let's recall something about a right-triangle.
it has a 90° angle, and the longest side, the hypotenuse, from the pythagorean theorem, is c² = a² + b², or namely c = √( a² + b²).
so, let's take a peek at the two smaller sides, 60 and 11, can we get the longest side from it using the pythagorean theorem?
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{61}\\ a=\stackrel{adjacent}{60}\\ b=\stackrel{opposite}{11}\\ \end{cases} \\\\\\ 61=\sqrt{60^2+11^2}\implies 61=\sqrt{3600+121} \\\\\\ 61=\sqrt{3721}\implies 61=61~~\stackrel{\textit{yeap, it is}}{\checkmark}[/tex]
The given lengths of 60ft, 61ft, and 11ft can form a right triangle. This has been confirmed by applying the Pythagorean theorem, which gives equal results for both sides of the equation.
Explanation:In the field of Mathematics, the formation of a right triangle with given side lengths can be verified using the Pythagorean theorem. The theorem states: If a triangle is a right triangle, then the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, as represented by this formula: a² + b² = c².
Applying this theorem to your question, we can use the three lengths you've provided: 60ft, 61ft, and 11ft. Let's assign the longest length (considered as the hypotenuse in a right triangle) as 'c', which is 61ft in this case. The other sides 'a' and 'b' would be 60ft and 11ft.
Here's how the theorem fits: 60² + 11² = 61².
Calculating the squares gives us 3600 + 121 = 3721 for the left-hand side, and 3721 for the right-hand side as well. Since the results are equal, the given lengths can indeed form a right triangle according to the Pythagorean theorem.
Learn more about Pythagorean theorem here:https://brainly.com/question/28361847
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On a piece of paper use a protractor to construct a triangle with angle measures of 40 and 60 what is the measure of the third angle?
Answer:
80°
Step-by-step explanation:
The angles of a triangle must add up to 180°.
40° + 60° + missing angle = 180°
100° + missing angle = 180°
subtract 100° from both sides
missing angle = 80°
lulu eats 5/8 pound of food a day. how many days will it take her to eat a 5-pound bag of food?
Answer:
[tex]8\ days[/tex]
Step-by-step explanation:
we know that
using proportion
[tex]\frac{1}{(5/8)}\frac{day}{pounds}=\frac{x}5}\frac{days}{pounds}\\ \\x=5*8/5\\ \\x=8\ days[/tex]
While at the zoo, you saw 20 monkeys in an exhibit. Then some of the monkeys go and hide while the zoo keeper moves 5 monkeys to another area for feeding. Now you only see 8 monkeys. How many monkeys are hiding?
It would be 7.
Because 20-5-15 then 15-8=7
Calculate the volume of this regular solid. What is the volume of the rectangular prism
The answer is 270cm cubed.
What is the volume of the rectangular prism?
270 cm^3
You roll a 6-Sided fair die What is the P that you get a number less then 4
Answer:
The answer is 66.6%
Step-by-step explanation:
All you have to do to solve this question is 6÷4
Answer:
66.6
Step-by-step explanation:
a computer store bought a program at a cost of $20 and sold it at a selling price$26. what is the percent markup
The markup percentage can be found by subtracting the cost price from the selling price, dividing by the cost price, and then multiplying by 100, resulting in a 30% markup.
The percent markup is calculated by finding the difference between the selling price and the cost price, then dividing that by the cost price and multiplying by 100.
Markup = (Selling Price - Cost Price) / Cost Price x 100
Markup = ($26 - $20) / $20 x 100
Markup = $6 / $20 x 100
Markup = 0.30 x 100
Markup = 30%
what is the sum? x/x+3 + 3/x+3 + 2/x+3
Answer: [tex]\frac{x+5}{x+3}[/tex]
Step-by-step explanation:
The problem gives you the following expression:
[tex]\frac{x}{x+3}+\frac{3}{x+3}+\frac{2}{x+3}[/tex]
Therefore, to add the fractions with equal denominator, you must rewrite the denominator (x+3) and add the numerators of each one of the fractions.
