Answers:
a = 21b = 42*sqrt(2)h = 14*sqrt(2)================================================
Explanation:
There are 3 right triangles here. They are all similar triangles allowing us to form the proportion
7/h = h/56
which solves to...
7/h = h/56
7*56 = h*h
392 = h^2
h^2 = 392
h = sqrt(392)
h = sqrt(196*2)
h = sqrt(196)*sqrt(2)
h = 14*sqrt(2)
Note: h is the geometric mean of 7 and 56.
---------------------
Use the pythagorean theorem to solve for 'a'. Focus on the smaller triangle on the left
7^2 + h^2 = a^2
7^2 + (sqrt(392))^2 = a^2
49 + 392 = a^2
441 = a^2
a^2 = 441
a = sqrt(441)
a = 21
---------------------
Then we can find b. Again use the pythagorean theorem. Focus on the largest right triangle this time.
a^2 + b^2 = (7+56)^2
21^2 + b^2 = 63^2
441 + b^2 = 3969
b^2 = 3969 - 441
b^2 = 3528
b = sqrt(3528)
b = sqrt(1764*2)
b = sqrt(1764)*sqrt(2)
b = 42*sqrt(2)
Amir wants to create a 4-digit password for his phone.
He wants to choose 4 different numbers between 1 and 5 inclusive.
Calculate the total number of 4-digit passwords that Amir can create.
Answer:
360
Step-by-step explanation:
Given that Amir wants to create a 4-digit password for his phone.
He wants to choose 4 different numbers between 1 and 5 inclusive.
The total number of 4-digit passwords that Amir can create will be achieved by using permutation
6P4 = 6!/ ( 6 - 4)!
6P4 = (6 × 5 × 4 × 3 × 2!)/2!
6P4 = 6×5×4×3 = 360
Therefore, the total number of 4-digit passwords that Amir can create is 360 different passwords.
Ship A and Ship B are 120 km apart when they pick up a distress call from another boat. Ship B estimates that they are 70 km away from the distress call. They also notice that the angle between the line from ship B to ship A and the line from ship A to the distress call is 28°. What are the two possible distances, to the nearest TENTH of a km, from ship A to the boat?
Answer:
The two possible distances from Ship A to the distress call boat are 64.4 km and 147.5 km
Step-by-step explanation:
The given parameters are;
The distance between Ship A and Ship B = 120 km
The distance of the distress call from Ship B = 70 km
The angle made between the line from Ship A to B and the line from Ship A to the distress call = 28° = Opposite angle to the line from the location of the distress caller to Ship B
Therefore;
70/(sin(28°)) = 120/(sin(x))
Where;
x = The angle opposite the line from Ship A to B
sin(x) = ((sin(28°))×120)/70 = 0.805
x = sin⁻¹(0.805) = 53.59°
Therefore, the angle opposite the line from Ship A to the distress caller, r = 180 - (28 + 53.59) = 98.4°
From sin rule, we have;
70/(sin(28°)) = r/(sin(98.4°))
r = (70/(sin(28°)))×(sin(98.4°)) = 147.5
However by cosine rule, we have;
70² = 120² + r² - 2×120×r × cos(28°)
4,900 = 14,400 + r² - 211.907·r
r² - 211.907·r + 14,400 - 4,900 = 0
r² - 211.907·r + 9,500 = 0
Factorizing, we have;
[tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]
[tex]r = \dfrac{211.907\pm \sqrt{211.907^{2}-4\times 1\times 9,500}}{2\times 1}[/tex]
r = 64.406 km or 147.501 km
Which gives;
The distance of the line from Ship A to the distress caller = 64.4 km or 147.5 km to the nearest tenth.
The two possible distances from Ship A to the distress call boat = 64.4 km and 147.5 km
what is (15-2)×3×2
Answer:
15−2(3−2x)=46
Step-by-step explanation:
15−2(3−2x)=46
the slope and y intercept of 3y+6x=18
Answer:
slope: -2
y-intercept: 6
Step-by-step explanation:
First, put the equation into slope intercept form.
