HELP I NEED THIS ASAP 20 POINTS
PLEASE ANSWER THESE 2 MATH QUESTIONS!!!

The possible rational zeros of [tex]f(x) = 5x^(4) - 9x^(3) - 7x^(2) + 9x - 2[/tex] are [tex]±1, ±2, ±1/5, and ±2/5.[/tex]

According to the Rational Zeros Theorem, the possible rational zeros of a polynomial function are the ratios of the factors of the constant term to the factors of the leading coefficient. In this case, the constant term is -2 and the leading coefficient is 5.

The factors of -2 are ±1 and ±2. The factors of 5 are ±1 and ±5. So, the possible rational zeros are:

[tex]±1/1, ±2/1, ±1/5, ±2/5[/tex]

Simplifying these gives us the following list of possible rational zeros:

[tex]±1, ±2, ±1/5, ±2/5[/tex]

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The distance is 35 units and the average speed is 5 units per min.

To find the distance that the bug ran, we need to take the difference between the final position and the initial position, it gives:

distance = -12 - (-47) = 12 + 47 = 35 units

And the average speed is the quotient between the distance and the time, so:

Average speed = distance/time.

And here we know that.

distance = 35 units.

time=  7 minutes.

Then we can replace these in the formula above to get:

s = (35 units)/7min = 5 units per min.

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The area of this trapezoid is 66 cm².

To find the area of a trapezoid, we use the formula:

Area = (a + b) x h / 2

Where:

a and b are the lengths of the parallel sides of the trapezoid

h is the height

If we assume that the 22 cm and 11 cm sides are parallel sides, that is

a = 22

b = 11

and h = 4 cm

Now we can use the formula to find the area:

Area = (22 cm + 11 cm) x 4 / 2

Area = 66 cm²

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Answer:

Below

Step-by-step explanation:

'k' shifts the graph of f(x)   UP   by  ' k'  units     k = 6   ( look how far the y-axis intercepts are shifted UP= 6 units  from -2 to + 4)

Answer: 5.25

Step-by-step explanation:

     First, a percent divided by 100 is a decimal.

15% / 100 = 0.15

     Next, we are finding 15% of 35. In mathematical terms, "of" usually represents multiplication. We will multiply 0.15 by 35 to find 15% of 35.

0.15 * 35 = 5.25

Answer:

D

Step-by-step explanation:

The line touches the graph at 2 different points so it doesnt pass the verticle line test

Thus, the drawing's scale factor is 8:1, or simply 8. This implies that each function measurement on the design is eight times bigger than its actual-world equivalent.

Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.

One inch on the illustration equals one eighth of an inch in reality if the scale is 1 inch = 1/8 inch.

We must divide the length of the drawing by the comparable length in reality to determine the scale factor. The scale factor is: because one inch on the design corresponds to 1/8 inch in reality.

1 / (1/8) = 8

Thus, the drawing's scale factor is 8:1, or simply 8. This implies that each measurement on the design is eight times bigger than its actual-world equivalent.

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Answer:

1. [tex]75[/tex]

2. [tex]4x^{8}[/tex]

3. [tex]128[/tex]

Step-by-step explanation:

[tex]\frac{3*5^9}{5^7}=\frac{3*5^2*5^7}{5^7}=3*5^2=75[/tex]

[tex]\sqrt{16x^{16}}=4\sqrt{x^{16}} =4x^8[/tex]

[tex]\frac{(-5)(2^8)}{-6+1}/2=\frac{(-5)(2^8)}{(-5)(2)}=\frac{2^8}{2}=2^7=128[/tex]

The depth of water is fount to be 2.0 fathom when its was 12 feet.

Given:

Conversion unit:

1 foot = 0.167 fathom

Then,

12 feet = 0.167*12 fathom

12 feet = 2.004 fathom

12 feet = 2.0 fathom

Thus, the depth of the water is fount to be 2.0 fathom when its was 12 feet.

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The expression b²/b⁻⁷ when simplified with a positive exponent only will become b⁹.

To simplify the expression b²/b⁻⁷, we can use the rules of exponents. The rules of exponents, also known as laws of exponents, are a set of mathematical rules that govern the manipulation of exponential expressions. These rules are essential in simplifying and solving various mathematical problems involving exponents.

Quotient rule of exponent states that when dividing two exponential expressions with the same base, we subtract their exponents, such that:

xᵃ / xᵇ = xᵃ⁻ᵇ.

In this case, we can simplify the expression b²/b⁻⁷ as follows:

b²/b⁻⁷ = b²⁻⁽⁻⁷⁾ = b⁹.

So, the simplified expression is b⁹. This answer is written with a positive exponent only, as requested.

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[tex]-\dfrac{3}{4}x-\dfrac{1}{3}+\dfrac{7}{8}x-\dfrac{1}{2} = -\dfrac{3}{4}x+\dfrac{7}{8}x -\dfrac{1}{3}-\dfrac{1}{2} = \\[/tex]

[tex]= -\dfrac{3(2)}{4(2)}x+\dfrac{7}{8}x -\dfrac{1(2)}{3(2)}-\dfrac{1(3)}{2(3)} = -\dfrac{6}{8}x+\dfrac{7}{8}x -\dfrac{2}{6}-\dfrac{3}{6} \\[/tex]

[tex]= \dfrac{-6+7}{8}x -\dfrac{2+3}{6} = \dfrac{1}{8}x -\dfrac{5}{6} \\[/tex]

G is linear.

To show that g:V→F defined by g(x)=⟨x,y⟩ for all x∈V is linear, we need to prove that g satisfies the following two properties:

1) g(x+z)=g(x)+g(z) for all x,z∈V
2) g(αx)=αg(x) for all x∈V and α∈F

Proof:

1) Let x,z∈V. Then g(x+z)=⟨x+z,y⟩=⟨x,y⟩+⟨z,y⟩=g(x)+g(z) by the distributive property of the inner product.

2) Let x∈V and α∈F. Then g(αx)=⟨αx,y⟩=α⟨x,y⟩=αg(x) by the scalar multiplication property of the inner product.

Therefore, g is linear.

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Answer: 10y - 3

Step-by-step explanation:

We just add the "+" sign between the two.

So we get:

8y - 6 + 2y + 3

The y terms are like, so we do :

(8y + 2y) - 6 + 3

Which is:

10y - 6 + 3

The integers are like (common), so we do:

10y (-6 + 3)

Which is :

10y - 3    

It is - 3 because -6 + 3 = -3, and we also add the "-" with the integer

So our final answer is=

10y - 3

1) a. 6     b. 5 - i     c. 1 + 4i    d.  -0.5 + 2.5i

2) x^3 - (7 - 3i)x^2 + (14 - 6i)x - (8 - 24i).

(1)
(a) 2 + 3i + 4 - 3i = 6 + 0i = 6

(b) (3 + 2i)(1 - i) = 3 + 2i - 3i - 2i^2 = 3 - i + 2 = 5 - i

(c) 2 + 3i - (1 - i) = 2 + 3i - 1 + i = 1 + 4i

(d) 2+3i / 1-i = (2+3i)(1+i) / (1-i)(1+i) = (2+2i+3i+3i^2) / (1-i+i-i^2) = (2+5i-3) / (1+1) = (-1+5i) / 2 = -0.5 + 2.5i

(2)

If x = 1 – 3i, x = 2, and x = 4 are roots of f(x),

then we can write f(x) as:
f(x) = (x - (1 - 3i))(x - 2)(x - 4)

Multiplying these factors out, we get:

f(x) = (x^2 - (1 - 3i)x - 2x + 2(1 - 3i))(x - 4)
f(x) = (x^2 - (3 - 3i)x + 2 - 6i)(x - 4)
f(x) = x^3 - (7 - 3i)x^2 + (14 - 6i)x - (8 - 24i)
So, the polynomial f(x) is x^3 - (7 - 3i)x^2 + (14 - 6i)x - (8 - 24i).

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[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{20})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{22}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{22}-\stackrel{y1}{20}}}{\underset{\textit{\large run}} {\underset{x_2}{-1}-\underset{x_1}{(-2)}}} \implies \cfrac{2}{-1 +2} \implies \cfrac{ 2 }{ 1 } \implies 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{20}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-2)}) \implies y -20 = 2 ( x +2) \\\\\\ y-2=2x+4\implies {\Large \begin{array}{llll} \end{array}} y=2x+6\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

The table of values is added below and and the graph is attached

From the question, we have the following parameters that can be used in our computation:

y < |4x + 1| - 3

To create a table of values for y < |4x + 1| - 3, we can choose different values of x and substitute them into the expression to find the corresponding values of y.

Let's choose some values of x: -2, -1, 0, 1, 2.

When x = -2, we have:

y < |4(-2) + 1| - 3

y < 4

When x = -1, we have:

y < |4(-1) + 1| - 3

y < 0

When x = 0, we have:

y < |4(0) + 1| - 3

y < |1| - 3

y < -2

When x = 1, we have:

y < |4(1) + 1| - 3

y < 2

When x = 2, we have:

y < |4(2) + 1| - 3

y < 6

Putting it all together, we have the following table:

x y values

-2 y < 4

-1 y < 0

0 y < -2

1 y < 2

2 y < 6

The graph is attached

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The population of the culture at the end of 24 hours will be 1600.

To find this answer, we can use the formula for exponential growth:

P = P₀ * 2^(t/h)

Where P is the final population, P₀ is the initial population, t is the total time in hours, and h is the time it takes for the population to double.

Plugging in the given values, we get:

P = 25 * 2^(24/4)

Simplifying the exponent:

P = 25 * 2^6

Solving for P:

P = 25 * 64

P = 1600

So the population of the culture at the end of 24 hours will be 1600.

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Answer:

See below.

Step-by-step explanation:

We are asked to find the result of the expression.

We have 3 proper fractions, and they don't have a common denominator.

Meaning, that in order to simply subtract the Numerators, we should have the same Denominator for each.

We can find the Denominator simplify by finding the LCM.

The LCM is the smallest multiple that 2 or more numbers share.

We can easily find the LCM by making a list of numbers that adds the number to itself. The previous explanation is simpler, but what really is happening is we're multiplying the number with a number that grows by 1 each time; A common multiple.

The list should look like;

[tex]4; 4 \times 1 ,\ 4 \times 2, \ 4 \times 3, \ 4 \times 4, \ 4 \times 5, \ 4 \times 6, \ 4 \times 7.\\4; 4, 8, 12, 16, 20, 24, 28.[/tex]

Let's find the LCM of 5, 3, and 15:

[tex]5; 5, 10, [15], 20, 25\\3; 3, 6, 9, 12, [15]\\15; [15], 30, 45, 60, 75[/tex]

These numbers share a LCM of 15.

Multiply the fractions by setting up a proportion:

[tex]\frac{4}{5} -\frac{1}{3} -\frac{1}{15} \\\frac{4 \times 3}{5 \times 3} = \frac{12}{15} \checkmark \\\frac{1 \times 5}{3 \times 5} = \frac{5}{15} \checkmark\\\frac{1}{15} \ stays \frac{1}{15} \checkmark[/tex]

Subtract:

[tex]\frac{12}{15} - \frac{5}{15} - \frac{1}{15} = \frac{6 \div 3}{15 \div 3} = \frac{2}{5} .[/tex]

Your final answer is [tex]\frac{2}{5} .[/tex]

The correct answer is c. 7/15.

To find the result of 4/5 - 1/3 - 1/15, you need to first find a common denominator for all three fractions. The smallest common denominator for these fractions is 15.

Next, you need to convert each fraction to an equivalent fraction with a denominator of 15.

4/5 = 12/15
1/3 = 5/15
1/15 = 1/15

Now you can subtract the numerators of each fraction and keep the common denominator of 15.

12/15 - 5/15 - 1/15 = 6/15 - 1/15 = 5/15

Finally, you can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 5.

5/15 = 1/3

So the result of 4/5 - 1/3 - 1/15 is 7/15, which is answer choice c.

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The simplified form of the radical expressions are:
a) −12x2y6
b) 284x7t4y3

To simplify the following radical expressions, we need to factor the radicand and then use the properties of radicals to simplify.

For a) −72x4y122x8y2, we can factor the radicand as follows:

−72x4y12 = −(2*2*2*3*3)x4y12 = −(2*2*2*3*3)(x4)(y12)

Now we can use the properties of radicals to simplify:

√−(2*2*2*3*3)(x4)(y12) = √−(2*2)(2*2)(3*3)(x4)(y12) = −(2*2*3)(x2)(y6) = −12x2y6

For b) 7z21128x14t8y6, we can factor the radicand as follows:

1128x14t8y6 = (2*2*2*2*71)(x14)(t8)(y6)

Now we can use the properties of radicals to simplify:

√(2*2*2*2*71)(x14)(t8)(y6) = √(2*2)(2*2)(71)(x14)(t8)(y6) = (2*2*71)(x7)(t4)(y3) = 284x7t4y3

So the simplified form of the radical expressions are:

a) −12x2y6
b) 284x7t4y3

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Quinn has 6 dimes and 15 quarters in his pocket.

Let's use a system of two equations to represent the given information:

d + q = 21      (1)   // The number of dimes and quarters adds up to 21

10d + 25q = 435 (2)   // The total value of the coins in cents is 435

where d represents the number of dimes and q represents the number of quarters.

We can use equation (1) to solve for d in terms of q:

d = 21 - q

Substituting this expression for d into equation (2), we get:

10(21 - q) + 25q = 435

210 - 10q + 25q = 435

15q = 225

q = 15

So, Quinn has 15 quarters. Substituting this value into equation (1), we get:

d + 15 = 21

d = 6

So, Quinn has 6 dimes.

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To graph a quadratic function, follow the steps explained to obtain the smooth curve of the quadratic function.

Graphing quadratic functions involves plotting the points on a coordinate plane that satisfy the equation of the function. Quadratic functions are typically written in the form:

f(x) = ax^2 + bx + c

where;

To graph a quadratic function, you can follow these steps:

x = -b / 2a

y = f(x)

You can find the x-coordinate of the vertex by using the formula above, and then substitute it into the function to find the corresponding y-coordinate.

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The value of angle x is 134°.

We have:

Angle ABD = 180° (straight line)

Angle ABE = 44° (given)

Angle BCE = 90° (as BC is perpendicular to AB)

Angle AEC = 180° - Angle BCE - Angle BAE = 180° - 90° - 44° = 46° (angle sum of triangle ABE)

Now, we can use the exterior angle property of triangles to find the value of angle x.

Angle AED = Angle AEC + Angle CED = 46° + x (exterior angle property of triangle CED)

Angle AED = Angle ABD = 180° (opposite angles of a cyclic quadrilateral)

Therefore, we have:

46° + x = 180°

x = 180° - 46°

x = 134°

Hence, the value of angle x is 134°.

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Y = 4114/5114

3 (a) To solve 2557⋅X=457 for X∈Z57 using Euclid's algorithm, take the GCD of 2557 and 457. That is, the GCD is:

GCD(2557, 457) = GCD(2557 - 457, 457)

                  = GCD(2157, 457)

                  = GCD(757, 457)

                  = GCD(357, 457)

                  = GCD(157, 457)

                  = 457


Therefore, the GCD of 2557 and 457 is 457, and thus the solution to the equation is X = 457/2557.

3 (b) To find all solutions to the equation 50114⋅Y=8114 for Y∈Z114, we need to rewrite the equation in terms of ordinary integers, since the inverse of 50114 does not exist. The equation can be rewritten as Y = 8114/50114 = 8114/(5114⋅2114) = 4114/5114. This equation is the same as the one in part (a), with 25 replaced by 5. Thus, the solution to this equation is Y = 4114/5114, which is the same solution found in part (a). Therefore, there is only one solution to this equation, and this solution is Y = 4114/5114.

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Answer:

the answer is 8

Step-by-step explanation:

subtract 11
67 - 11 = 56

Divide 7 to find the answer

56/7 = 8

Answer:

False

Step-by-step explanation:

...............

The function that is increasing at a faster rate, given the graph shown, is D. g ( x ) increases at a faster rate.

You can find which function is increasing faster by looking at the steepness of the line.

When the slope of a line is positive, it means that as we move from left to right along the line, the y-coordinate of a point on the line increases. This indicates that the line is moving upward and becoming steeper. The steeper the line, the larger the magnitude of the slope.

g ( x ) was more steep in the interval [ 0, 1 ] and so was increasing at a faster rate.

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The tangent trigonometry ratio can be used to determine the measure of m∠F using the length shown. Option C is correct

The given figure is a right triangle.

According to the question, we are to determine the trigonometry ratio that can be used to find m∠F.

Given the following sides

Hypotenuse = EF

Opposite to m∠F = DE

Adjacent = DF

Since tan m∠;F = opposite/adjacent = DE/DF

tan m∠F can be used to determine m∠F.

The same goes with tan and sine since we can determine the value of the hypotenuse but only tangent can be used to find the measure given the length shown.

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Based on the sample of the 48 South African households collected from the Census At School survey project, the mean number of people living in a household will be 6.208, and the standard deviation is 2.576.

However, it is important to note that this sample only represents a small fraction of the total number of the households in South Africa, so we cannot make definitive conclusions about the entire population based on this sample alone.

To get a more accurate estimate of the number of people living in the South African households, a larger and the more representative sample would need to be collected.

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