Answers
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.
Related Questions
Willa bought 5 tops that cost $72 after she applied a $20-off coupon. The tops all cost the same amount. Which equation can be used to find the cost in dollars of each top?
A5t + 20 = 72
B5t - 20 = 72
C20t = 5 = 72
D20t - 5 = 72
Answers
Answer:
B
Step-by-step explanation
5 tops minus the 20 from coupon, to get the total
Find each of the trigonometric ratios. I am going to give brainliest to whoever gets this right.
Answers
Answer:
Step-by-step explanation:
sin(Z) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{YZ}{XZ}[/tex]
= [tex]\frac{9}{15}[/tex]
= [tex]\frac{3}{5}[/tex]
cos(Z) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{XY}{XZ}[/tex]
= [tex]\frac{12}{15}[/tex]
= [tex]\frac{4}{5}[/tex]
tan(Z) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{XY}{YZ}[/tex]
= [tex]\frac{9}{12}[/tex]
= [tex]\frac{3}{4}[/tex]
sin(X) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{YZ}{XZ}[/tex]
= [tex]\frac{12}{15}[/tex]
= [tex]\frac{4}{5}[/tex]
cos(X) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{XY}{XZ}[/tex]
= [tex]\frac{9}{15}[/tex]
= [tex]\frac{3}{5}[/tex]
tan(X) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{YZ}{XY}[/tex]
= [tex]\frac{12}{9}[/tex]
= [tex]\frac{4}{3}[/tex]
The slope-intercept form of a linear equation
is y = mx + b, where x and y are coordinates of an
ordered pair, m is the slope of the line, and b is where
the line crosses the y-axis.
Which is an equivalent equation solved for the slope,
m?
m= yx +b
m= b
x
O m=-b
O m=y-
Answers
Answer:
The second option m=y-b/x
Step-by-step explanation:
Hope this helps :)
Answer:
B
Step-by-step explanation:
I have super human powers that tell me the correct answer
Blaise bought a used car for $3,250. He added a turbocharger that cost t dollars and a new air intake manifold that cost $178, bringing the total cost to $3,587. This situation can be represented by the equation $3,250 + $178 + t = $3,587. How much did the turbocharger cost?
Answers
Answer:
t = $159
Step-by-step explanation:
3587-3250-178 = t
t = 159
How many terms are in this expression? d + 8c + 7
Answers
Answer:
2
Step-by-step explanation:
solve for h in the parallelogram
Answers
Answer:
h = 5
Step-by-step explanation:
diagonals in a parallelogram bisect each other so:
2h = h + 5
h = 5
please help me put these in order if u can
Answers
Answer:
5x+8y=480
5(16)+8y=480
80+8y=480
8y=40
y=50
Step-by-step explanation:
x= kids ticket sold
y= adult tickets sold
5x+8y = sales
Plug in 16 for x and 480 for sales
5(16)+8y= 480
Solve for y
80+8y=480
400=8y
y=50
The boys' basketball team at Washington High School has been doing really well so far this year. In the past six games, they ve scored the following points.
84, 67, 74, 87, 67, 73
If the coach is discussing their year with the local newspaper, which measure of central tendency is he least likely to use?
Median
Mode
Mean
Range
Answers
Hope this helped :)
Answer:
Step-by-step explanation:
Median
Not 100 percent
Median is middle he is least likely to use.
Corey spent $17.00, inculding sales tax, on 2 sanwiches cost $5.25 each and the total sales tax was $0.92. What was the cost of each drink.
Answers
Answer:
Well to start you already know the sandwich cost 5.25 and the total sales tax .92.
To find the cost of each drink
5.25 x 2= 10.50
10.50+.92=11.42
17.00-11.42= 5.58
5.58/3= 1.86
So the cost per Drink is $1.86
Step-by-step explanation:
Hope this helped!
Please help! Will mark brainliest
Answers
I believe its 35 but im thinking it can be 40 too
What is the slope of the line passing through the points (3,5) and (-1,7)?
Answers
-1/2
To find the slope of the line between two points, we use the equation (y2-y1)/(x2-x1)
Substitute the values given for the xs and ys:
(7-5)/(-1-3)
2/(-4)
simplify: -1/2
Slope=-1/2
Hgvvvgssf
11. Determine the measure of the angles below.
12. Two lines intersect to form the four angles shown in the figure. Which term does not accurately describe the pair of angles 1 and 4?
