Answer:
135 and 315degrees
Step-by-step explanation:
Given the expression
4tan²θ+tanθ=−4tanθ−1
Equate to zero
4tan²θ+tanθ+4tanθ+1 = 0
4tan²θ+5tanθ+1 = 0
Let x = tanθ
4x²+5x+1 = 0
Factorize;
4x²+4x+x+1 = 0
4x(x+1)+1(x+1) = 0
4x+1 = 0 and x+1 = 0
4x = -1 and x = -1
x = -1/4 and -1
Since x = tanθ
-1 =tanθ
θ = arctan(-1)
θ = -45degrees
Since tan is negative in the 2nd and fourth quadrant;
In the second quadrant
θ = 180 - 45 = 135degrees
In the fourth quadrant;
θ = 360 - 45 = 315degrees
Hence the required angles are 135 and 315degrees
Abigail buys two cartons of strawberries. One carton has 19 berries and the other carton has 26 berries. She wants to divide the berries into bags so there are exactly 6 berries in each bag. How many bags will have 6 berries?
Answer:
7.5 bag
Step-by-step explanation:
Carton #1: 19 berries
Carton #2: 26 berries
^^add them up together to get hte total amount of berries! 19 + 26 = 45
She has 45 berries in total, then you divid it by 6 aka the amount of berries she wants in each bag 45 ÷ 6 = 7.5
When she divids them up she has 7 bags with 6 berries in each and 1 bag with 3 berries.
A boy is twice as old as his sister who is x years old now. In 2 years, the boy will be
Answer and Step-by-step explanation:
2x + 2 is the answer.
If the boy is twice as old, and the sister's age is represented by x, then we multiply 2 to x to represent the boy's age.
Then we add 2 when 2 years pass by.
#teamtrees #PAW (Plant And Water)
Please help kitty(
<3
Answer:
A. increasing curve
Step-by-step explanation:
exponential equations always have a curve, so you know it has to be the one about a curve.
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If
AC 18 and DC · 15, what is the length of BC in simplest radical
form？
what is the degree of polynomial x^2y^2+y^3+4?
Answer:
The degree of the polynomial ≈ 4
Step-by-step explanation:
The degree of a polynomial, is given by the highest value of the sum of the exponents (powers) of the of the variables (monomials) that are present in the polynomial expression
The given polynomial expression is x²·y² + y³ + 4
The sum of the exponents; 2 + 2 = 4, and 3
The sum of exponents 4 > 3
Therefore, the degree of the polynomial = 4.
How many moles are in 30.0g of N2
Answer:1.0709
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
To be very accurate 1.1
Please help! Must get done ASAP!!!
^^
Answer:
No
No
Yes
Yes
Step-by-step explanation:
Try it.
Answer: 1st: No, 2nd: No, 3rd: Yes, 4th: Yes
Step-by-step explanation: You only flip the inequality when you divide a negative number on both sides. The only reason why you would divide would be to get the variable by itself - in this case the coefficient would need to be negative. That only applies to the third and 4th equations.
it takes 2 1/2 cups of sugar to make 4 dozen sugar cookies. How much sugar is needed to make 120 sugar cookies
Answer:
6.25 cups of sugar
Step-by-step explanation:
Let's make a proportion expression:
2.5/48 = x/120
Let x be the amount of sugar needed to make 120 sugar cookies.
Cross multiply:
120*2.5=48x
48x=300
x=6.25
So, you would need 6 1/4 cups or 6.25 cups of sugar to make 120 sugar cookies.
Help With the answer Please
??????
Answer:
not sure
Step-by-step explanation:
Answer:
b) FIGURE A AND FIGURE B
Step-by-step explanation:
figure c has
all the sides equal so its not a rectangle
Help me please!!!!!!!!!!!!!
Answer:
The answer is 70 ways.
Step-by-step explanation:
8C4 = 70.
40320/576 is equal to 70.
PLEASE SOMEONE HELP ME FIGURE OUT THESE 4 Ill give you brainiest!
Answer: 5. 83 1/3*pi, or 261.8 (approx.) 6. 2*pi, or 6.28 (approx.) 7. 42 2/3*pi or 134.04 (approx.) 8. 144*pi or 452.39 (approx.)
