12 x (-2/3) =

A. 1/8
B. -8
C. 8
D. -1/8

Answer:

(First answer option)

Step-by-step explanation:

General form of an exponential function

\(y=ab^x+c\)

where:

Given exponential function:

\(y=4(10)^x-3\)

The x-intercept is the point at which the curve crosses the x-axis, so when y = 0.  To find the x-intercept, substitute y = 0 into the given equation and solve for x:

\(\begin{aligned}& \textsf{Set the function to zero}:& 4(10)^x-3 &=0\\\\& \textsf{Add 3 to both sides}:& 4(10)^x &=3\\\\& \textsf{Divide both sides by 4}:& 10^x &=\dfrac{3}{4}\\\\& \textsf{Take natural logs of both sides}:& \ln 10^x &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Apply the power log law}:&x \ln 10 &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Divide both sides by }\ln 10:&x&=\dfrac{\ln\left(\dfrac{3}{4}\right)}{\ln 10} \\\\& \textsf{Simplify}:&x&=-0.1\:\:\sf(1\:d.p.)\end{aligned}\)

Therefore, the x-intercept is (-0.1, 0) to the nearest tenth.

An asymptote is a line that the curve gets infinitely close to, but never touches.

The parent function of an exponential function is:

\(f(x)=b^x\)

As x approaches -∞ the function f(x) approaches zero, and as x approaches ∞ the function f(x) approaches ∞.

Therefore, there is a horizontal asymptote at y = 0.

This means that a function in the form  \(f(x) = ab^x+c\) always has a horizontal asymptote at y = c.  

Therefore, the horizontal asymptote of the given function is y = -3.

A graph representing exponential growth will have a curve that shows an increase in y as x increases.

A graph representing exponential decay will have a curve that shows a decrease in y as x increases.

The part of an exponential function that shows the growth/decay factor is the base (b).  

The base of the given function is 10 and so this confirms that the function is increasing since 10 > 1.

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Answer:

c took me a wiel but then realized it was just butterfly method to solve.

Step-by-step explanation:

The equation of the perpendicular bisector of the line segment with endpoints (-7, 2) and (-1, -6) is y = (3/4)x + 1.

To find the equation of the perpendicular bisector of a line segment, we need to determine the midpoint of the line segment and the slope of the line segment. The perpendicular bisector will have a negative reciprocal slope compared to the line segment and will pass through the midpoint.

Given the endpoints (-7, 2) and (-1, -6), we can find the midpoint using the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Midpoint = ((-7 + (-1))/2, (2 + (-6))/2)

= (-8/2, -4/2)

= (-4, -2)

The midpoint of the line segment is (-4, -2).

Next, we need to find the slope of the line segment using the slope formula:

Slope = (y2 - y1)/(x2 - x1)

Slope = (-6 - 2)/(-1 - (-7))

= (-6 - 2)/(-1 + 7)

= (-8)/(6)

= -4/3

The slope of the line segment is -4/3.

Since the perpendicular bisector has a negative reciprocal slope, the slope of the perpendicular bisector will be 3/4.

Now, we can use the midpoint (-4, -2) and the slope 3/4 in the point-slope form of a line to find the equation of the perpendicular bisector:

y - y1 = m(x - x1)

y - (-2) = (3/4)(x - (-4))

y + 2 = (3/4)(x + 4)

y + 2 = (3/4)x + 3

y = (3/4)x + 1.

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Answer:

3r

Step-by-step explanation:

there is an invisible 1 in front of the rs. Add them and you get 3r

Answer:

3r

Step-by-step explanation:

Let's replace r with a number.

For example,

r=3

3+3+3=9

We know also that 9=3 multiplied by 3. Therefore, r+r+r=3r

Answer:

x=3

Step-by-step explanation:

x-5+11=x

2x=-5+11

2x=6

x=3

For the given composite figure, the area of the shaded portion is 132 sq. yards.

What is a composite figure?

Composite geometric figures are made from two or more geometric figures. Finding the area of a composite shape can be done using one of two broad approaches.

This is a composite figure.

There is a trapezium inside which a triangle is present.

The separated figures are shown below.

Trapezium

Area of rectangle = 22 * 11 = 242

Area of triangle = 0.5 * 22 * 2  =22

Area of trapezium =242 + 22 = 264 sq. yards

Triangle

base = 22 yards

height = 12 yards

Area = 0.5 * 22 * 12 = 132 sq. yards

Area of shaded portion = area of trapezium - area of triangle = 264-132

                                                                           = 132 sq. yards

Therefore for the given composite figure, the area of the shaded portion is 132 sq. yards.

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Answer:

\(200 cm^2\)

Step-by-step explanation:

A = (1/2)bh

A = (1/2)(18)(30)

A = 270 square cm

A = (1/2)(16)(25)

A = 200 square cm

Answer:

200 square centimeters

Step-by-step explanation:

The area of a triangle can be calculated using the formula: \(A = \frac{1}{2}bh\) where b is the base and h is the height. So if the base is 16 cm and the height if 25 cm you simply plug the values into the equation to find the area

Plug Values In:

\(A = \frac{1}{2}(16 cm)(25 cm)\)

Multiply 16 cm and 25 cm:

\(A = \frac{1}{2}(400 cm^2)\)

Multiply by 0.5 (or technically divide by 2)

\(A = 200 cm^2\)

The value of function g(x + 2) is the one in option B.

g(x + 2) = 3x + 10

Here we know that the function g(x) is:

g(x) = 3x + 4

We want to find the value of g(x + 2), so we just need to change the argument, here we will get:

g(x + 2) = 3*(x + 2) + 4

Expanding the product:

g(x + 2) = 3x + 3*2 + 4

            = 3x + 10

The correct option is B.

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Answer: D- 20 to 60

I know this because the others are all equivalent to 1 to 2 but 20 to 60 simplified is 1 to 3

Answer:

13

Step-by-step explanation:

Explained on the last one

Answer:

she needs to buy 4 boxes since she can't buy a part of a box. assuming total boxes means completely filled boxes, then she fills 3

Step-by-step explanation:

The solution to the equation 3 / 5x-2 = 2 / 3x-1 is x = 1.

Given the equation in the question;

3 / 5x-2 = 2 / 3x-1

To solve for x, cross multiply the equation

3 / 5x-2 = 2 / 3x-1

3( 3x - 1 ) = 2( 5x - 2 )

Apply distributive property

3( 3x - 1 ) = 2( 5x - 2 )

3×3x + 3×-1 = 2×5x + 2×-2

9x - 3 = 10x - 4

Subtract 10x from both sides

9x - 10x - 3 = 10x - 10x - 4

9x - 10x - 3 = - 4

Add 3 to both sides

9x - 10x - 3 + 3 = - 4 + 3

9x - 10x  = - 4 + 3

-x = -1

Divide both sides by -1

-x/-1 = -1/-1

x = 1

Therefore, the value of x is 1.

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Answer: The probability that both events A and B will occur is 5/18 or 0.28.

Step-by-step explanation:

To determine the probability that both events A and B will occur, we need to calculate the probabilities of each event separately and then multiply them together.

Event A: The probability of rolling a 5 or 6 on the first die is 2 out of 6 (since there are two favorable outcomes out of six possible outcomes on a fair six-sided die). Therefore, the probability of event A is 2/6 or 1/3.

Event B: The probability of not rolling a 1 on the second die is 5 out of 6 (since there are five favorable outcomes out of six possible outcomes). Therefore, the probability of event B is 5/6.

To find the probability that both events A and B occur, we multiply the probabilities:

Probability(A and B) = Probability(A) * Probability(B) = (1/3) * (5/6) = 5/18.

Check the picture below.

Step-by-step explanation:

the answer is (c)

because 0 is 3 in number,

1 is 4 in number,

2 is 3in number

3 is 2 in number,

4 is 2 in number,

no 5,6,7

8 is 1 in number

and no 9

The dot plot ( C )is solved and each dot represents one student's response

A dot plot, also known as a dot chart or dot graph, is a type of data visualization that displays the frequency of values in a dataset. It is a simple graphing technique that uses dots to represent data points on a horizontal or vertical axis.

Each data point in the dataset is represented by a dot placed above the corresponding value on the axis. If there are multiple data points with the same value, the dots are stacked vertically above that value. The resulting plot shows the distribution of data points along the axis, with the height of the stack of dots representing the frequency of each value.

Given data ,

Let the data of the number of pets owned by student be represented as A

Now , the value of A = { 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8 }

The frequency of 0 = 3

The frequency of 1 = 4

The frequency of 2 = 3

The frequency of 3 = 2

The frequency of 4 = 2

The frequency of 8 = 1

In this dot plot, each dot represents one student's response. The number on the left indicates how many pets the students reported owning, and the dots are arranged vertically above that number.

For example, three students reported owning 2 pets, so there are three dots arranged above the number 2. This type of plot is useful for displaying the frequency of different values in a dataset.

Hence , the dot plot is solved

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Yes, there is statistical evidence that the drug is effective in reducing infarct size because p-value is less than the significance value.

Let us first define the hypotheses;

Null Hypothesis; H₀: µ = 25

Alternative Hypothesis; H₁: µ < 25

Standard Deviation; σ = 10

Sample mean; x' = 16

Sample size; n = 8

z-score is;

z = (16 - 25)/(10/√8)

z = -2.55

From online z-score table, the p-value is 0.005

Since p-value is less than the significance value, then we reject the null hypothesis and conclude that the drug is effective in reducing infarct size.

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Answer:   \(\bold{y=3sin\bigg(\dfrac{\pi}{2}x-\dfrac{\pi}{2}\bigg)-7}\)

Step-by-step explanation:

Minimum: (0, -10)

Maximum: (2, -4)

y = A sin (Bx - C) + D

\(A=\dfrac{-4-(-10)}{2}\quad =\dfrac{-4+10}{2}\quad =\dfrac{6}{2}\quad =\large\boxed{3}\)

\(\text{x-value of Max minus x-value of Min}= \dfrac{1}{2}\text{Period}\\\\2 - 0 = \dfrac{1}{2}P\quad \rightarrow \quad P=4\\\\\\B=\dfrac{2\pi}{P}\quad =\dfrac{2\pi}{4}\quad =\large\boxed{\dfrac{\pi}{2}}\\\)

\(D = \dfrac{\text{Max + Min}}{2}\quad = \dfrac{-4+(-10)}{2}\quad =\dfrac{-14}{2}\quad =\large\boxed{-7}\)

Sin usually starts at (0, 0).  For this graph, the midline touches 0 when x = 1 so the Phase Shift = 1.

\(C = B \times \text{Phase Shift}\quad = \dfrac{\pi}{2}\times 1\quad =\large\boxed{\dfrac{\pi}{2}}\)

\(A=3, \quad B=\dfrac{\pi}{2}, \quad C=\dfrac{\pi}{2},\quad D=-7\\\\\rightarrow \quad \large\boxed{y=3\sin \bigg(\dfrac{\pi}{2}x-\dfrac{\pi}{2}\bigg)-7}\)

Answer: (-1) x 2² x 3

Happy to help:)

The Volume of the solid formed by the curves y = 4x³ , y = 4x, x ≥ 0 ; about the x axis is 64π/21  .

In the question ,

it is given that ,

the given curves are y = 4x³ , y = 4x, x ≥ 0 ,

we have to find the volume about x axis ,

the region formed by the given curves about x axis is shown below in the figure .

So , the Volume of the required region is

V = \(\int\limits^1_0 {\pi [(4x)^{2} - (4x^{3} )^{2} }] \, dx\)

On simplification ,

we get ,

V = \(\pi \int\limits^1_0 { [16x^{2} - 16x^{6} }] \, dx\)

V = π[ x³/3 - x⁷/7 ]¹₀

= 16π( 1/3 - 1/7 - 0 - 0)

= 16π((7 - 3)/21)

= 64π/21

Therefore , the required Volume is 64π/21   .

The given question is incomplete , the complete question is

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 4x³ , y = 4x, x ≥ 0 ; about the x-axis  .

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Answer:

1.74

Step-by-step explanation:

0.58*(12/4) = 0.58*3 = 1.74

Answer:

1.74

Step-by-step explanation:

Multiply 0.58 times 3 to get your answer.

The expression L(x)/M(x) is (14 - 3/x)/2. To find the expression L(x)/M(x), we need to first determine the function L(x).

Given M(x) = 2x and N(x) = 7x^2 - 3x + 1, we can proceed with the following steps:

Express L(x) in terms of x. Let L(x) = ax + b, where a and b are constants.

Substitute M(x) and N(x) into the expression L(x)/M(x):

L(x)/M(x) = (ax + b)/(2x)

Multiply both the numerator and denominator by 1/x to eliminate the denominator:

L(x)/M(x) = (ax + b)/(2x) * (1/x) = (a + b/x)/2

Since L(x)/M(x) = (a + b/x)/2, we need to determine the values of a and b. To find them, we can equate N(x) with L(x)/M(x) and solve for a and b.

7x^2 - 3x + 1 = (a + b/x)/2

By comparing the coefficients of like terms, we have:

a = 14

b = -3

Substituting the values of a and b into L(x)/M(x), we obtain the final expression:

L(x)/M(x) = (14 - 3/x)/2.

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Answer:

x = 65

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the angles and equate to 360

x + 95 + 118 + 82 = 360

x + 295 = 360 ( subtract 295 from both sides )

x = 65

Answer:

7/30

Step-by-step explanation:

The difference means subtracting so 14/15 - 7/10 = 7/30 or decimal form is 0.23

Answer:

24

Step-by-step explanation:

That would be:

(3/8)(30)

---------------

(15/16)(1/2)

This can be reduced in various ways.  First, divide that 30 by 15, obtaining:

   6/8

-----------

   1/32

Now invert the divisor (1/32) and multiply:

(6/8)(32/1)

This reduces to 6*4, or 24.

Answer:

\(y=x^2+6x-16\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)

Given points on the curve:

The x-intercepts of a quadratic function are the points at which the line crosses the x-axis, so when y = 0.  

Therefore, the x-intercepts of the given function are -8 and 2.  

Substitute these into the intercept formula:

\(\implies y=a(x-(-8))(x-2)\)

\(\implies y=a(x+8)(x-2)\)

Substitute the other given point (-6, -16) into the equation and solve for a:

\(\begin{aligned} y&=a(x+8)(x-2)\\\textsf{When }(-6,-16)\implies -16&=a(-6+8)(-6-2)\\-16&=a(2)(-8)\\-16&=-16a\\\implies a&=1\end{aligned}\)

Therefore, the equation of the function in intercept form is:

\(y=(x+8)(x-2)\)

Expand to standard form:

\(\implies y=x(x-2)+8(x-2)\)

\(\implies y=x^2-2x+8x-16\)

\(\implies y=x^2+6x-16\)

Therefore, the quadratic function in standard form is:

\(\boxed{ y=x^2+6x-16}\)

Step-by-step explanation:

p+4<-24

collect like terms

p<-28

\(\\ \rm\Rrightarrow p+4<-24\)

\(\\ \rm\Rrightarrow p<-24-4\)

\(\\ \rm\Rrightarrow p<-28\)

So

\(\\ \rm\Rrightarrow p\in (-\infty,-28)\)

The order of reasons that best justifies each step of the equation's solution is as follows;

It follows from the task content that the reasons which best justify each step of the solution be identified.

Therefore; Given the equation; -2(x - 5) = 4x; we have;

Ultimately, the reasons which best justifies each of the steps as required are as provided above.

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Answer:  Justification for each step is provided below.

Step-by-step explanation:

Original Equation: -2(x - 5) = 4x

-2x + 10 = 4x  -->  Distributive property - simplify the left side

-2x + 10 + 2x = 4x + 2x  -->  Addition property of Equality - add 2x to both sides

10 = 6x  -->  Simplifying

10/6 = 6x/6   -->   Division Property of Equality - divide each side by 6

5/3 = x   -->  Simplifying

The range of the given equation is [-1, infinity).

We are given that;

Equation  y= underroot(x+5​)

Now,

The domain of this equation is the set of x values that make the expression under the square root non-negative.

That is, x+5 >= 0, or x >= -5. So the domain is [-5, infinity).

The range of this equation is the set of y values that are obtained by plugging in the domain values into the equation. Since the square root function is always non-negative, and we are subtracting 1 from it, the smallest possible value of y is -1, when x = -5. As x increases, y also increases, and there is no upper bound for y.

Therefore, by the range the answer will be [-1, infinity).

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