Answer:
Step-by-step explanation:
These problems are based on triangle ratios. You cannot use the Pythagorean theorem to solve them.
The first triangle is a 45 45 90 degree triangle (I'm talking about the angles), and so, the ratio is 1:1:[tex]\sqrt{2\\}[/tex], so I have to divide the hypotenuse by [tex]\sqrt{2\\}[/tex] to get the legs. The hypotenuse is 15[tex]\sqrt{6}[/tex], so that divided by [tex]\sqrt{2\\}[/tex] is 15[tex]\sqrt{3\\}[/tex]. X is the same length as y because of the triangle ratio, so both x and y for the first triangle are 15[tex]\sqrt{3\\}[/tex].
The second triangle is a 30 60 90 degree triangle, so the ratio is x:x[tex]\sqrt{3}[/tex]:2x. The short leg is 7[tex]\sqrt{3}[/tex], so 7[tex]\sqrt{3}[/tex] * 2 is the hypotenuse, which is 14[tex]\sqrt{3}[/tex]. The long leg is 7[tex]\sqrt{3}[/tex] * [tex]\sqrt{3}[/tex], which is 21. So, x for the second triangle is 14[tex]\sqrt{3}[/tex], and y for the second triangle is 21.
Answer:
Question 9: x = [tex]15\sqrt{3}[/tex], Question 10: y = [tex]15\sqrt{3}[/tex], Question 11: x = [tex]14\sqrt{3}[/tex], Question 12: y = 21
Step-by-step explanation:
Question 9-10: Right triangles with 45°, 45°, 90° have a special rule, the legs of the triangle are equal, so x = y. Now you can form the statement [tex]2x^2 = 1350[/tex], and because x = [tex]15\sqrt{3}[/tex], so does y.
Question 11-12: Right triangles with 30°, 60°, 90° also have a special rule, the side corresponding to 30° is half the length of the hypotenuse and the side corresponding to 60° is [tex]\sqrt{3}[/tex] times as great as the 60°. x is 2 times as big as [tex]7\sqrt{3}[/tex], so its length is [tex]14\sqrt{3}[/tex]. Y is [tex]\sqrt{3}[/tex] as great as [tex]7\sqrt{3}[/tex], so its length is 21.
6. The scatter plot shows the median household income, x, in thousands of dollars, and
the number of adults per 1,000 people with bachelor's degrees, y, of 50 U.S. states.
The line y = 4.08x + 63.13 is a good fit for this data.
The line y = 4.08x + 63.13 is a good fit for this data because it accurately represents the positive relationship between median household income and the number of adults with bachelor's degrees in the 50 U.S. states.
Given that a scatter plot of median household income x and the number of adults per 1,000 people with bachelor's degrees y for 50 U.S. states. The line y = 4.08x + 63.13 is suggested to be a good fit for this data.
To understand why this line is a good fit, to consider its equation. In this case, y represents the number of adults per 1,000 people with bachelor's degrees, and x represents the median household income in thousands of dollars.
The equation of the line is y = 4.08x + 63.13. This means that for every increase of $1,000 in median household income, the number of adults with bachelor's degrees increases by 4.08 per 1,000 people. The intercept of the line is 63.13, which represents the number of adults with bachelor's degrees when the median household income is $0.
By analyzing the scatter plot, we can see that the points are roughly linear and show a positive correlation between median household income and the number of adults with bachelor's degrees. The line represents the best fit for this data because it minimizes the distance between the line and the points on the scatter plot.
Hence, the line y = 4.08x + 63.13 is a good fit for this data because it accurately represents the positive relationship between median household income and the number of adults with bachelor's degrees in the 50 U.S. states.
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Jason needs to run 30 laps before basketball practice. His coach makes a deal with the team that on Friday’s they only need to complete 5/6 of that.
Write an expression or equation to represent the number of laps to complete on Friday.
Answer:
a little bit less than 30
Step-by-step explanation:
A 381 foot cable runs from the top of a radio tower to a skate in the ground. If it hits the ground 167 feet from the base of the tower , what is the angle of elevation that is makes with the ground?
Answer:
64°
Step-by-step explanation:
Using Pythagoras rule :
Cosθ = adjacent / hypotenus
Adjacent = 167
Hypotenus = 381
Cosθ = 167 / 381
Cosθ = 0.4383202
θ = Cos^-1(0.4383202)
= 64.003
Hence, angle of elevation = 64°
The perimeter of a rectangle is 260 yards. The length is 30 yards greater than the width. Find the dimensions of the rectangle.
Answer:
width: 50 yards
length: 80 yards
Step-by-step explanation:
I would write an equation to start
x = width
260 = 2x + 2(x + 30)
260 = 4x + 60
200 = 4x
x = 50
Width = 50 yards
Length = width + 30
Length = 50 + 30
Length = 80 yards
a collector purchased a rare book for $97.56 and then sold the book in an online auction for $141.82. The auction charged the collector $8.25 in fees for the use of its service. how much did the collector earn by selling the book
Answer:
$36.01
Step-by-step explanation:
141.82 - 8.25 = 133.57
133.57-97.56=36.01
The collector earned a total of $36.01 by selling the book.
