Answers
Explanation:
To solve you need to divide the three gallons of paint by the 5 cans. This can be solved in two ways.
Way 1 (fraction)
This is the easiest way, you simply put the first number in the equation on top and the second on the bottom, then simplify if possible. When we do this we get 3/5 and it can’t be simplified so we leave it as the fraction three fifths of 3/5.
Way 2 (decimal)
This way you divide 3 by 5, you can use long division to do this but it takes a long time. The answer is 0.6.
I hope this helps. Please mark me the Brainliest, it’s not necessary but I put time and effort into every answer and I would appreciate it greatly. Have a great day, stay safe and stay healthy ! :)
Related Questions
find the exact value of 6cos(105°)
Answers
Answer:
[tex]-\frac{3(\sqrt{6}-\sqrt{2})}{2}\text{ or } \frac{-3\sqrt{6}+3\sqrt{2}}{2}}\text{ or }\frac{3(\sqrt{2}-\sqrt{6})}{2}[/tex]
Step-by-step explanation:
There are multiple ways to achieve and even express the exact answer to this problem. Because the exact value of [tex]6\cos(105^{\circ}})[/tex] is a non-terminating (never-ending) decimal, it does not have a finite number of digits. Therefore, you cannot express it as an exact value as a decimal, as you'd either have to round or truncate.
Solution 1 (Cosine Addition Identity):
Nonetheless, to find the exact value we must use trigonometry identities.
Identity used:
[tex]\cos(\alpha +\beta)=\cos \alpha \cos \beta-\sin \alpha \sin \beta[/tex]
Notice that [tex]45+60=105[/tex] and therefore we can easily solve this problem if we know values of [tex]\cos(45^{\circ})[/tex], [tex]\cos(60^{\circ})[/tex], [tex]\sin (45^{\circ})[/tex], and [tex]\sin(60^{\circ})[/tex], which is plausible as they are all key angles on the unit circle.
Recall from either memory or the unit circle that:
[tex]\cos(45^{\circ})=\sin(45^{\circ})=\frac{\sqrt{2}}{2}[/tex] [tex]\cos(60^{\circ})=\frac{1}{2}[/tex] [tex]\sin(60^{\circ})=\frac{\sqrt{3}}{2}[/tex]Therefore, we have:
[tex]\cos(105^{\circ})=\cos(45^{\circ}+60^{\circ}}),\\\cos(45^{\circ}+60^{\circ}})=\cos 45^{\circ}\cos 60^{\circ}-\sin 45^{\circ}\sin 60^{\circ},\\\cos(45^{\circ}+60^{\circ}})=\frac{\sqrt{2}}{2}\cdot \frac{1}{2}-\frac{\sqrt{2}}{2}\cdot \frac{\sqrt{3}}{2},\\\cos(105^{\circ})=\frac{\sqrt{2}}{4}-\frac{\sqrt{6}}{4},\\\cos(105^{\circ})={\frac{-\sqrt{6}+\sqrt{2}}{4}}[/tex]
Since we want the value of [tex]6\cos 105^{\circ}[/tex], simply multiply this by 6 to get your final answer:
[tex]6\cdot {\frac{-\sqrt{6}+\sqrt{2}}{4}}=\frac{-3\sqrt{6}+3\sqrt{2}}{2}}=\boxed{\frac{3(\sqrt{2}-\sqrt{6})}{2}}[/tex]
Solution 2 (Combination of trig. identities):
Although less plausible, you may have the following memorized:
[tex]\sin 15^{\circ}=\cos75^{\circ}=\frac{\sqrt{6}-\sqrt{2}}{4},\\\sin 75^{\circ}=\cos15^{\circ}=\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]
If so, we can use the following trig. identity:
[tex]\cos(\theta)=\sin(90^{\circ}-\theta)[/tex] (the cosine of angle theta is equal to the sine of the supplement of angle theta - the converse is also true)
Therefore,
[tex]\cos (105^{\circ})=\sin (90^{\circ}-105^{\circ})=\sin(-15^{\circ})[/tex]
Recall another trig. identity:
[tex]\sin(-\theta)=-\sin (\theta)[/tex] and therefore:
[tex]\sin (-15^{\circ})=-\sin (15^{\circ})[/tex]
Multiply by 6 to get:
[tex]6\cos (105^{\circ})=-6\sin (15^{\circ})=-6\cdot \frac{\sqrt{6}-\sqrt{2}}{4}=\boxed{-\frac{3(\sqrt{6}-\sqrt{2})}{2}}[/tex] (alternative final answer).
HELP ASAP PLS Select the correct answer.
A light bulb's brightness is reduced when placed behind a screen. The amount of visible light produced by the light bulb decreases by 25% with
each additional layer that is added to the screen. With no screen, the light bulb produces 750 lumens. The lumen is a unit for measuring the total
quantity of visible light emitted by a source,
Select the correct equation that can be used to represent the lumens, L, after x screen layers are added.
Answers
Answer:
D. 750(0.75)ˣ
Step-by-step explanation:
Let the new brightness be L'. Since our initial brightness L₀ reduces by 25 %, we have that L' = L₀ - 25% of L₀
L' = L₀ - 0.25L₀
L' = 0.75L₀
Adding the second screen, the new intensity is L" = L' - 25 % of L'
L" = L' - 0.25 L'
L" = 0.75L'.
Since L' = 0.75L₀,
L" = 0.75L' = 0.75(0.75L₀) = 0.75²L₀
Adding the third screen, the new intensity is L"' = L'' - 25 % of L''
L'" = L" - 0.25 L"
L"' = 0.75L".
Since L" = 0.75L' = 0.75²L₀
L"' = 0.75L" = 0.75(0.75²L₀) = 0.75³L₀
So, we see a pattern here.
The intensity after x screens is L = (0.75)ˣL₀
Since L₀ = 750 lumens,
L = 750(0.75)ˣ
Which statement must be true if APQR = ASTU?
Answers
Answer:
(a) [tex]PQ \sim ST[/tex]
Step-by-step explanation:
Given
See attachment
Required
Which must be true
[tex]\triangle PQR \simeq \triangle STU[/tex] implies that:
The following sides are corresponding
[tex]PQ \sim ST[/tex]
[tex]PR \sim SU[/tex]
[tex]QR \sim TU[/tex]
The following angles are corresponding
[tex]\angle P \sim \angle S[/tex]
[tex]\angle Q \sim \angle T[/tex]
[tex]\angle R \sim \angle U[/tex]
From the given options, only option (a) is true because:
[tex]PQ \sim ST[/tex]
Mr. Pinter's class has twice as many students as Mrs. Rupert's class. Mrs. Althouse's class has 20 less than three times Mrs. Rupert's class. Together they have 106 students. How many are in each class?
Answers
Answer:
Mr. Pinter's class has 42 students, Mrs. Rupert's class has 21 students, and Mrs. Althouse's class has 43 students.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
Mr. Pinter's class has x students.
Mrs. Rupert's class has y students.
Mrs. Althouse's class has z students.
Mr. Pinter's class has twice as many students as Mrs. Rupert's class.
This means that:
[tex]x = 2y[/tex]
Mrs. Althouse's class has 20 less than three times Mrs. Rupert's class.
This means that:
[tex]z = 3y - 20[/tex]
Together they have 106 students.
This means that:
[tex]x + y + z = 106[/tex]
We have x and z has a function of y, so:
[tex]2y + y + 3y - 20 = 106[/tex]
[tex]6y = 126[/tex]
[tex]y = \frac{126}{6}[/tex]
[tex]y = 21[/tex]
And:
[tex]x = 2y = 2(21) = 42[/tex]
[tex]z = 3y - 20 = 3(21) - 20 = 63 - 20 = 43[/tex]
Mr. Pinter's class has 42 students, Mrs. Rupert's class has 21 students, and Mrs. Althouse's class has 43 students.
-2,6,-18,54, what is the common ratio of the sequence
Answers
Answer:
2
Step-by-step explanation:
Answer:
Common Ratio=-3
Step-by-step explanation:
To find any common ratio in a sequence, always take the second number in the sequence and divide it by the first number. However, you must be careful because the common ratio should only be negative if the values in the sequence are alternating between negative and positive. Therefore, if the sequence of numbers is simply decreasing in value, this does not mean that the common ratio is negative. The common ratio would still be positive. If the sequence is decreasing in value, this means that the common ratio would be a fraction or a decimal less than one.
3 Lizzie buys 3 clocks for a total cost of £50 at a car boot sale.
She sells 2 of the clocks for £22 each and the other clock for £20
Lizzie thinks she has made a profit of over 30% of the cost of the clocks.
