Answer:
[tex]\cos x=-\dfrac{\sqrt{21}}{5}\\ \\\tan x =-\dfrac{2}{\sqrt{21}}\\ \\\cot x=-\dfrac{\sqrt{21}}{2}[/tex]
Step-by-step explanation:
Given
[tex]\sin x=\dfrac{2}{5}\\ \\\cos x<0[/tex]
Use formula:
[tex]\cos^2x+\sin ^2x=1\\ \\\cos^2x+\left(\dfrac{2}{5}\right)^2=1\\ \\\cos^2x=1-\dfrac{4}{25}\\ \\cos^2x=\dfrac{21}{25}\\ \\\cos x=\pm \dfrac{\sqrt{21}}{5}[/tex]
Since [tex]\cos x<0,[/tex] then
[tex]\cos x=-\dfrac{\sqrt{21}}{5}[/tex]
By definition,
[tex]\tan x =\dfrac{\sin x}{\cos x}=\dfrac{\frac{2}{5}}{-\frac{\sqrt{21}}{5}}=-\dfrac{2}{\sqrt{21}}\\ \\ \\\cot x=\dfrac{1}{\tan x}=\dfrac{1}{-\frac{2}{\sqrt{21}}}=-\dfrac{\sqrt{21}}{2}[/tex]
How many 2/3 cup servings are in a 4 cup container of food
Answer:
6
Step-by-step explanation:
4 divided by 2/3 is 6, because 4 x 2 = 8, and 8/3 is 6.
Please help !!!!!!!!!
Answer:
Katherine invested $12,000
Step-by-step explanation:
Use formula
[tex]I=P\cdot r\cdot t,[/tex]
where
I = interest,
P = principal,
r = rate (as decimal),
t = time (in years).
In your case,
t = 1 year,
r = 0.06 (or 6%)
P + I =$12,720, thus
[tex]12,720-P=P\cdot 0.06\cdot 1\\ \\12,720-P=0.06P\\ \\12,720=P+0.06P\\ \\1.06P=12,720\\ \\P=\dfrac{12,720}{1.06}\\ \\P=\$12,000\\ \\I=\$12,720-\$12,000=\$720[/tex]
Two pieces of equipment were purchased for a total of $4000. If one piece cost $850 more than
the other, find the price of the less expensive piece of equipment. Assume all data are accurate
to two significant digits unless greater accuracy is given.
The price of less expensive equipment is $1575.
Step-by-step explanation:
Let,
Price of one equipment = x
Price of other equipment = y
According to given statement;
x+y=4000 Eqn 1
x = y+850 Eqn 2
Putting Eqn 2 in Eqn 1
[tex](y+850)+y=4000\\y+850+y=4000\\2y=4000-850\\2y=3150[/tex]
Dividing both sides by 2;
[tex]\frac{2y}{2}=\frac{3150}{2}\\y=1575[/tex]
Putting y=1575 in Eqn 2;
[tex]x=1575+850\\x=2425[/tex]
The price of less expensive equipment is $1575.
Keywords: linear equation, substitution method
Learn more about linear equations at:
brainly.com/question/11343416brainly.com/question/11416224#LearnwithBrainly
Final answer:
The price of the less expensive piece of equipment is $1575. This was calculated by setting up an equation based on the total cost and the difference in price between the two pieces of equipment and then solving for the unknown price.
Explanation:
To find the price of the less expensive piece of equipment, we will first assign variables to the two pieces of equipment. Let's call the cost of the less expensive piece of equipment x dollars. Since the other piece cost $850 more, the cost of the second piece would then be x + $850. We are given that the total cost of both pieces is $4000, so we can set up the following equation to represent this relationship:
x + (x + $850) = $4000
To solve for x, we combine like terms and get:
2x + $850 = $4000
Subtracting $850 from both sides gives us:
2x = $3150
Dividing both sides by 2, we find the value of x:
x = $1575
Therefore, the price of the less expensive piece of equipment is $1575.
When Dustin goes to work, he drives at an average speed of 55
miles per hour. It takes about 2 hour and 15 minutes for Dustin to
arrive at work. His car travels about 25 miles per gallon of gas. If
gas costs $2.75 per gallon, how much money does Justin spend to
travel each mile to work?
Dustin spends $13.6125 on going to work daily. It is 0.11 dollars per mile
Step-by-step explanation:
we have to caalculate the distance between Dustin's home and work
So
Given
Speed =s = 55 miles per hour
Time = t = 2 hours and 15 minutes
Converting time into fraction
Time = 2.25 hours
We know that
[tex]s = \frac{d}{t}\\d = s * t\\d = 55 * 2.25\\d = 123.75\ miles[/tex]
So the distance is 123.75 miles
The car travels 25 miles per gallon
We have to calculate the total number of gallon first
So,
[tex]No.\ of\ gallons = \frac{Miles}{Miles\ per\ gallon}\\=\frac{123.75}{25}\\=4.95\ gallons[/tex]
So the total amount is:
[tex]2.75*4.95\\= 13.6125\ dollars[/tex]
Total amount is $13.6125. Dividing it by total distance will give us the cost of each mile
So,[tex]Cost\ of\ mile = \frac{Total\ amount}{Distance}\\= \frac{13.6125}{123.75}\\=0.11\ dollars[/tex]
Hence,
Dustin spends $13.6125 on going to work daily. It is 0.11 dollars per mile
Keywords: Speed, Distance
Learn more about distance and speed at:
brainly.com/question/9590016brainly.com/question/9607945#LearnwithBrainly
The fraction 7/9 is in the lowest terms. True or false ??
Answer:
True
Step-by-step explanation:
This is true because there is no common factor for 7 annd 9
Please help! And if u do label the answers so Ik which is which if u answer n say idk I’ll report u
Answer:
5. y-intercept is 8
6. slope is -1/2
7. y=-1/2x+8
what is 4/9 divided by 7/9
Answer:
4/9
Step-by-step explanation:
(4/9)/(7/9) is equal to (4/9)*(9/7) because "keep change flip." So we keep the first number, change division into multiplication, and flip 4/9 (basically find the reciprocal) and that is 9/4. Thus, (4/9)*(9/7) is equal to 4/9 because the 7's cancel.
I hope this helped!
Answer: 4/7
Step-by-step explanation: In this problem, we have 4/9 ÷ 7/9. Dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division to multiplication and flip the second fraction.
So here, 4/9 divided by 7/9 can be rewritten as 4/9 × 9/7.
Now we are simply multiplying fractions.
To multiply fractions, we multiply across the numerators and multiply across the denominators.
Image provided.
Notice however that 36/63 is not in lowest terms so we divide both the numerator and denominator by 9 and we get the equivalent fraction 4/7.
Therefore, 4/9 divided by 7/9 = 4/7.
Given: E-midpoint of DA
F - midpoint of DB
E, F, C collinear, FC ≅ EF
Prove: EABC is a parallelogram.
By proving that triangles DEA and EFB are congruent due to the Side-Angle-Side postulate and demonstrating that AE is parallel to FB as well as AD parallel to BC, we can conclude that EABC is a parallelogram.
To prove that quadrilateral EABC is a parallelogram, we can use the properties of triangles and the definition of a parallelogram. According to the given information, E is the midpoint of DA and F is the midpoint of DB. Additionally, we know that E, F, and C are collinear and that FC is congruent to EF.
Leveraging these pieces of information, we observe that triangle DEA is congruent to triangle EFB because they have a side (EF or DE), an angle (at point E, since DE is an extension of EF), and another side (EA or FB, which are halves of DA and DB, respectively) in common (Side-Angle-Side postulate).
Since the two triangles are congruent, angle DEA is congruent to angle EFB, and angle DAE is congruent to angle FEB. These congruent angles imply that line AE is parallel to line BF. Since E and F are midpoints, AE is half of DA and BF is half of DB. If we continue the line AE to meet CD at point A and the line BF to meet CD at point B, EA will be parallel to FB, and AD will be parallel to BC, meeting the definition of a parallelogram.
EABC is a parallelogram because opposite sides are parallel and equal due to the Midpoint Theorem.
Given:
E - midpoint of DA
F - midpoint of DB
E, F, C collinear, FC ≅ EF
To Prove: EABC is a parallelogram.
