if angle X is an acute angle with tan X = 8/7, what is the value of sec X?
Answer: [tex]\frac{\sqrt{113}}{7}[/tex]
Step-by-step explanation:
As X is an acute angle, all 6 trigonometric functions with an argument of X are positive.
Using the identity [tex]1+\tan^{2} X=\sec^{2} X[/tex],
[tex]1+\left(\frac{8}{7} \right)^{2}=\sec^{2} X\\\\\sec^{2} X=\frac{113}{49}\\\\\therefore \sec X=\boxed{\frac{\sqrt{113}}{7}}[/tex]
If P(x) is a polynomial with lead term -x7, then
a) P(x) goes to negative infinity as x goes to negative infinity, and P(x) goes to infinity as x goes to infinity
b) P(x) goes to infinity as x goes to negative infinity, and P(x) goes to negative infinity as x goes to infinity
c) P(x) goes to negative infinity as x goes to negative infinity, and P(x) goes to negative infinity as x goes to infinity
d) P(x) goes to infinity as x goes to negative infinity, and P(x) goes to infinity as x goes to infinity
P(x) goes to infinity as x goes to negative infinity, and P(x) goes to negative infinity as x goes to infinity , Option B is the correct answer.
What is a Polynomial ?A polynomial is an expression which consists of variables , Coefficient , indeterminate and mathematical operations.
The polynomial given has lead term -x⁷
So when x --> ∞ , -x⁷---> - ∞
and when x ---> - ∞ , -x⁷ ----> ∞
Similarly for the function P(x)
So when x --> ∞ , P(x)---> - ∞
and when x ---> - ∞ , P(x) ----> ∞
P(x) goes to infinity as x goes to negative infinity, and P(x) goes to negative infinity as x goes to infinity
Therefore Option B is the correct answer.
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Find the domain and range of the function graphed below. Write your answers in interval notation.
Answer:
Domain: [tex](-\infty, \infty)[/tex]Range: [tex](-\infty, -1][/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
226,710 - 724,435 =
How to work this out without calculator
60 milllimeter equals kilograms
Answer: .00006kg
Step-by-step explanation:
What are the following expressions simplified?
(11 √40) (9 √5)
(2 √6) (10 √8)
5 √6 ÷ √7 - √5 ÷ √6
The simplified expressions are
1. 990√2
2. 80 √3
3. 30- √35 / √42
What is expression?An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
(11 √40) (9 √5)
= 11*9* √40*√5
= 99*√200
= 99* 10√2
= 990√2
(2 √6) (10 √8)
= 2*10 * √6 * √8
=20* √48
= 20* 4 √3
= 80 √3
5 √6 ÷ √7 - √5 ÷ √6
=30- √35 / √42
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What error did Lucia make?
Answer:
See below
Step-by-step explanation:
She combined 3x and - 9x incorrectly
she should have gotten - 6 x not - 12 x
what is the range of the ordered pairs shown in the graph
Answer:
D.
Step-by-step explanation:
It contains all the y-values of the points.
Answer:
Coordinates of all points
first = (-1 , 3)
second = (-2, 1 )
third = (-3 , -3)
fourth = (-4 , -5)
option 3
An object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second. The height h of the object after t seconds is given by the quadratic equation h= -16t^2 + 128t + 144. After how many seconds will the ball pass the top of the building
The time for the ball to pass the top of the building is determined as 4 s.
Time of motion of the ballThe time for the ball to pass the top of the building is obtained when the velocity of the ball is zero.
h = -16t² + 128t + 144
v = dh/dt
v = -32t + 128
at maximum height, v = 0
0 = -32t + 128
32t = 128
t = 128/32
t = 4 s
Thus, the time for the ball to pass the top of the building is determined as 4 s.
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After 8 seconds, the ball will pass the top of the building if the object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have:
An object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second.
