The new dimensions of the box are 5 feet, 4 feet, and 6 feet.
Given:
A rectangular box has dimensions of 4 feet by 3 feet by 5 feet.
So, Length = 4 feet ,width = 3 feet and height = 5 feet.
Volume of rectangular box = length × width × height
= 4 × 3 × 5 = 60 feet³
Now, increasing each dimension by the same amount yields a new box.
Let the increase in dimension be x feet.
The dimensions of the new box are,
Length = (4 + x) feet ,width = (3 + x) feet and height = (5 + x) feet.
Volume of new box = length × width × height
= (4 + x) (3 + x) (5 + x)
It is given that the volume of the new box is twice the volume of the old box, 2 × 60 feet³ = 120 feet³
So, equate the volume to find the value of x.
(4 + x) (3 + x) (5 + x) = 120
(12 + 7x + x²) (5 + x) = 120
60 + 12x + 35x + 7x² + 5x² + x³ = 120
60 + 47x + 12x² + x³ = 120
x³ + 12x² + 47x - 60 = 0
x = 1
Hence each dimension was increased by 1 foot.
The new dimensions of the box are 5 feet, 4 feet, and 6 feet.
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What is the value of x in the equation?
6x + 24 - 4x = 30
Answer:2x+ 24
Step-by-step explanation:
6x-4x=2x+ 24
Answer:
✨hello mark as branlist pls x=3
Step-by-step explanation:
6x+24−4x=30
6x+24−4x=30
6x+24+−4x=30
(6x+−4x)+(24)=30
2x+24=30
2x+24=30
2x+24−24=30−242x=6
2x
2
=
6
2
x=3
Make x the subject of the following equation:
[tex] \sqrt{4x} = 3a - y \\ \sqrt{4} \times \sqrt{x} = 3a - y \\ 2 \sqrt{x} = 3a - y \\ \frac{2 \sqrt{x} }{2} = \frac{3a}{2} - \frac{y}{2} \\ \sqrt{x} = \frac{3a}{2} - \frac{y}{2} \\ ( { \sqrt{x} })^{2} = {( \frac{3a}{2} - \frac{y}{2} })^{2} \\ x = ( \frac{3a}{2} - \frac{y}{2} ) ^{2} [/tex]
ATTACHED IS THE SOLUTION
State a true conclusion.
1) If Bis between A and C, then AB+ BC = AC.
2) Qis between Rand S.
Conclusion:
Both conclusion are correct and the second conclusion is RS = RQ + QS.
What is a midpoint of line segment?The midpoint is halfway between the two end points, Its x value is halfway between the two x values. Its y value is halfway between the two y values.
Given that,
Part 1, If B is between A and C then AB + BC = AC
Then, we need to find the conclusion in Part 2 if Q is between R and S.
The required conclusion can be find out by using the concept of deductive reasoning.
Deductive reasoning involves a pattern which is followed in one argument and by following the same pattern we reach to a conclusion for some other argument.
Now, If we see in Part 1 if B is between A and C then the length of line segment AC is equal to sum of its mid segments AB and BC
⇒ AB + BC = AC
Similarly, if Q is between R and S, then the length of line segment RS is equal to sum of its mid segments RQ and QS
⇒ RS = RQ + QS
Hence, The required Conclusion is RS = RQ + QS.
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-k-(-8k+7)
what is the answer
Answer:
7k-7
Step-by-step explanation:
[tex]-k-(-8k+7) \\ \\ =-k+8k-7 \\ \\ =7k-7[/tex]
2) you are comparing two investment options that each pay 6 percent interest, compounded annually. both options will provide you with $12,000 of income. option a pays $2,000 the first year followed by two annual payments of $5,000 each. option b pays three annual payments of $4,000 each. which one of the following statements is correct given these two investment options? assume a positive discount rate. (no calculations needed.) a) both options are of equal value since they both provide $12,000 of income. b) option a has the higher future value at the end of year 3. c) option b has a higher present value at time 0. d) option b is a perpetuity. e) option a is an annuity.
Answer:
The correct answer is B) Option B has a higher present value at time zero.
Step-by-step explanation:
We use spreadsheets to compare both options.
We have to calculate
future value
present value
Option A
Net Present Value (NPV) 10534,87
Future value 12.547
Option B
Net Present Value (NPV) 10692,05 is higher than option A
Future value 12.734 is higher than option A
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A city has a sales tax.
Is there a proportional relationship between the cost of items before tax and the cost of items after tax?
Yes
What is the constant of proportionality?
1. Yes. There is a proportional relationship between the cost of items before tax and the price after tax because they share a constant of proportionality.
2. The constant of proportionality refers to the relative ratio that establishes the proportional relationship between two values.
What other descriptions refer to the constant of proportionality?Other descriptions of the constant of proportionality include:
Constant ratioConstant rateUnit rateConstant of variationRate of change.Two variables possess a proportional relationship when their ratio or product produces a constant.
We can use the equation, k = y ÷ x, to find the constant of proportionality.
For instance, let the cost of items before tax be $100 with a 7% sales tax. The cost of the articles after tax is $107.
Therefore, the constant of proportionality is 1.07 ($107/$100).
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HELPPPPPPPPPPPPPPP MEEEE
Answer: 244.92 square inches
Step-by-step explanation:
The radius is half the diameter so is 3 inches
Substitute r=3 and pi= 3.14 into the equation:
SA= (2x3.14x9) + (2x3.14x3x10)
Put that into your calculator and you get 244.92
4.
Rectangle MATH was translated 7 units to the left and 4 urlits down to create rectangle M'ATH'. Which rule describes this transformation?
The rectangle MATH is translated by using the transformation rule P'(x, y) = (x - 7, y - 4) to create the rectangle M'A'T'H'.
What is the resulting rule transformation for the translation of a rectangle?
In this problem we have the case of a rectangle, a geometric locus, that is translated both horizontally (7 units to the left) and vertically (4 units down). Vectorially speaking, a translation is represented by the following vector sum:
P'(x, y) = P(x, y) + T(x, y) (1)
Where:
P(x, y) - Original point.P'(x, y) - Resulting point.T(x, y) - Translation vector.If we know that P(x, y) = (x, y) and T(x, y) = (- 7, - 4), then the transformation rule is derived below:
P'(x, y) = (x, y) + (- 7, - 4)
P'(x, y) = (x - 7, y - 4)
The rectangle MATH is translated by making use the transformation rule P'(x, y) = (x - 7, y - 4).
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Henry purchases $56.00 worth of clothing at the store. The sales tax in his city is 7.5%. What is the total cost of the clothing?
Answer:
$60.20
Step-by-step explanation:
7.5 percent of 56 can be found by multiplying 56 times .075, which equals 4.2. Add that to 56 and you get the total cost, which is $60.20
Increasing
decreasing
concave up
concave down
Answer:
won't that be concave up?
Please help!
In the diagram of triangle ABD shown below, point C is located on BD such that AB is congruent AC and AC DC. I
m/B=62°, what is the measure of angle ADC?
Step-by-step explanation:
follow the steps and apply the rules of geometry
Help -crys- "pacman traveled 18 feet every 6 seconds. pacman's distance is proportional to time. (im not in high school im in middle school i dont know why it says that)
Constant of Proportionality
k=___
Based on the distance that Pacman traveled for every 6 seconds, and the distance being proportional to time, the Constant of Proportionality is 3.
How to find the constant of proportionality?The Constant of Proportionality shows how the quantity of a variable increases of decreases as the quantity of another related variable increases or decreases as well.
In the distance traveled by Pacman, the constant of proportionality can be found by the formula:
= Distance traveled / Time traveled
= 18 feet / 6 seconds
= 3 feet per second
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What is the slope equation for (7,5) and (2,-5)
Answer:
2
Step-by-step explanation:
To find the slope, m, you use the equation:
[tex]m \: = \frac{y2 - y1}{x2 - x1} [/tex]
From our question, (x1 = 7, y1 = 5) ; ( x2 = 2, y2 = -5)
Substitute the values into the equation:
[tex]m \: = \frac{ - 5 - 5}{2 - 7} \\ = 2[/tex]
The slope, m is therefore 2
Identify the function that fits the description given below.
The function whose domain consists of all nonnegative real numbers.
Select all that apply.
The function which contains non-negative real number is y = (x - 1)² and the domain is [0, ∝).
What is real number?
In mathematics, real number are those numbers which contain negative numbers, whole numbers as well as natural numbers. And all the positive real number lies in the first quadrant in the graph. The set of real numbers (denoted by R) includes both rational numbers (positive, negative and zero) and irrational numbers.
According to the question, the given functions whose domain consists of all non-negative real numbers.
Non-negative real numbers lie in the first quadrant. Therefore, the function(d) contains all non-negative real numbers.
Given function: y = (x - 1)²
The domain for this function is: [0, ∝)
Hence, the function which contains non-negative real number is y=(x - 1)² and the domain is [0, ∝).
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What’s x-7-9=2-8x
Please I need it now
hope it's true.
yes
x-7-9=2-8x
-16-2 = -8x-x
x= 18/9
x= 2
A bakery made 9 cakes using 3 bags of flour. The bakery uses the same relationship between cakes made and the amount of flour used to make all their cakes.
Which table of values shows the relationship between the number of cakes the bakery makes and the number of bags of flour the bakery uses?
The table of values showing the relationship between the number of cakes the bakery makes and the number of bags of four the bakery uses is:
Cakes | 3 6 9 12 15
Bags of flour| 1 2 3 4 5
A bakery made 9 cakes using 3 bags of flour.
We can introduce a relation between the number of cakes and the bags of flour in the form of a ratio.
Then, cakes : bags of flour = 9 : 3
We can simplify this ratio into 3:1.
So the ratio between the number of cakes and bags of flour = 3:1
We take values for number of bags of flour from 1 to 5 and found the corresponding values for number of cakes using the ratio 3:1.
For each value of number of bags of flour, we just needed to multiply 3 with it to get the number of cakes made.
So using this relationship between cakes made and the amount of flour used to make all their cakes, we can makes table with values:
Cakes | 3 6 9 12 15
Bags of flour| 1 2 3 4 5
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please answer this question to do with shapes
please explain the steps in detail
Area of the shape formed by joining triangle , trapezium and rectangle with height 3.5cm is equal to 6.25cm².
As given in the question,
Height of the shape = 3.5cm
length of the rectangle =3cm
Base of a triangle= 8mm
= 0.8cm
Parallel sides of the trapezium
side1 = 0.8cm
side 2= 3cm
Let x represents the height
Ratio of the height of rectangle ,trapezium and triangle =2:3:2
2x +3x+2x =3.5
⇒7x =3.5
⇒x =0.5
Height of rectangle =2×0.5
= 1cm
Height of trapezium =3×0.5
= 1.5cm
Height of the triangle =2×0.5
= 1cm
Area of triangle = (1/2)× 0.8 ×1
= 0.4cm²
Area of trapezium = (1/2) ×(0.8+3)×1.5
= 2.85cm²
Area of rectangle = 3 ×1
=3cm²
Area of the shape =0.4 +2.85 +3
= 6.25cm²
Therefore, area of the shape formed by joining triangle , trapezium and rectangle with height 3.5cm is equal to 6.25cm².
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L2) In a class of 27 students, there are 13 male students and 14 female students. What is the probability of randomly choosing 2 male students for class representatives?
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Match the operation with it's inverse operation you would use to solve an equation
Answer:
1. e
2. c
3. f
4. b
5. a
6. d
Step-by-step explanation:
Addition - Subtraction
Subtraction - Addition
Multiplication - Division
Division - Multiplication
x^2 = square root X
square root x = x^2
Answer:
A to 5. B to 3. C to 1. D to 6. E to 2. F to 4.
Step-by-step explanation:
It makes sense.
Joaquin works at a loading dock. He has been asked to load 30 trucks today, and so far he has finished loading 12. Name the numerator and denominator of the fraction that represents the number of trucks that he has loaded out of the total needing to be loaded .
Answer:
first choice in the image.
numerator: 12
denominator: 30
Step-by-step explanation:
"Name the numerator and denominator of the fraction that represents the number of trucks that he has loaded out of the total needing to be loaded"
so numerator = "number of trucks that he has loaded"
and denominator = "total needing to be loaded"
Joaquin was asked to load 30 trucks today. So his/her total would be 30.
thus the denominator is 30.
Joaquin has finished loading 12 already, which means he/she has loaded 12. so, the numerator is 12.
Find the equation of the line that is parrallel to y=-x+9 and contains the point (7,-13)
Answer:
y = - x + 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - x + 9 ← is in slope- intercept form
with slope m = - 1
• Parallel lines have equal slopes , then
y = - x + c ← is the partial equation of the parallel line
to find c substitute (7, - 13 ) into the partial equation
- 13 = - 7 + c ⇒ c = - 13 + 7 = - 6
y = - x + 6 ← equation of parallel line
Answer:
[tex]\rm{y=-x-6}[/tex]Step-by-step explanation:
Parallel lines have the same slope. So the slope of the line that's parallel to
[tex]\sf{y=-x+9}[/tex] is[tex]\sf{-1}[/tex]Now, plug that into the Point-slope formula:
[tex]\rm{y-y_1=m(x-x_1)}[/tex]
Where:
[tex]\rm{y_1}[/tex] is the y-coordinate of the point[tex]\rm{m}[/tex] is the slope[tex]\rm{x_1}[/tex] is the x-coordinate of the pointPlug in the values:
[tex]\rm{y-(-13)=-(x-7)}[/tex][tex]\rm{y+13=-(x-7)}[/tex][tex]\rm{y+13=-x+7}[/tex][tex]\rm{y=-x+7-13}[/tex][tex]\rm{y=-x-6}[/tex]I hope this helps!!
20 POINTS A company uses functions to model the costs to produce and market a product.
The cost, in thousands of dollars, to produce x units of the product is modeled by function j:
j(x) = 17 + 0.05x.
The cost, in thousands of dollars, to market x units of the product is modeled by function k:
k(x) = 4 + 0.03x.
Which function correctly represents the total cost, in thousands of dollars, to produce and market x units of the product?
A.
c(x) = 21 + 0.08x2
B.
c(x) = 13 + 0.02x2
C.
c(x) = 13 + 0.02x
D.
c(x) = 21 + 0.08x
Answer:
D
Step-by-step explanation:
We can add the two functions.
[tex]j(x)+k(x)=(17+0.05x)+(4+0.03x)=21+0.08x[/tex]
If two dice are rolled at one time what's the probability of getting a sum less than or equal to 10
Answer
Step-by-step explanation:
When one dice is rolled, the total sample space = 6 When two dice is rolled, total sample space = 6*6=36 A) P(sum less than 9) = 1 - P(sum greater than or equal to 9) Sample outcomes for sum greater than or equal to 9 = {(3,6),(4,5),(5,4),(6,3),(4,6), (5,5),(6,4), (5,6), (6,5),(6,6)} P(sum greater than or equal to 9) = 10/36 = 5/18 or 0.2778 P(sum less than 9) = 1-5/18 = 13/18 or 0.7222 B)Sample outcomes for sum greater than or equal to 10 = {(4,6),(5,5),(6,4), (5,6),(6,5),(6,6)} P(sum greater than or equal to 10) = 6/36 = 1/6 or 0.1667 C) sample outcomes for event 3 on one die or both = {(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),(1,3),(2,3), (4,3),(5,3),(6,3)} P(3 on one die or both die) = 11/36 or 0.3056
Round to the nearest dollar $6.34
What is the measure of
The measure of angle AXY based on the information will be A. 70°.
How to calculate the angle?It should be noted that the value of a right angle is equal to 90°.
In this case, we will add the angles that are given and equate them to 90°. This will be:
6x + 40 + 10 + 2x = 90°
8x + 50 = 90°
Collect like terms
8x = 90° - 50°
8x = 40°
Divide
x = 40° / 8
x = 5°
Therefore, the value of angle AXY will be:
= 6x + 40
where x = 5.
= 6(5) + 40
= 30 + 40
= 70°
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Henry read 6 books in 2 months. if he reads at a constant rate, how many books did he read each month? give your answer as a whole number or a fraction in simplest form.
The number of books Henry read each number is 3 or 6/2 in a fraction.
A fraction is used to denote a portion or component of a whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
As given in the question,
The number of books read in 2 months is 4.
Henry read books at a constant rate.
The Number of books read by Henry in 1 month is ( 6/2 ) = 3 books.
Therefore, the number of books read by Henry as per the given condition of reading 6 books in 2 months at a constant rate is equal to 6/2.
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Help me please i dont get how to do it
The linear graph of y = 2x + 3 is shown below.
How to Draw the Graph of a Linear Equation?To graph the linear equation, plot each points from the table of values on a coordinate plane then connect the points to each other as a straight line.
Given the table, to fill it, substitute each value of x into y = 2x + 3:
For x = -2:
y = 2(-2) + 3
y = -4 + 3
y = -1
For x = -1:
y = 2(-1) + 3
y = -2 + 3
y = 1
For x = 0:
y = 2(0) + 3
y = 3
Thus, plot the points, (-2, -1), (-1, 1), (0, 3), (1, 5), and (2, 7) on a graph. The graph is shown below.
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3
5
of the fish in Carson's fish tank are guppies.
3
4
of the guppies are red. What fraction of the fish in Carson's tank are red guppies?
Answer:
9/20
Step-by-step explanation:
3/5 is the same as 12/20, so 12 fish are guppies, now 3/4 is also 9/12, so 9 of the fish are red guppies, 9/20 is in the simplest form
Use the number 2 4 6 and 8
__+(__-__)_=2
Ella needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 3 hours and charged her $61 for parts. The total was $226. Write and solve an equation which can be used to determine x, the cost of the labor per hour.
Answer:
x = 55
Step-by-step explanation:
61+3×X=226
61+3x=226-61
3x=165
x= 165/3
x= 55