Part (a)
Answer: x = -8------------------
Work Shown:
2(x-1) = 3(x+2)
2x-2 = 3x+6 .... distribute
2x = 3x+6+2 .... adding 2 to both sides
2x = 3x+8
2x-3x = 8 .... subtracting 3x from both sides
-x = 8
x = -8 ..... multiply both sides by -1
===========================================================
Part (b)
Answer: x = 5/11------------------
Work Shown:
-4(2x-2) = 3(x+1)
-8x+8 = 3x+3 ..... distribute
-8x = 3x+3-8 .... subtract 8 from both sides
-8x = 3x-5
-8x-3x = -5 ... subtract 3x from both sides
-11x = -5
x = -5/(-11) .... divide both sides by -11
x = 5/11
In decimal form, this is approximately equal to 5/11 = 0.4545
150 into the ratio 4:11
9514 1404 393
Answer:
40 : 110
Step-by-step explanation:
There are a number of ways you can go at this. One of my favorite is to consider the value of a "ratio unit." Here, a total of 4+11 = 15 "ratio units" represent the total to be divided: 150. So the value of each one is ...
150/15 = 10
Then the division is ...
4 : 11 = 10·4 : 10·11 = 40 : 110
_____
Alternate solution
Let x represent the larger share. Then the ratio is ...
(150 -x) : x = 4 : 11
Cross-multiplying gives ...
11(150 -x) = 4x
1650 = 15x . . . . . add 11x, simplify
110 = x . . . . . . . . . divide by 15; the larger share
150-x = 150-110 = 40 . . . . . . the smaller share
The division is 40 : 110.
The diagram shows a shape made from a solid cube and a solid cylinder.
The cube has sides of length 8.7 cm.
The cylinder has a radius of 2.7 cm and a height of 4.9 cm.
Calculate the total surface area of the solid shape.
Give your answer correct to 3 significant figures.
The total surface area of the solid shape made from the cube and cylinder is approximately 583.31 cm².
How to calculate the areaThe side length of the cube is 8.7 cm, so the surface area of one face is A = 8.7²
= 75.69 cm²
Since there are six faces, the total surface area of the cube is 6 * 75.69 = 454.14 cm²
Since there are two circular bases, the total surface area of the bases is 2 * 22.91 = 45.82 cm².
In this case, the radius of the cylinder is 2.7 cm and the height is 4.9 cm, so the curved surface area is A_curved = 2 * π * 2.7 * 4.9 ≈ 83.35 cm².
Total surface area = surface area of the cube + surface area of the cylinder
Total surface area = 454.14 cm² + 45.82 cm² + 83.35 cm²
Total surface area ≈ 583.31 cm²
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Lisa sees 10 birds. Cheyanne sees 6 times as many birds as lisa. How many birds do lisa and cheyanne see?
Answer:70
Step-by-step explanation:
Lisa sees 10
Cheyenne sees 10x6=60
10+60=70
4. Which of the following angles is vertical to angle /DEB?
A
C
109°
E
D
B
Answer:
A
Step-by-step explanation:
In Exercises 33–36, determine if the specified linear transforma- tion is (a) one-to-one and (b) onto. Justify each answer. 14. Let T : R2 R2 be a linear transformation with standard matrix A = aaz], where a, and a, are shown in the figure. Using the figure, draw the image of under the transformation T. [-] 1 |
If values prοvided then transfοrmatiοn οf vectοrs can be determined.
What is vectοr?In mathematics, a vectοr is a mathematical οbject that represents a quantity with bοth a magnitude and a directiοn. Vectοrs can be used tο represent physical quantities such as velοcity, fοrce, and acceleratiοn, as well as mοre abstract cοncepts such as cοlοr, sοund, and temperature.
Withοut seeing the figure οr the values οf a1, a2, and a3, it is nοt pοssible tο determine whether the specified linear transfοrmatiοn T : R2 → R2 is οne-tο-οne and οntο.
Hοwever, in general:
A linear transfοrmatiοn T : Rn → Rm is οne-tο-οne if and οnly if its kernel (i.e., the set οf vectοrs that are mapped tο the zerο vectοr) is trivial, meaning that the οnly vectοr that maps tο the zerο vectοr is the zerο vectοr itself.
A linear transfοrmatiοn T : Rn → Rm is οntο if and οnly if its range (i.e., the set οf all vectοrs that can be οbtained by applying T tο sοme vectοr in Rn) is equal tο Rm.
Tο determine whether a linear transfοrmatiοn is οne-tο-οne οr οntο, we can examine its prοperties and characteristics, such as its kernel, range, rank, and determinant. We can alsο use geοmetric intuitiοn and visualizatiοn tο understand hοw the transfοrmatiοn maps pοints and vectοrs in Rn tο Rm.
