What is the value of x?
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The figure shows 2 right triangles, triangle A B C with right angle B and triangle B D C with right angle D. The measure of angle B A C is 45 degrees. The measure of angle D B C is 60 degrees. The length of side C A is 6 square root 2. The length of side B D is x.
Answers
Answer:
x=3
Step-by-step explanation:
I took the test and I got it right but if you want an explanation see bellow.
so triangle ABC is a 45- 45 -90 and we are given the hypotenuse of [tex]6\sqrt{2}[/tex]
and on a 45-45-90 triangle we know that the hypotenuse is always [tex]s\sqrt{2}[/tex] s standing for the lengths of both of the legs since they are both equal, so this tells us that line segment AB and BC are equal to 6, SO triangle BCD hypotenuse is equal to 6.Triangle BCD is a 60-90-30 triangle as we can tell by the measures given, and in a 60-90-30 triangle the hypotenuse is equal to S and it's shorter length known as line segment BD on this triangle is equal to [tex]\frac{s}{2}[/tex] and since we know s=6 we can do [tex]\frac{6}{2}[/tex] giving us our answer 3.
Using the sine ratio and the cosine ratio, the value of x in the given triangle is calculated as: x = 6.
How to Find the Value of x?Using the sine ratio, find BC:
sin ∅ = opposite/hypotenuse
Given the following:
∅ = 45°
hypotenuse = 6√2
opposite = BC
Substitute:
sin 45 = BC/6√2
sin 45 = BC/6√2
√2 = BC/6√2 [sin 45 = √2]
BC = √2 * 6√2
BC = 12 units
Use the cosine ratio to find x:
cos ∅ = adjacent/hypotenuse
Thus, we have:
cos 60 = x/12
1/2 = x/12 [cos 60 = 1/2]
2x = 12
x = 6.
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Related Questions
5. Which side lengths form a right triangle?
Check all that apply.
Answers
Answer:
=> 6.5, 7.2 , 9.7
Step-by-step explanation:
By using Pythagorean theoram
H² = P² + B²
=> (9.7)² = (7.2)² + (6.5)²
=> 94.09 = 51.84 + 42.25
=> 94.09 = 94.09
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
c
Step-by-step explanation:
because 3 x 3 = 9
1 x 5 = 5
simplest form will be 1 4/5
What are the y-intercept and the horizontal asymptote of g(x) = 7x + 2?
(0, 3) ; y = 2
(0, 4) ; y = 7
(0, 7) ; y = 2
(0, 9) ; y = 7
please hurry
Answers
Put x =0 to find y intercept
7(0)+20+22Y intercept:-
(0,2)Horizontal asymptote=y=2
Adult tickets for the evening show at XD Theater are $16 and children's tickets are $8. If the theater seats 282 people, how many adult
tickets must be sold for $2416 of total sales?
Answers
What expression is equivalent to 4 (3x-2)
Answers
Answer:
12x-8
Step-by-step explanation:
In order to take away the parentheses, we have to multiply all terms inside the parentheses by 4. 4*3x = 12x, and -2*4 = -8. So we can determine at 4(3x-2) = 12x-8.
what is the median in 72 77 75 72 70 69 71 78 75 68 62 69 65 63 68 53 57 79 77 75 80 73 71 64 71 64 50 50 55 55
Answers
Answer:
The median is 69.5
Step-by-step explanation:
The median is also known as the middle value. To find the median, you first arrange your data in numerical order.
Numerical order:
50, 50, 53, 55, 55, 57, 62, 63, 64, 64, 65, 68, 68, 69, 69, 70, 71, 71, 71, 72, 72, 73, 75, 75, 75, 77, 77, 78, 79, 80
There are 30 numbers, which means that the median is between the 15th and 16th value (69 and 70).
69 + 70 = 139
139/2 = 69.5
Therefore, the median of this data set is 69.5
Hope this helps!
Last year the depth of the river was 4.2 feet deep. This year it dropped 9% Find the depth of the river this year
Answers
Answer: 3.822
Step-by-step explanation: 9/100 × 4.2 = 0.378
Deduct from 4.2
find the are of the shape below
Answers
Answer:
Area is 235
Step-by-step explanation:
Split the shape evenly so 11 x 14 and 9 x 9then multly and add
when slpitting up the number some times you have to add or subtract so to get 9 x 9 we just take 20 then take away 11 due to the line going through 20 and 20 - 11 = 9
9 x 9 = 81
11 x 14 = 154
81 + 154 = 235
or
Simular to the first one but the cutting line is different. this time the line cuts through 14
9 x 20 = 180
11 x 5 = 55
180 + 55 = 235
16 Select the correct answer. Jonathan opened an auto repair shop. In the first month, 11 cars were serviced at his shop. After the first month, the total number of cars serviced at Jonathan's shop increased by 9 cars per month. How many total cars were serviced at Jonathan's shop at the end of the 7th month? O A 75 cars OB. 86 cars Oc 74 cars OD 65 cars Reset Net l rights reserved.
I just need help please
Answers
Answer:
65 cars
Step-by-step explanation:
In the first month, there are 11, then the cars increased by 9 for the last 6 months, meaning you can do 6*9=54
You can then add that to 11, which is 11+54=65
What's the range of f(x)=x+6 if x ∈(-4,-1)
Answers
Answer:
the range of is (2 , 5)Step-by-step explanation:
f(x)=x+6
f is an increasing function then the range of is
f(-4,-1) = (f(-4) , f(-1))
f(-4) = -4 + 6 = 2
f(-1) = -1 + 6 = 5
Therefore
the range of is f(-4,-1) = (2 , 5)
please solve for x 3x + 22
Answers
Answer:
The x intercept is [tex](-\frac{22}{3} ,~0)[/tex]
The y intercept is [tex](0,~22)[/tex]
Sally's soccer team played 25
games this season and lost 9 of
those games. What percent of the
games did the team win?
Answers
Answer:
64%
Step-by-step explanation:
25 - 9 = 16, so 16 of the games were won by Sally's team.
16/25 = 64% of the games were won
Help pls
What is the value of RS?
Answers
Answer:
RS = 16
Step-by-step explanation:
If a line is parallel to a side of a triangle and intersects the other 2 sides , it divides those sides proportionally.
PR is such a line , then
[tex]\frac{QR}{RS}[/tex] = [tex]\frac{QP}{PT}[/tex] ( substitute values )
[tex]\frac{32}{RS}[/tex] = [tex]\frac{42}{21}[/tex] = 2 ( multiply both sides by RS )
32 = 2 RS ( divide both sides by 2 )
16 = RS
Answer:
Your answer is, RS- 16.
Step-by-step explanation:
I hope this helps you :)
pls mark brainleist :P
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Tori
Which equation represents the graphed function? –3x 2 = y –x 2 = y x – 3 = y 2x – 3 = y
Answers
Answer:
C) 3/2x-3=y
Step-by-step explanation:
-3 because that is the Y- intercept and 3/2 is the slope of the line. Y= mx +b is the formula and m is the slope and b is the y intercept.
What is the slope of a line parallel to the line whose equation is 2x + 4y = 56.
HELP ASAP
Answers
Hi there !
Lets first try to write given line in slope intercept form which is -
❄︎[tex]\green{ \underline { \boxed{ \sf{y=mx+c}}}}[/tex]
Here-
m = slope of linec = intercept cut on y- axisProceeding-
✰2x + 4y = 56
➪ 4y = -2x +56
➪ y =[tex]\dfrac{ -2x +56}{4}[/tex]
➪ y =[tex]\dfrac{ -2x }{4}+ \dfrac{56}{4}[/tex]
➪ y =[tex]\dfrac{ -x }{2}+ 14[/tex]
➪ y =[tex]\dfrac{ -1}{2}x + 14[/tex]
Comparing with slope intercept form -
❄︎[tex]\red{ \underline { \boxed{ \sf{m = - \frac{1}{2}}}}}[/tex]
Now,
✪ Since the parallel lines have same inclination with positive x-axis , their slopes are equal.
❀ So, the slope of a line parallel to the line whose equation is 2x + 4y = 56 would be [tex]-\dfrac{1}{2}[/tex]
The equation of a line is given as:
y = mx + c
where m = slope and c = y-intercept.
The slope of the line parallel to the line 2x + 4y = 56 is -(1/2).
i.e
Slope = -(1/2)
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
y = 2x + 5
Slope = 2
y-intercept = 5
We have,
Let the equation of the line be:
y = mx + c
m = slope.
The equation is parallel to the line 2x + 4y = 56.
2x + 4y = 56 can be written in the form y = mx + c.
2x + 4y = 56
Subtract 2x on both sides.
4y = 56 - 2x
Divide both sides by 4.
y = 14 - (1/2)x
y = -(1/2)x + 14
m = -(1/2)
Since the line is parallel to the line 2x + 4y = 56 which has a
slope m = -(1/2).
The slope of the line is m = -(1/2).
Thus,
The slope of the line parallel to the line 2x + 4y = 56 is -(1/2).
i.e
Slope = -(1/2)
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- A new rectangular lawn has a
perimeter of 298 ft. and a width of
67 ft. A bag of grass seed will cover
285 ft2 of ground. How many bags
of grass seed are needed to seed
the new lawn?
Answers
The number of bags of grass seed that are needed to seed the new rectangular lawn is approximately 19 bags .
Perimeter of a rectangle
The perimeter of a rectangle is the sum of the whole sides of the rectangle.
Therefore,
perimeter of the rectangle = 298 ft
The width is 67 ft.
Hence
perimeter of rectangle = 2(l + w)
where
l = lengthw = widthTherefore,
298 = 2 ( l + 67)
298 = 2l + 134
298 - 134 = 2l
164 = 2l
l = 164 / 2
l = 82 ft
Therefore,
area of the rectangle = 82 × 67 = 5494 ft²
285 ft² = 1 bag of grass seed
5494 ft² = ?
cross multiply
number of bag of grass seed to fill the new rectangular lawn = 5494 / 285
number of bag of grass seed to fill the new rectangular lawn = 19.2771929825
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What is the solution, if any, to the inequality 10x1207
O all real numbers
O no solution
Ox20
Ox50
Answers
Answer:
i am sure options 2 please go with option 2
no solution
option b
27
5
to a mixed number
a
decimal.
Answers
Answer: 5.4 and 5⅖
Step-by-step explanation:
27/5 to a mixed number 5⅖
Decimal 5.4
Can you please help me really quick I need help with this
Answers
Check the picture below.
The tank of a car holds 10 gallons of gas.
How many liters does the tank hold? Round to the nearest tenth.
Answers
Answer:
37.9 liters
Step-by-step explanation:
Multiply the number of gallons by 3.785 to convert to liters
Multiplying by ten moves the decimal point over to the right
3.785 * 10 = 37.85
The tenths place is where the 8 is, and since 5 is [tex]\geq[/tex] (greater than or equal to) 5 that makes the 8 round up to a 9
resulting in...
10 gallons = 37.9 liters
hope this helps:)
A sample of students is taken from the school's A honor roll. The school
estimates that there are 360 students on the A honor roll. Using this sample,
how many students on the A honor roll are 8th graders?
Answers
Answer:
There are 126 8th grade A honor roll students.
Step-by-step explanation:
What is the length of the missing leg? If necessary, round to the nearest tenth
Answers
Answer:
Solution
Here,
H=?
P=3
b=6
H=√p2+B2
=√6×6+3×3
=√36+9
=√45
=3√5
Answer:
23
Step-by-step explanation:
a^2 + b^2=c^2
3=a^2
6=b^2
3×3= 9
6x6=36
36+9=45
45÷2=22.5
Need help please 10 points
Answers
πr² = π.5.5 = π25 units² or 78.5 units²
hope it helps...!!!
Look at the image for the instructions! I need this asap! I will give points, 5 stars and brainliest ((:
(This is an essay)
Answers
Answer:
1. one is smaller by 5 cm and one is larger by 5 cm
2. well they are similar to each other, but one is dilated and isn't
f x + 12 ≤ 5 − y and 5 − y ≤ 2(x − 3), then which statement is true?
Answers
y<=-x-7
(-infinity ,-x-7)
This is statement is true
Interval notation for 5-y<=2(x-3)
y=>11-2x
[11 - 2 x, ∞)
‼️⚠️⚠️‼️ HELP PLEASE WILL GIVE POINTS
Answers
Answer:
m∠ABC=42°
Step-by-step explanation:
m∠ABD=70°
⇒m∠ABD=m∠ABC+m∠CBD
⇒70°=(3x+33°)+(5x+13°)
70°=8x+46°
70°-46°=8x
24°=8x⇒x=3°
x=3°
Then,
m∠ABC=3x+33°
put x=3°, we get
m∠ABC=3×3°+33°=9°+33°
m∠ABC=42°
30 points pls helppp
Select the equation of the line that passes through the point (2, –1) and has slope 3 in point-slope form.
(y + 1) = 3(x – 2)
(y – 1) = 3(x + 2)
(x + 2) = 3(y – 1)
(x – 2) = 3(y + 1)
Answers
Answer:
(y + 1) = 3( x +2)
Step-by-step explanation:
from equation,
y - y1 = m( x - x1)
given x1=2, y1= -1
m = 3 (slope)
substitute
y - (-1) = 3( x - 2)
ans: y+1= 3(x+2)
Let p(x) = x^2 + 8x + 12 and q(x) = x^3 + 5x^2 - 6x. Define r(x) = p(x) \cdot q(x).
Find all values of x for which r(x) = 0.
Answers
The roots of the entire polynomic expression, that is, the product of p(x) = x^2 + 8x + 12 and q(x) = x^3 + 5x^2 - 6x, are x₁ = 0, x₂ = -2, x₃ = -3 and x₄ = -6.
How to solve a product of two polynomials
A value of x is said to be a root of the polynomial if and only if r(x) = 0. Let be r(x) = p(x) · q(x), then we need to find the roots both for p(x) and q(x) by factoring each polynomial, the factoring is based on algebraic properties:
r(x) = (x + 6) · (x + 2) · x · (x² + 5 · x - 6)
r(x) = (x + 6) · (x + 2) · x · (x + 3) · (x + 2)
r(x) = x · (x + 2)² · (x + 3) · (x + 6)
By direct inspection, we conclude that the roots of the entire polynomic expression are x₁ = 0, x₂ = -2, x₃ = -3 and x₄ = -6. [tex]\blacksquare[/tex]
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lily and Aiko think of a whole number aiko's numbers of 2000 when rounded to the nearest 1000 lily's number 1900 when rounded to 100 Aiko says "my number larger than Lily's!" is Aiko correct?
Answers
he has a higher chance of having the larger number but that does not make him correct
Step-by-step explanation:
Aikos number can be any where from 1501 all the way to 2499 while lily's number would have to be between 1851 and 1949.
Solve the following inequalities, if it is known that the function g is decreasing on its domain. g(5-x^2)≤g(3x-5), Dg=(-∞,4)
Answers
For the following inequalities, if it is known that the function g is decreasing on its domain. g(5-x^2)≤g(3x-5) the solution is mathematically given as
1 ≤ x < 6
What is the following inequalities g(5-x^2)≤g(3x-5)?
Generally, the equation for the inequalities is mathematically given as
g(5-x^2)≤g(3x-5)
therefore,
x^2<5x+6
-1< x <6
In conclusion, the solution to the inequalities are
1 ≤ x < 6
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