The sandbox can hold 48 cubic feet of sand in it if the sandbox with dimensions of 4 feet, 6 feet, and 2 feet.
What is a cuboid?It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape.
We have a sandbox:
The length of the sandbox = 4 feet
The width of the sandbox = 6 feet
The height of the sandbox = 2 feet
Amount of sand can hold = volume of the sandbox
= 4×6×2
= 48 cubic feet
Thus, the sandbox can hold 48 cubic feet of sand in it if the sandbox with dimensions of 4 feet, 6 feet, and 2 feet.
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Solve the equation 4 sin x - cosec x =cot x for 0° < x < 360°.
For this question, I will be writing 'csc' instead of 'cosec'
[tex]4\sin x-\csc x=\cot x\\\\4\sin x-\frac{1}{\sin x}=\frac{\cos x}{\sin x}\\\\4\sin^{2} x-1=\cos x\\\\4(1-\cos^{2} x)-1=\cos x\\\\4-4\cos^{2} x-1-\cos x=0\\\\4\cos^{2} x+\cos x-3=0\\\\ (4\cos x-3)(\cos x+1)=0\\\\\cos x=\frac{3}{4}, 1\\\\\therefore \boxed{\cos^{-1} \left(\frac{3}{4} \right), 180^{\circ}, 360^{\circ}-\cos^{-1} \left(\frac{3}{4} \right)}[/tex]
Solve x+ 2y = -2 I’m really confused
Answer:
y=−1/2x−1
Step-by-step explanation:
I put it in slope intercept form as I assume that is what the question is asking.
The members of a golf team contributed a total of $14.30 for a party to be held after their practice. Each member contributed the same amount of money in dimes only. How many members are in the team and how much money did everyone contribute? Give all possible answers. I NEED FULL ANSWER!!!!!!!!!!!!!!!!!!
Answer:
each teammate contributed 1.43 sorry but i do not know how many members they have because my head hurts
Can someone help me please?
Answer:
B. <TSN and <ISW
C. <KSW and <NST
Answer:
D. ∠ISN and ∠TSW
Step-by-step explanation:
The meaning of vertical angles is each of the pairs of opposite angles made by two intersecting lines.
The angles ∠ISN and ∠TSW are made by two intersecting lines. This means that these angles are vertical angles.
Hope this helps!
If not, I am sorry.
There are boys and girls in a class in the ratio 1: 12 there are 77 more girls than boys. how many boys are there?
Let's set up some variables:
b: # of boysg: # of girlsLet's set up some equations based on the informative given:
boys to girls ratio ⇒ 1: 12(Mathematical form) g = 12b
77 more girls than boys(Mathematical form) g = b + 77
Let's put the equation together:
g = 12b -- equation 1
g = b + 77 -- equation 2
(equation 2)'s value of g into (equation 1)
12b = b + 77
11b = 77
b = 7
There are 7 boys.
Answer: 7 boys
Hope that helps!
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f(x) = 3x+2
What is f(5)?
Answer:
the answer will be 17.
Step-by-step explanation:
if, f (x) = 3x + 2
f (5) = 3 × 5 + 2 = 17.
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What is the circumference of the circle shown below? (Round your answer to the nearest tenth.) A. 33.0 B. 66.0 C. 346.4 D. 206.2
Answer:
B. 66.0
Step-by-step explanation:
The formula for circumference is 2*π*r where r is the radius. MS and MR are both radii, so we can plug in 10.5 to the formula to get 2* π*10.5, which would be about 65.97, which rounds to 66.0. Hope this helps!
(6, -5) reflected aross the y axis
Answer:
Then the new point is (-6,-5)
Step-by-step explanation:
PLEASE HELP (PRE-ALGEBRA) MULTIPLE CHOICE! WILL GIVE BRAINLEIST! (photo attached!)
If the triangle on the grid below is translated by using the rule (x,y) → (x−2.y+2), what will be the coordinates of A'?
(4,0)
(0,4)
(0,0)
(-2.2)
Answer:
(-4, 0)
Step-by-step explanation:
x-2 means ur gonna take coordinate A and move it back 2 places along the x axis, (-4,-2) and then y+2 means ur gonna go up to places alomg the y axis which brings coordinate A' to (-4,0)
Answer:
A'(-4, 0)
Step-by-step explanation:
(x, y) → (x - 2, y + 2)
A(-2,-2 )→ A'(-2-2,-2+2)
= A'(-4,0)
HELP ASAP PLS ILL MARK YOU BRAINLIEST
Answer:
c is the answer.
