Answer:
[tex]\boxed{3x - y = 5}}[/tex]
Step-by-step explanation:
The coordinates of the two points are (4, 7) and (3, 4).
(a) Calculate the slope of the line
[tex]\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\&= & \dfrac{7 - 4}{4 - 3}\\\\& = & \dfrac{3}{1}\\\\ & = &3\\\end{array}[/tex]
(b) Calculate the y-intercept
[tex]\begin{array}{rcl}y & = & mx + b\\7 & = & 3 \times 4 + b\\7 & = & 12 + b\\b & = & -5\\\end{array}[/tex]
(c) Write the equation for the line
y = 3x - 5
This is the point-slope form of the equation.
(d) Convert to standard form
[tex]\begin{array}{rcl}y & = & 3x - 5\\-3x + y & = & -5\\3x - y & = & -5\\\end{array}\\\text{The standard form of the equation is }\boxed{\mathbf{3x- y = -5}}[/tex]
The equation of the line in the form of Ax + By = C is 3x - y = 7.
Given that,
The equation of the line in the form Ax +By = C,
Which passes through the points (4, 3) and (3,4).
We have to determine,
The equation of the line.
According to the question,
The equation of the line in the form Ax +By = C,
The co-ordinate passes through the points (4, 3) and (3,4).
To determine the equation of the line following all the steps given below.
Step1; The slope of the two points can be written as,[tex]m = \dfrac{y_2-y_1}{x_2-x_2}\\\\m = \dfrac{4-7}{3-4}\\\\m = \dfrac{-3}{-1}\\\\m = 3[/tex]
The slope of the line is 3.
Step2; The y-intercept of the line,[tex]y = mx + c\\\\7= 3 \times 4 + c\\\\7 = 12+ c\\\\c = 7-12\\\\c = -5[/tex]
The y-intercept of the line is -7.
Step3; The equation for the line is,
[tex]y = mx + c \\\\y = 3x-7[/tex]
Step4; The equation can be written as standard form,[tex]y = 3x - 7\\\\3x -y = 7[/tex]
Hence, The equation of the line in the form of Ax + By = C is 3x - y = 7.
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What is the value of x? Enter your answer in the box
Answer:
x = 20
Step-by-step explanation:
Formula
x1/x2 = x3/x4
Givens
x = 11
x2 = 11 + 121 = 132
x3 = 10
x4 = 10 + 5x + 10
Solution
11/132 = 10 / (5x + 10 + 10) Combine
11/132 = 10/(5x + 20) Cross multiply
11*(5x + 20) = 132 * 10 Combine on the right.
11(5x + 20 ) = 1320 Divide by 11. (You could remove the brackets, but this is easier.
11(5x + 20)/11 = 1320/11 Do the division
5x + 20 = 120 Subtract 20 from both sides
5x + 20-20 = 120 - 20 Combine
5x = 100 Divide by 5
5x/5 = 100/5
x = 20
The recursive rule for a geometric sequence is given. a1=2; an=1/3a subscript (n−1) Enter the explicit rule for the sequence. an=
ANSWER
[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]
EXPLANATION
The recursive formula is given as:
[tex]a_n= \frac{1}{3} a_{n-1}[/tex]
where
[tex]a_1=2[/tex]
The explicit rule is given by:
[tex]a_n=a_1 {r}^{n-1}[/tex]
From the recursive rule , we have
[tex]r = \frac{1}{3} [/tex]
We substitute the known values into the formula to get;
[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]
Therefore, the explicit rule is:
[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]
8) Factor each sum or difference of cubes completely.
a. 8x3 + 27
Answer:
[tex]\large\boxed{(2x+3)(4x^2-6x+9)}[/tex]
Step-by-step explanation:
[tex]8=2^3\\\\8x^3=2^3x^3=(2x)^3\\\\27=3^3\\\\8x^3+27=(2x)^3+3^3\qquad\text{use}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(2x+3)\bigg((2x)^2-(2x)(3)+3^2\bigg)=(2x+3)(4x^2-6x+9)[/tex]
please help and thank you.
