55 Points! Multiple choice algebra question. State the number of real zeros for the function whose graph is shown. Photo attached. Thank you!

Answer:

\(x= 80^o\)

Step-by-step explanation:

Given

\(\angle Z = 36^o\)

\(\angle WYZ = 100^o\)

Required

Find x

\(\angle WYZ\) and x are on a straight line.

So:

\(\angle WYZ + x= 180^o\)

Make x the subject

\(x= 180^o -\angle WYZ\)

Substitute known value

\(x= 180^o -100^o\)

\(x= 80^o\)

Answer:

80 is correct

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

AD: AC=3:6, so the ratio is 1:2

AC:AB=6: AB, AB=12

Answer:

\(4\sqrt{2b}\)

Step-by-step explanation:

\(\sqrt{98b}-\sqrt{72b}+\sqrt{18b}\)

Apply radical rule \(\sqrt{ab} =\sqrt{a} \sqrt{b}\):

\(\implies \sqrt{98}\sqrt{b} -\sqrt{72}\sqrt{b} +\sqrt{18}\sqrt{b}\)

Factor out common term \(\sqrt{b}\):

\(\implies \sqrt{b}(\sqrt{98} -\sqrt{72}+\sqrt{18})\)

Rewrite 98, 72 and 18:

\(\implies \sqrt{b}(\sqrt{49 \cdot 2} -\sqrt{36 \cdot 2}+\sqrt{9 \cdot 2})\)

\(\implies \sqrt{b}(\sqrt{49}\sqrt{2} -\sqrt{36}\sqrt{2}+\sqrt{9}\sqrt{2})\)

\(\implies \sqrt{b}(7\sqrt{2} -6\sqrt{2}+3\sqrt{2})\)

Factor out common term \(\sqrt{2}\):

\(\implies \sqrt{b}\sqrt{2}(7 -6+3)\)

\(\implies \sqrt{b}\sqrt{2}(4)\)

\(\implies 4\sqrt{2b}\)

Answer:

512 ft and 1,232 ft

Step-by-step explanation:

area is length x width

the pool's area can be calculated doing 32ft x 16ft

the area of the pool is 512 ft

the deck's area can be calculated doing 28ft x 44ft

the area of the deck is 1,232 ft

you're welcome<3

Answer:

its 85

Step-by-step explanation:

The distance at which the Benson family would be from home after 412 hours of driving according to the task content is; 18,640 miles.

It follows from the task content that the equation which models the distance of the Benson's family from home after a given time t is;

d = 45t +100

Hence, when t = 412 hours.

d = 45(412) + 100

d = 18540 +100

d = 18,640miles.

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Answer:

1/4

Step-by-step explanation:

Since y/x = 3/12 = 1/4, the answer is 1/4.

Answer:

simplified: 6 + x/3

Step-by-step explanation:

(2/3x+2) - (1/3x - 4)

= 6 + x/3 .

Hope this helps !

Using the rate of the exponential growth to calculate the exponential function, the number of subscribers after 10 years is 3446

An exponential function is a function in which the variable appears in an exponent. It is of the form f(x) = aˣ, where a is a constant and x is the independent variable. The graph of an exponential function is a curve that increases or decreases at an increasing rate.

To solve this problem, we have to find the rate and then calculate the number subscribers after 10 years.

In a given exponential function;

A = P(1 + x)ⁿ

Since this is an exponential growth, we can calculate the rate as;

1 year = 250 subscriber

2 years = 3 * 250

rate = (250 / 750) * 100

rate = 30%

We can substitute the values into the formula and solve

A = 250(1 + 0.3)¹⁰

A = 3446.46

They are expected to have 3446 subscribers after 10 years

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The radius of the given circle is 2 units.

Here, we are given an equation of a circle as follows-

\(x^{2}+ y^{2} + 8x - 6y + 21 = 0\)

The general form of the equation of a circles is -

\((x- h)^{2}+ (y-k)^{2} = r^{2}\)

where (h, k) are the coordinates of the center of the circle and r is the radius of the circle.

Let us convert the given equation into the general form by completing the squares as follows -

\(x^{2}+ y^{2} + 8x - 6y + 21 = 0\)

\(x^{2}+ (2*4)x+ y^{2} - (2*3)y + 21 = 0\)

\(x^{2}+ (2*4)x+ 16 -16+ y^{2} - (2*3)y + 9 - 9+ 21 = 0\)

\([x^{2}+ (2*4)x+ 16] -16+ [y^{2} - (2*3)y + 9] - 9+ 21 = 0\)

\((x+4)^{2} -16+ (y - 3)^{2} - 9+ 21 = 0\)

\((x+4)^{2} + (y - 3)^{2} = 16 + 9 - 21\)

\((x+4)^{2} + (y - 3)^{2} = 4\)

\((x+4)^{2} + (y - 3)^{2} = 2^{2}\)

Thus, we have obtained the equation of the circle in the general form. From this, we can observe that the center coordinates will be (-4, 3) and the radius of the circle will be 2 units.

Therefore, the radius of the given circle is 2 units.

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Answer:

x = 6

Step-by-step explanation:

\(x = \sqrt{10 {}^{2} - 8 {}^{2} } \)

\(x = \sqrt{100 - 64} \)

\(x = \sqrt{36} \)

\(x = 6\)

Answer: X=10

Step-by-step explanation:

Step 1: Subtract x from both sides.

Step 2: Divide both sides by 5.

Answer:X=10

Step-by-step explanation:

s1 = 5

s2 = s1 × -2 = 5×-2 = -10

s3 = s2 × -2 = -10 × -2 = 20

...

now, we could do all that manually.

but there is also a formula for geometric sequence.

in fact, there are 2 - one for finite and one for infinite sequences.

and I was not completely honest, each of these 2 had some sub-forms depending on the size of the multiplier or ratio.

since we need the sum of the first 5 terms, which of the 2 do you think we need ?

of course, finite, because 5 is a normal number we can "touch". it is not infinity.

so, the formulas for finite sums of geometric sequences are :

if |r| < 1, Sn = a(1 - r^n)/(1 - r)

if |r| > 1, Sn = a(r^n - 1)/(r - 1)

if r = 1, Sn = na

if r = -1, then Sn = a or 0 depending on if n is odd or even.

the sequence is in general

s1 = a

sn = sn-1 × r

in our case a = 5, r = -2.

so, what form of the formula do we need ?

|-2| = 2, and 2 > 1, so ...

S5 = 5(-2^5 ‐ 1)/(-2 - 1) = 5(-32 - 1)/-3 = 5×-33/-3 =

= 5 × 11 = 55

quick check, as the 5 terms are

5

-10

20

-40

80

and their sum is : 55

correct !

The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.

Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:

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

Simplifying:

y - 3 = x + 1

Now, we can rewrite the equation in the standard form:

y = x + 4

Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

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The equation of the line in slope - intercept form is -

y = - 5x + 77.

The equation of a straight line in slope - intercept form is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the equation as -

77 - y = 5x

We have the equation in the slope - intercept form as -

77 - y = 5x

y = 77 - 5x

y = - 5x + 77

Therefore, the equation of the line in slope - intercept form is -

y = - 5x + 77.

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Answer:

5:20 to 9:20

Step-by-step explanation:

Answer:

x=-82

subtract 74 from -130 and then divide -164 by two

hello

the answer to the question is:

y = a cot(bx – c) + d

a = 1, b = 1/2, c = 0

the midline is y = d, so y = 0

the vertical stretch is 1, so label the y-axis so the inflection point of the curve is 1 above the midline, and the other inflection point is 1 below the midline

the period is:

T = π/b ----> T = 2π

the phase shift is:

PS = c/b ----> PS = 0

and also, there's no amplitude for tangent and cotangent, there is only the vertical stretch that takes the place of an amplitude

Answer:

amplitude does not exist. period = 2π (360°)

Step-by-step explanation:

there is no amplitude for tan θ or cot θ, since there is no limit up or down (positive/negative infinity).

period for cot θ is π (180°)

period for cot 1/2 θ is 2π (360°)

Answer:

3

Step-by-step explanation:

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Steps to solve:

b + 4.22 = 7.08

~Subtract 4.22 to both sides

b = 2.86

Best of Luck!

Answer:

1. continuous random variable

2. not a random variable

3. a continuous random variable

Step-by-step explanation:

The classifications are as follow

a)  The height of the player reported in the game day program is treated as a continuous random variable as these values could be determined through measuring them

b)  The color of student car is not a random variable as it does not contain any quantitative data or we can say numerical data

c)  The exact weight of the bag is a continuous variable as it is lie between the range

Answer:

x^2

Step-by-step explanation:

1^2=1

2^2=4

3^2=9

Answer:

7 hours

Step-by-step explanation:

here,

270/18=105/x

x=(105*18)/270

x=7

Chau made $270 for 18 hours of work. At the same rate,  Therefore Chau would have to work 7 hours at the same rate to make $105.

To find out how many hours Chau would have to work to make $105 at the same rate, we can set up a proportion using the given information:

Let x be the number of hours Chau needs to work to make $105.

We know that Chau made $270 for 18 hours of work, so the rate of earnings per hour is:

Rate = Total earnings / Number of hours

Rate = $270 / 18 hours

Rate = $15 per hour

Now, we can set up the proportion:

$15 per hour = $105 / x hours

To find x, we can cross-multiply:

$15 × x = $105

Now, solve for x:

x = $105 / $15

x = 7 hours

So, Chau would have to work 7 hours at the same rate to make $105.

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Answer:

(u + \(\frac{65}{2}\) )²

Step-by-step explanation:

u² + 65u

to complete the square

add ( half the coefficient of the u- term )²

= u² + 2(\(\frac{65}{2}\) )u + \(\frac{4225}{4}\)

= (u + \(\frac{65}{2}\) )²

Chay can use 3 bags of mulch per flower bed.

Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.

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'The amount of paint needed is 78.4π cm³. We can calculate it in the following manner.

We know that V= 2/3πr³ since we have a hemisphere here. So,

dV= (2/3)3πr²dr= 2πr²dr

Now the amount of paint needed is

ΔV≈ dV= 2πr²dr

In this,

dr= 0.05 cm and r= 28 cm ( because the diameter is 56 cm),

hence:

dV= 2π(28)²(0.05)= 78.4π cm³

Any straight line segment that cuts through the center of a circle and has ends that are on the circle is considered a circle's diameter in geometry. It is also known as the circle's longest chord. The diameter of a sphere can be defined using either of the two methods. The simplest place to start would be to use a ruler to measure the distance between the circle's outside edges starting from its very center. The diameter would be that.

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\(\cfrac{2y}{3}-\cfrac{3}{4}=\cfrac{1}{12}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{2y}{3}-\cfrac{3}{4} \right)=12\left( \cfrac{1}{12} \right)}\implies 8y-9=1 \\\\\\ 8y=10\implies y=\cfrac{10}{8}\implies y=\cfrac{5}{4}\)