Quadratic equation whose roots are -6 and -1 with leading coefficient is 1

Answer:

Therefore, the constant of proportionality for the given proportional relationship is 5.

Step-by-step explanation:

To determine the constant of proportionality in the given proportional relationship, we can use the formula:

Constant of Proportionality = Tickets / Games

Let's plug in the values from the table:

For the first set of values (4 games and 20 tickets):

Constant of Proportionality = 20 / 4 = 5

For the second set of values (7 games and 35 tickets):

Constant of Proportionality = 35 / 7 = 5

For the third set of values (10 games and 50 tickets):

Constant of Proportionality = 50 / 10 = 5

In all three cases, the constant of proportionality is equal to 5.

Therefore, the constant of proportionality for the given proportional relationship is 5.

Answer:

-10 :)

Hey champ! Here's the 'splination!

equation: 50-5x=100

50=-5x. (subtract 50 from both sides)

-10=x (divide both sides by -5)

Answer:

36

Step-by-step explanation:

81 x (4/9) =

36

The distance it will take to drive from Toronto to buffalo (distance between Toronto and buffalo is 154km) is 1.75 hours.

We are given that;

distance = 154 km speed = 88 km/hr

Now,

we need to use the formula:

time = distance / speed

where time is in hours, distance is in kilometers, and speed is in kilometers per hour.

Plugging these values into the formula, we get:

time = 154 / 88 time ≈ 1.75

Therefore, by speed the answer will be 1.75 hours.

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Answer:

  -64

Step-by-step explanation:

Undo the cube root by cubing both sides.

  (∛x)^3 = (-4)^3

  x = -64

Answer:

But, you didn't ask any question.

Step-by-step explanation:

Remember to post your question next time.

Answer:

y=2

Step-by-step explanation:

due to diagram have done the steps in the image

The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

\($\frac{AB}{BC} = \frac{AD}{AB}$\)

Cross-multiplying, we get:

\($AB^2 = BC \cdot AD$\)

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

\($\frac{AC}{BC} = \frac{AD}{AC}$\)

Cross-multiplying, we have:

\($AC^2 = BC \cdot AD$\)

Now, we can substitute the derived expressions into the original equation:

\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)

It was made possible by cross-product property.

Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

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Answer:

5 Hours

Step-by-step explanation:

He’s going 63 MPH

441/7 = 63 MPH

315/63 = 5 Hours

Answer:

5 hours

Step-by-step explanation:

First, divide 441 miles by 7 hours to get a rate of 63 miles/1 hour. Then divide 315 miles by 63mph to get 5 hours.

The vertices of the feasible region is (4, 3)

From the question, we have the following parameters that can be used in our computation:

x + y ≤ 7

x - 2y ≤ -2

x ≥ 0

y ≥ 0

Express as equations

So, we have

x + y = 7

x - 2y = -2

Subtract the equations

3y = 9

So, we have

y = 3

Next, we have

x + 3 = 7

This gives

x = 4

Hence, the vertex of the feasible region is (4, 3)

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Answer:

48

Step-by-step explanation:

Apply pythagorean theorem, a² = c² - b²

Where, a = third side

b = 55

c = 73

Plug in the values

a² = 73² - 55²

a² = 2,304

a = √2,304 = 48

a = 48

Answer:

The answer is D: 4

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer: Marian can pack 132 softballs in 11 boxes.

Step-by-step explanation:

Marian packed 60 bsoftballs in 5 boxes.

so, she packed (60÷5)=12 softballs in each box.

NOW, she can pack (12×11)=132 softballs in 11 boxes.

Answer:

Step-by-step explanation:

Marian can pack 132 softballs in 11 boxes. Hence option C is correct.

Here we can use the unitary method to solve this question, i.e.

Since we can fill 5 boxes with 60 softballs, that means a single box can contain 12 softballs.

Hence 11 boxes could contain, 11 x 12 = 132 softballs.

Hence, option C is the correct option.

To see more examples of the unitary method refer to the below links,

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Answer: b

Step-by-step explanation: a right triangle should have a right angle so you´d need atleast one right angle and two acute angles.

Answer:

1. choice number 3

2. choice number 1

3. choice number i dont know

Step-by-step explanation:

Answer:

$0.01 more

Step-by-step explanation:

To calculate this, subtract the larger number from the smaller number to find the difference. 0.98 - 0.97 = 0.01, so the yellow button costs $0.01 more than the teal button.

First, look for the zeroes of the integrand in the interval [0, 6] :

x² - 6x + 8 = (x - 4) (x - 2) = 0   ⇒   x = 2   and   x = 4

Next, split up [0, 6] into sub-intervals starting at the zeroes we found. Then check the sign of x² - 6x + 8 for some test points in each sub-interval.

• For x in (0, 2), take x = 1. Then

x² - 6x + 8 = 1² - 6•1 + 8 = 3 > 0

so x² - 6x + 8 > 0 over this sub-interval.

• For x in (2, 4), take x = 3. Then

x² - 6x + 8 = 3² - 6•3 + 8 = -1 < 0

so x² - 6x + 8 < 0 over this sub-interval.

• For x in (4, 6), take x = 5. Then

x² - 6x + 8 = 5² - 6•5 + 8 = 3 > 0

so x² - 6x + 8 > 0 over this sub-interval.

Next, recall the definition of absolute value:

\(|x| = \begin{cases}x & \text{for }x \ge0 \\ -x & \text{for }x < 0\end{cases}\)

Then from our previous analysis, this definition tells us that

\(|x^2 - 6x + 8| = \begin{cases}x^2 - 6x + 8 & \text{for }0<x<2 \text{ or } 4<x<6 \\ - (x^2-6x+8) & \text{for }2<x<4\end{cases}\)

So, in the integral, we have

\(\displaystyle \int_0^6 |x^2-6x+8| \, dx = \left\{\int_0^2 - \int_2^4 + \int_4^6\right\} (x^2 - 6x + 8) \, dx\)

Then

\(\displaystyle \int_0^2 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_0^2 = \frac{20}3 - 0 = \frac{20}3\)

\(\displaystyle \int_2^4 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_2^4 = \frac{16}3 - \frac{20}3 = -\frac43\)

\(\displaystyle \int_4^6 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_4^6 = 12 - \frac{16}3 = \frac{20}3\)

and the overall integral would be

20/3 - (-4/3) + 20/3 = 44/3

Step-by-step explanation:

\( \frac{30}{wz} = \frac{40}{32 + 40 } \\ wz = 54\)

\( \frac{40}{40 + 32} = \frac{28}{xz} \\ xz = 50.4\)

So the Perimeter is

\(54 + 50.4 + (40 + 32) = 176.4\)

9514 1404 393

Answer:

  g = 1/6(w+40)​

Step-by-step explanation:

The given equation is already solved for g. Nothing need be done.

  g = 1/6(w+40)​

The area of the shape, given the dimensions of the various parts of the shape, can be found to be 8, 100 ft ².

You can divide the shape into other shapes. Then you can find the areas of these shapes and then sum them up.

The area of the composite shapes would therefore be :

= ( 30 x 60 ) + ( 30 x 60 ) + ( ( 60 + 30 + 60) x 30 )

= ( 30 x 60 ) + ( 30 x 60 ) + ( 150 x 30 )

= 1, 800 + 1, 800 + 4, 500

= 8, 100 ft ²

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Complete Question

Suppose the weight of Chipotle burritos follows a normal distribution with mean of 450 grams, and variance of 100 grams2 . Define a random variable to be the weight of a randomly chosen burrito.

(a) What is the probability that a Chipotle burrito weighs less than 445 grams? (3 points)

(b) 20% of Chipotle burritos weigh more than what weight

Answer:

a

   \(P(X < 445 )= 0.3085\)

b

  \(k = 458.42\)

Step-by-step explanation:

From question we are told that

     The population mean is \(\mu = 450 \ g\)

      The variance is \(var = 100 \ g^2\)

      The  consider weight is  \(x = 445 \ g\)

The  standard deviation is mathematically represented as

     \(\sigma = \sqrt{var}\)

substituting values

     \(\sigma = \sqrt{ 100}\)

     \(\sigma = 10\)

Given that weight of Chipotle burritos follows a normal distribution the  the probability that a Chipotle burrito weighs less than x grams is mathematically represented as

        \(P(X < x ) = P ( \frac{X - \mu }{\sigma } < \frac{x - \mu }{\sigma } )\)

Where  \(\frac{X - \mu }{\sigma }\) is  equal to z (the standardized values of the random number X )

So

     \(P(X < x ) = P (Z < \frac{x - \mu }{\sigma } )\)

substituting values

     \(P(X < 445 ) = P (Z < \frac{445 - 450 }{10} )\)

      \(P(X < 445 ) = P (Z <-0.5 )\)

Now from the normal distribution table  the value for \(P (Z <-0.5 )\)  is  

      \(P(X < 445 ) = P (Z <-0.5 ) = 0.3085\)

=>   \(P(X < 445 )= 0.3085\)

Let the  probability  of the Chipotle burritos weighting more that k be 20% so  

       \(P(X > k ) = P ( \frac{X - \mu }{\sigma } > \frac{k - \mu }{\sigma } ) = 0.2\)

=>    \(P (Z> \frac{k - \mu }{\sigma } ) = 0.2\)

=>    \(P (Z> \frac{k - 450}{10 } ) = 0.2\)

From the normal distribution table the value of z  for  \(P (Z> \frac{k - \mu }{\sigma } ) = 0.2\) is  

    \(z = 0.8416\)

=>   \(\frac{k - 450}{10 } = 0.8416\)

=>   \(k = 458.42\)

Answer:

B and D

Step-by-step explanation:

<JKB = <FGC (SINCE BITH THEIR BISECTORS BISECT THEM MAKING A 90° ANGLE)

AND

<BKL = 90° (BECAUSE OF THE BISECTOR)

Answer:

B and D

Step-by-step explanation:

B and D

Answer:

52

Step-by-step explanation:

This is because the formula is dr

To make the profit of $5000, the temperature should be 290 degrees Fahrenheit.

The general equation of a straight line is -

y = mx + c

where -

{m} is the slope of the line.

{c} is the {y} - intercept.

Given is a scatter plot as shown in the image.

We can write the equation of the line of best fit as -

{m} = (400 - 0/(60 - 40)

{m} = 400/20

{m} = 20

We can write the y - intercept as -

y = 20x + c

0 = 800 + c

c = - 800

So, the equation of the line of best fit is -

y = 20x - 800

For {y} = 5000, we can write -

5000 + 800 = 20x

5800 = 20x

x = 5800/20

x = 290

Therefore, to make the profit of $5000, the temperature should be 290 degrees Fahrenheit.

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Answer:

18

Step-by-step explanation:

If 4 out of 10 wore glasses, then 6 out of 10 did not wear classes.  This would be 60% or .6

.6x30 = 18

Answer: D

Step-by-step explanation:

1 in.=1488 milesx5=7440 miles.

Area= pi x r^2

=pi x (7440)^2 or option D.

Hope this helps :)

The answer is,

\(x > - 7\)

hope it helps.

Answer:

x>-7

Step-by-step explanation:

4x-2x>-8-6

-2x>-14

x>-7

Answer:

5y+6

Step-by-step explanation:

-3 and 9 are like terms which can be simplified to 6.

Answer:

5y+6

Step-by-step explanation:

-3+5y+9

=-3+9+5y

=6+5y

=5y+6