Step-by-step explanation:
Volume of a circular cone : pi*r^2*h/3
I applied the formula to find these answers
what is the correct answer
Answer:
the answer is D
Step-by-step explanation:
from :
Tan(60) = x/4 then X = Tan(60) × 4
X = 4×√3
Express 0.0003754 in scientific notation
Answer:
Scientific Notation: 3754 × [tex]10^{-4}[/tex]
Step-by-step explanation:
Have a great summer :)
Answer:
3.754 • 10^-4
Step-by-step explanation:
Put decimal point back until in front of a whole number( not zero ;D). So it would be 3.754 and since it was going left or backwards the exponent would be negative. Therefore, giving our answer!
Hope this helped, good luck! :)
I really need help❤️
Answer:
about (-3,1.5)
Step-by-step explanation:
Hope this helps!
The area of a rectangle is (x^3 - 5x^2 + 3x - 15), and the width of the rectangle is (X2 + 3). If area = length x width, what
is the length of the rectangle?
Given:
Area of a rectangle = [tex]x^3-5x^2+3x-15[/tex]
Width of rectangle = [tex]x^2+3[/tex]
To find:
The length of the rectangle.
Solution:
The area of a rectangle is:
[tex]A=l\times w[/tex]
Where, l is length and w is the width.
It is can be written as:
[tex]\dfrac{A}{w}=l[/tex]
[tex]l=\dfrac{A}{w}[/tex]
Putting [tex]A=x^3-5x^2+3x-15[/tex] and [tex]w=x^2+3[/tex], we get
[tex]l=\dfrac{x^3-5x^2+3x-15}{x^2+3}[/tex]
[tex]l=\dfrac{x^2(x-5)+3(x-5)}{x^2+3}[/tex]
[tex]l=\dfrac{(x^2+3)(x-5)}{x^2+3}[/tex]
[tex]l=x-5[/tex]
Therefore, the length of the rectangle is [tex]x-5[/tex].
Below is a list of numbers. Use them to answer question 3.
2, 19, 31, 43, 59, 67
Question 3*
What type of numbers are shown?
A
B.
C.
composite numbers
even numbers
odd numbers
prime numbers
D.
Answer:
prime numbers
Step-by-step explanation:
not composite since,example, 2 is prime
not even since,example, 19 is odd
not odd since,example, 2 is even
Answer:
the answer is
prime numbers.
Find the volume of the cylinder.
Either enter an exact answer in terms of π or use 3.143.t, 14 for π.
Answer:
V = 75 pi
Step-by-step explanation:
We know the volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
V = pi ( 5)^2 (3)
V = pi (25)(3)
V = 75 pi
===============================================
Work Shown:
r = 5 is the radius
h = 3 is the height
V = pi*r^2*h .... volume of a cylinder
V = pi*5^2*3
V = pi*25*3
V = pi*75
V = 75pi ..... exact volume in terms of pi
V = 75*3.14
V = 235.5
If you used the approximation pi = 3.14, then the approximate volume is about 235.5 cubic units. Use more decimal digits of pi to get a more accurate answer.
Note how the pi*r^2 portion represents the area of the circular base. So we can say
volume = (area of base)*(height)
What expression would be easier to simplify if you use the associative property to change the grouping?
A.[(-0.2)+(-0.6)]+1.7
B.(2+5/2)+(-1/2)
C.(60+40)+(-27)
D.6+[4/9+(-2/9)]
Answer:
B
Step-by-step explanation:
2+5/2 is hard to add since first you have to make 2 into a fraction with the denominator 2. If you use the associative property, you can just easily combine -1/2 and 5/2 without any converting into fractions
8(2 + x) = 3x + 16 + 5x
Answer:
x = 0Step-by-step explanation:
8(2 + x) = 3x + 16 + 5x
=> 16 + 8x = 3x + 16 + 5x
=> 8x - 3x - 5x = 16 - 16
=> 0x = 0
=> x = 0 (Ans)
Answer:0
Step-by-step explanation:
everything cancels out
There were 8 fewer boys than girls in Mr. Taylor’s Algebra class. If he had 40 pupils, how many were girls?
Answer:
There are 24 girls in the class.
Step-by-step explanation:
Write out the problem like this:
40 = (g-8)+(g)
40 is the total amount of students. (g) is the unknown number of girls in the class, and (g-8) is the amount of boys since there are 8 fewer boys than girls.
