Find the missing length. Round to the nearest tenth if necessary. Find the missing side.
Answers
Given:
a = 4
b = 5
c = unknown
Let's find the length of c.
Here, we are given a right triangle, where c is the longest side.
The longest side of a right triangle is called the hypotenuse.
To find the hypotenuse, apply Pythagorean Theorem:
[tex]c^2=a^2+b^2[/tex]Input values into the equation above:
[tex]\begin{gathered} c^2=4^2+5^2 \\ \\ c^2=16+25 \\ \\ c^2=41 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{c^2}=\sqrt[]{41} \\ \\ c=6.4 \end{gathered}[/tex]Therefore, the length of the missing side, c =
Related Questions
11) Find the length of XZ.If WY = 15x -2 and XZ = 9x + 10,TVZY
Answers
Answer:
XZ = 28
Explanation:
The trapezoid is isosceles because it has two equal sides WZ and XY.
The diagonals of isosceles trapezoids have the same length. So, WY is equal to XZ and we can write the following equation:
WY = XZ
15x - 2 = 9x + 10
Then, solving for x, we get:
15x - 2 = 9x + 10
15x - 2 + 2 = 9x + 10 + 2
15x = 9x + 12
15x - 9x = 9x + 12 - 9x
6x = 12
6x/6 = 12/6
x = 2
Therefore, the value of XZ is equal to:
XZ = 9x + 10
XZ = 9(2) + 10
XZ = 18 + 10
XZ = 28
So, the answer is XZ = 28
What is the approximate area of a clock face with a diameter of eight inches?
Answers
The area formula of a circle is :
[tex]A=\frac{1}{4}\pi D^2[/tex]From the problem, the diameter is 8 inches.
The area will be :
[tex]\begin{gathered} A=\frac{1}{4}\pi(8)^2 \\ A=50.27 \end{gathered}[/tex]The answer is 50.27 in^2
Marco bought 12 roses for
$48. What was the original
cost of EACH rose before
the discount? Set up an
equation and solve to
answer this question
Super Saver
DEALS! Get $2
off each rose
when you buy 12
or more roses
Answers
Marco bought 12 roses for $48. Each rose was originally $4 before the discount, and Super Saver Get $2 off each rose when you buy 12 or more roses each rose is $6.
How to calculate discount?The discount formula is as follows: Discount = Marked Price - Selling Price. OR. Formula for Discount Percentage = Marked Price Discount Rate A 10% discount can be calculated in two steps: Step 1 is to convert your percentage to a decimal using the formula 10 / 100 = 0.1. As a decimal, 10% equals 0.1. Step 2 is to multiply your original price by the decimal you chose. The sweaters were originally priced at $80. The store would like to offer a 15% discount on the sweaters. The company converts 15% to the decimal 0.15 to calculate the discount. The result is a figure of $12 after multiplying 0.15 by the original price of $80.Therefore,
Marco bought 12 roses for $48. Each rose was originally $4 before the discount.
∴ 48/12 = $4 and,
Super Saver Get $2 off each rose when you buy 12 or more roses
each rose is $6.
∴ 12/2 = $6
To learn more about discount, refer to:
https://brainly.com/question/23865811
#SPJ9
Part II: Constructed Response15. An amusement park has two carousels. The first carousel has a circularplatform with a diameter of 13 meters, and the second carousel has acircular platform with a diameter of 19 meters. How much larger is thearea of the larger carousel's platform than the area of the smallercarousels platform? Show your work, using 3.14 for r.151st find Area of First Carousel:16. Next find Area of Second Carousel:127.6.417. What is the difference between the two areas?
Answers
- Area of First Carousel:
diameter = 13 m
[tex]\text{Area}=\pi\cdot\frac{d^2}{4}=(3.14)\cdot\frac{(13)^2}{4}=3.14\cdot\frac{169}{4}=\frac{530.66}{4}=132.7m^2[/tex]- Area of Second Carousel:
diameter = 19 m
[tex]\text{Area}=(3.14)\cdot\frac{(19)^2}{4}=3.14\cdot\frac{361}{4}=\frac{1133.54}{4}=283.4m^2[/tex]- The difference between the two areas is:
[tex]283.4-132.7=150.7m^2[/tex]Answer:
The platform area of the larger carousel is 150.7 m^2 larger than the platform area of the smaller carousel.
Match the one-to-one functions with their inverse functions.
Answers
Matching the following function
What is a Function?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The function of f^(-1)(x) = 5x is:
f(x)= x / 5
The function of f^(-1)(x) = x^3 / 2 is:
f(x)=3√2x
The function of f^(-1)(x) = x+10 is:
x - 10
The function of f^(-1)(x) = 3(x + 17) / 2 is:
(2x / 3) - 17
Hence, These are the Match of one-to-one functions with their inverse functions.
To learn more about Function click on the link
https://brainly.com/question/10439235
#SPJ9
The area of the triangle below is40 square meters. What is the length of the base?Express your answer as a fraction in simplest form.
Answers
Given the area of the triangle:
[tex]A=\frac{3}{40}m^2[/tex]You can identify in the figure provided in the exercise that the height of the triangle is:
[tex]h=\frac{1}{5}m[/tex]The area of a triangle can be calculated using this formula:
[tex]A=\frac{bh}{2}[/tex]Where "A" is the area, "b" is the base, and "h" is the height.
If you solve for "b", you obtain this formula:
[tex]\begin{gathered} 2A=bh \\ \\ b=\frac{2A}{h} \end{gathered}[/tex]Therefore, knowing the Area and the height of the triangle, you can substitute them into the formula and then evaluate, in order to find the length of its base:
[tex]b=\frac{(2)(\frac{3}{40})}{\frac{1}{5}}[/tex][tex]b=\frac{\frac{6}{40}^{}}{\frac{1}{5}}[/tex][tex]b=\frac{6\cdot5}{40\cdot1}[/tex][tex]b=\frac{30}{40}[/tex][tex]b=\frac{3}{4}m[/tex]Hence, the answer is:
[tex]b=\frac{3}{4}m[/tex]Hi, can you help me with this exercise please, Find the value of x. Round lengths of segments to the nearest tenth and angle measures to the nearest degree.
Answers
From the given figure , we will use the Sine function in order to find segment x .
Sin 70 ° = opposite /hypotaneus
Sin 70 ° =x /7
∴x = 7* Sin 70°
x = 6.5778
x ≈6.6 ...( rounded to the nearest 10 )
Solve the word problem. Show all the steps.
Two numbers add to 39. One number is 9 less than 7 times the other. What are the numbers?
Answers
The numbers represented by the word problems are 33 and 6
How to determine the solution to the word problem?The statements in the question are:
Two numbers add to 39. One number is 9 less than 7 times the other.Let the numbers in the expressions be x and y
So, we have
x + y = 39
x = 7y - 9
Substitute x = 7y - 9 in the equation x + y = 39
So, we have
7y - 9 + y = 39
Evaluate the like terms
8y = 48
Divide both sides by y
y = 6
Substitute y = 6 in x + y = 39
x + 6 = 39
Evaluate the like terms
So, we have
x = 33
Hence, the numbers are 33 and 6
Read more about word problems at
https://brainly.com/question/29118452
#SPJ1
For the following exercises, evaluate the function f at the indicated values.
a. f(-3) b. f(2) c. f(-a) d. -f(a)
4. f(x)=2x-5
5. f(x)=−5x²+2x−1
6. f(x)=x-1-x+1
Answers
After we evaluate the function f at the indicated values the results are
a. (4) −11, (5) −52, (6) 0
b. (4) -1, (5) −17, (6) -5
c. (4) −2a−5, (5) −5a² −2a−1, (6) −3+a
d. (4) −2a+5, (5) 5a² −2a+1, (6) 3+a
What is function?A relation in which there is only one possible pairing of each x and each y is called a function. It should be noted that while the reverse is true, the same y can be paired with different x. Vertical and horizontal lines are the only types of linear equations that are not functions.
