Step-by-step explanation:
The Pythagorean theorem is:
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
where c is the hypotenuse.
The two wires in the sketch are the hypotenuse so we just use the formula
let the wires=x
So:
[tex] {x}^{2} = {12}^{2} + {6}^{2} [/tex]
[tex] {x}^{2} = 144 + 36[/tex]
[tex] {x}^{2} = 180[/tex]
[tex]x = \sqrt{180} [/tex]
[tex]x = 13.42[/tex] feet
What order should you simplify like terms in? E.g. [tex]16-4\sqrt{5} -4\sqrt{5} +5[/tex] A video said to Simplify the numbers first as they will be positive?
But in [tex]6+3\sqrt{5} +2\sqrt{5}+5[/tex] You simplify the surds first.
Answer:
It does not matter, since, from your second case, [tex]5\sqrt5 +11 = 11+5\sqrt5[/tex].
In general is a matter of personal preference but in general I like to start with a positive number (I like [tex]\sqrt2 -1[/tex] more than [tex]-1+\sqrt2[/tex] since if there's an equal sign before I'm guaranteed to have the two signs mesh together in a few steps).
If everything you are adding together is positive, I just go first come first served and pick a new term in order it appears in the previous passage.
Find the intersection point for the following linear functions.
Rx) = 2x + 3
8(x) = -4x - 27
Answer:
(-5, -7)
Step-by-step explanation:
Answer:
[tex](-5,-7)[/tex]
Step-by-step explanation:
[tex]f(x)=2x+3[/tex]
[tex]g(x)=-4x-27[/tex]
[tex]2x+3=-4x-27[/tex]
[tex]6x+3=-27[/tex]
[tex]6x=-30[/tex]
[tex]x=-5[/tex]
[tex]f(-5)=2(-5)+3[/tex]
[tex]f(-5)=-10+3[/tex]
[tex]f(-5)=-7[/tex]
Therefore, the point of intersection is [tex](-5,-7)[/tex]
10. A wedding reception bartender is faced with a problem: how many litres of fruit juice must be
mixed with 4 litres of a 24% flavoured rum to make a rum punch of 8% strength?
9.14 liters of fruit juice must be mixed with 4 liters of a 24% flavored rum to make a rum punch of 8% strength.
To determine how many liters of fruit juice must be mixed with 4 liters of a 24% flavored rum to make a rum punch of 8% strength, the following calculation must be performed:
(4 x 24 + 4) / 8 = 12.5 (4 x 24 + 8) / 12 = 8.66 (4 x 24 + 9) / 13 = 8.07 (4 x 24 + 9.14) / 13.14 = 8
Therefore, 9.14 liters of fruit juice must be mixed with 4 liters of a 24% flavored rum to make a rum punch of 8% strength.
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please help I am so lost rn
(please put step by step if you can)
thanks!
Answer:
x=-5 and y= 4
Step-by-step explanation:
To eliminate x, add up both equations
9y= 36
divide both sides by 9
y=36/9
y= 8
To eliminate y, multiply the first equation by 8
-16x + 8y = 112
2x+ 8y= 22
Subtract equation 2 from equation 1
-18x = 90
Divide both sides by -18
x= 90/-18
x= -5
Rewrite in simplest terms: (-9x + 7y) - (-9x + 5y)
Answer:
3y
Step-by-step explanation:
(-9x+7y)-(-9x+5y)
Distribute the negative(-)
-9x+7y+9x-5y
-9 and 9 cancel each other
3y
The simplest terms of the given expression (-9x + 7y) - (-9x + 5y) will be 2y.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given expression,
(-9x + 7y) - (-9x + 5y)
Open the bracket
-9x + 7y + 9x - 5y
Combined likely terms together
-9x + 9x + 7y - 5y
0 + 2y = 2y
Hence "The formula (-9x + 7y) - (-9x + 5y) will have 2y as its simplest terms".
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QUESTION 21 PLEASE HELPPP
Answer:
one solution
Step-by-step explanation:
Since both are y-isolated equation, we can write as:
[tex]\displaystyle \large{6x-2=4x-2}[/tex]
Solve for x, first move 4x to subtract with 6x and -2 to add with -2
[tex]\displaystyle \large{6x-4x=-2+2}\\\displaystyle \large{2x=0}\\\displaystyle \large{x=0}[/tex]
Then substitute x = 0 in any of these equations which we receive y = -2.
And the solution is (0,-2) which only has one solution.
Mrs Ang bought k apples at 50% each from a supermarket. How much
change did she receive if she paid $10 to the cashier? Express your answer
in cents.
Answer:
The apples may have costed 0.50 cents each, and she may have bought 10, which would result in her paying 10 dollars, and receiving 5 dollars in change.
Step-by-step explanation:
Multiply 10 (the amount she gave to the cashier) by 0.50%, it equals 5, so that's how much she paid, and since she gave a 10 dollar bill, she should get 5 dollars in change.
T^T
In a parking lot 30% of the cars are white write this as a decimal
Answer:
0.3
Step-by-step explanation:
Answer:
[tex]{ \tt{30\% = 0.3}} \\ [/tex]
Solve 3-x/2<18.
A. X>-42
B. x > -30
C. X< -30
D. X<42
The solution of the given equation will be C -x< 30
What does it mean to solve an equation?An equation represents the equality of two or more mathematical expressions.
A Solutions to an equation are those values of the variables, involved in that equation for which the equation is true.
We have been given the equation as 3-x/2<18.
Now solving for x
3-x/2<18.
Eliminate 3
-x/2 < 18 - 3
-x/2 < 15
Multiply by 2 on both sides;
-x/2 < 15 (2)
-x< 30
Therefore, the solution of the given equation will be C -x< 30
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ST
16. (26)
A bag contains 3 green marbles and
7 yellow marbles. Find the probability of
drawing a green marble, keeping it, and
drawing another green marble. Write the
probability as a fraction in simplest form.
17.
Answer:
the probability would be 30% but as a fraction it would be 3/10
Step-by-step explanation:
Answer:
7/15
Step-by-step explanation:
The probability of the first one is 7/10 and the second one is 6/9. Multiply them together and you get 42/90, which simplifies to 7/15.
Find the square (8m-7)^2
Answer:
64m^2 - 112m + 49
Step-by-step explanation:
You just do the math lol.
Answer:
64m^2 + 112m + 49
Step-by-step explanation:
I got it right in Grandpoint.
Help help help math math
Answer:
Function
Step-by-step explanation:
Hope it help !!
What is the value of x in the equation 4
.
+
2
Answer:
x=-3
Step-by-step explanation:
Which of the following is equal to 2,952 ÷ 24?
A.
(2,400 ÷ 24) + (480 ÷ 24) + (72 ÷ 24)
B.
(2,400 + 24) ÷ (480 + 24) ÷ (72 + 24)
C.
(2,400 + 24) + (480 + 24) + (72 + 24)
D.
(2,400 ÷ 24) - (480 ÷ 24) - (72 ÷ 24)
Answer:
A
Step-by-step explanation:
After doing long division we then know that 2,952 ÷24 = 123
We 1st follow pemdas knowing this we solve the equations in parenthesis 1st
(2,400 ÷ 24) + (480 ÷ 24) + (72 ÷ 24)
2,400 ÷ 24 = 100
480 ÷ 24 = 20
72 ÷ 24 = 3
We can then rewrite the equation as
100 + 20 + 3 We then solve left to right
100 + 20 = 120
120 + 3 = 123
HELPPPP PLEASEEEEE
Ben currently has $70 in his trip fund. He makes $45 per week doing yard work for his neighbors. He keeps $18 of the $45 for weekly expenses. The remaining amount goes into his trip fund. Which function can be used to determine the amount of money (y), in dollars, that Ben has in his trip fund at the end of xx weeks?
y=70+27x
Answer:
he starts with 70 and $45-18=27 so he makes $27 to add to those $70
Step-by-step explanation:
find three solutions for 9x - 2y = 18
Answer:
[tex](x,y) = \left(5,\dfrac{27}2 \right), \left(0,-9), \left(9, -\dfrac 92 \right)[/tex]
Step-by-step explanation:
David's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs David $4.45 per pound, and type B coffee costs $5.85 per pound. This month, David made 123 pounds of the blend, for a total cost of $643.95. How many pounds of type B coffee did he use?
Step-by-step explanation:
x = pounds A
y = pounds B
x + y = 123
4.45x + 5.85y = $643.95
from the first equation we get
x = 123 - y
and we use that in the second equation :
4.45×(123 - y) + 5.85y = 643.95
547.35 - 4.45y + 5.85y = 643.95
1.4y = 96.6
y = 69
x = 123 - y = 123 - 69 = 54
so, he used 69 pounds of B coffee.
Help with this please?
In a group of workers, 16 belonged to a lottery syndicate and 4 did not.
What fraction of the workers did not belong to the syndicate?
1: 4/16
2: 1/5
3: 1/4
4: 3/4
Answer:
HI THEREthe answer is number 1 !!
• correct me if I'm wrong
"When I started here, there were 500 employees. Since then, we have
added 35% more employees, so we now have a total of employees."
Answer:
Assuming that the question is asking how many employees there are, your answer would be 675.
Step-by-step explanation:
First, to find 35% of 500, you can use this equation (35 x 500) / 100 Second, solve the equation (The answer is 175) Third, you add 500 + 175 to get 675What is the prime factorization of 32?
A. 32 = 2 x 4x4
B. 32 = 2x2x2x2x2
C. 32 = 2x2x2x2
D. 32 = 2 * 2 * 2 * 4
Answer:
2nd option
Step-by-step explanation:
Repeatedly divide by 2 until the value 1 is reached
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1 ← finish here
Then
32 = 2 × 2 × 2 × 2 × 2
help plsssssssssssssss
Answer:
Last answer, height is 150 ft
Step-by-step explanation:
from the graph, you can clearly see, when T=3, H=150
Which means The firework is at a height of 150 feet
Answer:
D
Step-by-step explanation:
At 3 seconds, the firework is at a height of 150 feet
Answer is D. third option
The firework is at a height of 150 feet
What is the molarity of a solution
made by dissolving 67.3 g of lithium
chloride (LiCl) in enough water to
make 2.37 L of solution?
Molar Mass Li: 6.94 g/mol
Molar Mass Cl: 35.45 g/mol
Answer:
0.670. M
Step-by-step explanation:
Molarity can be expressed like this:
molarity = number of moles /volume (L)
We know the volume, which is 2.37 L , but we need to find the number of moles. We can do this by dividing 67.3 g by the molar mass of L i C l :
number of moles = mass of sample /molar mass
number of moles = 67.3 g /(6.94 + 35.45) g/mol = 67.3 g /42.39 g/mol
number of moles = 1.59 mol
molarity = 1.59 mol /2.37 L = 0.670. M
Please answer. I will give brainliest to the best answer
Answer:
b
Step-by-step explanation:
took the test a bit ago
you went to a coffee house with 2 friends and ordered an iced coffee and dessert which came to $12.96 how much is your total bill
Answer:
$4.32
Step-by-step explanation:
If you are splitting it evenly, just divide 12.96 by 3
12.96 / 3 = $4.32
7362*637 help please
Answer:
4689594
Step-by-step explanation:
rewrite in simplest terms -6(-7u+6)+2u
Answer:
44u-36
Step-by-step explanation:
42u-36+2u
44u-36
Express the following surds in the simplest form
a)
[tex] \sqrt{128} [/tex]
b)
[tex] \sqrt{48} [/tex]
c)
[tex] \sqrt{300} [/tex]
[tex] \sqrt{128} \\ = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2} \\ = \sqrt{ {2}^{2} \times {2}^{2} \times {2}^{2} } \\ = 2 \times 2 \times 2 \\ = 8[/tex]
[tex] \sqrt{48} \\ = \sqrt{2 \times 2 \times 2 \times 2 \times 3} \\ = \sqrt{ {2}^{2} \times {2}^{2} \times 3 } \\ = 2 \times 2 \sqrt{3} \\ = 4 \sqrt{3} [/tex]
[tex] \sqrt{300} \\ = \sqrt{2 \times 2 \times3 \times 5 \times 5} \\ = \sqrt{ {2}^{2} \times 3 \times {5}^{2} } \\ = 2 \times 5 \sqrt{3} \\ = 10 \sqrt{3} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
A rectangular cube of iron is a side 8 cm. What is it volume.
[tex] = {8}^{3} \: \: cm ^{3} \\ = 512 \: \: {cm}^{3} [/tex]
Answer:
The volume is 512 cube centimetres.
Hope you could get an idea from here.
Doubt clarification - use comment section.