Answer:
x=100º
Step-by-step explanation:
The two angles are vertical angles, so they are congruent.
The solution to -12 + n = -15 is n = 3. true or false
Answer:
False
Step-by-step explanation:
Step 1: Write out equation
-12 + n = -15
Step 2: Add 12 on both sides
n = -3
So our answer is -3 and not 3.
Answer: \(False\)
The answer to this problem is \(n=-3\)
To get -3 here is the work shown
Simplify both sides of the equation
\(n-12=-15\)
Add 12 to both sides
\(n-12+12=-15+12\\n=-3\)
Choose all of the transformations that are rigid motions.
Answer:
The answer is below
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, dilation and rotation.
Rigid transformations are transformation that produces an image with the same size, shape and angle as the original object. Rigid transformations are translation, rotation and reflection.
Dilation is not a rigid transformation.
All the transformations attached are rigid transformations.
If f(x)=2x-3x^2 what is f(2)
f(2) is -8
According to the question,
Given that,
f(x)=2x-3x^2
Substitute x = 2 into f(x) = 2x-3x^2
f(2)=2x-3x^2
f(2)=2x2 - 3x \(2^{2}\)
f(2)= 4 - 3 x 4
f(2)= 4 - 12
f(2)= - 8
In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.
Example of an Equation:
4y + 2 = 18
4×2 + 3x − 28 = 0
9m = 49.5
Equation Types
Algebra considers two prominent families of equations, namely polynomial equations and linear equations. Polynomial equations with one variable can be written in P(x) = 0, where P is a polynomial, and ax + b = 0 is the general form of linear equations. Here, a and b are parameters. We can practice geometric or algorithmic methods from linear algebra or mathematical analysis to solve these equations. Also, there are different types of equations, such as:
Linear equations
Quadratic equations
Cubic equations
Quartic equations
Differential equations
Parametric equations
Equation of a line
The standard form of the equation of a line is A x + By + C = 0. The slope-intercept form of an equation is y = mx + b, where m is the slope of the line and b is the y-intercept. However, there are various types of equations to represent lines.
Equation of x-axis
Generally, we say that the equation of the x-axis equation is of the form y = 0. However, we can also write the x-axis equation as x = c where c is constant.
The x-axis comprises all the real values of x, although the value of y is equal to 0 on the complete x-axis.
Thus, x can be recognised as constant and y as 0.
In the coordinate system representation, we can represent any point on the x-axis as (c, 0), where c is any real number.
Therefore, the x-axis formula will be x= c + y
Here,
c = constant
y = 0
The x-axis formula is x = c, where c is constant.
Equation in One Variable
The equation in one variable means the equation containing only one variable. Let’s have a look at the below equations.
17 – 9 = 8
x + 4 = 4y + 22z
4x2 + 3x – 7 = 0
The three examples above represent equations that propose equality (could be true or not) between two expressions.
The first equation does not contain any variable.
The second equation has three different variables, such as x, y and z. Thus, it is a multivariate equation.
The third equation contains only one variable, i.e. x.
learn more about equation here : brainly.com/question/10413253
SPJ9
please help me with number 6 ....
The area of the given triangle is 24 square inches.
As per the shown triangle, the height is 4 inches and the base is 12 inches.
The area of a triangle can be found by multiplying the base by the height and dividing by 2.
So, the area of the triangle is:
The area of a triangle = (base x height) / 2
The area of a triangle = (12 inches x 4 inches) / 2
The area of a triangle = (48 inches) / 2
The area of a triangle = 24 square inches
Therefore, the area of the triangle is 24 square inches.
Learn more about the triangle here:
brainly.com/question/2773823
#SPJ1
How to find a coterminal angle between 0 and 360° ?
A coterminal angle is an angle that has the same initial side and terminal side as a given angle. The difference between the angle and the coterminal angle is a multiple of 360 degrees.
The following steps can be used to find a coterminal angle between 0 and 360 degrees:
Step 1: Identify the given angle. Let's assume that the given angle is 100 degrees.
Step 2: Add or subtract multiples of 360 degrees to the given angle to obtain a new angle that has the same initial and terminal sides. To obtain the angle that is between 0 and 360 degrees, add or subtract 360 degrees from the angle until the result is between 0 and 360 degrees.There are two ways to do this.
The first method is to add or subtract multiples of 360 until the result is between 0 and 360 degrees. The second method is to divide the given angle by 360 degrees and then multiply the quotient by 360 degrees.
The first method:Subtract 360 degrees from 100 degrees to get -260 degrees. Add 360 degrees to -260 degrees to get 100 degrees, which is between 0 and 360 degrees. Therefore, 100 degrees and 460 degrees are coterminal angles between 0 and 360 degrees.
The second method:Divide 100 degrees by 360 degrees to get a quotient of 0.27777777778. Multiply 0.27777777778 by 360 degrees to obtain 100 degrees, which is between 0 and 360 degrees.
Therefore, 100 degrees and 460 degrees are coterminal angles between 0 and 360 degrees.
For more such questions on angle
https://brainly.com/question/25716982
#SPJ11
Select the coff
A company that bottles mustard is allowed to advertise their bottle size as 21 ounces as long as the actual amount in the bottle is within
0.15 ounces of that amount. Which inequality shows all the possible actual bottle volumes (1) that the manufacturer would be able to advertise
as 21 ounces?
Answer:
d
Step-by-step explanation:
v+21
\(v + 21 \leqslant 0.15\)
The inequality is v+ 21 ≤ 0.15
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
A company that bottles mustard is allowed to advertise their bottle size as 21 ounces as long as the actual amount in the bottle is within 0.15 ounces of that amount.
So,
if the volume is v then the situation can be represented as
v+ 21 ≤ 0.15
As, the actual amount is within 0.15 ounces of that amount.
Learn more about inequality here:
https://brainly.com/question/20383699
#SPJ2
Fill in the missing number. 11 + __ = 91
Answer:
80
Step-by-step explanation:
why do you keep asking these questions that anyone can answer
Answer:
80
Step-by-step explanation:
91 - 11 = 80
80 + 11 =91
In the result x2(3) = 8.4, p < 0.05, what is x2? significance level chi square critical value degrees of freedom
The 3 represent the degree of the freedom in the given equation.
According to the statement
we have to find that the in the given statement the digit is 3 is represented the term and we have to find that term.
So, For this purpose, we know that the
The given statement is:
X^2(3) = 8.4, p < .05,
From this it is clear that the
Degrees of freedom refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample.
This represent the independent values in the given statement also.
So, The 3 represent the degree of the freedom in the given equation.
Learn more about Degrees of freedom here
https://brainly.com/question/17305237
Disclaimer: This question was incomplete. Please find the full content below.
Question:
In the result X^2(3) = 8.4, p < .05, what is 3 represent from the given questions?
a. the observed value
b. the critical value
c. the significant level
d. degrees of freedom
#SPJ4
solve 6 X + 1 / 3+1=×-3/6
find the area under y = 2x on [0, 3] in the first quadrant. explain your method.
The area under the curve y = 2x on the interval [0, 3] in the first quadrant is 9 square units.
To find the area under the curve y = 2x on the interval [0, 3] in the first quadrant, we can use the definite integral.
The integral of a function represents the signed area between the curve and the x-axis over a given interval. In this case, we want to find the area in the first quadrant, so we only consider the positive values of the function.
The integral of the function y = 2x with respect to x is given by:
∫[0, 3] 2x dx
To evaluate this integral, we can use the power rule of integration, which states that the integral of x^n with respect to x is (1/(n+1)) * x^(n+1).
Applying the power rule, we integrate 2x as follows:
∫[0, 3] 2x dx = (2/2) * x^2 | [0, 3]
Evaluating this definite integral at the upper limit (3) and lower limit (0), we have:
(2/2) * 3^2 - (2/2) * 0^2 = (2/2) * 9 - (2/2) * 0 = 9 - 0 = 9
Therefore, the area under the curve y = 2x on the interval [0, 3] in the first quadrant is 9 square units.
Visit here to learn more about area brainly.com/question/1631786
#SPJ11
What is
\( 6 \frac{1}{3} \div \frac{1}{6} \)
equal to?
options:
A. 6
B. 9
C. 12
D. 19
E. 38
Answer:
The answer is E, 38.
Step-by-step explanation:
6×1/3 can be written as 19/3.
Use the reciprocal of 1/6, which is 6, and multiply 19/3 and 6.
6 and 3 can be simplified with 2.
So: 19 × 2, which is 38.
Step-by-step explanation:
please it my steps to work on paper whorksheet
F = 9 over 5C + 32 solve for C
I'm not sure what you're asking here
Step-by-step explanation:
\( \frac{9}{5c} + 32 = f\)
\( \frac{9}{5c + 32} = f\)
Assuming the former
\( \frac{9}{5c} + 32 = f \\ \frac{9}{5c} = f - 32 \\ \frac{9}{5} = c(f - 32) \\ c = \frac{9}{5(f - 32)} \)
Assuming the latter
\( \frac{9}{5c + 32} = f \\ 9 = f(5c + 32) \\ 9 = 5cf + 32f \\ 9 - 32f = 5cf \\ \frac{9 - 32f}{5f} = c\)
What is a factor of p(x)=x^3-3x^2-2x+4
Answer:
\(p(x) = x^3-3x^2-2x+4\)
\(p(x) = (x-1)(x^2-2x-4)\)
A consumer group tested 11 brands of vanilla yogurt and found the numbers below for calories per serving.
a) Check the assumptions and conditions.
b) A diet guide claims that you will get an average of 120 calories from a serving of vanilla yogurt. Use an appropriate hypothesis test to comment on their claim.
130 165 155 120 120 110 170 155 115 125 90
a) The independence assumption _____ been violated, and the Nearly Normal Condition ______ justified. Therefore, using the Student-t model for inference been violated, _____ reliable.
b) Write appropriate hypotheses for the test.
H0: ___
НА: ___
The test statistic is t = ____
(Round to two decimal places as needed.)
The P-value is ___
(Round to three decimal places as needed.)
In the question, the independence assumption may have been violated, while the Nearly Normal Condition is likely justified. Therefore, the use of the Student-t model for inference may be unreliable.
a) In order to perform a hypothesis test on the claim made by the diet guide, we need to assess the assumptions and conditions required for reliable inference. The independence assumption states that the observations are independent of each other. In this case, it is not explicitly mentioned whether the yogurt samples were independent or not. If the samples were obtained from the same batch or were not randomly selected, the independence assumption could be violated.
Regarding the Nearly Normal Condition, which assumes that the population of interest follows a nearly normal distribution, it is reasonable to assume that the distribution of calorie counts in vanilla yogurt is approximately normal. However, since we do not have information about the population distribution, we cannot definitively justify this condition.
b) The appropriate hypotheses for testing the claim made by the diet guide would be:
H0: The average calories per serving of vanilla yogurt is 120.
HA: The average calories per serving of vanilla yogurt is not equal to 120.
To test these hypotheses, we can use a t-test for a single sample. The test statistic (t) can be calculated by taking the mean of the sample calorie counts and subtracting the claimed average (120), divided by the standard deviation of the sample mean. The p-value can then be determined using the t-distribution and the degrees of freedom associated with the sample.
Without the actual sample mean and standard deviation, it is not possible to provide the specific test statistic and p-value for this scenario. These values need to be calculated using the given data (calorie counts) in order to draw a conclusion about the claim made by the diet guide.
Learn more about hypothesis test here:
https://brainly.com/question/17099835
#SPJ11
Solve for x in the equation 3x^2-18x+5=47
Answer:
x=3±√23thats the answer ^^
Step-by-step explanation:
plz give me brainlyest i need it
Answer:
Option 1
Step-by-step explanation:
\(3 {x}^{2} - 18x + 5 = 47\)
\( = > 3 {x}^{2} - 18x + 5 - 47 = 0\)
\( = > 3 {x}^{2} - 18x - 42 = 0\)
\( = > 3( {x}^{2} - 6x - 14) = 0\)
\( = > {x}^{2} - 6x - 14 = 0\)
We know that
\(x = \frac{ - b + \sqrt{d} }{2a} \: or \: \frac{ - b - \sqrt{d} }{2a} \)
Where D = Discriminant of the eqn.
Discriminant of the above eqn.=
\( {b}^{2} - 4ac = {( - 6)}^{2} - 4 \times ( - 14) \times 1 = 92\)
So,
\(x = \frac{ - ( - 6) + \sqrt{92} }{2 \times 1} \: or \: \frac{ - ( - 6) - \sqrt{92} }{2 \times 1} \)
\( = > x = \frac{6 + 2 \sqrt{23} }{2} \: or \: \frac{6 - 2 \sqrt{23} }{2} \)
\( = > x = (3 + \sqrt{23} ) \: or \: (3 - \sqrt{23} )\)
What is the expanded form of this number?
14. 702
a(1×10)+(4×1)+(7×110)+(2×11,000)
b(1×10)+(4×1)+(7×1100)+(2×11,000)
c(1×10)+(4×1)+(7×110)+(2×1100)
d(1×10)+(4×1)+(7×1100)+(2×1100)
did the answer asap
The expanded form of the number 14.702 is given by the option B: (1 × 10) + (4 × 1) + (7 × 1000) + (2 × 10,000).
Expanded form of a number means representing a number as a sum of its place value. Each digit in a number represents a value of its place.
Let's consider the number 14.702.
Here, 1 is in the tens place, 4 is in the ones place, 7 is in the thousands place, 0 is in the hundreds place, and 2 is in the ten thousands place.
Therefore, the expanded form of 14.702 would be:
1 × 10 + 4 × 1 + 7 × 1000 + 2 × 10,000
= 10 + 4 + 7,000 + 20,000= 14,010
So, the expanded form of 14.702 is (1 × 10) + (4 × 1) + (7 × 1000) + (2 × 10,000).
To know more about expanded form visit:
https://brainly.com/question/26337896
#SPJ11
Factor out the GCF from the given polynomial. 10^3 + 16^2 - 18x 10^3 + 16^2 - 18x = (Type your answer in factored form.)
Answer:
2x
Step-by-step explanation:
Given the expression 10x^3 + 16x^2 - 18x, we are to find the GCF
First find the factors
10x^3 = 2 * 5 * x * x^2
16x^2 = 2 * 8 * x * x
18x = 2 * 9 * x
From the factors shown, you will see that 2 and x are the common factors. Hence the GCF of the expression is 2x
Suppose you are deciding whether to take a train or a car to travel 3,000 miles across a country. The train travels at 95 kilometers an hour, while a car will travel 65 miles per hour on average. Which mode of transportation will take less time? Note that 1 mi=1.6 km.
Answer:
The car
Step-by-step explanation:
Train:1mi = 1.6 km
95km = 95/1.6 = 59.375 km
95km/h = 59.375mi//h
Car65mi/h
Comparative:
65 > 59.375
then:
the car is more faster
Answer:
The answer is A : the car will take less time because it travels at a faster speed. the train will travel at 95/1.6=59.03 while the car travels at 65
Step-by-step explanation:
a line passes through the point (10, -9) and has a slope of -3/2. write an equation in slope-intercept form for this line.
Determine the area of the region D bounded by the curves: x = y³, x+y= 2, y = 0. b) Find the volume of the solid bounded by the paraboloid z = 4-x² - y². and the xy-plane. (5 marks) (5 marks)
a) The area of the region D bounded by the given curves is 6.094 units². b) The volume of the solid bounded by the paraboloid z = 4 - x² - y² and the xy-plane is zero
a) To determine the area of the region D bounded by the curves x = y³, x + y = 2, and y = 0, we need to find the intersection points of these curves and calculate the area between them.
First, let's find the intersection points of the curves x = y³ and x + y = 2.
Substituting x = y³ into the equation x + y = 2, we get:
y³ + y - 2 = 0
We can solve this equation to find the values of y. One of the solutions is y = 1.
Next, let's find the y-coordinate of the other intersection point by substituting y = 2 - x into the equation x = y³:
x = (2 - x)³
x = 8 - 12x + 6x² - x³
This equation simplifies to:
x³ - 7x² + 13x - 8 = 0
By factoring or using numerical methods, we find that the other solutions are approximately x = 0.715 and x = 6.285.
Now, let's integrate to find the area between the curves. We integrate with respect to x from the smaller x-value to the larger x-value, which gives us:
Area = ∫[0.715, 6.285] (x + y - 2) dx
We need to express y in terms of x, so using x + y = 2, we can rewrite it as y = 2 - x.
Area = ∫[0.715, 6.285] (x + (2 - x) - 2) dx
= ∫[0.715, 6.285] (2 - x) dx
= [2x - 0.5x²] evaluated from x = 0.715 to x = 6.285
Evaluating this integral, we get:
Area = [2(6.285) - 0.5(6.285)²] - [2(0.715) - 0.5(0.715)²]
= [12.57 - 19.84] - [1.43 - 0.254]
= -7.27 + 1.176
= -6.094
However, area cannot be negative, so the area of the region D bounded by the given curves is 6.094 units².
b) To find the volume of the solid bounded by the paraboloid z = 4 - x² - y² and the xy-plane, we need to integrate the function z = 4 - x² - y² over the xy-plane.
Since the paraboloid is always above the xy-plane, the volume can be calculated as:
Volume = ∫∫R (4 - x² - y²) dA
Here, R represents the region in the xy-plane over which the integration is performed.
To calculate the volume, we integrate over the entire xy-plane, which is given by:
Volume = ∫∫R (4 - x² - y²) dA
= ∫∫R 4 dA - ∫∫R x² dA - ∫∫R y² dA
The first term ∫∫R 4 dA represents the area of the region R, which is infinite, and it equals infinity.
The second term ∫∫R x² dA represents the integral of x² over the region R. Since x² is always non-negative, this integral equals zero.
The third term ∫∫R y² dA represents the integral of y² over the region R. Similar to x², y² is always non-negative, so this integral also equals zero.
Therefore, the volume of the solid bounded by the paraboloid z = 4 - x² - y² and the xy-plane is zero
To know more about paraboloid:
https://brainly.com/question/30634603
#SPJ4
James drove for 1.5 hours at an average speed of x km/h and then 2.5 hours at an average speed of y km/h. He drove a total distance of 327 km.
(a) Write down an equation in terms of x and y the total distance travelled and show that it simplifies to 3x + 5y = 654.
(b) Ryan drove for 4 hours at an average speed of x km/h and then 6 hours at an average speed of y km/h. He drove a total distance of 816 km. Write down an equation, in terms of x and y, to represent this information.
(c) Solve the two equations found in (a) and (b) to find the values of x and y.
The average speeds are 78 km/h and 84 km/h respectively
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operations like exponents, addition, subtraction, multiplication and division.
The equation for speed is:
Speed = distance / time
a) James drove for 1.5 hours at an average speed of x km/h and then 2.5 hours at an average speed of y km/h.
For distance 1:
x = distance 1 / 1.5
distance 1 = 1.5x
For distance 2:
y = distance 2 / 2.5
distance 2 = 2.5y
Total distance = distance 1 + distance 2
1.5x + 2.5y = 327
multiply through by 2:
3x + 5y = 654 (1)
b) Ryan drove for 4 hours at an average speed of x km/h and then 6 hours at an average speed of y km/h. He drove a total distance of 816 km
For distance 1:
x = distance 1 / 4
distance 1 = 4x
For distance 2:
y = distance 2 / 6
distance 2 = 6y
Total distance = distance 1 + distance 2
4x + 6y = 816 (2)
c) Solving equations 1 and 2 simultaneously:
x = 78; y = 84
The value of x and y are 78 and 84 respectively
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Find the lowest common multiple (LCM) of 30 and 42
Answer:
2-30,42
3-15,21
5-5,7
7-1,7
-1,1
LCM of 30 and 42 is 210
Answer:
210
Step-by-step explanation:
30*42 by HCF of 30,42
1260 by 6 =210
The volume of air inside a rubber ball with radius r can be found using the function V(r) = four-thirds pi r cubed. What does V and five-sevenths represent?
Answer:
The answer is explained below
Step-by-step explanation:
Given that The volume of air inside a rubber ball with radius r can be found using the function V(r) = \(\frac{4}{3}\pi r^3\), this means that the volume of the air inside the rubber ball is a function of the radius of the rubber ball, that is as the radius of the rubber ball changes, also the volume of the ball changes.
As seen from the function, the radius is directly proportional to the volume of the ball, if the radius increases, the volume also increases.
\(V(\frac{5}{7} )\) is equal to the volume of the ball when the radius of the ball is \(\frac{5}{7}\). Therefore:
\(V(\frac{5}{7} )=\frac{4}{3} \pi *(\frac{5}{7} )^3=1.53\ unit^3\)
If b > a, which of the following must be true? A -a > -b B 3a > b C a² < b² D a² < ab
If b > a, then -a>-b and a²<b². The correct answers are option(A) and option(C)
To find which of the options are true, follow these steps:
If the inequality b>a is multiplied by -1, we get -a<-b. So option(A) is true.We cannot determine the relationship between 3a and b with the inequality a>b. So, option(B) is not true.Since a<b, on squaring the inequality we get a² < b². This means that option(C) is true.We cannot determine the relationship between a² and ab with the inequality a>b. So, option(d) is not true.Therefore, the correct options are option(A) and option(B)
Learn more about inequality:
brainly.com/question/30238989
#SPJ11
10 points please help me
Answer:
(a)
A = 3
B = 17
C = 8
D = 15
(b)
surface area = 240
(using the formula)
A student graphs the function f (x) = 2(4)* using a graphing calculator. The student then replaces the 2 in the equation with an 8.
Which best describes the change the student sees when graphing the new function?
O The graph of the new function will be vertically shifted up 4 units when compared to the previously graphed function.
O The graph of the new function will be vertically shifted up 6 units when compared to the previously graphed function.
O The graph of the new function will be vertically stretched by a factor of 4 when compared to the previously graphed function.
O The graph of the new function will be vertically stretched by a factor of 6 when compared to the previously graphed function.
The equation will be changed into = f(x)= 32
What are equations?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
A statement is not an equation if it has no "equal to" sign.
A mathematical statement called an equation includes the sign "equal to" between two expressions with equal values.
Hence, The equation will be changed into = f(x)= 32
learn more about equations click here:
brainly.com/question/2972832
#SPJ1
What is the y-value for the solution to the system of equations below? 10x + 8y = -24 5x+6y = 2
help me and ill give brainliest
Answer:
cap 1,8
miu
Step-by-step explanation:
Indigo launches a toy rocket from a platform. The height of the rocket in feet is given by h(t)=-16t² + 80t + 96 where t represents the time in seconds after launch. What is the rocket's greatest height?
The calculated value of the rocket's greatest height is 196 feet
Calculating the rocket's greatest height?From the question, we have the following parameters that can be used in our computation:
height function, h(t) =-16t² + 80t + 96
So, we have
h(t) =-16t² + 80t + 96
The maximum value of t is calculated as
t = -b/2a
So, we have
t = -80/(2 * -16)
Evaluate
t = 2.5
The rocket's greatest height is at t = 2.5
So, we have
h(2.5) =-16(2.5)² + 80(2.5) + 96
Evaluate
h(2.5) = 196
Hence, the rocket's greatest height is 196 feet
Read more about height funcion at
https://brainly.com/question/10837575
#SPJ1
Mary says that 2−3 is equal to −8. Explain what Mary is doing wrong.
Answer:
2-3=-1
Step-by-step explanation:
Since 2 is only 1 number below 3
ussaully we would do 3-2=1 but this is 2-3 so the answer is -1