Area of the base of a rectangular box is 205 cm² and its height is 3 cm. Find the volume of the box
Answer:
V= 615 cm³
Step-by-step explanation:
the volume (V) of a rectangular box is calculated as
V = Ah ( A is the area of the base and h the height ) , then
V = 205 × 3 = 615 cm³
Answer:
Step-by-step explanation: In order to find the volume of box, we need to know the formula
The formula is
volume= LxBxH where L=length, B= breadth and H= height
SO, area= L x B
we can say,
Volume= area x height= 205 x 3= 615 cm^3
Hence, the volume of the box= 615 cm^3
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compare -2/5 and -0.3 -2/5 = /10 and -0.3 = /10. -4 is ? , so -2/5 ? than -0.3
-4 is less than -3
so:
[tex]\frac{-2}{5}\text{ is less than }-0.3[/tex]The equation for line j can be written as y =
= -5/7x-10. Line k, which is parallel to line j,
includes the point (-9, 5). What is the equation of line k?
The equation of the line which is parallel to the other equation is;
[tex]y + \frac{5x}{7} +\frac{10}{7} =0[/tex].
What is the Relation between two Parallel Lines?
To determine whether two lines are parallel or not, apply the parallel line's formula. When we have the slope of two lines that we want to compare, the parallel line formula can be used. The separation between the parallel lines remains constant. Parallel lines are those that never cross each other. Since the two lines are equal in this situation and the angle is 180 degrees, they will never intersect.
In the given equation, we have:
The equation of the line is y = -5/7x-10.
and, Line k, which is parallel to the line of the equation :
[tex]y = \frac{-5x}{7} -10.[/tex]
[tex]y + \frac{5x}{7} +10. =0[/tex]
So, the equation of the line which is parallel to the line of the equation is:
[tex]y + \frac{5x}{7} +k. =0[/tex]
and since the two lines are parallels
So, the slope of equation 1 and the slope of equation two will be the same;
Also, It is given that the line includes the point (-9, 5).
So,
[tex]5 + \frac{5 \times -9}{7} +k. =0[/tex]
⇒[tex]k = -\frac{5 \times -9}{7} -5[/tex]
⇒[tex]k = \frac{10}{7}[/tex]
So, The equation of the line which is parallel to the other equation is;
[tex]y + \frac{5x}{7} +\frac{10}{7} =0[/tex].
Hence,
The equation of the line which is parallel to the other equation is;
[tex]y + \frac{5x}{7} +\frac{10}{7} =0[/tex]..
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There are 128 teams entered in a basketball tournament. Half of the teams are eliminated each round. How many teams are left after 4 rounds?
We have 128 teams.
In each round, half of the teams remain, so if T is the number of teams and n is the number of rounds, we have:
[tex]T(n)=0.5\cdot T(n-1)[/tex]and we start with n=0 so T(0)=128.
Then, we can use this recursive expression to find T after four rounds (n=4), but it is better if we derive an explicit formula for T in function of n (and not in function of the past terms of the sequence):
[tex]\begin{gathered} T(1)=0.5\cdot T(0) \\ T(2)=0.5\cdot T(1)=0.5\cdot0.5\cdot T(0)=0.5^2\cdot T(0) \\ T(n)=0.5^n\cdot T(0)=0.5^n\cdot128 \end{gathered}[/tex]With the last expression we can calculate T for any value of n. Then, for n=4, we have:
[tex]T(4)=0.5^4\cdot128=(\frac{1}{2})^4\cdot128=\frac{1}{2^4}\cdot128=\frac{1}{16}\cdot128=8[/tex]NOTE: in this case, its better to express the factor 0.5 as a fraction instead of a decimal.
Answer: after 4 rounds there will be 8 teams left.
Question 1(Multiple Choice Worth 2 points)
(Converting Between Systems MC)
I need help pleaseeee
For a craft project you need 182 inches of ribbon, but it is only sold by the meter. Determine the amount of ribbon, in meters, you need to buy for the project. (1 inch = 2.54 centimeters and 1 centimeter = 0.01 meter)
462
47
12
5
The amount of ribbon needed to buy for the project in meters is (d) 5.
According to question,
1 centimeter = 0.01 meter
2.54 centimeter = 0.01*2.54
= 0.0254 meters
1 inches = 2.54 centimeters
= 0.0254 meters
Amount of ribbon needed for project = 182 inches
= 182 * 0.0254 meters
= 4.62 meters
≅ 5 meters
Hence, 5 meters of ribbon is needed for the project.
