The 4.2 inches base length and 36 in.² area of the given triangle and the 5.6 inches base length of the similar triangle gives the area of the similar triangle as 64 square inches
Which method can be used to find the area of the similar triangle given the dimensions?Area of a triangle = (Base length × Height)/2
Area of the given triangle = 36 in.²
Base length of the given triangle = 4.2 inches
Base length of the similar triangle = 5.6 inches
Therefore;
Area of the given triangle = (Base length × Height)/2
Which gives;
36 = (4.2 × h)/2
Where;
h = Height of the given triangle
36 × 2 = 4.2 × h
[tex]h = \mathbf{\frac{36 \times 2}{4.2}} = 17 \frac{1}{7} [/tex]
Height of the given triangle, h = 17+ 1/7
The ratio of corresponding sides of similar triangles are the same, which gives;
[tex] \frac{5.6}{4.2} = \frac{h'}{17 \frac{1}{7}} [/tex]
Where;
h' = The height of the similar triangle
Which gives;
[tex] h' = \frac{5.6}{4.2} \times 17 \frac{1}{7} = 22 \frac{6}{7} [/tex]
The area, A', of the similar triangle is therefore;
[tex] A' = \frac{1}{2} \times 5.6 \times 22 \frac{6}{7} = 64 [/tex]
The area of the similar triangle A' = 64 in.²The area can also be obtained using the scale factor of area as follows;
(4.2/5.6)² = 36/A'Which gives;
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6 A survey was given to 12th-grade students of West High School to
determine the location for the senior class trip. The results are shown
in the table below.
To the nearest percent, what percent of the boys chose Niagara Falls?
Total of 24.03% of boys choose Niagara falls.
What is a frequency table?
A frequency table is a list of objects with the frequency of each item shown in the table.
The quantity of times that an event or value occurs is its frequency.
A frequency table, then, is a table that contains some facts and their frequency.
Given,
Total number of boys
56 + 74 + 103 = 233
Number of boys who chose Niagara falls = 56
Percentage of 56 out of 233
(56/233) × 100⇒ 24.03%
Hence the percent of the boys chose Niagara Falls will be 24.03%.
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Solve for x. Please help I don’t understand how to do this
Answer:
x = 5
Step-by-step explanation:
There's a Secant Theorem that someone else figured out (waaaay back in history) we just need to memorize it. So a secant is a line that touches the circle in two places. Your picture has two secants that both go thru the same point that's outside the circle. The secants each have a bit that's inside the circle and a bit that's outside the circle. And we could add together the inside and outside bits and get a total for the whole thing.
The secant theorem says that the outside piece × the whole thing on one secant = the outside piece × the whole thing on the other secant.
For the secant on top the "outside" bit is 9 and the whole thing is (2x+1+9). We'll times these together.
For the bottom secant the outside piece is 10 and the whole thing is (x+3+10). We'll multiply these together.
9(2x+1+9)=10(x+3+10)
simplify.
9(2x+10) = 10(x+13)
distribute.
18x + 90 = 101x + 130
combine like terms.
8x + 90 = 130
subtract 90
8x = 40
divide by 8
x = 5
see image.
what is 4,928 will rounded to the nearest hundred
Answer:
4.93
See the discussion below if the number is 4928.
Step-by-step explanation:
Comment
Do you really mean hundred? If you do, the nearest hundred is 0 when the actual value is 4.928
If you mean the nearest hundredth that means that 2 is the value of the hundredth now. Rounded, the answer is 4.93
If the given value is 4928, the hundred's place is the 9. Look at the 10s place (2). Since the 2 is less than 5, the 9 is not changed. 2 zeros are at the end of 49 since the hundreds place is rounded.
4900 is the answer
Hi there,
please see below for solution steps :
__________
Let us revise the rounding rules :
1) if the number you’re rounding to is followed by a number from 0 to 4, you drop that number
2) if the number you’re rounding to is followed by a number equal to 5 or more, you add 1 to that number
________
Now,
Nearest Hundredth => 3 digits after the decimal point
Thus,
4.928 => 4.93
Hope the Answer - and steps - made sense to you,
Happy Studying !!
Frozen Melody
what is the area of a polygon with verticies of (-2,2), (3,2), (7,-5) and (-2,-5)
Check the picture below.
[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=5\\ b=9\\ h=7 \end{cases}\implies \begin{array}{llll} A=\cfrac{7(5+9)}{2}\implies A=\cfrac{7(14)}{2} \\\\\\ A=49 \end{array}[/tex]
A chemical balance needs to weigh 237g using weights of 50g, 20g, 10g and 1g. How many of each weight is needed?
Answer:
See below
Step-by-step explanation:
237/50 = 4 R 37
37/20 = 1 R 17
17 / 10 = 1 R 7
7 / 1 = 7 R 0
4 50gm's 1 20gm 1 10gm and 7 1g wts
The required number of weights used in chemical balance to weigh 237g is 4,1,1,7 respectively.
What is mathematical expression?
A mathematical expression expression in mathematical is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Here, it is given that :
A chemical balance needs to weigh 237g using weights of 50g, 20g, 10g and 1g.
Now, let us find the number of weights for each weight type :
For 50g weight the maximum number of weights needed will be 4 that is :
50g x 4 = 200g
Now, for 20g weight the maximum number of weights needed will be 1 that is :
20g x 1 = 20g
Now, for 10g weight the maximum number of weights needed will be 1 that is :
10g x 1 = 10g
Now, for 1g weight the maximum number of weights needed will be 7 that is :
1g x 7 = 7g
Adding all the weights we get :
200g + 20g + 10g + 7g = 237g;
which is the required weight and the number of weights used is 4,1,1,7 respectively.
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PLEASE ASAP!! ALSO PLEASE INCLUDE AN EXPLANATION OF HOW YOU GOT THE ANSWER!!! THANK YOU! BTW THERE ARE TWO PICTURES! :)
2/3 is 400% of 1/6
0.2 is 12.5% of 1 3/5
Calculating PercentagesFrom the question, we are to determine what percent of 1/6 is 2/3
Let the value be x
Thus,
We can write that
2/3 is x% of 1/6
This means
2/3 = x/100 × 1/6
Now, solve for x
2/3 = x/100 × 1/6
2/3 = x/600
x = (2×600)/3
x = 400
Hence, 2/3 is 400% of 1/6
We are to determine what percent of 1 3/5 is 0.2
Let the value be y
That is,
0.2 is y% of 1 3/5
This can be written as
0.2 = y% × 1.6
0.2 = y/100 × 1.6
Now, solve for y
0.2 = y/100 × 1.6
0.2 = 1.6y/100
1.6y = 0.2 × 100
1.6y = 20
y = 20/1.6
y = 12.5
Hence, 0.2 is 12.5% of 1 3/5
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16 cups are to 1 gallon as x cups are to 5 gallons.
Answer:
80 cups
Step-by-step explanation:
Graph the line passing through (−4,−1) whose slope is m=−4/5
the answer is (-4,-1) and (1,-5)
Draw a line between the points representing wicket 3 and wicket 9 on the diagram. Then, find the
area of the rectangle. Show your work and round your answer to the nearest hundredth.
Based on the calculations, the area of a rectangle to the nearest hundredth is equal to 1143.92 ft².
How to calculate the area of a triangle?Mathematically, the area of a triangle can be calculated by using this formula:
Area = 1/2 × b × h
Where:
b represents the base area.h represents the height.By drawing a line between the points representing wicket 3 and wicket 9, we can logically deduce that wicket 2 forms a perpendicular bisector. Thus, the distance between the points representing wicket 3 and wicket 9 is given by:
Distance = 1/2 × 36.77
Distance = 36.77/2
Distance = 18.39 ft.
For the height of this triangle, we would apply Pythagorean's theorem:
h² = 25.02² - 18.39²
h² = 626.0004 - 338.1921
h² = 287.8083
h = √287.8083
h = 16.97 ft.
Area of triangle = 1/2 × b × h
Area of triangle = 1/2 × 36.77 × 16.97
Area of triangle = 311.99 ft².
For area of the rectangle, we have:
Mathematically, the area of a rectangle can be calculated by using this formula;
Area = LW
Area = 36.77 × 31.11
Area = 1143.92 ft².
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I just need to know what the answer is
Answer:
C
Step-by-step explanation:
You will have to solve the equation to get the number. Put your math skills to the test! Make sure to put your number in numeric form and in 3 digits. (not using pemdas, left to right)
Equation:
2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000
The value of the expression 2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 is 400000
How to solve the equation?The equation is given as:
2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000
From the question, we understand that the expression is to be solved from left to right (without using the pemdas mathematical rule)
So, we start by multiplying 2 and 4
2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 8 + 48000 / 8 - 1 x 30 x 2 + 40000
Add 8 and 48000
2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 48008 / 8 - 1 x 30 x 2 + 40000
Divide 48008 by 8
2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 6001 - 1 x 30 x 2 + 40000
Subtract 1 from 6001
2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 6000 x 30 x 2 + 40000
Multiply 6000 and 30
2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 180000 x 2 + 40000
Multiply 180000 by 2
2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 360000 + 40000
Evaluate the sum
2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 400000
Hence, the value of the expression 2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 is 400000
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Explain why [tex]x[/tex] and [tex]3x + 5[/tex] are factors of the expression [tex]x(3x + 5)^{2}[/tex] and not terms of the expression.
[tex]x[/tex] and [tex]3x+5[/tex] are being multiplied to form the expression, and are not being added or subtracted.
Here, x and (3x+5) are given in the form of multiplication, instead of being separated by addition or subtraction. This is why x and (3x+5) are factors of the expression x(3x + 5)² and not terms of the expression.
What are terms and factors in an expression?
Terms of an expression can be a variable, a signed number, or a constant multiplied by one or more variables. On the other hand, the factors are the items that have been multiplied by another items. Any integer, variable, phrase, or lengthier expression can be a factor.
For instance, the expression 2x(y - 5) has three components: 2, x, and (y-3). These three components are its factors, since when multiplied, they produce the same expression. The factors may or may not be comprised of more than one terms.
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what is Z in the rhombus?
Answer: 27°
Step-by-step explanation:
The easiest way to find the measure of angle Z is to know that in a rhombus, the diagonals are perpendicular bisectors of each other. This means that all the four angles in the center are 90°.
Since we know that all angles in a triangle add up to 180°, we can set the sum of z, 63, and 90 to be 180 and solve for z.
[tex]z+63+90=180\\z+153=180\\z=27[/tex]
Hence, z is 27°.
Mathematics problem..
Answer:
a) x + 10 = 45
b) 3 = 6 - x
c) d = s * t
Step-by-step explanation: This is actually pretty simple. Let's put down one theorem.
SYMMETRIC THEOREM OF PROPERTIES: If a equals b, then b must equal a. Thus, a = b and b = a.
This is all we're really doing.
Take a) for example, 45 = x + 10. Let's label (45) as A, and (x + 10) as B. Thus we have A = B. Now we know by the Symmetric Property, we have B = A. Thus, substituting B and A again, we get x + 10 = 45.
Just keep doing this with all the equations.
Hope this helped!
A client named Tommy wants us to prepare a 3300-word Marketing Report + Poster. If a task is quantifiable by word count, we charge $110 per 1000 words. If a task is not quantifiable by word count, we estimate how many hours are required to complete the task and we charge based on $5 per hour. How much should we charge Tommy? Work out the total price.
The amount we should charge Tommy is $363.
What does the amount charged mean?When you charge someone money, you are requesting payment from them in exchange for something you have either sold to them or performed for them.The total sum that the Owner is obligated to pay under the charge obligations as outlined in the payment schedule is referred to as the "Total Charge Amount."How much should we charge Tommy:
The amount charged for 1000 words = $110
The amount charged per word = $110/1000
Amount to be charged for 3300 words = $(110/1000) × 3300
= $(0.11) × 3300
= $363
The amount we should charge Tommy is $363.
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Jocelyn has a ladder that is 15 ft long. She wants to lean the ladder against a vertical wall so that the top of the ladder is 13.5 ft above the ground. For safety reasons, she wants the angle the ladder makes with the ground to be less than 75°. Will the ladder be safe at this height? Show your work and equation to support your answer
By using trigonometric relations, we will see that the angle that the ladder makes with the ground is 64.2°, so we conclude that the ladder is safe.
Will the ladder be safe at this height?Notice that the ladder makes a right triangle with the wall.
Such that the hypotenuse (the ladder itself) measures 15 ft, and one of the catheti (distance between the ground and top of the ladder) measures 13.5ft
If we considerate the angle that the ladder makes with the ground, the known cathetus is the opposite cathetus.
Then we can use the relation:
sin(x) = (opposite cathetus)/(hypotenuse)
Then:
sin(x) = (13.5ft)/(15ft)
If we use the inverse sine function on both sides, we get:
Asin(sin(x)) = Asin( 13.5ft/15ft)
x = Asin(13.5/15) = 64.2°
So the angle is less than 75°, which means that in fact, the ladder is safe.
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Given the two similar octagons
shown below, find the perimeter
of the larger octagon.
28
Perimeter = 34
4
6 4
3
4
7
3
3
The perimeter of the bigger octagon that is similar to the smaller one is: 238 units.
What is an Octagon?An octagon can be described as a polygon that has 8 sides and 8 angles.
What are Similar Octagons?
Octagons are referred to as similar to each other if they have the same angle measure but corresponding sides that are proportional to each other. That is, they have the same shape but different sizes.
How to Find the Perimeter of Similar Polygons?
Given the two octagons in the diagram are similar, and:
Perimeter of the smaller octagon = 34 units
A side of the smaller octagon = 4 units
Perimeter of the bigger octagon = ?
A corresponding side of the bigger octagon = 28 units
Therefore:
Perimeter of the smaller octagon/Perimeter of the bigger octagon = side of the smaller octagon/corresponding side of the bigger octagon
Plug in the values
34/Perimeter of the bigger octagon = 4/28
Perimeter of the bigger octagon = (28 × 34)/4
Perimeter of the bigger octagon = 238 units.
In summary, the perimeter of the bigger octagon is: 238 units.
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1.
Berkley is flying a kite. The string is all the way out, which means it is 425 meters away. Berkley is looking up at the kite at an angle of 42°. Berkley's dog is watching the kite too and the angle from Berkley to the dog to the kite is 87°. How would you find the distance between the kite and the dog? Is it possible? Explain your answer using the law of sines.
Using the law of sines, it is found that the distance between the kite and the dog is of 284.77 meters.
What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A is a.The length of the side opposite to angle B is b.The length of the side opposite to angle C is c.The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
For the situation described, we have that:
The height is opposite to the angle of 42º.The 425 meters are opposite to the angle of 87º.Hence:
[tex]\frac{\sin{42^\circ}}{h} = \frac{\sin{87^\circ}}{425}[/tex]
Applying cross multiplication:
[tex]h = 425\frac{\sin{42^\circ}}{\sin{87^\circ}}[/tex]
h = 284.77 meters.
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Can u guys please give me the correct answer
Answer:
∠ 3 = 65°
Step-by-step explanation:
∠ 2 and 115° are a linear pair and sum to 180° , that is
∠ 2 + 115° = 180° ( subtract 115° from both sides )
∠ 2 = 65°
∠ 2 and ∠ 3 are corresponding angles and and are congruent , then
∠ 3 = 65°
chef John bought 3 dozen eggs for $16.20 what is the unit price a $10.80 per 2 dozen eggs b $5.40 per 12 eggs c $0.45 per eggs d $0.22 per eggs e none of these f I don't know this yet
If f ( x ) = x 2 and g ( x )= 2x - 2,
find f ( g ( 7 ) )
Answer:
144
Step-by-step explanation:
First find g(7) --
[tex]g(7)=2(7)-2\\=14-2\\=12[/tex]
Then plug 12 into f(x) --
[tex]f(12)=(12)^{2} \\=144[/tex]
What is the value of b?
The value of b as described in the task content by means of solving the two equations simultaneously is; b= -10.
What is the value of b from the given equations?The given simultaneous equations as indicated have been manipulated to determine the value of a which is; 0.5 in the task content.
Hence, by substituting a= 0.5 into the equation; 5 = 30a + b; we have;
5 = 30(0.5) + b
b = 5- 15 = -10.
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QUESTION IS DOW BELOW 15 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
a. Angle BAC is a central angle.
b. Arc BEC is a major arc.
c. Arc BC is a minor arc.
d. m(BEC) = 260°
e. m(BC) = 100°
What is a Major Arc?An arc that has a measure that is greater than 180 degrees or is greater than a semicircle (half a circle) is referred to as a major arc.
What is a Minor Arc?An arc that has a measure that is less than 180 degrees or is not up to a semicircle (half a circle) is referred to as a minor arc.
What is a Central Angle?A central angle can be described as an angle with a vertex at the center of a circle and has two radii of the circle at sides.
a. Angle BAC is a central angle.
b. Arc BEC is a major arc.
c. Arc BC is a minor arc.
d. m(BEC) = 360 - 100 [central angle theorem]
m(BEC) = 260°
e. m(BC) = angle BAC = 100° [central angle theorem]
m(BC) = 100°
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A box contains 5 reams of paper. How could you estimate the thickness of 2 sheets of paper? One ream of paper is 500 sheets.
Please provide deep explanation so i can learn and understand
The estimated thickness of 2 sheets of paper, given the parameters, is 0.0216 cm.
What is the thickness of a sheet of paper?The thickness of a sheet of paper can be measured using a screw gauge or vernier caliper.
If the thickness of a ream of paper, which contains 500 sheets, is given, a sheet will be x/500 thick.
The thickness of 2 sheets of paper will be the thickness of a sheet multiplied by 2.
Data and Calculations:
Number of reams of paper in a box = 5 reams
1 ream = 500 sheets
500 sheets = 5.4 cm thick
The thickness of 2 sheets of paper = 0.0216 cm {5.4cm x 2/500)}
Thus, the estimated thickness of 2 sheets of paper, given the parameters, is 0.0216 cm.
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Question Completion:Assume that one ream of paper is 5.4 cm thick.
Calculate the perimeter and area of this shape.
Perimeter =
Perimeter → 25cm
Area → 25.5cm²
Explanation:[tex]perimeter = > 2.5 \times 2 + 5.5 + 3.5 + 6 + 3 + 2 = 5 + 9 + 9 + 2 = 25[/tex]
[tex]area = > 3 \times \frac{1}{2} \times 2 + 3 \times 3.5 + 6 \times 2 = 3 + 12 + 10.5 = 25.5[/tex]
with the law of indices simplify 3a²b×2ab
Answer:
6a³b²
Step-by-step explanation:
3 × 2 = 6
a²× a¹ = a³
b × b = b²
I hope you could get this answer
Answer: -12
Step-by-step explanation: x is -4 so -(-4) is positive 4. d = 3 so -3 = -3. -3x4 = -12.
Will give 30 pts!
What is:
27+ 8 x 41- 23 =
Please help quick what is the answer thank you
Answer:
y= -3x+4
Step-by-step explanation:
y=mx+c
m= y2-y1 ÷ x2-x1
m= -3
y=-3x+c
7=-3(-1)+c
c=4
y=-3+4
Help asap please!
What is sin(B)?
5
√61
sin(B):
6 [?]√[]
B
=
Answer:5SQRT61/
61
Step-by-step explanation:
