If flagpole casts a shadow 18m long when the angle of elevation of the sun is 54° then the height of the flagpole will be 24.8 m .
In the question ,
it is given that ,
the length of the shadow of the flag pole = 18m
the angle of "elevation" of the sun = 54°
let the height of the flagpole be = "x" ,
The flagpole and the shadow form a right triangle ,
So , tan(54°) = (height of flag pole)/(shadow of flagpole)
Substituting the values from above ,
we get ,
tan(54°) = x/18
on cross multiplication ,
x = 18 × tan(54°)
x = 18 × 1.3763
x = 24.7734
x ≈ 24.8
Therefore , If flagpole casts a shadow 18m long when the angle of elevation of the sun is 54° then the height of the flagpole will be 24.8 m .
The given question is incomplete , the complete question is
A flagpole casts a shadow 18m long when the angle of elevation of the sun is 54°. What is the height of the flagpole ?
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(will mark brainlist) Which of the following expressions is equivalent to 2x +37
○ 6(2)
8(2)*
2*
6
2*
8
Answer:
B) [tex]8(2)^{x}[/tex]
Step-by-step explanation:
Using the Product Property of Exponents, we know that two exponents with the same base can have their exponents added together.
Step 1 - Convert 8 to an exponent with a base of 2:
[tex]8 = 2^{3}[/tex]
Step 2 - Use the Product Property of Exponents:
[tex]2^{3} *2^{x}[/tex]
[tex]2^{x+3}[/tex]
Hope this helps and have a great day! :)
Mr. Johnson is ordering new desks and tables for the school. He has a budget of $2000, no more. Each desk is $45 and each table $75 befine your variables and write an inequality representing what Mr. Johnson can order. pls help
Answer: 45x + 75y < 2000
Step-by-step explanation:
x = # of desks
45 = cost/desk
y = # of tables
75 = cost/table
2000 = maximum dollar amount that can be spent
inequality:
45x + 75y < 2000
Find the area of the circle pictured above.
Round your answer to the nearest tenth
Answer:
A ≈ 314.2 units
Step-by-step explanation:
To find the area of the circle, we will use the given formula. We are given the diameter (d), 20, and the radius (r) is half of the diameter. 20 units / 2 = 10 units for our radius (r).
A = πr²
A = π(10)²
A ≈ 314.15927
Now, we are asked to round to the nearest tenth.
A ≈ 314.2 units
The Gonzalez family drove 342 miles in 6 hours. The Wilson family drove 472 miles in 8 hours.
Which family traveled at the higher rate of speed and what was this rate?
Question 2 options:
A:Gonzalez; 57 mi/h
B: Gonzalez; 59 mi/h
C: Wilson; 57 mi/h
D: Wilson; 59 mi/h
Warning: Whoever Answers this wrong will be reported :l
If the Wilson family drove 472 miles in 8 hours. The family that traveled at the higher rate of speed and rate is: D: Wilson; 59 mi/h
How to find the rate of speed?'Using this formula to find the speed
Speed = Distance /Time
Let plug in the formula
Rate of speed for Gonzalez family
Rate of speed = 342 ÷ 6
Rate of speed = 57 mph
Rate of speed for Wilson family
Rate of speed = 472 ÷ 8
Rate of speed = 59 mph
Therefore the correct option is D.
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Translate this phrase into an algebraic expression.
Eight less than the product of 21 of goran’s score.
Use the variable g to represent Goran’s score.
Answer:
21g-8
Step-by-step explanation:
The product of Goran's score and 21 = 21g, then subtract 8 from that.
Answer:
lo siento no se mucho de este ap
HELP IM GOING TO FAIL
Answer:
23) $248,943.75
24) $384
Step-by-step explanation:
23) 266,250/100= 2662.5 which is 1%
2662.5×6.5=17,306.25 which is 6.5%
Since it is a mark up we subtract 17,306.25 from 266,250 to find the
original price.
24) 320÷10=32 which is 10%
32×2= 64 which is 20%
Since it is a discount we add 64 to 320 to find the original price.
;)
1. (8x10^5)+(9x10^4) in standard form
2. (5x10^-1)+(5x10^-2) in standard form
3. Work out (3.5x10^11)x(2x10^15) give answer in standard form
4. (9x10^4)x(2x10^6) in standard form
5. (8x10^10) divided by (2x10^6) in standard form
6. (4.9x10^-13) divided by (7x10^4) in standard form
7. (8x10^4)-(9x10^3) in standard from
8. (7x10^-3)-(4x10^-4) in standard from
9. (3x10^7)x(3x10^12) in standard form
10. (9x10^2)x(2x10^4) in standard form
11. (1.2x10^13) divided by (6x10^2) in standard form
12. (4.5x10^9) divided by (9x10^-2) in standard form
Answer:
1. 8.9x10^5
2. 5.05x10^1
3. 7x10^26
4. 1.8x10^11
5. 4x10^4
6. 7x10^-18
7. 7.1x10^4
8. 6.6x10^-3
9. 9x10^19
10. 1.8x10^7
11. 2x10^10
12. 5x10^10
At the local dairy farm, kareem buys a 32-oz container of yogurt for $2. 56. Jonah buys a 6-oz container of yogurt for $0. 48. Are the cost, y, in dollars and the amount of yogurt, x, proportional? explain. Write an equation to represent this relationship.
Yes, the cost y in dollars and the amount of yogurt x are proportional the equation is y = 0.08x.
Given:
At the local dairy farm, kareem buys a 32-oz container of yogurt for $2. 56. Jonah buys a 6-oz container of yogurt for $0. 48.
y varies directly as x :
y = kx
k = constant of proportionality
y = 2.56 and x = 32
y = kx
k = y/x
= 2.56/32
k = 0.08
substitute k we get
y = 0.08x.
so x and y are directly proportional.
Therefore Yes, the cost y in dollars and the amount of yogurt x are proportional the equation is y = 0.08x.
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y=-2x+10 rewrite in y=mx + b form
Answer:
it would already be in it the y is alone
Answer:
View explanation.
Step-by-step explanation:
y = -2x+10
M is the slope or how much the y value increases every time the x value increases by one. b is the y-intercept or when x=0.
It is already in y=mx+b form.
What is the value of the expression below when w=8?
w-2
The value of the expression w-8 is 6 when w=8
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is w minus 8
w-2
The w is the variable and 2 is the number and minus is the operator
Now given variable w is 8
So substitute the value 8 in the expression w-2
8-2=6
Hence 6 is the value of the expression w-2 when w=8
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Drag graphs to show a graph of each equation in the table.
Answer:
see screenshot
Step-by-step explanation:
the equation is always f(x) = m * x + b
with b being where the graph hits the y axis and m being how much the graph rises or drops (then m is negative) when you go 1 to the right on the x axis
Hello a girl out pls
Answer:
D
Step-by-step explanation:
Nathan invested $3,500 in an account paying an interest rate of 3. 5% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 19 years?.
Amount of money in the account after 19 years when no deposits or withdrawals are done for the invested amount $3,500 with 3.5% interest rate compounded quarterly is equal to $6,800(nearest hundred dollars).
As given in the question,
Amount invested by Nathan is principal 'P' = $3,500
Interest rate 'r' = 3.5% compounded quarterly
Number of compounding periods per year for given quarterly 'n' = 4
Time period 't'= 19 years
Amount of money in the account after 19 years when no deposits or withdrawals are done.
Let 'A' be the amount.
Formula used:
[tex]A = P \times ( 1+ \frac{r}{n} )^{nt}[/tex]
Substitute the value in the formula we get,
A = 3500 × [ 1 + (0.035/4) ]⁽⁴⁾⁽¹⁹⁾
= 3500 × [ 1 + 0.00875]⁽⁴⁾⁽¹⁹⁾
= 3500 × [ 1.00875]⁷⁶
= 6,786.06 (approximately)
= $6800 (nearest hundred dollars)
Therefore, amount of money in the account after 19 years when no deposits or withdrawals are done for the invested amount $3,500 with 3.5% interest rate compounded quarterly is equal to $6,800(nearest hundred dollars).
