A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The value of x, y and z is 90°, 53°, and 100°, respectively.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
In ΔABD is made on the diameter of the circle, therefore, the measure of ∠BAD = 90°. Therefore,
x° = 90°
In ΔAOD, the measure of ∠AOD is 74°, also, the triangle is an isosceles triangle with OA and OD of equal length. Therefore, the sum of the angles can be written as,
y° + y° + 74° = 180°
2y° = 106°
y = 53°
Similarly, ΔBOC is an isosceles triangle with OB and OC having an equal length. Therefore, ∠OBC=∠OCB. Also, the sum of all the angles can be written as,
∠BOC + ∠OBC + ∠OCB = 180°
∠BOC + 40° + 40° = 180°
∠BOC = 100°
Hence, the value of x, y and z is 90°, 53°, and 100°, respectively.
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This graph shows the solution to which inequality?
The graph shows the solution to inequality is; y > ¹/₃x - 2
How to interpret Inequality Graphs?From the given graph, we see that the line joining the two dotted coordinates is a dashed line and as such the inequality will be less than or greater than.
Now, If a line passing through two points, then the equation of line is;
y - y1 = [(y2 - y1)/(x2 - x1)](x - x1)
Using the two given coordinates, we have;
y - (-3) = [(-1 - (-3))/(3 - (-3))](x - (-3))
y + 3 = (2/6)(x + 3)
y = ¹/₃x - 2
Since the related line is dashed and the shaded region is above the line, therefore the sign of inequality is >.
The graph shows the solution to inequality is;
y > ¹/₃x - 2
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Laila guesses on all 20 questions of a multiple-choice test. each question has 4 answer choices. what is the probability of a success and a failure for this experiment? p (success) = one-fourth; p (failure) = three-fourths p (success) = one-fourth; p (failure) = one-half p (success) = three-fourths; p (failure) = one-fourth p (success) = 1; p (failure) = 0
The probability of a success and a failure is as follows,
P(success) = one - fourth
P(failure) = three - fourth
Definition of Probability
The area of mathematics that deals with numerical representations of the likelihood that an event will occur or that a statement is true is known as Probability. An event's probability is a number between 0 and 1, where, 0 generally denotes the event's impossibility and 1 denotes certainty of that event.
Calculating the Probability
The formula for finding the probability of an event to occur is given by,
P = (favorable outcomes)÷(total number of outcomes)
Now, it is given that each multiple choice question consists of 4 choices.
And, out of these four choices, only one answer is true.
Then, if Laila guesses the answer, the probability of choosing the right answer is given by,
P(success) =1/4
Thus, the probability of choosing the wrong answer will be,
p(failure) = 1 - P(success)
⇒ P(failure) = 1 - (1/4)
⇒ P(failure) = 3/4
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Find the value of X:
Answer:
15
Step-by-step explanation:
180-150 = 30
30 = 3x-15
45 = 3x
x = 15
Find the Value of -3/7 ÷ 4
please answer fast
Answer:
Step-by-step explanation:
george drives the first 30 miles of a trip at a constant rate of 40 miles per hour. if he drives the remaining 75 milse of the trip at a constrant rate of 50 miles per hour, what is his average speed for the entire trip
His average speed for the entire trip is 46.6 mph
We have,
30 miles at 40 mph
time taken at this speed = 30/40 = 3/4 hours
..
75 miles at 50mph
time taken = 75/50 = 3/2 hours
Total time taken = 3/4 +3/2 hours=3+6 /4
=9/4 hours
Total distance traveled = 30+75 = 105 miles
Average speed = 105/ 9/4
=105*4/9
46.6 mph is the average speed.
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Evaluate each polynomial when a=3, b=5 , c=10.
1. 10a - 15
2. -5b^3 +7b+10
3. 6abc+ 4a^2
Answer:
15; -580; 936
Step-by-step explanation:
1. 10a-15=10*3-15=15
2. -5b^3+7b+10=-5*5^3+7*5+10=-580
3. 6abc+4a^2=6*3*5*10+4*3^2=936
I’m a football game the home team scored 2 times as many points as the visiting team, if the game ended with a total of 21 points. How many points did the visiting team score?
The graph above is a transformation of the function x2 Write an equation for the function graphed above
Answer: y=0,5x²-x-1,5.
