Priya says the sum of 1 2/5 and 4/5 is 1 6/5. Kiran says the sum is 11/5. Elena says it is 1 6/10. Tyler says it is 2 1/5. Do you agree with any of them? Use this space to solve the addition problem. Then Justify whether each person's answer is right or wrong using full sentences. You may use drawings if it helps.

Answer: x=3

Step-by-step explanation:

3(x+6)-10=17

3x+18-10=17

3x+8=17

3x=17-8

3x=9

x=3

Answer: 3 , 4 and 5 are correct options

Step-by-step explanation:

The required solution of the given system of equations is x = 5 and y = -1/4.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
3x+4y=8 - - - - - (1)

x-4y=4 - - - - (2)

Put x from equation 2 to equation 1
12y + 12 + 4y = 8
16y = -4
y = -1/4

Now,
Put y in equation 2
x - 4 {1/4} = 4

x = 5

Thus, the required solution of the given system of equations is x = 5 and y = -1/4.

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Answer: 40 pupils

Step-by-step explanation:

 35           14

-------   =   --------

100             ?

find the denominator.

multiply 14 and 100:

14 x 100 = 1400

divide 1400 by 35

1400/35 = 40

Therefore there are 40 students

The first row of a bank statement shows -

Option D : The account's balance at the beginning of the period.

What is bank statement?

A bank statement, also known as an account statement, is a record that summarises all of an account's transactions for a given month and is normally issued by the bank to the account holder each month.

The transactions for a bank account over a specific time period, typically monthly, are listed in a bank statement.

The statement provides the beginning and ending balances for the period along with deposits, charges, and withdrawals.

Every month, account holders typically analyse their bank statements to assist them keep track of their spending and costs and to check for any erroneous or fraudulent charges.

Therefore, the first row shows the balance at the beginning period.

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The unit rate of Jana's ride is 0.3 Miles per minutes

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

The unit rate of Jane's ride is

= 15miles/50minutes

= 0.3miles per minute

therefore the unit rate of Jane's ride is 0.3 miles per minute.

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We know from the problem that l = 3w - 5. We also know the formula for area is A = w * l. Therefore, the area of the rectangle is A = w * (3w - 5). We can then set this equation equal to 50 as the question states and solve for w.

[tex]50 = w * (3w-5)[/tex]

Expand the multiplication

[tex]50 = 3w^{2}- 5w[/tex]

Subtract 50 from both sides.

[tex]0 = 3w^{2} - 5w - 50[/tex]

We now have a quadratic equation and can solve it using the quadratic formula to find w. We find that the solutions to the equation are 5 and -3.3. We know that the width can't be negative, so the width must be 5.

Finally, we can plug this solution into the length formula we found earlier to solve for length.

[tex]l = 3w - 5[/tex]

Plug in the solution to w.

[tex]l = 3(5) - 5[/tex]

Multiply 3 and 5.

[tex]l = 15-5[/tex]

Subtract 5

[tex]l = 10[/tex]

Therefore the width is 5 and the length is 10.

The value of x in the expression is 0.9429

From the question, we have the following parameters that can be used in our computation:

8 square root x^5 divided by square root x = 5/x^8 divided by 1/x^2

Express properly

So, we have

8√x⁵/√x = 5x²/x⁸

Evaluate the quotients

So, we have

8x² = 5/x⁶

Cross multiply

This gives

x⁸ = 5/8

Take the 8th root of both sides

x = 0.9429

Hence, the solution is 0.9429

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The equation of the line that runs through the point (0,-1) and (1,2) in slope-intercept form is y = 3x - 1.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

From the diagram, the line runs through the point (0,-1) and (1,2).

First, we determine the slope of the line

Slope m = change in y / change in x

Slope m = (2 - (-1)) / (1 - 0)

Slope m = (2 + 1) / (1 - 0)

Slope m = 3/1

Slope m = 3

Next, plug the slope m = 3 and point (0,-1) into the point slope formula.

y - y₁ = m( x - x₁ )

y - (-1) = 3( x - 0 )

y + 1 = 3x - 0

y + 1 = 3x

Subtract 1 from both sides

y + 1 - 1 = 3x -1

y = 3x - 1

Therefore, the equation of the line is y = 3x - 1.

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The given function is continuous at  x = 5,  RHL = LHL = F(5)

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  =  [x² - 49]/[x² + 6x -7][x² + 14x + 49]

To check whether it is continuous at x = 3

First taking LHL,

[tex]\lim_{h \to \00 } F(x)[/tex]  

[tex]\lim_{h \to \00 }[/tex]   [(5-h)² - 49]/[(5-h)² + 6(5-h) -7][(5-h)² + 14(5-h) + 49]

⇒  -24/(48x144)

⇒   -1/288

Now, taking RHL

[tex]\lim_{h \to \00 }[/tex]   [(5+h)² - 49]/[(5+h)² + 6(5+h) -7][(5+h)² + 14(5+h) + 49]

⇒  -24/(48x144)

⇒   -1/288

The value at x = 3

F(3)  =  [(5)² - 49]/[(5)² + 6(5) -7][(5)² + 14(5) + 49]

⇒  -24/(48x144)

⇒   -1/288

Hence Proved,   RHL = LHL = F(5)

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Answer:

To find the GCF of 2^5·5·11 and 2^3·5^2·7, we first prime factorize each number:

2^5·5·11 = 2^5 x 5 x 11

2^3·5^2·7 = 2^3 x 5^2 x 7

Next, we look for the highest power of each prime factor that they both have in common:

2^3 is the highest power of 2 that both numbers have.

5^2 is the highest power of 5 that both numbers have.

So, the GCF of 2^5·5·11 and 2^3·5^2·7 is 2^3 x 5^2 = 180.

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

Proportionately, if Hayden uses 4 cups of flour and 5 cups of sugar to make cupcakes, he will eat 20 cupcakes.

Proportion refers to the relative size or ratio of one value compared to another quantity.

Proportions are represented as fractional values with decimals, percentages, or fractions.

The quantity of flour for 1 cupcake = 1/5 cups

The quantity of sugar for 1 cupcake = 1/4 cups

The quantity of flour Hayden uses = 4 cups

The number of cupcakes from 4 cups = 20 (4 ÷ 1/5)

The quantity of sugar Hayden uses = 5 cups

The number of cupcakes from 5 cups of sugar = 20 (5 ÷ 1/4)

Thus, according to the proportion of cupcake ingredients to the available quantities of ingredients, Hayden will make and eat 20 cupcakes.

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A cupcake requires 1/5 cup of flour and 1/4 cup of sugar to make.

The total charge for the month is given as follows:

$123.93.

The total charge for the month is obtained applying the proportions in the context of the problem.

The costs are given as follows:

For a customer with 7 lines, the charges are given as follows:

Hence the total charge is then calculated as follows:

3 x 19.99 + 4 x 15.99 = $123.93.

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Based on the definition of an angle bisector, the measure of angle WUT is: B. 38°.

An angle bisector is a line, ray or segment that divides an angle into two congruent angles.

Therefore:

m<VUW = m<WUT

Substitute

4x + 6 = 6x - 10

Solve for x

4x - 6x = -6 - 10

-2x = -16

x = 8

m<WUT = 6x - 10

Plug in the value of x:

m<WUT = 6(8) - 10 = 38°

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Answer: 3 3/8 or 3.375

Step-by-step explanation:

Answer:

3.375

Step-by-step explanation:

A graph of the line with a slope of 3/4 and y-intercept of -9 is shown in the image attached below.

Mathematically, the standard form or slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Next, we would write an equation of this straight line based on the slope and y-intercept as follows;

y = mx + c

y = 3x/4 + (-9)

y = 3x/4 - 9

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Answer:

6561m^4

Step-by-step explanation:

(9m)^4 =

(9 * m)^4 =

9^4 * m^4 =   ==> distribute the power 4 to 9 and m

6561 * m^4 = ==> simplify

6561m^4

Since ΔABC and ΔACD are similar triangles, therefore the length of AC is 18 m.

Similar triangles are triangles with corresponding sides that have the same ratio.

Thus:

AD is parallel to BC (bases of a trapezoid are parallel)

Therefore:

∠ACB = ∠CAD (alternate interior angles)

This implies that, ΔABC ~ ΔACD by AA similarity theorem.

Thus:

AC/DA = CB/AC

Substitute

AC² = 12 × 27

AC = √324

AC = 18 m

Therefore, since ΔABC and ΔACD are similar triangles, therefore the length of AC is 18 m.

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If Jane took 30 min to drive her boat upstream to water-ski at her favorite spot. her boat speed in still water is;3 km/h.

Let's x represent the  Jane's boat speed in still water

Upstream, her speed was x - 2 km/h.

Downstream, her speed was x + 2 km/h.

Let's d represent the distance between the start and end point

Let the  time it takes to cover d at a speed of x - 2 km/h=  30 min.

Let the  time it takes to cover d at a speed of x + 2 km/h=  10 min.

So we have:

d / (x - 2) = 30 min and

d / (x + 2) = 10 min.

Multiplying both sides of each equation

d * x - 2d = 30 * (x - 2)

d * x + 2d = 10 * (x + 2).

Adding the two equations and solve for x

2d * x = 40 * x + 20

20 * x = 40 * x + 20

20 * x = 60 * x

x= 3 km/h

Therefore Jane's boat speed in still water is 3 km/h.

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Step-by-step explanation:

If you write down the amount of time Bryant spends sleeping every night, you will see a sequence of numbers between 6 and 9 hours inclusive.

Answer:

9 and 6

Step-by-step explanation:

7x - x + 9 ← collect like terms

= (7x - x) + 9

= 6x + 9

the constant term is the numeric term, with no variable ( letter) attached

the constant term is + 9

the coefficient of x is the numeric value before x

the coefficient of x is 6

The equation of the horizontal asymptote of f(x) is given as follows:

x = 5/4.

The rational function f(x) in the context of this problem is defined as follows:

f(x) = (-4x² + 54x - 47)/(4x - 5).

The horizontal asymptote of a function happens at a value of x which is outside the function's domain.

For a rational function, the denominator cannot be zero, hence the value of x that represents the horizontal asymptote of f(x) is obtained as follows:

4x - 5 = 0

4x = 5

x = 5/4.

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Part 1

E. There is a pair of congruent angles and a pair of congruent right triangles, so the triangles are similar by the AA [tex]\sim[/tex] postulate.

Part 2

Note that 4 ft 6 in = 4.5 ft. Using the fact that corresponding sides of similar triangles have proportional side lengths,

[tex]\frac{x}{14}=\frac{4.5}{4} \implies \boxed{x=15.75 \text{ ft}}[/tex]

The rate of increase is 150%.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Desk were on sale for $200 the sale is over,

and they have gone back up to the full price of $300.

The rate of increase,

= 300 x 100 / 200

= 150%

Therefore, the rate is 150%.

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The greatest number of biscuits Habib can make is 25

From the question, we have the following parameters that can be used in our computation:

Habib has 400 g of butter

150 g of sugar

675g of flour

Factor each number to determine the GCF

So, we have

400 = 2 * 2 * 2 * 2 * 5 * 5

150 = 2 * 3 * 5 * 5

675 = 3 * 3 * 3 * 5 * 5

So, we have

GCF = 5 * 5

Evaluate

GCF = 25

Hence, the number of biscuits is 25

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Answer:

working on a answer hold up

Step-by-step explanation:

Answer:

C) AB, AC, AD

Step-by-step explanation:

All of the line segments stem from point A and connect to a point on the circle.

Hope this helped! :)

Answer:

third option

Step-by-step explanation:

the radius of a circle is a line segment from the centre of the circle A to a point on the circumference of the circle.

the circle shown here with centre A has 3 segments to the circle.

AB , AC and AD

Regarding shopping for a new card, it would depend on the terms and conditions of the new card, including the annual interest rate and any fees. Rachel should compare the options available and weigh the benefits and drawbacks of each before making a decision.

The length of time it will take Rachel to pay off her credit card balance can be calculated by dividing the outstanding balance by the monthly payment amount and then adding the number of months needed to pay off the balance.

Balance = $8,281

Monthly payment = $250

Annual interest rate = 16%

To calculate the length of time it will take to pay off the balance, we would first need to calculate the monthly interest rate, which can be done by dividing the annual interest rate by 12:

Monthly interest rate = 16% / 12 = 1.33%

Next, we can calculate the monthly payment amount, including the interest:

Monthly payment amount = $250 + ($8,281 * 1.33%)

By continually subtracting the monthly payment amount from the balance and adding the monthly interest, we can determine the length of time it will take to pay off the balance.

Regarding shopping for a new card, it would depend on the terms and conditions of the new card, including the annual interest rate and any fees. Rachel should compare the options available and weigh the benefits and drawbacks of each before making a decision.

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