John paid $34 for 2 books and 3 pencils. He paid $36 for 3 books and 2 pencils. How much was each?

Answer:

The answer is option C [tex](x+1)^{2} + ( y-2)^2 =25[/tex]

Step-by-step explanation:

i) The answer is option C [tex](x+1)^{2} + ( y-2)^2 =25[/tex]

Answer: x = -6, and y = -6  (-6, -6)

Step-by-step explanation: What we have here is a pair of simultaneous equations. Since we have been instructed to solve by substitution, we shall begin with the one which has one of the variables as having a coefficient of 1. We shall start with equation 2 which is,

y = 2x + 6

Having taken note of this, we can now go on to the other equation and substitute for the value of y.

Hence, from equation 1,

4x - 4y = 0 (substitute for the value of y)

4x - 4(2x + 6) = 0

4x - 8x - 24 = 0

-4x -24 = 0

Add 24 to both sides of the equation

-4x = 24

Divide both sides of the equation by -4

x = -6

Having calculated the value of x, we can now go on to substitute for the value of x in equation 2.

Therefore,

y = 2x + 6

y = 2(-6) + 6

y = -12 + 6

y = -6.

So, x = -6 and y = -6

Answer:

49.5

Step-by-step explanation: 11x9=99/2

Answer:

Quotient =(3x²-5x-1)  and reminder = 1

Step-by-step explanation:

[tex]\frac{9x^3-18x^2+2x+2}{3x-1}[/tex]

3x-1)9x³-18x²+2x+2(3x²-5x-1

      9x³-3x²

    ------------------------

          -15x²+2x+2

          -15x²+5x

           ------------------

                  -3x+2

                   -3x+1

                    --------

                         1

Therefore 9x³-18x²+2x+2=(3x²-5x-1)(3x-1)+1

Quotient =(3x²-5x-1)  and reminder = 1

6 3/11 that well be the answer

Answer:6 3/5

Step-by-step explanation: 10 2/5 - 3 4/5 = 33

5

= 63

5

= 6.6

The problems relate to airspeed and altitude in avionics and involve using mathematical concepts such as differential equations and differentials. The differential pressure when the indicated airspeed is 157 knots can be found by rearranging the given equation. Changes in airspeed can be determined based on differences in differential pressures. The equation for true airspeed in terms of altitude and differential pressure can be found by substituting the equation for indicated airspeed into the equation for true airspeed.

The subject of these problems is differential calculus, which deals with differential equations and differentials. We're using these mathematical concepts to solve problems related to airspeed and altitude in avionics.

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To find differential pressure at 157 knots, solve the equation S = 136.4√p + 4.5, yielding p ≈ 1.25. For changes in pressure from 218 to 195 knots, calculate both pressures then find the difference: Δp ≈ 0.50 in Hg. For true airspeed in terms of altitude and differential pressure, use T = (1 + A/50,000) ⋅ (136.4√p + 4.5). Estimating differential pressure for a true airspeed of 280 knots at 20,000 feet involves solving the combined equation to find p ≈ 2.05.

Let's tackle each problem step-by-step.

Problem 1

Given the indicated airspeed, S, of 157 knots, we need to find the differential pressure p.

The relationship is given by:

S = 136.4√p + 4.5

Substitute S = 157 into the equation:

157 = 136.4√p + 4.5

Subtract 4.5 from both sides:

152.5 = 136.4√p

Divide both sides by 136.4:

√p = 152.5 / 136.4 ≈ 1.118

Square both sides to solve for p:

p ≈ 1.118² ≈ 1.25 inches of mercury

Problem 2

We need to find the change in the differential pressure when the airplane slows down from 218 knots to 195 knots.

First, find the differential pressure at 218 knots:

218 = 136.4√p + 4.5

213.5 = 136.4√p

√p = 213.5 / 136.4 ≈ 1.565

p1 ≈ 1.565² ≈ 2.45 inches of mercury

Next, find the differential pressure at 195 knots:

195 = 136.4√p + 4.5

190.5 = 136.4√p

√p = 190.5 / 136.4 ≈ 1.397

p2 ≈ 1.397² ≈ 1.95 inches of mercury

Change in differential pressure:

Δp = p1 - p2 ≈ 2.45 - 1.95 ≈ 0.50 inches of mercury

Problem 3

We need to write the equation for true airspeed T in terms of altitude A and differential pressure p.

From the given formulas:

S = 136.4√p + 4.5

T = (1 + A/50,000) ⋅ S

Combining these, we get:

T = (1 + A/50,000) ⋅ (136.4√p + 4.5)

Problem 4

An airplane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet. We need to estimate the differential pressure p.

First, express the indicated airspeed S in terms of true airspeed T:

T = (1 + A/50,000) ⋅ S

280 = (1 + 20,000/50,000) ⋅ S

280 = 1.4S

S = 280 / 1.4 ≈ 200 knots

Next, solve for p using S = 136.4√p + 4.5:

200 = 136.4√p + 4.5

195.5 = 136.4√p

√p = 195.5 / 136.4 ≈ 1.433

p ≈ 1.433² ≈ 2.05 inches of mercury

This estimate is correct because it falls within the logical range for differential pressure at this indicated airspeed.

Answer:

Step-by-step explanation:

Since 8^2+15^2 = 289 and 17^2 = 289 then 8^2+15^2 = 17^2

8^2+15^2 = 17^2 Then according to the reciprocal of the Pythagorean theorem

it’s a right triangle

Answer:

12.5% is the answer for this question. the other answer is not correct,

Final answer:

The number 18 expressed as a percent is 100%. This is found by using the formula (Number / Total × 100%) and considering 18 as both the part and the whole.

Explanation:

To express the number 18 as a percent, you need to understand that a percent is a way of expressing a number as a part of 100. The word percent comes from the Latin phrase 'per centum' which means 'by the hundred'. So, the task at hand is to determine what part of 100 is 18.

The formula for converting a number to a percent is:

Number / Total × 100%

Since we are converting the whole number 18 into a percent, we treat it as 18 out of 18 or the 'part' as 18 and the 'whole' as also 18:

18 / 18 × 100% = 100%

Therefore, the number 18 expressed as a percent is 100%.

Answer:

Jose has completed 60% of his total deliveries.

Step-by-step explanation:

Given:

Jose needs to make a total of 25 deliveries this week. So far he has completed 15 of them.

Now, to find the percentage of his total deliveries has Jose completed.

Total deliveries = 25.

Deliveries completed = 15.

Now, to get the percentage of his total deliveries has Jose completed:

[tex]\frac{Deliveries\ completed}{Total\ deliveries} \times 100[/tex]

[tex]=\frac{15}{25} \times 100[/tex]

[tex]=0.6\times 100[/tex]

[tex]=60\%.[/tex]

Therefore, Jose has completed 60% of his total deliveries.

180 is the speed of the motorboat. I don't know the speed of the current.

........................................

120÷4=30

30×6=180

Answer:

180km

Step-by-step explanation:

Times both values by 1.8

1.8 : 1800000

You have 1,800,000 dm

Turn to m by dividing by 10 you get 180,000 m

Turn to km by dividing by 1000 you get 180km

Answer:

180

Step-by-step explanation:

Answer:

Step-by-step explanation:

  x³ + 3x² + 2x

= x(x² + 3x + 2)  , notice that x is a common factor

= x(x + 1)(x + 2)

Remark: (x + 1)(x + 2) = x² + 3x + 2  ; just develop

The second option is correct. To factor x³ + 3x² + 2x completely, factor out the common factor of x and then factor the quadratic expression inside the parentheses.

To factor the polynomial x³ + 3x² + 2x completely, we look for common factors and factor out an x term. This gives us x(x² + 3x + 2). Then, we factor the quadratic expression inside the parentheses by finding two numbers that multiply to give 2 and add up to give 3. In this case, the numbers are 1 and 2. Therefore, the factored form of the polynomial is x(x + 1)(x + 2).

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step-by-step explanation:

1.

8m +4n +7m-2n

=8m+7m+4n-2n

=15m+2n

2.

12(5y+4)

=60y+48   [ Using distributive law]

Therefore it is binomial of one variable.

3.

[tex]-2(\frac{1}{3}x -\frac{1}{5} )[/tex]

[tex]=-\frac{2}{3} x +\frac{2}{5}[/tex]

4.

4d+12

=4(d+3)

5.

-4.5n+3

= -4(5n+3)

Answer:

hotdog is $7.50

Step-by-step explanation:

hotdog = d soda = s

s + 2.5 = d

2d + s = 20

3s + 5 = 20

s = 5

5 + 2.5 = d

7.5 = d

Answer:

s = 5/4

Step-by-step explanation:

Solve for s:

86 = 8 s + 76

86 = 8 s + 76 is equivalent to 8 s + 76 = 86:

8 s + 76 = 86

Subtract 76 from both sides:

8 s + (76 - 76) = 86 - 76

76 - 76 = 0:

8 s = 86 - 76

86 - 76 = 10:

8 s = 10

Divide both sides of 8 s = 10 by 8:

(8 s)/8 = 10/8

8/8 = 1:

s = 10/8

The gcd of 10 and 8 is 2, so 10/8 = (2×5)/(2×4) = 2/2×5/4 = 5/4:

Answer:  s = 5/4

Answer: s = 1.25

Step-by-step explanation:

Answer:

Step-by-step explanation:

 ∠ABC =   ∠ DEF         {GIVEN}

            =      ∠GHI      {   ∠DEF =   ∠GHI - given}

 ∠ ABC =  ∠GHI

Answer:

4x, 2y, 3

Step-by-step explanation:

The terms are the number and variables separated by the minus sign and plus sign.

The three terms in the expression 4x - 2y + 3 are 4x, -2y and 3.

The given expression is 4x-2y+3.

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms.

In the given expression 4x-2y+3, the three terms are 4x, -2y and 3.

Therefore, the three terms in the expression 4x - 2y + 3 are 4x, -2y and 3.

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Answer:

Decimal form: 10.75

Fraction form: 10 6/8 = 10 12/16 = 10 18/24 and so on.

Simplest form: 10 3/4

Fraction greater than 1 form: 43/4

[tex]\boxed{g(x)=2x^2+31x+130}[/tex]

Hello! Remember to write complete questions in order to get good and exact answers. Here you haven't provided any quadratic equation, so I could help you in a general way. A quadratic equation is given by the form:

[tex]f(x)=ax^2+bx+c \\ \\ a,b,c \ constant \ and \ a\neq 0[/tex]

Suppose you have the following quadratic equation:

[tex]f(x)=2x^2+3x+6[/tex]

Perform the following transformation:

Then, we get:

[tex]g(x)=2(x+\mathbf{7})^2+3(x+\mathbf{7})+6+\mathbf{5}[/tex]

[tex]\left(x+7\right)^2:\quad x^2+14x+49 \\ \\ g(x)=2\left(x^2+14x+49\right)+3\left(x+7\right)+6+5 \\ \\ \\ g(x)=\:2x^2+28x+98+3x+21+6+5 \\ \\ \boxed{g(x)=2x^2+31x+130}[/tex]

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Answer:

18.19

Step-by-step explanation:

$20-15%=$17

$17+7%=18.19

Lin's father pays $18.19 for the meal after the 15% discount and 7% sales tax.

To find out what Lin's father pays for the meal after the discount and sales tax, we need to follow these steps:

Let's apply these steps to the given information:

Step 1: Discount amount = $20 x 15% = $3

Step 2: Discounted price = $20 - $3 = $17

Step 3: Sales tax amount = $17 x 7% = $1.19

Step 4: Total amount paid = $17 + $1.19 = $18.19

Therefore, Lin's father pays $18.19 for the meal after the discount and sales tax.

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Answer:

2x-8d

Step-by-step explanation:

Answer:

  5.  C.  {(22, 10), (23, 10), (24, 7), (25, 5)}

  6.  C.  x = -2

Step-by-step explanation:

A relation is not a function if a vertical line intersects a graph of it in more than one place.

__

5. A set of ordered pairs is not a function if any of the first-values is repeated.

In set A, (22, ) is repeated.

In set B, (23, ) is repeated.

In set D, (24, ) is repeated.

In set C, no first-value is repeated, so the relation is a function.

__

6. The line x=-2 is a vertical line, so a vertical line intersect it in an infinite number of places. It is NOT a function.

Answer:

E

Step-by-step explanation:

Given the system of two equations:

[tex]\left\{\begin{array}{l}\dfrac{2}{3}x-\dfrac{1}{2}y=1\\ \\-\dfrac{4}{3}x+y=-3\end{array}\right.[/tex]

Multiply the first equation by 6 and the second equation by 3 to eliminate fractions:

[tex]\left\{\begin{array}{l}4}x-3y=6\\ \\-4x+3y=-9\end{array}\right.[/tex]

Add these two equations:

[tex]4x-3y-4x+3y=6-9\\ \\0=-3[/tex]

You get false equality [tex](0\neq -9)[/tex], so the system of two equations has no solution (two equations represent parallel lines)

Answer:

Hamburger = $2.5

Fries = $0.80

Step-by-step explanation:

set up a system of equations

y = total cost

x = number of hamburgers

y = number of fries

[tex]24=8x+5y\\16.60=6x+2y[/tex]

find a LCF and multiply the equations. I'll be using the LCF of 5 & 2, which is 10 for y. so I will mulitilpy the first equation by 2 to get 10y and then the second by NEGATIVE 5 (-5) so when I combine both equations the y will cancle out because I'll get -10. Doing this, you should end up with this:

[tex]48=16x+10y\\-83=-30x-10y[/tex]

when you have this combine the equations to get

[tex]-35=-14x[/tex]

then divide both sides by -14 to get

[tex]2.5=x[/tex] this is the cost of one hamburger

then you plug in x into one of the original equations (I'll use the first equation)

[tex]24=8(2.5)+5y[/tex]

then solve for y to get

[tex]0.80=y[/tex] this is the cost for fry

if you plug in both the value for x and y into the original equations (like so)

[tex]24=8(2.5)+5(0.8)\\16.60=6(2.5)+2(0.8)[/tex]

you'll see that they are true (they equal one another)

this means that the cost of a hamburger is $2.50 and the cost of fries is $0.80

The cost of each hamburger is $2.50, and the cost of each serving of fries is $0.80.

Let's use a system of equations to solve this problem. Let h represent the cost of a hamburger and f represent the cost of a serving of fries.

From the information given, we can create two equations:

8h + 5f = 24

6h + 2f = 16.60

Now, we can solve this system of equations. We can start by solving one of the equations for one of the variables and then substituting it into the other equation. Let's solve equation 1 for h:

8h = 24 - 5f

h = (24 - 5f)/8

Now, substitute this expression for h into equation 2:

6[(24 - 5f)/8] + 2f = 16.60

Now, we can simplify and solve for f:

(3/4)(24 - 5f) + 2f = 16.60

Multiply both sides by 4 to eliminate the fraction:

3(24 - 5f) + 8f = 66.40

Now, distribute the 3 on the left side:

72 - 15f + 8f = 66.40

Combine like terms:

-7f = 66.40 - 72

-7f = -5.60

Now, divide by -7 to solve for f:

f = -5.60 / -7

f = $0.80

Now that we've found the cost of a serving of fries (f), we can use this value to find the cost of a hamburger (h) using equation 1:

8h + 5(0.80) = 24

8h + 4 = 24

8h = 24 - 4

8h = 20

h = 20 / 8

h = $2.50

So, the cost of each hamburger is $2.50, and the cost of each serving of fries is $0.80.

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Answer:

YES

Step-by-step explanation:

Answer:500

Step-by-step explanation:you divide it in half

Answer:

The equation to this word problem are:

x ≥ 30    ...... (1)

x ≥ y    ...... (2)

x + y  ≤ 100  ..... (3)

Step-by-step explanation:

Here, the given question is INCOMPLETE.

A private school admits no more than 100 students every year. additionally, at least 30 of these students must be girls, x and the school admits at least as many girls as boys,  y. What are the equation to this word problem.

Let us assume the number of girls  admitted in the school  = x

At least 30 of these students must be girls.

⇒ x ≥ 30    ...... (1)

Let us assume the number of boys admitted in the school  = y

The school admits at least as many girls as boys.

⇒ x ≥ y    ...... (2)

Also, TOTAL STUDENTS = No more than 100

So, Total Number of ( Boys + Girls) ≤ 100

⇒ x + y  ≤ 100  ..... (3)

Hence, the the equation to this word problem are:

x ≥ 30    ...... (1)

x ≥ y    ...... (2)

x + y  ≤ 100  ..... (3)

Answer:

y=(x+1)(x-1)(x+8)

Step-by-step explanation:

When creating a factor with a known zero, use (x-ZERO)

For instance: a zero of -1 would be reprsented as (x+1)

Answer:

Scalene triangle

Step-by-step explanation:

It is a scalene triangle because none of the sides are equal .equilateral triangle have the three sides equal. isosceles triangle have only two equal sides