Answer:
Step-by-step explanation:
This is a negative x^2 quadratic. I'm not sure if there's anything else you need.
Solve the equation of exponential decay. The population of a city is expected to be 440,000 in 2020. This is a decline of 12% from 2010 to 2020. Assuming this continued what would the population of the city be in 2040? Round to the nearest ten thousand
Answer:
about 340,000
Step-by-step explanation:
In 10 years, the population dropped to 0.88 of what it was in 2010. At the same rate, in 20 more years, it will drop to 0.88² of what it was in 2020:
2040 population = 440,000·0.88² ≈ 340,000
Answer:
about 340,000
Step-by-step explanation:
In 10 years, the population dropped to 0.88 of what it was in 2010. At the same rate, in 20 more years, it will drop to 0.88² of what it was in 2020:
2040 population = 440,000·0.88² ≈ 340,000
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) ? 0.]f(x) = 10/x , a= -2f(x) = \sum_{n=0}^{\infty } ______Find the associated radius of convergence R.R = ______
Rewrite [tex]f[/tex] as
[tex]f(x)=\dfrac{10}x=-\dfrac5{1-\frac{x+2}2}[/tex]
and recall that for [tex]|x|<1[/tex], we have
[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]
so that for [tex]\left|\dfrac{x+2}2\right|<1[/tex], or [tex]|x+2|<2[/tex],
[tex]f(x)=-5\displaystyle\sum_{n=0}^\infty\left(\frac{x+2}2\right)^n[/tex]
Then the radius of convergence is 2.
The Taylor series for the function f(x) = 10/x, centered at a = -2, is given by the formula ∑(10(-1)^n*n!(x + 2)^n)/n! from n=0 to ∞. The radius of convergence (R) for the series is ∞, which means the series converges for all real numbers x.
Explanation:Given the function f(x) = 10/x, we're asked to find the Taylor series centered at a = -2. A Taylor series of a function is a series representation which can be found using the formula f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + .... For f(x) = 10/x, the Taylor series centered at a = -2 will be ∑(10(-1)^n*n!(x + 2)^n)/n! from n=0 to ∞. The radius of convergence R is determined by the limit as n approaches infinity of the absolute value of the ratio of the nth term and the (n+1)th term. This results in R = ∞, indicating the series converges for all real numbers x.
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Please help ASAP and help me find what the value of x is
Answer:
x=44
Step-by-step explanation:
33+103+x=180
136+x=180
x=44
The sum of all the angles of a triangle is 180 degrees.
Add all the angles together and set it equal to 180, then solve for x
33 + 103 + x = 180
(136 - 136) + x = 180 - 136
x = 44
Hope this helped!
Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.
ANSWER
[tex]\sin( \theta) = - \frac{15}{17} [/tex]
[tex]\csc( \theta) = - \frac{17}{15} [/tex]
[tex]\cos( \theta) = \frac{8}{17} [/tex]
[tex]\sec( \theta) = \frac{17}{8} [/tex]
[tex]\tan( \theta) = - \frac{15}{8} [/tex]
[tex]\cot( \theta) = - \frac{8}{15} [/tex]
EXPLANATION
From the Pythagoras Theorem, the hypotenuse can be found.
[tex] {h}^{2} = 1 {5}^{2} + {8}^{2} [/tex]
[tex] {h}^{2} = 289[/tex]
[tex]h = \sqrt{289} [/tex]
[tex]h = 17[/tex]
The sine ratio is negative in the fourth quadrant.
[tex] \sin( \theta) = - \frac{opposite}{hypotenuse} [/tex]
[tex]\sin( \theta) = - \frac{15}{17} [/tex]
The cosecant ratio is the reciprocal of the sine ratio.
[tex]\csc( \theta) = - \frac{17}{15} [/tex]
The cosine ratio is positive in the fourth quadrant.