Step-by-step explanation:
[tex](-1;0)\ \ \ \ (3;0)\ \ \ \ (1;-2) \ \ \ \ y=ax^2+bx+c\ ?\\\left\{\begin{array}{ccc}a*(-1)^2+b*(-1)+c=0\\a*3^2+b*3+c=0\\a*1^2+b*1+c=-2\end{array}\right \ \ \ \ \ \left\{\begin{array}{ccc}a-b+c=0\ \ (1)\\9a+3b+c=0\ (2)\\a+b+c=-2\ (3)\end{array}\right \\[/tex]
We summarize (1) and (3):
[tex]2a+2c=-2\ |:2\\a+c=-1\ \ \ \ \Rightarrow\\a+b+c=-2\\(a+s)+b=-2\\-1+b=-2\\b=-1.[/tex]
Substitute b=-1 into (2):
[tex]9a+3*(-1)+c=0\\9a-3+c=0\\9a+c=3\ \ (5).\\[/tex]
From (5) subtract (4):
[tex]8a=4\ |:8\\a=0,5.\ \ \ \ \Rightarrow\\[/tex]
Substitute a=0,5 into (4):
[tex]0,5+c=-1\\c=-1,5.[/tex]
Hense:
y=0,5x²-x-1,5.
URGENT NEED ANSWER NOWWWW!!! WORTH 27 POINTS!!!
Lauren has 108 pieces of candy leftover from Halloween. She would like to distribute them evenly to the 9 kids on her block. Write an equation to show how many pieces of candy each kid will receive.
A. 9+x=108
B. x=108-9
C. x=108/9
D. x=9/8
The equation that shoes the pieces of candy each kid would receive is x = 108 / 9.
How many pieces of candy would each kid receive?
Division is the process of dividing a number into equal parts using another number. The sign used to denote division is ÷.
Candy each kid would get = total number of candy / total number of kids
x = 108/9
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what is slope of line graped below?
The slope of the line is 1
to find the slope its rise (y value)/run (x value); the equation is
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
plugging the values from the graph into the equation:
[tex] \frac{4 - 2}{4 - 2} [/tex]
which simplifies to simply 1
HELP PLEASE. 3(2x+3)=15
If you are solving for X then we have to do a few process
What you would want most is to remove the parentheses, so to do that i would use distributive property
3*2x is 6x and 3*3 is 9 so our new equation will look like
6x+9=15 if you don't understand please tell me
now we must bring the 9 over
If you bring the 9 over than it would become negative
6x=15-9
so 6x=6
and now you can solve the answer is x=1
Answer:
The solution is x = 1
Step-by-step explanation:
3(2x+3) = 15
6x+9 = 15
6x = 15-9
6x = 6
x = 6/6
x = 1
help please!
| 2x^2 + 5x + 3 | > 0
solve the inequality
Factorize the quadratic.
[tex]2x^2 + 5x + 3 = (2x + 3) (x + 1)[/tex]
We have [tex]|ab| = |a||b|[/tex], so
[tex]|2x^2 + 5x + 3| = |2x + 3| |x + 1| > 0[/tex]
Now, both [tex]|2x+3|\ge0[/tex] and [tex]|x+1|\ge0[/tex] (since the absolute value of any number cannot be negative), so we just need to worry about when the left side is exactly zero. This happens for
[tex](2x + 3) (x + 1) = 0 \implies 2x+3 = 0\text{ or }x+1 = 0 \\\\ \implies x = -\dfrac32 \text{ or } x = -1[/tex]
So the solution to the inequality is the set
[tex]\left\{x \in \Bbb R \mid x\neq-\dfrac32 \text{ and } x\neq-1\right\}[/tex]
A store sells cards on each of which there are drawing of different flowers: either roses, either daisies, either tulips, either sunflowers. Each card also has a message "happy birthday!", Happy Holidays". Or "happy anniversary!". What is the greatest possible amount of different cards that this store sells?
The greatest number of different cards based on the permutations is 144.
How to compute the value?From the information given, there are 4 versions which are either roses, daisies, tulips, or sunflowers and this is further divided into either Happy birthday, anniversary, or holidays.
Therefore, the greatest number of different cards will be:
= 4! × 3!
= 24 × 6
= 144
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Solve each triangle – find any missing side and angle measures. Round answers to the nearest tenth.
Answer:
Step-by-step explanation:
Things we already know:
Angle B = 56 degrees
Angle C = 90 degrees
Side CB = 7 units
We need to find angle A and sides AC and AB.
We know that every triangle has its angles equal to 180 degrees
angle A + B + C = 180 degrees
angle A + 56 + 90 = 180 degrees
angle A + 146 = 180 degrees
subtract 146 from both sides.
angle A = 34 degrees
Now we know angle A.
To find side AC, we can use the tangent of theta.
The hyp (hypothenuse) = AB
The adjacent side = CB
And the opposite side = AC
The tangent of theta is the opposite side divided by the adjacent side.
[tex]tan(56) = \frac{AC}{7}[/tex]
Now we just need to solve for AC.
multiply 7 on both sides, to cancel it out on the right side.
7tan(56) = AC
10.3 = AC
Now we know the side AC.
AC = 10.3 units
To find the hypothenuse, we can use the sine, cosine, or the Pythagorean theorem.
I will choose the Pythagorean theorem, though.
[tex]7^{2} +10.3^{2} =AB[/tex]^2
49 +106.09 = AB^2
AB = 155.09 units^2
AB = 12.4 units
And now we know everything about this triangle.
A = 34 degrees
C = 90 degrees
B = 56 degrees
AC = 10.3 units
CB = 7 units
AB = 12.4 units
Hope I Helped!
(a) Work out
8 × 1/1/1
x
3
Give your answer as a mixed numbers
Answer:
well.. 1/1/1 would be 1.
8 x 3 = 24
24x 1 = 24
sooo the answer would be 24...
Step-by-step explanation:
The product of the given expression 8 × 1/1/1 x 3 would be equal to 24.
What are proper and improper fractions and how to convert mixed fraction to simple fraction?When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction.
A proper fraction is also called fraction which is less than 1.
And an improper fraction is ≥ 1
A mixed fraction contains a sum of whole number and a proper fraction.
We know that 1/1/1 would be 1.
So,
8 x 3 = 24
24x 1 = 24
Thus, the answer would be 24.
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Solve the proportion.
3/6 = 7/d
To solve this proportion:
[tex]\frac{3}{6} =\frac{7}{d}[/tex]
Simplify 3/6, it reduces to 1/2
[tex]\frac{1}{2} =\frac{7}{d}[/tex]
Then do the Criss cross method
1d = 7 ×2
d=14
Hope it helps!
Answer:
d = 14
Step-by-step explanation:
We can use cross products to solve the proportion
3/6 = 7/d
3*d = 7*6
3d = 42
Divide each side by 3
3d/3 = 42/3
d = 14
help please!!! need it asap
no wrong answers
Displacement at t = 0 :
x = 4 cos(π (0) + π/4)x = 4 cos(π/4)x = 4 × 1/√2x = 2√2 metersDisplacement at t = 1 :
x = 4 cos (π (1) + π/4)x = 4 cos (π + π/4)x = -4 cos(π/4) [∴ cos is negative in the interval (π, 3π/2)x = -4 × 1/√2x = -2√2 metersDisplacement between t = 0 and t = 1 :
-2√2 - 2√2[tex]\boxed {-4\sqrt{2}}[/tex]∴ The displacement between t = 0 and t = 1 is -4√2 meters.
Answer:
[tex]-4\sqrt{2} m[/tex]
Step-by-step explanation:
Similar question to the previous one you asked, and I swear I will not make the same mistake again :)
First we will find the displacement at t = 0 and t = 1 to find both displacements.
t = 0,
[tex]x(0)=4cos(\pi (0)+\frac{\pi }{4} )=4cos(\frac{\pi }{4} )\\=4(\frac{\sqrt{2} }{2} )\\=2\sqrt{2} m[/tex]
t = 1,
[tex]x(1)=4cos(\pi (1)+\frac{\pi }{4} )=4cos(\pi +\frac{\pi }{4} )\\=4(-\frac{1}{\sqrt{2} } )\\=-\frac{4}{\sqrt{2} }[/tex]
Total Displacement = Final Position - Initial Position
= x(1) - x(0)
= [tex]-\frac{4}{\sqrt{2} } -2\sqrt{2} \\=-4\sqrt{2} m[/tex]
Add: -8x8+ (-3x8 + 3)
Answer:
-11x^8 + 3
Step-by-step explanation:
-8x^8 + (-3x^8 + 3)
-8x^8 - 3x^8 + 3
-11x^8 + 3
How many square meters are there in a floor that is 9 meters long by 14 meters wide?
Answer:
126 sq. meters
Step-by-step explanation:
A = lw
= 9(14)
= 126 sq. meter
Select the correct answer. What are the zeros of the graphed function? A polynomial function graph where the solid line intersects X-axis on origin (0, 0), (2, 0) and (4, 0). The same line intersects Y-axis at (0.5, 4) and (3.5, 4) A. 0 and 4 B. -4, -2, and 0 C. 0, 2, and 4 D. -4 and 0
Considering the situation described, the zeros of the function are given by:
C. 0, 2, and 4.
What are the zeros of a function f(x)?The zeros of a function are the values of x when f(x) = 0, and can also be described as the values of x for which the line intersects the x-axis.
In this problem, the line intersects the x-axis at x = 0, x = 2, and x = 4, hence option C is correct.
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Can someone help me? It’s 7th grade geometry
The area, in square centimeters, of the shaded quarter of the circle is π cm² OR 3.14 cm²
Calculating the area of a sectorFrom the question, we are to determine the area of the shaded quarter of the circle
The shaded quarter of the circle is a sector.
The area of a circle is given by the formula,
[tex]A = \frac{\theta}{360^\circ}\times \pi r^{2}[/tex]
Where A is the area
θ is the angle subtended
and r is the radius
First, we will calculate the radius of the circle
The radius of the circle equals the length of a side of the square.
From the given information,
Area of the square = 4 cm²
∴ s² = 4 cm²
s =√4 cm²
s = 2 cm
∴ A side of the square is 2 cm in length
Thus,
r = 2 cm
and
θ = 90°
Then,
[tex]A = \frac{90^\circ}{360^\circ}\times \pi \times 2^{2}[/tex]
[tex]A = \frac{1}{4}\times \pi \times4[/tex]
[tex]A = \pi \ cm^{2}[/tex] OR 3.14 cm²
Hence, the area, in square centimeters, of the shaded quarter of the circle is π cm² OR 3.14 cm²
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The point P(6, –1) is translated according to the rule (x, y) → (x – 5, y – 2).
What are the coordinates of P'?
P’(1, 2)
P'(1, 1)
P'(1, –3)
P'(4, 4)
The resulting point by considering that P(x, y) = (6, - 1) and P'(x, y) = P(x, y) + (- 5, - 2) is equal to the coordinates P'(x, y) = (1, - 3). (Right choice: C)
How to determined a resulting point by translation
In this question we need to determine the new location of a point by using a translation formula. Translations are rigid transformations in which a point is translated on a Cartesian plane. We have the following formula:
P'(x, y) = P(x, y) + (- 5, - 2) (1)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointIf we know that P(x, y) = (6, - 1), then the resulting point is:
P'(x, y) = (6, - 1) + (- 5, - 2)
P'(x, y) = (1, - 3)
The resulting point by considering that P(x, y) = (6, - 1) and P'(x, y) = P(x, y) + (- 5, - 2) is equal to the coordinates P'(x, y) = (1, - 3). (Right choice: C)
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Answer:
c
Step-by-step explanation:
Question 3 of 10
Use the quadratic formula to find both solutions to the quadratic equation
given below.
2x² + 3x-5=0
A. x = 1
B. x=-1
C.
D. x==2
E.
F.
x==2
X
=
+√8
x = 3-1
SUBMIT
Step-by-step explanation:
[tex]therefore \: x = 1[/tex]
The roots of the quadratic equation 2x² + 3x - 5 = 0 are [tex]\frac{-5}{2}[/tex] and 1.
A quadratic equation is an equation of the form ax² + bx + c = 0. It is a polynomial with degree 2. In this equation, a is the coefficient of x², b is the coefficient of x, and c is the constant term.
The given quadratic equation is 2x² + 3x - 5 = 0.
Use the quadratic formula, also known as the Shreedharachrya formula to find the roots of the given equation:
[tex]x = \dfrac{-b\ \pm\ \sqrt{b^2-4ac}}{2a}[/tex]
[tex]= \dfrac{-3\ \pm\ \sqrt{3^2-4\times2\times(-5)}}{2\times 2}\\= \dfrac{-3\ \pm\ \sqrt{9+40}}{4}\\\\= \dfrac{-3\ \pm\ \sqrt{49}}{4}\\= \dfrac{-3\ \pm\ 7}{4}[/tex]
[tex]x = \dfrac{-3-7}{4}[/tex] or [tex]x = \dfrac{-3+7}{4}[/tex]
[tex]x = \dfrac{-10}{4}[/tex] or [tex]x = \dfrac{4}{4}[/tex]
[tex]x = \dfrac{-5}{2}[/tex] or [tex]x = 1[/tex].
Hence, the roots of the given quadratic equation are [tex]\frac{-5}{2}[/tex] and 1.
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Do all these angles equal 360 degrees?
Answer:
The sum of the interior angles of any quadrilateral is 360 °Step-by-step explanation:
Do all these angles equal 360 degrees?
The sum of the interior angles of any quadrilateral is 360 °
what would not be a step in solving 18=2(4+x)
Step-by-step explanation
Well you gave no answer choices so here are the steps and maybe you can just find out which one isn't here :)
18=2(4+x) first multiply 2 into 4+x
18=8+2x then subtract 8 from the other side
10=2x divide both sides by 2
x=5
Best of luck <3
Multiply Conjugates Using the Product of Conjugates Pattern
In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern
334. (9c − 2d)(9c + 2d)
Answer:
The product is the difference of squares is [tex]$$(9c-2d)(9c+2d)=81{{c}^2}-4{{d}^2}$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (9c-2d)(9c+2d).We have to multiply the given expression.Square the first term 9c. Square the last term 2d.[tex]$$\begin{aligned}&(9 c-2 d)(9 c+2 d)=(9 c)^{2}-(2 d)^{2} \\&(9 c-2 d)(9 c+2 d)=81 c^{2}-4 d^{2}\end{aligned}$$[/tex]
9 out of 20 students who graduate from J. H. S. of 1,2000 students gained admission to S. H. S. How many students gained admission?
540 students gained admission
How to determine the number of students?The given parameters are:
Students = 1200
Proportion that gain admission. p = 9/20
The number of student that gain admission is calculated as:
Admission = p * Students
So, we have:
Admission= 9/20 * 1200
Evaluate
Admission= 540
Hence, 540 students gained admission
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I NEED THIS FAST! :(
What was the original price of the sneakers?
Answer:
n=45
Step-by-step explanation:
[tex]n=\dfrac{54.100}{120} \\\\n=45[/tex]
Which equation represents a line that passes through (–2, 4) and has a slope of 2/5
Equation of a line is given by y - y1 = m(x - x1); where m is the slope.
y - 4 = 2/5 (x - (-2))
y - 4 = 2/5 (x + 2)
Hope this helps! :)
Answer:
Step-by-step explanation:
y = 2/5x + p
We now that passes through (–2, 4)
2/5 × (-2) + p = 4
⇔ -4/5 + p = 4
⇔ p = 4 + 4/5
⇔ p = 20/5 + 4/5
⇔ p = 24/5
⇒ y = 2/5x + 24/5
Let a, b, and c be positive integers that form a geometric sequence. Given that a has 3 factors and c has 9 factors, how many factors can b have, at most?
Answer choices: 14, 9, 6, 8, 10.
DO NOT ATTEMPT IF YOUR NOT 98% SURE
Answer:
9
Step-by-step explanation:
it’s clear that a ,b and c are in geometric progression.
Then we have :
a
b = q×a
c = q²×a
also , b² = a×c
………………………
NOTE : b² and b have the same factors
also ,since b² = a×c then b and a×c
have the same number of factors.
_______________________________
Since c = q²×a then any factor of a is also a factor of c
Which means the number of factors of a×c
is equal to the number of factors of c.
Therefore b at most has the same number of factors as c.
Conclusion:
at most b has 9 factors.
……………………
As a side note :
You can take as example the numbers 3 , 30 , 300.
3 ——-> 1 factor
30 = 3×5×2 ——-> 3 factors
300 = 3 × 5² × 2² ——-> 3 factors