Y = -27x + 577, where x represents the number of weeks and y represents the amount of money left in her account. After how many weeks will Alma have $145 left in her account?
What is the 100th term in the following arithmetic number pattern: 2,7,12
Mason deposited $763.21 in a savings account that earns 1.7% simple interest. What is Mason's account balance after nine years?
16 pound turkey cost $14.24 what is the price per pound
40 students are going on a field trip to the aquarium. Every student needs to be in a group, and all groups must have the same number of students. If there is 1 group, there will be students in the group. If there are groups, there will be 20 students in each group. If there are 4 groups, there will be students in each group.
If there is 1 group there will be 40 students in the group. There will be 20 students in each group if there are 2 groups. If there are 4 groups, there will be 10 students in each group.
What is Division?Division is one of the four basic operations of mathematics.
On performing the operation division, a number is divided into some number of equal parts.
The number which is being divided is called the dividend, the number which divides the dividend is called divisor and the number got when division is performed is called the quotient and the remaining number which has not divided is called the remainder.
Total number of students = 40
If there is 1 group, number of students in the group = 40/1 = 40
If there are 20 students in each group, then the number of groups = 40/20 = 2.
If there are 4 groups, then number of students in each group = 40/4 = 10.
Hence there will be 40 students in the group if there is 1 group. There are 2 groups if there will be 20 students in each group. There will be 10 students in each group if there are 4 groups.
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The sum of the first and third of three consecutive even integers is 128. find the three even integers.
Final answer:
The three even integers are 62, 64, and 66.
Explanation:
The sum of the first and third of three consecutive even integers is 128. To find the three even integers, we start by letting the first integer be x. Because the integers are consecutive even numbers, the second integer will be x + 2 and the third will be x + 4. The sum of the first and third integers gives us the equation:
x + (x + 4) = 128
Solving this equation:
Combine like terms: 2x + 4 = 128.
Subtract 4 from both sides: 2x = 124.
Divide both sides by 2: x = 62.
So, the first even integer is 62. Consequently, the second is 62 + 2 = 64, and the third is 62 + 4 = 66. Therefore, the three consecutive even integers are 62, 64, and 66.
Solve for c. a(b − c)=d
Is 0 prime odd or even prime or composite?
Answer:
0 is nor prime or composite
Step-by-step explanation:
The definition of a prime number is a positive integer that has exactly two positive divisors. Therefore, the simplest reason why 0 is not prime is that 0 is not a positive integer, and the axiom says that all whole numbers greater than 1 are either prime or composite.
Solve the following problem for the roots by completing the square
3x^2 -12x = 9
An exhibit at Tabu World Square in Japan includes a scale model of the Empire State Building. The model was built using a scale of 1 m : 25 m. The height of the actual Empire State Building is 443.2 meters. What is the height of the model? Round your answer to the nearest thousanths place.
If you only have a 1/3 measuring cup and a recipe calls for 8 2/3 cups of flour, how many 1/3 cups would you need to use?
Graph the image of the given triangle after the transformation with the rule (x, y)→(y, x) .
A kennel owner needs 4 1/2 feet of wall space for each crate. How many crates can she fit along a 27 foot wall?
Add the following military times: 0645 + 0745
Express the volume v of the box as a function of the length x of the sidfe of the square cut from each corner
Long Division for a quadratic polynomial and binomial, please show your work!
Quadratic polynomial: x^2-x-6=f(x)
Binomial: (x-3)
[tex]\(x^2 - x - 6\)[/tex] can be expressed as the product of [tex]\((x - 3)\) and \((x - 2)\)[/tex]. The long division image is given below.
Long division for polynomials is similar to long division for numbers. We'll divide the quadratic polynomial [tex]\(f(x) = x^2 - x - 6\)[/tex] by the binomial [tex]\((x - 3)\)[/tex].
Here's a step-by-step breakdown of the process:
1. Start by dividing the highest-degree term of the dividend (in this case, [tex]\(x^2\)[/tex]) by the highest-degree term of the divisor (in this case, [tex]\(x\))[/tex]. This gives us [tex]\(x\)[/tex].
