Answer:
C) [tex]-4x+2y[/tex]
Step-by-step explanation:
[tex]6x-3y+5y-10x[/tex]
[tex]6x-10x-3y+5y[/tex]
[tex]-4x-3y+5y[/tex]
[tex]-4x+2y[/tex]
To calculate the height of a tree, Sophie measures the angle of elevation from a point “A” to be 34°. She then walks 10 m directly toward the tree, and finds the angle of elevation from the new point “B” to be 41°. What is the height of the tree, to the nearest tenth of a metre?
Answer:
30.1 Metres
Step-by-step explanation:
For this problem, we will use the law of sines twice to find the height of the tree.
First, you need to draw the image of the tree with two triangles, one with an angle of 34 degrees, and the second with an angle of 41 degrees, both being a right triangle toward the tree. The distance between point A and point B should be 10 meters.
From here, your bottom line of the triangle should be represented as 10 + x for the unknown distance from where Sophie stood to the tree. The x represents the distance from point B to the tree, whereas 10 + x represents the distance from point A to the tree.
Now, let's use the scalene triangle created by the distance between point A and point B to the top of the tree, to calculate the diagonal distance from point B to the top of the tree.
Using this scalene, we have the angles, 34, 7, and 139. Now, use the law of sines to find the diagonal of point B to the top of the tree represented by r.
sin(7) / 10 == sin (34) / r
r == 10 * sin (34) / sin(7)
r == 10 * .55919 / .12187
r == 45.88
Now that we know this diagonal distance, we can use the law of sines again with the second triangle, 41, 49, 90, to find the height of the tree represented by y.
sin(41) / y == sin(90) / 45.88
y == 45.88 * sin(41) / sin(90)
y == 45.88 * .65606 / 1
y == 30.1
So the height of the tree to the nearest tenth of a metre would be 30.1 metres.
Cheers.
Answer:
Hight of the tree: h = 30,1 mStep-by-step explanation:
tan(34°)≈0.6745 tg(41°)≈0.8693
[tex]\tan(34^o)=\dfrac h{x+10}\\\\\tan(34^o)(x+10)=h\\\\x+10=\dfrac h{\tan(34^o)}\\\\x=\dfrac h{\tan(34^o)}-10[/tex] [tex]\tan(41^o)=\dfrac hx\\\\x\tan(41^o)=h\\\\x=\dfrac h{\tan(41^o)}[/tex]
[tex]\dfrac h{\tan(34^o)}-10=\dfrac h{\tan(41^o)}\\\\ h\tan(41^o)-10\tan(34^o)\tan(41^o)=h\tan(34^o) \\\\ h\tan(41^o)-h\tan(34^o)=10\tan(34^o)\tan(41^o) \\\\ h[\tan(41^o)-\tan(34^o)]=10\tan(34^o)\tan(41^o)\\\\h=\dfrac{10\tan(34^o)\tan(41^o)}{\tan(41^o)-\tan(34^o)}\\\\\\h\approx \dfrac{10\cdot0.6745\cdot0.8693}{0.8693-0.6745}=\dfrac{5.8634285}{0.1948}\approx30.1\ m[/tex]
What kind of writing is found in a scientific essay?
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
A high temperature of 128°F was recorded in a desert. Use the formula F = C + 32
to convert this temperature to degrees Celsius.
Answer:
F=C+32.
128=C+32.
C=128-32.
96°C
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.
To learn more about the equation;
https://brainly.com/question/12788590
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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
A ratio compares the relative sizes of ______ quantities .
Answer:
two
Step-by-step explanation:
A ratio compares the relative sizes of two quantities .
Answer:2
Step-by-step explanation:
I need help step by step Combining like terms 6 + x + 4=
What is the distance between 1240 feet above sea level and 620 feet below sea level
Answer:
1860
Step-by-step explanation:
First, we need to get to 0.
1240 above sea level. The distance to 0 is 1240.
Next, below sea level. The distance to 0 is 620.
So, add 1240 + 620 to find the distance between the 2 numbers.
1860
Hope this helps!!!
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.
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.
Learn more about slope here
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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)
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
The quadratic function g(x) has a vertex at
(-5, 0) and y-intercept of (0, -5). What is g(1)?
