Answer:
B. 3.64 to the nearest hundredth.
Step-by-step explanation:
3tan1/3theta=8
tan1/3theta = 8/3
1/3 theta = 1.212 radians, 1.212 + π radians.
theta = 1.212 * 3 = 3.636 radians, 3(1.212 + π) radians.
The second value is greater than 2π radians.
The correct answer is C. 1.21, 2.26, 3.31, 4.35, 5.40.
To solve the equation [tex]\( 3 \tan \frac{1}{3}\theta = 8 \)[/tex] in the interval[tex]\( 0 \) to \( 2\pi \)[/tex], we first isolate [tex]\( \tan \frac{1}{3}\theta \):[/tex]
[tex]\[ \tan \frac{1}{3}\theta = \frac{8}{3} \][/tex]
Next, we take the inverse tangent (arctan) of both sides to solve for
[tex]\[ \frac{1}{3}\theta = \arctan\left(\frac{8}{3}\right) \][/tex]
Now, we multiply both sides by 3 to solve for [tex]\( \theta \)[/tex]:
[tex]\[ \theta = 3 \cdot \arctan\left(\frac{8}{3}\right) \][/tex]
Using a graphing calculator, we find the values of [tex]\( \theta \)[/tex] that satisfy the equation within the interval [tex]\( 0 \)[/tex] to[tex]\( 2\pi \)[/tex]. The calculator will give us the principal value and we need to consider all solutions within the given interval, taking into account the periodicity of the tangent function.
The principal value for [tex]\( \arctan\left(\frac{8}{3}\right) \)[/tex] is approximately[tex]\( 1.21 \)[/tex] radians. Since the tangent function has a period of[tex]\( \pi \)[/tex], we add multiples of[tex]\( \pi \)[/tex] to find other solutions within the interval [tex]\( 0 \)[/tex] to [tex]\( 2\pi \).[/tex]
[tex]\[ \theta \approx 1.21 + k\pi \][/tex]
where [tex]\( k \)[/tex] is an integer such that[tex]\( \theta \)[/tex] remains within the interval [tex]\( 0 \)[/tex] to[tex]\( 2\pi \).[/tex]
For[tex]\( k = 0 \):[/tex]
[tex]\[ \theta \approx 1.21 \][/tex]
For [tex]\( k = 1 \):[/tex]
[tex]\[ \theta \approx 1.21 + \pi \approx 4.35 \][/tex]
For[tex]\( k = 2 \):[/tex]
[tex]\[ \theta \approx 1.21 + 2\pi \approx 7.49 \][/tex]
However, this value is outside our interval, so we do not include it.
For[tex]\( k = 3 \):[/tex]
[tex]\[ \theta \approx 1.21 + 3\pi \approx 10.63 \[/tex]]
This value is also outside our interval, so we do not include it.
Since the tangent function is periodic with a period of [tex]\( \pi \),[/tex] we also need to consider the solutions in the second half of the interval[tex]\( 0 \)[/tex] to [tex]\( 2\pi \),[/tex] which are obtained by subtracting the principal value from[tex]\( 2\pi \):[/tex]
[tex]\[ \theta \approx 2\pi - 1.21 + k\pi \][/tex]
[tex]\[ \theta \approx 2\pi - 1.21 + k\pi \][/tex]
For [tex]\( k = 0 \)[/tex]:
[tex]\[ \theta \approx 2\pi - 1.21 \approx 5.40 \][/tex]
For [tex]\( k = 1 \)[/tex]:
[tex]\[ \theta \approx 2\pi - 1.21 + \pi \approx 8.54 \][/tex]
This value is outside our interval, so we do not include it.
Therefore, the solutions within the interval[tex]\( 0 \)[/tex] to [tex]\( 2\pi \)[/tex], rounded to the nearest hundredth, are: [tex]\[ \boxed{1.21, 2.26, 3.31, 4.35, 5.40} \][/tex]
Note that [tex]\( 2.26 \)[/tex] and [tex]\( 3.31 \)[/tex] are obtained by adding [tex]\( \pi \) to \( 1.21 \)[/tex] and [tex]\( 2.26 \)[/tex]respectively, which are the first two solutions in the first half of the interval. These values are within the interval [tex]\( 0 \) to \( 2\pi \)[/tex] and are also solutions to the original equation.
Find the range of the following set of data.
13. 11, 4,5,6, 9, 10, 12, 15, 16
Answer:
12
Step-by-step explanation:
First put the set in order from least to greatest:
4, 5, 6, 9, 10, 11, 12, 15, 16
To find the range you subtract the largest number by the smallest number.
4, 5, 6, 9, 10, 11, 12, 15, 16
So 16 - 4 = 12
So the range is 12.
Answer:
12
Step-by-step explanation:
The greatest value in the data is 16.
The lowest value in the data is 4.
The range is the difference between the highest and the lowest values.
range = 16 - 4 = 12
Divide 1,600 by 84, and then divide the answer by 3
Answer:
6.3
Step-by-step explanation:
1,600 / 84 = 19.04
19.04 / 3 = 6.3
To answer the student's question, we first divide 1,600 by 84 which gives around 19.0476, and then divide this result by 3, which gives the final answer of 6.3492.
Explanation:To solve this problem, we first need to divide 1,600 by 84. That will give us the first result. Next, we must take this first result and divide it by 3.
Let's take it step by step:
1,600 ÷ 84 ≈ 19.0476 (You can take it to the nearest 4 decimal points for simplicity). Now, take this result (19.0476) and divide it by 3. The answer is around 6.3492.
So after you divide 1,600 by 84, and then divide the answer by 3, the final result should be around 6.3492.
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y=x2
x=-3 -2 -1 0 1 2 3
y=
Answer:
see below
Step-by-step explanation:
Y=x^2
x=-3 -2 -1 0 1 2 3
y=(-3)^2 (-2)^2 (-1)^2 0^2 1^2 2^2 3^2
9 4 1 0 1 4 9
What is this anwser? Thanks!
Answer:
v = -90.
Step-by-step explanation:
To isolate v you multiply both sides of the equation by 10:
v *10 / 10 = -9 * 10
v = -90.
Answer:
v = - 90
Step-by-step explanation:
Given
[tex]\frac{v}{10}[/tex] = - 9
Multiply both sides by 10
v = 10 × - 9 = - 90
f(x)=5x-10 and g(x)=x-16
Which of the following represents h(x)=F(x)+g(x)
Answer:
6x - 26
Step-by-step explanation:
f(x) + g(x) = 5x - 10 + x - 16 ← collect like terms
= 6x - 26
Answer:
B
Step-by-step explanation:
If f(x)=x-3/x and g(x)=5x-4, what is the domain of (f•g)(x)?
Answer:
{x|⅘ ≠ x} → Set-Builder Notation
(-∞, ⅘) ∪ (⅘, ∞) → Interval Notation
Step-by-step explanation:
Plug the g(x) function into the f(x) function for every x you see.
Answer:
domain is the set of all real numbers except 0
Step-by-step explanation:
If f(x)=x-3/x and g(x)=5x-4
(f•g)(x) is f(x) times g(x)
multiply f(x) and g(x)
(f•g)(x) is f(x) times g(x)
Replace f(x) and g(x)
[tex]f(x) \cdot g(x)= (x-\frac{3}{x})(5x-4)[/tex]
Apply FOIL method to multiply it
multiply x inside the parenthesis
[tex]5x^2-4x[/tex]
Multiply the fraction inside the parenthesis
[tex]-5 +\frac{12}{x}[/tex]
[tex]5x^2-4x -5 +\frac{12}{x}[/tex]
We have x in the denominator . Domain is the set of x value for which the function is defined.
When denominator x is 0 then the function is undefined
So domain is the set of all real numbers except 0
5 / 3 + 43 / 9 what is the answer
Answer:
58/9
Step-by-step explanation:
5/3 +43/9
Lets take the L.C.M first
The L.C.M would be 9
Solve the term by taking 9 as L.C.M
=15+43/9
Add the numerator.
=58/9
The answer is 58/9 ....
which is a step in the process of calculating successive discounts of 8% and 10% on a $50 item
Answer:
The process of calculating successive discounts of 8% and 10% on a $50 item is take 10% of $46.
Step-by-step explanation:
As given
successive discounts of 8% and 10% on a $50 item .
First find out for 8 % discount
8% is written in the decimal form
= 0.08
8 % of $50 item = 0.08 × 50
= $ 4
Price of item after 8% discount = 50 - 4
= $46
First find out for 10 % discount
10% is written in the decimal form
= 0.1
8 % of $48 item = 0.1× 46
= $4.6
Price of item after 8% discount = 46 - 4.6
= $41.4
Therefore in the successive discounts of 8% and 10% on a $50 item is $41.4 .
The final price after applying the successive discounts is $41.40
To calculate successive discounts of 8% and 10% on a $50 item, follow these steps:
First, convert the first discount of 8% to a decimal by dividing 8 by 100, which gives 0.08.
Multiply the original price of the item, $50.00, by 0.08 to find the amount of the first discount: $50.00 x 0.08 = $4.00.
Subtract the first discount from the original price to find the new price: $50.00 - $4.00 = $46.00.
Next, convert the second discount of 10% to a decimal by dividing 10 by 100, which gives 0.10.
Multiply the new price of the item, $46.00, by 0.10 to find the amount of the second discount: $46.00 x 0.10 = $4.60.
Finally, subtract the second discount from the new price to find the final price: $46.00 - $4.60 = $41.40.
The final price after applying the successive discounts is $41.40.
Which of the following graphs represents the translation of Rectangle ABDC over the following: (x,y) ---> (x+1, y-2) ???
I WILL MARK BRAINLIEST
please answer I'll do anything. I know I have the answer right, i just need to know how to show the work
Answer:
B.
Step-by-step explanation:
The spaces on the graph are x=3 nd y=7 so x+1= Move it up 1 space so it's at -4. And move y up 2 so it's at 3. That's why B is correct.
(I can't really be more specific, sorry.)
If m proportional to n and m=5 when n=4.what is the valuue of m?when n=18
Answer:
m=22.5
Step-by-step explanation:
m is proportional to n means there is some constant k such that:
m=kn
If m=5 when n=4 then we have the following equation to solve for our constant k:
5=k(4)
5=4k
Divide both sides by 4:
5/4 =k
So k=5/4 no matter what (m,n) pair they give you where the equation is m=kn.
m=(5/4)n
What is m when n=18?
m=(5/4)(18)
m=(5/2)(9)
m=45/2
m=22.5
Final answer:
To find the value of m when n=18 for a proportional relationship where m is 5 when n is 4, calculate the constant of proportionality (k=5/4) and multiply by 18 to get m=22.5.
Explanation:
The question asks to find the value of m when n=18 given that m is proportional to n and m=5 when n=4. To solve this, we first establish the relationship between m and n using the provided values:
m = kn
(where k is the constant of proportionality)
Given that m=5 when n=4:
5 = k × 4
k = 5/4
Now we can determine the value of m when n=18 with the constant k:
m = (5/4) × 18
m = 22.5
The value of m when n is 18 is 22.5.
Which expression is equal to a + (b + c)?
(a + b) + c
(a + b) ⋅ c
a + bc
b + ac
Answer:
The correct option is (a+b)+c
Step-by-step explanation:
The correct option is (a+b)+c
According to the Associative property for Addition:
a+(b+c)=(a+b)+c
The associative property states that you can add or multiply regardless of how the numbers are grouped.
.If you are adding or multiplying it does not matter where you put parenthesis.
Thus the correct option is A....
[tex]\huge{\boxed{(a+b)+c}}[/tex]
For example, [tex]2+(3+4)=2+7=9[/tex].
If we group the terms differently, it doesn't matter. [tex](2+3)+4=5+4=9[/tex]
This is called the associative property of addition. As long as you still have all of the terms, and there are no other operations (subtraction, multiplication, etc.), the final answer will remain the same no matter how the terms are grouped.
if f(x)=x/2-3 and g(x)=3x2+x-6, find (f+g)(x)
Answer:
[tex](f+g)(x) = 3x^2+\frac{3x}{2}-9\\or\\(f+g)(x) = \frac{6x^2+3x-18}{2}[/tex]
Step-by-step explanation:
We are given:
[tex]f(x)=\frac{x}{2}-3 \,\, and\,\, g(x) = 3x^2+x-6[/tex]
We need to find [tex](f+g)(x)[/tex]
(f+g)(x) can be found by adding f(x) and g(x)
(f+g)(x) = f(x) + g(x)
[tex](f+g)(x) = \frac{x}{2}-3+(3x^2+x-6) \\(f+g)(x) = \frac{x}{2}-3+3x^2+x-6\\(f+g)(x) = 3x^2+\frac{x}{2}+x-3-6\\(f+g)(x) = 3x^2+\frac{3x}{2}-9\\(f+g)(x) = \frac{6x^2+3x-18}{2}[/tex]
so, (f+g)(x) is:
[tex](f+g)(x) = 3x^2+\frac{3x}{2}-9\\or\\(f+g)(x) = \frac{6x^2+3x-18}{2}[/tex]
Answer:
Step-by-step explanation:
Find the perimeter of a triangle with sides that measure 55 cm, 48 cm, and 32 cm..
Answer:
The perimeter of the triangle is 135 cm
Step-by-step explanation:
* Lets explain how to find the perimeter of a triangle
- The perimeter of any triangle is the sum of the lengths of its three sides
- The perimeter of the scalene triangle is P = S1 + S2 + S3
- The perimeter of the isosceles triangle is P = 2S + S1
- The perimeter of the equilateral triangle is P = 3S
* Lets solve the problem
∵ The length of the 1st side is 55 cm
∴ S1 = 55 cm
∵ The length of the 2nd side is 48 cm
∴ S2 = 48 cm
∵ The length of the 3rd side is 32 cm
∴ S3 = 32 cm
∵ The triangle is scalene
∴ P = S1 + S2 + S3
∴ P = 55 + 48 + 32 = 135 cm
* The perimeter of the triangle is 135 cm
I have been looking at this for hours, please help!
Q.
One liter is approximately equal to 0.26 gallons. Find the volume rounded to the nearest hundredth of a gallon of a container that holds approximately 5.5 liters.
[tex]\bf \begin{array}{ccll} liters&gallons\\ \cline{1-2} 1&0.26\\ 5.5&x \end{array}\implies \cfrac{1}{5.5}=\cfrac{0.26}{x}\implies x=(5.5)(0.26)\implies x=1.43[/tex]
What is the solution to 3|–3x + 9| = –18?
Answer:
X=5
Step-by-step explanation:
i hope this helps
Answer:
equation has no solutions
Step-by-step explanation:
3|–3x + 9| = –18 (divide both sides by 3)
|–3x + 9| = –6
because by definition, for any value a, |a| must be non-negative
hence |–3x + 9| must give a value that is greater or equal zero
because the right side of the equation is a negative integer, hence the equation has no solutions.
Find the value of the discriminant. Then describe the number and type of roots for the equation. x2 + x + 7 = 0
Answer:
The value of the discriminate is -27 and there are 2 complex roots
Step-by-step explanation:
* Lets explain what is discriminant
- The form of the quadratic equation is y= ax² + bx + c
- The roots of the equation is the values of x when y = 0
- There are three types of roots:
# Two different real roots
# One real root
# No real roots or two complex roots
- We can know the types of roots of the equation without solve it by
using the discriminant which depends on the value of a , b , c
- The discriminant = b² - 4ac, where a is the coefficient of x² , b is the
coefficient of x and c is the numerical term
# If b² - 4ac > 0, then there are two different real roots
# If b² - 4ac = 0, then there is one real root
# If b² - 4ac < 0, then there is no real root (2 complex roots)
* Lets solve the problem
∵ x² + x + 7 = 0
∴ a = 1 , b = 1 , c = 7
∵ The discriminant = b² - 4ac
∴ The discriminant = (1) - 4(1)(7) = 1 - 28 = -27
∵ -27 < 0
∴ There is no real solution there are two complex roots
* The value of the discriminate is -27 and there are 2 complex roots
Answer:
The number of roots are 2 and type of roots is complex
Step-by-step explanation:
Points to remember
Discriminant of a quadratic equation ax² + bx + c = 0
x = b² - 4ac
To find the discriminant of the given equation
Here quadratic equation be x² + x + 7 = 0
a = 1, b = 1 and c = 7
discriminant = b² - 4ac
= 1² - (4 * 1 * 7)
= 1 - 28
= -27
To find number and type of roots
Here discriminant is negative
Therefore the number of roots are 2 and type of roots is complex
What is the complex conjugate?
Answer:
B. -3 - 5i
Step-by-step explanation:
To find the complex conjugate of a complex number, just change the sign of the imaginary part.
The complex conjugate of a + bi is a bi.
In this case, the complex conjugate of 3 + 5i is -3 - 5i.
A complex conjugate of a complex number a + bi is a - bi. It is obtained by changing the sign of the imaginary part. It is useful for performing mathematical operations with complex numbers.
Explanation:The complex conjugate of a complex number is defined as changing the sign of the imaginary part of that number. If the complex number is expressed in the form a + bi, where a and b are real numbers and 'i' is the square root of -1 representing the imaginary unit, its complex conjugate is a - bi. The definition of a complex conjugate is very important in the study of complex numbers because it allows for the multiplication and division of complex numbers in a way that results in real numbers. We use this conjugate to calculate the magnitude or modulus of a complex number as well.
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Vince bought 6 boxes of worms to use as bait while fishing with his friends. If each person uses exactly 3/8 of a box of worms, how many people can share the worms.
We are given the following information:
each person uses 3/8 a box
there are 6 boxes
Because each box is [tex]\frac{8}{8}[/tex], and there are 6 boxes, we know that 1 person is [tex]\frac{3}{8*6}[/tex], or [tex]\frac{3}{48}[/tex].
In order to find how many people can use the 6 boxes, we can divide it by 3 (for each use):
48 / 3 = 16
Therefore, 16 people can share the worms.
Hope this helps! :)
Which of the following is the measure of AXYif ray xy bisects AXB,
which measures 110°
Answer:
The measure of angle AXY is 55°
Step-by-step explanation:
we know that
If ray XY bisects AXB
then
∠AXY=∠YXB=∠AXB/2
therefore
∠AXY=110°/2=55°
see the attached figure to better understand the problem
Solve the inequality 2x2 + 10x < –8
Answer:
-4<x<-1
Step-by-step explanation:
To solve the problem, we divide the whole expression by 2:
2x^2 + 10x < –8 → x^2 + 5x < –4
→ x^2 + 5x + 4 < 0
Factorizing
→ (x+4)(x+1) < 0
The expression is ONLY negative when:
x>-4 and x<-1
Therefore, the solution is:
-4<x<-1
The inequality 2x2 + 10x < -8 should be rearranged to 2x2 + 10x + 8 < 0. It can't be factored so we must use the quadratic formula to solve it. The solution involves finding the values of x that make the function positive or negative.
Explanation:To solve the inequality 2x2 + 10x < -8, we first need to arrange the terms. To do so, we can subtract 8 from each side of the inequality obtaining 2x2 + 10x + 8 < 0.
However, this is a quadratic inequality that is best solved by factoring, if possible. Let's try to factor our quadratic expression, but keep in mind that not all quadratic expressions can be factored. In this case, it is not factorable. Therefore, it must be solved by using the quadratic formula, which is x = [-b ± sqrt(b2-4ac)]/2a.
Take note the a, b, and c values from our inequality (a=2, b=10, c=8), and substitute these values into the quadratic formula. However, this approach will solve for 'x' in an equation, not an inequality.
To solve for 'x' in the inequality, we have to find the values of 'x' that make the function positive or negative, depending on the type of the inequality. We determine those values by solving the equation f(x) = 0, where f(x) is the left side of our inequality.
It is a complex process that requires understanding of both quadratic functions and inequalities. Following these steps and calculating correctly should lead you to the solution.
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Find the value of X in the picture.
Answer:
The measure of the arc x is 130°
Step-by-step explanation:
we know that
The semi-inscribed angle is half that of the arc it comprises
so
65°=(1/2)[arc x]
solve for x
arc x=(2)(65°)=130°
The graph of y= -4x + 7 is:
Answer:
Your y-intercept is at (0,7). To plot other points, use your slope: -4. (go down 4, go right 1 OR go up 4 and left 1)
Step-by-step explanation:
Answer:
Graph is attached below
Step-by-step explanation:
[tex]y= -4x + 7[/tex]
To graph this linear function , we make a table
Assume some random number for x and find out y. Assume some positive and negative numbers for x
x y=-4x+7
-1 -4(-1)+7=11
0 -4(0)+7=7
1 -4(1)+7=3
The points we got are (-1,11) (0,7) (1, 3)
Plot all the points and join all the points by a line
The graph is attached below
Use function notation to write a recursive formula to represent the sequence: 3, 6, 9, …
A. f(n) = f(n − 1) + 3
B. f(n) = f(n − 1) + 2
C. f(n) = f(n − 1) ⋅ 3
D. f(n) = f(n − 1) ⋅ 2
Final answer:
The recursive formula for the sequence 3, 6, 9, ... is represented by option A: f(n) = f(n - 1) + 3, which states that each term is 3 more than the previous term, starting with f(1) = 3. Option a
Explanation:
To write a recursive formula for the sequence 3, 6, 9, ..., we need to observe the pattern of the sequence. Since each term increases by 3 from the previous term, we can express this as:
f(n) = f(n − 1) + 3 for n > 1,
with a starting value f(1) = 3. This represents the first term in the sequence. Therefore, the correct answer is A: f(n) = f(n − 1) + 3.
The other options suggest either multiplying the preceding term by 2 or 3, or adding 2 to the preceding term, but those operations do not describe the given sequence. Option a
how do i solve x+3y=7
Answer:
If you're trying to find x or y, you cannot find the exact value since there is one equation. If there was, for example, 2 equations, [a system of equations] you could solve that. But here we only have one equation.
So, if you're trying to solve for x;
x = 7 - 3y
And if you're trying to solve for y;
y = 7/3 - x
Which of the following functions gives the length of the base edge, a(v), of a right square pyramid that is 8 inches tall as a function of its volume, v, in
cubic inches?
Answer:
[tex]\large\boxed{a(V)=\sqrt{\dfrac{3V}{8}}}[/tex]
Step-by-step explanation:
The formula of a volume of a square pyramid:
[tex]V=\dfrac{1}{3}a^2h[/tex]
a - base edge
h - height of a pyramid
We have H = 8in.
Substitute and solve for a:
[tex]\dfrac{1}{3}a^2(8)=V\\\\\dfrac{8}{3}a^2=V\qquad\text{multiply both sides by}\ \dfrac{3}{8}\\\\\dfrac{3\!\!\!\!\diagup^1}{8\!\!\!\!\diagup_1}\cdot\dfrac{8\!\!\!\!\diagup^1}{3\!\!\!\!\diagup_1}a^2=\dfrac{3}{8}V\\\\a^2=\dfrac{3V}{8}\Rightarrow a=\sqrt{\dfrac{3V}{8}}[/tex]
Answer:
Answer:
Step-by-step explanation:
The formula of a volume of a square pyramid:
a - base edge
h - height of a pyramid
We have H = 8in.
Substitute and solve for a:
diavinad8 and 53 more users found this answer helpful
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!
The new middle school aquarium is a rectangular prism with these dimensions:
Length: 60 cm
Width: 25cm
Height: 30 cm
Find how much water it will take to fill the aquarium to the top (volume).
Find how much glass it will take to make the aquarium (surface area).
Note: There is no “top” to the aquarium. It may help to draw a net.
Answer:
Volume: 45000cm^3
Surface area: 6600cm^2
Step-by-step explanation:
The volume is all the side lengths multiplied, so 60*25*30 = 45,000 cm^3.
Now let's calculate the surface area.
The bottom is the width * the length, or 60*25 cm^2.
One of the sides is the length * the height, or 60*30 cm^2. This is multiplied by 2 because there are 2 of those sides.
The other pair of sides is the width * the height, or 25*30 cm^2, again multiplied by 2.
In total, the surface area is
60*25+2*60*30+2*25*30 = 6600cm^2
To fill the aquarium to the top with water, it will take 7800 cubic centimeters (cm³). To make the aquarium, it will take 7800 square centimeters (cm²) of glass.
Find the volume of the aquarium: Since there is no top to the aquarium, we will consider the volume as the combined volume of the five faces of the rectangular prism (4 faces with dimensions Length x Width and 1 face with dimensions Length x Height).
Volume = 4 * (Length * Width) + (Length * Height)
Volume = 4 * (60 cm * 25 cm) + (60 cm * 30 cm)
Volume = 4 * 1500 cm² + 1800 cm²
Volume = 6000 cm² + 1800 cm²
Volume = 7800 cm³
So, it will take 7800 cubic centimeters (cm³) of water to fill the aquarium to the top.
Find the surface area of the aquarium: To find the surface area, we will consider the area of each face and add them together.
Area of the 4 faces with dimensions Length x Width:
4 * (60 cm * 25 cm) = 4 * 1500 cm² = 6000 cm²
Area of the face with dimensions Length x Height:
(60 cm * 30 cm) = 1800 cm²
Total Surface Area = 6000 cm² + 1800 cm² = 7800 cm²
It will take 7800 square centimeters (cm²) of glass to make the aquarium.
The ratio of Holly's age to that her aunt is 4:9. When holly was born her aunt was 15 years old. How old is holly's aunt now?
Answer:
27 years
Step-by-step explanation:
Let Holly's age be h and Aunt's age be a. We can setup 2 equations and solve.
1. [tex]\frac{h}{a}=\frac{4}{9}[/tex]
2. a - 15 = h
We can plug in equation 2 into equation 1 to solve for aunt's age:
[tex]\frac{h}{a}=\frac{4}{9}\\\frac{a-15}{a}=\frac{4}{9}\\9(a-15)=4a\\9a-135=4a\\5a=135\\a=\frac{135}{5}=27[/tex]
Holly's aunt's age is 27
Find the slope of the line that passes through the points (1, -3) and (2, -1). a.) one half b). negative one half c). -2 d).2
Answer:
d).2
Step-by-step explanation:
Use the following equation:
slope (m) = (y₂ - y₁)/(x₂ - x₁)
Let:
(x₁ , y₁) = (1 , -3)
(x₂ , y₂) = (2 , -1)
Plug in the corresponding numbers to the corresponding variables:
m = (-1 - (-3))/(2 - 1)
Simplify. Combine like terms. Remember to follow PEMDAS. Remember that two negatives = one positive:
m = (-1 + 3)/(2 - 1)
m = (2)/(1)
m = 2
d).2 is your slope.
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Answer:
[tex]\displaystyle =2[/tex]
Step-by-step explanation:
The slope formula is ⇒ [tex]\displaystyle\frac{Y_2-Y_1}{X_2-X_1}[/tex]
[tex]\displaystyle Y_2=(-1)\\\displaystyle Y_1=(-3)\\\displaystyle X_2=2\\\displaystyle X_1=1\\[/tex]
[tex]\displaystyle \frac{(-1)-(-3)}{2-1}=\frac{2}{1}=2[/tex]
Therefore, the slope is 2, and the correct answer is 2.
Hope this helps!
Which are the solutions of x^2 = -13x – 4?
Using the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a) to find the solutions, which are (13 + √185) / 2 and (13 - √185) / 2.
Explanation:To find the solutions of the equation x^2 = -13x - 4, we can rearrange it to the form ax^2 + bx + c = 0.
In this case, we have a = 1, b = -13, and c = -4.
We can then use the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a) to find the solutions.
Substituting the values into the formula, we get x = (-(-13) ± √((-13)^2 - 4(1)(-4))) / (2(1)). Simplifying further, we have x = (13 ± √(169 + 16)) / 2. T
herefore, the solutions of the equation are x = (13 + √185) / 2 and x = (13 - √185) / 2.
Learn more about Quadratic Equations here:https://brainly.com/question/30098550
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A culture started with 1000 bacteria. After 6 hours it few to 1300 bacteria. Predict how many bacteria will be present after 10 hours.
Answer:
1350
Step-by-step explanation:
If a culture started with 1000 bacteria and after 6 hours it few to 1300 bacteria, there would be 1350 present after 10 hours.
1000 to 1100 is an increase of 100 bacteria per 6 hours.
1100+250= 1350
Answer:
1500
Step-by-step explanation:if it grows 300 in 6 hours you can assume that each hour would increase the pop by 50 so 10 hours times 50 it will become 1500.