Question
The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.
Answer:
[tex]Hypotenuse:37.56[/tex]
[tex]Other\ Legs: 26.56[/tex]
Step-by-step explanation:
Let the hypotenuse be y and the other legs be x.
So:
[tex]y = 11 + x[/tex]
Required
Determine the exact dimension of the triangle
Using Pythagoras theorem;
[tex]y^2 = x^2 + x^2[/tex]
[tex]y^2 = 2x^2[/tex]
This gives:
[tex](11+x)^2 = 2x^2[/tex]
Open bracket
[tex]121 + 22x + x^2= 2x^2[/tex]
Collect like terms
[tex]2x^2 - x^2 -22x - 121 = 0[/tex]
[tex]x^2 -22x - 121 = 0[/tex]
Using quadratic formula:
[tex]x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]x = \frac{-(-22)\±\sqrt{(-22)^2 - 4*1*-121}}{2*1}[/tex]
[tex]x = \frac{-(-22)\±\sqrt{968}}{2*1}[/tex]
[tex]x = \frac{22\±31.11}{2}[/tex]
Split
[tex]x = \frac{22+31.11}{2}\ or\ x = \frac{22-31.11}{2}\\[/tex]
[tex]x = \frac{53.11}{2}\ or\ x = \frac{-9.11}{2}[/tex]
x can not be negative.
So:
[tex]x = \frac{53.11}{2}[/tex]
[tex]x = 26.56[/tex]
Recall that:
[tex]y = 11 + x[/tex]
[tex]y = 11 + 26.56[/tex]
[tex]y = 37.56[/tex]
Hence, the dimensions are:
[tex]Hypotenuse:37.56[/tex]
[tex]Other\ Legs: 26.56[/tex]
Out of the 232 media executives, 6 of them control 90% of all media outlets. If there are a total of 400 major
media outlets, how many are controlled by those 6 executives.
Answer:
360
Step-by-step explanation:
6 executives control 90% of the 400 major media outlets
so we need to find 90% of 400
first, convert 90% to a decimal and multiply
0.9•400 gives us 360
so 360 media outlets are controlled by those 6 executives
hope this helps babe <3
What is the GCF of the terms of the polynomial −12y^4 + 8y^3 – 4y^2?
Answer:
the GCF of the terms of the polynomial −12y^4 + 8y^3 – 4y^2 is:
4 y^2
If a simple machine requires an effort of 20 newtons to lift a load of 100 newtons, its
mechanical advantage is:
a. 5
b. 5N
c. 5MA
Answer:
A. 5
Step-by-step explanation:
x+1/3=5
help plzzzzzzz
Answer:
x = 4 2/3
Step-by-step explanation:
x = 5 - 1/3
x = 4 2/3
Answer:
x = [tex]\frac{14}{3}[/tex]
Step-by-step explanation:
Subtract [tex]\frac{1}{3}[/tex] from both sides
x + [tex]\frac{1}{3}[/tex] - [tex]\frac{1}{3}[/tex] = 5 - [tex]\frac{1}{3}[/tex]
x = [tex]\frac{14}{3}[/tex] or 4 [tex]\frac{2}{3}[/tex]
On two separate occasions, Mr. Johnson needed some electrical work done on his house. He called an electrician from Electrical Outlet in town. The electrician worked 2.5 hours and charged $180 for the first visit. The second time he worked 4 hours and charged $243. Let be the number of hours the electrician works in a single visit, and let be the total amount, in dollars, that the electrician charged for the visit. A. Create the equation that relates the total cost to the time worked. [4 pts] Note: This will be a linear relationship, so start by finding the slope of the line based on the given information. Express the final equation in = + form.
Answer:
y = 42x + 75
Step-by-step explanation:
Using the equation of a line in the form
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁) = m where m is the slope of the line
Let x be the number of hours the electrician works in a single visit, and let y be the total amount, in dollars, that the electrician charged for the visit.
Since the electrician worked 2.5 hours and charged $180 for the first visit. The second time he worked 4 hours and charged $243. where x₁ = 2.5 hours, y₁ = $ 180, x₂ = 4 hours and y₂ = $ 243
We find the slope of the line, m
m = (243 - 180)/(4 - 2.5) = (243 - 180)/(4 - 2.5) = 63/1.5 = 42
Since m = (y - y₁)/(x - x₁) ,
42 = (y - 180)/(x - 2.5)
cross-multiplying, we have
42(x - 2.5) = (y - 180)
expanding the bracket, we have
42x - 105 = y - 180
adding 180 to both sides, we have
42x - 105 + 180 = y - 180 + 180
42x + 75 = y
y = 42x + 75
The linear equation that relates the total cost to the time worked is:
[tex]y = 42x + 75[/tex]
What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem, the function has two points: (2.5, 180) and (4, 243).
The slope is given by change in y divided by change in x, hence:
[tex]m = \frac{243 - 180}{4 - 2.5} = 42[/tex]
Then:
[tex]y = 42x + b[/tex]
Considering point (2.5, 180), we have that when x = 2.5, y = 180, which is used to find b.
[tex]y = 42x + b[/tex]
[tex]180 = 42(2.5) + b[/tex]
[tex]b = 75[/tex]
Hence, the function is:
[tex]y = 42x + 75[/tex]
More can be learned about linear equations at https://brainly.com/question/24808124
A farmer sows 100 seeds of a new type of corn and wants to quickly determine the yield, or total number of ears of corn, for the crop when it has matured. He decides to take a simple random sample of the crop. Which of the following correctly labels the population?
00–99
01–99
0–99
1–100
Answer:
00–99
Step-by-step explanation:
I got it Correct
The correct label for the population would be: 1-100 as per the given scenario.
What is population?In statistics, a population refers to the entire group of individuals, objects, or measurements that the researcher is interested in studying.
In this scenario, the population refers to the entire group of items or people that the farmer is interested in studying.
In this case, the population is the total number of ears of corn produced by all 100 seeds sown by the farmer.
As a result, the population's correct label would be: 1-100. Because the farmer is interested in the yield of all 100 seeds, the population includes all possible outcomes of the experiment, ranging from one to one hundred ears of corn.
Option A, B, and C do not include all possible outcomes, whereas option D includes the number 0, which is not an option in this scenario.
Thus, the answer is 1-100.
For more details regarding population, visit:
https://brainly.com/question/27991860
#SPJ7
3. Solve for the side length of BA and AC. * (image attached)
1 point
Captionless Image
BA = 8, BA = 30
BA = 8, AC = 16
BA = 8, AC = 8√2
BA = 8, AC = 8√3
Answer:
D. BA = 8, AC = 8√3
Step-by-step explanation:
First, because this is a right triangle, refer to the trigonometric ratios:
tangent = opposite side/adjacent side
sine = opposite side/hypotenuse
cosine = adjacent side/hypotenuse
BA is the opposite side to the angle measure given, ∠C—which is 30°—and we have the measure of BC. BC is the hypotenuse, as it is across from the right angle of the right triangle. So we can use sine:
sine = opposite side/hypotenuse
sin(30) = BA/16
sin(30) / 1 = BA / 16
Cross multiply:
BA = sin(30) (16)
BA = 8
AC is the adjacent side to the angle measure given, ∠C—which is 30°—and we have the measure of BC. BC is the hypotenuse, as it is across from the right angle of the right triangle. So we can use cosine:
cosine = adjacent side/hypotenuse
cos(30) = AC/16
cos(30) / 1 = AC / 16
Cross multiply:
AC = cos(30) (16)
AC = 8√3
You can check by using the Pythagorean Theorem:
a² + b² = c²
8² + (8√3)² = 16²
64 + 192 = 256
256 = 256
A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks the players to run from one corner to the corner diagonally across the field. How far do the players run?
