Answer:
θ = 5π/6 rad and 11π/6 rad
Step-by-step explanation:
Given the expression cotθ+√3=0
Subtract √3 from both sides
cotθ+√3-√3=0-√3
cotθ = -√3
Since cotθ = 1/tanθ
1/tanθ = -√3
Reciprocate both sides:
tanθ = -1/√3
θ = tan^-1(-1/√3)
θ = -30°
Since the angle is negative, and tanθ is negative in the second and fourth quadrant.
In the second quadrant;
θ = 180-30
θ = 150°
Since 180° = πrad
150° = 150π/180
150° = 5π/6 rad
In the fourth quadrant;
θ = 360-30
θ = 330°
Since 180° = πrad
330° = 330π/180
330° = 11π/6 rad
Hence the solutions are 5π/6 rad and 11π/6 rad.
write 7.48 as a mixed number in simplest form
[tex]7\frac{12}{25}[/tex]
Step-by-step explanation:7.48 = 748⁽⁴/100 = 187/25 = 7 12/25
3. What is the coefficient in the expression: 94a+2?
Answer:
The coefficient would be 94
Step-by-step explanation:
A coefficient is the number used to multiply the variable! Hope this helps!
Which expression is equal to 8x3+8x1?
A. 8(3 + 8)
B. 8(3+1)
C. 3(8+1)
D. 1(3 + 8)
Answer:
B. 8(3+1)
Explanation: 8x3 = 24. 8x1 = 8
Answer:
B. 8(3+1) = 32
Step-by-step explanation:
8 x 3 + 8 x 1 = 32
A. 8(3 + 8) = 88
B. 8(3+1) = 32
C. 3(8+1) = 72
D. 1(3+8) = 11
Now that you have x² - 8x + 16 = 9 + 16, apply the square root property to the equation.
Answer:
x=−1,−7
Step-by-step explanation:
Answer:
The solutions are {-1, 9}
Step-by-step explanation:
x² - 8x + 16 can be re-written as (x - 4)^2, and 9 + 16 as 25.
Taking the square root of both sides of (x - 4)^2 = 25, we get:
x - 4 = ±5, or:
x = 4 + 5 = 9, and
x = 4 - 5 = -1
The solutions are {-1, 9}
Helena builds a shed in her backyard. There is a larger square section for large tools, like her lawn mower, and a smaller square section for small tools. What is the length of the entire shed? What type of number is the length? List as many types of numbers for the length as are possible.
Answer:
Step-by-step explanation:
a) From the image attached, the area of the small section is 16ft² and the area of the large section is 50 ft². The area of a square = length × length = length².
For the small section: Area = length²
16 = length²
length = √16 = 4 ft
For the large section: Area = length²
50 = length²
length = √50
The length of entire shed = length of small area + length of large area = 4 + √50
The length of entire shed = 4 + √50
b) All square root of integers other than perfect squares are irrational numbers , hence 4 + √50 is an irrational number. All numbers belongs to the set of real numbers. Therefore 4 + √50 is an irrational number and real number
Jillian's school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales
for opening night totaled $2071.50. The equation 10.50 +3.750 - 2071.50, where a is the number of adult tickets sold and b
is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students
attended, how may adult tickets were sold?
adult tickets
Intro
Done
Answer:
168 adult tickets were sold
Step-by-step explanation:
$10. 50 per adults
$3. 75 per student
There are 82 students..
.. So...
$3. 75 × 82 = $307. 50
Overall the amount of money made was $2071.50
If you subtract $307.50 from $2071. 50 you will get $1,764
We now need to find out how many adults bought tickets by dividing $1, 764 by the price adults have to pay so..
Amount of adults who bought tickets are
= $1, 764 ÷ $10. 50
= 186 adults
In ABC, the measure of sides c is 3.9 cm If DEF is a dilation ABC with a scale factor of 2.5 what is the measure of side f
Answer:
[tex]F = 9.75cm[/tex]
Step-by-step explanation:
Given
In ABC;
[tex]C = 3.9cm[/tex]
[tex]Dilation = 2.5[/tex]
Required
Determine side F
In the given question;
DEF is a dilation of ABC
Comparing both triangles side by side,
Side F is a direct dilation of side C and this is calculated as follows
[tex]F = Dilation * C[/tex]
[tex]F = 2.5 * 3.9cm[/tex]
[tex]F = 9.75cm[/tex]
What fraction of box does each student receive?
Answer: 13/48
let me know if I'm wrong
I didn't have enough time to explain it though
Step-by-step explanation:
I WILL GIVE BRAINLIEST IF IT IS CORRECT! The Atlantic Ocean covers about 3.2 × 10^7 square miles. The Pacific Ocean covers about 6.4 × 10^7 square miles. About how much area does the Atlantic Ocean and Pacific Ocean cover? A. 3.2 × 10^7 square miles B. 9.6 × 10^7 square miles C. 3.2 × 10^14 square miles D. 9.6 × 10^14 square miles
Answer:
B
Step-by-step explanation:
3.2 * 10⁷ + 6.4 * 10⁷
= 10⁷ * (3.2 + 6.4)
= 10⁷ * 9.6
= 9.6 * 10⁷
Answer:
The Atlantic Ocean and Pacific Ocean covers about 9.6 x 10^7 mi^2
Step-by-step explanation:
Let
x -----> area covered by the Atlantic Ocean
y -----> area covered by the Pacific Ocean
we know that
The area that covers the Atlantic Ocean and Pacific Ocean is equal to the sum of the area covered by the Atlantic Ocean and the area covered by the Pacific Ocean
x = 3.2 x 10^7
y = 6.4 x 10^7
Substitute
x + y = 3.2 x 10^7 + 6.4 x 10^7 = 9.6 x 10^7.
Hope this helps! And good luck on your test!
Select all sets that the number is a part of. You may have to select more than one.
66
Group of answer choices
Rational Numbers
Real Numbers
Irrational Numbers
Integers
Natural Numbers
Whole Numbers
plsplsplspslspls help ill give you a kiss on the cheek :)
Answer:
A)
Important information:
The total cost includes the price of 2 tickets and the price of yogurt.
The total cost: 19.90$
The price of yogurt: 5.5
The price of 2 tickets: unknown
Each of the tickets costs the same amount of money.
Verbal Description:
For the unknown value, the letter x is often selected to represent this unknown value.
Here, we select x that is the price of 1 ticket, then the price of 2 tickets would be 2x.
=> We have the equation: 2x + 5.5 = 19.90
Transfer 5.5 to the right, and then divide both sides by 2, we have:
(2x)/2 = (19.9 - 5.5)/2
Take the simplification, we have:
x = 7.2$ (this is the price of a ticket)
B)
Use the same strategy as shown in A), we have:
Total number of stamps: 100
Mari's number of stamps: x
Carlos's number of stamps: x + 5
Amanda's number of stamps: 3x
=> 3x + x + x + 5 = 100
=> 5x = 100 - 5
=> 5x = 95
=> x = 19
Mari's number of stamps: 19
Carlos's number of stamps: 19 + 5 = 24
Amanda's number of stamps: 3 x 19 = 57
C)
The perimeter of the garden:
perimeter = (width + length) x 2
perimeter = 256
width = w
length = w + 8
=> We have:
256 = (w + w + 8) x 2
<=>256 = (2w + 8) x 2
<=> 256/2 = (2w + 8) x 2/2
<=> 128 = 2w + 8
<=> 128 - 8 = 2w
<=> 120 = 2w
<=> w = 60
=> width of garden: 60
=> length of garden: 60 + 8 = 68
Answer:
68
Step-by-step explanation:
Helpppppppppppp me I really need help
The daily demand for ice cream cones at a price of $1.20 per cone is 50 cones. At a price of $2.20 per cone, the demand is 30 cones. Use linear interpolation to estimate the demand at a price of $1.50 per cone.
Answer:
The demand at a price of $1.50 per cone is 44 conesStep-by-step explanation:
let us apply the interpolation formula to solve this problem
we have
[tex]\frac{y-y1}{x-x1} =\frac{y2-y1}{x2-x1}[/tex]
Now let us set the values to the notation above
x= $1.20
x1= $2.20
x2= $1.50
y = 50 cones
y1= 30 cones
y2= ?
[tex]y2= \frac{(y-y1)}{(x-x1)} (x2-x1)+y1[/tex]
Substituting our given data we have
[tex]y2= \frac{(50-30)}{(1.2-2.2)} (1.5-2.2)+30\\\\y2= \frac{20}{-1} (-0.7)+30\\\\y2= (20*0.7)+30\\y2= 14+30\\y2= 44[/tex]
the demand at a price of $1.50 per cone is 44 cones
What is the distance across the river in feet?
