we conclude that 900 cubes enter in the given box.
How many blocks are needed to fill the box?
We need to find the volumes of both figures.
The blocks are cubes of 2cm by 2cm by 2cm, then the volume of each block is:
[tex]V = (2cm)^3 = 8cm^3[/tex]
The box has dimensions of 10cm by 12cm by 60cm, then the volume is:
[tex]V = 10cm*12cm*60cm = 7,200 cm^3[/tex]
The number of cubes that enter in the box is N such that:
[tex]N*8cm^3 = 7,200cm^3[/tex]
Solving for N, we get:
[tex]N = 7200cm^3/8cm^3 = 900[/tex]
In this way, we conclude that 900 cubes enter in the given box.
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Select ALL the true statements.
Responses
−1−−−√
is an imaginary number.
square root of negative 1 is an imaginary number.
There are no real numbers that satisfy the equation x=−1−−−√
.
There are no real numbers that satisfy the equation x is equal to square root of negative 1.
Because −1−−−√
is imaginary, no one does math with it.
Because square root of negative 1 is imaginary, no one does math with it.
The equation x2=−1
has real solutions.
The equation x squared is equal to negative 1 has real solutions.
−1−−−√=−1
because −1⋅ −1 = −1
square root of negative 1 is equal to negative 1 because −1⋅ −1 = −1
The true statements are:
√(-1) is an imaginary number.
There are no real numbers that satisfy the equation x = √-1.
What is Imaginary Number?A number that produces a negative square root is referred to as an imaginary number. An imaginary number, which has no real-world equivalent, is essentially the square root of a negative number.
Given:
We know that the value of √(-1) is i (iota) which is imaginary number.
So, √(-1) is an imaginary number.
Now, Negative numbers don't have real square roots since a square is either positive or 0.
So, x = √-1 have no real solution.
Now, x² = -1 again have no real solution because
x = √-1 and , Negative numbers don't have real square roots.
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Once Cherokee stomp dance has 36 aldults dancing. There are 3 times as many aldults as children at the stomp dance. Which sentence describes how to find the number of children at the stomp dance?
Answer: B, the second answer is correct.
Step-by-step explanation: Hope it helps, mark brainliest and give thanks please!
(PRE CALC) I NEED HELP ASAP WITH THIS PROBLEM WILL GIVE BRAINLIEST
The center of the ellipse is (2, -8).
The endpoints of the major axis are 10 units from the center.
The endpoints of the minor axis are 9 units from the center.
To graph the ellipse, connects (2, 2), (11, -8), (2, -18) and (-7, -8) with smooth curve.
What is ellipse?
An ellipse in mathematics is a plane curve that has two focal points and is such that the sum of the two distances from any point on the curve to the focal points is a constant. It generalizes a circle, a special kind of ellipse in which the two focal points coincide.
Given:
The equation of ellipse is,
[tex]\frac{(x-2)^2}{81}+(\frac{(y+8)^2}{100}=1[/tex]
Since, the general form of ellipse is,
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
where,
(h, k) is the center of ellipse
a is the minor axis
b is the major axis.
Here (h, k) = (2, -8) is the center of the ellipse.
9 is the minor axis and 10 is the major axis of the ellipse.
Also the graph of ellipse connects (2, 2), (11, -8), (2, -18) and (-7, -8) with smooth curve.
Hence, the center of the ellipse is (2, -8).
The endpoints of the major axis are 10 units from the center.
The endpoints of the minor axis are 9 units from the center.
To graph the ellipse, connects (2, 2), (11, -8), (2, -18) and (-7, -8) with smooth curve.
The graph of the ellipse is attached below.
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HELP PLEASE.
In an experiment with a bag of marbles, P(green) = one-fourth. Interpret the likelihood of choosing a green marble.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event.
The likelihood of choosing a green marble is unlikely.
What is the probability?Probability is used to determine how likely it is that a random event would happen. The probability that a random event occurs lie between 0 and 1. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability of picking a green marble is 1/4 or 0.25. 0.25 is less than 0.5. This means it is unlikely the event would occur.
