25/35 and 10/14 simplified

Answer:

3x + 5y = -8

Step-by-step explanation:

to find an equation for a line parallel to 3x + 5y = -1 we need to find its slope because parallel lines have the same slope

so we convert from standard form, Ax+By=C, to slope-intercept form, y=mx+b

where 'm' refers to slope and 'b' is the y-intercept

5y = -3x - 1

y = -3/5x -1/5

now we know the slope is -3/5

we can use the slope and the point (2,-1) to find the y-intercept of our parallel line

-1 = -3/5(-1) + b

-1 = 3/5 + b

-5/5 = 3/5 + b

-8/5 = b

put it all together:

y = -3/5x - 8/5

now convert back to standard form:

multiply each side by 5 to get:

5y = -3x - 8

add 3x to each side to get:

3x + 5y = -8

The statement that applies to the sample math is:

B. the work shown to remove all fractions is not correct

The given steps are:

y = ¹/₄x + 2

- I first isolate the constant.

- After doing so, I get the equation: -¹/₄x + y = 2

- To remove the fraction, I multiply by –4, giving the equation x - 4y=2, which is the final answer.

The correct steps are as follows:

y = ¹/₄x + 2

First isolate the constant to get: y - ¹/₄x = 2

To remove the fraction, Multiply the obtained equation by –4

So, Equation : x - 4y = -8

On comparing both the work we can see that in the given work the removal of fraction is done incorrectly

They didn't multiply -4 on the right hand side .

Thus, option B applies.

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Answer:

i think it A

Step-by-step explanation:

Answer:

220mi

Step-by-step explanation:

Annie's dad drove a total of 490 miles before heading home. The correct option is D.

Distance is defined as the product of speed and time.

We can use the formula distance = rate x time to calculate the distance for each day.

On Monday, he drove for 4 hours at 55 mph, so the distance he traveled was:

distance = 55 mph x 4 hours = 220 miles

On Tuesday, he drove for 3 hours at 50 mph, so the distance he traveled was:

distance = 50 mph x 3 hours = 150 miles

On Wednesday, he drove for 2 hours at 60 mph, so the distance he traveled was:

distance = 60 mph x 2 hours = 120 miles

To find the total distance, we can add up the distances for each day:

220 miles + 150 miles + 120 miles = 490 miles

Therefore, Annie's dad drove a total of 490 miles before heading home.

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The probability that both players show rock in the first round is 1/9 or 0.1111 (rounded to four decimal places).

In rock, paper, scissors there are three possible outcomes for each player: rock, paper, or scissors. Assuming both players choose randomly and independently of each other, each player has a 1/3 chance of showing rock in the first round.

To find the probability that both players show rock in the first round, we can use the multiplication rule of probability for independent events. The multiplication rule states that the probability of the intersection of two independent events is the product of their probabilities.

Therefore, the probability that both players show rock in the first round can be calculated as follows:

P(both show rock) = P(player 1 shows rock) x P(player 2 shows rock) P(both show rock) = 1/3 x 1/3 P(both show rock) = 1/9

So the probability that both players show rock in the first round is 1/9 or approximately 0.111.

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9514 1404 393

Answer:

  A.  (f-g)(x) = -5^x +3x -2

Step-by-step explanation:

The only terms that can be combined are the constants.

  (f -g)(x) = f(x) -g(x)

  (f -g)(x) = (-5^x -4) -(-3x -2) = -5^x -4 +3x +2

  (f -g)(x) = -5x^4 +3x -2 . . . . . matches A

Answer:

\(Average = 10\)

Step-by-step explanation:

Given

\(First\ Three = 14\) --- Average

\(Next\ Seven= 4\) --- Average

Required

Determine the overall average

Represent the sum of the first three with x.

So:

\(\frac{x}{3} = 14\)

Solve for x

\(x = 14 * 3\)

\(x = 42\)

Represent the sum of the next seven with y.

So:

\(\frac{y}{7} = 4\)

Solve for y

\(y = 4 * 7\)

\(y = 28\)

The overall average is calculated as thus:

\(Average = \frac{x + y}{7}\)

\(Average = \frac{42 + 28}{7}\)

\(Average = \frac{70}{7}\)

\(Average = 10\)

Answer:

vertex= (4,-5)

Step-by-step explanation:

find the x and y values on the equation by solving

x= -56/2(-7) and y= -7x^2+56x-117

According to census the total number of male and female was 88,51,84,692, if number of male was 45,40,34,570 the number of female population is 43,11,50,122.

To find the wide variety of girl population, we will subtract the quantity of male population from the full population.

Total population = 88,51,84,692

Number of male = 45,40,34,570

Number of female = Total population - Number of male

= 88,51,84,692 - 45,40,34,570

= 43,11,50,122

Therefore, the number of female population is 43,11,50,122.