When the ball pass the top of the building, h = 144 foot
Plug h = 144 foot in h= -16t² + 128t + 144
144 = -16t² + 128t + 144
[tex]\rm -16t^2+128t=0[/tex]
t = 0 or t = 8 seconds
At t = 0, initially, the ball was thrown upward.
At t = 8 seconds, the ball passes the top of the building
Thus, after 8 seconds, the ball will pass the top of the building if the object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second.
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A shop is opened at 7.45 am and closed at 6.30 pm on each day from Monday to Friday. Calculate the total time the shop is opened from Monday to Friday.
Answer:
53 hours and 45 minutes
Step-by-step explanation:
since they open for 10 hours and 45 minutes a day.
10*5=50 hours, 45*5=225 minutes
add the minutes and hours together and it is 53 hours and 45 minutes
Transform each graph as specified below.
(a) The graph of y= f(x) is shown. Draw the graph of y=1/2f(x).
(b) The graph of y=g(x) is shown. Draw the graph of y=g(1/2x)
Answer:
x f(x)
0 0
-2 -4
4 -2
You need to draw y = 2 f (x-1)
So you need to choose x so that x-1 = 0, -2, 4 then you can use the above values
New function
x-1 = 0, x = 1, y = 2 f (x-1) = 2 f(0) = 2 x 0 = 0
x-1 = -2 x = -1 y = 2 f (x-1) = 2 f(-2) = 2 x -4 = -8
x-1 = 4 x = 5 y = 2 f (x-1) = 2 f (4) = 2 x -2 = -4
So 3 points on the new graph are (1, 0) (-1, -8) and (5, -4)
Basically going from y = f(x) to y = f(x-a) where a is a constant positive number you translate (move) y = f(x) a units to the right.
y = f(x) to y = 2 f(x), you dilate f(x) with center (0,0) factor 2, so (a,b) > (2a, 2b)
So basically here you are doing both things.
So if (a,b) is on y = f(x) then after the translation (a,b) > (a+1, b) then after the dilation (a+1,b) > (2a+2, 2b)
Our graph for A was the same, but my B was a bit different. I hope this helps regardless. :)
&= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} S = square numbers E = even numbers Complete the Venn diagram. E S D E & = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } S = square numbers E = even numbers Complete the Venn diagram . E S D E
Answer:
E = [1,2,3,4,5,6,7,8,9,10,11,12]
S = [4,9]
E = [2,4,6,8,10,12]
The number that satisfies both conditions S and E is [4]
A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
The numbers in the Venn diagram are given,
S S∩E E
1,9 4 2, 6, 8, 10, 12
What is a Venn diagram?A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
We have,
&= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
S = square numbers
This means,
1² = 1
2² = 4
3² = 9
S = {1, 4, 9}
E = even numbers
This means,
E = {2, 4, 6, 8, 10, 12}
Now,
S ∩ E = Numbers that are even and square.
S ∩ E = {4}
Thus,
The numbers in the Venn diagram are given,
S S∩E E
1,9 4 2, 6, 8, 10, 12
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A company pays $20 per hour for up to 7 hours of work, and $30 per hour for
overtime hours (hours beyond 7). If x is the total hours worked, and more
than 7 hours have been worked, what is the expression for just the overtime
hours worked?
Answer:
Step-by-step explanation:
current total of hours work earnings (7hrs): $140
total earnings: $980 per week
49 hours work per week (no overtime)
immagine you're working another 4 hours for overtime payment everyday:
current total of hours work earnings (11hrs): $280 including 4 hours overtime ($120)
total working hours: 77 hours per week
total earnings: $1,960 per week
In Triangle XYZ, XZ = XY and m∠Y=57°. The longest side of the triangle is ______.
YZ
XZ
XY
Both XZ and XY
Answer:
I think YZ 'cause the triangle is iscoceles triangle. As the two sides XY and XZ are equal the longest side is YZ.