[tex]\cos( \theta) = \frac{adjacent}{hypotenuse} [/tex]
[tex]\cos( \theta) = \frac{8}{17} [/tex]
The secant ratio is the reciprocal of the cosine ratio.
[tex]\sec( \theta) = \frac{17}{8} [/tex]
The tangent ratio is negative in the fourth quadrant.
[tex]\tan( \theta) = - \frac{opposite}{adjacent} [/tex]
[tex]\tan( \theta) = - \frac{15}{8} [/tex]
The reciprocal of the tangent ratio is the cotangent ratio
[tex]\cot( \theta) = - \frac{8}{15} [/tex]
Answer:
sin=-15/17
cos=8/7
tan=-15/8
csc=-17/15
sec=17/8
cot=-8/15
"Solve the problem of exponential growth. According to the U.S. Census Bureau, the population of the United States in 2010 was 308 million. This is a 9.6% increase over the 2000 count. Assuming this continued what would the population be in 2030?"
Answer:
370 million
Step-by-step explanation:
In the 10 years from 2000 to 2010, the population was multiplied by the factor ...
100% + 9.6% = 109.6% = 1.096
In the next 20 years from 2010 to 2030, the population will be multiplied by that factor twice, if it grows at the same rate:
2030 population = (308 million)·(1.096²) ≈ 370 million
Answer:
370 million
Step-by-step explanation:
In the 10 years from 2000 to 2010, the population was multiplied by the factor ...
100% + 9.6% = 109.6% = 1.096
In the next 20 years from 2010 to 2030, the population will be multiplied by that factor twice, if it grows at the same rate:
2030 population = (308 million)·(1.096²) ≈ 370 million
A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)=72t-16t^2. What is the maximum height that the ball will reach?
Do not round your answer
Answer:
The maximum height that the ball will reach is 81 ft
Step-by-step explanation:
Note that the tray of the ball is given by the equation of a parabola of negative main coefficient. Then, the maximum value for a parabola is at its vertex.
For an equation of the form
[tex]at ^ 2 + bt + c[/tex]
So
the t coordinate of the vertice is:
[tex]t =-\frac{b}{2a}[/tex]
In this case the equation is:
[tex]h(t)=72t-16t^2[/tex]
So
[tex]a=-16\\b=72\\c=0[/tex]
Therefore
[tex]t =-\frac{72}{2(-16)}[/tex]
[tex]t=2.25\ s[/tex]
Finally the maximum height that the ball will reach is
[tex]h(2.25)=72(2.25)-16(2.25)^2[/tex]
[tex]h=81\ ft[/tex]
The ball thrown vertically upwards will reach the maximum height of 81 feet after 2.25 seconds.
Explanation:To find the maximum height the ball will reach, first, we need to recognize that the equation 'h(t)=72t-16t^2' is a quadratic function in the form of 'f(t)=at^2+bt+c'. The maximum point of a quadratic function, also known as the vertex, happens at 't=-b/2a'. In this case, 'a' is -16 and 'b' is 72.
So the maximum height is achieved at 't=-72/(2*-16)' or 't=72/32 = 2.25' seconds.
To find out the maximum height, we just need to substitute this value of t into the equation for h(t):
h(2.25)=72*2.25-16*2.25^2
The above calculation gives a maximum height of 81 feet.
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what is the sum of the fractions
Answer:
[tex]6\frac{7}{9}[/tex]
Step-by-step explanation:
[tex]6\frac{2}{3}+\frac{1}{9} = 6\frac{6}{9}+\frac{1}{9}=6 \frac{7}{9}[/tex]
Answer:
Step-by-step explanation:
its D
3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi. The Radius is 7 inches and the Height is 12.
The formula for volume of a cone is V = PI x r^2 x h/3 where r is the radius and h is the height.
Volume of cone = 3.14 x 7^2 x 12/3
Volume of cone = 3.14 x 49 x 4
Volume of cone = 615.44 cubic inches.
The formula for volume of half a sphere is : 1/2 x (4/3 x PI x r^3)
Volume for half sphere = 1/2 x (4/3 x 3.14 x 7^3)
= 1/2 x 4/3 x 3.14 x 343
= 718.01 cubic inches.
Total volume = 615.44 + 718.01 = 1333.45 cubic inches.
Rounded to the nearest tenth = 1,333.5 cubic inches.
Write the product of the monomials (8x6y)2 and (x3y4).
Answer:
The product of the monomials is 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]
Step-by-step explanation:
* Lets explain how to solve the problem
- We need to find the product of the monomials (8x 6y)² and
[tex]x^{3}y^{4}[/tex]
- At first lets solve the power of the first monomial
- Because the power 2 is on the bracket then each element inside the
bracket will take power 2
∵ (8x 6y)² = (8)²(x)²(6)²(y)²
∵ (8)² = 64
∵ (x)² = x²
∵ (6)² = 36
∵ (y)² = y²
∴ (8x 6y)² = [64x² × 36y²]
∵ 64 × 36 = 2304 x²y²
∴ The first monomial is 2304 x²y²
∵ The first monomial is 2304 x²y²
∵ The second monomial is [tex]x^{3}y^{4}[/tex]
- Lets find their product
- Remember in multiplication if two terms have same bases then we
will add their powers
∵ [2304 x²y²] × [ [tex]x^{3}y^{4}[/tex] ] =
2304 [ [tex]x^{2}*x^{3}[/tex] ] [ [tex]y^{2}*y^{4}[/tex] ]
∵ [tex]x^{2}*x^{3}[/tex] = [tex]x^{2+3}[/tex] = [tex]x^{5}[/tex]
∵ [tex]y^{2}*y^{4}[/tex] = [tex]y^{2+4}[/tex] = [tex]y^{6}[/tex]
∴ [2304 x²y²] × [ [tex]x^{3}y^{4}[/tex] ] = 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]
The product of the monomials is 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]
Write these expressions in exponential form:
1. 10 * 10 * 10 * 10 *10
2. y * y * x * x * x * z * z * z * z *z
3. What is 14 to the zero power?
1. 10^5
2. z^5*x^3*y^2
3. 1
Please respond quickly!!
Answer:
Area of triangle = 6 in^2
Step-by-step explanation:
We need to find the area of triangle. The formula used is:
Area of triangle = 1/2 * b*h
where b=base and h= height
In the given question, b =2 and h= 6
Putting values in the formula:
Area of triangle = 1/2 *2*6
= 12/2
= 6 in^2
Answer:
The area is 6 in^2
Step-by-step explanation:
This Venn diagram shows sports played by 10 students
Let event A - The student plays basketball.
Let event B - The student plays soccer.
What is P(AB)?
Answer:
B. 1/10 or 0.10
Step-by-step explanation:
The question asks what's the probability that a student picked randomly will be playing both basketball and soccer.
The answer is right in the diagram.
We have only one student who plays both basketball and soccer: Ella
Since we have 10 students in the selected group, the probably you'll pick Ella is:
1 / 10 = 0.10 = 10%
So, the answer is B.
The value of P(A/B) is 0.33.
Given that, the Venn diagram shows sports played by 10 students.
What is P(A/B)?P(A/B) is known as conditional probability and it means the probability of event A that depends on another event B. It is also known as "the probability of A given B". The formula for P(A/B)=P(A∩B) / P(B).
Now, P(A/B)=1/3≈0.33
Therefore, the value of P(A/B) is 0.33.
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Given the function f(x)= -5+4x^2 calculate the following value:
f(a+h)
Please help ASAP!!! :(
Evaluating a function in a specific point means to substitute all occurrences of x with the specific value.
In your case, we have to substitute "x" with "a+h":
[tex]f(x)= -5+4x^2 \implies f(a+h) = -5+4(a+h)^2\\ = -5+4(a^2+2ah+h^2)=-5+4a^2+8ah+h^2[/tex]
Using the distributive property to find the product (y — 4)(y2 + 4y + 16) results in a polynomial of the form y3 + 4y2 + ay – 4y2 – ay – 64. What is the value of a in the polynomial?
Answer:
a=16
Step-by-step explanation:
Given
(y-4)(y^2+4y+16)
To find the value of a in the resulting polynomial we have to solve the given expression
=y(y^2+4y+16)-4(y^2+4y+16)
= y^3+4y^2+16y-4y^2-16y-64
To find the value of a, both the polynomials will be compared
y^3+4y^2+16y-4y^2-16y-64
y^3+4y^2+ay-4y^2-ay-64
Comparing the coefficients of both polynomials gives us that
a=16
So, the value of a is 16 ..
help please
greatest common factor find the GCF of each
must show work
11) Factors of 55 are 1,5,11,55 Factors of 75 are 1,3,5,15,25,75
The greatest common factor is 5.
12) With algebraic expressions you just simplify and multiplier in the simplification is the greatest common factor.
66yx + 30x^2y --) 6yx( 11 + 5x ) so the greatest common factor is 6yx.
13) 60y + 56x^2 --) 4( 15y + 14x^2 ) so the greatest common factor is 4.
14) 36xy^3 + 24y^2 --) 12y^2( 3xy + 2 ) so the greatest common factor is 12y^2.
15) 18y^2 + 54y^2 --) 18y^2( 1 + 3 ) so the greatest common factor is 18y^2.
16) 80x^3 + 30yx^2 --) 10x^2( 8x + 3y ) so the greatest common factor is 10x^2.
17) 105x + 30yx + 75x --) 15x( 7 + 2y + 5 ) so the greatest common factor is 15x.
18) 140n + 140m^2 + 80m --) 20( 7n + 7m^2 + 4m ) so the greatest common factor is 20.
If you want a further explanation step by step just ask :)
Jake is eating dinner at a restaurant. The cost of his meal, including sales tax, is m dollars. After leaving an 18% tip, the amount Jake pays at the restaurant is represented by the following expression. In this expression, what does the term 0.18m represent?
For this case we have that variable "m" represents the cost of Jake's food. They tell us that he left an 18% tip. That is to say:
m -------------> 100%
tip ------------> 18%
Where "tip" is the cost of the tip based on the cost of the meal.
[tex]tip = \frac {18 * m} {100}\\tip = 0.18m[/tex]
The amount Jake pays is represented by:
[tex]m + 0.18m[/tex]
Where 0.18m is the tip
ANswer:
Tip
Answer:
the tip amount jake pays
Step-by-step explanation:
A certain game consists of rolling a single fair die. If a four or five comes up, you win 8 dollars; otherwise, you lose 4 dollars. Find the expected winnings for this game
Answer:
3/1
Step-by-step explanation:
Well there's 6 sides on a dice and only 2 winning numbers. 6/2=3/1. You have a good chance of losing lol. Is this what you're looking for?
~Keaura/Cendall.
Follow below steps:
To find the expected winnings for the game described, we need to calculate the expected value of one roll of the die based on the outcomes and their corresponding probabilities and payoffs. This is a classic example of a discrete probability distribution problem where the random variable X represents the winnings from one roll of the die.
There are two winning outcomes, rolling a four and rolling a five, each of which has a probability of 1/6 and a payoff of 8 dollars. There are four losing outcomes, rolling a one, two, three, or six, each with the same probability of 1/6 and a loss of 4 dollars.
Therefore, the expected value E(X) is calculated as follows:
P(rolling a 4 or 5) = 1/6 for each, so 2/6 combined since the die is fair.P(rolling any other number) = 4/6 combined, since there are four other possibilities.E(X) = (2/6) * 8 + (4/6) * (-4) = (16/6) - (16/6) = 0
So the expected winnings for this game are 0 dollars, which means that, on average, a player neither wins nor loses money in the long term.
What is the value of x?
Answer:
Step-by-step explanation:
When an angle is bisected the opposite sides and the sides of the bisected angle are in a set ratio.
That translates into
(x + 8)/10 = (2x - 5)/14 Cross multiply
14* (x + 8) = 10* (2x - 5) Remove the brackets on both sides.
14x + 112 = 20x - 50 Subtract 14x from both sides.
112 = 20x - 14x - 50 Combine
112 = 6x - 50 Add 50 to both sides.
112+50 = 6x - 50 + 50 Combine
162 = 6x Switch
6x = 162 Divide by 6
x = 27
How do you simplify this expression step by step using trigonometric identities?
[tex]\bf \textit{Pythagorean Identities}\\\\ 1+tan^2(\theta)=sec^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sec^2(\theta )cos^2(\theta )+tan^2(\theta )\implies \cfrac{1}{\begin{matrix} cos^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\cdot \begin{matrix} cos^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} +tan^2(\theta ) \\\\\\ 1+tan^2(\theta )\implies sec^2(\theta )[/tex]
what is the solution in this equation -8x+4=36
Answer:
X=-4
Step-by-step explanation:
Answer:
x = -4
Step-by-step explanation:
-8x+4=36
-4
-8x =32
/-8 /-8
x = -4
A cylindrical container has a radius of 0.2 meter and a height of 1 meter. The container is filled with honey. The density of honey is 1417 kg/m³. What is the mass of the honey in the container? Enter your answer in the box. Use 3.14 for π . Round your final answer to the nearest whole number.
Answer:178
Step-by-step explanation: I took the test :)
Answer:
The mass of the container is 178 kg.
Step-by-step explanation:
Since, the volume of a cylinder is,
[tex]V=\pi (r)^2 h[/tex]
Where r is the radius of the cylinder
And, h is its height
Here, r = 0.2 meters,
h = 1 meter,
So, the volume of the cylindrical container is,
[tex]V=\pi (0.2)^2(1)[/tex]
[tex]=3.14\times 0.04=0.1256\text{ cubic meters}[/tex]
Now,
[tex]Density = \frac{Mass}{Volume}[/tex]
[tex]\implies Mass = Density\times Volume[/tex]
Given, Density of the container = 1417 kg/m³,
By substituting the values in the above formula,
[tex]\text{Mass of the container}=1417\times 0.1256=177.9752\text{ kg}\approx 178\text{ kg}[/tex]
how much string is left when 1 and 3/4 in are cut from a piece measuring 3 and 1 /6 inches
Answer:
1 5/12 inches.
Step-by-step explanation:
That is 3 1/6 - 1 3/4
= 19/6 - 7/4
The lowest common denominator of 4 and 6 is 12, so we have:
38/12 - 21/12
= 17 /12
= 1 5/12 inches (answer).
The remaining string length after cutting [tex]\(1 \frac{3}{4}\)[/tex] inches is [tex](1 \frac{5}{16}\)[/tex]inches.
The correct option is (a).
find out how much string is left when [tex]\(1 \frac{3}{4}\)[/tex] inches are cut from a piece initially measuring[tex]\(3 \frac{1}{16}\)[/tex]inches.
1. Convert the mixed numbers to improper fractions:
[tex]- \(1 \frac{3}{4}\) inches = \(\frac{7}{4}\) inches[/tex]
[tex]- \(3 \frac{1}{16}\) inches = \(\frac{49}{16}\) inches[/tex]
2. Make the denominators equal:
- Multiply the numerator and denominator of [tex]\(\frac{7}{4}\)[/tex]by 16 to make the denominators equal:
[tex]\(\frac{7}{4} = \frac{112}{64}\)[/tex]
- Now we have:
- Initial length = [tex]\(\frac{49}{16}\)[/tex] inches
- Cut length = [tex]\(\frac{112}{64}\)[/tex] inches
3. Subtract the two fractions:
- Subtract the cut length from the initial length:
[tex]\(\frac{49}{16} - \frac{112}{64}\)[/tex]
- To subtract, we need a common denominator. The least common multiple (LCM) of 16 and 64 is 64.
- Convert both fractions to have a denominator of 64:
[tex]\(\frac{49}{16} = \frac{196}{64}\)[/tex]
[tex]\(\frac{112}{64}\) remains the same.[/tex]
- Subtract the numerators:
[tex]\(\frac{196}{64} - \frac{112}{64} = \frac{84}{64}\)[/tex]
4. Simplify the result:
- Divide both the numerator and denominator by their greatest common factor (GCF), which is 4:
[tex]\(\frac{84}{64} = \frac{21}{16}\)[/tex]
5. Convert back to a mixed number:
- Divide the numerator by the denominator:
[tex]\(\frac{21}{16} = 1 \frac{5}{16}\)[/tex]
Therefore, the remaining string length after cutting [tex]\(1 \frac{3}{4}\)[/tex] inches is [tex](1 \frac{5}{16}\)[/tex]inches.
rx+2x=4r+3
Solving for X
Answer:
x = (4r +3)/(r +2)
Step-by-step explanation:
Collect x terms, then divide by the coefficient of x.
x(r +2) = 4r +3
x = (4r +3)/(r +2)
What are the solutions to the system of equations?
x = x^2 - 4x +3
y = -x +3
( , ) and ( , )
Answer:
(0,3) and (3,0)
Step-by-step explanation:
The first thing to do is graph the two equations to see where they intersect. Then you know what answer to look for. The graph is below. It was done on desmos.
I take it the first equation is a typo and should be y = x^2 - 4x + 3
Equate the two equations.
-x + 3 = x^2 -4x + 3 Subtract 3 from both sides
-x = x^2 - 4x + 3-3
-x = x^2 - 4x Add x to both sides.
0 = x^2 - 4x + x
0 = x^2 - 3x Factor
0 = x(x - 3)
So x can equal 0
or x can equal 3
In either case the right side will reduce to 0.
Case 1. x = 0
y= - x + 3
y = 0 + 3
y = 3
So the point is (0,3)
Case 2. x = 3
y = - x + 3
y = - 3 + 3
y = 0
So the point is (3,0)
A mother who is 40 years old has a daughter and a son. The son is twice as old as the daugther. In 15 years the sum of all their ages will be 100 years. How old are the siblings now?
Answer:
The son's age is 10 and the daughter's age is 5 now
Step-by-step explanation:
Let
x-----> the son's age now
y----> the daughter's age now
we know that
x=2y ----> equation A
(x+15)+(y+15)+(40+15)=100
x+y+85=100
x+y=15 -----> equation B
Substitute equation A in equation B and solve for y
2y+y=15
3y=15
y=5 years
Find the value of x
x=2(5)=10 years
therefore
The son's age is 10.
The daughter's age is 5
Charles factors the expression 4/3xy+1/3x using a factor of 1/3x. He writes the factored expression 1/3x(4y+1). Which best describes the accuracy of Charles solution?
A. His solution is accurate
B. His solution is inaccurate. The factor does not divide evenly into both terms.
C. His solution is inaccurate. The factoring of 4/3xy using the given GCF is incorrect.
D. His solution is inaccurate. The factoring of 1/3x using the given GCF is incorrect.
A. His solution is accurate
You can verify this by expanding his factored expression: 1/3x(4y+1), which gives you back the original expression 4/3xy+1/3x
Charles' solution is accurate because expression after factorization is similar to Charles factor's of expression option (A) is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
[tex]\rm = \dfrac{4}{3}xy+\dfrac{1}{3}x[/tex]
Taking common as (1/3)x
[tex]\rm = \dfrac{1}{3}x(4y+1)[/tex]
The above expression is similar to Charles factor's of expression.
Thus, Charles solution is accurate because expression after factorization is similar to Charles factor's of expression option (A) is correct.
Learn more about the expression here:
brainly.com/question/14083225
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