Answer:
375
Step-by-step explanation:
The ratio of d to 125 is the ratio of 30 to 10,so by comparison, 30:10=3÷1
X÷125=X=375
8(−5d−9)−3(−6d+10) in simplest terms
Answer:
-22d -102
Step-by-step explanation:
8(−5d−9)−3(−6d+10)
Distribute
-40d -72 +18d -30
Combine like terms
-40d +18d -72 - 30
-22d -102
Answer:
−22d − 102
Step-by-step explanation:
8 (−5d − 9) −3 (−6d + 10)
expand 8 (−5d − 9) to −40d − 72
= −40d − 72 − 3 (−6d + 10)
expand − 3 (−6d + 10) to 18d − 30
= −40d − 72 + 18d − 30
combine like terms
= −40d + 18d − 72 − 30
= −22d − 102
Which ordered pair is a solution bf 2x = y? . (-1,-2) (-1,-1) (1,1) (1.-1)
Answer:
(-1,-2)
Step-by-step explanation:
Ordered pairs go in the order x,y so the 2x would be the first number that then equals the second number. The answer is (-1,-2) because when you multiply 2*-1 you get -2 and what's the y? -2. Does -2 = -2? Yes.
what logaa equals??
Answer:
Logarithm I think
Step-by-step explanation:
If u need more explanation u can ask me
A man is twice as old as his son. five years ago, their ages was 9:4 .find the sons present
Answer:
five years ago
father:son = 9:4
= 45: 20
now
father: son = 45+5 : 20+5
= 50:25
ok
the son is now 25 years old
Please Help! I'm Stuck!
Answer:
A. y = -4x - 10
Step-by-step explanation:
See image below. The red line (y = -4x - 10) is parallel to the blue line (y = -4x + 3) and passes through (-3 , 2)
Answer:
y = -4x - 10 (Answer A)
Step-by-step explanation:
Any line parallel to the given y = -4x + 3 has the same slope: -4.
Starting with y = mx + b, and substituting -4 for m, -3 for x and 2 for y, we get:
2 = -4(-3) + b, or b = -10, and so the desired equation is
y = -4x - 10 (Answer A)
What is 1/5 of 30????
Answer: The answer is 6!
Step-by-step explanation:
5х – 11 = 3х + 3
Solve for x
Answer:
Hello☺️!
Step-by-step explanation:
[tex]5 x - 11 = 3x + 3[/tex]
[tex]5x - 3x = 3 + 11[/tex]
[tex]2x = 14[/tex]
[tex]x = \frac{14}{2} [/tex]
[tex]x = 7[/tex]
In countries that use the metric system of measurement, corn yields are sometimes expressed in quintals per hectare (q/ha) instead of bushels per acre (bu/ac). 1 quintal = 220.462 lbs 1 bushel of corn = 56 lbs In field trials in one of these countries, a particular corn hybrid yielded 151 q/ha. What is this in bushels per acre (bu/ac)? Margin of Error: +/- 1 bu/ac
Answer:
The answer is below
Step-by-step explanation:
Different countries have different metric system of measurement, but the metric system of measurement accepted all over the world is the international system of unit (SI unit)
1 quintal = 220.462 lbs and 1 bushel of corn = 56 lbs.
151 q/ha = (151 × 220.462) lbs/ha = 33289.762 lbs/ha
But 1 hectare = 2.471 acre, hence:
33289.762 lbs/ha = [tex]\frac{33289.762\ lbs}{1\ ha*\frac{2.471\ acre}{1 \ ha} } =13472.182\ lbs/acre[/tex]
Since 1 bushel of corn = 56 lbs, hence:
[tex]13472.182\ lbs/acre=\frac{13472.182\ lbs*\frac{1\ bushels}{56\ lbs} }{acre}=240.6\ bushels/acre[/tex] = 240.6 bu/ac
For a Margin of Error: +/- 1 bu/ac, the bushels per acre = (239.6 bu/ac, 241.6 bu/ac)
A concrete column has a diameter of 390 mm and a length of 3 m. If the density (mass/volume) of concrete is 2.45 Mg/m^3, determine the weight of the column in pounds.
Answer:
w= 0.83 NStep-by-step explanation:
The column has the shape of a cylinder hence the formula for the volume of a cylinder is
[tex]v=\pi r^2h[/tex]
Given
diameter d= 390 mm
radius r= 390/2= 195 mm to meter = 0.195 m
length or height h= 3 m
applying the data to the formula we have
[tex]v=\pi *0.195^2*3\\\\ v=\pi*0.0038*3\\\\ v=\pi*0.0114\\\\ v=0.035 m^3[/tex]
we can now use the volume in addition with the density given to solve for the mass using the expression for density
density= mass/volume
2.45= mass/0.035
mass= 2.45*0.035
mass= 0.085 mg
We know that weight
w= mass* acceleration
w= 0.085*9.81
w= 0.83 N
3.a. Use the distributive property to rewrite the equation.
Enter the new equation as your answer.
3(2x - 1) + 4 = 7
Enter your answer
4.b. Combine any like terms to rewrite the equation that you entered as an answer in part a.
Enter the new equation as your answer.
Enter your answer
5.c. Use addition or subtraction to rewrite the equation that you entered as an answer in part b.
Enter the new equation as your answer.
Enter your answer
6.d. Use multiplication or division to rewrite the equation that you entered as an answer in part c.
Enter the new equation as your answer.
Answer:
Hey there!
Part A
3(2x-1)+4=7
6x-3+4=7
Part B
6x+1=7
Part C.
6x+1-1=7-1
6x=6
Part D.
6x/6=6/6
x=1
Let me know if this helps :)
Answer:
3. 6x -3 +4 = 7
4. 6x +1 = 7
5. 6x = 6
6. x = 1
Step-by-step explanation:
3. The distributive property allows you to eliminate parentheses by multiplying the outside factor by every term inside.
3(2x -1) +4 = 7 . . . . . . given
3(2x) +3(-1) +4 = 7 . . . . using the distributive property
6x -3 +4 = 7 . . . . . . . finishing the evaluation of those products
__
4. The only like terms that can be combined are the two constant terms on the left side. We simply add them up.
6x +1 = 7
__
5. Using the subtraction property of equality, we can subtract 1 from both sides of the equation. We choose to do this so that the x-term is by itself.
6x +1 -1 = 7 -1
6x = 6
__
6. Using the division property of equality, we can divide both sides of the equation by 6. We choose to do this so the new coefficient of x is 1.
6x/6 = 6/6
x = 1
______
Additional comment
You're told to apply these steps without any explanation as to why or what the goal may be. We assume you're supposed to realize that you can use these steps to solve the equation. Of course, you can use different values for addition (or subtraction) or multiplication (or division). Doing so may satisfy the literal interpretation of the question, but won't get you a solution to the equation.
a) The marked price of a mobile is 25% above its cost price, When it is sold at a gain of
10%, the profit amounts to Rs 725. Find the marked price of the mobile.
Answer:
the marked price of a mobile is 25% above its cost price when it is sold at a gain of 10%, the profit amount to RS 725 find the marked price of the mobile
Step-by-step explanation:
Hope this helps.......
Smaller p-values indicate more evidence in support of the: A. the reduction of variance B. null hypothesis C. quality of the researcher D. alternative hypothesis
Answer:
D
Step-by-step explanation:
Smaller p values that there is evidence to show that the alternate hypothesis should be accepted. The smaller the p value, the more evidence there is that we are not to accept the null hypothesis. The p value during a hypothesis yet, tells us how significant our result is. It gives a measurement of how strong the evidence is, against the null hypothesis.
бx - 6 = 24х +6
Help
Answer: [tex]x=-2/3[/tex]
Subtract 24x from both sides
[tex]6x-6-24x=24x+6-24x\\-18x-6=6[/tex]
Add 6 to both sides
[tex]-18x-6+6=6+6\\-18x=12[/tex]
Divide both sides by -18
[tex]-18x/-18=12/-18\\x=-2/3[/tex]
Answer: x=-2/3.
Step-by-step explanation:6x-6 = 24х+6
6x-6-24x=6 -18x-6+6=6+6 -18x/-18=12/-18 x=-2/3
Which of the following numbers is rational? A. 4/5 B.√27 C.4.020020002000002.... D.√31
Greetings from Brasil...
First let's define the rational number....
→ Division between two numbers with the detail that the dividend or denominator cannot be zero
A/B or A ÷ B
where B ≠ 0
(just for the sake of knowledge. If B = 0 we would have +∞ as an answer)
A ∈ ℤ
and
B ∈ ℤ* (B ≠ 0)
In this way, when dividing A by B, we will obtain a whole number or a number with a decimal (finite decimal or periodic tenth)
Let's go to the alternatives
A = 4/5 = 0,8 (finite decimal)4 ∈ ℤ and 5 ∈ ℤ*, so we have a rational number
B = √27 = 5.1961524227066318805823390245176
(There is no repetition of tithing periods (numbers after the point) - non-periodic tithe). So we have an Irrational Number
C = 4.020020002000002
There is no periodic tenth - Irrational Number
D = √31 = 5.5677643628300219221194712989185
Irrational Number - Non-periodic tithe
A raffle game has a single gran prize that will be drawn randomly from among all the tickets. A total of 500 tickets are sold. If a man buys 25 tickets, what is the probability that he will win the grand prize?
Step-by-step explanation:
P = 25/500
P = 1/20, or 5%
how would you say "the function is positive from -9 to 3 over the x axis but -9 is not included" using interval notation
Answer:
The function would be positive in:
(-9, 3]
Step-by-step explanation:
A function is considered positive on the X-axis when the changed values in the function are greater than zero. f(x) > 0
And is considered negative when f(x) < 0.
In this case, the numbers that make the function positive are the numbers from -9 to 3, but not including -9.
This can be written as (-9, 3]
It means that -9 is not taken but any number greater than -9 is.