Answers
Answer:
x = 15
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² = 9² + 12² = 81 + 144 = 225 ( take square root of both sides )
x = [tex]\sqrt{225}[/tex] = 15
Answer:
x = 15
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
From inspection of the given right triangle:
a = 9b = 12c = xSubstitute the given values into Pythagoras Theorem and solve for x:
[tex]\implies 9^2+12^2=x^2[/tex]
[tex]\implies 81+144=x^2[/tex]
[tex]\implies 225=x^2[/tex]
[tex]\implies \sqrt{x^2}=\sqrt{225}[/tex]
[tex]\implies x=15[/tex]
Related Questions
Multiply and combine like terms to determine the product of these polynomials. (2x – 3)(5x + 6)
Answers
Answer:
Step-by-step explanation:
(2x – 3)(5x + 6)
10x2 + 12x - 15x - 18
10x2 - 3x - 18
The product of the given polynomials is 10x² - 3x - 18
What is a polynomial?A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
The given polynomials are:
(2x – 3)(5x + 6)
By multiplying the two polynomials, we get
10x² + 12x - 15x - 18
10x²- 3x - 18
Hence, 10x²- 3x - 18 is the product of the given polynomials.
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Pls awnser this Giving brainlest to the right person that has the awnser
Answers
Answer:
top one is dependent
bottom is independent
Step-by-step explanation:
the amount of money you pay is based off of the amount of time on your subscription
A recipe from Sally’s "Chocoholic’s Cookbook" requires 70\frac{1}{6} grams of chocolate for each chocolate fudge cake. How many grams of chocolate would she need if she made one chocolate cake for each of her 12 closest friends?
Answers
Answer:
842 grams
Step-by-step explanation:
[tex]70\frac{1}{6} =\frac{421}{6}[/tex]
[tex]\frac{421}{6} *12\\\\842[/tex]
One cake consists of 421/6 grams of chocolate.
Since Sally wants to give 1 cake to 12 friends, we multiply 421/6 and 12.
To make 12 cakes, she needs 842 grams of chocolate.
At what time t was the instantaneous velocity equal to the average velocity? (Round your answer to one decimal place.)
Answers
Answer:
Instantaneous velocity can be equal to average velocity when the acceleration is zero or velocity is constant because in this condition all the instantaneous velocities will be equal to each other and also equal to the average velocity.
2. Two sidewalks in a park are represented by lines on a coordinate grid.
Sidewalk 1: 3x + 3y = 6
Sidewalk 2: y = x + 6
(a) Find the solution to the system of equations by using the substitution method.
(b) Show ALL of your steps.
Answers
Answer: x is -2 and y is 4 if needed (-2,4) is the origin form
Step-by-step explanation: first we take side walk one we subtract -3x on both sides then you get 3y=-3x+6 divide both by 3 you get y=-x+2 finally we can substitute. substitute y for x+6 you get x+6 = -x+2 do the inverse of -x on both sides you get 2x+6=2 do the inverse of 6 on both sides you get 2x=-4 divide 2 on both sides you get x=-2. substitute x of y=-x+2 to y=-(-2)+2 mult -1 x -2 is 2, 2+2 is four so y= 4 put that together x is -2 and y is 4
determine the area of the parallelogram below
Answers
Answer:
A= BH
A=8cm ×2.2 cm
A= 17.6cm²
What is the vertex form to standard form?
Answers
Answer:
[tex]y=x^2+2x-2[/tex]
Step-by-step explanation:
Vertex Form:Vertex form is expressed as: [tex]y=a(x-h)^2+k[/tex], and is super useful when analyzing the vertex, which is given to be (h, k).
Standard Form:Standard form is expressed as: [tex]y=ax^2+bx+c[/tex], and is also useful in certain cases.
Converting Vertex to Standard Form:When converting standard to vertex we have to complete the square to rewrite the equation using a perfect square binomial, which is what really distinguishes the two. Now when we want to convert back into standard form, we simply need to get rid of this perfect square binomial, which we can do by expanding out the perfect square binomial into a trinomial.
So in other words, we want to multiply out the following: [tex](x+1)(x+1)[/tex], which becomes: [tex]x^2+2x+1[/tex] which you can solve by using polynomial multiplication, which is essentially just extending the logic of the distributive property. In general when given two polynomials to multiply, you look at one polynomial, and then multiply it by each term in the other polynomial, now repeat this for each term in the polynomial you were initially looking at. I'll provide a picture to better illustrate this. You can use FOIL if it helps you with multiplying binomials, but remembering how to generally use it, will help you when multiplying polynomials in general.
Now that we've multiplied out the expression, we can substitute it into the equation: [tex]y=x^2+2x+1-3[/tex], now just combine the constants: [tex]y=x^2+2x-2[/tex], and now you've converted it into standard form!
A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.65 hours, with a standard deviation of 2.43 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.37 hours, with a standard deviation of 1.73 hours. Construct and interpret a 90% confidence interval for the mean difference in leisure time between adults with no children and adults with children. (u1 - u2)
Let u1 represent the mean leisure hours of adults with no children under the age of 18 and u2 represent the mean leisure hours of adults with children under the age of 18. The 90% confidence interval for (u1 - u2) is the range from (???, ???) round to 2 decimals
Answers
Answer:
The 90% confidence interval for (u1 - u2) is the range from; ( 0.50 - 2.06 )
Step-by-step explanation:
Given the data in the question;
Adult with No children under 18 Adult with children under 18
x"₁ = 5.65 x"₂ = 4.37
s₁ = 2.43 s₂ = 1.73
n₁ = 40 n₂ = 40
with 90% confidence
significance level ∝ = 1 - 90% = 1 - 0.9 = 0.1
Degree of freedom df = 39
Now, since variance are not equal and are also unknown, we will use 2 sample t-distribution method;
Standard Error: σx"₁ - x"₂ = [tex]\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} }[/tex]
Critical value = [tex]t_{\alpha /2, df[/tex] = [tex]t_{0.05, df=39[/tex] = 1.645 { from standard normal table }
Now,
Margin of Error = E = [tex]t_{\alpha /2, df[/tex] × [tex]\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} }[/tex]
we substitute
E = 1.645 × [tex]\sqrt{\frac{2.43^2}{40} + \frac{1.73^2}{40} }[/tex]
E = 1.645 × √( 0.1476225 + 0.0748225 )
E = 0.7758478
Now, our point difference will be; x"₁ - x"₂ = 5.65 - 4.37 = 1.28
So Limit at 90% confidence interval will be;
x"₁ - x"₂ ± E
Lower Limit = x"₁ - x"₂ - E = 1.28 - 0.7758478 = 0.50415 ≈ 0.50
Upper Limit = x"₁ - x"₂ + E = 1.28 + 0.7758478 = 2.05584 ≈ 2.06
Therefore, The 90% confidence interval for (u1 - u2) is the range from; ( 0.50 - 2.06 )
Makayla has 2 yards of ribbon to use for a craft project she cuts the ribbon into pieces that are 1/4 yard long how many pieces of ribbon does Makayla have
Answers
Answer:
8
Step-by-step explanation:
2/ 1/4 = 8
Answer: 8
Step-by-step explanation: 2 / 1/4 = 8
HELP ME I'LL GIVE BRAINLIEST
DON'T YOU DARE STEAL THE POINTS OR I WILL HUNT YOU DOWN
Answers
11h+33
30p+15j
4p+8
i feel like im about to die, ur a lil scary
Please help me with this question
Answers
Answer:
cos(x -π/3) = (1/2)cos(x) +(√3/2)sin(x)
Step-by-step explanation:
You want cos(x -π/3) written in terms of sine and cosine.
Angle differenceThe formula for the cosine of the difference between two angles is ...
cos(a -b) = cos(a)cos(b) +sin(a)sin(b)
ApplicationWe have a=x, b=π/3, so the desired function is ...
cos(x -π/3) = cos(x)cos(π/3) +sin(x)sin(π/3)
We know that ...
cos(π/3) = 1/2sin(π/3) = √3/2so the rewrite is ...
cos(x -π/3) = (1/2)cos(x) +(√3/2)sin(x)
Malcom wrote the equivalent ratios shown below. Find the scale factor he used to write the equivalent ratios
9/40 and 54/240
Answers
In this question, we're looking for the number Malcom used to scale the two numbers. We can see there's a pattern, 9 is 1/6 of 54 and 40 is 1/6 of 240!
(54 divided by 9 is 6 and 240 divided by 40 is 6!)
therefore, the scale factor must be 6
The front of a house needs to be painted black. The garage door is 1.5 m high and 2 m wide,
A) How many square meters of black paint will be needed to paint the house not including the
garage door?
Show your work
Answers
Answer:
3 m
Step-by-step explanation:
To geg the answer you need to multiply 1.5 times 2.