First, eliminate the parentheses.
40 = g - 8 + g
Next, combine like terms. Both g's are positive, to we get 2g
40 = g - 8 + g
40 = 2g - 8
Then, add 8 to both sides of the equation, because the 8 that was already present is negative and needs to be canceled out.
40 + 8 = 2g - 8 + 8
48 = 2g
Lastly, divide both sides by 2, so that the (g) is by itself.
40/2 = 24, 2g/2 = g
g=24
This can be tested as the correct answer by subtracting 8 from 24 to count the boys...
24 - 8 = 16
...and adding the two amounts together to get the total amount of students.
24 + 16 = 40
There are 24 girls in the class.
What is the surface area of the cylinder if the height is 11in and the radius is 4in?
Answer:
Around 376.99
Step-by-step explanation:
the formula is 2πrh+2πr²
so if we plug in everything we get 2π(4)(11)+2π(4)²
When we simplify that, we would get 376.99
please help ty !!! :)
Answer: $9,240
Step-by-step explanation:
If the car was sold at 40% off,
That is 40/100=0.4
selling price=$6600
So, 40% of $6600= 0.4*$6600=$2640
this means that the seller deducted this amount from his cost price to sell it to you.
Therefore,original price he bought will be a sum of both,that is
the amount he sold to you + the amount he deducted =$6600+$2640=$9,240.
Therefore the original price is $9,240
hope it’s correct !
Answer:
Answer :-(40/100) × X = 6600
X = (6600×100)/40
X = 16500$
Hope it helped :)6 g of butter is used for making a cupcake. How many such cakes can be made by using 3 kg of butter?
Answer: 500
Step-by-step explanation:
Given
6 g butter is required to make a cupcake
If there is 3 kg butter
We know, 1 kg is equivalent to 1000 g i.e. 3 kg is 3000 gm
No of cup-cakes made
[tex]\Rightarrow \dfrac{3000}{6}=500\ \text{cupcakes}[/tex]
How much would $500 invested at 6% interest compounded monthly be
worth after 5 years? Round your answer to the nearest cent.
int
A09) P(124
A. $512.63
B. $669.11
C. $674.43
D. $886.41
Answer:
$669
Step-by-step explanation:
Given data
Principal= $500
Rate= 6%
Time= 5 years
The compound interest formula is given as
A= P(1+r)^t
A=500(1+0.06)^5
A=500(1.06)^5
A=500*1.338
A=$669
You roll a 6-sided die.
What is P(4)?
1/6 or 4/9 or 4/5 or 3/4
Answer:
1/6
Step-by-step explanation:
Because there is only a side that has the number 4 in a total of 6 sides
Drag the tiles to the correct boxes to complete the pairs. Match the systems of equations with their solutions.
Answer:
See explanation for matching pairs
Step-by-step explanation:
Equations
(1)
[tex]x - y = 25[/tex]
[tex]2x + 3y = 180[/tex]
(2)
[tex]2x - 3y = -5[/tex]
[tex]11x + y = 550[/tex]
(3)
[tex]x - y = 19[/tex]
[tex]-12x + y = 168[/tex]
Solutions
[tex](-17,-36)[/tex]
[tex](47, 33)[/tex]
[tex](51, 26)[/tex]
Required
Match equations with solutions
(1) [tex]x - y = 25[/tex] and [tex]2x + 3y = 180[/tex]
Make x the subject in: [tex]x - y = 25[/tex]
[tex]x = 25 + y[/tex]
Substitute [tex]x = 25 + y[/tex] in [tex]2x + 3y = 180[/tex]
[tex]2(25 + y) + 3y = 180[/tex]
[tex]50 + 2y + 3y = 180[/tex]
[tex]50 + 5y = 180[/tex]
Collect like terms
[tex]5y = 180-50[/tex]
[tex]5y = 130[/tex]
Solve for y
[tex]y =26[/tex]
Recall that: [tex]x = 25 + y[/tex]
[tex]x = 25 + 26[/tex]
[tex]x = 51[/tex]
So:
[tex](x,y) = (51,26)[/tex]
(2) [tex]2x - 3y = -5[/tex] and [tex]11x + y = 550[/tex]
Make y the subject in [tex]11x + y = 550[/tex]
[tex]y = 550 - 11x[/tex]
Substitute [tex]y = 550 - 11x[/tex] in [tex]2x - 3y = -5[/tex]
[tex]2x - 3(550 - 11x) = -5[/tex]
[tex]2x - 1650 + 33x = -5[/tex]
Collect like terms
[tex]2x + 33x = -5+1650[/tex]
[tex]35x = 1645[/tex]
Solve for x
[tex]x = 47[/tex]
Solve for y in [tex]y = 550 - 11x[/tex]
[tex]y = 550 - 11 * 47[/tex]
[tex]y = 550 - 517[/tex]
[tex]y = 33[/tex]
So:
[tex](x,y) = (47,33)[/tex]
(3)
[tex]x - y = 19[/tex] and [tex]-12x + y = 168[/tex]
Make y the subject in [tex]-12x + y = 168[/tex]
[tex]y = 168 + 12x[/tex]
Substitute [tex]y = 168 + 12x[/tex] in [tex]x - y = 19[/tex]
[tex]x - 168 - 12x = 19[/tex]
Collect like terms
[tex]x -12x = 168 + 19[/tex]
[tex]-11x = 187[/tex]
Solve for x
[tex]x = -17[/tex]
Solve for y in [tex]y = 168 + 12x[/tex]
[tex]y =168-12 *17[/tex]
[tex]y =-36[/tex]
So:
[tex](x,y) = (-17,-36)[/tex]
3 1/2 + 7/15 multiply 1 1/4
Answer:
3 1/2 +7/15×11/4
7/2 +7/15×11/4
119/30×11/4
1309/120
Answer:
[tex]{ \tt{(3 \frac{1}{2} + \frac{7}{15} ) \times 1\frac{1}{4} }} \\ \\ = { \tt{ \frac{119}{30} \times \frac{5}{4} }} \\ \\ = 4 \frac{23}{24} [/tex]
Expand and simplify (x - 2)(x - 1)
Answer:
x^2 -3x+2
Step-by-step explanation:
(x - 2)(x - 1)
FOIL
first: x*x = x^2
outer: -1*x = -x
inner: -2*x =-2x
Last: -2*-1 =2
Add together
x^2 -x-2x+2
Combine like terms
x^2 -3x+2
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{(x - 2)(x - 1)}[/tex]
[tex]\large\textsf{DISTRIBUTE}[/tex]
[tex]\large\textsf{x(x) + x(-1) - 2(x) -2(-1)}[/tex]
[tex]\large\textsf{x(x) = }\mathsf{\bf x^2}[/tex]
[tex]\large\textsf{x(-1) = -1(x) = \bf -1x}[/tex]
[tex]\large\textsf{-2(x) = \bf -2x}[/tex]
[tex]\large\textsf{-2(-1) = \bf 2}[/tex]
[tex]\mathsf{= \bf x^2 - 1x - 2x + 2}[/tex]
[tex]\large\textsf{COMBINE the LIKE TERMS}[/tex]
[tex]\mathsf{(-1x - 2x)}[/tex]
[tex]\mathsf{= \bf -3x}[/tex]
[tex]\large\textsf{SOLVE for the ANSWER:}[/tex]
[tex]\mathsf{x^2 - 3x + 2}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: }\mathsf{\bf x^2 - 3x + 2}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
What would be your first step in solving for x in this problem. Please EXPLAIN in words?
Answer:
Step-by-step explanation: distribute the 1.5 and the 2
Answer:
hey you need to multiple the number behind the parentheses by the number into the parentheses, like 1.5×2x
the you put Xs on the left side of the = and the numbers on the right side
then you do the sentence and at the end you got the amount for x :)
Yesterday, 37% of the drivers for Quinn's Taxi Service worked. At Bella's Taxi Express, 3 out of 10 drivers worked. Which taxi service had a greater percentage of its drivers working?
Answer:
Quinn's Taxi Service
Step-by-step explanation:
a) Yesterday, 37% of the drivers for Quinn's Taxi Service worked.
Hence, the percentage for Quinn's Taxi Service drivers that are working is 37%
b) At Bella's Taxi Express, 3 out of 10 drivers worked.
The percentage for Bella's Taxi drivers that are working is calculated as:
3/10 × 100
= 30%
Therefore, the taxi service that had a greater percentage of its drivers working is Quinn's Taxi Service with a high percentage of 37%