The length of the hypotenuse is 6.71
How to calculate the length of the hypotenuse ?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle. This theorem can be expressed as the Pythagorean equation, which is an equation relating the lengths of the sides a, b, and the hypotenuse c:
[tex]{\displaystyle a^{2}+b^{2}=c^{2},}[/tex]
Given ,
Pythagorean therum
a^2 + b^2 = c^2....a and b are ur legs and c is the hypotenuse
3^2 + 6^2 = c^2
9 + 36 = c^2
45 = c^2...take the sqrt of both sides....this eliminates the ^2
sqrt 45 = c
6.708 rounded = 6.71 = c
Therefore the length of the hypotenuse is 6.71
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If you rent a car from Caleb's Cars, you'll pay a $61 fee
and $24 per day. At Vinny's Vehicles, you'll pay a $105 fee and $20 per day. Determine the number of days you can rent a car from either place and pay the same amount. Use substitution or elimination.
11 days are required to rent a car at both locations at the same price.
What is a System of Equations?
A system of equations in algebra is made up of two or more equations that are solved together. "A group of equations satisfied by the same set of variables are called a system of linear equations. Finding the values of the variables employed in the system of equations is the first step towards solving it. While maintaining the balance of the equations on both sides, we compute the values of the unknown variables. Finding a variable whose value makes the condition of all the given equations true is the primary goal of solving an equation system.
1st equation: 61+24x=y
Equation 2: 105+ 20x Equals y
Eq. 1 - 2 - subtracted
105-61+20x-24x= 0
44-4x= 0
4x = 44
4 divided by both sides
x= 44/4
x= 11 days
Hence, 11 days are required to rent a car at both locations at the same price.
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Bart is writing lines on a chalkboard that is initially empty. It ordinarily takes Bart 50 minutes to cover the whole board; however, today, Nelson is erasing the board while Bart is writing. Nelson can erase the board in 80 minutes by himself. If they work simultaneously, how long will it be until the whole board is covered?
think about this conceptually first. The difference between their rates of work is going to be the total speed at which the chalk board fills up (speed of writing - speed of erasing).
Ok, so we need to find the speed that Bart is writing, and the speed at which Nelson is erasing.
Bart: 50 minutes/ 1 board
However, we want to find his speed, which will be in boards/minute. Flip the fraction to get 1 board/50 minutes. Then multiply top and bottom by 1/50 in order to get 1/50 board per minute.
Bart's Speed = 1/50 board per minute
Do the same for Nelson, to get 1/80 board per minute (erasing).
The difference between these will be 1/50 - 1/80 = 3/400 board per minute
Since we want to know how long it will take to fill the board at this rate, we multiply 1 board * 1/(3/400) minute per board - this is the same as 1 * 400/3
So, the answer is 400/3 minutes, or 133.33 minutes, or 2 hours, 13 minutes.
#2
This is the same idea as #1. His speed without the headwind is 2000 miles/5 hours = 400miles/hour.
His speed with the headwind is 2000 miles/8 hours = 250 miles/hour.
400m/h - 250m/h = 150m/h
The speed of the wind is 150 miles/hour.
help me with this please !!!!
Answer: 2 times!
Step-by-step explanation:
(-1,0)
(4/3, 0)
Answer:
C.2
Step-by-step explanation:
See attached: the graph of your function
How do you simplify 5+5x-3x+1
Answer:
6 + 2x
Step-by-step explanation:
5 + 5x - 3x + 1
add 5 + 1
6 + 5x - 3x
collect like terms 5x -3x
6 + 2x
Step-by-step explanation:
Please follow me the answer is 6+2x
or 2x+6
The ribbon on a spool is 13 yards long. How many 4 inch pieces of ribbon can be cut from the spool?
Answer:
117
Step-by-step explanation:
13 yards = 468 inches
468 ÷ 4 = 117
Simplify the expression |ab^3| if a>0 and b>0
The expression |ab^3| if a>0 and b>0 is even.
What is Parity Definition?
Even Function: A function is even if f(-x)=f(x) for all [tex]$x \in \mathbb{R}$[/tex] Odd Function: A function is odd if f(-x)=-f(x) for all [tex]$x \in \mathbb{R}$[/tex]
[tex]f(a): \quad|a|\left|b^3\right|[/tex]
[tex]f(-a): \quad|a|\left|b^3\right|[/tex]
[tex]-f(a):-|a|\left|b^3\right|[/tex]
Check parity of [tex]$|a|\left|b^3\right|$[/tex]
Check if Even: True
Check if Odd: False
Even
The expression |ab^3| if b>0
[tex]$$\begin{aligned}& f(a): \quad|a| b^3 \mid \\& f(-a): \quad|a|\left|b^3\right| \\& -f(a): \quad-|a| b^3 \mid\end{aligned}$$[/tex]
Check parity of [tex]$|a|\left|b^3\right|$[/tex]
Check if Even: True
Check if Odd: False
Even
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Solve for x
Note drawn to scale
Geometry
Answer:
x=2
Step-by-step explanation:
1. Set the proportions equal: 5/2x-3 = 15/27
2. Butterfly method: 27x5 = 3x-3 x 15
3. Continue solving: 135 = 45x-45
4. Break it down: 45x = 90
5. Solution: 2 because 45 x 2 is equal to 90
Answer:
x=4
Step-by-step explanation:
[tex]\frac{3x-3}{5}=\frac{24+3x}{20}[/tex] Original equation. A proportion can be set up so that
you can find x. One proportion can be one side over the
other side of one of the smaller triangle set equal
to the total length of the larger triangle. 27 and -3 can
combine forming 24, which continues to be added to 3x.
15 and 5 can be combined to become 20.
20(3x-3)=5(24+3x) Now, cross multiply. This involves the distribution of one
term to the terms it's multiplied by. 20*3x=60x and
20*-3=-60. 5*24=120 and 5*3x=15x.
60x-60=120+15x Now, the goal is to get x alone on one side. You can do
this by combining like terms. Subtract 15x from both
sides and add 60 to both sides.
45x=180 Then, divide by 45 to get x by itself.
x=4 This is your answer.
The congruency theorem can be used to prove that △wut ≅ △vtu.
As per the congruency theorem, the two triangles are congruent.
Congruency theorem:
Congruency theorem states that "if all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other."
Given,
Here we need to prove that congruency theorem can be used to prove that △wut ≅ △vtu.
Let us consider triangles WUT and VTU.
And in these triangles:
=> WU≅VT
And in those one, ∠T≅∠U,
Therefore, m∠T = m∠U = 90°
Here the side TU is common.
Now, we have to note that triangles WUT and VTU are right triangles, because m∠T = m∠U = 90°.
Then the side TU is common leg and sides WU and VT are hypotenuses.
Therefore, the HL theorem states: if the hypotenuse (WU) and one leg (TU) of a right triangle (ΔWUT) are congruent to the hypotenuse (VT) and one leg (TU) of another right triangle (ΔVTU), then the triangles are congruent.
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Answer: HL
Step-by-step explanation:
Find the value of each variable
I’ve figured out Z, but need help with Y.
Answer: Y=112
Step-by-step explanation: Add all of the interior angles you have to get 248 and subtract 248 from 360.
67+80+101 = 248.
360-248 = 112
What is the slope of the function
Y = -5/4x - 3
PLEASE HELP ASAP
Share 850 between 2
Give the answer in it's simplest form.
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
850 ÷ 2 = 425
The amount each person got is 425.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The total amount = 850
The number of people to share = 2
Now,
The amount each got.
= 850/2
= 425
Thus,
The amount each person got is 425.
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Pls help on my math question and for part c it’s 48 since the teacher gave us answer only for tht part and show work pls :)
a) Equation for length and width of the rectangular rug be [tex]x^{2}[/tex] + 8x - 42 = 0
b) Width of the rectangular rug be 3.5 feet
c) Diagonal of the rectangle is 12.5 feet
What is the area of the rectangle?
The area of a rectangle is the area occupied by the rectangle within its four sides or boundaries.
The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of the length and width of a rectangle. The perimeter of a rectangle is equal to the sum of all its four sides
It is given that area of a rectangular rug id 42 square feet. The rug is 8 feet longer than its wide
a) Let the width of the rectangular rug be x feet
Length of the rectangular rug = (x+8) feet
area of rectangular rug = Length × width = x × (x + 8) = [tex]x^{2}[/tex] + 8x
area of rectangular rug = 42
[tex]x^{2}[/tex] + 8x = 42
[tex]x^{2}[/tex] + 8x - 42 = 0
Therefore, equation for length and width of the rectangular rug be [tex]x^{2}[/tex] + 8x - 42 = 0
b) If the length of the rectangle is 12 feet
Area of rectangle = 42 square feet
length × width = 42 square feet
12 × width = 42 square feet
width = 42/12 = 3.5
Therefore, width of the rectangular rug be 3.5 feet
c) Length of the diagonal of the rectangle = [tex]\sqrt{length^2+width^2}[/tex]
= [tex]\sqrt{12^2+3.5^2}=\sqrt{144+12.25}=\sqrt{156.25}= 12.5[/tex]
Therefore, diagonal of the rectangle is 12.5 feet
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If If you can help that would be great
3n < 3
Answer:
n<1
Step-by-step explanation:
3n<3
/3. /3
n<1
hopes this helps
Answer:
n < 1
Step-by-step explanation:
3/3 n < 3/3
n < 1
a project has the following projected outcomes in dollars: $210, $320, and $540. the probabilities of their outcomes are 25%, 55%, and 20% respectively. what is the expected value of these outcomes?
The expected value of these outcomes are $262.5, $496 and $648 respectively
How to calculate expected values?You should know that the expected value are the proportion of the values when valued with the percentages
The given values are $210, $320 and $540
The given percentages are 25%, 55% and 20%
The expected values are
0.25*210 = $52.5+210=$262.5
0.55*320=176+320=$496
0.20*540=108+540=$648
Therefore the projected values of the project are $262.5, $496 and $648 respectively
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Please help me solve this I’ll give brainless
Answer:
a) Solving by factoring, you move 225 to the left side by subtracting then making the equation equal to 0.
b) x = -15
x = 15
Step-by-step explanation:
1. x^2 -225=0
2. Find what two numbers equal to -225 then factor by using the expression a^-b^2=(a-b)(a+b)
In this case, -15(15)=-225
(x-15)(x+15)=0
3. Find x
x-15=0
x+15=0
This equation has 2 solutions
x=-15
x=15
To check answer, one of the solutions into X
1) Triangle ABC has vertices A(6,2), B(3,4), and C (2,8). If the triangle is rotated
90° counterclockwise, what are the coordinates of the image A'B'C'?
The coordinates of the image A'B'C are A(-2, 6) B(-3, 4) C(-8, 2)
How do you find the coordinates of a triangle?A specific example of barycentric coordinates for a triangle is referred to as triangular coordinates, and it is also known as a ternary plot or areal coordinates. Triangular coordinates can also refer to any of at least three additional related systems of coordinates in the Euclidean plane.The coordinate geometry formula for the area of a triangle A = (1/2) |x1 1 (y2 2 y3 3) + x2 2 (y3 3 y1 1) + x3 3 (y1 1 y2 2)|, where (x1 1,y1 1), (x2 2,y2 2), and (x3 3,y3 3) are the coordinates of the triangle's vertices, gives the area of a triangle in coordinate geometry.y = mx + c. The points whose coordinates fulfil the equation y = mx + c, on the other hand, always lie on the line with gradient m and y-intercept c.Given data :
Triangle ABC has vertices A(6,2), B(3,4), and C (2,8).
Although I am aware that the coordinates must rotate around the origin, I am unsure of the signs (+ or -).
Consequently, the shape is in the second quadrant of the graph, and the 90-degree angle should be in the fourth quadrant rather than the first (which is 180 degrees anticlockwise) or third (.180 anticlockwise)
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pls help due tomm!! super easyy
Answer:see below
Step-by-step explanation:
a+4<b+4
if a/b=c, then a= bc
A. If a/b ≠ c, then a ≠ bc.
B. If a =bc then a/b=c.
C.Ff a ≠ bc, then a/b ≠c
D. If a/b=c. then a≠ bc
Even though A and B are both square, AB always equals BA.
How to Prove that if ab=ac, then b=c ?Could someone please assist me in demonstrating that b=c follows from ab=ac and a does not equal 0. You can only apply the field axioms. Here is my try.
ab=ac then, ab-ac=0
a(b-c)=0
a(0)=0 Since a cannot equal zero (this has already been shown), (b-c) must also equal zero, leaving us with...
b-c=0
b=c
The only issue I have with the above is that I presupposed that a did not equal 0. I'm not sure if this is okay because the original theorem I'm attempting to prove includes the claim that "a does not equal 0."
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Please find the equation that fits this chart
Answer: y = 3/4x
Step-by-step explanation:
(100, 75)
(200, 150)
find slope
150 - 75 / 200 - 100
75 / 100 = 3/4
plug values into formula y=mx+b to find y-intercept
y = 3/4x + b
75 = 3/4(100) + b
75 = 75 + b
b = 0
A new club sent out 250 coupons to boost sales for next year's memberships. They provided 4 times as many to potential members than to existing members. How many coupons did they send to existing members?
A.
4
B.
50
C.
5
D.
54
Answer: 50 existing members
1 A, B and C are points on a circle with centre O.
8 cm A-B
15 cm B-C
B
AOC is a diameter of the circle.
AB= 8 cm
BC= 15 cm
Angle ABC = 90°
Work out the total area of the regions shown shaded in the diagram.
Give your answer correct to 3 significant figures.
