Solve for x: 3(x + 1) = 2(x - 1)​

Answer: Pedro= 1205. Ricky= 1488

Step-by-step explanation:

It is found that Ricky hits 1202 base and Pedro hits = 1485 base

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given that

Pedro + Ricky = 2693 hits

Let Ricky hits = x

So, the Pedro hits will be = x + 283

( x + 283 ) + x = 2693

2 x + 283 = 2693

2 x = 2693 - 283

2 x = 2404

x = 1202

So, the Ricky hits 1202 base

Thus Pedro hits (1202 + 283) = 1485 base

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Answer:

Please read the answers below.

Step-by-step explanation:

a. If he rides at a rate of 3 miles per hour, how long will it take?

Time = Distance/Rate

Time = 24/3 = 8 hours

At 4 miles per hour?

Time = 24/4 = 6 hours

At 6 miles per hour?

Time = 24/6 = 4 hours

b. Write an equation that Han can use to find t, the time it will take to ride 24 miles, if his rate in miles  per hour is represented by r.

The equation is the same we used in the part a of the problem:

t = 24/r

c. On graph paper, draw a graph that shows t in terms of r for a 24-mile ride.

The graph is attached.

Answer:

Ten plus six hundredth plus 8 thousandth equals ten and sixty-eight thousandths

Step-by-step explanation:

0.06 is in the hundredth place

0.008 is in the thousandth place

Answer:

ten plus zero point zero six plus zero point zero zero eight

Step-by-step explanation:

The ten is 10 then plus + and then 0.06 plus + 0.008

Answer: the answer is 5 feet per second

Step-by-step explanation:

Answer:

9ft wide

Step-by-step explanation:

First we convert it to ratios

[tex]\frac{6}{x} \frac{2}{3}[/tex]

Then we cross-multiply

6*3=2x

Multiply 6 and 3

18=2x

Solve for x

x=18/2

x=9

Diaz family spend $ 20 if they bought 3 adults tickets and 1 children's ticket

Solution:

Let "a" be the cost of each adult ticket

Let "c" be the cost of each student ticket

The Spencer family bought 3 adult tickets and 2 children's tickets for $23.50

Therefore, we frame a equation as:

[tex]3 \times a + 2 \times c = 23.50[/tex]

3a + 2c = 23.50 --------- eqn 1

The Yang family bought 2 adult tickets and 4 children's tickets for $25

Therefore, we frame a equation as:

[tex]2 \times a + 4 \times c = 25[/tex]

2a + 4c = 25 ----------- eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 2

6a + 4c = 47 ---------- eqn 3

Subtract eqn 2 from eqn 3

6a + 4c = 47

2a + 4c = 25

( - ) --------------

4a = 47 - 25

4a = 22

Divide both sides of equation by 4

a = 5.5

Substitute a = 5.5 in eqn 1

3(5.5) + 2c = 23.50

16.5 + 2c = 23.50

2c = 23.50 - 16.5

2c = 7

Divide both sides of equation by 2

c = 3.5

Thus, cost of each adult ticket = $ 5.5

Cost of each student ticket = $ 3.5

How much would the Diaz family spend if they bought 3 adults tickets and 1 children's ticket?

Total cost = 3a + 1c

Total cost = 3(5.5) + 1(3.5) = 16.5 + 3.5

Total cost = 20

Thus Diaz family spend $ 20

Final answer:

The Diaz family would spend $20 for 3 adult tickets and 1 children's ticket at the zoo after solving the system of linear equations given by the Spencer and Yang families' purchases.

Explanation:

Let A be the price of an adult ticket and C be the price of a children's ticket. We are given:

3A + 2C = $23.50 (Spencer family)

2A + 4C = $25 (Yang family)

To solve this system, we can multiply the first equation by 2 and the second equation by 3:

6A + 4C = $47 (Spencer family doubled)

6A + 12C = $75 (Yang family tripled)

Subtracting the first equation from the second gives us:

8C = $28

Dividing both sides by 8 yields:

C = $3.50

Now that we know the price of a children's ticket, we can substitute this value back into one of the original equations to find the price of an adult ticket.

3A + 2(3.50) = $23.50

3A + $7 = $23.50

3A = $16.50

A = $5.50

With the price of both ticket types known, we can now calculate the cost for the Diaz family:

3A + 1C = 3($5.50) + 1($3.50)

3A + 1C = $16.50 + $3.50

3A + 1C = $20

Therefore, the Diaz family would spend $20 if they bought 3 adult tickets and 1 children's ticket.

Answer:

14/3

Step-by-step explanation:

7       x           6

9                    1

7x6=42

9X1=9

42/9     or 14/3

The product of 7/9 and 6 is 14/3.

To find the product of 7/9 and 6, multiply the numerator (7) by the number (6) and keep the denominator (9) the same.

The calculation is as follows:

(7/9) * 6

= (7 * 6)/9

= 42/9

To simplify the fraction, divide both the numerator and the denominator by their greatest common factor, which is 3.

The simplified answer is: 14/3

Answer: 4.647

Step-by-step explanation:

The 4 in the hundredths place, or before the 6, is less than 5 so it will not round the 6 to a 7, therefore making it not round to 4.7

I multiply 1200 times 5 and yet 6000 because it says what is the height

Answer:

9

Step-by-step explanation:

The two triangles [tex]\triangle MNP\sim \triangle RST[/tex].

Therefore the corresponding sides are proportional.

[tex]\frac{|ST|}{|PN|} =\frac{|TR|}{|MP|}[/tex]

From the diagram |MP|=4, |PN|=3, |MN|=5 |ST|=x and |TR|=12.

Let us substitute the values and solve for x.

[tex]\frac{12}{4}=\frac{x}{3}[/tex]

Multiply both sides by 3 to get:

[tex]3*\frac{12}{4}=\frac{x}{3}*3[/tex]

This implies that:

[tex]9=x[/tex]

Therefore x=9

Answer: a,c

Step-by-step explanation:

Answer:

A .. C

Step-by-step explanation:

the y-coordinate corresponding to x=4 is 12.

the equation y=3x represents a linear function. A linear function is a type of mathematical relationship where the graph of the function forms a straight line.

The equation y=3x is in slope-intercept form, where y represents the dependent variable (usually plotted on the vertical axis),

x represents the independent variable (usually plotted on the horizontal axis), and 3 represents the slope of the line.

To find the y-coordinate when the x-coordinate is 4 in the equation y=3x, we need to substitute x=4 into the equation and solve for y.

Substituting x=4 into the equation y=3x,

we get: y=3×4=12

So, when x=4, y=12.

Therefore, the y-coordinate corresponding to x=4 is 12.

This means that the point on the graph of y=3x where the x-coordinate is 4 has a y-coordinate of 12.

Step-by-step explanation:

In order to rationalise the denominator, numerator and denominator must be multiplied by [tex] \sqrt[3]{9x^{10}}[/tex]

A unit fraction is a fraction with a numerator of 1 and a positive integer denominator. Identifying unit fractions involves ensuring the numerator is 1. Examples include 1/2, 1/3, and 1/5.

A unit fraction is a fraction where the numerator is always 1, and the denominator is a positive integer. This means that a fraction of the form 1/b, where b is a positive integer, qualifies as a unit fraction. For example, 1/2, 1/3, and 1/5 are unit fractions because the numerators are all 1.

When working with fractions, it's important to understand their components. The numerator (top number) represents how many parts you have, while the denominator (bottom number) tells you into how many equal parts the whole is divided. This rule helps identify unit fractions, as the numerator must always be 1.

To summarize, determining unit fractions is straightforward: check if the numerator is 1 and the denominator is a positive integer. If both conditions are met, you have a unit fraction.

Answer:

[tex]Area\ of\ a\ trinagle = \frac{5}{12}x^2[/tex] [tex]or\ 0.42x^2[/tex]

Step-by-step explanation:

Given:

Height of the triangle [tex]h = x[/tex]

Base of the triangle [tex]b=\frac{5}{6}x[/tex]

We need to find the area of the triangle.

Solution:

Using given Formula:

[tex]Area\ of\ a\ trinagle = \frac{1}{2}bh[/tex]

Where:

b = Base of the triangle.

h = Height of the triangle.

Substitute [tex]h = x[/tex] and [tex]b=\frac{5}{6}x[/tex] in equation in given formula.

[tex]Area\ of\ a\ trinagle = \frac{1}{2}(\frac{5}{6})x\times x[/tex]

[tex]Area\ of\ a\ trinagle = \frac{5}{12}x^2[/tex]

[tex]Area\ of\ a\ trinagle =0.42x^2[/tex]

Therefore, Area of the triangle is [tex]\frac{5}{12}x^2[/tex] or [tex]0.42x^2[/tex].

Answer:

d

Step-by-step explanation:

Answer:

t = -8

Step-by-step explanation:

combine like terms, so -3t + 7t = 4t and 34 - 2 = 32

so 4t - 8 = 32 + 9t

then subtract 4t from both sides and subtract 32 from both sides. You will get: -40 = 5t.

Then divide both sides by 5 so you will get -8 = t

Answer: t= -8

Step-by-step explanation:

Answer:

The middle point is 3

Step-by-step explanation:

Yo sup??

The mid point can be found out by taking the sum of the two values and dividing it by 2

mid point=(12+(-7))/2

=5/2=2.5

Hope this helps

Answer:

4x - 3(2x - 3)= 7

4x - 6x + 9 = 7

-2x + 9 = 7

-2x = -2

x = 1

y = 2(1)-3= -1

(1,-1)

Answer:

The number of faculty member is 45.

Step-by-step explanation:

Ratio of faculty members to students = 1 : 15

Number of students = 675

Total = Number students + faculty members

Let the total be t

Let the faculty member be f

Representing the ratio, we have:

[tex]\frac{15}{16} * t = 675\\\frac{15t}{16} = 675\\15t = 16 * 675\\15t = 10800\\\frac{15t}{15} =\frac{10800}{15} \\t = 720[/tex]

Therefore, the total number of both the students and faculty member is 720. To get the number of faculty member:

Total = Number students + faculty members

[tex]720 = 675 + f\\f = 720 - 675\\f = 45[/tex]

The number of faculty member is 45.

Answer:

Step-by-step explanation:

180-78=102

102÷2=51

E=51

To solve the given proportional equation, it simplifies to 5 = a/(a-9), leading to 4a = 45 after simplification and solving, with the solution being a = 11.25.

To solve the proportional equation 10/2 = a/(a-9), we first simplify and then solve for a. The equation simplifies to 5 = a/(a-9). By cross-multiplication, we get 5(a - 9) = a, which simplifies to 5a - 45 = a. Bringing all terms to one side gives 4a = 45, and dividing both sides by 4 gives a = 11.25. Therefore, the correct answer is a. 11.25.

The linear equation representing the value of the car as it depreciates over time is y = -3,000x + 25,635, where y is the value of the car and x is the age of the car in years.

To write a linear equation that describes the depreciation of the SUV over time, we define two variables: y represents the total value of the car at any time x, where x represents the age of the car in years.

The car is purchased for $25,635 and depreciates at a rate of $3,000 per year, which means that the value of the car decreases by a constant amount each year. We can write this situation as a linear function:

Linear Depreciation Equation:

y = -3,000x + 25,635

Here, the y-intercept is $25,635 (the value of the car at the time of purchase when x is zero), and the slope is -$3,000 (the rate at which the value of the car decreases per year).

Answer:

lets consider an example like

20 divided by 2/4 so we can rewrite as

2/4*  x      =20

so , 2*   x     =20*4

2*     x      =80

x=80/2

x=40

similarly,we can write the fraction as (20*4/2)-we can see that reciprocal of the fraction 2/4 is 4/2

x=20*4/2=80/2=40

so, we can say that dividing by a fraction results in the same answer as multiplying by its reciprocal.

Answer:

1 necklace is $19!

Step-by-step explanation:

4•$8=$32

$70-$32=$38

$38/2=$19

Answer:

Option C

Step-by-step explanation:

We are given that

[tex]f(x)=-x[/tex]

The line passing through the points (0,0),(-6,6) and (6,-6).

[tex]g(x)=2x[/tex]

The line passing through the points (-3,-6),(0,0) and (3,6).

We have to find the graph of (g-f)(x).

[tex](g-f)(x)=g(x)-f(x)=2x-(-x)=2x+x[/tex]

[tex](g-f)(x)=3x[/tex]

Substitute x=0

[tex](g-f)(0)=3(0)=0[/tex]

[tex](g-f)(2)=3(2)=6[/tex]

[tex](g-f)(-2)=3(-2)=-6[/tex]

[tex](g-f)(-6)=3(-6)=-18[/tex]

Option C is true.

Final answer:

The scientist used 9/40 of a full bottle of solution.

Explanation:

To find out how much of a full bottle of solution the scientist used, we first need to calculate the amount that is left in the bottle. The bottle is currently 5/8 full, and the scientist used 2/5 of the solution. To calculate the amount left, we subtract the amount used from the initial amount:

Amount Left = Initial Amount - Amount Used

To subtract fractions, we need a common denominator. The common denominator for 8 and 5 is 40:

Amount Left = 5/8 - 2/5

To subtract the fractions, we need to have the same denominator, which is 40:

Amount Left = (5/8) * (5/5) - (2/5) * (8/8)

Amount Left = 25/40 - 16/40

Amount Left = 9/40

Therefore, the scientist used 9/40 of a full bottle of solution.

Answer:

4s+9c

Step-by-step explanation:

6s+9c-2s

-2s. -2s

4s+9

Answer:

{(-34/7, -16/7)}

Step-by-step explanation:

Rearrange values, multiply to solve for x.

(5) 2y = 3x + 10

(-2) 5y = 4x + 8

Solve for x.

10y = 15x + 50 ↓

-10y = -8x -16

Combine and evaluate.

0 = 7x + 34

Subtract 34 from both sides.

7x = -34

Divide both sides by 7.

x = [tex]\frac{-34}{7}[/tex]

Plugin x value into either equation to solve for y.

2y = (3 × [tex]\frac{-34}{7}[/tex]) + 10

2y = [tex]\frac{-102}{7}[/tex] + 10

2y = [tex]\frac{-32}{7}[/tex]

y = [tex]\frac{-16}{7}[/tex]

3 metres from one end to the third mark

Solution:

Total length of wood = 10 metre

Wood is marked into 10 equal length.

[tex]$\text{Length of each marking}=\frac{\text{Total length}}{\text{Number of marking}}[/tex]

                                     [tex]$=\frac{10}{10}[/tex]

                                     = 1 metre

Length of each marking = 1 metre

Number of metres from one end to third mark = 1 + 1 + 1 = 3 metre

The image of the marking is attached below.

Hence 3 metres from one end to the third mark.