(a) x² + 2xy - y² must be added to x² + xy + y² to get 2x² + 3xy. (b) 5a + b -6 must be subtracted from 2a + 8b + 10 to get -3a + 7b + 16.
a)
Here we are given the expression x² + xy + y²
Now we need to add something so that this expression becomes x² + 3xy
Let the expression to be added be p.
Hence we get
x² + xy + y² + p = 2x² + 3xy
or, p = 2x² + 3xy - (x² + xy + y²)
or, p = 2x² + 3xy - x² - xy - y²
or, p = x² + 2xy - y²
Hence, x² + 2xy - y² must be added.
b)
Here we are given the expression 2a + 8b + 10
We need to subtract another expression to get -3a + 7b + 16
Let the expression be t. Hence we get
2a + 8b + 10 - t = -3a + 7b + 16
or, t = 2a + 8b + 10 - (-3a + 7b + 16)
or, t = 2a + 8b + 10 + 3a - 7b - 16
or, t = 5a + b - 6
Hence 5a + b - 6 must be subtracted,
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Correct Question
(a) What should be added to x² + xy + y² to obtain 2x² + 3xy?
(b) What should be subtracted from 2a + 8b + 10 to get -3a + 7b + 16?
Molly is building a model roller coaster as part of a school project she chose the millennium force in cedar point which is 94 meters tall to model if molly uses a scale of 1 centimeter = 4 meters what will be the height of the model
Answer:
23.5 cm
Step-by-step explanation:
You want the height of the model of a 94 m tall roller coaster when the model scale is 1 cm = 4 m.
ProportionThe model dimensions are assumed to be proportional to the real-world dimensions, so the model height h will satisfy the proportion ...
h/(94 m) = (1 cm)/(4 m)
Multiplying by 94 m gives ...
h = (1 cm)(94/4) = 23.5 cm
The height of the model is 23.5 cm.
There are 3 people pulling on an object, the first person pulls with a force of 226 newtons at a direction of 145 degrees the second person pulls with a force of 331 newtons at a direction of 303 degrees. The third person pulls with a force of 377 newtons at a direction of 77 degrees. find the resultant vector . find the resultant force . find the direction
Answer:
[tex]R=883.74N[/tex]
Step-by-step explanation:
From the question we are told that:
Force 1 [tex]F_1=226N[/tex]
Force 2 [tex]F_2=331N[/tex]
Force 3 [tex]F_3=377N[/tex]
Direction 1 [tex]\theta_1=145 degrees \approx 35 \textdegree (2nd qudrant)[/tex]
Direction 2 [tex]\theta_2=303 degrees \approx 57 \textdegree (3rd qudrant)[/tex]
Direction 3 [tex]\theta_3=77 degrees[/tex]
Generally Resolving forces to X axis is mathematically given by
[tex]\sum f_x=337cos77+331cos57+226sin35[/tex]
[tex]\sum f_x=351.596N[/tex]
Generally Resolving forces to Y axis is mathematically given by
[tex]\sum f_y=337sin77+331sin57+226cos35[/tex]
[tex]\sum f_x=810.788N[/tex]
Generally the equation for Resultant force R is mathematically given by
[tex]R=\sqrt{\sum f_x^2+\sum f_x^2}[/tex]
[tex]R=\sqrt{351.596^2+810.788^2}[/tex]
[tex]R=883.74N[/tex]
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 87 m long and 69 m wide. What is the length of a training track running around the field? (Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.)
Answer:
607.32
Step-by-step explanation:
two semi circles make a whole circle so use the normal circumfrence formula 2 pi r
circumfrence = 433.32
the perimeter of the rectangle is 87 + 87, because they are on the outside of the field.
The answer is 607.32
In a market urvey, 100 trader ell fruit. 40 ell apple, 46 orange, 50 mangoe, 14 apple and orange, 15 apple and mangoe and 10 ell all three fruit each of the 100 trader ell at leat one of the three fruit. (A) how many trader ell only one fruit. (B) how many trader ell only two fruit
A)There are 88 trader sell only one fruit.
B) There are 46 trader sell only two fruit.
Since there are three sets, use the formula
n (A∪O∪M) = n(A) + n(O) + n(M) - n(A∩O) -n(O∩M) - n(A∩M) + n(A∩O∩M)
A represents apple traders = 40
O represents orange traders = 46
M represents mangoes traders = 50
A∪O∪M = total traders = 100
A∩O = 14
O∩M = ?
