Find the value of 9y+1 given that -2y-1=5.Simplify your answer as much as possible.
Answers
Answer
The value of 9y + 1 is -26
Explanation:
Given the below equation
-2y - 1 = 5
Step 1: find y
To find y, firstly collect the like terms
-2y = 5 + 1
-2y = 6
Divide both sides by -2
-2y / -2 = 6/-2
y = -3
Given 9y + 1
Substitute the value of y = -3
9(-3) + 1
= -27 + 1
= - 26
Therefore, the value of 9y + 1 is -26
Related Questions
=Given that f(x) = -22 +1 and g(x) =(f +9) (0)2find:2+1'7O 3O 2O undefined, you can't put a 0 in the denominatorO-3
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f(x) = -x^2 +1
g(x) = 2 / (x+1)
Find (f+g) (0)
We can find f(0) + g(0)
f(0) = -0^2 +1 = 1
g(0) = 2/(0+1) = 2/1 = 2
f(0) + g(0) = 1+2 = 3
8x^2+36x+30=10-x^2Round your answer to the nearest hundreth or write them as a fraction
Answers
Solve for x:
[tex]\begin{gathered} 8x^2+36x+30+x^2-10=0 \\ 9x^2+36x+20=0 \end{gathered}[/tex]Factor:
[tex]\begin{gathered} 9x^2+36x+20=(3x+2)(3x+10) \\ so\colon \\ (3x+2)(3x+10)=0 \end{gathered}[/tex]Split into 2 equations:
[tex]\begin{gathered} 3x+2=0_{\text{ }}(1) \\ 3x+10=0_{\text{ }}(2) \end{gathered}[/tex]For (1):
[tex]\begin{gathered} 3x=-2 \\ x=-\frac{2}{3} \end{gathered}[/tex]For (2):
[tex]\begin{gathered} 3x=-10 \\ x=-\frac{10}{3} \end{gathered}[/tex]Answer:
As a fractions:
[tex]\begin{gathered} x=-\frac{2}{3} \\ or \\ x=-\frac{10}{3} \end{gathered}[/tex]As a decimals:
[tex]\begin{gathered} x\approx-0.67 \\ or \\ x\approx-3.33 \end{gathered}[/tex]Use the given information to solve right triangle ABC for all missing parts. Find all parts missing A=31.5°, a =8 1/4 in.
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We know two angles and one side of a right triangle. We can find the missing angle as shown below (knowing that the sum of the inner angles of a triangle is equal to 180°)
[tex]\begin{gathered} 180=A+B+C=31.5+B+90 \\ \Rightarrow B=58.5 \end{gathered}[/tex]Finally, we can use the following two trigonometric identities to find the lengths of the missing sides.
[tex]\begin{gathered} \sin A=\frac{a}{c},\tan A=\frac{a}{b} \\ \Rightarrow c=\frac{a}{\sin A},b=\frac{a}{\tan A} \\ \end{gathered}[/tex]Thus,
[tex]\Rightarrow c=15.79,b=\text{13}.46[/tex]The answer are B=58.5°, b=13.46in, c=15.79in
A boxplot for a set of 68 scores is given below.How many scores are represented in the blue section of the boxplot?
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Remember that the line inside the box represents the median of the data set; thus, 50 percent of the data set is to the left, and the remaining part of the data set is to the right of that line.
On the other hand, the right side of the box represents the upper quartile and marks 75% of the data.
Thus, between the upper quartile and the median, we can find 75%-50%=25% of the data.
Therefore, since the data set consists of 68 scores, the answer is
[tex]68\cdot0.25=17[/tex]The answer is 17 scores
A baseball player gets 7 hits every 8 times. If this player comes up to bar 32 times in an entire series find how many he would be expected to get
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Given:
A baseball player gets 7 hits every 8 times.
So, the probability of the event is,
[tex]P=\frac{7}{8}[/tex]Probability of not getting the hits is,
[tex]1-P=1-\frac{7}{8}=\frac{1}{8}[/tex]If this player comes up to bar 32 times in an entire series.
As player hits 7 times in 8. So, it will form 4 set of 8 .
That means in a total of 32 he gets 4 chances.
Therefore,
[tex]7\times4=28[/tex]Answer: the player would have 28 hits.
Rewrite the equation in terms of base E express the answer in terms of natural logarithm
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The given equation is:
[tex]y=4.1(0.8)^x[/tex]The base of the equation is 0.8:
[tex]\begin{gathered} 0.8=0.8\ln e \\ =\ln e^{0.8} \end{gathered}[/tex]Therefore,
[tex]y=4.1(0.8)^x[/tex]
find the constant proportionalityy= X/6
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The function:
y = x/6
has the form:
y = kx
where k is the constant of proportionality
[tex]\begin{gathered} y=\frac{x}{6} \\ y=\frac{1}{6}x \end{gathered}[/tex]Then, the constant of proportionality is 1/6
what is the unit rate or price per oz. of chips at ingles
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$1.98 ------------------>5oz
$x----------------------->1oz
Using cross multiplication:
[tex]\begin{gathered} \frac{1.98}{x}=\frac{5}{1} \\ solve_{\text{ }}for_{\text{ }}x\colon \\ x=\frac{1.98}{5}=0.396 \end{gathered}[/tex]Suppose that the functions and s are defined for all real numbers x as follows. r(x) = 3x ^ 3; s(x) = x ^ 2 Write the expressions for (s*varphi)(x) and (s + r)(x) and evaluate (s - r)(- 2) .
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Solution
[tex]\begin{gathered} r(x)=3x^3 \\ s(x)=x^2 \\ (s.r)(x)=3x^3\times x^2 \\ =3x^5 \end{gathered}[/tex][tex](s+r)(x)=3x^3+x^2[/tex][tex]\begin{gathered} (s-r)(x)=x^2-3x^3 \\ (s-r)(-2)=(-2)^2-3(-2)^3 \\ =4-3(-8) \\ =4+24 \\ =28 \end{gathered}[/tex]THE CORNER POINTS OF THE SHADED REGION IN A LINEAR PROGRAMING PROBLEM ARE (7,0) (9,-1) (9,5) (8,6) AND (0,6) IF THE COST FUNCTION WAS GIVEN BY C=3X+Y WHAT WILL THE MINIMUM COST BE?
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Given:
The shaded region are (7,0) (9,-1) (9,5) (8,6), and (0,6).
The cost function is
[tex]C=3x+y[/tex]Required:
We need to find the minimum cost.
Explanation:
Consider the point (7,0).
Substitute x =7 and y=0 in the given function.
[tex]C=3(7)+0=21[/tex]Consider the point (9,-1).
Substitute x =9 and y=-1 in the given function.
[tex]C=3(9)+(-1)=27-1=26[/tex]Consider the point (9,5).
Substitute x =9 and y=5 in the given function.
[tex]C=3(9)+5=27+5=32[/tex]Consider the point (8,6).
Substitute x =8 and y=6 in the given function.
[tex]C=3(8)+6=24+6=30[/tex]Consider the point (0.6).
Substitute x =0 and y=6 in the given function.
[tex]C=3(0)+6=6[/tex]We know that the lowest value of 21, 26, 32, 30, and 6 is 6.
The minimum cost will be 6.
Final answer:
The minimum cost will be 6.
Try once more Booker's father sells computer software and earns a 4.25% commission on every software package he sells. How much commission would he eam on a software package that sold for $15.725? Round to the nearest cent
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He will earn the following amount:
[tex]x=(15.725)(0.0425)\Rightarrow x=0.6683125\Rightarrow x\approx0.67[/tex]So, he will earn a commission of approximately $0.67.