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5 - 3 * 2 + 8 * 5 - 2
Lisa sells raffle tickets at a charity event for $4 each. How many tickets does she have to sell to make $160? Select the correct equation and answer.
Responses
4t=160; 40 tickets4t=160; 40 tickets
t160=4; 40 ticketst160=4; 40 tickets
4(160)=t; 480 tickets4(160)=t; 480 tickets
t4=160; 480 tickets
Answer: 40 tickets
Step-by-step explanation:
1 ticket=$4
160/4=40
$4x40tickets=$160
Gabriel models the volume of a popcorn box as a right rectangular prism. Its dimensions are 2 1/2 in by 2 3/4 in by 5 in. If the box contains 26 cubic inches of popcorn, what percent is full? Round your answer to the nearest whole number if necessary. please really asap brainliest
To find the percent full of the popcorn box, we need to divide the volume of popcorn in the box by the total volume of the box, and then multiply by 100 to convert the result to a percentage.
First we need to find the total volume of the box:
V = l x w x h
V = (2 1/2 in x 2 3/4 in x 5 in) = (5/2 in x 7/4 in x 5 in) = (35/4 in^3) = 8.75 in^3
Now we can calculate the percent full:
percent = (26 in^3 / 8.75 in^3) x 100 = 2.97 x 100 = 297%
The popcorn box is 297% full.
It's worth noting that 297% means that the popcorn box is almost 3 times full
need help asap please help! 50 points!!!!!!!!!!!!!!!!!!!!!!!! Plese do all problems
Answer:
Step-by-step explanation:
8) a) In a parallelogram, opposite sides are equal and parallel.
BC = AD
12x - 1 = x + 21
12x = x + 21 + 1
12x = x + 22
12x - x = 22
11x = 22
x = 22 ÷ 11
x = 2
AD = x + 21
= 2 + 21
AD = 23
In a parallelogram, adjacent angles are supplementary.
∠A + ∠D = 180°
[tex]\sf y - 9 + \dfrac{y}{2}=180\\\\ \dfrac{2y}{2}+\dfrac{y}{2}=180+9\\\\[/tex]
[tex]\dfrac{3y}{2}=189\\\\y =189*\dfrac{2}{3}\\\\y=63*2\\\\y = 126[/tex]
∠D = 126 ÷2
= 63
In parallelogram, opposite angles are congruent.
∠B = ∠D
∠B = 63°
When you’ve finished solving an equation, it’s easy to check your work. Simply plug your answer for the variable into the original equation. Take, for example, the equation 4x + 9 = 45. After isolating the variable, you’ve come up with x = 9. To check your work, replace the x with 9: 4(9) + 9 = 45. Following the order of operations, multiply 4 by 9 first to get 36 + 9 = 45. Adding 36 plus 9 does equal 45, so you know you’ve found the right value for x. Which of these equations is correct when x = -2? A x + 8 = 5 B 3x - 1 = -10 C 2x - 7 = -11 D -95x = -190 BACK
The required correct equations are 2x - 7 = -11 and -95x = -190. Options C and D are correct.
What is the equation?
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
As of the given example in the question,
Putting x = -2 to in every op[tion,
A,
X + 8 = 5
-2 + 8 = 5
6 ≠ 5
Similarly,
B. -7 ≠ -10
C. -11 = -11
D. -190 = -190
Thus, the required correct equations are 2x - 7 = -11 and -95x = -190. Options C and D are correct.
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5
In August, Peter rakes 5 lawns. He earns $8 for each lawn he rakes.
In September, Peter earns $10 raking lawns.
The equation shown can be used to find m, the total amount of money Peter earns raking lawns in August and September.
5 x 8 + 10 = m
What is the total amount of money Peter earns raking lawns in August and September?
OA. 55
B. 58
OC. 50
D. 23
Reset
Next
Therefore , algebraic solution is 55 is the total amount of money Peter earns raking lawns in August and September
What is the total amount of money Peter earns raking lawns in August and September?The total amount of money Peter earns from raking lawns in August and September can be found by solving the equation 5 x 8 + 10 = m, where m represents the total money earned.
Here,
In this equation, 5 represents the number of lawns Peter raked in August, 8 represents the amount he earns for each lawn, and 10 represents the amount he earned from raking lawns in September.
When this equation is solved, the result is m = 55, meaning that Peter earned a total of $55 from raking lawns in August and September.
This can be seen by multiplying 5 times 8, which is 40, and then adding 10, which brings the total to 55.
Therefore, the total amount of money Peter earns from raking lawns in August and September is $55.
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Yesterday, Rachel went on a bike ride. Her average speed was 9 miles per hour. Today, she went on another ride, this time averaging 14 mlles per hour. In the two days, she biked for a combined total time of 12 hours. Let x be the number of hours she biked yesterday. Write an expression for the combined total number of miles she biked in the two days.
Rachel rode her bike a total distance in miles over the course of two days, as shown by the expression: -5x + 168.
What is meant by term speed of object?Velocity is the pace and directions of an object's movement, whereas speed is really the time rate which an object is travelling along a path. In other words, velocity is a vector, whereas speed is just a scalar value.Let x be the duration of Rachel's bicycle ride yesterday.
Distance = speed * time
According to information provided, Rachel's average speed yesterday was 9 miles per hour.Therefore, the distance travelled in x hours would be: 9x.Additionally, we are informed that Rachel biked nine times in total 12 hours.Therefore, the second day's biking time would be: 12 - x.At a pace of 14 miles per hour, the distance travelled would be: 14(12 - x)The total distance that Rachel would travel is: 9x + 14(12 - x)Thus, the equation becomes.
= 9x + 14(12 - x)
On solving;
= 9x + 168 - 14x
=-5x + 168
Rachel rode her bike a total of miles over the course of two days, as shown by the expression: -5x + 168.
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Are tan D and tan F ____.
a. complementary
b. supplementary
c. congruent
d. reciprocals
Reason:
tan = opposite/adjacent
tan(D) = EF/DE = d/f
tan(F) = DE/EF = f/d
Comparing d/f with f/d, and we find they are reciprocals. The two fractions multiply to 1.
A savings account is opened with an initial deposit of $425.00. Determine the account balance after 9 years if the account earns 2.7% simple interest annually.
$3,928.28
$1,457.75
$528.28
$103.28
For a savings account with an initial deposit of $425.00, the account balance after 9 years if the account earns 2.7% simple interest annually is
$528.28How to find the account balance after 9 yearsThe account balance is solved by adding the initial deposit to the simple interest.
The simple interest is solved using the simple interest formula
The formula is stated as
Simple interest = Principal * time * rate / 100
In the problem the give data include
principal = $425.00
rate= 2.7%
time = 9 years
plugging in the values
Simple interest = Principal * time * rate / 100
Simple interest = 425 * 9 * 2.7 / 100
Simple interest = 10327.5 / 100
Simple interest = 103.275
The account balance
= initial deposit + simple interest
= 103.275 + 425
= $528.28
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MODELING REAL LIFE A rhino with mass m (in kilograms) has an average heart rate of approximately 241m 0.25 beats
per minute and a lifespan of approximately (6 x 106)m0.2 minutes. Write an expression using an exponent that represents
the average number of lifetime heartbeats for a rhino with a mass of 2310 kilograms.
Expression:____
On solving the provided question, we can say that expression is as follows r(m) . s(m) = [tex]241.^{-0.25} ]( 6 * 10^6) m^{ 0.2 }][/tex] = [tex]1.4446 X 10^9 m^{0.05}[/tex]
what is expression ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
expression is as follows
r(m) . s(m) = [tex]241.^{-0.25} ]( 6 * 10^6) m^{ 0.2 }][/tex] = [tex]1.4446 X 10^9 m^{0.05}[/tex]
the average number of lifetime heartbeats for a rhino with a mass of 2310 kilograms is [tex]1.7 X 10^8 KG[/tex]
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Simplify (10−6)2 + 8 − 22 .
Answer:
18
Step-by-step explanation:
9+9
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{ASSUMING}[/tex]
[tex]\mathsf{(10 - 6)^2 + 8 - 22}[/tex]
[tex]\mathsf{= (4)^2 + 8 - 22}[/tex]
[tex]\mathsf{= 4^2 + 8 - 22}[/tex]
[tex]\mathsf{= 4 \times 4 + 8 - 22}[/tex]
[tex]\mathsf{= 16 + 8 - 22}[/tex]
[tex]\mathsf{= 24 - 22}[/tex]
[tex]\mathsf{= 2}[/tex]
[tex]\huge\text{Therefore, your answer should be: \huge\boxed{\mathsf 2}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
I need help 783.1 x 1.03
Answer: 806.59300
Step-by-step explanation:
Line C is represented by the line
y=-52-5. Line D is perpendicular to Line C. What is the slope of Line D?
from the given option the slope of the line -5/2 is shown by the equation [tex]$y=-\frac{5}{2} x-4$[/tex]that is option B).
What is slope of Line?An indication of how steep a line is is its slope. When calculating slope mathematically, "rise over run" is used (change in y divided by change in x). Measured by slope, a line's steepness. The slope increases in steepness as it gets larger. It becomes flatter the smaller the slope. Along with indicating whether a line is going up, down, horizontal, or vertical, slope also indicates the direction of the line.
From the given option the slope of the line [tex]$-5 / 2$[/tex] is shown by the equation [tex]$y=\frac{2}{5} x[/tex] that is option[tex]$\mathbf{B}$[/tex] ) and this can be determined by using the slop intercept form.
Given :
Equation -[tex]$y=\frac{2}{5} x-1$[/tex]
First, determine the slope of the given line by using the slope-intercept form. The slope-intercept is given by the equation:
[tex]$$y=m x+c$$[/tex]
Now, compare equation (1) with the above equation.
[tex]& \mathrm{m}_1=\frac{2}{5} \\[/tex]
[tex]& \mathrm{c}=-1[/tex]
For a line to be perpendicular to the other line the product of the slope of both the line is equal to -1, that is:
[tex]$$m_1 m_2=-1$$[/tex]
So, the slope of the line perpendicular to the line [tex]$y=\frac{2}{5} x-1$[/tex] is:
[tex]$$\mathrm{m}_2=-\frac{5}{2}$$[/tex]
So, from the given option the slope of the line [tex]$-5 / 2$[/tex] is shown by the equation [tex]$y=-\frac{5}{2} x-4$[/tex] that is option[tex]$\left.\mathbf{B}\right)$[/tex].
The complete question is,
Which of the following is the equation of a line that is perpendicular to the graph of y = 25x − 1?
A. y = 25x − 4
B. y = −52x − 4
C. y = −25x − 4
D. y = 52x −
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For each function graphed below, state whether it is one to one.
Answer:
1) yes 2) no 3) yes 4) no 5) no 6) no
Step-by-step explanation:
Horizontal line test
which is larger
8/k^2+2 and k^2+2
Answer:
Step-by-step explanation:
d e e z n u t z
Simplify the expression 8+10 (x+3) + x . Do not include spaces in your answer and type in the form similar to 2x+2.
Answer:
8+10(x+3)+x
=18(x+3)+x
=18x+54+x
=19x+54
Jan is looking for similar figures.
Which choice is similar to the figure shown?
Answer: Number 3 ( the one with the numbers added that are 4,13)
Step-by-step explanation:
Simplify the following set expressions.
(-2,4]∪[0,9]
Answer: (-2,4) x (0,9)=36 simplified
y= 5/2x + 9 is the slope
Step-by-step explanation:
.
Find the circumference of a circle that has a radius of 5 cm. Use 3.14 for pi.
A linear equation is a(n) _____ because the greatest degree of the variable is 1.
Linear equation: If the maximum power of the variable/symbol in an equation is one, then the equation is called a linear equation.
An example of a linear equation is x + y = 10.
Definition of Degree: The maximum power in an equation of variable is known as a degree.
So, the degree of a linear equation is 1.
Linear equations are equations based on the first order. The linear equations are explained for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e., only one variable), then it is known as a linear equation in 1 variable.
If a linear equation can have more than one variable. If the linear equation has two or more two variables, then it is called a linear equation with two variables, and so on.
