Answer:
cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]
Step-by-step explanation:
Using the 45- 45- 90 triangle with legs 1, 1 and hypotenuse [tex]\sqrt{2}[/tex] , then
cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] if the denominator is rationalised
Item 3 The Hampton family used 17,158 kilowatts of electricity last year. They used about the same amount of electricity each week. About how many kilowatts of electricity did the Hampton family use each week? (There are 52 weeks in a year).
Please Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1111
The image shows two angle measures. Which equation can be used to find the
value of x?
2x - 15 = 45
2x - 15 = 135
2x - 15 + 135 = 90
2x - 15 + 131 = 360
Answer:
(2x-15) = 45
Step-by-step explanation:
When two angles lie on a straight line, they are supplementary
what this mean is that the add up to equal 180 degrees
Mathematically, we have this as:
(2x-15) + 135 = 180
(2x-15) = 180-135
(2x-15) = 45
Answer:
Step-by-step explanation:
(2x-15) = 45
Step-by-step explanation:
When two angles lie on a straight line, they are supplementary
what this mean is that the add up to equal 180 degrees
Mathematically, we have this as:
(2x-15) + 135 = 180
(2x-15) = 180-135
(2x-15) = 45
In which quadrant does the terminal side of 225° angle in standard position lie
Answer:
4 th quadrant
Step-by-step explanation:
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What is the equation of the line that passes through the point (6,14) and is parallel to the line with the following equation? y= -4/3x - 1
Answer:
Which of the following is the equation of a line parallel to the line given by ... Parallel lines have the same slope and different y-intercepts. ... Thus the only one that fits the description is:.
can someone please help me
The measure of the angle formed at the center of anoxygen atom in a water molecule is about 105. The angles formed at each hydrogen atom are congruent. What is the size of the angle at each hydrogen atom?
Answer:
The size is 37.5 degrees
Step-by-step explanation:
The total angle in the triangle is 180
Since the other two angles are congruent. it means that they are equal
Let us call each of the angles x
Mathematically,
x + x + 105 = 180
2x = 180-105
2x = 75
x = 75/2
x = 37.5
Adam earn $25 per week for allowance plus an additional $10 per yard he mows around the neighborhood. Write an inequality to represent how many lawns Adam would have to mow in one week if he needs to earn more than $150 for a new bicycle. *Use y for the variable
Alex dumped out his piggy bank and there were only
nickels, dimes, and quarters.
There were three times as many dimes as nickels, and 40
more quarters than nickels.
If the total amount of money was $17.20, how many of each
type of coin were there?
"There are
nickels,
dimes, and
quarters.
Answer:
12 nickels
36 dimes
52 quarters
Step-by-step explanation:
Let x = no. of nickels
3x = no. of dimes
x + 40 = no. of quarters
5x = value of the nickels since each nickel is 5 cents
10(3x) = 30x = value of the dimes since each dime is 10 cents
25(x + 40) = 25x + 1000 = value of the quarters since each quarter is 25 cents
Now, 5x + 30x + 25x + 1000 = 1720 ($17.20 = 1720 cents)
60x + 1000 = 1720
60x = 720
x = 12 nickels
3x = 36 dimes
x + 40 = 52 quarters
Check: 12 nickels are worth $.60
36 dimes are worth $3.60
52 quarters are worth $13
.60 + 3.60 + 13 = 17.20
Write each polynomial in factored form.
h(x) = 3x^3 + 5x^2 +9x +15
Answer:
Step-by-step explanation:
[tex]3x^3+9x+5x^2+15\\ \\ 3x(x^2+3)+5(x^2+3)\\ \\ (3x+5)(x^2+3)[/tex]
Are the two triangles similar? If so, why
are
they similar?
Answer:
They aren't similar.
What is the slope (-2,0) and (1,-4)
Answer:
-4/3
Step-by-step explanation:
y2-y1
--------
x2-x1
comple the similarity statement for 2 triangles shown
HELP ASAP
What is an equation of the line that passes through the points (6,8) and (-3,2)?
Answer:
y=2/3x+4
Step-by-step explanation:
Wednesday: Solve for x (can't use decimals), must use the rules.
Start by: What are the missing angles of this triangle?
What in the picture hints on the answer above?
X =
16
Answer:
missing angle isosceles angle and side (a)
Pythagoras theorem
a²+a²=16²
a²=256/2
a=√128=11.3=11
Can someone plz help me the info is in the photo I'm begging you and I need the equation to show my work.
Answer:
$65.02
Step-by-step explanation:
15% of 85 = 12.75
sale price = 85-12.75 = 72.25
10% of 72.25 = 7.225 = 7.23
final cost = 72.25 - 7.23 = 65.02
If we all draw a triangle using the same three side lengths, will we all draw exactly the same triangle?
I JUST WANT POINTS /\ /\
_
1 less than 1/4 Question: Peggy is pp years old. Maggie is 11 year less than \frac{1}{4} 4 1 of Peggy's age. What is Maggie's age in terms of p? ___ years
Answer:
[tex]M=\dfrac{(p-44)}{4}\ \text{years}[/tex]
Step-by-step explanation:
Given that,
Peggy is p years old.
Maggie is 11 year less than 1/4 of Peggy's age.
It means,
Maggie's age,
[tex]M=\dfrac{1}{4}\times p-11\\\\M=\dfrac{p}{4}-11\\\\M=\dfrac{(p-44)}{4}[/tex]
So, Maggie's age is [tex]\dfrac{(p-44)}{4}[/tex] years.
Frank is buying birthday candles for his grandmother's birthday cake. Her age, in years, will determine how many boxes of candles Frank will need to
buy. Which is the dependent quantity?
O b= how many boxes of candles Frank will buy
O a = Grandmother's age in years
Answer:
I believe A because the grandmothers age affects how many boxs of candles Frank will buy. Hope this helps
Step-by-step explanation:
Rita paid $82 for 5 trees and 1 shrub. Lilly bought 2 trees and 1 shrub for $37. Find the cost per tree and the cost per shrub.
Answer:
trees cost $15
Shrub cost $7
Step-by-step explanation:
Given data
Rita paid $82 for 5 trees and 1 shrub
5x+y= 82---------1
Lilly bought 2 trees and 1 shrub for $37
2x+y= 37----------2
from 1
y= 82-5x
put the value of y in 2
2x+82-5x= 37
2x-5x= 37-82
-3x=-45
x= 45/3
x=$15
put the value of x in 1
5(x)+y= 82
5*15+y=82
75+y=82
y=82-75
y=$7
Hence, trees cost $15
Shrub cost $7
HELLO help lolllllllll
Answer:
x = 7
y = 12
Step-by-step explanation:
ABCD is a parallelogram.
Measures of opposite sides of a parallelogram are equal.
Therefore,
2y - 18 = y - 6
2y - y = 18 - 6
y = 12
2x + 2 = y + 4
2x + 2 = 12 + 4
2x = 16 - 2
2x = 14
x = 14/2
x = 7
A ski slope is 320 yards long with a vertical drop of 100 yards. Find the
angle of elevation of the ski run. Round to the nearest degree.
Answer:
18°
Step-by-step explanation:
A ski slope is 320 yards long with a vertical drop of 100 yards. Find the
angle of elevation of the ski run. Round to the nearest degree.
The formula for angle of elevation is given as:
sin θ =Opposite/ Hypotenuse
Opposite = Vertical drop = 100 yards
Hypotenuse = Ski slope = 320 yards.
Angle of elevation =
sin θ = 100/320
sin θ = 0.3125
θ = arc sin(0.3125)
= 18.209956864°
Approximately = 18°
8.12
Given the diagram below, what is cos(45") ?
450
Triangle not drawn to scale
A. 2-3
B. 4/2
C.
D. JE
The value of cos 45° in the given triangle is 1/√2, Option C is correct.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
In the given right triangle the hypotenuse is 8√2
In the given triangle the two legs are equal.
Let x be the length of the two legs
By Pythagoras theorem, let us find the length of a leg.
x²+x²=(8√2)²
2x²=64(2)
2x²=128
Divide both sides by 2
x²=64
Take square root on both sides
x=8
Now let us find the cosine function, the ratio of adjacent side and hypotenuse
cos45 = 8/8√2
=1/√2
Hence, the value of cos 45° in the given triangle is 1/√2, Option C is correct.
To learn more on trigonometry click:
https://brainly.com/question/25122835
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HELP QUICK!! WILL GIVE BRAINILIST
Find the value of x in the triangle shown below.
Answer:
58
Step-by-step explanation:
Since two of the sides are both 6.2, we know that this is an isosceles triangle. Thus, the two angles opposite of x are both equal (61 degrees).
The angles inside of a triangle always add up to 180, so now we have
180 = 61 + 61 + x
Solving for x, we get x = 180 - (61 + 61) = 180 - 122 = 58
Which point is located on the x-axis?
ТУ
D
A
B
3+
2
1
1
-4-3-2-1
-1
1
2
2
3
4 x
-2
-3+
-4
ОА
ОВ
Answer:
Point C
Step-by-step explanation:
Point C is located on the x-axis.
How to sketch an angle in standard position
Answer:
Drawing an angle in standard position always starts the same way, draw the initial side along the positive x-axis. To place the terminal side of the angle, you must calculate the fraction of a full rotation the angle represents.
Answer:
Get the number of rotations of the given angle by dividing 360 degrees with respect to positive x-axis.
Step-by-step explanation:
1. First draw a horizontal line (along x-axis).
2. Locate the terminal side of the angle by dividing 360 degrees. Recall that one full rotation is equal to 360 degrees. So, to sketch 360 degrees, we will divide it by 360 degrees resulting in 1.
3. Similarly to draw 180 degrees, divide 180 by 360. This will result in 1/2. Therefore, it is half the way from x-axis.
Can anyone tell me the area? I will give brainlist if I'm able to
Answer:
143 yds^2
Step-by-step explanation:
Helpp I’ll mark you brainlist
Answer: 1
hope it help
In equilateral triangles STU:
==========================================================
Explanation:
Equilateral triangles have three equal sides, ie the sides are all the same length.
Let's set sides ST and TU equal to each other and solve for x
7x-10 = 2x+25
7x-2x = 25+10
5x = 35
x = 35/5
x = 7
Then we use this to compute each side
ST = 7x-10 = 7*7-10 = 49-10 = 39TU = 2x+25 = 2*7+25 = 14+25 = 39US = x^2 - 10 = 7^2 - 10 = 49-10 = 39Each side is 39 units long, so this confirms we have the correct answer.
Two athletes practice for a marathon by running back and forth on a 11-mile course. They start running simultaneously, one at a speed 2 miles faster than the other. How fast does each run if they meet 1 hr 6 minutes after starting? (The faster one is already returning at this point.) How far from the starting point do the runners meet?
Answer:
Faster runner speed: 11 mph
Slower runner speed: 9 mph
Distance from starting point: 9.9 miles
Step-by-step explanation:
Let the slower runner speed be: x
Faster runner speed: x+2
1 hour 6 minutes = 1.1 hours
Slower: 1.1(x) = 1.1x miles
Faster: 1.1(x+2) = 1.1x+2.2 miles
This means that the faster runner had gone 2.2 miles more than the slower runner.
1.1x + 2.2 > 11 miles (This is true as we know the faster runner is coming back from the 11 mile run)
1.1x > 11 - 2.2 miles
1.1x > 8.8 miles
x > 8.8 / 2.2 miles
x > 8 mph
1.1x < 11 miles (we know this is true as the slower runner has to have gone less than 11 miles as the faster runner met him on his way back)
x < 11 / 1.1 miles
x < 10 miles
8 < x < 10
Although x could be any number including decimal between 8 and 10, the obvious first answer would be 9. However we need to check if this answer is correct.
Slower runner distance to the end:
1.1(9) = 9.9 miles
11 - 9.9 = 1.1 miles
Faster runners distance from the end (when coming back)
1.1(9+2) = 1.1(11) = 12.1 miles
12.1 - 11 = 1.1 miles
The speeds 9 mph and 11 mph are now proven to be the right speeds. Using our equation before, we can figure out the distance from the starting point that they meet at. This is just how far the slower runner has gotten. So, 1.1(9) = 9.9 miles from the starting point
The runners meet at a distance of 8.8 miles from the starting point.
How to determine the time required for two runners to meet each otherAccording to statement, each runner must run back and forth on a 11-mile course. After supposing that each runner moves at constant speed, expressions for each runner are presented below:
Fast runner reaches the end
[tex](v+2)\cdot 1.1 = 11[/tex] (1)
Fast runner comes back from the end
[tex]x = \left(v+2\right)\cdot (1.1-t)-(v+2)\cdot t[/tex] (2)
Slow runner meets fast runner
[tex]x = v\cdot 1.1[/tex] (3)
Where:
[tex]v[/tex] - Speed of the slow runner, in miles per hour.[tex]t[/tex] - Comeback time of fast runner, in hours.[tex]x[/tex] - Point of the track where runners meet each other, in miles.By (1), we obtain the speed of the slow runner:
[tex]v = \frac{11}{1.1}-2[/tex]
[tex]v = 8\,\frac{mi}{h}[/tex]
The position from the starting point is calculated by (3):
[tex]x = (8\,mi)\cdot \left(1.1\,h\right)[/tex]
[tex]x = 8.8\,mi[/tex]
The runners meet at a distance of 8.8 miles from the starting point. [tex]\blacksquare[/tex]
To learn more on linear functions, we kindly invite to check this verified question: https://brainly.com/question/17058347
Beyonce is solving a system of equations: 2x – 3y = -2
4x + y = 24
She decides to use the elimination method to find the solution. She multiplies the second equation by 3 and adds it to the first equation to find 14x = 70, showing her that x = 5. Beyonce finds that y = 4.
Step 3: 4x + y = 24
4(5) + y = 24
20 + y = 24
-20 -20
y = 4
Step 1: 3(4x + y = 24) → 12x + 3y = 72
Step 2: 2x – 3y = -2
Solution: (5, 4)
+ 12x + 3y = 72
14x = 70
→ x = 5
Thinking about this process, Beyonce says out loud, “There are lots of ways I could go about solving this problem. I could do the method above or I could multiply the first equation by -2 and add the second.
Step 3: 4x + y = 24
4x + 4 = 24
-4 -4
4x = 20
x = 5
Step 1: -2(2x – 3y = -2) → -4x + 6y = 4
Solution: (5, 4)
Step 2: -4x + 6y = 4
+ 4x + y = 24
7y= 28
→ y = 4
“I seem to find that there is only one solution to the two equations, but I wonder if I will get the same solution if I use a different method?”
If Beyonce uses a different method, would she get the same solution? Be sure to show work or explain your reasoning.
Answer:
Step-by-step explanation: