ANSWER
[tex]\tan(x) = \frac{3\sqrt{7}}{7} [/tex]
EXPLANATION
[tex] \sin(x) = \frac{Opposite}{hypotenuse} [/tex]
[tex]\sin(x) = \frac{3}{4} [/tex]
This means the opposite side is 3 units and the hypotenuse is 4 units.
We use Pythagoras Theorem to find
[tex] { |ZX| }^{2} + {3}^{2} = {4}^{2} [/tex]
[tex]{ |ZX| }^{2} +9=16[/tex]
[tex]{ |ZX| }^{2} =16 - 9[/tex]
[tex]{ |ZX| }^{2} = 7[/tex]
[tex]{ |ZX| } = \sqrt{7} [/tex]
[tex] \tan(x) = \frac{opposite}{adjacent} [/tex]
[tex] \tan(x) = \frac{3}{ \sqrt{7} } [/tex]
[tex] \tan(x) = \frac{3}{ \sqrt{7} } \times \frac{\sqrt{7}}{\sqrt{7}} [/tex]
[tex]\tan(x) = \frac{3\sqrt{7}}{7} [/tex]
Final answer:
Given sin(X) = 3/4 in a right-angled triangle XYZ, by using trigonometric identities and the Pythagorean theorem, we find that tan(Y) is 1/3.
Explanation:
In triangle XYZ with angle Z being a right angle (90 degrees or π/2 radians), if we are given that sin(X) = 3/4, we can use trigonometric identities to find tan(Y). Since sin(X) is the ratio of the opposite side to the hypotenuse in a right-angled triangle, we have a side opposite angle X which is 3 units long and a hypotenuse that is 4 units long. From this, we can deduce that the side adjacent to angle X, which is also the side opposite to angle Y, is 1 unit long (using the Pythagorean theorem, as the square of the hypotenuse is equal to the sum of the squares of the other two sides: 3² + 1² = 4²).
Now, to find tan(Y), which is the ratio of the side opposite to Y to the side adjacent to Y, we just take the length of the side opposite to X (which is the same as the side adjacent to Y) and the length of the hypotenuse. Therefore, tan(Y) = opposite side / adjacent side, which in this case is 1/3.
f(x) = X^2. what is g(x) A. g(x) = x^2 - 4 B. g(x) = x^2 + 4 C. g(x) = -4x^2 D. g(x) = -x^2 - 4
Answer:
D. g(x) = -x^2 - 4
Step-by-step explanation:
(A.P.E.X)
The required function g(x) = -x²- 4. Option D is correct.
f(x) = x², g(x) to be determine with help of graph.
Function is defined as y = f(x). For every x their is certain value of y.
Here, from the graph g(x) is reflection of f(x) at y = -4.
So g(x) = -f(x) - 4
negative sign for reflection.
g(x) = -x²-4
Thus, The required function g(x) = -x²- 4.
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What is the opposite of square root
the opposite is squared so,
square root of 4 is 2 and 2 squared is 4
The opposite of a square root √ is the squared exponent ²
If you have a number and find the square root of it, you can take the answer and square it to get the original number. Cool, huh?
Which of the following types of lines will never intersect one another?
parallel lines
perpendicular lines
transversal lines
intersecting lines
Parallel Lines, they always stay perfectly in line.
