Answer:
x = -5
y = -2
Step-by-step explanation:
-3x + 4y = 7 ⇒ ( 1 )
7x - 12y = -11 ⇒ ( 2 )
Multiply the equation ( 1 ) by 3.
( 1 ) × 3
3( -3x + 4y = 7 )
-9x + 12y = 21 ⇒ ( 3 )
Let us find the value of x.
Add equations ( 2 ) & ( 3 ).
( 2 ) + ( 3 )
7x - 12y - 9x + 12y = - 11 + 21
Combine like terms.
-2x = 10
Divide both sides by -2.
x = -5
Let us find the value of y.
For that, let us use equation ( 1 ) and replace x with -5 and make y the subject.
- 3x + 4y = 7
-3 × -5 + 4y = 7
15 + 4y = 7
Subtract 15 from both sides.
4y = 7 - 15
4y = -8
Divide both sides by 4.
y = -2
if Tn =5n +2 which term will have a value of 52
Answer:
10th term
Step-by-step explanation:
given [tex]T_{n}[/tex] = 5n + 2 and [tex]T_{n}[/tex] = 52 , then equate right sides and solve for n
5n + 2 = 52 ( subtract 2 from both sides )
5n = 50 ( divide both sides by 5 )
n = 10
that is the 10th term has a value of 52
How many times greater is 5.96 × 10^4 then 2.98 × 10^3?
A. 20
B. 500
C. 50
D. 200
The number 5.96 × 10⁴ is 20 times greater than 2.98 × 10³ , the correct option is (a) .
In the question ,
it is given that
the number is 5.96 × 10⁴ ,
we have to find that how many times greater is 5.96 × 10⁴ then 2.98 × 10³ .
to find that the number is how many times greater ,
we divide 5.96 × 10⁴ by 2.98 × 10³ .
So , on dividing the numbers we get
= ( 5.96 × 10⁴ ) / ( 2.98 × 10³ )
= 5.96/2.98 × 10⁴⁻³
= 2 × 10¹
= 20 times
Therefore , The number 5.96 × 10⁴ is 20 times greater than 2.98 × 10³ .
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3. Round 134.76821 to the nearest hundredth.
Answer:
134.77
Step-by-step explanation:
Round 134.76821 to the nearest hundredth
by placing each number in reference to what they represent.
1 - hundreds
3 - Tens
4 - units
.7=Tenth
.76=Hundredth
.768=Thousandth
.7682=Ten Thousandth
.76821= Hundred Thousandth
Nearest hundredth will be
134.[76]821
since 2,1 are both round down numbers they will produce approximately 0
since 8 is a round off number it will produce approximately 10
134.77000
or 134.77
you can award the answer as brainliest
Hello, I need help with this math exercise.
John buys 7 apples and 4 pears for $7.25. At the same prices, Hayley buys 5 apples and 9 pears for $10.40. What is the price of one pear? Use Cramer’s Rule to solve.
The price of one pear is $0.85
How to use Cramer’s Rule to solve the price of one pear?
Cramer's rule is one of the useful methods used for solving a system of equations. In this method, the values of the variables in the system are to be calculated using the determinants of matrices. Thus, Cramer's rule is also known as the determinant method.
Given that: John buys 7 apples and 4 pears for $7.25 and at the same prices, Hayley buys 5 apples and 9 pears for $10.40
We will use this given information to form equations in matrices form. Let a and p represent the prices of one apple and one pear respectively.
The equation is:
7a + 4p = 7.25
5a + 9p = 10.40
The matrix formed is:
[tex]C=\left[\begin {array}{ccc}7&4\\5&9\end{array}\right][/tex] , [tex]b=\left[\begin {array}{ccc}7.25\\10.40\end{array}\right][/tex]
Find the determinants,
D = (7 x 9) - (5 x 4) = 43
Da = (7.25 x 9) - (10.40 x 4) = 23.65
Dp = (7 x 10.40) - (5 x 7.25) = 36.55
a = Da/D = 23.65/43 = 0.55
p = Dp/D = 36.55/43 = 0.85
Since p = 0.85. Therefore, the price of one pear is $0.85
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What is the coefficient of the 7th term of (3x² - 2)14?
13492928512 is the last term (7th term )of binomial expansion of the given expression so therefore it has no coefficient .
What is binomial expansion ?The binomial theorem is a way to bring the formulation to a finite power.
The binomial theorem is a effective extension device with packages in algebra, probability, and more. A binomial is an algebraic expression containing wonderful terms.
Calculationit has been attached below b'coz' that was not possible to type here
hope that image is clear .
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The expression $25 + $10h gives the amount of money that Stephanie earns per day, where h is the number of hours she works. How much does she earn if she works 4 hours?
