The expression in the lowest term will be 3^-1x³.
What is a expression?It should be noted that an expression simply has to do with the relationship that can be illustrated having a mathematical operator.
It should be noted that based on the information given, this will be illustrated as:
= 1/3(x³)
This can be illustrated as:
1/3 = 3^-1 multiplied by x³.
= 3^-1x³
This shows the concept of exponents.
Learn more about expressions on;
brainly.com/question/7234
#SPJ1
How can I divide these5/614/3
Let's divide 5/6, we just place each part as an extended division
When the dividend is less than the divisor, we have a decimal point
What is the exact value of [tex] { \cos}^{ - 1} \frac{ \sqrt{2} }{2} [/tex]when0° < A < 360°Choices- A. 135°B. 225°C. 315°D. 45°
Assuming that the question is as follows:
[tex]\arccos (\frac{\sqrt[]{2}}{2})=\cos ^{-1}_{}(\frac{\sqrt[]{2}}{2}),0The question is asking for the function arccos (or inverse cosine) of the value, that is the angle, theta, that gives us a cosine(theta) = (sqrt(2)/2). Then, we have that this value is, in degrees, as follows:If we represented this angle as a right triangle (in fact, a right-angled isosceles triangle) with sides (legs) equal to one, then, we have that (for this case, the triangle has two angles that equal 45 degrees):
[tex]\cos (\theta)=\cos (45)=\frac{adj}{hyp}=\frac{1}{\sqrt[]{2}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}}=\frac{\sqrt[]{2}}{\sqrt[]{2^2}}=\frac{\sqrt[]{2}}{2}\Rightarrow cos(45)=\frac{\sqrt[]{2}}{2}[/tex]We need to multiply both, the numerator and the denominator by the square root of 2 to have no irrational number in the denominator.
Therefore, the value of the inverse cosine of sqrt(2)/2 is the angle 45 (the correct answer is option D).
Graph a line that is perpendicular to the given line. Determine the slope of the given line and the one you graphed in simplest form
Let's first identify at least two points that pass through the given line.
Let's use the following points:
Point A: x1, y1 = 0, -7
Point B: x2, y2 = 6, 2
a.) Let's determine the slope of the original line:
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{ = }\frac{2\text{ - (-7)}}{6\text{ - 0}}\text{ = }\frac{2\text{ + 7}}{6}[/tex][tex]\text{ m = }\frac{9}{6}\text{ = }\frac{\frac{9}{3}}{\frac{6}{3}}\text{ = }\frac{3}{2}[/tex]Therefore, the slope of the given line is 3/2.
b.) Let's determine the slope of the line perpendicular to the given line:
[tex]\text{ m}_{\perp}\text{ = -}\frac{1}{\text{ m}}\text{ }[/tex][tex]\text{ = -}\frac{1}{\frac{3}{2}}\text{ = -1 x }\frac{2}{3}[/tex][tex]\text{ m}_{\perp}\text{ = -}\frac{2}{3}[/tex]Therefore, the slope of the line perpendicular to the given line is -2/3.
c.) Let's plot the graph of the perpendicular line.
Let's first determine the equation of the given line.
m = 3/2
x,y = 0, -7
y = mx + b
-7 = (3/2)(0) + b
-7 = b
y = mx + b
y = 3/2x - 7
Let's determine the equation of the perpendicular line.
m = -2/3
x,y = 0, -7 ; let's use this as the point of intersection.
y = mx + b
-7 = -2/3(0) + b
-7 = b
y = mx + b
y = -2/3x - 7
Let's now plot the graph.
The two options I selected was incorrect, what would the answer be?
The question gives us the following function:
[tex]f(x)=\frac{3x}{x-2}[/tex]The X-intercept is where the function crosses the x-axis and the Y-intercept is where the function crosses the y-axis.
X-intercept:
Since the graph must cross the x-axis to have an x-intercept, we should equate f(x) to zero.
[tex]\begin{gathered} f(x)=\frac{3x}{x-2}=0 \\ \\ 3x=0 \\ \therefore x=0\text{ is the x-intercept} \end{gathered}[/tex]Y-intercept:
Since the graph must cross the y-axis to have a y-intercept, we should equate x = 0.
[tex]\begin{gathered} f(x)=\frac{3x}{x-2} \\ \\ f(0)=\frac{3(0)}{0-2} \\ \\ f(0)=0\text{ is a y-intercept} \end{gathered}[/tex]Answer
Thus, the x and y-intercepts are: x = 0 and y = 0 respectively
1/3 * 4/5 is <, >, or =,4/5
Answer:
4/15 ___ 4/5 {nothing further can be done}.
Step-by-step explanation:
1/3 * 4/5 = 4/15
4/15 = 0.26
4/15 ≠ 4/5
Thus, nothing further can be done
Evaluate the expression when y=30 and z=6 .y + z^2/y - 4z
The answer is 11.
A 70-meter vertical tower is braced with a cable secured at the top of the tower and tied 30 meters from the base. What angle does the cable form with the ground? round measure of the angle to the nearest degree
Given: The statement in the question
To Determine: The angle the cable form with the ground
Solution
The statement can be represented using the diagram below
Using trigonometry ratio
[tex]\begin{gathered} tan\theta=\frac{70m}{30m} \\ tan\theta=2.333 \\ \theta=tan^{-1}(2.333) \\ \theta=66.8^0 \\ \theta\approx67^0 \end{gathered}[/tex]Hence, the angle the cable makes with the ground approximately to the nearest degree is 67⁰
what is the remainder when 1234 is divided by 34
Answer:
10
Step-by-step explanation:
1234 / 34 = 1224
1234 - 1224 = 10
The remainder = 10
A bag of chips costs $2.42. Your total grocery bill, b, is a function of the number of bags of chips, n, you purchase. Write an equation to represent this function,
Answer:
[tex]b(n)=2.42n[/tex]Explanation:
We are told that the grocery bill b is a function of n (the number of bags of chips). This means that the grocery bill can be represented as b(n).
Furthermore, we know that each bag of chips costs 2.42, meaning n bags of chips will cost 2.42n - which is the grocery bill b(n); therefore,
[tex]b(n)=2.42n[/tex]which is the equation the gives the grocery bill (as a function of n, the number of chips bags bought).
Really need help on this
Simplify the expression -3 devided by (-2/5)
Answer:-7 1/2
Step-by-step explanation:-3 divided by -2/5. -3÷-2/5. -3×-5/2. 15/2=7.5.
15. Higher Order Thinking Jane bought three sheets
of poster board and a pack of markers. Denise
bought two packs of construction paper and a
tube of glue. Who spent more? How much more?
16. If Jane buys two more sheets of poster board, how
much does she spend all together?
DATA
Poster board
Markers
Tape
Glue
8.90
Craft Supplies
Construction paper
17.MP.2 Reasoning Julene has $25 to make posters. She buys
two packs of markers, one pack of construction paper, two tubes
of glue, and a roll of tape. How many sheets of poster board can
she buy with the money she has left? Explain your answer.
:
$1.29/sheet
$4.50/pack
$1.99/roll
$2.39/tube
$3.79/pack
Answer: Denise spent more than Jane.
Step-by-step explanation: Denise spent $9.97. We know now that Denise spent more than Jane. For the second part of the question how much more? We basically just subtract the two values. $9.97-$8.37 which is $1.60. There you go.
Alocal aquarium found that if the price of admission was $10, the attendance was about 1000 customers per week. When the price of admission was dropped to $6,attendance increased to about 2950 per week. Write a linear equation for the attendance in terms of the price,p. (A = mp+b)
Given:
$10 price = 1000 customers per week.
$6 price = 2950 customers per week.
Let's write a linear equation for the attendance in terms of the price, p.
Apply the slope-intercept form:
y = mx + b
In this case, let's use the form:
A = mp + b
Where m is the average rate of change(slope) and b is the y-intercept.
To find the slope, m, apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where:
(x1, y1) ==> (10, 1000)
(x2, y2) ==> (6, 2950)
Hence, we have:
[tex]m=\frac{2950-1000}{6-10}=\frac{1950}{-4}=-487.5[/tex]The average rate of change is -$487.5
To find the y-intercept, b, substitute either of the points for A and p, substitute -487.5 for x then evaluate.
Let's take the first point: (10, 1000)
A = mp + b
1000 = -487.5(10) + b
1000 = -4875 + b
Add 4875 to both sides:
1000 + 4875 = -4875 + 4875 + b
5875 = b
b = 5875
Therefore, the lineart equation for the attendance in terms of the price, p is:
A = -487.5p + 5875
ANSWER:
[tex]A=-487.5p+5875[/tex]The height of a windmill blade above the ground (in feet) is given by the function ff where f(k)=14sin(1.1k)+24. Match the following expressions with the appropriate quantity.expressions-sin(1.1k)-1.1-24-14sin(1.1k)-k-1.1k- 14sin(1.1k)+24quantitiesspeed of the blade (in feet per second)height of the blade above ground (in radii)speed of the blade (in radians per second)height of the horizontal diameter of the fan above the ground (in radii)height of the blade above the horizontal diameter of the fan (in feet)angle measure rotated from the 3 o'clock position (in radians)height of the blade above the horizontal diameter of the fan (in radii)height of the horizontal diameter of the fan above the ground (in feet)height of the blade above ground (in feet)number of seconds elapsed since windmill started rotating
f (k ) =14 sin ( 1.1 k) + 24
The expressions with the appropriate quantity is f ( k) = - 14sin(1.1k
What’s 10 17/20 simplified
[tex] = 10 \frac{17}{20} \\ = \frac{20 \times 10 + 17}{20} \\ = \frac{217}{20} [/tex]
ATTACHED IS THE SOLUTION
9. A rectangle is inscribed in a circle.
a. Calculate the area of the circle.
b. Calculate the area of the rectangle.
c. Calculate the area of the shaded region.
Answer:
a. 227 in.
b. 120 in.
c. 107 in.
Step-by-step explanation:
a. diameter is the radius 2x. divide 17 by 2 to get the radius which is 8.5 plug it in to the formula A=π(8.5)2 to get 226.98 rounded to 227
b. formula: length x width. length is 15 width is 8. 15x8 = 120
c. subtract the area of the circle & the area of the rectangle to get 107.
Can you help me understand how to do this please?
1/8
Explanation:The given expression is:
[tex]-\frac{1}{4}+\frac{3}{8}[/tex]Find the Least Common multiple(LCM) of the denominators
LCM of 4 and 8 = 8
After simplification, the addition expression then becomes:
[tex]\begin{gathered} \frac{-2(1)+1(3)}{8} \\ =\frac{-2+3}{8} \\ =\frac{1}{8} \end{gathered}[/tex]You have a jar of marbles in front of you 2 are green, 9 are yellow, 3 are white and 7 are red. What is e probability, as a decimal, of selecting a marble that is white or yellow, followed by a marble that is green?
Sample space = 21
Pr(White or Yellow) = Pr(White) + Pr(Yellow)
Pr(White) = 3/21 = 1/7
Pr(Yellow) = 9/21 = 3/7
Therefore,
Pr(White or Yellow)= 1/7 + 3/7 = 4/7
A. The graph of g(x) is the graph of f(x) compressed vertically.B. The graph of g(x) is the graph of f(x) compressed vertically andreflected over the x-axis.C. The graph of g(x) is the graph of f(x) stretched vertically.D. The graph of g(x) is the graph of f(x) stretched vertically andreflected over the x-axis.
The Solution:
Given:
Required:
to determine the best statement that compares the graph of g(x) with that of f(x).
Below is the graph of the given functions:
Thus, the graph of g(x) is the graph of f(x) compressed vertically and
reflected over the x-axis.
Answer:
[option B]
Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below.Which statements about the function are true? Select three options. Select three options.The vertex of the function is at (–4,–15). The vertex of the function is at (–3,–16). The graph is increasing on the interval x > –3. The graph is positive only on the intervals where x < –7 and where x > 1. The graph is negative on the interval x < –4.
The statements about the function that are true are
The vertex of the function is at (–3,–16). The graph is increasing on the interval x > –3. The graph is positive only on the intervals where x < –7 and where x > 1. How to interpret the graph?The equation of the graph is given as
f(x) = (x - 1)(x + 7)
The graph of the function is added as an attachment
On the graph, we have
Vertex = (-3, -16)
This is so because the graph has a minimum point of (-3, -16)
Also, the graph crosses the x-axis at x = 1 and x = -7
This means that the graph is positive at x >1 and x >-7
Because the vertex is a minimum, the graph is increasing at the left of its symmetry i.e. x > -3
Read more about quadratic functions at
https://brainly.com/question/14933288
#SPJ1
Data Collected by the Substance Abuse and Mental Health Services Administration (SAMSHA) suggest that 69.8% of 18-20 year olds consumed alcoholic beverages in 2008?
(A) calculate the probability that exactly 4 out of 12 randomly sampled 18 to 20 year old consume an alcoholic drink?
(B) what is the probability that exactly 8 out of 1218 to20 year olds have not consumed an alcoholic beverage?
(C) What is the probability that at most two out of four randomly sampled 18 to 20 year old
have consume alcoholic beverage?
(D) what is the probability that at least one out of four randomly sample 18 to 20 years has consumed alcoholic beverage?
(a) The probability that exactly 4 out of 12 randomly sampled 18 to 20 year old consumes an alcoholic drink is 0.008127.
(b) The probability that exactly 8 out of 12, 18 to 20-year-olds have not consumed an alcoholic beverage is 0.231991.
(c) The probability that at most two out of four randomly sampled 18 to 20 year old have consumed alcoholic beverages is 0.35.
(d) The probability that at least one out of four randomly sample 18 to 20 years has consumed alcoholic beverages is 0.99168.
What is probability?The possibility of an event happening is defined by probability. We may need to forecast an event's result in a variety of real-world circumstances. The outcomes of an event may be certain or uncertain to us.
Given that 69.8% of people of 18-20 yr old consume alcohol.
Then p=0.698
Now let X is the random variable denoting the number of people who drinks alcohol.
(a) Let the sample size, n = 12, p = 0.698
It can be seen that X follows a binomial distribution
Then,
P(X=4) = ¹²C₄p⁴(1-p)⁸
= 495 × (0.698)⁴(1-0.698)⁸
=495 × 0.2373 × 0.00006919
= 0.008127
(b) P(X=8) = ¹²C₈p⁸(1-p)⁴
= 12!/ (8!)(4!)(0.698)⁸(1-0.698)⁴
=495 × 0.05634344 × 0.0083181
= 0.231991
(c) Let sample size n=4
p= 0.698
Then,
P(X≤2) = P(X=0)+P(X=1)+P(X=2)
= ⁴C₀p⁰(1-p)⁴ + ⁴C₁p¹(1-p)³ + ⁴C₂p²(1-p)²
=1 × 1× 0.0083181 + 4× 0.698 × 0.0275 + 6× 0.4872 × 0.091204
=0.3516881
=0.35
(d)
For P(X≥1)= 1-P(X<1)
=1-P(X=0)
=1-⁴C₀ p⁰(1-p)⁴
=1-1 × 1 × 0.0083181
= 0.99168
To know more about probability, visit:
brainly.com/question/28146099
#SPJ1
How do i do this question
Answer:25.12
Step-by-step explanation: To find the circumference the equation is diameter time pie. Pie=3.14
Use the number line to find the coordinate of the midpoint of
¯¯¯¯¯¯¯
M
P
.
Answer: 2.5
Step-by-step explanation:
The midpoint of the segment is the average of the coordinates.
[tex]\frac{0+5}{2}=2.5[/tex]
Your class tried to construct a tetrahedron using four smaller congruent tetrahedra. However, the result left a gap in the center, as shown in the diagram below. If the volume of each small shaded tetrahedron is 50 in.3, what is the volume of the gap? Explain how you know.
Answer:
200 in³
Explanation:
The lengths of the sides of the constructed tetrahedron are twice the length of the side of the small tetrahedron of 50 in³. It means that the scale factor for the solid is 2. So, the complete volume of the constructed tetrahedron is equal to
Vn = 2³(50 in³)
Vn = 8(50 in³)
Vn = 400 in³
However, we only use 4 small tetrahedrons, so the volume of these four solids is
4(50 in³) = 200 in³
Then, the volume of the gap is the difference between the volume of the constructed tetrahedron and the volume of the 4 small tetrahedrons
400 in³ - 200 in³ = 200 in³
So, the answer is 200 in³
Please help with this question
The sum of the expression will be given as 26. Thus, option B is correct.
An expression may be defined as the collection of numbers and variables related to one another by arithmetic operations. A number x is said to be a perfect square of a certain number y if the number y is multiplied to itself again. The square root of the number y will be equal to x. For example, 25 is the perfect square of 5 and 9 is the perfect square of 3. Square root of a number may be defined as the number to the power of half. The square root of √121 = 11 as 121 is perfect square of 11 and square root of √225 = 15 as 225 is perfect square of 15.
Now, √121 + √225 =?
As, √121 = 11 and √225 = 15
=> 11 + 15 = 26 which is the required answer.
Learn more about Perfect Square at:
brainly.com/question/8598497
#SPJ1
Question 2A bag of marbles contains 8 black marbles, 4 redmarbles, 3 blue marbles, and 5 white marbles. What isthe probability of not drawing a black marble?
Probability of not drawing a black marble = (Number of marbles which are not black)/ (Total number of marbles)
Probability of not drawing a black marble = 12/ 20 (Replacing)
Probability of not drawing a black marble = 3/5 (Simplifying)
The answer is 3/5
45. Write an inequality that represents the graph. Explain it step by step please.
Answer:
-4>x
Step-by-step explanation:
R1.56P12TSIn the diagram, QT || RS, PQ = 6, QR = 1.5 and PT = 12. Find ST.STtype your answer...units
Answer:
[tex]ST=3\text{ units}[/tex]Explanation:
Let x represent the length of segment ST.
Given that the lines QT and RS are parallel, the, then the triangles QPT and RPS are similar.
So, the ratio of their sides will be equal;
[tex]\frac{QP}{PT}=\frac{RP}{PS}[/tex]Given;
[tex]\begin{gathered} QP=6 \\ PT=12 \\ RP=6+1.5=7.5 \\ PS=12+x \end{gathered}[/tex]substituting;
[tex]\begin{gathered} \frac{6}{12}=\frac{7.5}{12+x} \\ 12+x=\frac{7.5\times12}{6} \\ 12+x=15 \\ x=15-12 \\ x=3 \\ ST=3\text{ units} \end{gathered}[/tex]Therefore;
[tex]ST=3\text{ units}[/tex]When a rate is simplified so that it has a _ , it is called a unit rate
Answer:
When a rate is simplified so that it has a denominator of 1, it is called a unit rate
Step-by-step explanation:
Hope it helps!
1. The number of identity theft cases from 2005 through 2010 can be represented by
the function f(x) = 0.058x + 2.175x + 340.2x² - 1,500x+20,000, where x
represents the number of years since 2005. Approximately when will the number of
identity theft cases reach 50,000
We need to know about quadratic equation to solve the problem. The year when the number of cases will be 50,000 is 2017.
Quadratic equation is an equation that has a maximum degree of two. Quadratic equations always have two roots, it can be solved by factorization method. In this question we have been given a function that we can simplify to get a quadratic equation. We need to find the year when the identity theft cases reach 50,000, we need to equate the equation to 50,000 and then solve the quadratic equation to get x.
f(x)=0.058x+2.175x+340.2[tex]x^{2}[/tex]-1500x+20000 =340.2[tex]x^{2}[/tex]-1497.767x+20000
50000=340.2[tex]x^{2}[/tex]-1497.767x+20000
340.2[tex]x^{2}[/tex]-1497.767-30000=0
Using Sridharacharya's method,
x=1497.767±[tex]\sqrt{2243305.99+40824000}[/tex]/680.4=1497.767±6562.56855/680.4
x=11.85 or x=-7.44
Here x cannot be negative, so the right value of x is approximately 12,
year when cases is 50000= 2005+12=2017
Therefore the year when identity theft cases reach 50000 is 2017.
Learn more about quadratic equation here:
https://brainly.com/question/1214333
#SPJ1