At time t = 4 + 3i sec and t = 4 - 3i sec that the projectile will reach a height of 400 ft.
A projectile is launched from ground level with an initial velocity of v₀ feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by s = −16t² + v₀t.
To determine the time that the projectile will reach a height of 400 ft
⇒ s = −16t² + v₀t
Here v₀ = 128 ft/s and s = 400 ft
Substitute the value of v₀ = 128 and s = 400 in the above equation,
400 = -16t² + 128 × t
16t² - 128t + 400 = 0
Which is simplified as :
t² - 8t + 25 =0
Which gives t = 4 + 3i sec and t = 4 - 3i sec
Therefore, time t = 4 + 3i sec and t = 4 - 3i sec that the projectile will reach a height of 400 ft.
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pls help
Does this graph
show a linear,
quadratic, or
exponential
function?
Answer:
exponential
Step-by-step explanation:
You told your friend that you could eat 7/8 of a large pizza. If you only ate 2/3 of what you said you could eat, what fraction of a large pizza did you eat?
The fraction of the large pizza that you were supposed to eat is 7/8. You could only eat 2/3 of 7/8. Thus, the fraction that you ate would be
(2/3) / (7/8)
If we flip 7/8 such that it becomes 8/7, the division sign would change to multiplication sign. Thus, we have
2/3 * 8/7
= 16/21
The fraction of the large pizza pizza that you ate is 16/21
Write the point-slope form equation of the line that satisfies the given conditions. Also, rewrite the equation of the line such that it's in slope-intercept form.
f(3) = 18 and f(16) = -18
Equation of the line is y = [tex]\frac{-36x}{13}[/tex] + [tex]\frac{687}{13}[/tex].
Define slope intercept form.An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx+ c, where m denotes slope and c denotes the y-intercept. A line's equation written using a single point on the line and the line's slope is referred to as the point-slope form. The slope is the rise over run, or the ratio of the change in the y values over the change in the x values, and the point form is denoted as (x, y).
Given Data
f(3) = 18
f(16) = -18
Slope:
m = [tex]\frac{f(x_{2})-f(x_{1}) }{x_{2}-x_{1} }[/tex]
m = [tex]\frac{f(16)-f(3)}{16-3}[/tex]
m = [tex]\frac{-18-18}{13}[/tex]
m = [tex]\frac{-36}{13}[/tex]
Equation of the line in slope intercept form:
y - f(x₁) = m(x - x₁)
y - 3 = [tex]\frac{-36}{13}[/tex](x - 18)
y - 3 = [tex]\frac{-36x}{13}[/tex] + [tex]\frac{648}{13}[/tex]
y = [tex]\frac{-36x}{13}[/tex] + [tex]\frac{687}{13}[/tex]
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The owner of the deli recorded the number of costumers who ordered each of four sandwiches avaliable. If the deli has 50 customers the first hour it is open, predict how many customers will order turkey andwiches?Ham: 160Cheese: 100Turkey: 180Veggie: 60
First, we want to find the probability of having a costumer who choose Turkey sanwich.
In order to find it, we calculate the ratio of turkey sandwiches over the total number of orders.
Turkey sandwiches: 180
Total number of orders: 160 + 100 + 180 + 60 = 500
Ratio = turkey / total
Ratio = 180 / 500 = 0.36
Then, the probability of having a costumer who choose Turkey sanwich is
P(T) = 0.36 = 36%
Secondly, in order to find the 36% of 50, we just multiply 0.36 by 50:
[tex]0.36\cdot50=18[/tex]Answer: in the first hour there will be 18 costumers that will order Turkey sanwichesWhich inequality is true?А. Зп > 9B. 7 + 8< 11C. 27 -1 < 5D. 2 > 2SUBMIT< PREVIOUS
For the given options, we will find which inequality is true:
A)
[tex]\begin{gathered} 3\pi>9 \\ 3\pi=3\cdot3.14=9.42>9 \end{gathered}[/tex]so, the inequality is true
B) 7 + 8 < 11
7 + 8 = 15 > 11
So, the inequality is wrong
C) 27 - 1 < 5
27 - 1 = 26 > 5
So, the inequality is Wrong
D) 2 > 2
2 = 2
so, the inequality is wrong
So, the answer will be the true inequality option A) 3п > 9
[tex]undefined[/tex]This diagram is used to prove the Pythagorean Theorem, and to show that the purple square - the green square = the red square
A café has three different sizes of plate. The ratio of small to medium is 2:5 and the ratio of medium to large is 3:4What is the ratio of small plates, to medium plates to large plates?