Lets evaluate the function a. f(-3)
4. f(-3) = 2(-3)-5
= −11
5. f(-3) = −5(-3)²+2(-3)−1
= −52
6. f(-3) = -3-1-(-3)+1
= 0
Lets evaluate the function b. f(2)
4. f(2) = 2(2)-5
= −1
5. f(2) = −5(2)²+2(2)−1
= −17
6. f(2) = -3-1-(2)+1
= −5
Lets evaluate the function c. f(-a)
4. f(-a) = 2(-a)-5
= −2a−5
5. f(-a) = −5(-a)²+2(-a)−1
= −5a² −2a−1
6. f(-a) = -3-1-(-a)+1
= −3+a
Lets evaluate the function d. -f(a)
4. -f(a) = -(2(a)-5)
= −2a+5
5. -f(a) = -(−5(a)²+2(a)−1)
= 5a² −2a+1
6. -f(a) = -(-3-1-(a)+1)
= 3+a
Learn more about functions
https://brainly.com/question/11624077
#SPJ13
Line r passes through the point (3,6) and is parallel to line s is 3y=-6x+9 enter the equation of line r in y=ax+b form
Answers
Answer:
y = -6/3 + 12
Step-by-step explanation:
Step 1: Plot the point
Step 2: Simplify the given function then graph it
3y = -6x + 9 becomes:
y = -6/3x + 3
Step 3: Using the slope of -6/3 (because parallel lines will ALWAYS have the same slope) find 1 more point on the graph.
Step 4: Draw a line thru those points and find the y-int
y = ax + b, x and y are variables, a is the slope and b is the y-int
y = -6/3 + 12
(3^9)/(3^-9)simpilfy. write your answer using a positive exponent
Answers
Simplifying:
[tex]\frac{3^9}{3^{-9}}\rightarrow3^{9-(-9)}\rightarrow3^{9+9}\rightarrow3^{18}[/tex]Help mee pleasee!!
thank you <3
Answers
...................
What is the simplified form: (8m + 1)^2
Answers
Answer
(8m + 1)^2 = (8m + 1)² = 64m² + 16m + 1
Explanation
The question simply wants us to simplify the expression
(8m + 1)^2
= (8m + 1)²
= (8m + 1) (8m + 1)
= 8m (8m + 1) + 1 (8m + 1)
= 64m² + 8m + 8m + 1
= 64m² + 16m + 1
Hope this Helps!!!
Consider the functions f(x) and g(x). The function f(x)=2x-5 and g(x)= -f(x+1)+3. A. Describe the three transformations that are performed on f(x) to create g(x).1.2.3.B. Sketch a graph of g(x):
Answers
First we have to take a look at the expression f(x + 1). This represents an horizontal translation. So this is the first transformation:
1. Horizontal translation
Now we can see that we have to multiply f(x + 1) by -1. This represents a reflexion on the y-axis
2. Reflection on y-axis
Finally we can see that -f(x + 1) is added by 3 units. This represents a vertical translation:
3. Vertical translation
Answer:
1. Horizontal translation
2. Reflection on y-axis
3. Vertical translation
Now let's see the final function:
f(x) = 2x - 5
f(x+1) = 2(x + 1) - 5
f(x+1) = 2x + 2 - 5
f(x+1) = 2x - 3
g(x) = -2x + 3 + 3
g(x) = -2x + 6
So let's plot f and g on the same reference system:
graph triangle JKL with vertices j(2,3), k(-2,1), L(-1,5) and its image after the glide reflection: x-axis
Answers
Check the picture below.
Identify the property used in each step of solving the inequality 7x+4 <46,
Step
7x+4 <46
7x <42
x <6
Answers
Answer:
1) Given
2) Subtraction Property of Inequalities
3) Division Property of Inequalities
Bea is asked to graph this system of equations: 8x - 6y= 3 -3y + 4x = 4 How many times will the lines intersect?
Answers
Given the system of equations:
8x - 6y = 3
-3y + 4x = 4
To find how many times the lines will intersect. let's solve the system of equation using substitution method.
8x - 6y = 3 ........................................1
-3y + 4x = 4 ......................................2
From equation 1, make x the subject:
8x - 6y = 3
8x = 3 + 6y
[tex]\begin{gathered} x=\frac{3}{8}+\frac{6}{8}y \\ \\ x=\frac{3}{8}+\frac{3}{4}y \end{gathered}[/tex][tex]\text{Substitute (}\frac{3}{8}+\frac{3}{4}y)\text{ for x in equation 2}[/tex]We have:
[tex]\begin{gathered} -3y+4(\frac{3}{8}+\frac{3}{4}y)=4 \\ \\ -3y+\frac{3}{2}+3y=4 \\ \\ \end{gathered}[/tex]Multiply through by 2 to eliminate the fraction:
[tex]\begin{gathered} -3y(2)+\frac{3}{2}(2)+3y(2)=4(2) \\ \\ -6y+3+6y=8 \end{gathered}[/tex][tex]\begin{gathered} -6y+6y=8-3 \\ \\ 0=5 \end{gathered}[/tex]Since we have 0 = 5, it means the system of equations has no solution.
Therefore, the lines will not intersect, because this system has no solution.
ANSWER:
A. The lines will not intersect, because this system has no solution.
Convert 63°F to degrees Celsius. If necessary, round your answer to the nearest tenth of a degree. Here are the formulas. 5 C== (F-32) F=-6 +32 5 63 PF - I c
Answers
The given temperature is 63 F
The formula for convert temperature into Degree C from Degree F.
[tex]C=\frac{5}{9}(F-32)[/tex]Substitute all the value in the above equation.
[tex]\begin{gathered} C=\frac{5}{9}(63-32) \\ C=\frac{5}{9}\times31 \\ C=17.22C \end{gathered}[/tex]The nearest tenth is 17degree C.
14. Sort each number of miles and number of hours traveled into the appropriate bin to identify the rate in miles per hour. 6.NS.2 718 miles in 5.95 hours 45.8 miles In 4 hours 2,865 miles in 24.8 hours 419.72 miles in 80.6 hours 935.47 miles in 22.75 hours Las Toan 10 MIO por Hour Between 10 and 99 Miles per Hour Greater Than 100 Miles per Hour
Answers
we have
Find the unit rate in each case
so
718/5.95=120.67 miles per hour ---------> greater than 100 miles per hour
45.8/4=11.45 miles per hour ------> between 10 and 96 miles per hour
2,865/24.8=115.52 miles per hour -------> greater than 100 miles per hour
419.72/80.6=5.21 miles per hour ------------> less than 10 miles per hour
935.47/22.75=41.12 miles per hour ------> between 10 and 96 miles per hour
The points (−7,−4) and (3,8) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.
Answers
The length of the radius of the circle is √61.
Here there are two endpoints of the circle (-7,-4) and (3,8)
To find the distance between the two points we have a formula:
Distance = [tex]\sqrt{(x_{2} -x_{1} ^{2} + (y_{2} - y_{1})^{2} }[/tex]
So here we have
([tex]x_{1} , y_{1}[/tex]) = (-7, -4)
([tex]x_{2} , y_{2}[/tex]) = ( 3,8)
Putting the value we have,
=[tex]\sqrt{(3-(-4))^{2} + (8-(-7))^{2} }[/tex]
=[tex]\sqrt{10^{2} + 12^{2} }[/tex]
=√244
=2√61
The diameter is 2√61
radius = diameter/2
= 2√61/2
= √61
Therefore the length of the radius of a circle is √61.
To know more about the circle refer to the link given below:
brainly.com/question/24375372
#SPJ1
For each system to the best description of a solution if applicable give the solution
Answers
System A
[tex]\begin{gathered} x-4y=4 \\ -x+4y+4=0 \end{gathered}[/tex]solve the first equation for x
[tex]x=4+4y[/tex]replace in the second equation
[tex]\begin{gathered} -(4+4y)+4y+4=0 \\ -4-4y+4y+4=0 \\ 0=0 \end{gathered}[/tex]The system has infinitely many solutions, They must satisfy the following equation
[tex]\begin{gathered} x-4y=4 \\ -4y=4-x \\ y=\frac{4}{-4}-\frac{x}{-4} \\ y=\frac{x}{4}-1 \end{gathered}[/tex]System B
[tex]\begin{gathered} x-2y=6 \\ -x+2y=6 \end{gathered}[/tex]solve for x for the first equation
[tex]x=6+2y[/tex]replace in the second equation
[tex]\begin{gathered} -(6+2y)+2y=6 \\ -6-2y+2y=6 \\ -6=6 \end{gathered}[/tex]The system has no solution.
Evaluar la expresion numérica -8.5 (9.4 a 6.1
Answers
answer: b) - 28.05
URGENT!!) Which of the following served as the primary route for transporting cotton to Georgia's only sea port? (5 points)
a
The Savannah River
b
The Chattahoochee River
c
The Oconee River
d
The Suwanee River
Answers
Answer:
Correct answer:
a. The Savannah River
variables review find w if 67.1=29.7-0.2w
Answers
Given the following equation:
[tex]67.1=29.7-0.2w[/tex]You need to solve for the variable "w" in order to find its value. To do this, you can follow the steps shown below:
1. You can apply the Subtraction property of equality by subtracting 29.7 from both sides of the equation. Then:
[tex]\begin{gathered} 67.1-(29.7)=29.7-0.2w-(29.7) \\ 37.4=-0.2w \end{gathered}[/tex]2. Finally, you need to apply the Division property of equality by dividing both sides of the equation by -0.2. Then, you get:
[tex]\begin{gathered} \frac{37.4}{-0.2}=\frac{-0.2w}{-0.2} \\ \\ w=-187 \end{gathered}[/tex]The answer is:
[tex]w=-187[/tex]An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 45% probability of winning the first contract. If they win the first contract, the probability of winning the second is 75%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 52%.
Answers
1. The probability that they win both contract will be 23.4%.
How to calculate the probability?It should be noted that probability simply means the likelihood that an event will occur.
The probability of winning the contract will be:
= Probability of A winning × Probability of B winning
= 45% × 52%
= 0.45 × 0.52
= 0.234
= 23.4%
The probability is 23.4%
Learn more about probability on:
brainly.com/question/25870256
#SPJ1
Lashonda, Josh, and Brian sent a total of 90 text messages during the weekend, Lashonda sent 10 more messages than Josh. Brian sent 2 times as manymessages as Josh. How many messages did they each send?Number of text messages Lashonda sent:Number of text messages Josh sent:Number of text messages Brian sent:
Answers
Defining:
Number of messages of Lashonda = L
Number of messages of Josh = J
Number of messages of Brian = B
We know that:
L+J+B=90 (Equation 1)
We also know:
L = J+10 (Equation 2)
B=2J (Equation 3)
Now, we can substitue the values for L and B in the first equation
L+J+B=90
J+10 + J + 2J = 90
4J=90-10
4J=80
J=80/4
J=20
Since you found how many messages Josh sent, we can return to Equation 2 and 3:
L = J+10
L = 20 + 10
L = 30
B=2J
B=2*20
B=40
ANSWER:
Number of text messages Lashonda sent: 30
Number of text messages Josh sent: 20
Number of text messages Brian sent: 40
I need help with my math
Answers
Answer:
Sure
Step-by-step explanation:
Let me know what you want by making me brainliest
Write the equation of the line with the points (0, 2) and (4, 10) in standard form.
Answers
By definition, the of a line written in Standard form is:
[tex]Ax+By=C[/tex]Where "A", "B" and "C" are Integers ("A" is positive).
The Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
You know that this line passes through these points:
[tex](0,2);(4,10)[/tex]By definition, the value of "x" is zero when the line intersects the y-axis. Then, you can identify that, in this case:
[tex]b=2[/tex]Now you can substitute the value of "b" and the coordinates of the second point into the following equation and solve for "m":
[tex]y=mx+b[/tex]Then, the slope of the line is:
[tex]\begin{gathered} 10=m(4)+2 \\ 10-2=4m \\ 8=4m \\ \\ \frac{8}{4}=m \\ \\ m=2 \end{gathered}[/tex]Therefore, the equation of this line in Slope-Intercept form is:
[tex]y=2x+2[/tex]To write it in Standard form, you can follow these steps:
- Subtract 2 from both sides of the equation:
[tex]\begin{gathered} y-(2)=2x+2-(2) \\ y-2=2x \\ \end{gathered}[/tex]- Subtract "y" from both sides of the equation:
[tex]\begin{gathered} y-2-(y)=2x-(y) \\ -2=2x-y \\ 2x-y=-2 \end{gathered}[/tex]The answer is:
[tex]2x-y=-2[/tex]Answer:
2x-y =-2
Step-by-step explanation:
To find the equation of the line in standard form, first, we need to find the slope
m = ( y2-y1)/(x2-x1)
m = (10-2)/(4-0)
= 8/4 = 2
Then we can use the slope intercept form
y = mx+b where m is the slope and y is the y-intercept
y = 2x +b
Using the y-intercept ( 0,2)
y = 2x +2
The standard form is Ax +By =C where A is a positive integer and B is an integer
Subtract 2x from each side
-2x +y = 2
Multiply each side by -1
2x-y =-2
look at the circle below. identify an example of radius
Answers
we have taht
radius is
HG
HA
HE
HD
The radius is the distance from the center of the circle to any point that lies on the circle
In this problem
point H is the center of the circle
so
the distance from H to any point on the circumference of the circle is a radius
see the attached image
All those segments are radius
Part 2
Remember that
the circumference is equal to
[tex]C=\pi\cdot D[/tex]so
In the table
the value of C is about 3 times the diameter
therefore
the values of flying disc are inaccurate
because
if D=23 cm the circunference must be about 69 cm, not 28 cm
A company has determined that the demand function for a certain couch is given by
= 2700 − 0.75, where p is the price per couch, and x is the number of couches sold. The fixed costs associated with producing a line of couches is $760,000, and each couch costs $360 to make. Determine how many couches should be manufactured and sold in order to maximize profit. Start by finding functions to represent the revenue and the total cost, then find a function for profit
Answers
The number of couches manufactured and sold in order to maximise the profit is 1560.
The demand function will be
p = 2700 - 0.75x
Here p = price per couch and x = number of couch
Total Fixed cost = $760000
Variable cost per couch = $360
Total cost = Fixed cost + variable cost
T(x) = 760000 + 360x
Revenue function will be
R(x) = Px
(2700 - 0.75x)x
2700x - 0.75x²
Since profit function = Pr(x)
Pr(x) = R(x) - T(x)
= 2700x - 0.75x² -760000 -360x
- 0.75x² + 2700x - 360x - 760000
For maximum profit
[tex]\frac{d}{dx}(Pr(x)) = 0[/tex]
[tex]\frac{d}{dx}[-0.75x^{2} + 2340x -760000 ] = 0[/tex]
-1.5x + 2340 = 0
x = 2340/1.5
x = 1560
The couches sold for maximum profit = 1560
Therefore, the number of couches manufactured and sold in order to maximise the profit is 1560.
To learn more about deman function refer here
https://brainly.com/question/15234429
#SPJ1
