Scale the rectangle by finding 3A. What are the vertices of the scaled rectangle
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Given A, the matrix that contains the vertices of a rectangle on the plane, calculate 3A as shown below
[tex]3A=3\begin{bmatrix}{1} & {6} & {6} & {1} \\ {1} & {1} & {5} & {5} \\ {} & {} & {} & {} \\ {} & {} & {} & {}\end{bmatrix}=\begin{bmatrix}{3*1} & {3*6} & {3*6} & {3*1} \\ {3*1} & {3*1} & {3*5} & {3*5} \\ {} & {} & {} & {} \\ {} & {} & {} & {}\end{bmatrix}=\begin{bmatrix}{3} & {18} & {18} & {3} \\ {3} & {3} & {15} & {15} \\ {} & {} & {} & {} \\ {} & {} & {} & {}\end{bmatrix}[/tex]Where each column of the 4x2 matrix above represents a vertex of the new rectangle; therefore, the 4 vertices are
(3,3), (18,3), (18,15), (3,15). The second option.Related Questions
Simplify 310x + 16y + 310x + 56y ( i need help)
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Answer:
[tex]620x+72y[/tex]
Step-by-step explanation:
[tex]310x+16y+310x+56y \\ \\ =310x+310x+16y+56y \\ \\ =620x+72y[/tex]
Could I please get help with this. I can’t seem to figure out the answers to each of the figures after multiple tries.
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Explanation:
Two figures are congruent when they have the same size and shape and two figures are similar when they have the same shape but not necessarily the same size. In similar figures, the ratio of the corresponding sides is constant.
Answer:
Then, for each pair, we get:
Solve for v.37+1=-2v-8v-4
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which is equal to 73.5÷by 15
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The answer to this division is 4.9.
You can also multiply the numerator (dividend) and the denominator (divisor) by 10, so you can have the equivalent division:
[tex]\frac{73.5}{15}\cdot\frac{10}{10}=\frac{735}{150}=4.9[/tex]And proceed as before. The result will be the same.
find the odds of an event occurring given the probability of the event 6/7
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Odds is the ratio of favourable outcomes to non-favourable outcomes:
Let:
P = probability of an event occurring = 6/7
Q = probability of the event not occurring = 1 - P = 1 - 6/7 = 1/7
Therefore, the odds will be:
[tex]\frac{P}{Q}=\frac{\frac{6}{7}}{\frac{1}{7}}=6[/tex]1 ptsQuestion 5Jane started jogging 5 miles from home, at a rate of 2 mph. Write the slope-intercept form of an equation for Jane's position relative to home.
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Answer
[tex]y=2x+5[/tex]SOLUTION
Problem Statement
The question wants us to model the distance Jane is from her home given her initial starting point (5 miles from home) and her speed (2 mph)
Explanation
To solve the question, we simply need to model her jogging using the equation of a line.
The general equation of a line is given as:
[tex]\begin{gathered} y=mx+c \\ \text{where,} \\ m=\text{slope}=\text{this represents Jane's speed} \\ c=y-\text{intercept}=\text{this represents her initial position from her home} \\ x=\text{time taken for Jane to move} \\ y=\text{Jane's final position after moving for time, x} \end{gathered}[/tex]We have been told that her speed is 2 mph. Thus, m = 2. We have also been given her initial position from her house to be 5 miles.
Jane starts jogging 5 miles from her home, thus, her position relative to her home will continue to increase as she jogs on at 2 mph. Thus, c = 5 and NOT -5.
This means we can write the equation for her position is:
[tex]\begin{gathered} m=2,c=5 \\ \therefore y=2x+5 \end{gathered}[/tex]Final Answer
[tex]y=2x+5[/tex]Find an equation of the line through (1,8) and parallel to y = 4x + 8.y=(Type your answer in slope-intercept form.)
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First of all, remember that parallel lines are those with equivalent slope. So, the given line is
[tex]y=4x+8[/tex]If the new line we have to find is parallel to this one, that means the slope is
[tex]m=4[/tex]Because the coefficient of x is always the slope.
Now, we know that the new line must pass through (1,8) and it must have a slope of 4. We can use the point-slope formula
[tex]y-y_1=m(x-x_1)[/tex]Replacing the point and the slope, we have
[tex]y-8=4(x-1)[/tex]Then, we solve for y
[tex]y=4x-4+8\rightarrow y=4x+4[/tex]Therefore, the new parallel line is
[tex]y=4x+4[/tex]express in scientific notation (9.3 x 10^7) ÷ 23,000 = ? (round to the nearest tenth.)
