Answers
Answer:
x=4, y =5
Step-by-step explanation:
there's no factorization involved, just elimination and substitution. First subtract equation 1 and 2. The x's cancel out and you get y by itself and can solve for it. Then plug the value of y into equation 2 and solve for x and you get it. (In my picture I put value of y in equation 1 but your question asks for putting it in equation 2 so do that instead)
Related Questions
PLEASE HELP
A fly makes a bee-line from one corner of Mrs. Tomasi's room
to the opposite corner. The room is 30x 32 feet and 9 feet tall.
What angle is the angle of elevation of the flight path if he flies
straight there?
Answers
The angle of elevation of the fly's flight path is approximately 57.74 degrees.
What is hypotenuse?In a right triangle, the hypotenuse is the side opposite the right angle. It is always the longest side of the triangle and is the side opposite to the 90 degrees angle. It is also the side that forms the "hypotenuse" of the right triangle.
What is Pythagorean theorem?The Pythagorean theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as c^2 = a^2 + b^2, where a and b are the legs of the triangle and c is the hypotenuse. This theorem can be used to find the length of the hypotenuse of a right triangle when the lengths of the other two sides are known.
Let's call the angle we're trying to find "theta". The horizontal distance is 30 feet, the vertical distance is 32 feet and the height is 9 feet.
Using pythagorean theorem:
$c^2 = a^2 + b^2$
$c = \sqrt{30^2 + 32^2}$ = $\sqrt{900 + 1024}$ = $\sqrt{1924}$
Now we can use the tangent function:
$\tan(\theta) = \frac{opposite}{adjacent} = \frac{32}{30}$
Now we can find the angle, theta, by using the inverse tangent function:
$\theta = \tan^{-1}(\frac{32}{30})$
The angle of elevation of the fly's flight path is approximately 57.74 degrees.
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Express (x-12)^2(x−12)
2
as a trinomial in standard form.
Answers
The trinomial (x - 12)² in standard form is x² - 24x + 144
How to evaluate the trinomial in standard formFrom the question, we have the following parameters that can be used in our computation:
(x-12)^2
Express properly
So, we have the following representation
(x - 12)²
Expand the expression
This gives
(x - 12)² = (x - 12) * (x - 12)
Open the brackets
This gives
(x - 12)² = x² - 12x - 12x + 144
Evaluate the like terms
(x - 12)² = x² - 24x + 144
Hence, the trinomial is x² - 24x + 144
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Physical Fitness Dino works out regularly. When he first started exercising, he
could do 10 push-ups. After the first month he could do 14 push-ups. After the
second month he could do 19, and after the third month he could do 25. Predict
the number of push-ups Dino will be able to do after the fifth month of
working out. How confident are you of your prediction? Explain.
Answers
Answer:
he will do 34 the next month
For each order, the web site applies a 7.7% sales tax to the price of the cards, plus a one time mailing fee of 5.95. Based on the information in the table, what will be the total cost for an order for 280 cards?
Answers
Answer: $1794.28
Step-by-step explanation:
280*5.95= 1666
0.077*1666= 128.282
1666+128.282= 1794.282
We round cause its money
if you earn 3250 over the 10 year period, how much will be in the account at the end of the 10 year period?
Answers
If earning 3250 per month over 10year period, At the end of 10th year, the amount on the account will be 390,000
What is multiplication?To multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem. In the multiplication problem, 6 × 9 = 54, the numbers 6 and 9 are the factors, while the number 54 is the product.
The amount earned In a month is 3250.
There are 12 months In a year.
The total month in 10 years = 10× 12 = 120 months
The total amount in the account for 10years = 120×3250 = 390,000
Therefore there will be 390000 in the account at the end of 10th year.
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The odometer of a car reads 35,467.219 the 5 stands for 5 x1,000 miles. Use expanded form to show what each of the other digits in the odometer reading means.
Answers
So the expanded form of the odometer reading 35,467.219 is:
5 x 1000 + 3 x 100 + 4 x 10 + 6 x 1 + 7 x 1/10 + 2 x 1/100 + 1 x 1/1000 + 9 x 1/10000
What is expanded form?A number is divided up into its place values, then expanded to represent the value of each digit. The enlarged form of 943 is shown as an example. 9 blocks of 100s Three blocks of ones, and four blocks of tens. Nine hundred increased to 4 tens, 3 ones. Form: 900 + 40 + 3.
Define Decimal Numbers.The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.
In expanded form, the odometer reading of 35,467.219 can be broken down into the value of each digit in the number.