Then, keeping the above on mind, you obtain the sum shown below (You must remember to add the like terms):
[tex]\frac{x+3+2}{x+3}=\frac{x+5}{x+3}[/tex]
Answer:
(x + 5)/(x + 3)
Step-by-step explanation:
I take all three fractions have a denominator of x + 3. If that is correct, then the question should be written as
x/(x + 3) + 3/(x + 3) + 2/(x + 3)
(x + 3 + 2)/ (x + 3)
(x + 5)/(x + 3)
That's the answer
A isosceles triangle
B equilateral triangle
C right triangle
D scalene triangle
Answer:
um thats a Isosceles triangle s A is correct
Step-by-step explanation:
this is because it has a pair of congruent sides and a pair of congruent angles.
can i get brainiest
Answer:
A
Step-by-step explanation:
A triangle with 2 sides equal is an isosceles triangle
how do i graph y = 2x - 1
Answer:
Step-by-step explanation:
Make a table that has (x) on the left and (y) on the right. There should be a slash between them. After that, you should place the numbers (1,2,3,4,5...) on the x column or on the left. Then times the x in y = 2x - 1 with the numbers on the left and that would give the numbers on the right. Once you are done with that, then pair the numbers from the left to the right. Then simply graph it.
But always remember, left is (x) and right is (y)
Convert 40 ounces into pounds round your answer to the nearest tenth
Answer:
2.5 pounds
Step-by-step Explanation:
Since there are 16 ounces in a pound you do 40÷16, which would get you 2.49999.... But since you have to round to the nearest 10th, you would round to 2.5 pounds.
The quantity 40 ounces is equal to the quantity 2.5 pounds. Therefore, the correct answer is option A.
The given quantity is 40 ounces.
Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
We know that, there are 16 ounces in one pound.
Here, number of ounces = 40/16
= 20/8
= 10/4
= 5/2
= 2.5 pounds
Therefore, the correct answer is option A.
To learn more about the metric conversion visit:
brainly.com/question/21244256.
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Please help, I'm currently confused on telling whether an absolute value equation has a solution or doesn't. For example, -5|x + 1| = 10 has no solution, and if you actually did it, the x would be -3, and 1. Meanwhile 2|x − 6| + 14 = 38 has a solution of x = −6, x = 18 and it has a solution??? I'm so confused.
Which of the following combined with the equation −9x + 3y = 12 creates a system of linear equations with no solution?
Answer:
Step-by-step explanation:
You can't get an exact answer to this because there are no choices.
Add 9x to both sides.
3y = 9x + 12 Divide by 3
3y/3 = 9x/3 + 12/3 Combine
y = 3x + 4
Now to get anything at all that is parallel to this and providing no answer because there is no intersection of the two lines, just change the 4 to something else. Here's one example
y = 3x + 8
As long as the number in front of the x's is the same, they are parallel with no point in common.
what is log10(2.2)= x
Answer:
Step-by-step explanation:
plug in to the calculator
find the height of a right rectangular prism with surface area 286 m^2, length 10 m, and width 8 m.
I need this ASAP
Answer: The height of the right rectangular prism is 3.5 meters.
Step-by-step explanation:
To find the height of the right rectangular prism, you need to use the formula of the surface area of a rectangular prism, where [tex]l[/tex] is the lenght, [tex]w[/tex] is the width and the height is [tex]h[/tex]:
[tex]SA=2wh+2lw+2lh[/tex]
Substitute [tex]SA=286[/tex], [tex]l=10[/tex] and [tex]w=8[/tex] into the formula and solve for the height of the right rectangular prism:
[tex]SA=2wh+2lw+2lh\\\\286=2(8)h+2(10)(8)+2(10)h\\\\286=16h+160+20h\\\\286=160+36h\\\\286-160=36h\\\\126=36h\\\\\frac{126}{36}=h\\\\h=3.5\ m[/tex]
Final answer:
Using the surface area formula for a right rectangular prism, the height is calculated to be 3.5 meters after setting up the equation with given surface area, length, and width.
