Answer:
The systems that are guaranteed have the solution (3, -1) are;
a.) (P + F)·x + (Q + G)·y = R + H
F·x + G·y = H
d.) P·x + Q·y = R
(F - 2·P)·x + (G - 2·Q)·y = H - 2·R
e) P·x + Q·y = R
5·F·x + 5·G·y = 5·H
Step-by-step explanation:
The given system of equation are;
a) P·x + Q·y = R...(1)
F·x + G·y = H...(2)
The solution of the system of equation = (3, -1)
Adding equation (1) to equation (2) gives;
P·x + Q·y + F·x + G·y = R + H
(P + F)·x + (Q + G)·y = R + H...(3)
Therefore, given that equation (3) is obtained from equation (1) and (2) by addition, equation (3), (P + F)·x + (Q + G)·y = R + H, we have;
The system of equation;
(P + F)·x + (Q + G)·y = R + H
F·x + G·y = H, derived from the given system of equation Is bound to have the same same solution (3, -1) as the given system of equation
d.) By multiplying equation (1) by 2, we have;
2 × (P·x + Q·y) = 2 × R
2·P·x + 2·Q·y = 2·R...(4)
Subtracting equation (4) from equation (2) gives;
F·x + G·y - (2·P·x + 2·Q·y) = H - 2·R
F·x - 2·P·x + G·y - 2·Q·y = H - 2·R
(F - 2·P)·x + (G - 2·Q)·y = H - 2·R
Therefore, for the following system, obtained from the original system, we have that the solution is (3, -1);
P·x + Q·y = R
(F - 2·P)·x + (G - 2·Q)·y = H - 2·R
e) For the system of equation, we have;
P·x + Q·y = R
5·F·x + 5·G·y = 5·H
The above system of equation is obtained from the original system by multiplying equation (2) by 5, therefore the solution of the system P·x + Q·y = R, 5·F·x + 5·G·y = 5·H is the same as the solution for the original system of equations (3, -1).
par teme
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Bookwork code, 021
Cessss chance Review your workings and see if you can comes your make
Ria buys 19 textbooks, which cost £6.82 each,
By first rounding both numbers to 1 significant figure, estimate the total
amount of money Ria spends,
Give your answer in pounds (L),
Answer?
Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.
Define unitary method.By multiplying the value about one unit by the quantity of units required, one can apply the unit technique to solve a problem. The unit procedure is used to separate a single entity integer from a given many, to put it simply. One pen, or 400 rupees, would be needed to purchase 40 needle. There might be a common way to verify this. only one nation. Anything has a unique feature. Algebra, grid logic, and its laminates and reverse are all identical terms used to describe mathematical analysis.
Here,
Given : Ria purchases 19 books for £6.82 apiece.
Thus,
Total cost of book = 19 * 6.82
=> 129.58
Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.
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Jane set up a lemonade stand to sell lemonade. The total cost of making the lemonade was $1.50. She sold each cup of lemonade for $0.25. Enter an equation that can be used to find the number of cups of lemonade, x, Jane sold if her earnings were $9.75 after paying out the cost of the lemonade x=
A bag of 10 marbles has 4 blue, 4 green, and 2 red marbles. If a blue marble is randomly pulled and not replaced, what is the probability that the second marble randomly pulled will also be blue?
Lani is making a cake in the shape of a cone. to make the cake, she uses a cone shape mold. the mold has a diameter of 10 inches and a height of 12 inches. what is the volume of the cake? use 3.14 for pi. round to the nearest tenth, if necessary. responses 125.6 in³ 125.6 in³ 314 in³ 314 in³ 942 in³ 942 in³ 1256 in³
The volume of the cake Lani is making is 314 inches³.
Volume is defined as the amount of space a figure occupies. The formula for the volume of a cone is given by:
V = πr²h/3
where V = volume
r = radius of the base of the cone
h = height of the cone
π = 3.14
If the cone shape mold has a diameter of 10 inches, then its radius is equal to half of 10 which is 5 inches.
Plug in the values to the formula and solve for the volume.
V = πr²h/3
V = (3.14)(5 inches)²(12 inches)/3
V = 314 inches³
Hence, the volume of the cake is 314 inches³.
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What is the standard from of the equation for the line of y=1/4x+4. (Please help meeee)
Solve for x: 3(x+6)=21. A)1 B) 5 C)9 D) 13
Answer:
[tex]\boxed {\boxed {\sf A. \ x=1}}[/tex]
Step-by-step explanation:
We are given the equation:
[tex]3(x+6)=21[/tex]
We want to solve for x, so we must isolate the variable by performing inverse operations to both sides of the equation.
(x+6) is being multiplied by 3. The inverse of multiplication is division. Divide both sides of the equation by 3.
[tex]\frac {3(x+6)}{3}=\frac{21}{3}[/tex]
[tex](x+6)=\frac{21}{3}[/tex]
[tex](x+6)=7[/tex]
Now 6 is being added to x. The inverse operation of addition is subtraction. Subtract 6 from both sides of the equation.
[tex]x+6-6=7-6[/tex]
[tex]x=7-6[/tex]
[tex]x=1[/tex]
We can test our solution by plugging 1 in for x in the original equation.
[tex]3(x+6)=21[/tex]
[tex]3(1+6)=21[/tex]
[tex]3(7)=21\\21=21[/tex]
This checks out (21 is equal to 21) so we know our answer is x=1.
Answer:
A. X=1Step-by-step explanation:
To solve this problem, you have to use the distributive property.
Isolate the x from one side of an equation.
Distributive property:
[tex]\sf{A(B+C)=AB+AC}[/tex]
First, divide by 3 from both sides of an equation.
[tex]\dfrac{3(x+6)}{3}=\dfrac{21}{3}[/tex]
Solve.
21÷3=7
Rewrite the problem down.
x+6=7
Then, subtract by 6 from both sides.
[tex]\sf{x+6-6=7-6}[/tex]
Solve.
7-6=1
[tex]\Large\boxed{X=1}[/tex]
The solution is x=1, which is our answer.
Find the measure of the exterior angle with 24 degrees
(3x+6) and (2x+18)
The measure of the exterior angle of the triangle is 114 degrees.
How to find the angles of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
The measure of the exterior angle of the triangle can be found using exterior angle theorem.
Therefore, the exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
Hence,
24 + 2x + 18 = 3x + 6
2x - 3x = 6 - 18 - 24
-x = -36
divide both sides of the equation by -1
x = 36
Hence,
exterior angle = 3x + 6 = 3(36) + 6 = 108 + 6 = 114 degrees
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Squares $ABCD$ and $EFGH$ are equal in area. Vertices $B$, $E$, $C$, and $H$ lie on the same line. Diagonal $AC$ is extended to $J$, the midpoint of $GH$. What is the fraction of the two squares that is shaded
The fraction of the two squares that is shaded exists 5/16 area shaded.
What is the difference between diagonal and vertices?A diagonal is a line segment connecting two opposite corners (vertexes) of a polygon, however it is not an edge (side). In other words, it connects any two non-adjacent polygonal vertices. Therefore, by connecting any two vertices in a polygon directly (i.e., without using a side), we create a diagonal.
A line segment known as a diagonal joins two polygonal vertexes (corners), although it is not an edge (side). To put it another way, it joins any two polygonal vertices that are not adjacent. Therefore, by connecting any two vertices in a polygon directly (i.e., without using a side), we create a diagonal.
The triangle on the bottom exists 1/2 × 1/2 × 1/2 of the original area of the lower square = 1/8 of the lower square
2 square = [1/2 (square) + 1/8 (square) ] / 2 square
= 5/16 area shaded
Therefore, the fraction of the two squares that is shaded exists 5/16 area shaded.
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The fraction of the two squares that is shaded exists 5/16 area shaded.
What is the difference between diagonal and vertices?A diagonal is a line segment that joins two opposed polygonal corners (vertexes), although it is not an edge (side). In other words, it joins any two polygonal vertices that are not neighbouring. As a result, we can make a diagonal by directly joining any two vertices of a polygon (i.e., without utilising a side).
Although it is not an edge, a line segment known as a diagonal connects two polygonal vertexes (corners) (side). In other words, it connects any non-adjacent pair of polygonal vertices. As a result, we can make a diagonal by directly joining any two vertices of a polygon (i.e., without utilising a side).
The triangle on the bottom exists 1/2 × 1/2 × 1/2 of the original area of the lower square = 1/8 of the lower square
2 square = [1/2 (square) + 1/8 (square) ] / 2 square
= 5/16 area shaded
Therefore, the fraction of the two squares that is shaded exists 5/16 area shaded.