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If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

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The total amount paid over 30 years is $2,028,000 and the company needs to deposit $921,818.18 in an account earning 4% interest annually to cover the amount paid.

Simple interest is defined as interest paid on the original principal and calculated with the following formula:

S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100

Amount paid per week = $1300

Number of years = 30 years

The total amount paid = (Amount paid per week × number of weeks)

The number of weeks in 30 years :

1 year = 52 weeks

30 years = (30× 52) = 1560 weeks

The total amount paid for 30 years :

($1300× 1560) = $2,028,000

Using the simple interest formula : A = P(1 + rt)

A = total amount earned = 2,028,000

Principal = P

Interest rate, r = 4 %

Time, t = 30 years

A = P(1 + (0.04 × 30))

2,028,000 = P(1 + 1.2)

2,028,000 = P(2.2)

2,028,000/ 2.2 = P

P = $921,818.18

Hence, the total amount paid over 30 years is $2,028,000 and the company needs to deposit $921,818.18 in an account earning 4% interest annually to cover the amount paid

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The slope of the straight line passing through the two given points is undefined which means the line is parallel to the y-axis.

Let us consider the two points A(x₁,y₁) and B(x₂,y₂) be the two points (7,-6) and (6,-6) on the cartesian coordinates.

Let the slope of the line joining A (7,-6)  and B(6,-6)  be m.

We know that the slope of a line is given by:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Slope of the line

= (6-7) / (-6+6)

= -1 / 0

= undefined

Since the slope is undefined we can say that the straight line is parallel to the y axis.

we know that tan 90° = ∞

So any line parallel to this line will have the same slope as the y axis.

Hence the slope of the given line is undefined or infinity.

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The required measure of ∠1 is 121.5 degrees to the nearest tenth.

When two lines intersect at a location, vertical angles are generated. They are always equal to each other.

Since ∠1 and ∠2 forms a linear pair, their measures add up to 180 degrees.

So, we can write as:

∠1 + ∠2 = 180   ....(i)

As per the question,

m∠1 = x + 49

m∠2 = x - 14

Substituting these values into the equation (i) for the sum of the angles, we get:

(x + 49) + (x - 14) = 180

Simplifying this equation, we can combine like terms:

2x + 35 = 180

Subtracting 35 from both sides, we get:

2x = 145

Dividing both sides by 2, we get:

x = 72.5

So, the measure of ∠1 is:

m∠1 = x + 49

m∠1 = 72.5 + 49

m∠1 = 121.5 degrees (rounded to the nearest tenth)

Therefore, the measure of ∠1 is 121.5 degrees.

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The value of the missing part of the triangle such as PR and ST = 8 and 5 respectively

Triangle PQS is congruent with triangle PRS

Therefore, PQ = PR

That is;

PQ = 8

PR = 2x

8 = 2x

X = 8/2 = 4

PR = 2(4) = 8

For ST;

Triangle VST = VUT

That is, TU = ST

ST = 5z

TU = 2z+3

5z = 2z+3

5z+2z = 3

z= 3/3 = 1

ST = 5(1) = 5

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Answer: The range is 20, Standard Deviation, σ: 6.8702256149271

Step-by-step explanation:

I hope it helped!

<3

Answer:

x=-1

Step-by-step explanation:

given data:

-5|2x+2|-3>-3

let us simplify,

Answer:

d² - 24d + c = (d - 12)² - 144 + c

a) The solution to the equation is y = ( 21,600 - 3.6x ) / 7.5 , where y is the number of trucks and x is the number of cars

b) when x = 1,000 cars , y = 2,400 trucks and

when x = 4,250 cars , y = 840 trucks

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number of cars be x

Let the number of trucks be y

The total cargo the ship can hold = 21,600 tons

The weight of one car = 3.6 ton

The weight of one truck = 7.5 tons

Now , the equation will be

3.6x + 7.5y = 21,600

On simplifying the equation , we get

Subtracting 3.6x on both sides of the equation , we get

7.5y = ( 21600 - 3.6x )

Divide by 7.5 on both sides of the equation , we get

y = ( 21,600 - 3.6x ) / 7.5

The number of trucks y = ( 21,600 - 3.6x ) / 7.5

b)

Now , when x = 1000 cars

Substitute the value of x in the equation , we get

y = ( 21,600 - 3.6 ( 1000 ) ) / 7.5

y = 2,400 trucks

And , when x = 4250 cars

Substitute the value of x in the equation , we get

y = ( 21,600 - 3.6 ( 4250 ) ) / 7.5

y = 840 trucks

Hence , the equation is y = ( 21,600 - 3.6x ) / 7.5

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Answer:

37 miles

Step-by-step explanation:

74/2=37

If Nolan's car can go 74 miles for 2 gallons, then one gallon could last it for 37 miles.

The day, from the following two days, which would be the best to sell both stocks with the closing price is day 3 by an amount of $2.45.

