Given : (3x² - 2y² + 5x) + (4x² + 12y² - 7x)
Rearranging like terms, we get :
⇒ (3x² + 4x²) + (12y² - 2y²) - 7x + 5x
⇒ 7x² + 10y² - 2x
But, Marcus got the Answer as : 7x² - 10y² - 2x
Marcus combined the terms -2y² and 12y² Incorrectly
Following are the solution to the given expression:
Given:
[tex]\bold{(3x^2-2y^2+5x)+(4x^2+12y^2-7x)=7x^2-10y^2-2x}[/tex]
To find:
Solve equation=?
Solution:
[tex]\to \bold{(3x^2-2y^2+5x)+(4x^2+12y^2-7x)=7x^2-10y^2-2x}[/tex]
Solving the L.H.S part:
[tex]\to \bold{(3x^2-2y^2+5x)+(4x^2+12y^2-7x)}\\\\\to \bold{(3x^2-2y^2+5x+4x^2+12y^2-7x)}\\\\\to \bold{(7x^2+10y^2-2x)}\\\\[/tex]
Solving the R.H.S part:
[tex]\bold{=7x^2-10y^2-2x}[/tex]
Since in this question the [tex]L.H.S \neq R.H.S[/tex] , and when we solve the equation so, except the third choice all were correct.
Therefore, the final answer is " He combined the terms [tex]\bold{-2y^2\ and\ 12y^2}[/tex]incorrectly."
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PLEASE ANSWER I’LL GIVE YOU BRAINLIEST
What is the value of the expression?
5 (9/12 - 1/4) + 0.5
Enter your answer in the simplest form.
Answer:
The answer is 3
Step-by-step explanation:
5( 9/ 12 − 1/ 4 )+0.5
=5( 3/ 4 − 1/ 4 )+0.5
=5( 1/ 2 ) + 0.5
= 5/ 2 + 0.5
=3
Which statement is true
Answer:
Step-by-step explanation
You must find the common denominator for all of them.
A is correct. 13 x 2 is 26 and 14 x 2 is 28. Therefore, 13/14 is greater than 25/28.
B is not correct. 4 x 5 is 20 and 9 x 5 is 45. 4/9 is actually less than 21/45.
C is not correct. 5 x 2 is 10 and 6 x 2 is 12. 5/6 is actually less than 11/12.
D is not correct. 4 x 5 is 20 and 5 x 5 is 25. 4/5 is actually less than 8/25.
f(x) = x + 5 If you know that the range is {0, 10}, then... The domain must be
The range of f(x) = x + 5 is the set {0, 10}.
Therefore
x + 5 = 0 and x + 5 = 10
x = -5 and x = 5
The domain is {-5, 5}.find the excluded values
Answer:
0
Step-by-step explanation:
The only value I can see that won't work is a = 0. That value gives you 0 over 0 which has no definite answer at this level. It is best to call such a thing undefined or not permitted.
PLEASE HELP!!!!!!!!!
Can someone please answer these?? Soon??
The measures of the angles and side lengths are:
m∠ BED = 130°
m∠ BEA = 50°
x = 7
y = 16.4
BE ≈ 23
BC ≈ 34
8. m∠ BED
∠DEB and ∠BED are supplementary angles, so their measures add up to 180°.
Therefore, m∠BED = 180° - m∠DEB = 180° - 50° = 130°.
9. m∠ BEA
∠BEA and ∠DEB are vertical angles, so they have the same measure. Therefore, m∠BEA = m∠DEB = 50°.
10. x
We can use the fact that the sum of the angles in a triangle is 180° to find x.
In triangle ABE, we have ∠BAE + ∠ABE + ∠BEA = 180°.
Substituting the given values, we get (7x - 2)° + 80° + 50° = 180°.
Solving for x, we get 7x = 50, so x = 7.
11. y
We can use the fact that the measures of the angles in a triangle add up to 180° to find y.
In triangle BCE, we have ∠BCE + ∠BEC + ∠CEB = 180°.
We are given that ∠BCE = 20° (since ∠BDE = ∠BCE, and we found m∠BDE in part 8), and we can find ∠BEC using the fact that it is supplementary to ∠BEA (which we found in part 9).
Therefore, ∠BEC = 180° - 50° = 130°.
Substituting these values, we get 20° + 130° + ∠CEB = 180°.
Solving for ∠CEB, we get ∠CEB = 30°.
Now, we can use the fact that ∠CEB and ∠DEB are vertical angles to find that ∠DEB = 30°.
Finally, we can use the fact that the sum of the angles in a triangle is 180° to find y in triangle BCD.
We have ∠BCD + ∠CDB + ∠DBC = 180°.
Substituting the given values, we get 30° + 90° + (5y - 22)° = 180°.
Solving for y, we get 5y = 82, so y = 16.4.
12. BE
We can use the Pythagorean theorem to find BE in triangle ABE.
We have AB^2 = AE^2 + BE^2.
Substituting the given values, we get (5y - 22)^2 = (3y)^2 + BE^2.
Simplifying, we get 25y^2 - 220y + 484 = 9y^2 + BE^2.
Solving for BE^2, we get BE^2 = 16y^2 - 220y + 484.
Substituting the value of y that we found in part 11, we get BE^2 = 16(16.4)^2 - 220(16.4) + 484 ≈ 531.4.
Taking the square root of both sides, we get BE ≈ 23.
13. BC
We can find BC using the Pythagorean theorem in triangle BCE.
We have BC^2 = BE^2 + CE^2.
Substituting the values we found for BE and CE, we get BC^2 = 23^2 + (3y)^2.
Substituting the value of y that we found in part 11, we get BC^2 = 23^2 + 3(16.4)^2 ≈ 1163.
Taking the square root of both sides, we get BC ≈ 34.
SOMEONE PLEASE HELP ME!!! ILL GIVE YOU BRAINLIST <3 PLEASE THANK YOU
Step by Step Explanation:
16. x - 4 = 4
Isolate the variable (x). Note the equal sign, what you do to one side, you do to the other. Add 4 to both sides:
x - 4 (+4) = 4 (+4)
x = 4 + 4
x = 8
17. a/4 = 4
Isolate the variable (a). Note the equal sign, what you do to one side, you do to the other. Multiply 4 to both sides:
(a/4)(4) = (4)(4)
a = (4)(4)
a = 16
18. y * 20 = 30
Isolate the variable (y). Note the equal sign, what you do to one side, you do to the other. Divide 20 from both sides.
(y *20)/20 = (30)/20
y = 30/20
y = 3/2 or 1.5
19. x/5 = 20
Isolate the variable (x). Note the equal sign, what you do to one side, you do to the other. Multiply 5 to both sides
(x/5)(5) = (20)(5)
x = (20)(5)
x = 100
~
Need help on this
Z+4>2z
Answer: z < 4
z+4 > 2z
z+4-z > 2z-z ..... Subtract z from both sides
4 > z
z < 4
So the solution set for z is any number that is less than 4, which could be something like z = 2 or z = 3.
Trapezoid ABCD is similar to trapezoid EFGH. Side AD is proportional to side ___
Answer:
Side EH
Step-by-step explanation:
Side AD is proportional to side EH. If you look at ABCD, and compare it to EFGH, the ends of the name, AD, correspond with the ends of the other, EH.
Side AD of trapezoid ABCD is proportional to side EH of trapezoid EFGH due to the properties of similar geometric figures, where corresponding sides of similar shapes are in proportion.
The question asks which side of trapezoid EFGH is proportional to side AD of trapezoid ABCD, given that the two trapezoids are similar. In similar figures, corresponding sides are proportional. Therefore, if side AD of trapezoid ABCD corresponds to side EH of trapezoid EFGH, then these sides are proportional to each other.
Since we are discussing proportions and similarity of shapes, particularly trapezoids, we can reference several mathematical concepts. By the AAA theorem, which stands for angle-angle-angle, we know that if two or more corresponding angles in two figures are equal, then the figures are similar and the sides opposite these angles are proportional. Also, the proportions of corresponding sides can be determined using theorems regarding triangles and trapezoids.
We conclude that side AD is proportional to side EH because of the properties of similar geometric figures.
how many terms are in the following expression 6+2x-4y+5z
1
2
3
4
Answer:
4
Step-by-step explanation:
A term no matter how long it is, is ended by some sort of sign. so 6 is a term 2x is a term -4y is a term and 5z is a term. The term could be 5xyz^6a^2bc^7 + 2, and there are only 2 terms.
Answer:
4
Step-by-step explanation:
There are 4 terms in the expression. Terms are separated by the addition or subtraction sign.
In transaction (C) on 5/10, the Fees Earned account is a(n)
A. expense account, which increases.
B. revenue account, which increases.
C. revenue account, which decreases.
D. asset account, which decreases.
Answer:
(B) Revenue account which increases
Step-by-step explanation:
Hello, my dear friend, I am sure the question you are intending should be corrected as follows:
In transaction (C) on 5/10, the Fees Earned account is a(n) A. Expense account, which increases B. Revenue account, which increases C. Revenue account, which decreases D. Asset account, which decreases
If that is the case, then please note that whatever amount you earn, is an amount that will always increase. If you have no earnings, then nothing decreases nor decreases.
The Fees Earned account is a type of revenue account that increases when the company earns more fees. Therefore, option B (revenue account, which increases) is correct.
Explanation:In transaction (C) on 5/10, the Fees Earned account is usually classified as a revenue account. Therefore, when a company earns fees, it records the transaction as an increase in the fees earned account. The more fees the company earns, the higher the balance in this account, representing the income the company has made. So, if the Fees Earned account is increasing in value, it would be correct to say that it is a revenue account, which increases. This makes option B the correct answer.
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what is 2.1x(1+4.2x)=5.3
Simplifying
2.1x + -1(1 + 4.2x) = 5.3
2.1x + (1 * -1 + 4.2x * -1) = 5.3
2.1x + (-1 + -4.2x) = 5.3
Reorder the terms:
-1 + 2.1x + -4.2x = 5.3
Combine like terms: 2.1x + -4.2x = -2.1x
-1 + -2.1x = 5.3
Solving
-1 + -2.1x = 5.3
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '1' to each side of the equation.
-1 + 1 + -2.1x = 5.3 + 1
Combine like terms: -1 + 1 = 0
0 + -2.1x = 5.3 + 1
-2.1x = 5.3 + 1
Combine like terms: 5.3 + 1 = 6.3
-2.1x = 6.3
Divide each side by '-2.1'.
x = -3
Simplifying
x = -3
Hope i was helpful!
how much will it cost guys
Answer:
635 pounds hope you do good :)
Step-by-step explanation:
Answer:
Step-by-step explanation:
I would say probably 695E.The reason why I said that answer is because 30*2 equals 60.Then it took a additional 12 minutes and I know that 12*5 equals 60 so I divided 30 by 5.I got 6 and added it to 60 which got me 66.Then I multiplied that by 10.After that I just added the 35 to it.
what value of c makes x2-24x+c a perfect square trinomial?
Answer:
144
Step-by-step explanation:
Perfect square formula: a^2 - 2ab + b^2 (because that equals (a-b)^2)
x^2-2*12x+c
a = 1
b = 12
12^2 = 144
Answer:
The value of [tex]c =144[/tex] makes [tex]x^{2}-24x+c[/tex] perfect square.
Step-by-step explanation:
We have to make [tex]x^{2}-24x+c[/tex]
Since, Perfect square formula: [tex]a^{2} - 2ab + b^{2}=(a-b)^{2}[/tex]
Re-write [tex]x^{2}-24x+c[/tex] as,
[tex]x^{2}-2\times 12x+c[/tex]
Compare above with [tex]a^{2} - 2ab + b^{2}[/tex]
Where a = x and b= 12
so, [tex]b=12[/tex]
⇒ [tex]c =12^{2}=144[/tex]
Hence, [tex](a-b)^{2}=(x-12)^{2}[/tex]
Therefore, the value of [tex]c =144[/tex] makes [tex]x^{2}-24x+c[/tex] perfect square.
find the circumstances of a circle that has an area of 452.16 square feet
a) 37.6992 meters
b) 24 meters
c) 75.3984 meters
d) 12 meters
Rex mixed x liters of fruit syrup with y liters of water to make a fruit punch. Three times the number of liters of water he mixed was 6 more than twice the number of liters of syrup he mixed. The total number of liters of syrup and water he mixed was 7 liters. Which graph best shows the number of liters of fruit syrup and water that Rex added to make the fruit punch?
Answer:
the solution is (3,4) (the second one)
Step-by-step explanation:
The correct graph is attached to the answer.
The amount of fruit syrup Rex added is: 3 liters
and the amount of water he added is: 4 liters.
Step-by-step explanation:x denote the amount of fruit syrup added and y denote the amount of water added.
It is given that:
Three times the number of liters of water he mixed was 6 more than twice the number of liters of syrup he mixed.
i.e. the equation that satisfies this condition is:
[tex]3y=2x+6\\\\i.e.\\\\2x-3y=-6-----------(1)[/tex]
i.e. the graph of this equation is a line that passes through (-3,0) and (0,2)
Also, The total number of liters of syrup and water he mixed was 7 liters.
Hence, the equation is:
[tex]x+y=7------------(2)[/tex]
i.e. the graph of this equality is a line that passes through (7,0) and (0,7)
Also, from equation (2) we have:
[tex]x=7-y[/tex]
Now, on putting this value of x in terms of y in equation (1) we get:
[tex]2(7-y)-3y=-6\\\\i.e.\\\\14-2y-3y=-6\\\\i.e.\\\\14-5y=-6\\\\i.e.\\\\14+6=5y\\\\i.e.\\\\5y=20\\\\i.e.\\\\y=4[/tex]
Also, on putting the value of y in equation (2) we get:
[tex]x=3[/tex]
Hence, the solution to the system of linear equation is:
(3,4)
Find d and the measure of each side of equilateral triangle KLM if KL=d+2, LM=12-d, and KM=4d-13
Answer:
all sides are 7 units
Step-by-step explanation:
Since the triangle is equilateral then all 3 sides are equal in length
equate any 2 sides and solve for d
KL = LM
d + 2 = 12 - d ( add d to both sides )
2d + 2 = 12 ( subtract 2 from both sides )
2d = 10 ( divide both sides by 2 )
d = 5
KL = d + 2 = 5 + 2 = 7
LM = 12 - d = 12 - 5 = 7
KM = 4d - 13 = (4 × 5) - 13 = 20 - 13 = 7
In the figure to the right point O is the midpoint of segment
AB
. Through point O is drawn a line
OX
.perpendicular to
AB
. Prove that any point on line
OX
is equidistant from A and B.
Answer:
See proof below
Step-by-step explanation:
Point O is the midpoint of segment AB. Through point O is drawn a line OX perpendicular to AB. Consider two triangles AOX and BOX. These triangles are right triangles, because OX is perpendicular to AB. In these triangles:
OX=OX (reflexive property of congruence);AO=OB (by the definition of the midpoint O).Thus, [tex]\triangle AOX\cong \triangle BOX[/tex] by LL theorem.
Congruent triangles have congruent corresponding sides, then AX=BX. This means that point X is equidistant from points A and B.
is 124 a whole number
Answer:
yes, fractions are like 1/2 or 3/6 but a whole number is not a part or a fraction such as 124.
Step-by-step explanation:
Answer:
124 is a whole number
Step-by-step explanation:
The whole numbers are the numbers 0, 1, 2, 3, etc.
124 is a whole number
what is 2,190-2,910=
Answer:
-720
Step-by-step explanation:
2910 is obviously bigger than 2190 so your answer will result in a negative so what you could do is 2910-2190 which is 720 and add a negative in front of it.
Identify all the numbered angles that are congruent to the given angle
Answer:
1: 3 4 7
2: 5 6
3: 1 4 7
4: 1 3 7
5: 2 6
6: 2 5
7: 1 3 4
For the sequence -27, -12, 3, 18, ..., the expression that defines the nth term where a1 = -27 is
A. 15 --27n
B. 15-27 (n-1)
C. -27 + 15n
D. -27+15 (N-1)
Answer:
D. -27+15 (N-1)
Step-by-step explanation:
-27, -12, 3, 18
Take the second term and subtract the first term to find the common difference
-12 - (-27)
-12+27 = 15
The common difference is +15
We are adding 15 each time
The formula for an arithmetic sequence is
an = a1+d(n-1)
an = -27 +15(n-1)
The correct nth-term expression for the given sequence is -27 + 15(n - 1), reflecting the sequence's consistent increase of 15 between terms. So the correct option is D.
Explanation:The student's question asks for the expression that defines the nth term of the sequence -27, -12, 3, 18, ... given that a1 = -27. Observing the sequence, we can see that each term increases by 15 from the preceding term. Thus, to find the nth term, we start with the first term (-27) and add 15 to it n times (n - 1), because the first term is already included.
The correct expression for the nth term is therefore -27 + 15(n - 1), which simplifies to -27 + 15n - 15 and further simplifies to -42 + 15n. This corresponds to option D: -27 + 15 (n - 1).
What is the smallest number you can make that is divisible by 5 by using the following numbers: 6, 3, 5, 9, 4, and 1?
Answer:
5
Step-by-step explanation:
Steps:
1. 4 + 1 make five
2. 5 is divisible by five!!
Jamie rolls a 6-sided die 30 times and determines that the experimental probability of rolling a 2 is 1/5. The theoretical probability of rolling a 2 is 1/6. What could Jamie do to make his experimental results more closely match the theoretical probability?
Answer:He can increase the number of trials.
Step-by-step explanation:
He can increase the number of trials.
He can decrease the number of trials.
He can increase the number of sides on the die.
He can decrease the number of sides on the die.
Answer:
increase the number of trials
Step-by-step explanation:
hope this helped;) <3
A restaurant reports a net income of -1,242 over a three month period. What is the average income per month for that period, (Please give me the answer)
Answer:
-$414 per month
Step-by-step explanation:
If the net income over three months is -1242
Take that amount and divide by 3
-1242/3
-414
A 3 foot stick is broken into two pieces. The ratio of the two pieces is 5:7. How big are the two pieces
The 3 foot stick broken in a 5:7 ratio results in two pieces measuring 1.25 feet and 1.75 feet, respectively.
Explanation:The question involves a 3 foot stick that is broken into two pieces with a ratio of 5:7.
To find the lengths of the two pieces, we first add the parts of the ratio together, which gives us 12 parts in total.
Since the whole stick is 3 feet long, each part of the ratio represents \(\frac{3 feet}{12 parts}\) or \(\frac{1}{4} foot\) per part.
Thus, the length of the smaller piece is 5 parts (\(5 \times \frac{1}{4} = \frac{5}{4} feet\) or 1.25 feet) and the length of the larger piece is 7 parts (\(7 \times \frac{1}{4} = \frac{7}{4} feet\) or 1.75 feet).
The quadrilaterals ABBCD
and PQRS
are similar.
Find the length
of X
.
Final answer:
To find the length of X, we can use the concept of corresponding sides in similar figures. By establishing the ratio between corresponding sides AB and PQ, we can find the length of X. The length of X is found to be 2 units.
Explanation:
In order to find the length of X in the similar quadrilaterals ABBCD and PQRS, we need to find the corresponding sides that are proportional to each other. Let's say AB represents a side of ABBCD and PQ represents the corresponding side of PQRS. If AB is 6 units long and PQ is 3 units long, then the ratio of AB to PQ is 6:3, which simplifies to 2:1. Since the lengths of corresponding sides in similar figures are proportional, if AB has a length of 4 units, then PQ would have a length half of that, which is 2 units. Therefore, the length of X is 2 units.
Someone please help me with this question? Thanks if you do!
∠CBA it's an inscribed angle.
An inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords.
Inscribed Angle = 1/2 Intercepted Arc
Therefore
m∠CBA = 1/2(88°) = 44° → B.Declan has n baseball cards. Sam has 4 times as any baseball cards as Declan. Amaya has 7 fewer baseball cards than Sam. Which expression represents the number of baseball cards that Amaya has?
The expression that represents the number of baseball cards Amaya has, is x=4n-7 , where x=number of baseball cards Amaya has and n=number of baseball cards Declan has.
How to elaborate the given facts ?Given that, Declan has n baseball cards.
Sam has 4 times as any baseball cards as Declan.
So, Sam has 4n cards.
According to the question, Amaya has 7 fewer baseball cards than Sam.
So, Amaya has 7 less number of baseball cards than Sam.
What is the required expression ?If, Sam has 4n cards & Amaya has 7 less number of baseball cards than Sam.
∴ The expression is x=4n-7
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the length of a recta gular room is 7.9 m and its width is 8.6 what's the area
Answer:
Step-by-step explanation:
so multiply 7.9 * 8.6 which will give you 67.94
Answer:
The area is 67.94m.
A line is represented by the equation x + 2y=4. What is the slope of the line with that equation?
Answer:
the slope is 1
Step-by-step explanation:
Answer:
The slope is -1/2
Step-by-step explanation:
x + 2y=4
Lets get the equation in the form y= mx+b
where m is the slope and b is the y intercept.
x + 2y=4
Subtract x from each side
x-x+2y = -x+4
2y = -x+4
Divide each side by 2
2y/2 = -1/2 x +4/2
y = -1/2x +2
The slope is -1/2