We have the following:
[tex]\begin{gathered} -7x-2y=-13 \\ x-2y=11 \end{gathered}[/tex]solving by substitution:
[tex]\begin{gathered} x-2y=11\Rightarrow x=11+2y \\ \text{replacing} \\ -7\cdot(11+2y)-2y=-13 \\ -77-14y-2y=-13 \\ -16y=-13+77 \\ y=\frac{64}{-16} \\ y=-4 \end{gathered}[/tex]now, for x
[tex]\begin{gathered} x=11+2\cdot-4 \\ x=11-8 \\ x=3 \end{gathered}[/tex]The solution is
[tex](3,-4)[/tex]The ratio of pumpkins to apples are 3 to 1 if there are 60 pumpkins then how many apples are there.
Answer:
20 apples
Step-by-step explanation:
For every three pumpkins, there is one apple.
There are 60 pumpkins. Divide 60 by 3 to find how many apples there are.
60 ÷ 3 = 20
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.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)
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.
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.
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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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).
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.
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]“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]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
I need help with this question finding cos Y=?the options are the following5/1312/135/12
Cosy = Adjacent/Hypotanuse
[tex]\begin{gathered} \theta\text{ = y} \\ \text{Opposite = }5 \\ \text{Hypotanuse = 13} \\ \text{Adjacent = 12} \\ \cos y\text{ = }\frac{adjacent}{\text{Hypotanuse}} \\ \cos y\text{ = }\frac{12}{13} \end{gathered}[/tex]Complete the following by filling in the missing terms in the sequence
Let's begin with the first sequence:
[tex]?,2,6,18,54,\text{?}[/tex]We can see each term of the sequence after the 2 is the previous term multiplied by 3. So the missing terms would be 2/3 and 54*3:
[tex]\frac{2}{3},2,6,18,54,162.[/tex]For the second sequence, we have:
[tex]?,?,17,12,7,2.[/tex]We can see that after the 17, each term is the previous one minus 5. So the sequence is:
[tex]27,22,17,12,7,2.[/tex]The third and fourth sequences are written correctly in the image.
For the fifth sequence, the only information we have to determine the ruele it's following is that the next number after 9 is 16, and the 1 that is before the number before the 9.
One possible rule would be to consider the sequence
[tex]x_n=n^2\text{.}[/tex]This way, if we start from n=0 we get:
[tex]0,1,4,9,16,25,[/tex]which fits the numbers we were given perfectly.
P(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
- Describe at least one thing you would do to critique Mary's reasoning.
Process to critique the reasoning of others is to clarifying the question.
A critique is to evaluate somebody's work (a book, an essay, a movie, a painting...) in order to increase the reader's understanding of it.
A critical analysis is subjective writing because it expresses the writer's opinion or evaluation of a text. Analysis means to break down and study the parts.
Writing a critical paper requires two steps: critical reading and critical writing.
Process to critique the reasoning of others.
Ask clarifying questions as someone explains their plan to solve the problem. Ask clarifying questions as someone explains their answer and how they solved the problem. Cite similarities and differences between strategies for how the problem could be solved.
Hence the answer is the Process to critique the reasoning of others is to clarifying the question.
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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.
If the surface area of a sphere is equal to the volume of the sphere, then what is the length of its radius?A. 3 unitsB. 2 unitsC. 0.5 unitsD. 1 unit
Given:
That the surface area of a sphere is equal to the volume of the sphere.
[tex]\begin{gathered} \text{The surface area of a sphere is given by:} \\ A=4\pi r^2 \\ \\ \text{The volume of a sphere is given by:} \\ V=\frac{4}{3}\pi r^3 \end{gathered}[/tex]If area is equal to volume, then;
[tex]\begin{gathered} A=V \\ 4\pi r^2=\frac{4}{3}\pi r^3 \\ C\text{ ross multiplying,} \\ 4\pi r^2\times3=4\pi r^3 \\ 12\pi r^2=4\pi r^3 \\ \text{Dividing both sides by }4\pi r^2\text{ to get the radius,} \\ \frac{12\pi r^2}{4\pi r^2}=\frac{4\pi r^3}{4\pi r^2} \\ 3=r \\ r=3\text{units} \end{gathered}[/tex]Therefore, the length of the radius is 3units.
The correct answer is option A.
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
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
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
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
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:
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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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.
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.
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
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 TrueFind 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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A 21 oz bottle of dish soap sells for $8.47. A 25 oz bottle of dish soap sells for $9.78.(round all answers to four decimal places)The unit price of the 21 oz bottle is $ per ozThe unit price of the 25 oz bottle is $ per ozWhich of the two is a better deal?
To find the unit prices, divide the price by the number of ounces, this way:
For the 21oz bottle that costs $8.47:
[tex]\frac{8.47}{21}=0.4033[/tex]The unit price is $0.40 per oz
For the 25oz bottle that cost $9.78:
[tex]\frac{9.78}{25}=0.3912[/tex]The unit price is $0.39 per oz.
It means that the 25oz bottle is a better deal because it has a lower unit price.