For each of the following equations, say which one (d) has two rational solutions, (e) has two irrational
solutions, and (f) has two non-real solutions. Each answer (d, e, and f) is used once.

Answer:

4

Step-by-step explanation:

Answer:

[tex]x=\frac{3\pi }{4} ,\frac{7\pi }{4}[/tex]

If wrong then [tex]x=-\frac{\pi }{4}.[/tex]

Step-by-step explanation:

[tex]tan^2(x)-tan(x)=0[/tex]

Factor out the tan(x).

[tex]tan(x)*(tan(x)-1)=0[/tex]

Solve for x.

[tex]tan(x)\neq 0\\[/tex] thus only option is tan(x)-1=0

[tex]tan(x)-1=0\\tan(x)=1\\[/tex]

x=tan^-1(1)⇒

Either it is Quadrant 2 or 4.

[tex]x=\frac{3\pi }{4} ,\frac{7\pi }{4}[/tex]

If the teacher says its wrong. Then that could only mean that its range of tan(x) is between [tex]-\frac{\pi }{2} < x < \frac{\pi }{2}[/tex] thus it's only on quadrant 4. [tex]x=-\frac{\pi }{4}[/tex]

The equation to represent the situation is like so:

[tex]x+(x-12)+3(x-12)=332[/tex]

Simplify.

[tex]x+x-12+3x-36=332[/tex]

[tex]5x-48=332[/tex]

[tex]5x-380=0[/tex]

Solve for the variable x.

[tex]5x=380[/tex]

[tex]x=76[/tex]

[tex]first\ man =x\\second\ man =x-12\\machine=3(x-12)[/tex]

[tex]first\ man=76\\second\ man=64\\machine=192[/tex]

Verify.

[tex]x+(x-12)+3(x-12)=332[/tex]

[tex]76+(76-12)+3(76-12)=332[/tex]

[tex]76+64+192=332[/tex]

[tex]332=332[/tex]

[tex]LS=RS[/tex]

Using the conversion of exponent to power, the equivalent expression is given as follows:

[tex]\frac{\sqrt{x}}{\sqrt[4]{y}z^2}[/tex]

It happens according to the following rule, with the denominator as the root and the numerator as the exponent:

[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]

In this problem, we are given the following expression:

[tex]x^{\frac{1}{2}}y^{-\frac{1}{4}}z^{-2}[/tex]

Negative exponents go to the denominator, hence the equivalent expression is given by:

[tex]\frac{\sqrt{x}}{\sqrt[4]{y}z^2}[/tex]

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Answer:

Each person received 3/10 of pie

Step-by-step explanation:

3 dived by 10 equals 0.3 which is equivalent to 3/10

Answer:

arc = 9π units

Step-by-step explanation:

the arc is half the circumference of the circle, then

arc = [tex]\frac{1}{2}[/tex] × 2πr = πr , then

arc = π × 9 = 9π

Answer:

[tex]\boxed{\tt 9\pi }[/tex]

Step-by-step explanation:

What we want to find here is the arc length of 1/2 of a circle, we'll start by finding the of the circle.

Step 1:- find the circumference of the circle →

[tex]\boxed{\sf Circumference\; of\; the \:circle=2\pi r}[/tex]

[tex]\tt 2\pi \times 9[/tex]

[tex]\tt 9\times 2\pi[/tex]

[tex]=\tt 18\pi[/tex]

Step 2:- find the arc length of 1/2 of the circle →

The arc length is 1/2 of the circumference of the circle:-

[tex]\boxed{\sf Circumference \; of \;\cfrac{1}{2}\; of\; the \; circle=\cfrac{1}{2}\times 18\pi}[/tex]

[tex]\tt \cfrac{18}{2} \pi[/tex]

[tex]\boxed{\tt 9\pi}[/tex]

Therefore, the arc length of the semicircle is 9π.

Answer:

7x5x2 = 70

There are no other smaller factors that include all of the given numbers

Answer:

0.4 or 2/5

Step-by-step explanation:

If head is 18/30, then that means that tails must be 12/30, since they must add up to one whole.

Reduce it to simplest terms: 2/5 or 0.4

Answer:

try 36 but im not quite sure

Step-by-step explanation:

im sry if im wrong have a good rest of your day :)

The result of the exponential expression is 81

Indices are written in term of exponents

According to the expoenent law of indices

a^4 = a * a * a * a

Given the expression

(-3)^4

This means the product of -3 in four places. Mathematically

(-3)^4 = -3 * -3 * -3 * -3
(-3)^4 = 9 * 9
(-3)^4 = 81

Hence the result of the exponential expression is 81

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Answer:

False

Step-by-step explanation:

False.

Gross income is the total amount a person earns before any deductions are taken out.

Gross income is the amount of money you make after deductions for taxes and other expenses have been taken out. This statement is false.

Gross income is the income that is earned before any deductions are removed. For example, if a person sells a product for $20. The gross income is $20. Net income is the income after deductions have been taken out.

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Answer:(-2,0) and (3,0)

Step-by-step explanation:im not sure if its correct but it should be

Answer:

True; True; False; True

Step-by-step explanation:

Answer:

PQ = 4cm

QR = 3cm

PR = 5cm

Area = 6cm²

Step-by-step explanation:

Area of triangle = 0.5 × Base × Height

6 = 0.5 × 3 × PQ

6 = 0.5 × 3 × x

[tex] \frac{6}{0.5 \times 3} = x[/tex]

x = 4cm

PQ = 4cm

Since, it is a right angled triangle applying Pythagoras Theorem,

PR =

[tex] \sqrt{ {3}^{2} + {4}^{2} } \\ = \sqrt{9 + 6} \\ = 5cm[/tex]

PR = 5cm

Answer:

16 x ^ -1/5

Step-by-step explanation:

Answer: correct

Step-by-step explanation theoretically it is indeed correct by acknowledging by surface+height which both angles are evenly congruent now

in terms of the 990 Degree angle i know for a fact that it corresponds with it no more to say.

Answer:f^-1(x) = 1/3x + 5/3

Step-by-step explanation:

Answer:

option d 34⁰

Step-by-step explanation:

Your Required Answer is 34⁰

I hope It helped you

Answer:

4 x 2 (2WD) A 4x2 or 2WD is a vehicle that has a two-wheel drive (2WD) with four wheels.

Step-by-step explanation:

Answer:

289 m²

Step-by-step explanation:

First find the area of the flower bed

A=πr²= (3.14)(9.5)² = 283.385

Then get the area of everything including the sidewalk

A=πr²= (3.14)(13.5)² = 572.265

Then subtract and you'll get the area of just the sidewalk

572.265 - 283.385 = 288.88m²

The answer to this question is 289

Using the given bar graph, it is found that the statement that is supported by the data in the bar graph is given by:

The number of employees in Category I is three times the number of employees in Category II.

Research the problem on the internet, it is found that:

Hence the correct option is given by:

The number of employees in Category I is three times the number of employees in Category II, as 45% = 3 x 15%.

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Answer:

Step-by-step explanation:

The graph of f(x) = x² was transformed to create the graph of g(x) = f(x) + 1.5. Which statement about the graphs is true?

The vertex of the graph of g is 1.5 units to the left of

the vertex of the graph of f.

B

The y-intercept of the graph of g is 1.5 units above the

y-intercept of the graph of f.

The graph of g is a reflection of the graph of f across

the y-axis.

The graph of g is a reflection of the graph of f across

the x-axis.

The location final image from the mirror, which is made when an object is placed 1.00 m to the left of the lens, is 0.58 right to the mirror.

The focal length of the lens is the length of the distance between the middle of the lens to the focal point.

It can be find out using the following formula as,

[tex]-\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}[/tex]

Here, (v)is the distance of the image, (u) is the distance of the object, and (f) is the focal length of the lens.

The lens and mirror in the Figure are separated by 1.00 m and have focal lengths of +79.2 cm and -50.6 cm, respectively. Change the units of focal length in meters,

[tex]f_l=79.2\text{ cm=0.792 m}\\f_m=-50.6\text{ cm=0.506 m}[/tex]

An object is placed 1.00 m to the left of the lens. Put the value in the lens formula as,

[tex]-\dfrac{1}{v_l}+\dfrac{1}{1}=\dfrac{1}{0.792}\\-\dfrac{1}{v_l}=\dfrac{1}{0.792}-1\\v_1=3.81[/tex]

The distance of the image made by lens is 3.81 meters. The distance of this image from the mirror is,

[tex]u_2=3.81-1\\u_2=2.81\rm \; m[/tex]

This distance is work as object distance for the mirror. The focal length of mirror is -0.506 m. Thus, the location of the final image is,

[tex]-\dfrac{1}{v_2}+\dfrac{1}{3.81}=\dfrac{1}{-0.506}\\\dfrac{1}{v_2}=-\dfrac{1}{3.81}-(-\dfrac{1}{0.506})\\v_2=-0.58[/tex]

Thus, the location final image from the mirror which is made when an object is placed 1.00 m to the left of the lens, is 0.58 right to the mirror.

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Answer:

336, (B)

Step-by-step explanation:

To find the surface area, find the area of each square and triangle

10x12 + 2(6x8)/2 + 12x6 + 8x12

This would then be,

120 + 48 + 72 + 96

Surface area = 336, (B)

You made a mistake on step 2.

When finding the area of triangle, you have to divide by 2.

Hope this helps!

The function that describes the area of the rectangle in terms of one of the sides is A = 12L - L².

The perimeter of the rectangle is given as 24. Therefore, the area in terms of one of its side will be:

A = L(24 - 2L)/2

A = L(12 - L)

A = 12L - L²

The length side for the maximum area will be 6 and 6. The maximum area of the rectangle will be:

= 6 × 6

= 36

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The number of appetizers that Liz would have learnt after 4 weeks given the unit rate is  20.

The first step is to determine the unit rate of appetizers that Liz learns.

Unit rate = total number of appetizers / total number of weeks

10 /2 = 5 appetizers

Number of appetizers Liz would learn in 4 weeks = 4 x 5 = 20

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Answer:

Step-by-step explanation:

TSA of cube = 6a²

side = 2/3

= 6 x (2/3)²

= 6 x 4/9

= 2 x 4/3

=8/3

Ans = 8/3 units or 2.66.. units

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