Find the value of x. Round the length to the nearest tenth.
PLEASE EXPLAIN HOW YOU GOT THE ANSWER
Answers
35 squared +12 squared = 1369
[tex]\displaystyle{ tan(35^o)= \frac{opposite \ side }{adjacent \ side } [/tex],
where the "opposite side" means the opposite side to angle with measure [tex]35^o[/tex], and "adjacent side" means the adjacent side to angle with measure [tex]35^o[/tex].
[tex]tan(35^o)[/tex] is a constant which can be found using a calculator.
In the calculator of the pc press: view - scientific - 35 - tan.
This gives [tex]tan(35^o)=0.7[/tex]
Thus, back in the equation [tex]\displaystyle{ tan(35^o)= \frac{opposite \ side }{adjacent \ side } [/tex] we substitute as follows and solve:
[tex]\displaystyle{0.7= \frac{x }{12 }\\\\[/tex]
[tex]x=0.7\cdot12=8.4[/tex]
Answer: 8.4 cm
Related Questions
What is the product of −412 and 212 ? Enter your answer as a mixed number, in simplified form, in the box.
Answers
It seems that the two factors are - 4 + 1/2 and 2 + 1/2.
Let's use latex for better underestanding:
[tex](-4 \frac{1}{2} ).(2 \frac{1}{2} ) = (-4 - \frac{1}{2} ).(2+ \frac{1}{2} )=(- \frac{9}{2} ).( \frac{5}{2})=- \frac{45}{4} = -( \frac{44 + 1}{4} ) = - 11 \frac{1}{4} [/tex]
Answer: - 11 1/4
In Mrs. Johnson's class there are 28 student desks each desk measures 26.17 inches long if you were to line up all the desks end to end how long would all the desk be?
Answers
number of desks* how long it measures = total measurement
28*26.17
=732.76 inches
Jolinda scores 21 points during her basketball game. Her team scores a total of 28 points. What fraction of the team’s points does Jolinda score? Choose the answer in simplest form.
Answers
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
If Jolinda scored 21 points of 28 total, the fraction is:
[tex]\frac{21}{28}=\frac{3}{4}= 0.75(or75\%)[/tex]
Remember that a fraction is the representation of a portion among the total.
In addition, this fraction also would represent the effectiveness of Jolinda, we could say that she is able to score a 75% of team's points.
solve the inequality
6n-3 > -18
a. n > -2.5
b. n > -3.5
c. n < -2.5
d. n > 2
Answers
n > 2 {divided each side by -6 and changed the inequality sign}
B.) n > 2
Suppose a triangle has sides a, b, and c, and let theta be the angle opposite the side of length a. If cos theta > 0 what must be true?
A. a2 + b2 > c2
B. a2 + b2 = c2
C. b2 + c2 < a2
D. b2 + c2 > a2
Answers
When cosθ >0 then , b² + c² > a².
What is triangle?
" Triangle is a 2 dimensional shape which is having three sides and three vertices. Sum of all the interior angles of a triangle is 180°."
Formula used
As per Cosine Rule
For a given ΔABC,
cosθ = [tex]\frac{b^{2} + c^{2} - a^{2} }{2bc}[/tex]
According to the question,
cosθ >0
⇒ [tex]\frac{b^{2} + c^{2}-a^{2} }{2bc}[/tex] >0
⇒ b² + c² >a²
Hence, we conclude that Option D is correct.
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The probability that an event will occur is 100%. Which of these best describes the likelihood of the event occurring?
Likely
Certain
Unlikely
Impossible
Answers
Answer: Certain
Step-by-step explanation:
A probability is from 0 - 1, if not 0 or 1 it is a fraction, percentage, or decimal. 100% also equal to 1 is the highest amount you can get, therefore the answer is certain.
A solid right pyramid has a square base with an edge length of x cm and a height of y cm. Which expression represents the volume of the pyramid?
Answers
The correct expression representing the volume of the pyramid is:
[tex]\[ \frac{1}{3} \times x^2 \times y \[/tex]. Therefore the correct option is 2.
The volume [tex]\( V \)[/tex] of a pyramid is given by the formula:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
For a square pyramid, the base area is given by [tex]\( \text{Base Area} = \text{side length}^2 \)[/tex].
In this case, the side length is [tex]\( x \)[/tex] and the height is [tex]\( y \)[/tex]. Therefore, the expression for the volume [tex]\( V \)[/tex] is:
[tex]\[ V = \frac{1}{3} \times x^2 \times y \][/tex]
Now, let's compare this with the given options:
1. [tex]\( \frac{1}{3}xy \)[/tex] cm³
2. [tex]\( \frac{1}{3}x^2y \)[/tex] cm³
3. [tex]\( \frac{1}{2}xy^2 \)[/tex] cm³
4. [tex]\( \frac{1}{2}x^2y \)[/tex] cm³
Now, we can see that the correct expression representing the volume of the pyramid is:
[tex]\[ \frac{1}{3}x^2y \, \text{cm}^3 \][/tex]
So, the correct option is option 2: [tex]\( \frac{1}{3}x^2y \)[/tex] cm³.
