Answer:
Step-by-step explanation:
Comment
Begin by removing the brackets.
6+3(n-4)-8+2n
6 + 3n - 12 - 8 + 2n Collect like terms
3n + 2n + 6 - 12 - 8 Combine
5n - 14
Answer
5n - 14
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.
1.Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
Answer:
[tex]y = -\frac{2}{3}x + 490[/tex]
gradient = = [tex]-\frac{2}{3}[/tex]
y-intercept = [tex]490[/tex]
Step-by-step explanation:
• The slope-intercept form of an equation takes the general form:
[tex]\boxed{y = mx + c}[/tex],
where:
m = slope,
c = y-intercept.
• We are given the equation:
[tex]2x + 3y = 1470[/tex]
To change this into the slope-intercept form, we must make y the subject:
[tex]3y = -2x + 1470[/tex] [subtract [tex]2x[/tex] from both sides]
⇒ [tex]y = -\frac{2}{3}x + \frac{1479}{3}[/tex] [divide both sides by 3]
⇒ [tex]y = -\frac{2}{3}x + 490[/tex]
• Comparing this equation with the general form equation, we see that:
m = [tex]-\frac{2}{3}[/tex]
c = [tex]490[/tex].
This means that the gradient is [tex]\bf -\frac{2}{3}[/tex], and the y-intercept is [tex]\bf 490[/tex].
How do i solve this with the steps?
Does the graph represent a function? Why or why not?
A. No, because it fails the horizontal line test
B. Yes, because it passes the horizontal line test
C. No, because it fails the vertical line test.
•
D. Yes, because it passes the vertical line test.
Answer:
D.
Step-by-step explanation:
Yes, because it passes the vertical line test.
Under her cell phone plan, Sarah pays a flat cost of $69 per month and $4 per gigabyte. She wants to keep her bill at $83.80 per month. Write and solve an equation which can be used to determine gg, the number of gigabytes of data Sarah can use while staying within her budget.
Using a linear function, it is found that Sarah can use 3.7 gigabytes while staying within her budget.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Considering the flat cost as the y-intercept and the cost per gigabyte as the slope, the cost of using g gigabytes is:
C(g) = 4g + 69.
She wants to keep her bill at $83.80 per month, hence:
C(g) = 83.80
4g + 69 = 83.80
4g = 14.80
g = 14.80/4
g = 3.7.
Sarah can use 3.7 gigabytes while staying within her budget.
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Answer:
The other person is correct!
Step-by-step explanation:
Yes
The length of a rectangle is a inches. Its width is 5 inches less then the length. Find the area and perimeter of the rectangle
Answer:
Area = (a² -5a) in²
Perimeter = (4a -10) in
Step-by-step explanation:
Let the length of the rectangle be a.
Given that, its width is 5 in less than the length.
So,
length ⇒ a
width ⇒ (a - 5)
First, let's find the area of the rectangle.
Area = length × width
Area = a ( a - 5 )
Solve the brackets.
Area = (a² -5a) in²
Now, let us find the perimeter of the rectangle.
Perimeter = 2 ( l + w )
Perimeter = 2 ( a + a - 5 )
Perimeter = 2 ( 2a - 5 )
Perimeter = (4a -10) in
Write an equation that represents the line
Use exact. Numbers
Answer soon please
Find the smallest evan number that contains every digit once
Answer:
The smallest even number that contains every digit once is 1023456798.============================
Conditions we need to meet:
Use every digit once,Even number,Smallest possible number.To get the smallest number we'd use all 10 digits in the ascending order:
0123456789Here we can't have zero in the beginning as the number becomes 9-digit.
So swapping zero with the closest digit, 1.
Our number should be even, so we should swap 9 with one even digit.
Again it should be the closest one to 9, so it is 8.
We get the following number as a result:
1023456798To test you may swap digits, any number you get will be greater than this number.
Use the polynomial [tex]4x^{5} -3x^{2} + x[/tex]
a. How many terms are in this polynomial? _____
b. What is the degree of this polynomial? _____
c. What is the contrast? _____
(x+3)^0 Rewrite the equation with positive exponents and simplify. x≠-3.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{(x + 3)^0}[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{(x + 3)^0}[/tex]
[tex]\text{Anything raised to the 0 power it automatically equal to 1.}[/tex]
[tex]\huge\text{So, this mean that your answer should be: \boxed{\mathsf 1}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Two events, a and b, are independent of each other. p(a)= and p(a and b)=. what is p(b) written as a decimal? round to the nearest hundredth, if necessary.
if two occurrences A and B are unrelated to one another. Then, 3/4 or 0.75 is the likelihood of event B.
