Answer:
81 and -31
Step-by-step explanation:
x + (x - 112) = 50
2x - 112 = 50
2x = 162
x = 81
the other number is x-112 = 81 - 112 = -31
Final answer:
To find the two numbers, set up a system of equations based on the given information. Solve the system of equations to find the values of the two numbers, which are -31 and 81.
Explanation:
To find the two numbers, we can set up a system of equations based on the given information.
Let's assume one number is x, and the other number is y.
According to the problem, the sum of the two numbers is 50, so we can write the equation:
x + y = 50
We are also told that one number is 112 less than the other, so we can write another equation:
x = y - 112
Now we can solve this system of equations to find the values of x and y.
Substituting the value of x from the second equation into the first equation, we have:
(y - 112) + y = 50
Combining like terms, we get: 2y - 112 = 50
Adding 112 to both sides of the equation, we have: 2y = 162
Dividing both sides by 2, we get: y = 81
Substituting this value of y into the second equation, we have: x = 81 - 112
Simplifying, we get: x = -31
Therefore, the two numbers are -31 and 81.
Find the product of (x − 7)^2. Basically Simplify It
Answer:
(x - 7)² = x² - 14x + 49Step-by-step explanation:
[tex]\bold{METHOD\ 1:}\\\\\text{Use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-7)^2=x^2-2(x)(7)+7^2=x^2-14x+49\\\\\bold{METHOD\ 2:}\\\\\text{We know:}\ a^2=a\cdot a\\\\(x-7)^2=(x-7)(x-7)\\\\\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(x)(x)+(x)(-7)+(-7)(x)+(-7)(-7)\\\\=x^2-7x-7x+49\qquad\text{combine like terms}\\\\=x^2-14x+49[/tex]
Which describes the combined variation shown in the equation F= kxy/z ?
Answer:
First question is D: F varies directly with x and y, and inversely with z.
Second Question is B Y=kx^3/sq root z
Edge Verified
Answer:
part 1 = d
part 2= b
Step-by-step explanation:
I just got it right on edg
Solve the equation 24+0.44x=19+1.69x
Answer: X= 4
Step-by-step explanation:
24+0.44x=19+1.69x exp equation like:
24+44x/100=19+169x/100
Multiply left and right side of equation with 100
2400+44x=1900+169x
2400-1900=169x-44x
500=125x
x=500/125
x=4
The solution of the equation is 4.
To solve the equation 24+0.44x=19+1.69x, we want to collect like terms and isolate the variable x on one side. This type of equation is a linear equation, not a quadratic equation, since the highest power of x is one. First, let's move the terms containing x to one side and the constant terms to the other side:
Subtract 1.69x from both sides: 24 - 19 = 1.69x - 0.44x
Combine like terms: 5 = 1.25x
Divide both sides by 1.25: x = 5 / 1.25
Solving for x gives us: x = 4
A bakery makes 40 different flavors of muffins. 25% of the flavors have chocolate as one of the ingredients. Draw a tape to show how many flavors have chocolate and how many don't?
Answer:
10
Step-by-step explanation:
A bakery makes 40 different flavors of muffins.
25% of the flavors have chocolate as one of the ingredients.
Convert 25% to fraction:
[tex]25\%=\dfrac{25}{100}=\dfrac{1}{4}[/tex]
So, there are
[tex]40\cdot \dfrac{1}{4}=10[/tex]
muffins which have chocolate as one of the ingredients.
In attached tape diagram:
green - with chocolate
blue - without chocolate
Answer:
10 flavors with chocolate.30 flavors without chocolate.Step-by-step explanation:
The total number of flavors is 40.
25% of the flavors have chocolate.
To find the number of flavors which have chocolate, we just need to multiply 0.25 by 40, because 0.25 represents 25%
[tex]0.25(40)=10[/tex]
So, there are 10 flavors with chocolate.
Now, if 25% represents flavors with chocolate, then 75% represents flavors without chocolate
[tex]0.75(40)=30[/tex]
So, there are 30 flavors without chocolate.
Draw the image of the figure with the given vertices under a dilation with the given scale factor centered at the origin j(-2,2), K(4,2), L(4,-2), M(-2,-2); Scale factor: 1/2
To create the image of a figure under a dilation with a scale factor of 1/2 centered at the origin, multiply each vertex coordinate by 1/2. The new coordinates for vertices j, k, l, and m would be j'(-1, 1), k'(2, 1), l'(2, -1), and m'(-1, -1), respectively.
Explanation:The student is asking for the image of a figure after performing a dilation with a scale factor centered at the origin. To perform this dilation, you need to multiply the coordinates of each vertex by the scale factor. For a scale factor of 1/2, each coordinate of the vertices is halved. Therefore, the new vertices after the dilation will be:
j'(-2 \\times 1/2, 2 \\times 1/2) = j'(-1, 1)k'(4 \\times 1/2, 2 \\times 1/2) = k'(2, 1)l'(4 \\times 1/2, -2 \\times 1/2) = l'(2, -1)m'(-2 \\times 1/2, -2 \\times 1/2) = m'(-1, -1)These new vertices j', k', l', and m' will give you the dilated figure.
Dylan opened a credit card account with $750.00 of available credit. Now that he has made some purchases, Dylan's account only has $412.50 of available credit. What is the percentage decrease of the amount of available credit in Dylan's account?
Answer:
45%
Step-by-step explanation:
The formula to work out the decrease is:
Percentage Decrease= actual decrease / original amount X 100%
1) So firstly, we have to work out the decrease, to do this we have to do is do $750-$412.50= $337.50
2) We can now substitute this into our formula which will now be. (We will also add the original amount, which is $750.00)
Percentage Decrease= 337.50 / 750.00 X 100% = 45
The percentage decrease is 45%
A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 30 books. There were 4 times as many large boxes sent as small boxes, which altogether can hold 280 books. Write a system of equations that could be used to determine the number of small boxes sent and the number of large boxes sent. Define the variables that you use to write the system.
Answer:
20*s+30*l = 280
4*s=l
Step-by-step explanation:
Let's say that the number of small boxes is s and the number of large boxes is l. Then, 20*s equals the amount of books in small boxes (as there are 20 books per small box), and 30*l for the amount of books in large boxes. Then, we know that 4 times the amount of small boxes, s, equals l, so 4*s=l. Then, as we know that the amount of books that can be held is 280, we can add the amount of books for each type of box, or 20*s+30*l, to get 280. Our equations are as follows:
20*s+30*l = 280
4*s=l
As we can define l in terms of s, making it so that we can limit the top equation to 1 variable, we can use this to determine the number of each type of box
Which description best fits the distribution of
the data shown in the histogram?
A)skewed left
B)skewed right
C)uniform
D)approximately bell-shaped
Answer:
D) approximately bell-shaped
Step-by-step explanation:
a bell-shaped histogram is where you can draw a vertical line to the top of the histogram (in this case to the blue line at frequency 12) and a "mirror" line going back down (1 (200-249) ) where the bell-shape can make the shape going through all the lines of the histogram.
I hope I explained that well, and I hope that helps!
Sam bought a computer game that costs 15% more than a printer cartridge. The computer game costs $40. Write an equation that can be used to find c, the cost in dollars, of the printer cartridge. Then, find the cost of the printer cartridge. Equation: ____________ Solution: $_______________
Equation: 1.15 c = 40
Solution: $34.78
Step-by-step explanation:
The given is:
Sam bought a computer game that costs 15% more than a printer cartridgec is the cost in dollars, of the printer cartridgeWe need to write an equation that can be used to find c, and then
find the value of c
∵ The cost of the printer cartage = $c
∵ The computer game costs 15% more than a printer cartridge
- That means add the cost of the cartage by 15% of it to find the
cost of the computer game
∴ The cost of the computer game = c + 15% × c
∵ 15% = 15 ÷ 100 = 0.15
∴ The cost of the computer game = c + 0.15 c
- The two terms of c (1 + 0.15)
∴ The cost of the computer game = $1.15 c
∵ The cost of the computer game = $40
- Equate the two expressions of the cost of the game
∴ 1.15 c = 40
The equation that can be used to find c is 1.15 c = 40
Solve the equation to find c
∵ 1.15 c = 40
- Divide both sides by 1.15
∴ c = $34.78
The cost of the printer cartridge is $34.78
Equation: 1.15 c = 40
Solution: $34.78
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Given that n is an integer and that n>1, prove algebraically that n²-(n-2)²-2 is always an even number
Answer:
see explanation
Step-by-step explanation:
Any integer n > 1 multiplied by 2 will be even, that is
2n ← is even
Given
n² - (n - 2)² - 2 ← expand parenthesis
= n² - (n² - 4n + 4) - 2
= n² - n² + 4n - 4 - 2 ← collect like terms
= 4n - 6 ← factor out 2 from each term
= 2(2n - 3)
Hence 2(2n - 3) ← will always be even for n > 1
The statement can be proved by parenthesis that the expression [tex]n^{2} - (n - 2)^{2} - 2[/tex] is always an even number.
What is the process of expanding the polynomial and check whether it is a even number ?= [tex]n^{2} - (n - 2)^{2} - 2[/tex]
= [tex]n^{2} - (n^{2} - 4n + 4) - 2[/tex]
= [tex]4n - 4 - 2[/tex]
= [tex]4n - 6[/tex]
= [tex]2(2n - 3)[/tex]
As the expression 2(2n - 3) is always a multiple of 2 and also it is given that n>1 therefore by the parenthesis, the expression [tex]n^{2} - (n - 2)^{2} - 2[/tex] is always an even number.
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Mr. Hanson wants to have enough pencils for each student to have 36 pencils at the beginning of the year , a pencil for each week of the school year. If Mr. Hanson has 32 students on his roll this year, How many pencils does he need to purchase?
Answer:
1152? 36÷32=1152 I think?
Mr. Hanson needs to multiply the number of students (32) by the number of pencils required per student (36) to find out he needs to purchase a total of 1152 pencils for the school year.
Mr. Hanson needs to calculate the total number of pencils required for his class for the entire school year. With 32 students and the need for each student to have 36 pencils, the calculation is straightforward:
Multiply the number of students by the number of pencils each student requires.
32 students imes 36 pencils per student = 1152 pencils.
Therefore, Mr. Hanson needs to purchase 1152 pencils in total.
By having this quantity of pencils, Mr. Hanson ensures that each student has a pencil for each week of the school year, contributing to a well-prepared classroom environment.
Need help with this math problem
Answer:
So the value of u is [tex]24[/tex] degree.
Step-by-step explanation:
Given;
Three angle [tex]2u[/tex] , [tex](u+18)[/tex] degree and [tex]90[/tex] degree in a Triangle.
We know;
Addition of three angle in a triangle is equal [tex]180[/tex] degree
[tex]2u+u+18+90=180[/tex]
[tex]3u=180-90-18[/tex]
[tex]3u=72[/tex]
[tex]u=\frac{72}{3}[/tex]
[tex]u=24[/tex]
∴ The value of u is [tex]24[\tex] degree.
Solve each equation by completing the square
6) m² + 16m – 8 = 0
Answer:
m = - 8 ± 6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Given
m² + 16m - 8 = 0 ( add 8 to both sides )
m² + 16m = 8
To complete the square
add ( half the coefficient of the m- term )² to both sides
m² + 2(8)m + 64 = 8 + 64
(m + 8)² = 72 ( take the square root of both sides )
m + 8 = ± [tex]\sqrt{72}[/tex] = ± [tex]\sqrt{36(2)}[/tex] = ± 6[tex]\sqrt{2}[/tex]
Subtract 8 from both sides
m = - 8 ± 6[tex]\sqrt{2}[/tex]
Jina drove 240 miles using 9 gallons of gas.At this rate,how many gallons of gas would she need to drive 216 miles?
Answer:
8.1 gallons of gas
Step-by-step explanation:
240/9=216/x
simplify 240/9 into 80/3,
80/3=216/x
cross product
3*216=80*x
648=80x
x=648/80
x=8.1
i-Ready
Understand Categories of Shapes - Quiz --- Level
Which shape has right angles AND sides that are the same length?