Proof:
1. By the Midpoint Theorem, EF || AB and EF = 1/2 * AB. (Midpoint Theorem)
2. Since E, F, C are collinear and FC ≅ EF, EC bisects EF at C. Therefore, AB || EC. (Definition of a parallelogram)
3. Since E is the midpoint of DA and C is the midpoint of EF, EC = 1/2 * DA. Since DA = AB, EC = 1/2 * AB. Similarly, EF = 1/2 * AB. Hence, EC = EF. Therefore, EA || BC. (Midpoint Theorem)
4. Since E is the midpoint of DA and C is the midpoint of EF, EC = 1/2 * DA. Since DA = BC, EC = 1/2 * BC. Similarly, EF = 1/2 * BC. Hence, EC = EF. Therefore, EB ≅ AC. (Midpoint Theorem)
Therefore, EABC is a parallelogram.
Alicia conducted an experiment in which a spinner landed on green seven times if the experimental probability of the spinner landing on green is 1/5 how many trials did Alicia perform
Answer:
35 trials
Step-by-step explanation:
Probability = Favorable Outcome / Total Outcome
P = 1/5
Favorable Outcome = 7
Substitute the values,
1/5 = 7 / Total Outcomes
1/5 =7/x
Cross multiplication:
1x=5*7
x=35
Total Trials = 35
Leo has 9 times as many red marbles as blue marbles.
If he has 2288 more red marbles than blue marbles, how many red marbles does he have?
Answer:20592
Step-by-step explanation:
Because you multiply 5 times 2288
Leo has 2574 red marbles.
Explanation:Let's say that the number of blue marbles Leo has is x. According to the given information, Leo has 9 times as many red marbles as blue marbles. So the number of red marbles Leo has is 9x.
It is also given that he has 2288 more red marbles than blue marbles, which means 9x = x + 2288.
Simplifying the equation, we can subtract x from both sides: 8x = 2288. Dividing both sides by 8, we find that x = 286.
Therefore, Leo has 9 times 286 red marbles, which equals 2574 red marbles.
Please help meeee (1/2) to the 4th power
Answer:
[tex]\frac{1}{16}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2} *\frac{1}{2} *\frac{1}{2} *\frac{1}{2} =[/tex][tex]\frac{1}{16}[/tex]
[tex]\frac{1}{2}*\frac{1}{2} =\frac{1}{4}[/tex]
[tex]\frac{1}{4} *\frac{1}{2} =\frac{1}{8}[/tex]
[tex]\frac{1}{8}*\frac{1}{2}=\frac{1}{16}[/tex]
Determine the maximum number of zeros. Then, determine the x-intercepts of the function. x^3-3x^2-22x+24
Answer:
Three zeros [tex]x=-4,\ x=1,\ x=6[/tex]
x-intercepts: (-4,0), (1,0), (6,0)
Step-by-step explanation:
Plot the graph of the function [tex]y=x^3-3x^2-22x+24[/tex] on the coordinate plane. This graph intersects the x-axis at three different points (see attached diagram):
(-4,0);(1,0);(6,0).This means [tex]x=-4,\ x=1,\ x=6[/tex] are zeros of the function [tex]y=x^3-3x^2-22x+24[/tex]
Answer:
D
because i think
Determine which binomial is not a factor of 4x^4 – 21x^3 – 46x^2 + 219x + 180.
A. x
+ 4
B. x + 3
C. x
- 5
D. 4x + 3
Answer:
A. x + 4
Step-by-step explanation:
f(x) = 4x⁴ − 21x³ − 46x² + 219x + 180
Plug in the zero of each binomial. If it's also a zero of f(x), then that binomial is a factor of f(x).
f(-4) = 936
f(-3) = 0
f(5) = 0
f(-3/4) = 0
The binomial (x + 4) is not the factor of the polynomial. Then the correct option is A.
What is a Binomial factor?The algebraic factors with exactly two terms are known as binomial components. Although binomials are simple to solve and their roots are identical to those of polynomials, binomial factors are intriguing.
The polynomial is given below.
⇒ 4x⁴ – 21x³ – 46x² + 219x + 180
Let's check all the factors.
If the factor does not satisfy the polynomial, then the binomial is a factor of the polynomial.
For x + 4 = 0, then we have
The value of the polynomial at x = -4, will be
⇒ 4(-4)⁴ – 21(-4)³ – 46(-4)² + 219(-4) + 180
⇒ 4(256) – 21(-64) – 46(16) + 219(-4) + 180
⇒ 1024 + 1344 – 736 – 876 + 180
⇒ 2548 – 1612
⇒ 936
Thus, the binomial (x + 4) is not the factor of the polynomial.
Then the correct option is A.
More about the Binomial factor link is given below.
https://brainly.com/question/17010849
#SPJ2
2. Find 16.36 - 2.954
14.918
O 13.954
O 14.314
13.406
Answer:
13.406
The drawing will help
Answer:
13.406
Step-by-step explanation:
One positive number is five times another number is the difference between the two numbers is 1676 find the numbers
Answer:
The two numbers are -419 and -2095.
Step-by-step explanation:
5x=y
x-y=1676
----------------
x-5x=1676
-4x=1676
x=1676/-4
x=-419
5(-419)=y
y=-2095
24. The function f(t) = -16t^2 +20t +4 gives the height of a ball, in feet, t seconds after it is tossed.
What is the average rate of change, in feet per second, over the interval [0.75, 1.25]
Answer:
-12 feet per second
Step-by-step explanation:
average rate of change over [0.75, 1.25] = [tex]\frac{f(1.25) - f(0.75)}{1.25 - 0.75}[/tex]
f(1.25) - f(0.75) = 4 - 10 = -6
1.25 - 0.75 = 0.5
[tex]\frac{f(1.25) - f(0.75)}{1.25 - 0.75}[/tex] = [tex]\frac{-6}{0.5}[/tex] = -12
The average rate of change of the function f(t) over the interval [0.75, 1.25] is -12 feet per second.
We have,
To find the average rate of change of the function f(t) over the interval [0.75, 1.25], you can use the following formula:
Average Rate of Change = [f(1.25) - f(0.75)] / (1.25 - 0.75)
Calculate f(1.25):
f(1.25) = -16(1.25)^2 + 20(1.25) + 4
Calculate f(0.75):
f(0.75) = -16(0.75)^2 + 20(0.75) + 4
Plug these values into the formula:
Average Rate of Change = [f(1.25) - f(0.75)] / (1.25 - 0.75)
Calculate the numerator:
Average Rate of Change = [(-16(1.25)^2 + 20(1.25) + 4) - (-16(0.75)^2 + 20(0.75) + 4)] / (1.25 - 0.75)
Simplify the numerator:
Average Rate of Change = [-25 + 25 + 4 - (-9 + 15 + 4)] / (1.25 - 0.75)
Further, simplify:
Average Rate of Change = (4 - (-9 + 15 + 4)) / (1.25 - 0.75)
Continue simplifying:
Average Rate of Change = (4 - 10) / (1.25 - 0.75)
Calculate the final result:
Average Rate of Change = (-6) / (0.5)
Average Rate of Change = -12 feet per second
Thus,
The average rate of change of the function f(t) over the interval [0.75, 1.25] is -12 feet per second.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ3
Aunt Annie and her family traveled 253
miles on Tuesday and 157 miles on
Wednesday. It is 473 miles from Annie's
to Grandma's How many miles do they have
left to travel on Thursday?
Answer:
63 miles left
Step-by-step explanation:
253+157=410
473-410=63
What is log39 = x in exponential form?
3x = 9
o 9x = 3
o x3 = 9
o 39 = x
оооо
DONE
Answer:
9 = [tex]3^{x}[/tex]
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
[tex]log_{3}[/tex] 9 = x ⇔ 9 = [tex]3^{x}[/tex] ← in exponential form
Answer:
its A on edge
Step-by-step explanation:
Solution to system of equations
Answer: In general, a solution of a system in two variables is an ordered pair that makes BOTH equations true. In other words, it is where the two graphs intersect, what they have in common. So if an ordered pair is a solution to one equation, but not the other, then it is NOT a solution to the system
PLEASE ANSWER THIS QUICKLY BUT ALSO PLEASE GIVE ME THE RIGHT ANSWER. WHOEVER ANSWERS THE FASTEST GETS A BRAINLIEST!!!!!!!!
A carpenter has boards of lengths 24, 36, and 42 inches that must be cut into smaller boards of equal length, with no scrap wood left over.
What is the longest length of boards he can cut?
A. 2 inches
B.6 inches
Answer:
B.6 inches
Step-by-step explanation:
Given: Three boards with measurement 24, 36, and 42 inches.
For the longest length of board we have to find out the H.C.F.
And for H.C.F. we will find out the factors,
[tex]24=2\times2\times2\times3\\36=2\times2\times3\times3\\42=2\times3\times7[/tex]
Here 2 and 3 is the common factor of given length of boards.
So the H.C.F. is 6.
Hence the longest length of board that carpenter can cut is 6 inches.
Mr. Lee drove 8 miles from his house to pakside.parkside i 4 miles south of springfield.from parkside, he drove 3 miles to springdale .then he drove 20 miles from springdale to brookville. How far did mr. Lee drive in all , from his house to brookville ? Identify the extra or missing information .solve i possible.
Mr Lee drive 31 miles from his house to Brookville and there is an extra information that is parkside is 4 miles south of springfield which is not required.
Solution:Given that
Mr. Lee drove 8 miles from his house to park side .
Parkside is 4 miles south of springfield.
From Parkside he drove 3 miles to springdale
Then he drove 20 miles from springdale to brookville.
Need to determine how far Mr Lee drive in all, from his house to Brookville.
Also need to identify Extra or missing information.
Complete drive of Mr Lee from his house to Brookville is equal to 8 miles from his house to park side then 3 miles from Parkside to springdale , then 20 miles from springdale to brookville.
=> Complete drive of Mr Lee from his house to Brookville in miles = 8 + 3 + 20 = 31 miles
Information that is parkside is 4 miles south of springfield is extra information which is not required to determine mr. Lee drive , from his house to Brookville .
Hence Mr Lee drive 31 miles from his house to Brookville and there is an extra information that is parkside is 4 miles south of springfield which is not required.
help me answer this question please.
The right answer is Option B.
Step-by-step explanation:
Given expression is;
5x√2 - 3√2 + x√2
We can add or subtract square roots only when the values inside the square root are same and the variables are also same.
In the given expression, variable x is same with √2, therefore, adding both the roots
[tex]6x\sqrt{2} -3\sqrt{2}[/tex]
6x√2 - 3√2 is equivalent to 5x√2 - 3√2 + x√2.
The right answer is Option B.
Keywords: square roots, subtraction
Learn more about square roots at:
brainly.com/question/10435816brainly.com/question/10435836#LearnwithBrainly
Can someone please help me with this problem!
Answer:
11 yards
Step-by-step explanation:
The volume of a cone formula is:
[tex]V=\frac{1}{3}\pi r^2 h[/tex]
Where V is the volume,
r is the radius (half of diameter)
h is the height
Given,
h = 15
V = 475.17
We find the radius (r) first by substituting given values:
[tex]V=\frac{1}{3}\pi r^2 h\\475.17=\frac{1}{3}\pi r^2 (15)\\475.17=5\pi r^2\\r^2=30.25\\r=5.5[/tex]
The radius (r) is 5.5 yards
We need the diameter, which is DOUBLE THE RADIUS, so diameter would be:
Diameter = 5.5 * 2 = 11 yards
if Sin A = 0.5736, what is the Cos A =
The value of CosA is 0.8191
Step-by-step explanation:
Given SinA= 0.5736
We know that [tex]SinA^{2} + CosA^{2} = 1[/tex]
Replacing value of SinA,
[tex](0.5736)^{2} + CosA^{2} = 1[/tex]
[tex](0.3290) + CosA^{2} = 1[/tex]
[tex] CosA^{2} = 1-0.3290[/tex]
[tex] CosA^{2} = 0.6709 [/tex]
[tex] CosA = 0.8191 [/tex]
The value of CosA is 0.8191
What is the value of the red dot on the number line below?
Answer:
B, 9.625
Step-by-step explanation:
I know there's a more surefire method of doing this problem but since this is multiple choice, you can use process of elimination to solve it.
To begin a bacteria study, a petri dish had 1800 bacteria cells. Each hour since, the number of cells has increased by 15%.
Let t be the number of hours since the start of the study. Let y be the number of bacteria cells.
Write an exponential function showing the relationship between y and t.
Answer:
The exponential function is [tex]C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1[/tex]
Step-by-step explanation:
Given
[tex]t[/tex] be the number of hours.
[tex]y[/tex] number of bacteria cells.
And we know that an exponential function is [tex]C(t)=y(b)^t[/tex],where [tex]b[/tex] is a positive real number, and in which the argument [tex]t[/tex] occurs as an exponent
The petri dish has [tex]1800[/tex] bacteria cells we can say that [tex]y=1800[/tex]
In the equation as [tex]C[/tex] is function of time and [tex](t)[/tex] will vary as [tex]1,2,3[/tex] for respective hours.
To find the value of [tex]b[/tex] we have to understand that it is dependent on percent increase if there is increment of [tex]15\%[/tex] then [tex]b=1+15\%=1+\frac{15}{100}=1+0.15=1.15[/tex]
So the exponential function will be [tex]C(t)=y(b)^t[/tex] ,plugging the values it will be equivalent to [tex]C(t)=1800(1+0.15)^1[/tex]
Check:
[tex]15\% of 1800 =0.15\times 1800=270[/tex]
So in first hour the cells will increased by a quantity of [tex]270[/tex] cells.
The number of cells after an hour in the petri dish [tex]=(1800+270)=2070[/tex]
That can also be from the formula.
[tex]C(t)=1800(1.15)^1=2070[/tex]
So the exponential function is [tex]C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1[/tex]
[tex]y[/tex] will increase exponentially as the value of [tex]t[/tex] increase.
Final answer:
The exponential function to represent the growth of bacteria cells, y, after t hours with an initial amount of 1800 cells and a 15% hourly growth rate is y = 1800(1 + 0.15)^t.
Explanation:
To write an exponential function showing the relationship between the number of bacteria cells, y, and the time in hours, t, we begin by using the initial value of 1800 bacteria cells and apply a 15% increase each hour. The exponential growth formula is given by y = P(1 + r)^t, where P is the initial amount, r is the growth rate (expressed as a decimal), and t is the time.
Since the growth rate is 15%, we convert this to a decimal by dividing by 100, resulting in 0.15. The formula to model this bacterial growth would be y = 1800(1 + 0.15)^t. Therefore, for any given number of hours t, you can calculate the number of bacteria cells y.
Which of the following pairs are alternate exterior angles?
A.6 and 7
B.2 and 7
C.5 and 4
D.5 and 2
The perimeter of a rectangle is 10. The length of the rectangle is five less than four times the width. Find the width of the rectangle
L=4*W-5
10=W*2+(4*W-5)*2
10=W*2+8*W-10
20=10*W
2=W
L=4*2-5
L=3
Included side between < S and < W.
A) side SA
B) side WA
C) side SW
Answer:
C) Side SW
Step-by-step explanation:
Hello! The included side between <S and <W is side SW. According to the included side rule, this would be the correct answer. I know this is not much of an explanation, but there is not much to it! Hope this helps.
an inflatable swimming pool holds 1,000 gallons of water. It sprang a leak. and 5% of the water leaked out of the pool. How many gallons of water leaked out
50 gallons of water leaked out of swimming pool.
Step-by-step explanation:
Total no. of gallons in swimming pool = 1000
Percentage of leaked water = 5%
Gallons of water leaked = 5% of total no. of gallons
[tex]Gallons\ of\ water\ leaked=\frac{5}{100}*1000\\\\Gallons\ of\ water\ leaked=\frac{5000}{100}\\\\Gallons\ of\ water\ leaked= 50\ gallons[/tex]
50 gallons of water leaked out of swimming pool.
Keywords: percentage, division
Learn more about division at:
brainly.com/question/7297385brainly.com/question/729447#LearnwithBrainly