A person who is six feet tall casts a 3-foot-long shadow. A nearby pine tree casts a 15-foot-long shadow.What is the height hh of the pine tree?
person is 6 feet tall, shadow is 3 feet long
6/3 = 2
pine tree shadow is 15 feet
15 *2 = 30
tree is 30 feet tall
Find the volume of the composite solid.
A. 420 ft^3
B. 530 ft^3
C. 630 ft^3
D. 840 ft^3
Answer:
[tex]V=630ft^3[/tex]
Step-by-step explanation:
This solid is composite by a triangular prism and a rectangular prism. So, let:
[tex]V_1=Volume\hspace{3}of\hspace{3}the\hspace{3}rectangular\hspace{3}prism\\V_2=Volume\hspace{3}of\hspace{3}the\hspace{3}triangular\hspace{3}prism[/tex]
Hence, the volume of the composite solid is:
[tex]V=V_1+V_2[/tex]
The volume of the rectangular prism is given by:
[tex]V_1=l*w*h[/tex]
Where:
[tex]l=length=8ft\\w=width=7.5ft\\h=height=7ft[/tex]
So:
[tex]V_1=8*7.5*7=420ft^3[/tex]
The volume of the triangular prism is given by:
[tex]V_2=\frac{1}{2} l*b*h[/tex]
Where:
[tex]l=Distance\hspace{3} between\hspace{3} the\hspace{3} triangular \hspace{3}faces=8ft\\b=length\hspace{3}of\hspace{3} one\hspace{3} side \hspace{3}of\hspace{3} the \hspace{3}triangle=7.5ft\\h=length \hspace{3} of \hspace{3} an \hspace{3}altitude \hspace{3} drawn \hspace{3} to \hspace{3} that \hspace{3}side=7ft[/tex]
So:
[tex]V_2=\frac{8*7.5*7}{2} =210ft^3[/tex]
Therefore:
[tex]V=420ft^3+210ft^3=630ft^3[/tex]
Solve for L. p=2L+2w
A suit is on sale for 26% off. the sale price is $629.what is the regular price?
Sam buys one bag of flour for $2.50, three packages of shredded cheese for $3.00 each, and two packages of mushrooms for $3.50 each. How much does Sam pay in all?
Answer:
The Answer is 18.5 which could also be 18.50
Step-by-step explanation:
The amount that Sam pay should be $18.50
Given that,
Sam buys one bag of flour for $2.50, three packages of shredded cheese for $3.00 each, and two packages of mushrooms for $3.50 each.Based on the above information, the calculation is as follows:
[tex]= (1 \times \$2.50) + (3\times \$3) + (2\times \$3.50)[/tex]
= $2.50 + $9 + $7
= $18.50
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The coordinates of the vertices of △ABC are A(−1, 1) , B(−2, 3) , and C(−5, 1) . The coordinates of the vertices of △A′B′C′ are A′(−1, −4) , B′(−2, −6) , and C′(−5, −4) .
Which statement correctly describes the relationship between △ABC and △A′B′C′ ?
△ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a translation 3 units down followed by a reflection across the x-axis, which is a sequence of rigid motions.
△ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a translation 5 units down followed by a reflection across the x-axis, which is a sequence of rigid motions.
△ABC is not congruent to △A′B′C′ because there is no sequence of rigid motions that maps △ABC to △A′B′C′ .
△ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a reflection across the x-axis followed by a translation 3 units down, which is a sequence of rigid motions.
Answer:
△ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a reflection across the x-axis followed by a translation 3 units down, which is a sequence of rigid motions.
Step-by-step explanation:
I took the test/ other answer is somewhat correct
Which of the following values is equal to − (−3.7)?
−3.7
0
3.7
4 (not it)
Answer:
C) 3.7
Step-by-step explanation:
The given expression is -(-3.7)
Here we have to use the multiplication of sign rule.
- (-) = +
-(+) = -
+(-) = -
+(+) = +
So, we we multiply negative by negative, the result will be positive.
Therefore, -(-3.7) = +3.7
Hence, the answer is C) 3.7
Dario bought a new bike for $90.00. Sales tax is 5 1/2% How much tax does he have to pay? How much is his total bill?
10, 30, 90 continue the pattern
Answer:
geometric sequence: 10, 30, 90, 270, 810, 2430, ...quadratic sequence: 10, 30, 90, 190, 330, 510, ...Step-by-step explanation:
Three terms of a sequence can be the first three terms of many different kinds of sequences. Here the ratios of terms are constant:
30/10 = 90/30 = 3
so the pattern could be that of a geometric sequence. In that sequence, each term is 3 times the previous one.
This pattern continues ...
10, 30, 90, 270, 810, 2430, ...
___
Another way to look at sequences of numbers is to consider their differences. Here the differences are not constant, and there aren't enough terms to tell how the differences change.
30 -10 = 20
90 -30 = 60
The second of these differences can be viewed several ways. One is to say that it is 40 more than the first of the differences. If each successive difference is 40 more than the last, then the pattern is described by a quadratic function:
[tex]a_n=10+20(n-1)^2[/tex]
This pattern continues ...
10, 30, 90, 190, 330, 510, ...
Find the approximate side length of a square game board with an area of 164 in2
The side length of the square board would be 12.8 inches.
A square is a quadrilateral with four equal sides.
Characteristics of a square includes:
• The diagonals bisect each other at 90°.
• Opposite sides parallel and of equal length
• The four angles of a square are equal.
Area of a square = length²
To determine the side length, find the square root of the area of the board.
√164 = 12.806 inches
Approximating it to the nearest tenth is 12.8 inches
The tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero
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Keesha needs to save $331. To earn money she plans to babysit and charge $11 per hour. Write two estimates Keesha could use to determine how many hours she needs to babysit.
Final answer:
Keesha could make two estimates to determine how many hours she needs to babysit to save $331 by either rounding down to 30 hours or rounding up to 31 hours at her rate of $11 per hour.
Explanation:
Keesha needs to save $331 and plans to charge $11 per hour for babysitting. To estimate how many hours she needs to babysit, Keesha could use two different approaches for rounding her estimates.
Round Down Estimate: Keesha can round down the total amount she needs to save to the nearest multiple of her hourly rate. If she rounds $331 down to $330, she can then divide $330 by $11 per hour to find she would need to babysit for 30 hours.
Round Up Estimate: Alternatively, Keesha can round up the total amount to the next multiple of her hourly rate. If she rounds $331 up to $341, she can divide $341 by $11 per hour to estimate that she would need to babysit for approximately 31 hours.
Shirley wants to buy a skateboard for $64. She has $98 in her account. She spent $10.85 to buy stationary. She also wants to buy some cookies for $1.65 each. What is the maximum number of cookies, n, that Shirley can buy so that she has enough money left to buy the skateboard? a. n ≥ 14 b. n ≤ 16 c.n ≤ 14 d.n ≥ 16
Answer:
n ≤ 14
Step-by-step explanation:
Shirley wants a skateboard that's $64. She has $98. She spent $10.85. She wants to spend some money on a couple cookies $1.65 each. So $1.65* 14= $23.10
23.10+10.85+64= 97.95
while
$1.65*16= 26.4
26.4+ 10.85+ 64= 101.25
So, it would have to be that n is less than or equal to 14.
The maximum no of cookies is n ≤ 14.
Given that,
The purchase price of the skateboard is $64.The amount in the account is $98.The spending amount is $10.85.The per cookie price is $1.65.Based on the above information, the calculation is as follows:
The amount after spending to stationary is
= $98 - $0.5
= $87.15
And,
The remaining amount is
= $87.15 - $64
= $23.15
Now
1.65n≤23.15
n≤[tex]23.15\div1.65[/tex]
n≤14
Therefore we can conclude that the maximum no of cookies is n ≤ 14.
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Look at the rectangle and the square:
Anna says that the length of diagonal SQ is two times the length of diagonal OM.
Is Anna correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.
Finding the Length of the Diagonals
Rectangle PQSR
Diagonal SQ, using the Pythagorean Theorem (a^2 + b^2 = c^2), would be equal to:
14^2 + 7^2 = c^2 (Where c is the hypotenuse;)
196 + 49 = c^2
Square root of 245 = c
15.6 inches.
Square LMON
Diagonal OM, using the Pythagorean Theorem (a^2 + b^2 = c^2), would be equal to:
7^2 + 7^2 = c^2 (Where c is the hypotenuse;)
49 + 49 = c^2
Square root of 98 = c
9.9 inches.
Finding the Diagonal Relation
9.9 * 2 = 19.8
19.8 is not equal to diagonal SQ.
9.8 is therefore not two times the length of 15.6, so Anna is incorrect.
Anna says that the length of diagonal SQ is two times the length of diagonal OM which is incorrect.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Look at the rectangle and the square:
Anna says that the length of diagonal SQ is two times the length of diagonal OM.
The diagonal is given by the Pythagoras theorem.
Diagonal SQ will be
SQ² = QR² + SR²
SQ² = 7² + 14²
SQ = 15.65 inches
Diagonal OM will be
OM² = ON² + MN²
OM² = 7² + 7²
OM = 9.899 inches
Twice of OM will be
⇒ 2 x OM
⇒ 2 x 9.899
⇒ 19.798 which is not equal to SQ.
Anna says that the length of diagonal SQ is two times the length of diagonal OM which is incorrect.
More about the geometry link is given below.
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Write the number in scientific notation. 322,000,000
Answer:
[tex]3.22\times 10^{8}[/tex]
Step-by-step explanation:
In scientific notation we write a very large or very small number as the product of a number between 0 to 9 and the exponent of 10,
Here, the given number,
[tex]322,000,000[/tex]
[tex]=3.22\times 10^{8}[/tex]
Hence, the scientific notation of the given number is [tex]3.22\times 10^{8}[/tex]
MATH HELP PLEASE !!!!!!!!
w^2 +16 = 8w
w^2 +16-8w = 0
(w-4)^2 = 0
(w-4) = 0
w=4
answer is 4
2w +2(2w+1) = 50
2w +4w +2 =50
6w +2 =50
6w = 48
w = 48/6
w=8
A line contains the points (34, 12) and (32, 48) .
What is the slope of the line in simplified form?
An architect built a scale model of a shopping mall. On the model, a circular fountain is 27 inches tall and 63 inches in diameter. If the actual fountain is to be 6 feet tall, what is its diameter?
14 ft
12 ft
2.6 ft
42 ft
PLEASE HELP!
DUE TODAY!!!
You and three friends own a paint shop. The shop's profit was $536 in the first month. You always divide the profits equally. In two months, each of you had made $224. How much profit did the shop make in the second month?
Simplify 4(6 - 2x) - 3(3 - 4x)
True or false : There are more cups in 5 gallons than in 22 quarts ?
Whenever the population has a normal probability distribution, the sampling distribution of is a normal probability distribution for?
A work shift for an employee at a restaurant consists of 10 hours. What fraction of the employee's work shift is represented by 8 hours
Incomplete substance for an expression that doesn't mean anything and needs to be solved
the point slope form of X-3Y=-27
The equation in point slope form as -
y - 18 = (1/3)(x - 27)
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line in point slope form can be also written as-
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
We have the following equation -
x - 3y = -27
We can write the equation as -
x - 3y = -27
Rearranging, we get -
3y = x + 27
y = x/3 + 9
Plot the graph. The line passes through the point (27, 18). So, we can write the equation in point slope form as -
y - 18 = (1/3)(x - 27)
Therefore, the equation in point slope form as -
y - 18 = (1/3)(x - 27)
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The point slope form of the equation X - 3Y = -27 is Y = (1/3)X + 9. This equation represents a line with a slope of 1/3 and a y-intercept of 9.
Explanation:The point slope form of the equation X - 3Y = -27 is Y = (1/3)X + 9.
To convert the given equation to point slope form, isolate Y by subtracting X from both sides: -3Y = -X - 27. Then, divide both sides by -3 to solve for Y: Y = (1/3)X + 9.
This equation represents a line with a slope of 1/3 and a y-intercept of 9. This means that for every 1 unit increase in X, Y will increase by 1/3, and the line will intersect the y-axis at the point (0, 9).
Marisa is walking from her home to her friend Sanjay's home. When she is 12 blocks away from Sanjay's home she looks at her watch. she looks again when she is 8 blocks away from Sanjay's home and finds that 6 minutes have passed?
A.what do you need to assume in order to treat this as a linear situation
B. identified the variables for the linear situation and identify two points on the line explain the meaning of the points in the in the context of the problem
C. find the slope of the line and describe what it means in the context of the problem
D. write an equation in point slope form for the situation and use it to find the number of minutes It takes to reach Sanjay's home. show your work
Final answer:
Marisa walks at a constant speed to Sanjay's home, covering 1.5 blocks each minute.
Two points on the line representing her journey are (12, 0) and (8, 6).
The slope of line is -1.5.
The point-slope form of the equation is y = -1.5x + 18, and it takes 18 minutes to reach home.
Explanation:
To answer the question about Marisa walking to her friend Sanjay's home, we need to treat her journey as a linear situation.
A. Assumptions for a Linear Situation:
We need to assume that Marisa is walking at a constant speed between the two observed points.
In other words, there are no changes in her walking pace between being 12 and 8 blocks away from Sanjay's home.
B. Variables and Points on the Line:
The variables in this linear situation would be distance to Sanjay's home (x) and time passed (y).
Two points on the line are (12, 0) when she starts at 12 blocks away and looks at the watch, assuming 0 minutes have passed, and (8, 6) when she is 8 blocks away after 6 minutes.
C. Slope of the Line:
The slope of the line can be calculated using the formula slope = (y2 - y1) / (x2 - x1).
Hence, the slope equals (6 - 0) / (8 - 12) = 6 / (-4) = -1.5 blocks/minute.
This slope indicates that Marisa covers 1.5 blocks each minute.
D. Equation and Time to Reach Sanjay's Home:
The point-slope form of the equation is y - y1 = m(x - x1).
Using the point (8, 6) and the slope -1.5, the equation is y - 6 = -1.5(x - 8).
Rearranging, we get y = -1.5x + 18.
To find out how many minutes it takes to reach Sanjay's home when x = 0, we plug in the values to get
y = -1.5(0) + 18,
y = 18 minutes.
50 points
What are the steps for using a compass and straightedge to construct a square?
Put them in order!
Here are the steps for using a compass and straightedge to construct a square, in the correct order:
Use a straightedge to draw line t and label a point on the line as point B.Construct a line perpendicular to line t through point B. Label a point on this line as point C.With the compass open to the desired side length of the square, place the compass point on point B and draw an arc on line t and an arc on [tex]$\overleftrightarrow{B C}$[/tex]. Label the points of intersection as points D and E.Use the straightedge to draw [tex]$\overline{F D}$[/tex] and [tex]$\overline{F E}$[/tex].Keeping the same compass width, place the compass on point E and draw an arc in the interior of < DBE to intersect the previously drawn arc. Label the point of intersection as point F.Without changing the compass width, place the compass point on point D and draw an arc in the interior of < DBE.Constructing a square using a compass and straightedge involves a series of precise steps to ensure accuracy. This sequence ensures each step is correctly executed to construct the square.
To construct a square using a compass and straightedge, one must draw a base line, construct a perpendicular line, use a compass to measure out equal lengths, and finally connect the points to form a square.
Following these steps carefully will result in a precise square. The key is to maintain consistent compass width for accurate side lengths and to use the straightedge for clean, straight lines.
How many integers between 2 and 61 are prime numbers inclusive?
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True or false: Dilating a triangle changes the angles and side length of the triangle
Answer:
Statement is false.
Step-by-step explanation:
Dilating of a triangle produces another triangle having properties as
(1) Corresponding angles of parent and dilated triangle will be same
(2) Corresponding sides of both the triangles will be in the same ratio. They can not measure equal.
Therefore, given statement is false.
A store offers a 15% discount on all items in the store during a sale. All store employees get an additional 10% employee discount. In the equation below, C represents the cost of an item for an employee including tax and x represents the original price of the item:
C = 0.765x + 0.06(0.765x)
Chris is an employee at the store. He plans to buy a coat during the sale. The price of the coat before the discount is $100. How much will Chris pay for the coat during the sale? Remember, do not include the $ symbol.
Answer for Blank 1: