The given expression is
[tex]sec\frac{3\pi}{2}[/tex]Since sec is the opposite of cosine, then
[tex]sec\frac{3\pi}{2}=\frac{1}{cos\frac{3\pi}{2}}[/tex]Since the value of cos(3pi/2) is 0, then
[tex]\begin{gathered} cos\frac{3\pi}{2}=0 \\ \\ sec(\frac{3\pi}{2})=\frac{1}{cos\frac{3\pi}{2}}=\frac{1}{0} \end{gathered}[/tex]Since 1/0 is an undefined value, then
The answer is undefined
8x^2+8x-22 In (x-p)^2=q
The given function 8x^2+8x-22 rewritten using the completing the square method is (x+1/2)^2 = 3
Completing the square methodBy altering the equation's form so that the left side is a perfect square trinomial, a quadratic equation can be solved using the "Completing the Square" approach.
Given the quadratic equation below;
8x^2+8x-22 = 0
This can be simplified into the equation below;
8x^2+8x-22 = 0
4x^2+4x-11 = 0
Add 11 to both sides of the equation
4x^2+4x-11 + 11= 0 + 11
4x^2+4x = 11
Factor out 4x from the expression;
4(x^2+1) = 11
(x+1/2)^2 = 11/4 + 1/4
(x+1/2)^2 = 12/4
(x+1/2)^2 = 3
Hence the expression in the form of (x-p)^2=q is (x+1/2)^2 = 3
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A cell of some bacteria divides into two cells every 30 minutes. The initial population is 3 bacteria.
(a) Find the size of the population after t hours
y(t)
(function of t)
=
(b) Find the size of the population after 7 hours.
y(7)=
=
(c) When will the population reach 21?
T =
After t hours, the population is 3(2^2t).
After 7 hours, the population is 3(2^14).
In 2.33 minutes, the population would be 21.
What is the function representing bacterial growth?The following formula is used to calculate the bacteria population:
The formula for calculating future value is as follows:
FV = P (1 + r)^n
Where:
FV stands for Future Value.
P = Present value of three
R = growth rate = 100%
(hours x 60 minutes) / 30 = 2t = time
3(2^2t) = population in t hours
3(2 ^14) = population in 7 hours
The population of time would be 21 =[( FV /PV) / r] X 30.
2.33 minutes = ( 21 / 3) / 3.
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Find the surface area for the triangular prism below if AB = 16 m, AC = 33 m, AD = 12 m, and DP = 9 m. (Note: the bases are isosceles triangles.)
INFORMATION:
We have the following figure
And we must find its surface area
STEP BY STEP EXPLANATION:
To find the surface area of the triangular prism, we can divide the figure in:
- The two triangle bases:
We have the next triangle in the two bases:
We can calculate the area of the triangle
[tex]A=\frac{16\times9}{2}=72m^2[/tex]Since we have the same triangle in the two bases, the total area of the two triangles would be
[tex]72m^2\cdot2=144m^2[/tex]-
can someone help please.(the part cut out says" Slope intercept form)
we have that
the equation of the line in slope intercept form is
y-=mx+b
we have
m=2
b=3/2
substitute
y=2x+3/2
answer is option C
Aaliyah needs to bake 42 servings of treats. She has cooked 20 servings of treats already. She has bars left to
make and each bar is 2 servings. How many bars does she need to make?
Answer:
she needs to make 11 bars
Step-by-step explanation:
42-20
22
each bar is 2 servings so
22÷2
11 bars
Tina's kitchen has an area of 54 square feet the kitchen is 9 times as many square feet does Tina's pantry if the pantry is 2 feet wide what is the length of the Pantry in feet
From the information given, the area of the kitchen is 54 square feet and it is 9 times as many square feet as does Tina's pantry. This means that the area of Tina's pantry is
54/9 = 6 square feet
If the pantry is 2 feet wide, we would determine its length by applying the formula for determining the area of a rectangle which is expressed as length * width
Therefore,
2 * length = 6
length = 6/2 = 3 feet
Length of the pantry is 3 feet
14 more than greg’s savings is 58
translate into equation
Answer:
1-4<58
Step-by-step explanation:
poor Greg is broke and yea
Mr. Coffey bought a house for $195,000. He made a 20% down payment. The interest rate is 5.25% for 30 years. How much does he need to borrow? What is his monthly payment?
Explanation:
Mr. Coffey bought a house for $195,000 with a 20% down payment.
A 20% down payment, would be 0.20, so $195,000 times 0.20 equals $39,000. Then $195,000 - $39,000 = $156,000.
He bought the bouse for $156,000.
5.25% is 0.525, because you move the decimals back. Understanding the total cost of the house is $156,000 now, we can do $156,000 times 5.25% (0.0525) which equals $8,190.
He would pay $8,190 every 30 years. (if this was the interest rate.)
Assuming if the cost was 20% down payment with the 5.25% interest rate then it would have been: $39,000 times 5.25% = 2047.5.
He would pay $2,047.50 every 30 years. (if this was the interest rate.)
There was no context between the interest rate, so let's assume the obvious which is $2,047.50 every 30 years.
A basketball player had scored 879 points in 34 games. a) At this rate, how many games will it take him to score 1500 points? b) There are 82 games in an entire season. At this rate, how many points would he score in the entire season? a) It will take him approximately games to score 1500 points . (Round up to the next whole number of games.) b) At this rate, he would score approximately (Round to the nearest one if necessary.) points in the entire season. Enter your answer in each of the answer boxes.
We know that he scored 879 points in 34 games, so we can calculate the average rate as:
[tex]r=\frac{879\text{ points}}{34\text{ games}}=25.85\text{ points/game}\approx26\text{ points/game}[/tex]At this rate, we can calculate the total points P by multiplying the rate r by the number of games n:
[tex]P=r\cdot n=25.85\cdot n[/tex]We can calculate how many games are needed for P=1500 as:
[tex]\begin{gathered} P=26\cdot n=1500 \\ n=\frac{1500}{25.85}\approx58.02\approx58\text{ games} \end{gathered}[/tex]For n=82 games, the expected number of points P is:
[tex]P=25.85\cdot n=25.85\cdot82=2119.7\approx2120\text{ points}[/tex]Answer:
a) It will take him approximately 58 games to score 1500 points.
b) At this rate, he would score approximately 2120 points in the the entire season.
Name the number of degrees in the monomial.8abcd
Given: 8abcd
The number of degrees is the sum of the exponent of each variable in the monomial
The answer is 4
What is 3m+n evaluate the expression. I’m confused on how to solve this this is what my teacher gave me that’s it
Explanation:
The expression is given below as
[tex]3m+n[/tex]Concept:
The sum of two or more like terms is a single like term; but the two unlike terms cannot be added together to get a single term. Suppose, to find the sum of two unlike terms x and y, we need to connect both the terms by using an addition symbol and express the result in the form of x + y.
In this case,
The terms given ( 3m and n ) are unlike terms and as such the expression cannot be simplified further
Hence,
The final answer is
[tex]3m+n[/tex]such
In 2016, there were 34,602 burger restaurants worldwide, with 12,994 of them located in a country. Determine the percent of burger restaurants in that country in 2016Approximately % of the burger restaurants worldwide were in that country in 2016.
% of the burger restaurants worldwide were in that country in 2016 =
= 12994/ 34602 X 100
= 37.55 %
Which statement is true regarding the functions on the graph? 6 9) O f2) = g(2) O fO) = g(0) O f2) = g(0) Of(0) = g(2) 2 5 6 -421
F(x) is blue and G(x) is red
Have to find at which point both functions have the same value, or the same in which point both lines intercept
and looking at the graph ,theres only one point where both are equal. Its the point x= 2 y=0.
so the correct answer is f(2) = g(2)
five friends earn a total of $33.75 shovellimg snow. How much does each friend earn
Given:
Number of friends = 5
Total amount they earn = $33.75
Let's find how much each friend earn.
To find the amount each friend earn, take the formula below:
[tex]\text{ Amount each friend earn = }\frac{Total\text{ amount they earn}}{\text{Number of friends}}[/tex]Substitute values into the equation above and evaluate:
[tex]\text{ Amount each friend earn = }\frac{33.75}{5}=6.75[/tex]Therefore, each friend earns $6.75
ANSWER:
$6.75
Answer: $6.75
Step-by-step explanation: Divided 33.75 by 5 which is equal to $6.75
find the length of the base if the area of the trapezoid is 198 M2.
The area of a trapezoid is given by:
[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]where b1 and b2 are the bases of the trapezois and h is the height. In this case we have that A=198, b1=15 and h=12, plugging this values into the equation above and solving for b2 we have:
[tex]\begin{gathered} 198=\frac{1}{2}(b_2+15)12 \\ 2\cdot198=12(b_2+15) \\ 396=12(b_2+15) \\ \frac{396}{12}=b_2+15 \\ 33=b_2+15 \\ b_2=33-15 \\ b_2=18 \end{gathered}[/tex]Therefore b2 is equal to 18 m
Round your answer to two
decimal places.
7X = 77
Answer:
x = 11
Step-by-step explanation:
7X = 77
divide both sides by 7
x = 11
A chord of a circle is 56cm long. The distance of the chord to the centre of the circle is 20cm. a) calculate the radius of the circle b) calculate the length of a chord which is 24cm from the center of the circle.
Answer:
a) 34.4 cm,b) 49.4 cmStep-by-step explanation:
The distance from the center to the chord is the perpendicular bisector of the chord.
The three segments form a right triangle:
The radius - hypotenuse,The half-length of the chord - leg,The distance to the chord - another leg.a) Use Pythagorean to find the radius:
r² = (56/2)² + 20²r² = 28² + 20²r² = 1184r = √1184r = 34.4 cm (rounded)b) Let the half-chord is x cm long. Use Pythagorean to find the missing leg:
34.4² = x² + 24²1184 = x² + 576x² = 1184 - 576x² = 608x = √608x = 24.7 cm (rounded)The length of the chord is:
24.7*2 = 49.4 cmNEED ASAP PLS QUESTION IS IN THE PICTURE IF CORRECT ILL GIVE BRAINLIEST
The vertex and range of y = (x + 2) - 3 is [tex]$(0,-1) ;-3 \leq y < \infty[/tex]
What is vertex and range?We only need to think about the k as the vertex is determined by the coordinates (h, k). Consider the function f(x)=3(x+4)26 as an illustration. All real integers greater than or equal to 6 fall within the range since an is positive and the vertex lies at (4,6).A vertex is a place where two line segments come together at an acute angle or where two curved lines come together to form a parabola. Depending on the direction, a parabola's vertex is either its highest or lowest point.The set of values that a function can accept as input is known as its range.. After we enter an x value, the function outputs this sequence of values.To learn more about vertex and range refer to :
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Determine the slope given two points (-2,3) (6,-7)
Answer: m = -3/5
Step-by-step explanation:
Graph the line with slope 1/3
and y-intercept -2.
The equation of a straight line is y = mx + b where m is the slope and b is the y-intercept then the two points exist (0, -2) and (6, 0).
What is meant by the equation of a straight line?A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.
The equation of a straight line is:
y = mx + b where m is the slope and b is the y-intercept.
Therefore, the equation for this line is:
y = (1/3)x - 2
To graph it we can identify two points on the line and connect them.
If x = 0, then y = -2 this is the y-intercept given in the problem.
If x = 6, then y = 0 this is the x-intercept
Therefore, the two points exist (0, -2) and (6, 0).
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A local hamburger shop sold a combined total of 632 hamburgers and cheeseburgers on Saturday. There were 68 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday?
The number of hamburger is 350 and the number of cheeseburger is 282.
How to illustrate the information?It should be noted that an expression is simply used to show the relationship between the variables.
In this case, the local hamburger shop sold a combined total of 632 hamburgers and cheeseburgers on Saturday and there were 68 fewer cheeseburgers sold than hamburgers.
Let Cheeseburger = x
Hamburger = x + 68
This will be:
x + x + 68 = 632
2x + 68 = 632
2x = 632 - 68
2x = 564
x = 564/2
x = 282
Cheeseburger = 282
Hamburger = x + 68 = 282 + 68 = 350
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Please show work as if you didn’t have a calculator
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given function.
[tex]f(x)=\frac{1}{(x+3)}-2[/tex]STEP 2: Explain the means to use to find the required values
Since we were given a graph and can not use a caculator, we will be using the graph to get the values.
STEP 3: Plot the given function on a graph
STEP 4: Get the domain of the function
Domain: The domain is all x-values or inputs of a function. The domain of a graph consists of all the input values shown on the x-axis.
[tex]\begin{gathered} The\text{ domain from the graph is given as:} \\ x<-3\text{ or }x>-3 \\ \text{The interval notation is given as:} \\ (-\infty,-3)\cup(-3,\infty) \end{gathered}[/tex]STEP 5: Get the Range of the function
The range is all y-values or outputs of a function.
[tex]\begin{gathered} \mathrm{The\: set\: of\: values\: of\: the\: dependent\: variable\: for\: which\: a\: function\: is\: defined} \\ \text{The range of the graph is given as:} \\ f(x)<-2\text{ or }f(x)>-2 \\ \text{The interval notation is given as:} \\ (-\infty,-2)\cup(-2,\infty) \end{gathered}[/tex]STEP 6: Get the value on which the function is increasing on
[tex]\begin{gathered} \mathrm{If}\: f\: ^{\prime}\mleft(x\mright)>0\: \mathrm{then}\: f\mleft(x\mright)\: \mathrm{is\: increasing.} \\ \mathrm{If}\: f\: ^{\prime}\mleft(x\mright)<0\: \mathrm{then}\: f\mleft(x\mright)\: \mathrm{is\: decreasing.} \end{gathered}[/tex]STEP 7: Get the value on which the function is decreasing on
[tex]\begin{gathered} \mathrm{If}\: f\: ^{\prime}\mleft(x\mright)<0\: \mathrm{then}\: f\mleft(x\mright)\: \mathrm{is\: decreasing.} \\ It\text{ can be s}een\text{ that the function on the graph decreases on the point betw}een\text{ negative infinity} \\ \text{and -3 and the point betw}een\text{ -3 and infinity. }\therefore This\text{ can be written as:} \\ \: \\ \mathrm{Decreasing}\colon-\infty\:STEP 8: Get the values of the asymptotes
An asymptote is a line that a graph approaches without touching. Similarly, horizontal asymptotes occur because y can come close to a value, but can never equal that value. In the previous graph, there is no value of x for which y = 0 ( ≠ 0), but as x gets very large or very small, y comes close to 0.
[tex]\mathrm{Vertical}\colon\: x=-3,\: \mathrm{Horizontal}\colon\: y=-2[/tex]
3 1 1 1 Evaluate 2 when n = 10 5 1 3 3 2 10 10 1 3 3 + + 2 10 10 (Type integers or fractions.)
The given expression is
[tex]\frac{1}{2}n+\frac{3}{10}[/tex]Where n = 1/5.
Let's replace the variable for its value.
[tex]\frac{1}{2}(\frac{1}{5})+\frac{3}{10}[/tex]First, we solve the product.
[tex]\frac{1}{10}+\frac{3}{10}[/tex]Then, we sum fractions. Notice that we just have to sum numerators because the denominators are equal.
[tex]\frac{1+3}{10}=\frac{4}{10}=\frac{2}{5}[/tex]Therefore, the answer is 2/5.NEEEEEEEEDDDDDD HELPPPPP ASAPPPPPPP
Matching the specific Polygons with their descriptions, we have;
15-gon → An exterior angle measures 24°
16-gon → The Sum of interior angles is 2520°
12-gon → An interior angle measures 150°
18-gon → An interior angle measures 160°
What is the sum of interior angles of a Polygon?The formula for sum of interior angles of a Polygon is;
S = (n - 2) * 180
where n is number of sides of polygon. Thus;
1) For a 15 sided polygon;
Sum = (15 - 2) * 180
Sum = 13 * 180
Sum = 2340
Sum of exterior angles of a polygon is; 360°
Thus, external angles = 360/15 = 24°
2) For a 16 sided polygon;
Sum of interior angles = (16 - 2) * 180 = 2520°
3) The value of the interior angles of a polygon with 12 sides is;
(12 -2) * 180/12 = 150°
4) The value of the interior angles of a polygon with 18 sides is;
(18 - 2) * 180/18 = 160°
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3x+7x-28+31-8x for x=2043
The value of the function when x is equivalent to 2043 is 4089.
Solving linear equationLinear equations are equation that has a leading degree of 1. Given the linear equation;
3x+7x-28+31-8x
Collect the like terms
3x+7x-28+31-8x
3x+7x-8x-28+31
10x-8x-28+31
2x+3
If the value of x is 2043, substitute;
2x+3 = 2(2043) + 3
2x + 3 = 4086 + 3
2x + 3 = 4089
Hence the value of the function when x is equivalent to 2043 is 4089.
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6 singles, 7 fives, 3 twenties, and 2 hundred dollar bills are all placed in a hat. If a player is to reach into the hat and randomly choose one bill, what is the fair price to play this game?
Fair price to play this game is $16.72
Explanation:[tex]\begin{gathered} \text{Given:} \\ 6\text{ singles, 7 fives, 3 twenties and 2 hundred dollar bills in a hat} \\ \end{gathered}[/tex]To find the fair price, we divide the total amount by the number of bill denominations given
[tex]\text{fair price = }\frac{total\text{ amount in the hat}}{nu\text{mber of bills in the hat}}[/tex][tex]\begin{gathered} nu\text{mber of bills = }6\text{ + 7 + 3 + 2 = 18} \\ \\ \text{singles = 1} \\ 6\text{ singles = 6 }\times\text{ 1} \\ 7\text{ fives = 7}\times\text{ 5} \\ 3\text{ twenties = 3}\times20 \\ 2\text{ hundred = 2 }\times\text{ 100} \\ \\ \text{Total amount in the hat = 6 }\times\text{ 1 + 7}\times\text{ 5 + 3}\times20\text{ + 2 }\times\text{ 100} \\ \text{Total amount = 6 + 35 + 60 + 200 = 301} \end{gathered}[/tex][tex]\begin{gathered} \text{fair price = }\frac{301}{18} \\ \text{fair price = 16.72} \end{gathered}[/tex]Fair price to play this game is $16.72
A. 8 + 8 + 8 + 8B. 2 + 4C. 4 + 4 + 8 + 8 + 1 + 1D. 8 + 8 + 4 + 4 + 2 + 2These Are The Choices
The surface area of a rectangular prism can be represented below
[tex]\begin{gathered} A=2(lw+wh+lh) \\ l=4 \\ w=2 \\ h=1 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} A=2(8+2+4) \\ A=8+8+4+4+2+2 \end{gathered}[/tex]5 · 4 -3 + 10 ÷ 2 A. -65 B. -55 C. -35 D. -25
we have
5 · 4 · -3 + 10 ÷ 2
Applying PEMDAS
P ----> Parentheses first
E -----> Exponents (Powers and Square Roots, etc.)
MD ----> Multiplication and Division (left-to-right)
AS ----> Addition and Subtraction (left-to-right)
step 1
Multiplication
5.4.-3=-60
substitute
-60+10÷ 2
step 2
Division
10÷ 2=5
substitute
-60+5
step 3
Addition
-55
therefore
option B5 MATH QUESTIONS WILL MARK BRAINLIEST PLS HELP
The correct options regarding the functions are given as follows:
1. C. y = -2x - 7/9, m = -2, b = -7/9.
2. A. y = 1400x + 5000, 10,600 lbs.
3. A. t = 0.75m + 12, $23.25.
4. A. y = (x - 2) - 3.
5. B. 302.5 miles.
Item 1In slope-intercept formula, a linear function is given as follows:
y = mx + b.
In which:
m is the slope.b is the y-intercept.For this problem, the equation is:
-18x - 9y = 7.
Then:
9y = -18x - 7
y = -2x - 7/9, which slope -2 and intercept -7/9.
Thus option C is correct.
Item 2The table represents a linear function, in which:
The initial value is the intercept of b = 5000.Each week, the amount increases by 1400, hence the slope is of m = 1400.Thus the function is:
y = 1400x + 5000.
In four weeks, x = 4, hence the amount is of:
y = 1400(4) + 5000 = 10600.
Which means that option A is correct.
Item 3Also a linear function, in which:
The intercept is the flat fee of $12.The slope is the cost per mile of $0.75.Hence the function is:
t = 0.75m + 12.
For 15 miles, the cost is given as follows:
t = 0.75(15) + 12 = $23.25.
Which means that option A is correct.
Item 4In this graph, we have a concave up parabola with vertex at (2,-3), hence the rule is:
y = (x - 2) - 3.
Which means that option A is correct.
Item 5The distance function after t hours is given by:
d = 45t + 100.
Hence, after 4.5 hours, as 1/2 = 0.5, the distance is of:
d = 45(4.5) + 100 = 302.5 miles.
Which means that option B is correct.
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hii i have a question on the question below . in the photo
Solution
For this case we need to sort the values and we have:
Studied
79, 83, 84, 88, 89, 89, 91, 92, 93, 94, 95, 95, 96, 99, 100, 100, 100, 100
Q3= 98.25
Q1= 89
Therefore IQR = 98.25-89= 9.25
Not Studied
45, 58, 65, 72, 73, 77, 82, 83, 87, 89, 90, 91
Q3= 87.5
Q1= 70.25
Therefore IQR = 87.5-70.25= 17.25
From the results obtained we can conclude that the students who not studied havve larger variability compared to those who studied