Find the gradient of the line segment joining of
(1, 1) and (3, 5)
Answer:
2
Step-by-step explanation:
[tex]\text{First I'd recommend using this little equation:}\\\text{m}=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{Substitute the values::}\\\text{m}=\dfrac{5-1}{3-1} \\\text{m}=\dfrac{4}{3}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{The gradient is:: }\dfrac{4}{3}[/tex]
Simplify the expression when j = 5 and k = 3
*
1 point
Captionless Image
3
-9/5
41/3
6
Answer:
1 7
_
8
Step-by-step explanation:
5 x 3 = 15
5 + 3 = 8
=1 7
_
8
Given that x is an even number, express, in terms of x, the product of the next two odd numbers.
Answer:
Odd is the answer.
Step-by-step explanation:
An even number can be written in the form 2x, where x is an integer.
An odd number can be written in the form 2x + 1, where x is an integer.
So two odd numbers can be represented by 2a +1 and 2b +1, the product would be:
(2a + 1)(2b +1) = 4ab + 2a + 2b + 1 = which can be written as 2(2ab + a +b) + 1, but 2ab +a + b represents some integer, so 2ab + a + b = x.
So (2a + 1)(2b + 1) = 2(2ab + a + b ) + 1 = 2x +1 which is odd.
Pls help 25 points!!
diane started a hike with 24 ounces of water in her backpack. what fraction of a gallon of water did she start the hike with? show your work.
Your question was incomplete. Please check below the full content.
There are 8 ounces in 1 cup and 16 cups in 1 gallon.
(a) Diane brought 4.5 gallons of water to a campout. How many ounces of water did she bring? Show your work.
(b) Diane started a hike with 24 ounces of water in her backpack. What fraction of a gallon of water did she start the hike with? Show your work.
a) 576 ounces of water Diane brought.
b) 3/16 of a gallon of water did she start the hike with.
The cost price per ounce is the amount of money needed to buy one ounce of goods.To find cost price per ounce, divide the total of cost of the goods by total number of goods.Given that there are 8 ounces in 1 cup and 16 cups in 1 gallon.
a) Amount of water diana brought for campout = 4.5 gallons Ounce of water she brought = 4.5×16×8
= 576ounces
b) Diane started a hike with 24 ounces of water in her backpack.
The fraction of gallons in 24 ounces is calculated as follows:
The fraction of gallons in 24 ounces = 24 / (8×16)
= 3/16
Hence, a) 576 ounces of water Diane brought.
b) 3/16 of a gallon of water did she start the hike with.
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The graphs of f(x) and g(x) are shown below: graph of function f of x open upward and has its vertex at negative 7, 0. Graph of function g of x opens upward and has its vertex at negative 7, negative 2. If f(x) = (x + 7)2, which of the following is g(x) based on the translation? (5 points) a g(x) = (x + 9)2 b g(x) = (x + 5)2 c g(x) = (x + 7)2 + 2 d g(x) = (x + 7)2 − 2
The equation of the function is g(x)=(x+7)² -2 , Option D is the correct answer.
What is a Function ?A function is a mathematical statement that defines relation between two variables.
The f(x) = (x+7)²
The equation for g(x) is ?
graph of function f of x open upward and has its vertex at (-7,0).
Graph of function g of x opens upward and has its vertex at (-7,2).
g(x) is formed by the translation of the function f(x) such that it's vertex is (-7,-2)
Therefore the equation of the function is
g(x)=(x+7)² -2
Therefore , the translation is a shift of the function f(x) 2 units down
Option D is the correct answer.
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f(x)= x - 1. Find the inverse of f(x).
O A. f¹(x) = x
OB. f¹(x) = x + 1
O c. f¹(x) = x − 1
-
O D. f¹(x)=1-x
help please asap
Step-by-step explanation:
The right answer is d because inverse means power in minus
Two towns that are 32 km apart are 8 cm on a map. What is the scale of the map?
This question is urgent, I have grade 8 final exams tomorrow and I'm struggling with this type of question.
If two towns that are 32 km apart are 8 cm on a map. Then the scale factor will be 1 cm = 4 km.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
Two towns that are 32 km apart are 8 cm on a map.
