Answer:
[tex]\displaystyle \cos(2x)=-\frac{7}{25}[/tex]
Step-by-step explanation:
We want to find:
[tex]\displaystyle \cos(2x)\text{ given that }\sin(x)=-\frac{4}{5}[/tex]
And x is in QIII.
Recall that sine is the ratio of the opposite side to the hypotenuse.
Therefore, the adjacent side is (we can ignore the negative for now).
[tex]a=\sqrt{5^2-4^2}=\sqrt{25-16}=\sqrt{9}=3[/tex]
So, the adjacent side is 3, the opposite side is 4, and the hypotenuse is 5.
Using the double angle identity, we can rewrite:
[tex]\cos(2x)=\cos^2(x)-\sin^2(x)[/tex]
Since x is in QIII, cosine is positive, sine is negative, and tangent is negative.
Using the above values, we can conclude that:
[tex]\displaystyle \cos(x)=\frac{3}{5}\text{ and } \sin(x)=-\frac{4}{5}[/tex]
Substitute:
[tex]\displaystyle \cos(2x)=\Big(\frac{3}{5}\Big)^2-\Big(-\frac{4}{5}\Big)^2[/tex]
Evaluate:
[tex]\displaystyle \cos(2x)=\frac{9}{25}-\frac{16}{25}=-\frac{7}{25}[/tex]
(2+3) (4-1) simplify
Step-by-step explanation:
Given
(2+3) (4-1)
= 5 * 3
= 15
Hope it will help :)
Answer:
15
Step-by-step explanation:
(2+3) (4-1)
(5) (3)
15
12. A circle has a center at C(2,5) and a point on the circle has coordinates A(8, 13). Could the point B lie on
the same circle if lies at B(9.1)? Justify.
Answer:
No.
Step-by-step explanation:
A circle is defined as a figure in which all points are equidistant from the center, or C. In order to determine how far points A and B are from the center, we must first find the difference in positioning from (2,5) to each point and then use Pythagorean Theorem to calculate the length of the hypotenuse. Point A establishes that the radius of the circle must be 10 units, and Point Bis only about 8 units away.
A student is conducting a probability experiment and wants to know the total number of outcomes for the experiment. The student's experiment is comprised of three events
• rolling a six-sided number cube • •flipping a coin
• rolling a six-sided number cube again
How many outcomes are possible in this experiment?
A. 14
B. 24
C. 72
D. 38
Answer:So to get a 6 when rolling a six-sided die, probability = 1 ÷ 6 = 0.167, or 16.7 percent chance. So to get two 6s when rolling two dice, probability = 1/6 × 1/6 = 1/36 = 1 ÷ 36 = 0.0278, or 2.78 percent.
Step-by-step explanation:
Answer:
C.72
Step-by-step explanation:
rolling a six-sided number cube(6) x flipping a coin(2) x rolling a six-sided number cube again(6)= 72
6x6= 36
36 x 2 = 72
6x2=12
12 x 6 = 72
List all the 4-digit even numbers that can be created by rearranging these number tiles.
3
4
7
2
Answer:
3472
3274
3742
3724
7342
7324
7234
7432
4372
4732
2374
2734
i found this much
These are the 12 possible 4-digit even numbers that can be created by rearranging the number tiles (3, 4, 7, 2).
To create 4-digit even numbers by rearranging the given number tiles (3, 4, 7, 2), we need to consider the following conditions:
The last digit must be an even number (2 or 4).The thousand digits cannot be 0.Considering these conditions, the possible 4-digit even numbers that can be formed are:
2347
2374
3247
3274
3427
3472
4237
4273
4327
4372
4723
4732
These are the 12 possible 4-digit even numbers that can be created by rearranging the number tiles (3, 4, 7, 2).
Learn more about the even numbers here:
https://brainly.com/question/2142825
#SPJ4
Simplify the ratio 30:45
Answer:
2:3
Step-by-step explanation:
Here is the math to illustrate better:
30/15 = 2 and 45/15 = 3
Thus, 30:45 ratio simplified is 2:3
Answer:
2/3
Step-by-step explanation:
There 2 ways:-
The simple way in 2 steps
1.divide by 5
2. then divide by 3
The complicated way is to divide by 15
Express the recurring decimal 0.136 as a fraction in its simplest form.