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Given:
[tex]\frac{9.3\times10^7}{23000}[/tex]Let's perform the division and express the quotient in scientific notation.
We have:
[tex]\frac{9.3\times10^7}{23000}=\frac{9.3\times10000000}{23000}=\frac{93000000}{23000}=4043.478261[/tex]Express 4043.478261 in scientific notation:
[tex]undefined[/tex]Graph the function. Label the vertex and axis of symmetry. 1. f(x)=(x-2)^2
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We have the following:
Can you help explain how to solve this for me?
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SOLUTION:
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex][tex]\begin{gathered} d=\sqrt{(-4-8)^2+(5--6)^2} \\ d=\sqrt{-12^2+11^2} \\ d=\sqrt{265}=16.28 \end{gathered}[/tex]b.
[tex]\begin{gathered} m=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2} \\ m=(\frac{-6+5}{2},\frac{-4+8}{2}) \\ m=(-\frac{1}{2},2) \end{gathered}[/tex]consider all of the 4 digit numbers that can be made from the digits 0 to 9 (assume that the numbers cannot start with 0) . What is the probability of choosing a random number from this group that is less than or equal to 8000? Enter a fraction or round your answer to 4 decimal places, if necessary.
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First, we need to determine the total amount of numbers fulfilling the conditions:
- 4 digits
- Not starting with 0
For the first digit, we have then 9 possible numbers: 1, 2, 3, 4, 5, 6, 7, 8 and 9.
For the second, third and fourth, we have 10 possible numbers 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Then, to determine the amount of numbers available we just need to multiply the possibilities for each digit:
[tex]9\cdot10\cdot10\cdot10=9000[/tex]Then, randomly choosing one of the given numbers, we have 9000 possible outcomes. Those will be numbers from 1000 to 9999.
Now we just need to determine how many numbers among those 9000 are lower than or equal to 8000.
As the numbers start in 1000, we have 7001 cases where the randomly selected number is lower than or equal to 8000.
We obtain 7001 since 8000 - 1000 = 7000 but we need to consider also the number 1000.
The probability will be then:
[tex]\frac{7001}{9000}\approx0.7779[/tex]In the figure, ABCD and EFGF are rectangle. ABCD and EFGH are similar.(a) If the length of AB is a cm, try to use a to Indicate the length of EF(b) Find the ratio of the areas of ABCD and EFGH.(English isn't my native language. Please correct me if I have any grammatical mistakes.)
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Given:
BC = 3 cm, FG = 4 cm
Required: bLength of EF and ratio of areas
Explanation:
(a) Since the rectangles ABCD and EFGH are similar, the correponding angles are proportional. Hence
[tex]\frac{AB}{EF}=\frac{BC}{FG}[/tex]Plug the given values.
[tex]\frac{AB}{EF}=\frac{3}{4}[/tex]If AB = a cm, then
[tex]\begin{gathered} \frac{a}{EF}=\frac{3}{4} \\ EF=\frac{4a}{3} \end{gathered}[/tex](b) Ara of ABCD
[tex]\begin{gathered} =\text{ Length}\times\text{ Width} \\ =3a\text{ cm}^2 \end{gathered}[/tex]Area of EFGH
[tex]\begin{gathered} =\text{ Length}\times\text{ Width} \\ =4\times\frac{4a}{3} \\ =\frac{16a}{3}\text{ cm}^2 \end{gathered}[/tex]Ratio of areas
[tex]\begin{gathered} =3a:\frac{16a}{3} \\ =9:16 \end{gathered}[/tex]Final Answer: The ratio of areas of ABCD to EFGH is 916.