***Explanation***
*Since we are given that he will earn the 4.25% commission for each sale and he sold $15.725 we will operate as follows:
*The $15.725 will represent 100% of the price of the sale, and we will want to find what is 4.25% of that:
*We then multiply the total cost of the sale ($15.725) times the percentage we want to obtain (4-25%) and divide that by the percentage that the whole sale represents (100%), that is:
[tex]x=\frac{15.725\cdot4.25}{100}\Rightarrow x=15.725\cdot(0.0425)\Rightarrow x=0.6683125[/tex]So, we round to the nearest cent:
[tex]\Rightarrow x\approx0.67[/tex]So, the commission that he will earn for the $15.725 sale is approximately $0.67.
If the measure of angle GAT equals 30° in GT equal 60 cm, find GA & AT.
Answers
As a result of crossing the rectangle from one vertex to the opposite vertex we get a right triangle, like this:
With right triangles, we can use the trigonometric ratios:
[tex]\begin{gathered} \sin \theta=\frac{oc}{h} \\ \cos \theta=\frac{ac}{h} \end{gathered}[/tex]Where h is the length of the hypotenuse of the triangle, oc is the opposite leg and ac is the adjacent leg.
By taking θ as the angle whose measure equals 30°, we get:
[tex]\begin{gathered} \sin \theta=\frac{GT}{GA} \\ \cos \theta=\frac{AT}{GA} \end{gathered}[/tex]From the sine function, we can replace 30° for θ and 60 for GT, then solving for GA, we get:
[tex]\begin{gathered} \sin 30=\frac{60}{GA} \\ \sin 30\times GA=\frac{60}{GA}\times GA \\ \sin 30\times GA=60\times\frac{GA}{GA} \\ \sin 30\times GA=60\times1 \\ \sin 30\times GA=60 \\ \frac{\sin30}{\sin30}\times GA=\frac{60}{\sin30} \\ 1\times GA=\frac{60}{\sin30} \\ GA=\frac{60}{\sin30} \\ GA=120 \end{gathered}[/tex]Then, GA equals 120 cm.
Similarly, by means of the trigonometric function cosine, we get:
[tex]\begin{gathered} \cos 30=\frac{AT}{120} \\ \cos 30\times120=\frac{AT}{120}\times120 \\ \cos 30\times120=AT\times\frac{120}{120} \\ \cos 30\times120=AT\times1 \\ AT=\cos 30\times120 \\ AT=60\sqrt[]{3} \end{gathered}[/tex]Then the side AT has a length of 60√3 cm (about 104 cm)
Karl has six pairs of pants, seven shirts and four pairs of shoes. How many different combination outfits can Karl create?
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To find the total number of combinations, we just have to use the basic counting principle which indicates that we have to multiply
[tex]C=6\times7\times4=168[/tex]Hence, there are 168 possible combinations.Solve for (xy,z), if there is a solution for the given system of equations:-4x + 2v + 2 = 1X -y + 32 =-53x + y - 4z = 10
Answers
Adding the second and the third equations we get:
[tex]\begin{gathered} 3x+y-4z+x-y+3z=10-5, \\ 4x-z=5. \end{gathered}[/tex]Now, adding the first and two times the second equation we get:
[tex]\begin{gathered} -4x+2y+z+2x-2y+6z=1-10, \\ -2x+7z=-9. \end{gathered}[/tex]Then, we have the following system of equations:
[tex]\begin{gathered} 4x-z=5, \\ -2x+7z=-9. \end{gathered}[/tex]Adding the first equation to two times the second equation, and solving for z we get:
[tex]\begin{gathered} 4x-z-4x+14z=5-18, \\ 13z=-13, \\ z=-\frac{13}{13}, \\ z=-1. \end{gathered}[/tex]Substituting z=-1 in the first equation of the second system and solving for x we get:
[tex]\begin{gathered} 4x-(-1)=5, \\ 4x=5-1, \\ 4x=4, \\ x=1. \end{gathered}[/tex]Finally, substituting x=1, z=-1, and solving for y in the first equation of the first system we get:
[tex]\begin{gathered} -4(1)+2y+(-1)=1, \\ -4+2y-1=1, \\ 2y=6, \\ y=\frac{6}{2}, \\ y=3. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} x=1, \\ y=3,\text{ } \\ z=-1. \end{gathered}[/tex]I need help with this math problem question number 2 please
Answers
The first question is true because a one-to-one function always has a different value in y.
For the second you need to find the inverse function to conclude that the function that they give you is correct. So
The first step is to replace the x with y and the y with x:
[tex]y=4x+3[/tex][tex]x=4y+3[/tex][tex]4y=x-3[/tex][tex]y=\frac{x-3}{4}[/tex]We find the same function as g(x). So the question is true.
For question 3, to discard a slant asymptote subtract the grade of the denominator from the numerator, if it is one we have a slant asymptote, else we don't have a slant asymptote:
[tex]2-2=0[/tex]We don't have slant asymptote, now find the vertical asymptotes
Equal the denominator to 0 and solve:
[tex]9x^2-6=0[/tex][tex]9x^2=6[/tex][tex]x^2=\frac{6}{9}[/tex][tex]x^2=\frac{2}{3}[/tex][tex]x=\sqrt{\frac{2}{3}},-\sqrt{\frac{2}{3}}[/tex]We have vertical asymptotes in these 2 values of x
Finally for horizontal asymptotes:
Find the limit of the function when x tends to infinity:
[tex]\lim _{x\to \infty }\left(\frac{-5x+2x^2}{9x^2-6}\right)[/tex]Divide for the denominator with the greatest potency:
[tex]\lim _{x\to \infty \:}\left(\frac{-\frac{5}{x}+2}{9-\frac{6}{x^2}}\right)[/tex]Separate terms
[tex]\frac{\lim _{x\to \infty \:}\left(-\frac{5}{x}+2\right)}{\lim _{x\to \infty \:}\left(9-\frac{6}{x^2}\right)}[/tex]Solve each one:
[tex]\lim_{x\to\infty\:}\left(-\frac{5}{x}+2\right)=-\lim_{x\to\infty\:}\left(\frac{5}{x}\right)+\lim_{x\to\infty\:}\left(2\right)=0+2=2[/tex][tex]\lim_{x\to\infty\:}\left(9-\frac{6}{x^2}\right)=\lim_{x\to\infty\:}\left(9\right)-\lim_{x\to\infty\:}\left(\frac{6}{x^2}\right)=9-0=9[/tex]Replace:
[tex]\frac{\operatorname{\lim}_{x\to\infty}(-\frac{5}{x}+2)}{\operatorname{\lim}_{x\to\infty}(9-\frac{6}{x^{2}})}=\frac{2}{9}[/tex]So have a horizontal asymptote in 2/9
Evan is picking marbles out of a bag. The results are recorded below. Red 24 Blue 16Yellow 10 Green 22Black 8 What is the experimental probability of picking a black marble? A. 90% B. 10% C. 1%
Answers
Answer:
Choice B: 10%.
Explanation:
The experimental probability of an event is the probability determined from the results of the experiment.
Now, in our case the experimental probability of picking a black marble would be the number of black marbles picked divided by the total number of marbles:
Experimental probability =( # black marbles / # total marbles ) x 100%
Now,
# total marbles = 24 + 16 + 10 + 22 + 8 = 80 marbles
and
# black marbles = 8 black marbles
Therefore,
Experimental probability =( 8 / 10 ) X 100%
Experimental probability = 10%
Hence, the correct choice is B.
Round each number to the nearest ten, hundred and thousand:6,999
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ANSWER
[tex]\begin{gathered} Tens:7,000 \\ \\ Hundreds:7,000 \\ \\ Thousands:7,000 \end{gathered}[/tex]EXPLANATION
We want to round the given number to the nearest ten, hundred, and thousand.
To round a number to any given place, if the number in the place value after the given place is greater than or equal to 5, round up but if the number is less than 5, round down.
To round the number to the nearest ten, apply the rule above to the number in the units place value:
[tex]6,999\approx7,000[/tex]To round the number to the nearest hundred, apply the rule to the number in the tens place value:
[tex]6,999\approx7,000[/tex]To round the number to the nearest thousand, apply the rule to the number in the hundreds place value:
[tex]6,999\approx7,000[/tex]That is the answer.
What is that rounded to the nearest tenth as a decimal
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Let (c) t be the number of customers In any restaurant t hours after 8 AM . Explain the meaning of each statement.c(n)=29
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Let t = n
c(n) = 29 means that after n hours after 8AM, the number of customers in a restaurant is 29.
A fraction whose _____ and ______ are integers, is considered a rational number.
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A fraction whose numerators and denominators are integers, is considered a rational number.
A rational number is a number in the form
[tex]\begin{gathered} \frac{a}{b},b\neq0 \\ \text{where a and b are integers.} \end{gathered}[/tex]on rectangle DEFG, it D is located at (-1 -1) and F is located at (4 -8), what is the length of GE
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First we have to notice that the lenght GE is the same as the length DF, this comes from the fact that the diagonals in any rectangle have the same length. Now that we know that we have to remember that the distance between two points is given as:
[tex]d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]In this case we have that:
[tex]\begin{gathered} d(G,E)=d(D,F)=\sqrt[]{(4-(-1))^2+(-8-(-1))^2} \\ =\sqrt[]{(5)^2+(-7)^2} \\ =\sqrt[]{25+49} \\ =\sqrt[]{74} \end{gathered}[/tex]Therefore the distance between GE is
[tex]\sqrt[]{74}[/tex]this is appoximately 8.602
I’m new to this math and could use some help.
Answers
The operation A U B means "A union B" for which the elements of A is combined with the elements of B
Given that
A = {3,4,5,6,7,8,9,10,11,12} and B = {8,10,12,14,16,18}
Combine all the elements, and list the repeat elements from both sets A and B (such as 8, 10 and 12) only once.
Therefore, A U B = {3,4,5,6,7,8,9,10,11,12,14,16,18}.
which of these expressions is equivalent to -2(x-5)?a. -2x-5b. -2x+5c. -2x+10d. -2x-10
Answers
To find a equivalent expression you apply the distributive property on the given expression:
Distributive property:
[tex]a(b+c)=ab+ac[/tex]For the given expression:
[tex]\begin{gathered} -2(x-5)=-2\cdot x+2\cdot5 \\ \\ =-2x+10 \end{gathered}[/tex]As you can see the equavalent expression is option Cwhat would be the correct solution for 7x=42
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The given equation is
[tex]7x=42[/tex]We just have to divide the equation by 7
[tex]\begin{gathered} \frac{7x}{7}=\frac{42}{7} \\ x=6 \end{gathered}[/tex]Therefore, the solution is 6.Find the coordinates of A if M-1, 2) is the midpoint of AB and Bhas coordinates of (3.-5).
Answers
To find the x coordinate of the midpoint, we add the x coordinates of the endpoints together and divide by 2. We do not know the x coordinate of a so I will call it x
( x+3) /2 = -1
Multiply each side by 2
( x+3)/2 *2 = -1*2
x+3 = -2
Subtract 3 from each side
x+3-3 = -2-3
x = -5
The x coordinate of A is -5
We do the same thing for y
To find the y coordinate of the midpoint, we add the x coordinates of the endpoints together and divide by 2. We do not know the x coordinate of a so I will call it y
(y+-5) /2 = 2
Multiply each side by 2
(y-5)/2 *2 = 2*2
y-5 = 4
Add 5 to each side
y-5+5 = 4+5
y = 9
The y coordinate of A is 9
The coordinates of point A is ( -5,9)
Ari wants to know the volume of her gold ring in cubic centimeters. She gets a rectangular glass with a base 7 cm by 4.5 cm, and fills the glass 8.8 cm high with water. Ari drops her gold ring in the glass and measures the new height of the water to be 9.2 cm. What is the volume of Ari's ring in cubic centimeters?
Answers
Solution:
Given:
The volume of water only:
[tex]\begin{gathered} l=7cm \\ w=4.5cm \\ h=8.8cm \end{gathered}[/tex]Using the formula;
[tex]\begin{gathered} V=lwh \\ V=7\times4.5\times8.8 \\ V=277.2cm^3 \end{gathered}[/tex]The volume of water and ring (height of water changes:
[tex]\begin{gathered} l=7cm \\ w=4.5cm \\ h=9.2cm \end{gathered}[/tex]Using the formula;
[tex]\begin{gathered} V=lwh \\ V=7\times4.5\times9.2 \\ V=289.8cm^3 \end{gathered}[/tex]The volume of the gold ring is the difference in volumes.
Hence;
[tex]\begin{gathered} V=289.8-277.2 \\ V=12.6cm^3 \end{gathered}[/tex]Therefore, the volume of the gold ring is 12.6 cubic centimeters.
if XYZ equals ABC what is the scale factor to enlarge XYZ to create ABC
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step 1
Find out the scale factor
The ratio between corresponding sides is equal to the scale factor
so
scale factor=9/6
scale factor=1.5
therefore
the answer is 1.5$15,000 is invested at a rate of 8% compounded quarterly. Identify the compound interest function to model the situation. Then find the balance after 10 years. A = 15000(1.4)2t ; $31,044.81B = 15000(1.04)2t ; $32,866.85C = 15000(1.02)4t ; $33,120.59D = 15000(1.02)4t ; $30,582.44
Answers
Correct option C
which of the following equation does not have a solution
Answers
Step 1
Solve the equations to know which of them has no solution
[tex]\begin{gathered} A)x+4=2(x+4) \\ x+4=2x+8 \\ 2x-x=4-8 \\ x=-4 \\ \text{Option A has a solution} \end{gathered}[/tex][tex]\begin{gathered} B)3x+1=2x+5 \\ 3x-2x=5-1 \\ x=4 \\ \text{Option B has a solution} \end{gathered}[/tex][tex]\begin{gathered} C)\text{ 4(x-1)+2x=6x+5} \\ 4x-4+2x=6x+5 \\ 6x-6x=5+4 \\ 0=9 \\ \text{Option C has no solution} \end{gathered}[/tex][tex]\begin{gathered} D)3x+7=3x-6 \\ 3x-3x=-6-7 \\ 0=-13 \\ \text{Option D has no solution} \end{gathered}[/tex][tex]\begin{gathered} E)\text{ }4x=5x \\ 4x-5x=0 \\ -x=0 \\ x=0 \\ \text{Option E has solution} \end{gathered}[/tex][tex]\begin{gathered} F)x+1=2x \\ 2x-x=1 \\ x=1 \\ \text{Option F has solution} \end{gathered}[/tex][tex]\begin{gathered} G)x=x+7 \\ x-x=7 \\ 0=7 \\ G\text{ has no solution} \end{gathered}[/tex][tex]\begin{gathered} H)10x+1=5x-6 \\ 10x-5x=-6-1 \\ 5x=-7 \\ \frac{5x}{5}=-\frac{7}{5} \\ x=-\frac{7}{5} \\ H\text{ has a solution} \end{gathered}[/tex]Hence C,Dand G has no solution
Complete the table . On the coordinate plane below , plot the points represented by the pairs of coordinates from table . 3x - y = 1
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EXPLANATION
Given the table, we can see that the appropiate points are:
x y
-2 -2
-1 -1
0 0
1 1
2 2
Now, we can plot this on the coordinate plane as shown as follows: