Answer:
X= -9/10
y= -2 3/5
Step-by-step explanation:
Multiply equation one by 4 and equation two by 3 to eliminate X
it becomes
-12x + 8y =-12
12x - 3y = -1
add equation one and two,
you'll be left with 5y= -13
divide both sides by 5
y = -13/5 improper fraction
= -2 3/5
Now substitut y = -2 3/5 into any of the original equations to get x.
using equation two, we have
4x -(-2 3/5) = -1
4x + 2 3/5 = -1
4x = -1 - 2 3/5
the LCM of 5 is 5 , so
4x = -5-13/5
4x = -18/5
crossmultiply
4x x 5 = -18
20x = -18
divide both sides by 20
we have x = -18/20, when you cancel further , you have x = -9/10
PLEASEEEE HELPPP MEEE!!!! (15 PTS!)
can you use the commutative property for 12x²-3x+5 and x³-2x²+7 or not?? that's all i wanna know! =(
Answer:
332324
Step-by-step explanation:
b4hbf3hkrbf;h3bfh3bfc;khjbr3fkhbn;vb 4;khvcj3nc
What is the answer to 2(4x-3)-8= 4+2x
Answer:
The answer to the given equation is x=3
Step-by-step explanation:
Given equation is 2(4x-3)-8=4+2x
To find the answer for the given equation :
2(4x-3)-8=4+2x
Using the distributive property a(x+y)=ax+ay
2(4x)+2(-3)-8=4+2x
8x-6-8=4+2x
8x-14=4+2x
Subtracting (4+2x) on both sides we get
8x-14-(4+2x)=4+2x-(4+2x)
8x-14-4-2x=4+2x-4-2x ( by distributive property )
8x-2x-14-4=4-4-2x+2x ( combinig like terms on both sides)
6x-18=0
6x=8
[tex]x=\frac{18}{6}[/tex]
Therefore x=3
Therefore the answer to the given equation is x=3
What is the area of a square with a perimeter of 12 feet?
Will mark brainliest and 10 points
Answer:
Student 3
Step-by-step explanation:
Part of the 3-4-5 Pythagorean triples.
which ordered pair is the solution to the system of linear equations -5x+y=26 and 2x-7y=16
A.(-4 6)
B.(6 -4)
C. (-4 -6)
D (-6 -4)
Answer:
D(-6,-4)
Step-by-step explanation:
-5x + y = 26
2x - 7y = 16
-5x/-5 = 26-y/-5
x = -26/5 + y/5
2(-26/5 + y/5) = 7y = 16
-52/5 + 2y/5 = 16 + 52/5
-33y/5 = 80/5 + 52/5
-33y/5 = 132/5
-33y = 132
y = -4
2x - 7(-4) = 16
2x + 28 = 16
2x = -12
x = -6
Awodden doll of height 8cm is made of with a pyramid of slant height 5cm on its upper part and a prism of base 6×6 on its lower part. if all the faces of the doll is painted at the rate of Rain 200 per cm^2, what will be the total cost? Find it.
Answer:
Total cost of painting the pyramid including the base = 19,200
Total cost of painting the pyramid excluding the base = 12,000
Step-by-step explanation:
Data provided in the question:
Height of the doll = 8 cm
Slant height of the pyramid, s = 5 cm
Base dimensions = 6 × 6
Cost of painting = 200 per cm²
Now,
Area of the base = 6 × 6 = 36 cm²
Area of the Pyramid = Area of the base + [tex]\frac{1}{2} \times P\times s[/tex]
here,
P is the perimeter of the base = 4 × side
= 4 × 6
= 24 cm
Thus,
Area of the Pyramid = 36 + [tex]\frac{1}{2} \times24\times 5[/tex]
or
Area of the Pyramid = 36 + 60 = 96 cm²
Total cost of painting the pyramid including the base = 96 cm² × 200
= 19,200
Total cost of painting the pyramid excluding the base = 60 cm² × 200
= 12,000
Hardy is packing his book collection into a box. Each book measures 4inches by 6 inches by 1 inch. The box he uses measures 24 in by 24in by 8in.
If Hardy fills the box completely, what is the greatest number of books that fit into the box?
If Hardy fills the box completely with the least number of layers, there will be (blank) books on the bottom layer.
To fill the box completely, Hardy places 8 layers of books in the box. There are (blank) books in each layer.
Thank you in advance for the help! Just a mom who hates math trying to help her kid with volume.
Answer:
1. 192 books.
2. 96 books.
3. 24 books.
Step-by-step explanation:
1. Let's find the volume of each book and the volume of the box, this way:
Volume of a book = 4 * 6 * 1 = 24 inches ³
Volume of the box = 24 * 24 * 8 = 4,608 inches ³
2. If Hardy fills the box completely, what is the greatest number of books that fit into the box?
Greatest number of books = Volume of the box/Volume of a book
Greatest number of books = 4,608/24
Greatest number of books = 192
3. If Hardy fills the box completely with the least number of layers, there will be (blank) books on the bottom layer.
The height of the box is 8 inches, so it can only can hold 2 or 8 layers of books, since the books are 4 * 6 * 1 inches.
Greatest number of layers = Height of the box/Width of a book
Greatest number of layers = 8/1 = 8
Minimum number of layers = Height of the box/Height of a book
Minimum number of layers = 8/4 = 2
Upon saying that, we have:
Number of books per layer = Greatest number of books/Minimum number of layers
Number of books per layer = 192/2 = 96
4. To fill the box completely, Hardy places 8 layers of books in the box. There are (blank) books in each layer.
Number of books per layer = Greatest number of books/Number of layers
Number of books per layer = 192/8
Number of books per layer = 24
Note: Same answer to question 14559894, answered by me today.
Final answer:
The greatest number of books Hardy can fit into the box is 192. With the least number of layers and the box completely filled, there would be 24 books on the bottom layer. And if there are 8 layers of books in the box, there would be 24 books in each layer.
Explanation:
Hardy is packing books into a box and wants to maximize the number of books while also considering different arrangements. The dimensions of each book are 4 inches by 6 inches by 1 inch, and the dimensions of the box are 24 inches by 24 inches by 8 inches. The volume of a book is 4in x 6in x 1in = 24in³, and the volume of the box is 24in x 24in x 8in = 4,608in³. Therefore, the greatest number of books that fit into the box is the volume of the box divided by the volume of one book, which gives us 4,608in³ / 24in³ = 192 books.
If Hardy fills the box completely with the least number of layers, he would place the books so that the largest book dimensions are aligned with the box's. This means laying the books down in layers where each layer measures 24in by 24in. Since each book has a 6-inch side, we can fit four books along the width of the box (24in / 6in = 4 books), and similarly, we can fit six books along the length of the box (24in / 4in = 6 books), resulting in 4 x 6 = 24 books on the bottom layer.
If Hardy fills the box completely with 8 layers of books, he is dividing the height of the box by the height of a book (8in / 1in = 8 layers). In this case, since there are 24 books per layer (as calculated previously), and there are 8 layers, it means there are still 24 books in each layer.
Fin find the slope of the line passing through the points (-2, -7) and (9, -7)
Answer:
The slope of the line passing through the given points (-2,-7) and (9,-7) is m=0
Step-by-step explanation:
Given that the line passing through the points (-2,-7) and (9,-7)
To find the slope of the line passing through the points :
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] be the given points (-2,-7) and (9,-7) respectively
Substitute the points in the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-7-(-7)}{9-(-2)}[/tex]
[tex]=\frac{-7+7}{9+2}[/tex]
[tex]=\frac{0}{11}[/tex]
Therefore m=0
Therefore Slope m is 0
Therefore the slope of the line passing through the given points (-2,-7) and (9,-7) is m=0
Drag the amounts to order them from greatest to least.
