Suppose y varies directly with x.When x is 7,y is 21 Write the equation that relates x and y
Answers
Given that y varies directly with x, we have:
[tex]\begin{gathered} y\propto x \\ \Rightarrow y=kx \end{gathered}[/tex]Where k is constant.
When x = 7, y = 21. From here, we can obtain the value of k
21 = 7k
k = 21/7 = 3
Since k = 3, the equation that relates x and y is:
[tex]y=3x[/tex]Related Questions
I have a few different questions :) first off I need this domain and range found
Answers
ANSWER
[tex]\begin{gathered} \text{Domain: -7 }\leq x\leq3 \\ \text{Range: }-1\text{ }\leq y\leq9 \end{gathered}[/tex]EXPLANATION
We want to find the domain and range of the function.
The domain of a function is the set of all input values of the function. Basically, the set of all x values of a function.
The range of a function is the set of all output values of the function. Basicallly, the set of all y values of a function.
To find the domain of the function, we have to look at the smallest and largest values of x.
The smallest value of x is -7.
The largest value of x is 3.
So, the domain is:
[tex]-7\text{ }\leq x\text{ }\leq3[/tex]To find the range of the function, we have to look at the smallest and largest values of y.
The smallest value of y is -1.
The largest value of y is 9.
So, the range is:
[tex]-1\text{ }\leq y\leq9[/tex]If you travel southeast from one city to another city that is 314 km away, and the trip takes you 4.00 hours, what is your average velocity?
Answers
Answer:
78.5
Step-by-step explanation:
i just know
You were using a ladder at your construction job. You started off at ground level and climbed down 10 feet to see the basement. Then you climbed up 20 feet to see the second floor. Finally, you climbed down 9 feet. What is your height relative to ground level?
Answers
Answer:
1 foot above the ground, positive 1
Step-by-step explanation:
you start at ground level let's call that 0
you go 10 down 0-10=-10
Now you climb up 20 feet so -10+20=10
Then you finally climb down 9 feet and 10-9=1
So you are one foot above the ground.
Good morning I could really use some help with this question please!!
Answers
Given:
center of the circle = (3, -2)
radius = 4
To find:
the standard form of the equation of a circle
The standard form of the equation of circle is given as:
[tex]\begin{gathered} (x\text{ - h\rparen}^2\text{ + \lparen y - k\rparen}^2\text{ = r}^2 \\ center\text{ = \lparen h, k\rparen} \end{gathered}[/tex][tex]\begin{gathered} h\text{ = 3, k = -2, r = 4} \\ \\ substitute\text{ the values into the formula:} \\ (x\text{ - 3\rparen}^2\text{ + \lparen y - \lparen-2\rparen\rparen}^2\text{ = 4}^2 \\ (x\text{ - 3\rparen}^2\text{ + \lparen y + 2\rparen}^2\text{ = 16} \end{gathered}[/tex]The equationof the circle in standard form:
[tex](x\text{ - 3\rparen}^2\text{ + \lparen y + 2\rparen}^2\text{ = 16 \lparen option B\rparen}[/tex]a group of six people has 10 pizzas to share if they divide the pizzas evenly how much does each person get
Answers
We will have that if they divide them evenly they will end up with:
[tex]\frac{10}{6}=\frac{5}{3}[/tex]So, each one will end up with option D.
5x+10+11x+2=58 please help i’m confused
Answers
5x + 10 + 11x + 2 = 58
Reorder the terms:
10 + 2 + 5x + 11x = 58
Combine like terms: 10 + 2 = 12
12 + 5x + 11x = 58
Combine like terms: 5x + 11x = 16x
12 + 16x = 58
Solving
12 + 16x = 58
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-12' to each side of the equation.
12 + -12 + 16x = 58 + -12
Combine like terms: 12 + -12 = 0
0 + 16x = 58 + -12
16x = 58 + -12
Combine like terms: 58 + -12 = 46
16x = 46
Divide each side by '16'.
x = 2.875
Simplifying
x = 2.875
Answer:
x = [tex]\frac{23}{8}[/tex] or 2 [tex]\frac{7}{8}[/tex]
Step-by-step explanation:
1. Add the numbers
10 + 2 = 12
5x+12+11x = 58
2. Combine like terms
5x + 11x = 16x
16x+12 = 58
3. Subtract 12 from both sides
16x + 12-12 = 58-12
x = [tex]\frac{23}{8}[/tex]
Redondea 5,951 a la decena más cercana
Answers
Answer:
6
Step-by-step explanation:
5.951
porque 1 no es mas o menos que 5, no vamos arriba
5.95
porque 5 es igual o mas que 5, vamos arriba
1 mas 9, es 10
pero este diez en el .9 is basicamente 1.0
entonces se combireta a uno entero
dejando nos con
6
During a sale, a store offered a 15% discount on a stereo system that originally sold for $400. After the sale the discount price of the stereo system was marked up by 15%. To the nearest whole number, what percent of the original price was the price after mark up
Answers
Problem Statement
We are told a store offers 15% discount on the sale of a stereo originally costing $400. After the sale, the new price is marked up by 15%.
We are asked to find what percentage of the original price is the new marked up price.
Method
T
You order seventeen burritos to go from a Mexican restaurant, eight with hot peppers and nine without. However, the restaurant forgot to label them. If you pick three burritos at random, find the probability of the given event.
Answers
The probability of at most two hot peppers = 0.918
Total number of burritos ordered = 17
Number of burritos with hot peppers = 8
Number of burritos without hot pepper = 9
Number of burritos picked = 3
We need to find the probability of the event that at most two have hot peppers.
At most two have hot peppers means either there is one with hot pepper or there are two with hot pepper. So there should not be 3 burritos all with hot peppers.
Thus we can rewrite the probability that at most 2 out of 3 burritos are with hot peppers as, Total probability - the probability that all 3 burritos are with hot peppers.
So the probability that all three burritos are with hot peppers = P(3 with hot peppers) = (8C3x9C0)/17C3
= 56 x 1/680
= 0.082
Then the probability that at most two burritos out of three are with hot peppers = 1 - P(3 with hot peppers)
= 1 - 0.082
= 0.918
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What is the value of z for the equation fraction 1 over 4z = −fraction 7 over 8 + fraction 1 over 8z? −3−737
Answers
-7
Explanation
Step 1
given
[tex]\frac{1}{4}z=-\frac{7}{8}+\frac{1}{8}z[/tex]subtrac (1/4)z in both sides
[tex]\begin{gathered} \frac{1}{4}z=-\frac{7}{8}+\frac{1}{8}z \\ \frac{1}{4}z-\frac{1}{4}z=-\frac{7}{8}+\frac{1}{8}z-\frac{1}{4}z \\ 0=-\frac{7}{8}-\frac{1}{8}z \end{gathered}[/tex]Step 2
add 7/8 in both sides
[tex]\begin{gathered} 0=-\frac{7}{8}-\frac{1}{8}z \\ 0+\frac{7}{8}=-\frac{7}{8}-\frac{1}{8}z+\frac{7}{8} \\ \frac{7}{8}=-\frac{1}{8}z \\ \end{gathered}[/tex]finally, multiply both sides by -8 in order to isolate z
[tex]\begin{gathered} \frac{7}{8}=-\frac{1}{8}z \\ \frac{7}{8}*-8=-\frac{1}{8}z*-8 \\ -7=z \end{gathered}[/tex]therefore, the answer is
-7
I hope this helps you
f(x)=ln(2x+1) inverse
Answers
Answer:
f−1(x)=ex+11−2ex
Step-by-step explanation:
Let y=f(x)=ln(x−1)−ln(2x+1). ⇒y=ln(x−12x+1). ⇒x−12x+1=ey. ⇒2xey+ey=x−1. ⇒x(1−2ey)=ey+1.
Given point Q equals negative 6 radical 3 comma negative 6 in rectangular coordinates, what are the corresponding polar coordinates?
Answers
Given the rectangular coordinates of point Q:
[tex]Q(-6\sqrt{3},-6)[/tex]You need to remember that the form from rectangular oordinates to polar coordinates is:
[tex](x,y)\rightarrow(r,\theta)[/tex]By definition:
[tex]\begin{gathered} r=\sqrt{x^2+y^2} \\ \\ \theta=tan^{-1}(\frac{y}{x}) \end{gathered}[/tex]In this case, you can identify that:
[tex]\begin{gathered} x=-6\sqrt{3} \\ y=-6 \end{gathered}[/tex]Then, you can determine that:
[tex]\begin{gathered} r=\sqrt{(-6\sqrt{3})^2+(-6)^2}=12 \\ \\ \theta=tan^{-1}(\frac{-6}{-6\sqrt{3}})=\frac{5\pi}{6} \end{gathered}[/tex]Therefore, the polar coordinates are:
[tex](12,\frac{5\pi}{6})[/tex]Hence, the answer is: Second option.
why do trees have wood (fre3 po1nts
Answers
Answer: The tree takes the Carbon dioxide from the air and converts it to wood.
EFG and GFH are a linear pair, mEFG = 2n +17, and mGFH = 4n +31. What are mEFG and mGFH?
Answers
mEFG and mGFH is 61 and 119 respectively.
What is linear pair of angle?
Linear pair of angle are formed when two lines intersect each other at a single point and sum of angles of linear pair is always 180.
given, mEFG = 2n+17 and mGFH = 4n+31 and they both are linear.
Hence,
mEFG+mGFH = 180
2n+17+4n+31 = 180
6n+48=180
6n = 132
n = 22
hence, mEFG = 2(22)+17= 61 and mGFH = 4(22)+31 = 119
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Question 15Please answer quickly, i don’t need much explanation and just want this to be done so I can use it as an example
Answers
SOLUTION:
Step 1:
In this question Number 15, we are given the following:
adult female Labrador Retrievers weigh an average of 65 lbs with a standard deviation of 4 lb adult female German Shepherds weigh an average of 62 pounds with a standard deviation of 3 lbs one sets teacher owns and underweight lab in an underweight German Shepherd the lab weighs 58 pounds and the German Shepherd weighs 59 pounds what is the Z score for the lab.
Answers
Labrador Retrievers weigh an average of 65 lbs with a standard deviation of 4 lb
German Shepherds weigh an average of 62 pounds with a standard deviation of 3 lbs
(1 point) Use the figure below to estimate the indicated derivatives. If a derivative does not exist, enter dne in the answer blank. The graph of f(x) is black and has a sharp corner at x=2. The graph of g(x) is blue.
Let j(x)=g(x)f(x). Find
j'(3)
Answers
Applying the quotient rule, the derivative of the given function at x = 3 is of -2/3.
What is the quotient derivative rule?A quotient function is defined as follows:
i(x) = g(x)/f(x)
Applying the quotient rule, the derivative of the function defined above is of:
i'(x) = [g'(x)f(x) - f'(x)g(x)]/f(x)².
Hence, at x = 3, the numeric value of the derivative is given as follows:
i'(3) = [g'(3)f(3) - f'(3)g(3)]/f(3)².
Function f(x) is a linear function with slope of -3/2, hence:
f'(3) = -3/2 (for a linear function, the derivative is constant).f(3) = 3/2 (from the graph).Function g(x) is a linear function with slope of -1/2, hence:
g'(3) = -1/2.g(3) = 1/2.Then the derivative is given as follows:
[tex]g^{\prime}(3) = \frac{-\frac{1}{2} \times \frac{3}{2} - \frac{3}{2} \times \frac{1}{2}}{\left(\frac{3}{2}\right)^2} = -\frac{\frac{6}{4}}{\frac{9}{4}} = -\frac{6}{9} = -\frac{2}{3}[/tex]
Hence the numeric value of the derivative at x = 3 is of -2/3.
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Jon just received a job offer that will pay him 12% more than what he makes at his current job. If the salary at the new job is 68,000. What is his current salary? Round to the nearest cent.
Answers
Let be "x" Jon's current salary.
According to the information given in the exercise, the salary at the new job is 68,000 and this is 12% more than his salary at his current job.
To convert from percent to a Decimal number, you can divide by 100. Then:
[tex]\frac{12}{100}=0.12[/tex]Therefore, knowing that information, you can set up the following equation:
[tex]x+0.12x=68,000[/tex]Now you can solve for "x" in order to find its value:
[tex]\begin{gathered} 1.12x=68,000 \\ \\ x=\frac{68,000}{1.12} \\ \\ x\approx60,714.29 \end{gathered}[/tex]The answer is:
[tex]60,714.29[/tex]Which equation represents a line that is perpendicular to the line passing through (-4,7) and (1,3)?A. y =x + 8B.y =-x + 6C.y =x - 3D. y = -x - 2
Answers
If two lines of slopes m1 and m2 are perpendicular, then:
[tex]m_1\cdot m_2=-1[/tex]The slope of a line passing through points (x1, y1) and (x2, y2) is:
[tex]\begin{equation*} m=\frac{y_2-y_1}{x_2-x_1} \end{equation*}[/tex]We are given the points of the first line (-4, 7) and (1, 3). Calculate the slope
[tex]m_1=\frac{3-7}{1+4}=-\frac{4}{5}[/tex]The slope of the perpendicular line is:
[tex]m_2=-\frac{1}{m_1}=-\frac{1}{-\frac{4}{5}}=\frac{5}{4}[/tex]The equation of the perpendicular line has the form:
[tex]y=\frac{5}{4}x+b[/tex]None of the options has the correct answer.
