Given:
Volume of cuboid container = 2 litres
The container has a square base.
Its height is double the length of each edge on its base.
To find:
The height of the container.
Solution:
We know that,
1 litre = 1000 cubic cm
2 litre = 2000 cubic cm
Let x be the length of each edge on its base. Then the height of the container is:
[tex]h=2x[/tex]
The volume of a cuboid is:
[tex]V=l\times w\times h[/tex]
Where, l is length, w is width and h is height.
Putting [tex]V=2000,\ l=x,\ w=x,\ h=2x[/tex], we get
[tex]2000=x\times x\times 2x[/tex]
[tex]2000=2x^3[/tex]
Divide both sides by 2.
[tex]1000=x^3[/tex]
Taking cube root on both sides.
[tex]\sqrt[3]{1000}=x[/tex]
[tex]10=x[/tex]
Now, the height of the container is:
[tex]h=2x[/tex]
[tex]h=2(10)[/tex]
[tex]h=20[/tex]
Therefore, the height of the container is 20 cm.
A jeweler had a fixed amount of gold to make bracelets and necklaces. The
amount of gold in each bracelet is 6 grams and the amount of gold in each
necklace is 16 grams. The jeweler used 178 grams of gold and made 7 more
necklaces than bracelets. Write a system of equations that could be used to
determine the number of bracelets made and the number of necklaces made.
Define the variables that you use to write the system.
Answer:
6b+16n=178
n=b+7
Step-by-step explanation:
Let b=the number of bracelets made
Let n=the number of necklaces made
System of Equations:
6b+16n=178
n=b+7
Which graph represents y-1 = 2(x - 2)?
Answer:
I only see 1 graph...
hksjfjf
Which triangles are similar?
20°
100°
100°
60°
А
B
20°
60°
с
O A. Triangles A and B are similar to each other.
B. Triangles A, B, and C are similar to each other.
C. Triangles A and C are similar to each other.
D. Triangles B and C are similar to each other.
Answer:
B because when at B angels are the same qnd A and c are also same
The increases (in cents) in cigarette taxes for 6 states in a 11-month period are 70,12,42,45,50,51,60,69,8,40,18
Answer:
The range is 62
Step-by-step explanation:
Given
[tex]x:70,12,42,45,50,51,60,69,8,40,18[/tex]
Required
The range
This is calculated as:
[tex]Range = Highest - Least[/tex]
From the given data
[tex]Highest = 70[/tex]
[tex]Least=8[/tex]
So:
[tex]Range = Highest - Least[/tex]
[tex]Range = 70-8[/tex]
[tex]Range = 62[/tex]
[tex]\frac{1}{3}x^{2} +5x+\frac{4}{3}=2x-\frac{1}{3} x^{2}[/tex]
Simplify\left(2-\sqrt{3}\right)^2
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { C) \:7 + 4 \sqrt{3}}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] {( - 2 - \sqrt{3} )}^{2} [/tex]
[tex] = ({ - 2})^{2} - 2.( - 2). \sqrt{3} + { (\sqrt{3}) }^{2} [/tex]
[tex] = 4 + 4 \sqrt{3} + 3[/tex]
[tex] = 7 + 4 \sqrt{3} [/tex]
Note:[tex] ({a - b})^{2} = {a}^{2} - 2ab + {b}^{2} [/tex]
[tex] \sqrt{a} \times \sqrt{a} = a[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
The directrix of the parabola -40x= y2 is:
y=-10
x= 10
x=-10
y= 10
Answer:
y=10
Step-by-step explanation:
Answer:
[tex]{ \tt{y {}^{2} = 4 {ax} }} \\ = - 10[/tex]
Someone Help if they can ASAP!
Answer:
The answer is D.
Step-by-step explanation:
Since (4x+20) and 60 are vertically opposite angles. They both are equal. Hope this helped!
Find the value of F
Answer:
f = 13[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Given that f and e are congruent then e = f
Using Pythagoras' identity in the right triangle
f² + e² = 26² , that is
f² + f² = 676
2f² = 676 ( divide both sides by 2 )
f² = 338 ( take the square root of both sides )
f = [tex]\sqrt{338}[/tex] = [tex]\sqrt{169(2)}[/tex] = 13[tex]\sqrt{2}[/tex] ≈ 18.4 ( to 1 dec. place )
Answer:
f = 25.85751233
Step-by-step explanation:
f^2+E^2=26^2
Thực hiện phép nhân, rút gọn rồi tính giá trị của biểu thức :
a) x(x - y) + y(x + y)
tại x = -6 và y = 8;
b) x(x - y) = x^(x + y) + yx2 – x) tại x =
1
và y = -100,
2
Answer:
i do not understand what youre asking
Step-by-step explanation:
see^^^^^
How can you solve X^2 +2x=-1
Một xưởng dệt thảm được giao làm một số thảm trong 30 ngày. Thực tế xưởng dệt đã tăng năng xuất lên 25% nên sau 25ngay không những đã làm xong số thảm mà còn làm thêm được 20 chiếc nữa. Tính số lượng thảm mà xưởng đã dệt trong 25 ngày
Gọi số tấm thảm xưởng dệt dệt theo dự định là x ( tấm, x >0 )
⇒ số tấm thảm xưởng dệt dệt trong 1 ngày theo dự định x/30 (tấm)
xưởng dệt dệt đc số tấm thảm trong thực tế là x/20 (tấm)
⇒số tấm thảm xưởng dệt dệt trong 1 ngày thực tế là x+20/25 (tấm)
Vì năng suất tăng 25% nên số tấm thảm dệt được trong 1 ngày thực tế sẽ bằng 125% số tấm thảm dệt đc trong 1 ngày theo dự định nên ta có PT : x+20/25=125% * x/30
me lười làm khúc dưới quá nên tự xử nha.
In a right triangle, one angle measures x°, where sin xº 4/5
What is cos(90° - xº)?
==========================================================
Rule:
if A+B = 90, then cos(A) = sin(B) and sin(A) = cos(B)
This can be rephrased into cos(A) = sin(90-A) and sin(A) = cos(90-A)
We'll focus on the second case sin(A) = cos(90-A)
Simply replace A with x and we have the same idea.
---------
So,
sin(x) = cos(90-x)
cos(90-x) = sin(x)
cos(90-x) = 4/5
You can prove this by drawing out a right triangle as shown below.
Please answer it all this is very important
Answer:
6.)
The answer is 63 inches because this value is closer to the mean and while the data is positively skewed (as in the mean is greater than the median) it's not by that much.
7.)
This would mean that the data is symmetric. By this, I mean that there would have to be an equal amount of data on either side of the mean. For example, for every entry 2 units below from the mean there must be one 2 units above the mean and so on. There would also have to be many entries on the mean/median (so that it would also be the mode)
8.)
We can observe that there are no real outliers that would heavily influence the data and so we can just take the mean
the mean of student A is: (68+72+73+67)/4= 70
The mean of student B is: (74+73+73+74)/4=73.5
We can see that student A, on average, is closer to 70 than student B and can therefore conclude that student A is more percise
Find MN. See image below.
Answer:
Step-by-step explanation:
Tangents from the point outside the circle are equal
NL = JL
NM + ML =JK + KL
2x - 7 + 9 = 8 + 10
2x + 2 = 18 {Subtract 2 from both sides}
2x = 18 - 2
2x = 16 {Divide both sides by 2}
x = 16/2
x = 8
MN = 2*8 - 7 = 16 - 7 = 9
MN = 9
How will you calculate it's surface area?
The general formula for the total surface area of a right prism is T. S. A. =ph+2B where p represents the perimeter of the base, h the height of the prism and B the area of the base.
another question about angles
Answer:
ㄥBEC=70；ㄥABE=160
Step-by-step explanation:
(x-5)+(3x-5)+90=180
x-5+3x-5+90=180
4x+80=180
4x=100
x=25
ㄥBEC=3*25-5=70
ㄥABE=180-(25-5)=160
What is the resulting ordered pair if the value of the independent variable is -1?
f(x)= -5x - 4x +2
A. (-1, 1)
B. (-1, 11)
C. (2,-6)
D. (1, -1)
I need help on this please!
Answer: The correct answer is D, also for part B, do you need help with that one too?
Step-by-step explanation:
Whoever answers these 2 right gets brainliest and 25 points!
Answer:
1. C) 8•9
2. D) 4•2
Step-by-step explanation:
1. multiplication come first before division
2. You have to resolve parenthesis first (3+4•2)
3•24÷12-(3+8)
Answer:
i think c and d
Step-by-step explanation:
math
Find csc 0, sin 0, and cot 0, where is the angle shown in the figure.
Give exact values, not decimal approximations.
PLZ HELP I BEEN STUCK FOR AN HOUR I WILL MARK BRAINLIEST!!!
Answers:
[tex]\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\[/tex]
=============================================
Explanation:
Before we can find the trig ratios, we need to determine the length of the missing side. Apply the pythagorean theorem
[tex]a^2+b^2 = c^2\\\\4^2+b^2 = 7^2\\\\16+b^2 = 49\\\\b^2 = 49-16\\\\b^2 = 33\\\\b = \sqrt{33}[/tex]
The vertical side is [tex]\sqrt{33}[/tex] units long.
------------------------------------
The side we just found is the opposite side to angle [tex]\theta[/tex] (greek letter theta)
The hypotenuse is 7 units long. The hypotenuse is always opposite the right angle.
Divide the hypotenuse over opposite to get the cosecant.
[tex]\csc(\theta) = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc(\theta) = \frac{7}{\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33*33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33^2}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\[/tex]
Note: In the third step, I multiplied top and bottom by sqrt(33) to rationalize the denominator.
------------------------------------
Recall that sine is the reciprocal of cosecant, and vice versa.
So we'll use the same idea as before, but flip the original fraction.
[tex]\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\[/tex]
The denominator is already a rational number, so there's not much else to do here.
--------------------------------------
Cotangent is the ratio of adjacent over opposite
[tex]\cot(\theta) = \frac{\text{adjacent}}{\text{opposite}}\\\\\cot(\theta) = \frac{4}{\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33*33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33^2}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\[/tex]
The steps are pretty much nearly identical as the section involving csc, except we're using the adjacent in place of the hypotenuse (so that means we use 4 in place of 7).
you can use the expression 5n to determine the amount of money you have in cents, when you have n nickels. Find the amount of money you have, in cents, when you have 18 nickels
Answer:
90 cents
Step-by-step explanation:
Find how much money you have by plugging in 18 as n into the expression:
5n
5(18)
Multiply:
= 90
So, when you have 18 nickels, you have 90 cents
PLEASE HELPPPPPP FINDING CIRCUMFERENCE AND AREA OF A CIRCLE
Answer:
The circumference of the circle is 28.26 m.
The area of the circle is 63.585 [tex]m^{2}[/tex].
Step-by-step explanation:
To solve for the circumference of the circle, start by using the circumference formula of a circle, which is [tex]C= 2\pi r[/tex]. However, 3.14 will be used instead of [tex](\pi)[/tex] for this formula.
First, the radius of the circle needs to be found. To find the radius of the circle, divide the diameter by 2 because the radius equals half of the diameter. The radius is 9 m divided by 2, which equals 4.5 m.
Next, plug in the radius into the formula, and the formula will look like [tex]C=(2)(\pi )(4.5 m)[/tex]. Then, solve the equation, and the answer will be 28.26 m.
To solve for the area of the circle, start by using the area formula of a circle, which is [tex]A=\pi r^{2}[/tex]. However, 3.14 will be used instead of [tex](\pi)[/tex] for this formula.
For the area, plug the radius into the formula, and the formula will look like [tex]A= (3.14)(4.5m)^{2}[/tex]. Then, solve the equation, and the answer will be 63.585 [tex]m^{2}[/tex].
Tanya has 130 ml of juice
Answer:
The answer is below
Step-by-step explanation:
A drink is made by adding water to juice.
Instructions
Add an amount of water that is between 3 times and 5 times the amount of juice
Tanya has 130 ml of juice.
If she follows the instructions, work out the minimum and maximum amounts
of the drink she can make.
Solution:
The minimum amount of water that can be added to the juice is 3 times the amount of the juice, hence:
Minimum amount of water = 3 * 130 ml of juice = 390 ml of water
Therefore minimum amount of drink = 390 ml of water + 130 ml of juice
minimum amount of drink = 520 ml
The maximum amount of water that can be added to the juice is 5 times the amount of the juice, hence:
Maximum amount of water = 5 * 130 ml of juice = 650 ml of water
Therefore maximum amount of drink = 650 ml of water + 130 ml of juice
Maximum amount of drink = 780 ml
A rancher planned to fence 6 1/2 acres of land to grow some experimental grasses. After he had finished fencing 4 3/4
acres of the land, it started snowing. How many acres of the land remained to be fenced?
Answer:
1 3/4 acres
Step-by-step explanation:
6 1/2 - 4 3/4 = the remaining acres to be fenced.
we can bring all numbers to "quarters" (1/4th) to be able to make that subtraction.
6 1/2 = 13/2 = 26/4
4 3/4 = 19/4
so, 26/4 - 19/4 = 7/4 = 1 3/4 acres still to be fenced.
What’s the answer????????????
Answer:33
Step-by-step explanation:
trust
The diagram shows a door lock.
B
2
3
4
The code is a letter followed by a number.
Write down all the possible codes,
write your answers like this: (A, 1)
You must write all of your answers on one line.
Trong đợt xảy ra một loại dịch bênh X ,người ta điều tra ngẫu nhiên 1600 nhười dân ở một vùng thấy có 160 người đã được tiêm vaccine đủ liều và đúng lịch
Answer:
Probability of an event = 1 / 10
Step-by-step explanation:
Given:
Total number of people in particular area = 1,600
Number of people vaccinated = 160
Find:
Probability[people vaccinated]
Computation;
Probability of an event = Number of favorable outcomes / Total number of outcome
Probability of an event = 160 / 1600
Probability of an event = 16 / 160
Probability of an event = 1 / 10
[(-2)⁴ + 3.(3² - 1)]: [(-2)³ + 3.2² ]
I don’t know what to do?
Answer:
I geuss because the scale factor is 2 that the resulting triangle will be almost twice the size. Because in a dilation you multiply it. If you dont know how to dilate a triangle with a compass I would suggest looking for a video online. But I know for the part that says "Is the image of ABC similar to the original triangle" the answer would be yes it is similar because you are just dilating the triangle not changing its orientation. I hope this helps! Good luck!