Answer:
25+10(4)= 65
Step-by-step explanation:
think of it as she makes 10 dollars an hour plus then she gets a 25 dollar bonus so you multiply the number of hours by 10 then and the bonus
Answer: $65
Step-by-step explanation:
25+10h h=4
25+10x4=
25+40=
65
the product of a number and 12 increased by two
After solving the formed equation from the question, the result will be equal to 4.
What is an arithmetic operation?The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.
The given statement of the question in the equation form will be,
5x + 12 = 32
5x = 20
x = 4
Therefore, the value of x will be equal to 4.
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Your complete question must be like this:
The product of a number and 5 is increased by 12 the result is 32 to find the number.
Tiffany borrows $8,000 to pay for college. The loan has a 7% interest rate that compounds monthly. She plans to pay off the loan in 15 years. How much will she pay in total?
Tiffany needs to pay $8,084.44 in total.
what is Compound Interest?In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. You will then be left with the principal amount of the loan plus compound interest.
Given:
P= 8000
R= 7%= 0.07
Time= 8 years.
Now, Amount = P[tex](1 + r/n)^{nt[/tex]
Amount = 8000 [tex](1 + 0.07/15)^{12 . 15[/tex]
Amount = 8000 x (1 + 5.8333333333333E-5)
amount = $8,084.44
Hence, Tiffany needs to pay $8,084.44 in total
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Carl is making accessories for the soccer team. He uses 773.85 inches of fabric on headbands for 29 players and 4 coaches. He also uses 279.56 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
Your answer might be 16.31 inches for each headband and wristband for each player.
---------------------------------------
Hope this helps!
Joke: What has ears but can’t hear a thing?
Answer: A cornfield.
Have a great day and God bless! :D
In chapters 5-8 of Frankenstein, Victor feels, for the first time in a long time, a sense of joy and calm. What causes these feelings
A. A visit from his father
B. A letter from Elizabeth
C. The arrival of Henry Clerval
D. An award for creating the monster
Frankenstein, Victor feels, for the first time in a long time, a sense of joy and calm, An award for creating the monster causes these feelings.
How does Victor first react to the monster and what happens to both after the first encounter?Victor is the first to enter and is relieved to see no evidence of the creature. But, exhausted by months of labour and the horror of the creature he has created, he becomes ill with a nervous fever that lasts several months.Victor begins to grasp, for the first time, that what he has made is not only the scientific result of an experiment in animated matter, but a genuine living entity with needs and desires.He informs Victor that all of his horrible deeds stemmed from his desperate loneliness. He offers to take his new friend to South America, where they will hide in the bush away from human interaction. He claims that with the sympathy of a fellow monster, he will no longer be compelled.'Frankenstein,' by Mary Shelley, is the narrative of Victor, who creates a monster with the goal of generating life. He was a genius in college, and he created a monster. His own creation was a failure.To learn more about Frankenstein, refer,
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Frankenstein, Victor feels, for the first time in a long time, a sense of joy and calm, An award for creating the monster causes these feelings.
How does Victor first react to the monster and what happens to both after the first encounter?Victor is the first to enter and is relieved to see no evidence of the creature. But, exhausted by months of labor and the horror of the creature he has created, he becomes ill with a nervous fever that lasts several months.Victor begins to grasp, for the first time, that what he has made is not only the scientific result of an experiment in animated matter, but a genuine living entity with needs and desires.He informs Victor that all of his horrible deeds stemmed from his desperate loneliness. He offers to take his new friend to South America, where they will hide in the bush away from human interaction. He claims that with the sympathy of a fellow monster, he will no longer be compelled.'Frankenstein,' by Mary Shelley, is the narrative of Victor, who creates a monster with the goal of generating life. He was a genius in college, and he created a monster. His own creation was a failure.To learn more about Frankenstein, refer,
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1. The cost of bell peppers varies directly with the weight of bell peppers, as shown in the table. Write a direct variation equation to represent this relationship. Then identify the constant of variation and interpret its meaning.
The constant of variation is 1.75 for every unit increase in x (weight), and the cost(y) value increases by $ 1.75.
What is the equation?
The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The difference between two consecutive entries is constant, as we can see = 1.75
⇒ 7 - 5.25 = 1.75
⇒ 8.75-7 = 1.75
⇒ Slope(m) = 1.75
The slope represents the variable's rate of change.
y - 3 = m(x - 5.25)
y - 5.25 = 1.75(x-3)
y = 1.76x
Thus, the constant of variation is 1.75
This indicates that for every unit increase in x (weight), the cost(y) value increases by $ 1.75.
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The question seems to be incomplete the correct question has been attached
Please only answer if you know the answer for sure,
URGENT
The area of a rectangular garden is 224 square meters. The width is 6 meters longer than one-half of the length. Find
the length and the width of the garden. Use the formula, area = length • width.