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Multiply. −16√3⋅5√3 Enter your answer by filling in the boxes.
Answer:
-240
Step-by-step explanation:
−16√3⋅5√3
-16(5)√(3*3)
When you multiply numbers with the same radical (in this case square root) the numbers inside the radical can be multipled with each other. The numbers outside (in this case -16 and 5) should also be multiplied with each other.
-16(5)√9
-80√9
-80*3
-240
HOMEWORK Khadijah has at most three hours to work on a math assignment
3
and a history project. If the math assignment will take hour, how much time
can Khadijah spend working on her history project?
The time spent by Khadijah to work on her history project is 2 hrs.
Addition and Subtraction:Addition and subtraction are the two basic arithmetic operations in Mathematics. In Addition, we sum up two or more numbers to get another number and it is denoted by the symbol (+).
In subtraction, we take away a number from another number and it is denoted by (-).
Here we have
Khadijah has at most 3 hrs to work on a math assignment and a history project.
The time taken by Math assignment = 1 hrs
Here we need to find the time that can be spent working on her history project.
[ Here we will use subtraction to get the answer ]
From given data
The time can be spent on History = Total time - Time taken by Math
= 3 hrs - 1 hr = 2hrs
Therefore,
The time spent by Khadijah to work on her history project is 2 hrs.
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An artist charges $980 for a portrait but gives 5% discount for cash. Calculate the cash Price of the portrait
UT
T
10. FIND THE ERROR A classmate is calculating the amount in a savings
account after 10 years. The deposit is $13,000 and the annual
simple interest rate is 2%. Describe the error. What support can
you provide to help them correct the error?
The interest when the classmate is calculating the amount in a savings account after 10 years is $2600.
How to calculate the interest?From the information, the classmate is calculating the amount in a savings account after 10 years and the deposit is $13,000 and the annual simple interest rate is 2%.
It should be noted that interest is calculated as:
= (Principal × Rate × Time) / 100
= ($13000 × 2 × 10) / 100
= $2600
The simple interest is $2600.
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Which expression is equivalent to -6(-3m-5)?
Answer:
18m + 30
Step-by-step explanation:
times everything in the bracket by 6
which of the following ratios are equalvalent to 5/20
1/4
1/5
20/100
25/100
Answer:
1/4 is a equivalent ratio
Step-by-step explanation:
hope it helped :)
The vertex angle of an isosceles triangle is 5 degrees more than 3 times the measure of one of the
base angles. Determine the measure of each angle of the triangle.
The measure of each angle of the triangle are 35°, 35°, 110°.
What is an isosceles triangle?
An isosceles triangle has two equal sides as well as two equal angles.The Greek words iso (same) and skelos are the source of the name (leg).An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.Let's Base angle =x°
Vertex angle = 5° +3x°
The sum of measure of angles of triangle are supplementary.
i.e., Sum of triangle = 180°
So,
x° + x° + 5° + 3x° =180°
5x° + 5° = 180°
5x° = 175°
x° = 175° /5°
x = 35°
Base angle = 35°
Vertex angle = 5°+ 3x°
= 5° + 3×35°
= 5° +105°
Vertex angle = 110°
Hence, the measure of each angle of the triangle are 35°, 35°, 110°.
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Warren and Dirk are baking cookies for a charity bake sale. First they bake gingersnaps, which are Warren's favorite cookie. Then they bake 120 chocolate crinkles, which are Dirk's favorite. In all, Warren and Dirk bake 204 cookies. Use an equation to find the number of gingersnaps Warren and Dirk bake. gingersnaps Ver en españ
Answer:
g = 204 - 120
Step-by-step explanation:
T - CC = amount of gingersnaps
204 - 120 = 84
Warren and Dirk baked 84 gingersnaps
What is the equation of the trend line in the scatter plot?
Use the two yellow points to write the equation in slope-intercept form. Write any coefficients
as integers, proper fractions, or improper fractions in simplest form.
PLS RN!!
The equation in slope intercept form is y = -4x + 24.
From the graph:
yellow points are (6,0) and (4,8).
slope intercept form is y = mx + c.
slope m = 8 - 0 / 4 - 6
= 8/-2
= -8/2
= -4
Substitute m and (6,0)
y = mx + c
0 = -4*6 + c
c = 24
y = mx + c
y = -4x + 24.
Therefore The equation in slope intercept form is y = -4x + 24.
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If the original quantity is 5 and the new quantity is 7, what is the percent of change?
A painter can paint 15 square feet every 1/4 hour. How many square feet can they paint in one hour?
A painter can paint 60 square feet every 1 hour.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A painter can paint 15 square feet every 1/4 hour.
Now,
Since, A painter can paint 15 square feet every 1/4 hour.
Let painter can paint in every 1 hour = x square feet
So, By definition of proportional as;
⇒ 15 / (1/4) = x / 1
Solve for x as;
⇒ 15 × 4 = x
⇒ x = 60 square feet
Thus, A painter can paint 60 square feet every 1 hour.
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HELPPP so the man bought a tv worth $1,700, and then each week he continued to spend $700 weekly WHAT IS THE EXPRESSION???? HELP (variable is X)
6.
Using a line of best fit equation to predict values between actual data points is an example of
O extrapolation
O correlation
O linear relation
O interpolation
For the given line of best fit, equation which represents the prediction of values between the actual data points is representing an example of interpolation.
As given in the question,
Given line of best fit equation,
Here prediction is to be done for the values which are between the actual data points.
The predicted values are within the range.
Predicted values represents either extrapolation or interpolation
If predicted values are outside the actual points it is extrapolation.
Here it is between the actual data points.
So, it is interpolation.
Therefore, for the given line of best fit, equation which represents the prediction of values between the actual data points is representing an example of interpolation.
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the scores on a mathematics exam have a mean of 70 and a standard deviation of 5. find the x-value that corresponds to the z-score 2.33.
x-value that corresponds to the z-score of 2.33 is 81.65.
Mean = 70
Standard deviation = 5
z score = 2.33
Using the z-score formula:
z = (x - mean) / SD
Plug the values:
2.33 = (x-70)/5
x = 5(2.33) +70
x = 81.5
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Solve the system by substitution.
y = x + 6
y = 3x
Answer:
y=9
x=3
Step-by-step explanation:
Answer:
x = 3y = 9Step-by-step explanation:
y = x + 6y = 3xBring one of the equations into the other one:
3x = x + 6
3x - x = 6
2x = 6
x= 3
Then, bring the found value to find the value other variable:
y = 3x = 3(3) = 9
What is the coordinate for midpoint D?
Answer:
B
Step-by-step explanation:
You Basically need to find halfway between 5a and -3 which has a difference of 8 so halfway is 4 so 3a +4=a
and as it is on the same line it would be (a,-2b)
Can someone help me
The graph of the given table of data is attached below. And the best scale for this one is x axis 1 cm = 20 units and y axis 1 cm = 1 units. The value of A is 60 and the value of B is 140.
Graph:
Graph can be used to view the table of data in a visual manner for the easy understanding of the given range of data.
Given,
Here we have the table of data that contains the details about the length and their corresponding mass in kg.
Now, we have to plot this data on the graph and then we have to find the best scale suitable for this graph.
Finally, we have to find the value of A and B in the plotted graph.
In order to plot the graph for the given table, we have to input the values on the graphing calculator,
Then we get the graph like the following.
While we lookin into the graph we have identified then the best scale suitable for this graph is
x axis
1 cm = 20 units and
y axis
1 cm = 1 units.
Now, the value of A is 60 and the value of B is 140.
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