Answer: Square
Step-by-step explanation: It has 4 equal sides that are all the same length.
The shape with four equal right angles and sides of the same length is a square, a fundamental concept in Euclidean geometry discussed in middle school mathematics.
The shape that has right angles and sides that are the same length is a square. In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or right angles). To identify a square, you can look for these two characteristics. .
The understanding of similar triangles is relevant when considering shapes and their properties, such as when using the properties of similarity to prove that two right triangles are similar based on their equal angles.
In isosceles triangle RST shown below, RS = RT,
Mand N are midpoints of RS and RT , respectively,
and MN is drawn. If MN = 3.5 and the perimeter
of RST is 25, determine and state the length of
NT.
The length of NT in isosceles triangle RST is 7.
Explanation:In an isosceles triangle, the base angles are congruent, and the sides opposite those angles are also congruent. Let's denote the length of RS (and RT) as r, and the length of MN as m Since M and N are midpoints, MN is parallel to the base, and its length is half the length of the base. Therefore, [tex]\( m = \frac{r}{2} \).[/tex]
The perimeter of the triangle is the sum of the three sides, so [tex]\( 2r + r = 25 \) (as RS = RT).[/tex] Solving for r, we get [tex]\( r = \frac{25}{3} \).[/tex]
Now, we know that [tex]\( m = \frac{r}{2} \),[/tex] so [tex]\( m = \frac{25}{6} \)[/tex]. Finally, the length of NT is the difference between RT and MN, which is [tex]\( \frac{25}{3} - \frac{25}{6} = 7 \).[/tex]Therefore, the length of NT is 7 units.
QUESTION:Consider isosceles triangle RST, where RS = RT. Let M and N be the midpoints of sides RS and RT, respectively. A segment MN is drawn with a length of 3.5 units. The perimeter of triangle RST is given as 25 units. Determine and state the length of NT.
Please provide a comprehensive solution to this problem, including step-by-step calculations and explanations.
Final answer:
By applying properties of isosceles triangles and the given conditions, we calculate that the length of segment NT is 4.5 units.
Explanation:
The subject matter is a geometrical problem involving an isosceles triangle with given conditions. In isosceles triangle RST, RS and RT are equal in length, M and N are the midpoints of RS and RT respectively, and MN is drawn with a length of 3.5 units. Given that the perimeter of the triangle is 25 units, we need to find the length of segment NT.
To solve this, we first understand that in an isosceles triangle, the perpendicular from the vertex to the base bisects the base. Therefore, segment MN cuts the base ST equally in two, making each half 3.5 units, since MN = 3.5 units. Furthermore, because M and N are midpoints, segments MS and NT are equal. Finally, by knowing the perimeter, we can deduce that RS + ST + RT equals 25 units.
Thus, we can derive the lengths of RS and RT (which are equal) and then use that information to calculate the length of NT. If RS = RT and we call that length x, then 2x + 2(3.5) = 25. Solving for x gives us x = (25 - 7)/2 = 9. Thus, segment NT as the half of either RS or RT is 9/2 = 4.5 units.
Enter the unknown value that makes this statement true.
20% of _______ is 120
Answer:
600
Step-by-step explanation:
20%=0.2
120/0.2=600
-7x+4y=-26
+7x – 4y = -2
Answer:
Its no Solution
Step-by-step explanation:
If you use elimination both 7x and the 4y will be 0 and you'll get
0=-26 and 0=-2
So
No Solution
sorry for my hand writing
the square root of a number is 2k. what is half of the number?
Answer:
2 milion
Step-by-step explanation:
2,000 x 2,000= 4,000,000
4,000,000÷ 2= 2,000,000
Half the number of square root of a number is 2k is [tex]2k^2[/tex].
Let's break down the problem step by step to find half of the number. We start with the given information: the square root of a number is [tex]2k[/tex]. Our goal is to find half of this number.
Let the number be [tex]x[/tex]. The problem tells us that the square root of [tex]x[/tex] is [tex]2k[/tex].