5 stands for 5 x 1,000 miles
3 stands for 3 x 100 miles
4 stands for 4 x 10 miles
6 stands for 6 x 1 miles
7 stands for 7 x 1/10 of a mile
2 stands for 2 x 1/100 of a mile
1 stands for 1 x 1/1000 of a mile
9 stands for 9 x 1/10000 of a mile
So the expanded form of the odometer reading 35,467.219 is:
5 x 1000 + 3 x 100 + 4 x 10 + 6 x 1 + 7 x 1/10 + 2 x 1/100 + 1 x 1/1000 + 9 x 1/10000
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7 3
What is another way to write the equation +--62
O
7+3
8+4
7 3
08
x=-6
7
X=-6
3
Answers
an equation to model this situation is 200 = x+ 2 *t and 220 pounds is his total weight after 30 weeks
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
x initial weight of John
weight gained 1 week = 2 pounds
no. of weeks = 20=t
Final weight of John = 200 pounds
200 = x+ 2 *t ---------(1)
no. of weeks = 20=t
From eq(1)
x = 160 pounds= intial weight
So,
[tex]y = 160+ 2 *t\\y = 160 + 2X 30\\y= 160+ 60\\y = 220 pounds[/tex]
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Tell whether the angles are complementary or supplementary. Then find the value of x.
Answers
The angles add up to 180° so the angles are supplementary.
The value of x is 31.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
From the figure,
Two angles:
3x + 25 and 2x
These two angles form a straight angle.
Now,
3x + 25 + 2x = 180
5x = 180 - 25
5x = 155
x = 31
When the sum of two angles is 90°, then the angles are known as complementary angles.
When the sum of two angles is 180°, then the angles are known as supplementary angles.
Now,
3x + 25
= 3 x 31 + 25
= 93 + 25
= 118
2x
=2 x 31
= 62
Now,
118 + 62 = 180
Thus,
The angles are supplementary.
The value of x is 31.
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The sum of two numbers is 210 and their difference is 30. What are the two numbers?
Answers
Answer:
120 and 90
Step-by-step explanation:
let one number be x and the other y
x + y = 210 (sum = 210)
x - y = 30 (difference = 30)
add the two equations together
2x = 240
divide both sides by 2 to isolate x
x = 120
plug into 1st equation
120 + y = 210
subtract 120 from both sides
y = 90
We take the 2 numbers as 'x' and 'x-30' in order to find those numbers
We plug the values into the given equation
[tex]x + x - 30 = 210\\2x - 30 = 210\\\\2x = 240\\x = \frac{240}{2} \\x = 120\\x - 30 = 120 - 30 = 90\\[/tex]
[tex]120 - 90 = 30[/tex]
Hence , the two numbers are 120 and 90
There is a pair of parallel sides in the following shape.
Answers
Answer:
A = 38.5 units²
Step-by-step explanation:
the figure has one pair of parallel sides and is therefore a trapezium.
the area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
b₁ and b₂ are the parallel bases and h the perpendicular height between them.
here h = 7 , b₁ = 5 , b₂ = 6 , then
A = [tex]\frac{1}{2}[/tex] × 7 × (5 + 6) = 3.5 × 11 = 38.5 units²
The width of a rectangle measures (k+3)(k+3) centimeters, and its length measures (k-9)(k−9) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answers
Answer:
(k+3)(k+3) + (k-9)(k-9), or p = (k+3)^2 + (k-9)^2, or p = 4k^2 - 24k + 180
Step-by-step explanation:
A rectangle has four sides, two sides both have equal width, while the other two have equal length. The perimiter is the total sum of these sides. We can use the following equation to represent the perimiter using the width and length:
p = 2w + 2l
We know that the width equals (k+3)(k+3), so 2w would equal 2(k+3)(k+3). In the form of a quadratic equation, this would equal 2k^2+12k+18.
We also know that the length equals (k-9)(k-9), so 2l would equal 2(k-9)(k-9). As a quadratic equation, this would equal 2k^2-36k+162.
Plugging these values into our equation we get:
p = (k+3)(k+3) + (k-9)(k-9), or p = (k+3)^2 + (k-9)^2.
Or in the form of a quadratic equation:
p = 2k^2 + 12k + 18 + 2k^2 - 36k + 162
=
p = 4k^2 - 24k + 180
Hope this helps!
The perimeter of the rectangle can be calculated using the formula 2(length + width). Substituting the given expressions for length and width, we get 2[(k+3)(k+3)+(k-9)(k−9)]. This simplifies to the expression 4k^2-24k+180.
Explanation:The perimeter of a rectangle is calculated by adding the lengths of all its sides. With the width given as (k+3)(k+3) centimeters, and the length as (k-9)(k−9) centimeters, we can substitute these into the formula for the perimeter of a rectangle, which is 2(length + width).
Therefore, the expression representing the perimeter of the rectangle is 2[(k+3)(k+3)+(k-9)(k−9)]. This simplifies to 2[(k^2+6k+9)+(k^2-18k+81)], which further simplifies to 2[2k^2-12k+90], and ultimately simplifies to 4k^2-24k+180.
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correct 0.00798516 to three significant figures
Answers
Explanation:
The zeros in 0.00798516 are not considered significant because they are not between nonzero values.
If we had something like 1.207, then that zero would be considered significant.
The first three significant values we come across in 0.00798516 are 7, 9 and 8 in that order. The next digit 5 meets the criteria of "5 or larger", which means the 798 bumps up to 799. Erase everything to the right of that.
Therefore, 0.00798516 rounds to 0.00799 when rounding to 3 significant figures.
Answer: 0.00799
0.00798516 rounded off to three significant figures is 0.00799
hope that helps...
Select ALL composite numbers with their correct prime factors(I need help)
Answers
Answer:
The answer would be the second and fourth options.
Step-by-step explanation:
This can be solved by using a calculator, the prime factor method, etc. Good luck on your math journey!
In 2-4, write yes or no to indicate whether the expressions are equivalent. Grade 6 math, please help
Answers
Discrete Mathematics
For each language L1 to L5, described below, you need to do the following:
• Create a regular expression that defines the language accurately.
The alphabet A = {a, b} will be used.
The languages are:
1. L1 which has exactly one a but any number of bs.
2. L2 which has an odd number of as and an even number of bs.
3. L3 which contains exactly two as or exactly two bs, although not necessarily adjacent.
4. L4 which has all the bs appearing before any of the as, or all the as appearing before any of the bs.
5. L5 where there can be any number of as but the number of bs must be even, although the bs do not have to be adjacent.
Answers
Note: ^ is for Start of the line, $ is for end of the line ,* means 0 or more, + means 1 or more, [ab] means either a or b and {} is for specific number of times, () is for grouping.
How to create regular expressions?A task in which it is necessary to create regular expressions to define five different languages. The alphabet used is A = {a, b}. The languages are:
L1, which has exactly one "a" but any number of "bs".
L2, which has an odd number of "as" and an even number of "bs".
L3, which contains exactly two "as" or exactly two "bs", although not necessarily adjacent.
L4, which has all "bs" appearing before any "a" or all "as" appearing before any "b".
L5, where there can be any number of "as", but the number of "bs" must be even, although the "bs" need not be adjacent.
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Please someone help me !!
Answers
Answer: $26.81
Step-by-step explanation: the tank holds 16.5 gallons. Meaning, half of the tank is 8.25 gallons. Multiply that by the cost of the gas, 3.25, and you get 26.81
Carlos measures an angle x. He then finds that the complement of the angle is 35 degrees. A. What is the measure of angle x? B. What is the supplement of angle x?
Answers
Therefore , the solution of the given problem of complementary angles comes out to be x = 55° and y =125°.
Describe complimentary angles.A pair of angles is considered to be complementary if their sum equals 90 degrees. Two angles are referred to as submissive if their sums total 180 degrees. Follow-up pain Utilizing fresh gruesome milk, as usual Prior to, before, ahead of The angles of thirty and sixty degrees, for example, are supplementary. In contrast to a supplemental angle, which is two angles joined to create a 90 degree angle, a supplementary triangle tilt is two possible approaches combined to create a 180 degree angle. If the sum of two angles is 90 degrees, they are said to be complementary. A straight angle, to put it another way
Here,
Given : complementary angle one of the angle is 35°
=> x+ 35° = 90°
=> x = 55°
Let y be the supplement of angle x
=> x+ y = 180°
=>55° + y =180°
=>y =125°
Therefore , the solution of the given problem of angle comes out to be
x = 55° and y =125°.
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Will mark brainliest!
Answers
Angle 7 = 126 degrees
Explanation below
Mark bought five packs of markers for $12.25. What is the cost of a pack of markers, in dollars, if all the packs cost the same?
Answers
Answer:
The cost of a single pack would be $2.45.
Step-by-step explanation:
If a 5 pack costs 12.25 then to find the cost of 1 packet we need to divide.
We would divide by 5.
$12.25/5=$2.45
Need to find the x and y
Answers
Need to find the x and y: The Graph asking in question is attached below:
What is Graph?A graph is a type of data structure used to represent relationships between different objects. It consists of nodes, which are connected by edges. The nodes represent the objects, while the edges represent the relationships between them. Graphs can be used to represent many different types of information, such as road networks, social networks, and even computer networks. Graphs can be used to solve a variety of problems, such as finding the shortest path between two nodes, or finding the most efficient way to route data throughout a network. Graphs can be represented in a variety of ways, such as in the form of a table, a map, or a diagram. In addition, graphs can be used to represent abstract concepts such as relationships between individuals.
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Jorge gives 3 chocolate bars to his friend. HE GIVES 1/12 OF CHOCOLATE BAR TO EACH FRIEND. HOW MANY FRIENDS DOES HE GIVE A PIECE OF CHOCOLATE TO
Answers
Solve the equation Sin(X)=-1 on the interval [0,360)
Answers
Therefore , the solution of the given problem of trigonometry comes out to be x = nπ where nЄ Z (where n is an integer).
What is trigonometry?The mathematical field of trigonometry investigates relationships between triangle sides and angles. Because every straight-sided form may be reduced to a collection of triangles, trigonometry is a fundamental concept in all of geometry. The relationships between trigonometry and other branches of mathematics, particularly calculus, real or complex, infinite series, logarithms, and infinite series, are astonishingly intricate.
Here,
[tex]e^{x}[/tex] is a function that increases across all of space (d[[tex]e^{x}[/tex] ]/dx = [tex]e^{x}[/tex] which is never negative), it must be that so it must be that [tex]e^{u}[/tex] crosses y=1 just once, or at u = 0. To demonstrate this:
In[tex]e^{sinx}[/tex]= In 1
sin x = 0
And when x = "0, 0", "2", we would have that sin x = 0 in [0, 2"]. In general, we would then have that x = n, where n Z, because of the periodicity of sin (where n is an integer).
Therefore , the solution of the given problem of trigonometry comes out to be x = nπ where nЄ Z (where n is an integer).
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If c = d, then a + c = d + a true or false
Answers
Answer:
True
Step-by-step explanation:
First, you need to subtract a then that would make a 0
Answer: true
Step-by-step explanation: c and d are the same, so a+c and a+d will be the same
Determine if each of the following statements are true or false (HELP!!! ARE MY ANSWERS CORRECT?)
Answers
Answer:
yes
Step-by-step explanation:
3y+2=2x is this a direct variation
Answers
The equation 3y + 2 = 2x is not a direct variation
How to determine if the equation is a direct variation
From the question, we have the following parameters that can be used in our computation:
Variation = direct variation
3y + 2 = 2x
A direct variation is represented as
y = kx
Where k is the constant of proportion
When the equations y = kx and 3y + 2 = 2x are compared, we can see that
The equation 3y + 2 = 2x has a constant term
Hence, the equation is not a direct variation
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How much is the monthly amortization on an automobile loan of ₱ 900,000 to be amortized over a 5-year period at a rate 9.5% compounded monthly?
Answers
The monthly amortization on the automobile loan, given the loan amount, the period, and the compounding frequency, is ₱ 18, 901.68
How to find the amortization ?The monthly amortization is constant so it will be an annuity. Seeing as we have the loan amount, this means that the present value of an annuity formula can be used to find the monthly amortization.
First, find the period in months:
= 5 x 12 months a year
= 60 months
The interest in months :
= 9 . 5 % / 12 months per year
= 9.5 / 12 %
The monthly amortization is:
= Loan amount / ( Present value interest factor of annuity, 60 periods, 9.5 / 12 %)
= 900, 000 / 47.614827336156
= ₱ 18, 901.68
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NEED HELP ASAP DUE TMR
Answers
1. The length of the altitude is 15 units.
2. The perimeter of trapezoid ABCD is 132 units.
Perimeter of a trapezoid.An altitude is the vertical height of a given object from the sea level. This is majorly a height reached by an object to the sea level as a reference.
The perimeter of a trapezoid is the sum of all its sides.
From the question;
1. To determine AE,
DE = (DG - EF)/ 2
= (22 - 6)/ 2 (since AB = EF = 6)
= 8
DE = 8 units
The altitude AE can be determined by applying the Pythagorean theorem to triangle ADE. So that;
/hyp/^2 = /opp/^2 + /adj/^2
AD^2 = DE^" + AE^2
17^2 = 8^2 + AE^2
289 = 64 + AE^2
AE^2 = 225
AE = 15
Thus the length of the altitude is 15 units.
2. To determine the perimeter of the trapezoid, we have;
AE = (AD - EF)/ 2
= (58 - 16)/ 2 (since BC = EF = 16)
= 21
AE = 21 units
So that from triangle ABE, applying the Pythagorean theorem to determine the value of AB, we have;
/hyp/^2 = /opp/^2 + /adj/^2
AB^2 = BE^2 + AE^2
= 20^2 + 21^2
AB = 841^1/2
AB = 29
Perimeter of the trapezoid = 29 + 16 + 29 + 58
= 132 units
Thus, the perimeter of the trapezoid is 132 units.
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3/8 = 8/X still not able to solve. Can you me how to solve by breaking down?
Answers
Answer: 21.3
Step-by-step explanation:
1. Cross multiply
8(8) = 3(x)
2. Simplify
64 = 3x
3. Divide by 3 on both sides to get the variable by itself
64/3 = 3x/3
4. Simplify
21.3333333333 = x
you can round the answer to the nearest tenth, which would be 21.3
Radius of 256/3π cm³
Answers
What is the answer to 156 x 13
Answers
Answer:
2028
Step-by-step explanation:
156 x 13 = 2028