Answer:
System 2 and system 3, because the second equation in system 3 is obtained by adding the first equation in system 2 to two times the second equation in system 2
Step-by-step explanation:
We are given four systems of equations. We are asked to find which two sets have the same solution.
We find that in all the 4 systems, first equation 4x-5y =2 remains the same.
I option is wrong because
Equation I + 2times equation 2 in II system
gives 10x-7y =10 but given is 10x-21y =10 hence wrong.
Now compare 2 and 3
In system 2, I equation +2times second equation gives
24x-5y-42y =2+20 or
24x-47y =22
Hence system 2 and 3 are the same set of equations and give the same solution.
ONLY THE BRAINLIEST OF USERS ANSWER THIS QUESTION 30 POINTS!!!!!!!!!!!!!!!
Give the function that defines the given sequence.
-8,-20,-50,-125,-625/2
PLEASE NEED HELP NOW
Answer:
8*5^n-1 / 2^n-1 = n
This is the function for your sequence
8*5^n-1 / 2^n-1 = n
The Sequence Calculator finds a equation of the sequence or also allows you to view the next terms in a sequence. Arithmetic Sequence Formula: an = a1 +d(n −1) a n = a 1 + d (n - 1) Geometric Sequence Formula: an = a1rn−1 a n = a 1 r n - 1
What does the word function mean in math?f (3) f ( 3) and g(3) g ( 3)f (−10) f ( − 10) and g(−10) g ( − 10)f (0) f ( 0)f (t) f ( t)f (t +1) f ( t + 1) and f (x +1) f ( x + 1)f (x3) f ( x 3)g(x2−5) g ( x 2 − 5)How do you find the Fraction form in math?Divide the numerator by denominatorWrite down the whole number resultUse the remainder as the new numerator over the denominator. This is the fraction part of the mixed number.Learn more about function here https://brainly.com/question/12431044
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Todd simplifies the radius of pond A this way:
5√(164 ) meters
Step 1: 5(√100+√64)
Step 2: 5(10+8)
Step 3: 5(18)
Step 4: 90
One of Todd’s steps is incorrect. Identify which step is incorrect; and rewrite the step so it is correct.
A textbook costs 65.49 before tax the tax on the textbook is 6.5% what is the cost of the text book
Answer:
69.75
Step-by-step explanation:
6.5% = 0.065
So the cost of the textbook = 65.49 + 0.065*65.49
= 69.75 to nearest hundredth
Solve for u, z, y, and t:
A;
y/a-b=y/b-a, if a≠b (/ means fractions)
B;
t+ b^2/a=bt/a +a, if a≠b
[tex]A.\\\\\dfrac{y}{a}-b=\dfrac{y}{b}-a\qquad\text{multiply both sides by }\ ab\neq0\\\\by-ab^2=ay-a^2b\qquad\text{add}\ ab^2\ \text{to both sides}\\\\by=ay+ab^2-a^2b\qquad\text{subtract}\ ay\ \text{from both sides}\\\\by-ay=ab^2-a^2b\qquad\text{distributive}\\\\(b-a)y=ab^2-a^2b\qquad\text{divide both sides by}\ (b-a)\\\\\boxed{y=\dfrac{ab^2-a^2b}{b-a}}\to y=\dfrac{ab(b-a)}{b-a}\to\boxed{y=ab}[/tex]
[tex]B.\\t+\dfrac{b^2}{a}=\dfrac{bt}{a}+a\qquad\text{multiply both sides by}\ a\neq0\\\\at+b^2=bt+a^2\qquad\text{subtract}\ b^2\ \text{from both sides}\\\\at=bt+a^2-b^2\qquad\text{subtract}\ bt\ \text{from both sides}\\\\at-bt=a^2-b^2\qquad\text{distributive}\\\\(a-b)t=a^2-b^2\qquad\text{divide both sides by}\ (a-b)\neq0\\\\\boxed{t=\dfrac{a^2-b^2}{a-b}}\to t=\dfrac{(a-b)(a+b)}{a-b}\to\boxed{t=a+b}[/tex]
Answer:
Where are y and t?