Let f(x) = 9 - x, g (x) = x*2 + 2x - 8, and h (x) = x - 4
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Solution
We are given the following functions
[tex]\begin{gathered} f(x)=9-x \\ g(x)=x^2+2x-8 \\ h(x)=x-4 \end{gathered}[/tex]g(x) + f(x)
[tex]\begin{gathered} g(x)+f(x)=(x^2+2x-8)+(9-x) \\ \\ g(x)+f(x)=x^2+2x-8+9-x \\ \\ g(x)+f(x)=x^2+x+1 \end{gathered}[/tex]h(x) - f(x)
[tex]\begin{gathered} h(x)-f(x)=(x-4)-(9-x) \\ \\ h(x)-f(x)=x-4-9+x \\ \\ h(x)-f(x)=2x-13 \end{gathered}[/tex]f o h(10)
[tex]\begin{gathered} First \\ h(x)=x-4 \\ h(10)=10-4 \\ h(10)=6 \\ and \\ f(x)=9-x \\ f(6)=9-6 \\ f(6)=3 \\ Now,\text{ to solve} \\ foh(10)=f(h(10)) \\ foh(10)=f(6) \\ \\ foh(10)=3 \end{gathered}[/tex]3 * g(-1)
[tex]\begin{gathered} First, \\ g(x)=x^2+2x-8 \\ g(-1)=(-1)^2+2(-1)-8 \\ \\ g(-1)=1-2-8 \\ \\ g(-1)=-9 \\ Now\text{ to solve} \\ 3g(-1)=3\times g(-1) \\ \\ 3g(-1)=3\times-9 \\ \\ 3g(-1)=-27 \end{gathered}[/tex]h(x) * h(x)
[tex]\begin{gathered} h(x)=x-4 \\ Now, \\ h(x)*h(x)=(x-4)(x-4) \\ \\ h(x)*h(x)=x^2-8x+16 \end{gathered}[/tex]g(x)/h(x)
[tex]\frac{g(x)}{h(x)}=\frac{x^2+2x-8}{x-4},\text{ }x\ne4[/tex]Help with this plsss !!!
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The average rate of change of function f(x) over the interval 12 ≤ x ≤ 21 is 2/3
We use the formula of average rate of change of function over the interval [x1, x2],
r = [f(x2 - f(x1)]/ (x2 - x1)
We need to find the average rate of change of function f(x) over the interval 12 ≤ x ≤ 21
r = [f(21) - f(12)] / (21 - 12)
r = (31 - 25) / 9
r = 6/9
r = 2/3
Therefore, the average rate of change of function f(x) over the interval 12 ≤ x ≤ 21 is 2/3
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How many men and women should the sample include. What were the steps you took to solve?
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We are asked to determine the sample size to determine the difference in the proportion of men and women who own smartphones with a confidence of 99% and an error of no more than 0.03. If we assume that both samples are equal then we can use the following formula:
[tex]n=\frac{Z^2_{\frac{\alpha}{2}}}{2E^2}[/tex]Where Z is the confidence and E is the error. Replacing the values we get:
[tex]n=\frac{(0.99)^2}{2(0.03)^2}[/tex]Solving the operations we get:
[tex]n=544.5\cong545[/tex]Therefore, each sample of men and women should be of 545.
The parent tangent function is horizontally compressed by a factor of 1/2 and reflected over the x-axis. Which equation could represent function g.the result of this transformation?OA. g(x) = -tan(2x)O B. g(x) = tan(-1/2x)OC. g(x) = tan(-2x)OD. g(x) = -tan(1/2x)
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Given :
The parent tangent function is horizontally compressed by a factor of 1/2 and reflected over the x-axis.
Explanation :
To find the equation of g.
The tangent function is
[tex]f(x)=\tan x[/tex]It is horizontally compressed by a factor of 1/2.
Then the function becomes
[tex]g(x)=\tan (\frac{1}{2}x)[/tex]After that it is reflected over x-axis.
[tex]g(x)=-\tan (\frac{1}{2}x)[/tex]Answer :
Hence the result of the transformation is
[tex]g(x)=-\tan (\frac{1}{2}x)[/tex]The correct option is D.
8. Su, who is 5 feet tall, is standing at point D in the drawing. The top of her head is at point E. A tree yard is at point B with the top of the tree at point C. Su stands so her shadow meets the end of the t shadow at point A. What is the length of side BC? C С + E 5 ft А 8 ft D 24 ft A) 20 feet B 15 fut B C) 22 feet D) 18 feet
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Explanation:
We would be applying similar triangles theorem.
If you check the image, there is a small triangle and a big triangle
For similar triangles, the ratio of the corresponding sides are equal.
Trianglke AEB is similar to triangle ECB
AD corresponds to AB
ED corresponds to CB
AD/AB = ED/CB
AD = 8 ft,
AB = AD + DB = 8+24 = 32
ED = 5 ft
CB = ?
The box-and-whisker plot shows the ages of employees at a video store. What fraction of the employees are 20 years or older Ages of Employees + 16 + 18 + 28 + Age 14 20 22 24 26 30 32 34 About of the employees are 20 years or older.
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Based on the given box-and-whisker plot. Consider that 20 years concides with the second quartile or median of the sample.
It means that one half of the employees at the video store are 20 years or older.
Hence, the fraction of such employees related to the total number of employess is 1/2.
Two trees are leaning on each other in the forest. One tree is 19 feet long and makes a 32° angle with the ground. The second tree is 16 feet long.What is the approximate angle, x, that the second tree makes with the ground?
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39º
1) Considering what's been given we can sketch this out:
From these trees leaning on each other, we can visualize a triangle (in black).
2) So now, since we need to find the other angle, then we need to apply the Law of Sines to find out the missing angle:
[tex]\begin{gathered} \frac{a}{\sin(A)}=\frac{b}{\sin (B)} \\ \frac{16}{\sin(32)}=\frac{19}{\sin (X)} \\ 16\cdot\sin (x)=19\cdot\sin (32) \\ \frac{16\sin(X)}{16}=\frac{19\sin (32)}{16} \\ \sin (X)=\frac{19\sin(32)}{16} \\ \end{gathered}[/tex]As we need the measure of the angle, (not any leg) then we need to use the arcsine of that quotient:
[tex]\begin{gathered} X=\sin ^{-1}(\frac{19\cdot\sin (32)}{16}) \\ X=38.996\approx39 \end{gathered}[/tex]3) Hence, the approximate measure of that angle X is 39º
A correlation cannot have the value:A) 0.0B) 0.4C) -1.01D) -0.5E) 0.99
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The possible range of values for the correlation coefficient is -1.0 to 1.0. In other words, the values cannot exceed 1.0 or be less than -1.0. A correlation of -1.0 indicates a perfect negative correlation, and a correlation of 1.0 indicates a perfect positive correlation.
Therefore, the value that is not within the range -1.0 to 1.0 is -1.01
Answer: C)
Graph the function?Can you also make a chart or like try to edit onto the graph in the picture
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For x = 0 , x = 2 and x = 1, we have the following values:
[tex]\begin{gathered} f(0)=2(\frac{1}{2})^0=2\cdot1=2 \\ f(2)=2(\frac{1}{2})^2=\frac{2}{4}=\frac{1}{2} \\ f(1)=2(\frac{1}{2})^1=\frac{2}{2}=1 \end{gathered}[/tex]thus, the graph would look like this taking these point as references:
Allison stated that 48/90 is a terminating decimal equal to 0.53. Why is she true or why is she wrong.
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Answer:
She was Wrong, because it is not a terminating decimal
Explanation:
Given the fraction;
[tex]\frac{48}{90}[/tex]Let us reduce the fraction to its least form, then convert it to decimal.
[tex]\frac{48}{90}=\frac{8}{15}[/tex]converting to decimal we have;
The decimal form of the given fraction is;
[tex]\begin{gathered} 0.533\ldots \\ =0.53\ldots \end{gathered}[/tex]Which is not a terminating decimal, because it has an unending, repeatitive decimal.
Therefore, she was Wrong, because it is not a terminating decimal
A single die is rolled 4 times. Find the probability of getting at least one 6.
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When a dice is rolled the probability of getting one 6 is,
[tex]P(\text{Getting one 6) = }\frac{1}{6}[/tex]The probability of not getting 6 when a dice is rolled is ,
[tex]P(\text{Not getting 6) = }\frac{5}{6}[/tex]The probability of getting 6 is independent on how many times the dice is rolled.
The probability of not getting 6 is given as,
[tex]P(\text{ getting atleast one 6) = 1 - P(Not getting 6)}[/tex]Therefore the probability of getting atleast one 6 when a dice is rolled 4 times is calculated as,
[tex]\begin{gathered} P(\text{Getting 6) = 1 - (}\frac{5}{6})^4 \\ P(\text{Getting 6) = 1 - }\frac{625}{1296} \\ P(\text{Getting 6) = }0.5177 \\ \end{gathered}[/tex]Thus the probability of getting atleast one 6 when a dice is rolled 4 times is 0.5177 .
Given the system of equations: 8x + 14y = 4 and -6x - 7y = - 10, what would youmultiply the bottom equation by to eliminate y when adding the two equationstogether?
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We need to multiply the second equation by 2 to eliminate y when adding the two equations
|x-2|-3 >or equal to 2
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By solving the linear inequation it is obtained that [tex]x \leq -3[/tex] or [tex]x \geq 7[/tex].
What is linear inequation?
Expressions with linear inequalities compare any two values using inequality symbols like ‘<’, ‘>’, ‘≤’ or ‘≥’. These values could be either numerical, algebraic, or both. Examples of numerical inequalities include 1011 and 20>17, while algebraic inequalities include x>y, y19-x, and x z > 11 (also called literal inequalities). Here is a lesson on linear inequalities for class 11. Inequality in mathematics, linear inequalities, graphing of linear inequalities, as well as detailed examples are all covered in this article.
Here,
The given linear inequation is
[tex]|x - 2| - 3 \geq 2[/tex]
Now,
[tex]|x -2| - 3 \geq 2\\|x - 2| \geq 2+3\\|x-2| \geq 5\\[/tex]
For [tex]x \geq 2\\[/tex]
[tex]x - 2 \geq 5\\x \geq 2 + 5\\x\geq 7[/tex]
For [tex]x < 2[/tex]
[tex]2 - x \geq 5\\x \leq 2 - 5\\x \leq -3[/tex]
So the solution set is [tex]x \leq -3[/tex] or [tex]x \geq 7[/tex]
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The diameter of a bicycle wheel is 26 inches. What is its circumference? (Round to the nearest inch.)
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Bicycle wheel:
diameter = 26 in
circumference = ?
Step 02:
Circumference
C = π d
C = π * (26 in) = 81.68 in
The answer is:
C = 82 in
Answer:
82 inches.
Step-by-step explanation:
diameter = 26 inches
radius = 13 inches
circumference = 2πr
π = 22÷7 or 3.142
... 2 × 22÷7 × 13 = 81.714
(to nearest inch) = 82inches.
Which is the graph of y = = where k is a constant?TO A.R०B.कOD. REE.
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Step 1
Given;
[tex]\begin{gathered} y=\frac{k}{x} \\ where\text{ k is a constant.} \end{gathered}[/tex]Required; To find the graph of the function.
Step 2
Since the graph is that of a fraction it will be a graph that may have a discontinuity and the answer will be;
I struggle with word problems please helpYou are ordering a new home theater system that consists of a TV, surround sound system, and DVD player. You can choose from 6 different TVs, 8 types of surround sound systems, and 20 types of DVD players. How many different home theater systems can you build?
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We are given the following :
• Number of different Tvs = 6
,• Number of different surround system = 8
,• Number of different Dvds = 20
In order to determine How many different home theater systems you can build: just multiply the items as follows :
=6*8*20 = 960 You can build 960 home theater systems.
Help me with math and explain it in a short solution
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The perimeter is the sum of all the sides of a geometric figure. Since it is a parallelogram, then its opposite sides are equal, so
[tex]\begin{gathered} QR=TS \\ \text{and} \\ QT=RS \end{gathered}[/tex]In the graph, we can see that the distance between points Q and R is 7 units. To find the distance between points Q and T we can use the formula of the distance between two points in the plane, that is,
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{ Where} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are the coordinates of the points } \end{gathered}[/tex]Then, we have
[tex]\begin{gathered} Q(-3,3) \\ T(-5,-3) \\ d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{ Replace} \\ d=\sqrt[]{(-5-(-3))^2+(-3-3)^2} \\ d=\sqrt[]{(-5+3)^2+(-3-3)^2} \\ d=\sqrt[]{(-2)^2+(-6)^2} \\ d=\sqrt[]{4+36} \\ d=\sqrt[]{40} \end{gathered}[/tex]Finally, we have
[tex]\begin{gathered} \text{ Perimeter }=QR+RS+TS+QT \\ \text{ Perimeter }=7+\sqrt[]{40}+7+\sqrt[]{40} \\ \text{ Perimeter }=26.65 \end{gathered}[/tex]Therefore, the perimeter of parallelogram QRST is 26.65 units and the correct answer is option B.
can you please help me
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AB = 3x + 4
BC = 7x + 9
AB + BC = AC
AC = 143
Let us add AB and BC then equate their sum by 143
[tex]AC=AB+BC=3x+4+7x+9=(3x+7x)+(4+9)[/tex]First, step add the like terms
[tex]AC=10x+13[/tex]Equate AC by its length 143
[tex]10x+13=143[/tex]Now we have an equation to solve it
To solve the equation let us move 13 from the left side to the right side by subtracting 13 from both sides
[tex]\begin{gathered} 10x+13-13=143-13 \\ 10x=130 \end{gathered}[/tex]To find x divide both sides by 10 to move 10 from the left side to the right side
[tex]\begin{gathered} \frac{10x}{10}=\frac{130}{10} \\ x=13 \end{gathered}[/tex]Now let us find AB and BC
Substitute x by 13 in each expression
AB = 3(13) + 4 = 39 + 4 = 43
BC = 7(13) + 9 = 91 + 9 = 100
The length of AB is 43 units
The length of BC is 100 units