Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 8 people took the trip. She was able to purchase coach tickets for ​$290 and first class tickets for ​$980. She used her total budget for airfare for the​ trip, which was ​$5080. How many first class tickets did she​ buy? How many coach tickets did she​ buy?

Answer:

Graph of quadratic opening downward and linear sloping up to the left. They intersect at point negative 3, negative 1 and point 1, negative 5

Step-by-step explanation:

we have

[tex]-x^{2} -3x-1=-x-4[/tex]

we can separate the expression above into two equations

[tex]y=-x^{2} -3x-1[/tex] ----> equation A

This is a quadratic equation ( vertical parabola) open downward (the leading coefficient is negative)

[tex]y=-x-4[/tex] ----> equation B  

This is a linear equation with negative slope (decreasing function).so linear sloping up to the left

The solution of the original expression are the x-coordinates of the intersection point both graphs

using a graphing tool

The intersection points are (-3,-1) and (1,-5)

see the attached figure

Answer: C is the correct choice

Step-by-step explanation:

Answer:

B) 36 + 9 = 3(12 + 3)

Step-by-step explanation:

The distributive property of multiplication over addition is:

a(b + c) = ab + ac

This is demonstrated by switching the sides of option B) 36 + 9 = 3(12 + 3)

Answer:

B

Step-by-step explanation:

B  Because 12*3 = 36 and 3*3 =9

Answer:

C. Negative three-fourths

Step-by-step explanation:

Step-by-step explanation:

Given two fractions -1 1/4 and 1/2, the sum of the fractions is expressed as shown below:

-1 1/4 + 1/2

Converting the improper fraction -1 1/4 to mixed fraction will give -5/4. The expression will now become:

-5/4 + 1/2

Taking the LCM of the expression

= (-5+2)/4

= -3/4

Hence the sum of fraction Negative 1 and one-fourth and one-half is negative three-fourths

Final answer:

To add negative three-fourths and one-half, we first convert 1/2 to 2/4 to have the same denominator as -3/4. Adding the numerators gives us -1/4 as the sum, which can be visualized on the number line.

Explanation:

The student has asked how to find the sum of the fractions negative three-fourths (-3/4) and one-half (1/2) using a number line and equivalent fractions. To solve this problem intuitively, we can use our understanding of fractions as parts of a whole. First, we need to find a common denominator which is the least common multiple of 4 and 2, which is 4 in this case. So, we convert 1/2 to 2/4 since one half of one-half is one quarter, and then add it to -3/4.

Now, we have -3/4 + 2/4, which simplifies to -1/4 when we add the numerators, -3 and +2. This result can be visually confirmed on a number line. If we start at -3/4 on the number line and move 2/4 (which is half) to the right, we'll end up at -1/4, between -1 and 0.

Through this intuition and number line visualization, we have determined that -3/4 plus 1/2 equals -1/4. This highlights how our intuition about everyday things like parts of a pie or quarters in a dollar can help us with fraction operations like addition and finding common denominators.

Answer:

3x(9x^2+1) or C on edge

Step-by-step explanation:

did the test on edge and i got it right :

The polynomial that is factored completely is 5x^2 - 17x + 14, as it can be fully factored into (5x - 7)(x - 2) using the quadratic formula or factoring by inspection.

The question requires us to determine which polynomial is factored completely. We have four options to consider.

Hence, the polynomial that is factored completely is 5x^2 - 17x + 14.

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[tex]\text{Hey there!}[/tex]

[tex]\text{Is 6(6 + x) equivalent to 6x + 3?}[/tex]

[tex]\text{Kind of yes, and kind of no}[/tex]

[tex]\text{But in order for you to solve for this equation you have to use the distribute}\\\text{ property}[/tex]

[tex]\text{The distributive property formula is}\rightarrow\text{a(b + c) = a(b) + a(c) = ab + ac}[/tex]

[tex]\text{Let's solve for the equation, shall we?}[/tex]

[tex]\text{6(6 + x)}\\\text{6(6) + 6(x)}\\\text{6(6) = 36}\\\text{36 + 6(x)}\\\text{6(x) = 6x}\\\boxed{\text{\underline{36+6x}}}[/tex]

[tex]\text{36 + 6x}\neq \text{6x+ 36}[/tex]

[tex]\text{So, thus your answer has to be NO}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

The sum of the roots of a polynomial is 5/3, the product of the same polynomial is -11. Write the polynomial function in standard form.n:

Answer:

f(x) = x³ - 7x - 6

Step-by-step explanation:

Given that the zeros are x = - 1, x = - 2 and x = 3 then the corresponding factors are

(x + 1), (x +2) and (x - 3)

The polynomial is then the product of the factors, that is

f(x) = (x + 1)(x + 2)(x - 3) ← expand the first pair using FOIL

     = (x² + 3x + 2)(x - 3) ← distribute

     = x³ - 3x² + 3x² - 9x + 2x - 6 ← collect like terms

     = x³ - 7x - 6

Answer:

Explanation:

add 13 to both sides of the equation.

17+13=−8x.

30=−8x.

divde both sides by −8.

30−8=x⇒x=−308=−154.

As a check.

Step-by-step explanation:

Answer:

Step-by-step explanation:

17 = -13 - 8x....add 13 to both sides

17 + 13 = -13 + 13 - 8x

30 = -8x...now divide both sides by -8

-30/8 = (-8/-8)x

-30/8 = x.....reduce

- 15/4 = x <===

Answer:

Its the first option.

Step-by-step explanation:

120 is not a perfect square.

Its close to one though - 121 is a perfect square ( 11 * 11 = 121).

Answer:

a

Step-by-step explanation:

I toolk the test (:  :)

The solution to the inequality 2x<8 is x<4.

Step-by-step explanation:

Given inequality is;

2x < 8

For solving this inequality, we will divide both sides by 2 to find the value of x, therefore;

Dividing both sides by 2

[tex]\frac{2x}{2}<\frac{8}{2}\\x<4[/tex]

It means that x is less than four.

Thus,

The solution to the inequality 2x<8 is x<4.

Keywords: inequality, division

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The cost to rent the canoe for 7 hours is $ 104

Solution:

At eagle bay it cost $12 per hour to rent a Canoe

Nate and his friends rented a canoe for 4 hours and paid $68

Let "x" be the number of hours rented

We can solve use the point slope equation

[tex]y-y_1 = m(x-x_1)[/tex]

Where, "m" is the rate of change

[tex](x_1, y_1)[/tex] is the sample point

From given,

m = 12

[tex](x_1, y_1) = (4, 68)[/tex]

Therefore,

[tex]y - 68 = 12(x-4)[/tex]

[tex]y - 68 = 12x -48\\\\y = 12x -48+68\\\\y = 12x + 20[/tex]

Thus the linear equation is found

Here, "y" represents the amount paid for "x" hours

Find the cost to rent the canoe for 7 hours

Substitute x = 7 in linear equation

y = 12(7) + 20

y = 84 + 20

y = 104

Thus cost to rent the canoe for 7 hours is $ 104

To find the cost to rent the canoe for 7 hours, we can use the equation: Cost = Rate x Time. Given that the rate is $12 per hour and the time is 4 hours, the cost can be calculated as $68. Therefore, the cost to rent the canoe for 7 hours would be $119.

To find the cost to rent the canoe for 7 hours, we can use the equation:

Cost = Rate x Time

Given that the rate is $12 per hour and the time is 4 hours, we can substitute these values into the equation:

68 = 12 x 4

Solving for the rate, we get:

Rate = 68 ÷ 4

Therefore, the rate is $17 per hour. To find the cost to rent the canoe for 7 hours, we can multiply the rate by the time:

Cost = Rate x Time = 17 x 7 = $119

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Speed of boat in still water is 12 km/hr and speed of current is 9 km/hr

Solution:

From given,

Downstream distance = 213 km

Time taken for downstream = 11 hours

Thus, speed is given as:

[tex]\text{Downstream speed} = \frac{\text{Downstream distance}}{\text{time taken}}[/tex]

[tex]\text{Downstream speed} = \frac{231}{11} = 21[/tex]

Thus downstream speed is 21 km/hr

Also,

Upstream distance = 213 km

Time taken for upstream = 77 hours

Thus, speed is given as:

[tex]\text{Upstream speed} = \frac{\text{Upstream distance}}{\text{time taken}}\\\\\text{Upstream speed} = \frac{231}{77} = 3[/tex]

Thus upstream speed is 3 km/hr

If the speed downstream is "a" km/hr and the speed upstream is "b" km/hr , then:

[tex]\text{Speed in still water } = \frac{1}{2}(a+b)\\\\\text{Speed of current } = \frac{1}{2}(a-b)[/tex]

Here, a = 21 and b = 3

Therefore,

[tex]\text{Speed in still water } = \frac{1}{2}(21+3) = \frac{24}{2} = 12\\\\\text{Speed of current } = \frac{1}{2}(21-3) = \frac{18}{2} = 9[/tex]

Thus speed of boat in still water is 12 km/hr and speed of current is 9 km/hr

The speed of boat in still water is 12 km/hr as:

Let speed of Boat be 'b' and speed of Current be 'c'.

Distance given is 210 miles.

Therefore speed for downstream = 210 ÷ 10=21 mph

speed for upstream =3mph

Now we can form the two equations as :

i) b+c = 21 ......(i) For downstream

ii) b-c = 3.........(ii) For Upstream

Solving by substitution method :

From equation (ii) c = b - 3 Substitute this value of c in equation

(i) we get b + b - 3 = 21

Therefore b = 12. Now substitute the value of b in any of the equations above (i) or (ii) and get c= 9

b= 12 and c = 9.

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Each multiplication problem was evaluated individually, revealing that two products are greater than 1 and one is less than 1.

When evaluating whether each product is less than 1, equal to 1, or greater than 1, it's important to consider the values being multiplied. Let's examine each multiplication problem provided:

2 x 1/3: Multiplying 2 by one-third gives us 2/3, which is less than 1.

5 x 1/3: Multiplying 5 by one-third gives us 5/3, which simplifies to 1 and 2/3, meaning it is greater than 1.

1/2 x 3: Multiplying one-half by 3 gives us 3/2, which simplifies to 1 and 1/2, so this is also greater than 1.

Answer:

The coordinate  to the given equations is (3,1)

Step-by-step explanation:

Given equation is [tex]2x+6y=12\hfill (1)[/tex]

and [tex]4x-3y=9\hfill (2)[/tex]

To find the coordinate of the given equations :

Multiply the equation (2) into 2 we get

[tex]8x-6y=18\hfill (3)[/tex]

Now adding the equations (1) and (3) we get

[tex]2x+6y=12[/tex]

[tex]8x-6y=18[/tex]

_______________

[tex]10x=30[/tex]

[tex]x=\frac{30}{10}[/tex]

Therefore x=3

Substitute x=3 in (1)

2(3)+6y=12

6y=12-6

[tex]y=\frac{6}{6}[/tex]

Therefore y=1

The coordinate  to the given equations is (3,1)

To find the coordinates of the intersection point of the equations 2x+6y=12 and 4x-3y=9, we can solve the system of equations using the method of substitution. The coordinates of the intersection point are (3, 1).

To find the coordinates of the intersection point of the equations 2x+6y=12 and 4x-3y=9, we can solve the system of equations by using the method of substitution or elimination. Let's use the method of substitution:

The coordinates of the intersection point are (3, 1).

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The correct inequality is: C. $114,840.00(1 + 0.04)^2 > $115,362.00.

It correctly applies compound interest to determine when the house value exceeds $114,840.00.

To determine the number of years [tex](\( f \))[/tex] after purchase that the value of Isaac's house will be more than $114,840.00, we can use the formula for compound interest.

The formula for compound interest is given by:

[tex]\[ A = P(1 + r)^n \][/tex]

Where:

- A is the future value of the investment/asset.

- P is the initial principal amount (the initial value of the investment/asset).

-  r  is the annual interest rate (expressed as a decimal).

- n is the number of years the asset is invested for.

In this case:

- [tex]\( P = \$104,400.00 \)[/tex] (the initial value of the house).

- r = 0.04 (the annual rate of increase, which is 4% expressed as a decimal).

- We want to find the value of n when [tex]\( A > \$114,840.00 \)[/tex].

So, the inequality to represent this scenario is:

[tex]\[ \$114,840.00 < \$104,400.00(1 + 0.04)^n \][/tex]

Now, let's compare this inequality with the options provided:

A. [tex]\( \$114,840.00(1 + 0.04)^{n+1} > \$115,362.00 \)[/tex] - This option is incorrect because it uses [tex]\( n + 1 \) instead of \( n \)[/tex] in the exponent.

B. [tex]\( \$114,840.00(0.04)^2 > \$115,362.00 \)[/tex] - This option is incorrect because it uses [tex]\( (0.04)^2 \)[/tex] instead of [tex]\( (1 + 0.04)^n \)[/tex].

C. [tex]\( \$114,840.00(1 + 0.04)^2 > \$115,362.00 \)[/tex] - This option is correct. It uses the correct formula for compound interest and compares it to the threshold value of [tex]\$114,840.00[/tex].

D. [tex]\( \$114,840.00(1 - 0.04)^2 > \$115,362.00 \)[/tex] - This option is incorrect because it uses [tex]\( (1 - 0.04)^2 \) instead of \( (1 + 0.04)^n \).[/tex]

Therefore, the correct inequality is option C:

[tex]\[ \$114,840.00(1 + 0.04)^2 > \$115,362.00 \].[/tex]

Correct question is:

Isaac purchased a house for $104,400.00.

Every year, Isaac makes improvements so that the value of the house goes up by 4% Which of the following inequalities can be used to determine the number of years after purchase, f, that the value of Isaac's house will be more than $114,840.00?

[tex]A. $114,840.00(1+0.04)^r+1 > $115,362.00[/tex]

[tex]B. $114,840.00(0.04)^2 > $115,362.00[/tex]

[tex]C. $114,84000(1+0.04)^2 > $115,362.00[/tex]

[tex]D. $114,84000(1-0.04)^2 > $115,362.00[/tex]

Answer:

Step-by-step explanation:

5/y + 7/x =24.........(1)

12/y + 2/x =24........(2)

Let 1/y = a and 1/x = b

5a + 7b = 24 ...........(3)

12a + 2b = 24...........(4)

Multiply (3) by 2 and (4) by 7

10a + 14b = 48..........(5)

84a + 14b = 168.........(6)

Substracting (5) from (6)

84a - 10a = 168 - 48

74a = 120

a = 120/74

a = 60/37

Putting a = 60/37 in (3)

5a + 7b = 24

5(60/37) + 7b = 24

300/37 + 7b = 24

Multiply each term 37

300 + 259b = 888

259b = 888 - 300

259b = 588

b = 588/259

And a = 1/y

60/37 = 1/y

Cross multiply

60y = 37

y = 37/60

Also

b = 1/x

588/259 = 1/x

Cross multiply

588x = 259

x = 259/588

The ratio of the variables 'x' and 'y' will be 5/7.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of equations is given below.

5/y + 7/x =24

12/y + 2/x =24

Let 1/x = X and 1/y = Y. Then the equation is given as

5Y + 7X = 24            ...1

12Y + 2X = 24          ...2

From equations 1 and 2, then we have

12[(24 - 7X) / 5] + 2X = 24

288 - 84X + 10X = 120

74X = 168

X = 168 / 74

1/x = 168/74

x = 74/168

The value of the variable Y is given as,

12Y + 2(168 / 74) = 24

12Y = 720 / 37

Y = 60/37

1/y = 60/37

y = 37/60

The ratio of the variable 'x' and 'y' will be given as,

Ratio = x / y

Ratio = (74 / 168) / (37 / 60)

Ratio = (74 / 168) x (60 / 37)

Ratio = 5/7

The ratio of the variables 'x' and 'y' will be 5/7.

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9514 1404 393

Answer:

  45 cm

Step-by-step explanation:

The ratio of length to width is the same for the drawing as for the field.

  length/width = L/(30 cm) = (120 yd)/(80 yd)

  L = (30 cm)(3/2) = 45 cm . . . . . . multiply by 30 cm and simplify

The field should be 45 cm long on the drawing.

Final answer:

The soccer field in Lexie's scale drawing should be 45 centimeters long, using a scale factor based on the given width of 30 centimeters and the real soccer field's dimensions.

Explanation:

Lexie is scaling a real soccer field to a drawing, with the real field's dimensions being 120 yards long and 80 yards wide. When converting these dimensions to a scale drawing where the width is 30 centimeters, we need to find the drawing's length. To do this, we will use a scale factor.

First, we find the actual scale factor based on the given dimensions:

Actual width of soccer field = 80 yards

Width in the drawing = 30 centimeters

To convert yards to centimeters, we need to know that 1 yard equals 91.44 centimeters. Given this, the actual width in centimeters is 80 yards * 91.44 cm/yard = 7312 centimeters.

Now, we calculate the scale factor:

Scale factor = Width in the drawing / Actual width in centimeters = 30 cm / 7312 cm

Using this scale factor, we can find the length for the drawing:

Actual length of soccer field = 120 yards

Actual length in centimeters = 120 yards × 91.44 cm/yard = 10972.8 centimeters

Length in the drawing = Actual length in centimeters × Scale factor = 10972.8 cm × (30 cm / 7312 cm)

Calculating this gives us:

Length in the drawing = 45 centimeters

Therefore, the length of the soccer field in Lexie's drawing should be 45 centimeters.

Answer: 81

Step-by-step explanation:

The pattern of the sequence is :

[tex]1^{2}[/tex] , [tex]3^{2}[/tex] , [tex]5^{2}[/tex] , [tex]7^{2}[/tex] , [tex]9^{2}[/tex] ...

Which will be :

1 , 9 , 25 , 49 , 81 , ...

Therefore , the next pattern in the sequence is 81

Answer:

The correct answer is 1/4(n - 64).

Step-by-step explanation:

1/4n - 16  Write Original expression

0.25n -16     Simplify the fraction

0.25(n - 64)      Distribute(take out) 0.25 from n-16

1/4(n - 64)      

According to the construction described  ∠ DEF ≅ ∠GEF by SSS congruence theorem

How to show that the two angles are congruent

Statement        Reason

DE ≅ GE              given

DF ≅ GF               given

EF ≅ FE                reflexive property

Δ DEF ≅ Δ GEF   SSS congruence theorem

∠ DEF ≅ ∠GEF    CPCTC

The function is definately defined at x=0 but not x=1.

But its just one part of the coordinate (x,y).

If the value of y or f(x) is considered, you'll see that it is never possible to attain f(x)=0. In other terms (x,y)= (0,0) is not a defined point in the graph of the function because the graph doesnt pass through that point.

Now I hope you understood what I meant!

Conclusion- The above function is not defined at all points in the space having the abscissa or x=1 in the coordinate and also at ordinate or y=0 in the coordinate.nation:

The value of x for which the function g(x)=x/1-x is not defined is at x = 1.

A value of a function becomes not defined when the denominator of that function becomes zero.

The function is g(x)=x/1-x.

We can substitute the different values of x to find which makes the function not defined.

g(-1) = -1/1-(-1)

= -1/2

The function is defined.

g(0) = 0/1-0

= 0

The function is defined.

g(1) = 1/1-1

= 1/0 = not defined

The function is not defined.

g(2) = 2/1-2

= 2/-1 = -2

The function is defined.

Therefore, we have found that the value of x for which the function g(x)=x/1-x is not defined is at x = 1.

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308 is greater than 215.06

Solution:

Given data: 215.6 ÷ 0.7

Let us first convert the fraction without decimal.

To remove a decimal point multiply and divide the fraction by 10.

[tex]\frac{215.6}{0.7}=\frac{215.6\times10}{0.7\times10}[/tex]

       [tex]=\frac{2156}{7}[/tex]

If we divide 2156 by 7, we get quotient as 308.

Now, to compare the quotient with the number 215.06.

308 > 215.06

Hence, 308 is greater than 215.06.

It is greater than 215.06.

[tex]= 215.06 \div 0.7[/tex]

= 308

This 308 should be more or greater than 215.06

Therefore we can conclude that It is greater than 215.06.

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Answer:

two solutions : 9   ; -9

Step-by-step explanation:

x²=81

means : x² - 81 =0   but 81 = 9²

use identity ; a² - b² = (a-b)(a+b)

x² -9² = 0     : (x-9)(x+9)=0

x-9=0 or x+9 = 0

x =9 or x = -9

Answer:

y= 2(2x-1) -4

Step-by-step explanation:

you subtract 4 from both sides and it cancel outs at the y side(because 4-4 is 0) leaving just y.

Option C: 126° is the correct answer

Step-by-step explanation:

When two lines intersect, the four angles are formed. The angles vertically opposite with same vertex are called vertical opposite angles.

The opposite vertical angles are equal.

In the given figure, the pairs of vertically opposite angles are e,h and f,g.

Given

∠e = 126°

The measurement of e and h will be equal as they are vertically opposite

So,

m∠e = m∠h

m∠h = 126°

Hence,

Option C: 126° is the correct answer

Keywords: Vertical angles, lines

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=============================================

Explanation:

A triangle is only possible if you can add two sides and have that sum be larger than the third side. This is the triangle inequality theorem.

Choice A is ruled out because the second and third sides add to 7+7 = 14, but that's not larger than the first side 15.

Choice B is a similar story: 6+8 = 14 is not larger than 14 (the first side)

Choice C as well: 6+7 = 13 is not larger than 14

------

Choice D is the answer because

15+7 > 9

15+9 > 7

7+9 > 15

These three inequalities show that picking any two sides of this triangle, then adding them up, leads to a sum larger than the third side.

Answer:

5

Step-by-step explanation:

One step equation. You would subtract 7 from 12 to get 5 because x would be alone now.

[tex]

kx+12=3kx \\

12=2kx \\

x=\frac{12}{2k} \\

x=\frac{6}{k}

[/tex]

Hope this helps.

Answer: x=6/k

Step-by-step explanation:

kx + 12 = 3kx and subtract k from both sides

12=3kx-kx then simplify

12=2kx, now divide both sides by two

12/2=kx simplify again

6=kx divide next

6/k=x finally, switch sides to get x=6/k

Hope this helps, have a BLESSED and wonderful day, as well as a safe one!

-Cutiepatutie ☺❀❤

Answer:

x = 18.5

Step-by-step explanation:

Multiply 5 and 3.7.

Which equals 18.5.

Check: 18.5 / 3.7 = 5.√