Explanation
The Inscribed Quadrilateral Theorem states that a quadrilateral can be inscribed in a circle if and only if the opposite angles of the quadrilateral are supplementary
Answer 1: True
Also, Given a triangle, the circumscribed circle is the circle that passes through all three vertices of the triangle. The center of the circumscribed circle is the circumcenter of the triangle, the point where the perpendicular bisectors of the sides meet.
Answer 2: True
Given the system below. What is the x value of the solution? 3x + 5y = 8 y = x + 8
We are given the following system of equations:
3 x + 5 y = 8
y = x + 8
So we can use the "substitution method" to solve it, since the second equation is already giving us a possible substitution to make:
Replace y with x + 8 in the other equation.
We proceed as shown below:
3 x + 5 y = 8
3 x + 5 (x + 8) = 8
Use distributivr property to remove the parenthesis:
3 x + 5 x + 40 = 8
8 x + 40 = 8
subtract 40 from both sides to isolate the term in "x"
8 x = 8 - 40
8 x = - 32
divide both sides by 8 to isolate "x"
x = - 32 / 8
x = - 4
We found the requested x value
We are also asked to find y , so we use the value for x in the substitution equation:
y = x + 8
y = -4 + 8 = 4
Then y = 4
The pair that satisfies this system is x = -4 and y = 4 or in pair form: (-4, 4)
What is the image of (−9,−12) after a dilation by a scale factor of 1/3
centered at the origin?
By dilation with a scale factor of 1 / 3 centered at the origin, the image of the resulting point is (- 3, - 4).
How to determine the location of the image of a point by using a dilation formula
In this problem we find the coordinates of a point set on Cartesian plane, whose image is the result of using a dilation centered at the origin, whose definition is introduced below:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilationP(x, y) - Original pointP'(x, y) - Resulting pointk - Scale factorIf we know that O(x, y) = (0, 0), k = 1 / 3 and P(x, y) = (- 9, - 12), then the image of the original point is:
P'(x, y) = (0, 0) + (1 / 3) · [(- 9, - 12) - (0, 0)]
P'(x, y) = (- 3, - 4)
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Which equation represents a line which is perpendicular to the line y =- +522x - 5y = -302x + 5y = 152y-53 = 10O 5x + 2y 12
Answer:
The equation that represents the perpendicular line is;
[tex]2y-5x=-10[/tex]Explanation:
We want to find the equation of a line perpendicular to the line;
[tex]y=-\frac{2}{5}x+5[/tex]Recall that for two lines to be perpendicular to each other, their slope must be a negative reciprocal of one another.
[tex]m_1.m_2=-1_{}_{}[/tex]so;
[tex]m_2=-\frac{1}{m_1}[/tex]For the given equation, the slope of the given line is;
[tex]m_1=-\frac{2}{5}[/tex]To get the slope of the perpendicular line, let us substitute m1 to the equation above;
[tex]\begin{gathered} m_2=-\frac{1}{m_1} \\ m_2=-\frac{1}{(-\frac{2}{5})_{}} \\ m_2=\frac{5}{2_{}} \end{gathered}[/tex]So, the equation of the perpendicular line would be of the form;
[tex]\begin{gathered} y=m_2x+c \\ y=\frac{5}{2}x+c \\ mu\text{ltiply through by 2} \\ 2y=5x+c \\ 2y-5x=c \end{gathered}[/tex]The equation of the perpendicular line will be of the form;
[tex]2y-5x=c[/tex]Where c is a constant;
From the options, the only equation that is similar to the derived equation is;
[tex]2y-5x=-10[/tex]Therefore, the equation of the perpendicular line is;
[tex]2y-5x=-10[/tex]how are rational munbers written as decimalsfYI:I was listening but I just don't understand
We have 4 rational numbers which we are asked to express in decimal numbers.
To do this, we divide the numerator of each rational number by its denominator, when we do that, we get the following results:
[tex]undefined[/tex]Find the area of each. 'Use your calculator's value of r. Round your answer to the nearest tenth.
To find the area of a circle given the radius;
[tex]undefined[/tex]Grpah the image of square ABCD after a translation 10 units up.
We have to take the points A, B, C, and D from the original square and move all of them 10 units up as shown in the following diagram:
After translating the points we get the image points A', B', C' and D'.
Finally, connecting the image points we get the image of the square:
si en un determinado lugar el metro cuadrado de terreno cuesta 250 dolares cuanto vale el lote de 400 metros cuadrados
If a square meter of land costs $250 in a certain place, then 1.6 sq. m. of land can be bought there for $400, calculated using the unitary method.
As per the question statement, the cost of per square meter of land in a certain place is $250,
And we are required to calculate the amount of land that can be bought in the above mentioned place for $400.
To solve this question, we will use the unitary method, that is,
Given, the cost of per square meter of land in a certain place is $250,
Or, in $250, one can buy 1 sq. m. of land in this place,
Or, in $1, one can buy (1/250) sq. m. of land,
And, in $400, one can buy [{(1/250) * 400} = (40/25) = (8/5) = 1.6 sq. m.] of land in that place.
Unitary Method: In Mathematics, the unitary method is a technique for solving a problem by first finding the value of a single unit, and then multiplying this single unit value into the number of concerned units, to obtain our desired resultant.To learn more about Unitary Method, click on the link below.
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What is the slope and y intercept of the line whose equation is y = -4x + 2?b =m=
To find the slope and the intercept of the line
y = -4x + 2
y = mx + b
so in this case the m = -4, because is the coefficient on x rigth over there
and b is going to be the constant term
b = 2
I need help with the third question where it says segment addition
ANSWER
EXPLANATION
We have that the line EG = 71.
We are given that
EF = 8x - 17
and
FG = 5x - 3
We see from the diagram that:
EF + FG
Work out the lenght off x
Using the Pythagorean theorem, the length of the side x is √147.
What is the Pythagorean theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.So, the formula of the Pythagorean theorem:
H² = l² + w², where H is the hypotenuse.Now, substitute the values and calculate as follows:
14² = 7² + x²x² = 14² - 7²x² = 196 - 49x² = 147x = √147Therefore, using the Pythagorean theorem, the length of the side x is √147.
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Below, the two-way table is given for aclass of students.FreshmenSophomoreJuniorsSeniorsTotal46246Male2Female 33TotalIf a student is selected at random, find theprobability the student is a junior given that it'smale. Round to the nearest whole percent.[?]%
Male students. 14
Female students: 16
Total students: 30
Since there are 2 male juniors, the probability of being junior and male is: 6.67%
[tex]\frac{2}{30}\cdot100=6.67[/tex]If we round to the nearest whole porcent: 7%
A teacher bought 28 books for her class. She spent a total of $112.00. What is the price, p, for each book? Let p = price for each book
Locker codes at Lincoln High School consist of 4 digits. No digit can be used more than once. How many locker codes are available at Lincoln High School? A 210 B 3,024 C 5,040 D 10,000
To obtain the number of locker codes available, the following steps are necessary:
Step 1: Create a diagram to represent the slot for each of the digits, as below;
Step 2: State the number ways that each digit can be used to fill any of the spots, as below:
Given that there are the numbers 0,1,2,3,4,5,6,7,8,9 - a total of 10 numbers,
- The first slot can be filled with any of the digits above, and thus can be filled in 10 ways
- The second slot can be filled with any of the remaining 9 numbers after one of them has already been used to fill the first slot. Thus, there are 9 ways the second slot can be filled.
- The same line of reasoning tells us that the third slot will be filled in 8 ways
- Lastly, the fourth slot will be filled in 7 ways
The diagram below gives a better illustration:
Step 3: Multiply the numbers of ways to find the total number of locker codes that are available, as follows:
[tex]10\times9\times8\times7\text{ = 5040}[/tex]Therefore, there are a total of 5040 available locker codes at Lincoln High School
Correct answer = Option C
A bike wheel as a radius of 13 inches. a. About how far does the bike wheel tra in 1 rotation? 5 rotations? 30 rotations? b. Write an equation relating the distance the bike travels in inches, b, to the number of wheel rotations, x. c. About how many rotations does the bike wheel make when the bike travels 1 mile?
The radius of the bike wheel is given as 13 inches. One rotation would be equal to the entire circumference of the bike wheel. Hence;
[tex]undefined[/tex]Evaluate the left hand side to find the value of aa in the equation in simplest form. 4
Given
[tex]\frac{x^{\frac{1}{2}}}{x^{\frac{1}{6}}}[/tex]Solution
Apply exponent rule
[tex]\begin{gathered} x^{\frac{1}{2}-\frac{1}{6}}=x^{\frac{3-1}{6}} \\ \\ \\ x^{\frac{2}{6}}=x^{\frac{1}{3}} \end{gathered}[/tex][tex]a=\frac{1}{3}[/tex]We have
[tex]\frac{x^{\frac{1}{2}}}{x^{\frac{1}{6}}}=x^{\frac{1}{3}}[/tex]what is the equation in point slope form of the line that passes through the point (5, 0) and has a slope of 1.2?
To see the equation we know that the general equation of a line is:
[tex]y=mx+b[/tex]Where m is the slope. So you know that the slope is 1.2, then you have an equation like this:
[tex]y=1.2x+b[/tex]Since b is just a number we can say that this is also equal to:
[tex]y=1.2(x+c)[/tex]We'll write it this way so it's similar to the options.
Then you know that the line pases through point (5,0). To find the value of constant c we replace the value of x and y from this point (x = 5 and y=0):
[tex]0=1.2(5+c)[/tex]And clear c from this expression
[tex]0=5+c\Rightarrow c=-5[/tex]So the answer is:
[tex]y-0=1.2(x-5)[/tex][tex]1144 \times \frac{25}{3699} + 114 \sqrt[1441]{36} - y + x \div 15663 = 2 - \sqrt[44410]{3651} + {2554}^{2} [/tex]first equation. then text
how does equation look in session history???
3. Determine the missing length in the following triangle. Round to thenearest tenth. (2 points: 1 point for correct answer, 1 point for showingyour work) *1214Your answer
7.2
1) Examining the picture, we can assume this is a Right Triangle, and then use the Pythagorean Theorem
a²=b² +c²
14² = 12² +c² The hypotenuse is the larger side a
196=144 +c²
196-144 = c²
52 =c²
√52 =√c²
c= √52
2) Rounding off to the nearest tenth we can write
c= √52 is approximately 7.2
If reciangle ABCD is in quadrant II, and rotated 270 degrees counterciockwise around the origin, then what quadrant will rectangle A'B'C'D' be in ? Quadrant l Quadrant II Quadrant lll Quadrant IV
Quadrant IV.
1) Let's Draw this to give us a better idea.
In a 270º CCW Rotation, the rule is every coordinate to be translated
(x.y) ---(y,-x)
2) Let's give to our quadrilateral
A(-2,3) ---- A'(3,2)
B(-4, 3) -----B'(3,4)
C(-6, 4) -----C' (4,6)
D( -8, 4) ---- D' (4, 8)
And so forth
So Quadrant IV is the answer.
If a quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors, then which statement would be true?
The figure must be an isosceles trapezoid because it has 2 congruent base angles.
The figure must be a rectangle because all rectangles have exactly 2 lines of symmetry.
The figure could be a rhombus because the 2 lines of symmetry bisect the angles.
The figure could be a square because the diagonals of a square bisect the right angles.
The third option is correct. That is, the figure could be a rhombus because the 2 lines of symmetry bisect the angles.
What is rhombus?
A rhombus is a quadrilateral that is an equilateral parallelogram and has all of its opposite pairs of sides parallel. Sometimes the word "rhombus" is substituted with "rhomb," and a rhombus is also referred to as a "diamond."
Given: A quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors.
Since the two lines of symmetry in a quadrilateral are angle bisectors, the figure may be a rhombus if the quadrilateral has exactly two lines of symmetry. Figures with four sides and angles are called quadrilaterals. Rectangle is a type of quadrilateral.
Therefore, If a quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors, then the figure could be a rhombus because the 2 lines of symmetry bisect the angles.
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Answer:
third option
Step-by-step explanation:
how do you solve y=x-2 and graph it
The equation
y = x - 2
is the equation of a line in the slope-intercept form with a slope of 1 and a y-intercept at (0, -2).
You can graph it by locating two points on the line. One point is (0, -2). The other one can be found with the slope. The slope of 1 means that the next point is 1 unit to the left and 1 unit up, respect the previous point. In this case, the next point is (1, -1). After you locate these two points, draw the line that connects them, as follows
Please help me with this geometry problem. i don’t understand.
Tangent theorem states that when two tangents intersect out a circle they are said to be equal
Therefore,
Tangent 2x+13 is equal to tangent 4x-8
[tex]\begin{gathered} 4x-8=2x+13_{} \\ by\text{ collecting like terms we will have that,} \\ 4x-2x=13+8 \\ 2x=21 \\ to\text{ find x we will dive both sides by the coefficent of x which is 2} \\ \frac{2x}{2}=\frac{21}{2} \\ x=10\frac{1}{2} \\ x=10.5 \end{gathered}[/tex]Hence,
The value of x =10.5
what is the value of the square root of -25+10
Celeste, this is the solution to the exercise:
Let's recall that √-1 = i, therefore:
The first term of the sum is √-25 = √25 * -1 = 5i
The second term remains the same. + 10
Thus, the correct answer is D. 5i + 10
What is the slope of a line that is perpendicular to the line y = - 1x +5?
○-2
-1/2
1/2
○ 2
The slope of the line that is perpendicular to the line y = - 1x +5 is -1.
What is the slope?The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same).
Given:
The equation of the line, y = -x + 5
The slope of the line can be calculated by the intercept form,
so m = -1, Here, m is the slope.
The slope of the perpendicular line will be the opposite
So, M = -1
Therefore, the slope of the line that is perpendicular to the line y = - 1x +5 is -1.
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What is the accumulated value if the money is compounded semiannually?
Given:
[tex]\begin{gathered} P=20,000 \\ t=6years \\ r=5.5\% \end{gathered}[/tex]Required:
To find the accumulated value.
Explanation:
Consider
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Here
[tex]\begin{gathered} =20000(1+\frac{0.055}{2})^{2\times6} \\ \\ =20000(1+0.0275)^{12} \\ \\ =27,695.68 \end{gathered}[/tex]Final Answer:
The accumulated value is $27,695.7
Evaluate the expression xy - 3x when x = 4 and y = 5
Answer:
xy - 3x = 8
when x = 4 and y = 5
Explanation:
Given the expression
xy - 3x
When x = 4 and y = 5, the equation becomes
(4)(5) - 3(4)
= 20 - 12
= 8
What steps should be followed to solve the following equation for x: -3x - 8 1 point= 4*Add 8 to both sides, then divide by 3Divide by -3, then add 8 to both sidesAdd 8 to both sides, then divide by -3Add 8 to both sides, then add 3 to both sides
1) Evaluating
-3x -8= 4 Adding 8 to both sides
-3x -8 +8=4+8
-3x = 12 Dividing both sides by 3
x=-4
2) Examining the options then
C Add 8 to both sides then divide both sides by 3
Select all the correct answers Each of these scatter plots has a line of fit for its data points. Which graphs have a line that is a line of best for the data
There should be as much as many dots above the line and below the line . The line of best fits represent the trend of the data whether positive or negative correlation
The graphs that have a line that is best for the data are
Graph 1
Graph 4
a. A random sample of 43 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $18.58 per car. The population standard deviation is $6.22. Estimate the mean bill for all cars from the drive-thru with 97% confidence. Round intermediate and final answers to two decimal places.
Given
[tex]\begin{gathered} n=43 \\ Mean\text{ = \$18.58} \\ \sigma=\text{ \$6.22} \end{gathered}[/tex]Solution
Formula
[tex]\text{Confident interval =M }\pm\frac{Z\sigma}{\sqrt[]{n}}[/tex]where
[tex]\begin{gathered} M=\text{ mean or Average} \\ Z-score=Z_{97}=2.17 \\ n=43 \end{gathered}[/tex]Substitute the parameters into the Confident Interval formula
[tex]\text{Confident interval =18.58}\pm\frac{2.17\times6.22}{\sqrt[]{43}}[/tex]Then we calculate the Addition and subtraction
First the Addition
[tex]\begin{gathered} \text{Confident interval =18.58+}\frac{2.17\times6.22}{\sqrt[]{43}} \\ \\ \text{Confident interval =18.58+}\frac{13.4974}{\sqrt[]{43}} \\ \\ \text{Confident interval =18.58+}\frac{13.4974}{6.5574} \\ \text{Confident interval =18.58+}2.05833 \\ \text{Confident interval =}20.63833342 \\ \\ \text{Confident interval =}20.64\text{ two decimal places} \end{gathered}[/tex]Then now for subtraction
[tex]\begin{gathered} \text{Confident interval =18.58-}\frac{2.17\times6.22}{\sqrt[]{43}} \\ \\ \text{Confident interval =18.58-}\frac{13.4974}{\sqrt[]{43}} \\ \\ \text{Confident interval =18.58-}\frac{13.4974}{6.5574} \\ \text{Confident interval =18.58-}2.05833 \\ \text{Confident interval =}16.5216658 \\ \\ \text{Confident interval =16.52 two decimal places} \end{gathered}[/tex]The final answer
[tex](16.52,\text{ 20.64)}[/tex]solve the equation T = 2x + 3y - z for y.
In order to solve this equation for y, we just need to isolate the variable y in the equation.
So, we have that:
[tex]\begin{gathered} T=2x+3y-z_{} \\ 3y=T-2x+z \\ y=\frac{T-2x+z}{3} \end{gathered}[/tex]So we have that y = (T - 2x + z) / 3