Answers
14. Each leg is [tex]21\sqrt{2}[/tex] units long.
15 (a). The longer leg is [tex]7\sqrt{3}[/tex] units long
15 (b). The hypotenuse is [tex]14[/tex] units long
=====================================================
Explanations:
For a 45 degree right triangle, aka 45-45-90 triangle, the hypotenuse is equal to sqrt(2) times the short leg. Algebraically we can say
[tex]y = x\sqrt{2}[/tex] where x is the leg and y is the hypotenuse
Let's solve for x
[tex]y = x\sqrt{2}\\\\x\sqrt{2} = y\\\\x = \frac{y}{\sqrt{2}}\\\\x = \frac{y\sqrt{2}}{\sqrt{2}*\sqrt{2}} \ \text{rationalizing denominator}\\\\x = \frac{y\sqrt{2}}{2}\\\\[/tex]
Now plug in the given hypotenuse y = 42, this leads to,
[tex]x = \frac{y\sqrt{2}}{2}\\\\x = \frac{42\sqrt{2}}{2}\\\\x = \frac{42}{2}\sqrt{2}\\\\x = 21\sqrt{2}\\\\[/tex]
---------------------------
For a 30-60-90 triangle, the hypotenuse is double that of the short leg. So the hypotenuse is 2*7 = 14.
The longer leg is equal to sqrt(3) times the short leg. The longer leg is [tex]7\sqrt{3}[/tex]
Related Questions
What is the completely factored form of f(x) = 683 – 1332 - 4x + 15?
Answers
Answer:-637
Step-by-step explanation:
what is 100 divided by 3?
Answers
Answer:
0.003
Step-by-step explanation:
100 / 3 = 0.003
When dividing with (10, 100, 100 etc) you go this way <—
According to survey records, 75.4% of women aged 20-24 have never been married. In a random sample of 25 young women aged 20-24, find the mean, variance and standard deviation for the number who are or who have been married.
Answers
Answer:
mean = 6.15
variance = 4.637
standard deviation = 2.15
Step-by-step explanation:
It is given that 75.4% of women aged 20-24 have never been married.
We are interested in finding the mean, variance and standard deviation for the number who are or who have been married.
So the percentile of women who have been married is given by
[tex]p = 1 - 0.754 \\\\ p = 0.246 \\\\q = 1 - p \\\\q = 1 - 0.246 \\\\q = 0.754[/tex]
The mean is given by
[tex]mean = n\times p[/tex]
Where n is the sample size
[tex]mean = 25\times 0.246 \\\\mean = 6.15[/tex]
Therefore, the mean is 6.15
The variance is given by
[tex]variance = n \times p \times q \\\\variance = 25 \times 0.246 \times 0.754 \\\\variance = 4.637[/tex]
Therefore, the variance is 4.637
The standard deviation is given by
[tex]standard \: deviation = \sqrt{variance} \\\\standard \: deviation = \sqrt{4.637} \\\\standard \: deviation = 2.15[/tex]
Therefore, the standard deviation is 2.15
YEAR 9 MATHS PLEASE QUICKLY HELP THIS WONT TAKE LONG
Here are six shapes made from centimetre squares.
Write down the letter of a shape with rotational symmetry of order 2.
(1 mark)
Answers
Answer:
letter of a shape with rotational symmetry of order 2 is B,D and F
Answer:
Step-by-step explanation:
i strongly believe it is rotational symmetry of order 2 is B,D and F .
hope it helps
-Delilah
−12 − (−25) + 8
plzz helpp im not sure is it 21??
Answers
Answer:
21
Step-by-step explanation:
−12 − (−25) + 8
Subtracting a negative is like adding
-12 +25+8
First do -12 +25 25-12 = 13 Replace in the equation
13+8
21
Answer:
Yes, the answer is
[tex]21[/tex]
Step-by-step explanation:
we know that,
[tex]( - ) \times ( - ) = ( + )[/tex]
Now let's solve the problem,
[tex] - 12 - ( - 25) + 8 \\ - 12 + 25 + 8 \\ = 21[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Help me solve please
Answers
Answer:
44Please see the attached picture for full solution
hope it helps...
Good luck on your assignment
Answer:
[tex]44[/tex]
hope this helps you.
brainliest appreciated
good luck! have a nice day!
Sam is buying presents for his family.
He buys a bracelet for his wife for $50. He
buys a game for his son, and the same game
for his daughter. He spends a total of $72.
How much does one game cost?
Answers
Answer:
$ 11
Step-by-step explanation:
A game costs $ x.
Two games costs 2x.
50 + 2x = 72
2x = 72 - 50
2x = 22
x = 11
factorise a)2x+8 b)3x-12 c)6x+4 d) 18x-9
Answers
Simplify C^5 x c
Plz can someone figure it out cuz I don’t get it
Answers
Answer:
c^6
Step-by-step explanation:
So, c is the same as c^ 1 ... therefore
c^5 x c
= c^5 x c^1
When we multiply two numbers with same base and different exponent, we add the exponents which in this case as 5 and 1
So c^5 x c^1
= c^(5+1)
= c^6
This is the simplest form
Answer: c⁶
Step-by-step explanation:
Notes: A variable without a given exponent has an "invisible" exponent of 1.
When multiplying two values with the same base, add the exponents.
[tex]\bold{c^5 \times c\qquad \rightarrow \quad c^5 \times c^1\quad =\quad c^{5+1}\quad = \large\boxed{c^6}}[/tex]
jenny has 36 cupcakes. how many kids (including jenny) can share these cupcakes evenly?
Answers
Answer:
2 people can have 18 cupcakes each
3 people can have 12 cupcakes each
4 people can have 9 cupcakes each
9 people can have 4 cupcakes each
Step-by-step explanation:
Answer: 1,2,3,4,6,9,12,18,36
Step-by-step explanation:
What is the result of 36 divided by 9? Use the number line to find the answer. A number line going from 0 to 39. The numbers 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, and 39 are marked on the line.
Answers
Answer:
4
Step-by-step explanation:
36/9=4
Answer:
4
Step-by-step explanation: division
rationalize the denominator of 5√3+3√5 ÷ 5√3+3√5
Answers
Answer:
[tex]1[/tex]
Step-by-step explanation:
[tex]\frac{5\sqrt{3}+3\sqrt{5} }{5\sqrt{3}+3\sqrt{5} }[/tex]
[tex]=1[/tex]
3(a-2/3)= 3/4a+2 1/4
Answers
Steps:
Step 1: Simplify both sides of the equation.
3(a−2/3)=3/4a+21/4
(3)(a)+(3)(−2/3)=3/4a+21/4(Distribute)
3a+−2=34a+2143a−2=3/4a+21/4
3a+−2=34a+2143a−2=3/4a+21/4
Step 2: Subtract 3/4a from both sides.
3a−2−3/4a=3/4a+21/4−3/4a
9/4a−2=21/4
Step 3: Add 2 to both sides.
9/4a−2+2=21/4+2
9/4a=29/4
Step 4: Multiply both sides by 4/9.
(4/9)*(9/4a)=(4/9)*(29/4)
Answer:
A=29/9
Please mark me brainliest
Hope this helps.
a linear function has the same y-intercept as x + 4y= 8 and its graph contains the point (6,3). what is the y intercept?
Answers
Answer:
The y-intercept b = 9/2
Step-by-step explanation:
A line has equation x + 4y = 8 or y = (-1/4)x + 2
=> The slope of this line is -1/4
Another line y = ax + b has the slope a = -1/4 and passes (6, 3)
=> 3 = (-1/4)*6 + b
=> 3 = -3/2 + b
=> b = 9/2
=> The y-intercept b = 9/2
Answer: y-intercept = 2
Step-by-step explanation:
Slope-Intercept form of an equation is: y = mx + b where
m = slopeb = y-interceptx + 4y = 8
4y = -x + 8
[tex]y=-\dfrac{1}{4}x+\dfrac{8}{4}[/tex]
[tex]y=-\dfrac{1}{4}x+2[/tex]
The y-intercept (b) = 2
I am not sure why you gave a point that goes through the y-intercept because it does not relate to the question , however, I have shown below the equation of point (6, 3) that goes through b = 2.
y = mx + b
3 = m(6) + 2
1 = 6m
[tex]\dfrac{1}{6}=m[/tex]
Equation: [tex]y=\dfrac{1}{6}x+2[/tex]
Please help! Correct answer only please! I need to finish this assignment by today.
