Answer:
Shorter leg=3
Longer leg=4
Step-by-step explanation:
Equations
In a right triangle, Pythagora's Theorem is satisfied. Being a the hypotenuse, b and c the legs of the triangle, then:
[tex]a^2=b^2+c^2[/tex]
Let's call
x=the shorter leg of the triangle
The longer leg is 1 cm longer than the shorter leg, thus:
x+1=the longer leg.
Since the hypotenuse is 5 cm long:
[tex]5^2=x^2+(x+1)^2[/tex]
Operating:
[tex]25=x^2+x^2+2x+1[/tex]
Swapping sides and simplifying:
[tex]2x^2+2x+1=25[/tex]
Subtracting 25:
[tex]2x^2+2x-24=0[/tex]
Dividing by 2:
[tex]x^2+x-12=0[/tex]
Factoring:
[tex](x-3)(x-4)=0[/tex]
We have two possible solutions:
x=3, x=4
The longer leg is x+1.
If x=3, x+1=4
If x=4, x+1=5. This solution is not valid because one leg would be equal to the hypotenuse.
Thus, the solution is:
Shorter leg=3
Longer leg=4
Gina wants to make
hamburgers for 12 people.
Her recipe serves 8 people
and calls for 4.5 pounds of
ground beef. How much
ground beef should
Gia purchase?
h
Answer:
6.75 pounds
Step-by-step explanation:
This question is of direct variation. We will use x as our answer. 8 is 2/3 of 12, so 4.5 should be 2/3 of x. We can now make an equation.
[tex]4.5=\frac{2}{3} x\\4.5*\frac{3}{2} =\frac{2}{3} x*\frac{3}{2} \\6.75=x[/tex]
In order to solve the equation, we multiply both sides by the reciprocal of 2/3, which is 3/2.
* stands for multiplication
From solving our equation, we get 6.75. We can't forget the units, so the answer is 6.75 pounds.
What is the nth term rule of the linear sequence below?
-9, -5, -1,3,7,...
Answer:
Step-by-step explanation:
Given sequence
-9, -5, -1,3,7,...
Is A.P(,airthmetic progression)
So
nth term of an A.P =a+(n-1)d
Where a=first term (-9)
D=difference=(-5)-(-9)=4
So nth term=-9+(n-1)4
=4n-13
Answer is 4n-13
What is the following product?
(5-12-4/5)(512-43
PLEASE HELP ):
Answer:
-3658.2
Step-by-step explanation:
-4-5(2x -4) = 76
-6
9
-4
7
9514 1404 393
Answer:
x = -6
Step-by-step explanation:
-4 -10x +20 = 76 . . . . . eliminate parentheses
-10x = 60 . . . . . . . . . . . subtract 16
x = -6 . . . . . . . . . . . . . . divide by -10
A downtown parking garage charges individuals to park a car according to the following rate schedule: $1.00 for the first hour, then $2 for each subsequent hour until the daily maximum charge of $9.00 is reached. These charges are represented in the graph below.
which of the following is true?
Answer:
In the graph, a white dot means that the value does not belong to the set, while the colored dot means that the value does belong.
Let's analyze each statement (from top to bottom)
1)The x-axis represents the number of hours, and the y-axis the charge.
Then let's find x = 2.
You can see that there is a colored dot at y = $3, and a white dot at y = $5.
Then the price for exactly two hours is $3, not $5.
Then this first statement is wrong.
2) You can assume that 20 minutes is in between x = 0 and x =1, then from that point, you can see that the equivalent value of y is $1. Then the individuals who park only for 20 minutes will be charged with $1,
This statement is wrong.
3) 1 hour and 15 minutes is in between 1 and 2 hours.
And as you can see, for 1 < x ≤ 2, the price is $3. Then this statement is correct.
4) Here we have x > 4.
In the graph you can see that all values of x > 4 are mapped into the black part of the graph, which is equivalent to the maximum charge of $9.
Then this statement is correct.
What would the set notation for the domain and range of the function, (-3, 6), (-2, -3), and (-1, 6)
Answer:
Domain: {-3, -2, -1}
Range: {-3, 6}
General Formulas and Concepts:
Domain is the set of x-values that can be inputted into function f(x). Range is the set of y-values that are outputted by function f(x).Step-by-step explanation:
Step 1: Define
(-3, 6)
(-2, -3)
(-1, 6)
Step 2: Identify x-values
x = -3, -2, -1
Step 3: Identify y-values
y = -3, 6, 6
A company that makes hair-care products had 6,000 people try a new shampoo. Of the 6,000 people, 48 had a mild allergic reaction. What percent of the people had a mild allergic reaction?
Answer:
I would say 2880 sorry if am wrong
Step-by-step explanation:
6000*48=288,000 then divide by 100 because percent means 100. 288,000/100= 2,880. hope this helps can I get brainlist and add effort before you come to look for anwer.
Does -3 and -2 make a right triangle
Answer:
There is no such thing as negative distances. In order to do Pythagoras theorem you need to know which one is the hypotenuse
Plz answer quick I need to get it bc it’s a quiz
Answer:
slope equals 2
Step-by-step explanation:
graph points and calculate rise over run
A bike travels 24 miles in 3 hours. How many miles will the bike travel in 12 hours?
Answer:
72
Step-by-step explanation:
24 / 3 = 8
so
8*7 = 72
Answer:
72
Step-by-step explanation
24 / 3 = 8
so
8*7 = 72
EMILY COOKIE RECIPE CALLS FOR 3 CUPS OF FLOUR AND 1 CUP OF SUGAR WHAT IS THE RATIO OF FLOUR TO SUGAR
Use a calculator, spreadsheet, or another tool to solve for the unknown sides of the given right triangle. The length of the hypotenuse is 12. a is the length of the side opposite the 10 degree angle and b is the length of the opposite angle B. Round your answers to four decimal places.
Answer:
27
Step-by-step explanation:
2 TIMES 3
The length of the side a and b is 2.0837 and 11.8176 respectively.
Length of side a and b to be determine, hypotenuse is 12 and a is the length of the side opposite the 10 degree angle and b is the length of the opposite angle B.
Trigonometry is branch of mathematics that helps in elevation and angle problems.
Let assume that one angle of triangle is right angle.
So in right angles triangle,
hypotenuse = 12
cos10 = length of b /12
length of b = 12 cos10
length of b = 11.8176
Now,
sin 10 =length of a/ 12
length of a = 12 sin10
length of a = 2.0837
Thus, the length of the side a and b is 2.0837 and 11.8176 respectively.
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help, I’ll give brainliest and thanks
Answer:
1/2
Step-by-step explanation:
Rise over Run... 2/4
Find the value of the missing angle
Which equation represents the number of points in the problem below?
A test is worth 60 points. Multiple-choice questions are worth 2 points, and
short-answer questions are worth 5 points. If the test has 15 questions, how
many multiple-choice questions are there?
O A. 2m+ 5s = 60
B. m + s = 60
O C. 2m + 5s +15 = 60
O D. 2m + 5s = 15
Answer:
Step-by-step explanation:
Let the number of MC questions = x
Let the number of SA questions = y
x + y = 15
2x + 5y = 60
Multiply the top equation by 2
2x + 2y = 30
Put this underneath the second equation and subtract
2x + 5y = 60
2x + 2y = 30 Subtract
3y = 30
y = 10 Subtract
2y = 20
y = 10
x + y = 15
x + 10 = 15
x = 5
classify the triangle based off of the measurements of its sides 30m, 30m
Answer:
i got it
its an isosceles triangle bc two sides are equal.
Multiply 8674 x 678 is what
Answer:
5880972
hope it helps..
the cube_____of 27 is 3.
Answer:
3
Step-by-step explanation:
Answer:
the cube ROOT of 27 is 3.
Step-by-step explanation:
Simplify: 5 -3 • 5 5
25 8
25 -15
5 -3
5 2
What are steps I need to take to find a? Please include working out ❤️❤️
What additional information could be used to prove that triangle XYZ is congruent to triangle Fe.g. using asa or aas check all that apply
Answer:
its the first one and the last one ..that's the answer.
WILL GIVE BRAINLIEST 20 POINTS!!! PLS HELP!!!?!?!?!?! DO NOT COPY AND PASTE FROM OTHER QUESTIONS OR I WILL REPORT U AND DELETE UR ANSWER!!!!
The functions f(x) and g(x) in the table below show Jane's and Mariah's savings respectively, in dollars, after x days. Some values are missing in the table.
x(years) 1 2 3
g(x) = 3x
Jane's savings in dollars 3 9
f(x) = 3x + 3
Mariah's savings in dollars 6 9
Which statement best describes Jane's and Mariah's savings in the long run?
Jane will save more than Mariah.
Mariah will save more than Jane.
The savings will increase by the same factor for both.
The savings will increase by the same percentage for both.
Answer:
Mariah will save more than Jane.
Step-by-step explanation:
i think
Find the value of n.
9 x -1 x n = 9 x -3
Answer:
n=3
Step-by-step explanation:
9 x -1 x n = 9 x -3
-9n=-27
9n=27
n=27/9
n=3
So value of n is 3
I don't know how to solve this.Please help!
3^x=2
A child has fewer than 40 baseball cards. If he puts them in piles of 2, 4, 8, or 12 he has one card left over each time. How many baseball cards does he have?
The child has 25 baseball cards.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The total number of cards the child has can be calculated using the steps below.
We can use the following steps:
- Prime factorization of each number:
2= 2
4= 2²
8 = 2³
12 = 2² x 3
- For each prime factor, choose the maximum exponent in any row, and multiply those together to get the least common multiple.
i.e
The maximum exponent of 2 is 3 and the exponent of 3 is 1.
- The least common multiple.
= 2³ x [tex]3^1[/tex]
= 24
- Add one to get the total number of cards.
Now,
The child's baseball cards.
= 24 + 1
= 25
Therefore,
The child has 25 baseball cards.
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a company has recently been hiring new employees. today the company has 26% more employees than it did a year ago. if there are currently 69300 employees, how many employees did the company have a year ago
Answer:
Did you just assume my gender?
Mark me brainliest please :)
Love ya!
Step-by-step explanation:
A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. An SRS of 28
stores this year shows mean sales of 64 units of a small appliance, with a standard deviation of 13.8 units. During the same point in time last year, an SRS of 28 stores had mean sales of 48.958 units, with standard deviation 15.4 units. An increase from 48.958 to 64 is a rise of about 24%.
1. Construct a 99% confidence interval estimate of the difference μ1−μ2
μ1−μ2, where μ1 is the mean of this year's sales and μ2 is the mean of last year's sales.
(b) The margin of error is
2. At a 0.01 significance level, is there sufficient evidence to show that sales this year are different from last year?
Answer:
Confidence interval = (4.61972, 25.46428)
Margin of Error = 3.9078675
Step-by-step explanation:
Given that :
This year:
Mean (μ1) = 64
Standard deviation (s1) = 13.8
Sample size (n1) = 28
Last year:
Mean (μ2) = 48.958
Standard deviation (s2) = 15.4
Sample size (n2) = 28
99% confidence interval estimate of the difference μ1−μ2
α = 1 - 99% = 0.01
(μ1−μ2) ± t0.01,27 * (√s1²/n1 + s2²/n2)
t0.01, 27 = 2.770683 (t value calculator)
√s1²/n1 + s2²/n2 = √13.8^2/28 + 15.4^2/28 = 3.9078675
(64 - 48.958) ± 2.667(3.9078675)
15.042 ± 10.42228
(15.042 - 10.42228), (15.042 + 10.42228)
(4.61972, 25.46428)
The margin of error :
√(s1²/n1) + (s2²/n2)
√(13.8^2/28) + (15.4^2/28)
√(6.8014285 + 8.47)
√15.2714285
= 3.9078675
What is the slope m in the equation y= -2x + 5
Answer:
Answer -2/1
Step-by-step explanation:Slope is the number in front of x
Help please! I’ll give brainliest!
Answer:
i think the answer is B
i am sorry if this is wrong
Step-by-step explanation:
Find the product. Enter your final answer as a simplified fraction.
-1/8•7•2/5=
Answer:
-7/20
Step-by-step explanation:
Answer:
-1/140
Step-by-step explanation:
-1/8*7*2/5
-7/8*2/5
-7/20