Then the scale factor will be
8 cm = 32 km
1 cm = 4 km
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Menna is traveling in a country that measures its temperature in degrees Celsius. If the high temperature for tomorrow will be 25
∘
C, what is the equivalent temperature in
∘
F?
a. 102.6∘
F
b. 57∘
F
c. 77∘
F
d. 45.9∘
F
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: Temp = 77° F[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: f = \bigg (c \sdot \cfrac{9}{5} \bigg) + 32[/tex]
[ convert 25° C to °F ]
[tex]\qquad \tt \rightarrow \: \bigg (25 \sdot \cfrac{9}{5} \bigg) + 32[/tex]
[tex]\qquad \tt \rightarrow \: (5 \sdot9) + 32[/tex]
[tex]\qquad \tt \rightarrow \: 45 + 32[/tex]
[tex]\qquad \tt \rightarrow \: 77 \degree \: \: f[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
77
Step-by-step explanation:
took the quiz
Someone please help with this !!!
Answer:
[tex]\dfrac 5{13}[/tex]
Step-by-step explanation:
[tex]\sin \theta =\dfrac{\text{Perpendicular}}{\text{Hypotenuse}} = \dfrac{5}{\sqrt{5^2 +12^2}} = \dfrac 5{\sqrt{169}} = \dfrac 5{13}[/tex]
How do I solve an endless amount of numbers with a common ratio
..........
etc. 10+1+0.1+0.01+0.001....
Answer:
11 .21 add the number together
Notice that the given sum is equivalent to
[tex]10 + 1 + \dfrac1{10} + \dfrac1{10^2} + \dfrac1{10^3} + \cdots \\\\ ~~~~~~~~~~~~ = 10 \left(1 + \dfrac1{10} + \dfrac1{10^2} + \dfrac1{10^3} + \dfrac1{10^4} + \cdots\right)[/tex]
or 10 times the infinite geometric series with ratio 1/10.
To compute the infinite sum, consider the [tex]n[/tex]-th partial sum
[tex]S_n = 1 + \dfrac1{10} + \dfrac1{10^2} + \cdots + \dfrac1{10^{n-1}}[/tex]
Multiply both sides by the ratio.
[tex]\dfrac1{10} S_n = \dfrac1{10} + \dfrac1{10^2} + \dfrac1{10^3} + \cdots + \dfrac1{10^n}[/tex]
Subtract this from [tex]S_n[/tex] to eliminate all but the outermost terms,
[tex]S_n - \dfrac1{10} S_n = 1 - \dfrac1{10^n} \implies S_n = \dfrac{10}9 \left(1 - \dfrac1{10^n}\right)[/tex]
As [tex]n\to\infty[/tex], the exponential term will decay to 0, leaving us with
[tex]1 + \dfrac1{10} + \dfrac1{10^2} + \cdots = \dfrac{10}9[/tex]
Then the value of the sum we want is
[tex]10\times\dfrac{10}9 = \boxed{\dfrac{100}9}[/tex]
Susan makes purple paint by mixing red and blue paint in the ratio 2:3
She has 12ml of red and 15ml of blue
What is the maximum amount of purple she can make?
Question 11 of 20
What is the solution to the equation below? (Round your answer to two
decimal places.)
log₂ x = 5.6
Step-by-step explanation:
log2(x) = 5.6
so,
x = 2^5.6 ≈ 48.50293013... ≈ 48.50
factorise:y(x+z)+z(x+y)+y^2+z^2
Answer: (x+z+y)(y+z)
Step-by-step explanation:
y(x+z)+z(x+y)+y^2+z^2
Factor out y and z from the expression
= y(x+z+y)+z(x+y+z)
Factor out x + z + y from the expression
= (x+z+y)(y+z)
Can you help find m<1
Answer:
69 degrees
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
<1 = 39+ 30
<1 = 69
To determine whether a graph of a relation is also a function, Shayla declares that the y-axis is a vertical line and counts the number of times that the graph intersects the y-axis. If the graph has exactly one y-intercept, Shayla concludes that the graph shows a function. In all other cases, she declares that it is not a function.
Is Shayla applying the vertical line test correctly?
No, because the y-axis is a horizontal line.
No, because using the y-axis tests only whether x = 0 is mapped to multiple values.
Yes, because multiple y-intercepts represent multiple x-values being mapped to y = 0.
Yes, because the y-axis represents all vertical lines of the x-values.
Answer: Choice B
No, because using the y-axis tests only whether x = 0 is mapped to multiple values.
===================================================
Further Explanation:
Shayla stating that the y axis being used to conduct a vertical line test is part of the process. But she needs to move the vertical line around and not have it fixed in place.
If it is possible to have a vertical line (on the y axis or not) pass through more than one point on the curve, then we don't have a function. It is said the curve fails the vertical line test.
Otherwise, the graph passes the vertical line test and we have a function.
Using the basic identities, find the value of cosΘ if cotΘ = -12/5.
Step-by-step explanation:
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Trout Street and Salmon Street are the same distance from the boardwalk to the intersection of 1st Street, Trout Street, and Salmon Street as shown in the diagram. Abby walks down 1st Street and stops when she reaches the boardwalk.
How far of a walk does she have to get to Trout Street?
Abby's walk to Trout Street is _______ yards.
Answer:
800
Step-by-step explanation:
I did it on the test
Answer:
800
Step-by-step explanation:
I just fifnished test
1. A comfortable ambient temperature is called room temperature. Approximately,
how hot or cold is it?
A. 20 OC B. 20 OF C. 40 OC D. 40 OF
2. Convert: 5da = _______hr
A. 300 B. 240 C. 120 D. 60
3. Pasig river can discharge a maximum of 56 m3 per second of water. How many
liters per second can it discaharge?
A. 56 B. 560 C. 5 600 D. 56 000
4. A snail moves at a constant rate of 25 cm per minute. At this rate, how many
hours will it take the snail to crawl 75 m?
A. 3 B. 4 C. 5 D. 6
5. The human body can normally endure a temperature of 105 0F but for a short
period of time only, otherwise, there will be permanent damage to the brain and
vital organs. What is the equivalent temperature in 0C?
A. 37 B. 37.5 C. 40.56 D. 45.56
Answer:
Using the simple mathematical relations and formulas we get the following correct answers.
1. Option A
2. Option C
3. Option D
4. Option C
5. Option D
Step-by-step explanation:
1. The approximate room temperature is 20°C. Option A is correct.
2. 1 day has 24 hrs. 5 days will have 5×24 = 120 hrs. Option C is correct.
3. The discharge is 56m³/sec. 1m³ has 1000L. So the discharge is 56000L/sec. Option D is correct.
4. The speed is 25cm/min or (25×0.01×60)m/hrs. = 15m/hrs. For 75m the snail would take 75/15 = 5hrs. Option C is correct.
5. The relation between °C and °F is (F-32)/1.8. The equivalent temperature is (105-32)/1.8 = 40.56°C. Option D is correct.
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Study the table.
x
y
–2
8
–1
2
0
0
1
2
2
8
Which best describes the function represented by the data in the table?
linear with a common ratio of 4
linear with a common second difference of 4
quadratic with a common ratio of 4
quadratic with a common second difference of 4
Answer:
quadratic with a common second difference of 4
Step-by-step explanation:
quadratic equations: Quadratic equations are the polynomial equations of degree 2 example - a[tex]x^2\\[/tex]+ b[tex]x[/tex] + c = 0.
[tex]\begin{array}{cc}x&y\\-2&8\\-1&2\\0&0\\1&2\\2&8\end{array}\right][/tex]
from the table it is clear that,
function is y = 2[tex]x^2\\[/tex]
so the function is not linear as the equation specifies.
formula to find second difference of a quadratic equation:
f(x + 2) - 2f(x + 1) + f(x)
therefore;
[tex]2(x+2)^2[/tex] - [tex]4(x+1)^2[/tex] + [tex]2x^2[/tex]
[tex]2(x^2 + 4x + 4) - 4(x^2 + 2x+ 1 ) + 2x^2[/tex]
[tex]2x^2 + 8x + 8 - 4x^2 - 8x - 4 + 2x^2[/tex]
[tex]4x^2 - 4x^2 + 8x - 8x +8 - 4[/tex]
4
therefore, the answer is quadratic with a common second difference of 4
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Ben, Tara and Liam are playing hide and seek. They start playing at quarter past 11. They play for 45 minutes, before stopping for a drink and a cookie. They continued to play for 45 minutes and head inside at 10 minutes past 1.
How long did they stop for a drink and a cookie. Explain your reasoning.
Answer:
25 minutes
Step-by-step explanation:
they started at a quarter past 11, which is 11:15
they then played for 45 minutes, which would be until 12:00
you also know that they stopped playing at 10 minutes past 1, at 1:10.
before 1:10, they had been playing for 45 minutes, which means they started playing for the second time at 12:25.
all that's left is the time between 12:00 and 12:25, which is 25 minutes, so they spent 25 minutes stopping for a drink and a cookie.
