Question 2 (10 points)

The simplified form of the exponential expression [tex]64^{\frac{1}{4} }[/tex] is  [tex]2\sqrt{2}[/tex]

The given expression = [tex]64^{\frac{1}{4} }[/tex]

The exponential function is the function in the form of f(x)= [tex]a^{x}[/tex], where x is the variable and a is the constant. The constant term is the base of the exponential function.

The given expression = [tex]64^{\frac{1}{4} }[/tex]

Here we have to use the power rule of the exponents

[tex](a^{m})^{n}=a^{mn}[/tex]

To increase a number with an exponent to the power, we have to multiply the exponent times the power

We know

64 = [tex]2^{6}[/tex]

Then

[tex]64^{\frac{1}{4} }[/tex] = [tex](2^{6})^{\frac{1}{4} }[/tex]

Apply the power rule of the exponent

[tex](2^{6})^{\frac{1}{4} }[/tex] = [tex]2^{(6)(\frac{1}{4} )}[/tex]

= [tex]2^{\frac{3}{2} }[/tex]

= [tex]2\sqrt{2}[/tex]

Hence, the simplified form of the exponential expression [tex]64^{\frac{1}{4} }[/tex] is  [tex]2\sqrt{2}[/tex]

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The 146°, and the x and 58° which are vertical angles formed by the two intersecting lines where the x and 58° are formed by the ray gives the measure of x as 88°

Vertical angles or vertically opposite angles are the angles formed by two intersecting lines and which are on either side to each other

The description parameters are;

The objects in the figure includes; Two intersecting lines and a ray

The measure of one of the angles formed by the intersecting lines = 146°

The vertically opposite angle to the 146° angle is broken into = x and 58°

Required; The value of x

Solution; The vertical angles theorem states that vertically opposite angles that are formed when two lines intersect, are congruent.

In geometry, two figures are congruent when they exactly coincide when they are superimposed, which means that the two figures have the same measurement.

Given that 146° is congruent to x + 58°, we have;

146° = x + 58° Definition of congruency and angle addition postulate

x = 146° - 58° = 88°

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The graph plotted represents a discrete data

The domain of the function is -2 ≤ x ≤ 2

The range of the function is 1 ≤ y ≤ 5

The graph plotted is represent circle functions

This is a term used to represent data that can be estimated by counting. The circle graph is an instance of methods of representing discrete data.

The term domain refers to the input variables on a graph, the domain is usually plotted on the x axis.

Range is a term that describes the output functions and are usually plotted on the y axis.

The function plotted is a circle with a radius of 2 units.

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The ordered pair that satisfies the inequality is (aₓ ,bₓ) .

In mathematics, an inequality is a link that compares two numbers or other mathematical expressions unfairly.

Therefore we can conclude that (aₓ, bₓ) satisfies the inequality.

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Yes she made a wise decision as she will get an amount of 4500 after 5 years which is better than getting 4000 after 5 years.

Given that ,

Let us assume that the person takes the amount 3000 from the college, and invests it on a annual rate of 10% for a period of 5 years,

means,

Principal amount = 3000

Rate of Interest = 10%=0.1

Time = 5 years

The future value simple interest formula is the addition of the principal amount that we have in the beginning and the interest earned on that principal amount after the completion of the period. The Future Value Simple Interest Formula is given as,

F V = P + I or F V = P(1 + rt)

Here,

P is the principal amount,

I is the interest,

r is the rate, and

t is the time.

So, We know that

Simple Interest = Principal amount * Rate of Interest * Time

Simple Interest = 3000*0.1*5

Simple Interest = 1500

So, The person will have a Future value of

Principal amount + Simple Interest

= 3000+1500

=4500

Therefore, If the person invests after 5 years will get a amount of 4500 in return which is a wise decision than not investing and getting a amount of 4000 .

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Check the picture below.

Answer:

Step-by-step explanation:

Horizontal line is y = 1

Vertical lone is x = 8.

Answer:

0.103 acres

Step-by-step explanation:

This question tests on the concept of Conversion.

Given from the question, we know that:

107 pounds of seed = 11 acre field

To find the acres of field we can plant per pound of seed, we simply divide both sides of the equation by 107.

(107 ÷ 107) pounds of seed = (11 ÷ 107) acres of fiels

1 pound of seed = 0.103 acres of field (Rounded off to 3 significant figures)

Answer:

B

Step-by-step explanation:

The range of |x| is [tex]{y|0 \leq y <\infty\}[/tex]. Adding 3 to this yields option B.