Given are the closing prices of two stocks in three days.

If you purchase 65 shares of Metropolis stock and 50 shares of Suburbia stock on Day 1 at the closing price,

Amount invested = (65 × 17.95) + (50 × 5.63) = $1448.25

If the stock is sold in day 2,

Amount received = (65 × 18.25) + (50 × 4.98) = $1435.25

Profit = $1435.25 - $1448.25 = -$13

If the stock is sold in day 3,

Amount received = (65 × 18.28) + (50 × 5.25) = $1450.7

Profit = $1450.7 - $1448.25 = $2.45

The profit is more for day 3 than day 2.

Hence it is best to sell on day 3 by $2.45.

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Answer:

the last one

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Here

Profit = SP-CP

=Rs490 - Rs 450

=Rs 40

Answer:

Step-by-step explanation:

The two equations you want to graph for your graphical solution are ...

  16x +8y = 80 . . . . . . total earnings

  y = 3x . . . . . . . . . . relation between clearing and tutoring hours

The attached graph shows the solution to be (x, y) = (2, 6).

Eva worked 2 hours tutoring and 6 hours clearing tables.

For constant A to be -4 (option 1) the system of equations have exactly one real solution.

NOTE: We are working with the problem statement: Y=-3 Y=Ax2+4x-4 In the system of equations above, a is constant. For which of the following values of a does the system of equations have exactly one real solution?

We have given, y=-3

y= Ax^2+4x-4

Therefore, -3= Ax^2+4x-4

or, Ax^2+4x-1=0

For second order equation of ax^2+bx+c=0 have a solution for

x= [-b± (√b^2-4ac)]/2a]   [Ax2 + Bx + C = 0 is the Sridharacharya equation, where a, b, and c are real values and a 0. The Sridharacharya formula, which is stated as x = (-b (b2 - 4ac)) / 2a, provides the answer to the Sridharacharya equation.]

For single solution b^2-4ac=0

here, Ax^2+4x-1=0

4^2 - 4a(-1)=0

16+4a=0

a= -(16)/4

a= -4

option A is correct .

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This is only true equation when A is equal to -2. Therefore, the correct answer is B) -2.

B) -2

The given system of equations can be written as:

Y = A*x^2 + 4*x - 4

We can solve this equation by using the Quadratic Formula. The Quadratic Formula states that the solutions to the equation are given by:

x = [-b +/- sqrt(b^2-4ac)]/2a

where a, b, and c are the coefficients of the equation. In this case, a = A, b = 4, and c = -4.

Substituting these values into the equation, we get:

x = [-4 +/- sqrt(4^2-4*A*(-4))]/2A

Simplifying this, we get:

x = [-4 +/- sqrt(16 + 16A)]/2A

For the system of equations to have two real solutions, the value of the square root must be greater than or equal to zero. This means that 16 + 16A must be greater than or equal to zero.

This is only true when A is equal to -2. Therefore, the correct answer is B) -2.

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Answer:

x^8/3

Step-by-step explanation:

The nominal rate per annum compounded half-yearly, equivalent to an effective rate of 14.5% per annum, is approximately 14.900625%.

To convert an effective rate to a nominal rate compounded half-yearly, we can use the formula:

Nominal rate \(= (1 + r/m)^m - 1\)

Where:

r = effective rate

m = number of compounding periods per year

In this case, the effective rate is 14.5% per annum, and we want to convert it to a nominal rate compounded half-yearly.

Since compounding is done semi-annually, m would be 2.

Plugging in the values:

Nominal rate \(= (1 + 0.145/2)^2 - 1\)  

Simplifying the expression inside the parentheses:

Nominal rate \(= (1 + 0.0725)^2 - 1\)

Calculating the exponent:

Nominal rate \(= (1.0725)^2-1\)

Performing the calculations:

Nominal rate = 1.14900625 - 1

Nominal rate = 0.14900625

Converting the nominal rate to a percentage:

Nominal rate = 14.900625%

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Yes, she did buy additional carrot seed. No, the total number of seeds was 1120. No, the total price is $171. She did buy more maize and beans than carrots.

Multiplication is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and division. A product is the outcome of a multiplication operation. Multiplication is a way of calculating the product of two or more integers in mathematics. It is one of the most fundamental mathematical operations that we utilize every day. When we multiply two numbers, the result is known as the product. The multiplicand is the number of items in each group, and the multiplier is the number of such equal groupings. In our situation, the multiplicand is, the multiplier is, and the product is 6.

Here,

Beans=12*40

=480

cost of beans=12*5

=$60

Carrot=15*36

=540

cost of carrot=15*7

=$105

Corn=2*50

=100

cost of corn=2*3

=$6

Total seeds=1120

Total cost=$171

Yes she bought more of carrot seed. No the total seeds was 1120. No the total cost is $171. Yes she bought more corn and beans than carrot.

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