We write this mathematically as:
[tex]\sqrt{x} = 2k[/tex]
To find [tex]x[/tex], we square both sides of the equation to remove the square root:
[tex]x = (2k)^2[/tex]
Simplify the right side:
[tex]x = 4k^2[/tex]
Now, we need to find half of [tex]x[/tex]. Half of [tex]x[/tex] is:
[tex]\text{Half of } x = \frac{x}{2} = \frac{4k^2}{2}[/tex]
Simplify the fraction:
[tex]\frac{4k^2}{2} = 2k^2[/tex]
Logan and Sarah work at a dry cleaners ironing shirts. Logan can iron 40 shirts per hour, and Sarah can iron 35 shirts per hour. Logan and Sarah worked a combined 13 hours and ironed 490 shirts. Determine the number of hours Logan worked and the number of hours Sarah worked.
29 points! Simplify. So uh yeah thats it.
Answer:
27[tex]\frac{27}{4x^{6}y^{8} }[/tex]
Step-by-step explanation:
your going to raise the power on the numerator by 3 and the denominator 4 so you get [tex]\frac{4*27x^{6} y^{12} }{16x^{12}y^{20} }[/tex] then reduce and simplify
[tex]\rightsquigarrow[/tex] [tex]\bold{\dfrac{4(3x^2 y^4)^3}{(2x^3 y^5)^4} }[/tex]
[tex]\rightsquigarrow[/tex] [tex]\bold{\dfrac{4(3x^5 y^{12})}{2x^{12} y^{20}} }[/tex]
[tex]\rightsquigarrow[/tex] [tex]\bold{\dfrac{ 12x^5 y^{12}}{2x^{12} y^{20}} }[/tex]
[tex]\rightsquigarrow[/tex] [tex]\bold{ \dfrac{\cancel{12x^5 y^{12}}}{\cancel{2x^{12} y^{20}}}}[/tex]
[tex]\rightsquigarrow[/tex] [tex]\bold{\dfrac{6}{x^7 y^8} }[/tex]
..
(3x + 4)(2x - 5)
i don’t know how to use foil
Answer: 6x^2-9x-20
Step-by-step explanation:
(3x+4)(2x-5)
6x^2-15x+6x-20
6x^2-9x-20
the area of a rectangle wall of a barn is 320 square feet. it's length is12 feet longer than twice it's width. find the length and width of the wall of the barn.
Answer:
Length = 32 feet
Width = 10 feet
Step-by-step explanation:
The area of a rectangle = length (L) x width (W)
The relationship between the length and width is that
L = 12 + 2W -------------- (i)
therefore
Area = L x W can be rewritten as (12 + 2W) x W
320 = (12 + 2W) x W
320 = 12W + 2W^2
this can then be turned into a quadratic equation:
2W^2 + 12W - 320 = 0
Divide through by 2
W^2 + 6W - 160 = 0
W^2 - 10W + 16W - 160 = 0
W(W- 10) + 16(W- 10) = 0
(W- 10)(W + 16) = 0
hence W = -16 and 10
since width cannot be a negative value,
Width = 10
hence substituting for width = 10 into equation (i)
L = 12 + 2(10)
L = 12 +20 = 32
A number increased by negative eight is equal to fourteen. Which equation could be used to find the number? n + 8 = 14 n - (-8) = 14 n + (-8) = 14 8 - n = 14
im confused?
Answer:
n +(-8)=14
Step-by-step explanation:
a number is 'n'
is adding negative of 8
i. e. -8
is eaual to 14
then n=14+8
or; n =22
therefore the number is 22.
Calculate:
(−16)3 ÷ (4−2)−3
Need explanation!
Answer:
Factor the numerator and denominator and cancel the common factors.
−1
Answer:
it is -1 when all calculated
Step-by-step explanation:
Rewrite the radical expression as an expression with a rational exponent.
the cube root of five to the seventh power
A: x21
B: x4
C: five to the seven thirds power
D: five to the three sevenths power
Answer:
C.
Step-by-step explanation:
(∛5)^7
= (5 ^ 1/3)^7
= 5^(7/3)
The cube root of five to the seventh power can be rewritten as a rational exponent as five to the seven thirds power. This is achieved by making the denominator of the exponent the index of the radical and the numerator the power of the radicand.