A∩M = 15
A∩O∩M = 10
B) Substitute values into the formula
100 = 40 + 46 + 50 - 14 - 15 - O∩M + 10
100 = 146 - 29 - O∩M
100 = 117 - O∩M
Make O∩M subject of formula
O∩M = 100 -117
O∩M = 17 traders
Now,
n(A∩O) -n(O∩M) - n(A∩M)
= 14 + 17 + 15
= 46
Therefore, the number of traders that sells two fruits are 46.
A) oranges n(O)
= 46-(4+10+ x)
= 32
Again,
mangoes n(M).
= 50-(5+10+x)
= 35
Now,
apple n(A)
= 40-(4+10+5)
= 21
Now, adding all of them we get:
n(o) + n(M) + n(A) = 32 + 35 + 21
= 88
Therefore, 88 trader sells only two fruit
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Rafael claims it's easiest to score points when a scatterplot has a linear association. Sahana says it's easiest when a scatterplot has a strong association.
Who is correct?
Rafael claims it's easiest to score points when a scatterplot has a linear association. Sahana says it's easiest when a scatterplot has a strong association. Both Rafael and Sahana are correct, in their own way.
A scatterplot with a linear association means that there is a straight line relationship between the two variables being plotted. In such a scatterplot, it is relatively easy to make predictions based on the line of best fit, as well as to calculate the correlation coefficient(r), which can indicate the strength and direction of the linear relationship.
On the other hand, a scatterplot with a strong association means that the points in the plot are closely grouped together, indicating a high degree of correlation between the variables. It is relatively easy to make predictions based on the overall pattern of the points in the scatterplot, even if there is no clear linear relationship.
So, Rafael is correct that scoring points is easiest when a scatterplot has a linear association because it is relatively easy to make predictions based on the line of best fit and correlation coefficient. And Sahana is correct that scoring points is easiest when a scatterplot has a strong association because it is relatively easy to make predictions based on the overall pattern of the points in the scatterplot.
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what is the area of this figure?
Answer:
602
Step-by-step explanation:
First find area of the rectangle portion
L x W
22 x 15
330
Second find area of trapezoid
B1+B2/2 times height
12+22/2 times 16
34/2 times 16
17 times 16
272
Lastly, add areas together
pleasee help!!! this is geometry
Answer:
Step-by-step explanation:
F TV day job cut hv h the BBC gg was the only time I had a chance of playing it for the last night of my life lol I love you and you are ok with your such good friends I know I love it but it’s ok I’m not sure how to get it away I don’t think you can get me to type in the car.
⚠️⚠️GIVING BRAINLIST⚠️⚠️
GIVING BRAINLIST HELP!
Answer:
I agree with Helen because she is right that the volume is about 175 cubic inch. and it is a triangular prism.
Step-by-step explanation:
helen is swaggy so i must agree with her
what other reason is there not to agree?
Tommy earned $225 washing cars with his mobile car washing business. He charges $30 per appointment and earned $45 in tips, but he also has to pay $10 per appointment for water. Write an equation to represent this situation.
A.
(30 + 10)y + 45 = 225
B.
30y + 45 = 225 - 10y
C.
30y + 45y - 10y = 225
D.
(30 - 10)y + 45 = 225
An equation representing this situation where Tommy earned $225 washing cars per appointment charge of $30 and tips of $45 while paying $10 for water per appointment is D. (30 - 10)y + 45 = 225.
What is an equation?An equation is a mathematical statement that states that two or more mathematical expressions are equivalent or equal.
Equations depict the equality of mathematical expressions using the equation symbol (=).
The total amount earned = $225
Variable charge per appointment = $30
Tips earned = $45
Variable cost per appointment for water = $10
Contribution margin per unit = $20 ($30 - $10)
Let each appointment = y
Total earnings: 225 = (30 - 10y) + 45
Thus, the equation that represents the situation of Tommy's net earnings from washing cars is Option D.
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Find the measure of the missing angle? please help :)
The measure of the angle ∠SUT will be 30°. Then the correct option is C.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The exterior angle of a triangle is almost always equal to the addition of the interior and opposing interior angles. The term "external angle property" refers to this feature.
The measure of the angle ∠SUT is calculated as,
∠SUT + ∠UTS = ∠JST
∠SUT + 80° = 110°
∠SUT = 110° - 80°
∠SUT = 30°
The measure of the angle ∠SUT will be 30°. Then the correct option is C.
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please answer correctly !!!!! Will mark brainliest !!!!!!!!!!!!!!
Answer:
0.44
Step-by-step explanation:
Sin∠ D= EC/DC
⇒ Sin D= 39/89⇒ Sin D= 0.44-------------------------------
hope it helps...
have a great day!!
Answer:
sin D = 0.44
Step-by-step explanation:
sin D = opp/hyp
The side opp D must be CE since the side opp D cannot contain D
opp = CE = 39
The hypotenuse must be DC since it's the longest
hyp = DC = 89
sin D = 39/89
sin D = 0.4382022472
To the nearest hundredth
sin D = 0.44
which of the following statements is true? a. the radius of a circle is twice its diameter b. to find the diameter of a circle, divide its circumference by pie. c. the circumference of a circle is grater than its diameter
Answer:
Statement B, C, E are correct
Solution:
We have to find the true statements
We know that,
To find the diameter of a circle, multiply its radius by two
Thus statement E is correct
Also,
To find the diameter of a circle, divide its circumference by π
Thus statement B is correct
circumference of a circle is obtained by multiplying diameter with pi
The circumference of a circle is greater than its diameter
Thus, Statement C is correct
C.
The circumstances is a circle that is greater than the diameter
Meada scored 24 points. If this was 4 less than the number
of points scored Jill scored, how many points did Jill score?
Define a variable. Then write an equation that could be
used to solve the problem.
Answer:
the answer is 28
Step-by-step explanation:
Maeda scored 24 points and if 4 less then jill
x is variable
x-4=24 add 4 on both sides
x=28
Complete the square to find the vertex of this parabola
Answer:
[tex](2,-6)[/tex]
Step-by-step explanation:
[tex]x^2-4x+y+10=0[/tex]
[tex]y=x^2+4x-10[/tex]
[tex]y=-(x^2-4x)-10[/tex]
[tex]=-(x^2-4x+4)-10+4[/tex]
[tex]=-(x-2)^2-6[/tex]
[tex]y=-(x-2)^2+(-6)[/tex]
[tex]h=2 ~and~ k=-6[/tex]
So, vertex → (2,-6)
[tex]------------[/tex]
hope it helps..
have a great day!!
A small radio transmitter broadcasts in a 31 mile radius. If you drive along a straight line from a city 41 miles north of the transmitter to a second city 42 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter
On solving the provided question, we can say that the slope's the intersection points are: (20.698, 42.197) and (43.998,16.527), the transmitter is within range between those to points along the line.
what is slope?A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
city - north at (0,65)
city-east at (59,0)
Slope is m=(-65/59)
[tex]B= y - mx = 65 - (-65/59)(0) = 65[/tex]
The equation of the line between the cities is y = (-65/59)x + 65
[tex]x^2 + ( (-65/50)x + 65) )^2 = 47^2[/tex]
the intersection points are:
(20.698, 42.197) and (43.998,16.527)
The transmitter is within range between those to points along the line.
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What are the 4 types of real numbers?
Real numbers are every number that exists in the real line, The four types of real numbers are rational, irrational, Natural and Integers.
What is a real number?In mathematics, a real number is a value that can be represented on the number line. The set of real numbers includes both rational numbers (such as integers, fractions, and decimals) and irrational numbers (such as √2 and π). Real numbers also include positive numbers, negative numbers, and zero. The set of real numbers is usually represented by the symbol R, and it has the properties of being closed under the operations of addition, subtraction, multiplication, and division (except for division by zero).
What are ideal and real solutions?In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.
Rational number = 3/4, -6/2, or 0.5.
Irrational number = √2, π, or e.
Natural number = 1,2,3,4....
Integers = -4, -1, 0, 1, 4.
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Given ΔRST : ΔLMN, which of the following is true? PLZZZZZZ ANSWER FOR 50 POINTS!!!!!!!!
R L
S L
S N
R M
Answer:
hope this helps you pls give me brainless.
A certain television is advertised as a 90-inch TV (the diagonal length). If the height of the TV is 63 inches, how wide is the TV? Round to the nearest tenth of an inch.
Answer:
The TV is 64.3 in. wide.
Step-by-step explanation:
a
2
+(63)
2
=
\,\,90^{2}
90
2
Use the Pythagorean Theorem.
a^{2}+3969=
a
2
+3969=
\,\,8100
8100
Simplify.
-3969\phantom{=}
−3969=
\,\,-3969
−3969
Subtract 3969 from both sides.
a^{2}=
a
2
=
\,\,4131
4131
\sqrt{a^{2}}=
a
2
=
\,\,\pm\sqrt{4131}
±
4131
Square root both sides.
a=
a=
\,\,64.272855...
64.272855...
Simplify. Ignore negative root, as length must be positive.
a\approx
a≈
\,\,64.3
64.3
Round to the nearest tenth.
The rectangle TV's width is determined by the formula W = 64.3 inches.
What is the diagonal of a rectangle?The formula determines a rectangle's diagonal.
From the Pythagoras Theorem , The hypotenuse² = base² + height² , and
Diagonal of a Rectangle = √ ( Length )² + ( Width )²
Given data ,
Let D represent the diagonal of the rectangular TV.
D is now equal to 90 inches.
Let the TV's rectangle size be 63 inches.
Let W be the TV's rectangular width.
And , Diagonal of a Rectangle = √ ( Length )² + ( Width )²
D² = L² + W²
90² = 63² + W²
Subtracting 63² on both sides of the equation , we get
W² = 90² - 63²
On simplifying the equation , we get
W² = 4131
Taking square roots , we get
W = √4131 inches
W = 64.3 inches
Thus , W is equal to 64.3 inches.
Hence, the rectangular TV is 64.3 inches wide.
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The radius of a circle is 7 cm what is the area
Answer:
153.94 cm²
Step-by-step explanation:
Area of circle = πr² = π(7)² = 49π = 153.94 cm²
Answer:
7^2 = 49
49 x 3.14 = 153.86
Step-by-step explanation:
Formula of an Area of a circle:
pi(3.14 or 22/7 or whatever they tell you to use for pi) x radius squared
help plz 20 points help plz its math
Answer: A
Step-by-step explanation:
Please help me find the circumference of the circle!
Answer:
[tex]C=59.6902604182[/tex]
Step-by-step explanation:
The formula to calculate the circumference of a circle given the diameter is:
[tex]C=\pi d[/tex]
Substitute and solve:
[tex]C=\pi \times19=59.6902604182[/tex]
[tex]C=59.6902604182[/tex]
Since the question doesn't say to round your answer is "59.6902604182."
Hope this helps.
Bart and April are purchasing a house with a 15-year, 2/1 ARM for $315,000 at 5. 85% with a 2/8 cap structure. What will the difference in
payments be from year 2 to year 3?
$309. 69
$595. 18
$333. 68
$86. 56
The monthly payment for this difference would be $1,361.21. An Adjustable Rate Mortgage (ARM) is a type of mortgage in which the interest rate on the loan changes over time.
An Adjustable Rate Mortgage (ARM) payment is based on various factors such as the loan amount, interest rate, and the terms of the ARM. The interest rate is usually tied to a specific financial index, such as the U.S.
Here is the calculation format for the difference in payments between year 2 and year 3 for Bart and April's mortgage:
Total amount to be paid for the mortgage: $315,000
Rate of interest: 5.85% (Depreciating rate)
Time = 2 years:
a. Remaining amount to be paid after 2 years:
Principal × (1 - Rate/100)^time
= $315,000 × (1 - 5.85/100)²
= $315,000 × (1 - 0.0585)²
= $279,223.01
Time = 3 years:
a. Remaining amount to be paid after 3 years:
Principal × (1 - Rate/100)^time
= $315,000 × (1 - 5.85/100)³
= $315,000 × (1 - 0.0585)³
= $262,888.46
Difference in payments from year 2 to year 3:
= Remaining amount after 2 years - Remaining amount after 3 years
= $279,223.01 - $262,888.46
= $16,334.55
The monthly payment for this difference would be $1,361.21, which is calculated by dividing the difference in payments by 12:
$16334.546/12 = $1361.21
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What type of correlation (association)? The outside temperature and the amount of layers you wear.
Answer:
negitive corralation
Step-by-step explanation:
The outside temperature and the number of layers you wear. represents a negative correlation.
What is correlation?It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
As we know a negative correlation is a relationship between two variables in which one increases while the other decreases and a positive correlation is a relationship in which one variable increases while the other decreases.
The case of the two variables that are outside temperature and the number of layers you wear represents the negative correlation because in the summer temperature increases and the number of layers decreases that you wear.
In the winter when the temperature goes down the number of layers increases that you wear.
Thus, the outside temperature and the number of layers you wear. represents a negative correlation.
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Find the height of a trapezium whoe area i 420 q. Cm and the um of the length of it parallel ide i 30 cm
The sum of length of the parallel sides of a trapezium exists 300 cm.
What is meant by trapezium?A trapezoid, which is often referred to as a trapezium, is a flat, closed object with four straight sides and one set of parallel sides. A trapezium's parallel bases and non-parallel legs are referred to as its bases and legs, respectively. Also possible are parallel legs on a trapezium.
Four sides, four corners/vertices, and four angles make up a trapezium, which is a closed shape or polygon. A trapezium has parallel sides on each of its opposing angles.
One set of the sides of a trapezium is parallel only. Since no trapezium is a rectangle, they are not all the same.
Area of trapezium = (a + b)/2 × h
where h is the perpendicular height, and a and b are parallel sides.
So, (a + b) exists sum of length of bases of a trapezium.
Let the equation be
Area of trapezium = (a + b)/2 × h
substitute the values in the above equation, we get
⇒ 4.2 × 100² = (a + b) / 2 × 280 {1 m = 100 cm}
simplifying the equation, we get
⇒ (84/280) × 10000 = a + b
⇒ a + b = 300 cm
Therefore, the sum of length of the parallel sides of a trapezium exists 300 cm.
The complete question is:
Find the sum of length of the parallel sides of a trapezium whose area is 4.2 m² and whose height is 280 cm.
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The sum of length of the parallel sides of a trapezium exists 300 cm.
What is meant by trapezium?A trapezoid, also known as a trapezium, is a closed, flat object with one pair of parallel sides and four straight sides. The parallel bases and the non-parallel legs of a trapezium are called the bases and the legs, respectively. A trapezium with parallel legs is another option.
A trapezium is a closed shape or polygon with four sides, four corners, and four angles. Each of the opposing sides of a trapezium has parallel sides.
A trapezium has only one set of parallel sides. They are not all the same since no trapezium is a rectangle.
Area of trapezium = (a + b)/2 × h
where h is the perpendicular height, and a and b are parallel sides.
So, (a + b) exists sum of length of bases of a trapezium.
Let the equation be
Area of trapezium = (a + b)/2 × h
substitute the values in the above equation, we get
⇒ 4.2 × 100² = (a + b) / 2 × 280 {1 m = 100 cm}
simplifying the equation, we get
⇒ (84/280) × 10000 = a + b
⇒ a + b = 300 cm
Therefore, the sum of length of the parallel sides of a trapezium exists 300 cm.
The complete question is:
Find the sum of length of the parallel sides of a trapezium whose area is 4.2 m² and whose height is 280 cm.
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The scale on a map is 1 : 30 000 What is the actual distance represented by 1 centimeter? Give your answer in meters
Write an equation in slope-intercept form of the line that passes through the points
(12,10)and (16,8).
Answer:
y=-1/2x+16
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(8-10)/(16-12)
m=-2/4
m=-1/2
y-y1=m(x-x1)
y-10=-1/2(x-12)
y=-1/2x+12/2+10
y=-1/2x+6+10
y=-1/2x+16
Sorry for the quality, if anyone could help. It’s geometry.
Answer:
5
Step-by-step explanation:
Percent of change. What is 40 decreased to 33
Answer:
13.2
Step-by-step explanation:
40 decreased by 33% = 26.8
Absolute change (actual difference):
26.8 - 40 = - 13.2
Daphine flips a coin four times. What is the probability that it lands on rails all four times?
Answer:
4/8 if you need simplified version its 1/2
Step-by-step explanation:
A coin has 2 sides. If you flip a coin one time, the possibility of getting a tails would be 1/2.
times 1/2 by 4 (since your flipping it four times)
two families with four people in each family go to a movie theater. in how many ways can they be seated
According to probability, if both families want to sit together, they can be seated in a row a maximum of two times.
What seating configuration?The direction that each person is facing is crucial when arranging the people.
In order to determine how many ways they can be seated in a row if both families want to sit together, imagine that two families with four members each attend a movie theatre.
Given that the arrangement is important, we will apply the permutation rule. We'll divide the remaining four into two groups of four each.
There are two different ways to arrange the groups so they can sit together.
2! = 2 * 1
2! = 2ways
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