Work out the size of angle X ?
Answer:
x = 121°
Step-by-step explanation:
∠ 1 + 115° = 180°
∠ 1 = 180 - 115
∠ 1 = 65°
∠ 2 + 304° = 360°
∠2 = 360 - 304
∠ 2 = 56°
∠ 1 + ∠ 2 + ∠ 3 = 180°
65° + 56 ° + ∠ 3 = 180°
∠3 = 180 - 65 - 56
∠ 3 = 59°
∠3 + x = 180°
59° + x = 180°
x = 180 - 59
x = 121 °
Suppose cos(x)= -1/3, where π/2 ≤ x ≤ π. What is the value of tan(2x). EDGE
A.) -2√8/7
B.) -√8
C.) √8
D.) 2√8/7
Answer:
D
Step-by-step explanation:
We are given that:
[tex]\displaystyle \cos x = -\frac{1}{3}\text{ where } \pi /2 \leq x \leq \pi[/tex]
And we want to find the value of tan(2x).
Note that since x is between π/2 and π, it is in QII.
In QII, cosine and tangent are negative and only sine is positive.
We can rewrite our expression as:
[tex]\displaystyle \tan(2x)=\frac{\sin(2x)}{\cos(2x)}[/tex]
Using double angle identities:
[tex]\displaystyle \tan(2x)=\frac{2\sin x\cos x}{\cos^2 x-\sin^2 x}[/tex]
Since cosine relates the ratio of the adjacent side to the hypotenuse and we are given that cos(x) = -1/3, this means that our adjacent side is one and our hypotenuse is three (we can ignore the negative). Using this information, find the opposite side:
[tex]\displaystyle o=\sqrt{3^2-1^2}=\sqrt{8}=2\sqrt{2}[/tex]
So, our adjacent side is 1, our opposite side is 2√2, and our hypotenuse is 3.
From the above information, substitute in appropriate values. And since x is in QII, cosine and tangent will be negative while sine will be positive. Hence:
[tex]\displaystyle \tan(2x)=\frac{2(2\sqrt{2}/3)(-1/3)}{(-1/3)^2-(2\sqrt{2}/3)^2}[/tex]Simplify:
[tex]\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{(1/9)-(8/9)}[/tex]
Evaluate:
[tex]\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{-7/9} = \frac{4\sqrt{2}}{7}[/tex]
The final answer is positive, so we can eliminate A and B.
We can simplify D to:
[tex]\displaystyle \frac{2\sqrt{8}}{7}=\frac{2(2\sqrt{2}}{7}=\frac{4\sqrt{2}}{7}[/tex]
So, our answer is D.
Calculate the area of triangle ABC with altitude CD, given A (−3, −4), B (−6, 2), C (0, 0), and D (−4, −2). (5 points)
Question 8 options:
1)
14 square units
2)
15 square units
3)
18 square units
4)
20 square units
Answer: 2) 15 square units
Step-by-step explanation:
The area of the triangle is 15 square units if the triangle ABC with altitude CD, given A (-3, -4), B (-6, 2), C (0, 0), and D (-4, -2) which is correct option (2)
What is the distance between two points?The distance between two points is defined as the length of the line segment between two places represents their distance. Most significantly, segments that have the same length are referred to as congruent segments and the distance between two places is always positive.
The formula of distance between two points is P(x₁, y₁) and Q(x₂, y₂) is given by: d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².
Given that a triangle ABC with altitude CD.
The coordinates for the triangle are A (-3, -4), B (-6, 2), C (0, 0), and D (-4, -2)
Given that the distance between C and D will be the height of the triangle
Since, the distance between the points by using the distance formula:
= √ (x₂ – x₁)² + (y₂ – y₁) ².
height = √ (-4 – 0)² + (-2 – 0) ²
height = √20
base = √45
Area of triangle = (1/2)base x height
Area of triangle = (1/2)√20×√45
Area of triangle = (1/2)30
Area of triangle = 15 square units
Hence, the area of the triangle is 15 square units if the triangle ABC with altitude CD
Learn more about distance between two points here:
https://brainly.com/question/15958176
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Complete the table for the given rule.
Rule: y=x+3
Answer:
1
5
2
Step-by-step explanation:
4-3=1
8-3=5
5-3=2
Hope this helps! :)
If a1 = 6 and an = 3 + 2(an-1), then a2 equals
no links
Answer:
15
Step-by-step explanation:
Given that a1 = 6
an = 3 + 2(an-1),
Substitute n = 2 into the formula
a2 = 3 + 2(a1)
a2 = 3 + 2(6)
a2 = 3+12
a2 = 15
Hence the second term of the sequence is 15
Find the range for the following list of values:
1, 2, 4, 7
Answer:
below
Step-by-step explanation:
Rage =
highest value - lowest value
= 7 - 1
=6
Round to the nearest cent or whole number as needed. How many males had fatal car accidents last year if there were 1761 fatal car accidents and about 42% of the fatalities were male?
Answer:
740
Step-by-step explanation:
42% of 1761 = 0.42 * 1761 = 739.62
Answer: 740
Find the value of x
Answer:
[tex]x=14[/tex]
Step-by-step explanation:
The given triangle is a right triangle, meaning it is a triangle with a right angle, this is indicated by the box around one of the angles. When given a right triangle, one can use the right triangle trigonometric ratios. These ratios describe the relationship between an angle in a right triangle, and the sides in a right triangle. Such ratios are as follows,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
Bear in mind that the way one names the sides, in the sense of (opposite or adjacent) will change based on the angle one uses to describe the triangle. However, the hypotenuse is the same no matter the angle, as the hypotenuse is the side opposite the right angle.
In this case, one is given one of the angles, and the side opposite the angle. One is asked to find the hypotenuse of the triangle. One can use the sine (sin) ratio to achieve this.
[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
Substitute,
[tex]sin(30)=\frac{7}{x}[/tex]
Inverse operations,
[tex]x=\frac{7}{sin(30)}[/tex]
Simplify,
[tex]x=14[/tex]
At a middle school, 30% of students buy lunch in the cafeteria and the remaining students bring lunch from home. A spinner with 10 equal-sized sections numbered 0-9 will be used to simulate the lunch trend. How can you design a simulation to guess whether the next 20 students buy lunch or bring lunch from home?
A:Assign the numbers 0–3 to represent students who buy lunch and the numbers 4–9 to represent students who bring lunch from home. Spin the spinner 20 times and count how many spins are between 0–3 and how many are between 4–9.
B:Assign the numbers 0–2 to represent students who buy lunch and the numbers 3–9 to represent students who bring lunch from home. Spin the spinner 10 times and count how many spins are between 0–1 and how many are between 4–6, then multiply the counts by 2.
C:Assign the numbers 0–2 to represent students who buy lunch and the numbers 3–9 to represent students who bring lunch from home. Spin the spinner 20 times and count how many spins are between 0–2 and how many are between 4–9.
D:Assign the numbers 0–3 to represent students who buy lunch and the numbers 4–9 to represent students who bring lunch from home. Spin the spinner 10 times and count how many spins are between 0–3 and how many are between 4–9.
Answer:
B
Step-by-step explanation:
I'm pretty confident that it is B
Ms. Cortez was building doll houses to sell at a toy store. She had to spend $184 on tools before she could begin to work. Each doll house cast $17 to make. She planned to sell the doll houses for $29 each. How many doll houses did she need to sell to make a profit?
Answer:
A minimum of 16 dollhouses
Step-by-step explanation:
profit on each dollhouse= sp-cp= 29-17= $12
if we divide 184 by 12 we get abt 15.33, which means, she has to sell more than 15 Dollhouses to make a profit.
so the minimum number of dollhouses to be sold are 16
Colin and Dan win some money and share it in the ratio 4:5. Colin gets £52. How much did they win in total?