Mary is going down a straight waterslide that is 150 feet above the ground. The waterslide is 225 feet long. What is the angle of elevation with the ground to the top of the waterslide?round to two decimals places
Answers
Step by step solution: see photo
Frank's father came home from San Francisco by airplane. He had to wait 1 hour and 45 minutes at the airport in San Francisco. Then Frank's
father had to wait another 35 minutes while the plane was in Portland.
How long did Frank's father spend waiting?
Answers
Answer:
2 hrs and 20 minutes
Step-by-step explanation:
45 + 35 = 80
How many ways can you arrange 4 of 6 trophies on a shelf?
Answers
Answer:
24
Step-by-step explanation:
i did 4x6
4x6=24
the reason i did this is because that is how i do this the rest of the class has their fancy diagrams and are being hyponthageese and not listening to me to find that it is the easiest way to find the answer
Please help will mark Brainly
Answers
Answer:
x=-1 and y=4
Step-by-step explanation:
When you draw a graph you will see point of intersection which is solution
($75,000 - $80,000) x (1 - .21)
Answers
Answer:
-3,950
Step-by-step explanation:
First -5,000(1-0.21)
Then multiply -5,000 x 0.79 = -3,950
I NEED HELP. PLEASE ANSWER QUICK. BRAINLIEST WILL BE GIVEN. THERE IS A BOT AUTO ANSWERING. PLEASE ANSWER ANYWAY
Answers
Answer:
The answer is A
Step-by-step explanation:
The shape is a rhombus when plotted on a quardanent plane. The shape is similar to a diamond.
Sam had 5 fish. She ate 2 how many did she have left
Answers
Answer:
3
Step-by-step explanation:
find the value of x !!
thanks :)
Answers
According to question as both side are equal so it is an isosceles triangle and the value of X is 18.
What are the properties of Isosceles Triangle?An isosceles triangle is a triangle with two sides of equal length. Some properties of an isosceles triangle include:
The two equal sides are called the legs of the triangle and the remaining side is called the base.The angle between the legs is always equal to the angle between the base and one of the legs.The altitude (perpendicular line segment from a vertex to the opposite side) bisects the base of the triangle.The median (line segment from a vertex to the midpoint of the opposite side) and the altitude from the same vertex to the opposite side are also congruent.The circumcenter (center of the circle that passes through all three vertices) of an isosceles triangle is always located at the midpoint of the line connecting the two vertices of the congruent sides.The line that is bisecting the angle between the congruent sides (also known as the angle bisector) also bisects the side opposite to that angle.so In this triangle ,
The mid point on horizontal side is given and 5m line cut the mid point of both the sides.
both side are equal as it is an isosceles triangle.
and given in the question,
side/2 =9
and one side is equal to x.
and both sides are equal,
therefore
side = 9*2 = 18
so the value of x = 18.
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Which of the following rational functions is graphed below?
Answers
Answer:
B
Step-by-step explanation:
Cuz I graphed it, and it looked the same
What is the volume of the rectangular prism? Please Help
Answers
Answer:
60 cm cubed I think
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
use the Area formula
L*W*H
3*5*4=60
Please help me solve it
Answers
Step-by-step explanation:
D
Equations of Exponential Functions
The population, P, of six towns with time t in years are given by the following exponential equations:
(i) P = 1000(1.08)t (ii) P = 600(1.12)t
(iii) P = 2500(0.9)t (iv) P = 1200(1.185)t
(v) P = 800(0.78)t (vi) 2000(0.99)t
Which town is growing the fastest?
a. i c. iv
b. iii d. vi
Please select the best answer from the choices provided
Answers
Answer:
C. iv
Step-by-step explanation:
I calculated it logically
What is the scale factor? Will mark brainlest
Answers
Answer:
The answer is -1
Step-by-step explanation:
X
Let f(x) = 3x2 - 6x + 2. Find f(2)
A
B
10
16
C 12
E
D 2
8
Answers
On solving the provided question, we can say that - f(x) = 3x2 - 6x + 2, and the value of the equation f(x) = +2
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
f(x) = 3x2 - 6x + 2
x = 1
f(x) = +2
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Which graph is represented by the equation (X + 3)2 + (y – 4)2 = 9?
Unit test
Answers
Answer:
center (2, -3)
radius r = 3
Graph c
Step-by-step explanation:
Answer:
Graph A on edge
Step-by-step explanation:
how many sides does a polygon have whose total number of diagonals is 20?
Answers
Answer:
there would be 8 sides if there are 20 diagonals
Can a triangle have sides with the given lengths ? Explain . 1 ft , 2 ft , 4ft