From the given figure the value of angle x is 40 degrees

|AC| = | CD |

Δ ( ACD ) = Δ ( DCB )

< ( BAC ) = 70 degrees

Since |AC| = | CD | then the base angles are equal, hence

< ( ADC ) =  < ( BAC ) 70 degrees. ( base angles of isosceles triangle )

< ( ADC ) + < ( BAC ) + < ( ACD ) = 180 degree ( sum of angles in a triangle)

note < ( BAC ) = < ( DAC )

< ( ACD ) = 180 - 70 - 70

< ( ACD ) = 180 - 140

< ( ACD ) = 40 degrees

If Δ ( ACD ) = Δ ( DCB ) then the angles should be equal

Δ ( ACD ) has angles:

< ( ADC )  = 70

< ( DAC ) = 70

< ( ACD ) = 40

Then Δ ( DCB ) should have angles 70, 70, and 40. The figure did not give enough information to put the angles where it should be.

Comparing with the options, only angle 40 degrees is in the option, hence the correct answer

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The number is (x/2)+15=5+3x if Half of Number augmented by 15 equals the sum of 5 and the product of 3 and the number.

A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.

Decimal Number System is one of the four popular forms of number systems and other 3 are -

System of binary numbers.

System of Octal Numbers.

System of Hexadecimal Numbers.

From the given question,

X is the number. first we have to halve it , then we add 15.

Next ,set it equal to the other side . the second side is 5+ ( because it is the sum)

3x( the product of 3 and x means multiply them)

Hence the number is (x/2)+15=5+3x

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Answer:

Step-by-step explanation:

your answer along with the work is down below please go and check it out also sorry I'm wrong have nice day:)

The rate at which Portia reads is 2.3 pages per minute, at this rate, she can read 126.5 pages in 55 minutes.

We know that Portia can read 23 pages in 10 minutes, so the number of pages she reads per minute is given by the rate:

R = (23 pages)/(10 minutes) = 2.3 pages per minute.

Now, the number of pages she can read in 55 minutes is given by the product between the rate and 55 min, so we will get:

(2.3 pages/min)*55 min = 126.5 pages

We conclude that Portia can read 125.6 pages in 55 minutes.

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Answer:

I don't understand the equation....pls rewrite it

Answer:

if x=4 y=12

if y=4 x=-4

Step-by-step explanation:

y=4+8 (add)

y=12

4=x+8 (subtract 8 from each side)

-4=x

Answer:

12

Step-by-step explanation:

Did you mean 7+5?

If so, then 7 + 5 = 12

a)Midpoints are (-6.5,-4).

b)Midpoints are (-6.5,-4).

In geometry, a line segment's midpoint is referred to as the midpoint. It serves as both the segment's and the ends' centroid, and it is equally spaced from both. The portion is halved by it. The midpoint formula is employed when it is important to pinpoint the exact intersection of two given points. The point that splits a line segment described by two points in half can thus be found using this method. The halfway is the precise numerical intersection of two integers. The two-number average computation and the midpoint calculation are equivalent. Consequently, you may get the halfway point between any two integers by adding any two numbers together and dividing by two.

Given Data

Mid point formula = [tex]\frac{x+x}{2}[/tex]¹ , [tex]\frac{y+y}{2}[/tex]¹

a) (2,-1) (-8,6)

Equating values in formula,

[tex]\frac{2-8}{2}[/tex] , [tex]\frac{-1+6}{2}[/tex]

(-4,2.5)

Midpoints are (-4,2.5)

b) (-8,-9) (-5,1)

Equating,

[tex]\frac{-8-5}{2}[/tex] , [tex]\frac{-9+1}{2}[/tex]

[tex]\frac{-13}{2}[/tex] , [tex]\frac{-8}{2}[/tex]

(-6.5,-4)

Midpoints are (-6.5,-4).

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Answer: 3.6

20

8.25

Step-by-step explanation:

7 - 10 = 3

-6 - -8 = 2

[tex]\sqrt{3^{2} +2^{2} } =3.6[/tex]

Answer:

D. reflection over the y-axis.

Step-by-step explanation:

Reflections are the samere same shapes, but mirrored and over a certain axis (x or y axis). In this case, we see a reflection over the y-axis.

Using the given information, the value of 6a + 9b is 21 and the value of 3x + 5y is 20

From the question, we are to determine the values of the given expressions.

From the given information,

2a + 3b = 7

and

6x + 10y = 40

To determine the value of 6a + 9b, multiply the first equation by 3.

That is

3 × [ 2a + 3b = 7

6a + 9b = 21

∴ The value of 6a + 9b is 21

To determine the value of 3x + 5y, we will divide the second equation by 2

That is,

6x + 10y = 40 ] ÷ 2

3x + 5y = 20

The value of 3x + 5y is 20

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Check the picture below.

[tex]\stackrel{\measuredangle N}{(5x-8)}~~ + ~~\stackrel{\measuredangle O}{(x-5)}~~ + ~~\stackrel{\measuredangle P}{(6x+1)}~~ = ~~180 \\\\\\ 12x-12=180\implies 12x=168\implies x=\cfrac{168}{12}\implies x=14 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle O}{(x-5)}\implies (14)-5\implies {\Large \begin{array}{llll} \stackrel{\measuredangle O}{9} \end{array}}[/tex]

Answer:

-3

Step-by-step explanation:

[tex] \frac{a - 15}{2 - 0} = \frac{ - 6}{2} = - 3 \\ \frac{3 - 9}{4 - 2} = - 3 \\ \frac{ - 3 - 3}{6 - 4} = - 3 \\ \frac{ - 9 - ( - 3)}{8 - 6} = - 3 \\ so \: slop \: is \: - 3[/tex]

It is impossible to give a value for f(-1) because -1 is not in the domain of the function f.

It is given in the question that function f(x) is defined by the set of coordinate pairs {(-3,8),(2,5),(7,-1),(11,3)}.

Here, the ordered pair (a,b) represents (x ,f(x))

Which means:-

f(-3) = 8 , f(2) = 5, f(7) = -1, f(11) = 3.

Here, the elements of domain are -3, 5, -1 and, 3 and the elements of range are 8, 5, -1 and, 3.

We cannot find the value of f(-1) because -1 is not present in the domain of the function.

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Answer:

Step-by-step explanation:

yes it is

Answer:

if x = -6, r = 180/pi and D = 360/pi

without knowing the actual D or r, one cannot truly solve for x.

Step-by-step explanation:

looking at the angle, [tex]125^o[/tex], it is part of two supplementary parts of the circle, let us call the angle between [tex]55^o\ \&\ 125^o[/tex] y. given that 125 is supplementary to y:

125+y=180

and so...

y=55

now, let us call the angle associated with the arc-length, x+76 z.

Knowing that y+55 and z are supplementary (given the length is a diameter), we can write the equation:

y + 55 + z = 180

substituting y=55 gives:

55 + 55 + z = 180

combining like terms gives:

110 + z = 180

further simplifying gives:

z = 70

x + 76 is the arc-length of the section of the circle, whose angle is now denoted by z = 70.

Arc-length = Circumference * percentage of circle

circumference is given as C = π * D OR C = 2r * π (because 2r = D)

percentage of circle is simply (number of degrees covered ÷ total degrees of a circle)

so, we have that the percentage = 70/360 [360 degrees in a circle, 70 degrees covered by the angle, z]

and the circumference is unknown without a radius or diameter length, so we will use the equation C = π * D

using the formula for arc-length:

Arc-length =  π * D * 70/360

Arc-length also happens to equal x + 76, so:

x + 76 =  π * D * 70/360

reduce:

x + 76 =  π * D * 7/36

simplify by getting x alone:

x =  π * D * 7/36 - 76

we can further simplify by creating one fraction:

[tex]x = \frac{7D\pi - 2736}{36}[/tex]

it can also be shown as:

[tex]x = \frac{7r\pi - 1368}{18}[/tex]

because, D = 2r and you could factor 2 from (7*2*r*pi - 2736) and then reduce by dividing top and bottom each by 2.

You can divide top and bottom by 2 because:

[tex]\frac{2}{36} = \frac{1}{18}[/tex]

which is because [tex]\frac{km}{ln}=\frac{k}{l} * \frac{m}{n}[/tex]

if we say km = 2 and ln = 36, then k = 2, m = 1 is the only options for k and m

and l and n can be any set of factors of 36, which include 2*18, 3*12, 6*6, 9*4.

if we choose l = 2 and n = 18, then k = l = 2 and:

[tex]\frac{k}l=\frac{2}2 = \frac{r}{r}[/tex]

which is to say that k = r = l = 2, which I only show to say generally that when k = l or you have r ÷ r, it is equal to 1.

1 * s = s

and if s =  m ÷ n, then [tex]\frac{km}{ln} = \frac{m}{n}\ whenever\ k = l[/tex]

given that the answer to what is x, is -6, the arc length is therefore 70. we can plug in this 70 now to find r and therefore, D.

[tex]70 = \pi * D * \frac{70}{360}\\\\multiply\ by\ \frac{360}{70}\ on\ both\ sides\ to\ get:\\360=\pi * D\\divide\ by\ \pi\ on\ both\ sides\ to\ get:\\360/\pi = D\ OR\ 180/\pi=r[/tex]

Answer:

m=y2-y1/x2-X1 so the slope is equal to -3

Answer:

AB = 4.5 cm

Step-by-step explanation:

the total area (A) of the 2 rectangles is calculated as

A = x(x - 4) + 3x(x - 2)

   = x² - 4x + 3x² - 6x

   = 4x² - 10x

Given A = 36 , then equating

4x² - 10x = 36 ( subtract 36 from both sides )

4x² - 10x - 36 = 0 ( divide through by 2 )

2x² - 5x - 18 = 0 ← as required

To factorise the equation

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 18 = - 36 and sum = - 5

the factors are + 4 and - 9

use these factors to split the x- term

2x² + 4x - 9x - 18 = 0 ( factor the first/second and third/fourth terms )

2x(x + 2) - 9(x + 2) = 0 ← factor out (x + 2) from each term

(x + 2)(2x - 9) = 0

equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

2x - 9 = 0 ⇒ 2x = 9 ⇒ x = 4.5

but x > 0 , then x = 4.5

Then

AB = x = 4.5 cm

Answer:

AB = 4.5 cm

Step-by-step explanation:

[tex]\boxed{\textsf{Area of a rectange}=\sf width \times length}[/tex]

Area of the smaller rectangle:

[tex]\implies A=x(x-4)[/tex]

[tex]\implies A=x^2-4x[/tex]

Area of the larger rectangle:

[tex]\implies A=(2x+x)(x-2)[/tex]

[tex]\implies A=3x(x-2)[/tex]

[tex]\implies A=3x^2-6x[/tex]

The area of the compound shape is the sum of the areas of the two rectangles:

[tex]\implies A=(x^2-4x)+(3x^2-6x)[/tex]

[tex]\implies A=x^2+3x^2-4x-6x[/tex]

[tex]\implies A=4x^2-10x[/tex]

If the area of the compound shape equals 36 cm² then:

[tex]\implies 36=4x^2-10x[/tex]

[tex]\implies 36-36=4x^2-10x-36[/tex]

[tex]\implies 0=4x^2-10x-36[/tex]

[tex]\implies 4x^2-10x-36=0[/tex]

[tex]\implies \dfrac{4x^2}{2}-\dfrac{10x}{2}-\dfrac{36}{2}=\dfrac{0}{2}[/tex]

[tex]\implies 2x^2-5x-18=0[/tex]

The length of AB is x cm.  

To find the value of x, factor the quadratic.

To factor a quadratic in the form [tex]ax^2+bx+c[/tex] find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].

[tex]\implies ac=2 \cdot -18=-36[/tex]

[tex]\implies b=-5[/tex]

Therefore, the two numbers are: -9 and 4.

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies 2x^2-9x+4x-18=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(2x-9)+2(2x-9)=0[/tex]

Factor out the common term (2x - 9):

[tex]\implies (x+2)(2x-9)=0[/tex]

Apply the zero-product property:

[tex](x+2)=0 \implies x=-2[/tex]

[tex](2x-9)=0 \implies x=\dfrac{9}{2}=4.5[/tex]

As length is positive, x = 4.5 only.

Therefore, AB = 4.5 cm.

If C is the midpoint of AB then the length of CD is 11 units.

The midpoint of a line segment is referred to as the midpoint in geometry.

Given C is the midpoint of AB.

AD = 15 and BD = 7

Now AB = 15 - 7 = 8

Again AC = BC

Therefore = BC = 8 / 2 = 4

Now CD = BC + BD = 4 + 7 = 11

Therefore the length of CD is 11 units.

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-9

Constants are terms that are only numbers, without any variables.

Terms

First, let's define what a term is. Within a polynomial, a term is an expression that is added to other terms to create a polynomial. It is important to note that terms are always added. So, if there is subtraction, that means one of the terms is negative.

Constants

The easiest way to identify constants is to look for terms without variables. In the polynomial above, the only constant is -9. All of the other terms have x to some power as a factor. Since they have variables, they cannot be a constant.

Numbers cannot be changed; this is why there are called constants. No matter the x-value, -9 will not change.