Answer:
Step-by-step explanation:
Multiply the 6 and 4 together. 6*4 = 24
The next part is a bit tricky. Add the powers on the base 10. Keep the base 10.
10^(6 - 1) = 10^5
Now put the two parts together. 24 * 10^5
The number in front of the 10 must be between 1 and 10.
So 24 can be written as 24 = 2.4 * 10^1
2.4 * 10^1 * 10^5 = 2.4 * 10^(5 + 1) = 2.4 * 10^6
Diego and Anya live 72 miles apart. They both meet at
their favorite restaurant, which is (16x – 3) miles from
Diego's house and (5x + 2) miles from Anya's house.
Diego argues that in a straight line distance, the restaurant
is halfway between his house and Anya's house. Is Diego
right? Justify your reasoning.
Answer:
The restaurant is not at half way
Step-by-step explanation:
Given
[tex]Total\ Distance = 72[/tex]
[tex]Diego = 16x - 3[/tex]
[tex]Anya = 5x + 2[/tex]
Required
Accept or reject Diego's claim
To do that, we need to determine the value of x by:
Diego + Anya =Total Distance
Substitute values for each parameter
[tex]16x - 3 + 5x + 2 = 72[/tex]
Collect Like Terms
[tex]16x + 5x = 72 + 3 - 2[/tex]
[tex]21x = 73[/tex]
Divide both sides by 21
[tex]x = \frac{73}{21}[/tex]
Substitute the value of x in Diego and Anya's distance
[tex]Diego = 16x - 3[/tex]
[tex]Diego = 16 * \frac{73}{21} - 3[/tex]
[tex]Diego = \frac{1168}{21} - 3[/tex]
[tex]Diego = \frac{1168 - 63}{21}[/tex]
[tex]Diego = \frac{1105}{21}[/tex]
[tex]Diego = 52\frac{13}{21}[/tex]
[tex]Anya = 5x + 2[/tex]
[tex]Anya = 5 * \frac{73}{21} + 2[/tex]
[tex]Anya = \frac{365}{21} + 2[/tex]
[tex]Anya = \frac{365 + 42}{21}[/tex]
[tex]Anya = \frac{407}{21}[/tex]
[tex]Anya = 19\frac{8}{21}[/tex]
Since, both distances are not equal,
Then Diego's claim is false and incorrect
What number should be placed in the box to help complete the division calculation?
(Long division setup showing an incomplete calculation). 13 is in the divisor, 4231 is in the dividend, and 3 hundreds and 2 tens is written in the quotient. 3900 is subtracted from 4231 to give 331. An unknown value represented by a box is being subtracted from 331.
Answer:
299
Step-by-step explanation:
Lisa purchased a hat for $10, a purse for $20, and a book for $23. The sales tax rate was 7.2 percent. What was the total amount she paid?
Answer:
$56.82
Step-by-step explanation:
The sum of all the stuff she bought is 10+20+23, so 53.
Now you need to find the tax, so you multiply 53 x 7.2%, and to change a % to a number you move the decimal place two to the left, so you get .072
$53 x .072 = $3.816 sales tax
$53 for the stuff plus $3.816 tax = $56.816
and since money is only two decimal places and the 6 is higher than 5, you have to round up to the nearest penny, so $56.82!
Answer:
56.81$ she paid
Step-by-step explanation:
Select all that apply which expressions are equivalent to 6X +12
(A) 6(x+12)
(B) x(6+12)
(C) 3(2x+4)
(D) 2(3x+6)
(E) 6(x + 2)
3(2x+4), 2(3x+6) and 6(x + 2) are the expressions are equivalent to 6X +12
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 6X +12
We have to find the equivalent expressions of 6x+12
Let us take 6 as a common factor we get
6(x+2)
so 6(x+2) is equivalent expression of 6X +12
Now let us take 3 as common factor
3(2x+4)
so 3(2x+4) is equivalent expression of 6X +12
Now let us take 2 as common factor
2(3x+6)
so 2(3x+6) is equivalent expression of 6X +12
Hence, 3(2x+4), 2(3x+6) and 6(x + 2) are the expressions are equivalent to 6X +12
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Twice a number increased by three times the number?
this is the answer
Step-by-step explanation:
2x+3
Answer:
2x+3x
Step-by-step explanation:
help please
pleaseeee i dont understand
:(
Which of the following sets are equal? A = {2, 3, 4} n B = {XER 1 4 x < 5} n C = { ERI 1 < x < 5} n D = {xEZ| 1 < x < 59} n E = {xez | 1 < x < 59} n
Answer:
Step-by-step explanation:
The question is not too clear. check the attachment for better view of the question.
From the options The set A = {2, 3, 4} will be compared to other options to determine which of the remaining set is equivalent to the set A.
x e R means the values in the set are real numbers and real numbers can either be rational or irrational. R= Hence the real numbers between 1 and 5 are not restricted to only positive integer values but also decimal numbers. and since set A does nit contain ant rational number, hence both set B and C are not equivalent to set A.
Also, set B is not equivalent to set C even though the values in both sets are integers. They are not equal because 1 is included in set B but not in set C.
Set D and E are equivalent because they both contains integers between 1 and 5. Integers are positive whole numbers between 1 and 5 since the both sets doesn't contain any negative value. Hence the set A = set D = set E
answer reeeeeeeeeeeeeeeeeeeeeeeee
Answer:
36 and 49
Step-by-step explanation:
6x6 and 7x7
Find the equation of the tangent line to the curve at the given point?
y = x cot(x) at the point with x-coordinate= π/4
Answer:
The equation of the tangent line
[tex]y - \frac{\pi }{4} = (\frac{-\pi }{2} +1)( x - \frac{\pi }{4} )[/tex]
Step-by-step explanation:
Step(i):-
Given function y = x cot (x) ....(i)
Differentiating equation (i) with respective to 'x' , we get
[tex]\frac{dy}{dx} = x (-Co sec^{2} (x)) +cot(x) (1)[/tex]
Step(ii):-
The slope of the tangent line
[tex]\frac{d y}{d x} = -x Co-sec^{2} (x) +cot x[/tex]
[tex](\frac{d y}{d x} )x_{=\frac{\pi }{4} } = -\frac{\pi }{4} Co-sec^{2} (\frac{\pi }{4} ) +cot \frac{\pi }{4}[/tex]
We will use trigonometry formulas
[tex]Cosec(\frac{\pi }{4} ) = \sqrt{2}[/tex]
[tex]sec(\frac{\pi }{4} ) = \sqrt{2}[/tex]
[tex]Cot(\frac{\pi }{4} ) = 1[/tex]
Now the slope of the tangent
[tex]\frac{dy}{dx} =-\frac{\pi }{4} (\sqrt{2})^{2} )+1[/tex]
[tex]\frac{dy}{dx} =-\frac{\pi }{2} +1[/tex]
Step(iii):-
Given
Substitute [tex]x=\frac{\pi }{4}[/tex] in y = x cot (x)
[tex]y = \frac{\pi }{4} cot (\frac{\pi }{4} )[/tex]
[tex]y = \frac{\pi }{4}[/tex]
The point of the tangent line [tex](x ,y ) = (\frac{\pi }{4} , \frac{\pi }{4} )[/tex]
The equation of the tangent line
[tex]y - y_{1} = m ( x - x_{1} )[/tex]
[tex]y - \frac{\pi }{4} = (\frac{-\pi }{2} +1)( x - \frac{\pi }{4} )[/tex]
Find the slope of the given line, if it is defined. 2x + 1 = 0
Given :
A line 2x + 1 =0 .
To Find :
The slope of the given line .
Solution :
We know , slope of line is given by the tangent of the angle between the x-axis and the line .
Now, for line 2x + 1 =0 i.e [tex]x=\dfrac{-1}{2}[/tex] .
The line is perpendicular to x-axis and cuts the x-axis at [tex]\dfrac{-1}{2}[/tex] .
Therefore , the angle between the line and x-axis is [tex]90^o[/tex] .
So , slope [tex]m=\tan\ 90^o[/tex] i.e undefined .
Therefore , the slope of given line is not defined .
Hence , this is the required solution .
Select all that apply.
Which expressions are equivalent to 6x +18?
6(2+3)
3(2x + 6)
2 (32 +9)
6(x + 18)
3(x+6)
The expression equivalent to 6x + 18 is 3(2x + 6) thus option (B) is correct.
What is an expression?An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that are all constrained and create an equation.
Expression is very useful to determine the end or root value of constraint.
As per the given,
6x + 18
Take 3 as common,
3(2x + 6)
Hence "The expression equivalent to 6x + 18 is 3(2x + 6)".
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46 winners divided $33 equally. what decimal is equivalent to the fraction of a dollar that each winner received? round to the nearest hundredths.
Answer:
1.39
Step-by-step explanation:
Lydia owns a food truck that sells tacos and burritos. She only has enough supplies to make 115 tacos or burritos. She sells each taco for $4 and each burrito for $6.75. Lydia must sell at least $680 worth of tacos and burritos each day. If 32 tacos were sold, determine the minimum number of burritos that the Lydia must sell in order to meet the requirements. If there are no possible solutions, submit an empty answer.
Answer:
Lydia must sell 552 burritos
Step-by-step explanation:
Mark made a business trip of 259.5 miles. He averaged 59 mph for the first part of the trip and 57 mph for the second part. If the trip took 4.5 hours, how long did he
travel at each rate?
Answer: He spends 1.5 hours on the first part of trip and 3 hours on the second part of trip
Step-by-step explanation:
Let x = the number of hours for first part
Let y = the number of hours for second part
Concept: speed × time = distance
----------------------------------------------------------------
x+y=4.5
59x+57y=259.5
-----
y=4.5-x
59x+57y=259.5
-----
59x+57(4.5-x)=259.5
59x+256.5-57x=259.5
2x+256.5=259.5
2x=3
x=1.5
4.5-1.5=3 hrs
When finding all the roots of polynomials, how do you find the possible rational zeros to know which numbers you plug back into the function to get the number you synthetically divide by?
Answer:
You would have to break the polynomial down into smaller binomials or monomials. Take x^2-6x-9 for instance. It would break down into (x+3)(x-3) through the a^2+2ab+b^2 formula. After that set the two nomials equal to zero and solve for x. After that, you would plug back in x to see whatever x works. You may more than two nomials after breaking it apart so keep that in mind.
Which of the following would be considered the most conservative alpha level?
a. .01
b. .05
c. .10
d. .15
Answer:
C.0.1
Step-by-step explanation:
Because this is 10% confidence confirmed
The sphere weighs 4 pounds. sorry no picture but you can ask me for it in the comments What is the weight of the cylinder? What is the weight of the cube?
Answer:
The weight is 4 pounds :D
Step-by-step explanation:
Divide rs 21000 between Nisha and Nishan so that Nisha gets double than Nishan
let the nisha be x and nishan be y
Step-by-step explanation:
ATQ
your statement is x=2y
Study the example on the right to help you complete the problem below. please help!:(
Answer : The equation for 'h' is [tex]h=\frac{2A}{b}[/tex]
Step-by-step explanation :
The given equation is:
[tex]A=\frac{1}{2}bh[/tex]
Now we have to determine the equation for 'h'.
[tex]A=\frac{1}{2}bh[/tex]
Multiplying the equation by 2.
[tex]2\times A=2\times \frac{1}{2}\times bh[/tex]
on simplifying, we get:
[tex]2\times A=bh[/tex]
Dividing the equation by 'b'.
[tex]\frac{2\times A}{b}=\frac{bh}{b}[/tex]
[tex]\frac{2\times A}{b}=h[/tex]
or,
[tex]h=\frac{2A}{b}[/tex]
Therefore, the equation for 'h' is [tex]h=\frac{2A}{b}[/tex]
Answer: B
Step-by-step explanation:
67.9 is ten times as much as what number?
A. 6.79
B. 6,790
C. 607.9
D. 6.7
Answer:
6.79
Step-by-step explanation:
6.79 x 10 = 67.9
The unknown number z would be 6.79
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
WE have been given that 67.9 is ten times as much as unknown number;
Let the unknown number be z;
Z x 10 = 67.9
Now divide by 10 on both sides, we get;
Z = 67.9/10
Z = 6.79
Therefore,
6.79 x 10 = 67.9
Hence, the unknown number z would be 6.79
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Why did I get this question wrong?
Answer:
9.25
Step-by-step explanation:
M₄ means the area using 4 rectangles with heights equal to the function evaluated at the midpoints.
The width of each rectangle is (4−0)/4 = 1.
The area of each rectangle is:
M₁ = (1) (1.12) = 1.12
M₂ = (1) (1.80) = 1.80
M₃ = (1) (2.69) = 2.69
M₄ = (1) (3.64) = 3.64
The total area is therefore:
M = 1.12 + 1.80 + 2.69 + 3.64
M = 9.25
Your favorite dog groomer charges according to your dog’s weight. If your dog is 15 pounds and under, the groomer charges $35. If your dog is between 15 and 40 pounds, she charges $40. If your dog is over 40 pounds, she charges $40, plus an additional $2 for each pound over 40 pounds.
A. Write a piecewise function for the cost of a dog grooming based on the number of pounds at this grooming salon.
B. Sasha weighs 30 pounds, Link weighs 15 pounds, and their friend Bailey weighs 85 pounds. How much will it cost them all together to get groomed?
Answer:
it would cost them $100
Answer:
it would cost them $100
Step-by-step explanation:
Derive the positive square root of 982081
Answer: 991
square root of 982081 hope this helps
Zero equals two-thirds a number decreased by twelve?
Answer:
X= 12 or 18 (see below)
Step-by-step explanation:
This could be read two different ways.
0=2/3x-12
12=2/3x
12÷2/3=x
12*3/2=x
18=x
—-OR—-
0=2/3(x-12)
0=2/3x-8
8=2/3x
8÷2/3=x
8*3/2=x
12=x
if x+y = 10
and xy 21
find 2(x² + y ² )
Answer:
158
Step-by-step explanation:
2(x square + y square)
2 (X+y) square -2 xy
2(10) square -2(21)
2×100-42
200-42
=158
ILL GIVE YOU BRAINLIST !!
Nick's mom gave him $10 allowance. His little sister was given $4 less than Nick. Write an expression for the amount that Nick's little sister was given
Answer:
Let x be the amount Nick's little sister is given.
x = 10 - 4
The sum of five times a number, and 1, is equal to four times the number
I need help with the
translation part!
Answer:
5x + 1 = 4x
You can really put any letter for "a number":
5n + 1 = 4n
Evaluate the expression when a=-7. a^2+4a-2
Plug in the value to solve the expression.
[tex](-7)^2+4(-7)-2[/tex]
[tex]49-28-2[/tex]
[tex]19[/tex]
Hope this helps.
頑張って!
Hey there!
a^2 + 4a - 2
= -7^2 + 4(-7) - 2
= -49 - 28 - 2
= -77 - 2
= -79
Therefore, your answer is: -79
Therefore, your answer is: -79
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Simplify 0.5x-2y > 3
I will assume you want it in the form of y>mx+b
0.5x-2y>3
0.5x-3>2y
0.25x-1.5>y
Answer:
[tex]x>4y+6[/tex]
Step-by-step explanation:
[tex]0.5x-2y>3[/tex]
First, we will have to add 2 to both sides.
[tex]0.5x-2y+2y>3+2y[/tex]
This equals to
[tex]0.5x>2y+3[/tex]
Now, we will make this into a fraction and divide. We will divide by 0.5.
[tex]\frac{0.5x}{0.5} >\frac{2y+3}{0.5}[/tex]
Now that we divided, we got our answer!
[tex]x>4y+6[/tex]
Hope this helps!
Which pair of expressions have equivalent values?
Answer:
5 + y - 2 - 6 y + y; 8 y + 3
Step-by-step explanation: