Answers
1. Given that AD is perpendicular to BC, this tells us angle ADC and ADB are both right angles and are therefore congruent.
2. We know AD = AD, since it's the same line segment.
3. Since AD bisects angle BAC, we know angle CAD and BAD are congruent.
Based on Angle-Side-Angle, triangles ADC and ADB are congruent.
Related Questions
Samantha is designing a vidèo game where players get 3 free revives per level. She wanted O test howmany revives players might use on a new level.Samantha recruited 50 players to play the level, and she recorded how many revives each player used.Fill in the blanks to complete the probability distribution.Do not round your answers.Revives used023Frequency6228Probability0.120.44 0.16
Answers
Frequency = 14
Probability = 0.28
Explanation:The sample size is given to be 50
Frequency must sum to 50
Let the missing frequency be x
6 + x + 22 + 8 = 50
x + 36 = 50
x = 50 - 36 = 14
The corresponding probability for the frequency above is:
14/50 = 0.28
Frequency = 14
Probability = 0.28
HURRY! Which numbers below are even Check all that apply
Answers
Answer:
A. 934
C. 8402
E. 2120
F. 9154
Step-by-step explanation:
Even numbers must contain have a 0, 2, 4, 6, or 8 at the last digit of an integer.
Example:
1326 (Even)
4377 (Odd)
Here is a crde with center H and some line segments and curves joining points on the circle,DBE1. Identify and select all of the segments that form a diameter of the circle.AEОаObAHDGdDHCEfBH
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we know that
A diameter of the circle is a chord that passes through the center
so
In this problem we have that
the diameter are
EADGWhich of the following transformations would map CD on C'D'
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hello, first we need to know what color represents each line segment.
Look at the figure: CD is represented in green, and C'D is represented in blue.
Now, let's look at the points of each one:
CD: (2,1) and (3(-4)
C'D': (-1,2) and (4,3)
To solve this question, we need to rotate the green line segment to the same position as the blue line segment.
So, if we rotate 90 degrees in the clockwise, we will have:
(-2, 1) and (-3, -4)
If we rotate 90 degrees in the counterclockwise, we will have:
(-1,2) and (4,3). This are the same points of the line segment C'D'
Let g(x) = 2x and h(x) = x^2 + 4. Find the value.(g o h) (0)a) 4b) 8c) 0d) 16
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Solve for (g o h)(x)
[tex]\begin{gathered} (g\circ f)(x)=g\big(f(x)\big) \\ (g\circ f)(x)=g(x^2+4) \\ (g\circ f)(x)=2(x^2+4) \\ (g\circ f)(x)=2x^2+8 \end{gathered}[/tex]Next substitute x = 0
[tex]\begin{gathered} (g\circ f)(x)=2x^2+8 \\ (g\circ f)(0)=2(0)^2+8 \\ (g\circ f)(0)=8 \end{gathered}[/tex][tex]\text{Therefore, }(g\circ f)(0)=8[/tex]Please help with part a b and c, C says “compre the functions algebraically by rewriting them using a common denominator”
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Given:
[tex]\begin{gathered} f(x)=\frac{x+2}{x+3} \\ g(x)=\frac{x+5}{x} \end{gathered}[/tex]Required:
To find the values of the given functions at the given values of x.
Explanation:
At x = 0.5, Put x=0.5 in f(x) and g(x).
[tex]\begin{gathered} f(0.5)=\frac{0.5+2}{0.5+3} \\ f(0.5)=\frac{2.5}{3.5} \\ f(0.5)=0.714 \\ g(0.5)=\frac{0.5+5}{0.5} \\ g(0.5)=11 \end{gathered}[/tex]Now put x=1 in f(x) and g(x)
[tex]\begin{gathered} f(1)=\frac{1+2}{1+3} \\ f(1)=\frac{3}{4} \\ f(1)=0.75 \\ g(1)=\frac{1+5}{1} \\ g(1)=6 \end{gathered}[/tex]Now put x=2 in f(x) and g(x).
[tex]\begin{gathered} f(2)=\frac{2+2}{2+3} \\ f(2)=\frac{4}{5} \\ f(2)=0.8 \\ g(2)=\frac{1+5}{2} \\ f(2)=\frac{6}{2} \\ f(2)=3 \end{gathered}[/tex]Similarly, we will put the other values of x in f(x) and g(x), and then make the table by putting the values.
find the x- and y-intercepts of the graphs of each equation6x+12y=24-5x+3y=-24
Answers
To find the x-intercept we replace y=0 and solve for x
To find the y-intercept we repalce x=0 and solve for y
First equation
[tex]6x+12y=24[/tex]x-intercept
[tex]\begin{gathered} 6x+12(0)=24 \\ 6x=24 \\ x=\frac{24}{6} \\ \\ x=4 \end{gathered}[/tex]x-intercept is
[tex](4,0)[/tex]y-intercept
[tex]\begin{gathered} 6(0)+12y=24 \\ 12y=24 \\ y=\frac{24}{12} \\ \\ y=2 \end{gathered}[/tex]y-intercept is
[tex](0,2)[/tex]Second equation
[tex]-5x+3y=-24[/tex]x-intercept
[tex]\begin{gathered} -5x+3(0)=-24 \\ -5x=-24 \\ x=\frac{-24}{-5} \\ \\ x=\frac{24}{5} \end{gathered}[/tex]x-intercept is
[tex](\frac{24}{5},0)[/tex]Y-intercept
[tex]\begin{gathered} -5(0)+3y=-24 \\ 3y=-24 \\ y=\frac{-24}{3} \\ \\ y=-8 \end{gathered}[/tex]y-intercept is
[tex](0,-8)[/tex]d = -gt^2 + vt + c. the equation expresses the distance, d, in feet, of a ball t seconds after it is thrown straight up with an initial velocity of v feet per second and from a starting point of c feet. which of the following expresses v in terms of d, g, t, and c? A) v = d - c - + g/t B) v = d + c + g/t C) v = d + c/t - gt D) v = d - c/t + gt
Answers
Given:
[tex]d=-gt^2+vt+c[/tex]To express v in terms of d, g, t, and c, take the following steps:
Step 1:
Subtract c from both sides
[tex]\begin{gathered} d-c=-gt^2+vt+c-c \\ \\ d-c=-gt^2+vt \end{gathered}[/tex]Step 2:
Divide through by t:
[tex]\begin{gathered} \frac{d}{t}-\frac{c}{t}=\frac{-gt^2}{t}+\frac{vt}{t} \\ \\ \\ \frac{d}{t}-\frac{c}{t}=-gt+v \end{gathered}[/tex]Step 3:
Add gt to both sides
[tex]\begin{gathered} \frac{d}{t}-\frac{c}{t}+gt=-gt+gt+v \\ \\ \frac{d}{t}-\frac{c}{t}+gt=v \\ \\ v=\frac{d}{t}-\frac{c}{t}+gt \end{gathered}[/tex]Therefore, the expression of v in terms of d, g, and c is:
[tex]v\text{ = }\frac{d}{t}-\frac{c}{t}+gt[/tex]ANSWER:
[tex]v=\frac{d}{t}-\frac{c}{t}+gt[/tex]farmer has 100 m of fencing to enclose a rectangular pen.
Which quadratic equation gives the area (A) of the pen, given its width (w)?
Answers
Considering the area and the perimeter of a rectangle, the quadratic equation that gives the area (A) of the pen, given its width (w), is:
A = -w² + 50w.
What are the area and the perimeter of a rectangle?Considering a rectangle of length l and width w, we have that the area and the perimeter have equations presented as follows:
The area is given by A = lw.The perimeter is given by P = 2(l + w).In the context of this problem, the farmer has 100 m of fencing to enclose a rectangular pen, meaning that the perimeter is of 100 m, hence:
2(l + w) = 100
l + w = 50
l = 50 - w.
Hence the area of the pen is given by the following quadratic equation:
A = lw
A = (50 - w)w
A = -w² + 50w.
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Eric jogged 3 1/4 on Mon, 5 5/8 >; Tues and 8 miles on Wed. Suppose he continues this pattern for the remainder of the week. how far will Eric jog on Fri?
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Sequences
The distance in miles jogged by Eric in the week are shown below:
Mon: 3 1/4
Tue: 5 5/8
Wed: 8
The distances form a pattern which we will recognize below.
Let's compute the differences in the distance of each day with respect to the previous day:
[tex]r=5\frac{5}{8}-3\frac{1}{4}[/tex]Converting each mixed fraction into improper fractions:
[tex]r=(5+\frac{5}{8})-(3+\frac{1}{4})=\frac{45}{8}-\frac{13}{4}[/tex]The LCM of the denominators is 8, thus:
[tex]r=\frac{45}{8}-\frac{13}{4}=\frac{45}{8}-\frac{26}{8}=\frac{19}{8}[/tex]Now we find the same difference between the third and the fourth terms of the sequence:
[tex]r=8-\frac{45}{8}=\frac{64-45}{8}=\frac{19}{8}[/tex]Since both differences have the same value, the terms of the distances jogged by Eric form an arithmetic sequence. The general term of an arithmetic sequence is:
[tex]a_n=a_1+(n-1)\cdot r[/tex]Where a1 is the first term, n is the number of the term, and r is the common difference.
We have the values a1=3 1/4= 13/4. r=19/8, thus the distance jogged by Eric on Friday (n=5) is:
[tex]a_5=\frac{13}{4}+(5-1)\cdot\frac{19}{8}[/tex]Calculating:
[tex]a_5=\frac{13}{4}+4\cdot\frac{19}{8}=\frac{13}{4}+\frac{19}{2}[/tex]The LCM of 2 and 4 is 4, thus:
[tex]a_5=\frac{13}{4}+\frac{38}{4}=\frac{51}{4}[/tex]Converting to mixed fraction:
[tex]a_5=\frac{51}{4}=\frac{48+3}{4}=12+\frac{3}{4}=12\frac{3}{4}[/tex]Eric jogged 12 3/4 miles on Friday
Write an equation in slope-intercept form for the line that passes through (4,-3) and is parallel to the line described by y=1/2+5
Answers
Given:
The point, (4, -3)
The line,
[tex]y=\frac{1}{2}x+5[/tex]To find an equation in slope-intercept form for the line that passes through (4,-3) and is parallel to the given line:
The slope of the line is,
[tex]m=\frac{1}{2}[/tex]Since the given line is parallel to the new line, so the slope will be same for the both.
Using the point-slope formula,
[tex]y-y_1=m(x-x_1)[/tex]Substitute the point and slope we get,
[tex]\begin{gathered} y-(-3)=\frac{1}{2}(x-4) \\ y+3=\frac{1}{2}x-2 \\ y=\frac{1}{2}x-2-3 \\ y=\frac{1}{2}x-5 \end{gathered}[/tex]Hence, the equation in slope-intercept form for the line is,
[tex]y=\frac{1}{2}x-5[/tex]Flying against the wind, a jet travels 6320 miles in 8 hours. Flying with the wind, the same jet travels 5950 miles in 5 hours. What is the rate of the jet in stillair and what is the rate of the wind?Rate of the jet in still air:Rate of the wind:
Answers
Given,
A jet travels 6320 miles in 8 hours.
Flying with the wind, the same jet travels 5950 miles in 5 hours.
To find: The rate of the jet in still air, and the rate of the wind.
Solution:
The jet's velocity against the wind is
[tex]\frac{6320}{8}=790\text{ miles per hour}[/tex]The jet's velocity with wind is
[tex]\frac{5950}{5}=1190\text{ miles per hour}[/tex]Let the velocity of the jet in still air be x miles per hour and velocity of wind be y miles per hour.
As such its velocity against wind is x-y and with wind is x+y and therefore
[tex]\begin{gathered} x-y=790.......(1) \\ x+y=1190.......(2) \end{gathered}[/tex]Solve both equations (1) and (2)
[tex]\begin{gathered} 2x=1980 \\ x=\frac{1980}{2} \\ x=990 \end{gathered}[/tex]And
[tex]\begin{gathered} y=1190-990 \\ y=200 \end{gathered}[/tex]Hence, the velocity of the jet in still air is 990 miles per hour and the velocity of wind is 200 miles per hour.
If the graph of h was transformed to create the graph of g(x)=x^2+3, which statement is true?D.) The graph of g is 3 units below the graph of h.
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The answer is letter C. The graph of g is 3 units above the graph of h.
Note: A vertical translation is generally given by the equation y= f(x) + b. In this example, g(x) = x^2 + 3, the +3 means to move the graph of x^2 up by 3 units. Thus, The graph of g is 3 units above the graph of h.
The revenues of a company increased by 40% in year one and decreased by 28% in year two. What is the overall change over the two-year period?
What is the overall change?
Answers
The revenues of a company increased by 40% in year one and decreased by 28% in year two, then the overall change over the two-year period is 0.8%
Consider the revenue of the company = x
The revenues of a company increased by 40%
New revenue = x + x(40/100)
= (1+0.4)x
= 1.4x
In next year the revenue decreased by 28%
= 1.4x - (1.4x ×28/100)
= 1.4x - 0.392x
= 1.008x
The over all change in revenue = [tex]\frac{1.008x-x}{x}[/tex] × 100%
= 0.008×100%
= 0.8%
Hence, the revenues of a company increased by 40% in year one and decreased by 28% in year two, then the overall change over the two-year period is 0.8%
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Part A:The Radius of earth = 6,378,100 metersThe radius of earth in single-digit number multiplied bypower of 10.Step by step solution:R= 6.378.100 metersR= 6.3781 × 10^6Part B:The radius of Saturn is approximately 6x10^7 meters. Use the answer from Part A to estimate how many times greater the radius of Saturn is than the radius of Earth. Show or explain how you got your answer.
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Given:
[tex]\begin{gathered} \text{ Radius of earth }=6.3781\times10^6 \\ \\ \text{ Radius of Saturn }=6\times10^7 \end{gathered}[/tex]Find-:
How many times greater the radius of Saturn is than the radius of Earth
Explanation:-
Let "x" times greater than the radius of Saturn is than the radius of Earth
So,
[tex]\begin{gathered} 6\times10^7=x\times6.3781\times10^6 \\ \\ x=\frac{6\times10^7}{6.3781\times10^6} \\ \\ x=\frac{6\times10}{6.3781} \\ \\ x=9.407 \end{gathered}[/tex]So Saturn's radius is 9.407 times greater than the radius of the earth.
Give exact values, not decimal approximations. If the sum does not exist, click on "No sum". [tex](5) + (5) {}^{2} + (5) {}^{3} + ...[/tex]
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first
[tex]undefined[/tex]Expand the expression using the distributive property. Then, simplify by combining like terms.5(3m + 7) – 4Part A: What is the expanded form of 5(3m + 7),Part B: What is the simplified expression,53m + 7) - 4
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The answer for part A is 5(3m+7) = 15m + 35
And the answer for part B is 15m+31
What are the zeros of the function represented by the quadratic expression?A. x= 3/2 and x = 1B. x= -2/3 and x = 1c x= -1 and x = 2/3d. x= -1 and x = -3/2
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so the zeros of the function are 1 and -3/2. So the answer is option A
Two friends, Andrew and Liz, are playing a game using this spinner. If thespinner lands on region 4, Andrew wins. If it lands on region 3, Liz wins. If itlands on any other region, neither wins. Is this a fair game?
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Since we have the following probabilities:
[tex]\begin{gathered} P(1)=P(4)=\frac{1}{4} \\ P(2)=P(3)=P(5)=P(6)=\frac{1}{8} \end{gathered}[/tex]then, this is not a fair game, since Andrew has a 1/4 probability of winning and Liz has a 1/8 probability of winning
summer is planning to build a small snowcone shed that is walkable from three different schools. It is7/8 miles from north junior high .0.68 from South elementary, and 5/6 miles from Westside Elementary. Order the schools from closest to farthest away from summer snow cones.
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The order of the schools from the closest to farthest away from summer snow cones is South Elementary < West Side Elementary < North Junior High .
In the question ,
it is given that
the Summer is planning to build a small snow cone shed .
the distance from north junior high = 7/8 miles = 0.875 miles
the distance from South elementary = 0.680 miles
the distance from West Side elementary = 5/6 miles = 0.833 miles
From , above result we see that
the farthest from summer snow cone is north junior high which is 0.875 miles .
the nearest from summer snow cone is South Elementary which is 0.680 miles .
So , the order from closest to farthest is
South Elementary < West Side Elementary < North Junior High
Therefore , The order of the schools from the closest to farthest away from summer snow cones is South Elementary < West Side Elementary < North Junior High .
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Answer these questions please ?
Answers
In the parallelogram PQRS
PS = 5 and ∠Q = 105 What is defined as the parallelogram?A parallelogram is a type of quadrilateral created by parallel lines. A parallelogram's angle between adjacent sides can vary, however the opposite sides must be parallel in order to be a parallelogram. A parallelogram is formed when the opposite sides of a quadrilateral are parallel as well as congruent.For the given question;
In the parallelogram PQRS,
QR = PS = 5 (opposite side of parallelogram are parallel and equal).
Sum of all angles is 360.
∠Q = ∠S (opposite angles of parallelogram are equal)
∠P + ∠Q + ∠R + ∠S = 360
2∠P + 2∠Q = 360
2∠Q = 360 - 2∠P
2∠Q = 360 - 1502∠Q = 210
∠Q = 105
Thus, the angle Q is found as 105 degrees.
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Sonny and Cher are both members of a population, and a simple random sample is being conducted. If the chance of Sonny being selected is 1/2900, what is the chance of Cher being selected?
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In the case of a simple random sampling, each member of the population has an equal chance of being selected.
Therefore, if the chance of Sonny being selected is 1/2900, the change of Cher being selected is 1/2900.
The answer is 1/2900, option D.Which expression results in a rational number? (1) V2.VIS (3) V2 + 2 (2) 5.5 (4) 3V2 +213
Answers
Step 1
Consider all options
[tex]\begin{gathered} \sqrt[]{2}+\sqrt[]{2}=\text{ 2}\sqrt[]{2}\text{ and 2}\sqrt[]{2\text{ }}is\text{ irrationl} \\ 5\times\sqrt[]{5}=\text{ 5}\sqrt[]{5}\text{ and 5}\sqrt[]{5\text{ }}is\text{ irrational} \end{gathered}[/tex][tex]\begin{gathered} 3\sqrt[]{2\text{ }}+\text{ 2}\sqrt[]{3}=\text{ 3}\sqrt[]{2\text{ }}_{_{_{_{_{_{_{_{_{_{_{}}}}}}}}}}}+2\sqrt[]{3}\text{ and this is irrational} \\ \sqrt[]{2}\times\sqrt[]{18}=\sqrt[]{36\text{ }}=6\text{ and 6 is rational} \end{gathered}[/tex]Hence the answer is option A
There are 10 boys and 13 girls in an eighth grade class.Which of the following is a correct way to write the ratio of boys to girls?A) 10 to 13B) 10:13C) /D) 13:10
Answers
Answer:
D) 13:10
Explanation:
Given:
Total number of boys = 10
Total number of girls = 13
We can show ratios in different ways. We can use the ":" to separate the values , and we also use the word "to". In addition, we can also write like a fraction.
Since "boys" is mentioned first, the correct ways to write the ratio of boys to girls are:
Using the word "to":
By using the colon or ":"
By using fraction,
Therefore, 13:10 is NOT the correct way to write the ratio of boys to girls.
What is the value of x − 9 if x = −24?
Options :33 15 −15 −33
Answers
The value of x - 9 is -33 when x is -24
Given,
x - 9
x = -24
In algebra, the letter "x" is frequently used to denote an unknown value. It is referred to as a "variable" or occasionally a "unknown."
Apply arithmetic operations to both sides of the equation to bring the variable to one side and all other values to the other side in order to find the value of x. To determine the outcome, simplify the values.
We have to find the value of x - 9 when x = -24.
That is,
x - 9
-24 - 9 = -33
Here,
The value of x - 9 is -33 when x is -24
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Answer:
what de person said above ME
Look at Picture for further clarification round to nearest minute
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To determine A we will use the inverse function of the sine ( the arcsine):
[tex]\begin{gathered} \sin ^{-1}(\sin A)=\sin ^{-1}(0.573) \\ A\approx34.9596^{\circ}. \end{gathered}[/tex]Now, we convert A from degrees to degrees and minutes:
[tex]A\approx34.9596^{\circ}=34^{\circ}57.576^{\prime}\approx34^{\circ}58^{\prime}\text{.}[/tex]Answer:
[tex]A\approx34^{\circ}58^{\prime}\text{.}[/tex]Which of the following equations has a graph that is a rose?
Answers
Solution
The answer is
What is the slope of the line that passes through the points (−2,2) and (−4,−1)? Write your answer in simplest form.
Answers
Answer:
[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
The formula for slope is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].
Using points (-2,2) and (-4,-1), this gives us:
[tex]\frac{-1-2}{-4-(-2)}[/tex], which simplifies to [tex]\frac{3}{2}[/tex].
Find the domain and the range please help fast 20 points
Answers
Answer:
See below
Step-by-step explanation:
Domain is the values of x a graph can have
-5 < x <= 6
Range is the y-values a graph can have
-5 < y <= 3
For each expression, select all equivalent expressions from the list.(a) 2x+1402.X+272(x+7)2(7x+1)16x(b) 16 +12y-6-y11 +10y10y+1110y +11 y11 y +10
Answers
We must find equivalent expressions by performing some algebraic operations
Let's start with the first expression:
(a) 2x+14
Please note that both 2x and 14 are divisible by 2.
Take 2 as a common factor like this:
2x+14 = 2(x+7)
Note that if we multiply 2(x+7) we get 2x+14
Thus, the expression is equivalent to 2(x+7)
Now for the following expression:
(b) 16 + 12y - 6 - y
We can note there are numbers apart from variables. The numbers that appear without any variable, can be joined. The variables with the same letter can also be joined:
16 - 6 = 10
12y - y = 11y
Thus, the equivalent expression is
11y+10