The length of a rectangle is 6 cm more than its width. The area of the rectangle is 256 cm,superscript,2,baseline,. Let x represent the width of the rectangle in centimeters. Which equation represents the situation? Answer Options with 4 options A
. 6x,superscript,2,baseline, − 256 = 0 B
. 6x,superscript,2,baseline, + 256 = 0 C.
x ,superscript,2,baseline, − 6x + 256 = 0 D.
x ,superscript,2,baseline, + 6x − 256 = 0
The equation which represents the situation is:
[tex]x^2+6x-256=0[/tex]
Step-by-step explanation:Let x represent the width of the rectangle in centimeters.
The length of a rectangle is 6 cm more than its width.
This means that the length of the rectangle is: x+6 cm.
Also, we know that the area of a rectangle is the product of the length and width of the rectangle.
Here, the area of the rectangle is 256 cm².
i.e.
[tex]x(x+6)=256\\\\x^2+6x=256\\\\i.e.\\\\x^2+6x-256=0[/tex]
Given the linear equation y=5x+7, fill in the table by choosing values for x, and calculating the corresponding y values. Use integer values for x.
Final answer:
To fill in the table for the equation y=5x+7, integer values for x are chosen and substituted into the equation to find the corresponding y values. The (x, y) pairs are then recorded in the table and can be plotted on a graph.
Explanation:
Filling in a Table for a Linear Equation
To fill in the table for the linear equation y=5x+7, let's choose integer values for x and calculate the corresponding y values. Here's how you do it step by step:
Pick an integer value for x (e.g., -1, 0, 1, 2, etc.).
Substitute this value of x into the equation to solve for y.
Record the (x, y) pair in the table.
For example:
If x = -1, then y = 5(-1)+7 = 2, so the point is (-1, 2).
If x = 0, then y = 5(0)+7 = 7, so the point is (0, 7).
If x = 1, then y = 5(1)+7 = 12, so the point is (1, 12).
If x = 2, then y = 5(2)+7 = 17, so the point is (2, 17).
Remember, the dependence of y on x represents the fact that y changes when x changes, according to the equation of the line. After calculating several points, you can plot these points on a graph, and they should form a straight line because they belong to a linear equation.
Write the number 60 as a product of its prime factors in the same way. Write the factors in order, from smallest to largest
Four pieces of wood each 11 1/2 inches long are required to build a cabinet. If all four pieces are cut from one board and 1 inch is allowed for waste in cutting each piece, how long should the board be?
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I need help ASAP. And, when done solving, how did you get your answer and what was your thought process (not steps). Thank you!!
finding the domain and range and answering in interval notation.
The domain is [-3,2)
The range is [-5,4]
How to get the domain and range of functionsDetermining the domain and range involves analyzing the behavior and restrictions of the function. The domain and range may vary depending on the type of function and any restrictions imposed by the function's definition, such as square roots, division by zero, or logarithms.
Understanding the domain and range is crucial in analyzing and describing the behavior and output of functions in mathematics and various fields where functions are applied.
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325 people were in a tour group. Six buses were completey filled and 7 people chose to walk.How many people did the bus hold?
An average person in the United States throws away 4.5 × 10² g of trash per day. In 2013, there were about 3.2×10^6 people in the U.S.
About how many grams of trash was thrown away in the United States in 2013?
Enter your answer in the box.
5.3 × 10^ g
A fossil is 254 millimeters long. How many meters long is the fossil? Enter your answer, as a decimal, in the box.
The length of a rectangle is one unit shorter than one-sixth of the width, x.
Which expression represents the perimeter of the rectangle?
7/3x−2
7/3x−8
1/3x−2
13x−4
A machine factory produces 2 parts per second. One shift is 10 hours long.
What is the production rate in parts per shift?
Enter your answer in the box.
What the answer to this
Which expression represents the calculation “subtract 10 from 36, then divided by 6”?
A) 6 ч (36 − 10)
B) (36 − 10) ч 6
C) (36 ч 6) − 10
D) (10 − 36) ч 6
3.55 divided by 5=..... tenths divided By 5+......... hundredths divided by 5
3.55 divided by 5 = 35 tenths divided by 5 + 5 hundredths divided by 5
To solve 3.55 divided by 5 using place values, we can break 3.55 into tenths and hundredths:
3.55 can be written as 3.5 + 0.05.
Tenths: 3.5 = 35 tenths
Hundredths: 0.05 = 5 hundredths
Now, we can write:
3.55 divided by 5 = 35 tenths divided by 5 + 5 hundredths divided by 5
Let's verify.
3.55/ 5 = 0.71
35 tenths /5 = 7 tenths
5 hundredths /5 = 1 hundredths
Adding them: 7 tenths + 1 hundredths = 0.71
Thus, it is verified.
Hence, 3.55 divided by 5 = 35 tenths divided by 5 + 5 hundredths divided by 5
Write in slope-intercept form an equation of the line that passes through the given points.
(−1, −1), (1, 5)
Answer: y= ??????
13 + 3p = 7 I need help finding what p stands for.
4x-8y=9 what is the slope of a line perpendicular to this line
A package of blank CDs usually costs $8.50. This week it's on sale for 15% off. What's the discount?
Use the vocabulary term "absolute value" to explain the term opposite as it pertains to positive and negative numbers. Explain why zero is the opposite of itself
Answer:
zero is the opposite of itself because there is no negative zero to be its opposite so it is itselfs opposite.
Bridget works part time in a shoe store. Sometimes when it is not busy, she rearranges the shoes for fun. If she takes six different pairs of shoes and rearranges them in a row, in how many ways can she rearrange them so that no two shoes match?
Alyssa received $30,000 from an inheritance and invests part in a certificate of deposit (CD) paying 5% annual interest and the rest in Apple Inc. offering an annual return of 11%. If the annual income from her investments is $2,220, how much did Alyssa invest in each?
Which set does not contain –3? the set of all real numbers the set of all integers the set of all whole numbers the set of all rational numbers
The set of whole number since it is defined as positive integers + zero.
We have given that,
The set of all real numbers the set of all integers the set of all whole numbers the set of all rational numbers.
We have to determine the Which set does not contain –3
What is the set of all whole numbers?Integers are the set of whole numbers and negative of natural numbers. Hence, integers include both positive and negative numbers including 0. Real numbers are the set of all these types of numbers natural numbers, whole numbers, integers and fractions.
Therefore we get,
The set of whole number since it is defined as positive integers + zero.
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The basketball coach made up a game where each player takes 10 shots at the basket. For every basket made, the player gains 10 points. For every basket missed, the player loses 15 points. The player with the highest score sank 7 baskets and missed 3. What was the highest score?
Jeff is saving to purchase a new basketball that will cost at least $88. He has already saved $32. At least 7) Jeff is saving to purchase a new basketball that will cost at least how much more does he need to save for the basketball?
The cost of the ball is $0.05. This is determined through a simple algebraic calculation that takes into account that the bat costs $1.00 more than the ball and the total cost is $1.10.
The student's question is about solving a simple algebraic problem involving the cost of two items with a given difference in their prices. In the problem statement, a bat and ball cost a combined total of $1.10. The bat costs $1.00 more than the ball.
Let's denote the cost of the ball as x dollars.Consequently, the cost of the bat will be x + $1.00, since it costs one dollar more than the ball.According to the information provided, the combined cost of the ball and bat is $1.10. Therefore, we can write the following equation: x + (x + $1.00) = $1.10.Simplifying this equation: 2x + $1.00 = $1.10.Subtracting $1.00 from both sides of the equation, we get 2x = $0.10.Dividing both sides of the equation by 2, we find that x = $0.05.Therefore, the cost of the ball is $0.05.
you are given the measure of angle 4. You also know the following angles are supplementary: Angles 1 and 2, angles 2 and 3, angles 1 and 4. Explain how you can determine the measures of angles 1, 2, and 3.
To find the measures of angles 1, 2, and 3, use the fact that angle 1 is supplementary to both angles 2 and 4, and angles 2 and 3 are supplementary. Set up equations and solve them simultaneously to find the measures of the angles.
Explanation:To determine the measures of angles 1, 2, and 3, we can use the information that angle 1 is supplementary to both angles 2 and 4, and angles 2 and 3 are supplementary. Since angles that are supplementary add up to 180 degrees, we can set up equations to solve for the measures of angles 1, 2, and 3.
Let's represent the measure of angle 4 as x. Then we can write the equations:
Angle 1 + Angle 4 = 180 degreesAngle 2 + Angle 3 = 180 degreesAngle 1 + Angle 2 = 180 degreesSubstituting x for the measure of angle 4, we can solve these equations simultaneously to find the measures of angles 1, 2, and 3.
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Which three points in the figure are collinear?
a) F, E, G
b) A, B, D
c) E, C, A
d) A, B, C
In the figure, the points F, E, and G are collinear. Collinear points are points that lie on the same straight line. The correct option is A).
Point F is clearly on the same straight line as points E and G because it falls directly in line with them, creating a continuous sequence.
It can visualize this by a line passing through points F, E, and G. This line would pass through all three points without any interruption.
No other points in the figure form such a straight-line arrangement with F and G, further confirming that F, E, and G are the collinear points.
In summary, points F, E, and G are collinear because they lie on the same straight line, and no other points in the figure share this property with them.
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How do I solve for x?
3x+4(-4x+4)= -75
Please solve
Identifytwonumbers,onerationalnumber and one irrational number, that are between 1.4 and 1.6. Include the decimal approximation of the irrational number to the nearest hundredth.
1.5 is rational
1.58472679422222.... is irrational because it doesn't end
LCM of 15, 30, and 45
What is 8.61×10−8 in decimal form?
0.000000861
0.0000000861
8,610,000
861,000,000
What's a rational number between 8 and 8.1
The rational number between 8 and 8.1 is 8.05 / 1 or 16.1 / 2.
What is Number system?
A system of writing to express the number is called number system.
Given that;
The numbers are,
⇒ 8 and 8.1
Now,
Find the rational number between 8 and 8.1 as;
The rational number = (8 + 8.1) / 2
= 16.1 / 2
= 8.05 / 1
Thus, The rational number between 8 and 8.1 is 8.05 / 1 or 16.1 / 2.
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6. Identify an equation that models the situation and find its solution.
It’s going to be Lindsay’s birthday soon, and her friends Mary, Jacqui, Tadeusz, Opal, and
Tony have contributed equal amounts of money to buy her a present. They have $45.00 to
spend between them. Determine how much each contributed.
(1 point)
5y = 45.00; y = $9.00
5y = 45.00; y = $10.00
5 + y = 45.00; y = $39.00
5 + y = 45.00; y = $40.00