Use the given information to match the answers.
ABC is a right triangle.
1. 2√13
2. √5
3. 3√3
1. If b = 2 and c = 3, then a =
2. If a = 3 and c = 6, then b =
3. If a = 4 and b = 6, then c =
Answers
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
1)
[tex] {3}^{2} = {a}^{2} + {2}^{2} \\ a = \sqrt{ {3}^{2} - {2}^{2} } \\ a = \sqrt{5} [/tex]
2)
[tex] {6}^{2} = {3}^{2} + {b}^{2} \\ b = \sqrt{ {6}^{2} - {3}^{2} } \\ b = \sqrt{27} \\ b = \sqrt{9} \sqrt{3} \\ b = 3 \sqrt{3} [/tex]
3)
[tex] {c}^{2} = {4}^{2} + {6}^{2} \\ c = \sqrt{ {4}^{2} + {6}^{2} } \\ c = \sqrt{52} \\ c = \sqrt{4} \sqrt{13} \\ c = 2 \sqrt{13} [/tex]
Solve them by using
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
1.
[tex] {a}^{2} + {2}^{2} = {3}^{2} \\ {a}^{2} + 4 = 9 \\ {a}^{2} = 9 - 4 \\ {a}^{2} = 5 \\ a = \sqrt{5} [/tex]
2.
[tex] {3}^{2} + {b}^{2} = {6}^{2} \\ 9 + {b}^{2} = 36 \\ {b}^{2} = 36 - 9 \\ {b}^{2} = 27 \\ b = \sqrt{9 \times 3} \\ b = 3 \sqrt{3} [/tex]
3.
[tex] {4}^{2} + {6}^{2} = {c}^{2} \\ 16 + 36 = {c}^{2} \\ {c}^{2} = 52 \\ c = \sqrt{13 \times 4} \\ c = 2 \sqrt{13} [/tex]
Hope this helps. - M
Related Questions
Ross and 5 of his friends are going kayaking. They rented 6 kayaks for 420. then they brought food for all 6 people , which costs 144. if all 6 people shared the cost 144. if all 6 people shared the cost of the trip equally, how much did each person pay?
A. 70
B.76
C.88
D.94
please help me
Answers
adding $420 + $144 = 564
then divide 564 and 6 to get 94.
Answer:
its $95
Step-by-step explanation:
i got it right
Baby Kelsey wants to arrange 12 blocks in a row. How many different arrangements can she make?
Answers
To find the number of arrangements Baby Kelsey can make with 12 blocks, we calculate 12 factorial (12!), which equals 479,001,600. This represents the total number of unique ways to arrange the blocks in a row.
Explanation:The student has asked how many different arrangements can be made with 12 blocks in a row. To determine the number of different arrangements, we use the concept of factorial, which is represented by an exclamation mark (!). In this case, we want to find 12!, which represents the product of all positive integers from 1 to 12.
Specifically, the calculation is 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1. This multiplication results in the number of unique ways to arrange the 12 blocks since each block is distinct and can be placed in any position within the arrangement.
Therefore, there are 479,001,600 different arrangements possible when organizing 12 unique blocks in a row, showcasing the vast number of combinations for even a small number of objects.
The volume of two spheres are 327\pi in^{3} and 8829\pi in^{3}
What is the ratio of their radii?
Answers
[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\ -----------------------------[/tex]
[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ %The volume of two spheres are 327\pi in^{3} and 8829\pi in^{3} \cfrac{small}{large}\qquad \cfrac{s}{s}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{s}{s}=\cfrac{\sqrt[3]{327}}{\sqrt[3]{8829}}\qquad \begin{cases} 8829=3\cdot 3\cdot 3\cdot 327\\ \qquad 3^3\cdot 327 \end{cases}[/tex]
[tex]\bf \cfrac{s}{s}=\cfrac{\sqrt[3]{327}}{\sqrt[3]{3^3\cdot 327}}\implies \cfrac{s}{s}=\cfrac{\underline{\sqrt[3]{327}}}{3\underline{\sqrt[3]{327}}}\implies \cfrac{s}{s}=\cfrac{1}{3}[/tex]
Which of the following is equivalent to the midpoint between the points (8, -9) and (0, 5)?