6: 15 : 20
Explanation:Ratio of small to medium = 2 : 5
Ratio of medium to large = 3 : 4
We need to make the medium in both ratios equivalent since medium is common to both:
[tex]\begin{gathered} \frac{small}{\text{medium}}\text{ = }\frac{2}{5} \\ \frac{medium}{\text{large}}=\frac{3}{4} \\ \text{for medium to be equivalent, we multiply ratio by 3} \\ we\text{ multiply the second ratio by 5} \\ \text{LCM = 3}\times5\text{ = 15} \end{gathered}[/tex]We multiply the numerator by same amount we multiply the denuominator in both ratios:
[tex]\begin{gathered} \frac{small}{\text{medium}}\text{ = }\frac{2}{5}\times\frac{3}{3}\text{ } \\ \frac{small}{\text{medium}}=\text{ }\frac{6}{15} \\ \\ \frac{medium}{\text{large}}=\frac{3}{4}\times\frac{5}{5} \\ \frac{medium}{\text{large}}=\text{ }\frac{15}{20} \end{gathered}[/tex]The ratio of small to medium to large:
[tex]\begin{gathered} \text{The medium is the same so we can bring all thr}ee\text{ together:} \\ \text{small: medium: large} \\ 6\colon\text{ 15 : 20} \end{gathered}[/tex]Solve the equation. log, (-x) + log, (x - 10) = log, 24 Select one: O a. {-6 O b. O O c. {-6, -4) O d. {4,6
start by applying the log properties on the left side
[tex]\log (-x^2+10x)=\log (24)[/tex]remember that when we talk about the logs they are defined for values greater than 0, determine the range in which will be defined
[tex]\begin{gathered} -x^2+10x>0 \\ -x(x-10)<0 \\ x<0 \\ x-10<0 \\ x<10 \\ x=\mleft\lbrace0,10\mright\rbrace \end{gathered}[/tex]knowing that the values in order for the log to be true must be between 0 and 10, apply base 10 on both sides to cancel the log
[tex]10^{log(-x^2+10x)}=10^{\log (24)}[/tex][tex]\begin{gathered} -x^2+10x=24 \\ -x^2+10x-24=0 \\ \text{using the quadratic equation} \\ a=-1;b=10;c=-24 \\ x_1=4;x_2=6_{} \end{gathered}[/tex]after having the values of the quadratic replace them on the equation
[tex]\begin{gathered} x=4 \\ \log (-4)+\log (4-10)=\log (24) \\ \log (-4)+\log (-6)\ne\log (24) \end{gathered}[/tex][tex]\begin{gathered} x=6 \\ \log (-6)+\log (6-10)=\log (24) \\ \log (-6)+\log (-4)\ne\log (24) \end{gathered}[/tex]after seeing that with both solutions is false the statement, we can conclude that there are no solutions for x.
[tex]x\in\varnothing[/tex]HELP QUICK PLEASE
all i need is 6,10,&12
In exercises 1-8, the table or graph represents a quadratic function. Write an equation of the function in standard form.
In exercises 9-12, write a quadratic function in standard form whose graph has the given characteristics.
Answer:
y= - 104/125 (x - 1/2 2) +1
Step-by-step explanation:
hope this helps
Hello I need help with question 6! I will give you a great rating! Please help, I’m not sure how to do this. Also this is not a quiz this is practice
6.
cos a = adjacent side / hypotenuse
Replacing with the values given:
Cos 45 = 13 / y
y= 13/cos45
y= 13/ (1 /√2 )
Y= 13√2
For x apply the Pythagorean theorem
c^2 = a^2 + b^2
Where:
c= hypotenuse
a & b = the other 2 legs
(13 √2 )^2 = x^2 + 13^2
338 = x^2 + 169
338 - 169 = x^2
169 =x^2
√169 = x
x = 13
consider the line y=7/5x+4
The genral equation of line can be written as y=mx+c, where m is the slope of the line.
Comparing y=7/5x+4 with y= mx+c, we get slope m=7/5.
The slope of two parallel lines are equal. Hence, the slope of a parallel line to y=7/5x+4 is 7/5.
Now, the point slope form of a line which passes through a point (x1, y1) and habing slope m is,
[tex]\frac{y-y_1}{x-x_1}=m[/tex]Given (x1,y1)=(-7,-5). Therefore,
[tex]\begin{gathered} \frac{y-(-5)}{x-(-7)}=\frac{7}{5} \\ \frac{y+5}{x+7}=\frac{7}{5} \\ 5y+25=7x+49 \\ 5y=7x+49-25 \\ 5y=7x+24 \\ y=\frac{7}{5}x+\frac{24}{5} \end{gathered}[/tex]Therefore, the equation of line parallel to y=7/5x+4 and passing through point(-7,-5) is y=(7/5)x+(24/5).
(2)The slope of a line perpendicular to y=mx+c is -1/m.
So, slope of a line perpendicular to y=7/5x+4 is
[tex]Slope,m_1=\frac{-1}{m}=\frac{-1}{\frac{7}{5}}=\frac{-5}{7}[/tex]If (x1,y1)=(-7-5), then using point slope form,
[tex]\begin{gathered} \frac{y-y_1}{x-x_2}=m_1 \\ \frac{y-(-5)}{x-(-7)}=\frac{-5}{7} \\ \frac{y+5}{x+7}=\frac{-5}{7} \\ 7y+35=-5x-35 \\ 7y=-5x-70 \\ y=\frac{-5}{7}x-10 \end{gathered}[/tex]Therefore, the equation of line perpendicular to y=7/5x+4 and passing through point(-7,-5) is y=-(5/7)x-10.
can I get help please
we have the equation
y=-4x+4
step 1
Find the x-intercept (value of x when the value of y is zero)
so
For y=0
0=-4x+4
4x=4
x=4/4
x=1
x-intercept is (1,0)step 2
Find the y-intercept (value of y when the value of x is zero)
so
For x=0
y=-4(0)+4
y=4
y-intercept is (0,4)A golf ball is dropped out of an airplane. The downward velocity of the ball at various times is given in the table below. What is the slope of the line that fits this data?
Let:
[tex]\begin{gathered} (x1,y1)=(1,21.8) \\ (x2,y2)=(2.2,33.56) \\ \text{Slope}=m=\frac{y2-y1}{x2-x1}=\frac{33.56-21.8}{2.2-1}=\frac{11.76}{1.2}=9.8 \end{gathered}[/tex]3)
A 10-person team competes in a 24-hour cycling race. In total, they cover 443 miles.
Each person cycles the same distance. How far did each person cycle?
The distance covered by each person in hour cycling race is 44.3 miles.
What is defined as the method of unitary?The unitary method is employed to determine the value of a single unit given a multiple.The unitary method is used in a wide range of applications, from speed, distance, and time problems to determining the material cost.The technique is employed to calculate the cost of a product.It is used to calculate how long it takes a vehicle or even a person to travel a certain distance in an hour.For the given question;
The total distance covered by is 443 miles.
Total number of person cycling in a race = 10.
Distance covered by each person is same.
Each person's distance = 443/ 10
Each person's distance = 44.3 ,miles.
Thus, distance covered by each person in hour cycling race is 44.3 miles.
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uh hey can you help me with my hw if you help send me your snap and if you want I will send pics
The question says 900,000 /556040 x 190600
[tex]\begin{gathered} \frac{900,000}{556040}\text{ x 190600 } \\ \text{cancel the zero in the denominator and one zero above, then divide by 4 } \\ \frac{900000}{13901}\text{ x 47650} \\ \text{divide the dirst expression into decimal, that gives } \\ 64.74\text{ x 47650 = 3085029.85} \end{gathered}[/tex]Hence, 3085029.85 isthe solution to the question.
Answer: why
Step-by-step explanation: help me
Main street, Broad Street, and Park Street all intersect to form a right triangle. If broad Street is 75 yards ling and Park is 100 yards long, how long must Main Street be?
Option (D) is the correct answer.
Given:
The length of broad street is 75 yards.
The length of park street is 100 yards.
The objective is to find the length of the main street.
The length of the main street can be calculated using Pythagorean theorem.
[tex]\begin{gathered} \text{Park}^2=Main^2+Broad^2 \\ \text{Main}^2=Park^2-Broad^2 \\ \text{Main}^2=100^2-75^2 \\ \text{Main}^2=10000-5625 \\ \text{Main}^2=4375 \\ \text{Mai}n=\sqrt[]{4375} \\ \text{Main}^{}=66.144\text{ yards} \end{gathered}[/tex]Thus, the length of the Main street is 66.144 yards.
Hence, option (D) is the correct answer.
