What is the right answer to this?
Quadrilateral $abcd$ is a parallelogram. if the measure of angle $a$ is 62 degrees and the measure of angle $adb$ is 75 degrees, what is the measure of angle $adc$, in degrees?
In the given parallelogram ABCD, angle $a$ is 62 degrees and angle $adb$ is 75 degrees. Angle $bd$ is calculated to be 105 degrees making angle $adc$ the supplementary to $bd$, and therefore also 75 degrees.
Explanation:In a parallelogram, opposite angles are equal and consecutive angles are supplementary (adding up to 180 degrees). In your given quadrilateral $abcd$, the measure of angle $a$ is 62 degrees and $a$ and $adb$ are consecutive angles. Therefore, knowing that angle $adb$ is 75 degrees, angle $bd$ should be the supplementary to $adb$, which is 180 - 75 = 105 degrees. Finally, since $adc$ is a straight line and $bd$ and $dc$ are parts of it, therefore angle $dc$ = 180 - angle $bd$ = 180 - 105 = 75 degrees. So, the measure of angle $adc$ is 75 degrees.
Learn more about Angles in a Parallelogram here:https://brainly.com/question/16578666
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Which inequality is correctly represented by this graph
A) 3x-y>3
B) x-3y>=2
C) 3x-y<=3
D)x-3y>2
You should first solve each equation for y.
Eliminate answer choices with wrong slopes or y intercepts.
Then, because it is a dotted line, the answer will only be < or >.
And because the area is shaded to the right, it would mean that x > y.
So the answer is A) 3x - y > 3
Answer:
The correct option is A.
Step-by-step explanation:
If a line passing through two points then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
From the given graph it is clear that the related line passing through the points (0,-3) and (1,0). So, the equation of related line is
[tex]y-(-3)=\frac{0-(-3)}{1-0}(x-0)[/tex]
[tex]y+3=3x[/tex]
The (0,0) is not in the solution set. So check the equation be (0,0).
[tex]0+3=3(0)[/tex]
[tex]3=0[/tex]
This condition is false if the sign of inequality is < or ≤. Since the related line is a solid line, therefore the sign of inequality must be <.
The required inequality is
[tex]y+3<3x[/tex]
[tex]3<3x-y[/tex]
It is also written as
[tex]3x-y>3[/tex]
Therefore the correct option is A.
A man wishes to construct a pultry house 12 feet long, in which to keep 20 hens. if each hen requires 4 square feet of floor space, how wide should he contruct the poultry house
Best explained and correct answer gets brainliest.
3275 = x * (1+0.075/12)^(12*10)
3275 = x * (2.11206463)
x= 3275/2.11206463 = 1550.6154
x=1550.62
she needs to deposit $1,550.62
Alive the equation 2 k+2= k+1
What is [tex] 3\sqrt{18} [/tex] + [tex] 2\sqrt{50} [/tex] simplified?
F.[tex] 19\sqrt{2} [/tex]
G.[tex] 39\sqrt{2} [/tex]
H.[tex] 77\sqrt{2} [/tex]
I. [tex] 90\sqrt{2} [/tex]
IF THERE IS WORK PLEASE SHOW THANKS:)
Richard has just been given a 4-question multiple-choice quiz in his history class. each question has four answers, of which only one is correct. since richard has not attended class recently, he doesn't know any of the answers. assuming that richard guesses on all four questions, find the indicated probabilities. (round your answers to three decimal places.) (a) what is the probability that he will answer all questions correctly
The probability of answering all the question correctly is [tex]\boxed{\bf \dfrac{1}{256}}[/tex]
Further Explanation:
Given:
The total number of question is [tex]4[/tex].
Each question has [tex]4[/tex] options and one is correct.
Concept used:
Probability is defined as the ratio of number of favorable outcomes to number of total outcomes.
[tex]\boxed{\text{Probability}=\dfrac{\text{favorable outcomes}}{\text{total outcomes}}}[/tex]
Calculation:
The probability of getting the correct answer is calculated as follows:
[tex]\begin{aligned}P&=\dfrac{1}{4}\\&=0.25\end{aligned}[/tex]
The probability of getting the incorrect answer is calculated as follows:
[tex]\begin{aligned}P&=1-\dfrac{1}{4}\\&=1-0.25\\&=0.75\end{aligned}[/tex]
The formula for probability of answering all question correctly is as follows:
[tex]\boxed{P'=^nC_{r}P^{r}(1-P)^{n-r}}[/tex]
Here, [tex]n[/tex] is number of question and [tex]r[/tex] is number of correct answer, [tex]P'[/tex] is the probability of answering all question correctly.
Solve the above equation to obtain probability of answer all question correctly.
Substitute [tex]4[/tex] for [tex]n[/tex], [tex]0.25[/tex] for [tex]P[/tex] and [tex]4[/tex] for [tex]r[/tex] in above equation to obtain probability of answering all question correctly.
[tex]\begin{aligned}P'&=^4C_{4}(0.25)^{4}(1-0.25)^{4-4}\\&=\dfrac{4!}{(4-4)!\cdot 4!}\left(\dfrac{25}{100}\right)^{4}(0.75)^{0}\\&=\left(\dfrac{1}{4}\right)^{4}\\&=\dfrac{1}{256}\end{aligned}[/tex]
Therefore, the probability of the correct answer is [tex]0.25[/tex].
The probability of the incorrect answer is [tex]0.75[/tex].
The probability of answering all question correctly is [tex]\dfrac{1}{256}[/tex].
Thus, the probability of answering all question correctly is [tex]\boxed{\dfrac{1}{256}}[/tex].
Learn more:
1. Simplification: https://brainly.com/question/1602237
2. Quadratic equation: https://brainly.com/question/1332667
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Probability
Keywords: Probability, Question, Richard, multiple choice, four answer, class, attend, guesses, correctly answer, favorable outcomes, total outcomes.
The probability that Richard will answer all four questions correctly is 0.004.
Explanation:The probability that Richard will answer all four questions correctly can be determined by multiplying the probability of getting one question correct by itself for each question. Since each question has four answer choices and only one is correct, the probability of guessing the correct answer for one question is 1/4.
Therefore, the probability of Richard answering all four questions correctly is (1/4) * (1/4) * (1/4) * (1/4) = 1/256. Rounded to three decimal places, this probability is approximately 0.004.
Thus, the probability that Richard will answer all questions correctly is 0.004.
PLEASE HELP!!!!!
Which function has the following domain and range?
Domain: {−7,−3,0,4,12}
Range: {−5,1,2}
Select one:
a. {(−7,12),(−5,2)}
b. {(−7,−5),(−3,1),(0,2),(−4,5),(3,−1)}
c. {(4,1),(−3,−5),(12,2),(0,−5),(−7,1)}
d. {(−5,4),(2,12),(1,−3),(−5,−7),(1,0)}
Find the number of ways to listen to 4 different cds from a selection of 15 cds.
Answer:
The First person who answered it was wrong! Its 32,760 I took the test lol!
Step-by-step explanation:
nPr = n!/(n-r)! <-- The equation used for this.
Identify the y-intercept of the function, f(x) = 2x 2 + x - 4. (0,-4) (0,4) (-4,0) (4,0)
Answer:
The y-intercept of the function [tex]f(x)=2x^{2}+x-4[/tex] is [tex](0,-4)[/tex]
Step-by-step explanation:
The y-intercept of a function is the intersection between the graph of the function and the y-axis.This particular point will have a ''0'' in its x-coordinate (because all points over the y-axis have a ''0'' on its x-coordinate).Therefore, we can write the y-intercept as :
[tex]y-intercept=(0,a)[/tex]
We obtain the another coordinate ''a'' replacing ''x'' by a ''0'' in the function.
In this exercise, the function is:
[tex]f(x)=2x^{2}+x-4[/tex]
If x = 0 ⇒
[tex]f(0)=2(0)^{2}+0-4=-4=a[/tex]
We find that ''-4'' is the coordinate ''a'' that we were looking for.
We conclude that the point [tex](0,a)=(0,-4)[/tex]
And [tex](0,-4)[/tex] is the y-intercept of the function.
which equation represents the statement thirteen less then a number is forty two
Answer:
The equation which represents the statement thirteen less then a number is forty two is:
x-13=42
Step-by-step explanation:
Let x be any number
we are given that:
thirteen less then a number is forty two
i.e. x-13=42
Hence, the equation which represents the statement thirteen less then a number is forty two is:
x-13=42
Find the function h(x) = f(x) ∘ g(x) if f(x) = x(2 - x) and g(x) = 3x.
h(x) = 0
h(x) = -32x
h(x) = 2(32x)
h(x) = 3x(2 - 3x)
Answer: h(x) = 3x(2 - 3x)
Step-by-step explanation:
Here the given functions are,
[tex]f(x) = x(2-x)[/tex]
[tex]g(x) = 3x[/tex]
[tex]h(x) = f(x) \circ g(x) = (f\circ g)(x) = f[g(x)][/tex]
[tex]= f( 3x )[/tex]
[tex]= (3x)[2-(3x)][/tex]
[tex]= 3x(2-3x)[/tex]
Hence,
[tex]h(x) = 3x(2-3x)[/tex]
⇒ Fourth option is correct.
What is the factored form of 2x2 − 7x − 15? (2x + 3)(x − 5) (2x + 5)(x − 3) (2x − 7)(x + 8) (2x + 8)(x − 7)
Justin wants to use 376 ft of fencing to fence off the greatest possible rectangular area for a garden what dimensions should he use what will be the area of the garden
the greatest rectangular area is actually a square
so 376/4 = 94 feet.
each side will be 94 feet
area of a square is 94^2
= 94 * 94 = 8836 square feet
The function f(x) = –x2 + 60x – 116 models the monthly profit, in dollars, a shop makes for repairing windshields, where x is the number of windshields repaired, and f(x) is the amount of profit. Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points) Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
Answer:
I believe Homer "the genius" math to be incorrect for Part A. (-30)^2+60(30)-116= 900+1800-116=2584; not 784 as he got -900 when squaring -30.
Step-by-step explanation:
A plane's airspeed is 400 miles per hour on a heading of 45 degrees south of east (compass: 135 degrees, babylonian 315 degrees). if a wind is blowing from the west with a speed of 50 miles per hour, what is the ground speed and direction of the plane?
a factor of the quadratic 6x2-11x-35
The tangent of an angle is 3.4. what is the measure of the angle to the nearest tenth? 99.8° 73.6° 68.2° 52.9°
Find the polynomial f(x) that has the roots of -2, 5 of multiplicity 2. Explain how you would verify the zeros of f(x).
Trey went to the batting cages to practice hitting. he rented a helmet for $4 and paid $0.75 for each group of 20 pitches. if he spent a total of $7 at the batting cages, how many groups of pitches did he pay for?
What is -4x - 5x <18 need help
What type of equation would best model this data
The wildflowers at a national park have been decreasing in numbers. There were 300 wildflowers in the first year that the park started tracking them. Since then, there have been one fourth as many new flowers each year. Create the sigma notation showing the infinite growth of the wildflowers and find the sum, if possible.
I chose C, but can someone check for me? Thanks :)
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
Initial wildflowers in the first year = 1200
Every year, the number of wildflower is one fourth of the previous year.
So, it form a geometric series:
1200,300,75............
so, using sigma notation we can express the infinite growth of the wildflowers:
[tex]\sum ^{\infty}_{i=1}1200(\dfrac{1}{4})^{i-1}[/tex]
As we know that sum of infinite terms in case of geometric series is given by
[tex]S_{\infty}=\dfrac{a}{1-r}\\\\S_{\infty}=\dfrac{1200}{1-0.25}\\\\S_{\infty}=\dfrac{1200}{0.75}\\\\S_{\infty}=1600[/tex]
Therefore, there are 1600 wildflowers.
Hence, Third option is correct.
What is the solution set of the equation x^2 - 7x - 18 = 0
Factoring this trinomial as the product of two binomials,
we have (x - 9)(x + 2) and set that equal to 0.
So we have (x - 9)(x + 2) = 0.
So either x - 9 = 0 or x + 2 = 0.
Solving for x in each equation, we find that our solution is {9, -2}.
Write a compound inequality that represents the situation:
all real numbers at least -6 and at most 3
A) -6 < x ≤ 3
B) -6 ≤ x ≤ 3
C) -6 ≥ x ≥ 3
D) -6 < x < 3
Please help!!! (-x/2)+(1/2x)=(-4/x)
What is the slope of y-9=-2(x-8)
help me please help me
What is the simplified form of the quantity of x plus 5, all over the quantity of 9 − the quantity of x plus 4, all over the quantity of x plus 6