Slope-intercept form: y = mx + b
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, subtract 6x from both sides:
3y + 6x (-6x) = 18 (-6x)
3y = -6x + 18
Next, divide 3 from both sides. Remember to divide from all terms:
(3y)/3 = (-6x + 18)/3
y = (-6x)/3 + (18)/3
y = -2x + 6
Slope-intercept form: y = -2x + 6
Again, note the slope-intercept form.
> Slope-intercept form: y = mx + b
The variables:
y = (x ,y)
m = slope
x = (x , y)
b = y-intercept
Your answers:
slope: -2
y-intercept: 6
If g(x) = a f(x + b), how is f(x) transformed to get g(x)?
02/(x + 4)
02/(x-4)
O f(x + 4)
Of(x-4)
Answer:
There was a Horizontal translation left b units and then Vertical stretch or compression
Step-by-step explanation:
Given : [tex]g(x) = a f(x + b)[/tex]
We are supposed to show the transformation
Rule : f(x)→f(x+c)
Horizontal translation left c units
So, f(x+b) is the Horizontal translation left b units
Rule : f(x)→cf(x)
Vertical stretch or compression
So,[tex]g(x) = a f(x + b)[/tex]
So, Initially there was a Horizontal translation left b units and then Vertical stretch or compression
Answer:
-2f(x+4), A
Step-by-step explanation:
Vertically stretch the function by 2, flip it over the x-axis and add 4 to shift right
(The explaination might be BS but the answer is 100% correct, took the quiz)
What is the value of vba? be sure to give the correct algebraic sign?
Answer:
V = Vab from the drawing.
So if V = –10 volts, then Vab = –10v and Vba = +10v
"the figure is the same in the link below except that the voltage is from a to b" but the drawing shows that V = Vab
Hoped I helped
All of the following represent the same concept except _____. 47 take away 28 47 minus 28 47 less than 28 47 subtract 28
Answer:
C. 47 less than 28
Step-by-step explanation:
A. 47 take away 28
Equivalent to counting 47 and taking away 28
= 47 - 28
= 19
B. 47 minus 28
Simply
47 - 28
= 19
C. 47 less than 28
47 < 28
The less than sign is <
D. 47 subtract 28
= 47 - 28
= 19
Answer:47 less than 28
Step-by-step explanation:the rest are subtracting 28 from 47 , 47 less than 28 is subtracting 47 from 28.
3/4 - 1/2n =5/8. solve for n
The solution to the equation (3/4) - (1/2)n = 5/8 is n = 1/4 as per the rule of fraction's operations.
To solve the equation (3/4) - (1/2)n = 5/8 for n, we can follow these steps:
Start by subtracting 3/4 from both sides of the equation:
(3/4) - (1/2)n - 3/4 = 5/8 - 3/4
Simplifying, we have:
(1/2)n = 5/8 - 6/8
Combine the fractions on the right-hand side:
(1/2)n = -1/8
To eliminate the fraction coefficient, multiply both sides by -2:
(-2)(-1/2)n = (-2)(-1/8)
This gives us:
n = 2/8
Simplify the right-hand side:
n = 1/4
Therefore, the solution to the equation (3/4) - (1/2)n = 5/8 is n = 1/4.
It's important to note that when solving equations involving fractions, it's crucial to perform the same operation on both sides of the equation to maintain the equality. By isolating the variable n on one side, we were able to find its value.
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the average number of spectators at a football competition for the first five days was 3144.the attendance on the sixth day was 3990.find the average attendance for the 6 days
Answer:
3285
Step-by-step explanation:
5x3144=15720
3990
15720+3990=19710
19710/6=3285
IF Tunde, who has n eggs, has three
more than Sola, how many eggs has
Sola?
Answer:
Sola has n-3 eggs
Step-by-step explanation:
Tunde = n
Tunde has 3 more = Sola has 3 less than tunde
= Tunde - 3
= n - 3
Calculate the slope of the line that passes through the following points:
(-4,-7) and (1, -7)
Apply the following formula:
Tise
m =
(y2-91)
(22-21)
TUT
0
O Undefined
Answer:
0
Step-by-step explanation:
Slope is -7--7/1--4
=0/5
=0
Slope of the line passing through (-4,-7) and (1, -7) is equals to 0.
What is slope?
"Slope of a line is defined as the ratio of change in y-coordinates to the change in x-coordinates."
Formula used
Slope = ( y₂ - y₁) / (x₂ - x₁)
According to the question,
Line passing through two points (-4, -7) and ( 1, -7)
x₁ and x₂ are x- coordinates on the line.
y₁ and y₂ are the y-coordinates on the line.
Here,
( x₁ , y₁ ) = ( -4, -7)
(x₂ , y₂) = ( 1 , -7)
Substitute the given value in the formula we get,
Slope = [ -7 -(-7)] / [ 1 - (-4)]
= (-7 +7) / ( 1 +4)
= 0 / 5
= 0
Hence, slope of the line passing through (-4,-7) and (1, -7) is equals to 0.
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5u+5(1-u)=u+8
I need help finding the answer
I hope this helps you
5u+5-5u=u+8
5-8=u
u=-3
What is the Decimal Represention of 9/11
Answer: the answer is A 0.81
What is the probability of getting dealt a hand equal to 21?
Answer:
The odds to get a blackjack (natural) as arrangement: 128 / 2652 = . 0483 = 4.83%. 4.83% is equivalent to about 1 in 21 blackjack hands.
select the correct descriptor of the following problems: from a pack of 52 cards, two cards drawn together at random. What is the probability od both the cards being kings?
Answer:
[tex]\frac{1}{221}[/tex]
Step-by-step explanation:
We have to note that there are 4 kings in a deck of 52 cards.
This makes the probability of choosing a king the first time [tex]\frac{4}{52} = \frac{1}{13}[/tex].
We now know that we can choose another king from the deck, but it's important to note that it's not a [tex]\frac{1}{13}[/tex] chance. We now only have 51 cards in the deck, and 3 kings left. This means the probability of choosing a king now is [tex]\frac{3}{51} = \frac{1}{17}[/tex].
To find the probability of doing both these, we need to multiply the fractions.
[tex]\frac{1}{13}\cdot\frac{1}{17}=\frac{1}{221}[/tex]
Hope this helped!
If x is a rational number and y is a rational number than x + y is a rational number.
Answer:
True.
Step-by-step explanation:
The sum of two rational numbers is rational.
By definition, a rational number can be expressed as a fraction with integer values in the numerator and denominator (denominator not zero). So, adding two rational numbers produces another rational number.
Rewrite in mathematical language. Every negative integer J is less than or equal to its inverse.
Answer:
[tex]-J \leq J[/tex]
Step-by-step explanation:
Given
Negative integer J
Required
Represent as an inequality of its inverse
The question didn't state if it's additive inverse or multiplicative inverse;
Since the question has to do with negation, I'll assume it's an additive inverse
The inverse of -J is +J
To represent as an inequality (less than or equal), we have:
[tex]-J \leq +J[/tex]
Solving further, it gives
[tex]-J \leq J[/tex]
I have no idea how to do any of these so please explain I'm already struggling and school just started
1.
[tex]5g + h = g[/tex]
solve for g
2.
[tex]y = mx + b[/tex]
solve for m
3.
[tex]3y + z = am - 4y[/tex]
solve for y
4.
[tex]km + 5x = 6y[/tex]
solve for m
5.
[tex] \frac{3ax - n}{5} = - 4[/tex]
solve for x
6.
[tex] \frac{by + 2}{3} = c[/tex]
solve for y
7.
[tex]at + b = ar - c[/tex]
solve for a
Answer:
See below!