Answer:
$65
Step-by-step explanation:
Collin gets 4x dollars which equals 52, so 4x = 52
Dan gets 5x dollars which equals y (the answer). solve for x = 13. 5 • 13 = 65.
What is the surface area of the cylinder with height 4 yd and radius 7 yd? Round your answer to the nearest thousandth.
Answer:
483.87yd^2
Step-by-step explanation:
Given data
Height= 4yd
Radius= 7yd
The expression for the surface area of a cylinder is given as
Surface area= 2πr (4+ 7)
Surface area= 2*π*7 (4 + 7)
Surface area = 14π (11)
Surface area= 154*3.142
Surface area= 483.87yd^2
Hence the surface area is 483.87yd^2
can someone help me with this problem!
C. -1
Hope this helps! :)
______________
Answer:
-1
Step-by-step explanation:
Simplify the real and imaginary parts of the expression. That’s probably as simple as i can get it.
Hope this helps! :)
What is 16.99 times 0.80
Answer:
Hi, there your answer is 13.592
Step-by-step explanation:
Can someone help me? It's urgent and thank you!
Put either A,B,C,D,E in r= and also put A,B,C,D,E in the find the 6th term put whatever your answer's lead you too
number a is too low so we will work with c after all I put that and got it eight
Your answer is C. - 972
I found 3 by dividing 36 by 12. I hope the image is self- explanatory.
Please help find volume of cone
Answer:
5275.2 m³
Step-by-step explanation:
We need the radius first:
[tex]\sqrt{l^2- h^2}[/tex] = 12
Formula for volume = πr²*h/3
Volume = 3.14 * 144 * 35/3
Volume = 5275.2
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Use the function shown in the table to answer the questions below .
Answer:
a) -6
b) 3
c) Y = -6x + 3
Step-by-step explanation:
Pick two points and find rise/run = slope
rise y1 - y2 = 9 - 3 = 6
run x1 - x2 = -1 - 0 = -1
slope = 6 / -1 = -6
The y intercept is where x = 0 which is given in the table (0,3) so
y intercept = 3
Point slope form is y = mx + b , so
y = -6x + 3
Box A has 14 black pens and 6 blue pens box B has 9 black pens and 3 blue pens a pen is randomly chosen from each box list these events from least likely to most likely
Answer:
The list of these events from least likely to most likely is Blue-Blue -> Black-Blue -> Blue-Black -> Black-Black
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Possible outcomes:
Black - Black
Black - Blue
Blue - Black
Blue - Blue
Probability of each outcome:
Black-Black:
14 out of 20, and then 9 out of 12. So
[tex]P_{BkBk} = \frac{14}{20} \times {9}{12} = \frac{14*9}{20*12} = \frac{126}{240}[/tex]
Black-Blue:
14 out of 20, then 3 out of 12. So
[tex]P_{BkBl} = \frac{14}{20} \times {3}{12} = \frac{14*3}{20*12} = \frac{42}{240}[/tex]
Less likely than black-black.
Blue - Black:
6 out of 20, then 9 out of 12. SO
[tex]P_{BlBk} = \frac{6}{20} \times {9}{12} = \frac{6*9}{20*12} = \frac{54}{240}[/tex]
More likely than black-blue, less likely than black-black.
Blue - Blue
6 out of 20, then 3 out of 12
[tex]P_{BlBl} = \frac{6}{20} \times {3}{12} = \frac{6*3}{20*12} = \frac{18}{240}[/tex]
Least likely of the outcomes.
List these events from least likely to most likely:
The list of these events from least likely to most likely is Blue-Blue -> Black-Blue -> Blue-Black -> Black-Black
Use the expression 5(6 + 4x) to answer the following:
Part A: Describe the two factors in this expression. (4 points)
Part B: How many terms are in each factor of this expression? (4 points)
Part C: What is the coefficient of the variable term? (2 points)
Answer:
6 and 4
Step-by-step explanation:
Answer:
Part A: 4 and x are factors of 4x
Part B: 6 and 4
Part C: 4
Step-by-step explanation:
Can someone pleaseeee help and if you’re correct i’ll give brainliest
Answer:
70
Step-by-step explanation:
the figure shown is a parallelogram with a base length of 10 ft and a height of 7 ft
the area of a parallelogram can simply be calculated by multiplying the base length by the height
hence, area = 7 * 10 = 70
Answer: 10 times 7
Step-by-step explanation: 10 times 7
How do I do this ? no links please
Hey there!
ASSUMING….
-14.4 = -1.2m
-1.2m = -14.4
DIVIDE -1.2 to BOTH SIDES
-1.2m/-1.2 = -14.4/-1.2
SIMPLIFY IT!
m = -14.4/-1.2
m = 12
Therefore, the answer should be:
m = 12
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A runs 25% faster than B and is able to give him a start of 7 metres to end a race in dead heat. What is the length of race?
Answer:
35 metres
Step-by-step explanation:
The question states that A runs 25% faster than B. This means that, for every 1 second that B runs, A runs 1.25 second
Assuming that the total length of the race, that we're looking for, is D. Then we can say that B made a total distance of D-7 meters, and A runs D.
time taken by A = [tex]\frac{D}{1.25}[/tex]
time taken by B = [tex]\frac{D-7}{1}[/tex]
equating both together, we have
[tex]\frac{D}{1.25}[/tex] = [tex]\frac{D-7}{1}[/tex]
1.25D - 8.75 = D
1.25D - D = 8.75
0.25D = 8.75
D = 8.75/0.25
D = 35
On the number line below, length
AB = [?]
A
В
16
45
Answer:
29
Step-by-step explanation:
45 - 16 =
PLEASE HELP ME. this is due TONIGHT and i need this done so i have time for other assignments. thank you so much
explaining your answer = brainliest.
the area of this parallelogram is 504 square centimeters.
y = ___ cm
Answer:
28cm
Step-by-step explanation:
Area of a parallelogram equals the base length, which is y cm, multiplied by the height, which is 18cm.
So
Area= 504cm
y cm (base) x 18 cm (height) = 504cm^2 (area)
y cm = 504cm^2 / 18cm
y cm = 28cm
Answer:
28 cm
Step-by-step explanation:
Just use some good ol' algebra:
18y = 504
y = 28 cm
A parallelogram is basically a wonky rectangle, so it uses the same formula for area.
how to simplify (a+3b)+3(4a+b)
Answer:
13a + 6b
Step-by-step explanation:
Given
(a + 3b) + 3(4a + b) ← distribute parenthesis
= a + 3b + 12a + 3b ← collect like terms
= 13a + 6b
Answer: 13a+3b+18
Step-by-step explanation:
First distribute the 3 to 4a+b
Then you get 12a+18
Add 12a+18 with a+3b
Please give me the answer and tell me how you solved it
Answer:
6x-3
Step-by-step explanation:
that is the procedure above
Step-by-step explanation:
5+4X+2x-8
=6x-3
answer is third option
WILL GIVE BRAINLIST
WRITE THE PHRASE AS A VARIABLE EXPRESSION. USE X TO REPRESENT “a number”
THE PRODUCT OF 4 AND A NUMBER
Answer:
x+14.
Sum of a number and 14 is x+14.
Round 187.890 to the nearest 10 000
Answer:
190,000
190,000
190,000
Step-by-step explanation:
190,000
190,000
Find m 22 in the figure below.
95°
2
72°
Answer:
<2= 23°
Step-by-step explanation:
180°- 95°= 85°
(95° is on a straight line, angles on a straight line adds up to 180° so 95° is being subtracted from 180°. Therefore the next angle in the triangle will be 85°)
To find <2
180- (85°+ 72°)
(Angles on a triangle adds up to 180°)
180- 157
= 23
Someone I need help plzzz
Answer:
sorry this question is confusing
Step-by-step explanation: