Use the diagram below to answer the following questions.
The value of x is
The measure of 1 is
The measure of 2 is
The measure of 3 is
The measure of 4 is
The measure of 5 is
The measure of 6 is
The measure of 7 is
The measure of 8 is
Answer:
The value of x is 24. The measures of angles 1,2,3,4,5,6,7,8 are 101, 79, 101, 101, 79, 79, 89, 89 respectively.
Step-by-step explanation:
If two line intersect each other, then vertical opposite angles are same.
[tex]3x+19=5x-29[/tex] (Vertical opposite angles)
[tex]19+29=5x-3x[/tex]
[tex]48=2x[/tex]
Divide both sides by 2.
[tex]24=x[/tex]
The value of x is 24.
Measure of angle 2 is
[tex]\angle 2 =3x+7=3(24)+7=79[/tex] (Vertical opposite angles)
The measure of angle 2 is 79°.
Measure of angle 1 is
[tex]\angle 1 =180-\angle 2=180-79=101[/tex] (Angle 1 and 2 are supplementary angles)
The measure of angle 1 is 101°.
Measure of angle 3 is
[tex]\angle 3 =180-\angle 2=180-79=101[/tex] (Angle 3 and 2 are supplementary angles)
The measure of angle 3 is 101°.
Measure of angle 4 is
[tex]\angle 4 =4x+5=4(24)+5=101[/tex] (Vertical opposite angles)
The measure of angle 4 is 101°.
Measure of angle 5 is
[tex]\angle 5 =\angle 2=79[/tex] (Alternate Interior Angles)
The measure of angle 5 is 79°.
Measure of angle 6 is
[tex]\angle 5 =\angle 6=79[/tex] (Vertical opposite angles)
The measure of angle 6 is 79°.
Measure of angle 7 is
[tex]\angle 7 =180-(5x-29)=180-(5(24)-29)=89[/tex] (Supplementary angles)
The measure of angle 7 is 89°.
Measure of angle 8 is
[tex]\angle 8 =\angle 7=89[/tex] (Vertical opposite angles)
The measure of angle 8 is 89°.
An experiment consists of rolling two fair(not weighted) dice and adding the dots on the two sides facing up. Each die has the number 1 on two opposite faces, the number 2 on two opposite faces, and the number 3 on two opposite faces.
Compute the probability of obtaining the indicated sums in problem.
Final answer:
The student is performing a probability calculation involving rolling two dice and must enumerate all possible outcomes. The probability of a specific sum is determined by dividing the number of ways to achieve that sum by the total number of possible outcomes, 36 in the case of rolling two dice.
Explanation:
The student's experiment consists of rolling two fair dice and adding the numbers that appear on the faces that land upwards. Each die in this scenario has the numbers 1, 2, and 3 on two opposite faces. When calculating the probability of specific sums resulting from this experiment, we need to consider all the possible outcomes (the sample space) and the number of ways to achieve the sum in question.
To find the probability of any particular sum, one must enumerate each distinct way that sum can occur. There are a total of 36 possible outcomes when rolling two dice (6 outcomes per die × 2 dice). For example, to calculate the probability of getting a sum of 4, we need to consider the possible dice combinations (1+3, 2+2, 3+1) that would result in that sum.
As for the probability of an event, it is the number of favorable outcomes over the total number of possible outcomes. If the event is 'rolling a sum of 4', and there are three combinations out of 36 total that yield that sum, the probability would be 3/36 or 1/12. Remember that we must count each die distinctly; although the numbers are the same (1, 2, 3), a roll of 1 on the first die and 3 on the second die is a different outcome from a roll of 3 on the first die and 1 on the second die.
What is the exact circumference of the circle?
A. 10π feet
B. 20π feet
C. 40π feet
D. 60π feet
circumference of a circle= pi multiplied by the diameter
= 20ft x pi
=20 pi feet so the answer is b
All real numbers that are less then -3 or greater then or equal to 5
What is the exact value of the expressions the square root of 180. − the square root 125. + the square root of 5.? Simplify if possible.
A) 2the square root of 2.
B) 12the square root of 2.
C) 2the square root of 5.
D) 12the square root of 5.
Answer:
[tex]2\sqrt{5}[/tex]
C is the correct option.
Step-by-step explanation:
The given expression is [tex]\sqrt{180}-\sqrt{125}+\sqrt{5}[/tex]
In order to simplify the expression, we find the factors.
180 =6 ×6×5
125 = 5 ×5×5
Hence, we can rewrite the expression as
[tex]\sqrt{6\times6\times5}-\sqrt{5\times5\times5}+\sqrt{5}[/tex]
We can further write this expression as
[tex]\sqrt{6^2\times5}-\sqrt{5^2\times5}+\sqrt{5}[/tex]
Now, we can use the rule [tex]\sqrt{x^2}=x[/tex]
[tex]6\sqrt{5}-5\sqrt{5}+\sqrt{5}[/tex]
Finally, we can combine these like terms
[tex]2\sqrt{5}[/tex]
Hence, C is the correct option.
This table shows the input and output values for an exponential function f(x)
What are the ratios of outputs for any two inputs that are 1 apart?
A. 1/2
B. 4
C. 1/8
D. 2
x −3, −2, −1, 0, 1, 2, 3
f(x) 1/256, 1/64, 1/16, 1/4, 1, 4, 16
Answer:
B. 4
Step-by-step explanation:
This table that shows the input and output values for an exponential function f(x) is,
x -3 -2 -1 0 1 2 3
f(x) 1/256 1/64 1/16 1/4 1 4 16
Taking [tex]x=2[/tex] and [tex]x=3[/tex] as input (because they are 1 apart), the ratio of output is,
[tex]=\dfrac{f(3)}{f(2)}[/tex]
[tex]=\dfrac{16}{4}[/tex]
[tex]=4[/tex]
Answer:
The correct answer is B. 4
Step-by-step explanation:
Find the range of y = 3cos4x - 2. -5 ≤ y ≤ 5 -5 ≤ y ≤ 1 -3 ≤ y ≤ 3 1 ≤ y ≤ 3
Answer:
{y|−5≤y≤1}
Step-by-step explanation:
The range of the function is y ∈ [-5, 1] or -5 ≤ y ≤ 1 if the function is y = 3cos4x - 2 option second is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
y = 3cos4x - 2
As we know, cosx ∈ [-1, 1]
-1 ≤ cosx ≤ 1
-1 ≤ cos4x ≤ 1
-3 ≤ 3cos4x ≤ 3
-5 ≤ 3cos4x - 2 ≤ 1
-5 ≤ y ≤ 1
Thus, the range of the function is y ∈ [-5, 1] or -5 ≤ y ≤ 1 if the function is y = 3cos4x - 2 option second is correct.
Learn more about the function here:
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how many solutions does the system of equations have 2x = -10y + 6 and x + 5y = 3
The equation x2 – 1x – 90 = 0 has solutions {a, b}. What is a + b?
Answer:
The value of a+b is 1.
Step-by-step explanation:
The given equation is
[tex]x^2-1x-90=0[/tex]
It is given that this equation has two solutions {a,b}.
First of all find the factors of given equation. The middle term can be written as -10x+9x.
[tex]x^2-10x+9x-90=0[/tex]
[tex](x^2-10x)+(9x-90)=0[/tex]
Taking out common from each parenthesis.
[tex]x(x-10)+9(x-10)=0[/tex]
[tex](x-10)(x+9)=0[/tex]
Using zero product property, we get
[tex]x-10=0\Rightarrow x=10[/tex]
[tex]x+9=0\Rightarrow x=-9[/tex]
The value of a is 10 and b is -9. The sum of both the solutions is
[tex]a+b=10-9=1[/tex]
Therefore the value of a+b is 1.
p and q are prime numbers. p3 x q = 56. Find p and q.
Which of the following statements is true?
A.A radius is always a chord.
B.A tangent is always a secant.
C.A diameter is always a chord.
D.A chord is always a diameter.
scores on a test are normally distributed with a mean fo 69.2 and a standard deviation of 9.4, find p81
The length of the rectangle is 2(x+1) meters and the perimeter is 60 meters. Find the length of the rectangle
State the y-coordinate of the y-intercept for the function below.
ƒ(x)=x^3-x^2-x+1 ...?
Answer:
1
Step-by-step explanation:
Answer is 1 for Apex Precal
Mary baked 21 cookies on saturday and twice that many on sunday for a school fundraiser. 4 cookies fell on the ground and had to be thrown out. if she packaged 3 cookies to a bag, how many cookies were left over?
Will upvote and tip
A smart phone costs $149.99 before tax. The tax on the smart phone is 7%.
What is the total cost of the smart phone?
Round your answer to the nearest cent.
Answer/Step-by-step explanation:
149.99+(149.99*0.07)=160.4893. Round to $160.49
I don't really know how to do this and I have to explain to my class how I got my answer. Help me!!!
30inches increased by 30 percent
Which statement correctly describes a kite
A movie theater charges $11 for each adult and $6 for each ticket. one day, they sold 163 tickets and made $1578. How many of each ticket did they sell?
The movie theater sold 117 adult tickets and 46 child tickets.
Explanation:To solve this problem, we can set up a system of equations. Let's say the number of adult tickets sold is x and the number of child tickets sold is y. We can then write two equations based on the given information:
x + y = 163 (equation 1, representing the total number of tickets sold)11x + 6y = 1578 (equation 2, representing the total amount earned)We can solve this system of equations by either substitution or elimination. Let's use elimination:
Multiply equation 1 by 6 to make the coefficients of y in both equations equal:6x + 6y = 978
Subtract equation 1 from equation 2 to eliminate y:(6x + 6y) - (11x + 6y) = 978 - 163
-5x = -585
Divide by -5:
x = 117
Substitute x back into equation 1 to find y:117 + y = 163
y = 163 - 117
y = 46
Therefore, 117 adult tickets and 46 child tickets were sold.
What is 3/4 x 2/3 in simplest form?
Please help !!
Answer correct for a brainliest and also a thanks ! Don't answer if you don't know it .
which of the following is the correct factorization of the polynomial below?
27x^3+64
a) (3x+4)(9x^2-12x+16)
b) (9x+8)(3x^2-16x+8)
c) (3x^2+8)(9x-16x+8)
d) the polynomial is irreducible
...?
Answer:
a) (3x+4)(9x^2-12x+16)
Step-by-step explanation:
A parallelogram has a base that measures 5 units and a height that measures (x + 6) units. The area of this parallelogram is 20 square units. What must be the value of x?
Choose one answer.
a. x=4
b. x=-2
c. x=5
d. x=15
To solve for 'x' in the parallelogram area equation, we multiplied the given base (5 units) by the height (x + 6 units) and set it equal to the given area (20 square units). After simplifying, we found that x must be -2 to satisfy the equation 5x + 30 = 20.
Explanation:The question presented is a typical algebra problem where we need to find the value of 'x' in the context of the area of a parallelogram. The base of the parallelogram is given as 5 units and its height is given as (x + 6) units, with the total area given as 20 square units. Since the formula for the area of a parallelogram is base × height, we can set up the equation 5 × (x + 6) = 20 to find the value of x.
Now, we will solve for x:
Multiply the base by the height: 5(x + 6) = 20.Distribute the 5: 5x + 30 = 20.Subtract 30 from both sides to solve for x: 5x = -10.Divide both sides by 5 to find x: x = -2.Hence, the correct answer is b. x=-2.
A 1250-kg slippery hippo slides down a mud-covered hill inclined at an angle of 18º to the
horizontal. If the coefficient of sliding friction between the hippo and the mud is 0.0900, what
force of friction impedes the hippo’s motion down the hill? ...?
Solve each compound inequality. Graph the solution
Help explain step by step
4x<=12and-7x<=21
Three identical coins, labeled A, B, and C in the figure, lie on three corners of a square 10.0 cm on a side. Determine the x coordinate of each coin, xA, xB, and xC. (See figure.)
The [tex]x[/tex] coordinates of the point A is [tex]\boxed{\bf 0}[/tex].
The [tex]x[/tex] coordinates of the point B is [tex]\boxed{\bf 0}[/tex].
The [tex]x[/tex] coordinates of the point C is [tex]\boxed{\bf 10}[/tex].
Further explanation:
Given:
The coin labeled as A lies on the [tex]y[/tex]-axis.
The coin labeled as B lies on the origin.
The coin labeled as C lies on the [tex]x[/tex]-axis.
The distance of the point B and C is [tex]10\text{ cm}[/tex].
Concept used:
The point which lies on the [tex]x[/tex]-axis, the value of its [tex]y[/tex]-coordinate is [tex]0[/tex].
The point which lies on the [tex]y[/tex]-axis, their [tex]x[/tex]-coordinate is [tex]0[/tex].
The coordinate of the origin is [tex](0,0)[/tex].
Calculation:
The coin labeled as A lies on the [tex]y[/tex]-axis therefore the [tex]x[/tex]-coordinate of the point is [tex]0[/tex].
The coin labeled as B lies on the origin therefore the [tex]x[/tex]-coordinate of the point is [tex]0[/tex].
The distance from point B to the point C is [tex]10\text{ cm}[/tex] and the coin labeled as C lies on the x axis it means that the [tex]x[/tex]-coordinate of the point is [tex]10[/tex].
Therefore, the [tex]x[/tex] coordinate of the point A is [tex]0[/tex].
The [tex]x[/tex] coordinate of the point B is [tex]0[/tex].
The [tex]x[/tex] coordinate of the point C is [tex]10[/tex].
Learn more:
1. Coordinate of the point : https://brainly.com/question/1286775
2. Equation: https://brainly.com/question/1473992
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Coordinate geometry
Keywords: Coordinate geometry, x-axis, y-axis, x-coordinate, y-coordinate, coin, square, three corners, three identical coins.
Faith is 1/5 get morthers age. their combined ages are 30. how old is faith
What are the factor pairs of 23?
Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 2.4 h, and Car B traveled the distance in 4 h. Car A traveled 22 mph faster than Car B.
How fast did Car A travel?
_____mph