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An electrician leans an extension ladder against the outside wall of a house so that it
reaches an electric box 27 feet up. The ladder makes an angle of 62° with the ground.
Find the length of the ladder. Round your answer to the nearest tenth of a foot if
necessary?
Answer: 59.5 ft
Step-by-step explanation:
When the ladder lay on the wall it makes a triangle. And for this equation, we have to use the sin to find the length.
Sin = opposite / hypotenuse
Sin 62 = 27 / h
27 / 0.4539
h= 59.48
h=59.5 feet
Answer:
30.6
Step-by-step explanation:
I AM HIM
If Miss. lora has 4 people in her class and she has 28 more. How many people are in her class.
Answer:
32
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
sorry no Step-by-step explanation
Answer the question below.
The formula that can be used to find the nth term of the sequence is aₙ = 4n + 1
How to find the formula of an arithmetic sequence?The sequence follows an arithmetic patterns. Therefore, the formula for arithmetic progression can be used to find the nth term as follows:
aₙ = a + (n - 1)d
where
n = number of termsd = common differencea = first termTherefore, using the sequence 5, 9, 13, 17, 21
a = 5
d = 9 - 5 = 4
Hence,
aₙ = 5 + (n - 1)4
aₙ = 5 + 4n -4
aₙ = 5 - 4 + 4n
Therefore,
aₙ = 4n + 1
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Where is the center of dilation located?
inside figure A
outside figure A
on a vertex of figure A
B
A
The center of dilation is outside figure A
In this question, rectangle A is dilated to rectangle B.
We know that, the center of a dilation is nothing but a fixed point about which all points are expanded or contracted.
We can observe that B = 1/2 * A
This means, the scaling factor is k = 1/2
Let's determine the center of dilation:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilation.
k - Scale factor
P(x, y) - Original point
P'(x, y) - Resulting point
(3, 1) = O(x, y) + 1/2 [(6, 2) - O(x, y)]
(3, 1) = O(x, y) - 1/2 O(x, y) + (3, 1)
1/2O(x, y) = (0, 0)
so, the center of dilation is the origin (0, 0)
So, in this case the center of dilation is outside figure A.
Therefore, the center of dilation is outside figure A
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Write all integers that belong to the intervals:[-1, 1]
Okay, here we have this:
Considering that the intervals are closed, we have the following integers in this interval: -1,0,1.
A towns population is 53,350 about 100 people move out of the town each month 200 people on average move into town. A nearby town has a population of 56,375.It has no one moving in and an average of 175 people moving away every month in about how many months will be population of the town be EQUAL?
11
this is just words because it doesn't let me submit this with just the answer
Simplify 9/16 + 1/16 • (2_3)-1
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
9/16 + 1/16 * (2/3)^(-1)
Step 02:
we must apply the algebraic rules to find the solution
[tex]\frac{9}{16}+\frac{1}{16}\cdot(\frac{2}{3})^{-1}=\frac{9}{16}+\frac{1}{16}\cdot\frac{3}{2}=\frac{9}{16}+\frac{3}{32}[/tex][tex]\frac{9\cdot2+3\cdot1}{32}=\frac{21}{32}[/tex]The answer is:
21 / 32
Choose the line parallel to the following equation through the given point
Answer:
y = 2x + 1
Step-by-step explanation:
→ Find the gradient of this line
2
→ Write in standard format
y = 2x + c
→ Substitute in ( 0 , 1 )
1 = 0 + c ⇒ c = 1
What is 106/200 written as a decimal
Answer:
0.53
Step-by-step explanation:
you just take 106 and divide it by 200
Parallel line of y=-1/2x-2
The parallel line of y=-1/2x-2 is y=-1/2x
Slope-intercept form y=mx+b of linear equations the slope-m and the y-intercept -b of a line,
here y=-1/2x-2 slope of the linear equation is m=-1/2,
whereas the y-intercept is b=-2,
Parallel lines are those lines that are equidistant from each other, the condition for representing two lines is parallel their slopes should be equal or the same.
here slope of the line is -1/2, and the fundamental equation of a line in slope intercept form is y=mx+b, taking the assumption the parallel line is passing through the origin hence the y-intercept of the parallel line is 0, b=0.
therefore, the parallel line of y=-1/2x-2 is y=-1/2x
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Pls help i need this answered quickly
Tess builds a sandbox in the shape of a regular hexagon in which all the sides are 40 inches long. She then takes a photo of the sandbox and prints the photo. In the photo, the sides of the hexagon are each 4 inches long. Identify the scale factor that was used to create the printed photo of the sandbox. Express your answer as a decimal.
