Answer:
[tex]10a + 5(a - 3) = 15 \\ 10a + 5a - 15 = 15 \\ 15a = 30 \\ a = \frac{30}{15} \\ a = 2 \\ 10 \times 2 + 5(2 - 3) = 15 \\ 20 + - 5 = 15 \\ 15 = 15 \\ lhs = rhs\\ thank \: you[/tex]
Answer: a = 2
Solve:
Given
10a + 5 (a - 3) = 15
Expand parentheses and apply the distributive property
10a + 5 · a - 5 · 3 = 15
10a + 5a - 15 = 15
Combine like terms
(10a + 5a) - 15 = 15
15a - 15 = 15
Add 15 on both sides
15a - 15 + 15 = 15 + 15
15a = 30
Divide 15 on both sides
15a / 15 = 30 / 15
[tex]\boxed{a=2}[/tex]
Check:
Left-hand side = 10a + 5 (a - 3)
Left-hand side = 10(2) + 5 (2 - 3)
Left-hand side = 20 + 5(-1)
Left-hand side = 20 - 5
Left-hand side = 15
Right-hand side = 15
15 = 15, therefore, [tex]\boxed{a=2}[/tex] would make the equation true.
Hope this helps!! :)
Please let me know if you have any questions
Identify the errors made in the finding the inverse of y= x^2 +12x
X= y^2+12x
Y^2= x- 12x
Y^2 = -11x
Y=√11x, for x greater than or equal to 0
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Answer:
y was not substituted for every x
Step-by-step explanation:
To find the inverse of ...
y = f(x)
you need to solve ...
x = f(y)
Here, f(x) = x^2 +12x, so f(y) = y^2 +12y
This is not the expression we see on the right of ...
x = y^2 +12x
Apparently y was not properly substituted into f(x).
Vectors u and v are perpendicular. ||u|| = 5√2 units, and ||v|| = 6√2 units. ||u + v|| ≈ ? units
A. 11.04
B. 11.05
C. 15.55
D. 15.56
Answer:
15.56
Step-by-step explanation:
Given the vectors ||u|| = 5√2 units, and ||v|| = 6√2 units.
||u + v|| ≈ 5√2 + 6√2
||u + v|| ≈ (5+6)√2
Since √2≈ 1.4142
||u + v|| ≈ 11(1.4142)
||u + v|| ≈ 15.56
Hence the correct option is D
Answer: 11.05
Step-by-step explanation: got it right
Jenny bought scrapbooking supplies for $156.50. She paid $10.17 in sales tax. What was the sales tax rate on the supplies? If necessary, round your answer to the nearest tenth.
Answer:
6.5%
Step-by-step explanation:
sales price x sales tax rate = sales tax
156.50 x sales tax rate = 10.17
sales tax rate = 10.17/156.50
sales tax rate = .065 or 6.5%
please help me with geometry
Answer:
x = 8
Step-by-step explanation:
Set 2x + 3 = 3x - 5
Solve for x
x = 8
To host an event at a popular convention center, it costs $300 plus $45 per person attending. Step 1 of 3 : Write a rational expression that represents how much you would need to charge each attendee in order to cover the cost of hosting the event. Let x be the number of attendees.
Answer: (300 + 45x) / x
Step-by-step explanation:
Based on the information given in the question, the total cost will be the addition of the fixed cost and the variable cost which will be:
= 300 + (45 × x)
= 300 + 45x
The amount that needs to be charge for each attendee in order to cover the cost of hosting the event will be:
= (300 + 45x) / x
Select the statement that best justifies the conclusion based on the given information.
a. Definition of bisector.
b. Definition of midpoint.
c. If two lines intersect, then their intersection is exactly one point.
d. Through any two different points, exactly one line exists.
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Answer:
a. Definition of bisector.
Step-by-step explanation:
Line l is a line through the midpoint M. We can conclude it is a bisector, because, by definition, a bisector is a line through the midpoint.
The conclusion is justified by the definition of a bisector.
Question 6 a-c if plz show ALL STEPS like LITERALLY EVERYTHING
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Answer:
a) quadrant III
b) 4π/3, -2π/3
c) (1/2, (√3)/2)
d) ((√3)/2, -1/2
Step-by-step explanation:
a) The attachment shows the point P and the numbering of the quadrants (in Roman numerals). Point P lies in quadrant III.
__
b) Measured counterclockwise, the angle to point P is 240° or 4π/3 radians. Measured clockwise, the angle is -120° or -2π/3 radians. In the diagram, these are shown in green and purple, respectively.
__
c) Adding π/2 to the angle 4π/3 or -2π/3 brings it to 11π/6, or -π/6. This point is marked as P' (blue) on the diagram. The coordinate transformation for π/2 radians CCW rotation is ...
(x, y) ⇒ (-y, x)
P(-1/2, -√3/2) ⇒ P'(√3/2, -1/2)
In terms of trig functions, the coordinates of the rotated point are ...
P'(cos(-π/6), sin(-π/6)) = P'(√3/2, -1/2)
__
d) Adding or subtracting π radians to/from the angle moves it directly opposite the origin. Both coordinates change sign. This point is P'' (red) on the diagram.
How many significant figures are there in the number: 76000?
Answer:
2 significant figures
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
2
Only the 7 and the 6 are significant. The zeros are place holders and not significant figures.
-2y^2 - (y^2 + y) answer please
Answer:
The answer is −3y^2−y.
Steps:
Distribute the Negative Sign:
=−2y2+−1(y2+y)
=−2y2+−1y2+−1y
=−2y2+−y2+−y
Combine Like Terms:
=−2y2+−y2+−y
=(−2y2+−y2)+(−y)
=−3y2+−y
Answer:
-3y^2 - y
Step-by-step explanation:
-2y^2 - (y^2 + y)
Find the opposite of y^2 + y, so distribute the negative sign to the values inside the parentheses to get:
−2y^2 −y^2 − y
Then combine like terms to get:
-3y^2 - y
help me this EQUATION please help help help !
Please how do I solve this.
Answer:
Horizontal Shift: Right 1
Vertical Shift: Down 5
Reflection: None
Explanation: To find the transformation, compare the function to the parent function (being in this case g(x)=1/x) and check to see if there is a horizontal or vertical shift or a reflection.
So, the answer would be Right 1, and down 5
Hope this helps you out :)
2) Consider the quadratic sequence 72, 100, 120, 132
2.1.1) Determine Tn the nth term of the quadratic.
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Answer:
Tn = -4n² +40n +36
Step-by-step explanation:
A graphing calculator readily performs the quadratic regression, yielding the formula ...
Tn = -4n² +40n +36
__
The first and second differences of the given sequence terms are ...
28, 20, 12 and -8, -8
The coefficient of the squared term is half the second difference, so is -4. Then the sequence of squared terms is -4n²:
-4, -16, -36, -64
Subtracting these values from the original sequence gives the linear sequence ...
76, 116, 156, 196
which has first term 76 and common difference 40. The equation for the n-th term of this is ...
an = 76 +40(n -1) = 36 +40n
Adding this linear sequence to the sequence of squared terms, we get ...
Tn = -4n² +40n +36
Aliana is supposed to get back to a customer with an answer about a refund by the end of the day, but she won't have all the approvals she needs to process the refund by that time. What should she do? O a) Call the customer only when she has processed the refund Ob Tell the customer that she should have called about the problem earlier Oc) Explain to the customer that her bosses are the ones that are taking forever O di Apologize to the customer and say that she will call her tomorrow with an update
Answer:
"ob" is the answer of this long question
Answer:
D
Step-by-step explanation:
reason:
not A cuz the customer has to wait for a long time, and she feel waste of time
not B cus it's the store's responsiblity, not customer. if she said that, the customer would feel be disrespected. and i swear she never comes back that store.
C if she said that, customer also feel waste of time when she has to talk with Aliana who cant solve her problem
and the boss will think Ali couldnt have no problem-solving skills
Area of a triangle
A/12 = 12/12bh
solve for b
Step-by-step explanation:
I hope this works for ya.
what is factorization of the trinomial below? -x2+2x+48
Answer:
-(x+6) (x-8)
Step-by-step explanation:
-(x^2-2x-48)
two values the multiply to get 48 and the difference of those two numbers gives you -2.
6,-8
6 x -8 =-48
6-8=-2
In this case we factored out the negative so leave it outside
-(x+6) (x-8)
Answer:
-1(x-8)(x+6) is the answer just took the test
Step-by-step explanation:
Analyze the diagram below and complete the instructions that follow. Find a, b, and c.
Answer:
The correct answer is the letter C.
Step-by-step explanation:
We can use the following trigonometric identity:
[tex]cos(60)=\frac{6}{b}[/tex] (1)
[tex]cos(45)=\frac{c}{b}[/tex] (2)
Solving each equation by b and equaling we have:
[tex]\frac{6}{cos(60)}=\frac{c}{cos(45)}[/tex]
[tex]\frac{6}{cos(60)}=\frac{c}{cos(45)}[/tex]
Let's recall that:
[tex]cos(45)=\frac{1}{\sqrt{2}}[/tex]
[tex]cos(60)=\frac{1}{2}[/tex]
Then we have:
[tex]c=\frac{cos(45)*6}{cos(60)}[/tex]
[tex]c=\frac{2*6}{\sqrt{2}}[/tex]
[tex]c=\frac{12}{\sqrt{2}}[/tex]
[tex]c=6\sqrt{2}[/tex]
Using equation (1) we can find b.
[tex]cos(60)=\frac{6}{b}[/tex]
[tex]b=12[/tex]
Finally, we can find a using the next equation:
[tex]tan(60)=\frac{a}{6}[/tex]
[tex]a=6*tan(60)[/tex]
[tex]a=6\sqrt{3}[/tex]
Therefore, the correct answer is the letter C.
I hope it helps you!
The question is attached, please help.
Answer:draw a triangle
Step-by-step explanation:
A scale drawn on the map shows that 1 inch represents 40 miles. If tuo cities
are 25 inches apart on the map, what is the distance between them in real
life?
Answer:
Im pretty sure its 1,000 miles (dont forget the unit)
Step-by-step explanation:
Determine if this problem is a inverse variation or direct variation problem! This means that:
equation would be:
1=40
25=x
cross multiply*
x=25*40
x=1,000 miles apart! (dont forget the unit)
If this doesnt work then try this equation!
1=40
25=x
Multiply 1*40 and 25 *x
40=25x......
40/25= 1.6
x=1.6! (Extra step)
Cheers!
Answer: 100 Miles
Step-by-step explanation: took the miles and got it correct.
(Also it's 2.5 inches apart, not 25.)
Which expression is equivalent to
-32 3/5
-8
-3/325
3/325
1/8
Answer:
[tex]-32^\frac{3}{5} = -8[/tex]
Step-by-step explanation:
Given
[tex]-32^\frac{3}{5}[/tex]
Required
The equivalent expression
We have:
[tex]-32^\frac{3}{5}[/tex]
Rewrite as:
[tex]-32^\frac{3}{5} = (-32)^\frac{3}{5}[/tex]
Expand
[tex]-32^\frac{3}{5} = (-2^5)^\frac{3}{5}[/tex]
Remove bracket
[tex]-32^\frac{3}{5} = -2^\frac{5*3}{5}[/tex]
[tex]-32^\frac{3}{5} = -2^3[/tex]
[tex]-32^\frac{3}{5} = -8[/tex]
Which equation describes this graph?
Step-by-step explanation:
The graph clearly has a positive slope. So Answer D couldn't be correct. Next: the y-intercept of this line is (0, -2), so b in the formula y = mx÷ b must be -2.
Therefore the correct equation of this line is
y = x - 2 (choice a)
Please help me will vote the person who does brainiest person or something
Answer:
quadratic
y=mx+c
Step-by-step explanation:
fridays high temp was -1. the low temp was -5. what was the difference between the high and low temps
Answer:
4
Step-by-step explanation:
count up from -5 to -1
so -5,-4,-3,-2,-1 and there are four numbers excluding-5
If P(x): x < |2x|. b) What is the value of ∃x P(x)?
Answer:
true
Step-by-step explanation:
because some of x if x=3 then 3<6 is true
Which expression describes this graph?
A. x -5
B. x -5
C. x < -5
D. x > -5
Answer:
C
Step-by-step explanation:
The equation that described the graph is x<-5
AM and CM
BM and BM
AB and CB
These are variables on your graph
A car rental agency rents 480 cars per day at a rate of $20 per day. For each $1 increase in rate, 10 fewer cars are rented. At what rate should the cars be rented to produce the maximum income? What is the maximum income?
Answer:
340 cars at $ 34 should be rented to produce the maximum income of $ 11,560.
Step-by-step explanation:
Given that a car rental agency rents 480 cars per day at a rate of $ 20 per day, and for each $ 1 increase in rate, 10 fewer cars are rented, to determine at what rate should the cars be rented to produce the maximum income and what is the maximum income, the following calculations must be performed:
480 x 20 = 9600
400 x 28 = 11200
350 x 33 = 11550
300 x 38 = 11400
310 x 37 = 11470
320 x 36 = 11520
330 x 35 = 11550
340 x 34 = 11560
Therefore, 340 cars at $ 34 should be rented to produce the maximum income of $ 11,560.
Can someone help me please. I am struggling and I would be so happy if any of you helped me. Thank you for your help!
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Answer:
$19.36
Step-by-step explanation:
Any average is the sum of numbers, divided by the number of them.
Here, the numbers are grouped, but the computation of the average works the same way.
The total value of donations received is ...
$100×10 +$50×20 +$20×30 +$10×100 +$5×35
= $1000 +1000 +600 +1000 +175 = $3775
The total number of donations received is ...
10 +20 +30 +100 +35 = 195
Then the average (mean) donation is the total value divided by the total number ...
$3775/195 ≈ $19.35897 ≈ $19.36 . . . mean donation
Find the quotient of -196/4
Answer:
this is the answer
Step-by-step explanation:
thank you
Answer:
-196/4 = -49
Step-by-step explanation:
Mental math. If you can't do that then use a calculator. It's faster to type it in on g oogle
Solve the following equation by using the addition principle. Check the solution.
-4/5 + y = -1/4
Answer:
y = 11/20
Step-by-step explanation:
-4/5 + y = -1/4
Add 4/5 to each side
-4/5 +4/5 + y = -1/4+4/5
y = -1/4 + 4/5
Get a common denominator
y = -1/4 *5/5 + 4/5 *4/4
y = -5/20 + 16/20
y = 11/20
Check
-4/5 +11/20 = -1/4
Get a common denominator
-4/5*4/4 + 11/20 = -1/4*5/5
-16/20 +11/20 = -5/20
-5/20 = - 5/20
Check
Step-by-step explanation:
[tex] - \frac{4}{5} + y = - \frac{1}{4} \\ y = \frac{ - 1}{4} + \frac{4}{5} \\ y = \frac{ - 5 + 16}{20} \\ y = \frac{11}{20} [/tex]
[tex]y = \frac{11}{20} [/tex]
A simple random sample of 41 men from a normally distributed population results in a standard deviation of 10.7 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.10 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts(a) through (d) below.
a. Identify the null and alternative hypotheses.
b. Compute the test statistic; χ2 = ___ (Round to three decimal places as needed.)
c. Find the P-value; P-value = ____ (Round to four decimal places as needed.)
d. State the conclusion. (choose one from each ( x, y) set)
(Do not reject, Reject) Upper H0, because the P-value is (greater than, less than, or equal to) the level of significance. There is
(sufficient, insufficient) evidence to warrant rejection of the claim that the standard deviation of men's pulse rates is equal to
10 beats per minute.
Answer:
H0 : σ²=10²
H1 : σ²>10²
χ² = 45.796
Pvalue = 0.2442
Do not reject H0 because Pvalue is greater Than significance level
There is insufficient evidence to warrant rejection of the claim that the standard deviation of men's pulse rates is equal to 10 beats per minute.
Step-by-step explanation:
Given that :
Sample size, n = 41
Sample standard deviation, s = 10.7
Population standard deviation, σ = 10
Significance level, α = 0.10
The Hypothesis :
H0 : σ²=10²
H1 : σ²>10²
Using the χ² test for population variance :
The test statistic, χ² = (n-1)*s²/σ²
χ² = (41 - 1) * 10.7²/ 10²
χ² = (40 * 114.49) / 100
χ² = 4579.6 / 100
χ² = 45.796
The Pvalue ;
df = n - 1 ; 41 - 1 = 40
Pvalue(45.796, 40) = 0.2442
Since Pvalue > α ; WE fail to reject H0
Do not reject H0 because Pvalue is greater Than significance level
There is insufficient evidence to warrant rejection of the claim that the standard deviation of men's pulse rates is equal to 10 beats per minute.
