Solve the following system of equations: (2 points) 5x + y = 9 3x + 2y = 4

Cost of admission for a group of 3 people is $ 120

Solution:

Given that amusement park charges an admission fee of 40 dollars per person

The cost, C (In dollars), of admission for a group of p people is give by the following expression:

C = 40p

Here "p" denotes the number of people

To find: cost of admission for a group of 3 people

For a group of 3 people, p = 3

Substituting p = 3 in given cost formula, we get the cost of admission for a group of 3 people

[tex]c = 40p\\\\c = 40(3) = 120[/tex]

Thus cost of admission for a group of 3 people is $ 120

Answer:

(3x+2)(2x-5)

Step-by-step explanation:

you can use process of elimination on this one just distribute the equations:

3x(2x-5)+2(2x-5)

6x^2-15x+4x-10 <------ Combine like terms

6x^2-11x-10

Final answer:

Factor completely [tex]6x^2[/tex] - 11x - 10 to find the equivalent binomials involves finding two numbers that multiply to -60 and add to -11. In this case, the numbers are -15 and +4, and using factor by grouping, the correct factorization is (3x + 2)(2x - 5).

Explanation:

When asked to factor the expression [tex]6x^2[/tex] − 11x − 10 completely, we're looking for two binomial expressions that multiply together to produce the original quadratic equation. To do this, we seek two numbers that multiply to give [tex]6x^2[/tex] times -10 (which is -[tex]60x^2[/tex]) and add to give -11x. Factoring is a method to express an equation as a product of its factors.

Let's find two such numbers: -15 and +4. These numbers give a product of -60 and a sum of -11, which fits our criteria. Now we replace the middle term (-11x) with -15x+4x to use factor by grouping.

Original equation: [tex]6x^2[/tex] − 11x − 10
Rewritten with new terms: [tex]6x^2[/tex] − 15x + 4x − 10
Factor by grouping: ([tex]6x^2[/tex] − 15x) + (4x − 10)
Factor out common terms: 3x(2x − 5) + 2(2x − 5)
Factor out the common binomial: (2x − 5)(3x + 2)

The completely factored form of the quadratic equation is (3x + 2)(2x − 5).

Answer:

G. 17.3

solution:

Answer: Avery's bottle holds 300 milliliters. If Dashawn's container holds 3/4 as much, then his container can hold 225 milliliters. Added together, both containers can hold 525.

Step-by-step explanation: 3/4 of 300 is 225. 300 + 225 = 525.

Paulo's family has 1 hour and 45 minutes before the trip to Scenic Lake Park after their arrival at the reunion.

The question asks how long Paulo's family has before the trip to Scenic Lake Park if they arrived at a family reunion at 8:30 A.M. and the trip is scheduled to start at 10:15 A.M. To solve this, we need to calculate the time difference between 8:30 A.M. and 10:15 A.M.

Here's how you calculate the time difference:

Answer:

9

Step-by-step explanation:

x= hk/ (k+h)(a-2)

10*15 (15+10) (7/2-2)= 9

Answer:

m=16/39

Step-by-step explanation:

-5(4m-2)=-2/3+6m

-20m+10=-2/3+6m

-20m-6m=-2/3-10

-26m=-2/3-30/3

-26m=-32/3

26m=32/3

m=(32/3)/26

m=(32/3)(1/26)

m=32/78

m=16/39

Answer:

The area of the pool increasing at the rate of 653.12[tex]cm^2/min[/tex]  when the radius is 13 cm

Step-by-step explanation:

Given:

radius of the pool increases at a rate of 8 cm/min

To Find:

How fast is the area of the pool increasing when the radius is 13 cm ?

Solution:

we are given with the circular pool

hence the area of the circular pool =

A =[tex]\pi r^2[/tex]-----------------------------(1)

The area of the pool os increasing at the rate of 8 cm/min, meaning that the arae of the pool is changing with respect to time t

so differentiating eq (1)  with respect to t , we have

[tex]\frac{d A}{d t}=\pi \cdot 2 r \cdot \frac{d r}{d t}[/tex]

we have to find  [tex]\frac{d A}{d t}[/tex] with [tex]\frac{d r}{d t}[/tex] = 8 cm/min and  r =  13cm

substituting the values

[tex]\frac{d A}{d t}=\pi \cdot 2 (13) \cdot 8[/tex]

[tex]\frac{d A}{d t}=\pi \cdot 26 \cdot 8[/tex]

[tex]\frac{d A}{d t}=\pi \cdot 208[/tex]

[tex]\frac{d A}{d t}= 208 \pi[/tex]

[tex]\frac{d A}{d t}=653.12[/tex]

Answer:

208pi cm^2/min

Step-by-step explanation:Take the derivative of the formula for Area and substitute the values

Answer:

no because it is just a straight line. a dot is plotted at (0,-3) and a straight line is horizontal.

Answer:

The probabilities are 0.4 and 0.6 respectively.

Step-by-step explanation:

We are given two spinning wheels with numbers on it and we have to find the probability of getting 3.

In the first wheel, there are 5 slots and the numbers are 3, 3, 2, 5 and 4.

So the probability of getting 3 =[tex]\frac{number of 3's}{total number of slots}[/tex]

                                            = [tex]\frac{2}{5}[/tex]

                                            = 0.4

In the second spinner there are three 3's and total of 5 slots.

So probability of getting 3 = [tex]\frac{number of 3's}{total number of slots}[/tex]

                                             = [tex]\frac{3}{5}[/tex]

                                             = 0.6

Hence the probabilities are 0.4 and 0.6 respectively.

Answer:

Cost of a box of brownies = $5

Cost of a loaf of banana bread = $4

Step-by-step explanation:

Let, x= box of brownies.                                              

y=loaf of banana bread.

Now,

Sarah bought 4 boxes of brownies and 6 loaves of banana at $44, after expressing this in equation form we get:-

[tex]4x+6y=44[/tex] --------------------------(equation 1)

And George bought 5 boxes of brownies and 3 loaves of banana at $37, after expressing this in equation form we get:-

[tex]5x+3y=37[/tex] --------------------------(equation 2)

Now,

[tex]4x+6y=44[/tex]

[tex]4x=44-6y[/tex]

[tex]x=\frac{44-6y}{4}[/tex]

[tex]x=11-\frac{6}{4}y[/tex]

[tex]x=11-\frac{3}{2}y[/tex]------------------(equation 3)

Now substituting equation 3 in equation 2 we get,

[tex]5x+3y=37[/tex]

[tex]5(11-\frac{3}{2}y)+3y=37[/tex]

[tex]55-(\frac{15}{2}\times y) +3y=37[/tex]

[tex]55-37=(\frac{15}{2}\times y)-3y[/tex]

[tex]18=7.5y-3y[/tex]

[tex]18=4.5y[/tex]

[tex]y=4[/tex] ----------------------------------(Equation 4)

Now putting value of y from equation 4 in  equation 3

i.e. [tex]x=11-\frac{3}{2}y[/tex]

[tex]x=11-\frac{3\times 4}{2}[/tex]

[tex]x=11-6[/tex]

[tex]x=5[/tex]

Therefore the cost of a box of brownies = $5

the cost of a loaf of banana bread = $4                                                        

Answer:

The principal amount invested is $4395.93 .

Step-by-step explanation:

Given as :

The Amount that saved for future = A = $5,000

The bank applied rate of interest = r = 4.3% compounded monthly

The time period of loan = t = 3 years

Let the principal amount invested = $p

Now, From monthly Compound Interest method  

Amount = principal × [tex](1+\dfrac{\textrm rate}{12\times 100})^{12\times time}[/tex]

Or, A = p × [tex](1+\dfrac{\textrm r}{12\times 100})^{12\times t}[/tex]

Or, $5000 = p × [tex](1+\dfrac{\textrm 4.3}{12\times 100})^{12\times 3}[/tex]

Or, $5000 = p × [tex](1.003583)^{36}[/tex]

Or, $5000 = p × 1.137414

∴ p = [tex]\dfrac{5000}{1.137414}[/tex]

i.e p = $4395.93

So, The principal amount invested = p = $4395.93

Hence, The principal amount invested is $4395.93 . Answer

Answer:

20,000

Step-by-step explanation:

Step-by-step explanation: Using the diagram shown which I have provided in the image attached, the definition of a midpoint states that M is the midpoint of segment LN, then segment LN ≅ to MN.

The definition of a midpoint can also be stated the other way around. using the diagram shown, if segment LN ≅ to segment MN, then M is the midpoint of segment LN.

We can use hash marks in the figure to show that are 2 segments are congruent.

Answer:

[tex]x \approx 31.8[/tex]

Step-by-step explanation:

[tex]\frac{\sin(75)}{22}=\frac{\sin(x)}{12}[/tex]

Cross multiply:

[tex]\sin(75) \cdot 12=\sin(x)\cdot 22[/tex]

Divide both sides by 22:

[tex]\frac{\sin(75) \cdot 12}{22}=\sin(x)[/tex]

Take [tex]\sin^{-1}( )[/tex] of both sides:

[tex]\sin^{-1}(\frac{\sin(75) \cdot 12}{22}=x[/tex]

Put left hand side into a calculator now:

[tex]31.7941 \approx x[/tex]

To the nearest tenth that is: [tex]x \approx 31.8[/tex]

Answer: -47 - 48x

Step-by-step explanation: When you first take a look at this problem, it's tempting to want to subtract -7 - 8 to get -15 and then distribute the -15 through the parentheses.

You wouldn't want to subtract however before you distribute because the distributive property is a form of multiplication and remember from your order of operations that multiplication comes before subtraction.

So the first thing you want to do here is distribute and change the minus sign in front of the -8 to plus a negative 8 so that you know you are distributing a -8 through your parentheses.

So we have -7 + -8 times 6x which is -42x + -8 times 5 which is -40.

Now we have -7 + -48x + -40.

Now just combine your like terms. -7 + -40 is -47 and plus a negative 48x can be written as -48x so we have -47 - 48x.

So your answer is just -47 - 48x.

Real word problem ⇒ constant of proportionality

$4.16 for 4 pounds of bananas ⇒ 1.04

$16.48 for 8 pounds of potatoes  ⇒ 2.06

$18.36 for 2 pizzas  ⇒ 9.18

2 cups of flour to make 36 cookies ⇒ 18

Solution:

A proportional relationship is one in which two quantities vary directly with each other.

We say the variable y varies directly as x,

if for x ∝ y

then,  x = y k

Where "k" is called constant of proportionality

[tex]k = \frac{x}{y}[/tex]

$4.16 for 4 pounds of bananas

x = 4.16 and y = 4

[tex]k = \frac{4.16}{4} = 1.04[/tex]

Thus constant of proportionality is 1.04

$16.48 for 8 pounds of potatoes

x = 16.48 and y = 8

[tex]k = \frac{16.48}{8} = 2.06[/tex]

Thus constant of proportionality is 2.06

$18.36 for 2 pizzas

x = 18.36 and y = 2

[tex]k = \frac{18.36}{2} = 9.18[/tex]

Thus constant of proportionality is 9.18

2 cups of flour to make 36 cookies

x = 36 and y = 2

[tex]k = \frac{36}{2} = 18[/tex]

Thus constant of proportionality is 18

Answer:

210 people.

Step-by-step explanation:

Here is the correct question: At a school fair, 70% of the people are under 16 years old. One third of the people  remaining are teachers. If there are 21 teachers at the fair, how many people are there at the fair?

Now, solving to find total number people in the fair.

Lets assume total number of people in the fair is "x".

As given, there is 70% of total number of people are under 16 year old.

∴ People under 16 year old= [tex]70\% of x= \frac{7x}{10}[/tex]

Next, finding the number of remaining people.

∴ Number of remaining people= [tex]x-\frac{7x}{10} = x-0.7x[/tex]

Number of remaining people is 0.3x

As given, One third of the people  remaining are teachers.

∴ Number of teachers= [tex]\frac{1}{3} \times 0.3x= 0.1x[/tex]

As given there are 21 teachers at the fair.

⇒ [tex]0.1x= 21\ teachers[/tex]

∴ x= [tex]\frac{21}{0.1} = 210[/tex]

Hence, total number of people in the fair are 210.

Answer:

Step-by-step explanation:

CD and AB are parallel; DB transverse

∠D + ∠B = 180     {co interior angles}

112 + 27 + y = 180

139 + y = 180

y = 180 - 139

y = 41

In ΔABC,

49 + x + y = 180   ( sum of all angles of triangle}

49 + x + 41 = 180

90 + x = 180

x = 180 - 90

x = 90

Answer:

x<-3

Step-by-step explanation:

-9x>27

x>27/-9

x>-3

The most accurate measurement of the boiling point of water is  option B: 212.1 degrees F.

The most accurate measurement of the boiling point of water is option B: 212.1 degrees F.

When measuring the temperature of boiling water, it is important to consider the accuracy and precision of the measuring instrument. The given options range between 205.46 and 213.15 degrees F, but the boiling point of water is widely accepted to be 212 degrees F at standard atmospheric pressure.

Therefore, the measurement closest to this accepted value is the most accurate, which is option B: 212.1 degrees F.

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Step-by-step explanation:

0.2x² − 0.8x = 1.6

Multiply both sides by 5.

x² − 4x = 8

Complete the square by adding 4 to both sides.

x² − 4x + 4 = 12

(x − 2)² = 12

x − 2 = ±√12

x = 2 ± √12

The positive solution is x = 2 + √12 ≈ 5.46.

Answer

THE REAL ANSWER IS c and f

Step-by-step explanation:

I just finished and they are the only 2 and I got it right

Nikki's and Dylan's Both proposed placements will light the same sized area.

A = 1/2 × b × h.

The steps are as follow:

A= 1/2×60×38

A= 30×38

A = 1,140ft.

So, Nikki's and Dylan's Both proposed placements will light the same sized area.

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Answer:

49x

Step-by-step explanation:

Answer:

Therefore the value of x is 15.

Step-by-step explanation:

Given:

AD || BC

m∠ B = (9x + 15)°

m∠ A = (3x - 15)°

To Find:

x = ?

Solution:

AD || BC       ...............Given

If two lines are parallel and sum of the interior angles are supplementary.

i.e m∠ B and m∠ A are interior between Parallel lines.

∴ [tex]\angle B + \angle C =180\\[/tex]

Substituting the given values we get

∴ [tex](9x + 15)+( 3x - 15)=180\\12x=180\\\\x=\frac{180}{12} \\\\\therefore x =15[/tex]

Therefore the value of x is 15.

The number is -11.

Step-by-step explanation:

Let,

the number be x.

According to given statement;

Sum of a number and five is doubled;

2(x+5)

is equals to one less than the number

= x-1

Combining both the sides and forming an equation

2(x+5)=x-1

[tex]2x+10=x-1\\2x-x=-1-10\\x=-11\\[/tex]

The number is -11.

Keywords: addition, subtraction

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Answer:

LA=6 WA=4 LB=6 WB=2

Step-by-step explanation:

Its a square so the sides are 6cm. 2:1 ratio means A is 6*4=24 cm while B is 6*2=12cm.

The angle of elevation from point C to point A is [tex]32^{\circ}[/tex]

Solution:

Given that we have to find the angle of elevation from point C to Point A

Given in figure that, angle A = [tex]58^{\circ}[/tex]

Given is a right angled triangle ABC where angle B = [tex]90^{\circ}[/tex]

We have to find angle C

The angle sum property of a triangle states that the angles of a triangle always add up to 180°

Therefore, in given triangle ABC

angle A + angle B + angle C = 180

[tex]58^{\circ} + 90^{\circ} + C = 180^{\circ}[/tex]

[tex]148^{\circ} + C = 180^{\circ}\\\\C = 180^{\circ} - 148^{\circ}\\\\C = 32^{\circ}[/tex]

Therefore angle C = [tex]32^{\circ}[/tex]