Not sure how to do this. (I'm aware this is wrong lol)
A box has a rectangular base with a length of 3x + 2 and width of 2x - 2, and the base has a perimeter of 60 centimeters. If the height of the box is x, what is the volume of the box?
The volume of the box is determined by finding the value of x from the perimeter equation, substituting it back into the expressions for length and width, and finally multiplying the dimensions with the height. Calculating these steps, the volume of the box is 1200 cm³.
Explanation:To find the volume of a box, we multiply its length, width, and height. The student has provided the length as 3x + 2, the width as 2x - 2, and the height as x. We also know the perimeter of the base is 60 centimeters.
First, we calculate the perimeter of the base, which is 2(length + width). Hence, we set up the equation: 2(3x + 2 + 2x - 2) = 60. Simplifying this, we get 2(5x) = 60, therefore x = 6 cm.
Second, we substitute x into the expressions for length and width to get the actual dimensions of the box base: length 3(6) + 2 = 20 cm, and width 2(6) - 2 = 10 cm.
Finally, we calculate the volume of the box as length × width × height = 20 cm × 10 cm × 6 cm = 1200 cm³.
Two lines intersect to form a linear pair with equal measures. One angle has the measure 3x° and the other angle has the measure (8y − 70)°. Find the values of x and y.
Answer:
Substitute by equation 1 in equation 2:
3x+3x = 180
6x = 180
x = 30
Substitute with the value of x in equation 1 to get y as follows:
3x = 8y-70
3(30) + 70 = 8y
160 = 8y
y = 20
How does finding the square root of a number compare to finidng the cubic root of a number?
Final answer:
Square rooting and cube rooting are processes to find a number that, when raised to the second or third power respectively, equals the original number. Square roots are related to squares, and cube roots are related to cubes; both functions are essential in solving various mathematical problems, including equilibrium and Pythagorean Theorem problems.
Explanation:
Finding the square root of a number is the process of determining a number which, when multiplied by itself, gives the original number. For example, the square root of 25 is 5, because 5 squared (5²) is 25. This can be expressed using exponents as x¹⁄₂ = √x.
On the other hand, finding the cube root of a number involves determining a number which, when multiplied by itself twice (or cubed), results in the original number. For instance, the cube root of 27 is 3, since 3 cubed (3³) equals 27. The formula for a simple equilibrium problem that involves cubic roots is a³ = M₁ × P², where you would then find the cube root of the result to solve for 'a'.
Both operations are inverse functions: square rooting is the inverse of squaring, and cube rooting is the inverse of cubing. When dealing with equilibrium problems or Pythagorean Theorem applications, it's important to know how to perform these operations, often requiring a calculator. Make sure you are comfortable with your calculator's functions for these operations, or seek assistance from your instructor if needed.
Nadine is constructing a line perpendicular to KE←→ . She has constructed the arcs as shown. What is the next step in her construction? Use a straight edge to draw a line through D and M. Use a straight edge to draw a line through M and E. Use a straight edge to draw a line through M and K. The image shows a horizontal line with points K, D, and E from left to right. Point D looks halfway between points K and E. An arc is shown at point K turning inwards towards point D. An arc is shown at point E turning inwards towards point D. Above point D is point M. Two arcs go through point M. One arc faces southwest towards point K and one points southeast towards point E.
Write an equation for the line that is parallel to the given line and that passes through the given point.
y equals five halves x minus 10; the point negative 6, negative 29
A. y equals five halves x plus one hundred thirty three halves
B. y equals five halves x minus 14
C. y equals two fifths x minus 14
D. y equals negative two fives x plus 14
Answer:
The correct option is B.
Step-by-step explanation:
The slope intercept form of a line is
[tex]y=mx+b[/tex]
where, m is slope and b is y-intercept.
The given equation is
[tex]y=\frac{5}{2}x-10[/tex]
It means the slope of the line is 5/2 and y-intercept is -10.
The slope of two parallel lines is same. So, the slope of required line is 5/2.
The equation of required line is
[tex]y=\frac{5}{2}x+b[/tex]
It is given that the line passes through the point (-6,-29).
[tex](-29)=\frac{5}{2}(-6)+b[/tex]
[tex]-29=-15+b[/tex]
[tex]-29+15=+b[/tex]
[tex]-14=b[/tex]
The y-intercept of required line is -14. So the equation of required line is
[tex]y=\frac{5}{2}x-14[/tex]
Therefore the correct option is B.
Answer:
the answer is B. y equals five halves x minus 14
Step-by-step explanation:
hope it helps
Please help asap!!! I will mark brainliest!
Estimate 27.89 • 10.3 divided by 4.37 using compatible numbers
Markus receives dollar bills from his grandfather for one week on the first day he received $1 on the second day he received $2 on the third day he received $4 and on the fourth day he received $8 if this continues how much money will Marcos have by the end of the week
Answer:
127
Step-by-step explanation:
It gas geometric sequence,
We has a sequence: 1, 2, 4, 8, 16, 32, 64.
It can be solved by two method either sum these digits individually or use formula of sum of geometric sequence
We have formula: [tex]S_n=\frac{a_1(1-r^n)}{(1-r)}[/tex]
Here r = Common Ratio = 2 ÷ 1 = 4÷2 = 2
and a = First term = 1
⇒ [tex]S_n= \frac{1\times(1-2^7)}{(1-2)} \\\Rightarrow S_n=\frac{(1-128)}{-1}\\ \Rightarrow S_n=127[/tex]
The volume of a cone is 1004.8 cubic inches. The height of the cone is 15 inches. What is the radius of the cone, rounded to the nearest inch? (Use π = 3.14.)
64
32
8
4
Select the coordinates of two points that are on the line x = 5.
(5, 0) and (0, 5)
(5, 0) and (5, −2)
(5, 0) and (0, 2)
(0, 5) and (0, 2)
The line x=5 is the vertical line consisting of all points with x-coordinate equal to 5 (see attached graph).
A. Point (0,5) has first coordinate 0 (not 5).
C. Point (0,2) has first coordinate 0 (not 5).
D. Points (0,5) and (0,2) have first coordinates 0 (not 5).
B. Only in this option both points have first coordinates 5.
Answer: correct choice is B
A rectangular persian carpet has a perimeter of 176 inches. the length of the carpet is 20 inches more than the width. what are the dimensions of the carpet?
The dimension of the carpet are 54 inches and 34 inches.
What is mean by Rectangle?
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given,
A rectangular Persians carpet has a perimeter of 176 inches.
Now,
The perimeter of a rectangle is;
P =2W + 2L
In this case;
⇒ 176= 2W + 2L
Also, the 2nd sentence says;
⇒ L = W + 20
We can substitute this value of length in the perimeter formula as;
176 = 2W + 2(W+20)
176 = 2W+ 2W + 40
176 = 4W + 40
136 = 4W
34 = W
W = 34
Since, L = W +20
L = 34 + 20
= 54
Thus, The dimensions are 54 inches and 34 inches.
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The dimensions of the carpet are 54 inches in length and 34 inches in width. This was determined by setting up and solving the perimeter equation for a rectangle, after which we calculated the length by adding 20 to the width.
To determine the dimensions of a rectangular Persian carpet with a perimeter of 176 inches where the length is 20 inches more than the width, first, let's let the width be represented by w inches. The length will then be w + 20 inches. The perimeter of a rectangle is calculated by adding together twice the width and twice the length (P = 2w + 2l).
The formula with the given values will look like this:
176 = 2w + 2(w + 20)
Simplifying this equation gives us the width and subsequently the length:
176 = 2w + 2w + 40
176 = 4w + 40
136 = 4w
w = 34
So, the width of the carpet is 34 inches. To find the length, we add 20 inches to the width:
Length = w + 20 = 34 + 20 = 54 inches
Therefore, the dimensions of the carpet are 54 inches in length and 34 inches in width.
Simplify the expression (20-14)^2 divided by 12
A)1
B)3
C)17
D)0.5
Answer:
The correct option is B) 3.
Step-by-step explanation:
Consider the provided expression.
(20-14)^2 divided by 12
The above statement can be written as:
[tex]\frac{(20-14)^2}{12}[/tex]
[tex]\frac{(6)^2}{12}[/tex]
[tex]\frac{6\times 6}{12}[/tex]
[tex]\frac{36}{12}[/tex]
3 times 12 is 36,
[tex]3[/tex]
Hence, the simplified form of the provided expression is 3.
Therefore, the correct option is B) 3.
Constructed Response 1: A student thinks that the sum of 4.3 and 8.4 is 12.7 because 4 + 8 = 12 and 3 + 4 = 7. The student then adds 3.6 and 2.7 and gets 5.13 because 3 + 2 = 5 and 6 + 7 = 13. Identify the mistake in the student’s procedure and explain why this procedure won’t always work.
The game of clue involves 6 suspects, 6 weapons, and 9 rooms. one of each is randomly chosen and the object of the game is to guess the chosen three. (a) how many solutions are possible? in one version of the game, the selection is made and then each of the players is randomly given three of the remaining cards. let s, w, and r be, respectively, the numbers of suspects, weapons, and rooms in the set of three cards given to a specified player. also, let x denote the number of solutions that are possible after that player observes his or her three cards. (b) express x in terms of s, w, and r. (c) find e[x].
Answer:
(a) 324 solutions are possible
(b) (6 - s)(6 - w)(9 - r)
(c) 198/78
Step-by-step explanation:
Just a pure guess and also give brainliest to the other person
Find the specific formula for the sequence. [−3,1,5,9,13,...]
x+4 is the specific formula for sequence [−3,1,5,9,13,...]
What is Sequence?A sequence is defined as an arrangement of numbers in a particular order.
The given sequence is
−3,1,5,9,13,...
-3+4=1
1+4=5
5+4=9
9+4=13
As we can see above, to get from one number to the next it is simply adding 4. So the formula for sequence is x + 4.
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Write a function g in terms of f so that the statement is true.
The graph of g is a reflection in the y-axis of the graph of f
g(x)=
The function g(x) in terms of f(x) that represents a reflection in the y-axis is g(x) = -f(x).
Explanation:The function g(x) in terms of f(x) that represents a reflection in the y-axis is g(x) = -f(x).
To reflect a point across the y-axis, we change the sign of the x-coordinate. So, to reflect the graph of f(x) across the y-axis, we need to change the sign of f(x). This can be achieved by multiplying f(x) by -1, giving us g(x) = -f(x).
For example, if f(x) = 2x+3, then g(x) = -(2x+3) = -2x-3.
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The function g(x) that represents a reflection in the y-axis is g(x) = -f(x).
Explanation:The function g(x) in terms of f(x) that represents a reflection in the y-axis is g(x) = -f(x).
To reflect a graph in the y-axis, we replace each x-coordinate with its opposite (negative value) while keeping the y-coordinate unchanged. In this case, since g is the reflection of f in the y-axis, the function g(x) will have the same y-values as f(x), but the x-values will be their negatives.
For example, if f(x) = 2x + 3, then g(x) = -f(x) would be g(x) = -2x - 3, where the graph of g(x) is the reflection of f(x) across the y-axis.
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Math problem : suppose you cut a sheet of papper into fourths and throw away three of the fourths. you cut the reminding fourths into fourths you repeat the process , each time cutting the paper into fourths and throwing away three of the fourths. after the sixth repetition what fraction of the original sheet of paper id left?
Ashley runs 6 miles in 49 minutes. how many miles does she run per minute?
Solve 4(c + 2) < 4c + 10.
Divide 7/24 by 34/48 and reduce the quotient to the lowest fraction
The area of a circle is found with the formula a = , where represents 3.14. if a tile artist is placing tiles in a circular mosaic pattern and the area of the circle is 658 square feet, what is the approximate radius of the circle in feet?
Answer:
14
Step-by-step explanation:
Area = 3.14πr^2
We know that the area of the circle is 658. Divide 658 by 3.14 which equals 209.5 ( rounded to the nearest whole number is 210). The square root of 210 is 14.4 and rounding to the nearest whole number is 14.
Two angles are supplementary. The first angle measures 40°. What's the measurement of the second angle?
Write an additional word problem in which the estimated sum is 14,000
The problem is about estimating the total sales sum of 7 TVs sold in a day, each priced at approximately $2,000, which gives us a total estimate of $14,000.
Explanation:The mathematics problem could be something along the lines of this: In a local electronics store, 7 high-definition smart TVs were sold in one day. If each TV is approximately priced at $2,000, what is the estimated total sales sum for that day?
First, analyze the problem. We want to find the estimated total sales sum for the smart TVs.Then, we use estimation to solve it. We know each TV costs around $2,000 and that 7 TVs were sold.Just multiply $2,000 by 7. Thus, $2,000 * 7 = $14,000So, the estimated sum is $14,000This estimation gives us a total sum of $14,000, which is close to the actual total if each TV is priced at $2,000.
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The three interior angle measures of this triangle are x = °, y = °, and z = °.
Answer:
30-70-80
Step-by-step explanation:
Which inequality will have a shaded area above its graph?
a
x − 9y ≤ 1
b
4x + 3y < 6
c
2x − y ≥ 4
d
x − 3y > 4
In a mixture of concrete, there are fourfour lb of cement mix for each pound of gravel. if the mixture contains a total of 110110 lb of these two ingredients, how many pounds of gravel are there?
Find the x -intercept and the y -intercept. Then use them to graph the line of 6x+2y=-12
Sharon is twice as old as brian, and in 5 years the sum of their ages will be 25 years. find their present ages.
Answer:
sharon=10
Step-by-step explanation:
The present age of Sharon and Brain is 10 years old and 5 years old.
Given,
Sharon is twice as old as brian.
In 5 years the sum of their ages will be 25 years.
We need to find their present ages.
What are the important terms in solving age problems?Some of the terms are:
In x years - add x years to the present age
x years ago - Subtract x years with the present age
Before x years - subtract x years to the present age
After x years - add x years to the present age
Find the present age of Sharon and Brain.
Let the present age of:
Sharon - S
Brain - B
Now,
Sharon is twice as old as brian.
We can write this as:
S = 2B ____(1)
In 5 years the sum of their ages will be 25 years.
It can be written as:
(S + 5) + (B + 5) = 25
S + B + 10 = 25
S + B = 25 - 10
S + B = 15 _____(2)
From (1)
We get,
2B + B = 15
3B = 15
B = 5. ______(3)
Putting (3) in (2)
S + 5 = 15
S = 15 - 5
S = 10
We have,
B = 5 and S = 10
Thus the present age of Sharon and Brain is 10 years old and 5 years old.
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For what values of x does 25^x = 5^x^2-3?
The values of x that satisfy the given equation are -1 and 3
What is an indical equation?From the question, we are to determine the values of x that satisfy the given equation
The given equation is
25^x = 5^x^2-3
The can be written as
[tex]25^{x} =5^{x^{2} -3}[/tex]
Expressing 25 in index form, we get
[tex]5^{2x} =5^{x^{2}-3 }[/tex]
Now, equate the powers (since the bases are equal)
[tex]2x =x^{2}-3[/tex]
Then, we have that
[tex]x^{2} -2x-3 =0[/tex]
Solve quadratically
Using the factorization method, we get
[tex]x^{2} -2x-3 =0[/tex]
[tex]x^{2} -3x+x-3 =0[/tex]
[tex]x(x-3)+1(x-3)=0[/tex]
[tex](x+1)(x-3) =0[/tex]
∴ x+1 = 0 OR x-3 = 0
x = -1 OR x = 3
Hence, the values of x that satisfy the given equation are -1 and 3.
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The numbers on two consecutively numbered gym lockers have a sum of 129129. what are the locker numbers?