First, we will find the weight of each oranges and grape fruit
Let x be the unit weight of orange
Let y be the unit weight of grape fruit
If "10 oranges and 20 grapefruits weigh 35 pounds total"
Then this implies;
10x + 20 y = 35 -----------------(1)
And
If " 16 oranges and 10 grapefruits weigh 23 pounds total"
This implies;
16x + 10y = 23 ---------------------(2)
We can solve the two equations simultaneously.
Using elimination method;
we eliminate y and to do that, the y variables in the two equations must be same, Hence we can achieve that by multiply equation (1) by 10 and then multiply equation (2) by 20
100x + 200y = 350 ----------------------------(3)
320x + 200y = 460 ------------------------------(4)
subtract equation (3) from equation (4)
220x = 110
divide both-side of the equation by 220
x = 0.5
substitute x=0.5 into equation(1) and then solve for y
10(0.5) + 20y = 35
5 + 20y = 35
subtract 20 from both-side of the equation
20y = 35 - 5
20y = 30
divide both-side of the equation by 20
y = 1.5
"13 oranges and 15 grape fruits" = 13 x + 15y
substituting x = 0.5 and y= 1.5 in the above;
13(0.5) + 15(1.5)
=6.5 + 22.5
=29
Hence;
13 oranges and 15 grapefruits will weigh 29 pounds
factor the triminal
3x squared -15x+12
Choose the equation that represents the graph.
graph of a line passing through points negative 2 comma 0 and 0 comma negative 4
y = −2x − 4
y = 2x + 4
y = −2x + 4
y = 2x − 4
Answer:
The equation is y=2x+4.hope it's solved
[tex]compare 2.01 x 10 and 2.8 x 10 which number is larger[/tex]
When you compare 2.01 x 10 and 2.8 x 10, the larger number is 2.8 × 10.
What is multiplication?It should be noted that multiplication simply means the product of a number. This is usually illustrated by the symbol ×.
In this case, it should be noted that 2.01 × 10 = 20.1
It should also be noted that 2.8 × 10 = 28
Therefore, the larger number is 2.8 × 10.
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A carpenter has 2 pipes which are 60 dm and 72 dm long respectively. he cuts them into equal lengths. what is the greatest possible length of each pipe?
Using greatest common factor (GCF), the greatest possible length of each pipe is 12 dm.
The greatest common factor (GCF) of a set of numbers is defined as the largest common positive integer that divides each number into equal parts with zero remainder.
If a carpenter has 2 pipes which are 60 dm and 72 dm long, respectively and he cuts them into equal lengths, then the greatest possible length of each pipe is the GCF of 60 and 72.
60 : 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
72 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 24, 36, 72
common factors : 1, 2, 3, 4, 6, 12
GCF = 12
Hence, he should cut the two pipes into 12 dm long.
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graph the line y=-3x+b if its graph goes through the given point A(-2,4)
The graph of the linear equation, y = -3x - 2, that passes through (-2, 4) is shown in the attachment below.
How to Graph The Line of a Linear Equation?The linear equation of a line is expressed in slope-intercept form as y = mx + b. The y-intercept of the line, which is the point where the line intercepts the y-axis, is represented as "b" in the equation.
The slope is represented as "m".
Given that the line, y = -3x + b passes through the point A(-2, 4), find the value of the y-intercept of the line, b, by substituting x = -2 and y = 4 into y = -3x + b:
4 = -3(-2) + b
4 = 6 + b
4 - 6 = 6 + b - 6
-2 = b
b = -2
Substitute b = -2 into the equation:
y = -3x - 2
The graph of y = -3x - 2 is given in the attachment.
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Make x the subject of m= n + x/p
Answer:
[tex]x[/tex] = m - n x p
Step-by-step explanation:
m - n = [tex]x[/tex]/p
[tex]x[/tex] = m - n x p
Answer:
x = pm - pn
Step-by-step explanation:
Make x the subject:To make 'x' as the subject, isolate 'x'.
[tex]\sf n + \dfrac{x}{p}=m\\\\\text{Subtract 'n' from both sides,}\\\\\dfrac{x}{p}=m-n\\\\\text{Multiply both sides by p,}\\\\p*\dfrac{x}{p}=p*(m-n)\\\\[/tex]
x = pm - pn
11. Write a function rule for the area of a rectangle with a length 7 m more than three
times its width. What is the area of the rectangle when its width is 3 m?
The area of the rectangle when its width is 3 m is 39m².
What is area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares. The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Given Data
A function rule for the area of a rectangle with a length 7 m more than three times its width.
Area of rectangle = Length(Width)
Area of function = (w) (3w+7)
Area of function = 3w² + 7w
If w = 3m
Area of function = 3(3)² +7(3)
Area of function = 3(9) + 21
Area of function = 18 + 21
Area of function = 39
the area of the rectangle when its width is 3 m is 39m².
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Can you please help me with 37
Solution:
The equation of the ellipse in the question is given as
[tex]\frac{(y-3)^2}{9}-\frac{(x-3)^2}{9}=1[/tex]Concept:
The general formula of a hyperbola is
[tex]\begin{gathered} \frac{(y-h)^2}{b^2}-\frac{(x-k)^2}{a^2}=1 \\ \text{Where } \\ h,k\text{ are the centres} \end{gathered}[/tex]From the above equation by comparing coeficient, we will have
[tex]\begin{gathered} a^2=9 \\ a=3 \\ b^2=9 \\ b=3 \\ (a,b)\Rightarrow(3,3) \\ h=3,k=3 \end{gathered}[/tex]The linear eccentricity c, will be
[tex]\begin{gathered} c=\sqrt[]{a^2+b^2} \\ c=\sqrt[]{3^2+3^2} \\ c=\sqrt[]{9+9} \\ c=\sqrt[]{18} \\ c=3\sqrt[]{2} \end{gathered}[/tex]The vertices of the hyperbola will be calculate using the formula below
[tex]\begin{gathered} (h,k-b)\Rightarrow(3,3-3)\Rightarrow(3,0) \\ (h,h+b)\Rightarrow(3,3+3)\Rightarrow(3,6) \end{gathered}[/tex]The co-vertex are calculated using the formula below
[tex]\begin{gathered} (h-a,k)\Rightarrow(3-3,3)\Rightarrow(0,3) \\ (h+a,k)\Rightarrow(3+3,3)\Rightarrow(6,3) \end{gathered}[/tex]The foci of the hyperbola will be calculated using the formula below
[tex]\begin{gathered} \mleft(h,k-c\mright)\Rightarrow(3,3-3\sqrt[]{2)} \\ \mleft(h,k+c\mright)\Rightarrow\Rightarrow\Rightarrow\mleft(3,3+3\sqrt[]{2}\mright) \end{gathered}[/tex]The eccentricity, e is
[tex]e=\frac{c}{b}=\frac{3\sqrt[]{2}}{3}=\sqrt[]{2}[/tex]Hence,
The sketch of the graph is given below as
The foci is represented with the two red dots on the graph
The vertices are represented above by the two coordinates
find the equation of the line passing through the points (2, 11) and (-8, -18)
y = [ ? ]x + [ ]
i would appreciate the help!
The equation of the line passing through the points (2, 11) and (-8, -18) is y = 29 / 10 x + 26 / 5
How to find the equation of a line?The equation of a line can be express as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line passes through the points (2, 11) and (-8, -18).
Hence,
m = -18 - 11 / -8 - 2
m = - 29 / - 10
m = 29 / 10
Therefore, let's find the y-intercept using (2, 11)
The equation is as follows:
11 = 29 / 10(2) + b
11 = 58 / 10 + b
b = 11 - 58 / 10
b = 110 - 58 / 10
b = 52 / 10 = 26 / 5
Therefore,
y = 29 / 10 x + 26 / 5
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Is 5/8 a reciprocals
Answer:8/5
Step-by-step explanation:
TO find the reciprocal, divide 1 1 by the number given
1/(5/8)
=8/5
sold for missing side length when necessary round to nearest tenth.
Answer: missing side length = 12.5
Step-by-step explanation:
1. Identify what equation to use
there are 2 side lengths, and no Pythagorean triples present therefore using the Pythagorean theorem a^2+b^2=c^2 would be a good approach
2. plug in numbers
knowing the missing side length is the hypotonus we can plug 6 and 11 for a and b: 6^2+11^2=c^2
3. Solve equation
6^2+11^2=c^2
36+121=c^2
157=c^2
12.52=c | to cancel square (^2) you must square root the number
12.5=c | round
The length of the base of a rectangular prism is given as x + 4, and the width of the base is x +2. The height of the rectangular prism is three more than two times the length. Build a function to model the volume of the rectangular prism. (Hint: volume is l•w•h)
3) Isaac has 18 coins, all quarters and nickels. The total value of the coins it $3.50.
Determine the number of quarters and the number of nickels that Isaac has.
By using the method subtraction,
1 quarter is 0.25
1 nickel is 0.05
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.
Given that,
Isaac has 18 coins, all quarters and nickels.
The total value of the coins it $3.50.
Let the quarters be x and nickels be y
x+ y= 18
x= 18 - y... equation 1
1 quarter is 0.25
1 nickel is 0.05
So,
0.25x+ 0.05y= 3.50
substitute x value in above equation
0.25(18-y)+0.05 = 3.50
4.5-0.25y+ 0.05 = 3.50
4.55 - 3.50 = 0.25y
1.05= 0.25y
y= 4.2
y in equation 1
x= 18 - y
x= 18-4.2
x= 13.8
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Last night, Luis read 75% more pages than Dayja, and Dayja read 75% more pages than Michael. If Dayja read 84 pages, how many pages did Luis, Dayja, and Michael read all together?