Answer:
parallel lines
Step-by-step explanation:
lines that never cross one another and are the same distance apart at all times
You made 1/2 quart of lemonade.How many 1/4 quart-sized glasses will you be able to fill with lemonade
Well answer is 2 cause 1/4+1/4 is 1/2
Classwork 12.1 surface area
Answer:
6) LA = 90 units² and SA = 202 units²
7) LA = 377 units² and SA = 477.5 units²
8) LA = 208 units² and SA = 232 units²
9) LA = 455 units² and SA = 591 units²
Step-by-step explanation:
* Lets revise the rules of lateral area and surface area
- Lateral area of the solid = perimeter of its base × its height
- Surface area = lateral area + 2 × area of its base
* Now lets solve the problems
6) The solid is a rectangular prism
- Its base is a rectangle with dimensions 8 units and 7 units
- Its height is 3 units
∵ Perimeter of the rectangle = 2(L + W)
∴ Perimeter of the base = 2(8 + 7) = 2(15) = 30 units
∴ LA = 30 × 3 = 90 units²
∵ Area of the rectangle = L × W
∴ Area of the base = 8 × 7 = 56 units²
∴ SA = 90 + 2 × 56 = 90 + 112 = 202 units²
7) The solid is a cylinder
- Its base is a circle with diameter 8 units
∴ Its radius = 8 ÷ 2 = 4 units
- Its height is 15 units
∵ The perimeter of the circle is 2πr
∴ The perimeter of the base = 2π(4) = 8π
∴ LA = 8π(15) = 120π = 376.99 ≅ 377 units²
∵ The area of the circle = πr²
∴ The area of the base = π(4)² = 16π
∴ SA = 120π + 2 × 16π = 120π + 32π = 152π = 477.5 units²
6) The solid is a triangular prism
- Its base is a triangle with sides 5 , 5 , 6 units and height 4 units
- Its height is 13 units
∵ Perimeter of the triangle is the sum of the 3 sides
∴ Perimeter of the base = 5 + 5 + 6 = 16 units
∴ LA = 16 × 13 = 208 units²
∵ Area of the triangle = 1/2 × base × height
∴ Area of the base = 1/2 × 6 × 4 = 12 units²
∴ SA = 208 + 2 × 12 = 208 + 24 = 232 units²
9) The solid is a prism
- Its base is an isosceles trapezium with parallel bases 7 units and 10
units, 2 non-parallel bases 9 units and height 8 units
- Its height is 13 units
∵ Perimeter of the trapezium is the sum of its sides
∴ Perimeter of the base = 7 + 10 + 9 + 9 = 35 units
∴ LA = 35 × 13 = 455 units²
∵ Area of the trapezium = 1/2(b1 + b2) × h
∴ Area of the base = 1/2(7 + 10) × 8 = 68 units²
∴ SA = 455 + 2 × 68 = 455 + 136 = 591 units²
If (x, 1/100) lies on the graph of y = 10x, then x =
The value of x in the coordinate is 1/1000
Using the coordinates of the point given:
(x , 1/100)Equation of the graph:
y = 10xTo find the value of x for the coordinate given; substitute into the equation:
1/100 = 10x
1/100 × 100 = 100 * 10x
1 = 1000x
x = 1/1000
Hence, x = 1/1000
Factor 27a^3 b^9+8c^18
For this case we must factor the following expression:
[tex]27a ^ 3b ^ 9 + 8c ^ 18[/tex]
So, we rewrite the terms like:
[tex]27a ^ 3b ^ 9 = (3ab ^ 3) ^ 3\\8c ^ {18} = (2c ^ 6) ^ 3[/tex]
So, we have:
[tex](3ab ^ 3) ^ 3 + (2c^6) ^ 3 =[/tex]
Being both perfect cube terms, we factorize by applying the cube sum formula:
[tex](a ^ 3 + b ^ 3) = (a + b) (a ^ 2-ab + b ^ 2)[/tex]
Where:
[tex]a = 3ab ^ 3\\b = 2c ^ 6\\(3ab ^ 3 + 2c ^ 6) ((3ab ^ 3) ^ 2- (3ab ^ 3) (2c ^ 6) + (2c ^ 6) ^ 2) =\\(3ab ^ 3 + 2c ^ 6) (9a^2b ^ 6-6ab ^ 3c ^ 6 + 4c ^ {12})[/tex]
Answer:
[tex](3ab ^ 3 + 2c ^ 6) (9a2b ^ 6-6ab ^ 3c ^ 6 + 4c ^ 12)[/tex]
Find u*v, if u=13j and v=i+3j
Answer:
u * v = 39 ⇒ 2nd answer
Step-by-step explanation:
* Lets explain how to solve the problem
- u and v are two vectors
- u * v means the scalar product of the two vectors
- The scalar product is a way of multiplying vectors
- The result of a scalar product is always a number not a vector
- Ex: If u = ai + bj ⇒ <a , b> and v = ci + dj ⇒ <c , d> then the scalar
product of them is ac + bd where ac + bd is a number
* Lets solve the problem
∵ Vector u = 13j ⇒ <0 , 13>
∵ Vector v = i + 3j ⇒ <1 , 3>
- Lets find the scalar product
∴ u * v = (0)(1) + (13)(3)
∴ u * v = 0 + 39
∴ u * v = 39
The following graph plots the batting averages of 29 players of a baseball team against the weekly time (in hours) they spend in batting practice.
Which statement is a reasonable conclusion that may be drawn from the graph?
Practice and batting average have no direct relationship.
The best batter has an average of 0.33.
Batting practice increases batting averages.
The worst batter has an average of 0.
Answer:
Batting practice increases batting averages.
Step-by-step explanation:
By looking at the graph, we clearly see a trend, almost a straight line (if you regroup the points a bit) going up.
So, it's clear that batting practice increases batting averages; they're directly related. The more a player practices at bat, the better will be his average.
Answers B and D (best and worst batters) are not proved at all by the graph, since there's data higher than those two cases.
If a boy threw 8 books in to a pond and originally had 147 books how many books does he now have?
Answer:
139
Step-by-step explanation:
He originally had 147 books and threw 8 into a pond.
147-8=139
Solve for x. (x - 5)(x - 5) = 0
Answer:
x=5
Step-by-step explanation:
(x - 5)(x - 5) = 0
x-5=0
x=5
If the divisor is eight tenths and the dividend is forty eight hundredths what is the quotient?
Answer:
3737
Step-by-step explanation:
njrdndjfjdjdjjekekekekekekekewkekke
[tex]\bf \stackrel{dividend}{\cfrac{48}{100}}\div \stackrel{divisor}{\cfrac{8}{10}}\implies \cfrac{48}{100}\cdot \cfrac{10}{8}\implies \cfrac{10}{100}\cdot \cfrac{48}{8}\implies \cfrac{1}{10}\cdot \cfrac{6}{1}\implies \cfrac{6}{10}\implies \cfrac{3}{5}[/tex]
select the true statement about triangle ABC
Answer:
The answer is C.
The true statement about triangle ABC is sin A=cos C. Therefore, option C is the correct answer.
From the given triangle ABC, CA=13 units, BA=12 units and BC=5 units.
What are heights and distances?Heights and Distances is a study about the applications of Trigonometry. It has many real-life applications, such as measuring the object’s height, depth of the object, the distance between two celestial objects etc. The formulas and the ratios of trigonometry are helpful in the study of heights and distances.
Here,
sin A= Opposite/Hypotenuse
BC/CA=5/13
cos C= Adjacent/Hypotenuse
BC/CA=5/13
So, sin A=cos C
The true statement about triangle ABC is sin A=cos C. Therefore, option C is the correct answer.
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Help me in this question please
The least number 4 and 10 go into is 20. (4 goes into 20 five times and 10 goes into 20 two times)
State the plot overview of the movie Inside out. Please help ASAP.
Inside Out is a film about an 11 year old girl named Riley who moves across the country from Minnesota to San Francisco with her parents. Riley experiences a transformation in her mind and in who she is as a person as she tries to adjust to her new life in San Francisco and to the difficult process of growing up. The viewer follows Riley’s five emotions, Joy, Sadness, Anger, Fear, and Disgust, on a journey in her mind to help her through her transition to adolescence, and to assist her in making what they think are the right decisions.
Inside Out is an animated movie detailing the emotional journey of an 11-year-old girl named Riley who moves to San Francisco. The film personifies Riley's core emotions: Joy, Sadness, Anger, Fear, and Disgust, outlining how they shape her actions and memories. The movie communicates a crucial message about the importance of all emotions, including sadness.
Explanation:Inside Out is a movie presented by Pixar Animation Studios and released by Walt Disney Pictures. It showcases the story of an 11-year-old girl named Riley who moves from her hometown in Minnesota to San Francisco due to her father's new job. But this story is not a typical animation, as it transcends the usual plot setup. The unique aspect of this film is that it personifies Riley's five core emotions: Joy, Sadness, Anger, Fear, and Disgust, who live inside her mind and guide her actions and memories.
At the start of the movie, Riley's actions are primarily dictated by Joy, but the move to San Francisco triggers a series of events leading to Joy and Sadness getting lost in the depths of Riley's mind, leaving Anger, Fear, and Disgust in control. Throughout their journey to return to the headquarters, Joy and Sadness traverse various parts of Riley's mind, including Long-Term Memory, Imagination Land, and even the Subconscious, all the while Riley struggles with her new life.
In the end, the movie beautifully illustrates that all emotions are vital for a healthy mind - highlighting that sadness is as essential as joy. This plot overview simplifies a deep and complex movie, conveying a profound message about understanding and managing emotions.
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Which number is irrational
For this case, we have by definition, that an irrational number is a number that can not be expressed as a fraction [tex]\frac {a} {b}[/tex], where a and b are integers and b is nonzero.
Some examples are:
[tex]\sqrt {2}, \sqrt {3}, e, \pi.[/tex]
So, that the answer is [tex]\pi.[/tex]
Answer:
Option C
For the function f(x) = x + 7, what is the ordered pair for the point on the graph when x = 2b?
Answer:
The ordered pair is the point [tex](2b,2b+7)[/tex]
Step-by-step explanation:
we have
[tex]f(x)=x+7[/tex]
For [tex]x=2b[/tex]
Substitute the value of x in the function
so
[tex]f(2b)=2b+7[/tex]
therefore
The ordered pair is the point [tex](2b,2b+7)[/tex]
Answer:
(2b, 2b+7)
Step-by-step explanation:
Since the value of x is 2b, we just have to insert that value into the function in order to solve the ordered pair, we have the first part of the ordered pair, which is (2b), now we just insert the value of x into the function:
[tex]f(x)=x+7\\f(x)=2b+7[/tex]
Now we know that the value of y would be 2b +7, and the ordered pair will be (2b,2b+7)
Flora is making salsa for a party. Every 1 cup of chopped tomatoes makes 2 3/4 cups of salsa. She uses 1 2/3 cups of tomatoes. How much salsa does she make?
I will make BRAINLIEST
Answer:
4[tex]\frac{7}{12}[/tex] cups of Salsa.
Step-by-step explanation:
Flora is making Salsa for a party.
Every 1 cup of chopped tomatoes makes 2[tex]\frac{3}{4}[/tex] = [tex]\frac{11}{4}[/tex] cups of Salsa
She uses 1[tex]\frac{2}{3}[/tex] = [tex]\frac{5}{3}[/tex] cups of tomatoes
1[tex]\frac{2}{3}[/tex] cups of tomatoes makes:
[tex]\frac{5}{3}[/tex] × [tex]\frac{11}{4}[/tex] ÷ 1 = [tex]\frac{55}{12}[/tex] = 4[tex]\frac{7}{12}[/tex] cups of Salsa.
it is estimated that on a daily basis 15% of the custoners at a local supermarket use the express checkout. What is the probability that one of the first five customers on a given day uses the express checkout?
Answer:
the answer is 1/5 for the probability
If g(x) = 3(x − 2), find the value of x if g(x) = 6.
Answer:
x=4
Step-by-step explanation:
From the statement we know that g(x)=3(x-2) and g(x)=6. Then we know that:
6=3(x-2)
Solving for "x":
6=3x-6
12=3x
x=12/3
x=4
Then, the solution is x=4.
For this case we have a function of the form [tex]y = g (x)[/tex]
Where:
[tex]g (x) = 3 (x-2)[/tex]
We want to find the value of "x" if the function is 6, that is, if y = 6
So, we have:
[tex]3 (x-2) = 6\\3x-6 = 6[/tex]
We clear "x":
[tex]3x = 6 + 6\\3x = 12\\x = \frac {12} {3}\\x = 4[/tex]
So, if the function has a value of 6, then [tex]x = 4[/tex]
ANswer:
[tex]x = 4[/tex]
How do I answer this?
Check the picture below.
What is the sum of the infinite geometric series represented by?
A. 600
B. 360
C. 480
D. 720
Answer:
B. 360 hope it helps
faze up
Complete the ratio
4 : 32 = 1 : ?
Answer:
1: 8
Step-by-step explanation:
4 : 32
Divide both the left and right side by 4
4/4 =1
32/4 = 8
4:32 becomes 1:8
Answer:
sorry i do not know
Step-by-step explanation:
Suppose Colby rolls the number cube 1000 times, about how many times can she expect to roll an odd number?
Since there are 3 odd numbers ( 1, 3 and 5) and 3 even numbers ( 2, 4 and 6) in the cube ,
The chance of getting an odd number is 50/50 or 50%
So out of 1000 she will probably get 500 odd since 1000 × 0.5 (which is 50%) is 500
Choose the equation that models the following problem.
When the side of a square is doubled, its area is increased to 28 cm^2.
Answer:
[tex](2x)^2=28[/tex]
Step-by-step explanation:
The equation for the area of a square is [tex](x)^2=A[/tex]
In this case, the value within the parenthesis are the lengths of each side.
As you are doubling the length of the side and know the area, the equation can be written as follows
[tex](2x)^2=28[/tex]
how do you find the measure of each angle of m<8=115
You would do 180 - 115 and that gives you the < for 7
Answer:
1. 65 deg
2. 115 deg
3. 115 deg
Step-by-step explanation:
1.
Angles 7 and 8 are supplementary. Their measures add to 180 deg.
m<7 + m<8 = 180
m<7 + 115 = 180
m<7 = 180 - 115
m<7 = 65
2.
Since lines p and q are parallel lines cut by a transversal, corresponding angles 6 and 8 are congruent.
m<6 = m<8
m<6 = 115
3.
Angles 1 and 6 are vertical angles, so they are congruent.
m<1 = m<6
m<1 = 115
What's 30 inches decreased by 30%
Answer:
21
Step-by-step explanation:
First, we would find 30% of 30, which would be 9. Then we would subtract 9 from 30 because we are decreasing it by 30%. That means the answer is 30-9, which is 21.
Divide. (11x^2+2x^3+14+17x) / (2x+5)
(11x2 + 2x3 + 14 +17x) ÷ (2x + 5)
= (2x^3 + 11x^2 + 17x + 14) ÷ (2x + 5)
= x^2 + 3x + 1 r 9
Answer:
2.2x^2+.4x^2+2.8+3.4x
Step-by-step explanation:
We can factor out a few numbers right off the bat-
(11x^2+2x^3+14+17x) / (2x+5)
(11x^2+2x^2+14+17x) / (5)
Now make the denominator disappear.
(11x^2+2x^2+14+17x) / (5)
2.2x^2+.4x^2+2.8+3.4x
(please contact if wrong)
another one :) thank you ahead of time!!
[tex]x = 0.4828282[/tex]
[tex]1000x = 482.828282[/tex]
[tex]999x = 482.346[/tex]
[tex]x = \frac{482}{999} + \frac{362}{1000} [/tex]
[tex]x = \frac{843638}{999000} [/tex]
Answer:
[tex]\dfrac{239}{495}[/tex]
Step-by-step explanation:
[tex]\text {Let x = } 0.4 \overline {82}[/tex]
[tex]1000x = 482. \overline {82}[/tex]
[tex]10x = 4. \overline {82}[/tex]
[tex]1000x - 10x = 482. \overline {82} - 4. \overline {82}[/tex]
[tex]990x = 478[/tex]
[tex]x = \dfrac{478}{990}[/tex]
[tex]x = \dfrac{239}{495}[/tex]
what is the area of this triangle h = 5 in. b = 10 in.
The area of a triangle is 1/2 base times height so, the answer is 25
The area of the triangle is 25 square inches.
What is a triangle?A 2-dimensional geometric figure bounded by three sides and has 3 corners and hence has 3 angles is called a triangle. In a triangle sum of all 3 angles is equal to 180°.
How to find the area of the triangle?Area of triangle can be found by the formula, base x height/2In the given problem,
base = 10 in.height = 5 in.∴ Area of triangle = ( 10 x 5 /2) square inches = 25 square inches
So, the area of the triangle is 25 square inches.
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