What is the Subtraction operation?Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
The collector earned $141.82 - $97.56 = $44.26 by selling the book.
To find the total amount the collector earned, we need to subtract the price they paid for the book from the price they sold it for. This gives us the profit that the collector made on the sale of the book.
However, we also need to subtract the auction fees that the collector had to pay.
The collector paid $8.25 in fees, so their total earnings from the sale of the book were :
⇒ $44.26 - $8.25
Apply the subtraction operation, and we get
⇒ $36.01.
Therefore, the collector made a total of $36.01.
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The ratio of a:b is 3:4.
the ratio of b:c is 5:3.
work out the ratio of a:c
12:53:34
What is most often given a value of zero to describe an object’s position on a straight line?
displacement
reference point
distance
ending location
Answer:
Reference Point
Step-by-step explanation:
The answer is reference point. This is because reference point is used to determine if an object is in motion or if it has changed is direction.
Thus, reference point has to be a value of zero for us to use it to determine if an object has moved.
Match each problem to the inequality that models it. Once choice will be used twice *
Answer:
yes
Step-by-step explanation:
1 sentences- c
2 sentence - b
3 sentence- d
4 sentence- a
5 sentence- c
Five integers have a mean of 8. The
integers are 7, 3, 10, 13, X. Find the
value of x.
The ratio of men to women working for a company is 5 to 6. If there are 198 employees total, how many women work for the company?
Answer: 110 Women !
Step-by-step explanation:
Call their numbers 4x to 5x.
Since there are a total of 198 people,
4x + 5x = 198
9x = 198
x = 22
so that there are
88 men and 110 women.
Find the unknown side of the triangle below.
9 in
18.8 in
15 in
8 in
Answer:
its actually 15 inches, cause if you bring the bottom line up and compare it to the 17 line its a smidge shorter so go with the largests number the less then 17. theres proof for the quiz itself
Step-by-step explanation:
Help please look at the image
Thanks
Answer: Option 1
Reason: Math
Help me please !!!
And thank you
Answer:
804.4
Step-by-step explanation:
the formula for the volume of a cube is the side length cubed,
so:
(9.3)(9.3)(9.3) = 804.357
then round it to 804.4
hope this helped!
at a basketball game, 18% were supporting the visiting team. if 2624 people attending supported the home team, what was the total number of people attending the game?
Answer:
2624= 82%
18%= 2624/82=32. 32*18=576
Step-by-step explanation:
If 2624 people attending supported the home team, the total number
of people attending the game will be 3200.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
It is given that 18% were supporting the visiting team and 2624 people attending supported the home team as a result 82 % were supporting the home team,
Let the total number of people attending the game be x.
⇒82% of x = 2624
⇒(82/100)×x= 2624
⇒x= (2624×100)÷82
⇒x=3200
Hence, if 2624 people attending supported the home team, the total number of people attending the game will be 3200.
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name each of the shapes below
1Wht2
2The3
3Frick4
4Is5
5that6
The name of the shape in the figure is a hexagon.
What are polygons?A polygon is often a plane figure in geometry that is enclosed by a closed chain made up of a finite number of straight-line segments that end in a loop. The spots where two of these segments meet are referred to as the polygon's vertices (plural: vertices) or corners. These segments are known as its edges or sides.
Given a shape,
the shape is a polygon,
to name a polygon first count the number of sides of the figure,
as we count there are 6 sides for the shape,
There are some specific names for the shapes according to their number of sides, like
Number of Sides Name
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
The name for the shape is Hexagon.
Hence the name of the figure is Hexagon.
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60 people were asked the colour of their car and the pictogram shows the results.
a) 16 cars are red. Complete the key.
b) How many cars are silver?
KEY: One circle represents __ cars
Red = 4 circles
White = 3 circles and a half
Silver = 5 circles and 3/4
Grey = 1 circle and 3/4
The number of silver cars in the pictogram is 23.
How many cars are silver?If 16 cars are red, then, each circle represents 4 cars.
If each circle represents 4 cars, then, each quarter of a circle represents 1 car
White car = 4 + 4 + 4 + 2
= 14 cars
Silver = 4 + 4 + 4 + 4 + 4 + 3
= 23 cars
Grey = 4 + 3
= 7 cars
Total cars = red + white + silver + grey
= 16 + 14 + 23 + 7
= 60 cars
It can therefore be concluded that silver cars is 23 in number.
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The vertices of parallelogram DEFG are E(-1,4) F(5,6) and G (8,0). Find the coordinates of D
Answer:
The coordinates of D are (2,-2)
Step-by-step explanation:
The coordinates of point D are (2,-2)
The coordinates of the parallelogram are given as:
E(-1,4), F(5,6) and G (8,0)
For the coordinates to represent a parallelogram, the following must be true
[tex]x_D - x_E = x_G - x_F[/tex]
[tex]y_D - y_E = y_G - y_F[/tex]
So, the equations become
[tex]x_D -(-1) =8-5[/tex] and
[tex]y_D -4 =0-6[/tex]
Solve for x and y in the above equations
[tex]x_D -(-1) =8-5[/tex]
[tex]x_D +1 = 3[/tex]
[tex]x_D = 3-1[/tex]
[tex]x_D = 2[/tex]
[tex]y_D -4 =0-6[/tex]
[tex]y_D - 4 = -6[/tex]
[tex]y_D = 4-6[/tex]
[tex]y_D =-2[/tex]
Hence, the coordinates of point D are (2,-2)
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I NEED THIS FOR A TEST PLZ HELP!!!
Triangle ABC has been dilated from center D.
If the length of segment BC = x, which is the
length of segment
ST?
A. 2x
B. 3x
C. 4x
D. 5x
Answer:
4x
Step-by-step explanation:
Answer:
A. 2x is correct.
Step-by-step explanation:
Finding the measure of the segment BC and ST by the Distance formula: B (5, 7), C (8, 8), S (1, 11), T (7, 13).
BC = √(8-5)² + (8 - 7)²
BC = √10
ST = √( 7 - 1)² + ( 13 - 11)²
ST = 2√10
Scale Factor = Image/ Pre-image = ST/BC = 2√10/√10 = 2
This means that the image, ST, is twice as large as the pre-image BC.
ILL GIVE BRAINLIESAT FOR FIRST ANSWER!
Divide
3÷1/12
Step-by-step explanation:
is 36 hello my name is santiago i am fron Colombia
A rectangular football field is 6x meters long and 3x meters wide. If its
perimeter is 360 meters, then the value of x is
Answer:dgrgfhtbsdvdsvs
Step-by-step explanation:dssfdfd
Answer:
x = 20
Step-by-step explanation:
perimeter = 2(width) + 2(length)
2(6x) + 2(3x) = 360
12x + 6x = 360
18x = 360
divide both sides by 18
x = 20
over which of the following approximate intervals is the water level decreasing
pls help !
Answer:
B and C
Step-by-step explanation:
It is going down
2x+1 cual es su respuesta ??
Answer:??
Step-by-step explanation:
¿A qué es igual la ecuación? x no se puede resolver sin un signo igual al final. por favor responda para que pueda ayudar! :D
Answer:
x= -1/2
Step-by-step explanation:
2x+1=0
-1 -1
2x= -1
➗ por 2
x= -1/2
find the area of an equilateral triangle of side 12 cm
Step-by-step explanation:
root 3 by 4a²
root3/4*(12)²
36root3
Answer:
A≈62.35cm²
Step-by-step explanation:
A=3
4a2=3
4·122≈62.35383cm²
Assume that x = x(t) and y = y(t). Let y = x^2 + 6 and
dx/dt=4 when x=1
Find dy/dt when x = 1
Answer:
[tex]\frac{dy}{dt}[/tex] = 8
Step-by-step explanation:
Given:
x = x(t) and y = y(t)
Let y = x² + 6
By differentiating the given equation with respect to t,
[tex]\frac{dy}{dt}=\frac{d}{dt}(x^{2}+6)[/tex]
[tex]\frac{dy}{dt}=\frac{d}{dt}(x^{2})+\frac{d}{dt}(6)[/tex]
Since, [tex]\frac{dx}{dt}=4[/tex] when x = 1
[tex]\frac{dy}{dt}=2x\frac{dx}{dt}+\frac{d}{dt}(6)[/tex]
[tex]\frac{dy}{dt}=2(1)(4)+0[/tex] [By substituting the values of [tex]\frac{dx}{dt}[/tex] and x = 1]
[tex]\frac{dy}{dt}[/tex] = 8
Write the approximate value of 0.12456
upto 3 significant figures.
Step-by-step explanation:
be62vw6vwebe6e6be6ev6eb6eb6eb7eb7eebe73
what is 8.154 to 1 decimal place?
Please answer the correctly in the picture below 8TH GRADE MATHENMATICS?!
Answer:
B 3.5
Step-by-step explanation:
Hope it Helps!
someone please show me the steps on how to solve this.
Answer:
1. BC=26
Step-by-step explanation:
1• because it is an equiangular triangle (i guess that would be low I describe it), all of the sides & angles are =.
I’m not 100%sure on number two but i hope this helps fir number one
A retailer marks up the price of a coffee mug from $6.25 to $8.77. By what percent did the price increase? Round to
two decimal places
a. 28.73%
b. 39.68%
40.32%
45.97%
C
d
Answer:
c
Step-by-step explanation:
edg 20/21
If a store raises a coffee mug's price from $6.25 to $8.77. The price increase was 40.32%. Option C is correct.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
It is given that, A retailer marks up the price of a coffee mug from $6.25 to $8.77.
We have to find the percentage by which the price increase,
% increment = New rate - old rate / old rate × 100
% increment =(8.77 - 6.25)× 100
% increment =40.32%
Thus, if a store raises a coffee mug's price from $6.25 to $8.77. The price increase was 40.32%. Option C is correct.
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Which is the graph of y = 3x + 1?
Answer:
X dot on graph (-0.333,0) Y dot on graph (0,1)
Step-by-step explanation:
It intercepts on the X line on (-0.33,0)
It intercepts on the Y line on (0,1)
Answer:
Hi so the graph will look like this
Hope This Helps!