Write your working in the box, below, and use x in the working.
Write fractions using the / sign. Eg you would write as 1/2
Forgot how to solve, i need help man..
Answer:
3x + x + 100° = 180°
⇔ 4x = 80°
⇔ x = 20°
Step-by-step explanation:
The store is offering 15% discount. The regular price of a T shirt is $23 , what is the discount?
Answer:
$3.45
Step-by-step explanation:
15% of 23 is 3.45
4) Find the area.
7 points
7 in
18 in
10 in
18 in
236
180
125
56
Answer: its 236
Step-by-step explan
This recipe makes 12 flapjacks.
How much of each ingredient is needed to make 30 flapjacks by following this recipe?
Recipe: Makes 12 flapjacks
140 g margarine
120 g sugar
100 mL syrup
240 g oats
50 g raisins
Ingredients for 30 flapjacks:
margarine = 350g
sugar : 300g
syrup :250g
oats : 600g
raisins : 125g
What are the ingredients needed for 30 flapjacks?The first step to determine the amount of ingredients needed to make one flapjack.
Ingredients for one flapjack:
margarine = 140 / 12
sugar : 120 / 12
syrup : 100 / 12
oats : 240 / 12
raisins : 50 / 12
Ingredients for 30 flapjacks:
margarine = (140 / 12) x 30 = 350g
sugar : (120 / 12 ) x 30 = 300g
syrup : (100 / 12) x 30 = 250g
oats : (240 / 12) x 30 = 600g
raisins : (50 / 12) x 30 = 125g
To learn more about division, please check: https://brainly.com/question/13281206
#SPJ1
The radius of a circle is 3 units.
expand 2x(5x-2)
answer needed asap
Answer:
10[tex]x^{2}[/tex] - 4x
Step-by-step explanation:
Answer:
10x^2-4x
Step-by-step explanation:
Information is given about a polynomial f(x) whose coefficient are real numbers. Find the remaining zeros of f.
Degree 3; zeros: -2,4-i
Please help!
Answer:
Remaining zeros x= 4+i
Step-by-step explanation:
since complex roots always occur in conjugate pairs.
so if one root is 4-i the other one will be 4+i
8th grade math, please help.
Answer:
140 degrees
Step-by-step explanation:
because they're congruent
since this is no where on here
Answer:
B)
Hope that helps! Or is it for our own good? Either way, thanks!
Step-by-step explanation:
If X + 3Y = 5 and 2X - Y = 3, then X is equal to
Answer:
X=2
Y=1
That's the answer
Negative X plus negative one equals 3X plus -5 what is X
Pleases help with 4-9!
Step-by-step explanation:
The answer is
4_
[tex]m = \frac{4 - 0}{0 - ( - 2)} = \frac{4}{2} = 2[/tex]
9_
[tex]m = \frac{3 - 0}{0 - 4} = \frac{ - 3}{4} [/tex]
ILL GIVE BRAINLIEST
SHOW ALL WORK
Answer:
9/20 mile^2
Step-by-step explanation:
9/10 x 1/2 = 9/20
Answer:
The area of the field is [tex]\frac{9}{20}[/tex] [tex]miles^{2}[/tex]
Step-by-step explanation:
To get the area, multiply the length and the width together: [tex]\frac{9}{10}[/tex] * [tex]\frac{1}{2}[/tex] = [tex]\frac{9 * 1}{10*2}[/tex] = [tex]\frac{9}{20}[/tex][tex]miles^{2}[/tex].
find the derivative of f(x) = 6 / x at x = -2.
Answer:
Substitute the given value into the function and evaluate.
−3
Step-by-step explanation:
I think I'm not really sure but use math-way it helps a lot
Round 291 to the nearest hundredth
Answer:
291 rounded to the nearest hundredth = 291.00
Step-by-step explanation:
QUESTION 8
In this question, you will be assessed on the quality of your organisation, communication and
accuracy in writing
A rod is 4 yards long and another rod is 1į yards long.
What is the total length of these rods in inches?
You must show all your working.