If yοu prοvide mοre infοrmatiοn abοut the values οf a1, a2, and a3 and the figure that shοws the standard matrix A, it can help yοu determine whether the transfοrmatiοn is οne-tο-οne and οntο and draw the image οf the vectοr [-1, 1] under the transfοrmatiοn T.
Therefοre, if values prοvided then transfοrmatiοn οf vectοrs can be determined.
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Complete question -
In Exercises 33–36, determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify each answer. 14. Let T : R2 R2 be a linear transformation with standard matrix A = aaz], where a, and a, are shown in the figure. Using the figure, draw the image of under the transformation T. [-] 1
which expresions are equivalent to 3 1/4 - _ 5/8 select all that apply
if n = 2 b = 6 y = 1,
find 2b + 3n +y
Answer:
19
Step-by-step explanation:
Answer:
b= 1/2 n+3y
Step-by-step explanation:
What is the minimum value of the absolute value parent function on
-10 SX< 10?
eWhat are the zeros of the function f(x) = (2x+6)(x-4)?OA. x = 6 and x = -4OB. x=-6 and x = -4OC. x=3 and x = -4OD. x=-3 and x = 4
Hello there. To solve this question, we have to remember some properties about roots of polynomials.
Given the following function:
\(f(x)=(2x+6)\cdot(x-4)\)We want to determine its roots.
For this, we want to determine the values of x such that
\(f(x)=0\)Then we have that
\((2x+6)\cdot(x-4)=0\)We know that a product of two values is equal to zero if and only if one of them is equal to zero.
So we have that
\(2x+6=0\text{ or }x-4=0\)Subtract 6 on both sides of the first equation, we get
\(2x=-6\)Divide both sides of the equation by a factor of 2
\(x=-3\)Now for the second equation, add 4 on both sides of the equation
\(x=4\)Hence we say that the roots of this function are
\(x=-3\text{ and }x=4\)This is the answer contained in the last option.
How to solve \(\frac{dy}{dx} =2|x|\) ?
dy= 2|x|dx
integral dy= integral 2|x|dx
y= X² + c
x2+10x+=()2
step by step
The value of the expression x² + 10x, when x = 2 is 24.
In the expression x² + 10x, x represents a variable, which is a placeholder for a value that can change. We are given that x = 2, which means we substitute 2 for x in the expression:
x² + 10x = 2² + 10(2)
Here, 2² means 2 raised to the power of 2, which is 2 multiplied by itself: 2² = 2 x 2 = 4.
10(2) means 10 multiplied by 2, which is 20.
So we can substitute these values in the expression:
x² + 10x = 2² + 10(2)
= 4 + 20
= 24
Therefore, when x is equal to 2, the value of the expression x² + 10x is 24.
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The complete question:
Evaluate the expression x² + 10x, when x = 2.
Celeste is planting a rectangular flower garden in which the width will be 4 feet less than its length. She has decided to put a birdbath within the garden that will occupy a space 3feet by 4 feet how many feet are now left for planting? Express your answer on factored form
Answer:
(L-6)(L+2)
Step-by-step explanation:
Let L be the length of the flower garden.
Then the width will be L-4.
The area of the flower garden = L*(L-4) =L²-4L
The area of the birdbath is 3*4 = 12 ft²
The area of the remaining space for planting is
= Area of flower garden - area of birdbath
L² - 4L - 12We can factor the expression as follows:
L² - 4L - 12 L²-(6-2)L-12L²-6x+2x-12taking common frome each two terms
L(L-6)+2(L-6)(L-6)(L+2)Therefore, the number of feet left for planting is (L-6)(L+2) in factored form.
Question 2 of 5
AABC DEF. What sequence of transformations will move AABC onto ADEF?
10
9876 5 4 3 2 +
A(0,4)
-1
D(5,8)
1 2 3 4 5 6 7 8 9 10 1
B(0,0) C(3, 0) E(5.0) F(11,0)
A. A dilation by a scale factor of 2, centered at the origin, followed by
a reflection over the wavic
Answer:
s
sStep-by-step explanation:
Julian has a rectangular picture. He enlarges the picture so that each dimension is 9 times its original dimension Which statement about the areas of the pictures is true?
Given Data:
The dimension of the rectangle is 9 times the original dimension i.e.
\(\frac{l_f}{l_i}=\frac{b_f}{b_i}=9\)The ratio of the area of the rectangle can be determined as,
\(\begin{gathered} \frac{A_f}{A_i}=(\frac{l_f}{l_i})^2 \\ =9^2 \\ =81. \end{gathered}\)Thus, area of the enlarged picture is 81 times the area of the original picture.
Thus, option (E) is the correct solution.
Find the equation for the circle with center (2,5) and passing through (3,5).
Write the equation for the circle.
(Simplify your answer.)
Answer:
\((x-2)^2 + (y-5)^2 = 1\)
Step-by-step explanation:
The radius is the distance from the center to a point oh the circle, in this case 1.
