Let the missing exponent be a,
[tex]w^3\times w^a=w^{-6}[/tex]From the law of indices stated below which satisfies the above equation,
[tex]\begin{gathered} x^a\times x^b=x^{a+b} \\ \text{relating the equation to the formula,} \\ w^3\times w^a=w^{-6} \\ w^{3+a}_{}=w^{-6} \\ \text{solving the exponents,} \\ 3+a=-6 \\ \text{Collect like terms} \\ a=-6-3 \\ a=-9 \end{gathered}[/tex]Hence, the missing exponent a is -9.
Which of these is an exponential parent function?  A. f(x) = 2^x – 3  B. f(x) = 2^x + 2  C. f(x) = 2^x  D. f(x) = 2^x + 1/3
An exponential parent function is the option C. f(x)= [tex]2^{x}[/tex], from the given options.
What do you mean by exponential parent function?
The formula for their parent function is y = [tex]b^{x}[/tex], where b is any non zero constant. Below is a graph of the parent function, y = [tex]e^{x}[/tex], which demonstrates that it will never equal 0. And at y = 1 when x = 0, y crosses the y-axis.
According to options in the given question,
We have the option below in the given question:
A. f(x) = 2^x – 3 
B. f(x) = 2^x + 2 
C. f(x) = 2^x 
D. f(x) = 2^x + 1/3
We know from the above definition that the option C. is the right answer to the given question.
Therefore, the exponential parent function is f(x)= [tex]2^{x}[/tex].
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If I have found my slope intercept form and I need to graph the line but my slope and y intercept are fractions do I need to make the denominators the same to graph the line?
The formula for the slope-intercept form of a line is:
[tex]\begin{gathered} y=mx+b \\ m=slope \\ b=intercept \end{gathered}[/tex]If you have found the slope-intercept form and need to graph the line, but your slope and y-intercept are fractions, you do not really need to make the denominators the same. All you need to do is make a table of values on a range of values from which your graph can be plotted.
16) Select the sequence of transformations that will carry triangle A onto triangle A'Atranslate 6 units down, then reflect acrossA)'the y-axis5B) reflect over the y-axis, reflect over the x-axis,then 2 units upC)reflect over the x-axis, translate 2 units up,then 8 units left-5D)reflect over the x-axis, rotate 90° clockwise,then translate 4 units down
C
16) Let's first locate the points that make up the pre-image A, and the image A' picking them from each one of those three vertices.
A
(-3,5)
(-5, 5)
(-5,3)
A'
(5,-1)
(5,-3)
(3,-3)
16.2) Then let's pick just one point and apply the transformations, in this case, let's pick point (-3,5)
Counting on the graph
So if we reflect it over the x-axis, we'll get from (-3,5) to (3,-5) and translating up two units, we'll arrive at (-3,-3) and finally to (5,-3) one of the coordinates of the Image A'
16.3) Hence, the answer is C
Choose a natural number between 1 and 36, inclusive. What is the probability that the number is a multiple of 3 (enter the probability as a fraction.)
List of multiples of 3 in the interval:
3,6,9,12,15,18,21,24,27,30,33,36. (12 numbers)
The probability of choosing a number multiple of 3 is:
Number of multiples of 3 in the interval / Total number of values in the interval
12/36 (Replacing)
1/3 ( Simplifying the fraction)
The answer is 1/3.
8. Jenise throws a ball 75 times and hits the larget 41 times. What is the experimental probability that she will hit the target? State your answer as a percent. The experimental probability that she will hit the target is (Round to the nearest hundredth as needed.)
OK
Number of throws = 75
Number of targets = 41
Probability = number of targets / number of throws
Probability = 41/75 x 100
Probability = 0.54666 x 100
Probability = 54.67 %
f(x)=3x+12 find f(15)
f(15) = 57
Explanation:Given that
f(x) = 3x + 12
To find f(15), perform the following:
Step 1: Replace x by 15 in the given function
f(15) = 3(15) + 12
Step 2: Evaluate the expression
f(15) = 45 + 12
= 57
If y varies directly as x, and y = 6 when x= 3, find y when x = 9.
y =when x= 9.
We know that:
- y varies directly as x
- y = 6 when x= 3
And we must find y when x = 9
To find it:
1. we must use that y varies directly as x
[tex]y=kx[/tex]2. We must find k using that y = 6 when x = 3
[tex]\begin{gathered} 6=k\cdot3 \\ k=\frac{6}{3} \\ \Rightarrow k=2 \end{gathered}[/tex]3. Finally, to find y when x = 9 we must replace x = 9 and k = 2 to solve it for y
[tex]\begin{gathered} y=2\cdot9 \\ y=18 \end{gathered}[/tex]ANSWER:
y = 18 when x = 9
Consider the figure below.MGiven:PM 2PN, LM I MN,MNI ONLN bisects ZMNO, OM bisects LMNAMPL XANPO?Which of the following statements is enough to prove
Since PM=PN
And
[tex]LM\perp MN[/tex]While
[tex]MN\perp ON[/tex]We can assume that
[tex]\begin{gathered} LN=OM\text{ and bisect each other} \\ \text{Therefore,} \\ PM=OP\text{ and }PN=LP \end{gathered}[/tex]Then we can conclude that
[tex]\begin{gathered} LP=PO\text{ ( Isosceles triangle theorem)} \\ \angle\text{MPL}=\angle NPO(\text{ Vertically opposite angles)} \\ \text{hence,} \\ \Delta MPL=\Delta NPO(By\text{ sides angle side)} \end{gathered}[/tex]Therefore,
The correct answer IS OPTION C
A sample has mean 97 and standard deviation 12.Part: 0/2Part 1 of 2(a) What value is 2.5 standard deviations above the mean?The value that is 2.5 standard deviations above the mean is
The value that is 2.5 standard deviations above the mean is 127
A car was valued at $32,000 in the year 1995. The value depreciated to $14,000 by the year 2001.A) What was the annual rate of change between 1995 and 2001?T =Round the rate of decrease to 4 decimal places.B) What is the correct answer to part A written in percentage form?T =%.C) Assume that the car value continues to drop by the same percentage. What will the value be in the year2005 ?value = $Round to the nearest 50 dollars.
Givn:
Value of the car in 1995 = $32,000
Value of the car in 2001 = $14,000
Let's solve for the following:
• (A). What was the annual rate of change between 1995 and 2001?
Apply the exponential decay formula:
[tex]f(t)=a(1-r)^t[/tex]Where:
• t is the number of years between 2001 and 1995 = 2001 - 1995 = 6
,• a is the initial value = $32000
,• r is the rate of decay.
,• f(t) is the present value
Thus, we have
[tex]\begin{gathered} 14000=32000(1-r)^6 \\ \end{gathered}[/tex]Divide both sides by 32000:
[tex]\begin{gathered} \frac{14000}{32000}=\frac{32000(1-r)^6}{32000} \\ \\ 0.4375=(1-r)^6 \end{gathered}[/tex]Take the 6th root of both sides:
[tex]\begin{gathered} \sqrt[6]{0.4375}=\sqrt[6]{(1-r)^6} \\ \\ 0.87129=1-r \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} r=1-0.87129 \\ \\ r=0.1287 \\ \\ r=0.1287*100=12.87\text{ \%} \end{gathered}[/tex]Therefore, the rate of change between 1995 and 2001 is 0.1287
• (B). What is the correct answer to part A written in percentage form?
In percentage form, the rate of change is 12.87 %
• (C),. Assume that the car value continues to drop by the same percentage. What will the value be in the year 2005?
We have the equation which represents this situation below:
[tex]f(t)=32000(1-0.1287)^t[/tex]Here, the value of t will be the number of years between 1995 and 2005.
t = 2005 - 1995 = 10
Now, substitute 10 for t and solve for f(10):
[tex]\begin{gathered} f(10)=32000(1-0.1287)^{10} \\ \\ f(10)=32000(0.8713)^{10} \\ \\ f(10)=32000(0.25216) \\ \\ f(10)=8069.14\approx8100 \end{gathered}[/tex]Therefore, the value in the year 2005 rounded to the nearest 50 dollars is $8100
ANSWER:
• (a). 0.1287
,• (b). 12.87%
,• (c). $8100
Find the area of a regular hexagon with side lengths of 12 in.
Answer:
[tex]216\sqrt{3\text{ }}\text{ in}^2[/tex]Explanation;
Here, we want to get the area of the regular hexagon
Mathematically, we have that as:
[tex]A\text{ = }\frac{3\sqrt{3}}{2}a^2[/tex]where a represents the length of one of the sides which is 12 in
Substituting the value, we have it that:
[tex]\begin{gathered} A\text{ = }\frac{3\sqrt{3}}{2}\times\text{ 12}^2 \\ \\ A\text{ = 216}\sqrt{3\text{ }}\text{ in}^2 \end{gathered}[/tex]Find the slope of the line(Question in photo sorry) (Pre algebra)
Given that
There are two points and we have to find the slope of the line passing through these points.
Explanation -
The given two points are (19/2, -8/3) and (-7/2, -1/15)
The general formula to find the slope through two points is given as
[tex]\begin{gathered} If\text{ points are \lparen x}_1,y_1)\text{ and \lparen y}_1,y_2) \\ Then \\ slope=m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]So on substituting the values we have
[tex]\begin{gathered} Slope=m=\frac{-\frac{1}{15}-(-\frac{8}{3})}{-\frac{7}{2}-\frac{19}{2}}=\frac{-\frac{1}{15}+\frac{8}{3}}{-\frac{7}{2}-\frac{19}{2}} \\ \\ m=\frac{\frac{-1\times1+5\times8}{15}}{\frac{-7-19}{2}}=\frac{\frac{-1+40}{15}}{\frac{-26}{2}}=\frac{\frac{39}{15}}{-\frac{13}{1}} \\ \\ m=\frac{39}{15}\times\frac{-1}{13}=-\frac{3}{15}=-\frac{1}{5} \end{gathered}[/tex]So the required slope passing through the given two points is -1/5.
Final answer -
Therefore the final answer is -1/5.What is the efficiency of a lever if you push 100 N over 5m to move 350 N over 1 m?
The efficiency of a lever is 70%.
From the question, we have
Efficiency = F_out/F_in
=350*1/100*5 = 350/500 = 0.7*100% = 70%
Efficiency:
Efficiency is the proportion of work done by a machine or throughout a process to the overall amount of energy or heat used.
Efficiency is the degree to which a given input may produce a specific outcome with the least amount of waste possible. Efficiency is the capacity to minimize wastage of resources, labor, time, and energy when completing an action or achieving a goal.
The ratio of usable output to total input can be used to objectively measure efficiency. The efficiency of the device is defined as the ratio of energy converted to a useable form to the original amount of energy supplied.
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[tex] \sqrt[3]{80} [/tex]simplify in simplest radical form
Start by decomposing the number inside the root into primes
Then group the terms into cubes if possible
[tex]\begin{gathered} 80=2\cdot2\cdot2\cdot2\cdot5 \\ 80=2^3\cdot2\cdot5 \\ 80=10\cdot2^3 \end{gathered}[/tex]rewrite the root
[tex]\sqrt[3]{80}=\sqrt[3]{10\cdot2^3}[/tex]then cancel the terms that are cubes and bring them out of the root
[tex]\sqrt[3]{80}=2\sqrt[3]{10}[/tex]como se resuelve esto? 3x²+10x=O
3 x^2 + 10 x = 0
x ( 3 x + 10 ) = 0
x = 0 or 3 x+ 10 = 0
x = 0 or 3 x = -10
x = 0 or x = -10/3
tell whether the red line segment is the height or Stan height.
The slant height is the height that can be found using the height of the pyramid and the half length from the center of one of the sides to the center of the pyramid, this would be the hypotenuse.
The red line in this case represents the height of the pyramid.
What is the solution set to this equation?1054(= + 3) + 108.7
ANSWER
[tex]C.\text{ }x=1\text{ and }x=-4[/tex]EXPLANATION
We want to find the solution set to the equation given:
[tex]\log_4(x+3)+\log_4x=1[/tex]According to the laws of logarithm, we have that:
[tex]\begin{gathered} \log_ax+\log_ay=\log_a(x*y) \\ \\ and \\ \\ \log_aa=1 \end{gathered}[/tex]Therefore, we can rewrite the equation as follows:
[tex]\log_4[(x+3)*x]=\log_44[/tex]Since the logarithms on both sides have the same base, it implies that:
[tex](x+3)*x=4[/tex]Simplify and solve for x:
[tex]\begin{gathered} x^2+3x=4 \\ \\ x^2+3x-4=0 \\ \\ x^2+4x-x-4=0 \\ \\ x(x+4)-1(x+4)=0 \\ \\ (x-1)(x+4)=0 \\ \\ x=1\text{ and }x=-4 \end{gathered}[/tex]Hence, the correct answer is option C.
To make 6 cups of ramen, 2/3 cups of noodles is needed. How many cups of ramen can you make with 1 3/4 cups of noodles?
Explanation
The question calls for using the direct proportion concept. This can be seen below.
Let the number of cups of ramen you can make with 1 3/4 cups of noodles be x. Therefore;
[tex]\frac{6}{x}=\frac{\frac{2}{3}}{1\frac{3}{4}}[/tex]We can them crossmultiply
[tex]\begin{gathered} \frac{2}{3}x=\frac{7}{4}\times6 \\ \frac{2}{3}x=21 \\ 2x=63 \\ x=\frac{63}{2} \\ x=31\frac{1}{2} \end{gathered}[/tex]Answer:
[tex]31\frac{1}{2}\text{cups}[/tex]Answer:
31.5
Step-by-step explanation:
Find the equation of the line through (2,-4) and parallel to the line 5x-2y-4=0. Write your answer in general form.
We can find the equation of a line given one point and its slope.
Remember that two parallel lines have the same slope; therefore, the slope of 5x-2y-4=0 is equal to the slope of the line we are trying to find.
[tex]\begin{gathered} 5x-2y-4=0 \\ \Rightarrow2y=5x-4 \\ \Rightarrow y=\frac{5x}{2}-\frac{4}{2}=\frac{5x}{2}-2 \\ \Rightarrow y=\frac{5x}{2}-2 \\ \Rightarrow m=\frac{5}{2} \end{gathered}[/tex]Then, we have got everything we need, the slope is equal to 5/2 and a point in the line is (2,-4)
The equation is:
[tex]\begin{gathered} y-(-4)=\frac{5}{2}(x-2) \\ \Rightarrow y+4=\frac{5}{2}(x-2) \\ \Rightarrow y+4=\frac{5x}{2}-5 \\ \Rightarrow y=\frac{5x}{2}-9 \\ \Rightarrow y+9=\frac{5}{2}x \\ \Rightarrow2y+18=5x \\ \Rightarrow5x-2y-18=0 \end{gathered}[/tex]The answer is 5x-2y-18=0
I need to find the value of x. can you help me?
The angle on a line is 180°
The sum of the three given angles is 180°:
[tex](6x-10)+(x-5)+(x-5)=180[/tex]Use this equation to find the value of x:
[tex]\begin{gathered} 6x-10+x-5+x-5=180 \\ 8x-20=180 \\ 8x=180+20 \\ 8x=200 \\ x=\frac{200}{8} \\ \\ x=25 \end{gathered}[/tex]Then, the value of x is 25Create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answers to four decimal places. If an answer does not exist, enter DNE.)
Answer:
Explanations:
Given the limit of the function expressed as:
[tex]\begin{gathered} \lim _{n\to0}\frac{\sin8x}{x} \\ f(x)=\frac{\sin 8x}{x} \end{gathered}[/tex]First, we need to create a table for the given values in the table:
If x = -0.1
[tex]\begin{gathered} f(-0.1)=\frac{\sin8(-0.1)}{-0.1} \\ f(-0.1)=\frac{\sin(-0.8)}{-0.1} \\ f(-0.1)=0.1396 \end{gathered}[/tex]If x = -0.01
[tex]\begin{gathered} f(-0.01)=\frac{\sin8(-0.01)}{-0.01} \\ f(-0.01)=\frac{\sin(-0.08)}{-0.01} \\ f(-0.01)=0.1396 \end{gathered}[/tex]If x = -0.001
[tex]\begin{gathered} f(-0.001)=\frac{\sin8(-0.001)}{-0.001} \\ f(-0.001)=\frac{\sin(-0.008)}{-0.008} \\ f(-0.001)=0.1396 \end{gathered}[/tex]From the values above, we can conclude that the values of f(x) will all tend to be 0.1396 for the positives values of x
Therefore, we can conclude that as you approach the value 0 from the positive and negative directions, they approach the same value, hence the limit does exist.
A cell phones was purchased for $400 and depreciates at a rate of 17% per year. How much is the cell phone worth after 4 years? Round to the nearest cent .
1) Gathering the data
Cell phone
$400
Depreciates at -17% yearly
Period: 4 yrs
2) Let's write an exponential function to calculate that depreciation:
y = The brand new price x (depreciation rate)^time
17%= 0.17
[tex]\begin{gathered} y=400(1-0.17)^4 \\ y=400(0.83)^4 \\ y=189.83 \end{gathered}[/tex]3) So 4 years from the data of the purchase, the cell phone worths $189.83
If the radius of the circle is 6cm, what is the length of arc BC? Round to the neare:thousandth (3 decimal places) and use the pi button on the calculator.
Given that:
Radius of the circle = 6 cm
Central angle of the arc = 120 degrees
The formula to find the arc length of a circle of radius is
[tex]Arc\text{ length=}\frac{\theta}{360^{\circ}}\cdot2\pi r[/tex]Substitute the given values into the formula.
[tex]\begin{gathered} Arc\text{ length=}\frac{120^{\circ}}{360^{\circ}}\cdot2\pi\cdot6 \\ =12.566\text{ cm} \end{gathered}[/tex]Write the given fraction in simplest form 25/27
Notice that:
[tex]\begin{gathered} 25=5\cdot5, \\ 27=3\cdot3\cdot3. \end{gathered}[/tex]Then 25 and 27 have no common factors.
Since the denominator and the numerator have no common factors, then the given fraction is in its simplest form.
Answer: 25/27.
[tex]\frac{25}{27}\text{.}[/tex]Which shows another way to write 6*3? A.3 + 3 + 3 + 3 + 3 + 3 B.3 × 3 × 3 × 3 × 3 × 3 C.6 × 6 × 6 D.6 + 6 + 6
Another way to write the given expression 6×3 is by use of addition operator 6+6+6 .
We know that multiplying a number by another number is another way of adding the number that many times.
If we multiply a with n it can be written as
a × n = a + a + a + a +.... n terms
Similarly we can use the same formula for 6×3.
6×3 = 6+6+6
Addition can be defined and carried out using abstractions known as numbers, such as integers, real numbers, and complex numbers, in addition to counting things.
Addition is a part of the arithmetic branch of mathematics. In algebra, a different area of mathematics, addition can also be performed on abstract objects like vectors, matrices, subspaces, and subgroups.
The words, addends, or summands collectively refer to the quantities or components that must be combined to make a whole number; this terminology also includes the summing of multiple terms. This needs to be differentiated from multiple factors.
Hence the given expression can be written as 6+6+6 .
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Find the slope of the lines between two points (4,8);(-1,8)
We want to find the slope, the slope formula is;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Inserting the values, (4,8), (-1,8), we have;
[tex]m=\frac{8-8}{-1-4}=\frac{0}{-5}=0[/tex]Thus, the slope is zero
Part A in. (a) For the following figure, the value of x is 45° 8 in. 459 B 45
Answer
The value of x = 8 in.
y = 8√2 = 11.31 in.
For the second question,
x = 8.3 units
Explanation
Isoscelles triangles have two of their sides being of the same lengths and those two sides are the ones whose base angles are the same.
From the image, we can see that two angles of the triangle have the same measures, hence, we can easily conclude that
x = 8 inches.
To find y, we will use pythagoras theorem.
The Pythagorean Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For this triangle,
hyp = y
a = 8 in
b = x = 8 in
a² + b² = (hyp)²
8² + 8² = y²
64 + 64 = y²
y² = 128
Take the square roots of both sides
√(y²) = √128
y = 8√2 = 11.31 in
For the other question.
In a right angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
For that triangle,
Hyp = 11 units
Opp = ?
Adj = x
θ = 41°
We can then use trignometrical identities to solve this
CAH allows us to say
Cos 41° = (Adj/Hyp)
Cos 41° = (x/11)
x = 11 Cos 41°
x = 11 (0.7547)
x = 8.3 units
Hope this Helps!!!
Anetha wants to eam at least $90 per month. She babysits for $8 per hour (x) and cleans houses for $5 per hour (y). She cannot work more than 15 hours per month. Which pairs (x,y) represent hours that Anetha could work to meet the given conditions?
ANSWER
(6, 9) and (7, 8)
EXPLANATION
We have that x represents the number of hours she spends babysitting and y represents the number of hours she spends cleaning houses.
She cannot work for more than 15 hours per week. This means that:
[tex]x\text{ + y }\leq\text{ 15 \_\_\_\_\_\_\_\_(1)}[/tex]She wants to earn at least $90 per month. This means that:
[tex]8(x)\text{ + 5(y) }\ge\text{ 90 \_\_\_\_\_\_\_\_\_\_(2)}[/tex]We can solve this by plotting the graphs of the inequalities. We have:
The solution of the inequalities is the region that the two shaded regions intersect.
Due to the fact that we are considering number of hours (x and y), we will only concern ourselves with the positive portion of the graph.
So, the pairs (x, y) that can represent the number of hours that Anetha can work are the pairs that fall in the positive x and y axis of the shaded part of the graph.
They are:
(6, 9) and (7, 8)
What is the area of a circle with a circumference of 31.4Area-
The circumference of a circle is give by:
[tex]C=2\pi r[/tex]Plugging the value we have for the circunference we can find the radius:
[tex]\begin{gathered} 31.4=2\pi r \\ r=\frac{31.4}{2\pi} \\ r=\frac{15.7}{\pi} \end{gathered}[/tex]Now that we have the radius we remember that the area of a circle is:
[tex]A=\pi r^2[/tex]Plugging the value of r we have that:
[tex]A=\pi(\frac{15.7}{\pi})^2=78.46[/tex]Therefore the area of the circle is 78.46
Plot the value of 8 x 1/2 on the number line shown.
Step 1: Firstly, simplify the expression
[tex]\begin{gathered} 8\text{ }\times\text{ }\frac{1}{2} \\ =\text{ }\frac{8\text{ x 1}}{2} \\ =\text{ }\frac{8}{2} \\ =\text{ 4} \end{gathered}[/tex]Step 2: The value may be less than or greater than 4.
Positive numbers are plotted to the right of the origin while negative numbers are plotted to the left of the origin.
Step 3: Plot the number line