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3 years ago

Find two consecutive integers whose sum is 67. Which of the following equations could be used to solve the problem?

1 answer:

3 0

The desired answer is probably that
2x + 1 = 67
is the equation that can be used to solve the problem. In this case, x represents the smallest integer.

_____
I like to work problems in consecutive integers by considering their average. Here, it is 67/2 = 33.5. The two consecutive integers whose average is 33.5 are 33 and 34, the solution to the problem. For this, the first equation applies, where x is the value halfway between the two integers. (This answer (2x=67) would likely get marked wrong by your computer grading system.)

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Help only plz only 10 minutes

Allisa [31]

Answer:

2.5

Step-by-step explanation:

If i am correct the first rectangle is 3 and the second is 7.5.

7.5 divided by 3 equals 2.5

7 0

3 years ago

Read 2 more answers

Write a quadratic equation given the roots -1/3 and 5, show your work

Travka [436]

$\boxed{(x - a)(x - b) = 0}$

The equation above is the intercept form. Both a-term and b-term are the roots of equation.

$x = - \frac{1}{3} \\ x = 5$

These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.

$(x + \frac{1}{3} )(x - 5) = 0$

Here we can convert the expression x+1/3 to this.

$x + \frac{1}{3} = 0 \\ 3x + 1 = 0$

Rewrite the equation.

$(3x + 1)(x - 5) = 0$

Simplify by multiplying both expressions.

$3 {x}^{2} - 15x + x - 5 = 0 \\ 3 {x}^{2} - 14x - 5 = 0$

Answer Check

Substitute the given roots in the equation.

$3 {(5)}^{2} - 14(5) - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0$

$3( - \frac{1}{3} )^{2} - 14( - \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) + \frac{14}{3} - 5 = 0 \\ \frac{1}{3} + \frac{14}{3} - \frac{15}{3} = 0 \\ \frac{15}{3} - \frac{15}{3} = 0 \\ 0 = 0$

The equation is true for both roots.

Answer

$\large \boxed {3 {x}^{2} - 14x - 5 = 0}$

8 0

3 years ago

Solve for x. 50 = x^2 Show your work.

Tanzania [10]

50 = x^2

To isolate x you need to do the opposite of an exponent, which would be square root.

$\sqrt{50} = x Next solve what the square root of 50 is[tex]5\sqrt{2}$ = x

That is the exact form, in other words your answer, if teacher is looking for a decimal, it would be

7.07 = x

6 0

3 years ago

Read 2 more answers

Suppose that you are conducting a survey on how many students have blue eyes in each first period classroom at Garfield Middle s

rusak2 [61]

Answer:

The correct statement is the first one: The number of blue-eyed students in Mr. Garcia's class is 2 standard deviations to the right of the mean

Explanation:

To calculate how many standard deviations a particular value in a group is from the mean, you can use the z-score:

$z-score=(x-\mu )/\sigma$

Where:

$z-score$ is the number of standard deviations the value of x is from the mean

$\mu$ is the mean

$\sigma$ is the standard deviation

Substitute in the formula:

$z-score=(10-6)/2=4/2=2$

Which means that the number of blue-eyed students in Mr. Garcia's class is 2 standard deviations above the mean.

Above the mean is the same that to the right of the mean, because the in the normal standard probability graph the central value is Z = 0 (the z-score of the mean value is 0), the positive values are to the right of the central value, and the negative values are to the left of the central value.

Therefore, the correct statement is the first one: The number of blue-eyed students in Mr. Garcia's class is 2 standard deviations to the right of the mean,

4 0

4 years ago

The radius is 6 and the height is 15 what is the volume in terms of pi the shape is a cone

Alenkinab [10]

Answer:

565.49 or if rounded to the nearest tenth, 565.5

Explanation:

The formula for finding the volume of a cone is V=1/3Bh

B = pi times the radius squared

h = height

Substitute 6 for r and 15 for h.

V= 1/3· $\pi$ ·( $6^{2}$ )·15

Multiply.

V= 565.49 or 565.5 rounded to the nearest tenth.

4 0

3 years ago