City Donuts recently sold 12 donuts, of which 6 were maple donuts. What is the experimental probability that the next donut sold will be a maple donut?
Simplify your answer and write it as a fraction or whole number.
P(maple donut) =
Answers
Answer:
1/2
Step-by-step explanation:
Out of a total 12 donuts, 6 of them are maple. Assuming this ratio stays constant, the experimental probability that the next one sold is a maple donut is 6/12=1/2. Hope this helps!
Answer:
P(maple donut) = 0.5
Step-by-step explanation:
If they sold 12 donuts, of which 6 of them were Maple Donuts.
The experimental probability of donuts sold that were maple donuts is:
[tex]\frac{6}{12}=\frac{1}{2}=0.5[/tex]
Therefore donuts sold in the future, would follow this probability, so our answer is 0.5.
Write down the order of rotational symmetry of the shape.
Answers
Answer:
the order of rotational symmetry of the shape is 2
Fully Factorise 5D^2+11d
Answers
Answer:
d × (5d + 11)
Step-by-step explanation:
5d² + 11d
Factor out d from the expression
When d is factored out;
5d² becomes 5d
11d becomes 11
And d multiplies it all;
d × (5d + 11)
is the ordered pair (-4,3) a solution of the equation y=5x + 21
Answers
Answer:
Step-by-step explanation:
If you substitute x = -4 in the equation, you should get the y value as 3
y = 5x + 21
= 5* -4 + 21
= -20 + 21
y = -1 ≠ 3
So, (-4, 3) is not a solution
(6x?+ 5) - (4x - 3)
A. 6x2 - 4x + 2
B. 2x2 + 2
C. 2x2 + 8
O D. 6x2 - 4x + 8
Answers
Answer:
6x^2 -4x +8
Step-by-step explanation:
(6x^2+ 5) - (4x - 3)
Distribute the minus sign
(6x^2+ 5) - 4x + 3
Combine like terms
6x^2 -4x +8
Answer:
Step-by-step explanation:
C
can somone answer number 12, I really need it bad, please help .
Answers
Answer:
-24
Step-by-step explanation:
f(x) = 3x^3 -12x^2
f(2) = 3 * (2)^3 - 12 (2)^2
= 3 (8) - 12 (4)
= 24 - 48
= -24
Answer:
D. f(2)= -24
Step-by-step explanation:
To solve this problem, we want to find what f(x), or y is, when x is equal to 2.
f(x)=3x³-12x²
Therefore, we can substitute 2 in for every x.
x=2
f(2)=3(2³)-12(2²)
Evaluate the exponents first.
2³ is equal to 2*2*2, which equals 8.
2² is equal to 2*2, which equals 4.
f(2)=3(8)-12(4)
Multiply 3 and 8.
f(2)=24-12(4)
Multipy 12 and 4
f(2)=24-48
Subtract 48 from 24.
f(2)=-24
Therefore, the correct answer is D. f(2)= -24
Given the function ƒ(x) = 8x^2 − 14x − 10, find ƒ(−2). A) ƒ(−2) = 50 B) ƒ(−2) = 60 C) ƒ(−2) = −6 D) ƒ(−2) = −70
Answers
Answer:
50
Step-by-step explanation:
f(x) = 8x² - 14x - 10
f(-2) = 8(-2)² - 14(-2) -10
f(-2) 8*4 + 28 - 10
f(-2) = 32 + 28 - 10 = 50
a vegetable garden surrounding path are shaped like a square that together are 10 ft wide. The path is 3 ft wide. Find the total area of the vegetable garden and path.
Answers
Answer: Garden = 36 ft², Path = 64 ft²
Step-by-step explanation:
Path is 3 ft wide ON EACH SIDE of the garden
Garden + 2(Path) = 10 ft --> Garden = 6 ft wide.
Since the garden is a square, Area = 6² = 36
Garden + 2(Path) = 10 ft
Since the Garden + Path form a square, Area = 10² = 100
Area of Garden + Area of Path = Total Area
36 + Area of Path = 100
Area of Path = 64
Helppp pleaseeeee The object below is made of solid plastic. It is a cylinder with an indentation at the top in the shape of a cone.What is the volume, to the nearest tenth of a cubic inch, of the plastic object? Explain your answer.