(4, -2)
(4, 2)
(-2, 4)
(2, 4)
Answers
_____________
What is the y-value of sin(x) when x = -90°?
Answers
You can use the unit circle to find this value, if you wish.
sin(-90) = -1
Which is closer to the x-axis (1.4 , 2.2) and (4.1 , 2.4) or (3.9) and (8,9) or (1 1/4 , 2) and 1 1/4 , 8)?
Answers
A circle is centered at (−8, −13) and has a radius of 13.
What is the equation of the circle?
Enter the equation in the box using lower case variables x and y.
Answers
the equation of a circle is
(x-h)²+(y-k)²=r²
where
(h,k) is the center
r is the radius
so
for a circle is centered at (−8, −13) and has a radius of 13
the equation is
(x+8)²+(y+13)²=13²--------------> (x+8)²+(y+13)²=169
the answer is
(x+8)²+(y+13)²=169
(x+8)²+(y+13)²=169
Find 3 consecutive odd numbers where the product of the smaller two numbers is 46 less than the square of the largest number.
Answers
___________________________________________________
Explanation:
___________________________________________________
Let the "3 consecutive odd numbers" be represented by:
___________________________________________________
"x" ;
___________________________________________________
"x + 2 " ;
___________________________________________________
"x + 4 " ;
___________________________________________________
→ Solve for "x" ; and then solve for "(x + 2)" and "(x + 4)" .
___________________________________________________
The product of the smaller two numbers, is "46 less than" (the square of) the largest number:
___________________________________________________
→ " x* (x + 2) = (x + 4)² − 46 " ;
___________________________________________________
Note the "distributive property" of multiplication:
___________________________________________________
a(b + c) = ab + ac ;
a(b − c) = ab − ac .
___________________________________________________
Start with simplifying the "left-hand side" of the equation:
___________________________________________________
" x(x + 2)" = (x * x) + (x * 2 ) = (x² + 2x) ;
___________________________________________________
Then simplify the "right-hand side" of the equation:
___________________________________________________
" (x + 4)² − 46 " ;
___________________________________________________
→ (x + 4)² = (x + 4) (x + 4) ;
Note: " (a + b)(c + d) = ac + ad + bc + bd " .
→ (x + 4)² = (x + 4) (x + 4) = (x *x) + (x *4) + (4 *x) + (4 * 4) ;
= x² + 4x + 4x + 16 ;
= x² + 8x + 16;
→ Bring down the " − 46 " ;
___________________________________________________
→ x² + 8x + 16 − 46 ;
= x² + 8x + 16 − 46 ;
= x² + 8x − 30 ;
____________________________________________________
Now, rewrite the entire equation:
____________________________________________________
→ x² + 2x = x² + 8x − 30 ;
Subtract "x² " & "2x" from EACH SIDE of the equation:
→ x² + 2x − x² − 2x = x² + 8x − 30 − x² − 2x ;
to get:
→ 0 = 6x − 30 ;
→ 6x − 30 = 0 ;
Add "30" to each side of the equation:
→ 6x − 30 + 30 = 0 + 30 ;
→ 6x = 30 ;
Divide each side of the equation by "6" ;
to isolate "x" on each side of the equation; & to solve for "x" ;
→ 6x / 6 = 30 / 6 ;
to get;
→ x = 5 ;
→ "(x + 2)" = "(5 + 2)" = 7 ;
→ "(x + 4)" = "(5 + 4)" = 9 ;
______________________________________________________
Answer: The numbers are: " 5, 7, and 9 " .
______________________________________________________
Solve the equation.
left parenthesis x plus 4 right parenthesis left parenthesis x minus 9 right parenthesis equals 4 x
x =
nothing
(Use a comma to separate answers as needed.)
Answers
To solve the equation (x + 4)(x - 9) = 4x, expand and rearrange the terms. Then solve the quadratic equation by factoring or using the quadratic formula.
Explanation:To solve the equation (x + 4)(x - 9) = 4x, we can expand the left side of the equation and then rearrange the terms:
x^2 - 5x - 36 = 4x
Next, we can move all the terms to one side of the equation:
x^2 - 9x - 36 = 0
Finally, we can solve this quadratic equation by factoring or using the quadratic formula to find the values of x.