The accompanying frequency distribution represents the square footage of a random sample of 500 houses that are owner occupied year round. Approximate the mean and standard deviation square footage.
Savings Lower Limit Upper Limit Frequency
0-199 0 199 345
200-399 200 399 97
400-599 400 599 52
600-799 600 799 21
800-999 800 999 9
1000-1199 1000 1199 8
1200-1399 1200 1399 3
The mean and the standard deviation are 233 and 208.95 respectively.
The mean of a distribution is its average, while the standard deviation is the summary of how far each data in the dataset, is to the mean.
First, we calculate the class midpoint (x) from the given intervals.
The class midpoint is the average of the intervals. So, we have:
X1 = (0+199)/2 = 99.5
X2 = (200+399)/2 = 299.5
X3 = (400+599)/2 = 499.5
X4 = (600+799)/2 = 699.5
X5 = (800+999)/2 = 899.5
X6 = (1000+1199)/2 = 1099.5
X7 = (1200+1399)/2 = 1299.5
So, the table becomes:
X values Frequency (f)
99.5 345
299.5 97
499.5 52
699.5 21
899.5 9
1099.5 8
1299.5 3
The mean of the distribution is:
This gives:
Mean = (99.5*345)+(299.5*97)+(499.5*52)+(699.5*21)+(899.5*9)+(1099.5*8)+(1299.5*3)/(345+97+52+21+9+8+3)
Mean = 124832.5/535 = 233
Therefore, Mean = 233
The standard deviation is calculated as follows:
So, we have:
Б =
√(99.5*(345-233)²+((299.5-233)² * 97)+((499.5-233)² * 52)+((699.5-233)² * 21)+((899.5-233)² * 9)+((1099.5-233)² * 8)+((1299.5- 233)² * 3)/ (345+97+52+21+9+8+3)
Standard Deviation = √(23357155.5)/535
= √43658.23
= 208.95
Б = 208.95
Hence, the mean and the standard deviation are 233 and 208.95 respectively.
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What is the equation of a circle with center (8, 6) and radius 5?
The equation of the circle is [tex](x-8)^2 + (y-6)^2 = 25[/tex].
Derek works 43 hours at a rate of pay of $15 per hour. He receives double pay over 40 hours. What is his gross pay?
The Gross pay which Derek gets is 690 dollars.
What is Gross Pay?Gross pay is what employees earn before taxes, benefits and other payroll deductions are withheld from their wages. The amount remaining after all withholdings are accounted for is net pay or take-home pay.
Here, Total hours worked by Derek = 43 hours
Rate of pay = $15 per hour
Rate of pay beyond 40 hours = $30 per hour
Now,
Rate of pay for the first 40 hours = 40 X 15 = $ 600
Since the pay rate doubles after 40 hours,
Rate of pay for the remaining 3 hours = 3 X 30 = $ 90
Gross Pay = 600 + 90 = $ 690
Thus, the Gross pay which Derek gets is 690 dollars.
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Let E be the event where the sum of two rolled dice is greater than or equal to 7. List the outcomes in Ec.
Answer:
(1, 1) (1, 2) (1, 3) (1,4)
(1,5) (2,1) (2,2) (2,3)
(2,4) (3,1) (3,2) (3,3)
(4,1) (4,2) (5,1)
Step-by-step explanation:
An event is a specified set of results of a random experiment in probability theory. The number of possible outcomes that Event E has is 21.
What is an event?An event is a specified set of results of a random experiment in probability theory. Because the sample space is the collection of all potential outcomes of a random experiment, another definition of an event is any subset of a sample space.
Let E be the event where the sum of two rolled dice is greater than or equal to 7. Therefore, the outcomes in E are represented in red in the given table below.
(1, 6)
(2, 6)
(3, 6)
(4, 6)
(5, 6)
(6, 6)
(2, 5)
(3, 5)
(4, 5)
(5, 5)
(6, 5)
(3, 4)
(4, 4)
(5, 4)
(6, 4)
(4, 3)
(5, 3)
(6, 3)
(5, 2)
(6, 2)
(6, 1)
Hence, the number of possible outcomes that Event E has is 21.
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) The correlation between a car’s engine size and its fuel economy (in mpg) is r= -0.774. What fraction of the variability in fuel economy is accounted for by the engine size?
The fraction of the variability in fuel economy is accounted for by the engine size is 59.91%.
Given that, r= -0.774.
To solve such problems we must know about the fraction of the variability in data values or R-squared.
What fraction of the variability in fuel economy is accounted for by the engine size?The fraction by which the variance of the dependent variable is greater than the variance of the errors is known as R-squared.
It is called so because it is the square of the correlation between the dependent and independent variables, which is commonly denoted by “r” in a simple regression model.
Fraction of the variability in data values = (coefficient of correlation)²= r²
Now, the variability in fuel economy = r²= (-0.774)²
= 0.599076%= 59.91%
Hence, the fraction of the variability in fuel economy accounted for by the engine size is 59.91%.
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hi i really need help with this it is due tonight
Answer:
[tex]1)\text{ Friday}\\2)\text{ }7:00\\3a)\text{ }0\\3b)\text{ }4\\3c)\text{ }0\\4a)\text{ }6\\4b)\text{ }4\\4c)\text{ }2[/tex]
Find the principal needed now (the present value) in order to get $10,000 after 15 years, compounded
semiannually at a rate of 5%.
Answer:
10000×(1+5%)^(15×2)=43219.4238
help Which statement describes the pattern shown?
*
1 point
Captionless Image
A. Each figure has 3 fewer squares than the one before it.
B. Each figure has 6 fewer squares than the one before it.
C. Each figure has 3 more squares than the one before it.
D. Each figure has 6 more squares than the one before it.
A pattern is a recurring arrangement of numbers, forms, colours, and so on.
What is a pattern?In mathematics, a pattern is a recurring arrangement of numbers, forms, colours, and so on. The Pattern may be applied to any form of event or object. A pattern is defined as a group of integers that are connected to each other in a specified way.
As per the pattern, Each figure has 3 more squares than the one before it.
Hence, the correct option is C.
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3z^2-4z+11 -(12z^2+2z-11 find the difference . polynomials functions
Answer:
−135z
2
−2z
The 2 is representing Square
Step-by-step explanation:
(3z)
2
−4z+11−(12z)
2
+2z−11
Expand (3z)
2
.
3
2
z
2
−4z+11−(12z)
2
+2z−11
Calculate 3 to the power of 2 and get 9.
9z
2
−4z+11−(12z)
2
+2z−11
Expand (12z)
2
.
9z
2
−4z+11−12
2
z
2
+2z−11
Calculate 12 to the power of 2 and get 144.
9z
2
−4z+11−144z
2
+2z−11
Combine 9z
2
and −144z
2
to get −135z
2
.
−135z
2
−4z+11+2z−11
Combine −4z and 2z to get −2z.
−135z
2
−2z+11−11
Subtract 11 from 11 to get 0.
−135z
2
−2z
In the year 2015, New Jersey had 1,218 people per square mile. The land area of New Jersey is 7,354 square miles. What was the approximate population of New Jersey in 2015? In the year 2015 , New Jersey had 1,218 people per square mile . The land area of New Jersey is 7,354 square miles . What was the approximate population of New Jersey in 2015 ?
Answer:
8,957,172 people
Explanation:
Population = 1,218 people per square mile
Land area of New Jersey = 7,354 square miles
Total population:
people living in per square mile × total land area
1,218 × 7,354
8,957,172
factorise 4ab +6bn-2a-3n
Answer:
(2b - 1)(2a + 3n)
-----------------------------------------------
Given polynomial
4ab + 6bn - 2a - 3nFactorize it as below:
4ab + 6bn - 2a - 3n =
(4ab - 2a) + (6bn - 3n) = Regroup
2a(2b - 1) + 3n(2b - 1) = Factorize each group using common factors
(2b - 1)(2a + 3n) Factorize using common factor
Answer:
[tex](2b-1)(2a+3n)[/tex]
Step-by-step explanation:
Given expression:
[tex]4ab+6bn-2a-3n[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 2b(2a+3n)-1(2a+3n)[/tex]
Factor out the common term (2a + 3n):
[tex]\implies (2b-1)(2a+3n)[/tex]
Which measure of center is shown in a box plot?
mean
median
mode
range
Answer:
(b) median
Step-by-step explanation:
A box-plot is a graphical representation of the 5-number summary of a data set. It includes the minimum, maximum, median, and 1st and 3rd quartiles.
__
The measure of center shown in a box plot is the median.
Cai drove 189 miles in 7 hours. If he continued at the same rate, how far would he
travel in 12 hours?
Can anyone help me solve this? Please and thank you!
It's the sum of a geometric sequence.
Let's rewrite it a bit:
[tex]\displaystyle\\\sum_{n=1}^{10}8\left(\dfrac{1}{4}\right)^{n-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot \left(\dfrac{1}{4}\right)^{-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot 4=32\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n[/tex]
And now let's calculate this sum [tex]\displaystyle \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n[/tex]:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}\\\\a=\dfrac{1}{4}\\n=10\\r=\dfrac{1}{4}\\\\S_{10}=\dfrac{\dfrac{1}{4}\cdot\left(1-\left(\dfrac{1}{4}\right)^{10}\right)}{1-\dfrac{1}{4}}=\dfrac{\dfrac{1}{4}\cdot\left(1-\dfrac{1}{1048576}\right)}{\dfrac{3}{4}}=\dfrac{\dfrac{1048575}{1048576}}{3}=\dfrac{1048575}{3145728}=\\=\dfrac{349525}{1048576}[/tex]
Now let's calculate the initial sum:
[tex]\displaystyle 32\cdot \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n=32\cdot \dfrac{349525}{1048576}=\dfrac{349525}{32768}\approx10.67[/tex]
Question 6b
6b of 6
The width of a rectangle is 15 centimeters less than its length. If the area of the
rectangle is 100 square centimeters, find the length and the width using the formula
A = lw.
O Length = 25 centimeters and Width = 10 centimeters
○ Length = 20 centimeters and Width = 5 centimeters
O Length = 115 centimeters and Width = 100 centimeters
○ Length = 5 centimeters and Width = 20 centimeters
Answer:
○ Length = 20 centimeters and Width = 5 centimeters
Step-by-step explanation:
Let the length = L
Then the width is L - 15
A = lw
100 = L(L - 15)
L² - 15L - 100 = 0
(L - 20)(L + 5) = 0
L - 20 = 0 or L + 5 = 0
L = 20 or L = -5
Since a length of a rectangle cannot be negative, we discard the solution L = -5 and keep the solution L = 20.
L = 20
width = L - 15 = 20 - 15 = 5
Answer: ○ Length = 20 centimeters and Width = 5 centimeters
Brad wants to buy flowers for his friend
with $33. The daisies are $1 each and
the roses are $2 each. He buys 3 more daisies than roses.
how much did the roses cost?
Answer:
20
Step-by-step explanation:
Answer:
20$ For the Roses
Step-by-step explanation:
Think about it like this. For each daisy (1$), the price is double for roses (2$).
Brad has a limit of 33$. And he bought 3 more daisies than roses.
If each daisy is 1$, and he bought 3+ over roses, take away 3$ to get 30$. If he bought 10 (excluding 3+) Daisies, He must have bought 10 roses.
(10 Daisies = 10$) + (10 Roses = 20$) = 30$
30$ + (3 Daisies = 3$) = 33$