1 in. = 2.54 cm
1 ft = 12 in.
A 20 in.
B 1.8 in.
C 56 cm.
Answer:
answer is c i did the test
Step-by-step explanation:
Find the difference
83456 - 728.88
Final answer:
To find the difference between 83456 and 728.88, subtract the second number from the first, resulting in the answer 82727.12.
Explanation:
To find the difference between the two numbers 83456 and 728.88, we simply subtract the second number from the first:
Write the numbers in a vertical column, aligning the digits by place value.
Perform the subtraction, starting from the rightmost digits (the ones place) and moving to the left, borrowing as needed.
Subtract each digit in the smaller number from the corresponding digit in the larger number.
83456
- 728.88
_______
82727.12
The difference is 82727.12.
Consider the following system of equations and their graph as picture
Answer:
(-2,5) and (7,23)
Step-by-step explanation:
we have
[tex]y=x^{2} -3x-5[/tex] ---> equation A
[tex]y=2x+9[/tex] ---> equation B
Solve the system by graphing
Remember that the solution of the system is the intersection point both graphs
Using a graphing tool
The intersection points are (-2,5) and (7,23)
see the attached figure
therefore
The solutions are (-2,5) and (7,23)
The solution points are [tex](-2,5)[/tex] and [tex](7,23)[/tex].
It is given equations are,
[tex]y=x^2-3x-5[/tex][tex]y=2x+9[/tex]Explanation:
From the given graph it is clear that the curve and line intersect each other at two points. These points are the solutions for the given system of equations.
The graph of line and curve intersect each other at [tex](-2,5)[/tex] and [tex](7,23)[/tex].
Thus, the solution points are [tex](-2,5)[/tex] and [tex](7,23)[/tex].
Learn more:
https://brainly.com/question/14300335
Ramesh bought 63 oranges for RM34.65. The oranges were packed in small packets with 3 oranges in each packet. Calculate the price Ramesh sold for each packet of oranges if he had made a profit of RM51.45 after he sold all the oranges.
Answer:
He sold a packet for RM4.1
Step-by-step explanation:
number of Oranges = 63
Bought Oranges for. = RM 34.65
Number of packets. = 63/3
= 21
profit. = RM 51.45
the value that he sold a packet =
[tex] \frac{34.65 + 51.45}{21} = \frac{86.1}{21} = rm4.1[/tex]
ating a Line with a Positive Slope
A line passes through the point (0, –1) and has a positive slope. Which of these points could that line pass through? Check all that apply.
(12, 3)
(–2, –5)
(–3, 1)
(1, 15)
(5, –2)
Answer:
The points (12,3), (-2,-5) and (1,15) through which the line can pass.
Step-by-step explanation:
A line passes through the point (0, –1) and has a positive slope.
(i) The slope of the line passing through the points (0,-1) and (12,3) will be
[tex]\frac{- 1 - 3}{0 - 12} = \frac{1}{3} > 0[/tex]
(ii) The slope of the line passing through the points (0,-1) and (-2,-5) will be
[tex]\frac{- 1 + 5}{0 + 2} = 2 > 0[/tex]
(iii) The slope of the line passing through the points (0,-1) and (- 3,1) will be
[tex]\frac{- 1 - 1}{0 + 3} = - \frac{2}{3} < 0[/tex]
(iv) The slope of the line passing through the points (0,-1) and (1,15) will be
[tex]\frac{- 1 - 15}{0 - 1} = 16 > 0[/tex]
(v) The slope of the line passing through the points (0,-1) and (5,-2) will be
[tex]\frac{- 1 + 2}{0 - 5} = - \frac{1}{5} < 0[/tex]
Therefore, the points (12,3), (-2,-5) and (1,15) through which the line can pass. (Answer)
Answer:
A, B, D
Step-by-step explanation:
just took it on edg
Factor the expression completely. 1/4x + 19/4
The expression 1/4x + 19/4 can be factored by taking out the common factor of 1/4, resulting in the completely factored form (1/4)(x + 19).