Answer:
150 meters
Step-by-step explanation:
Answer:
150 metresStep-by-step explanation:
We can imagine the rectangle, when cut diagonally it forms a Right angled Triangle
Using this we can find the diagonal i.e hypotenuse.
From the question we know that,
Length = 120 metres
Width = 90 metres
So we can find the diagonal by keeping it as x using the pythogorean theorem.
[tex] {120}^{2} + {90}^{2} = {x}^{2} \\ 14400 + 8100 = {x}^{2} \\ 22500 = {x}^{2} \\ x = \sqrt{22500} \\ x = 150[/tex]
What is the volume of a hemisphere with a diameter of 37.6 m, rounded to the nearest tenth of a cubic meter?
Answer:
13916.6m^3
Step-by-step explanation:
1. Are two congruent figures similar? Explain.
Answer:
Yes
Step-by-step explanation:
Congruence means two objects (whether two dimensional or three dimensional) are identical in size and shape. Everything about them -- their angles, lengths of sides, overall dimensions -- are identical. Similar means being the same shape. Two congruent figures must be the same shape, so they are similar.
Hope that helps!
-Sabrina
Which of the following is NOT a linear function?
y=x
y=5
y=-3x-5
y=x^2+6
Sally invests £8000 in a savings account.
The account pays 2.8% compound interest per year.
Work out the value of her investment after 4 years.
Give your answer to the nearest penny.
Answer:
£8934.34
Step-by-step explanation:
[tex]8000 * 1.028^4 = 8934.34[/tex]
rounding to 2dp
if trunctuated at 2dp however, 8934.33
the number is multiplied by 1.028 to the power of four as you go through the equation four times, so it would be the same as
x * n * n * n * n, where it would simplify to x * n^4
Maddie and Josh are trying to clean the roof of their house. They place the base of the ladder 3 feet away from the base of the house. Their ladder is 27 feet long. What angle does the ladder make with the ground?
Answer:
83.6 degrees
Step-by-step explanation:
Can someone plz help me plz I beg u the answer choices are at the bottom just pls
Answer:
Step-by-step explanation:
PLEASE HELP !!! ILL GIVE BRAINLESS
Answer:
a. ∠G = 180 - (90 + 32)
b. ∠G = 58°
c. ∠J = 180 - 58°
d. ∠J = 122°
Step-by-step explanation:
Angles are added to result in 180°
when the line is straight; thus:
a.
∠G = 180 - (90 + 32)
b.
∠G = 180 - 122
∠G = 58°
c.
∠J = 180 - 58°
d.
∠J = 122°
_____________________
#IndonesianPride - kexcvi
Hi can someone tell me what this is in y=mx+b please?
Answer: y= 5x +7
Slope is rise over run. From the two given points we rise 10 and run 2 which is 10/2 or 5.
7 is how high/low we are when we are at x=0
Answer:
Hi!
y= 5x+7
The five is the slope and i counted from the point on the y axis until the next point on the line. Which is 10/2. simplified that is 5/1 or just 5.
The seven in where the line intercepts the y axis.
Hope this helps! Have a good day and don't forget to be tiger fierce!! :)
10=0.5f
What’s the answer to “f”?
Answer: 20
Step-by-step explanation: to find f, you divide 10 by 0.5 to see what’s left. When you divide it you get 20. To check your work multiply 0.5 by 20 and you’ll see that it equals 10.
Problem to solve:
b) The Smith family has five members. They go to the beach for a day. Each member has a small towel and a
beach towel. How many towels did they bring to the beach?
Answer:
25 towels hahha
Step-by-step explanation:
In ΔBCD, the measure of ∠D=90°, the measure of ∠B=71°, and DB = 67 feet. Find the length of BC to the nearest tenth of a foot.
Answer:
in triangle BCD
relationship between base and hypotenuse is given by cos angle
cos 71=b/h
cos71=BD/BC
cos71=67/x
x=67/cos71=205.8ft.
the length of BC to the nearest tenth of a foot is 206ft.
Write the equation of a line that has a slope of 3 and passes through the point (5, 7).
O y = 3x + 8
O y = 5x + 7
O y = 3x - 8
O y = 7x + 5
Answer:
y = 3x - 8
Step-by-step explanation:
All the options are written in slope-intercept ( [tex]y = mx + b[/tex]) form. So, what we can do with the given information is write the equation in point-slope form first, then convert it to slope-intercept form.
1) First, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] to find the point-slope equation of the line. Substitute [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] for real values.
Since [tex]m[/tex] represents the slope, substitute 3 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line intersects, substitute the x and y values of (5,7) into the appropriate places in the formula as well. This gives the following equation of the line in point-slope form:
[tex]y-7 = 3(x-5)[/tex]
2) Now, isolate y in the above equation to find its slope-intercept form.
[tex]y-7=3(x-5)\\y-7 = 3x-15\\y = 3x -8[/tex]
Thus, the answer would be the third option as it matches the result we received.
Question 1: How much fabric is needed for a round table cloth?
Assume the radius is 10 inches. How much fabric would you need?
Answer:
50 yards because of the roundness of the table
Charlie grew 3/4 of an inch on her 7th birthday. Her twin sister Lucy grew 1/2 of an inch. How much more did charlie grow more than lucy?
Answer: 1/4
Step-by-step explanation: 3/4-1/2= 1/4
What is the slope of the line?
-3/2
slope = rise/run
We can use the two points to calculate rise (y value change) and run (x value change)
slope = (-6)/4 = -3/2
I need help with this
Answer:
13.5
Step-by-step explanation:
4+5 = 9.
9/2 = 4.5
4.5 * 3 = 13.5
What is categorical data
Answer:
Categorical variables represent types of data which may be divided into groups. It can not measure.
Step-by-step explanation:
what is the solution to the system of equations x-y=5 and 3x+7y=-5
Answer:
Step-by-step explanation:
3(x-y)-3x-7y=3(5)-(-5)
3x-3y-3x-7y=15+5
-10y=20
y=-2, since x-y=5
x-(-2)=5
x+2=5
x=3
So the solution is the point (3,-2)
Which equation matches the hanger?
y = 6.3
3y = 6.3
y/3 = 6.3
y + 3 = 6.3
Answer:
B 3y=6.3
Step-by-step explanation:
On the hangers left side there are 3 Y's so we would put that together as 3y
On the hangers right side there is a rectangle with a whole of 6.3
The 3y would equal with the 6.3
HELP IT'S DUE IN 10 MINUTES
Noelle rode her bike 5/10 of a kilometer to the library, and then another 22/100 of a kilometer to her friend's house. How far did Noelle ride her bike in all?
A. 27/110
B. 7/10
C. 72/100
D. 225/100
Answer:
C. 72/100
Step-by-step explanation:
does -7/10 = -4/5? plz hurry
Answer:
False
Step-by-step explanation:
_7/10 does not equal -4/5
Answer: No.
Step-by-step explanation: The left side, -0.7 doesn't equal the right side, -0.8, so it is false.
To find equivalent fractions, multiply the the numerator and denominator by the same whole number.
[tex]-\frac{7}{10}\times\frac{2}{2} =-\frac{14}{20}[/tex]
[tex]-\frac{7}{10}\times\frac{3}{3} =-\frac{21}{30}[/tex]
[tex]-\frac{7}{10}\times\frac{4}{4} =-\frac{28}{40}[/tex]
And so on...
[tex]-\frac{4}{5}\times\frac{2}{2} =-\frac{8}{10}[/tex]
[tex]-\frac{4}{5}\times\frac{3}{3} =-\frac{12}{18}[/tex]
[tex]-\frac{4}{5}\times\frac{4}{4} =-\frac{16}{20}[/tex]
And so on...
If we keep doing this, they won't equal each other.
So no, they're not equivalent.
Can y’all do 5-6 please.I have this whole thing due at 12:00 lol.