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Can some please help me with this questions
9514 1404 393
Answer:
y = 100,000(1 + 0.15)^t y = 1200(1 -0.06)^t y = 49.50(1 -0.07)^t y = 135(1 +0.05)^t value of $200 decreases (decays) by 25% each yearStep-by-step explanation:
It should be no stretch to understand that "increases" means the function is a growth function (+ sign), and "decreases" means the function is a decay function (- sign).
The multiplier in front (a) is the initial value — the value when t=0.
ILL BRAINLIEST YOU AND GIVE YOU 10 extra points
Answer:
it's b
Step-by-step explanation:
it satifies Pythagoras theorem.
29² = 20²+21²
The average sale price of new one-family houses in the United States for a recent year was . Find the range of values in which at least of the sale prices will lie if the standard deviation is . Round your to the nearest whole number
The price range for 75% of sales will be between $149,300 and $343,300.
What is meant by Chebyshev's Theorem?The minimum percentage of observations falling within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous probability distributions can use this theorem. Also known as Chebyshev's Inequality, Chebyshev's Theorem.
Between $149,300 and $343,300 is where 75% of transactions are priced. Only 75% of the distribution's numbers must fall within two standard deviations for Chebyshev's theorem to hold, which makes it weaker than the proportion of numbers that are within two standard deviations of the mean.
Since the standard deviation given exists 48500, 2 standard deviations will be 2 × 48500 = 97000.
The lower limit will be 246300 - 97000 and the upper limit will be 246300 + 97000.
Lower limit = 246300 - 97000 = 149300
Upper limit = 246300 + 97000 = 343300
So 75% of the sales prices will be between $149,300 and $343,300
The complete question is:
The average sale price of new one-family houses in the United States for 2003 was $246,300. Using Chebyshev's theorem, find the range of values in which at least 75% of the sale prices will lie if the standard deviation is $48,500. Hint: You should memorize that when k is 2, it is 75% and when k is 3 it is 88.89%. Please answer with whole numbers: ex. 55,232 to 65,450 with commas
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Which number sentence is true?
I need help with this bc i dont understand it can somebody help me plzzzzz i'll give you 40 points for it!!!! And name you brainly!!!!!!!
Answer:
8.79 in
Step-by-step explanation:
23 = 150/360 × 2×3.14× r
23 = 5/12 × 6.28 x r
23 = 31.4×r / 12
31.4 r = 23×12
31.4 r = 276
r = 276/31.4
r = 8.79 in
Suppose x is 5 and y is 7. Choose the value of the following expression: (x != 7) && (x <= y) a. false b. true c. 0 d. null Suppose that x is an int variable. Which of the following expressions always evaluates to true? a. (x > 0) || ( x <= 0) c. (x > 0) && ( x <= 0) b. (x >= 0) 11 (x == 0) d. (x > 0) && (x == 0)
1)correct option is b) true
2)Which of the following expressions always evaluates to true?
correct option is d)(x > 0) && (x == 0)
given that
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Many authors make a distinction between an expression and a formula, with the former designating a mathematical object and the latter a claim about such objects.
x = 5 and y = 7
Choose the value of the following expression: (x != 7) && (x <= y)
a. false
b. true
c. 0
d. null
(5! = 7) && (5<=7)
5 ≠ 7
correct option is b) true
Suppose that x is an int variable.
Which of the following expressions always evaluates to true?
a. (x > 0) || ( x <= 0)
b. (x > 0) && ( x <= 0)
c. (x >= 0) 11 (x == 0)
d. (x > 0) && (x == 0)
a) x = 1,2,3.... || x =0,-1,-2,-3......
b)x = 1,2,3.... && x = 0,-1,-2,-3,.....
c) x = 0,1,2,3..... 11 x = 0
d) x = 1,2,3.... && x = 0
correct option is d)(x > 0) && (x == 0)
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1. Write two word expressions for each problem using different math vocabulary for each
expression
5d-10
a/b+2
Step-by-step explanation:
for the first one
subtract 10 from 5 times a certain number
i’m not sure how to find the slope of the lines
Answer:
Step-by-step explanation:Select any two random points on the graph of the line (preferably with integer coordinates).
Label them as A and B (in any order).
Calculate the "rise" from A to B. While going vertically from A to B, if we have to go
"up", then the rise is positive;
"down", then the rise is negative.
Calculate the "run" from A to B. While going horizontally from A to B, if we have to go
"right", then the run is positive;
"left", then the run is negative.
Now, use the formula: slope = rise/run.
How do you solve a 45 45 90 and 30 60 90 triangle?
All 45-45-90-degree triangles have sides that are in a unique ratio. The two legs are exactly the same length.
This triangle is important because any time we're given one side of a 45-er triangle, we can figure out the other two sides.
If one leg is given, the hypotenuse is calculated by multiplying this length by the square root of 2.The hypotenuse is given, and the leg is calculated by dividing the hypotenuse by the square root of 2.The 30-60-90 degree triangle is half of an equilateral triangle, cut straight down the middle along its altitude. This triangle has angles of 30°, 60°, and 90°.
The shortest leg is over from the 30-degree angle, the length of the hypotenuse is always double the length of the shortest leg,If the hypotenuse is given, the long leg is calculated by dividing the hypotenuse by 2.If the long leg is given, the hypotenuse is calculated by dividing this side by the square root of 3.Read more about 30-60-90 degree triangle:
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A rectangle measures 1 3/4
inches by 3 3/4
inches. What is its area?
please help!
Answer:
6 and 9/16
Step-by-step explanation:
The area of a rectangle can be calculated by multiplying the width and length. So 1 3/4*3 3/4=7/4*15/4=105/16 or 6 and 9/16
Can some one help me with this question its hard :( down below ill give brainliest
Can you please help me with this problem
Answer: what’s the problem
Step-by-step explanation:
with what problem there isn't one posted
formula of quadratic function and their graph
Answer:
-b +/- √b^2-4ac
_____________
2a
Hey I need some help,
If you were typing an 300 page essay and you finished 6 3/5 pages every hour, how long would it take you to complete a 300-page essay?
What types of lines are coplanar and intersect at a right angle?
A. parallel
B. perpendicular
C. skew
D. transversal
Answer:
B
Step-by-step explanation:
perpendicular is right angle
Find the value of x.
Answer: X = 121
Step-by-step explanation:
Because 180 degrees is a flat line, you subtract 59 from 180 to get the remaining angle values
PLEASE ANSWER ASAP!
Help please??????????????
Answer:
The answer is B. 1/8
Step-by-step explanation:
Half of the garden is planted by seeds. The quarter of that half will be equal to 1/8 for the whole garden.
9) $36,500 at 2% compounded
semiannually for 2 years
A) $37,993.74 B) $37,982.05
C) $37,960.00 D) $37,974.60
Answer: I think it is B
Step-by-step explanation:
Sry if wrong pls don’t be mad
Help me, please pleeeeeeeeeeeease
Answer:done
Step-by-step explanation:
A geologist visits 60 volcanoes in Alaska and California. What if 40% of the volcanoes were in California? How many volcanoes would the geologist have visited in California and how many in Alaska?
Answer : in California there are 24 volcanoes while in Alaska there are 36 volcanoes.
Step-by-step explanation:
Total number of volcanoes = 60.
40% of the volcanoes where in California.
i.e 100% - 40% = 60%.
60% of the volcanoes were in Alaska.
In California = 40/100 × 60 = 24 volcanoes.
In Alaska = 60/100 × 60 = 36 volcanoes.
is 120,110,105… a geometric sequence
Answer: No
Step-by-step explanation:
Look at the 3 numbers in the sequence,
Geometric sequence means the ratio between two consecutive numbers in the sequence is a constant (eg. 10, 5, 2.5 is a geometric sequence as the ratio is a constant at 1/2)
However, for the sequence listed above
Looking at 1st and 2nd term,
Ratio = 110/120 = 11/12
Looking at 2nd and 3rd term,
Ratio = 105/110 = 21/22 which is not the same as 11/12.
Hence, since the ratio is not the same, this sequence is not a geometric sequence.
1. Combine the like like terms
14 + 8x + 2y -5x - 2
Answer: 12 +3x +2y
Step-by-step explanation:
like terms:
14 and -2
8x and -5x
2y
combine and there you go. hope this helped.
(btw. the equation can vary in different forms, like 3x+2y+12 or 2y+3x+12. They are all correct.)