What is the length of the hypotenuse? If necessary, round to the nearest tenth.
Answers
Answer:
c = 68 m
Step-by-step explanation:
Pythagorean theorem:To find the hypotenuse 'c' use Pythagorean theorem
hypotenuse² = base ² + altitude²
c² = 60² + 32²
= 3600 + 1024
= 4624
[tex]\sf c=\sqrt{4624}\\\\ c= \sqrt{2*2*2*2*17*17}=2*2*17\\\\\boxed{\bf c = 68 \ m }[/tex]
Related Questions
Reflection across X=1
Answers
It should be noted that a reflection is known as a flip and it's a mirror image of the shape.
How to illustrate the reflection?An image will reflect through a line, known as the line of reflection.
Reflecting around x = 1 never touches the y coordinate, and the x coordinate transforms.
In other words, if a point were at x=π, it's distance to x=1 was π−1 so the new location is π−1 to the left of x=1.
The reflection is attached.
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I dare u to solve this!
Answers
Answer:
? = 26
Step-by-step explanation:
Challenge accepted!
For the bottom left corner:
[tex]10^{2} + 6^{2} \\= 100 + 36\\= 136[/tex]
Now, 10 - 6 = 4
136 / 4 = 34
For the top left corner:
[tex]7^{2} + 5^{2} \\= 49 + 25\\= 74[/tex]
Now, 7 - 5 = 2
74 / 2 = 37
For the top right corner:
[tex]8^{2} + 4^{2} \\= 64 + 16\\= 80[/tex]
Now, 8 - 4 = 4
80 / 4 = 20
For the bottom right corner:
[tex]6^{2} + 4^{2} \\= 36 + 16\\= 52[/tex]
Now, 6 - 4 = 2
52 / 2 = 26
Another method:
5×6+7=37
7×6-5=37
6×4+10=34
10×4-6=34
4×3+8=20
8×3-4=20
So, 4×5+6=26
6×5-4=26
Firstly we have to multiply number with smaller number from the both number, then, multiply that constant number with larger number and then subtract smaller number you will get same number, in this with 4 only 5 constant number following this rule 4×5+6=26, 6×5-4=26, if you multiply 4 with 6, then, 4×6+6=30, 6×6-4=32, and with 7, 4×7+6=34, 6×7-4=38. So, 26 is the right answer of this question
Simplify this radical
[tex]\sqrt{84} \\\\A: 2\sqrt{21} \\B: 2\sqrt{42} \\C: 4\sqrt{21} \\D: 4\sqrt{42} \\[/tex]
Answers
The given radical root 84, the simplification is option B; [tex]2\sqrt{21}[/tex].
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
The given radical;
[tex]\sqrt{84} \\\\\sqrt{42 \times 2} \\\\\sqrt{7\times3\times 2 \times 2} \\\\2\sqrt{21} \\[/tex]
Thus, the correct option is B; [tex]2\sqrt{21}[/tex].
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Could I get some help on this pls, and most importantly how you could solve it.
Thank you.
Using your choice of technology, find the line of best fit using the data below for the women’s 100-meter Olympic records. Interpret the y-intercept, and explain the significance of the slope.
Answers
The equation of the line of best fit is y = -0.03x + 69.94
How to determine the line of best fit?The column headers are given as:
Year Time(s)
To enter the data values in a graphing calculator, we use the following representations:
x ⇒ Year
y ⇒ Time (s)
Using the above representations, we have the following calculation summary from a graphing calculator:
Sum of X = 72209Sum of Y = 432.95Mean X = 1951.5946Mean Y = 11.7014Sum of squares (SSX) = 17242.9189Sum of products (SP) = -514.5997The equation of the line of best fit is:
y = bx + a
Where
b = SP/SSX = -514.6/17242.92 = -0.02984 ≈ -0.03
a = MY - bMX = 11.7 - (-0.03*1951.59) = 69.94497 ≈ 69.94
So, we have:
y = -0.03x + 69.94
A linear equation is represented as:
y = Slope * x + y intercept
So, we have:
Slope = -0.03
y intercept = 69.94
The y-intercept implies that the initial time is 69.94 seconds, while the slope implies that the time decreases by 0.03 seconds each year
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5.7x10^6 as an ordinary number
Answers
Answer:
5700000
Step-by-step explanation:
A,B and C are points in the cartesian plane. the coordinates of A are (3,-2),BA=(4,-3)and AC=(4,9). Calculate
i. the coordinates of B and C
Answers
Then B is at (3 - 4, -2 + 3) = (-1, 1)
and C is at (3 + 4, -2 + 9) = (7, 7)
write a function rule for the table
hours worked 2,4,6,8 and pay 15,30,45,60
Answers
Answer:
f(x) = 7.5x
Step-by-step explanation:
you can find the slope by using the slope formula (y2-y1)/(x2-x1). you can use any of the values but for this example I'll be using (2, 15) and (4, 30).
(30-15)/(4-2) = 15/2 = 7.5.
now we can use one of the coordinates to find the y-intercept by plugging the known values in the equation y=mx+b where m is the slope and b is the y-intercept.
for this example I'll be using (2, 15) but you could use any of the values you gave.
15 = 7.5(2) + b
15 = 15 + b
0 = b
so now we have the function rule
f(x) = 7.5x + 0 or just f(x) = 7.5x
Cullumber company had $170,000 of net income in 2021 when the selling price per unit was $152, the variable costs per unit were $96, and the fixed costs were $574,800. management expects per unit data and total fixed costs to remain the same in 2022. the president of cullumber company is under pressure from stockholders to increase net income by $106,400 in 2022.
Answers
The number of units sold in 2021 = 13,300 units.
The number of units that would have to be sold in 2022 to reach the stockholder's desired profit level = 15,200 units.
Assuming that Cullumber company sells the same number of units in 2022 as it did in 2021, the selling price in order to reach the stockholder's desired profit level = $160.
The net income of a company is its profit function, derived by the formula:
Profit = Sales - Cost.
Sales are the product of the number of units sold and per unit selling price.
Cost is the sum of fixed costs and the product of the number of units produced to the variable cost per unit.
Assuming the number of units sold in 2021 to be x,
we can say sales = $152x, and
cost = ${574800 + 96x}.
Therefore, profit = sales - cost,
or, 170000 = 152x - {574800 + 96x},
or, 170000 = 56x - 574800
or, 56x = 574800 + 170000 = 744800,
or, x = 744800/56 = 13300.
Therefore, the number of units sold in 2021 was 13,300.
In 2022, the desired profit = $170,000 + $106,400 = $276,400.
Assuming the number of units sold in 2022 to be n, at the same unit data and fixed cost, we can say that:
Sales = $152n, and
Cost = ${574800 + 96n}.
Therefore, profit sales - cost,
or, 276400 = 152n - {574800 + 96n},
or, 276400 = 56n - 574800,
or, 56n = 574800 + 276400 = 851200,
or, n = 851200/56 = 15200.
Therefore, the number of units sold in 2022 should be 15,200 to reach the desired profit of the stakeholders.
When the number of units sold in 2022 is the same as in 2021, that is, the number of units = 13,300, we assume the per unit selling price to be $P.
Now we can say that,
Sales = $13300P.
Costs = ${574800 + 96*13300} = ${574800 + 1276800} = $1851600.
Therefore, profit = sales - cost,
or, 276400 = 13300P - 1851600,
or, 13300P = 1851600 + 276400 = 2128000,
or, P = 2128000/13300 = 160.
Therefore, the new selling price per unit to reach stockholders' desired profit, assuming the number of units sold in 2022 to be the same as in 2021 is $160.