Pls help
[tex]\textit{area of a rectangle}\\\\ A=Lw ~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ A=224\\ w=\stackrel{\textit{half-length plus 6}}{\frac{L}{2}+6~\hfill } \end{cases}\implies 224=L\left( \cfrac{L}{2}+6 \right)\implies 224=\cfrac{L^2}{2}+6L[/tex]
[tex]\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2(224)=2\left( \cfrac{L^2}{2}+6L \right)}\implies 448=L^2+12L \\\\\\ 0=L^2+12L-448\implies 0=(L-16)(L+28)\implies \boxed{L= \begin{cases} -28\\\\ 16 ~~ \textit{\LARGE \checkmark} \end{cases}} \\\\\\ \stackrel{\textit{since we know that}}{w=\cfrac{L}{2}+6}\implies w=\cfrac{16}{2}+6\implies \boxed{w=14}[/tex]
now, let's notice, "L" has two valid values but for this case "L" cannot be negative.
if p is false,which row represents when p v(q^r) is true?
E
F
G
H
Answer:
f and g 231
Step-by-step explanation:
Need help please someone
The equation of the linear function is y=8x+(-8).
What do you mean by equation?
A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation. Take the example of 3x + 5 = 15. Equations can be of several sorts, including linear, quadratic, cubic, and others.
According to data in the given question,
We have points (0,-8) and (1,0), thus
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\=\frac{(0-(-8))}{1-0} \\=8[/tex]
Then
y=8x+b
Points (0,-8) means that when x=0, y=-8 and we use this to find b,
y=8x+b
-8=8(0)+b
-8=0+b
b=-8
So, y=8x+(-8)
Therefore, the equation of the linear function is y=8x+(-8).
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The height of a building is proportional to the number of floors The figure shows the height of a building with 9 floors
a. Reasoning write the ratio of height of the building to the number of floors. Then find the unit rate, and explain what it means in this
b. How tall would the building be if it had 15 floors
THIS IS FOR MIDDLE SCHOOL 7TH GRADE
Answer: B
Step-by-step explanation:
it has to do with simallar mathematics of 12th grade so you can do the sum
its pretty ez cuz im a 12th grader
x+13
2x +1
x-8
Find x
X = 43.5 .............
what is meter × meter
[tex]meter^{1`} *meter^{1} \\=meter^{1+1} \\=meter^{2}[/tex]
⇒Mote I used the laws of exponents : [tex]=x^{m} *x^{n} \\=x^{m+n}[/tex]
ASAP
10 yellow, 6 green, 9 orange, and 5 red cards facedown. Once a card selected, NOT replaced.
a. P(two cards that are not orange)
b. P(two cards that are neither red nor green)
The probability of selecting two cards that are not orange, is 0.483 and the probability of selecting two cards that are not red and green, is 0.393.
In the given question we have to find the probability.
From the question it is given that,
10 yellow, 6 green, 9 orange, and 5 red cards facedown.
Total number of cards = 10+6+9+5
Total number of cards = 30
Once a card selected, NOT replaced.
a.) Now finding the probability of selecting two cards that are not orange.
There are total orange cards = 9
The number of cards except orange card = 21
Then the probability of selecting one card except orange = 21/30
Then the probability of selecting other card except orange = 20/29
Then the probability of selecting two cards that are not orange is
P(O) = 21/30 * 20/29
P(O) = 420/870
P(O) = 0.483
Then the probability of selecting two cards that are not orange, is 0.483.
(b) Now finding the probability of selecting two cards that are neither red nor green.
The total number of cards except red and green card = 19
Then the probability of selecting one card except red and green card = 19/30
Then the probability of selecting other card except red and green card = 18/29
Then the probability of selecting two cards that are not red and green card is
P(RG) = 19/30 * 18/29
P(RG) = 342/870
P(RG) = 0.393
Then the probability of selecting two cards that are not red and green, is 0.393.
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The cost to produce x units of wire is C= 45x + 450, while the revenue is R= 70x. Find the interval where the product will at least break even.
The interval where the product will be at least break even equals to 18 units.
What is a break even point?In accounting, the break-even point refers to the production level at which total revenues equal total expenses.
Given data
Cost is given as C = 45x + 450
Revenue is given as: R = 70x
In this case, the point of breakeven will be:
Cost = Revenue
45x + 450 = 70x
We will collect like terms:
70x - 45x = 450
25x = 450
We will divide both side by 25:
25x/25 = 450/25
x = 18
Therefore, the interval where the product will be at least break even equals to 18 units.
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James shares 5/8 of a cake between 6 people.
What fraction of the cake do they each receive?
Answer:
5/48
Step-by-step explanation:
The fraction of people getting cake will be 1/6 of 5/8 thus it will be 5/48.
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
In another word, if we divide two numbers by each other then the upper word is called the numerator, and the lower word is called the denominator.
As per the given,
James shares 5/8 of a cake between 6 people.
Now, 1/6 of 5/8 will be as,
1/6(5/8) = 5/48
Hence "The fraction of people getting cake will be 1/6 of 5/8 thus it will be 5/48".
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For f(x)=3x+18, what is the value of x for which f(x) =21
a. x=2
b. x=5
c. x=1
d. x=-1
Answer:
I believe the answer is C
Step-by-step explanation:
a. would = 24b. would = 33c. would = 21d. would = 15 :)Point M is the midpoint of AB. If the coordinates of A are ( -3 , 6 ) and the coordinates of M are ( -5 , 2 ), what are the coordinates of B? (reference sheet on the left side)
The coordinates of B are (-7,-2).
What do you mean by x and y coordinates?
The x and y coordinates are a component of the x-axis and y-axis in a 2D space in the Cartesian coordinate system. The x and y coordinates for a point in space are expressed as an ordered pair (x, y). The position of the point on the x-axis is shown by the first number, while its location on the y-axis is indicated by the second number.
According to the given data in the question,
if M is the location where line segment AB meets its midpoint.
Then, we will using the midpoint formula,
[tex](-5,2)=(\frac{-3+x}{2},\frac{6+y}{2})..............(1)[/tex]
Putting the x-coordinates in (1),
[tex]-5=\frac{-3+x}{2}\\ -10=-3+x\\-10+3=x\\x=-7[/tex]
Similarly, putting the y-coordinates in (1),
[tex]2=\frac{6+y}{2} \\4=6+y\\4-6=y\\y=-2[/tex]
Hence, the coordinates of B are (-7,-2).
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The measure of the largest angle in a triangle is 110° larger than the sum of the measures of the other two angles. The measure of the smallest angle is three-
quarters the measure of the middle angle. Find the measure of each angle.
Measure of largest. smallest and middle angle of a triangle under given conditions is 145°, 15° and 20° respectively.
What is angle sum property of a triangle?
Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
According to the given question:
Let the measure of middle angle = x
The measure of the smallest angle is three-quarters the measure of the middle angle.
∴ Smallest angle = (3/4)x
The measure of the largest angle in a triangle is 110° larger than the sum of the measures of the other two angles.
∴ Largest angle = 110° + x + (3/4)x
Now, by Angle sum property of a triangle
x + (3/4)x + 110° + x + (3/4)x = 180°
On solving for the value of x we get
2x + (3/2)x = 70°
7x = 140°
x = 20°
Therefore,
measure of middle angle x = 20°
measure of smallest angle (3/4)x = 15°
measure of the largest angle 110° + x + (3/4)x = 145°
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Emma wrote one hundred thousand as 1,000,000. Explain what she did wrong.Then write the number correctly
Answer:
she wrote 1 million. It's 100,000
Step-by-step explanation:
she wrote 1 million. It's 100,000
Solve for y 4(7y+x)=4
Answer:
Step-by-step explanation:
y= 1/7 - x/7
Answer:
y = 1/7 - x/7
Step-by-step explanation:
4(7y + x) = 4 Distribute the 4 to 7y and x
28y + 4x = 4 Subtract the 4x on both sides
28y = 4 - 4x To get 'y' by itself divide 28 on both sides
y = 4/28 - 4x/28 You can simplify the 4/28 since 4 goes into 28 7 times
y = 1/7 - x/7
A rectangular ground is 121/4m long and 41/2 m broad. Find the perimeter and area of the ground.
Answer:
Thank you,Hope you like it and it will help you
In which quadrant does the point (10, -9) lie?
Answer:Qadrant 4
Step-by-step explanation:
[tex]4x^{2} +12x+8=0[/tex]
Step-by-step explanation:
4x² + 12x + 8 = 0
this has the same solutions as
x² + 3x + 2 = 0
as we simply divided everything by 4. 0/4 = 0.
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case that is
x = (-3 ± sqrt(3² - 4×1×2))/(2×1) =
= (-3 ± sqrt(9 - 8))/2 = (-3 ± sqrt(1))/2
x1 = (-3 + 1)/2 = -2/2 = -1
x2 = (-3 - 1)/2 = -4/2 = -2
so, the 2 solutions are
x = -1
or
x = -2
According to the general equation for conditional probability, if P(AB) =3/7 and P(B)=7/8,
what is P(AIB)? O A. O B. O c. O D. 16 49 32 24 49
Answer:
(d) 24/49
Step-by-step explanation:
You want to know P(A|B) when P(AB) = 3/7 and P(B) = 7/8.
Conditional probabilityThe general equation for conditional probability tells you ...
P(A|B) = P(AB)/P(B)
P(A|B) = (3/7)/(7/8) = (3/7)·(8/7)
P(A|B) = 24/49