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x-y=5
find y
write out the steps
Answer:
y is x - 5.
Step-by-step explanation:
x - y = 5
x = y + 5
we can isolate y by subtracting 5 from both sides of the equation:
x = y + 5
x - 5 = y
Therefore, the solution for y is x - 5.
[tex]solve \: each \: equation \: for \: 0 \: \leqslant 0 < 2\pi[/tex]
btw the second 0 is a 0 with a / but i don't have the symbol
[tex] - 1 = - 2 + \cot(0) [/tex]
The sine, cosine, and tangent are the three fundamental trigonometry operations. The cotangent, secant, and cosecant functions are derived from these three basic functions.
Is trigonometry a practical tool?Numerous applications of trigonometry and its operations can be found in daily life. For instance, it is used in astronomy to determine how far away nearby stars are, in geography to determine the distance between landmarks, and in the satellite navigation system.
Here,
The three basic categories of trigonometric functions are sine, cosine, and tangent.
And
from the primary functions, one can derive the three cotangent, secant, and cosecant functions.
Therefore , the solution is cotangent, secant, and cosecant functions are derived from these three basic functions .
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The complete question is " Is a slash used on a zero or an O to differentiate between the two trigonometric ratios? ".
PLEASE HURRY I WILL GIVE BRAINLT The function f(x) represents the number of texts sent this week, and g(x) represents the number of texts sent last week. Given f(x) = 8x + 14 and g(x) = 5x − 2, find (f − g)(x) to find how many more texts were sent this week than last week.
(f − g)(x) = 3x + 12
(f − g)(x) = 3x + 16
(f − g)(x) = 13x + 12
(f − g)(x) = 13x + 16
The function that represents how many more texts that were sent this week than last week is: B. (f − g)(x) = 3x + 16.
How to Evaluate Functions?To find the value of a given functional expression, we have to apply the basic knowledge of how to solve algebraic expressions.
For example, if we are given that (f - g)(x), it means we are to subtract the function g(x) from f(x). That is (f - g)(x) = f(x) - g(x).
Given the following functions:
Number of texts sent this week is represented as the function, f(x) = 8x + 14
Number of texts sent last week is represented as the function, g(x) = 5x - 2.
Number of texts that were sent this week than last week = (f - g)(x)
(f - g)(x) = (8x + 14) - (5x - 2)
(f - g)(x) = 8x + 14 - 5x + 2
(f - g)(x) = 3x + 16
Therefore, the answer is: (f − g)(x) = 3x + 16.
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Therefore, the answer is: (f − g)(x) = 3x + 16.
Find the differential of each function. (a) y - x^2 sin 8x
The differential of the function y - x² sin 8x with respect to x is dy/dx - 2x sin 8x + 8x² cos 8x
To find the differential of the function y = x² sin 8x, we can use the standard notation dy/dx which represents the rate of change of y with respect to x.
To calculate dy/dx, we need to use the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.
Let z be the given function,
z= y - x² sin 8x
The derivative of x² is 2x
The derivative of sin 8x is 8 cos 8x
So,
dz/dx= dy/dx - (2x)(sin 8x) + (x²)(8cos 8x)
= dy/dx- 2x sin 8x + 8x² cos 8x
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PLEASE HELP!! DUE TMR!
Answer:
Answers below
Step-by-step explanation:
a)solving for f(2)
f(2)= 5(2) - 3 (input the given value for the letter x)
f(2) = 10 -3 (multiply your inputed value with whatever is infront of it)
f(2) = 7 (Connect simmilar terms)
b) solving for f(32)
remember to follow the steps from above
f(32) = 5(32) - 3
f(32) = 160 -3
f(32) = 157
c) solving for f(-8)
we are going to end up on the negatives and thats okay. Not all answers have to be positive
f(-8) = 5(-8) -3
f(-8) = -40 -3
f(-8) = -43
I need help with this please hurry asap due right now in 10 minutes!!! p.s x is not multiplying.
Answer:
31.80
Step-by-step explanation:
20.53
× 1.55=
31.82
-.02
32.80