If a 45-gal hot water tank holds 375 lb of water, what weight of water will a 55-gal tank hold? (Round to the nearest pound.)
Answers
Given:
A 45-gal hot water tank holds 375 lb of water.
[tex]\begin{gathered} 45\text{ gal }\rightarrow375\text{ lb} \\ 55\text{ gal}\rightarrow x?\text{ lb} \end{gathered}[/tex]To find the values of x,
[tex]\begin{gathered} \frac{45}{375}=\frac{55}{x} \\ 45x=55\cdot375 \\ 45x=20625 \\ x=458.33\text{ lb} \end{gathered}[/tex]Answer: The weight of water which will hold 55 gal tank is 458 lb.
What is the value of sin^-1(0)
a= -1
b= 0
c = 1
d = pi
Answers
Answer:
B: 0
Step-by-step explanation:
At the unit circle, we can see that sin(x) = 0 for x = 0 and for x = pi
This gives us directly that sin^-1(0) = 0 or x = pi
However, the function sin^-1(x) is only defined for -pi/2 \leq 0 \geq pi/2, since otherwise it is very unclear which answer is the right one.
By this definition, we directly see that the only right aswer is 0
What is the solution to the rational inequality?
3 - x / 2x + 1 ≥ 2
( - 1/ 2 , 1 / 5)
( - ∞ ; - 1 /2)
( - 1 / 2 , 1 / 5)
( - ∞ , - 1/ 2 ) ∪ ( 1 /5 , ∞ )
Answers
The solution to the rational inequality given in this problem is as follows:
(-1/2, 1/5].
Rational inequalityThe rational inequality is defined as follows:
[tex]\frac{3 - x}{2x + 1} \geq 2[/tex]
The first step to solve the inequality is isolate 0 on the right side of the inequality, hence:
[tex]\frac{3 - x}{2x + 1} - 2 \geq 0[/tex]
Then the least common multiplied is applied to represent the left side of the inequality as a single fraction, as follows:
[tex]\frac{3 - x - 2(2x + 1)}{2x + 1}\geq 0[/tex]
[tex]\frac{3 - x - 4x - 2}{2x + 1}\geq 0[/tex]
[tex]\frac{-5x + 1}{2x + 1}\geq 0[/tex]
There are two cases for the solution to the inequality:
Case 1: numerator and denominator positive.Case 2: numerator and denominator negative.The solution is the union of the solution of each of these cases.
Case 1-5x + 1 ≥ 0
-5x ≥ -1
5x ≤ 1
x ≤ 1/5
2x + 1 > 0 (only > as the denominator cannot be zero)
2x > -1
x > -1/2
The intersection of these solutions is given by the following interval:
(-1/2, 1/5].
Case 2-5x + 1 ≤ 0
-5x ≤ -1
5x ≥ 1
x ≥ 1/5
2x + 1 < 0
2x < -1
x < -1/2.
The intersection of these two cases is empty, hence the solution to the inequality is given by the following interval:
(-1/2, 1/5].
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Kira, Justin, and Reuben have a total of $82 in their wallets. Kira has $10 more than Justin. Reuben has 2 times what Kira has. How much do they have in their wallets?
Answers
Kira have $23 in his wallet.
Justin have $13 in his wallet.
Reuben have $46 in his wallet.
Given,
There are three persons, Kira, Justin, Reuben.
The total amount in their wallet = $82
The amount in Justin's wallet = x
The amount in Kira's wallet = x + 10
The amount in Reuben's wallet = 2(x + 10)
We have to find the amount in their wallets.
Here,
x + x + 10 + 2(x + 10) = 82
2x + 10 + 2x + 20 = 82
4x + 30 = 82
4x = 82 - 30
x = 52/4 = 13
Now,
The amount in Justin's wallet = x = $13
The amount in Kira's wallet = x + 10 = 13 + 10 = $23
The amount in Reuben's wallet = 2(x + 10) = 2(13 + 10) = 2 × 23 = $46
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Is 21.23 a rational number Show evidence
Answers
Answer:
Yes, 21.23 is a rational number.
[tex]21.23=\dfrac{2123}{100}[/tex]
Step-by-step explanation:
Terminating decimal numbers are decimals that have a finite number of decimal places.
A Rational Number is the division of an integer by another integer.
Therefore, 21.23 is a terminating decimal since it has a finite number of decimal places.
Let x be the rational number.
[tex]\implies x=21.23[/tex]
Multiply both sides by 100 so that the right side is an integer:
[tex]\implies 100x=2123[/tex]
Divide both sides by 100:
[tex]\implies x=\dfrac{2123}{100}[/tex]
(This fraction cannot be reduced any further).
Therefore, we have proved that 21.23 is a rational number.
Answer:
It is a rational number.
Step-by-step explanation:
Given value,
→ 21.23
Converting into rational number,
→ (21.23/1) × (100/100)
→ (21.23 × 100)/(1 × 100)
→ 2123/100
Hence, it is a rational number.
HELP ASAP!!
Find the product of (x − 6)^2 and is the product a polynomial.
x^2 − 12x + 36; is a polynomial
x^2 − 12x + 36; may or may not be a polynomial
x^2 − 36; is a polynomial
x^2 − 36; may or may not be a polynomial
Answers
Answer: Choice A
x^2-12x+36; is a polynomial
===================================================
Explanation:
Use the rule that (A-B)^2 = A^2 - 2AB + B^2 to show (x-6)^2 = x^2-12x+36 is an identity. In this case, A = x and B = 6
You could also use the FOIL rule or the distributive property as two alternatives.
The result is a polynomial because it consists of summing or subtracting various monomials. If we had terms that had say exponents of decimal numbers or negative values, then we wouldn't have a polynomial.
Write the equation of the line (in standard form) that goes through point (5,-1) and is parallel to the equation 3x + 2y = 19.
Answers
3x+2y=10 This is the equation of the new line in standard form
Calculate the equation of the line in standard form?Two parallel lines have the same slope, to compute the slope (m) of the equation 3x+2y=19. This can be obtained by converting the equation into slope-intercept form (i.e., y=mx+b, where m is the slope):
by subtracting 3x from both sides, and then simplifying:
3x+2y-3x=19-3x
2y =-3x+19
Then, let's divide both sides by 2, to obtain slope-intercept form:
y = (-3/2)x+(/2) From this, we know that the slope (m) is -3/2
To determine the equation of the line we're being asked to solve for. If we know the slope (in this case m=-3/2) along with any given point on the line ((x0,y0); in this case (4,1)), the equation of the line can be determined as y-y0=m(x-x0)
So substituting, the equation of the line is y-1=(-3/2)(x-5)
We now need to put this into standard form, with both x and y terms on the left side of the equation:
First, distribute the 3/2 on the right side: y-1=(-3/2)x+(3/2)5 or y-1
= (-3/2)x+6
Next, add (3/2)x to both sides, add 1 to both sides, and simplify:
(3/2) x + y = 5
multiply both sides by 2, to eliminate the fraction (3/2): 3x+2y = 10 This is the equation of the new line in standard form
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What property is used to solve 9x + 5 = 21 and 9x + 5 -5 = 21 - 5
Answers
Problem
What property is used to solve 9x + 5 = 21 and 9x + 5 -5 = 21 - 5
Solution
9x +5 =21
If we subtract 5 in both sides we got:
9x +5-5 =21-5
Subtraction property of equality
Given that P(B AND A)=0.07 and P(B|A)=0.20, what is P(A)?
Answers
Answer: P A is paranthathesis add
Step-by-step explanation: so frist u do ( + ( = ((
then ((-)))=-)
Can anyone help me with this true or false question
Answers
ANSWER
A. True
EXPLANATION
Let the complex number be z = a+ ib, so its complex conjugate is z* = a - ib, where a and b are real numbers. Let's find the product,
The product is,
[tex](a+ib)(a-ib)=a\cdot a-a\operatorname{\cdot}ib+ib\operatorname{\cdot}a-ib\operatorname{\cdot}ib[/tex]Solve the products,
[tex](a+ib)(a-ib)=a^2-iab+iab-i^2b^2[/tex]Simplify: note that the second and third terms are opposites, so they cancel out. Remember that i² is equal to -1,
[tex](a+ib)(a-ib)=a^2+0-(-1)b^2=a^2+b^2[/tex]Since a and b were real numbers, then the sum of their squares is also a real number.
Hence, this statement is true.
Which experession is equivalent to 4(9+7)
Answers
Answer:
64
Step-by-step explanation:
9+7=16
16(4)=64