Answers
============================================================
Explanation:
Use the pythagorean theorem to tie together the three sides of the right triangle.
[tex]a = x-3 = \text{horizontal leg}\\b = x+5 = \text{vertical leg}\\c = 9 = \text{hypotenuse}[/tex]
[tex]a^2 + b^2 = c^2\\(x-3)^2 + (x+5)^2 = 9^2\\x^2-6x+9 + x^2+10x+25 = 81\\2x^2+4x+34 = 81\\2x^2+4x+34-81=0\\2x^2+4x-47=0\\[/tex]
From here, we use the quadratic formula to solve for x.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(4)\pm\sqrt{(4)^2-4(2)(-47)}}{2(2)}\\\\x = \frac{-4\pm\sqrt{392}}{4}\\\\x \approx \frac{-4\pm19.79898987}{4}\\\\x \approx \frac{-4+19.79898987}{4} \ \text{ or } \ x \approx \frac{-4-19.79898987}{4}\\\\x \approx \frac{15.79898987}{4} \ \text{ or } \ x \approx \frac{-23.79898987}{4}\\\\x \approx 3.94974747 \ \text{ or } \ x \approx -5.94974745\\\\[/tex]
We'll ignore the negative x value because it makes the sides x+5 and x-3 to be negative numbers. Negative side lengths make no sense.
The only practical solution is roughly x = 3.94974747; rounding to 3 sig figs leads to the final answer of x = 3.95
In this case, 3 sig figs means that we're rounding to 2 decimal places.
Related Questions
. Find the range of the function y
1/4x +1 if the domain is {-8, -4, 0}.
Answers
The range of a function is the possible output values the function can have.
The range of the function is all real values except 0
The function is given as:
[tex]\mathbf{y = \frac{1}{4x + 1}}[/tex]
When the denominator of the function is 0, the function would not have a real value.
This means that:
[tex]\mathbf{y \ne 0}[/tex]
i.e. the value of y cannot be 0.
Hence, the range of the function is all real values except 0
Read more about domain and range at:
https://brainly.com/question/21853810
a
Kenny took a total of 10 quizzes over the course of 2 weeks.
How many weeks of school will Kenny have to attend this quarter
before he will have taken a total of 45 quizzes?
weeks
Helppp <3
Answers
Answer:
he would do 9 weeks of school
Step-by-step explanation:
count by fives
Suppose that a department contains 8 men and 17 women. How many ways are there to form a committee with 6 members if it must have strictly more women than men
Answers
2. A trader received a commission of 25 percent on the sales he made in a month. His commission was CH¢ 180.00. find his total sales for a month.
Answers
Answer:
CH¢ 720.00Step-by-step explanation:
25% commission equals 180.00
Total sales amount is x:
x*25/100 = 1800.25x = 180x = 180/0.25x = 720simplify the expression.
20a^4 × (1/2 a^3 )^2
Answers
Answer:
5a^10
Step-by-step explanation:
Which ordered pair is NOT in the solution set of −2x + 3y ≥ 12?
A. (-3,5)
B. (-5,0)
C. (0,6)
D. (-5,3)
Answers
Answer:
B
Step-by-step explanation:
Complete the description of the piecewise function graphed below.
Answers
Step-by-step explanation:
not everything is visible, and the points' coordinates have to optically estimated (particularly for the leftmost point).
I assume, we have the following points :
(-6, 1.5) (-3, 3)
(-3, 2) (1, 2)
(1, 1) (6, -9)
all 3 segments are lines with the basic function definition
y = ax + b
a is the slope of the line function and is always the factor of x.
it is the ratio y/x indicating how many units y changes, when x changes a certain amount of units when going from one point on the line to another.
b is the y-intercept (the y value when x = 0).
the first segment goes from (-6, 1.5) to (-3, 3).
x changes by +3 units (from -6 to -3).
y changes by +1.5 or 3/2 units (from 1.5 to 3).
the slope of the line is 3/2 / 3 = 3/(2×3) = 1/2
giving us the first part
y = (1/2)x + b
b we get by using the coordinates of one point (e.g. -3, 3) as x and y values and solve for b :
3 = (1/2)×-3 + b
3 = -3/2 + b
6/2 + 3/2 = b
9/2 = b
the full equation is
y = (1/2)x + 9/2 = (x + 9)/2
the second segment is a flat, horizontal line and is simply
y = 2
the third segment goes from (1, 1) to (6, -9) :
x changes by +5 units (from 1 to 6).
y changes by -10 units (from 1 to -9).
the slope of the line is -10/5 = -2
giving us the first part
y = -2x + b
b we get by using the coordinates of one point (e.g. 1, 1) as x and y values and solve for b :
1 = -2×1 + b
1 = -2 + b
3 = b
the full equation is
y = -2x + 3
The answer is in the pic below!
Evaluate the expression for x = 5:
2•(x-2)^2+5
Answers
Answer:
2•(x-2)^2+5 3x + 3 = x + 13, 3x = x + 10, 2x = 10, and x = 5.
I hope that this helps :P (and thx for the ez pointsss)
What is the Factor of 3/9+8/9
Answers
Step-by-step explanation:
the lcm is 9 so....
3/9+8/9
multiply both sides by their lcm which is 9...
so....
9 (3/9)+9 (8/9)
3+8=11
5. The lengths of the sides of a triangle are x, 2x + 1 and 5x + 4 inches. If the perimeter is 53
inches, what is the value of x?
Equation: Xt2x+/+5x+4-53
Solution:
Answers
Answer:
x = 6
Step-by-step explanation:
The perimeter is the sum of the 3 sides
Sum the 3 sides and equate to 53
x + 2x + 1 + 5x + 4 = 53 , simplify left side
8x + 5 = 53 ( subtract 5 from both sides )
8x = 48 ( divide both sides by 8 )
x = 6
2x2-2x3-2x4-2x5-2x6-2x7
Answers
Answer:
-46
Step-by-step explanation:
first multiply
add
and last subtract
The area in square feet of a rectangular field is x^2-80x+1500. the width, in feet, is x-30. what is the length in feet.
Answers
Answer:
Step-by-step explanation:
Area = x² - 80x + 1500
= x² -30x - 50x + 1500
= x(x - 30) - 50(x - 30)
= (x -30) (x - 50)
Length =(x -50) ft
1.8 0.087 − 0.947 + 2.2 0.044
Answers
Answer:
2
Step-by-step explanation:
im smart
Write the equation of a horizontal line going through the point (8, -1)
Answers
Answer:
y =-1
Step-by-step explanation:
An easy way to answer any type of these questions is looking at the part where it said "Write the equation of a horizontal line", if this is the case you have to look at the 2nd point given to you which is -1 and simply make y = to that. Having y = -1 covers every possible x value which is why it is valid.
1 year = 12 months
3/4 year =
Answers
Answer:
3/4 year = 9
Step-by-step explanation:
To find 3/4 of a year you first need to find 1/4 of a year so you do 12/4 and get 3. Now we know that 1/4 of a year is 3 months so you just multiply that by 3 to get 9. So 3/4 of a year is 9 months.
I hope this helps!
Your answer to 3/4 of a year is 9 months
FOR 3 graders learn and pay attention in class its important Ask me any multiplacation equation or time tables
Answers
Answer:
c
Step-by-step explanation:
write each power as a product of the same factor. Then find the value. 4^4
Answers
Answer:
256
Step-by-step explanation:
4^4 means 4raise to power 4. so, it's typically 4x4x4x4 which is 256
Fibd the distance and midpoint between each pair of points. C(-2,2) d(5,-3)
Answers
Answer:
D=[tex]\sqrt{10}[/tex] or about 3.2 M=(1.5,-0.5)
Step-by-step explanation:
D=[tex]\sqrt{(x2+x1)^2 +(y2-y1)^2}[/tex] M=[tex](\frac{x1+x2}{2} , \frac{y1+y2}{2} )[/tex]
Lets find the distance first:
D=[tex]\sqrt{(5+-2)^2 + (-3+2)^2}[/tex]
D=[tex]\sqrt{(3)^2+(-1)^2}[/tex]
D=[tex]\sqrt{9+1}[/tex]
D=[tex]\sqrt{10}[/tex]
D is about = 3.2
Lets find the midpoint now:
M= [tex](\frac{-2+5}{2} , \frac{2+-3}{2} )[/tex]
M=[tex](\frac{3}{2} ,\frac{-1}{2} )[/tex]
M= (1.5,-0.5)
can some one help me
Answers
Answer:
y=x-3
Hope This Helps!!!
Select the correct answer.
If you roll a fair die twice, what is the probability of getting an even number at least once?
A.
0.75
B.
0.36
C.
0.5
D.
0.25
Answers
Answer:
A
Step-by-step explanation:
Got this right on edmentum
Events A and B are disjoint. Find P(AorB) when P(A) = 0.55 and P(B) = 0.2
P (A or B)=
Answers
Answer:
0.75 = P(A or B)
Step-by-step explanation:
Since the events are disjoint, we can find the probability of one or the other occurring merely by adding P(A) and P(B): 0.55 + 0.2 = 0.75 = P(A or B)
PLEASEEEEEEE HELP ME GUYS!!
Answers
What is the value of y? y = 40 y = 80 y = 100 y = 120.
Answers
Answer:
I think it is 80. But I am also not sure because this question is not briefly described.
Answer:
80
Step-by-step explanation:
got it right on edge
onique bought 2 hot dogs and 1 large soda. She spent $7. Scott
bought 4 hot dogs and 1 large soda. He spent a total of $12.
What is the cost of one hot dog and one large soda?
Answers
Find the perimeter.Simplify your answer.
Answers
Answer:
20c+14
Step-by-step explanation:
To find the perimeter we have to add up all the sides
4c+6c+7+4c+6c+7
Combine light terms
20c+14
Answer:
Well your not given C so we just leave that be and we can just add up all 4 sides since perimeter means outside length total. Now when added up,
6c+7+6c+7+4c+4c= 20c+14
20c+14 is the perimeter
The simple process of counting the number of observations (cases) that are classified into certain categories is called
Answers
Answer:
tabulation. the simple process of counting the number of observations (cases) that are classified into certain categories; a frequency count; counting the number of responses in categories. one-way tabulation. categorization of single variable existing in a study.
Step-by-step explanation:
How do I graph y=-2x+7?
Answers
Answer:
Step-by-step explanation:
A food truck sells tacos, burritos, and drinks.
Let event A = A customer buys a taco.
Let event B = A customer buys a drink.
What does PA or B) = 0.55 mean in terms of this problem?
A. The probability that a customer buys both a taco and a drink is
55%.
B. Buying a taco and buying a drink are mutually exclusive events.
C. The probability that a customer buys neither a taco nor a drink is
55%.
O D. The probability that a customer buys a taco, a drink, or both is
55%.
Answers
Answer:
D. The probability that a customer buys a taco, a drink, or both is
55%.
What is the equation of a line with a y-intercept at (0, 2) and a slope of 3? a. y = 2 x + 3 c. y = 3 x + 2 b. y = 3 x minus 2 d. y = negative 2 x + 3
Answers
Answer:
C) y = 3x + 2
Step-by-step explanation:
Given the slope of the line, m = 3, and the coordinates of the y-intercept, (0, 2).
We can substitute these values into the following slope-intercept form, y = mx + b, where:
m = slope
b = the y-coordinate of the y-intercept.
Therefore, the correct answer is option C, where it shows the equation of the line in slope-intercept form is: y = 3x + 2.
Plz help .!$&&&&&&&&&
Answers
The thing dosnet show