6. Find (G + G) then subtract H from the result H = (2x^2 + 6x + 5) and G = (6x^2 + 3x + 5)
ANSWER
[tex]10x^2\text{ + 5}[/tex]EXPLANATION
We have that:
[tex]\begin{gathered} G=6x^2\text{ + 3x + 5} \\ \text{and} \\ H=2x^2\text{ + 6x + 5} \end{gathered}[/tex]Let us find G + G:
[tex]\begin{gathered} 6x^2\text{ + 3x + 5 + }6x^2\text{ + 3x + 5} \\ 6x^2+6x^2\text{ + 3x + 3x + 5 + 5 } \\ 12x^2\text{ + 6x + 10} \end{gathered}[/tex]Now, let us subtract H:
[tex]\begin{gathered} 12x^2+6x+10-(2x^2\text{ + 6x + 5)} \\ 12x^2+6x+10-2x^2\text{ - 6x - 5} \\ 12x^2-2x^2\text{ + 6x - 6x + 10 - 5} \\ \Rightarrow10x^2\text{ }+\text{ 5} \end{gathered}[/tex]That is the answer
If the reference angle is 47° label the sides accordingly:
Answer:
side c = 10.72 = Opposite
side d = 14.66 = Hypotenuse
Side 10 = Adjacent side
Explanation:
The given sides are given from the triangle;
Adjacent = 10
Angle of elevation = 47degrees
Required
Opposite = c
Hypotenuse = d
Using the SOH CAH TOA identity;
Tan theta = opposite/adjacent
Tan 47 = c/10
c = 10tan47
c = 10(1.0724)
c = 10.72
hence side c = 10.72 = Opposite
Similarly;
Cos theta = adjacent/Hypotenuse
Cos 47 = 10/d
d = 10/Cos47
d = 10/0.6819
d = 14.66
Hence Side d = 14.66 = Hypotenuse
Side C: Adjacent
Side D: Hypotenuse
Side length of 10 units: Opposite
Graph a line with an undefined slope that goes through the point (-14,0)Identify the slope:And the Intercept:Write special equation of the line:
We need to first graph a line that goes through the point (-14, 0).
The chosen line passes through the point (-14,0) and (0, 28).
The slope of a line is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where m is the slope, (x1,y1) is the first point and (x2,y2) is the second point. Applying these points to the problem:
[tex]m=\frac{28-0}{-0-(-14)}=\frac{28}{14}=2[/tex]The slope of the line is 2.
The intercept of the line is the point at which it crosses the "y" axis. In this case this point is (0,28).
We can write the line in its slope-intercept form, since we already calculated those values. This form is given by:
[tex]y(x)=m\cdot x+b[/tex]Where "m" is the slope and "b" is the intercept, therefore the equation of the line is:
[tex]y(x)=2\cdot x+28[/tex]a) CF for 21,72 and 62
The three numbers given in the question : 21 , 72 and 62 do not have any common factor.
What do you mean by common factor ?The common factors are those that are found in both lists
Example: Factors of 12 and 30
Factors of 12 are 1, 2, 3, 4, 6 and 12
Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30
Thus common factor = 1, 2, 3, 6
-------------------------------------------------------------------------------------------------------------
Given numbers : 21,72 and 62
Factors of 21 = 3 and 7
Factors of 72 = 2 and 3
Factors of 62 are 2 and 31
Thus these three numbers do not have any common factor.
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help
subtracting integers
1. 9 - 13 =
2. 10 - (-20) =
3.36 - (-11) =
4.-15 - (-16) =
5.-8 - 30 =
find a rational number lying at one fourth of the way between 3/4 and 2/3 from the greater side
(with steps)
Answer:
13 / 20
Step-by-step explanation:
This question does not require an understanding of number theory.
NUMBER THEORY
A rational number is any real number that can be represented as a fraction or an integer. This group of numbers excludes imperfect squares or constants like pi.
THE MATH PART
We can use a bit of logic and algebra to do this.
(2/3) > (3/5)
This means we need to find a number relative to (2/3).
Calculate the distance between (2/3) and (3/5) by finding the least common multiple denominators. Two brackets placed together mean multiplication.The rational number is ( 13 / 20 ).
I could have probably made step 2 easier by subtracting ( 1 / 4 ) of ( 1 / 15 ) from ( 2 / 3 ).
Write and solve an equation to find the unknown side length x (in inches).
Perimeter =24.2 in.
An equation is
=24.2.
The unknown side length is
inches.
The value of side length x is equal 6.05 in
Perimeter of a SquareThe perimeter of a square is given as the sum of the total sides in the square or 4 multiplied by the side length of the square since they all have equal sides.
Mathematically, this can be written as
[tex]P = 4 *L\\P = 4l\\[/tex]
L = side lengthIn this given question, the side length is equal to x and the perimeter of the square is given as 24.2in.
Let's substitute the values
[tex]P = 4L\\24.2 = 4L\\but l = x\\24.2 = 4x\\x = 6.05in[/tex]
The side length of the square is equal to 6.05in
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complete question
Write and solve an equation to find the unknown side length x (in inches).
Perimeter =24.2 in. assuming the figure is a square
6) A new home is bought for $254,000, and home values appreciate by 1.5% each year. If you wantto sell your home in 8 years, how much will your house be worth? Round to the nearest hundredth.
Step 1:
Write the formula worth of the house after 8 years.
[tex]\begin{gathered} \text{Amount = P(1 + r)}^t \\ P\text{ = Cost price of the house} \\ r\text{ = rate} \\ t\text{ = time} \end{gathered}[/tex]Step 2: Given data
P = $254000
r = 1.5% = 0.015
t = 8 years
Step 3: Substitute the values of P, r and t.
[tex]\begin{gathered} \text{Amount = 254000 }\times(1+0.015)^8 \\ =\text{ 254000 }\times1.015^8 \\ =\text{ 254000 }\times\text{ 1.126}492587 \\ =\text{ \$286,}129.12 \end{gathered}[/tex]Step 4: Final answer
The house worth
$286,129.12
What is the total cost of a $717 tablet computer that is on sale at 12% off of the local sales tax rate is 7%? The cost of the tablet is ? (Round to two decimal places as needed)
Given: The cost of a table as
[tex]\begin{gathered} Cost=717 \\ Discount=12\% \\ Sales-tax=7\% \end{gathered}[/tex]To Determine: The cost of the tablet
Solution
Let us first determine the discount
[tex]\begin{gathered} Discount=12\%\times717 \\ =0.12\times717 \\ =86.04 \end{gathered}[/tex]Then calculate the discounted price
[tex]Discount-price=717-86.04=630.96[/tex]We would also calculate the sales tax
[tex]\begin{gathered} sales-tax=7\%\times discount-price \\ =0.07\times630.96 \\ =37.86 \end{gathered}[/tex]The total price of the tablet would be
[tex]\begin{gathered} Total-cost=discount-price+sales-tax \\ =630.96+37.86 \\ =668.82 \end{gathered}[/tex]Hence, the cost of the tablet is $668.82
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeee
thank you
Based on the graph of the function shown, we can logically deduce the following information:
A. The domain can be best described using interval notation. The domain is (-∞, ∞).
B. The range can be best described using the roster method. The range is {y | y = -∞, -3}.
How to identify the domain and range of this graph?The horizontal extent of a graph represents all domain values and they are also read and written from smaller to larger numerical values, and from the left of the graph to the right.
Similarly, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph of the continuous function shown above, we can reasonably infer and logically deduce the following information:
The domain is equal to (-∞, ∞).The range is equal to {y | y = -∞, -3}.Read more on range here: brainly.com/question/17003159
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Graph the given equation by evaluating integer values of x from −2 to 2 and plotting the resulting points.y=−2x+3
Explanation
to evaluate a function replace the x place
so
[tex]y=-2x+3[/tex]Step 1
a) when x=-2
replace
[tex]\begin{gathered} y=-2x+3 \\ y=-2(-2)+3 \\ y=4+3 \\ y=7 \\ \end{gathered}[/tex]so
[tex]P1(-2,7)[/tex]b) when x= -1
[tex]\begin{gathered} y=-2x+3 \\ y=-2(-1)+3 \\ y=2+3 \\ y=5 \\ \end{gathered}[/tex]so
[tex]P2(-1,5)[/tex]c) when x= 0
[tex]\begin{gathered} y=-2x+3 \\ y=-2(0)+3 \\ y=0+3 \\ y=3 \\ \end{gathered}[/tex]so
[tex]P3(0,3)[/tex]d)when x= 1
[tex]\begin{gathered} y=-2x+3 \\ y=-2(1)+3 \\ y=-2+3 \\ y=1 \\ \end{gathered}[/tex]so
[tex]P4(1,1)[/tex]e) when x= 2
[tex]\begin{gathered} y=-2x+3 \\ y=-2(2)+3 \\ y=-4+3 \\ y=-1 \\ \end{gathered}[/tex]so
[tex]P4(2,-1)[/tex]Step 2
now, draw a line that connects the points, so
50 points help (show ur work)
Answer all of them
Answer:
5. $40
6. 500 students
7. 60 books
8. 63 pages
Step-by-step explanation:
Question 5Given:
Aiden spent $18 on souvenirs.$18 is 45% of the money he brought on the trip.Let x be the money Aiden brought on the trip.
Create equivalent ratios with the given information and defined variable, and solve for x:
[tex]\implies 18:45\%=x:100\%[/tex]
[tex]\implies 18:0.45=x:1[/tex]
[tex]\implies \dfrac{18}{0.45}=\dfrac{x}{1}[/tex]
[tex]\implies 18=0.45x[/tex]
[tex]\implies x=\dfrac{18}{0.45}[/tex]
[tex]\implies 40[/tex]
Therefore, Aiden brought $40 on the trip.
Question 6Given:
Angel received 300 votes.300 votes was 60% of all the votes.Let x be the number of students who voted in the election.
Create equivalent ratios with the given information and defined variable, and solve for x:
[tex]\implies 300:60\%=x:100\%[/tex]
[tex]\implies 300:0.6=x:1[/tex]
[tex]\implies \dfrac{300}{0.6}=\dfrac{x}{1}[/tex]
[tex]\implies 300=0.6x[/tex]
[tex]\implies x=\dfrac{300}{0.6}[/tex]
[tex]\implies x = 500[/tex]
Therefore, there were 500 students who voted in the election.
Question 7Given:
The students sold 80% of the books.The total number of books they sold is 48.Let x be the number of books in the sale.
Create equivalent ratios with the given information and defined variable, and solve for x:
[tex]\implies 80\%:48=100\%:x[/tex]
[tex]\implies 0.8:48=1:x[/tex]
[tex]\implies \dfrac{0.8}{48}=\dfrac{1}{x}[/tex]
[tex]\implies 0.8x=48[/tex]
[tex]\implies x=\dfrac{48}{0.8}[/tex]
[tex]\implies x=60[/tex]
Therefore, there were 60 books in the book sale.
Question 8Given:
Aiyana read 147 pages of the book.She completed 70% of the book.If she has completed 70% of the book, then she still has 30% left to read, as 100% - 70% = 30%.
Let x be the number of pages Aiyana still has to read.
Create equivalent ratios with the given information and defined variable, and solve for x:
[tex]\implies 70\%:147=30\%:x[/tex]
[tex]\implies 0.7:147=0.3:x[/tex]
[tex]\implies \dfrac{0.7}{147}=\dfrac{0.3}{x}[/tex]
[tex]\implies 0.7x=44.1[/tex]
[tex]\implies x=\dfrac{44.1}{0.7}[/tex]
[tex]\implies x=63[/tex]
Therefore, Aiyana still has 63 pages left to read.
Question 13(Multiple Choice Worth 4 points)(06.04 MC)The function f(x) = 4x + 30 represents the length of a rectangle. The function g(x) = x - 1 represents the width of the rectangle. Use (f•g)(5) to determine the area of the rectangle.44650200
From the problem, the length of the rectangle is f(x) = 4x + 30 and the width is g(x) = x - 1.
To find the area, use (f · g)(5)
That will be :
[tex]\begin{gathered} (f\cdot g)(x)=(4x+30)(x-1) \\ (f\cdot g)(5)=(4\times5+30)(5-1) \\ (f\cdot g)(5)=50(4) \\ (f\cdot g)(5)=200 \end{gathered}[/tex]ANSWER :
The area is 200
An English test contains 8 short-answer questions.
If Ebony must choose 5 to answer, how many ways can she select the questions?
In 56 ways, she can select the questions.
Define combination.
Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up. A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant. The digits 0 through 9 can be put together in one of 10,000 different ways to create a four-digit code.
Given Data
An English test contains 8 short-answer questions.
If Ebony must choose 5 to answer.
h = x
r = 5
Number of ways for selecting the questions are, through combination,
ˣC₅ = [tex]\frac{x!}{r!(x-r)!}[/tex]
ˣ C ₅ = [tex]\frac{x!}{5!(x -r)!}[/tex]
ˣC₅ = [tex]\frac{x(7)(6)5!}{5!(3)}[/tex]
ˣC₅ = 56
In 56 ways, she can select the questions.
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