Answers
Answer:
11 - 125 and 55
12 - supplementary
Step-by-step explanation:
5x+20+3x-8=180
step 1 combine like terms
8x+12=180
step 2 subtract 12 from each side
8x=168
step 3 divide each side by 8
x=21
then you just plug in 21 to each equation to find that angle 1 = 125 and angle 2=55
Problem 11
Answers:
5x+20 = 1253x-8 = 55--------------------
Explanation:
The two angles shown here form a linear pair. They supplementary so they add to 180.
(5x+20)+(3x-8) = 180
(5x+3x) + (20-8) = 180
8x+12 = 180
8x = 180-12
8x = 168
x = 168/8
x = 21
We then find the angles to be
5x+20 = 5*21+20 = 125
3x-8 = 3*21-8 = 55
Note how 125+55 = 180 to help confirm the answers
===================================================
Problem 12
Answer: B) Vertical angles
--------------------
Explanation:
Vertical angles are angles that form after intersecting two lines, and the angles are opposite one another. So one example of a vertical angle pairing would be angles 1 and 3. The other vertical angle pair of this diagram are angles 2 and 4. Vertical angles are always congruent to one another.
In this diagram, angles 1 and 4 are adjacent since they are next to each other. In other words, they share a common line (think of apartment neighbors sharing a common wall). Since they are adjacent angles, there is no way they are vertical angles.
Angles 1 and 4 are also supplementary since they form a straight line. They are a linear pair for very similar reasons. This allows us to rule out choices A, C and D.
Side note: the term "linear pair" means that the angles are adjacent and supplementary.
The laptop was $500
and is now $400. What
is the percent of change?
Answers
Answer:
20%
Step-by-step explanation:
Answer:
It's -20.00% I have a link to a website that calculate percent of change for you if you want it, just comment and tell me
Step-by-step explanation:
Every two years, there is a local election in a small town. In 2015, a total of 29,000 voters turned out in the election. In 2017, the number of voters decreased by 16%. In 2019, the number of voters increased by 22%. How many voters turned out in the election for 2019?
Answers
Answer:
29730 voters
Step-by-step explanation:
so:
in 2017- 16/100=0.16 x 29,000=4640 so 29,000-4640=24360 voters
in 2019-22/100=0.22 x 24369=5361.18 so 24369+5361.18=29730.18 voters
I hope this helped
Can someone please help me with this questions
Answers
Step-by-step explanation:
a. 3⁴
b. 7⁵
c. 10²
d. 5⁷
Hope this helps?
Yolanda is making a springboard to use for gymnastics. She has 8-inch-tall springs and wants to form a 16.5° angle with the base, as modeled
in the diagram below.
X
8 in
16.5
To the nearest tenth of an inch, what will be the length of the springboard, x?
27.0
b
28.2
ООО
8.3
d
2.3
Answers
Answer: Hi! The answer is 28.2
Step-by-step explanation:
The value of x from the given diagram is 28.3 in
SOH CAH TOA identityFrom the diagram shown, we are given the following:
Opposite = 8inHypotenuse = xAngle of elevation = 16.5 degreesTo get the value of x, we will use the relatinship;
Sin theta = opp/hyp
Sin 16.5 = 8/x
x = 8/sin16.5
x = 8/0.2840
x = 28.16
x = 28.2in
Hence the value of x from the given diagram is 28.3 in
Learn more on SOH CAH TOA here: https://brainly.com/question/20734777
Change to y = mx + b form. 3y - 3x = 9
Answers
Answer:
y = x+3
Step-by-step explanation:
3y-3x = 9
3y-3x+3x = 9+3x
3y = 3x+9
3y/3 = 3x/3+9/3
y = x+3
Hey there!
The answer is [tex]y=x+3[/tex]
[tex]3y-3x=9[/tex]
[tex]\frac{3y}{3} -\frac{3x}{3} =\frac{9}{3}[/tex]
[tex]y-x=3[/tex]
[tex]y-x+x=3+x[/tex]
[tex]y=x+3[/tex]
Have a great day!
Caleb purchased video games for $45 each. He bought $540 worth of video games. If x is the number of video games, which equation can be used to find the total number of video games Caleb purchased?