Diagram NOT
accurately drawn
The total area of the shaded region is solved to be 154.93 cm²
How to find the total area of the shaded regionThe diameter is solved using Pythagoras theorem given by the the formula
hypotenuse² = opposite² + adjacent²
plugging the values as in the problem
let x be the required distance
x² = 8² + 15²
x² = 289
x = √289
x = 17
Work out the area of the triangle using the formula
= 1/2 * base * height
base = hypotenuse or diameter
height = radius = diameter/2
= 0.5 * 17 * 8.5
= 72.25 cm²
Area of the circle
= Π * radius²
= 22/7 * 8.5²
= 226.98 cm²
shaded portion
= Area of the circle - area of the triangle
= 226.98 - 72.25
= 154.93 cm²
the area of the shaded portion is 154.93 cm²
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Name two sets of alternate interior angles
Answer:
1st and 3rd ones.
Step-by-step explanation:
<BAD and <ADE are equal because the transversal connects the two angles on alrenate sides. Also <CBA and <CED are equal, as they are again, alternate and the transversal (the diangonal line) connects them.
A department store buys 400 shirts at a cost of $4,800 and sells them at a selling price of $20 each. Find the percent markup.
40% is the percent markup.
What does math mean by percentage?
A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a percentage. Divide the number by the total and multiply by 100 to find the percent of a given number. , a.
an a, the in the an in the an in the an in the an in the Per 100 is what the word percentage signifies.
= 1 - 4800 /20 ÷ 400
= 1 - 12/20
= 1 - 3/5
= 5 - 3/5
= 2/5
Multiply a number to both the numerator and the denominator
2 *20/5 *20
= 40/100
= 40%
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The surface area of this cylinder is 118.378 square yards. What is the height?
Use ≈ 3.14 and round your answer to the nearest hundredth.
r = 2.9 yd
The surface area of this cylinder is 118.378 square yards. 3.6 yard is the height.
What is surface area?The quantity of space enclosing a three-dimensional shape's exterior is its surface area.
For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. Square units are used to measure it at all times.
The terms "lateral surface area," "curved surface area," and "total surface area" refer to three different forms of surface area.
Surface area and volume are the cylinder's two main characteristics because it is a three-dimensional form. The area of the two circular bases combined with the cylinder's curved surface area equals the cylinder's overall surface area. Its volume is the three-dimensional area that a cylinder takes up.
Given that,
Surface area (A) of the cylinder = 118.378 square yards.
radius (r) = 2.9 yard
As we know, A = 2πrh + 2πr²
putting the values we get -
or, 118.378 = 2πr (h + r)
or, 118.378 = 2 × 3.14 ×2.9 × (h + 2.9)
or, 118.378 = 18.212 × (h + 2.9)
or, 6.5 = h + 2.9
or, h = 6.5 - 2.9
or, h = 3.6 yard
Thus, 3.6 yard is the height of the cylinder.
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Ohdhhdhdhdgdueyehehehhegehehehgegr
Answer:
JSHKAKSBKSBAK?
Step-by-step explanation:
3x + 4y =8 write equation in slope intercept
Answer:
[tex]y=2-\frac{3}{4} y[/tex]
Step-by-step explanation:
Slope intercept form is y=mx+b
m is the slope; b is the y-intercept
Therefore, we need to isolate the y variable first
3x + 4y = 8
-3x -3x
4y=8-3x Divide both sides by 4 to leave y by itself.
/4 /4
[tex]y=2-\frac{3}{4} y[/tex]
0.4x+6.1forx= -5
show work
Solve over the complex number x^2+16=0
EXERCISE 12.1 There are 20 girls and 15 boys in a class. (a) What is the ratio of number of girls to the number of boys? (b) What is the ratio of number of girls to the total number of students in the class?
Answer:
(a) 4 : 3
(b) 4 : 7
Step-by-step explanation:
a)
20:15
divide both by the HCF which is 5
4:3
b) 20 + 15 = 35
20 : 35
divide both by HCF which is 5
4:7
I need an explanation on how to solve it!
The factored form of f(x) is f(x) = (x+2) (x+2)(x+4)
What is a factor?
A factor is a number/expression that divides another number/expression, leaves zero remainder . In other words, if multiplying two numbers/expressions gives us a product, then the numbers/expressions we are multiplying are factors of the product because they are divisible by the product.
f(x) = x³ +8x² + 20x + 16
The value of x at which f(x) is zero, is the root
x= -2 is a root
so, ( x- (-2) ) = ( x+2) is a factor
Divide the polynomial x³ +8x² + 20x + 16 by ( x+2) using long division method:
x+2) x³ +8x² + 20x + 16 ( x² + 6x + 8
x³ + 2x²
_______________________
6x² + 20x + 16
6 x² + 12x
____________________________
8x + 16
8x + 16
__________________________
00
f(x)= (x+2) (x² + 6x + 8 )
Factors of (x² + 6x + 8 ) are (x+2)(x+4)
f(x) = (x+2) (x+2)(x+4)
Thus, the factored form of f(x) is f(x) = (x+2) (x+2)(x+4)
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