A scale factor of 0.1 was used to create the printed photo of the sandbox
How to find the scale factor used for the printed photo of the sandbox?A scale factor is the size by which a shape is enlarged or reduced. It is used in increasing or reducing the size of a 2D shape, such as circle, triangle, square, rectangle, hexagon, etc.
Given that: Tess builds a sandbox in the shape of a regular hexagon in which all the sides are 40 inches long, and in the photo, the sides of the hexagon are each 4 inches long
The scale factor will be:
4/40 = 1/10 = 0.1
This means the sandbox has been reduced by 10 times the original size
Therefore, the scale factor that was used to create the printed photo of the sandbox is 0.1
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Which is the domain and range of the parabola with the equation y = 0.5(x²-10x-5)?
The domain of the given function is the set of all real numbers that is represented as x ∈ (-∝,∝ ) and range of the function is [-15,∝).
What is domain and range of a function?The set of values that can be plugged into a function is known as its domain. The range of a function is the collection of all potential values that can result from the dependent variable, or the collection of all possible values after substituting the domain.
Domain of a polynomial function is the set of all real numbers which is given by x ∈ (-∝,∝ ).
Since the given function y = 0.5(x^2 - 10x - 5) is a polynomial function, it's domain is x ∈ (-∝,∝ ).
To obtain the range of the function, plot the graph of the parabola which is shown in the figure.
The vertex of the parabola is at (5,15). Value of y does not go below 15. Therefore the set of all possible values that the function takes is given by [-15,∝).
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help me please, correct answer gets brainliest
Answer:
Only D and B
Step-by-step explanation:
Which of the following relations is NOT a function?
OA. (-6, 4), (1, 3), (-2, 1), (6, 2)
• B. (1, 4), (-2, 2), (1, 1), (-6, 2)
• C.
(-2, 4), (1, 2), (6, 1), (-6, 5)
O D.
(6, 4), (-2, 2), (1, 1), (-6, 2)
Answer:
B
Step-by-step explanation:
2 x values must be the same to not be a function, therefore b must be the answer.
Complete the statements by writing the number from the graph.
The substance is in the gas phase only in region _.
The substance is in both the liquid and the solid phase in region _.
The substance is in only the liquid phase in region _.
The melting point is the temperature at region _.
The boiling point is the temperature at region _.
A. The substance is in the gas phase only in region 5.
B. The substance is in both the liquid and the solid phase in region 2.
C. The substance is in only the liquid phase in region 3.
D. The melting point is the temperature at region 2.
E. The boiling point is the temperature at region 4.
What is meant by the term temperature?Temperature is a measure of how hot or cold something is conveyed in terms of one of several scales, such as Fahrenheit and Celsius.For the given question, the correct depiction of the expressions are is;
Melting or fusion is a process wherein the phase transitions from solid to liquid at a constant temperature.Freezing is a process wherein the phase transitions from liquid to solid at a constant temperature.Evaporation is a process where the phase transitions from liquid to gaseous at a constant temperature.Condensation is a process where the phase transitions from gaseous to liquid at a constant temperature.Sublimation is a process during which the phase transitions from solid to gaseous without passing through a liquid state at a constant temperature.Thus, the result for the graph will be-
A. The substance is in the gas phase only in region 5.
B. The substance is in both the liquid and the solid phase in region 2.
C. The substance is in only the liquid phase in region 3.
D. The melting point is the temperature at region 2.
E. The boiling point is the temperature at region 4.
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Answer:
A. The substance is in the gas phase only in region 5.
B. The substance is in both the liquid and the solid phase in Region 2.
C. The substance is in only the liquid phase in region 3.
D. The melting point is the temperature at region 2.
E. The boiling point is the temperature at region 4.
Step-by-step explanation:
Determine weather the statement is true or false. Justify your answer
As we know:
[tex]\begin{gathered} \cos (x)=0 \\ for \\ x=\pi n-\frac{\pi}{2} \\ n\in Z \end{gathered}[/tex]For:
[tex]\begin{gathered} n=2 \\ x=2\pi-\frac{\pi}{2}=\frac{3\pi}{2} \\ for \\ n=-3 \\ x=-3\pi-\frac{\pi}{2}=-\frac{7\pi}{2} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \cos (-\frac{7\pi}{2})=0 \\ and \\ \cos (\frac{3\pi}{2})=0 \\ so\colon \\ 0=0 \\ This_{\text{ }}is_{\text{ }}true \end{gathered}[/tex]Therefore, the statement is true
True or False? Every quadrilateral is a rhombus. Every parallelogram is a quadrilateral. Every square is a quadrilateral. Every rhombus with four right angles is a square. X Ś True False O True False O True False True False ?
First of all it's important to note that all parallelograms, rhombuses and squares are quadrilateral and they meet the following properties:
- Rhombus: quadrilateral whose four sides have the same length.
- Parallelogram: quadrilateral that has two pairs of parallel sides.
- Square: quadrilateral whose four sides and internal angles have the same length/measure.
With these definitions in mind we can solve the True or False table in the picture.
The first statement is false not every quadrilateral is a rhombus. For example rectangles that are not squares are not rhombuses since their four sides aren't all equal.
The second is true, as we saw before parallelograms are quadrilaterals. The same reason applies to the third statement, squares are qudrilaterals.
Now let's see the last statement. A rhombus with four right angles is a quadrilateral that has four equal sides (because it's a rhombus) and four equal angles (all measuring 90°). These are the conditions required for a quadrilateral to be considered a square so this last statement is true.
AnswersThen the answers are:
F
What is the measure of n?
5
15
m
n= [?l
The measure of the hypotenuse n is 5√3
Hypotenuse
Hypotenuse refers the longest side of a right-angled triangle, the side opposite the right angle. And the length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.
Given,
Here we have the triangle with some measures on it.
Here we need to find the value of n.
While we looking into the diagram, we have identified that, n is the hypotenuse of the triangle,
So, the value of n is the root of the product of the two hypotenuse segments it touches:
=> n = √(5·15)
=> n = √75
It can be simplified as,
=> n = √(3 x 25)
=> n = 5√3
Therefore, the value of n is 5√3.
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Carlos had 194 seeds and 11 flower pots. He put the same number of seeds in each flower pot. Which is the best estimate for the number of seeds in each flower pot?
a:10
b:20
c:30
d:40
Answer: B
Step-by-step explanation: The question says estimate, meaning you'll have to round the numbers. 194 gets rounded up to 200, while 11 gets rounded down to 10.
200 / 10 = 20, thus the answer is B
PLEASEEE HELP I REALLY NEED HELP ITS MENTAL MATH!!!!!!!!!!!!
Answer:
6y+12
Step-by-step explanation:
4(y+3)+2y
= 4y+12+2y
=6y+12
Answer:
[tex]\sf 6y+12[/tex]Step-by-step explanation:
[tex]\sf 4(y+3)+2y[/tex]
Expand (Distributive property):-
[tex]\sf 4y+12+2y[/tex]
Combine like terms:-
[tex]\sf 4y+2y+12[/tex]
[tex]\sf (4y+2y)=6y[/tex]
[tex]\sf 6y+12[/tex]
__________________
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The track team has 11 distance runners but can only enter five in the meet. How many combinations of five runners can the coach create?.
Answer:
55
Step-by-step explanation:
11 x 5 = total combinations
11 x 5 = 55
Write the first five terms of the geometric sequence with a1 = 16 and common ratio r= 3/2
From the problem, we need to find the first five terms of the geometric sequence.
The first term, a1 = 16 and the common ratio, r = 3/2
Note that the succeeding term is the previous term multiplied by the common ratio.
This will be :
[tex]\begin{gathered} a_2=a_1r=16(\frac{3}{2})=24 \\ a_3=a_2r=24(\frac{3}{2})=36_{} \\ a_4=a_3r=36(\frac{3}{2})=54 \\ a_5=a_4r=54(\frac{3}{2})=81 \end{gathered}[/tex]The geometric series is :
an = {16, 24, 36, 54, 81, ...}
The answer is B. an = {16, 24, 36, 54, ...}
Write an inequality for the graph below.
Answer: y < -4
Step-by-step explanation:
What’s the answer asp
Answer:
Step-by-step explanation:
35
Solve this system of equations by graphing. First graph the equations, and then type the solution.x+y=13x+5y=15Click to select points on the graph.
Solution
For this case we have the following system of equations:
x + y= 1
3x + 5y= 15
We can create the following plot:
Then the solution for this case is:
x= -5
y= 6