Answer:
The length is 10 inches, and the width is 4 inches.
By creating a quadratic equation using the known facts and algebra, we can determine that the dimensions of the rectangle with an area of 40 square inches are length= 10 inches and width= 4 inches.
Explanation:This problem is a classic example of using algebra to solve for unknown dimensions. Given that the area (A) of a rectangle equals its length (L) times its width (W), written as A = L x W, you can substitute the given values into this formula. You're told the length is 6 inches longer than the width, which you can denote in algebra as L = W + 6. Secondly, you're given that the area is 40 square inches. Substituting these values gives us the following equation: 40 = W(W + 6).
Solving this equation will give us the width, and substituting the width into the formula L = W + 6, gives us the length.
Solving the Equation:
First, distribute the width on the right side of the equation to get 40 = W^2 + 6W. Re-arranging terms gives W^2 + 6W - 40 = 0. Factoring this quadratic equation yields (W - 4)(W + 10) = 0. Setting each factor equal to zero and solving for W gives W = 4 and W = -10. Because a width cannot be negative, the width of the rectangle is 4 inches. Substituting W = 4 into the length equation results in L = 4 + 6 = 10 inches. Hence, the dimensions of the rectangle are Length = 10 inches and Width = 4 inches.
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Select the action you would use to solve x-3= 12. Then select the property that justifies that action.
A. Action: Add 3 to both sides.
B. Action: Multiply both sides by 3,
C. Action: Subtract 3 from both sides.
D. Property: Addition property of equality
E. Property: Multiplication property of equality
F. Property: Subtraction property of equality
Answer:
a
Step-by-step explanation:
you would add three to both sides because you are subtracting on the left side, so you would use inverse operations
Answer:
A &d
Step-by-step explanation:
A pex
Write the equation of the sequence in the form y = mx + b:
0.5, 2.5, 4.5, ...
Answer:
y= 2x + 0.5
Step-by-step explanation:
Mrs. Lyons is playing Jeopardy against Mr.Browen. Mr. Bowen incorrectly answers questions with 40 points five times in a row. What is his score so far?
Answer:
-40 x 5 = -200. his score is -200
]
Perform 4.629 + 78.2 - 57
With appropriate number of significant figures
Final answer:
The calculation 4.629 + 78.2 - 57, when rounded to the appropriate number of significant figures, results in 25.8. This takes into account the number with the least decimal places in the original equation.
Explanation:
To solve the calculation 4.629 + 78.2 - 57 with the appropriate number of significant figures, follow these steps:
Add 4.629 to 78.2 to get 82.829.
Subtract 57 from 82.829 to get 25.829.
When considering significant figures, the least number of decimal places in the given numbers is one (in the number 78.2), which means our final answer should also be rounded to one decimal place. Therefore, the correct answer, rounded and with the appropriate number of significant figures, would be 25.8.
What is 5/1 • 7 3/6 and 3 1/3 • 2 2/4 simplify?
Answer:
The first one is 35 5/6. The second is 8 1/3
Step-by-step explanation:
5/1 * 7 3/6
= 5/1 * 45/6
=215/6
= 35 5/6
3 1/3 * 2 2/4
= 10/3 * 10/4
= 100/12
= 8 1/3
6.) A box of candy had 4 cherry pieces for
every 10 lemon pieces. If the box had 45
lemon pieces, how many cherry pieces
would there be?
Answer:
18 cherries
Step-by-step explanation:
45 lemon pieces
40 lemons=16 cherries
5 lemons=2 cherries
Be Precise, One kilometer is About 0.62 mile.
It is 12 Kilometers from Noah's house to the ice skating rink. About how many miles is it from Noah's house to the ice skating rink?
Answer:
about 7.4 miles
exact is 7.44 miles
Step-by-step explanation:
0.62×12=7.44
What is the solution to 4x−1=7 ? Plot the solution on the number line.
Answer: x is 2
Step-by-step explanation:
Add the 1 to 7 and get 8 then 4x=8 then divide 4 into 8 and x=2 to plot it on the line just go to 2 I’m guessing
Answer:
x=2
Step-by-step explanation:
Evaluate the expression when a=6 and y=7-a+5y
Answer:
29
Step-by-step explanation:
Substitute a = 6 and y = 7 into the expression
- a + 5y = - 6 + (5 × 7) = - 6 + 35 = 29
Shaunee won 79 tickets at Chuck e' Cheese's. She
kept 25 of them, and split the rest evenly between 3
friends. How many did each friend get?
Answer:
Step-by-step explanation:
From the problem statement, we can set up the following equation:
[tex]3N + S = 79[/tex]
where [tex]N[/tex] is the number of tickets each friend got, and [tex]S[/tex] is the number of tickets that Shaunee got. We know that Shaunee got 25, so we know [tex]S = 25[/tex] and can plug that into the equation:
[tex]3N + 25 = 79[/tex]
Subtracting 25 from each side gives us the following:
[tex]3N = 54[/tex]
Dividing both sides by 3 gives us the answer:
[tex]N = 18[/tex]
79 tickets minus 25 is 54
Shawnee has 54 tickets to split between her friends.
54 divided by 3 friends equals 18 tickets.
You can check the answer by multiplying: 18x3 equals 54.
Hence, her friends each got 18 tickets...
The sum of three numbers is 95. The first number is 5 more than the third. The second number is 4 times the third. What are the numbers?
Answer:
20, 60, 15
Step-by-step explanation:
Let the third number be n, then
The first number is n + 5 and the second number is 4n
Sum the 3 numbers and equate to 95, that is
n + 5 + 4n + n = 95 ← collect like terms on left side
6n + 5 = 95 ( subtract 5 from both sides )
6n = 90 ( divide both sides by 6 )
n = 15
Thus
The first number is 15 + 5 = 20
The second number is 4 × 15 = 60
The third number is 15
the ordered pairs(1,4), (3,12), and (5, 20)represent the distance y that Jario walks after x seconds. Plot the ordered pairs on the coordinate plane and drawn a line through the points and find the slope of the line and explain what the slope represents.
Check the picture below.
Answer: 4 meters per sec.
A set of stairs is being built as shown.
The length of each stair is 11 inches. What is the rise, r, for each stair? Round to the nearest inch.
2 inches
7 inches
17 inches
24 inches
Answer:
The correct answer is A. Two inches.
HELP needed!!
Completely the steps to find the value of x in the angle?
8x + 6 = m<4
m<4 = 180 - 118 = 62
8x + 6 = 62
8x = 56
x = 7
Ripley told his mom that multiplying whole numbers by multiples of 10 was easy because you just count zeros in the factors and put them in the product. He used these two examples to explain his strategy.
7,000 × 600 = 4,200,000
(3 zeros) (2 zeros) (5 zeros)
800 × 700 = 560,000
(2 zeros) (2 zeros) (4 zeros)
Ripley’s mom said his strategy will not always work. Why not? Give an example.
Answer:
She is right, it won´t always work.
Step-by-step explanation:
Hi, in the examples this tactic works because the first numbers, when multiplied, don´t equal 10 (7x6=42 and 8x7=56). If you multiply both numbers and give you 10, you will have to add another zero to the final number and the trick would crash.
Example:
200 x 500 = 100,000
(2 Zeros) (2 zeros) (5 zeros)
Best of luck.
The sum of two numbers is 72 and one of them is five times the other
Answer:
60+12
Step-by-step explanation:
5x12=60
Answer:
12 and 60
Step-by-step explanation:
Create an equation to solve:
x + 5x = 72
6x = 72 combine like terms
x = 12 divide both sides by 6
the first number is 12
then the other number is 5 times this one
12 x 5 = 60
ANSWER: 12 & 60
Check your work:
12 + 60= 72
The volume of a sphere is 3,052.08 units cubed. What is its diameter?
18 units
20 units
31 units
47 units
Evaluate 6-(5-(3×2-3))
[tex]\bf \stackrel{\mathbb{P~~E~~M~~D~~A~~S}}{6-(5-(3\times 2-3))\implies 6-(5-(\stackrel{\downarrow }{6}-3))\implies 6-(5-(\stackrel{\downarrow }{3}))} \\\\\\ 6-(\stackrel{\downarrow }{2})\implies 4[/tex]
How can u solve for x when there is a y in the like y=4x+8x
Answer:
x = [tex]\frac{1}{12}[/tex] y
Step-by-step explanation:
Given
y = 4x + 8x, that is
y = 12x ( divide both sides by 12 )
[tex]\frac{y}{12}[/tex] = x, or
x = [tex]\frac{1}{12}[/tex] y
Based on the graph, what is the initial value of the linear relationship?
(A) −2
(B) 0
(C) 2/3
(D) 3
Check the picture below.
The sum of a number and its additive inverse is equal to ?
Answer:
Zero
Step-by-step explanation:
To find the additive inverse, you merely change the sign of the number
For Example 5 {5 is the number} + (-5) {-5 is the additive inverse} = 0.
i.e. 6 + (-6) = 0
i.e (-7) + 7 = 0
6. What word describes the equal
shares of the shape?
Answer:
bisection, trisection etc.
Step-by-step explanation:
It depends on how many parts a shape will be divided in. for example if a shape is divided in two equal parts, it will be called as halves or bisection or if a shape is divided in three equal shapes it will be known as trisection and so on.
❗❗❗❗❗❗❗HELP❗❗❗❗❗❗❗
Select the table of values where the quadratic function changes direction at a different value of x than the others.
Imagine that this is a graph.
A.
x -3 -2 -1 0 1 2 3
y 2 3 2 -1 -6 -13 -22
B.
x -3 -2 -1 0 1 2 3
y 2 3 2 -1 -6 -13 -22
C.
x -3 -2 -1 0 1 2 3
y 4 3 4 7 12 19 28
D.
x -3 -2 -1 0 1 2 3
y 1 -1 1 7 17 31 49
Answer:
x -3 -2 -1 0 1 2 3
y 28 19 12 7 4 3 4
Step-by-step explanation:
The point where the quadratic function changes direction (which is the maximum or the minimum of the function) is called the turning point. In options A, B and C the turning point is at (-2, 3), and in option D the turning point is at (-2, -1).
Given that all of them correspond to the same x-value and options A and B are the same, I assume one of them was mistyped. Given the following option:
x -3 -2 -1 0 1 2 3
y 28 19 12 7 4 3 4
we see that the turning point is at (2, 3) which represents a different x-value.
Which numbers are 3 units from −6 on this number line?
Drag and drop all of the numbers that are 3 units from −6 to their correct position on the number line.
-9 and -3 are both 3 units from -6 on the number line.
Answer: -9 and -3 are numbers which are 3 units from -6 on the number line.
Step-by-step explanation:
Since we have given that
3 units from -6 on the number line.
As we know that
there is right hand side and left hand side on the number line.
Left hand side is for negative numbers, and right hand side is for positive numbers.
So, the number which is 3 units from -6 on the left is given by
[tex]-6-3=-9\ units[/tex]
The number which is 3 units from -6 on the right is given by
[tex]-6+3=-3\ units[/tex]
Hence, -9 and -3 are numbers which are 3 units from -6 on the number line.
How many numbers between 650 and 780 leave the remainders 4 and 6 when divided by 7 and 11, respectively?
There are 120 numbers between 650 and 780 that leave remainders of 4 when divided by 7 and remainders of 6 when divided by 11.
To find the numbers between 650 and 780 that leave remainders of 4 when divided by 7 and remainders of 6 when divided by 11, we can analyze the problem systematically.
For a number to leave a remainder of 4 when divided by 7, it must be of the form [tex]\(7k + 4\)[/tex].
Similarly, for a number to leave a remainder of 6 when divided by 11, it must be of the form [tex]\(11m + 6\).[/tex]
We need to find the intersection of these two sets of numbers between 650 and 780.
Let's start by finding the smallest number of the form \(7k + 4\) greater than or equal to 650:
[tex]\[7k + 4 \geq 650\][/tex]
[tex]\[7k \geq 646\][/tex]
[tex]\[k \geq \frac{646}{7} \approx 92.2857\][/tex]
Since [tex]\(k\)[/tex] must be an integer, the smallest integer greater than or equal to [tex]\(92.2857\)[/tex] is 93.
So, the smallest number of the form [tex]\(7k + 4\)[/tex] greater than or equal to 650 is [tex]\(7 \times 93 + 4 = 655\).[/tex]
Now, let's find the largest number of the form [tex]\(7k + 4\)[/tex] less than or equal to 780:
[tex]\[7k + 4 \leq 780\][/tex]
[tex]\[7k \leq 776\][/tex]
[tex]\[k \leq \frac{776}{7} \approx 110.857\][/tex]
Again, since [tex]\(k\)[/tex] must be an integer, the largest integer less than or equal to [tex]\(110.857\)[/tex] is 110.
So, the largest number of the form [tex]\(7k + 4\)[/tex] less than or equal to 780 is [tex]\(7 \times 110 + 4 = 774\).[/tex]
Next, let's find the smallest number of the form [tex]\(11m + 6\)[/tex] greater than or equal to 650:
[tex]\[11m + 6 \geq 650\][/tex]
[tex]\[11m \geq 644\][/tex]
[tex]\[m \geq \frac{644}{11} \approx 58.5455\][/tex]
Since [tex]\(m\)[/tex] must be an integer, the smallest integer greater than or equal to [tex]\(58.5455\)[/tex] is 59.
So, the smallest number of the form [tex]\(11m + 6\)[/tex] greater than or equal to 650 is[tex]\(11 \times 59 + 6 = 655\).[/tex]
Finally, let's find the largest number of the form[tex]\(11m + 6\)[/tex]less than or equal to 780:
[tex]\[11m + 6 \leq 780\][/tex]
[tex]\[11m \leq 774\][/tex]
[tex]\[m \leq \frac{774}{11} \approx 70.3636\][/tex]
Since [tex]\(m\)[/tex] must be an integer, the largest integer less than or equal to [tex]\(70.3636\)[/tex] is 70.
So, the largest number of the form [tex]\(11m + 6\)[/tex] less than or equal to 780 is [tex]\(11 \times 70 + 6 = 776\).[/tex]
Now, we need to find the intersection of the sets of numbers [tex]\([655, 774]\) and \([655, 776]\).[/tex]
This can be done by finding the range of overlap between these two sets.
The range of overlap is [tex]\([655, 774]\),[/tex] which contains 774 - 655 + 1 = 120 numbers.
So, there are 120 numbers between 650 and 780 that leave remainders of 4 when divided by 7 and remainders of 6 when divided by 11.
On a coordinate plane, solid circles appear at the following points: (negative 2, negative 5), (negative 1, 3), (1, negative 2), (3, 0), (4, negative 2), (4, 4). Which explains why the graph is not a function? It is not a function because the points are not connected to each other. It is not a function because the points are not related by a single equation. It is not a function because there are two different x-values for a single y-value. It is not a function because there are two different y-values for a single x-value.
Answer:
Last option: It is not a function because there are two different y-values for a single x-value.
Step-by-step explanation:
It is necessary to remember that, by definition, a relation is a function if each input value (x-value) has one and only one output value (x-value) .
In this case, the following points:
[tex](-2, -5), (- 1, 3), (1, -2), (3, 0), (4,- 2), (4, 4)[/tex]
You can observe that the input value 4 ([tex]x=4[/tex]) has two ouput values. These are:
[tex]y=-2\\\\ y=4[/tex]
Therefore, since there are two different y-values for a single x-value, you can conclude that the given graph is not a function.
Answer:
t represents time, which is the input of the function, so we know that 10 is the time in minutes. h(t) represents the altitude, which is the output of the function after time, t. So, we need to substitute 10 into 210 – 15t in place of t. Simplifying 210 – 15(10), we get that 60 is the altitude in feet. So, after 10 minutes, the hot air balloon is at 60 feet.
Step-by-step explanation:
(This is the answer form the assignment if it helps)
Simplify. 11-19i/8-5i
Good evening ,
______
Answer:
[tex]\frac{183-97i}{89}[/tex]
____________________
Step-by-step explanation:
(11-19i)/(8-5i)
=(11-19i)(8+5i)/(8-5i)(8+5i)
=(88+55i-152i+95)/(8²+5²)
=(183-97i)/89.
:)
(8x-11)-(15-x)=1 dont know where to start with it
Answer:
x = 3
Step-by-step explanation:
First open the brackets. While opening brackets, you've to be careful about signs. So when you open bracket of (15-x), there's negative sign in front of it, so it makes the signs inside the brackets to change. Then you solve the it.
Answer: x=3
Step-by-step explanation:Step 1: Simplify both sides of the equation.
(8x-11)-(15-x)=1
(8x-11)+-1(15-x)=1 (distribute the negative sign)
8x+-11+-15+x=1
8x+x+(-15+-11)=1 (combine like terms)
9x+-26=1
Step 2: Add 26 to both sides
9x-26+26=1+26
9x=27
Step 3: Divide both sides by 9.
9x/9=27/9
x=3
which equation could be used to create the graph?
Answers
A y=x -2
B y=x -4
C y= x/3
D y=3x
Answer:
C
Step-by-step explanation:
The equation of a line passing through the origin is
y = mx ( m is the slope )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (9, 3) ← 2 points on the line
m = [tex]\frac{3-0}{9-0}[/tex] = [tex]\frac{3}{9}[/tex] = [tex]\frac{1}{3}[/tex], thus
y = [tex]\frac{1}{3}[/tex] x
Or
y = [tex]\frac{x}{3}[/tex] → C
Answer:
C
Step-by-step explanation:
The equation of a line passing through the origin is
y = mx ( m is the slope )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (9, 3) ← 2 points on the line
m = \frac{3-0}{9-0} = \frac{3}{9} = \frac{1}{3}, thus
y = \frac{1}{3} x
Or
y = \frac{x}{3} → C
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Evaluate the expression below
4 - 2 2x2 + 3
Is my answer right
Answer:
3
Step-by-step explanation:
first mulitply 2×2 then add 3 it equals in total 7. then subtract 7-4 and your final answer is 3.