Answer:
[tex]\displaystyle x=\biggr\{\frac{\pi}{6},\frac{11\pi}{6}\biggr\}[/tex]
Step-by-step explanation:
[tex]\displaystyle 5\cos x-\sqrt{3}=3\cos x;\:0\leq x < 2\pi\\\\5-\frac{\sqrt{3}}{\cos x}=3\\ \\-\sqrt{3}\sec x=-2\\\\\sec x=\frac{2}{\sqrt{3}}\\\\\sec x=\frac{2\sqrt{3}}{3}\\ \\\cos x=\frac{3}{2\sqrt{3}}\\ \\\cos x=\frac{3\sqrt{3}}{6}\\ \\\cos x=\frac{\sqrt{3}}{2}\\\\x=\biggr\{\frac{\pi}{6},\frac{11\pi}{6}\biggr\}[/tex]
Chen is given the graph below.
What type of graph is shown, and what is the growth factor?
linear function; growth factor of 2
linear function; growth factor of 4
exponential function; growth factor of 2
exponential function; growth factor of 4
a boat is traveling east across a river that is 112 meters wide at 8 meters per second. if the river has a northwest current of 5 meters per second, what is the resultant speed of the motorboat rounded to the nearest 10?
boat speed= 8 m/s
river current= 5 m/s
to find:the resultant speed of the motorboat rounded to the nearest 10.
solution:use pythagorean theorem.
let the unknown be "x".
[tex] {a}^{2} = {b}^{2} + {c}^{2} [/tex]
[tex] {c}^{2} = \sqrt{ {a}^{2} + {b}^{2} } [/tex]
[tex]x = \sqrt{ {8}^{2} + {5}^{2} } [/tex]
[tex]x = \sqrt{64 + 25} [/tex]
[tex]x = 9.4 \: m |s[/tex]
hence, the resultant speed of the motorboat is 9.4 m/s
NEED HELP PLEASE ANSWER ASAP! (42)
Answer:
(1) (4x - 5y)(4x + 5y)
Step-by-step explanation:
Question 42
16x² - 25y²The identity to be used is : a² - b² = (a - b)(a + b)(1) (4x - 5y)(4x + 5y)Answer:
(1) (4x - 5y)(4x + 5y)
Step-by-step explanation:
Difference of Two Squares: [tex]a^2-b^2=(a-b)(a+b)[/tex]
Therefore, we can use The Difference of Two Squares to factor this expression quickly.
Given expression: [tex]16x^2-25y^2[/tex]
[tex]16=4^2 \implies 16x^2=4x \cdot 4x=(4x)^2[/tex]
[tex]25=5^2 \implies 25y^2=5y \cdot 5y=(5y)^2[/tex]
Therefore:
[tex]16x^2-25y^2=(4x)^2-(5y)^2[/tex]
Using The Difference of Two Squares:
[tex](4x)^2-(5y)^2=(4x-5y)(4x+5y)[/tex]
Carlos wrote a check for $44.92 to pay his gas bill. he’ll use the check register to record his transaction. what will be his new balance? a check register has a balance of 415 dollars and 1 cent. $345.09 $370.09 $434.93 $459.93
His new balance after the check is deducted will be $370.09
How to determine his new balance?From the question, we have the following parameters:
Initial Balance = $415.01 Check amount = $44.92The new balance is then calculated using:
New balance = Initial Balance - Check
So, we have:
New balance = 415.01 - 44.92
Evaluate
New balance = 370.09
Hence, his new balance will be $370.09
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Answer:
c
Step-by-step explanation:
A teacher assigns 10 questions for homework and wants to randomly pick 3 questions to be graded. Which of the following procedures would produce a simple random sample? 1.Assign the homework questions the numbers 1-10. Use a random number table to select the first three numbers between 1 and 10. These represent the questions that will be graded. 2.Assign the homework questions the numbers 0 to 9. Use a random number table to select the first three numbers between 0 and 9. These represent the questions that will be graded. 3.Assign the homework questions the numbers 01–10. Use a random number table to select the first three 2-digit numbers between 01 and 10. These represent the questions that will be graded.
3. Assign the homework questions the numbers 0–9. Use a random number table to select the first three unique numbers between 0 and 9. These represent the questions that will be graded.
The answer will be option D which is to Assign the homework questions the numbers 0–9. Use a random number table to select the first three unique numbers between 0 and 9.
What is randomization?
Randomization allows a sample or small groups with similar characteristics to determine a probability or to hypothesize an event, that is why this type of sample is important in an experiment, that is, to carry it out in a random way.
Given that:-
A teacher assigns 10 questions for homework and wants to randomly pick 3 questions to be graded.
Assign the homework questions the numbers 0–9. Use a random number table to select the first three unique numbers between 0 and 9. These represent the questions that will be graded.
Hence the answer will be option D which is to Assign the homework questions to the numbers 0–9. Use a random number table to select the first three unique numbers between 0 and 9.
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Which functions have a y-intercept that is greater than the y-intercept of the function g(x) = |x 3| 4? check three options. f(x) = –2 (x – 8)2 h(x) = –5 |x| 10 j(x) = –4(x 2)2 8
Using it's concept, it is found that the functions that have a greater y-intercept than g(x) = |x + 3| + 4 are given as follows:
h(x) = -5|x| + 10.k(x) = 0.25(x - 4)² + 4.m(x) = 0.25|x - 8| + 6.What is the y-intercept of a function?It is the value of the function when the input is of zero, that is, f(0).
For g(x) = |x + 3| + 4, we have that g(0) = 7. As for the other functions, we have that:
f(x) = -2(x - 8)² -> f(0) = -128.h(x) = -5|x| + 10 -> f(0) = 10 -> Greater than g(x).j(x) = -4(x + 2)² + 8 = f(0) = -8.k(x) = 0.25(x - 4)² + 4 -> f(0) = 8 -> Greater than g(x).m(x) = 0.25|x - 8| + 6 -> f(0) = 8 -> Greater than g(x).More can be learned about the y-intercept of a function at https://brainly.com/question/24737967
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PLSSS HELP ME WITH MATH
Step-by-step explanation:
always remember, equations and inequalities are like a scale with 2 pans (left and right).
a variable is like a placeholder, an empty spot on the pans. and the expressions on both sides are kind of the conditions for the things to put in these empty spots so that the status of the scale stays unchanged.
for an equation the scale has to stay balanced all the time.
and in an inequality one side is heavier that the other (it normally does not matter how much heavier) with "<" or ">" signs, or the scale can be also balanced with "<=" or ">=" signs. just the other side must never be heavier.
A
so, in our case here
2x - 5 = 3
yes, the solution (the ONLY solution, actually) is x = 4. no other value of x allows the scale to be balanced.
2x - 5 >= 3
well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = 4 is therefore a valid solution for the inequality too.
but so is every other value of x that makes the left side "heavier". what about e.g. 5 ?
2×5 - 5 >= 3
10 - 5 >= 3
5 >= 3
true, great ! so, e.g. x = 5 is also a valid solution.
what else ?
let's simplify the inequality
2x - 5 >= 3
2x >= 8
x >= 4
so, really every value of x that is greater or equal to 4 is a valid solution for the inequality.
B
-2x - 5 = 3
yes, the solution (the ONLY solution, actually) is x = -4. no other value of x allows the scale to be balanced.
-2x - 5 >= 3
well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = -4 is therefore a valid solution for the inequality too.
but so is every other value of x that makes the left side "heavier". what about e.g. -5 ?
-2×-5 - 5 >= 3
remember, -×- = +
10 - 5 >= 3
5 >= 3
true, great ! so, e.g. x = -5 is also a valid solution.
what else ?
let's simplify the inequality
-2x - 5 >= 3
-2x >= 8
x <= -4
a multiplication or division by a negative value flips the inequality sign, because such an operation makes a light weight heavy and a heavy weight light.
so, really every value of x that is less or equal to -4 is a valid solution for the inequality.
Question 3 of 10
The minimum monthly payment for Janet's credit card is 2% of her balance or
$10, whichever is higher. If Janet's balance at the end of her last billing cycle
was $760, what is her minimum monthly payment?
A. $10.00
O B. $5.20
C. $25.20
OD. $15.20
(1) the fear of genetically modified foods is not based in facts. (2) the food and drug administration holds genetically modified foods to the same standard as traditional foods, which means that these new products are equally as safe as products that are already on grocery shelves. (3) in addition, common fruits, including nectarines and seedless grapes, are a result of genetic breeding. what would be the best way of revising the second sentence for a presentation?
In order to revise the second sentence for a presentation, the best thing to do would be to break it up into two sentences.
How can we revise the second sentence?The second sentence is quite long and so would not be the best fit for a presentation.
We can solve this by breaking it into two sentences such as:
The Food and Drug Administration holds genetically modified foods to the same standard as traditional foods. This means that these new products are equally as safe as products that are already on grocery shelves.This makes the presentation more readable and ensures that the information is better passed on.
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Answer:
B - Breaking into two sentences
Step-by-step explanation:
Edge 2023
If anyone can help me with this, please feel free to answer
Pam has 15 candies in a jar, her sister threw in some more ( the ones she doesn’t like) and now Pam has 27. Write an equation to determine how many candies ( x) her sister put in the jar. Solve using both inverse operations and balance scale.
Answer:
Step-by-step explanation:
Number of candies that her sister gave = x
Total candies that Pam has now = 27
x + 15 = 27
Inverse operation:
x + 15 = 27
x + 15 - 15 = 27 - 15
x = 12
Answer:
Equations :
27 - 15 = x
15 + x = 27
Step-by-step explanation:
So, we know that 1. Pam starts with 15 candies. and 2. Pam ends up having 27 candies. This means, that she gained candy.
To figure out how many candies her sister gave, her, we have to find the difference between 27 and 15 becuase she goes from having 15 to having 27 after her sister had given some.
x will represent how many cadies Pams' sister had given her :
27 - 15 = x
12 = x
This means Pams' sister gave 12 candies to Pam. To make sure we are correct, we can simply start with how many candies Pam started with (15). And add how many we think her sister added (12)
15 + 12
15 + 12 = 27
Therefore proving, and meaning, that Pams' sister gave her 12 candies.
Possible Equations :
27 - 15 = x
End total (27) minus starting total (15).
15 + x = 27
Starting total (15) plus how many she gained (x) equal to end total (27).
What is the range of the function represented by this graph?
Answer:
The range of the function given in the graph is the values of all y for any input x.
Therefore, as shown in the graph the value of y for any input of x is below y = 1. Therefore, the range is y <= 1
see attached image.
Answer:
whats the question?
Step-by-step explanation:
Help its a math problem * please see attached images below ....The graph of f(x) is shown below on the coordinate grid. Which graph shows the transformed linear function f(x) +2?
Answer:
4th graph
Step-by-step explanation:
I believe that they are just saying f(x) and then adding 2 to each of the corrdnants to x+2 y+2
Answer:
See below ~
Step-by-step explanation:
The +2 in the equation : f(x) + 2, indicates the y-intercept of the graph lies at (0, 2). The 4th graph (attached below) is the correct answer.
Find the area of the kite or rhombus.
Answer:
126 cm^2 (please mark me brainliest)
Step-by-step explanation:
(14x16)/2+(2*14)/2=
112+14=126
Hudson was marked wrong on this problem, but why? Explain what error he made and include the correct method for solving this problem.
Help me pleaseeeeeee
Answer:
See below ~
Step-by-step explanation:
A lies between 665 and 670.
Let's answer the questions asked.
A rounded to the nearest ten
As the ones place value of A is clearly greater than 5, it will round upThe nearest ten is 670A rounded to the nearest hundred
As the tens place value of A is greater than 5, it will round upThe nearest hundred is 700Answer:
try 660
Step-by-step explanation:
because get to think it already says 670 and 680 so i believe the answer is 660
part of a line having two end points
Answer:
a line segment
Step-by-step explanation:
Answer:
A line segment is part of a line that has two endpoints and is finite in length. A ray is a line segment that extends indefinitely in one direction.
Step-by-step explanation:
hope this helps
You score an 84 on the first of two exams. Write and solve an equation to find the score x that you need on the second exam to have a mean score of 92. I got the answer -76 I need to know if that's correct.
Answer: 100
Step-by-step explanation:
▪︎ To find the mean we take the sum of the values and divide it by the number of values.
▪︎ Let x be your score on the second exam.
(84 + x) / 2 = 92
84 + x = 92*2
84 + x = 184
x = 100
20. Which formula would you use to calculate the floor space of Firm 3's structure? Explain your choice. (Refer to the Formula table on page 3.) (2 points: 1 point for the formula, 1 point for the explanation)
The formula would you use to calculate the floor space of Firm 3's structure is πr²h.
How to depict the formula?It should be noted that the formula that can be used on this scenario will be:
= πr²h
where,
h = 60
r = 70/2 = 35
The volume will be:
= πr²h
= 3.14 × 35² × 60
= 230790 feet ³
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The following spinner has four sections. There are equal sections for 1, 4, and 3. The section for 2 is twice as large as each of the other sections. 1 2 4 3
Answer:
it would be 39t for the extra 8s
Step-by-step explanation:
Find the value of x if the perimeter is 20
Answer:
x = 3Step-by-step explanation:
Find the value of x if the perimeter is 20
20 = X + 4X - 6 + X + 8
20 + 6 - 8 = 6X
18 = 6X
x = 18 : 6
x = 3
-----------------
check
20 = 3 + 3 * 4 - 6 + 3 + 8
20 = 20
the answer is good
Answer:
Value of x is 3
Step-by-step explanation:
Given perimeter of figure = 20
x + (x+8) + (4x-6) = 20
x + x + 8 + 4x - 6 = 20
6x + 2 = 20
6x = 20 - 2
6x = 18
x = 18 / 6
x = 3
What does this graph show
inverse
direct
neither
Answer:
i think the given graph is inverse
5 cm
3 cm
5 cm
8 cm
2 cm
7 cm
what is the volume of the prism? show your thinking. organize it so it can be followed by others.
8400
Step-by-step explanation:
use multiplication
I cant reveal any more things that I know
Solve this problem and get 15 points
d. 32.6°
explanation:
tan(×)= 0.6396
tan(x)= 0.6396/1000
tan(×)= 1599/2500
(×)= arctan (1599/2500)
(×)≈ 0.569029 or 32.6°
Charlie raked 23 piles of leaves. jessie raked 14 piles of leaves.
how many more piles of leaves did charlie rake than jessie?
What is more than 11 but less than 12?
Answer:
136
Step-by-step explanation:
Answer:
There are infinite numbers that fit this range, but one is 11.5
I need help me with math homework please .?
[tex]x = 5 \\ y = 4 \\ m = \frac{1}{5} [/tex]
y= mx+b
[tex]4 = ( \frac{1}{5} \times( 5) )+ b \\ 4 = 1 + b \\ 4 - 1 = b \\ 3 = b \\ y = \frac{1}{5} x + 3[/tex]
Answer:
y = 1/5x + 3
Step-by-step explanation:
Only 4 students have won the track races this year gina has won 4 times Hal has won 3 times Isabel has won 3 times and Jamal has won 4 times
Tickets for a concert are sold at a rate of 370 tickets per hour. At this rate, how long will it take to sell all the tickets for a 2100-seat auditorium?
Answer:
5 hours and 42 mins
Step-by-step explanation:
Jillian guessed at random for each question on a true-false quiz of ten questions. what is the probability that she got exactly seven questions correct?
Answer:
11/64
Step-by-step explanation:
Each question can be answered in 2 ways
∴ Total ways in which 10 questions can be answered
=2¹⁰
No. of ways of guessing at least 7 questions
out of 10
=7 questions correct +8 questions correct
+9 questions correct +10 questions correct
= ¹⁰C7(1)⁷+ ¹⁰C8(1)⁸+ ¹⁰C9(1)⁹+ ¹⁰C10(1)¹⁰
= 120 + 45 + 10 +1
=176
..Required Probability =176/2¹⁰
.. =11×16/2¹⁰
=11/64
