Answer:
The first questions unknown equals
[tex] \frac{3025}{49} [/tex]
The second question is unclear. I assume it is to simplify if that is the case the answer will be.
[tex] \frac{1}{2} [/tex]
Step-by-step explanation:
First Question I made ?=x for simplicity.
[tex]7 \sqrt{x} = 55[/tex]
then I divide both sides by 7
[tex] \sqrt{x} = \frac{55}{7} [/tex]
then I square both sides
[tex]x = \frac{3025}{49} [/tex]
Question 2
I simplified by dividing both the denominator and the numerator by their HCF (highest common factor) which is 5
[tex] \frac{5 \div 5}{10 \div 5} [/tex]
which equals
[tex] \frac{1}{2} [/tex]
Answer:
[tex]\textsf{1.} \quad 7\sqrt{\dfrac{3025}{49}}=55[/tex]
[tex]\textsf{2.} \quad \dfrac{5}{10}=\dfrac{1}{2}[/tex]
Step-by-step explanation:
Question 1Let x be the unknown number:
[tex]\implies 7\sqrt{x}=55[/tex]
Divide both sides of the equation by 7:
[tex]\implies \dfrac{7 \sqrt{x}}{7}=\dfrac{55}{7}[/tex]
[tex]\implies \sqrt{x}=\dfrac{55}{7}[/tex]
Square both sides of the equation:
[tex]\implies \left(\sqrt{x}\right)^2=\left(\dfrac{55}{7}\right)^2[/tex]
[tex]\implies x=\dfrac{55^2}{7^2}[/tex]
[tex]\implies x=\dfrac{3025}{49}[/tex]
Question 2Divide the numerator and the denominator by the highest common factor:
[tex]\implies \dfrac{5 \div 5}{10 \div 5}=\dfrac{1}{2}[/tex]
a manufacturer produces a metal box with a square base, no top, and a volume of h w w 50 cm3 what dimensions minimize the amount of metal used to make the box.
the dimensions of the box that minimize the amount of material used is 4.641cm by 4.641cm by 2.32cm
Let the side of the square base be x
h be the height of the box
Volume V = x²h
50 = x²h
h = 50/x² ..... 1
Surface area = x² + 2xh + 2xh
Surface area S = x² + 4xh ...... 2
Substitute 1 into 2;
From 2; S = x² + 4xh
S = x² + 4x(50/x²)
S = x² + 200/x
To minimize the amount of material used; dS/dx = 0
dS/dx = 2x - 200/x²
0 = 2x - 200/x²
0 = 2x³ - 200
2x³ = 200
x³ = 100
x = ∛100
x = 4.6416cm
Since V = x²h
50 = 4.642²h
h = 50/21.548
h = 2.32cm
Hence the dimensions of the box that minimize the amount of material used is 4.641cm by 4.641cm by 2.32cm
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Jamie thinks that 1 is neither prime
nor composite.
Show why you agree or disagree with him.
Yes, I do agree with Jamie.
1 is NEITHER a prime number NOR a composite number.
Reason for agreeing:-
We know that a PRIME NUMBER is any given number that has only one as a factor. I.e it is only divisible by 1 AND ITSELF.
And, a COMPOSITE NUMBER is any number that is divisible by a number other than one and itself.
Here in the case of 1, we see that it is divisible by 1 and itself, and since it cannot have any other factor we can't put in either of the two categories
Walter pays 2.53 to ship a package that weighs 5.5 onces. which is the cost to ship 1 ounce
To determine the price per ounce walter paid to ship the package you can use cross multiplication.
If 5.5 ounces ______$2.53
Then 1 ounce______$x
[tex]\begin{gathered} \frac{2.53}{5.5}=\frac{x}{1} \\ x=0.46 \end{gathered}[/tex]He will pay $0.46 per ounce
can someone help me really quick
Answer:
6.75
Step-by-step explanation:
Consider the ratio:
$4.50 : 6 apples
We need to multiply this ratio by a value such that the right side is 9 because there are 9 apples in array p. This value is 9/6 = 3/2.
$4.50 : 6 apples
× 3/2 × 3/2
$6.75 : 9 apples
So, the value of p, or 9 apples, is $6.75, which you will input as 6.75.
please anyone pleaseee help with explanation
The slope of the line = change in y / change in x = 4/3.
How to Find the Slope of a Line?The slope of a line is the rise over the run, which is the change in y/change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
To calculate the slope of the line that is given, chose any two points on the line as plotted in the given graph, say:
(30, 20) = [tex](x_1, y_1)[/tex]
(60, 60) = [tex](x_2, y_2)[/tex]
Substitute each of these values into the slope formula, [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]:
Slope for the given line (m) = (60 - 20)/(60 - 30)
Slope for the given line (m) = 40/30
Slope for the given line (m) = 4/3.
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Match each pair of angles to their angle pair name.
<2&<7
<5 & <8
<9 & <16
<1 & <3
<4 & <3
<14 & <15
The name for the angle <2&<7 is an alternate interior angle by a transversal x.
What are vertically opposite angles?It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
The angle pairs are given.
From the diagram:
<2&<7 = Alternate interior angle by a transversal x
<5 & <8 = Consecutive exterior angle by a transversal x
<9 & <16 = Consecutive exterior angle by a transversal x
<1 & <3 = Corresponding angles by transversal x
<4 & <3 = Adjacent angle by transversal g
<14 & <15 = Consecutive interior angle by a transversal y
Thus, the name for the angle <2&<7 is an alternate interior angle by a transversal x.
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A group of friends go to the store buy some fruit. marcus buys 5 pounds of apples for $13.75 at this rate ,how many pounds of apples can marcus buy with $22
Answer:
He can buy 8 pounds
Step-by-step explanation:
13.75/5=2.75
22/2.75=8 or 8 pounds the to check your answer 2.75x8=22
On Wednesday night in St. Petersburg, Russia, the temperature is -11°C.
On the same night in Bombay, India, the temperature is 17°C.
What is the difference in the temperature?
The difference in the temperature of Bombay to St. Petersburg is 28° C.
What is the difference between two numbers and how is it calculated?
An arithmetic operation called subtraction simulates the process of deleting items from a collection. The negative symbol, or, denotes subtraction. Subtraction is the process of subtracting a matrix, vector, or other quantity from another according to predetermined criteria in order to find the difference.
Subtracting two numbers from each other is a type of subtraction. The difference between two numbers is calculated by deducting the smaller of the two values from the larger.
Given, the temperature in St. Petersburg = T₁ = -11° C
The temperature in Bombay = T₂ = 17° C
Using general comparison, we get T₂>T₁, since one is positive and the other is negative.
Therefore following available literature,
Difference in temperature = T₂ - T₁ = 17 - (-11) = 17 + 11 = 28° C
Thus, the required difference in temperature of Bombay to St. Petersburg is 28° C.
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12] Will's salary is three times Nathan's salary. Together they earn $192 per week. Find the salary of each boy.
Nathan's salary is $48 and Will's salary which three times of Nathan's salary is $144.
What is salary?
An employment contract may include a salary clause as a type of recurring payment from an employer to an employee. In contrast, piece wages are paid separately for each job, hour, or other unit rather than on a regular schedule. Salary can also be seen from the perspective of operating a corporation as the expense of obtaining and keeping employees to carry out operations; this is known as a personnel expense or salary expense. Payroll accounts are used in accounting to record salaries.
It is given in the question that Will's salary is three times Nathan's salary.
So, lets assume that Nathan's salary is X it implies that Will's salary will be 3 times X = 3X
Together they earn $ 192.
So,
X + 3X = 192
4X = 192
X = 192/4
X = 48
Therefore, Nathan's Salary is $48
Since, Will's salary is 3 times of Nathan's salary,
So,
Will's salary = 3 (48) = 144
Therefore, Will's Salary is $144
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Identify which of the twelve basic functions listed below fit the description.
The four functions with a local minima are:
y = x², y = |x|, y = sin x, y = cos x
A function f(x) has a local minima if its second derivative, f''(x) > 0 at the point where f'(x) = 0.
We use this to find which among the functions y = x, y = x², y = x³, y = |x|, y = 1/x, y = eˣ, y = √x, y = ln x, y = sin x, y = cos x, y = int(x), y = 1/(1+e⁻ˣ) has a local minima.
y = xy' = 1. There is no point x such that y' = 0. So it has no local minima.
y = x²y' = 2x
y' = 0
⇒ 2x = 0
⇒ x = 0
y'' = 2 > 0
So y = x² has a local minima at x = 0
y = x³y' = 3x²
y' = 0
⇒ 3x² = 0
⇒ x = 0
y'' = 6x = 0 at x = 0
So y = x³ has no local minima.
y = |x|i.e., y = x, when x ≥ 0 and y = -x , when x < 0
So y ' = 1, when x ≥ 0 and y' = -1, when x < 0
But at x = 0, y = 0 and y' = 0.
Now y'' = 0 everywhere. But the graph of y = |x| clearly shows that y = |x| has a local minimum at x = 0.
y = 1/xy' = -1/x²
Here, y' is nowhere zero and hence doesn't has a local minima.
y = eˣy' = eˣ
eˣ is nowhere zero and hence it does not has a local minima.
y = √xy' = 1/2√x
Here also y' is nowhere zero and hence it does not has a local minima.
y = ln xy' = 1/x
Here also y' is nowhere zero and hence it does not has a local minima.
y = sin xy' = cos x
y' = 0
⇒ cos x = 0
⇒ x = (2n+1)π/2, n = 0,1,2,....
y'' = -sin x
-sin ((2n+1)π/2) = -1, when n = 0,2,4,... and -sin ((2n+1)π/2) = 1, when n = 1,3,5,....
So y = sin x has local minima at x = (2n+1)π/2, where n = 1,3,5,....
y = cos xy' = -sin x
y' = 0
⇒ -sin x = 0
⇒ x = nπ
y'' = -cos x
-cos(nπ) = (-1)ⁿ⁺¹
So, -cos(nπ) = 1, when n = 1,3,5,.... and -cos(nπ) = -1, when n = 0,2,4,...
Hence y = cos x has local minima at x = nπ with n = 1,3,5,....
y = int(x)y' = x
y' = 0
⇒ x = 0
y'' = 1 >0
So y = int (x) has local minima at x = 0
y = 1/(1+e⁻ˣ)y' = e⁻ˣ/(1+e⁻ˣ)²
y' = 0
⇒ e⁻ˣ/(1+e⁻ˣ)² = 0
⇒ e⁻ˣ = 0
⇒ 1/eˣ = 0 which is not possible anywhere.
Hence y = 1/1+e⁻ˣ has no local minima.
Finally the four functions with local minima are:
y = x², y = |x|, y = sin x, y = cos x
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Dennis's curtain company is making curtains for a local hotel. He wants each curtain to be 48 inches long. At the fabric store, fabric is sold by the foot. If Dennis's curtain company wants to make 63 curtains, how many feet of fabric will he need?
Dennis's curtain company needs 252 feet long fabric to make 63 curtains.
Given,
The length of a curtain = 43 inches
Number of curtains they want to make = 63
We have to find the length of fabric in foot needed to make 63 curtains.
1 foot = 1/12 inches
Now,
The total length of fabric needed in inches = Number of curtains × Length of 1 curtain = 63 × 48 = 3024 inches
Convert this into feet.
That is,
3024 × 1/12 = 252 feet.
Therefore,
Dennis's curtain company needs 252 feet long fabric to make 63 curtains.
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Swim team members can race or dive. At a meet, 18 members race. The ratio of racers to divers is 6:2. How many members are on the team?
Answer:
24
Step-by-step explanation:
If the ratio of racers to divers is 6:2 then compare that to 18:x
6 times 3 is 18
2 times 3 is 6
x is 6
Now add 6 and 18
You get 24
how do you Graph the line y=4x-1
Answer: Look at photo. Your y intercept is -1 and the line goes up 4 and right 1.
Step-by-step explanation: Look at your last number, the -1. That should be on the y axis. Put that number there and then take 4x which can also be read as 4/1x and from the point of -1, go up 4 and right 1.
Marta does 30 minutes of exercise a day. greg des 40 minutes of exercise a day. how many more minutes does marta exercise greg in one month of 31 days? answers
Answer:
Martha exercises 310 minutes more than Greg in a 31-day month!
Step-by-step explanation:
30x
40x
Where x equals the number of days.
Let's plug it in:
30(31) = 930
40(31) = 1240
Let's subtract:
1240 - 930 = 310
MEANING Marta exercises 310 minutes more than Greg in a 31-day month!
-27 = -w/5 solve for w simplify your answer as much as possible
Answer:
w = 135
Step-by-step explanation:
-27 = -w/5
multiply both sides by 5:
5(-27) = 5(-w/5)
- 135 = -w
divide both sides by -1:
- 135/-1 = -w/-1
w = 135
33 1/3 of 66 is i will give points if help
Answer: 2200
Step-by-step explanation:
33 1/3 of 66
What is 150 + 1/6 + 1/2
Answer:
150 and 2/3 or 150.6666...
Step-by-step explanation:
1/6 + 1/2 = 1/6 + 3/6.
1/6 + 3/6 = 4/6 = 2/3
150 + 2/3 = 150 and 2/3
Mark as brainliest please
Answer: exact form is 452/3
decimal form is 150.6
Step-by-step explanation:
Simplify the expression. Show your work.
[tex]\sqrt{\frac{4x^2}{3y} }[/tex]
[tex]\sqrt{\cfrac{4x^2}{3y}}\implies \cfrac{\sqrt{4x^2}}{\sqrt{3y}}\implies \cfrac{\sqrt{2^2x^2}}{\sqrt{3y}}\implies \cfrac{2x}{\sqrt{3y}}[/tex]
Answer:
[tex]\frac{2x}{\sqrt{3y} }[/tex]
Step-by-step explanation:
Hope that's helps.
Margie’s work for adding linear expressions is shown below. After checking her answer key, she solved it incorrectly.
Given: (-3.78b + 12) - (4.82b - 16)
Step 1: -3.78b + 12 + -4.82b - 16
Step 2: -3.78b + -4.82b + 12 - 16
Step 3: (-3.78b + 4.82b) + (12 - 16)
Step 4: -8.6b + (-4)
Part A: Identify and explain the first step where Margie made an error
Part B: Explain how to correctly write the expression in the fewest terms by correcting the error in Part A.
There is a mistake in the first step. The correct way to add the linear expression is (−3.78b + 12) − (4.82b − 16) = -8.6b + 18
How to correctly write adding linear expression?An expression is used to show the relationship between the variables.
The linear expression to add is as follows: (−3.78b + 12) − (4.82b − 16)
Firstly we open the bracket on the right side by multiplying the negative sign by the numbers in the brackets.
(−3.78b + 12) − (4.82b − 16)
−3.78b + 12 - 4.82b + 16
Combine like terms
−3.78b + 12 - 4.82b + 16
-3.78b - 4.82b + 12 + 16
Add the like terms
-3.78b - 4.82b + 12 + 16
-8.6b + 18
Therefore, she made the mistake in the first step.
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Ten granola bars and twelve bottles of water cost $23. Five granola bars and four bottles of water cost $10. How much do one granola bar and one bottle of water cost?Part BFor a fundraiser, a group plans to sell granola bars and bottles of water at the same prices as described in Part A. The group wants the income from the fundraiser to be at least $150.Choose the inequality to show the number of granola bars x and the number of bottles of water y that must be sold.
Let g = cost of granola bars
b = cost of a bottle of water
10g+12b = 23
5g + 4b = 10
Multiply the second equation by -2
-10g -8b = -20
Add this to the first equation
10g+12b = 23
-10g -8b = -20
---------------------
4b = 3
Divide by 4
4b/4 = 3/4
b = 3/4 or .75
Now find g
5g + 4(3/4) = 10
5g + 3 = 10
5g = 7
g = 7/5
g = 1.4
We want to find 1g+ 1b
1.4+ .75 =2.15
Part B
We want our income to be at least 150
The cost of granola bars is 1.4 and we are selling x of them
The cost of water is .75 and we are selling y of them
It must be at least >=
1.4x + .75y >= 150
Landon had 56 playing cards. He kept 12 for himself and
dealt the rest evenly to his 4 friends. Which expression best
represents the number of cards each friend received?
We need to use simple division to solve the problem. The number of cards each friend received is 11.
It is said that Landon has 56 cards, he kept 12 cards for himself, so we can subtract 12 cards from the whole lot to get the total number of cards he distributes among his friends.
56-12=44
There are 44 cards that he will distribute among his friends equally, we can get that by simply dividing the total number of cards by the number of friends which is 4.
number of cards for each friend=44/4=11
Therefore the number of cards each friend received is 11.
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Determine which integer(s) from the set S:{−40, 2, 20, 42} will make the inequality three eighths m minus three is less than one fourth m plus 2 false.
S:{42}
S:{−40, 2}
S:{−40, 2, 20}
S:{−40}
The set S:{42} will make the inequality false.
By definition, one can apply any monotonically rising function to both sides of an inequality without affecting how they relate to one another (provided that both expressions are in the domain of that function).
An inequality relation would be reversed if a monotonically dropping function were applied to both sides of the inequality. Examples of how to employ a monotonically declining function are the rules for the additive and multiplicative inverses for positive values. The inequality (a b, a > b) remains stringent if the function is monotonic in a strict sense.If only one of these requirements is met, the inequality that results is not rigid. In fact, the requirements for both additive and multiplicative inverses serve as evidence that a strictly.Given inequality is :
3/8 m - 9 < 1/4 m + 2
Solving the inequality we get:
or, m < 40
Therefore of all the elements of the set 42 makes the inequality false.
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how many apples does john eat
Answer:
you gave no context....so ill just guess 3.
Simplify before multiplying 15/20 x 2/5
Thanks!
Answer:
3/10 hope this helps you answer your question!
Find the slope of the line passing through the points (-2, 7) and (—9,4)
The slope of the line is 3/7.
The slope of line will be calculated using the formula :
Slope = [tex] \frac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]
The first point is (-2, 7) and second point is (-9, 4). So, [tex] y_{2}[/tex] = 4, [tex] y_{1}[/tex] = 7, [tex] x_{2}[/tex] = -9 and [tex] x_{1}[/tex] = -2. Keep the values in formula to find the values of slope of the line.
Slope = (4 - 7)/(-9 - -2)
Performing subtraction in numerator and denominator
Slope = -3/-7
Cancelling the negative signs we get -
Slope = 3/7
Thus, the slope of the line is 3/7.
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For one journey from London to Marseille, the ratio number of adults: number of children = 11: 2. There were 220 adults in total on this journey. All of the children and 70% of the adults paid the standard fare. The remaining adults paid the premier fare. Calculate the total of the fares paid by the adults and the children.
Answer: 174
Step-by-step explanation: ok so we divide 220 by 11 to get 20 and times that by two to get 20 children on this journey then see that all children paid and 70 percent of adults so 70 percent of 220 is 154 and then 154 + 20 is 174 so thats the number of fares paid
Which table is linear?
2)
X
-2
-1
0
1
2
у
0.111
0.333
1
3
9
8)
X
-2
-1
0
1
2
у
7
2
-1
-2
-1
X
-2
-1
0
1
2
у
-2
1
4
7
10
Answer:
The last one
Step-by-step explanation:
this is really hard to read but you have to see which y values increase by a constant amount. Only the last case is linear in which each value increases by 3
i need help with this. it’s just geometry
Answer:
27. 48°, 132°
28. The expressions resolve to both angles being 0°, a contradiction to the lines being distinct.
Step-by-step explanation:
Given a figure showing parallel lines crossed by a transversal with marked angles, you want to know (27) the measures of consecutive interior angles that have a ratio of 4:11, and (28) the contradiction in corresponding angles being marked (60-2x)° and (2x-60)°.
27. Algebra.The two marked angles are consecutive interior angles, so are supplementary. Using x for the smaller angle value, we can write the equation ...
x/(180-x) = 4/11 . . . . . the given ratio of the two angles
Multiplying by 11(180-x) gives ...
11x = 4(180-x)
15x = 4(180) . . . . add 4x and simplify
x = 48 . . . . . . . . divide by 15
Then the obtuse angle is ...
180 -48 = 132
The measures of the angles are ∠1 = 48°, ∠2 = 132°.
2. Error Analysis.The two marked corresponding angles are congruent, so ...
(60 -2x)° = (2x -60)°
4x = 120 . . . . . . . . . . . divide by °, add 2x+60
x = 30 . . . . . . . . . . divide by 4
60 -2x = 60 -2(30) = 0
2x -60 = 2(30) -60 = 0
The marked values require the angles to be 0°, which means the transversal is coincident with each of the "parallel" lines.
The given angle values require the lines not to be distinct, as the diagram shows they are.
The measures of the angles of a triangle are shown in the figure below. Solve for x
need help asap!!!)
Answer:
x=36
Step-by-step explanation:
(3x+3)^0+x+54= 90
x+54=90
x=90-54
x=36
Write the domain for the following piecewise-defined function using intervalnotation,2 if x < 1f(x) =1 2 – x2 if x > 1
The domain of a function are the values for which the function is defined or in the other words, it is the set of all possile values that the function accepts.
Therefore:
[tex](-\infty,1)U(1,\infty)[/tex]