Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle:
A(2, 1), B(5, 1), C(5, 6), and D(2, 6).
Given these coordinates, what is the length of side AB of this rectangle?
FIND THE GCF. Mathematics
The G.C.F of the given algebraic expression is; ⁴⁹/₆a xy
What is the G.C.F (Greatest Common Factor)?The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. For example, for the set of numbers 18, 30 and 42 the GCF = 6.
We are given the algebraic expression;
(3 x y * 4x²y * ¹/₁ * 5x³y ^ z * 4)7a * 1/1 * 7*6
Expanding this further gives;
⁴⁹/₆a((3xy * 4x²y * 20x³y ^ z )
Now, the GCF of the terms inside the bracket would be x y. Thus, expanding the GCF we have;
⁴⁹/₆a xy((3 * 4x * 20x²y^(z - 1))
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What are the coordinates of the point on the
directed line segment from (4, 3) to (9, 8) that
partitions the segment into a ratio of 2 to 3?
The required coordinates are (6, 5).
Let A denotes the point (4, 3), and B denotes the point (9, 8).
Let C denote the point which divides the line segment AB in the ratio of 2:3.
The distance between A(4, 3) and B(9, 8) is given by
AB = √{(x₂ - x₁)² + (y₂ -y₁)²}
= √{(9 - 4)² + (8 - 3)²
= √{5² + 5²}
= √(2×5²)
= 5√2
We have AC + BC = AB
AC and BC are in the ratio 2:3.
Therefore 2x + 3x = AB
⇒5x = 5√2
⇒x = √2.
Therefore, AC = 2√2 and BC = 3√2.
Using the distance formula,
AC = √{(x - 4)² + (y - 3)²}
⇒ 2√2 = √{(x - 4)² + (y - 3)²}
⇒ √(2² + 2²) = √{(x - 4)² + (y - 3)²} (taking the 2 inside the square root.)
⇒ x - 4 = 2 ⇒ x = 6
⇒ y - 3 = 2 ⇒ y = 5.
Therefore the required coordinates are (6, 5).
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How can the graph rule y=2x+1 be used to predict the result for an input (x-Value) of 7
The value of y for the given input x=7 is 15.
The given function is y=2x+1.
We need to graph the given function.
How to graph the given function?Graphing functions is the process of drawing the graph (curve) of the corresponding function. Graphing basic functions like linear, quadratic, cubic, etc is pretty simple, graphing functions that are complex like rational, logarithmic, etc, need some skill and some mathematical concepts to understand.
Now,
Graph the line using the slope and y-intercept, or two points.
Slope: 2
y-intercept: (0, 1)
Plot the points (0, 1) and (1, 3)
The value of y for x=7 is y=2(7)+1=15
Therefore, the value of y for the given input x=7 is 15.
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Find the derivative of the function using the definition of derivative. g(t) = 3 t
The derivative of the function using the definition of derivative is 3.
The given function is g(t) = 3t.
We have to find the derivative of the function using the definition of derivative.
We know that,
Definition of derivative:-
The derivative of a function is the rate of change of the function's output relative to its input value.
Here,
Input value = t
Output value = g(t)
Given y = g(t), the derivative of g(t), denoted g'(t) (or dg(t)/dt), is defined by the following limit:
[tex]g'(t)= \lim_{h \to 0} \frac{g(t+h)-g(t)}{h}[/tex]
We have the function:-
g(t) = 3t
Hence, according to the data given in the question, we can write,
g'(t) =
[tex]\lim_{h \to 0} \frac{g(t+h)-g(t)}{h} \\\\ \lim_{h \to 0} \frac{3(t+h)-3(t)}{h}\\\\ \lim_{h \to 0} \frac{3t+3h-3t}{h}\\\\ \lim_{h \to 0} \frac{3h}{h}\\\\\lim_{h \to 0} 3[/tex]
g'(t) = 3
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A gaming company claimed that their role-playing games take over 65 hours to complete. A sample of 300 gamers played their role-playing games and were able to complete them with a mean time of 63, hours with a standard deviation of 10 hours. Using a 1% level of significance, test the gaming company's hypothesis.
A. Reject the null hypothesis. There is enough evidence to oppose the gaming company's claim.
B. Reject the null hypothesis. There is not enough evidence to oppose the gaming company's claim.
C. Fail to reject the null hypothesis. There is not enough evidence to oppose the gaming company's claim.
D. Fail to reject the null hypothesis. There is enough evidence to oppose the gaming company's claim.
Answer:
D. Fail to reject the null hypothesis. There is enough evidence to oppose the gaming company's claim.
Step-by-step explanation:
Let μ = mean time to complete a role-playing game.
The company claims that their role-playing games take over 65 hours to complete, so the hypotheses are:
H₀: μ = 65 H₁: μ > 65
Therefore, this is a one-tailed test.
The significance level is 1%, so α = 0.01.
Find the value of the test statistic (z):
[tex]\textsf{sample mean }\overline{x}=63,\quad \sigma=10, \quad n=300[/tex]
[tex]\implies z=\dfrac{\overline{x}-\mu}{\sigma / \sqrt{n}}=\dfrac{63-65}{10 / \sqrt{300}}=-2\sqrt{3}=-3.4641...[/tex]
Using the “Percentage Points of The Normal Distribution” table, the critical value is z = 2.3263 meaning the critical region is Z > 2.3263.
Since z = -3.4641... < 2.3263, the observed value of the test statistic lies outside the critical region. Therefore, the result is not significant.
Conclusion
There is sufficient evidence at the 1% level of significance to fail to reject H₀ and to oppose the alternative hypothesis that the mean time to complete the role-playing game is more than 65 hours.
Answer:
A) Reject the null hypothesis. There is enough evidence to oppose the gaming company's claim.
Step-by-step explanation:
The test statistic needs to fall within the rejection regions that are above and below the critical z-score associated with a 1% level of significance in order to reject the null hypothesis. Otherwise, we will fail to reject the null hypothesis.
how do you turn this root into a power?
√5
Answer:
5^(1/2)
Step-by-step explanation:
Square root means to the power of (1/2)
cube root means to the power of (1/3)
and so on
Solve for X. Show work
The value of x in the figure is 5
How to solve for x?From the figure, we have the following parameters are:
NM = 9
ML = 2x - 7
NL = x + 7
This means that
NL = NM + ML
So, we have:
x + 7 = 9 + 2x - 7
Collect the like terns
x - 2x = 9 - 7 - 7
Evaluate
-x = -5
This gives
x = 5
Hence, the value of x in the figure is 5
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what is the answer for this 3x+4x+5x+...+43x
Answer:
1032x
Step-by-step explanation:
[tex]3x+4x+\cdots+43x=x(3+4+\cdots+45) \\ \\ =43x\left(\frac{45+3}{2} \right) \\ \\ =43(24x) \\ \\ =1032x[/tex]
Describe the transformation from the parent function to the graph f(x) = 3|x+1|−6
the 3 will make the parent function (vertical or horizontal) (shift or stretch or compass or reflect) (up or down or left or right or by a factor) (3 or -3 or 1 or -1 or 6 or -6)
the x+1 will make the parent function (vertical or horizontal) (shift or stretch or compass or reflect) (up or down or left or right or by a factor) (3 or -3 or 1 or -1 or 6 or -6)
the -6 will make the parent function (vertical or horizontal) (shift or stretch or compass or reflect) (up or down or left or right or by a factor) (3 or -3 or 1 or -1 or 6 or -6)
Using translation concepts, we have that:
The 3 will make the parent function vertically stretch by a factor of 3.The x + 1 will make the parent function shift horizontally left 1 unit.The -6 will make the parent function shift vertically down 1 unit.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the parent function is:
g(x) = |x|.
The translated function is:
f(x) = 3|x + 1| - 6.
The multiplication by 3 means that the function was stretched vertically by a factor of 3, hence:
The 3 will make the parent function vertically stretch by a factor of 3.
At x -> x + 1, we have that the function was shifted one unit left, hence:
The x + 1 will make the parent function shift horizontally left 1 unit.
For the subtraction by 6, the function was shifted down 6 units, hence:
The -6 will make the parent function shift vertically down 1 unit.
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The volume of the cone shown in the figure below is 1/3 the volume of the cylinder. In terms of h,
what is the volume of the
cone?
Answer:
It is the last answer [tex]\frac{16\pi }{3}[/tex]
Step-by-step explanation:
the volume of the cylinder is the area of the base times the height. The area of a circle is
a = [tex]\pi r^{2}[/tex] We are give the diameter is 8. The radius is 1/2 of the diameter so the radius is 4. [tex]4^{2}[/tex] = 16
a = 16[tex]\pi[/tex] If the cone is 1/3 of that, we divide this answer by 3 to get
a = [tex]\frac{16\pi }{3}[/tex]
If (m-1÷m)=3 , find the value of m^3 - 1÷m^3
The value of given equation i.e. [tex]m^{3} -\frac{1}{m^{3} }[/tex] is [tex]\frac{63}{8}[/tex]
Given a equation i.e.[tex]\frac{m-1}{m}[/tex]=3 and asked to calculate the value of the equation [tex]m^{3} -\frac{1}{m^{3} }[/tex]
To calculate the value of [tex]m^{3} -\frac{1}{m^{3} }[/tex] , Need to use various operations like subtraction and division)
Given .[tex]\frac{m-1}{m}[/tex]=3
⇒m-1=3m ( cross multiplies 3 and m)
⇒2m=-1( subtraction is used)
⇒m=-[tex]\frac{1}{2}[/tex]( division is used)
Thefore the value of m in the given equation i.e.[tex]\frac{m-1}{m}[/tex]=3 is -[tex]\frac{1}{2}[/tex]
⇒ [tex]m^{3} -\frac{1}{m^{3} }[/tex]
Here the value of m =-[tex]\frac{1}{2}[/tex]
Substituting the value of m in the given equation
⇒[tex](\frac{-1}{2} )^{3}[/tex]-[tex](-2)^{3}[/tex]
⇒[tex]\frac{-1}{8}[/tex]+8(addition is used)
⇒[tex]\frac{64-1}{8}[/tex]
⇒[tex]\frac{63}{8}[/tex]
Therefore, the value of the given equation i.e. [tex]m^{3} -\frac{1}{m^{3} }[/tex] is [tex]\frac{63}{8}[/tex]
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Find the unit vectors that are parallet to the tangent line to the parabola y=x^2 at the point (3,9)
The unit vector is [tex]\left.\pm \frac{1}{\sqrt{17}} \overline{(i}+\overline{4}\right)[/tex].
What are unit vectors?Unit vectors have a magnitude of exactly one unit. They are extremely useful for a variety of reasons.In particular, the unit vectors [0,1] and [1,0] can be combined to form any other vector.To find the unit vector:
Differentiate y = x² with respect to x.
We get, dy/dx = 2x.
The slope of a tangent:
[tex]\mathrm{P}(2,4)=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)_{\mathrm{atP}(2,4)}=2 \times 2=4[/tex]
Tangent P equation is:
y - 4 = 4(x - 2)y = 4x - 4y = 4xy = 4x is the equation of a line passing through the origin O and parallel to the tangent at P.
4x = y, z = 0x/1 = y/4, z = 0This line's direction ratios are 1, 4, and 0, and its direction cosines are:
[tex]\pm \frac{1}{\sqrt{1^2+4^2+0^2}}, \pm \frac{4}{\sqrt{1^2+4^2+0^2}}, 0\\\pm \frac{1}{\sqrt{17}}, \pm \frac{4}{\sqrt{17}}, 0[/tex]
The number of unit vectors parallel to the tangent line at P(2,4) is:
[tex]\left.\pm \frac{1}{\sqrt{17}} \overline{(i}+\bar{j}\right)[/tex]
Therefore, the unit vector is [tex]\left.\pm \frac{1}{\sqrt{17}} \overline{(i}+\overline{4}\right)[/tex].
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The correct question is given below:
Find the unit vectors that are parallel to the tangent line to the parabola y=x^2 at the point (2, 4).
For which value of a does 4 = a +| x – 4| have no solution?
-6
0
4
6
Answer:
a = 6
Step-by-step explanation:
Hello!
First, let's isolate the Absolute Value bracket.
4 = a + |x - 4|4 - a = |x - 4|Based on the definition of Absolute value, the outcome should always be a positive number. Therefore, if the product, 4 - a, is a negative number, it will have no solutions.
That means a has to be greater than 4 for it to be negative. a should be 6.
a = 6
A 10-lb bag of flour costs $3.69. A 5-lb bag costs $1.55. How much can you save if you buy the big bag instead of 2 small bags?
You will $0.29, if you will purchase 2 small bags of flour instead of 1 big bag.
What exactly is the unitary method?The unitary method is an approach that calculates the value of a specific unit utilizing the values of multiple units, in addition to determining the value of multiple units based on the value of a single unit.To figure out the value of one item, we must first divide it, and then multiply it by the number of things we want to find the value of.For the given question;
The total cost of one big bag that is 10-lb bag of flour = $3.69.
Now, the cost of one small bag that is 5-lb = $1.55.
Thus, the cost for two small bag that is 5-lb = $3.10.
The difference in the cost = big bag cost - 2 small bag costs.
The difference in the cost = $3.69 - $3.10
The difference in the cost = $0.29.
Thus, you will save $0.29 for the purchase of 2 small bags of floor instead of one big bag.
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606060+28282 pls help
Answer:
634342
FACTOR:
2 x 317171
The approximate weights of two animals are 5.36 x 104 lbs. and 6.2 x 104 lbs. Find the total weight of the two animals. Write the final answer in scientific notation with the correct number of significant digits.
Answer:
12*10^4 lbs.
Step-by-step explanation:
This is the correct answer because you have to count using scientific notation by seeing the amount of times the decimal point has moved to the left which makes it positive.
The total weight of the two animals is 12x10⁴ lbs if the approximate weights of the two animals are 5.36 x 10⁴ lbs. and 6.2 x 10⁴ lbs.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
It is given that:
The approximate weights of the two animals are 5.36 x 10⁴ lbs. and 6.2 x 10⁴ lbs.
The total weight = 5.36 x 10⁴ + 6.2 x 10⁴
The total weight = (5.36+ 6.2)10⁴
The total weight = 11.56x10⁴
Or
The total weight = 12x10⁴ lbs
Thus, the total weight of the two animals is 12x10⁴ lbs if the approximate weights of the two animals are 5.36 x 10⁴ lbs. and 6.2 x 10⁴ lbs.
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Quadrilateral BASE is located at B (3, 4), A (-2, 3), S (4, 0), and E (-2, 5). BASE was dilated with a scale factor of 5 to create B’A’S’E’. Where is A’ located? Group of answer choices
A. (-10, 15)
B. (5, 5)
C. (15, 12)
D. (10, 15)
will give brainliest
The location of the point A' after dilation is; A'(-10, 15)
What is the result of dilation transformation?We are given that the Quadrilateral BASE is located at the following coordinates;
B(3, 4), A(-2, 3), S(4, 0), and E(-2, 5).
Now, if it is dilated by a scale factor of, it means that each of the coordinates values would be multiplied by 5 to get the new coordinates as;
B'(15, 20), A'(-10, 15), S'(20, 0), and E'(-10, 25).
Thus, we can conclude that the location of the point A' after dilation is; A'(-10, 15)
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He bought a pair of boots that cost 10 and spent the rest on hats that cost 8 each
Answer:
Oh! WoW
Very nice questions .
Step-by-step explanation:
Please provide full question
5x + 3y = 26
6x+ 7y=21
Answer:
x = -1
Step-by-step explanation:
5x + 3y = 26
- (6x + 7y = 21)
_________
-x - 4x = 5
-5x = 5
x = -1
The school band will sell pizzas to raise money for new uniforms. The supplier charges $100
plus $4 per pizza. The band members sell the pizzas for a 50% upcharge. How many pizzas will
the band need to sell to make a profit?
Answer:
35
Step-by-step explanation:
what fraction is equivalent to -0.5
Mrs. Martina wants to put a wire fence around her garden which is 12 feet long and 6 feet wide. How much fencing does she need?
If fencing costs $3 per foot, how much will it cost her to purchase the fence?
The cost for her to purchase the fence is $108.
How to calculate the cost?Since she wants to put a wire fence around her garden which is 12 feet long and 6 feet wide, the total perimeter will be:
= 2(length + width)
= 2(12 + 6)
= 36 feet
Therefore, the cost will be:
= Total feet × Amount
= 36 × $3
= $108
Therefore, the cost for her to purchase the fence is $108.
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Camille wants to crochet a blanket for her new baby cousin. her pattern calls for 900 yards of thick, soft wool. she already has 200 feet of wool left from another project. at the craft store, she notices that each ball has 500 feet of wool. how many balls of wool should she buy?
Camille need 5 balls of wool to crochet a blanket for her new baby cousin.
Unitary Method:
Unitary method is the method in which the value of a unit quantity is first calculated to get the value of any quantity is called the unitary method.
Given,
Camille wants to crochet a blanket for her new baby cousin. her pattern calls for 900 yards of thick, soft wool. she already has 200 feet of wool left from another project. at the craft store, she notices that each ball has 500 feet of wool.
Here we need to find the number of wool balls she need.
Let us consider x be the amount of wool balls she need.
Then,
wool needed - 900 yards
We know that,
1 yard = 3 feet
Then 900 yards will be equal to
=> 900 x 3 = 2700 feet
Now, She has - 200 feet
And we know that,
each ball at store contains - 500 feet
So it can be written as,
=> 200 + 500x = 2700
=> 500x = 2500
=> x = 2500/500
=> x = 5
Hence she need to buy 5 balls of wool from the store to get the required length of wool.
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A traditional unit of length in japan is the ken (1 ken = 1.97 m). what are the ratios of (a) square kens to square meters?
The ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88
For given question,
We have been given the unit conversion.
A traditional unit of length in Japan is the ken
and 1 ken = 1.97 m
We need to find the the ratios of (a) square kens to square meters.
First we find the square of 1 ken.
⇒ 1 square kens = (1.97 m)²
⇒ 1 square kens = 1.97 × 1.97 m²
⇒ 1 square kens = 3.88 m² ..................(1)
And 1 square meters = 1 m² ................. (2)
Now we take the ratio of square kens to square meters.
From (1) and (2),
⇒ 1 ken² / 1 m² = 3.88 / 1
⇒ 1 ken² / 1 m² = 3.88
Therefore, the ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88
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I need help right now!
Which expression is equivalent to 5(−2.3b − 4.1) − (7b + 0.7)?
−18.5b − 21.2
18.5b − 21.2
−18.5b − 3.4
18.5b + 3.4
Answer: B (18.5b-21.2)
The required expression −18.5b − 21.2 is equivalent to the given expression which is the correct answer that would be option (A).
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
We have been given the expression below as
5(−2.3b − 4.1) − (7b + 0.7)
Open the parentheses and apply the distributive property of multiplication,
⇒ −2.3b × 5 − 4.1 × 5 − 7b - 0.7
⇒ -11.5 - 20.5 − 7b - 0.7
Rearrange the likewise terms and apply the arithmetic operation,
⇒ −18.5b − 21.2
Hence, the required expression −18.5b − 21.2 is equivalent to the given expression.
Thus, the correct answer would be an option (A).
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1.) Raisins and nuts were mixed in a
bowl. If 34 of the mixture was
made up of nuts, what was the
ratio of raisins to nuts?
Answer:
8−5=3
Step-by-step explanation:
Does the fugue below appear to have line symmetry if so how many lines of symmetry
Answer:
It has 1 line off symmetry.
Step-by-step explanation:
it has one straight from the top point all the way down.
Find the general solution to the differential equation put the problem in standard form. find the integrating factor, . find . use c as the unknown constant.
y = \frac{-x}{2 } + \frac{1}{4} + ce^-{2x} is the general solution to the differential equation put the problem in standard form.
What is meant by integrating factor?
A function called an integrating factor is used to solve differential equations in mathematics. It is a function that can be made integrable by multiplying it by an ordinary differential equation. Ordinary differential equations are typically solved using this method. This factor is also applicable to multivariable calculus.x² + 2xy + x . dy/dx = 0
x dy/dx + 2xy = [tex]- x^{v}[/tex]
[tex]\frac{dy}{dx} =+ 2y = -x[/tex]
[tex]left u(x) = e^{\int\limits^_ {} } 2dx = e^{2x}[/tex]
integration factor p(x) = u(x) = [tex]e^{2x}[/tex]
Now ,multiply [tex]e^{2x}[/tex] both sides
[tex]e^{2x} ( \frac{dy}{dx} + 2y ) = -x . e^{2x}[/tex]
[tex]e^{2x} \frac{dy}{dx} + 2e^{2x} . y = -x e^{2x}[/tex]
[tex]\frac{d}{dx} (e^{2x} .y) = -x e^{2x}[/tex]
integrate both sides
∫ [tex]d .( e^{2x} .y )[/tex] = ∫[tex]-xe^{2x} .dx[/tex]
[tex]e^{2x} .y = -\frac{e^{2x}}{2} . x + \frac{e^{2x}}{4} + c[/tex]
[tex]y = \frac{-x}{2 } + \frac{1}{4} + ce^-{2x}[/tex]
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The complete question is -
Find the general solution to the differential equation 2 dy X+ + 2xy + x dx = 0 Put the problem in standard form. Find the integrating factor, p(x) = 2x - Find y(x) Use C as the unknown constant.
What is
greater than
-3/8?
Answer:
give a situation where you are adapted a holistic view in looking at a problem or situation: my own
