The height of the tree which is the opposite side of the right triangle is 145 meters.
How to find height when given angle of elevation?The angle of elevation is 36 degrees.
The situation forms a right angle triangle.
Therefore,
base of the triangle = 200 m
Hence, using trigonometric ratios,
tan 36 = opposite / adjacent
tan 36 = x / 200
x = 200 tan 36
x = 200 × 0.726542528
x = 145.308505601
x = 145.31 m
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if you starting salary is $350000 and you receive a 6% increase at the end of every year, what is the total amount, in dollars. you will earn over the first 16 years that you work
The total amount will be $889123 after 16 years if the starting salary is $350000
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent [tex]y = a^x[/tex]
where a is a constant and a>1
We have:
Starting salary is $350000 and you receive a 6% increase at the end of every year.
We can find the total amount, from the exponential formula:
T = a(1 + r)ⁿ
T is the total amount
a is the starting amount
r is the rate
n is the total number of years
T = 350000(1 + 6%)¹⁶
T = 350000(1 + 0.06)¹⁶
T = 889123.08 ≈ $889123
Thus, the total amount will be $889123 after 16 years if the starting salary is $350000
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A triangle with side lengths of 5 meters, 7 meters and 9 meters.
Answer:
obtuse triangleStep-by-step explanation:
A triangle with side lengths of 5 meters, 7 meters and 9 meters is
an obtuse triangle
Solve the following system of equations. Express your answer as an ordered
pair in the format (a,b), with no spaces between the numbers or symbols.
2x + 7y = -1
4x - 3y = - 19
Isolate x:
2x + 7y = -1
2x = -1 -7y
x = -1/2 - 7/2y
Substitute the equation of x:
4x - 3y = -19
4(-1/2 - 7/2y) - 3y = -19
-2 - 14 - 3y = -19
-3y = -19 + 14 + 2
-3y = -3
y = 1
Substitute to find x:
2x + 7y = -1
2x + 7(1) = -1
2x = -1 - 7
2x = -8
x = -4
(-4, 1)
What are the rules of the system of equations?
Multiply one or both equations through an integer in order that one time period has the same and contrary coefficients within the equations. Add the equations to provide a single equation with one variable. clear up for the variable. alternative the variable back into one of the equations and resolve for the other variable.
Conclusion: A system of equations is fixed of 1 or greater equations related to some of the variables. The solutions to systems of equations are the variable mappings such that every one component equations are satisfied—in other phrases, the locations at which all of these equations intersect.
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Follow the steps to find the
area of the shaded region.
First, use the formula
below to find the area
of the whole sector.
Sector Area
(angle of sector ) p2
360
Sector Area = [?] cm2
Round to four decimal places.
The area of the sector rounded to 4 decimal place is 78.6396 cm²
How to find the area of a sector?area of sector = ∅/ 360 × πr²
Therefore,
r = radius∅ = 46 degrees.Hence,
area of a sector = 46 / 360 × 3.14 × 14²
area of a sector = 46 / 360 × 3.14 × 196
area of a sector = 46 / 360 × 615.44
area of a sector = 28310.24 / 360
area of a sector = 78.6395555556
Hence,
area of a sector = 78.6396 cm²
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12x+10y=2
-x+4y= -5
Without actually solving, explain whether substitution or elimination would be a better method for solving the system.
Answer:
Elimination would be a better method for solving the system.
Given equation [tex] \sf12x+10y=2[/tex][tex] \sf-x+4y= -5 [/tex]Solution :-[tex]\Rrightarrow \sf12x+10y=2[/tex]
[tex]\Rrightarrow \sf6x+5y=1.......(i)[/tex]
[tex] \sf\Rrightarrow-x+4y= -5 ............(ii)[/tex]
[tex]\large \sf \red{ \blue{[ (ii)×6]}}[/tex]
[tex]\sf\Rrightarrow-6x+24y= -30 ............(iii)[/tex]
[tex] \large \sf \red{(i) + \blue{ (iii)}}[/tex]
[tex]\Rrightarrow \small\sf6x+5y=1+(-6x+24y= -30)[/tex]
[tex]\Rrightarrow \sf29y = - 29 \\ [/tex]
[tex]\Rrightarrow \blue{\sf \: y = - 1}[/tex]
putting the value in equation (i)
[tex]\Rrightarrow \sf6x+5 \times - 1=1[/tex]
[tex]\Rrightarrow \sf6x - 5=1[/tex]
[tex]\Rrightarrow \sf6x = 6[/tex]
[tex]\Rrightarrow \red{\sf \: x = 1}[/tex]
[tex]\overline{\underline{\rule{209pt}{2pt}}}[/tex]
Point Y is the center of dilation. Triangle A B C is dilated to form triangle A prime B prime C prime.
If CA = 8, what is C'A'?
10 units
12 units
16 units
20 units
Using the rule of dilation, 5/4, the length of C'A' is: A. 10 units.
What is Dilation?Dilation is a form of transformation that creates a new image that is similar to the original one.
The images formed are similar images shown in the diagram given, therefore, using the rule of dilation, Dy = 5/4, we would have:
CA × 5/4 = C'A'
Plug in the given value
8 × 5/4 = C'A'
10 = C'A'
C'A' = 10 units
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A recipe for nut bread calls for 1/4 cup of walnuts and 2/6 cup
cup of pecans. What is
the total amount of walnuts and pecans needed for the recipe?
Answer:
[tex]\sf Total \ amount \ of \ walnuts \ and \ pecans \ needed = \dfrac{7}{12}[/tex]
Step-by-step explanation:
Fraction addition:[tex]\sf Amount \ of \ walnut \ needed = \dfrac{1}{4}[/tex]
[tex]\sf Amount \ of \ pecans \ needed =\dfrac{2}{6} =\dfrac{1}{3}[/tex]
To find the total amount of walnut and pecans, we have to add the fractions.
Find the LCM of the denominators.Find equivalent fractions using the LCMNow, add the fractionsLCM of 4 & 3 = 12
Equivalent fractions:
[tex]\sf \dfrac{1}{4}=\dfrac{1*3}{4*3}=\dfrac{3}{12}\\\\\dfrac{1}{3}=\dfrac{1*4}{3*4}=\dfrac{4}{12}[/tex]
Now, add
[tex]\sf \dfrac{3}{12}+\dfrac{4}{12}=\dfrac{3+4}{12}[/tex]
[tex]\sf = \dfrac{7}{12}[/tex]
A sequence is defined recursively by the formula f(n 1) = f(n) 3 . the first term of the sequence is –4. what is the next term in the sequence?
The next term in the sequence is -1.
Given a sequence is defined recursively by the formula f(n+1)=f(n)+3.
An ordered list of integers that frequently follows a pattern or function is known as a sequence. Sequences can have a finite or indefinite length. Terms refer to the distinct components of a sequence. The individual numbers or parts that make up a sequence are known as its terms.
The first term of the sequence is -4.
That means f(1)=-4 .......(1)
When compare f(1) with f(n+1), we get
n=0
So, when n=0 then it is the first term of the sequence.
When n=1 then substituting this in the given formula, we get
f(1+1)=f(1)+3
f(2)=f(1)+3
Now, Substitute the value of f(1) from equation (1), we get
f(2)=-4+3
f(2)=-1
Hence, the next term in the sequence when the sequence is defined recursively by the formula f(n+1) = f(n)+3 and the first term of the sequence is –4 is -1.
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What is the expression of g(x) when we perform the following sequence of transformations onto the parent function fx=1x:
a) stretch horizontally by a factor of 2
b) shift left 1 unit
c) shift up 3 units
The expression of function g(x) is [tex]\sqrt{\frac {x - 1}2} + 3[/tex]
How to determine the expression?The function is given as:
[tex]f(x) = \sqrt{x[/tex]
When the function is stretched horizontally by a factor of 2, the rule is:
f'(x) = f(x/2)
So, we have:
[tex]f'(x) = \sqrt{\frac x2[/tex]
When the function is shifted left by 1 unit, the rule is:
f"(x) = f(x + 1)
So, we have:
[tex]f"'(x) = \sqrt{\frac {x - 1}2[/tex]
When the function is shifted up by 3 units, the rule is:
g(x) = f"(x) + 3
So, we have:
[tex]g(x) = \sqrt{\frac {x - 1}2} + 3[/tex]
Hence, the expression of function g(x) is [tex]\sqrt{\frac {x - 1}2} + 3[/tex]
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Find the average rate of change of each function over the interval [0, 3]. Match each representation with its respective average rate of change.
3
-2
5
-1
6
-3
The average rate of change is illustrated below.
How to illustrate the average rate?The average rate of change over interval [a,b]: r=[f(b)-f(a)]/(b-a).
In this case the interval is [0,2], then a=0, b=2
r=[f(2)-f(0)]/(2-0)
r=[f(2)-f(0)]/2
1) First function: h(x)
r=[h(2)-h(0)]/2
x=2→h(2)=(2)^2+2(2)-6
h(2)=4+4-6
h(2)=2
x=0→h(0)=(0)^2+2(0)-6
h(0)=0+0-6
h(0)=-6
r=[h(2)-h(0)]/2
r=[2-(-6)]/2
r=(2+6)/2
r=(8)/2
r=4
2) Second function: f(x)
A function, f, has an
x-intercept at (2,0)→x=2, f(2)=0
and a y-intercept at (0,-10)→x=0, f(0)=-10
r=[f(2)-f(0)]/2
r=[0-(-10)]/2
r=(0+10)/2
r=(10)/2
r=5
3) Third function: g(x)
r=[g(2)-g(0)]/2
From the graph:
g(2)=6
g(0)=2
r=(6-2)/2
r=(4)/2
r=2
4) Fourth function: j(x)
r=[j(2)-j(0)]/2
From the table:
x=2→j(2)=-8
x=0→j(0)=4
r=(-8-4)/2
r=(-12)/2
r=-6
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Choose the 5 numbers that give a remainder of 5 when divided by 7 ASAp
Answer:
was there a list to choose from
Step-by-step explanation:
19, 26, 33, 40, 47
A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 29° From a point 1000 feet closer to the mountain along the plain, they find that the angle of elevation is 34° How high (in feet) is the mountain?
The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The height of the mountain is 3110.5767 feet.
What is Tangent (Tanθ)?The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
The height of the mountain from the first point,
[tex]\tan(29^o) = \dfrac{H}{x+1000}\\\\H = (1000+x) \times \tan(29^o)[/tex]
The height of the mountain from the second point,
[tex]\tan(34^o) = \dfrac{H}{x}\\\\H = x \times \tan(34^o)[/tex]
Equating the height,
H = H
(1000+x) × tan(29°) = x tan( 34°)
x = 4611.5767 feet
Now, the height of the mountain is,
H = x tan(34°)
H = 3110.54776 feet
Hence, the height of the mountain is 3110.5767 feet.
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Members of the swim teams at a competition want to wash their hair. The bathroom has less than 5600 liters of water and at most 1.5 liters of shampoo.
70L+60S < 5600 represents the number of long-haired members L and short-haired members S who can wash their hair with less than 5600 liters of water.
0.02L+0.01S ≤1.50 represents the number of long-haired members and short-haired members who can wash their hair with at most 1.5 liters of shampoo.
Does the bathroom have enough water and shampoo for 35 long-haired members and 40 short-haired members? Does the bathroom have enough water and shampoo for 35 long-haired members and 40 short-haired members based on the feasible region? Why or why not?
Yes, the bathroom have enough water and shampoo for 35 long haired and 40 short haired members.
Inequality can be define as the relation of equation contains the symbol of ( ≤, ≥, <, >) instead of equal sign in an equation.
For 35 long haired and 40 short haired member.
Put this values in the given equation.
For water 70L+60S < 5600
70 x 35 + 60 x 40
2450+2400
4850 <5600
inequality holds
For shampoo 0.02L+0.01S ≤ 1.50
0.02 x 35 + 0.01 x 40
0.7 + 0.4
1.1 < 1.50
inequality holds
Thus, the bathroom have enough water and shampoo for 35 long haired and 40 short haired members.
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Mike bought a photo frame which measured 8 inches in length and 7 inches in width. Determine the diagonal length of the photo frame
Answer:
10.63 inches
(b)2+(h)2=(H)2
(8)2+(7)2=(H)2
64+49=(H)2
113=(H)2
H=10.63
The diagonal length of the photo frame having measurements of 8 inches in length and 7 inches in width is 10.63 inches.
How is the diagonal of a rectangle determined?The diagonal of a rectangle having a length l and width w will be:
d = √(l² + w²).
How to solve the question?In the question, we are asked to determine the diagonal length of the photo frame bought by Mike, having measurements of 8 inches in length and 7 inches in width.
We know the photo frame is in the shape of a rectangle, as it has a length and a width.
We also know that the diagonal of a rectangle having a length l and width w will be:
d = √(l² + w²).
So, by substituting l = 8 and w = 7, in the above relation, we can calculate the diagonal of the photo frame as:
d = √(8² + 7²),
or, d = √(64 + 49),
or, d = √113,
or, d = 10.63.
Therefore, the diagonal length of the photo frame having measurements of 8 inches in length and 7 inches in width is 10.63 inches.
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can someone help me with this i dont know what im doing
Answer:
ok sure will do the answer is
Step-by-step explanation:
I need help asap! Thank you guys
Answer:
Y intercept: (0,2) Slope: 1/3
Step-by-step explanation:
X is horizontal. Y is vertical the slope touches at (0,2).
The slope goes up by one and right by three cause it connects to the line
for the second one all you would have to do is increase the slope first number like 4/3
list both the negative and positive factors of -30 and sum is 1
Answer:
-5 and 6
Step-by-step explanation:
-5 * 6 = -30
-5 + 6 = 1
4(2x-1)+2x+2= 28
solve for X
Answer:
X=3
Step-by-step explanation:
First you can distribute the 4 to 2x-1 making is 8x-4
8x-4+2x+2=28
Now add like terms
8x+2x-4+2=28, 10x-2=28
Add 2 to both sides
10x=30
Divide both sides by 10
x=3
Abhasra won 68 lollipops playing
basketball at her school's game night.
Later, she gave two to each of her friends.
She only has 8 remaining. How many
friends does she have?
Answer:
8
Step-by-step explanation:
because there is 8 in the question
A cheerleading team plans to sell t-shirts as a fundraiser. The team's
goal is to make a profit of at least $1248. The profit on each t-shirt sold
is $6.50. The team's goal is written as the inequality shown below.
6.50t ≥1248 where t=number of t-shirts sold
Which graph represents the solution to this inequality?
Answer:
t ≥ 192
Step-by-step explanation:
To isolate t in the inequality 6.50t ≥1248, divide by 6.50 on both sides. There you are left with t ≥ 192 which means the cheerleading team must sell 192 t-shirts or more to make their profit goal. Graph this using a closed circle at 192 moving upwards. (You didn't include a picture of the given graphs in your problem)
Find an equation perpendicular to y = (3/₂)x+ 1 and has a y-
intercept of 2.
Step-by-step explanation:
ATTACHED IS THE SOLUTION!!!!!!if you pick a card at random from a well shuffled deck, what is the probability that you get a face card or a spade
Answer: 42.308%
Step-by-step explanation:
erena is writing an expression that is equivalent to 12ab – 6b, but she has not completed it.
__?__ (2 a minus 1)
What is missing from the expression?
The missing term in the expression ___( 2a-1) is 6b.
What is an Expression?An expression is an algebraic statement that consists of variables, constants, and mathematical operators.
The expression 12ab-6b is equivalent to
6b( 2a-1)
(By taking the common factors out of the given expression.)
Therefore, the missing term in the expression is 6b.
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Jian Hui can do 14 pages of homework every 3 hours. How many pages can he finish if he works from 8pm to 11pm?
14 pages
-------------
3 hours
Find the solution to the equation z – 7 = 8.
Answer:
z=15
Step-by-step explanation:
z-7+7=8+7 ( add 7 on btoh sides to cancel out)
z=15 ( left with 7)
ANSWER ASAP PLS..........
The length of one leg of the right triangle is 5√10
How to find the leg of a right triangle?The leg of a right triangle can be found as follows;
Therefore, using trigonometric ratios,
sin 45 = opposite / hypotenuse
sin 45 = x / 10√5
1 / √2 = x / 10√5
cross multiply
10√5 = x√2
divide both sides by √2
x = 10√5 / √2
x = 10√5 / √2 × √2 / √2
x = 10√10 / 2 = 5√10
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Which equation is equivalent to the given equation?
x² - 6x = 8
The number of math classes offered online in the summer is 15 less than the number of math classes offered face-to face in the summer . Let Frepresent the number of face-to face summer classes . Which of the following expressions gives the number of online math classes ?
The expressions that gives the number of online math classes is as follows:
y = x - 15
How to express an equation?The number of math classes offered online in the summer is 15 less than the number of math classes offered face-to face in the summer.
Let
the number of math classes offered face-to face = x
the number of math classes offered online = y
Therefore, the expression that gives the number of online math classes is as follows:
y = x - 15
x = y + 15
Hence,
y = x - 15
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Workers are required to pay 4½% of their salaries into an Educational Fund. A worker's salary is 120 Ghana cedis . How much does he pay into the Educational Fund?
Answer:
He will need to pay 5.4 Ghana cedis into his educational fund.
Step-by-step explanation:
We need to multiply 4 1/2 by 120 since it is a percentage. We convert 4 1/2 into a decimal which is 4.5. Now, we just need to multiply 120 by 4 1/2 to get an answer of 5.4.
80 more points ez ez!
Answer:
{(-3, -2), (-4, 3), (-1, 0), (3, -7)}
Step-by-step explanation:
When you find the inverse of a function you swap the x and the y. So let's look at a couple examples and see what happens to the x and y values
Radical:
[tex]y=\sqrt{x}[/tex]
So let's just look at perfect squares so it's a bit easier to understand
(0, 0)
(4, 2)
(9, 3)
Now let's find the inverse:
[tex]x=\sqrt{y}[/tex]
Now to make this concept a bit easier to understand let's leave it in this form. Well the first notable thing, is that any operations applied to y will now apple to x, and any operations applied to x will apply to y (in this case the square root).
So if I input 9 as the y, the x will be 3
If I input 4 as y, the x will become 2
Some points are
(0, 0)
(2, 4)
(9, 3)
You'll notice the x and y values are swapped, well it's simply because you swap the x and y's place. this is also why the domain and range are swapped
So given the points {(-2, -3), (3, -4), (0, -1), (-7, 3)} you simply swap the x and y to get: {(-3, -2), (-4, 3), (-1, 0), (3, -7)}
Answer:
D
Step-by-step explanation: