Answer:20%
Step-by-step explanation:216-180=36. 36/180=.20
choose the best answer:
the area of a right triangle is 12in^2. the ratio of the length of its legs is 2:3. Find the length of the hypotenuse.
a) square root is 13 in
b) 26 inches
c) 2 square root of 13
d) 52 inches
e) 4 square root of 13
Answer:
The length of the hypotenuse is 2 square root of 13 ⇒ c
Step-by-step explanation:
The rule of the area of the right triangle is A = [tex]\frac{1}{2}[/tex] × leg1 × leg2, where
leg1 and leg2 are the sides of the right angle
∵ The area of a right triangle is 12 in²
∵ The ratio of the length of its legs is 2: 3
→ Let leg1 = 2x and leg2 = 3x
∵ leg1 = 2x and leg2 = 3x
→ Substitute them in the rule of the area above
∴ 12 = [tex]\frac{1}{2}[/tex] × 2x × 3x
∵ 2x × 3x = 6x²
∴ 12 = [tex]\frac{1}{2}[/tex] × 6x²
∴ 12 = 3x²
→ Divide both sides by 3 to find x²
∴ 4 = x²
→ Take √ for both sides
∴ x = 2
→ Substitute x in the expressions of leg1 and leg2 to find them
∴ leg1 = 2(2) = 4 inches
∴ leg2 = 3(2) = 6 inches
∵ hypotenuse = [tex]\sqrt{(leg1)^{2}+(leg2)^{2}}[/tex]
∴ hypotenuse = [tex]\sqrt{(4)^{2}+(6)^{2}}=\sqrt{16+36}=\sqrt{52}[/tex]
∵ The simplest form of [tex]\sqrt{52}[/tex] = 2[tex]\sqrt{13}[/tex]
∴ The length of the hypotenuse = 2[tex]\sqrt{13}[/tex] inches
What is the solution of the system? Use elimination.
2x + 2y +z = 7
-X – y +z = -5
x + 3y – 4z = 12
Answer:
The solutions to the system of the equations by the elimination method will be:
[tex]x=2,\:z=-1,\:y=2[/tex]
Step-by-step explanation:
Given the system of the equations
[tex]2x\:+\:2y\:+z\:=\:7[/tex]
[tex]-x-\:y\:+z\:=\:-5[/tex]
[tex]x+3y-4z=12[/tex]
solving the system of the equations by the elimination method
[tex]\begin{bmatrix}2x+2y+z=7\\ -x-y+z=-5\\ x+3y-4z=12\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}-x-y+z=-5\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-2x-2y+2z=-10[/tex]
[tex]\begin{bmatrix}2x+2y+z=7\\ -2x-2y+2z=-10\\ x+3y-4z=12\end{bmatrix}[/tex]
[tex]-2x-2y+2z=-10[/tex]
[tex]+[/tex]
[tex]\underline{2x+2y+z=7}[/tex]
[tex]3z=-3[/tex]
[tex]\begin{bmatrix}2x+2y+z=7\\ 3z=-3\\ x+3y-4z=12\end{bmatrix}[/tex]
[tex]2x+6y-8z=24[/tex]
[tex]-[/tex]
[tex]\underline{2x+2y+z=7}[/tex]
[tex]4y-9z=17[/tex]
[tex]\begin{bmatrix}2x+2y+z=7\\ 3z=-3\\ 4y-9z=17\end{bmatrix}[/tex]
Rearranging the equations
[tex]\begin{bmatrix}2x+2y+z=7\\ 4y-9z=17\\ 3z=-3\end{bmatrix}[/tex]
solve [tex]3z=-3[/tex] for z:
[tex]z=-1[/tex]
[tex]\mathrm{For\:}4y-9z=17\mathrm{\:plug\:in\:}z=-1[/tex]
solve [tex]4y-9\left(-1\right)=17[/tex] for y:
[tex]4y-9\left(-1\right)=17[/tex]
[tex]4y+9=17[/tex]
[tex]4y=8[/tex]
[tex]y=2[/tex]
[tex]\mathrm{For\:}2x+2y+z=7\mathrm{\:plug\:in\:}z=-1,\:y=2[/tex]
solve [tex]2x+2\cdot \:2-1=7[/tex] for x:
[tex]2x+2\cdot \:2-1=7[/tex]
[tex]2x+3=7[/tex]
[tex]2x=4[/tex]
[tex]x=2[/tex]
Therefore, the solutions to the system of the equations by the elimination method will be:
[tex]x=2,\:z=-1,\:y=2[/tex]
To prepare for wrestling season, Tommy wants to eat 24 grams of protein at breakfast. He knows that there are 3 grams of protein in a slice of bacon and 6 grams of protein in an egg. Let x represent the number of slices of bacon he will eat and let y represent the number of eggs he will eat.
Write an equation that relates the number of slices of bacon to the number of eggs he will eat, assuming he eats exactly 24 grams of protein. **Rewrite your equation in slope-intercept form.
Answer:
1) The equation that represents the number of slices of bacon to the number he will eat, assuming he eats 24 grams is;
3·x + 6·y = 24
2) The equation in slope and intercept form is;
y = 4 - 0.5·x
Step-by-step explanation:
1) The given parameters are;
The amount of protein Tommy wants to eat for breakfast = 24 grams
The quantity of protein in a slice of bacon = 3 grams
The quantity of protein in an egg = 6 grams
Let x represent the number of slices of bacon he will eat and let y represent the number of eggs he will eat
The equation that represents the number of slices of bacon to the number he will eat, assuming he eats 24 grams is given as follows;
3·x + 6·y = 24
2) The equation in slope and intercept form is given by making y the subject of the above equation as follows;
3·x + 6·y = 24
6·y = 24 - 3·x
y = 24/6 -1/2·x
y = 4 - 0.5·x, which is in the slope and intercept form y = m·x + c
Where;
m = The slope = -0.5
c = The y-intercept = 4
HELP ME PLEASE I'LL MARK YOU THE BRAINEST!!!!!!!!
Determine the missing values.
Answer:
Hi it’s me
Step-by-step explanation:
7is the first one
10 is the second
Nvm you already got the answer cause yo asked this 2 weeks ago anyways hi
PLS PLS HELPPPPP ASAP
Answer:
Wht u need help on?
Step-by-step explanation:
Holler sold 150 frozen yogurts. Out of these frozen yogurts sold, 40% included toppings. How many frozen yogurts included toppings?
Hi. I need help with these questions.
See image for question.
Answer:
Step-by-step explanation:
Plug in the stated values for x
(a) 2(1)^4 + 3(1)^3 - (1)^3 + 2(1) - 3
2 + 3 - 1 + 2 - 3 = 1 + 2 = 3
f(1) = 3
(b) 2(-1)^4 + 3(-1)^3 - (-1)^2 + 2(-1) - 3
2 * 1 + 3(-1) - 1 + 2(-1) - 3
2 + -3 -1 -2 - 3 = 2 - 9 = -7
f(-1) = -7
(c) 2(0) + 3(0) - 0 + 0 - 3
0 - 3 = -3
f(0) = -3
d) 2(-1/2)^4 + 3(-1/2)^3 - 2(-1/2) - 3
1/8 - 3/8 - (-1/2)^2 - 2 * 1/2 - 3
16/4 - 1/4 - 1/4 = -16-1-1/4 = -18/4
f(-1/2) = -9/2
1
Prove that
1: sin/1-cot + cos/1-tan=cos+sin
Answer:
have:
[tex]\frac{sin}{1-cot}+\frac{cos}{1-tan}\\\\=\frac{sin}{1-\frac{cos}{sin} }+\frac{cos}{1-\frac{sin}{cos} }\\\\=\frac{sin^{2} }{sin-cos}+\frac{cos^{2} }{cos-sin} \\\\=\frac{sin^{2} }{sin-cos}-\frac{cos^{2} }{cos-sin}\\\\=\frac{sin^{2}-cos^{2} }{sin - cos}\\\\=\frac{(sin-cos)(sin+cos)}{sin-cos}\\\\=sin+cos[/tex]
Step-by-step explanation:
graph the line y=1/2x+3
Answer:
to find the line you must find x and y
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}x&-6&0\\y&0&3\end{array}\right][/tex]
graph the line using slope and y intercept
slop:1/2
y-intercept:3
find the values of mx and b
[tex]m=\frac{1}{2}\\b=3[/tex]
find x intercept
[tex]0=\frac{x}{2}+3[/tex]
re wright the equasion
[tex]\frac{x}{2}+3=0[/tex]
subtract 3
[tex]\frac{x}{2} +3-3=0-3[/tex]
[tex]\frac{x}{2}=-3[/tex]
multiply by 2
[tex]*2\frac{x}{2}=-3*2[/tex]
x intercept = -6
now find y intercept
[tex]y=\frac{0}{2}+3[/tex]
divide by 2
[tex]y=0+3[/tex]
add 0 and 3
y=3
create a table of x and y [tex]\left[\begin{array}{ccc}x&-6&0\\y&0&3\end{array}\right][/tex]
graph the line using y-intercept and slope
so your answer is (-6,3)
Write the polynomial in standard form. State the degree and leading coefficient:
−9 + 7m^3 − 11m + 3/5m^5
Degree:_____________
Leading Coefficient:_____________
Answers:
Standard form = [tex]\frac{3}{5}m^5 + 7m^3 - 11m-9[/tex]Degree = 5Leading coefficient = 3/5===================================================
Explanation:
The largest exponent term is what will go first. Then the term with the second largest goes next, and so on. We count the exponents down. The exponents will count down in this case as 5, 3, 1, 0
Note: -9 = -9*1 = -9m^0 and -11m = -11m^1
So that's why standard form is [tex]\frac{3}{5}m^5 + 7m^3 - 11m-9[/tex]
We can write this as (3/5)m^5 + 7m^3 - 11m - 9
------------------------
The leading term is the first term after getting everything in standard form. The coefficient of the leading term is the leading coefficient. So in this case, it would be 3/5.
The degree is the largest exponent. So the degree is 5. This is a quintic polynomial.
How would you solve |10+4x|<14
And how would you graph it on a number line?
Answer:
x < 1
Step by step explanation:
10 + 4x < 14
4x < 14 -10
4x < 4
x < 1
When you graph it on a number line, draw a line that extends from 1 towards the left side (since x is less that 1) and use unshaded circles.
What is the value of x?
60"
95
A. 250
B. 350
C. 60°
D. 1550
PREVIOUS
Answer:
it's B ==35
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
A because u know its not 60 bc its already there and 35 would be to big also it cant be 155 bc that is way to big for that angle
1. Jun needs to review for the entrance exam with his remaining 5 3/5 hours fo the 7 subjects. how long will he spend for each subject?
2.Mar purchased 6 3/4 meters of wall paper for the boxes he will cover. if each box needs 2 1/4 meters, how many boxes will get covered?
3.Joana has 12 1/4 meters of ribbon, joy has 3meters ribbon shorter than joana. they split the ribbon to have the an equal length of ribbon. how long is each piece
Answer: See explanation
Step-by-step explanation:
1. Jun needs to review for the entrance exam with his remaining 5 3/5 hours fo the 7 subjects. how long will he spend for each subject?
The time spent on each subject will be the remaining hours left divided by 7. This will be:
= 5 3/5 ÷ 7
= 28/5 ÷ 7
= 28/5 × 1/7
= 28/35 = 4/5 hours
Since 60 minutes make one hour
4/5 hours = 4/5 × 60 = 48 minutes
2.Mar purchased 6 3/4 meters of wall paper for the boxes he will cover. if each box needs 2 1/4 meters, how many boxes will get covered?
This will be:
= 6 3/4 ÷ 2 1/4
= 27/4 ÷ 9/4
= 27/4 × 4/9
= 3 boxes
3.Joana has 12 1/4 meters of ribbon, joy has 3meters ribbon shorter than joana. they split the ribbon to have the an equal length of ribbon. how long is each.
Joana ribbon = 12 1/4 meters
Joy's ribbon = 12 1/4 - 3 = 9 1/4 meters
We then add both length of ribbons and divide by 2. This will be:
= 12 1/4 + 9 1/4
= 21 1/2 meters
= 21 1/2 meters ÷ 2
= 43/2 ÷ 2
= 43/2 × 1/2
= 43/4
= 10 3/4 meters
a new theater is being built for the city ballet. the balcony has 100 seats. The floor has 20 rows with x seats in each row. the number of people in the theater must be under 400 to meet fire safety regulations. what is the solution of this inequalit,y, and what is its meaning?
The answers are in the picture
Answer:
A
Step-by-step explanation:
How can ure out the next number in the pattern below? Write a conjecture that describes the pattern.
29, 28, 26, 23, 19
The difference between consecutive first and second integers is increased by 1 thus the next number 19 - x = 5 → x = 14.
What is the pattern?A pattern is a specific arrangement of numbers or any term which will follow a specific code or hint.
For example 2,4,6,8 in this, the difference between any two-term is only 2 and this will be its specific pattern.
As per the given pattern,29, 28, 26, 23, 19
29 - 28 = 1
28 - 26 = 2
26 - 23 = 3
23 - 19 = 4
Since the difference is increasing by 1
So the difference of 19 and the next number (x) will be 4 + 1 = 5.
19 - x = 5
x = 14
Hence "The difference between consecutive first and second integers is increased by 1 thus the next number 19 - x = 5 → x = 14".
For more information about the pattern,
brainly.com/question/14013716
#SPJ2
The Wright family budget allows
twice as much money for rent as
for food. Their budget allows
less than $720 for both food and
rent. What is the most they can
spend on food?
Answer:
The most that they can spend in food is $239
Step-by-step explanation:
Their budget allows for less than $720 for both food and rent.
We are told that this budget allows
twice as much money for rent as
for food.
Thus,
Let x be amount of spent on food.
Thus, money spent on rent is 2x
Thus,
2x + x < 720
3x < 720
x < 720/3
x < 240
Since x should be less than 240,it means that the most that they can spend in food is $239
1l) HAO WENT TO A HOBBY SHOP AND SAW A DISPLAY OF TOY TRAINS. THE SIGN IN FRONT OF THE DISPLAY SAID THAT THE TOY TRAINS WERE A REPLICA OF THE LONG ISLAND RAILROAD TRAINS. HAO ESTIMATED THAT ONE OF THE RAILROAD CARS WAS APPROXIMATELY 15 INCHES LONG AND 4 INCHES WIDE. THE SIGN IN FRONT OF THE DISPLAY STATED "SCALE- 2 /9". WHAT IS THE LENGTH OF THE RAILROAD CAR ON THE LONG ISLAND RAILROAD? WHAT IS THE WIDTH OF THE LONG ISLAND RAILROAD CAR?
Answer:
Step-by-step explanation:
Given that :
Dimension of rail road toy trains :
Length = 15 inches
Width = 4 inches
Scale = 2/9
Dimension of car on the long Island rail road :
Let length = x
Length = 2/9 of x = 15 inches
= 0.22222x = 15 inches
LENGTH = 67.5 inches
WIDTH = 2/9 of x = 4 inches
0.22222x = 4 inches
Width = 18
Width = 6 inches
f. How many times greater is the area of triangle DEF
than the area of triangle ABC? Show/explain.
Answer:
Area of ΔDEF is 2.25 times the area of ΔABC.
Step-by-step explanation:
Since, ΔDEF is the enlarged form of ΔABC,
Scale factor = [tex]\frac{\text{Side length of triangle ABC}}{\text{Corresponding side length of image triangle}}[/tex]
= [tex]\frac{15}{10}[/tex]
= 1.5
Since, ratio of the areas of image and preimage triangles = (Scale factor)²
[tex]\frac{\text{Area of image triangle}}{\text{Area of triangle ABC}}[/tex] = (Scale factor)²
[tex]\frac{\text{Area of image triangle}}{\text{Area of triangle ABC}}=(1.5)^2[/tex]
Area of image ΔDEF = 2.25(Area of ΔABC)
Therefore, area of ΔDEF is 2.25 times the area of ΔABC.
I NEED HELP QUESTION IN PICTURE!!!!!!HAVE A NICE DAY
Henri bought a swim suit at a cost of $8. Which statements are true regarding the cost of the suit? Select three options
Answer:
where are the options
Step-by-step explanation:
Answer:
it cost $8, it was a swimsuit and he bought it
Step-by-step explanation:
is 48/6 an integer?
No, because intergers don't include fractions.
Answer:
No
Step-by-step explanation:
Integers cannot have any fractions.
If you simplify this to get 8/1 and then 8, 8 is an integer
The expression (x^3)(x^−17) is equivalent to xn. What is the value of n?
Answer:
-14Step-by-step explanation:
(x^3)(x^−17) =x^(3 - 17) =x^-14n = -14n = -14
(x^3)(x^−17) =
x^(3 - 17) =
x^-14
Dan Miller has been granted $120,000 mortgage loan. When signing the papers to purchase his new home, he will need to pay closing costs, what's are the total costs?
Answer:1222
Step-by-step explanation:
this is why this the answer
[tex]776{x} 34344[/tex]Also need help on this one thx u guys and girls who are helping meeeeee!!!!!! :)
Answer:
B
Step-by-step explanation:
big line= divide
[tex]-2 1/4 to improper = -9/4\\/ -2/3[/tex]
so -9/4 / -2/3 or
B
Hope this helps :D
Answer:
B!
Step-by-step explanation:
if you calculate the original expression given you get [tex]3\frac{3}{8}[/tex] so i just went down the line calculating the rest of the equations and B was the one equivalent to the original expression! hope this helped.
PLEASE HELP, MARKING BRAINLIEST!!!!
Which congruence statement do the triangles show?
A. SAS
B. AAS
C. ASA
D. SSS
E. HL
F. Not enough information
Answer:
A ( SAS )
Step-by-step explanation:
ahhhhhhhhh come on I'm so stupid
Answer:
1. -32
2. -46
Step-by-step explanation:
1. When muliplying a number with a postive number and a negative number the answer will be a negative number
2. When you have a negative number and when you have a postive number and you are subtracting your answer has to be a negative answer
Answer:
cvgbnm,m
Step-by-step explanation:
bxxcvn vn
Solve the proportion. If necessary, round to the nearest hundredth. 9/(y +1) = 18/54 *
22
18
30
26
help find the missing side length???
Answer:
you look at the numbers and add the other numbers.
Step-by-step explanation:
Nathan took his car in for service and repairs. He had a coupon for 15% off.
Original Prices
• Labor $220.43
• Parts $340.47
• Other $61.97
Which amount is closest to Nathan's total costs after the 15% discount and including 7% sales tax? [Assume tax is applied after the discount is applied.]
A.
$486
B.
$567
C.
$529
D.
$492
What is the value of the expression below?
36÷103
Answer:
0.3495.
Step-by-step explanation:
............................