.28 cost per dozen. Finally, $2.28 divided by 12 equals $0.60, so each egg costs $0.60.