Susan uses the function p(x) = 4x to determine the perimeter of a square when she knows the side length, x. Which statements are true about the function?

The perimeter is the dependent variable.
The length of the side of the square is the dependent variable.
The value of p(x) depends on the value of x.
The length of the side of the square is the independent variable.
The value p(x) can be found by multiplying p by x.
The perimeter is the independent variable.

Answer:

[tex]x=2+\sqrt{21}\\\\x=2-\sqrt{21}[/tex]

Step-by-step explanation:

One is given the following equation;

[tex]x^2-4x-9=29[/tex]

The problem asks one to find the roots of the equation. The roots of a quadratic equation are the (x-coordinate) of the points where the graph of the equation intersects the x-axis. In essence, the zeros of the equation, these values can be found using the quadratic formula. In order to do this, one has to ensure that one side of the equation is solved for (0) and in standard form. This can be done with inverse operations;

[tex]x^2-4x-9=29[/tex]

[tex]x^2-4x-38=0[/tex]

This equation is now in standard form. The standard form of a quadratic equation complies with the following format;

[tex]ax^2+bx+c[/tex]

The quadratic formula uses the coefficients of the quadratic equation to find the zeros this equation is as follows,

[tex]\frac{-b(+-)\sqrt{b^2-4ac}}{2a}[/tex]

Substitute the coefficients of the given equation in and solve for the roots;

[tex]\frac{-(-4)(+-)\sqrt{(-4)^2-4(1)(-38)}}{2(1)}[/tex]

Simplify,

[tex]\frac{-(-4)(+-)\sqrt{(-4)^2-4(1)(-38)}}{2(1)}\\\\=\frac{4(+-)\sqrt{16+152}}{2}\\\\=\frac{4(+-)\sqrt{168}}{2}\\\\=\frac{4(+-)2\sqrt{21}}{2}\\\\=2(+-)\sqrt{21}[/tex]

Therefore, the following statement can be made;

[tex]x=2+\sqrt{21}\\\\x=2-\sqrt{21}[/tex]

Step-by-step explanation:

[tex] \frac{1}{3 } \times \frac{30}{1} = 10 \\ \\ \frac{10}{1} \times \frac{5}{6} = 8.33 \\ \\ \frac{833}{100} \times \frac{6}{10} = 4.998 \\ \\ \frac{4998}{1000} \times \frac{12}{1} = 59.976[/tex]

Answer:

The equation of line d is [tex]y + 8 = 6(x + 3)[/tex]

Step-by-step explanation:

Equation of a line:

The equation of a line, in point-slope form, is given by:

[tex]y - y_0 = m(x - x_0)[/tex]

In which the slope is m and the point is [tex](x_0,y_0)[/tex]

Perpendicular lines:

If two lines are perpendicular, the multiplication of their slopes is -1.

Perpendicular to y=-1/6x+5

Slope of - 1/6, so:

[tex]-\frac{1}{6}m = -1[/tex]

[tex]m = 6[/tex]

So

[tex]y - y_0 = 6(x - x_0)[/tex]

Passes through the point (-3,-8).

This means that [tex]x_0 = -3, y_0 = -8[/tex]. So

[tex]y - y_0 = 6(x - x_0)[/tex]

[tex]y - (-8) = 6(x - (-3))[/tex]

[tex]y + 8 = 6(x + 3)[/tex]

Answer:

The 98% confidence interval to estimate the proportion of watermelon seeds that germinate is (0.4443, 0.6557). This means that we are 98% sure that the true proportion of all watermalong seeds of the company that germinate is between these two values, which means that there is good evidence that the proportion is below the 70% standard.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

Once a week for 12 weeks, he purchases a pack of 10 watermelon seeds to act as his sample. He plants the seeds in a greenhouse with good soil to maintain a consistent temperature and watering routine. He finds that the germination rate for the company's watermelon seeds is 55%.

This means that [tex]n = 12*10 = 120, \pi = 0.55[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 - 2.327\sqrt{\frac{0.55*0.45}{120}} = 0.4443[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 + 2.327\sqrt{\frac{0.55*0.45}{120}} = 0.6557[/tex]

The 98% confidence interval to estimate the proportion of watermelon seeds that germinate is (0.4443, 0.6557). This means that we are 98% sure that the true proportion of all watermalong seeds of the company that germinate is between these two values, which means that there is good evidence that the proportion is below the 70% standard.

9514 1404 393

Answer:

  A, C

Step-by-step explanation:

A: -3 -(-8) = -3 +8 = 5

B: -2 -3 = -5

C: 1 -(-4) = 1 +4 = 5

D: 7 -(-2) = 7 +2 = 9

__

Differences A and C are 5.

Answer: A: -3- (-8)

B:1 -(-4)

Step-by-step explanation:

in A your subtracting them in B your adding them

Answer:

Step-by-step explanation:

11 22 6 34 19

Answer:

4.575

Step-by-step explanation:

365.085/79.8=4.575

Answer:

B = 25 because 180-25-130 = 25 and all angles within triangle add to 180 degrees

a = 6  because the triangle is isosceles and we can see symmetry and draw this to prove on two opposite lines, therefore we can now find height easier.

c = 10. 876  because 130/2 = 65 degree and with new central height we can find Right Angle and using 6 x sin (65) = 5. 438 then we multiply by 2 to find c  

Then all you have to do is re-write and round to the nearest 10th and check the units and write degree sign where required.

Step-by-step explanation:

Answer:

Event 4 (0%), Event 2 (45%), Event 3 (80%), Event 1 (100%)

Step-by-step explanation:

Step-by-step explanation:

how many people in the party please ?

Answer:

Its speed is 14 mph.

Step-by-step explanation:

Given that regarding racer called The Whirlwind, its poster says that in 1/20 hour it covers 7/10 mile, to determine what is the Whirlwind’s speed in miles per hour the following calculation must be performed:

1/20 x 60 = 0.05 x 60 = 3 minutes

7/10 = 0.7

Therefore, every 3 minutes the Whirlwind travels 0.7 miles.

60/3 = 20

0.7 x 20 = 14

Thus, in an hour it travels 14 miles, with which its speed is 14 mph.

Answer:

m(∠y) = 64°

Step-by-step explanation:

From the figure attached,

m(∠e) = 90°

m(∠b) + 67° = 180° [Linear pair of angles]

m(∠b) = 180 - 67

          = 113°

m(∠c) + 75° = 180°  [Linear pair of angles]

m(∠c) = 105°

m(∠a) = m(∠d)

By the property of a polygon,

Sum of the interior angles of a polygon is given by,

Sum of interior angles = (n - 2) × 180°

Here, n = number of sides of the polygon

For n = 5,

Sum of interior angles = (5 - 2)×180°

                                     = 540°

m(∠a) + m(∠b) + m(∠c) + m(∠d) + m(e) = 540°

2m(∠d) + 113° + 105° + 90° = 540°

2m(∠d) + 308 = 540°

2m(∠d) = 540 - 308

m(∠d) = 116°

m(∠d) + m(∠y) = 180°

m(∠y) + 116° = 180° [Linear pair of angles]

m(∠y) = 64°

Answer: Just create an account and you have unlimited skips.

Answer:

y = -3x + 13

Step-by-step explanation:

First, find the slope:

[tex]m=\frac{y_1-y_2}{x_1-x_2}\\\\m=\frac{4-10}{3-1}\\\\m=\frac{-6}{2}\\\\m=-3[/tex]

Finally, find the equation:

[tex]y-y_1=m(x-x_1)\\\\y-4=-3(x-3)\\\\y-4=-3x+9\\\\y=-3x+13[/tex]

Answer: 144

Step-by-step explanation:

If 1 pound is 16 ounces then you have to do 9 X 16

9x16 = 144

Therefore the answer is 144 ounces

Hope this helped!

Answer:

The correct answer will be "[tex]\frac{8}{9}[/tex]".

Step-by-step explanation:

The given expression is:

= [tex]\frac{1}{2}\times \frac{16}{9}[/tex]

By applying multiplication, we get

= [tex]\frac{16}{18}[/tex]

= [tex]\frac{8}{9}[/tex]

Thus, the above is the lowest form.

9514 1404 393

Answer:

  D

Step-by-step explanation:

The sine function is negative only for angles greater than 180°. This eliminates choice B.

The sine function is periodic with a period of 360°, eliminating choices A and C.

The only viable choice is D, which is the correct one.

mass = force / area

this is second law of motion ( Newton's 2nd law)

[tex]\longrightarrow{\blue{ m = \frac{F}{a} }}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Explanation}}{\red{:}}}}}[/tex]

F = ma

➺ m = [tex]\frac{F}{a} [/tex]

where,

F = Force

m = mass

a = acceleration

"F = ma" is Newton's second law of motion, which states that force is equal to mass times acceleration.

The SI unit of force is newton, symbol N.

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Answer:

show the graphs?

Step-by-step explanation:

F(1) is saying the value of x is 1

Look at the graph where x is 1 and find the y value of where the line is.

At x = 1, the line is at y = 1 ( there is actually a dot showing you the location.

The answer is 1

=====================================================

Explanation:

Set the expression equal to 100 and get everything to one side

[tex]d^2 - 12d + 45 = 100\\\\d^2 - 12d + 45 - 100 = 0\\\\d^2 - 12d - 55 = 0\\\\[/tex]

Now use the quadratic formula. We'll plug in a = 1, b = -12, c = -55.

[tex]\ d = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\ d = \frac{-(-12)\pm\sqrt{(-12)^2-4(1)(-55)}}{2(1)}\\\\\ d = \frac{12\pm\sqrt{364}}{2}\\\\\ d \approx \frac{12\pm19.07878403}{2}\\\\\ d \approx \frac{12+19.07878403}{2}\ \text{ or } \ d \approx \frac{12-19.07878403}{2}\\\\\ d \approx \frac{31.07878403}{2}\ \text{ or } \ d \approx \frac{-7.07878401}{2}\\\\\ d \approx 15.53939201\ \text{ or } \ d \approx -3.53939201\\\\d \approx 15.54 \ \text{ or } \ d \approx -3.54[/tex]

We'll ignore the negative d value as we can't have a negative number of days.

This means d = 15.54 is the only approximate solution we'll consider.

If we plugged in d = 15, then,

d^2 - 12d + 45

(15)^2 - 12(15) + 45

90

This tells us that 90 masks were sold on day d = 15.

Now try d = 16

d^2 - 12d + 45

(16)^2 - 12(16) + 45

109

We see that 109 masks were sold on day d = 16. Somewhere between those days, 100 masks were sold. At the end of the 15th day, we got to 90. So in the middle of day 16 is when we reach the exact 100 mark we're after.

In short, we would round d = 15.54 up to d = 16 so that we clear the hurdle.

In other words, if you rounded d = 15.54 to d = 15, then you'd be 10 masks short of the goal. Besides, 15.54 rounds to 16 when rounding to the nearest whole number.

Answer:

I am not to sure how the actual grade was calculated, maybe there are some other factors to it, but from the three grades you got, the weighted total is 70.2%, if we add the weighted average of 68 on the exam (with the weight being 20%), we get 83.3%.

Answer:

x = 10

y = 6

Step-by-step explanation:

x/2 - y/3 = 3 - - - (1)

4x - 3y = 22 - - - (2)

From (1):

x/2 - y/3 = 3

(3x - 2y)/6 = 3

3x - 2y = 18 - - - - (11)

4x - 3y = 22 - - - - (2)

Multiply (11) by 1.5

4.5x - 3y = 27 _____(111)

4x - 3y = 22 - - - (2)

Subtract :

0.5x = 5

x = 5 / 0.5 = 10

From :

4x - 3y = 22

Put x = 10

4(10) - 3y = 22

40 - 3y = 22

-3y = 22 - 40

-3y = - 18

y = 6

Answer:

Step-by-step explanation:

1.4 m = 1.4 * 100 = 140.0  = 140 cm

Answer:

C. 47 deg

Step-by-step explanation:

m<A = 180 - 94 - 39 = 47

m<D = m<A = 47

Answer:

In explanation

Please let me know if something doesn't make sense.

Step-by-step explanation:

a)

*This relation is not reflexive.

0 is an integer and (0,0) is not in the relation because 0(0)>0 is not true.

*This relation is symmetric because if a(b)>0 then b(a)>0 since multiplication is commutative.

*This relation is transitive.

Assume a(b)>0 and b(c)>0.

Note: This means not a,b, or c can be zero.

Therefore we have abbc>0.

Since b^2 is positive then ac is positive.

Since a(c)>0, then (a,c) is in R provided (a,b) and (b,c) is in R.

*The relation is not antisymmretric.

(3,2) and (2,3) are in R but 3 doesn't equal 2.

b)

*This relation is reflective.

Since a^2=a^2 for any a, then (a,a) is in R.

*The relation is symmetric.

If a^2=b^2, then b^2=a^2.

*The relation is transitive.

If a^2=b^2 and b^2=c^2, then a^2=c^2.

*The relation is not antisymmretric.

(1,-1) and (-1,1) is in the relation but-1 doesn't equal 1.

c)

*The relation is reflexive.

a/a=1 for any a in the naturals.

*The relation is not symmetric.

Wile 4/2 is an integer, 2/4 is not.

*The relation is transitive.

If a/b=z and b/c=y where z and y are integers, then a=bz and b=cy.

This means a=cyz. This implies a/c=yz.

Since the product of integers is an integer, then (a,c) is in the relation provided (a,b) and (b,c) are in the relation.

*The relation is antisymmretric.

Assume (a,b) is an R. (Note: a,b are natural numbers.) This means a/b is an integer. This also means a is either greater than or equal to b. If b is less than a, then (b,a) is not in R. If a=b, then (b,a) is in R. (Note: b/a=1 since b=a)

Answer:

z(max)  = 2350

x₁  =  18          x₂  =  10

Step-by-step explanation:

                             Vol (ft³)         W (p)    Income ($)

Cargo A  (x₁)             50              200          75

Cargo B  (x₂)            10               360          100

Max load limit       1000            7200

Objective Function

z  =  75*x₁   +  100*x₂

Constraints:

Volume constraint:

50*x₁  +  10*x₂  ≤ 1000

Weight constraint:

200*x₁  +  360*x₂  ≤ 7200

Model:

z  =   75*x₁   +  100*x₂       to maximize

Subject to:

50*x₁  +  10*x₂  ≤ 1000

200*x₁  +  360*x₂  ≤ 7200

x₁  ≥  0        x₂  ≥ 0    x₁  and x₂  integers

After 6 iterations with an on-line solver optimal solution is:

z(max)  = 2350

x₁  =  18          x₂  =  10