A fish tank in the shape of a rectangular prism has these dimensions: length = 20 inches width = 10 inches height = 12 inches What is the volume of water in the tank when it is 45 full?
Answers
The volume of water in the fish tank when it is 45% full is 1080 cubic inches.
Explanation:To find the volume of water in the tank when it is 45% full, we first need to calculate the volume of the tank.
The formula for the volume of a rectangular prism is length × width × height.
Given that the length is 20 inches, the width is 10 inches, and the height is 12 inches, we can substitute these values into the formula: 20 × 10 × 12 = 2400 cubic inches.
Next, we need to find 45% of this volume. To do this, we multiply the volume by 0.45: 2400 × 0.45 = 1080 cubic inches.
Therefore, the volume of water in the tank when it is 45% full is 1080 cubic inches.
The ratio of height between Joey and his girlfriend is 8:7. If Joey is 72 inches tall, how tall is his girlfriend in inches
Answers
8x is height of Joey.
8x=72
x=72/8=9
7x is height of Joey's girlfriend.
7x=7*9=63 in.
Answer: 63 in.
Multiply the ratio by 9:
Joey : Girlfriend = 8x9 : 7x9
Joey : Girlfriend = 72 : 63
Answer: His girlfriend is 63 inches tall.
if f(x) = x-1 and g(x) =2x-3 find the sum, difference, product and quotient of these two functions
Answers
f (x) = x-1
g (x) = 2x-3
For the sum we have:
f (x) + g (x) = (x-1) + (2x-3)
f (x) + g (x) = 3x - 4
For subtraction we have:
f (x) - g (x) = (x-1) - (2x-3)
f (x) - g (x) = -x + 2
For the product we have:
f (x) * g (x) = (x-1) * (2x-3)
f (x) * g (x) = 2x ^ 2 - 3x - 2x + 3
f (x) * g (x) = 2x ^ 2 - 5x + 3
For the quotient we have:
f (x) / g (x) = (x-1) / (2x-3)
HELP!!! - The lunch special at a diner is a bowl of soup with either a salad or a sandwich. The diner offers chicken noodle, potato, or lentil soup as part of the special. Which statement best describes how this tree diagram represents the number of different ways the lunch special can be ordered?
A: The diagram is flawed because it should show there are four different ways the special can be ordered.
B: The diagram is flawed because it should show there are five different ways the special can be ordered.
C: The diagram models the situation correctly, and it shows there are six different ways the special can be ordered.
D: The diagram models the situation correctly, and it shows there are nine different ways the special can be ordered.
Answers
The correct answer is C) The diagram models the situation correctly, and it shows there are six different ways the special can be ordered.
Answer:
C: The diagram models the situation correctly, and it shows there are six different ways the special can be ordered.
Step-by-step explanation:
A package of cookies contains 6 cookies. Each package of cookies costs $1.49.
A function, f(x), is written to represent the cost of purchasing x packages of cookies.
What is the practical domain for the function f(x)?
A: all positive integers
B: all real numbers
C: all whole numbers that are multiples of 6
D: all whole numbers
Answers
Given are 6 cookies in a package.
Given that the cost of a package = 1.49 dollars.
Let's assume we purchase 'x' numbers of packages.
So, total cost of 'x' packages = '1.49x' dollars.
f(x) is the function that represents the cost of 'x' packages, i.e. f(x) = 1.49x
Since the number of packages can not be negative or can't be decimal numbers, so 'x' should be positive integral values.
So, the practical domain of f(x) would be "positive integral values".
Hence, option A is correct, i.e. "all positive integers".
If i walk 4 miles an hour how long will it take to walk 1 mile
Answers
x= portion of 1 hour
4 miles/1 hour= 1 mile/ x hour
cross multiply
4 * x= 1 * 1
4x= 1
divide both sides by 4
x= 1/4 of an hour
To find number of minutes:
1 hour= 60 minutes
=1/4 of an hour * 60 minutes
=60/4
=15 minutes
ANSWER: It would take 1/4 of one hour ( or 15 minutes) to walk 1 mile.
