Solution
For this case the correct formula for the circumference of a circle is given by:
[tex]C=2\pi r=2\pi\cdot\frac{d}{2}=\pi d[/tex]Then the best option would be:
C = pi d
A line is drawn on a scatter plot, as shown below:
The line of best fit is the line which closely fits the data points.
Therefore from the look of the graph the statement which best defines the line is that it is the line of best fit because it closely fits the data points. Hence the fourth option is right.
the terminal side θ passes through the point (8,-7) what is the exact value of θ in simplified form?
Given:
the terminal side θ passes through the point (8,-7)
so,
[tex](x,y)=(8,-7)[/tex]The point lying in quarter number 4
so,
[tex]\begin{gathered} \tan \theta=\frac{y}{x}=-\frac{7}{8} \\ \\ \theta=\tan ^{-1}(-\frac{7}{8})=-41.186 \\ \\ \theta=360-41.186=318.814 \end{gathered}[/tex]
Consider the following advertisement.Which of the following calculations represents the cost of 2 dozen iris bulbs?
Answer:
C: (6 x $5)+(6 x $4)+(12 x $3)
Explanation:
The total number of bulbs bought = 2 dozens = 2 x 12 = 24
• The cost per bulb for the first half-dozen = $5
[tex]\text{Cost for the first half-dozen=6 x \$5}[/tex]• The cost per bulb for the next half-dozen = $4
[tex]\text{Cost for the next half-dozen=6 x \$}4[/tex]Out of 24 bulbs, we have calculated the cost for 12.
• The number of bulbs left = 24 - 12 = 12.
,• Each additional bulb is $3 per bulb.
The cost for the last 12 will be:
[tex]12\times\$3[/tex]Therefore, the cost for the 2 dozen iris bulbs will be:
[tex](6\times\$5)+(6\times\$4)+(12\times\$3)[/tex]The correct choice is C.
•
•
Geometry Angle of Depression and Angle of Elevation. 2. - 3.
2) We can draw this situation as:
We can now find the angle x.
We can use trigonometric ratios as:
[tex]\begin{gathered} \tan(x)=\frac{Opposite}{Adjacent}=\frac{23}{34} \\ x=\arctan(\frac{23}{34}) \\ x\approx34.08\degree \end{gathered}[/tex]3) We can draw this situation as:
We can find x as:
[tex]\begin{gathered} \tan(x)=\frac{Opposite}{Adjacent}=\frac{12}{17} \\ x=\arctan(12/17) \\ x\approx35.22\degree \end{gathered}[/tex]Answer:
2) 34.08°
3) 35.22°
Multiply 2 2/3 • 1 5/6 Simplify the answer and write as a mixed number.
Answer:18 and 1/3
Step-by-step explanation:22
3
(15)
6
=
55
3
(Decimal: 18.333333) and then as a mixed number is:
PLEASE HELP DUE IN 23 and I’ll be giving 25 points to whoever helps me.Thank you
Answer:
x = 17
Step-by-step explanation:
(6x - 20) and the angle vertically opposite (6x - 4) are same- side interior angles and sum to 180° , that is
6x - 20 + 6x - 4 = 180
12x - 24 = 180 ( add 24 to both sides )
12x = 204 ( divide both sides by 12 )
x = 17
( 5b. A square has an area of 9 cm². What is its side length?
Answer: 2.25
Step-by-step explanation:
9 divided by 4 = 2.25
4 sides on the shape
2.25 cm on one side!
Lance had 24 apps on his phone. If the ratio of educational apps to gaming apps is 5:1, how many educational apps are there?
help me with this
Which of the following products is irrational?
Answer:
B, C are irrational
Step-by-step explanation:
Not a ratio
Rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.
Answer:
The expression becomes;
[tex]\frac{3}{8}-\frac{1}{2}\cos 2x+\frac{1}{8}\cos 4x[/tex]Explanation:
Given the trigonometric expression;
[tex]\sin ^4x[/tex]Simplifying and rewriting the expression;
Recall that;
[tex]\begin{gathered} \cos 2x=1-2\sin ^2x \\ \sin ^2x=\frac{1-\cos 2x}{2} \end{gathered}[/tex]So, the expression becomes;
[tex]\begin{gathered} \sin ^4x=(\sin ^2x)(\sin ^2x) \\ =(\frac{1-\cos2x}{2})(\frac{1-\cos2x}{2}) \\ =(\frac{1-2\cos2x+\cos^22x}{4}) \\ =\frac{1}{4}-\frac{2}{4}\cos 2x+\frac{1}{4}\cos ^22x \end{gathered}[/tex]Also;
[tex]\begin{gathered} \cos 4x=2\cos ^22x-1 \\ \cos ^22x=\frac{\cos 4x+1}{2} \end{gathered}[/tex]substituting to the above expression;
[tex]\begin{gathered} =\frac{1}{4}-\frac{2}{4}\cos 2x+\frac{1}{4}(\frac{\cos4x+1}{2}) \\ =\frac{1}{4}-\frac{1}{2}\cos 2x+\frac{1}{8}\cos 4x+\frac{1}{8} \\ =\frac{1}{4}+\frac{1}{8}-\frac{1}{2}\cos 2x+\frac{1}{8}\cos 4x \\ =\frac{3}{8}-\frac{1}{2}\cos 2x+\frac{1}{8}\cos 4x \end{gathered}[/tex]Therefore, the expression becomes;
[tex]\frac{3}{8}-\frac{1}{2}\cos 2x+\frac{1}{8}\cos 4x[/tex]4)PQRS is a rectangle. The length of the diagonal PR is 10cm. If PQ = 8cm, find the perimeter of the
rectangle.
The perimeter of the rectangle PQRS would be 28 cm which is the addition of all lengths of sides.
The given rectangle PQRS that has a length of the diagonal PR is 10 cm and PQ = 8 cm
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
To determine the perimeter of the rectangle.
Since opposite sides of the rectangle and diagonal are equal.
⇒ PQ = SR = 8 cm
⇒ PR = QS = 10 cm
⇒ PS = QR = x cm (suppose)
In the rectangle, all the angles are right angles
Now in △QRS,
Using Pythagoras' theorem, we have
QS² = QR² + SR²
10² = x² + 8²
x² = 100 - 64
x =√36
x = 6 cm
So length of PS = QR = 6 cm
The perimeter of the rectangle = PQ + SR + PS + QR
The perimeter of the rectangle = 8 + 8 + 6 + 6 = 28 cm
Therefore, the perimeter of the rectangle PQRS would be 28 cm.
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6 3/4 ÷ 1 7/8=how do I figure those out?
6The given expression is 6 3/4 ÷ 1 7/8 is :
[tex]6\frac{3}{4}\div1\frac{7}{8}=\text{ }\frac{}{\square}[/tex]Express the mixed frcation in the normal forM :
[tex]\begin{gathered} 6\frac{3}{4}=\frac{6\times4+3}{4} \\ 6\frac{3}{4}=\frac{27}{4} \end{gathered}[/tex]Similarly with the 1 7/8
[tex]\begin{gathered} 1\frac{7}{8}=\frac{1\times8+7}{8} \\ 1\frac{7}{8}=\frac{15}{8} \end{gathered}[/tex]Substitute the value and simplify :
[tex]\begin{gathered} 6\frac{3}{4}\div1\frac{7}{8}=\frac{27}{4}\div\frac{15}{8} \\ 6\frac{3}{4}\div1\frac{7}{8}=\frac{27}{4}\times\frac{8}{15} \\ 6\frac{3}{4}\div1\frac{7}{8}=\frac{9}{1}\times\frac{2}{5} \\ 6\frac{3}{4}\div1\frac{7}{8}=\frac{18}{5} \end{gathered}[/tex]18/5 in the mixed fraction :
18/5 = 3 3/5
Answer : 6 3/4 ÷ 1 7/8 = 18/5 or 3 3/5
Question 13 of 50
A function is when each domain has only one range.
False
True
Answer:true
Step-by-step explanation:It’s on khan
Answer:
True
Step-by-step explanation:
A function is when each element of the domain has only one corresponding element in the range.
True
Determine which of the following points is a solution to the inequality 3x + 9y < 18 i (2, 2) ii. (-3,-4) iii. (0.2)
Given the inequality:
[tex]3x+9y<18[/tex]to find which point is a solution to the inequality, there are 2 methods to solve :
by graphing or by substitution by the point in the given inequality
Solving by substitution :
1) point (2 , 2)
so,
[tex]3\cdot2+9\cdot2=24>18[/tex]So, this point is not a solution
2) Point (-3 , -4)
[tex]3\cdot-3+9\cdot-4=-45<18[/tex]This point is a solution
3) Point (0 , 2)
[tex]3\cdot0+9\cdot2=18[/tex]So, this point is not a solution
Another sol
Which decimal equivalent is NOT correct for the given set of numbers
EXPLANATION
Since the value 7/10 is equivalent to 0.7, not to 0.07, the last equivalence is NOT correct.
What makes the value of X that makes l1 l2?
A. 10
Explanation:From the figure provided:
<(4x)⁰ and <(2x+20)⁰ are alternate interior angles
Note that:
Alternate interior angles are equal
4x = 2x + 20
Collect like terms
4x - 2x = 20
2x = 20
x = 20/2
x = 10
find the value of x using the kite below (work required)
Since the diagonals in a kite intersect creating a right angle, the angles 2x° and (10x - 6)° are complementary angles. So we have:
[tex]\begin{gathered} 2x+(10x-6)=90 \\ 12x-6=90 \\ 12x=96 \\ x=\frac{96}{12} \\ x=8 \end{gathered}[/tex]So the value of x is 8.
Classify the equation 6x + 4x - 1 = 2(5x + 4) as having one solution, infinitely many solutions, or no solution. Enter integers or expressions to complete the solution. (Simplify your answers.) Since - 1 = 8, the equation has no solution(s).
Solve;
[tex]\begin{gathered} 6x+4x-1=2(5x+4) \\ \text{Solve the parenthesis,} \\ 10x-1=10x+8 \\ \text{Collect all like terms} \\ 10x-10x=8+1 \\ 0=9 \\ \text{This equation has no solution because 0=9 is not possible} \end{gathered}[/tex]The answer is
No solution
Unit Rates can also be used to solve problems....hello I'm a 7th grader can u please help me with my math summer package and explain it in a way that a 7th grader can understand
10)
Given:
The cost of 8 ounces of shampoo is $0.89.
The cost of 12 ounces of shampoo is $1.47.
Required:
We need to find a better deal.
Explanation:
Consider the first deal.
The cost of 8 ounces of shampoo is $0.89.
Divide the cost of 0.89 by 8 to find the cost for one ounce.
[tex]The\text{ cost of shampoo for one ounce=}\frac{0.89}{8}[/tex][tex]The\text{ cost of shampoo for one ounce=\$}0.11125[/tex]Consider the second deal.
The cost of 12 ounces of shampoo is $1.47.
Divide the cost of 1.47 by 12 to find the cost for one ounce.
[tex]The\text{ cost of shampoo for one ounce=}\frac{1.47}{12}[/tex][tex]The\text{ cost of shampoo for one ounce=}0.1225[/tex]We know that $0.11125 is less than $0.1225.
The first deal is better than the second deal.
Final answer:
The best deal is,
The cost of 8 ounces of shampoo is $0.89.
The equation below describes a circle. What are the coordinates of the centerof the circle?(x-4)^2 + (y+12)^2 = 17²O A. (4,12)OB. (-4,-12)O C. (-4,12)OD. (4, -12)21
Solution:
The equation is given below as
[tex](x-4)^2+(y+12)^2=17^2[/tex]Concept:
The general equation of a circle is given below as
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ where, \\ (h,k)=center \end{gathered}[/tex]Hence,
By comparing coefficients, we will have the center of the circle be
[tex](h,k)\Rightarrow(4,-12)[/tex]Hence,
The final answer is
[tex]\Rightarrow(4,-12)[/tex]OPTION D is the right answer
The table below shows a probability density function for a discrete random variable X. What is the probability that X is 2 or 3?
Answer:
Step-by-step explanation:
a ____ polynomial is a polynomial with a degree of 3
Let's understand some definitions first:
Polynomial - an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). (oxford languages)
When we have 1 term, we call it a monomial.
When we have 2 terms, we call it a binomial.
When we have 3 terms, we call it a trinomial.
Now,
• When the power of a variable is 1, we call it a line:
[tex]\begin{gathered} x \\ 2x \\ \text{etc.} \end{gathered}[/tex]• When the highest power is 2, we call it a quadratic polynomial:
[tex]\begin{gathered} x^2 \\ 3x^2 \end{gathered}[/tex]• When the highest power is 3, we call it a cubic polynomial:
[tex]\begin{gathered} x^3 \\ -2x^3 \end{gathered}[/tex]Question
A ____ polynomial is a polynomial with a degree of 3
Answer
A cubic polynomial is a polynomial with a degree of 3
The value of a house increased by 6%.
The house then had a value of £265 000
Work out the value of the house before the increase
In a case whereby value of a house increased by 6% and the house then had a value of £265, the value of the house before the increase is £250000.
How can the value of the house before the increase be calculated?To calculate the value of the house before the increase then the formular below can be used in making the calculation:
V = [V₀(1+r)]
where
V = the final price
V₀ = initial price
r = the rate.
V = £265,000
r = 6%,
V₀ = unknown?
Then since we know the variables now, we can substitutes the values into the above equation so that we can simplify the expression as :
we can rearrange the formular by making the unknown the subject of the formula as :
V₀ = [V/(1+r)]
= [265000/(1 + 6%)]
= [265000/(1 + 6/100)[]
= 265000/(106/100)
then the final expression will now be
V₀ = [265000*100/106 ]
= £250000
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What is 1875 divided by 41
The value when 1875 is divided by 41 is 45.73.
What is division?
Division is the opposite of multiplication. If 3 groups of 4 make 12 in multiplication, 12 divided into 3 equal groups give 4 in each group in division.
Given,
1875 ÷ 41
= 45.73
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Two friends drive off in different directions from the same place. one heads north at 25 miles per hour, while the other heads east at 40 miles per hour. complete an equation for the distance between the friends after t hours.