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You just looked at the graph of this system of equations. Why will the lines never intersect? y = –x + 5 y = –x – 3
Answers
Answer: same slope, y int are different
Step-by-step explanation:
Both these lines never intersect because they have the same slope.
they both go down 1 over 1, and also their y interecepts are different
find y in terms with z. help me please :)
Answers
Answer:
y = 5z
Step-by-step explanation:
added in the picture
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow y = 5z [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[ let the point at which line segments SV and RT intersects be O ]
[tex]\qquad \tt \rightarrow \: \angle ROV + \angle ROS = 180° [/tex]
[ linear pair ]
[tex]\qquad \tt \rightarrow \: \angle ROV = 180 - \angle ROS[/tex]
[tex]\qquad \tt \rightarrow \: \angle ROV = 180 -2y[/tex]
____________________________________
[tex]\qquad \tt \rightarrow \: \angle SVU = \angle ROV + \angle TRV[/tex]
[ Exterior angle = sum of opposite interior angles ]
[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - 2y + y[/tex]
[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y [/tex]
( let it be equation 1 )
____________________________________
[tex]\qquad \tt \rightarrow \: \angle SVU + \angle SUV + \angle VSU = 180°[/tex]
[ Sum of angles of Triangle ]
[tex]\qquad \tt \rightarrow \: \angle SVU + 4z + z = 180°[/tex]
[tex]\qquad \tt \rightarrow \: \angle SVU + 5z = 180°[/tex]
[tex]\qquad \tt \rightarrow \: \angle SVU = 180° - 5z[/tex]
( let it be equation 2 )
____________________________________
By comparing both equations :
[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y = 180 - 5z[/tex]
[tex]\qquad \tt \rightarrow \: 180 - y = 180 - 5z[/tex]
( Add 180° on both sides )
[tex]\qquad \tt \rightarrow \: 180 - y + 180 = 180 - 5z + 180[/tex]
[tex]\qquad \tt \rightarrow \: - y = - 5z[/tex]
[tex]\qquad \tt \rightarrow \: y = 5z[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Please please help what is equivalent to this??
Answers
The correct option is Option A: [tex]16^{3x/4}[/tex] is equivalent to the expression [tex](\sqrt[4]{16})^{3x[/tex].
The rules of the exponent are
(a) [tex]a^m*a^n=a^{m+n[/tex]
(b)[tex]a^m/a^n=a^{m-n[/tex]
(c)[tex](a^b)^c=a^{bc}[/tex]
(d) [tex]\sqrt[n]{a}=a^{1/n[/tex]
here the given expression is [tex]16^{3x/4}[/tex]
we can rewrite the expression as
[tex]16^{3x/4}[/tex]
as we know by the rule of the exponent that [tex](a^b)^c=a^{bc}[/tex]
=[tex](16^{1/4})^{3x[/tex]
as we know by the rule of the exponent [tex]\sqrt[n]{a}=a^{1/n[/tex]
=[tex](\sqrt[4]{16})^{3x[/tex]
Therefore the correct option is Option A: [tex](\sqrt[4]{16})^{3x[/tex]
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3. Adjacent sides of a rectangle are in the ratio 5:12, if the perimeter of the rectangle is 34 cm, find the length of the diagonal. 3. Adjacent sides of a rectangle are in the ratio 5:12 , if the perimeter of the rectangle is 34 cm , find the length of the diagonal.
Answers
Answer:
Adjacent sides are in the ratio 5 : 12
That means,
Let length = 12x and breadth = 5x
Perimeter = 34
2(l+b) = 34
12x + 5x = 17
17x = 17
x = 1
Lenth =12 cm
Breadth = 5 cm
By Pythagorean theorem
The length of the diagonal of rectangle = 13 cm
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A circle centered at the origin contains the point
(0, -9). Does (8, √17) also lie on the circle? Explain.
O No, the distance from the center to the point
(8, √17) is not the same as the radius.
O No, the radius of 10 units is different from the
distance from the center to the point
(8, √17).
O Yes, the distance from the origin to the point
(8, √17) is 9 units.
O Yes, the distance from the point (0, -9) to the point
(8, √17) is 9 units.
Answers
Approximate value of √17
~4+So the point is (8,4)
As we can see in graph the point is contained by the circle
Hence the distance
√(0-8)²+(9-4)²√8²+5²√89Approximately 9 units
Option D
Answer:
Yes, the distance from the origin to the point (8, √17) is 9 units
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) is the centerr is the radiusGiven:
center = (0, 0)r = 9Substitute the given values into the formula to create the equation of the circle:
[tex]\implies (x-0)^2+(y-0)^2=9^2[/tex]
[tex]\implies x^2+y^2=81[/tex]
To find if point [tex]\sf (8, \sqrt{17})[/tex] lies on the circle, substitute x = 8 into the found equation and solve for y:
[tex]\implies 8^2+y^2=81[/tex]
[tex]\implies 64+y^2=81[/tex]
[tex]\implies y^2=81-64[/tex]
[tex]\implies y^2=17[/tex]
[tex]\implies y=\sqrt{17}[/tex]
As y = √17 when x = 8, this proves that point (8, √17) lies on the circle.
The distance from the origin to any point on the circle is the radius.
Therefore, as the radius is 9 units, the distance from the origin to the point (8, √17) is 9 units.
What is the inverse of f(x)=5x/3+5
Answers
Answer:
f^-1(x)=8x/5
Step-by-step explanation:
The inverse of f(x)=5x/3+5 is 8x/5
The inverse function of f(x)=5x/3+5 is f-1(x) = 3x/5 - 15
How to determine the inverse?We have:
f(x)=5x/3+5
Rewrite as:
y=5x/3+5
Swap x and y
x = 5y/3 + 5
Subtract 5 from both sides
5y/3 = x - 5
Multiply through by 3
5y = 3x - 15
Divide through by 5
y = 3x/5 - 15
Rewrite as:
f-1(x) = 3x/5 - 15
Hence, the inverse function of f(x)=5x/3+5 is f-1(x) = 3x/5 - 15
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. put these numbers in order, from least to greatest. if you get stuck, consider using a number line. 3.5 -1 4.8 -1.5 -0.5 -4.2 0.5 -2.1 -3.5 2. write two numbers that are opposites and each more than 6 units away from 0.
Answers
hi can some one help me
Answers
-5≥
so 8 x -5 = -40 - 16 = -56 and that's the smallest number you can get that will be greater than -64 hope this helps! :)
Answer:
x> -6
Step-by-step explanation:
Drag the -16 to -64. This will change the -16 to a positive 16. Add -64 and 16. The answer is -48. All that should be left is 8x>-48. Now we need to divide -48 and 8 so we can leave x. The answer should be -6 on one side, and x on the other side. x> -6
A shoe making company makes 256 pairs of boots in a day how many pairs of boots do they make in 260 days
Answers
Answer:
66560 pairs
Step-by-step explanation:
let the number of pairs of boots the company makes in 260 days = X
1day -----------------256pairs
260days-------------X
cross multiplying
1×X = 260×256
X= 66560
therefore, in 260days, he makes 66560 pairs
I need help on this question
pls help yes
Answers
The arc length of the semicircle is 5π units
Calculating length of an arcFrom the question, we are to calculate the arc length of the semicircle
Arc length of a semicircle = 1/2 the circumference of the circle
∴ Arc length of a semicircle = 1/2 × 2πr
Arc length of a semicircle = πr
Where r is the radius
From the given information,
r = 5
∴ Arc length of the semicircle = 5 × π
Arc length of the semicircle = 5π units
Hence, the arc length of the semicircle is 5π units
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cosA/secA+sinA/cosecA=1
Answers
Step-by-step explanation:
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A plant grows at a constant rate . daniel records the height of the plant each week . the unit reat is meausred in inches per week . what is the constant of proportionality ?
Answers
By the consideration of direct proportionality, the constant of proportionality for the height of the plant is equal to 3 inches per week.
How to find a constant of proportionality in direct proportional equation
Let x and y the number of weeks and the height of the plant, respectively. Given the consideration of direct proportionality, the height of the plant inasmuch as the number of weeks increases. Then, the constant of proportionality (in inches per week) is found by dividing the height of the plant by the number of the respective week:
k = 18 inches /6 weeks = 15 inches /5 weeks = 12 inches/4 weeks = 3 inches/week
By the consideration of direct proportionality, the constant of proportionality for the height of the plant is equal to 3 inches per week.
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Question 1
swere
>
Find the equation for the line that passes through (2, 8) that has slope 4. Give your answer in point-slope
form. You do not need to simplify.
Answers
Answer:
The point-slope form is y - 8 = 4(x - 2)
Step-by-step explanation:
Given:
slope = 4passes through (2, 8)the point-slope form is y - y1 = m(x - x1)
(x1, y1) is a known pointm is the slope of the line(x, y) is any other point on the lineHence the point-slope form is y - 8 = 4(x - 2)
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Which expression is equivalent to 2 (14x-37+28x+12.2-5y-17.5)?
A. 84x-16y-10.6
B. 28x-6y-10.6
C. 42x-8y-5.3
D 84x-16y-5.3
Answers
Answer:
A. 84x - 16y - 10.6
Explanation:
[tex]\sf \rightarrow 2(14x-3y+28x+12.2-5y-17.5)[/tex]
[tex]\sf \rightarrow 2 (42x-8y-5.3)[/tex]
apply distributive method: a(b + c) = ab + ac
[tex]\sf \rightarrow 2 (42x) -2(8y)-2(5.3)[/tex]
[tex]\sf \rightarrow 84x -16y-10.6[/tex]
NOTE: I DO NOT NEED A LONG ANSWER
Figure B is a scaled copy of Figure A.
What is the scale factor from Figure A to Figure B?
Answers
Answer:
Scale factor is 3
Given lJK , which is an isosceles right triangle, IJ=4 and m
Answers
As IJK is isosceles
IJ=JKHypotenuse must not counted counted among equal sides so
IK²=2(LJ)²Apply roots
IK=LJ√2Option C
0.738×0.28 is 0.20664 but is rounded to 0.21. which rule or rules are applied to this calculation? select all that apply.
Answers
The rules of the calculation are:
Round the result to the same number of significant figures as the value with the least number of significant figuresRound up if the digit to be dropped is 5 or greater.How to determine the rule?The complete question is added as an attachment
The equation is given as:
0.738 × 0.28 = 0.20664
When approximated, we have:
0.738 × 0.28 ≈ 0.21
The above approximation can mean any of the following:
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If the diagonal of the rectangle is 10.5 inches and the length of the rectangle is 7.25, what is the width of the rectangle?
Answers
Answer:
w≈7.6in
Step-by-step explanation:
L= 7.25
D= 10.5
Using the formula [tex]d=\sqrt{w^{2} + l^{2} } \\[/tex]Solving for w [tex]w=\sqrt{d^{2} -l^{2} }[/tex] [tex]\sqrt{10.52^{2}-7.25^{2} } = 7.59523in[/tex]Answer:-
The width of this rectangle is = 7.59
Given:-
In this question, it is given that -
The diagonal of this rectangle is = 10.5
the length of this rectangle is = 7.25
To find:-
We have to find the width of this rectangle.
Solution:-
We can easily solve this problem using the Pythagorean theorem.
In this problem, it is given that the length of this rectangle is = 7.25 and the diagonal is =10.5
so by the Pythagorean theorem, we can get-
(length)² + (width)² = (diagonal)²
or, (7.25)² + (width)² = (10.5)²
or, (width)² = (10.5)² - (7.25)²
= 17.75 × 3.25
= 57.6875
or, width = 7.59
So, the width of the rectangle is 7.59.
Solve the compound inequality for x and identify the graph of its solution.
x+7> 3 and x-5≤-1
OA. Solution: x<-4 or x ≥ 4
++
-5-4-3 -2 -1 0 1 2 3 4 5
OB. Solution: x>-4 and x≤ 4
--
-5-4-3 -2 -1 0 1 2 3 4
OC. Solution: x>-4 and x≤ 4
+
H
-5 -4 -3 -2 -1 0 1
2
4 5
OD. Solution: x2-4 and x < 4
44
-5-4-3 -2 -1 0 1 2 3 4 5
3
5
Answers
Answer:
C is the answers for the question
Step-by-step explanation:
please mark me as brainlest
The compound inequality can be expressed as "x > -4 or x ≤ 4."
The correct graph of the solution is:
OC. Solution: x > -4 and x ≤ 4
Let's solve the compound inequality step by step:
x + 7 > 3
Subtract 7 from both sides to isolate x:
x > 3 - 7
x > -4
and, we have,
x - 5 ≤ -1
Add 5 to both sides to isolate x:
x ≤ -1 + 5
x ≤ 4
Now, we have two inequalities for x:
x > -4
x ≤ 4
The compound inequality can be expressed as "x > -4 or x ≤ 4."
The correct graph of the solution is:
OC. Solution: x > -4 and x ≤ 4
The graph will include all values greater than -4 (open circle) and all values less than or equal to 4 (closed circle) on the number line.
The correct representation is:
OC. Solution: x > -4 and x ≤ 4
Graph:
-5 -4 -3 -2 -1 0 1 2 3 4 5
+---|---|---|---|---|---|---|---|---|---+
-4 0 4
The open circle at -4 indicates that x is greater than -4, and the closed circle at 4 indicates that x is less than or equal to 4.
The shaded area between -4 and 4 represents the solution to the compound inequality.
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given f(x)=2x+2 and g(x) =-5x-3 find (f-g)(x)
Answers
Answer:
(f-g)(x) = 7x+5
Step-by-step explanation:
Given that,
f(x)=2x+2 and g(x) =-5x-3
To Find:
(f-g)(x)Solution:
[tex](f - g)(x)[/tex]
Re-write as:
[tex]f(x) - g(x)[/tex]Now substitute the values on the polynomial/function:
Simplify using this order:BPEMDAS
[tex]2x + 2 - ( - 5x - 3)[/tex][tex]2x + 2 + 5x + 3[/tex][tex]2x + 5x + 2 + 3[/tex][tex] \boxed{ ( f - g)(x) = 7x + 5}[/tex]Hence,(f-g)(x) = 7x+5.
A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compare over the interval
The exponential function decays at one-half the rate of the quadratic function.
The exponential function decays at the same rate as the quadratic function.
The exponential function decays at two-thirds the rate of the quadratic function.
The exponential function decays at three-fourths the rate of the quadratic function.
Answers
Answer:
The ratio of decay rates is 3:4. So, option D is correct.
Step-by-step explanation:
Concept: The Decay rate for any function can be calculated by the formula Decay rate = Difference in y values / Difference in x values in given interval
Decay Rate for the exponential function in the interval -2 ≤ x ≤ 0 is (4-1) / (-2-0) = 3/2.
Decay rate for quadratic function in same interval = [(4-0) ÷ -(-2-0)] = 2.
Ratio of decay rates = (3/2) : (2) = 3:4
Option D, the exponential function decays at three-fourths the rate of the quadratic function is the correct answer.
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PLS HELP ASAP FIRST CORRECT ANSWER GETS BRAINLEIST
Answers
2. 43 cm
Explanation: take the 15m and subtract 8 cm and for 2 add all the sides together to get 43
