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In the lower triangle, one of the angles of which is 45 degrees, we know:
In the triangle, the side facing the angle 45° is √2 / 2 times the hypothenuse.
Thus ;
[tex]10 = hypothenuse \times \frac{ \sqrt{2} }{2} \\ [/tex]
[tex]hypothenuse \times \frac{ \sqrt{2} }{2} = 10 \\ [/tex]
Multiply sides by 2
[tex]hypothenuse \times \sqrt{2} = 2 \times 10[/tex]
Divide sides by √2
[tex]hypothenuse = \frac{2 \times 10}{ \sqrt{2} } \\ [/tex]
[tex]hypothenuse = \frac{ \sqrt{2} \times \sqrt{2} \times 10 }{ \sqrt{2} } \\ [/tex]
[tex]hypothenuse = 10 \sqrt{2} [/tex]
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♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
The common side of the triangles is hypothenuse for both.
[tex]hypothenuse \times \cos(60) = x[/tex]
[tex]10 \sqrt{2} \times \frac{1}{2} = x \\ [/tex]
[tex]x = \frac{2 \times 5 \sqrt{2} }{2} \\ [/tex]
[tex]x = 5 \sqrt{2} [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
The correct answer is the Third Option .
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Related Questions
During a 60-minute period, a traffic engineer counted 66 trucks and cars that crossed a bridge. The ratio of trucks to cars that travel across the bridge is usually 3:8. The equation 3 8 = t 66 − t 3 8 = t 66 − t can be used to predict the number of trucks, t, the engineer should have counted. How many trucks should the engineer have counted?
Answers
Answer:
18
Step-by-step explanation:
t = Number of trucks counted
c = Number of cars
Ratio of trucks to cars = [tex]\dfrac{t}{c}=\dfrac{3}{8}[/tex]
Total number of cars and truck = 66
[tex]t+c=66[/tex]
Divide the left and right side by the number of cars
[tex]\dfrac{t+c}{c}=\dfrac{66}{c}\\\Rightarrow \dfrac{t}{c}+1=\dfrac{66}{c}\\\Rightarrow \dfrac{3}{8}+1=\dfrac{66}{c}\\\Rightarrow \dfrac{11}{8}=\dfrac{66}{c}\\\Rightarrow c=66\times \dfrac{8}{11}\\\Rightarrow c=48[/tex]
Total number of cars is 48
so
[tex]t=66-c\\\Rightarrow t=66-48\\\Rightarrow t=18[/tex]
Total number of trucks counted is 18.
Pls help i will mark brainliest シ♡︎
Answers
Answer:
D:95 mm Hg
Step-by-step explanation:
Using the linear model, y=x+95, x represents the age and y represents the blood pressure.
For a newborn, x=0 this gives us
> y=0+95 = 95<
Answer: 1mm hg per year
Step-by-step explanation:
PLEASE HELP I WILL MARK AND 5 STARS SOLVE AND EXPLAIN THANKS
Answers
I have 1 word problem and a math problem. (word prob)A light-year is the distance that light travels in a year and is equivalent to 9.461 * 10^12. Write this distance in standard form.
(math prob) Order the list of numbers from least to greatest.
8.5*10^12,3.6*10^8,5.85*10^-3, 2.5*10^-1,8.5*10^8. ( This ^ means there are square roots for the numbers).
My math class is real soon. Pls, answer them. Thanks!!
Answers
Answer:
1. 9461000000000
move the desimal in 9.461 12 places to the right to get:
9461000000000
2.
5.85 x 10^-3,
2.5 x 10^-1,
3.6 x 10^8,
8.5 x 10^8,
8.5 x 10^12
the smallest exponent is the smallest. Since 8.5 x 10^8 and 3.6 x 10^8 have the same exponent, go to the desimal
1. The circle C has centre (5,k), where k is a constant. The line y = 2x + 1 is tangent to C at point
A (3,7). Find the equation of C.
Answers
Answer:
[tex](x-5)^2+(y-6)^2=5[/tex]
Step-by-step explanation:
Equation of the Circle
A circle centered at (h,k) and radius r can be written with the equation:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We are given the center (5,k), thus:
[tex](x-5)^2+(y-k)^2=r^2[/tex]
We know the point (3,7) belongs to the circle. This means the distance between the center and this point is the radius.
Given two points (x1,y1) and (x2,y2), the distance between them satisfies:
[tex]d^2=(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Calculating the radius, we have:
[tex]r^2=(7-k)^2+(3-5)^2[/tex]
[tex]r^2=(7-k)^2+4\qquad\qquad [1][/tex]
Now we use the fact that the line y=2x+1 and the circle are tangent at (3,7). The radius and the line are perpendicular at that point. Two perpendicular lines with slopes m1 and m2 satisfy the condition:
[tex]m_1\cdot m_2=-1[/tex]
The line y=2x+1 has a slope of m1=2, thus the slope of the segment from (5,k) to (3,7) has a slope of -1/2:
The slope is calculated as:
[tex]\displaystyle \frac{7-k}{3-5}=-\frac{1}{2}[/tex]
Operating:
[tex]\displaystyle \frac{7-k}{-2}=-\frac{1}{2}[/tex]
Multiplying by -2
[tex]\displaystyle 7-k=1[/tex]
Solving:
k=6
From [1] the radius is:
[tex]r^2=(7-6)^2+4[/tex]
[tex]r^2=1+4[/tex]
[tex]r^2=5[/tex]
Finally, substituting into the equation of the circle:
[tex]\mathbf{(x-5)^2+(y-6)^2=5}[/tex]
The graph can be seen in the figure below.
Answer:
Step-by-step explanation:
Which number sentence is true?
A. –2.0 + (–0.5) = 2.5
B. –4.5 + 6.5 = –2.0
C. 3.0 + (–0.5) = –2.5
D. 5.5 + (–2.5) = 3.0
answer soon please!
Answers
Answer:
B. and D.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Here are the correct sums:
A. –2.0 + (–0.5) = -2.5
B. –4.5 + 6.5 = 2.0
C. 3.0 + (–0.5) = 2.5
D. 5.5 + (–2.5) = 3.0
Only D is correct.
Answer: D
Guys can you plz help me Answer this QUESTION!!!!!!
Answers
Answer:
C - 9
Step-by-step explanation:
pls give branliest
ANSWER ASAP PLEASE AND SHOW YOUR WORK!!!!
Algebraically determine whether the following function is Even, Odd, or Neither.
f(x)= x^3-2x
Answers
Answer:
f(-x)= -f(x) so, the given function [tex]f(x)= x^3-2x[/tex] is Odd
Step-by-step explanation:
We need to determine if the function [tex]f(x)= x^3-2x[/tex] is Even, Odd, or Neither.
Determining if a function f(x) is even or not we put x=-x and check
If f(-x)=f(x) the function is even
if f(-x)= -f(x) the function is odd
So, Putting x =-x and determining if the given function [tex]f(x)= x^3-2x[/tex] is Even, Odd, or Neither.
[tex]f(x)= x^3-2x\\Put \ x=-x\\f(-x)=(-x)^3-2(-x)\\f(-x)=-x^3+2x\\f(-x)=-(x^3-2x)\\f(-x)=-f(x)[/tex]
As f(-x)= -f(x) so, the given function [tex]f(x)= x^3-2x[/tex] is Odd
ASAP answer it please.!!!!!!!!!!!!!!!!!!! thank uuu
Answers
Answer:
X=120 and y=10,z=120
Step-by-step explanation:
corresponding angles
thus 120=(13y-10)=x
A biker cycles 9 miles in 2 3 of an hour. b The distance here varies directly with time. What is the constant of variation? (It is the hikers’ rate .)
Answers
Answer:
27/2
Step-by-step explanation:
Hope this helps! Also dont add comments to get gems like bruh ;-;
Answer: 27/2
Step-by-step explanation:
[tex]9\cdot \:1=x\frac{2}{3}[/tex]
[tex]x\frac{2}{3}=9\cdot \:1[/tex]
[tex]x\frac{2}{3}=9[/tex]
[tex]3x\frac{2}{3}=9\cdot \:3[/tex]
2x= 27
x= 27/2
Add Me Brainliest!
The temperature at midnight was −11°C. By midday, the temperature was 5°C.
What was the temperature during the morning?
Explain what method you used to find the temperature change.
Answers
Answer:
-3 celcius
Step-by-step explanation:
Answer:
6 ℃
Step-by-step explanation:
by substacring u will see it
Evaluate each value expression for the given value of x : 22-x/5 , x=20
HURY!!!!!!!!!!!
Answers
22-20/5
22-4
=18
Answer:
10 maybe sorry if wrong
Step-by-step explanation:
22-x x=20 so that should be 2 then u do 2x5 =10
On your last math quiz, you got 15
out of 20 questions correct. What is
your percentage of correct answers?
Answers
Answer: 75%
Step-by-step explanation: So 15/20 simplified is 3/4 and 3 divided by 4 equals 0.75. To convert a decimal to a percentage, you multiply 0.75 by 100 to get 75%.
What is the slope of the line passing through the points (-6, 33) and (-2, 15)?
Please answer quick
Answers
Answer:
The slope is -9/2
Step-by-step explanation:
m=y²-y¹/x²-x¹
m=15-33/(-2)-(-6)
m=-18/4
m=-9/2
Ed wants to buy a basketball for $5, but
his bank account only contains $3. If Ed
purchasos tho baskotball, how much
money will his bank account show?
Answers
solve for x: -5|x + 1| = 10
Answers
Answer:
x=-3
Step-by-step explanation:
-5(x+1)=10
-5x-5=10
-5x= 15
x=-3
What is the square root of 40000 step by step
Thx for everything that answers
Answers
The answers 200 of u have an iPhone u can ask siri what the square root of whatever number is and it will tell u the correct answer
Which of the following shows 2.736 correctly rounded to the tenths place?
2.74
2.7
2.8
3
Answers
Answer:
2.7
Step-by-step explanation:
The 3 does not round up the 7, so it stays as 2.7
Answer:
2.7
Step-by-step explanation:
the tenths place is the first number after the decimal. When rounding numbers 5 and higher can increase the number next to it by 1. So 2.736 becomes 2.74 then becomes 2.7 as the 4 is not able to round the number since it is below 5.
What is the formula for the area of this triangle?
Answers
Answer:
A = h b/2
Step-by-step explanation:
Answer:
J =6,L=5,K=3
Step-by-step explanation:
this is kinda hard to do bur I'll try to do it.
HEELLLPP MEEEE PLZZZZ!!!!!
Answers
Use the distance formula to find base and height.
No rush on this one:)
The price of a shirt decreases by 13$. Which integer represents the decrease in the shirt’s price?
Answers
Answer:
-13
Step-by-step explanation:
-13 since it's going down in price
How do you find the slope of the table below
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Pick any two sets and plug in.
(24-16)/(21-14) = 8/7
The median of the set (n, n+5, n+6, n+9, n+15) is 9. What is the mean?
HELP ME
Answers
Answer: 10
Step-by-step explanation:
tbh its too long to explain i gtg now but plz just trust me
b+b-1+b+b+10=___b+9
whats the blank spot??
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The distance from Philadelphia to Harrisburg is 5 inches on the map. The actual distance is 100 miles. The distance from Allentown to Harrisburg is 4 1/20 inches on the map. What is the actual distance, in miles, from Allentown to Harrisburg?
A.) 81 miles
B.) 405 miles
C.) 65 miles
D.) 84 miles
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Answer:
A. 81 miles
Step-by-step explanation:
ANSWER PLSSS THANK YOUUUUU
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Answer:
As a fraction: 81/100 (cannot be simplified) Decimal: 0.81 and a percent 81%
Step-by-step explanation:
Count the blocks and convert (you can also use an array.) Hope this helps you!
Answer:
Fraction: 81/100
Decimal: 0.81
Percent: 81%
Step-by-step explanation:
The box is a 10x10 so it has 100 squares inside.
There are 81 squares shaded so the fraction would be 81/100
To get the decimal just divide 81 by one hundred so the decimal is .81
As a percent is would be 81%
Hope this helps ya!!
15. Which expression has the greatest value?
A. 142-(-172)
B. 1 12+ -1 12
C. -142 - (-14)
D. 142
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Answer:
i think that its D
Step-by-step explanation:
hopes this helps
(BRAINLYEST TO RIGHT ANSWER) pls i need help!
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Answer:
What is the question?
Step-by-step explanation:
Answer:
where is the question
Step-by-step explanation:
Need help with this pls
Answers
Answer:
hi
Step-by-step explanation:
hi
Complete the following statement.
24 ft = in.
Answers
Answer:
288
Step-by-step explanation:
1 foot= 12 inches
24x12=288
Answer:288
Step-by-step explanation:24x12=288 hope this helps