Answer: [tex]5t\sqrt{89}[/tex] miles
=======================================================
Explanation:
Draw a right triangle. The legs of this triangle represent the directions the two friends travel (one going east, the other going north).
The horizontal leg has side length 40t and the vertical leg has length 25t, where t is the number of hours.
I'm using the idea that distance = rate*time.
We'll use the pythagorean theorem to find the hypotenuse in terms of t.
[tex]a = 40t, \ b = 25t\\\\a^2 + b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{(40t)^2+(25t)^2}\\\\c = \sqrt{1600t^2+625t^2}\\\\c = \sqrt{2225t^2}\\\\c = \sqrt{25*89t^2}\\\\c = \sqrt{25t^2}*\sqrt{89}\\\\c = 5t\sqrt{89}\\\\[/tex]
At time t hours, the distance between the two friends is exactly [tex]5t\sqrt{89}[/tex] miles.
Identify the slope and y-intercept of equation y= 3x-10
To answer this question, we need to remember that the slope-intercept form of the line is given by:
[tex]y=mx+b[/tex]Where
• m is the slope of line
,• b is the y-intercept of the line, that is, the point where the line passes through the y-axis. At this point, x = 0.
Since we can see that the given equation is in slope-intercept form:
[tex]y=3x-10[/tex]We can see that the slope of the line is:
[tex]m=3[/tex]And the y-intercept is:
[tex]\begin{gathered} b=-10 \\ (0,-10) \end{gathered}[/tex]In summary, we have that
• The slope of the line is m = 3.
,• The y-intercept of the line is (0, -10)
My family has 12 member coming for Christmas dinner. Each person eats an average of 4 lbs of food. How much food should I prepare?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Family
12 members
4 lb food per person
total food = ?
Step 02:
total food
[tex]\begin{gathered} \text{total food = 12 people}\cdot\frac{4lb}{\text{person}} \\ \end{gathered}[/tex]total food = 48 lb
The answer is:
You should prepare 48 lb of food
Evaluate the following expression when m = 7. Enter your answer as a simplified fraction in the form a/b. (m/3)^2 = ___
Evaluating m = 7:
[tex](\frac{m}{3})^2=(\frac{7}{3})^2[/tex]Answer:
[tex]\frac{49}{9}[/tex]Plot points between and beyond the Exitir serves in the vertical asymptote evaluate the function at -5, -2,2,5 and 6 Simplify
Step 1: Write out the definition of the function f:
The function f is given by:
[tex]f(x)=\frac{x^2-9}{x}[/tex]Step 2: Calculate the value of the function f at t=-5:
[tex]\begin{gathered} f(-5)=\frac{(-5)^2-9}{(-5)} \\ \text{Hence,} \\ f(-5)=\frac{25-9}{-5}=-\frac{16}{5} \end{gathered}[/tex]Step 3: Calculate the value of the function f at t=-2:
[tex]\begin{gathered} f(-2)=\frac{(-2)^2-9}{(-2)} \\ \text{Hence,} \\ f(-2)=\frac{4-9}{-2}=\frac{-5}{-2}=\frac{5}{2} \end{gathered}[/tex]Step 4: Calculate the value of the function f at t=2:
[tex]\begin{gathered} f(2)=\frac{(2)^2-9}{(2)} \\ \text{Hence,} \\ f(2)=\frac{4-9}{2}=-\frac{5}{2} \end{gathered}[/tex]Step 5: Calculate the value of the function f at t=5:
[tex]\begin{gathered} f(5)=\frac{(5)^2-9}{(5)} \\ \text{Hence,} \\ f(5)=\frac{25-9}{5}=\frac{16}{5} \end{gathered}[/tex]Step 6: Calculate the value of the function f at t=6:
[tex]\begin{gathered} f(6)=\frac{(6)^2-9}{(6)} \\ \text{Hence,} \\ f(6)=\frac{36-9}{6}=\frac{27}{6}=\frac{9}{2} \end{gathered}[/tex]Hence
HELP HELP PLEASE!!!!!!!!!!!!!!!!!!!!
There are 5.65 milliliters of water in a jar. Tess wants only 3.85 milliliters of water in the jar. She calculates that she should remove 1.8 milliliters of water. Which statement shows whether Tess is correct? (1 point)
She is correct. 5.65 + 1.8 = 3.85.
She is correct. 3.85 + 1.8 = 5.65.
She is incorrect. 5.65 + 1.8 = 7.45.
She is incorrect. 3.85 + 1.8 = 4.65.
Answer:
She is incorrect
Step-by-step explanation:
5.65 + 1.8 = 7.45
Answer:
She is correct. 3.85 + 1.8 = 5.65
Step-by-step explanation:
She is correct. 3.85 + 1.8 = 5.65