The correct expression representing the volume of the pyramid is:
[tex]\[ \frac{1}{3} \times x^2 \times y \[/tex]
Complete question:
A solid right pyramid has a square base with an edge length of x cm and a height of y cm. Which expression represents the volume of the pyramid?
1. [tex]\( \frac{1}{3}xy \)[/tex] cm³
2. [tex]\( \frac{1}{3}x^2y \)[/tex] cm³
3. [tex]\( \frac{1}{2}xy^2 \)[/tex] cm³
4. [tex]\( \frac{1}{2}x^2y \)[/tex] cm³
Suppose you need to buy fabric to make costumes for a school play. The budget is $16 for each costume.
You need 12 costumes made from brown fabric. Each brown costume needs 3.25 yards of fabric. You need 8 costumes made from red fabric. Each red costume needs 3.5 yards of fabric.
You have gotten prices from two stores.
Store A: Brown fabric is $4.25 per yard. Red fabric is $4.75 per yard. On any purchase over $40, you will receive a $10 coupon for your next purchase. This store is 5 miles from school.
Store B: Both fabrics are $4.50 per yard. This store is walking distance from school.
What is the maximum budget for the fabric?
Answers
Hope this helped!
20 x 16 = 320
The maximum budget for the fabric is $320
Consider the following equation, bh+hr=25 when solving for h
Answers
2.) Divide out b+r: h=25/(b+r)
The answer is 25/(b+r)
Answer:
[tex]h=\frac{25}{b+r}[/tex]
Step-by-step explanation:
Given equation,
[tex]bh+hr=25[/tex]
For solving this equation for h,
We need to isolate h in the left side of the equation,
We can write,
[tex]h(b+r) = 25[/tex] ( by the converse of distributive property ),
Divide both sides by b + r,
[tex]h=\frac{25}{b+r}[/tex]
Which is the required equation.
Decide which of the two points lies on the graph of the line
X= -3
A. 2,-3
B. -3,2
Answers
hope this helps
How to find the slope of a line perpendicular to each given line?
Answers
Ex:
slope= 2/3
perpendicular slope= -3/2
A train travels from city a to city b and then to city
c. the distance from a to b is 200 miles and the distance from b to c is 70 miles. the average speed from a to b was 50 miles per hour, and the average speed from b to c was 35 mph. what was the average speed from a to c (that is for the entire trip) in miles per hour?
Answers
sam and bethan share £54 pounds in the ratio 5:4 workout how much each person gets
Answers
ratio is 5:4
5+4 =9
54 pounds divided by 9 = 6
6*5 = 30
6*4 = 24
Sam gets 30 pounds Bethan gets 24 pounds
Rectangle ABCD is transformed to AB’C’D’ by a dilation .What is the scale factor used for the dilation ?
Answers
Answer: The required scale factor that is used for the dilation is 3.
Step-by-step explanation: Given that the rectangle ABCD is transformed to A'B'C'D' by a dilation.
We are to find the scale factor that is used for the dilation.
We know that
the scale factor of dilation is defined as
[tex]S=\dfrac{\textup{the length of a side of the dilated figure}}{\textup{the length of the corresponding side of the original figure}}.[/tex]
From the graph, we see that
in rectangle ABCD, the length the side AB is 2 units
and
the length of the corresponding side A'B' in the dilated rectangle A'B'C'D' is 6 units.
Therefore, the scale factor of dilation is given by
[tex]S=\dfrac{A'B'}{AB}=\dfrac{6}{2}=3.[/tex]
Thus, the required scale factor that is used for the dilation is 3.
solve the system by substitution
2x-y+z=-4
z=5
-2x+3y-z=10
Answers
To solve the system by substitution, substitute the value of z in the equations and solve them simultaneously.
Explanation:To solve the system by substitution, we need to substitute the value of z in the other equations. Given that z=5, we can substitute this value in the first and third equations:
2x - y + 5 = -4
-2x + 3y - 5 = 10
Now, we can solve these two equations simultaneously to find the values of x and y.
To solve a system of equations by substitution, express one variable in terms of the other and substitute it into the other equations to eliminate that variable before solving for the remaining variables.
Explanation:To solve this system of equations by substitution:
Start by expressing one variable in terms of the other variable from one of the equations. In this case, we can express z as 5 since it is given.Substitute the value of z into the other two equations to eliminate the variable z.Solve the resulting system of equations for the remaining two variables.By following these steps, you can find the values of x, y, and z that satisfy the system of equations.
5k+(−2k)−(−1) what is the answer please give it to me
Answers
What is the value of y?
Enter your answer in the box.
y =
Answers
Answer-
[tex]\boxed{\boxed{y^{\circ}=26^{\circ}\ 45'}}[/tex]
Solution-
As the triangle ABC is an isosceles triangle, with AC = BC.
So the angles A and B will be same, i.e
[tex]\Rightarrow \angle A=\angle B[/tex]
[tex]\Rightarrow 34^{\circ}=(x-5)^{\circ}[/tex]
[tex]\Rightarrow x^{\circ}=34^{\circ}+5^{\circ}[/tex]
[tex]\Rightarrow x^{\circ}=39^{\circ}[/tex]
As sum of all angles in a triangle is 180°, so
[tex]\Rightarrow \angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]\Rightarrow 34^{\circ}+39^{\circ}+4y^{\circ}=180^{\circ}[/tex]
[tex]\Rightarrow 4y^{\circ}=180^{\circ}-34^{\circ}-39^{\circ}[/tex]
[tex]\Rightarrow 4y^{\circ}=107^{\circ}[/tex]
[tex]\Rightarrow y^{\circ}=\dfrac{107^{\circ}}{4}[/tex]
[tex]\Rightarrow y^{\circ}=26.75^{\circ}[/tex]
[tex]\Rightarrow y^{\circ}=26^{\circ}\ 45'[/tex]
Walter's savings account has a balance of $273. After 5 years, what will the amount of interest be at 5% compounded quarterly? a. $6.83 c. $77.00 b. $68.00 d. $82.00
Answers
Answer:
c
Step-by-step explanation:
Consider kite FGHJ. What are the values of a and b?
Answers
Answer:
Hmmm... interesting on my final I answered B: a=14, b=8 and got it wrong but, when I did it again I got C: a=17, b=6
Step-by-step explanation
Answer:
The value of a=17 cm and b=6 cm
C is correct option.
Step-by-step explanation:
Given: FGHJ is a kite.
Kite has property their adjacent sides are equal. Top two side of the kite is equal and bottom two side of the kite is equal.
FG=GH because ∠F=∠H.
30=2a-4
2a=34
a=17 cm
Similarly, ∠F=∠H
FJ=HJ
3b+6=24
3b=18
b=6 cm
Hence, The value of a=17 cm and b=6 cm
factor by grouping: 12x^3-20x+3x-5
Answers
1,705x-5
F(x) = 4x^2+1
Group 1: 3x-5
Group 2: 12x3-20x2
This is going to take a long time to explain so the answer is just (12x2 - 12x - 5) • (x + 1)
F(x) = |x − 1| find the derivative from the left at x = 1. if it does not exist, enter none.
Answers
A graph of the function is shown below.
The function is either
f(x) = x-1, for x>1
or
f(x) = 1-x, for x<1
Therefore
f'(x) = 1, for x>1
and
f'(x) = -1, for x<1
Answer: -1
What Is The Perimeter Of The triangle ? A(1,2) B(4,6) C(4,2)
Answers
you can pretty much get AC and BC right off the grid.
now, let's check how long is AB then.
[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ 1}}\quad ,&{{ 2}})\quad % (c,d) B&({{ 4}}\quad ,&{{ 6}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ AB=\sqrt{(4-1)^2+(6-2)^2}\implies AB=\sqrt{3^2+4^2} \\\\\\ AB=\sqrt{9+16} \implies AB=\sqrt{25}\implies AB=5[/tex]
so the perimeter will then be AB + BC + AC.
Translate the following phrase into an algebraic expression or equation.
the square of the difference of two numbers
Answers
(x - y)^2
Done.
Twice a number decreased by seven
Answers
Which element is located at B42?
Answers
Introduction to addition or subraction of fractions with different denominator 2/3+1/4
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finding lcm which is 12. 2/3 + 1/4=8+3/12
=11/12
A water tank can hold 234 cubic meters of water. How many gallons can the water tank hold?
A. 6,176 gallons
B. 61,776 gallons
C. .886 gallons
D. 23,400 gallons
Answers
Approximately, 1 cubic meter is equal to 264.172 gallons.
i hope this helps you
1 cubic meter of water = 264 gallons of water
264*234 would be your equation :)
The measurement of the complement of an angle exceeds the measure of the angle by 25%. Find the measurement of the angle and its complement.
Answers
Complimentary angles, therefor
A + C = 90
The measurement of the complement of an angle exceeds the measure of the angle by 25% (you used a % sign so I'll use % instead of degrees)
C = 1.25A
Substitute
A + 1.25A = 90
2.25A = 90
A = 40º <-----
C = 50º <-----
------------------------------
If you meant 25º
A + (A + 25) = 90
2A + 25 = 90
2A = 65
A = 32.5º
C = 57.5º
The angle measures 40 degrees, and its complement, which is 25% larger than the angle, measures 50 degrees. This is solved using elementary algebra by setting up an equation with the angle as 'x' and its complement as '90-x', and then simplifying the equation to solve for 'x'.
Explanation:The question involves finding the measure of an angle and its complement when given that the complement exceeds the measurement of the angle by 25%. To solve this, let's use algebra. Let the measure of the angle be x degrees.
Since the complement of an angle adds up to 90 degrees with the angle itself, the complement can be represented as 90 - x degrees. According to the problem, the complement is 25% more than the angle, so we can write the equation:
90 - x = x + 0.25x
Simplifying, we get:
90 - x = 1.25x
90 = 2.25x
Dividing both sides by 2.25 gives us the measure of the angle x:
x = 40 degrees
Since the complement is 90 - x, we find:
Complement = 90 - 40 = 50 degrees
Therefore, the angle measures 40 degrees, and its complement measures 50 degrees.
PLEASE HELP ME BOTH MY TUTORS LEFT AT THE SAME TIME I NEED MAJOR HELP!!! PPPPLLLLEEEEAAAASSSSEEE
What is the length of an arc with a central angle of 5/4π radians and a radius of 34 centimeters?
Use 3.14 for pi.
Enter your answer, as a decimal, in the box.
What is the value of y?(picture)
Enter your answer in the box.
Round your final answer to the nearest whole number.
What is tanB ? (picture)
Enter your answer, as a simplified fraction, in the box.
Based on the diagram, what is tanA ?(picture)
Enter your answer in the boxes.
What is the value of x?
sin(x+34)°=cos(2x+20)°
Enter your answer in the box.
What is the value of x?
cos63°=sinx
Enter your answer in the box.
Answers
The formula to use is
s = r*theta
where,
s = arc length
r = radius
theta = angle in radians
Note: if the angle is not in radians, you have to convert it over to radians. However, in this case we are told the angle is "5pi/4 radians". So no conversion is needed.
In this case,
s = unknown (this is what we want to solve for)
r = 34
theta = 5pi/4
keep in mind that 5pi/4 is the same as (5/4)*pi
----------------------------
Plug the value of r and theta into the formula to get...
s = r*theta
s = 34*(5pi/4)
s = (34*5/4)*pi
s = 42.5*pi
s = 42.5*3.14
s = 133.45
----------------------------
----------------------------
Final Answer: 133.45
===============================================
Problem 2
sin(angle) = opposite/hypotenuse
sin(61.7) = 8/y
y*sin(61.7) = 8
y = 8/sin(61.7)
y = 9.08598042654456 ... use a calculator
y = 9 ... rounding to the nearest whole number
----------------------------
----------------------------
Final Answer: 9
===============================================
Problem 3
We need to know the length of BC. Let's call this x for now. Use the pythagorean theorem to find x
x^2 + 14^2 = 50^2
x^2 + 196 = 2500
x^2 + 196-196 = 2500-196
x^2 = 2304
sqrt(x^2) = sqrt(2304)
x = 48
So BC = 48 units long
Now we can compute the tangent of angle B
----------------------------
tan(angle) = opposite/adjacent
tan(B) = AC/BC
tan(B) = 14/48
tan(B) = 7/24
----------------------------
----------------------------
Final Answer: 7/24
===============================================
Problem 4
In this current stage, I cannot answer this question because the image isn't showing up. On my end, all I see is a black rectangle with no triangle showing. It seems like some kind of glitch is happening. Please repost this image. Thank you.
===============================================
Problem 5
There are multiple answers here so it seems like there should be a restriction. Does it state what the restriction must be? Please let me know. Thank you.
===============================================
Problem 6
Rule:
sin(x) = cos(90-x)
where x is an angle in degrees
----------------------------
Using that rule mentioned above, we can replace the "sin(x)" term with "cos(90-x)" then solve for x
cos(63) = sin(x)
cos(63) = cos(90-x)
both arguments must be equal, so 63 must be equal to 90-x
63 = 90-x
63+x = 90-x+x
x+63 = 90
x+63-63 = 90-63
x = 27
----------------------------
----------------------------
Final Answer: 27
Which of the following points is a solution of the inequality y < -|x|?
a. (1,-2)
b. (1,-1)
c. (1,0)
Answers
You can substitute each point into the inequality which gives you the answer of a
None of the given points is the solution to the inequality y < -|x|.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given inequality,
y < -|x|
As per the given below, the dotted line is not included in the region thus, point (1,-1) is not included.
Hence "None of the given points is the solution to the inequality y < -|x|".
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