Step-by-step explanation:
Your favorite baseball player is doing much better this year than he did last year. Last year he got 56 hits. This year he has 3 times as many hits. How many hits does he have this year?
Answer:168
Step-by-step explanation:
56 x 3 = 168
There are 15 pieces of fruit in a bowl and six of them are apples. What percentage of the pieces of fruit in the Bowl are apples
Answer:
40% of the pieces of fruit in the Bowl are apples.
Step-by-step explanation:
Given the statement:- There are 15 pieces of fruit in a bowl and six of them are apples.
⇒ Total number of pieces of fruit in a bowl = 15 pieces
and
Number of pieces of apple in a bowl = 6 pieces.
To find the percentage of the pieces of fruit in the Bowl are apples.
[tex]Percentage = \frac{Number of pieces of apple in bowl}{Total number of pieces of fruit in Bowl} \times 100[/tex]
= [tex]\frac{6}{15} \times 100 = 40\%[/tex]
Therefore, 40% of the pieces of fruit in the Bowl are apples.
The percentage of apples present in the bowl is [tex]40\%[/tex].
According to the question, there are 15 pieces of fruit in a bowl and 6 of them are apples.
So, the percentage of apples present in the bowl is evaluated as-
[tex]Percentage\;of\;apples=\dfrac{Apples}{Total\;number\;of\;fruits}\times 100\%\\Percentage\;of\;apples=\dfrac{6}{15}\times 100\%\\Percentage\;of\;apples=40\%[/tex]
Hence, the percentage of apples present in the bowl is [tex]40\%[/tex].
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Molly can drive her car 112 miles on 4 gallons of gas and 182 miles on 6.5 gallons write an equation that represented between g the number of gallons she has in her car and m the number of miles she can drive then use the equation to find how many gallons she would need to drive 420 miles
Answer:
Step-by-step explanation:
You will always get the same result in a numerical expression no matter the order in which you perform the operations
Answer:
i just did the quiz and its FALSE i got it wrong so i thought you should have a right answer
Step-by-step explanation:
The order of operations in mathematics ensures that the result of a numerical expression is the same regardless of the order in which the operations are performed. - True
Explanation:In mathematics, the order of operations is a set of rules that dictate the order in which mathematical operations should be performed in an expression. Following these rules ensures that you always get the same result, regardless of the order in which the operations are performed.
The order of operations, also known as PEMDAS, stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). For example, in the expression 4 + 5 × 2, according to the order of operations, you would perform the multiplication first and then the addition. So, the correct way to evaluate this expression would be 4 + (5 × 2) = 4 + 10 = 14.
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Complete Question:
You will always get the same result in a numerical expression no matter the order in which you perform the operations. True/False ?
HELPPPP WILL GIVE BRAINLIEST
Answer:
79
Step-by-step explanation:
Since the triangles are similar, the sides that are the same length have angles that are the same size at the top.
solve the inequality a-3 ≤-8
Answer:
a is less than or equal to -5
Step-by-step explanation:
Answer:
a ≤-5
Step-by-step explanation:
a-3 ≤-8
Add 3 to each side
a-3 +3≤-8+3
a ≤-5
Seattle, wa and san francisco, ca lie on the same longitudinal line. san francisco is at 38° latitude and seattle is at 47° latitude. if the earth is a sphere of radius 4000 miles, use arc length to find the distance between the cities. [use π = 3.14, and round to the nearest mile.]
Step 1.
Calculate measure of angle α:
[tex]47^o-38^o=9^o[/tex]
Step 2.
Calculate what fraction of the angle 360° is the angle α:
[tex]\dfrac{9^o}{360^o}=\dfrac{1}{40}[/tex]
Step 3.
Calculate the circumference of the Earth (circle):
[tex]C=2\pi r\to C=2\pi\cdot4000=8000\pi\ mi[/tex]
Step 4.
The length of arc is equal 1/40 of the circumference:
[tex]\dfrac{1}{40}C=\dfrac{1}{40}\cdot8000\pi=200\pi\ mi[/tex]
[tex]\pi\approx3.14\to\dfrac{1}{40}C\approx200\cdot3.14=628\ mi[/tex]
The distance between San Francisco, CA, and Seattle, WA, along the longitudinal line is approximately 628 miles, calculated using the formula for arc length of a sphere, considering the Earth's radius and the difference in degrees of latitude.
Explanation:The question revolves around the concept of calculating the arc length in degrees, which is a topic in mathematics, specifically trigonometry.
The formula for calculating the arc length of a sphere is arc length = radius x angle (in radians).
We already know the radius of the earth (4000 miles) and the difference in latitude between Seattle and San Francisco (47°-38°=9°).
However, in the formula, we need the angle to be in radians. To convert degrees to radians, we use the formula 1 degree = π/180 radians.
So, 9° equals 9*(π/180) = 0.157 radians.
Now, we substitute the values into the formula: arc length = 4000 miles * 0.157 radians. This gives an answer of approximately 628 miles.
Therefore, the distance between San Francisco, CA, and Seattle, WA, along the longitudinal line is about 628 miles.
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A solid rectangular metal box of 8 inches long, 2 inches wide and 4 inches deep is melted down. All the liquid metal is used to case a cube. What is the length of one side of the cube?
Find the volume of the rectangle:
8 x 2 x 4 = 64 cubic inches.
This means the square can have a volume of 64 cubic inches.
The formula for the volume of a square is V = S^# where S is the length of the side.
Replace V with 64 to solve for S:
64 = S^3
To find S, take the cubic root of 64:
S = ∛64
S = 4
The length of a side is 4 inches.
If a room is 16 1/2 feet by 18 1/2 feet in size and the carpet cost 17.50per square yard what is the total cost of the room
if a normal distribution has a mean of 132 and a standard deviation of 20 what is the value that has a z score of 1.8?
Answer:
168 = x
Step-by-step explanation:
mean = u=132
standard deviation =sigma = 20
z score =z=1.8
The formula is
z = (x-u)/ sigma
Substituting what we know
1.8 = (x-132)/20
Multiply by 20
1.8*20 = (x-132)/20 *20
36 = x-132
Add 132 to each side
36+132 = x-132+132
168 = x
Multiply the standard deviation by the z-score and add that to the mean:
Value = 132 + (20*1.8) = 132 + 36 = 168
The value would be 168.
1) How much greater than m^2+3mn−n^2 is 4m^2+5mn+6n^2?
2)How much less than 3x^2−7x+9 is 2x^2+4x−8? What is the value of the result when x=2?
^=power
Answer:
[tex]3m^2+5n^2+8mn[/tex]
[tex]x^2-11x+17[/tex];0
Step-by-step explanation:
We have been given [tex]m^2+3mn−n^2 [/tex] and [tex]4m^2+5mn+6n^2[/tex]
for (1) we will subtract [tex]4m^2+5mn+6n^2[/tex] from [tex]m^2+3mn−n^2 [/tex] that is:
[tex]4m^2+5mn+6n^2-m^2+3mn-n^2[/tex]
Now, simplify the like terms we get:
[tex]4m^2-m^2+6n^2-n^2+5mn+3mn[/tex]
After simplification we get:
[tex]3m^2+5n^2+8mn[/tex]
Hence, [tex]3m^2+5n^2+8mn[/tex] is the required result.
(2) Now, we need to find how much less than [tex]3x^2-7x+9[/tex] is [tex]2x^2+4x-8[/tex]
Subtract [tex]3x^2-7x+9[/tex] from [tex]2x^2+4x-8[/tex] we get:
[tex]3x^2-7x+9-2x^2-4x+8[/tex]
After simplifying like terms
[tex]x^2-11x+17[/tex]
When x=2 the the above expression becomes:
[tex](2)^2-11(2)+17[/tex]
[tex]4-22+17=0[/tex]
For the first question, 4m^2+5mn+6n^2 is 3m^2+2mn+7n^2 greater than m^2+3mn-n^2. For the second question, 3x^2-7x+9 is x^2 -11x + 17 less than 2x^2+4x−8 and the value of the result when x=2 is 12.
Explanation:For the first question, begin by subtracting the given expressions (m^2 + 3mn - n^2) from (4m^2+5mn+6n^2). This equates to:
(4m^2 + 5mn + 6n^2) - (m^2 + 3mn - n^2) = 3m^2 + 2mn + 7n^2
For the second question, we subtract (2x^2+4x−8) from (3x^2−7x+9). This is equal to:
(3x^2−7x+9) - (2x^2+4x−8) = x^2 -11x + 17
To find the value of the result when x=2, simple plug in '2' wherever x is in the equation, giving the result 17 - 22 + 17 = 12
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A company makes and sells charm bracelets. The cost of producing x bracelets is represented by the function. C(x)=180+8x. The revenue earned for selling x bracelets is represented by the function R(x)=20x. Write and simplify a function P the represents the profit made from selling x bracelets. How many must the company sell to break even
Answer:
Minimum 15 bracelets to be sold to meet the break even.
Step-by-step explanation:
The cost price of bracelets is represented by C(x) =180+8x
The revenue earned (selling price) is represented by R(x) =20x
In these two functions x represents number of bracelets.
If P represents the profit then P = 20x-(180+8x)
P = 20x-180-8x = (12x-180)
For break even profit P = 0
12x-180 =0
12x = 180
x = 180÷12
x = 15
So minimum quantity of bracelets to be sold is 15 for the break even.
Which compound sentence has its solution set shown on the graph below?
2x - 4 > 6 or 3x < 9
2x - 4 < 6 and 3x > 9
3x + 8 > -7 or -4x < 12
3x + 8 < -7 and -4x > 12
There might be a simpler way to do this, if there is, sorry.
If you look at the graph, x is greater than 3 but less than 5.
So: x > 3 and x < 5
I would simplify each solution set and get "x" by itself (until I get the right answer):
A.) 2x - 4 > 6 or 3x < 9
2x - 4 > 6 Add 4 on both sides
2x > 10 Divide 2 on both sides
x > 5 (you could stop here and go to the next choice since you know this does not match the graph)
3x < 9 Divide 3 on both sides
x < 3
x > 5 and x < 3
B.) 2x - 4 < 6 and 3x > 9
x < 5 and x > 3
Your answer is B or the 2nd option
[C and D would have given a negative number]
The compound sentence that has its solution set shown on the graph is 3x + 8 > -7 and -4x < 12.
The solution set for the given compound inequalities is represented by the graph where the shaded region includes the points -1, 0, 1, 2, 3, 4, and 5. The compound sentence that has this solution set is:
3x + 8 > -7 and -4x < 12
Let's break down the compound sentence step by step:
Solve the first inequality: 3x + 8 > -7. Subtract 8 from both sides to get 3x > -15. Divide both sides by 3 to get x > -5.
Solve the second inequality: -4x < 12. Divide both sides by -4 and flip the inequality sign to get x > -3.
Combine the two inequalities by using the word 'and': x > -5 and x > -3.
The solution to this compound sentence is the values of x that satisfy both inequalities, which is x > -3.
Therefore, the compound sentence 3x + 8 > -7 and -4x < 12 has its solution set shown on the given graph.
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PLEASE HELP (SEE ATTACHMENTS)
Answer:
Question 1 is A.
The measures of two consecutive angles of a parallelogram are in the ratio 6:3. What is the measure of an acute angle of the parallelogram?
A) 15° B) 30° C) 60° D) 90°
Help Plz I'm Almost Done
Answer: choice C) 60 degrees
smaller angle = 3*x; larger angle = 6*x
The two angles are supplementary, so they add to 180
6x+3x = 180
9x = 180
x = 180/9
x = 20
If x = 20, then,
smaller angle = 3*x = 3*20 = 60 degrees
(the other angle being 6*x = 6*20 = 120; note how 60+120 = 180)
Answer:
try going with C
Step-by-step explanation:
Christine baked a pumpkin pie she ate 1/6of the pie. Her brother ate 1/3 of it and gave leftovers to his friends. What fraction of the pie did he give to his friends
Answer:
[tex]\frac{1}{2}[/tex] of the pie.
Step-by-step explanation:
We have been given that Christine baked a pumpkin pie. She ate 1/6 of the pie. Her brother ate 1/3 of it and gave leftovers to his friends.
Let us find out pie given to friends by subtracting amount of pie eaten by Christine and her brother from 1 pie, that will be 6/6.
[tex]\text{The pie given to friends}=\frac{6}{6}-(\frac{1}{6}+\frac{1}{3})[/tex]
[tex]\text{The pie given to friends}=\frac{6}{6}-(\frac{1}{6}+\frac{2*1}{2*3})[/tex]
[tex]\text{The pie given to friends}=\frac{6}{6}-(\frac{1}{6}+\frac{2}{6})[/tex]
[tex]\text{The pie given to friends}=\frac{6}{6}-\frac{3}{6}[/tex]
[tex]\text{The pie given to friends}=\frac{6-3}{6}[/tex]
[tex]\text{The pie given to friends}=\frac{3}{6}[/tex]
[tex]\text{The pie given to friends}=\frac{1}{2}[/tex]
Therefore, he gave [tex]\frac{1}{2}[/tex] of the pie to his friends.
what is the value of x?
Answer:
The answer is 5
Find the value of 64 ÷ 2 · 16.
Answer:
512
Step-by-step explanation:
64 / 2 = 32
32 * 16 = 512
64 / 2 * 16 = 512
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[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{62 \div 2 \times 16}\\\\\mathsf{= \dfrac{62}{2} \times 16}\\\\\mathsf{= \bold{32}\times16}\\\\\mathsf{= \bf 512}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak{512}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Does anyone know how to solve this? A motorist and a bicyclist leave the same place and proceed in opposite directions. If the bicycle is traveling 15 mph and the auto is traveling 55 mph, in how many hours will they be 140 miles apart?
Answer:
3.5
Step-by-step explanation:
The speed difference is 40 mph
then divide the distance by the speed difference and you get 3.5
Answer:
they will be 140 miles apart in 2 hours
Step-by-step explanation:
in one hour they will be 70 miles apart since 15 + 55 = 70 and then they get 70 more miles apart in the second hour and 70 + 70 = 140 so 2 hours
Caroline has 201?4 pounds of pastrami in her deli. If she uses 3?8 of a pound for each sandwich she makes, how many pastrami sandwiches can she make with the 201?4 pounds of pastrami?
Answer:
76
Step-by-step explanation:
Caroline can make 804 full pastrami sandwiches with 201 1/4 pounds of pastrami, using 3/8 of a pound for each sandwich.
To find out how many pastrami sandwiches Caroline can make with 201 1/4 pounds of pastrami, we first need to determine the total number of sandwiches that can be made from a single pound of pastrami. As each sandwich uses 3/8 of a pound, we can calculate this as follows:
1 pound / (3/8 pound per sandwich) = 8/3 sandwiches per pound.
Next, we multiply the number of sandwiches that can be made per pound by the total pounds of pastrami:
201 1/4 pounds * 8/3 sandwiches/pound = 804 sandwiches + 2/3 of a sandwich.
Since Caroline can't make 2/3 of a sandwich, she can make a total of 804 full sandwiches with the pastrami she has.
20 POINTS AND BRAINLIEST!
IT WILL TELL ME WHICH ONES ARE WRONG!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Megan constructed triangle ABC. In Megan’s triangle, m∠A is represented by x°, m∠B is 4 times greater than m∠A, and m∠C is 30° less than 5 times m∠A.
m∠A = x°
m∠B = (4x)°
m∠C = (5x − 30)°
~~~~~~~~~~~~~~~~~~~~~~~~
What is the measure of each angle in Megan’s triangle?
1) m∠A = °
A) 21 B) 20 C) 36 D) 30
2) m∠B = °
A) 80 B) 84 C) 120 D) 112
3) m∠C = °
A) 85 B) 75 C) 82 D) 120
Answer:
<A =21
<B = 84
<c = 75
Step-by-step explanation:
<A =x
<B = 4x
<C =5x-30
The sum of A+B+C = 180
x+ 4x + 5x-30 = 180
Combine like terms
10x -30 = 180
Add 30 to each side
10x-30+30 = 180+30
10x = 210
Divide by 10
10x/10 = 210/10
x= 21
Since x =21 we can find the value of the angles
Substituting x into the equations for angles A, B and C
<A =21
<B = 4x = 4*21 = 84
<C = 5x-30 = 5*21-30 = 105-30 = 75
Answer
a,b,c
Step-by-step explanation:
21
84
75
What is sinB ?
Express your answer as a fraction.
Answer:
sinB = 8/17
Step-by-step explanation:
sinB = Opposite/Hypotenuse
Here we have to find the opposite side using the Pythagorean theorem.
AB^2 = AC^2 + BC^2
17^2 = AC^2 + 15^2
AC^2 = 17^2 - 15^2
AC^2 = 289-225
AC^2 = 64
Taking the square root on both sides, we get
AC = 8
Opposite side = 8
SinB = 8/17
Answer:
sin B = 8/17
Step-by-step explanation:
sin B can be expressed as the opposite over the hypotenuse in a right triangle. But we don't know the opposite yet. We can use the Pythagorean theorem to solve for it
a^2 + b^2 = c^2
15^2 +b^2 = 17^2
225+b^2 = 289
Subtract 225 on each side
225-225 +b^2 = 289-225
b^2 = 64
Take the square root of each side
b=8
The opposite side is 8
sin B = opp/hyp
sin B = 8/17
Karen uses her credit card to purchase a new television for $695.20. She can pay off up to $325 per month. The card has an annual rate of 17.9% compounded monthly. How much will she pay in interest?
$6.28
$16.96
$20.44
$62.16
Answer: $ 16.96
Step-by-step explanation:
Here, the present value of the loan, PV = $695.20
Annual Interest rate = 17.9%
⇒ Monthly interest rate = 17.9/12 = 1.41666666667
Thus, the monthly interest rate (decimal ) , r = 0.014167 ( approx)
Monthly payment, P = $ 325
Let the time period of the loan = n.
Since, [tex]P= \frac{r(PV)}{1-(1+r)^{-n}}[/tex]
⇒ [tex]325= \frac{0.014167(695.20)}{1-(1+0.014167)^{-n}}[/tex]
⇒ [tex]1-(1+0.014167)^{-n}= \frac{10.37008984}{325}[/tex]
⇒ [tex]1-(1+0.014167)^{-n}= 0.03190796873 [/tex]
⇒ n = 2.19
Thus, her total payment = 2.19 × 325 = 711.75
⇒ Her total interest = 711.75 - 695.20 = $16.55
Since only 16.96 is near to 16.55
Thus, second option is correct.
The times for three runners in a 100-meter race are 9.85 s, 9.6 s and 9.625 s. What is the winning time?
Help me please lots of points
Given quadrilateral ABCD, if diagonals AC and BD bisect each other, and angle ABC=91°, but you know nothing about any lengths in the diagram, what special figure MUST ABCD be? A rhombus or a parallelogram? HOW DO YOU KNOW.
Answer:
ABCD must be a paralellogram
Step-by-step explanation:
In parallelogram, rectangle, square and rhombus the diagonals bisect each other. Since angle ABC=91°, then this quadrilateral cannot be rectangle and cannot be square, because rectangle and square have all right angles (90°).
If diagonals of a quadrilateral bisect each other, then quadrilateral is parallelogram. A rhombus is a parallelogram with all congruent sides.
You know nothing about any lengths in the diagram, then you can state that this quadrilateral is parallelogram (always) and can be rhombus (sometimes).