Substituting into the general formula for the equation of a circle, we get the equation to be
\((x-2)^2 + (y-5)^2 = 1\)
Which of the following calculations described in the following statements require that you use the addition rule?
A)Calculate the probability of black offspring from the cross AaBb × AaBb,when B is the symbol for the black allele.
B)Calculate the probability of children with both cystic fibrosis and polydactyly when parents are each heterozygous for both genes.
C)Calculate the probability of each of four children having cystic fibrosis if the parents are both heterozygous.
D)Calculate the probability of a child having only sickle-cell anemia or cystic fibrosis if each parent is each heterozygous for both traits.
If probability each parent is heterozygous for both features, determine the likelihood that a child will only have cystic fibrosis or sickle-cell anaemia.
P(Sickle-cell Anemia)
= 0.25
P(Cystic Fibrosis)
= 0.25
P(Sickle-cell Anemia or Cystic Fibrosis) = P(Sickle-cell Anemia) + P(Cystic Fibrosis)
P(Sickle-cell Anemia or Cystic Fibrosis)
= 0.25 + 0.25
P(Sickle-cell Anemia or Cystic Fibrosis)
= 0.5
The likelihood that a child will have either cystic fibrosis or sickle-cell anaemia is 0.5 or 50%. This is because both parents are heterozygous for both features. This means that each parent has a 25% chance of passing on either one of the conditions to their child. The probability of having either one of the conditions is the sum of the individual probabilities, which is 0.25 + 0.25 = 0.5 or 50%.
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Happy Card Co. designs personalized cards which cost $1.10 per card. The fixed cost to make the cards is $264 per day. If the company charges $5.10 per card, how many cards must be delivered daily to make a profit of $52? Show work below.
Step-by-step explanation:
x = number of cards
the production costs (PC) per day are
PC(x) = 264 + 1.1x
the sales (S) are
S(x) = 5.1x
the profit (P) per day is sales minus costs
P(x) = S(x) - PC(x) = 5.1x - (264 + 1.1x) =
= 5.1x - 264 - 1.1x = 4x - 264
we need to find the value of x, so that P(x) = 52.
52 = 4x - 264
316 = 4x
x = 316/4 = 79
79 cards must be delivered daily to make a profit of $52.
Divide
14 divided by 2/7
Answer:
49
Step-by-step explanation:
The numbers in 14 divided by 2/7 are labeled below:
14 = whole number
2 = numerator
7 = denominator
To make it a fraction form answer, you multiply the whole number by the denominator and make the result the new numerator. The old numerator becomes the new denominator:
\(\frac{14*7}{2}=\frac{98}{2}\)
Thus, the answer to 14 divided by 2/7 in fraction form is:
\(\frac{98}{2}\)
To make the answer to 14 divided by 2/7 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
98 / 2 = 49
The answer is rounded to the nearest two decimal points if necessary.
98/2 can be simplified to 49/1.
49/1 is an improper fraction and should be written as 49.
[RevyBreeze]
The division of 14 by 2/7 gives the quotient 49.
What is Division?The division is one of the four introductory fine operations, the other three being addition, deduction, and addition. In simple words, division can be defined as the splitting of a large group into lower groups similar that every group will have an equal number of particulars. It's an operation used for equal grouping and equal sharing in calculation.
We have to divide 14 by 2/7.
So, We have to multiply the fraction by reciprocate the number 2/7 to 7/2.
So, the division is
= 14 x 7/2
= 7 x 7
= 49.
Thus, the quotient is 49.
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Select a counter-example that makes the conclusion false. 7 - 3 = 4, 8 - 5 = 3, 9 - 8 = 1 Conclusion: the difference o...
A counter-example to the given conclusion is the difference between the numbers 15 and 25, where both are positive, but the difference gives a negative result.
How to find the counter-example?Here we are shown some differences between positive numbers:
7 - 3 = 4
8 - 5 = 3
9 - 8 = 1
And the conclusion is:
"The difference of two positive numbers is always positive".
To find a counter-example we just need to find two positive numbers such that the difference between these two positive numbers gives a negative number as a result.
An example of that can be the numbers 15 and 25, if we take the difference we will get:
15 - 25 = -10
Here we can see that the difference between two positive numbers gives a negative number as an outcome, so this is our counter-example.
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5/7 of what is 1/7???
Answer:
0.2
Step-by-step explanation:
5/7*x/1=1/7
5x/7=1/7
5x=1/7*7/1
5x=1
x=1/5 or 0.2
There are 52 playing cards in a standard deck. Each card is assigned to one of four suits: diamonds, hearts, spades, or clubs. Within each suit, there are 13 ranks: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King.
pls help
Answer:
Plzzzz answer fast......
Noah’s remote control car moved 12 feet in 6 seconds. Which graph has a slope that best represents Noah’s car’s average rate of speed?
We want to find a graph that represents Noah's average speed.
We define the average speed as the quotient between the distance moved and the time it takes to move that distance, then in this case we will have:
s = 12ft/6s = 2ft/s
Then we can define a linear equation:
y = (2ft/s)*x
As the distance that Noah travels in x seconds.
The graph of the given linear function can be seen below, and that is the graph with the slope that best represents Noah's average speed.
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2 more than the number of frogs is 4 ( writing Equations )
Answer:
4f+2
Step-by-step explanation:
Step-by-step explanation:
Answer:-Let the number of frogs be x.
According to statement,
2 more than the number of frogs is 4 .
So,
\(\boxed{\tt{2 + x = 4}}\) is the required Equation.
If solution, then,
\(x = 4 - 2\)
\(x = 2\)
Hope it helps :)
Question 9 of 10 Which of the following is most likely the next step in the series? OA. O B. O C. O D.
Answer: B
Step-by-step explanation:
The most likely the next pattern in the series is 2 lines with red color. Therefore, option B is the correct answer.
What is pattern?A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.
From the given patterns
Figure 1 has 5 lines and it is blue in color.
Figure 2 has 4 lines and it is red in color.
Figure 3 has 3 lines and it is blue in color.
So, Figure 4 must has 2 lines and red in color.
Therefore, option B is the correct answer.
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GEOMETRY 100 POINTS
Find the length of BC
Answer:
x = 16
Step-by-step explanation:
Opposite sides are equal in a parallelogram
AD = BC
5x - 12 = 3x + 20
5x - 3x = 20 + 12
2x = 32
x = 32/2
x = 16
What is the mean of 0.8, 1.0, 2.7, 2.8, 3.1, 13.3
Answer:
2.75
Step-by-step explanation:
Questions 16. Santhosh and Co. Chennai, opened a branch at Trichy on 1.1.2018. The following Information relate to the branch for the year 2018.
40,000
36,000
9,000
7200
3,600
30,000
16,200
300
3,000
Prepare branch account to find out the profit or loss of branch. Santosh & Co, Chennai opened its branch in Trichy on 1.1.2018. The action for 2018 is as follows
Credit sales at branch
Office expenses by Head office
Cash remittance to branch for petty cash Stock 31.12.2018
Goods sent to Branch
Salaries paid by head office
Debtors 31.12.2018
Petty cash on 31.12.2018
Cash sales at branch
of
The preparation of the branch's income statement for Santosh & Co. Chennai is as follows:
Branch of Santosh & Co. Chennai
Income StatementFor the year ended December 31, 2018
Sales revenue $40,300
Cost of goods sold 4,200
Gross profit $36,100
Expenses:
Office expenses $36,000
Salaries 3,600
Total expenses $39,600
Loss $3,500
What is an income statement?An income statement is a financial statement prepared at the end of an accounting period to determine the profit or loss generated by a business or branch.
The profit or loss is the difference between the total revenue and the total expenses for the accounting period.
Credit sales at branch 40,000
Office expenses by Head office 36,000
Cash remittance to branch for petty cash 9,000
Goods sent to Branch 7,200
Salaries paid by head office 3,600
Debtors 31.12.2018 30,000
Petty cash on 31.12.2018 16,200
Cash sales at branch 300
Stock of 31.12.2018 3,000
Sales revenue $40,300 ($40,000 + $300)
Cost of goods sold $4,200 ($7,200 - $3,000)
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△
ABC has vertices A(1, 3), B(2, 5), and C(5, 3). What are the coordinates of B′ after the transformation (x, y) ⟶ (–y, x), then translation 1 unit right and 4 units up?
Answer: we first need to apply the transformation to the x- and y-coordinates of the point individually
Step-by-step explanation:
To transform the coordinates of a point (x, y) using the transformation (x, y) ⟶ (–y, x), we first need to apply the transformation to the x- and y-coordinates of the point individually. This means that the x-coordinate becomes –y and the y-coordinate becomes x.
In the case of point B, the original coordinates are (2, 5), so the transformed coordinates are (–5, 2). This means that the x-coordinate becomes –5 and the y-coordinate becomes 2.
Next, we need to apply the translation that moves the point 1 unit right and 4 units up. To do this, we simply add 1 to the x-coordinate and add 4 to the y-coordinate. After this translation, the coordinates of B′ become (–4, 6). Therefore, the final coordinates of B′ are (–4, 6).
Find the greatest common factor of 9c and 11c? HEIM
Answer:
1
Step-by-step explanation:
Prime Factorization of the numbers-
3 x 3 = 9
11 = 11
GCF(9,11)
=1
alyssa does jumping jacks in her spare time she does 300 jumping jacks on 2.5 minutes how many jumpin jacks can she do per minute?