Answer: -7.2
Step-by-step explanation:
The vertex form of quadratic equation :[tex]f (x) = m(x - a)^2 + b,[/tex] where (a,b) is the vertex.
Given: The quadratic function g(x) has a vertex at (-5, 0).
Put (a,b)= (-5,0) for function g(x), we get
[tex]g(x)=m(x-(-5))^2+0\\\\\Rightarrow\ g(x)=m(x+5)^2[/tex]
Also, its y-intercept is (0, -5).
Put x= 0 and g(x) =-5
[tex]-5=m(0+5)^2\\\\\Rightarrow\ -5=m(25)\\\\\Rightarrow\ m=\dfrac{-5}{25}\\\\\Rightarrow\ m=\dfrac{-1}{5}[/tex]
so, [tex]g(x)=-\dfrac{1}{5}(x+5)^2[/tex]
For g(1), put x=1
[tex]g(1)=-\dfrac{1}{5}(1+5)^2\\\\=-\dfrac{1}{5}(6)^2=-\dfrac{1}{5}(36)\\\\=-7.2[/tex]
Hence, g(1) is -7.2.
He first term in the sequence is 1, and each other term is 5 more than three times the previous term. 1, , , , Blank 1: Blank 2: Blank 3: Blank 4:
Answer:
The complete sequence is: 1, 8, 29, 92, 281.
Step-by-step explanation:
The series to be completed is:
1, _, _, _, _
The information provided is:
The first term in the sequence is 1.Each other term is 5 more than three times the previous term.Then the nth term can be determined using the expression:
[tex]a_{n}=3a_{n-1}+5[/tex]
Compute the 2nd, 3rd, 4th and 5th term as follows:
[tex]a_{2}=3a_{2-1}+5 = 3a_{1}+5=(3\times 1)+5=8\\\\a_{3}=3a_{3-1}+5 = 3a_{2}+5=(3\times 8)+5=29\\\\a_{4}=3a_{4-1}+5 = 3a_{3}+5=(3\times 29)+5=92\\\\a_{5}=3a_{5-1}+5 = 3a_{4}+5=(3\times 92)+5=281[/tex]
Thus, the complete sequence is:
1, 8, 29, 92, 281.
Please help me i am in a bit of a rush
Answer:
0.505 in fraction is 101/200.
it can't be divided into simplest form
Roisin is a price analyst for a food distributor. One week she put together bids for 680 cases, 507 cases, 830 cases, 391 cases, and 587 cases. What was the average
number of cases per bid?
The average number of cases per bid is
Answer: The average number of cases per bid is 599.
Step-by-step explanation:
Given: One week she put together bids for 680 cases, 507 cases, 830 cases, 391 cases, and 587 cases.
Total cases = 680 + 507 + 830 + 391+587
= 2995
Number of bids = 5
Now, average number of cases per bid = [tex]\dfrac{\text{Total cases }}{\text{Number of bids}}[/tex]
[tex]=\dfrac{2995}{5}\\\\=599[/tex]
Hence, the average number of cases per bid is 599.
step linear equation
-2a+6=18
Answer: a = -6
Step-by-step explanation:
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
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]
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!
evaluate 9/m+4 when m=3
Answer:
[tex] \frac{9}{7} \: or \: 1.28[/tex]
Step-by-step explanation:
[tex] \frac{9}{m + 4} = \frac{9}{3 + 4} = \frac{9}{7} \: or \: 1.28[/tex]
Part B: Plot point C(2,7). If M is the midpoint of CD, what are the
coordinates of D?
There are 5 pencils and 8 pens. What is the ratio of pens to pencils?
Answer:
8/5
Step-by-step explanation:
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! :)
What is the solution to the following equation? (1 point)
3(7x − 12) + 26 = 3x − 10
Answer:
x = 0
Step-by-step explanation:
3(7x − 12) + 26 = 3x − 10
Distribute
21x - 36 +26 = 3x-10
21x -10 = 3x-10
Add 10 to each side
21x = 3x
Subtract 3x from each side
21x-3x = 0
18x =0
x =0
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
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]
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.