WXYZ is an isosceles trapezoid with legs WX and YZ and a base XY. If the length of WX is 6x+5, the length of XY is 10x+4 and the length of YZ is 8x-3, find the VALUE OF Y.

The total time for two game is 32 minutes. The time for each game can be determine using system equation.

The time for game is 10 minute and 22 minute respectively.

Given:

Total time to complete two game is 32 minutes.

Let [tex]x[/tex] is the time took to complete one game.

Write the system equation for the given condition.

[tex]\begin{aligned}\\ x+x+12=32\\2x=32-12\\x=10 \:\rm min\\\end{aligned}[/tex]

As per the question, one game took 12 minutes longer than other. So the time for second game is,

[tex]x+12=10+12=22 \:\rm minutes[/tex]

Thus, the time took to complete game is [tex]10\:\rm minutes[/tex] and [tex]22\:\rm minutes[/tex] respectively.

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length= 93 width=31

248=2L+2w

L=3w

248=2x3w+2w

248=6w+2w

248=8w      (248/8=31)

31=w

L=3 x 31

L=93

check answer: 248= 2x93 + 2x31

                       248=186+62

                         248=248

The cost of the flour per ounce will be $0.06 per ounce. Then the correct option is A.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A 5-pound of flour costs $4.80.

We know that in one pound, there are 16 ounces. Then the number of ounces in 5 pounds is calculated as,

⇒ 5 x 16

⇒ 80 ounces

Then the cost of the flour per ounce will be given as,

⇒ $4.80 / 80

⇒ $0.06 per ounce

The cost of the flour per ounce will be $0.06 per ounce. Then the correct option is A.

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Answer:

17 heartbeats in 15 seconds as a unit rate is-

1.13 over 1

hope it is clear to you

When using elimination to solve the system of equations, subtracting the first equation from the second eliminates the y variable, resulting in the equation 3x = 3, which simplifies to x = 1.

When solving the system of equations by elimination, we align the equations vertically and subtract or add them to eliminate one of the variables. Let's consider the given system:

3x - y = 7
6x - y = 10

By subtracting the first equation from the second, we eliminate variable y. The subtraction works as follows:

(6x - y) - (3x - y) = (10) - (7)

Which simplifies to:

3x = 3

From this resulting equation, we can easily solve for x:

x = 3 / 3
x = 1

This is the first part of the solution. After finding the value of x, we substitute back into either of the original equations to solve for y.

The answer is Jasons!

Answer:

Step-by-step explanation:

There are 3 data sets given as

I)   x                         7 8 9 10 11 12 13    Total

   Frequ                  1  2  1   2  2 0     2

Mean dev|x-10|*f    3 4  1   0    3  0   6      17

II)     x                         7 8 9 10 11 12 13    Total

   Frequ                     2  3 0  0  1  1   3

Mean dev|x-10|*f        6  6  0  0 1  2 9     24

III)   x                         7 8 9 10 11 12 13    Total

   Frequ                     0 0 4  4  1  0 1

Mean dev|x-10|*f        0  0 4 0 1  0 3        8

Thus we find the middle one Jason has the highest deviation.

The total cost is $2,260.

The question involves calculating the total cost of purchasing dining room furniture with an initial down payment and subsequent monthly payments. First, we account for the down payment: $1,900 (cash price) - $100 (down payment) = $1,800 remaining balance. This balance will be paid over 24 months at $90 per month, thus 24 * $90 = $2,160. The total cost of the furniture, including the down payment, would then be the sum of the down payment and the total of the monthly payments: $100 + $2,160 = $2,260.

The total cost of the dining room furniture with this payment plan is $2,260.00.

The total cost for the dining room furniture with the given payment plan.

1. Down Payment: $100.00

2. Monthly Installments: $90.00 for 24 months

Calculate the total cost of the furniture before any payments are made:

[tex]\[ \text{Cash Price} = \$1,900 \][/tex]

The total amount paid through monthly installments:

[tex]\[ \text{Monthly Installment} = \$90.00 \times 24 \text{ months} = \$2,160.00 \][/tex]

Finally, let's add the down payment to the total amount paid through installments to find the overall cost:

[tex]\[ \text{Total Cost} = \$100.00 + \$2,160.00 = \$2,260.00 \][/tex]

The height of Mel in the air is decreasing at a faster rate than victor's height in the air.

Given information:

Mel slides down water-slide A and Victor slides down water-slide B.

After 1 second, height achieved by [tex]\rm{Mel}= 50\; \text{Ft}[/tex]

After 5 seconds, the height remained is 35 feet.

In another case,

Now, the expression is used for evaluating the slope of the equation are formulated below:

[tex]\bold{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Where, [tex]m[/tex] is the slope and [tex]x[/tex] and [tex]y[/tex] are respective coordinates.

Hence, for Mel's case, apply the formula of slope and solve it further:

[tex]\begin{aligned}m_1&=\dfrac{35-50}{5-2} \\m_1&=-5 \end{aligned}[/tex]

So, the rate of change of Mel's height is 5 feet per second.

And for victor's case, slope will be:

[tex]m_2=\dfrac{50-60}{4-1} \\\\m_2=-3.33[/tex]

The rate of change of victor's height is 3.33 feet per second.

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The matching of the given numbers to there standard notation is given as follows:

     232,000,000------ 2.32E8

     0.00000431 ------  4.31E-6

 2,320,000,000 ----- 2.32E9

 0.000000000000431 ----- 4.31E-13

We know that the standard  notation of a number is given by:

There must be only one digit before the decimal and rest after that.

Also, it there is a shift of the decimal to the right then the power goes to negative and positive if shift is to the left.

1)

        232,000,000

Here we have to take the decimal 8 digits from the left and the number in standard notation will be given by:

              [tex]2.32\times 10^8[/tex]

which is written as:  2.32E8

2)

      0.00000431

Here we have to shift the decimal 6 digits to the right.

Hence, the number is expressed as:

           [tex]4.31\times 10^{-6}[/tex]

which is written as: 4.31E-6

3)

       2,320,000,000

Here the decimal is to be put 9 digits from the left and hence the number is represented as:

           [tex]2.32\times 10^9[/tex]

which is given by: 2.32E9

4)

         0.000000000000431

Here we will shift the decimal 13 places to the right and hence the number is given by:

            [tex]4.31\times 10^{-13}[/tex]

which is given by:  4.31E-13

Final answer:

The solution to the system of equations y = -1/5x + 1 and y = x + 4 is found by setting the equations equal to each other, solving for x, and then substituting back to find y. The solution is the ordered pair (-5, -1).

Explanation:

The student is asking to find the ordered pair that represents the best estimate for the solution to a system of linear equations. The given system of equations is: y = −1/5x + 1 and y = x + 4. To find the solution, we need to determine where the two lines intersect, which will give us the coordinates (x, y) of the solution.

To find the intersection, we can set the two equations equal to each other since they both equal y: −1/5x + 1 = x + 4. Then, we would solve for x:

Add 1/5x to both sides to get 1 = 6/5x + 4

Subtract 4 from both sides to get −3 = 6/5x

Multiply both sides by 5/6 to get x = −3 × (5/6)

Which simplifies to x = −5

Now we substitute x back into either of the original equations to find y. For instance, using the second equation y = x + 4, we find that:

y = (−5) + 4 = −1

Therefore, the ordered pair that is the solution to the system of equations is (-5, -1).

Final answer:

The equivalent expression to 15x+50, by factoring out the greatest common divisor, is 5(3x+10).

Explanation:

The question is asking for an equivalent expression to the linear algebraic expression 15x+50. By examining the coefficient and constant term, we note that both terms are divisible by 5. Therefore, we can factor out 5 to simplify the expression. The steps for simplification are as follows:

Find the greatest common divisor (GCD) of the coefficients, which in this case is 5.

Divide each term by the GCD.

Express the factored form using the distributive property.

By applying these steps:

The GCD of 15 and 50 is 5.

Dividing each term by 5 gives us 3x + 10.

Thus, we can write the expression as 5(3x + 10), which is equivalent to the original expression 15x + 50.

To compare Sandra's unit rate with Terrance's and Jesse's, we must calculate their speeds in mph. Terrance runs at 12 mph, Jesse at 8 mph, and Sandra at 10.67 mph. Therefore, Sandra is faster than Jesse but slower than Terrance.

To compare Sandra's unit rate to Terrance's and Jesse's, we need to determine the speed at which each person runs in miles per hour (mph). The given information is:
Terrance runs 6 miles every half hour.
Jesse runs 2 miles every 15 minutes.
Sandra runs 8 miles in 45 minutes.

First, we calculate each person's running speed:

Terrance: 6 miles in 0.5 hours (30 minutes), so we multiply by 2 to find his speed per hour: 6 miles ÷ 0.5 hours = 12 mph.

Jesse: 2 miles in 0.25 hours (15 minutes), so we multiply by 4 to find his speed per hour: 2 miles ÷ 0.25 hours = 8 mph.

Sandra: 8 miles in 0.75 hours (45 minutes), so we divide her distance by the time in hours: 8 miles ÷ 0.75 hours = 10.67 mph.

Therefore, compared to Terrance and Jesse, Sandra's running speed is:

Faster than Jesse's (10.67 mph > 8 mph)

Slower than Terrance's (10.67 mph < 12 mph)