Answer:
B, second option: the product of three fourths is not equal to 9
The error made by Sameer while creating the algebraic equation: Sameer did not use the correct equation to model the given information.
What is algebraic equation?An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other.
It is given that Three-fourths of the total number of different toppings available at the make-your-own sundae shop = 12
The algebraic equation given by Sameer is wrong, the correct equation will be:
Let the total number of toppings be x.
[tex]\frac{3}{4} x = 12\\ \\x = 12 (\frac{4}{3} ) = 16[/tex]
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Hansen and his good buddy Xavier are both mechanics at a shop that does oil changes. They are in a friendly competition to see who can complete the most oil changes in one day. Hansen has already finished 7 oil changes today, and can complete more at a rate of 2 oil changes per hour. Xavier just came on shift, and can finish 3 oil changes every hour. Sometime during the day, the friends will be tied, with the same number of oil changes completed. How many oil changes will Hansen and Xavier each have done? How long will that take?
Prove that: (sin x - 2 sin³ x)/(2 cos³ x - cos x) = tan x
[tex]\large\underline{\sf{Solution-}}[/tex]
We have to prove that:
[tex]\rm\longmapsto \dfrac{ \sin(x) - 2 \sin^{3} (x) }{2 \cos^{3} (x) - \cos(x) } = \tan(x) [/tex]
Taking LHS, we get:
[tex]\rm = \dfrac{ \sin(x) - 2 \sin^{3} (x) }{2 \cos^{3} (x) - \cos(x) }[/tex]
We can take sin(x) as common from numerator part. We get:
[tex]\rm = \dfrac{ \sin(x) \{1- 2 \sin^{2} (x) \}}{2 \cos^{3} (x) - \cos(x) }[/tex]
Similarly, we can take cos(x) as common from first two terms. We get:
[tex]\rm = \dfrac{ \sin(x) \{1- 2 \sin^{2} (x) \}}{ \cos(x) \{ 2 \cos^{2} (x) -1\}}[/tex]
[tex]\rm = \dfrac{ \sin(x) }{ \cos(x) } \cdot \dfrac{\{1- 2 \sin^{2} (x) \}}{\{ 2 \cos^{2} (x) -1\}}[/tex]
As we know that:
[tex]\rm\longmapsto \dfrac{ \sin(x) }{ \cos(x) } = \tan(x) [/tex]
We get:
[tex]\rm = \tan(x) \cdot \dfrac{\{1- 2 \sin^{2} (x) \}}{\{ 2 \cos^{2} (x) -1\}}[/tex]
Now, we will expand the terms in fraction:
[tex]\rm = \tan(x) \cdot \dfrac{\{1- \sin^{2} (x) - { \sin }^{2}(x) \}}{\{\cos^{2} (x) + \cos^{x}(x) -1\}}[/tex]
As we know that:
[tex]\rm \longmapsto \sin^{2}(x)+cos^{2}(x)=1[/tex]
[tex]\rm \longmapsto\cos^{2}(x)=1-sin^{2}(x)[/tex]
[tex]\rm \longmapsto\cos^{2}(x) - 1=-sin^{2}(x)[/tex]
Now substitute the values in the expression, we get:
[tex]\rm = \tan(x)\cdot \dfrac{ \cos^{2} (x)-{ \sin }^{2}(x)}{\cos^{2} (x) - \sin^{2} (x) }[/tex]
[tex]\rm = \tan(x)\cdot1[/tex]
[tex]\rm = \tan(x)[/tex]
Here, we notice that LHS = RHS
Proved.
Your friend identifies the terms and like terms in the expression
3x - 5 - 2x + 9x
is your friend correct?
explain your reasoning :
Answer:
The like-terms equation would be:
10x - 5
Step-by-step explanation:
help pelase i need help
Answer:
:P
Step-by-step explanation:
:P
A boy needs to grill 13 pounds of meat for a cookout. Determine the Maximum cost per pound that he can afford if he wants to spend the most $70 on his meat purchase
Answer:
$5.38 per pound
Step-by-step explanation:
70/13=5.384615
5.38x13=69.94
How much is does 8×10 equal to?
Answer:
80
Step-by-step explanation:
8x10= 80
the area of the floor in George Square bedroom is 25 feet squared what is the length of his bedroom?
If the height of his room is 6 feet how much wall surface does he have in his room?
Answer:
1. 6.25 square feet
2. 37.5 square feet
Step-by-step explanation:
25 divided by 4=6.25
6.25x6=37.5
Answer:
Length of his bedroom is 5 Ft
Wall Surface he have in his room is 120 ft^2
Step-by-step explanation:
Help with test review homework please.
Answer:
11p^(13)
10m^(15)
Step-by-step explanation:
11×11=121 so sqrt(121)=11
Since 26/2=13, then p^(13)×p^(13)=p^(26). This implies sqrt(p^26)=p^13.
sqrt(121p^26)=11p^(13)
In short, you just find sqrt of 121 since 121 is a perfect square and then do p^(26/2) since 26 is even and be done.
Other problem is similar.
Sqrt(100)=10 and m^(30/2)=m^(15).
The answer is 10m^(15).
La suma de cuatro números consecutivos es 938 cuál es el valor del número menor
De acuerdo con los cálculos realizados en el presente desarrollo, el valor del número menor es 233.
Dado que la suma de cuatro números consecutivos es 938, para determinar cuál es el valor del número menor se debe realizar el siguiente cálculo:
X + X + 1 + X + 2 + X + 3 = 9384X + 6 = 9384X = 938 - 6X = 932 / 4X = 233233 + 234 + 235 + 236 = 938Por lo tanto, el valor del número menor es 233.
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Please help me fast thank you for your help I’ll give 50 points
Answer:
C
Step-by-step explanation:
Answer:
It's option 3
Step-by-step explanation:
Some banks now use continuous compounding of an amount invested. In this case, the equation that models the value of an initial investment of P dollars in t years at an annual
interest rate of r is given by A = Pelt. Using this equation, find the value in 5 years of an investment of $2000 that earns 7% annual interest. (Round your answer to the nearest cent.)
Answer:
In this case, the equation that models the value of an initial investment of P dollars in t years at an annual interest rate of r is given by A = Pert.
Step-by-step explanation:
given the right triangle ABC with the altitude BD drawn to hypotenuse………. please help asap i’ve failed this so many times
Answer:
plz mark me as a brainliest
At a comic book convention vendor I was selling a set of 5 comics for $38.70.
Vendor 2 was selling a set of 4 comics for $30.76. Which vendor has the higher
unit price?
Answer:
Vendor I sells more by 0.05
Step-by-step explanation:
First, you do Vendor I, divide 38.70/5, which gives you $7.74.
Then, you go to Vendor 2, divide 30.76/4 and that makes the answer $7.69.
7.74 - 7.69 = 0.05
Vendor 1 has more then Vendor 2 by 5 cents.
Juan is making a cake for his mom's birthday. For every three cups of
flour, there are four teaspoons of sugar. If Juan used 33'cups of flour,
how many teaspoons of sugar did he use? Be sure to identify the
multiplicative rule.
Answer:
44 teaspoons
Step-by-step explanation:
33 divided by 3 is 11 and 4 x 11 is 44 if juan used 4 teaspoons of sugar every 3 cups of flour then 3 goes into 33 11 times and 4 x 11= 44
3 (1 2t) = 3t + 5 !!
Answer:
2/3
Step-by-step explanation:
3+6t=3t+5
like terms together
6t-3t=5-3
3t=2
t=2/3
A department store sells shoes with an 70% markdown. If one pair of shoes is originally $148, then with the markdown, what is the new selling price for those shoes?
Answer:
$44.40
Step-by-step explanation:
100%-70%=30%
30/100x148=44.40 (discounted price)
Appreciate to be marked brainliest. Hope this helps!
What is the slope of the line that contains these points
Answer:
Slope = - 5
Step-by-step explanation:
Let,
x1 = 13
x2 = 14
y1 = 11
y2 = 6
Formula : -
Slope = ( y2 - y1 ) / ( x2 - x1 )
Slope = ( 6 - 11 ) / ( 14 - 13 )
= - 5 / 1
Slope = - 5
Answer:
[tex]\boxed{\sf slope:-5}[/tex]
Step-by-step explanation:
Slope :
[tex]\boxed{\sf m=\cfrac{rise}{run} =\cfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf ^*m=slope[/tex]
[tex]\sf (x_1, y_1): first \: coordinates[/tex]
[tex]\sf (x_2, y_2): second\: coordinates[/tex]
___________________
[tex]\sf \left(x_1,\:y_1\right):\left(13,\:11\right)[/tex]
[tex]\sf \left(x_2,\:y_2\right):\left(14,\:6\right)[/tex]
[tex]\sf slope\:(m)=\cfrac{6-11}{14-13}[/tex]
[tex]\sf slope\:(m)=-5[/tex]
____________________
The American Association of Individual Investors (AAII) conducts a weekly survey of its members to measure the percent who are bullish, bearish, and neutral on the stock market for the next six months. For the week ending March , , the survey results showed bullish, neutral, and bearish. Assume these results are based on a sample of AAII members. a. Over the long-term, the proportion of bullish AAII members is . Conduct a hypothesis test at the level of significance to see if the current sample results show that bullish sentiment differs from its long-term average of . What are your findings
What is the common ratio between
1,-5, 25, -125
Answer:
1/5
Step-by-step explanation:
hope this helps!
Mrs. Jackson had 493 canned goods that she collected for the annual canned food drive. She put all the cans in 7 equal piles. About how many cans are in each pile?
Answer:
about 70 cans
Step-by-step explanation:
493÷7=70.42
what is proportion mean
Answer:
a part, share, or number considered in comparative relation to a whole.
Step-by-step explanation:
hope it helps
mark me brainliest pls
How many combinations are possible? Assume the items are distinct.
10 items chosen 10 at a time
A kennel charges $15 per day board dogs. Upon arrival, each dog must have a flea bath that costs $12.
Part A: Write a function rule for the total cost for n days of boarding plus a bath.
Part B: How much does a 10-day stay cost?
Part C: Does a 5-day stay cost half as much as a 10-day stay? Explain.
What I Think:
I think the function rule is C=15+12n.
10-day stay cost: 135
5-day stay: 75. No, a 5-day stay does not cost half as much as the 10-day stay.
Is this correct???
Your answer makes sense. Though I would recommend using a different variable for each dog at the kennel. Like D. But other than that you're good!
Compute the difference quotient
Answer:
Step-by-step explanation:
f(x) = -x^2+6x-2
-x^2+6x-2 here we use work sheets or log books
What is this answer need reply ASAP
Answer:
how many boxes is the line on
A figurine of a lighthouse is shown. if the actual lighthouse is 30feet wide, how tall is the lighthouse
Answer:
30× 60 ( 3×2= 6 + tens= 60 )= minimum- 180 fery
Convert the 144 km/h into meters per second
Answer:
144 Kilometers per Hour = 40 Meters per Second
Step-by-step explanation:
multiply the value in kilometers per hour by the conversion factor '0.27777777777778'.
So, 144 kilometers per hour = 144 × 0.27777777777778 = 40 meters per second.
please mark 4 brainliests.
Answer: 40 m/s
Step-by-step explanation: you can multiplied by 5/18 to convert km/h to m/s ,and you can multiplied by 18/5 to convert m/s to km/h.
Two gasoline stations along an expressway have six gas pumps each. An experiment involves determining how many pumps are in use at a particular time for each station. Describe S by listing the elements.
The sample space is used to prepare a list of all possible outcomes or element in an experiment. The sample space containing all elements attainable for the number of working pumps at a particular station is listed below :
Number of stations = 2 Number of pumps per station = 6Let the number of pumps in use at each station be listed on the row and column respectively :
P1/P2_0 _ 1__ 2 __ 3 __ 4 __ 5 __ 6
0__ 0,0 _0,1 _0,2 _0,3 __0,4_ 0,5_0,6
1__ 1,0 __1,1 _1,2 __1,3 __1,4 __1,5_ 1,6
2__2,0 _2,1 _2,2 _2,3 __2,4 __2,5_2,6
3__3,0_3,1 _3,2 _ 3,3 __3,4 __3,5 _3,6
4__4,0_4,1 _4,2 _ 4,3 __4,4 __ 4,5 _4,6
5__5,0_5,1 _5,2 _ 5,3 __5,4 __ 5,5 _5,6
6__6,0_6,1 _6,2 _ 6,3 __6,4 __ 6,5 _6,6
Therefore, all possible outcomes relating to the number of working pumps are available in the sample space created.
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Q: What is the product of (a-5) and (a+3)?
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Let's solve for a :
[tex](a - 5) \times (a + 3)[/tex][tex](a \times a) + (a \times 3) + ( - 5 \times a) + ( - 5 \times 3)[/tex][tex] {a}^{2} + 3a - 5a - 15[/tex]yE2 ÷(3Z)= _______
if y=12, and Z=8
Answer:
45
Step-by-step explanation: