Complete the table by giving the length and area for each
width. (The width is the side perpendicular to the building.)
width (feet) length (feet)
area (square feet)
10
30
40
W
of the play area

Answer:

C neither

the coordinates shows that only the x intercepts are moving not y the line of the graph will be horizontal and straight . it is not a function

Answer:

275

Step-by-step explanation:

20 x 9 = 180

180 + 95 = 275

Answer:

1 m^2

Step-by-step explanation:

A = W * L

1 * 1 = 1

Using it's concept, it is found that the average rate of change of the function from x = -1 to x = 5 is of -1.

It is given by the change in the output divided by the change in the input.

In this problem, the output changes by -6(from 7 to 1) when the input changes by 6(from -1 to 5), hence the average rate is given by:

r = -6/6 = -1.

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Step-by-step explanation:

always remember, equations and inequalities are like a scale with 2 pans (left and right).

a variable is like a placeholder, an empty spot on the pans. and the expressions on both sides are kind of the conditions for the things to put in these empty spots so that the status of the scale stays unchanged.

for an equation the scale has to stay balanced all the time.

and in an inequality one side is heavier that the other (it normally does not matter how much heavier) with "<" or ">" signs, or the scale can be also balanced with "<=" or ">=" signs. just the other side must never be heavier.

A

so, in our case here

2x - 5 = 3

yes, the solution (the ONLY solution, actually) is x = 4. no other value of x allows the scale to be balanced.

2x - 5 >= 3

well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = 4 is therefore a valid solution for the inequality too.

but so is every other value of x that makes the left side "heavier". what about e.g. 5 ?

2×5 - 5 >= 3

10 - 5 >= 3

5 >= 3

true, great ! so, e.g. x = 5 is also a valid solution.

what else ?

let's simplify the inequality

2x - 5 >= 3

2x >= 8

x >= 4

so, really every value of x that is greater or equal to 4 is a valid solution for the inequality.

B

-2x - 5 = 3

yes, the solution (the ONLY solution, actually) is x = -4. no other value of x allows the scale to be balanced.

-2x - 5 >= 3

well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = -4 is therefore a valid solution for the inequality too.

but so is every other value of x that makes the left side "heavier". what about e.g. -5 ?

-2×-5 - 5 >= 3

remember, -×- = +

10 - 5 >= 3

5 >= 3

true, great ! so, e.g. x = -5 is also a valid solution.

what else ?

let's simplify the inequality

-2x - 5 >= 3

-2x >= 8

x <= -4

a multiplication or division by a negative value flips the inequality sign, because such an operation makes a light weight heavy and a heavy weight light.

so, really every value of x that is less or equal to -4 is a valid solution for the inequality.

Recall that for all [tex]z\in\Bbb C[/tex],

[tex]\sin(z) = \dfrac{e^{iz} - e^{-iz}}{2i}[/tex]

so that

[tex]\sin(z) = a \iff e^{iz} - e^{-iz} = 2ia[/tex]

Multiply both sides by [tex]e^{iz}[/tex] to get a quadratic equation,

[tex]e^{2iz} - 2iae^{iz} - 1 = 0[/tex]

Solve for [tex]e^{iz}[/tex]. By completing the square,

[tex]e^{2iz} - 2ia e^{iz} + i^2a^2 = 1 + i^2a^2[/tex]

[tex]\left(e^{iz} - ia\right)^2 = 1 - a^2[/tex]

[tex]e^{iz} - ia = \pm \sqrt{1-a^2}[/tex]

[tex]e^{iz} = ia \pm \sqrt{1-a^2}[/tex]

[tex]iz = \log\left(ia \pm \sqrt{1-a^2}\right)[/tex]

[tex]iz = \ln\left|ia \pm \sqrt{1-a^2}\right| + i \left(\arg\left(ia \pm \sqrt{1-a^2}\right) + 2\pi n\right)[/tex]

[tex]\boxed{z = -i \ln\left|ia \pm \sqrt{1-a^2}\right| + \arg\left(ia \pm \sqrt{1-a^2}\right) + 2\pi n}[/tex]

where n is any integer.

We are given with:

[tex]{\quad \qquad \longrightarrow \sin (z)={\sf a}\:,\:z\in \mathbb{C}}[/tex]

Recall the identity what we have for the sine function of complex numbers

Put the values to thus obtain:

[tex]{:\implies \quad \sf \dfrac{e^{\iota z}-e^{-\iota z}}{2\iota}=a}[/tex]

[tex]{:\implies \quad \sf e^{\iota z}-e^{-\iota z}=2a\iota}[/tex]

Multiply both sides by [tex]{\sf e^{\iota z}}[/tex]

[tex]{:\implies \quad \sf e^{\iota z}\cdot e^{\iota z}-e^{-\iota z}\cdot e^{\iota z}=2a\iota e^{\iota z}}[/tex]

[tex]{:\implies \quad \sf (e^{\iota z})^{2}-2a\iota e^{\iota z}-1=0}[/tex]

Put x = [tex]{\sf e^{\iota z}}[/tex]:

[tex]{:\implies \quad \sf x^{2}-2a\iota x-1=0}[/tex]

Find the discriminant, here D will be, D = (-2ai)² - 4 × 1 × (-1) = 4 - 4a² = 4(1-a²)

Now, By quadratic formula:

[tex]{:\implies \quad \sf x=\dfrac{-(-2a\iota)\pm \sqrt{4(1-a^{2})}}{2}}[/tex]

[tex]{:\implies \quad \sf x=\dfrac{a\iota \pm \sqrt{1-a^{2}}}{2}}[/tex]

[tex]{:\implies \quad \sf e^{\iota z}=\dfrac{a\iota \pm \sqrt{1-a^{2}}}{2}}[/tex]

[tex]{:\implies \quad \sf \iota z=log\bigg(\dfrac{a\iota \pm \sqrt{1-a^{2}}}{2}\bigg)}[/tex]

Using the formula for logarithms, we have:

[tex]{:\implies \quad \sf \iota z=log(a\iota \pm \sqrt{1-a^{2}})-log(2)}[/tex]

[tex]{:\implies \quad \sf z=\dfrac{1}{\iota}log(a\iota \pm \sqrt{1-a^{2}})-\dfrac{1}{\iota}log(2)}[/tex]

The sine function is periodic on 2πn and zero on (π/2), and the logarithmic expression becomes undefined for all ia±√(1-a²) < 0, so we will take modulus of it

[tex]{:\implies \quad \boxed{\bf{z=\dfrac{1}{\iota}log\bigg|a\iota \pm \sqrt{1-a^{2}}\bigg|-\dfrac{1}{\iota}log(2)+\dfrac{\pi}{2}+2\pi n\:\:\forall \:n\in \mathbb{Z}}}}[/tex]

Answer:

true

Step-by-step explanation:

Answer:

x=3, Aly is correct.

Step-by-step explanation:

a. angle YWZ

b. ZY = 9

c. the triangles are congruent so 7x-20=2x-5, 5x=15, and x=3

Answer:

  (6x² +4x -20)/(x² +x -3) cm

Step-by-step explanation:

The perimeter of a rectangle is twice the sum of its length and width. Here, length and width are rational functions. The same relation to perimeter applies.

__

  [tex]P = 2(L+W)\\\\P=2\left(\dfrac{2x^2 +3x-5}{x^2+x-3}+\dfrac{x^2-x-5}{x^2+x-3}\right)\qquad\text{use given values for $L$ and $W$}\\\\P=2\left(\dfrac{2x^2+3x-5+x^2-x-5}{x^2+x-3}\right)=\dfrac{2(3x^2 +2x-10)}{x^2+x-3}\\\\P=\dfrac{6x^2+4x-20}{x^2+x-3}\\\\\underline{\ \qquad}\\\\\textsf{It would take $\dfrac{6x^2+4x-20}{x^2+x-3}$ cm of ribbon to go around the package.}[/tex]

Answer:

15%

Step-by-step explanation:

see the picture for explanation

Answer:

28%.

Step-by-step explanation:

That would be 100 * 7/25

= (100/25) * 7

= 4*7

= 28.

The equation that represents the total of $400 based on the hot dog and drink sales is $400= $1.50H + $2.00D

The amount sold for each hot dog = $1.50

The total number of hot dogs sold = H × $1.50

The amount sold for each drink = $2.00

The total number of drinks sold = D× $2.00

The total sales made was = $400

Therefore the equation that represents the total of $400 based on the hot dog and drink sales is;

$400= $1.50H + $2.00D

The relationship that exists between the hot dog sales is that the cost is the drinks is higher than the cost of the hot dog.

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Answer:

Step-by-step explanation:

   Number of candies that her sister gave = x

Total candies that Pam has now = 27

  x +  15 = 27

       x + 15 = 27

   x + 15 - 15 = 27 - 15

               x  = 12

Answer:

Equations :

27 - 15 = x

15 + x = 27

Step-by-step explanation:

So, we know that 1. Pam starts with 15 candies. and 2. Pam ends up having 27 candies. This means, that she gained candy.

To figure out how many candies her sister gave, her, we have to find the difference between 27 and 15 becuase she goes from having 15 to having 27 after her sister had given some.

x will represent how many cadies Pams' sister had given her :

27 -  15 = x

12 = x

This means Pams' sister gave 12 candies to Pam. To make sure we are correct, we can simply start with how many candies Pam started with (15). And add how many we think her sister added (12)

15 + 12

15 + 12 = 27

Therefore proving, and meaning, that Pams' sister gave her 12 candies.

Possible Equations :

27 - 15 = x

End total (27) minus starting total (15).

15 + x = 27

Starting total (15) plus how many she gained (x) equal to end total (27).

Answer:  [tex]y = 850(0.943)^t[/tex]

Reason:

The exponential of the form [tex]y = a*b^x[/tex] has 'a' as the initial term and b as the growth or decay factor.

a = 850 is the starting amount

b = 1 + r = 1 + (-0.057) = 0.943 is the decay factor

If the sample loses 5.7% of its mass each year, then it keeps the remaining 94.3% of it.

Answer:

10y - 70z + 10.

Step-by-step explanation:

10(y-7z+1)    Multiply each term in the brackets by 10:

= 10y - 70z + 10

Using the Empirical Rule, it is found that Tariq scores between 80 and 140 in 99.7% of the games that he bowls.

It states that, for a normally distributed random variable:

In this problem, considering the mean of 110 and the standard deviation of 10, scores between 80 and 140 are within 3 standard deviations of the mean, hence Tariq scores between 80 and 140 in 99.7% of the games that he bowls.

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Answer: 8 meters

Step-by-step explanation: 72/9 = 8

Answer:

8 meters

Step-by-step explanation:

Since there is so little information given, I'm assuming this is just the area of a rectangle. The formula you used to find the area of a rectangle is "area = length * width" or "A = l*w".

We are given the area and the length, so we can fill in those spaces in the formula-

72 = 9 * w

Now, in order to find the width. we have to undo in reverse order. We have to divide 72 by 9.

72 (/ 9) = 9 * w (/ 9)

8 = w

Therefore, the width is 8 meters. I hope this helps! Have a lovely day!! :)

Step-by-step explanation:

We can use long division to solve this

First place a 5 in the tens place, this means we are multiplying 5 by 50. This will subtract 250 from 280, leaving us with 30.

Next place a 6 in the ones place, this means we are multiplying 5 by 6. This will subtract 30 from 30, leaving us with 0.

This means we have found our answer of 56.

Answer:

See explanation

Step-by-step explanation:

Basically, division is just saying "how many numbers would go into this number this many times?" We can break this problem down into 200/5 and 80/5. 200/5 is 40, and 80/5 is 16. 40+16 is 56, so the answer is 56.

(I can elaborate further if needed)

Hope this helps!

Answer:

C. 5f +25

Step-by-step explanation:

Answer:

[tex](x+1)^{2} +4[/tex]

a = 1

b = 4

Step-by-step explanation:

hope this helps!! p.s. i really need brainliest :)

Yes

Step-by-step explanation:

[tex] \cos( \alpha ) = \frac{base}{hypoteneuse} [/tex]

Its just correct..

Answer:

260 cm^2

Step-by-step explanation:

Area of rectangle = 20 x 10 = 200 cm^2

Area of triangle = 6 x 20 /2 = 60 cm ^2

Area of figure = 200 + 60 = 260 cm^2

Using it's concept, it is found that there is a 0.1087 = 10.87% probability Sung chose a milk chocolate then a white chocolate.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that:

Thus, the probability of milk then white is given by:

[tex]p = \frac{5}{12} \times \frac{6}{23} = \frac{30}{12 \times 23} = 0.1087[/tex]

0.1087 = 10.87% probability Sung chose a milk chocolate then a white chocolate.

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Answer:

Area of the prism = 2(lw + lh + wh)

l = length = 6 m

w = width = 3 m

h = height = 12 m

—

Area of the prism = 2(6*3 + 6*12 + 3*12) = 2(18 + 72 + 36) = 2(126) = 252 m²

—

Have a nice day!!

The probability that the spinner will land on a number greater than 4 or on a shaded section is 2/3

The given parameters are:

Using the above parameters, we have the following probabilities

P(Greater than 4) = 2/6

P(Shaded) = 3/6

P(Shaded section and greater than 4) = 1/6

The required probability is then calculated using:

P = 2/6 + 3/6 - 1/6

Evaluate

P = 4/6

Simplify

P = 2/3

Hence, the probability that the spinner will land on a number greater than 4 or on a shaded section is 2/3

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Answer:

  6.1 km

Step-by-step explanation:

The Pythagorean theorem tells you the relationship between the lengths of the sides of a right triangle.

  c² = a² +b² . . . . a, b are the short sides; c is the hypotenuse

__

The geometry of this problem can be modeled by a right triangle with legs 3.7 km and 4.9 km. The distance of interest is the hypotenuse of the triangle.

  c² = 3.7² +4.9² = 13.69 +24.01 = 37.70

  c = √37.70 ≈ 6.1

The straight-line distance is about 6.1 km.

Answer:

[tex]\huge{\red{\angle ABC = \boxed{30}\degree}}[/tex]

Step-by-step explanation:

Answer:

The inequality for this diagram is x≥-1

Please the explanation... it always helpsssss....

Step-by-step explanation:

The first step is to look at the circle... is it filled in or not... in this case it is...

meaning the symbol is greater than or equal to  OR less than or equal to

next the arrow is pointing to the right meaning the symbol must be greater than or equal to

then look at the value at the filled in circle (which in this case is -1)

meaning the inequality must be x≥-1

i really hope this helps!!!!