Answers
Answer:
Total volume = (145/3)π in³
Step-by-step explanation:
First find the volume of the entire cylinder. The correct formula to use here is:
V = πr²h, where r is the radius and h is the height. Here, with the radius being 5/2 inches and the height being 8 inches, the cylinder volume is
V = π(2.5 in)²(8 in) = 50π in³
Next find the volume of the conical shape: V = (1/3)π(2.5 in)²(0.8 in)
The desired volume is equal to the volume of the entire cylinder LESS the volume of the cone:
π(2.5 in)²(8 in) = 50π in³ LESS (1/3)π(2.5 in)²(0.8 in), which simplifies as follows:
Total volume =
50 π in³ - (1/3)π(2.5 in)²(0.8 in), or
(2.5 in)²π[8 in - 0.8/3 in] = π(6.25 in²)(8 in - 8/30 in) = π( 6.25 in²)(116/15 in), or
Total volume = (145/3)π in³
A 2-column table with 2 rows. The labels for the columns and rows are blank. First column entries are 5 x squared, 10 x. Second column entries are negative 2 x, negative 4. Which factors can be multiplied together to make the trinomial 5x2 + 8x – 4? Select two options. (x + 1) (2x + 1) (x + 2) (5x + 1) (5x – 2)
Answers
Answer:
(5x – 2) and (x + 2)Step-by-step explanation:
In order to know the two factors we are to multiply together to get the trinomial function 5x² + 8x – 4, we need to factorize the quadratic function given. On factorizing;
[tex]= 5x^{2} +8x-4\\= (5x^{2} +10x)-(2x-4)\\\\factoring\ out\ the\ common\ term\\= 5x(x+2)-2(x+2)\\= (5x-2)(x+2)\\[/tex]
The factors that can be multiplied together are (5x – 2) and (x + 2)
Answer:
The Answer On Edge Is C.) and E.), Have Fun Dreamers!
Step-by-step explanation:
Pablo has 0 pieces of candy and wants to divide them into 2 equal piles. You want to know how many pieces will be in each pile? Can you divide zero into 2 equal parts?
Answers
Answer:
no
Step-by-step explanation:
you cannot divide zero into two equal parts because there is nothing there to start. Since Pablo has no candy, he cannot divide it into two piles because there isn't anything to divide.
Answer: No because 0 means nothing and you can't divide nothing among something so that is like undefined.
Step-by-step explanation:
Write a four-digit whole number that is divisible by 2. Use a divisibility rule and explain how you know that your number is divisible by 2.
Answers
Answer:
2378
Step-by-step explanation:
it is even. plus 8 is a multiple of 2
Answer:
2738
Step-by-step explanation:
2738 divided by 2 is 1369, and 1369 multiplied by 2 is 2738 also I checked on a calculator lol.
Triangle XYZ has vertices X(-6, 3), Y(4,5), and Z(-2,-1).
View
f Step-by
Part 1 out of 3
Find the vertices of triangle X'Y'Z' after a translation of 9 units to the right.
Video T
The vertices are X
and Z
Pls I don’t get this !!!!
Answers
Answer:
see explanation
Step-by-step explanation:
A translation of 9 units to the right means adding 9 to the x- coordinates of the original points, while the y- coordinate remains unchanged, thus
X(- 6, 3 ) → X'(- 6 + 9, 3 ) → X'(3, 3 )
Y(4, 5 ) → Y'(4 + 9, 5 ) → Y'(13, 5 )
Z(- 2, - 1 ) → Z'(- 2 + 9, - 1 ) → Z'(7, - 1 )
6. Classify this kind of triangle:
Answers
Answer:
Number 3
Step-by-step explanation:
It is an acute isosceles because all the angles are acute and two sides are congruent.
Answer:
Acute and isosceles
Step-by-step explanation:
All the angles are less than 90
2 sides are equal
Please answer !!!!!!!!!!! Will mark brainliest !!!!!!!!!!!
Answers
Answer:
f ⁻¹ (-2)=3
f ⁻¹ (1)= 0
Step-by-step explanation:
inverse functions are switching x and f(x) coordinates so f ⁻¹ (-2)=3 and f ⁻¹ (1)= 0
What is the name of this shape?
Please help!
Answers
Answer:
It is an isosceles triangle
Step-by-step explanation:
because there are 2 straight lines