Explanation:The student has asked to factor the expression 1/4x + 19/4 completely. To begin with, we note that both terms in the expression share a common factor of 1/4. Thus, we can factor out this common factor. The expression becomes:
(1/4)(x + 19)
The 1/4 is factored out, and we are left with the binomial x + 19 inside the parentheses. This is the completely factored form of the expression. Remember that factoring is essentially reversing the distribution process. In this case, we took out the common factor of 1/4 that was distributed across the x and 19.
The first Ferris wheel was built in 1893 in Chicago. It's diameter was 250 feet. How many feel did the Ferris wheel rotate with one complete turn?
The wheel covered 785 feet in one complete turn
Solution:
Given that, The first Ferris wheel was built in 1893 in Chicago
Diameter of wheel = 250 feet
Let us find the radius of wheel
[tex]Radius = \frac{diameter}{2}\\\\Radius = \frac{250}{2}\\\\Radius = 125[/tex]
Thus radius of wheel is 125 feet
We have to find the distance covered in one complete turn
The number of feet the wheel rotated in one turn is equal to its circumference
The circumference of circle is given as:
[tex]C = 2 \pi r[/tex]
Where, "r" is the radius and [tex]\pi[/tex] is a constant equal to 3.14
Substituting the values we get,
[tex]C = 2 \times 3.14 \times 125\\\\C = 785[/tex]
Thus the wheel covered 785 feet in one complete turn
without doing any calculations or modeling, explain how you know that the 24 inch by 32 inch mirror and the 20 inch by 32 inch mirror are not similar. Explain
What is (6 x 10^2) divide (3x10^-5) in standard form?
Thank you.
Answer:
Step-by-step explanation:
[tex]\frac{6*10^{2}}{3*10^{-5}}=2*10^{2}*10^{5}\\\\=2*10^{(2+5)}=2*10^{7}[/tex]
The scale on a map is 1 : 320 000
What is the actual distance represented by 1 centimetre
Give your answer in kilometres.
Step-by-step explanation:
Given that , the scale on map is 1 : 320000.
Its means that if the scale shows 1 unit then actual length is 320000 units
So If the shows 1 cm then the actual distance = 320000 cm
=[tex]\frac{320000}{100000}[/tex] km = 3. 2 km
Therefore the actual distance represented by 1 centimeter is = 3.2 kmThe diagram represents the process of creating a scale
drawing from an original using a scale factor of 0.4. The
base of the original drawing must be:
A. 17.6
B. 18 cm
C. 33.5 cm
D. 45 cm
Answer: 18cm
Step-by-step explanation:
Let original drawing's base be b.
We are using scale factor of 0.4, so
0.4 of b = 7.2cm
0.4 × b = 7.2cm
b = (7.2/0.4)cm
b = 18cm
The base of the original drawing must be 18 cm.
Option B is the correct answer.
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object,
We have,
Scale factor = 0.4.
From the figure,
Original height = 25.6 cm
Original base = b cm
Scale height.
= 25.6 x 0.4
= 10.24 cm
Scale base = 7.2 cm
Now,
Original base.
b x 0.4 = 7.2
b = 7.2 / 0.4
b = 18 cm
Thus,
The base of the original drawing must be 18 cm.
Learn more about scale factors here:
https://brainly.com/question/20759556
#SPJ6
Seven years ago Maya opened a savings
account with her bank. She started with a
balance of $218. If her interest rate is 6%
per year, how much interest has accrued
using simple interest? What is Maya's
new total balance?
Answer:
accrued interest: $91.56total balance: $309.56Step-by-step explanation:
The amount of simple interest is ...
I = Prt = $218·0.06·7 = $91.56
The total account balance is this amount added to the original deposit:
$218.00 + 91.56 = $309.56
Correctly solve 7-4.59 with explanation step by step
Answer:
2.41
Step-by-step explanation:
First you make 7 a decimal that matches 4.59. if you understand decimals then you know its 7.00. after that you just subtract. borrow is necessary in this problem.
To solve 7-4.59, subtract 4.59 from 7 to get 2.41.
Explanation:To solve 7-4.59, we need to subtract 4.59 from 7.
Step 1: Write down the subtraction problem: 7-4.59
Step 2: Subtract the ones place value: 7 - 4 = 3
Step 3: Subtract the tenths place value: 0 - 5 = -5
Step 4: Combine the values: 3 - 0.59 = 2.41
Therefore, 7 - 4.59 equals 2.41.
I need help please help
Answer:
B
Step-by-step explanation:
Substitute the value of (2,1) into the equations, and you find that only B works.
What is 7 and 1/2 plus 9 and 1/4
Answer:
16.75
Step-by-step explanation:
7.5+9.25=16.75
Line up the digits and use traditional algorithm.
A baker has 10 cups of sugar to make cookies. Each batch calls for 113 cups of sugar.
How many batches of cookies can he make?
Enter your answer, as a mixed number in simplest form, in the box.
The number of batches of cookies made is [tex]7\frac{1}{2}[/tex]
Solution:
Given that, baker has 10 cups of sugar to make cookies
Each batch calls for [tex]1\frac{1}{3}[/tex] cups of sugar
To find: Number of batches of cookies can be made
From given information,
Total number of cups of sugar = 10
Cups of sugar for 1 batch = [tex]1\frac{1}{3} = \frac{3 \times 1 + 1}{3} = \frac{4}{3}[/tex]
Therefore, number of batches of cookies can be made is found by dividing the total number of cups of sugar by cups of sugar for 1 batch
Thus we get,
[tex]\text{Number of batches of cookies can be made} = \frac{\text{Total number of cups of sugar}}{\text{Cups of sugar for 1 batch}}[/tex]
Substituting the values, we get
[tex]\text{Number of batches of cookies can be made} = \frac{10}{\frac{4}{3}}\\\\\text{Number of batches of cookies can be made} = 10 \times \frac{3}{4}\\\\\text{Number of batches of cookies can be made} = \frac{15}{2}\\\\\text{In mixed form, we get }\\\\\rightarrow \frac{15}{2} = 7\frac{1}{2}[/tex]
Thus number of batches of cookies made is [tex]7\frac{1}{2}[/tex]
8. Water flows out of a hose at a constant rate. After 2 minutes, 97 gallons of water have come
se. At what rate, in gallons per minute, is water flowing out of the hose?
Answer:
48.5 gal/min
Step-by-step explanation:
I used a ratio to solve this problem.
If 97 gallons flow in 2 minutes, the ratio is 97/2
To find the flow per one minute, the ratio is x/1
You can then cross multiply to get 97=2x
When solved, this gives you 48.5 gal/min.
To check, you can multiply x2.
Help trigonometry (angles of evaluation and depression)
Answer:
x ≈ 745.5 ft
Step-by-step explanation:
The angle at the lower right of the triangle is 28° ( alternate angle )
Using the sine ratio in the right triangle
sin28° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{350}{x}[/tex]
Multiply both sides by x
x × sin28° = 350 ( divide both sides by sin28° )
x = [tex]\frac{350}{sin28}[/tex] ≈ 745.5 ft ( to the nearest tenth )
Beach ball with diameter of 24 inches what is the volume of air in the beach ball to the nearest of a cubic foot?
Final answer:
The volume of a beach ball with a diameter of 24 inches is approximately 4.19 cubic feet, which is rounded to 4 cubic feet.
Explanation:
To find the volume of a beach ball with a diameter of 24 inches, we first need to find the radius by dividing the diameter by 2, giving us a radius of 12 inches. The formula for the volume of a sphere is V = (4/3) * π * r^3, where V is the volume and r is the radius of the sphere.
Using the formula:
V = (4/3) * π * (12 inches)^3
V = (4/3) * π * 1,728 cubic inches
V ≈ 7,238 cubic inches (rounded to the nearest whole number)
Now, we need to convert cubic inches to cubic feet since 1 cubic foot equals 1,728 cubic inches.
V = 7,238 cubic inches / 1,728 cubic inches per cubic foot
V ≈ 4.19 cubic feet
Rounded to the nearest cubic foot, the volume of air in the beach ball is approximately 4 cubic feet.
12+b=
26
Solve by using substitution
Answer:
14
Step-by-step explanation:
12+b=26
b=26-12
b=14
Answer:14
Step-by-step explanation:You first want to do 12+12 because that =24 and then keep on adding until u get 26
The following table shows the consumer price index(CPI) for a fictional country from 1992-2000.during which of these time periods was there a period deflation?please help!!!!!!!!!!!!!!!!!
Answer:
d) 1998 to 2000
Step-by-step explanation:
Consumer price index (CPI) is an economic indicator that shows the average change in prices of items, goods and services. Basically, if CPI is increasing over a period of time that means that there is inflation, and if it decreases that means that there is deflation (lowering of prices).
Now, looking at our table, we see that:
- 1992-1994: CPI increased from 44.3 to 58.2 -> inflation
- 1994-1996: CPI increased from 58.2 to 65.9 -> inflation
- 1996-1998: CPI increased from 65.9 to 70.4 -> inflation
- 1998-2000: CPI decreased from 70.4 to 69.1 -> deflation
Answer:
The correct answer is D. 1998 to 2000
Step-by-step explanation:
Marlene only has enough ingredients to make a 1/4 batch of cookies. For the smaller batch, she only needs 2/3 cup of sugar. How much sugar does the recipe for a full batch of cookies call for? Include all your work in your answer.
Answer:
A full batch of cookies will require [tex]\hspace{0.15cm} \frac{8}{3} cup \hspace{0.15cm}of\hspace{0.15cm} \hspace{0.15cm} sugar,\hspace{0.15cm} or \hspace{0.15cm}2\hspace{0.15cm}whole\hspace{0.15cm} cups\hspace{0.15cm} and \hspace{0.15cm} \frac{2}{3} cup\hspace{0.15cm} of \hspace{0.15cm}sugar.[/tex]
Step-by-step explanation:
i) [tex]\hspace{0.15cm}\frac{1}{4} batch \hspace{0.15cm}of \hspace{0.15cm}cookies\hspace{0.15cm} requires\hspace{0.15cm} \frac{2}{3} cup \hspace{0.15cm}of\hspace{0.15cm} sugar[/tex]
ii) multiplying the above by 4 we get
[tex]\hspace{0.15cm}(4\times\frac{1}{4}) batch \hspace{0.15cm}of \hspace{0.15cm}cookies\hspace{0.15cm} requires\hspace{0.15cm}( 4 \times\frac{2}{3} )cup \hspace{0.15cm}of\hspace{0.15cm} sugar[/tex]
iii) Therefore [tex]\hspace{0.15cm}1 batch \hspace{0.15cm}of \hspace{0.15cm}cookies\hspace{0.15cm} requires\hspace{0.15cm} \frac{8}{3} cup \hspace{0.15cm}of\hspace{0.15cm} sugar[/tex]
iv) Therefore a full batch of cookies will require [tex]\hspace{0.15cm} \frac{8}{3} cup \hspace{0.15cm}of\hspace{0.15cm} \hspace{0.15cm} sugar,\hspace{0.15cm} or \hspace{0.15cm}2\hspace{0.15cm}whole\hspace{0.15cm} cups\hspace{0.15cm} and \hspace{0.15cm} \frac{2}{3} cup\hspace{0.15cm} of \hspace{0.15cm}sugar.[/tex]