Answer:
A) cotx = cosx/sinx
C) tanx = 1/cotx
Step-by-step explanation:
A)
cosx/sinx = 1/(sinx/cosx) = 1/tanx = cotx
Therefore, cotx = cosx/sinx
C)
Similarly;
1/tanx = cotx
Therefore,
1 = tanxcotx
1/cotx = tanx
and
tanx = 1/cotx
B) cscx=1/cosx is not true since;
1/cosx = secx
and
cscx = 1/sinx
I need answers for both please!!
1 = a
2 = h
have a good day
A county government says that a safe level of chlorine in a hot tub is within 1.75 ppm of 3.25 ppm.
a. Write and solve an absolute value inequality to represent this situation.
b. A lifeguard measures the chlorine level in the pool and finds it is 1.0 ppm. Should he add more chlorine? Explain.
Answer:
Part A : |x-2.5| ≤ 0.75 , x ∈ [1.75,3.5]
Part B : yes, the lifeguard should add more chlorine.
Step-by-step explanation:
Part A:
Let C is the variation of the level of chlorine in a hot tub.
Level of chlorine in a hot tub is within 1.75 ppm of 3.25 ppm.
To find absolute value inequality, need to find the standard level of chlorine 1.75 + C or 3.25 - C
1.75 + C = 3.25 - C
2C = 5
C = 2.5
So, the standard level would be 2.5 ppm,
If x represents the present level of chlorine,
Then it would be lie within 1.75 ppm of 3.25 ppm.
1.75 ≤ x ≤ 3.25
Subtract 2.5 from all sides
1.75 - 2.5 ≤ x -2.5 ≤ 3.25 - 2.5
-0.75 ≤ (x-2.5) ≤ 0.75
which is equivalent to the following absolute value inequality.
|x-2.5| ≤ 0.75
And the solve of the inequality : x ∈ [1.75,3.5]
Part B: If x = 1.0 ppm,
∴ |1.0-2.5| = 1.5 which is not less than equal to 0.75.
Another explanation:
the minimum safe level of chlorine in a hot tub is 1.75 ppm
Since 1 < 1.75
Therefore, lifeguard should add more chlorine.
FACTOR: 36−(5+2a)^2
QUICKLY PLS!
36-(4+2a)^2=0
36-16+4a^2=0
4a^2+20=0
a^2+5=0 <— Factored form
A right rectangular pyramid is sliced parallel to the base as shown.
What is the area of the resulting two-dimensional cross-section?
A. 2
B. 3
C. 9
D. 12
Answer:
[tex]A=2\ m^{2}[/tex]
Step-by-step explanation:
we know that
The resulting two-dimensional cross-section is a rectangle 1 m x 2 m
so
the area of this rectangle is equal to
[tex]A=2*1=2\ m^{2}[/tex]
Which line is the line of best fit for this scatter plot?
The last one. It goes and touches the most points.
The 4th line is the line of best fit for this given scatter plot.
What is a scatter plot?"A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed."
Here, 4 different lines are drawn for a given scatter plot.
We know, a line drawn on a scatter plot fits it the best is the line that is closer to most of the points.
Here, the 4th line is closer to most of the points on the scatter plot.
Therefore, 4th line is the best fit.
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Please help, what is x?
Answer:
x = 18
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{x+x+3}{x+3}[/tex] = [tex]\frac{14+12}{14}[/tex]
[tex]\frac{2x+3}{x+3}[/tex] = [tex]\frac{26}{14}[/tex] ( cross- multiply )
14(2x+3) = 26(x + 3) ← distribute both sides
28x + 42 = 26x + 78 ( subtract 26x from both sides )
2x + 42 = 78 ( subtract 42 from both sides )
2x = 36 ( divide both sides by 2 )
x = 18
(20 points) Please answer and explain!
multiply and simplify -3x^2y^2 * y^4x3
a. -3x^5y^6
b. -3x^6y^2
c. 9x^5y^2
d. -3x ^5y^2
Answer:
[tex]\large\boxed{a.\ -3x^5y^6}[/tex]
Step-by-step explanation:
[tex]-3x^2y^2\cdot y^4x^3=(-3)(x^2x^3)(y^2y^4)\\\\\text{use}\ a^na^m=a^{n+m}\\\\=-3x^{2+3}y^{2+4}=-3x^5y^6[/tex]
Consider the function f (x) = x2.
What effect does subtracting 2 from the input have on the graph of the function?
Answer: The graph is shifted 2 units to the right.
Step-by-step explanation:
Given a function f(x), we know that one transformation rule is:
If [tex]f(x-k)[/tex] then the function is shifted "k" units to the right.
Therefore, for the function [tex]f(x)=x^{2}[/tex], when we subtract 2 from the input, then we get the function g(x) in the form:
[tex]g(x)=(x-2)^{2}[/tex]
We can conclude that subtracting 2 from the input of the function [tex]f(x)=x^{2}[/tex], then the graph is shifted 2 units to the right.
The answer is right graph shifted 2 units to the right
Which statement describes the speed of the remote control car over time?
Answer:
Step-by-step explanation:
D
Find the volume of the figure. Round your answer to the nearest hundredth, if necessary.
Answer:
Step-by-step explanation:
3.14 x 10.6^2= 352.81 pi
Answer is...
Volume = 4988.92
See attached photo
15) f(x) = 3x + 5
g(x)=-4x + 3
Find f(x) + g(x)
17) f(x) = 2x +4
g(x)= x - 5
Find f(x) - g(x)
how do u solve these equations?
Answer:
15) f(x) + g(x) = -x + 8
17) f(x) - g(x) = x + 9
Step-by-step explanation:
15)
f(x) = 3x + 5
g(x)= - 4x + 3
Find f(x) + g(x)
f(x) + g(x) = 3x + 5 + ( - 4x + 3 )
f(x) + g(x) = 3x + 5 - 4x + 3
f(x) + g(x) = -x + 8
17)
f(x) = 2x +4
g(x)= x - 5
Find f(x) - g(x)
f(x) - g(x) = 2x +4 - (x - 5 )
f(x) - g(x) = 2x +4 - x + 5
f(x) - g(x) = x + 9
[tex]
f(x)=3x+5 \\
g(x)=-4x+3 \\
(f+g)(x)=f(x)+g(x)=(3x+5)+(-4x+3) \\
3x+5-4x+3=\boxed{-x+8} \\ \\
f(x)=2x+4 \\
g(x)=x-5 \\
(f-g)(x)=f(x)-g(x)=(2x+4)-(x-5) \\
2x+4-x+5=\boxed{x+9}
[/tex]
Hope this helps.
r3t40
The radius of a circle is three meters. What is the circle’s diameter
The diameter of a circle is the radius times 2.
Diameter = 3 x 2 = 6 meters.
Answer:
6 is the answer.
3 x 2 = 6
Step-by-step explanation:
For Spirit Day, each 8th-grade
homeroom designs a unique two-
color T-shirt. They get to choose from
the colors red (R), blue (B), green (G),
violet (V), and orange (O). Each T-shirt
is a solid color with a different color
used for the student's name. What is
the probability that a homeroom will
have a T-shirt with a combination of
blue and violet?
(A) P(B and V)=10%
(B) P(B and V)=20%
(C) P(B and V)=30%
(D) P(B and V)=40%
Answer: Option A
P(B and V)=10%
Step-by-step explanation:
To solve this poroblema we use the formula of combinations:
[tex]nCr =\frac{n!}{r!(n-r)!}[/tex]
Where n is the number of objects that can be chosen and you choose r from them.
There are 5 colors of shirts.
The number of shirts that can be made by combining 2 of the 5 possible colors is calculated as:
[tex]5C2[/tex]
[tex]5C2=\frac{5!}{2!(5-2)!}[/tex]
[tex]5C2=10[/tex]
The number of shirts that can be made by combining 2 of the 2 possible colors (B) and (V) is calculated as:
[tex]2C2 = 1[/tex]
Then the probability is:
[tex]P(B\ and\ V)=\frac{2C2}{5C2}\\\\P(B\ and\ V)=\frac{1}{10}\\\\P(B\ and\ V)=0.1=10\%[/tex]
Answer: the answer is D
Step-by-step explanation:
Cause you have to do 100% divided by 5 you will get 20%
So if you have two of the five colors you will have two multiple 20% times 2 and get 40%
solve for K thanks!!!
4.5 + 1.5k = 18 - 3k
Bring -3k to the other side by adding 3k to both sides
4.5 + (1.5k + 3k) = 18 + (-3k + 3k)
4.5 + 4.5k = 18 + 0
4.5 + 4.5k = 18
Bring 4.5 to the other side by subtracting it to both sides
(4.5 - 4.5) + 4.5k = 18 - 4.5
0 + 4.5k = 13.5
4.5k = 13.5
Isolate k by dividing 4.5 to both sides
4.5k / 4.5 = 13.5 / 4.5
k = 3
Hope this helped!