Answers
Answer:
y=45x-540
Step-by-step explanation:
need help im dum (not really but i dont get it)
i will give brainliest
Answers
Answer:
20
Step-by-step explanation:
to do % you have to multiply your number (50) by the % which is 40%
but you have to turn your number into a decimal (.40) then multiply
you'll get 20 and there is your answer!
hope this helps!
UM what is 53 x 4? I need to know right now.
Answers
Answer:
212 is the correct answer hope it helps
The point ( -3, 15 ) undergoes a translation of 9 units right and 10 units down. What are the coordinates of the new point?
Answers
Answer:
The new coordinates would be (6,5)
Step-by-step explanation:
I'm pretty sure o-O
x^2+5x+4=0 how do I factor this because Im trying to solve quadratic equations by factoring and i dont understand it
Answers
Answer:
(x + 4)(x + 1)
Step-by-step explanation:
The slope of line M between (-6,-8) and (-2,-5) is 3/4. What is the slope of line M between (2,-2) and (10,4)?
Answers
find the difference of (6x^2+3x-5) and (4x^2-2x+3)
Answers
Answer:
ummm
Step-by-step explanation:
cz points
Trigonometric functions
Answers
Answer:
in mathematics,the trigonometric functions are real function which relate an angle of a right angle triangle to ratios of two side lengths.They are widely used in all sciences that are related to geometry,such as navigation,solid mechanics,celestial mechanics,geodesy,and many others.
Select all the systems of equations that have exactly
one solution.
y = 3x + 1
y =− 3x + 7
y = 3x + 1
y = x + 1
y = 3x + 1
y = 3x + 7
y =− x + 10
y =− 1x + 10
y =− x + 10
y =− x + 12
Answers
Answer:
a, c
Step-by-step explanation:
because they have the same equations
what is the slope of a line that contains the points (-6, 1)and (4 negative 4)
Answers
Btw check if it is correct
help me please, i don’t get it loll
Answers
Answer:
subtract to find A
Step-by-step explanation:
Maths question, will give Brainliest! Estimate the solution to the system:
y=4x−2
y=x+3
Answers
Answer:
C
Step-by-step explanation:
Answer:
C or (5/3, 14/3)
Step-by-step explanation:
y = 4x - 2 = x + 3
3x - 3 = 3
3x = 5
x = 5/3 or 1 2/3
y = 5/3 + 3
y = (5 + 9)/3
y = 14/3 or 4 2/3
A shop sells packs of black pens, packs of red pens and packs of green pens.
There are
2 pens in each pack of black pens
5 pens in each pack of red pens
6 pens in each pack of green pens
On Monday, the ratio of number of packs of pens sold was Black : Red : Green = 7 : 3 : 4
A total of 212 pens were sold.
Work out the number of green pens sold.
Answers
Answer:
The number of green pens sold are 96 green pens
Step-by-step explanation:
The given parameters for the packs of pens sold by the shop are;
The number of pens in each pack of black pens = 2 pens
The number of pens in each pack of red pens = 5 pens
The number of pens in each pack of green pens = 6 pens
The ratio of number of packs of pens sold Black : Red : Green = 7 : 3 : 4
The total number of pens sold = 212
Let 'x' represent the number of packs of pens sold
Therefore, the fraction of the packs the pens sold that are black pens = 7/(7 + 3 + 4) = 7/14 = 1/2
∴ 1/2 of the number of packs of pen sold = packs black pens = x/2
The fraction of the packs the pens sold that are red pens = 3/14
∴ 3/14 of the number of packs of pen sold = packs of red pens = 3·x/14
Similarly, we have;
The fraction of the packs the pens sold that are green pens = 4/14 = 2/7
∴ 2/7 of the number of packs of pen sold = packs of green pens = 2·x/7
Therefore, we have;
x/2 × 2 + 3·x/14 × 5 + 2·x/7 × 6 = 212
Where;
x/2 × 2 = The number of black pens sold
3·x/14 × 5 = The number of red pens sold
2·x/7 × 6 = The number of green pens sold
∴ 53·x/14 = 212
x = 212 × 14/53 = 56
∴ The number of packs of pens sold = x = 56 packs
The number of green pens sold = 2·x/7 × 6 = 2 × 56/7 × 6 = 96
The number of green pens sold = 96 pens.