We have the system of equations:
[tex]\begin{gathered} 4x-2y=20 \\ -8x+4y=-40 \end{gathered}[/tex]We can tell that the equations are linear combination of each other: if we multiply the first equation by -2 we get the second equation.
[tex]\begin{gathered} -2(4x-2y)=-2(20) \\ -8x+4y=-40 \end{gathered}[/tex]So in fact we have only one equation and two unknowns, so there are infinite solutions to this system.
We can write the solution as:
[tex]\begin{gathered} 4x-2y=20 \\ 2y=20-4x \\ y=10-2x \\ y=-2x+10 \end{gathered}[/tex]Answer: the system has infinte solutions, expressed in the line y=-2x+10.
If a triangle ABC is at: A = (10, 7) B = (4, -4) C= (- 11, -9) and if it is translated right 2 and down 7, find the new point B'
B' (6, -11)
Explanations:
Translations is a transformation technique used to change the position of an object in an xy-plane.
Given the coordinate of a triangle ABC given as A (10, 7) B (4, -4) C (- 11, -9). If it is translated right 2 and down 7, the translation rule will be;
(x, y) -> (x+2, y-7)
Determine the new point B'
B' = (4+2, -4-7)
B' = (6, -11)
Therefore the coordinate of the new point B' is (6, -11)
“Rewrite the following expression with the fewest terms possible:14x + 6 - 12x + 9y - 1” i need help.please?
Given the following expression:
[tex]14x+6-12x+9y-1[/tex]You must simplify it if you want to rewrite it with the fewest terms possible.
To simplify the expression you must add the like terms (or combine like terms). Like terms are defined as those terms whose variables and exponents are the same.
Based on the above, you can add the like terms in the expression as following:
[tex]14x+6-12x+9y-1=(14x-12x)+9y+(6-1)=2x+9y+5[/tex]The answer is:
[tex]2x+9y+5[/tex]In the equation y = mx + b, m is the slope.TrueFalse
Remember that
The equation of the line in slope-intercept form is given by
[tex]y=mx+b[/tex]where
b is the y-intercept and m is the slope
therefore
The answer is TrueP(A) = 3/4P(B) = 1/3If A and B are independent, what is P(A n B)?9/125/121/413/12
If A and B are independent events, then:
[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]Then, we have:
[tex]\begin{gathered} P\mleft(A\mright)=\frac{3}{4} \\ P\mleft(B\mright)=\frac{1}{3} \\ P(A\cap B)=P(A)\cdot P(B) \\ P(A\cap B)=\frac{3}{4}\cdot\frac{1}{3} \\ \boldsymbol{P(A\cap B)=\frac{1}{4}} \end{gathered}[/tex]Therefore, if A and B are independent events, the probability of their
I need help with this question please. I also have options available
Okay, here we have this:
We need to identify which of the graphs corresponds to the following imaginary number:
-3+4i
Using the x-axis for real numbers and the "y" axis for imaginary numbers:
So, considering that in the number -3 is the real number and 4 is the coefficient of the imaginary number. The correct option must have the point located at -3 on the x-axis and 4 on the y-axis.
The option that satisfy the mentioned conditions is the option C, that's the correct option.
6) Which type of transformation creates an image where the area of the shape changes? A) translations B) rotations C) reflections D) dilations
The transformation that changes the area of a shape is dilation (Option D)
Step by step explanation
Option A: Translation
A translation is a geometric transformation that moves every point of a figure, shape, or space by the same distance in a given direction. For this type, the image is congruent with the original shape.
Option B: Rotation
A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point. For this type, the image is congruent with the original shape.
Option C: Reflection
A reflection is a transformation where each point in a shape appears at an equal distance on the opposite side of a given line - the line of reflection. For this type, the image is congruent with the original shape.
Option D: Dilations
Dilation in math is a transformation that changes the size of a figure so it becomes larger or smaller without changing shape. This type changes the area since the area is the size of a figure.
Will the slope here be -7? I’m not sure on this
In the given graph, the line passes through at y = -7
Thus equation of line is y = -7
The general equation of line represent as;
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ or\text{ } \\ y-y_1=m(x-x_1),m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Consider any two coordinate as; (0 ,-7) and (2, -7)
Substitute this coordinate in the equation of line as;
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-(-7)=\frac{-7-(-7)}{2-0}(x-0) \\ y+7=\frac{-7+7}{2}x \\ y+7=0x \end{gathered}[/tex]Thus, here slope = 0
For the vertical intercept, x= 0 and y = -7
Therefore;
....................
The distance between Bricktown and Koala Creek is 75 km. A person travels from Bricktown to Koala Creek at an average speed of 50 km/h.How long does it take the person to complete the journey?
distance = 75 km
speed = 50 km/h
Speed = distance / time
time = Distance / speed
Time = 75 km / 50 km/h = 1.5 hours = 1 hour 30 minutes
Multiply pair conjugates using Product of Conjugates Pattern ( xy-9)(xy +9)
Given the following pair of conjugates:
[tex]\mleft(xy-9\mright)\mleft(xy+9\mright)[/tex]As shown, the same terms and the different signs
This is called the factor of the square difference
The product will be as follows:
[tex]\mleft(xy-9\mright)\mleft(xy+9\mright)=(xy)^2-(9)^2=x^2y^2-81[/tex]So, the answer will be:
[tex]x^2y^2-81[/tex]1000C The formula that relates the wattage of an appliance to the cost to run the appliance is W = 1000/tcwhere W is the wattage of appliance, C is the cost to use the appliance per month, t is the time in hours per month, and c is the cost of electricity per kilowatt hour. Use $0.15 per kilowatt-hour for the cost of electricity. How much does it cost to run a 60-watt light bulb 720 hours a month? A. $0.15 B.$6.48 C.$12.32 D.$288
Hence, the correct option is Option C
Task 2Graphing Proportional RelationshipsGraph each leg of Kiley’s trip with the time (in hours) along the x-axis and the distance (in miles) along the y-axis. First you will answer some questions below to find the correct coordinates to use for your graph. In part H, you will create the graph using this spreadsheet.Part AThe starting coordinates of the graph will be (0, 0), or the origin. This point represents Kiley’s house. From here, if you drew a line segment that represents Kiley’s car ride from her house to the airport, at what point would the line segment end?
We want to draw a graph with a y-axis equal to the distance from Kiley's home, and the x-axis represents the amount of time the trip will take. Then, each point point on this graph represent a location. Since our origin(0, 0) is Kiley's house, if we drew a line segment that represents Kiley’s car ride from her house to the airport, this line would end at the location of the airport, the y-axis would inform how far is the airport and the x-axis how much time it is needed to get there.
Since Kiley drove 24.3 miles from their house to the airport in 1/2 hour, this means the end of this line will be at (0.5, 24.3).
is the prime factorization of what composite number?
A factor of a number is called a prime factor.
The prime factor of a number is obtained by a factor tree method or by a division method.
The expression of a given number as a product of factors is called prime factorisation.
The prime number has 1 and the number itself is a factor.
The composite number will have more than one factor.
A number which is not a prime number is a composite.
1 and the number itself are not included in the prime factorisation of a composite number.
let us take the example
For the number 20, the prime factors are 2*2*5.
The above example is an example of the prime factorization of the composite number. where 1 and the number itself are not included in the prime factorisation of a composite number.
Answer:
But they can be broken down into prime numbers the process of writing out the prime numbers that make up a composite number is known as prime factorization
Step-by-step explanation:
What are the coefficients?12x + 8 < 9 + 2X
This problem is about coefficients.
It's important to know that a coefficient is a number used to multiply a variable. In other words, coefficients are all numbers placed in front of a variable.
Being said that, in this case, coefficients are 12 and 2, because these numbers multiply a variable.
Therefore, the right answer is 12 and 2.Question 33R, it is one am for me and I have exams tomorrow, please be very quick and include the answer in bold. Thanks
Given:
scale rated 2.2
other rating is 4.6
Magnitude diff. is:
[tex]\begin{gathered} =4.6-2.2 \\ =2.4 \end{gathered}[/tex]how to draw a double number line representing a 1:4 ratio
e are asked to draw a double number line representing a 1:4 ratio. To do that we will follow the next steps.
1. Draw two parallel lines each ending in arrows, like this:
2. Label the beginning of each line with zero, like this:
3. Label the first line with units, like this:
4. Each corresponding unit in the second line will be the unit in the first line multiplied by 4, since we need a ratio of 1:4
Find the slope-intercept equation of the line satisfying: Y-Int is 4 and goes through (1,8).
Let's recall that the slope-intercept equation of a line has the form
[tex]y=mx+b,[/tex]where "m" is the slope, and "b" is the y-intercept. We know that the y-intercept is 4; then, our equation becomes
[tex]y=mx+4.[/tex]The trick to finding the slope is to note that the point (1,8) lies on the line; namely, we can evaluate the equation of the line in this point:
[tex]8=m\cdot1+4.[/tex]Solving this equation for m, we get
[tex]\begin{gathered} 8=m\cdot1+4, \\ 8=m+4, \\ 8-4=m+4-4, \\ 4=m, \\ m=4. \end{gathered}[/tex]AnswerThe equation of the line satisfying the provided conditions is
[tex]y=4x+4.[/tex]Find the area of the square.10 cm^225 cm^220 cm^25 cm^2
Answer:
25 cm^2
Explanation:
Given:
To find:
Area of the square
The area(A) of a square can be determined using the below formula;
[tex]A=s^2[/tex]where s = side length = 5 cm
So the area of the given is;
[tex]A=5^2=25\text{ cm}^2[/tex]Area of the given square is 25 cm^2
i need help with math Can you
The result of the parallel rail supports are-
∠BCD = ∠CFG (corresponding angle)∠HIK = 180° - x (supplementary angles)∠CFE + ∠EFI = 180°What is meant by the parallel line?Two lines (on same plane) are said to be parallel if they never intersect, regardless of how far they have extended along either side. Parallel lines run parallel to each other, like train tracks.Many pairs of angles are formed when two parallel lines are intersected by some other line known as a transversal. A few angles are congruent (equal), while others are supplementary (different).For the given question;
The measure of the angles are given in the diagram.
Thus, the relation between the angles are found as-
∠BCD = ∠CFG (corresponding angle)∠HIK = 180° - x (supplementary angles)∠CFE + ∠EFI = 180°Therefore, the result for the intersecting railing are found.
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To estimate the total number of people in the photography club, begin by rounding 48% to Select Choice% and
round 26 to Select Choice Since this is about Select Choice of the members in the club, then
Select Choice+ Select Choice or Select Choice
people is the approximate number of people in the
club.
Answer:
i believe its 74
Step-by-step explanation:
Select Choice+ Select Choice
48+26
Which equation represents the graphed function?1. y=4x-22. y=-4x-23. y=1/4x-24. y=-1/4x-3
The general equation of a line is:
[tex]y=m\cdot x+b[/tex]Where m is the slope of the line and b its the value of the y-intercept of the line.
Q) The question asks about the equation of a graphed line.
A) In order to find the equation of the line, we note that it passes through the points:
[tex]\begin{gathered} (x_1,y_1)=(0,-2) \\ (x_2,y_2)=(4,-1) \end{gathered}[/tex]The first point give us the value of the y-intercept of the line (b), so the y-intercept is y = -2, and we have:
[tex]b=-2[/tex]Now we must calculate the slope (m) of the line. In general the slope of a line is given by the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1,y1) and (x2,y2) are the coordinates of two points of the line. Using the points of above and the last formula we find that:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-(-2)}{4-0}=\frac{2-1}{4}=\frac{1}{4}[/tex]Answer
Using the values of m and b, and the general equation, we find that the equation of the line is:
[tex]y=m\cdot x+b=\frac{1}{4}x-2[/tex]Or: y = 1/4 x - 2
So the correct option is option number 3.
Find the exact value of cos (u-v) given that sin u=-7/25, π
c0s v= 12/25,3π/2
a) -3/5
b) -117/25
c) -28/125
d) 13/25
The exact value of the cosine of the subtraction of angles is equal to - 3 / 5. (Correct choice: A)
How to determine the exact value of a trigonometric expression
In this problem we find the exact value of the sine of an angle set in the third quadrant and the exact value of the cosine of an angle set in the fourth quadrant. Herein we need to determine the cosine of subtraction of two angles:
cos (u - v) = cos u · cos v + sin u · sin v
First, determine the missing cosines and sines by the fundamental trigonometric formula:
cos u < 0, sin v < 0
cos u = - √(1 - sin² u)
cos u = - √[1 - (- 7 / 25)²]
cos u = - 24 / 25
sin v = - √(1 - cos² v)
sin v = - √[1 - (12 / 15)²]
sin v = - 3 / 5
Second, determine the exact value of the trigonometric equation:
cos (u - v) = (- 24 / 25) · (12 / 15) + (- 7 / 25) · (- 3 / 5)
cos (u - v) = - 3 / 5
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Diamond spends a total of 45 minutes singing and She burns 5 calories per minute singing and 15 calories per minute dancing.Create an equation comparing the number of minutes Diamond spends singing (s) and the number of minutes she spends dancing (d) to the total number of calories she burns (C).Solve the equation to determine the total number of calories Diamond burns if she spends 20 minutes of her time singing.my teacher said base the on her spending 20 minutes singing
Answer:
475 calories.
Explanation:
The number of minutes Diamond spends singing = s
The number of minutes she spends dancing =d
Since she spends a total of 45 minutes singing
• s+d=45
Since she spends 20 minutes of her time singing.
• s=20 minutes
Substitution into: s+d=45
[tex]\begin{gathered} 20+d=45 \\ d=45-20=25 \end{gathered}[/tex][tex]\text{Rate}=\frac{Number\text{ of calories burned}}{Time}[/tex]The number of calories burned = Time X Rate
Therefore:
[tex]C=5s+15d[/tex]We then substitute s=20 minutes, d=25 minutes into C.
[tex]\begin{gathered} C=5s+15d \\ =5(20)+15(25) \\ =100+375 \\ =475 \end{gathered}[/tex]The total number of calories Diamond burns is 475 calories.
The following refer to the following data set:31.8 63.4 47.2 26.8 44.632.8 63.4 63.4 45.4 59.4What is the arithmetic mean of this data set?mean -What is the median of this data mset?median -What is the mode of this data set?mode
A book sold 39,800 copies in its first month of release. Suppose this represents 9.3% of the number of copies sold to date. How many copies have been sold to date?
Round your answer to the nearest whole number.
The number of copies is 3,701 which has been sold to date.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The book sold 39,800 copies in its first month of release.
Given that 9.3% of the number of copies sold to date.
To determine the number of copies has been sold to date.
⇒ 9.3% of 39,800 copies
⇒ (9.3/100) × 39,800
⇒ (0.093) × 39,800
⇒ 3,701.4
Round to the nearest whole number.
⇒ 3,701
Thus, the number of copies is 3,701 which has been sold to date.
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What is the simple interest on $4000 principal at 5% for 3/4 years
Answer:
$150
Explanation:
The simple interest can be calculated using the following equation
I = Prt
Where P is the principal, r is the rate as a decimal and t is the number of years.
So, replacing P = $4000, r = 5% = 0.05 and t = 3/4 years, we get:
I = ($4000)(0.05)(3/4)
I = $150
Therefore, the simple interest is $150
Activity 1: Determine MeDetermine if the given pair of triangle is congruent. Justify your answer using triangle congruence postulate and theorem
Answer:
1)
From the given two triangles ABC and DEF
angle B= angle E
side AB= side ED
side BC= side EF
By SAS criterion
If any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule., triangles ABC and DEF are congruent.
2)
From the given triangles HJI and KLI
side HJ=side KL
side JI=side LI
side HI= side KI
By SSS criterion,
If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
triangles HJI and KLI are congruent.
Which of the following ordered pairs could Briggs add to the graph?
Answer: B
Step-by-step explanation:
The next point where the gap is would be B but you're looking for the point that comes after (8,4) it would be C
a. an 9. Find the explicit formula for the given sequence. -4,0,4,8,... = 4+ -4(n-1) b. an = – 4 · 8(n − 1) -4 + 4(n − 1) -4 · 4(n-1) c. an d. an
The given sequence is
-4 , 0 , 4 , 8 , ......
the given sequence is arithmetic sequence
because there is a common difference between the terms of the sequence
common difference = 0 - (-4) = 4
as a check = 4 - 0 = 4 and 8 - 4 = 4
and the first term is -4
So,
The explicit formula is an = a1 + d ( n - 1)
an = -4 + 4 ( n - 1)
The answer is option c
the missing angle men
Answer:
x = 16.
Explanation:
The angels x and 164 are supplementary, meaning they add up to 180; therefore, we can say
[tex]x+164^o=180^o[/tex]Subtracting 164 from both sides gives
[tex]x+164^o-164^o=180^o-164^o[/tex][tex]x=16^o\text{.}[/tex]Hence, the value of x is 16 degrees.
How many terms are in the expansion of the binomial below? (x^3 + 2/x)^8A: 9B: 8C: 11D: 10
Given expression is
[tex](x^3+\frac{2}{x})^8[/tex]This is of the form
[tex](a+b)^n[/tex][tex]\text{where}a=x^3,\text{ b=}\frac{2}{x}\text{ and n=8}[/tex]Recall that
[tex]In\text{ the binomial expansion of }(a+b)^n,\text{ there are total n+1 terms.}[/tex]Here n=8.
[tex]In\text{ the binomial expansion of }(x^3+\frac{2}{x})^8,\text{ there are total 8+1=9 terms.}[/tex]Hence option A is correct.