What is probability?The field of mathematics known as probability studies numerical descriptions of the likelihood of an event occurring or of a statement being true.. The probability of an event is a number between 0 and 1, with 0 generally signifying the event's impossibility and 1 generally signifying its certainty.
What pair of events is referred to as an independent event?These occurrences are referred to as independent events when the occurrence or non-occurrence of one event has no bearing on the occurrence or non-occurrence of any other events.
Figuratively, we have:
If we have the following, two events A and B are said to be independent.
[tex]\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B})[/tex]
Events A and B happen apart from one another. P(A) = 1/6, while P(A and B) = 1/8.
The likelihood of the event B will then be.
[tex]\begin{aligned}&\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B}) \\&\mathrm{P}(\mathrm{B})=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{A})} \\&\mathrm{P}(\mathrm{B})=\frac{1 / 8}{1 / 6} \\&\mathrm{P}(\mathrm{B})=\frac{6}{8} \\&\mathrm{P}(\mathrm{B})=\frac{3}{4}=0.75\end{aligned}[/tex]
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I understand that the question you are looking for is:
Two events, A and B, are independent of each other. P(A) = 1/6 and P(A and B) = 1/8. What is P(B) written as a decimal? Round to the nearest hundredth, if necessary.
If (a2b−3c)34a−1b4c5=apbqcr What is the value of p+2q?
Use BODMAS and algebra to arrive at the values of P = 5/2, q = -25/4 and r = -9/2.
Then substitute the values of p and q into p+2q to get -10
Identify the indicated sum for the geometric series.
S7 for 162 − 54 + 18 − 6 + .....
The indicated sum for the geometric series is 121.5
How to identify the indicated sum for the geometric series?The series is given as:
162 − 54 + 18 − 6 + .....
Start by calculating the common ratio of the geometric series.
This is calculated using
r = -54/162
Evaluate
r = -1/3
The indicated sum for the geometric series is then calculated as:
S = a(1 - r^n)/1 - r
Substitute the known values in the above equation
S = 162(1 - (-1/3)^7)/1 + 1/3
Evaluate the exponent and the sum
S = 162(1 + 1/2187)/4/3
Evaluate the sum
S = 162(2188/2187)/4/3
Express as products
S = 162 * (2188/2187)* 3/4
Evaluate the product
S = 162 * 547/729
Evaluate the product
S = 121.5
Hence, the indicated sum for the geometric series is 121.5
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What is the slope of a line that is parallel to the line whose equation is y=45x−3?
The slope is (B) -5/4.
What is a slope?The slope is the inclination of a line relative to the horizontal as a numerical value. The slope of any line, ray, or line segment in analytic geometry is the ratio of the vertical to the horizontal distance between any two points on it ("slope equals rise over run").To find the slope:
We're going to assume that we don't mean, y = 45x -3; which has a perpendicular line with a slope of -1/45.Rather, we're going to assume that we mean, y = 4/5x -3; so that the slope of the perpendicular line is -5/4.Similarly, we're going to assume that the answer choices are supposed to represent fractions so that the above slope matches choice B.If the slope of a line is m, the slope of the perpendicular line is -1/m.The reciprocal of a fraction is the fraction that has the numerator and denominator swapped, -1/(4/5) = -5/4.Therefore, the slope is (B) -5/4.
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The complete question is given below:
What is the slope of a line that is parallel to the line whose equation is y=45x−3?
A. −4/5
B. −5/4
C. 5/4
D. 4/5
Circle A has center of (2, 3) and a radius of 5, and circle B has a center of (1, 4) and a radius of 10. What steps will help show that circle A is similar to circle B? (5 points) Dilate circle A by a scale factor of 2. Translate circle A using the rule (x + 1, y − 1). Rotate circle A 180° about the center. Reflect circle A over the y-axis.
To prove the similarity between the two circles we must translate circle A by <- 1, 1> and dilate the figure by a factor of 2.
How to prove that two circles are similar
Herein we must prove that two circles are similar by taking advantage of two key characteristics: (i) Center, (ii) Radius. Based on such facts, we must apply the following rigid transformation:
Translating the circle from A to B.Enlarging the circle A by a dilation factor.Step 1 - Traslating the circle from A to B: Translation vector - (- 1, 1).
(x, y) = (2, 3) + (- 1, 1)
(x, y) = (1, 4)
Step 2 - Dilate the circle by a factor of 2.
r = 2 · 5
r = 10
To prove the similarity between the two circles we must translate circle A by <- 1, 1> and dilate the figure by a factor of 2.
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2 [{2-2(2÷2-2)} ÷2]÷2
Answer:
read below or other answer
Step-by-step explanation:
2 [{2-2(2÷2-2)} ÷2]÷2
2 [ { 2 - 2 ( 1 - 2 ) } ÷ 2 ] ÷ 2
2 [ { 2 - 2 ( - 1 ) } ÷ 2 ] ÷ 2
2 [ { 2 + 2 } ÷ 2 ] ÷ 2
2 [ 4 ÷ 2 ] ÷ 2
2 ( 2 ) ÷ 2
4 ÷ 2
2 divided by 2
Answer: 2
Step-by-step explanation:
PLS ANSWER ILL MARK U BRAINLIEST
Given the length of the two diagonals of the kite, the area of kite ABDC is 33 squared centimeters.
What is the area of kite ABDC?Formular for the area of a kite is expressed as;
A = pq/2
Where p and q are the two diagonals of the kite.
Given the data in the question;
Diagonal p = line BC = BM + MC = 3 + 3 = 6Diagonal q = line AD = AM + MDLine AM = ?Line MD = ?From the diagram, we can determine line AM and line MD using Pythagoras theorem.
c² = a² + b²
First, we find line AM
c² = a² + b²
5² = 3² + b²
25 = 9 + b²
b² = 25 - 9
b² = 16
b = √16
b = 4
Line AM = 4
Next, we determine Line MD
c² = a² + b²
(√58)² = 3² + b²
58 = 9 = b²
b² = 58 - 9
b² = 49
b = √49
b = 7
Line MD = 7
Now, we can find the area of the kite.
Diagonal p = BC = 6
Diagonal q = AD = AM + MD = 4 + 7 = 11
Area = pq/2
Area = [ 6 × 11 ]/2
Area = 66 / 2
Area = 33cm²
Given the length of the two diagonals of the kite, the area of kite ABDC is 33 squared centimeters.
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Angle Sum Theorem
y = ?
Answer:
140°
Step-by-step explanation:
The exterior angle is equal to the sum of the 2 remote interior angles. (The 2 angles farthest from the angle on the outside of the triangle)
20 + 120 = 140
Answer:
y= 140
Step-by-step explanation:
first you find x by using the sum of angles in a triangle(180-120-20). so x is 40.and then you do 180-40 ( adjustment angles on a straight line. let me know if it makes sense.
Which of the following equations is an example of inverse variation?
Since this is the result of the second function, hence equations I and II are inverse of each other.
Inverse of a function
Inverse of a function is s a function that serves to undo another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.
Given the function f(x) = 3x
Find its inverse
Replace with y with x
y = 3x
x =3y
Make y the subject of the formula
3y = x
y = x/3
Since this is the result of the second function, hence equations I and II are inverse of each other.
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Choose the best answer from the choices below: the perpendicular bisector of a chord ____.
The perpendicular bisector of a chord passes through the center of a circle.
What is a chord?In geometry, a chord is a straight line segment that connects two points on the circumference of a circle. It is the longest possible segment within the circle.
The perpendicular bisector of a chord is a line that passes through the midpoint of the chord, creating two equal halves, and is perpendicular to the chord.
Notably, for any chord in a circle, its perpendicular bisector always intersects at the center of the circle, making it a significant geometric property.
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Determine whether the series is convergent or divergent. 1 1 2 2 1 3 3 1 4 4 1 5 5 ⋯
Step-by-step explanation:
clearly divergent.
the elements of the series are getting bigger and bigger intercepted by some constant "1" (but they don't help here - after every intercepting "1" are 2 numbers that are larger by 1 than the 2 numbers before the intercepting "1", and that continues into infinity, so, the numbers will go to infinity, and that shows that the series is divergent).
c) Shin thinks of a number. She multiplies it bye 5 then subtract 7. The answer is he
same as 3 times a number plus 11. What number did shin think of?
Answer:
9
Step-by-step explanation:
let the number be y
5×y - 7 = 3×y + 11
5y-7 = 3y+11
collect like terms
5y-3y = 11+7
2y = 18
y = 18/2
y = 9
The drama club sold bags of candy and cookies to raise money for the spring show. Bags of candy cost $8.50, and bags of cookies cost $4.50, and sales equaled $79.00 in total. There were 6 more bags of cookies than candy sold.
Find the number of bags of candy and cookies sold by the drama club. Show your work.
The number of bags of candy and cookies sold by the drama club is 4 and 10 respectively
Simultaneous equationlet
number of bags of candy = xnumber of bags of cookies = yThe equation:
8.50x + 4.50y = 79
y = x + 6
Substitute x = y + x into
8.50x + 4.50y = 79
8.50x + 4.50(x + 6) = 79
8.50x + 4.50x + 27 = 79
8.50x + 4.50x = 79 - 27
13x = 52
x = 52/13
x = 4
Recall,
y = x + 6
y = 4 + 6
y = 10
Therefore, the number of bags of candy and cookies sold by the drama club is 4 and 10 respectively.
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find the ratio with step
1] 900ml and 3L
2]8cm and 8mm
3] 2kg and 750gm
4] 1m and 7cm
please help me with step by step
please immediately
Answer:
3:10
10:1
8:1
100:7
Step-by-step explanation:
900:3000
300:1000
3:10
80:8
10:1
2000:750
8:1
100:7
If you are playing a game using this spinner, what is the probability of not
landing on yellow or purple?
blue
green
yellow
orange
Your answer should be in the form of a fraction. Type it like this: 15/52.
Answer:
3/4
Step-by-step explanation:
Fraction of total area of the circle each color occupies in the spinner.
purple = 1/8
red = 1/4
orange = 1/8
yellow = 1/8
green = 1/4
blue = 1/8
Landing on yellow or purple: 1/8 + 1/8 = 1/4
Not landing on yellow or purple = 1 - 1/4 = 3/4
Let a_n be the integer obtained by writing all the integers from 1 to n from left to right. For example, a_3 = 123 and a_{11} = 1234567891011. Compute the remainder when a_44 is divided by 45.
Answer:
9
Step-by-step explanation:
The 79-digit number of interest can be formulated as a sum of shorter numbers whose remainders can be computed.
Expanded formThe expanded form of the number can be written as ...
a_44 = 01×10^78 +23×10^76 +45×10^74 +67×10^72 +89×10^70 +...
+10×10^68 +11×10^66 +... +43×10^2 +44×10^0
Powers of 10Each number except the last is multiplied by a power of 10. Powers of 10 modulo 45 are ...
10 mod 45 = 10
100 mod 45 = 10
This lets us conclude that any positive power of 10 mod 45 is 10.
Parts of the sumIn short, all of the multiplication by powers of 10 can be collapsed to a single multiplication by 10. Hence, the mod 45 value of a_44 will be ...
a_44 mod 45 = (((01 +23 +45 +67 +89) +10 +11 +12 +... +43)×10 +44) mod 45
= (((01 +23 +45 +67 +89) mod 45 + sum(10 .. 43) mod 45)×10 +44) mod 45
= (((225 mod 45) +(901 mod 45))×10 +44) mod 45
= ((0 +1)×10 +44) mod 45
Final valuea_44 mod 45 = 54 mod 45 = 9
__
Additional comment
The result can be confirmed by a suitable calculator.
__
The sum of the 34 numbers from 10 to 43 is the product of their average value (10+43)/2 = 26.5 and their number, 34. (26.5×34) = 901.
Answer: 9
Step-by-step explanation:
we can manually do this by dividing 1234567891011121314151617181920212223242526272829303132333435363738394041424344
on the calculator. I saw multiple hate comments on the answer above, and I wanted to test it manually - it still is 9.
Evaluate the integral, show all steps please!
Answer:
[tex]\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x=\dfrac{x}{9\sqrt{9-x^2}} +\text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given indefinite integral:
[tex]\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x[/tex]
Rewrite 9 as 3² and rewrite the 3/2 exponent as square root to the power of 3:
[tex]\implies \displaystyle \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x[/tex]
Integration by substitution
[tex]\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}[/tex]
[tex]\textsf{Let }x=3 \sin \theta[/tex]
[tex]\begin{aligned}\implies \sqrt{3^2-x^2} & =\sqrt{3^2-(3 \sin \theta)^2}\\ & = \sqrt{9-9 \sin^2 \theta}\\ & = \sqrt{9(1-\sin^2 \theta)}\\ & = \sqrt{9 \cos^2 \theta}\\ & = 3 \cos \theta\end{aligned}[/tex]
Find the derivative of x and rewrite it so that dx is on its own:
[tex]\implies \dfrac{\text{d}x}{\text{d}\theta}=3 \cos \theta[/tex]
[tex]\implies \text{d}x=3 \cos \theta\:\:\text{d}\theta[/tex]
Substitute everything into the original integral:
[tex]\begin{aligned}\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x & = \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x\\\\& = \int \dfrac{1}{\left(3 \cos \theta\right)^3}\:\:3 \cos \theta\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{\left(3 \cos \theta\right)^2}\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{9 \cos^2 \theta} \:\: \text{d}\theta\end{aligned}[/tex]
Take out the constant:
[tex]\implies \displaystyle \dfrac{1}{9} \int \dfrac{1}{\cos^2 \theta}\:\:\text{d}\theta[/tex]
[tex]\textsf{Use the trigonometric identity}: \quad\sec^2 \theta=\dfrac{1}{\cos^2 \theta}[/tex]
[tex]\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}[/tex]
[tex]\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta = \dfrac{1}{9} \tan \theta+\text{C}[/tex]
[tex]\textsf{Use the trigonometric identity}: \quad \tan \theta=\dfrac{\sin \theta}{\cos \theta}[/tex]
[tex]\implies \dfrac{\sin \theta}{9 \cos \theta} +\text{C}[/tex]
[tex]\textsf{Substitute back in } \sin \theta=\dfrac{x}{3}:[/tex]
[tex]\implies \dfrac{x}{9(3 \cos \theta)} +\text{C}[/tex]
[tex]\textsf{Substitute back in }3 \cos \theta=\sqrt{9-x^2}:[/tex]
[tex]\implies \dfrac{x}{9\sqrt{9-x^2}} +\text{C}[/tex]
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2/13 = 0.153846 In the decimal above, 1 is the first digit in the repeating pattern. What is the 279th digit?
Answer:
F
Step-by-step explanation:
There are 6 digits in the repeating pattern.
279 / 6 = 46.5 remainder 3.
we care about the remainder as this is how many digits in. it is the 3rd digit in so is 3.
write a solution system for the inequality 3x-2>10
Answer:
x>4
Step-by-step explanation:
3x - 2 >10 add 2 to both sides
3x > 12 Divide both sides by 3
x >4
Answer:
[tex]x > \bf 4[/tex]
Step-by-step explanation:
To find a solution to this inequality, we have to rearrange this equation to make [tex]x[/tex] its subject:
[tex]3x - 2 > 10[/tex]
⇒ [tex]3x - 2 + 2 > 10 + 2[/tex] [Add 2 to both sides]
⇒ [tex]3x > 12[/tex]
⇒ [tex]\frac{3x}{3} > \frac{12}{3}[/tex] [Divide both sides by 3]
⇒ [tex]x > \bf 4[/tex]
3. The diagram on the right shows the pattern drawn on a Cartesian plane. The final line on the plan is parallel to the y-axis and passes through x = -10. Find the sum of the length of the overall pattern.
The sum of the length of the overall pattern in the given cartesian coordinate is calculated as; 44
How to find the lengths of a cartesian?We are told that The final line on the plan is parallel to the y-axis and passes through x = -10
Now, looking at the pattern, the lengths of each side are as follows;
1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5
Thus, the sum of the length of the overall pattern is calculated as;
1.5 + 2 + 2.5 + 3 + 3.5 + 4 + 4.5 + 5 + 5.5 + 6 + 6.5 = 44
Therefore we can conclude from all the deductions and calculations above that the sum of the length of the overall pattern in the given cartesian coordinate is calculated to be; 44
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Round 219.2 to the nearest whole number
❄ Hi there,
let us revise the two rounding rules before getting down to the actual process of rounding.
[tex]\sf{Rules:}[/tex]
If the number you ought to round to is followed by a number from 0 to 4, you round down, or in other words, just drop that number.If the number you ought to round to is followed by a number that's 5 or more, you add 1 to that number.Let's see these rules in action!
The number is – [tex]219.2[/tex].
Nearest whole number – [tex]219[/tex], which is followed by a number between 0 and 4, so we just drop that number :
[tex]\sf{219.2- > > 219}[/tex]
❄