The pages read by Luis, Dayja and Michael read all together is 252.
What is Percentage?
A relative value indicating hundredth part of any quantity is called percentage.
Given that;
The conditions is,
Luis read 75% more pages than Dayja, and Dayja read 75% more pages than Michael.
Total pages read by Dayja = 84
Now,
Since, Luis read 75% more pages than Dayja.
So, The pages for Luis = 75% of 84
= 75/100 × 84
= 6,300 / 100
= 63
Thus, Pages for Luis = 84 + 63
= 147
And, Number of pages read by Michael = 84 - 63
= 21
Thus, Number of pages read by Michael = 21
So, Total number of pages read by Luis, Dayja and Michael all together is;
= 84 + 147 + 21
= 252
Therefore,
The pages read by Luis, Dayja and Michael read all together is 252.
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What is the slope of (15,-51) and (-29,-45)
Answer:
slope = (-3/22)
Step-by-step explanation:
(15, -51), (-29, -45)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -45 - (-51) -45 + 51 6 ÷ 2 -3
m = ------------ = ----------------- = -------------- = ------------ = --------
x₂ - x₁ -29 - 15 -44 -44 ÷ 2 22
I hope this helps!
Answer:
Gradient/slope: y2-y1/x2-x1
y1= -51
y2= -45
x1= 15
x2= -29
Slope:
-45-(-51)/-29-15
= -45+51/-44
= -6/44
divide both by 2
= -3/22
Felipe is having a party. He'll have 4 tables for every 20 guests. Complete the table below showing the number of tables and the number of guests.
( Table: ?, 1 20,4 35,? ?,8 50,?)
Answer:
8
Step-by-step explanation:
( Someone please help me, I'll mark brainliest )
Answer the question in the photo.
Answer: 5/3
Step-by-step explanation:
The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.
We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.
Question
Which table represents a proportional relationship between x and y?
Responses
x 3 9 10 15
y 1 3 4 5
x 3 9 10 15 y 1 3 4 5
x 1 5 8 10
y 15 75 120 150
x 1 5 8 10 y 15 75 120 150
x 4 6 8 10
y 6 8 10 12
x 4 6 8 10 y 6 8 10 12
I don't know.
The table that represents a proportional relationship between x and y is table 2.
What is a proportional relationship?A relationship is proportional if each pair of data values are related in the same way, by multiplying by a factor.
A proportional relationship is one in which two quantities vary directly with each other.
For example,
y = kx
where,
k = constant of proportionality
You can tell if a table shows a proportional relationship by calculating the ratio of each pair of values.
If those ratios are all the same, the table shows a proportional relationship.
Therefore, let's calculate the ratios of the table
1 / 155 / 75 = 1 / 158 / 120 = 1 / 1510 / 150 = 1 / 15Hence, the table 2 has a proportional relationship.
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HELP ANSWER ASAP!! WILL GIVE BRAINLIEST!
Please give description and how to do problem ! NO LINKS !!!
Just answer questions 12 and 13 !
Answer:
Step-by-step explanation:
12. We have : angle ABF = angle ABE + angle FBE = 2(w+11) + angle FBE = 8w - 6
-> angle ABE = 8w - 6 - [2(w+11)] = 8w - 6 - 2w - 22 = 6w - 28.
13. As we can see, angle EBA and angle EBC is a linear pair, therefore they're supplementary angles, adding up to 180.
-> 3r + 10 + 2r - 20 = 180
5r - 10 = 180
r = 38.
So, angle EBF = 2r - 20 = 76 - 20 = 56.
(pls just don't blur the question next time cause im very confused why the 2 angles are marked equal)
Urgent | Find the angles of the following shape
Step-by-step explanation:
easy so first you are going to subtract 130 from 180 since any angle that is made on a straight line segment if subtracted you get the answer of the other angle
180-130 =50
I want you to draw this diagram on paper and extend the line S that is 50° since we know the angle SRQ =130
Now you will be able to see a Z formation PQR and the other half of the S is making a Z formation the interior angles of a z formation are always equal to each other
so the interior x =50°
extend the line P or Q out wards that will also be equal to the other side now since it also makes a Z formation
As we know that the angle SRQ is equal 130 we will half it or divide it by 2 the answer will be 65
one angle in R angle will be 65 while the other one will also be 65
Now we know two angles in the triangle PQR and one angle in triangle PRS
applay the formula that all interior angles sum =189
x + 65 + z =180 (name the left unknown angle z)
50 + 65 + z= 180
105+ z =180
z=180-105
z=75
we now all the angles in the triangle x
y angle =65 again apply the z formation to get the answer
What is the pressure when 650N is applied over 40m2?
Answer:
16,25 Pa
Step-by-step explanation:
P=F/A;
650/40 = 16,
If you multiply two polynomials, will you always get a polynomial? Try combining some polynomials to answer your question. Use the ones given by your teacher or make up your own polynomials. Keep a record of what polynomials you tried, and the results. When you think you have an answer to your question, explain your reasoning using equations, graphs, visuals, calculations, words, or in any way that will help others understand your reasons.
Polynomials are closed under the multiplication operation, meaning that the result of the multiplication between two polynomials will always be a polynomial.
How to multiply polynomials?To multiply polynomials, we first apply the distributive property, multiplying all terms, then we combine the like terms, that is, adding all the terms that have the same exponents.
Since all the factors of the multiplications will be of polynomial terms, the results of the multiplication will be polynomial, and so will the like terms combined, hence polynomials are closed under the multiplication operation.
One example of multiplication of polynomials is given as follows:
(x² - 1)(x² + 1) = x²x² + x² - x² - 1 = x^4 - 1.
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Which expression is equivalent to [tex]5^{4} x (5-^{2} )^{3}[/tex]
The simplified expression of 5^4 * 5^-6 is 5^-2
How to evaluate the expression?The expression is given as
5^4 * (5^-2)^3
Evaluate the product of exponents
So, we have
5^4 * 5^-6
The base of the above expression are the same
i.e. Base = 5
This means that we can apply the law of indices
So, we have
5^4 * 5^-6 = 5^(4 -6)
Evaluate the sum in the above equation
So, we have
5^4 * 5^-6 = 5^(4 -6)
Evaluate the difference in the above equation
So, we have
5^4 * 5^-6 = 5^-2
Hence, the simplified expression of the expression given as 5^4 * 5^-6 is 5^-2
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Complete the two-way frequency table below, which shows the relationship between students who enroll in advanced algebra and physics in a particular high school. From a sample of 40 students, it is found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both. How many students are enrolled in either algebra or physics?
Algebra Not in Algebra Total
Physics 5 14
Not in Physics
Total 29 40
33
38
2
5
Answer:38
Step-by-step explanation:
sense it subteact between
Answer: 38
Step-by-step explanation: subtract between
I need help with this fraction problem! It can be either adding, subtracting, dividing, or multiplying fractions.
Given: 1 || m; 21 = 23
Prove: p | q
m
Р
3
9
2
Complete the missing parts of the paragraph proof.
We know that angle 1 is congruent to angle 3 and that
line I is parallel to line m because
We see that
is congruent to
by the alternate
interior angles theorem. Therefore, angle 1 is
congruent to angle 2 by the transitive property. So, we
can conclude that lines p and q are parallel by the
Parallel lines l and m are intersected by p and q, which are also parallel. The parallelism of the lines p and q can be inferred.
What is meant by transitive property?According to the transitive property, "all the quantities are equal to each other if two quantities are equal to the third quantity."
Given: Line l is parallel to line m.
Angle 1 exists equal to angle 3.
Angles 1 and 3 are shown in the figure as equivalent angles that are equal.
Angle 1 created by line p and line l is equivalent to angle 3 created by lines q and m. Lines l and m are parallel as well. Since p and q form the same angle as two parallel lines, they too should be parallel.
In light of this, it can be said that lines p and q are parallel.
Therefore, it can be concluded that the lines p and q are parallel.
The complete question is:
Given: l || m; ∠1 ∠3 Prove: p || q Complete the missing parts of the paragraph proof. We know that angle 1 is congruent to angle 3 and that line l is parallel to line m because . We see that is congruent to by the alternate interior angles theorem. Therefore, angle 1 is congruent to angle 2 by the transitive property. So, we can conclude that lines p and q are parallel by the
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What is the range? 0 2 0 3 3 1 5 3 1 6 Submit
Solution
0 2 0 3 3 1 5 3 1 6
For this case the range is defined like this:
Range = Max -Min
The maximum = 6
Minimum =0
Then the solution would be:
Range = 6-0 =6
does anyone know what 4/5 x 2/5 in simplest form is?
Help please, geometry
PLEASE HELP I AM GROUNDED AND MY MOM IS FURIOUS WITH MY GRADE
Answer:
p = 11, I hope this helps and I hope you can improve your grade.
Step-by-step explanation:
Adjacent Angles = 90 degrees, or a right angle.
90 = (5p + 7) + (3p - 5)
1. Subtract the numbers
90 = 5p + 2 + 3p
2. Combine Like Terms
90 = 5p + 2 + 3p
90 = 8p + 2
3. Subtract 2 from both sides
90 - 2 = 8p + 2 - 2
88 = 8p
4. Divided 8 from both sides
88/8 = 8p/8
p = 11