Answers
Answer:
28% She didn't make a profit over 30%
Step-by-step explanation:
She buys the clocks for 50 pounds
She sells them for 22 + 22 + 20 = 64 pounds.
The profit is 14 pounds
What's the % profit.
Profit % = 14/50*100 = 28%
She's not quite right.
Using the following distribution, calculate the following measures of central tendency:
State Proportion of Residents Without Health Insurance Louisiana 0.19 New Jersey 0.13 New York 0.16 Pennsylvania 0.11 Rhode Island 0.09 South Carolina 0.13 Texas 0.25 Washington 0.14 Wisconsin 0.10
N = 9
Identify the variable:
Identify the median:
Identify the mean:
How would you describe the shape of the distribution:
Answers
Answer:
(a) Residents
(b) [tex]Median = 0.13[/tex]
(c) [tex]\bar x = 0.14[/tex]
(d) Right skewed
Step-by-step explanation:
Given
The data of residents without health insurance
Solving (a): The variable
The variable is the residents
Solving (b): The median
First, we sort the data
[tex]Sorted: 0.09, 0.10, 0.11, 0.13, 0.13, 0.14, 0.16, 0.19, 0.25[/tex]
So, the median position is:
[tex]Median = \frac{n + 1}{2}[/tex]
[tex]Median = \frac{9 + 1}{2}[/tex]
[tex]Median = \frac{10}{2}[/tex]
[tex]Median = 5th[/tex]
The 5th element of the dataset is: 0.13
So:
[tex]Median = 0.13[/tex]
Solving (c): The mean
This is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
[tex]\bar x = \frac{0.09+ 0.10+ 0.11+ 0.13+ 0.13+ 0.14+ 0.16+ 0.19+ 0.25}{9}[/tex]
[tex]\bar x = \frac{1.3}{9}[/tex]
[tex]\bar x = 0.14[/tex]
Solving (d): The shape of the distribution
In (b) and (c), we have:
[tex]Median = 0.13[/tex]
[tex]\bar x = 0.14[/tex]
By comparison, the mean is greater than the median.
Hence, the shape is: right skewed.
Algebraically show that each of the given combinations are equivalent to the given functions. f(x) – g() is
equivalent to m(x) given:
f(0)
= - 3x + 5; g(x)
- 5x – 7; m(x) = 2x + 12
f(x) – g(x) = (
=
Is f(x) – g(x) equivalent to m(x)? yes
Answers
Answer:
[tex]f(x) - g(x) = 2x + 12[/tex]
[tex]m(x) = f(x) - g(x)[/tex] --- True
Step-by-step explanation:
Given
[tex]f(x) = -3x + 5[/tex]
[tex]g(x) = -5x - 7[/tex]
[tex]m(x) = 2x + 12[/tex]
Solving (a): [tex]f(x) - g(x)[/tex]
From the given parameters, we have:
[tex]f(x) = -3x + 5[/tex]
[tex]g(x) = -5x - 7[/tex]
So:
[tex]f(x) - g(x)=-3x+5 + 5x + 7[/tex]
Collect like terms
[tex]f(x) - g(x) = 2x + 12[/tex]
Solving (b) m(x) = f(x) = g(x)?
In (a), we have:
[tex]f(x) - g(x) = 2x + 12[/tex]
And
[tex]m(x) = 2x + 12[/tex] --- given
By comparison:
[tex]m(x) = f(x) - g(x)[/tex]
NEEED HELP FROM BRAINLIEST??????
If the point (1,4) is on the graph of an equation, which statement must be
true?
A. The values x= 1 and y= 4 make the equation true.
B. The values x= 4 and y= 1 make the equation true.
C. The values x= 1 and y= 4 are the only values that make the
equation true.
D. There are solutions to the equation for the values x= 1 and x= 4.
Answers
Answer:
A
Step-by-step explanation:
Please help ASAP!!! Thank you!!!
Answers
Please I need help!!!!!!!!
Answers
Answer:
10 is the correct answer
Answer:
Go with the third option 10!
i hope this helped!
What is the growth factor that corresponds to a product that increases its value first by 2%, and then increases by 5% of
its value, and finally increases by 12% of its value? Round to the tenths place.
a. 1.20
C. 1.19
b. 3.19
d. 1
Answers
Answer:
1.19
Step-by-step explanation:
1+0.02+0.05+0.12 = 1.19
The greatest common factor of 45a^2b^3 and 18a^4b
Answers
Answer:
9a²b
Step-by-step explanation:
Hi there!
We need to find the greatest common factor out of 45a²b³ and 18[tex]a^{4}[/tex]b
We can split apart the monomials to make it easier
45a²b³ is 45*a²b³
18[tex]a^{4}[/tex]b is 18*[tex]a^{4}[/tex]b
First, let's find the GCF out of 45 and 18 (the number coefficients)
we can find all of the multiples of the 2 numbers:
45 is made up of 9 and 5
9 is made up of 3 and 3
so 3*3*5 is 45
18 is made up of 2 and 9
9 is made up of 3 and 3
so 2*3*3 is 18
3*3 is in both 45 and 18, so 9 is the GCF out of 45 and 18
Now let's find the GCF out of a²b³ and [tex]a^{4}[/tex]b
a²b³ made up of a² and b³
so a²b³ is a*a*b*b*b
[tex]a^{4}[/tex]b is made up of [tex]a^{4}[/tex] and b
so [tex]a^{4}[/tex]b is a*a*a*a*b
a*a*b is in both a²b³ and [tex]a^{4}[/tex]b, so the GCF out of a²b³ and [tex]a^{4}[/tex]b is a²b
Now multiply 9 and a²b together, as they are only the GCF of the parts of the monomials
9*a²b=9a²b
there's the greatest common factor of the 2 monomials
Hope this helps!
Find m<1. Please answer by tomrrow
Answers
Answer:
59
Step-by-step explanation:
Just get the supplement of 121.
So angle 1 is 180-121 = 59 degrees
Please help it’s kinda confusing only got 20 minutes left !!
Answers
Write the expression in complete factored form.
5n(x - 2) + 8(x - 2) =
Answers
x − 2 out of 5n ( x −2 ) + 8 ( x − 2) . ( x − 2 ) ( 5 n + 8 )
I hope this is correct and helps!
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{5n(x - 2) + 8(x - 2) =}[/tex]
[tex]\large\text{DISTRIBUTE 5 and 8 WITHIN the PARENTHESES}[/tex]
[tex]\large\textsf{= 5n(x) + 5(-2) + 8(x) + 8(-2)}[/tex]
[tex]\large\textsf{= 5nx - 10n + 8x - 16}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf (x - 2)(5n + 8)}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Which could be the function graphed below?
Answers
[tex]f(x)=\sqrt{x} -2[/tex] is the correct option
what is the circumference of a circle whose radius squared is 113
Answers
Answer:
[tex] C = 2 \pi \sqrt{113} [/tex]
[tex] C \approx 66.79 [/tex]
Step-by-step explanation:
[tex] C = 2 \pi r [/tex]
[tex] r^2 = 113 [/tex]
[tex] r = \sqrt{113}} [/tex]
[tex] C = 2 \pi \sqrt{113} [/tex]
[tex] C \approx 66.79 [/tex]
There are two numbers. The sum of 4 times the first number and 3 times the second number is 34 the difference between 2 times the first number and 3 times the second number is 12 . Find the two numbers
Answers
Answer:
10/9
23/3
Step-by-step explanation:
4x + 3y = 34
2x - 3y = 12
2x = 12 + 3y
2×(12 + 3y) + 3y = 34
24 + 6y + 3y = 34
24 + 9y = 34
9y = 10
y = 10/9
3×10/9 + 4x = 34
10/3 + 4x = 34
4x = (102 - 10)/3 = 92/3
x = (92/3)/4 = (92/3)/(4/1) = 92/(4×3) = 23/3
Please help asap i will give brainliest. Find the exact perimeter and area of the triangle.
Answers
Answer:
perimeter=9cm
Area=2cm^2
step by step explanation:
Firstly solve the sides that don't have figures using trigonometry
#1..sin15°=opposite/hypotenuse
sin15=opposite/4
opposite=sin15×4
=1.035, round off to 1cm
Then find the value of the base
tan15=opposite/adjacent
tan15=1/adjacent
1=tan15adjascent
1/tan15=adjacent
adjacent or base=3.7 round off to 4cm
After finding these values find the perimeter
p=side+side+side
p=4cm+4cm+1cm
p=9cm
Find the area
1/2bh
1/2×4×1
A=2cm2
Can you tell me the procedure of these
x-7 = -2
x-1 = 7
9-x = -10
Answers
I
Don’t
Know
write the expression x^2+8x-5 and x^2-4x-2 in the form (x+a)^2 +b
Answers
If 2x^2 + 3x + 3 = Kx - K has real roots, find the possible values of k.
Answers
Answer:
Step-by-step explanation:
Dd
If the smallest angle of a triangle is 20° and it is included between sides of 4 and 7, then (to the nearest tenth) the smallest side of the triangle is _____.
Answers
Answer:
[tex]3.5[/tex]
Step-by-step explanation:
The smallest side of a triangle is formed by the smallest angle in the triangle.
To find the side opposite (formed by) the 20 degree angle, we can use the Law of Cosines. The Law of Cosines states that for any triangle, [tex]c^2=a^2+b^2-ab\cos \gamma[/tex], where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are the three sides of the triangle and [tex]\gamma[/tex] is the angle opposite to [tex]c[/tex].
Let [tex]c[/tex] be the side opposite to the 20 degree angle.
Assign variables:
[tex]a\implies 4[/tex] [tex]b\implies 7[/tex] [tex]\gamma \implies 20^{\circ}[/tex]Substituting these variables, we get:
[tex]c^2=4^2+7^2-2(4)(7)\cos 20^{\circ},\\c^2=16+49-56\cos 20^{\circ},\\c^2=12.377213236,\\c=\sqrt{12.377213236}=3.51812638147\approx \boxed{3.5}[/tex]
Therefore, the shortest side of this triangle is 3.5.
Yes again but pls if you don’t know don’t answer.
Answers
Answer:
90deg +20deg.
Step-by-step explanation:
Angle RST can be broken down into RSQ and QST, whose measures are 90 deg and 20 deg, respectively. So you just add up the two parts to get the whole.
Hope this helps!
F(x) = x2. What is g(x)?
need help asap!!!
Answers
Answer:
Dear the answer is 100% D
Good luck
identify an equation in slope-intercept form for the line parallel to y=-3x+7 that passes through (2,-4)
Answers
Answer:
y = -3x + 2
Step-by-step explanation:
If two lines are parallel to each other, they have the same slope.
The first line is y = -3x + 7. Its slope is -3. A line parallel to this one will also have a slope of -3.
Plug this value (-3) into your standard point-slope equation of y = mx + b.
y = -3x + b
To find b, we want to plug in a value that we know is on this line: in this case, it is (2, -4). Plug in the x and y values into the x and y of the standard equation.
-4 = -3(2) + b
To find b, multiply the slope and the input of x (2)
-4 = -6 + b
Now, add 6 to both sides to isolate b.
2 = b
Plug this into your standard equation.
y = -3x + 2
This equation is parallel/perpendicular to your given equation (y = -3x + 7) and contains point (2, -4)
Hope this helps!
If m and n are positive integers and m^2 - n^2 = 9, which of the following could be the value of
n?
A) 1
B) 16
C) 9
D) 4
Answers
Answer:
4
Problem:
If m and n are positive integers and m^2 - n^2 = 9, which of the following could be the value of
n?
A) 1
B) 16
C) 9
D) 4
Step-by-step explanation:
One approach would be to plug in the choices and see.
If n=1, then we have m^2-1=9.
This would give m^2=10 after adding 1 on both sides. There is no integer m when squared would give us 10. ( Square root of 9 is a decimal )
If n=16, then we would have m^2-256=9.
This would give m^2=265 after adding 256 on both sides. There is no integer m when squared would give us 265. ( Square root of 265 is a decimal )
If n=9, then we would have m^2-81=9.
This would give m^2=90 after adding 81 on both sides. There is no integer m when squared would give us 90. ( Square root of 90 is a decimal )
If n=4, then we would have m^2-16=9.
This would give m^2=25 after adding 16 on both sides. There is an integer m when squared would give us 25. ( Square root of 25 is a 5)
Which choice is equivalent to √10*√5
Answers
Answer:
5√2
Step-by-step explanation:
Given √10*√5
Using surd, the expression can be evaluated further as :
√10*√5 = √50
√50 can be expressed as :
√50 = √25*2 = √25 * √2
√25 = 5
Hence,
√50 = √25 * √2 = 5√2
Hence, √10*√5 = 5√2
Water lilies are often used to decorate ponds, as shown in the photo. But they are also famous for their unusual growth pattern!
Answers
Answer:
what is the question
pls mark me as brainlist
Thank you for the points