2. Multiply the divisor [tex]\((x - 3)\)[/tex] by the result from step 1, which is [tex]\(x\),[/tex] and write the result below the dividend, aligning like terms. So, [tex]\(x \cdot (x - 3) = x^2 - 3x\)[/tex].
3. Subtract the result from step [tex]2 (\(x^2 - 3x\))[/tex] from the dividend ([tex]\(x^2 - x - 6\)[/tex]). This gives us [tex]\(x^2 - x - 6 - (x^2 - 3x)\)[/tex], which simplifies to [tex]\(-x + 3x - 6\),[/tex] resulting in [tex]\(2x - 6\)[/tex].
4. Now, we repeat the process with the new expression [tex]\(2x - 6\)[/tex]. We divide the highest-degree term ([tex]\(2x\)[/tex]) by the highest-degree term of the divisor [tex](\(x\)),[/tex] which gives us [tex]\(2\).[/tex]
5. Multiply the divisor [tex]\((x - 3)\)[/tex] by the result from step 4, which is [tex]\(2\)[/tex], and write the result below the previous result: [tex]\(2 \cdot (x - 3) = 2x - 6\)[/tex].
6. Subtract the result from step [tex]5 (\(2x - 6\))[/tex] from the previous expression [tex](\(2x - 6\))[/tex], which results in [tex]\(0\)[/tex].
Since we have a remainder of [tex]\(0\),[/tex] this means that [tex]\(x^2 - x - 6\)[/tex] is evenly divisible by [tex]\((x - 3)\)[/tex], and the quotient is [tex]\(x - 2\).[/tex] The final result is:
[tex]\[ \frac{x^2 - x - 6}{x - 3} = x - 2 \][/tex]
This tells us that [tex]\(x^2 - x - 6\)[/tex] can be expressed as the product of [tex]\((x - 3)\) and \((x - 2)\)[/tex].
Find f(x) and g(x) so the function can be expressed as y=f (g (x)).
y=2/x^2 +3
Can someone help me with these maths questions? I totally don't get them.
Do the following coordinates lie on the following graphs?
1) y=2x+4 (7,20)
2) y=4x-14 (-1,-18)
3) y=5x-1 (0.5,2.5)
4) y=-2x+6 (0.8,5.4)
[tex] 5) y=\frac{1}{2}x+2 (0.7,1.6) [/tex]
1. 2(7) +4 = 18, does not = 20, does not lie on graph
2. 4(-1) -14 = -18, equals -18, does lie on the graph
3. 5(.5)-1 = 1.5, does not = 2.5, does not lie on the graph
4. -2(0.8)+6 = 4.4, does not = 5.4 does not lie on graph
5. 1/2(0.7) +2 = 2.35, does not = 1.6, does not lie on graph
Four times the difference of a number and seven is 32
I NEED HELP ASAP
Definition: This is an expression that includes monomials, binomials and more. There is no limit to the number of terms.
Example: 2x+ 3y+ 4xy+ 5xyz What is the term?
What is the area of a circle with a radius of 14 feet? use 22/7 for π?
PLEASE HELP?!
Both trapezoids are similar. The area of the larger trapezoid is 61 ft2. Which is the best approximation for the area of the smaller trapezoid?
39 ft2
34 ft2
49 ft2
44 ft2
The best approximation for the area of the smaller trapezoid is 39 [tex]ft^2[/tex].
Since the trapezoids are similar, the ratio of their corresponding side lengths is constant. We know the base of the larger trapezoid is 30 ft and the smaller one is 24 ft. Therefore, the ratio of their bases is:
ratio of bases = [tex]\frac{30 ft}{24 ft}[/tex] = [tex]\frac{5}{4}[/tex]
The area of a trapezoid is given by:
Area = [tex]\frac{1}{2}[/tex] * base * height
For similar shapes, the ratio of their areas is proportional to the square of the ratio of their corresponding side lengths. In this case, the ratio of areas will be:
Ratio of areas = [tex](Ratio \ {of \ { bases)^2[/tex] = [tex]({\frac{5}{4} })^2[/tex] = [tex]\frac{25}{16}[/tex]
We know the area of the larger trapezoid is 61 [tex]ft^2[/tex]. Applying the ratio of areas:
Area of smaller trapezoid = (61 [tex]ft^2[/tex]) * [tex]\frac{16}{25}[/tex]
Area of smaller trapezoid ≈ 38.91 [tex]ft^2[/tex] ≈ 39[tex]ft^2[/tex]
How do I do these only need to do 1 I just need to see how to do it!
Lets do the first one(7). Fist change 10x -2y = 3,which is in standard form to point slope form so you can see the slope.
10x - 2y = 3
-2y = -10x + 3
-2y/-2 = -10x / -2 + 3/-2
y = 5x - 3/2
The slope is the m in y = mx + b so our slope is 5x, well it wants you to find the equation of a line that passes through (0,1) that is parallel to the equation this (Parallel) mean has the same slope.The slope is 5. Now that we know the slope is 5 we can find the equation by using the point slope form of an equation of a line.
point slope form = y – y1 = m(x – x1)
Remember m = slope = 5. Now plugin our x and y cord from the point (0,1) and our slope of 5
y - y1 = m(x - x1)
y - 1 = 5(x - 0)
y - 1 = 5x - 0
y - 1+1 = 5x + 1
y= 5x + 1
So the point (0,1) passes through y = 5x + 1
Number 8 is already in slope intercept form so you don't have to do anything to find the slope. You can see that the slope is 7 so just plug your point into y - y1 = m(x - x1) and then put it into slope intercept form.
8)
Point = (5,8)
Slope = 7
y - y1 = m(x - x1)
y - 8 = 7(x - 5)
y = 7x - 27
So for number 8 the point (5,8) passes through y = 7x - 27
(9) For nine they want an equation that is perpendicular, which means to flip the slope. For instance, if you have a slope of 2/5 the perpendicular slope would be 5/2. For 9 we see that the slope is 2/5 so its perpendicular slope would be 5/2. Now just plug your point into the point slope form equation.
Point = (-4, 6)
Slope = 2/5
perpendicular slope = 5/2
y - 6 = 5/2(x - (-4))
y = 5/2 x + 16
So point (-4, 6) passes through y = 5/2 x + 16
(10) Point (4,1) passes through y = 7/5 x - 23/5
Amber has 4/5-pound bag of colored sand. She uses 1/2 of the bag for the project. How much sand does she use for the project?
Answer:
[tex]\frac{2}{5}[/tex]-pound of sand
Step-by-step explanation:
We have been given that Amber has [tex]\frac{4}{5}[/tex]-pound bag of colored sand. She uses 1/2 of the bag for the project.
We need to find 1/2 'of' the 4/5 as:
[tex]\frac{4}{5}\times \frac{1}{2}[/tex]
[tex]\frac{4\times1}{5\times2}[/tex]
[tex]\frac{2\times1}{5\times1}[/tex]
[tex]\frac{2}{5}[/tex]
Therefore, Amber used [tex]\frac{2}{5}[/tex]-pound of sand for the project.
Explain why the following statement are equivalent 4(x+y)=4x+4y
The equation 4(x+y)=4x+4y represents the same value after solving.
What is Distributive Property?This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.
Given:
We have 4(x+y)=4x+4y.
We have the Distributive Property
a x ( b+ c )= a x b + a x c
let x= 2 and y = 5
So, 4 (x+ y) = 4 (2+ 5)= 4(7) = 28
and, 4x+ 4y= 4(2)+ 4(5) = 8+ 20 = 28
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Do you know the answer to this question
The perimeter of a rectangle is 44 inches, and its area is 105 square inches. find the length and width of the rectangle.
How do you solve this ?
width = w
length = w+8
perimieter = 256 feet
formla for perimeter is p=2L+2w
so you have: 256 =2(w+8) +2w =
256 = 2w+16 +2w
256= 4w+16
240=4w
w=240/4 = 60
width is 60 feet
length = 60+8 = 68 feet
How to draw a grid of area of 12 square centimeters and a perimeter of 16 centimeters?
Two thirds of a number is no more than -10