Explanation:
To find the height of a right rectangular prism with a given surface area, length, and width, we can use the surface area formula for a prism: SA = 2lw + 2lh + 2wh, where SA is the surface area, l is the length, w is the width, and h is the height.
Given that the surface area is 286 m2, the length is 10 m, and the width is 8 m, we can set up the equation 286 = 2(10)(8) + 2(10)h + 2(8)h.
Simplify this to 286 = 160 + 20h + 16h, which further simplifies to 286 = 160 + 36h. Subtracting 160 from both sides, we get 126 = 36h. Dividing both sides by 36 gives us h = 3.5 m.
Therefore, the height of the prism is 3.5 meters.
Which expression represents the calculation “subtract 3 from 7, then multiply by 9"? A) (3 − 7) × 9 B) 7 − (3 × 9) C) 9 − (7 × 3) D) 9 x (7 − 3)
Answer:
D. 9 x (7 - 3)
Step-by-step explanation:
Subtracting 3 from 7 is (7-3), then multiplying by 9 is (7-3)x9.
A. Because it says three subtracted from seven so that goes first in the parentheses
how many ounces of pure oil should be mixed with an oil-gas solution that is 4.51% oil, to get 100 ounces of an oil-gas mixture that is 15% oil
Answer:
≈ 11 ounces
Step-by-step explanation:
(This is the easiest method I can explain, there is probably a simpler one)
We can make a system of equations (x = oz. of pure oil, y = oz. of mixture):
x + y = 100 oz. -> y = 100 - x
x + 0.0451y = 0.15(100) -> x + 0.0451y = 15
Using substitution, we get that x + 0.0451(100 - x) = 15.
This is equal to x + 4.51 - 0.0451x = 15.
Subtracting both sides by 4.51 and combining like terms gets us
0.9549x = 10.49.
Dividing both sides gives us about 11 ounces.
Final answer:
To obtain 100 ounces of a 15% oil-gas mixture from a 4.51% oil-gas solution, 10.49 ounces of pure oil should be added to the solution.
Explanation:
To solve the problem of how many ounces of pure oil should be mixed with an oil-gas solution that is 4.51% oil to get 100 ounces of an oil-gas mixture that is 15% oil, we can use a simple mixture equation. Let's denote the unknown quantity of pure oil to be added as x ounces.
First, we calculate the amount of oil already present in the 4.51% oil-gas mixture. If we have a total of 100 ounces, the existing oil in the mixture is 4.51% of this, that is 4.51 / 100 × 100 = 4.51 ounces.
Next, we know that the final mixture will have to be 15% oil. Therefore, in 100 ounces of this mixture, we will need 15% oil, which is 15 / 100 × 100 = 15 ounces of oil.
To find out how much pure oil to add, we subtract the amount of oil already present in the mixture from the total amount of oil needed. So, x + 4.51 = 15, which gives us x = 15 - 4.51 = 10.49 ounces of pure oil needed to be added.
may somebody help me please.
Answer:
X= -8. (-8,8)
Step-by-step explanation:
If -4x-y=24 and y = 8 then it is -4x-8=24. +8 on both sides. -4x=32. divide -4 on both sides and you get that x = -8 because 32 divided by -4 is -8.
if im right sub to my you tube channel:
Josiah Rowell
and can i get brainliest
Answer:
(-8,8)
Step-by-step explanation:
-4x-y = 24
We know that y =8
Substitute that into the equation
-4x-8 = 24
Add 8 to each side
-4x-8+8 = 24+8
-4x = 32
Divide by -4
-4x/-4 = 32/-4
x = -8
Q1. A number cube is rolled twice. What is the probability of getting an even number twice
Q2. Mei Lee spins a spinner 50 times. The spinner lands on red 25 times. What is the experimental probability of landing on red?
Q1. Answer: [tex]\bold{\dfrac{1}{4}}[/tex]
Step-by-step explanation:
[tex]\dfrac{even\ numbers}{total\ numbers}\times \dfrac{even\ numbers}{total\ numbers}\\\\\\=\dfrac{3}{6}\times \dfrac{3}{6}\\\\\\=\dfrac{1}{2}\times\dfrac{1}{2}\\\\\\=\large\boxed{\dfrac{1}{4}}[/tex]
Q2. Answer: [tex]\bold{\dfrac{1}{2}}[/tex]
Step-by-step explanation:
[tex]\dfrac{red\ spins}{total\ spins}=\dfrac{25}{50}=\large\boxed{\dfrac{1}{2}}[/tex]
The best command denominator for 3/4 + 5/6
Answer:
12
Step-by-step explanation:
If 70 is increased by 30%, what is the new amount?
Answer:
91
Step-by-step explanation:
70 * .30 = 21
21 + 70 = 91
Find the missing value to the nearest whole number.
cos xº = 0.39
Answer:
1
Step-by-step explanation:
cos^-1(0.39)=1.17... so i rounded to the nearest whole number, 1
Answer:
67°
Step-by-step explanation:
Apply the inverse cosine function to both sides, obtaining:
x = arccos 0.39
Using a calculator, obtain the value of x:
x = 1.17 (radians)
or
1.17 180°
x = ---------- · ------------ = 67 degrees (to the nearest whole degree)
1 π
1
What is the AREA of this figure?
Answer:
532m squared is the answer
Step-by-step explanation:
Split the shape into two shapes
one will be a square and the other one a triangle
1) since the length and the width of the square is 18m just Multiply
18x18=324m squared
2) look carefully the width of the square you split is equal to the base of the triangle, so you connect the 18 and the 8 together.
18+8=26m squared
3) Now solve the triangle since you know the height which is 16m squared.
A=lw/2
26x16=416
416 divided by 2 is 208
4) finally just Add
208+324=532m squared
Hopes this helps!
there are 28 other students in Tiana's class,not including her self. her teacher is going to randomly choose one student's name for a prize how many outcomes are possible.
I’m not sure what you mean but I will say that the probability of Tiana getting chosen is 1/29z
10................/......
Answer:
-1 + √3 or -(1 - 2√3)Step-by-step explanation:
(1 + √3) (2 - √3) = 2 - √3 + 2√3 - 3 = 2 - 3 - √3 + 2√3 = -1 + √3 or -(1 - 2√3)
For this case we must simplify the following expression:
[tex](1+ \sqrt {3}) (2- \sqrt {3})[/tex]
We apply distributive property:
[tex]2- \sqrt {3} +2 \sqrt {3} - \sqrt {3} * \sqrt {3} =[/tex]
We take into account that different signs are subtracted and the sign of the major is placed:
[tex]2+ \sqrt {3} - (\sqrt {3}) ^ 2 =\\2+ \sqrt {3} -3 =[/tex]
We take into account that different signs are subtracted and the sign of the major is placed:
[tex]-1+ \sqrt {3}[/tex]
Answer:
[tex]-1+ \sqrt {3}[/tex]
solve the simultaneous equations using an algebraic method:
2x+5y=0
3x-4y=23
Answer: The required solution is (x, y) = (5, -2).
Step-by-step explanation: We are given to solve the following system of equations :
[tex]2x+5y=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x-4y=23~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From equation (i), we have
[tex]2x+5y=0\\\\\Rightarrow 2x=-5y\\\\\Rightarrow x=-\dfrac{5}{2}y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the value of x from equation (iii) in equation (ii), we get
[tex]3\times\left(-\dfrac{5}{2}y\right)-4y=23\\\\\\\Rightarrow -15y-8y=46\\\\\Rightarrow -23y=46\\\\\Rightarrow y=-\dfrac{46}{23}\\\\\Rightarrow y=-2.[/tex]
From equation (iii), we get
[tex]x=-\dfrac{5}{2}\times(-2)=5.[/tex]
Thus, the required solution is (x, y) = (5, -2).
Final answer:
To solve the simultaneous equations 2x+5y=0 and 3x-4y=23, you can multiply the first equation by 4 and the second by 5 to eliminate y, solve for x, and then substitute back to find y. The solution is x = 5 and y = -2.
Explanation:
To solve the simultaneous equations 2x+5y=0 and 3x-4y=23 using an algebraic method, one effective technique is to eliminate one of the variables to solve for the other. Let's eliminate y and solve for x.
Multiply the first equation by 4, and the second equation by 5, to make the coefficients of y equal but opposite in sign.
4(2x+5y) = 4(0) → 8x+20y = 0
5(3x-4y) = 5(23) → 15x-20y = 115
Add the two resulting equations to eliminate y.
8x + 20y + 15x - 20y = 0 + 115
23x = 115
x = 115/23
x = 5
Substitute x back into one of the original equations to solve for y. Using the first equation:
2(5) + 5y = 0
10 + 5y = 0
5y = -10
y = -2
The solution to the simultaneous equations is x = 5 and y = -2.
Erik spends $680 for cable television service. The cable company offers a deal that promises Erik 3 free months of cable if he signs a contract with them for $40 per month.
complete the equation below to find th number of months that Erik will have cable television service with his deal. use m to represent the number of months.
Answer:
20
Step-by-step explanation:
Can someone help me please? Thanks
Answer:
The volume of juice is 38.4 pi in^3
Step-by-step explanation:
First we need to find the volume of the cylinder
V = pi r^2 h
We need the radius
r = d/2 = 8/2 =4
V = pi * 4^2 *12
V = pi *16*12
V = 192 pi in^3
Remember we need the exact volume so we cannot approximate pi
Now it is 20% full of juice
Multiply the volume by 20 percent
192 pi * 20%
192 pi * .20
38.4 pi
The volume of juice is 38.4 pi in^3
11. Solve 5(2x – 3) = x – 15 + 9x for x.
Answer:
[tex]\boxed{\bold{True \ For \ All \ x}}[/tex]
Explanation:
[ Step One ] Group Like Terms
[tex]\bold{5\left(2x-3\right)=x+9x-15}[/tex]
[ Step Two ] Combine Similar Elements: [tex]\bold{x+9x=10x}[/tex]
[tex]\bold{5\left(2x-3\right)=10x-15}[/tex]
[ Step Three ] Expand [tex]\bold{5\left(2x-3\right): \ 10x-15}[/tex]
[tex]\bold{10x-15=10x-15}[/tex]
[ Step Four ] Add 15 To Both Sides
[tex]\bold{10x-15+15=10x-15+15}[/tex]
[ Step Five ] Simplify
[tex]\bold{10x=10x}[/tex]
[ Step Six ] Subtract 10x From Both Sides
[tex]\bold{10x-10x=10x-10x}[/tex]
[ Step Seven ] Simplify
[tex]\bold{0=0}[/tex]
[ [tex]\boxed{\bold{Final \ Answer}}[/tex] ]
➤ [tex]\bold{Both \ Sides \ Are \ Equal, \ True \ For \ All \ x}[/tex]
[tex]\boxed{\bold{Mordancy}}[/tex]
To solve the equation, distribute the 5 into the parentheses, combine like terms, and simplify to find that the solution for x is 0.
To solve the equation 5(2x \\- 3) = x \\- 15 + 9x for x, we start by distributing the 5 into the parentheses on the left side:
5(2x) - 5(3) = x - 15 + 9x
which simplifies to:
10x - 15 = x - 15 + 9x
Combine like terms by subtracting x from both sides:
10x - x - 15 = 9x - x - 15
Leaving us with:
9x - 15 = 8x - 15
Next, we can cancel the -15 on both sides, since they are equal and opposing, which simplifies the equation to:
9x = 8x
Subtract 8x from both sides to isolate x:
9x - 8x = 0
And we find that:
x = 0
If f(x) = 6x-4, what is f(x) when x = 8
Answer:
The correct answer is 44
Step-by-step explanation:
6(8)-4
48-4
44
Answer:
f(8) = 44
Step-by-step explanation:
Plug in 8 for x. Then evaluate the expression.
f(x) = 6x - 4
Where you see x, substitute it with 8.
f(x) = 6x - 4
f(8) = 6(8) - 4
f(8) = 48 - 4
f(8) = 44
-0.06 as a mixed number is what
Answer:
-3/50
Step-by-step explanation:
-0.06 = -6/100
-6/100 = -3/50