Hope this helps! :)
What is 40.15 divided by 7.3, written as a decimal?
Answers
hope this helps!!
Final answer:
To calculate 40.15 divided by 7.3, we can use long division. The final quotient is 5.5, and there is no remainder. Therefore, 40.15 divided by 7.3 written as a decimal is 5.5.
Explanation:
To calculate 40.15 divided by 7.3, we can use long division.
First, we write the division problem with 40.15 as the dividend and 7.3 as the divisor:
5.5
________
7.3 | 40.15
We start by dividing 40.15 by 7.3. The quotient is 5.5.
Next, we subtract 5.5 multiplied by 7.3 from 40.15:
5.5
________
7.3 | 40.15
- 36.5
________
37.65
Since the remainder, 37.65, is greater than the divisor, 7.3, we can continue dividing.
We bring down the next digit from the dividend, which is 0, and divide it by 7.3:
5.5
________
7.3 | 40.15
- 36.5
________
4.15
3.65
We repeat the process of dividing and subtracting until the remainder is less than the divisor:
5.5
________
7.3 | 40.15
- 36.5
________
4.15
3.65
5.5
0
The final quotient is 5.5, and there is no remainder. Therefore, 40.15 divided by 7.3 written as a decimal is 5.5.
Find an explicit formula for the sequence 30\,,\,150\,,\,750\,,\,3750,...30,150,750,3750,...30, space, comma, space, 150, space, comma, space, 750, space, comma, space, 3750, comma, point, point, point.
Answers
an=ar^(n-1)
where
a=first term
n=number of terms
r=common ratio
from the sequence:
a=30
r=5
thus the explicit formula will be:
an=30(5)^(n-1)
hence the answer is:
an=30(5)^(n-1)
Answer:750+3750=4,500
Step-by-step explanation:
Ryan wants to use the Fermi process to estimate the number of basketballs that would fill a gymnasium. As part of the process, he needs to estimate the volume of a basketball. The diameter of a basketball is about 10 in.
Which estimate best approximates the volume of a basketball?
5×10^1 in³5×10^2 in³
5×10^3 in³
5×10^4 in³
Answers
The volume of a sphere is given by
[tex]V= \frac{4}{3} \pi r^3[/tex]
Given that the diameter of the basketball is 10 in., thus the radius is 10 / 2 = 5 in.
Thus, the volume of the basketball is given by
[tex]V= \frac{4}{3} \pi(5)^3 \\ \\ = \frac{4\times125}{3} \pi=523.6\ in^3[/tex]
Therefore, The best approximate of the volume of the basketball is [tex]5\times10^2\ in^3[/tex]
An equation of a function y(t) is shown. y(t)=−t2+14t−40 Which of the following statements are true about the graph of y(t) for 6≤t≤8 and WHY? a. The value of y(t) increases over the interval 6≤t≤7. b. The value of y(t) increases over the interval 7≤t≤8. c. The average rate of change over the interval 6≤t≤8 is 0. d. The value of y(t) is constant over the interval 6≤t≤8. e. The average rate of changer over the interval 6≤t≤7 is the same as the average rate of change over the interval 7≤t≤8. Make sure you use complete sentences and capitalize!
Answers
Hope this helps :)
What is the input to a trigonometric function?
a ratio
the x position of a point on the circle
a central angle of a circle
the y position of a point on the circle
Answers
Answer: A central angle of a circle
Step-by-step explanation:
The trigonometric functions are also known as circular functions.
The two fundamental trigonometric functions are defined as the coordinates of a any point A travelling around on the unit circle of radius 1 .
The input variable in trigonometric functions is the central angle of the circle 'x' such that we get sin x and cos x which give the x and y coordinates of A.
Hence, the input to a trigonometric function is a central angle of a circle.
What is the excluded value of
-2x/17
a. x=0
b. x=2
c. x=17
d. no excluded values
Answers
There is only excluded values if the variable x is in the denominator.
Tammy and Wyatt are sales associates at the same used car dealership. Their supervisor is planning to promote the employee with the best sales numbers, on average. The box plots below show their sales, in thousands of dollars, for the past 2 weeks:
box plot labeled Tammy with min at 19, Q1 at 21, median at 25.5, Q3 at 26.75, max at 27.75. Box plot labeled Wyatt with min at 18.5, Q1 at 20.5, median at 24, Q3 at 27.5, max at 28.25
Who should get the promotion, and why?
A) Wyatt should get the promotion. His data is more evenly distributed, so his sales are more consistent.
B) Wyatt should get the promotion because he had the highest sales in a single day.
C) Tammy should get the promotion because her lowest value is higher than Wyatt's lowest value.
D) Tammy should get the promotion. She has a higher median with a smaller IQR, so her sales are better on average.
Answers
Answer:
Tammy should get the promotion. She has a higher median with a smaller IQR, so her sales are better on average.
Jack's father let jack use a rectangular section of the back yard that had dimensions of 10 feet by 12 feet for his garden. he wanted to put a fence around the outside of the garden. how long should the piece of fencing he needs to buy be?
Answers
shawna and amanda are selling pies for a school fundraiser. customers can buy cherry pies and pumpkin pies. shawna sold 1 cherry pie and 3 pumpkin pies for a total of $55. amanda sold 3 cherry pies and 3 pumpkin pies for a total of $69. what is the cost of each one cherry pie and one pumpkin pie?
PLEASE SHOW WORK
Answers
Shawna: c + 3p = 55
Amanda: 3c + 3p = 69
We want to find the cost of c + p. To do this, the easiest way is to divide the second equation by 3:
(3c + 3p)/3 = 69/3
c + p = 23
Therefore, 1 cherry pie & 1 pumpkin pie cost $23.
Find the volume of a right prism with height h=10 cm, if: a The base is equilateral triangle with side 4 cm, base altitude of ≈ 3.5 cm. Help me!!!
Answers
A(triangle)=(4×3.5)/2=7cm²
V(prism)=7×10=70cm³
Hope this helped!
To find its Volume of Right prism we multiply the base of the triangle times the height and divide that by 2.Then, multiply the area times the length, or the depth, of the prism to find the volume.
Area of the equilateral triangle = [tex]\frac{1}{2}x4x3.5.[/tex]
Area of triangle = 7 square cm.
Volume of the right prism = Area of triangle x Height of prism = 7x10 =70 cubic cm.
Volume of right prism = 70 cubic cm.
How do I do this ??
Answers
-4x^2 *-7 = +28x^2
So since you can’t add them together the answer is the second one
how many real solutions does y = (-x + 4)^2 have?
Answers
1.y = -1
2.y = 4/3 = 1.333
Comment
There are a couple of ways of doing this to show there there is just one solution. The most easily done way is to graph the quadratic. I have done that for you.
Notice that the quadratic touches the x axis, it does not cut it in two places or no places. When a quadratic just touches the x axis, it has only one solution.
Method 2
The quadratic is shown in the vertex form. If there was a number outside he bracket showing squares then you would get
y = (-x + 4)^2 + 4 (drawn in blue)
y = (-x + 4)^2 - 6 (drawn in green)
These two examples show what the vertex form would look like if the axis was cut in 2 places or no places and there would be no solution for the first one and 2 places for the second one.
9. Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale
Answers
tan (theta) = C.O / C.A
Where,
theta: angle
C.O: opposite leg
C.A: adjoining catheto
Substituting values:
tan (25) = x / 5
Clearing x:
x = 5 * tan (25)
x = 2.33
Answer:
x = 2.3
A scatter plot has a correlation coefficient of -0.159. What does this suggest about the relationship between the two variables?
Answers
the value of r is closer to 0 than it is to -1, so the data is very weakly linear associated. The scatter plot points are too spread out for one single line to be close to them all. A different curve (such as a parabola) may be a better fit.
The fact that r is negative suggests that there is negative association. What this means is that as x goes up, y goes down. As you move from left to right, you go downhill. The regression line will have a negative slope.
Given the two expressions shown below:
A. \sqrt{3} +\sqrt{2}
B. \sqrt{3} +\sqrt{6}
Which statement best describes the two expressions?
Both are rational.
Both are irrational.
A is rational, but B is irrational.
A is irrational, but B is rational.
Answers
Answer: Both are irrational.