Step-by-step explanation:
1. 5g + h = g
4g = -h
g = [tex]-\frac{h}{4}[/tex]
2. y = mx + b
y - b = mx
m = [tex]\frac{y - b}{x}[/tex]
3. 3y + z = am - 4y
7y = am - z
y = [tex]\frac{am - z}{7}[/tex]
4. km + 5x = 6y
km = 6y - 5x
m = [tex]\frac{6y - 5x}{k}[/tex]
5. [tex]\frac{3ax - n}{5} = -4[/tex]
3ax - n = -20
3ax = n - 20
x = [tex]\frac{n-20}{3a}[/tex]
6. [tex]\frac{by+2}{3}= c[/tex]
by + 2 = 3c
by = 3c - 2
y = [tex]\frac{3c-2}{b}[/tex]
7. at + b = ar - c
at - ar = -b - c
a(t - r) = -(b + c)
a = [tex]-\frac{b+c}{t-r}[/tex]
There are 75 people in a room. Of these people, 2/5 are from Germany. If 4/9 of the people who are not from Germany are from France, how many of the people in the room are from neither Germany nor France
Answer:
25 people are not from Germany or France.
Step-by-step explanation:
1. You first want find out what is the number of people from Germany.
So you would find...
2/5 of 75
or
2/5*75= 30 people from Germany
2. Next you want to to find out the number of people from France.
So you would do the following...
75-30=45 (Subtract the number of people from Germany from 75 so you can get the total number of people from France and other countries)
4/9 of 45 to find the number of people from France.
4/9 *45= 20
3. Lastly you need to find the people who are from neither of the countries listed above.
Add 30+20= 50
Then subtract that number from 75.
75-50= 25 people who are from neither France or Germany.
Voila! This is your answer. Hope this helps! :)
Part B: Plot point C(2,7). If M is the midpoint of CD, what are the
coordinates of D?
9-2x=7x
How do I solve for x?
Answer:
The answer to the equation is 1.
Step-by-step explanation:
When having an algebraic equation, you have to move all of the variables on one side. Therefore, you can move the -2x or the 7x. However, to make a positive number, I would recommend to move the -2x.
To move the -2x to the other side, you add 2x to the both sides of the equation. Since the original equation is 9-2x=7x, you will add the 2x to it, so your equation will now look like this: 9-2x+2x=7x+2x. Once simplifying that down, you will have 9=9x. Then, you can divide the coefficient, so the 9 on the left side, and the 9 on the right side. After this, you will have 1=x. AKA x=1, which is the answer to the equation!
The solution to the equation 9 - 2x = 7x is x = 1 as per the algebraic operations.
To solve the equation 9 - 2x = 7x for x, we need to isolate the variable on one side of the equation. Here's the step-by-step process:
Start by combining like terms. Add 2x to both sides of the equation to move the variable terms to one side:
9 - 2x + 2x = 7x + 2x
9 = 9x
Divide both sides of the equation by 9 to isolate x:
9/9 = 9x/9
1 = x
Therefore, the solution to the equation 9 - 2x = 7x is x = 1.
By performing the necessary algebraic operations, we found that x is equal to 1. This value satisfies the original equation, making it the solution. It's important to check the solution by substituting x = 1 back into the original equation to ensure that it holds true. In this case, when we substitute x = 1 into the equation, we have 9 - 2(1) = 7(1), which simplifies to 7 = 7, confirming that x = 1 is indeed the correct solution.
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What is the value of x in equation 6x + 2= 9x - 1?
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
So we have the equation:
[tex]6x+2=9x-1[/tex]
Subtract 6x from both sides:
[tex](6x+2)-6x=(9x-1)-6x\\2=3x-1[/tex]
Add 1 to both sides:
[tex](2)+1=(3x-1)+1\\3=3x[/tex]
Divide both sides by 3:
[tex](3)/3=(3x)/3\\x=1[/tex]
So, the value of x is 1 :)
P.S. Welcome to Brainly!
Find the asymptotes of the hyperbola described by the equation: y2/9 - x^2/81=1. ANSWERS ATTACHED, due in 2 HOURS, will give Brainliest!
Answer:
Solution : y = ± 1/3x
Step-by-step explanation:
Remember that the equation of a hyperbola is in the form (y - k)² / a² - (x - h)² / b² = 1. Therefore we have a² here = 9, and b² here = 81.
To determine the asymptotes we can use the equation y = k ± a/b(x - h). What makes this equation really simple, is that k = 0 and h = 0, giving us y = ± a/b(x). Let's isolate a and b given a² = 9, and b² = 81 --- (1)
a² = 9
a = 3
b² = 81
b = 9
Therefore our asymptotes will be in the form y = ± a/b(x) = ± 3/9(x) = ± 1/3x. Our solution is thus option a.
Dylan can paint a wall in 4 hours, while Brett can paint the same wall in 3 hours. If Dylan paints the wall for 2 hours, how much time will it take for Brett to finish painting the wall
Answer:
n 1 hour Dylan can paint 1/4 of the wall, and Brett can paint 1/3 of the wall.
Therefore together they can paint 1/4+1/3 = 7/12 of wall
Therefore they can paint entire wall in 12/7 hours
Step-by-step explanation:
you ' re welcome grandma loves youu ! < 33 ; )
mark meee branliest pleaseeee ; )
Kenya is reserving a room in a hotel in France where they use euros (€). The room charge is €75. Suppose the conversion rate is €1 = $1.298. What is the cost of the room in dollars? (1 point)
Add 113+(−56) using the number line.
Answer:
Step-by-step explanation:
Start at 1 1/3
Add the negative number.
1 1/3 + (-5/6)
Adding a negative number means to go left on a number line.
-5/6 is equal to -2/3 plus -1/6.
Move 2/3 to the left.
1 1/3 (Start)
1 (1/3)
2/3 (2/3)
Now, move 1/6th to the left.
2/3 is equal to 4/6
4/6 - 1/6 = 3/6
So, put the point at 3/6 or 1/2.
The value of addition of 1 1/3+(−5/6) is 1/2 and plotted on a number line.
What is addition?The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
Start at 1 1/3
Add the negative number;
1 1/3 + (-5/6)
Here Adding a negative number means to go left on a number line.
-5/6 is equal to -2/3 plus -1/6.
Now Move 2/3 to the left;
1 1/3 (Start)
1 (1/3)
2/3 (2/3)
Now, move 1/6th to the left;
2/3 is equal to 4/6
4/6 - 1/6 = 3/6
Thus 1 1/3+(−5/6) = 3/6 = 1/2
The value of addition of 1 1/3+(−5/6) is 1/2 and plotted on a number line.
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There are 5 pencils and 8 pens. What is the ratio of pens to pencils?
Answer:
8/5
Step-by-step explanation:
The parent function, Rx) = 5*, has been vertically compressed by a factor of one-half, shifted to the left three units and
down two units. Choose the correct function to represent the transformation.
Answer:
see below
Step-by-step explanation:
For a vertical scale factor of 'b', and a translation by (h, k) in the (right, up) direction, the transformed function is ...
g(x) = b·f(x -h) +k
For a scale factor of 1/2 and translation left 3 and down 2, the transformed function is ...
g(x) = (1/2)f(x +3) -2
g(x) = (1/2)5^(x +3) =2 . . . . matches the 2nd choice
If A = 3x power 2+2y + 2 and B=6x power 2 - 8y + 1 then A+B and A-B
Answer:
see explanation
Step-by-step explanation:
Given A = 3x² + 2y + 2 and B = 6x² - 8y + 1 , then
A + B
= 3x² + 2y + 2 + 6x² - 8y + 1 ← collect like terms
= 9x² - 6y + 3
-------------------------------
A - B
= 3x² + 2y + 2 - (6x² - 8y + 1) ← distribute parenthesis by - 1
= 3x² + 2y + 2 - 6x² + 8y - 1 ← collect like terms
= - 3x² + 10y + 1
I need help step by step Combining like terms 6 + x + 4=