(3 + 2 OCW]
You are given that:
1 yard = 3 feet
1 foot = 12 inches
Answer:
180
Step-by-step explanation:
First you do 3 feet or 36 inches and multiply that by 5 to get 180.
a class has eight boys and 12 girls. what is a ratio of boys to girls?
Answer:
8:12
Step-by-step explanation:
Answer:
8:12
= 2:3
hope
this
helps
1. Find the area of the shaded sector.
2. Find the length of the arc defined by the sector.
Answer:
1. 150π sq.ft 2. 10π ft
Step-by-step explanation:
Part 1Equation: Area of a sector = [tex]\frac{x}{360}[/tex] × π[tex]r^{2}[/tex]
Where:
x = internal angle
r = radius of circle
Values from problem:
x = 60
r = 30
Plug values into equation:
Area of sector = [tex]\frac{60}{360}[/tex] × π[tex]30^{2}[/tex]
Simplify:
60 divided by 30 equals [tex]\frac{1}{6}[/tex] and 30 squared equals 900 so...
[tex]\frac{1}{6}[/tex] × 900π
900π divided by 6 equals 150π so...
[tex]\frac{900}{6}[/tex] × π = 150π
150π sq. ft
Part 2Equation: Arc length = [tex]\frac{x}{360}[/tex] × 2πr
Where:
x = internal angle
r = radius of circle
Values from Problem:
x = 60
r = 30
Plug values into equation:
Arc length = [tex]\frac{60}{360}[/tex] × 2π30
Simplify:
60 divided by 360 equals [tex]\frac{1}{6}[/tex], and 2π × 30 equals 60π so...
[tex]\frac{1}{6}[/tex] × 60π
60π divided by 6 is 10π
[tex]\frac{60}{6}[/tex]π = 10π
10π ft
The radius of a circle measures 12 centimeters.
What is the circumference of the circle?
Answer:
C=24π
Step-by-step explanation:
C=2πr
C=2π12
C=24π
≈75.39
1. Find the slope of the line that passes through the points (9, 7) and (2, 9).
11
16
7
2
2
-7
7
2
Answer:
Step-by-step explanation:
Slope of line passing through (x₁, y₁) and (x₂, y₂) = (y₂-y₁)/(x₂-x₁)
Slope of line passing through (9, 7) and (2, 9) = (9-7)/(2-9) = -2/7
Answer:
The slope is [tex] - \frac{2}{7} [/tex]
_
Step-by-step explanation:
☆Remember: [tex]m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
---
☆We need to find the slope . So just plug in according to the slope formula!
[tex]m = \frac{9 - 7}{2- 9} = \frac{ \: \: 2}{ - 7} = - \frac{2}{7} [/tex]
---
▪Happy To Help <3
Suppose y varies directly with x, and y=98 when x=14. Write the direct
variation equation that relates x and y.
===========================================================
Explanation:
Since y varies directly with x, this means y = kx for some constant k.
Plug in y = 98 and x = 14 to solve for k
y = kx
98 = k*14
98/14 = k
7 = k
k = 7
Therefore, y = kx updates to y = 7x which is the equation we're after.
Answer:
y = 7x
Step-by-step explanation:
The general formula for direct variation is y = kx, where k is the constant of proportionality. If y = 98 when x = 14, then k must be 98/14. or 7, and so
y = 7x is the desired direct variation equation.
Find the Y intercept of the following quadratic function.
Answer:
The Y-intercept is 6
Step-by-step explanation:
Please solve this problem for me.
Answer:
It is 63 or 63/1. Billy used change in x over change in y, and the correct formula for slope is the change in y over the change in x.
He might have done it backwards.
1/63
and could be 63 miles in 1 hour
63/1.
Because the graph looks good. (i think)
A spinner is divided into sections of equal size, some of which are red, some are blue, and the remaining are green. The probability of the arrow landing on a red section is 40%. The probability of the arrow landing on a blue section is 25%.
What is the probability of the arrow landing on a green section?
Group of answer choices
35%
65%
25%
50%
Answer:
35%
Step-by-step explanation:
X=the probability of the arrow landing on a green section.
Equation:
40+25+ x = 100
65 +x = 100
(65-65) + x = 100-65
X= 35
Hope this helps!