Explanation:In mathematics, radical expressions can be rewritten as expressions with rational exponents. In your case, the cube root of five to the seventh power, is represented as [tex]5^(^7^/^3^)[/tex], which is your rational exponent form. So the answer is C: five to the seven thirds power.
To convert a radical expression to an expression with a rational exponent, the denominator of the exponent becomes the index of the radical, and the numerator of the exponent becomes the power of the radicand. In this case, the cube root is the index, which is 3, and the power of the radicand (five) is 7. Hence, five to the seven thirds power.
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simplify 8(p+7+2q) using the distributive property
Answer:
8p + 56 + 16q
Step-by-step explanation:
To distribute, we must multiply all numbers/terms inside the paranthesis by '8.'
So:
8(p) = 8p
8(7) = 56
8(2q) = 16q
So your expression would be 8p + 56 + 16q ^-^
Answer:
[tex]\rm{8p+56+16q[/tex]
Step-by-step explanation:
Hi there!
The Distributive Property states that
a(b+c)=ab+ac
Let's use this property to simplify our expression:
[tex]\rm{8(p+7+2q)[/tex]
[tex]\rm{8p+56+16q[/tex]
Thus, [tex]\rm{8p+56+16q[/tex] is our final answer.
[tex]\star\star[/tex]Hope it helps! Enjoy your day!
[tex]\bold{GazingAtTheStars(:}[/tex]
You earn $72 for every 8 hours you spend shoveling snow. You earn $60 for every 5 hours you spend babysitting. For every 3 hours you spend babysitting, you spend 2 hours shoveling snow. You babysit for 15 hours in January. How much money do you earn in January?
Answer:
$270.00
Step-by-step explanation:
The ratio of house of babysitting and house is 3:2. If you change the 3 into a 15, you would have to change the 2 into a 10 because 3 x 5 = 15, so 2 x 5 = 10.
After you do those calculations you divide 15 by 5 and that is 3. You then multiply 60 by 3 = 180.
After that you have to divide 10 by 8 and you get 1.25. You then multiply 72 by 1.25 = 90.
Then you add 180 and 90 together to get $270.00
HELP ME 30 points and Brainliest.
The area of a rooftop can be expressed as 9x^2+6x+1. The rooftop is a quadrilateral.
Part A. What type of quadrilateral is the rooftop? Justify your answer.
Part B. If the area of the rooftop is 361 m^2, what is the length of one side of the rooftop?
Part A: The type of the quadrilateral of the rooftop is a square
Part B: The length of one side of the rooftop is 19 m
Step-by-step explanation:
Let us revise some notes about quadratic expression
(a + b)² = a² + 2ab + b², where a² + 2ab + b² is a perfect square trinomial because it gives square binomial (a + b)²Area of a square can be represented by perfect square trinomial, where the side of the square represented by the binomialThe area of a rooftop can be expressed as 9x² + 6x +1
The rooftop is a quadrilateral
We need to find the type of the quadrilateral and the length of
one side of the rooftop
∵ The area of the rooftop = 9x² + 6x +1
- Check if 9x² + 6x +1 is a perfect trinomial
∵ [tex]\sqrt{9x^{2}}=3x[/tex]
∵ [tex]\sqrt{1}=1[/tex]
∵ [tex](3x)(1)(2)=6x[/tex]
∴ 9x² + 6x +1 = (3x + 1)²
∴ 9x² + 6x +1 is a perfect square trinomial
∵ Perfect square trinomial can represent the area of a square
∴ The quadrilateral is a square
Part A: The type of the quadrilateral of the rooftop is a square
∵ The area of the rooftop is 9x² + 6x +1
∵ 9x² + 6x +1 = (3x + 1)²
∵ Area of the rooftop = 361 m²
∴ (3x + 1)² = 361
- Take square root for both sides
∴ 3x + 1 = 19
∵ The area of a square = (side)²
∵ The area of a square = (3x + 1)²
∴ 3x + 1 is the length of the side of the square
∵ 3x + 1 = 19
∴ The length of the side of the square is 19 m
Part B: The length of one side of the rooftop is 19 m
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