~Just a girl in love with Shawn Mendes
a small box has a length of (x) a width of (x+1) and a height of (x+2). what is the volume of the box
Answer:
Step-by-step explanation:
The volume of a box with dimensions length x, width (x+1), and height (x+2), is given by the formula x^3 + 3x^2 + 2x cubic units.
Explanation:The volume of the box can be calculated by multiplying its length, width, and height together. Given that the length is x, width is (x+1), and height is (x+2), the volume would be x*(x+1)*(x+2).
To further expand this, apply the distributive law which first multiplies x*(x+1), resulting in x^2 + x. Then multiply this result by (x+2), giving the final volume V = x^3 + 3x^2 + 2x.
Therefore, the volume of the box given the stated dimensions is x^3 + 3x^2 + 2x cubic units.
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A cube has an edge length 12cm. If the edge length of the cube is doubled, what happens to the surface area?
Answer:
Surface area of original cube:
6(12²) = 6(144) = 864 cm²
Surface area of new cube:
6(24²) = 6(576) = 3,456 cm²
If the edge length of the cube is doubled, the surface area of the cube will be quadrupled.
Doubling the edge length of a cube from 12 cm to 24 cm increases the surface area by a factor of four, from 864 cm^2 to 3456 cm^2, because surface area is a two-dimensional measure and each dimension has been doubled.
If a cube has an edge length of 12 cm, its surface area is calculated by the formula 6s^2, where s is the length of a side. So the surface area of the original cube is 6 imes 122 cm^2 = 864 cm^2.
When the edge length of the cube is doubled to 24 cm, to find the new surface area, we also apply the formula 6s^2. Therefore, the new surface area is 6 imes 242 cm^2 = 3456 cm^2.
Comparing the new surface area to the original, we see that it has increased by a factor of 4, which is the square of the factor by which the edge length was multiplied (22 = 4). This occurs because surface area is a two-dimensional measure (involving length by width), so when each dimension is doubled, the overall area increases by a factor of four (2 imes 2).
what is the value of x to the nearest tenth?
tan 24 = x/12
0.4452 · 12 = X
5.34 = X
HELPPP IDK WUT THE HECK THIS IS
ANSWER:
The 100 one is 10 and the 1,728 one is 12!
I think this is right and I hope I helped!
Tell me if it was right!
somebody help fast??????
Answer:
Option 3 (angle WXY + angle YXZ = 180) is the answer.
Which of the following is the product of the rational expressions shown below x+2/x-4•3x/x+4
Answer:
Final answer is [tex]\frac{3x^2+6x}{x^2-16}[/tex].
Step-by-step explanation:
Given rational expressions are [tex]\frac{x+2}{x-4}[/tex] and [tex]\frac{3x}{x+4}[/tex].
Now we need to find about what is the product of given rational expressions.
to multiply the rational expressions, we simply multiply numerator with numerator. Then multiply denominator with denominator.
[tex]\frac{x+2}{x-4}\cdot\frac{3x}{x+4}[/tex]
[tex]=\frac{\left(x+2\right)\cdot3x}{\left(x-4\right)\cdot\left(x+4\right)}[/tex]
[tex]=\frac{3x^2+6x}{x^2+4x-4x-16}[/tex]
[tex]=\frac{3x^2+6x}{x^2-16}[/tex]
Hence final answer is [tex]\frac{3x^2+6x}{x^2-16}[/tex].
6. Mr Wade works for 5 straight
hours when he opens his stand
After a 1 hour break he works
6 hours and 15 minutes before
Closing at 6:10p.m. What time
does Mr Wade open his stand
5:55am
Start by finding how long the stand was open. Add 5 hours + 1 hour + 6 hours 15 minutes to get 12 hours 15 minutes.
Now, just find the time that is 12 hours and 15 minutes before 6:10pm. Start by subtracting 12 hours, which just switches the time from a.m. to p.m. This brings you to 6:10am. Finally, subtract the 15 minutes to get 5:55am.
what i 36 divide by 86.4
If your asking whats 86.4 divided by 36 its 2.4
A 4-PINT carton of ice cream costs $12.04. What is the price per QUART
1 quart = 2 pints.
This means a 4 pint container is 2 quarts.
To find the price for 1 quart divide the price by 2:
12.04 / 2 = $6.02 per quart.
adults have 32 teeth children have 62.5% as many teeth as adults. how many teeth do children have
The answer would be 20
You multiply 62.5% by 32
32*0.625=20
They are correct it is 20.
Determine the total annual FICA tax for an annual salary of $165,000. Use $106,800 for maximum taxable earnings.
Answer:
FICA Tax =$8170.2
Step-by-step explanation:
Given
Total income=$165000
Taxable income=$106800
FICA tax includes Social security tax and medicare tax.
Medicare tax is 1.45% of the taxable wage and social security tax is6.2% of the taxable wage.
1.45% of medicare is paid by the employer and similarly 6.2% social security tax is paid by the employer.
0.9% of medical surtax is deducted if the employee earns more than $200000
So,
Medicare Tax=Taxable income*1.45/100
=106800*0.0145
=$1548.6
Social Security Tax=Taxable Income*6.2/100
=106800*0.062
=$6621.6
As the income of the employee is less than $200000, so there will be no medical surtax.
Total FICA tax=$1548.6+$6621.6
=$8170.2
What percentage kf the rolls are greater than 3?
Add the total number of rolls that were greater than 3.
This would be the number 4, 5 and 6.
8 + 11 + 10 = 29 rolls higher than 3.
Now divide the number of rolls higher than 3 by the total number of rolls which is given as 50:
29 / 50 = 0.58
Multiply by 100 to get the percent:
0.58 x 100 = 58% of the rolls were higher than 3.
Lydia bought a car for $20,000. It is expected to depreciate at a continuous rate. What will be the value of the car in 2 years? Use k = 0.105 and round to the nearest dollar.
Answer:
[tex]\$16,021[/tex]
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]V=P(1-k)^{x}[/tex]
where
V is the depreciated value
P is the original value
k is the rate of depreciation in decimal
x is Number of Time Periods
in this problem we have
[tex]P=\$20,000\\k=0.105\\x=2\ years[/tex]
[tex]V=\$20,000(1-0.105)^{2}=\$16,020.50[/tex]
round to the nearest dollar
[tex]\$16,020.50=\$16,021[/tex]
the value of the car after 2 years will be approximately $16,212.
To find the value of the car after 2 years with continuous depreciation, we will use the formula for continuous exponential decay:
[tex]V(t) = V_0 \times e^{-kt}[/tex]
Where V(t) is the value after time t V_0 is the initial value, k is the decay constant and t is time
Plugging in the values:
[tex]V(2) = 20000 \times e^{-0.105 \times 2}[/tex]
Simplifying the exponent:
[tex]V(2) = 20000 \times e^{-0.21}[/tex]
[tex]V(2) = 20000 \times 0.8106 \approx 16212[/tex]
Thus, the value of the car after 2 years will be approximately $16,212.
Follow the process of completing the square to solve x2 - 10x + 8 = 0. How will the left side of the equation factor in step 5?
Answer:
[tex]x=5(+/-)\sqrt{17}[/tex]
Step-by-step explanation:
we have
[tex]x^{2}-10x+8=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]x^{2}-10x=-8[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]x^{2}-10x+5^{2}=-8+5^{2}[/tex]
[tex]x^{2}-10x+25=-8+25[/tex]
[tex]x^{2}-10x+25=17[/tex]
Rewrite as perfect squares
[tex](x-5)^{2}=17[/tex]
Take square root both sides
[tex](x-5)=(+/-)\sqrt{17}[/tex]
Adds 5 both sides
[tex]x=5(+/-)\sqrt{17}[/tex]
A total of 430 dogs and people attend a fundraising dog walk. Altogether, 1210 legs participated in the walk. How many dogs were there?
1210÷4=302.5 and u can have a half of a dog so there would be 302
A student pulls out a marble from a pag containing blue, green, and red marbles. He records the color and places it back into the bag The table below shows the frequency of
each color after 100 marbles are pulled out
Color of Marbles Blue Green Red
Number of Draws 13 29 58
How many green draws can you expect if the marbles are pulled out 1,000 times?
Answer:
Answer is B - 290.
Step-by-step explanation:
The idea here is that we're assuming the frequency each colour is drawn is a reflection of the proportion of marbles in the bag that are that colour. The more of a particular colour you have, the more likely you are to draw it, and vice versa.
Therefore we can assume the proportion of blue, gree, and red marbles is 13%, 29%, and 58% respectively based on the first 100 draws.
These percents should stay relatively similar as more draws are done, approaching the true proportions of each colour better the higher the number of draws. That means 29%, or 290, of the 1000 draws will be green.
Answer: 290
Step-by-step explanation: