Answer:
c
Step-by-step explanation:
Answer: 32
Step-by-step explanation:
Apply exponent rule: 1/4 times 2^3/4^-2 = 2^7 times 1/4.
1 times 2^7 divided by 4 (all numbers)
2^4 divided by 4
Factor 2^7 / 2^2
Cancels out to 2^5
which is 32
Instructions: Problem 2 ! Find the missing angle in the image below. Do not include spaces in your answers
Step-by-step explanation:
since angles in a triangle add up to 180
<vuw=180-(71+23)
=86°
since angles in a straight line add up to 180
<vuf=180-86
=94
Say I have a graph. The points plotted make a straight line, but the textbook did not draw a straight line, they drew dots. Would that make my graph Discrete or Continuous?
Answer:
A Discrete.
Step-by-step explanation:
Answer:
C. Graphs are used to demonstrate numerical concepts visually
Step-by-step explanation:
The radius of the wheel on a car is 19 inches. If the wheel is revolving at 277 revolutions per minute, what is the linear speed of the car in miles per hour? Round your answer to the nearest tenth. Provide your answer below: miles per hour
The linear speed of the car is approximately 31.2 miles per hour (rounded to the nearest tenth).
To find the linear speed of the car in miles per hour, we need to calculate the distance traveled by the car in one minute and then convert it to miles per hour.
First, let's calculate the distance traveled by the car in one revolution of the wheel. The circumference of a circle can be calculated using the formula: circumference = 2 × π × radius.
Circumference of the wheel = 2 × π × 19 inches
Since the question asks for the answer in miles per hour, we need to convert the units from inches to miles. There are 12 inches in a foot, and 5280 feet in a mile. Therefore, there are 63360 inches in a mile.
To convert inches to miles, we divide by 63360:
Distance traveled in one revolution = (2 × π × 19) / 63360 miles
Now, let's calculate the distance traveled by the car in one minute. The car is making 277 revolutions per minute:
Distance traveled in one minute = 277 revolutions × distance traveled in one revolution
Next, we need to convert the time from minutes to hours. There are 60 minutes in an hour:
Distance traveled in one hour = Distance traveled in one minute × 60 minutes
Finally, we can calculate the linear speed of the car in miles per hour:
Linear speed = Distance traveled in one hour
Let's perform the calculations:
Circumference of the wheel = 2 × π × 19 inches = 119.38 inches
Distance traveled in one revolution = (2 × π × 19) / 63360 miles = 0.001879... miles
Distance traveled in one minute = 277 revolutions × 0.001879... miles = 0.5206... miles
Distance traveled in one hour = 0.5206... miles × 60 minutes = 31.24... miles
Therefore, the linear speed of the car is approximately 31.2 miles per hour (rounded to the nearest tenth).
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Given the following expressions
1. - 5/8 + 3/5
2. 1/2 + square root 2
3. (Square root 5 ) x ( square root 5
4. 3 x ( square root 49)
Which expression result in a irrational number
1. 2 only
2. 3 only
3 . 1, 3 ,4
4. 2,3,4
The expression that results in an irrational number is option 2 only: 1/2 + square root 2.
To determine which expression results in an irrational number, let's analyze each expression:
-5/8 + 3/5:
The result of this expression can be computed by finding a common denominator, which is 40. The expression simplifies to (-25 + 24) / 40 = -1/40. This is a rational number, not an irrational number.
1/2 + square root 2:
The expression involves adding a rational number (1/2) to an irrational number (square root 2). When adding a rational and an irrational number, the result is always an irrational number. Therefore, this expression results in an irrational number.
(Square root 5) x (square root 5):
The expression simplifies to 5, which is a rational number, not an irrational number.
3 x (square root 49):
The square root of 49 is 7. Therefore, the expression simplifies to 3 x 7 = 21, which is a rational number, not an irrational number.
Based on the analysis above, the expression that results in an irrational number is:
1/2 + square root 2.
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compute the lower riemann sum for the given function ()=2 over the interval ∈[−1,1] with respect to the partition =[−1,−14,14,34,1].
The function is f(x)=2 over the interval [−1,1]. Compute the lower Riemann sum with respect to the partition P=[−1,−14,14,34,1].
The formula for calculating the lower Riemann sum is given by:L(f,P)=∑i=1n−1miΔxiWhere mi is the infimum of f on [xi,xi+1], and Δxi is the length of the subinterval [xi,xi+1].To compute the lower Riemann sum with respect to the partition P=[−1,−14,14,34,1], we have to calculate the infimum of the function over each subinterval, and multiply it by the length of the subinterval.Subinterval [-1, -1/4]The infimum of f(x)=2 on [-1, -1/4] is f(-1) = 2.
Therefore, m1 = 2.The length of the subinterval [-1, -1/4] is Δx1 = (-1/4) - (-1) = 1/4.Subinterval [-1/4, 1/4]The infimum of f(x)=2 on [-1/4, 1/4] is f(-1/4) = 2. Therefore, m2 = 2.The length of the subinterval [-1/4, 1/4] is Δx2 = 1/2.Subinterval [1/4, 3/4]The infimum of f(x)=2 on [1/4, 3/4] is f(1/4) = 2. Therefore, m3 = 2.The length of the subinterval [1/4, 3/4] is Δx3 = 1/2.Subinterval [3/4, 1]The infimum of f(x)=2 on [3/4, 1] is f(3/4) = 2. Therefore, m4 = 2.The length of the subinterval [3/4, 1] is Δx4 = 1/4.Therefore, the lower Riemann sum is:L(f,P) = m1Δx1 + m2Δx2 + m3Δx3 + m4Δx4= 2(1/4) + 2(1/2) + 2(1/2) + 2(1/4)= 1/2 + 1 + 1 + 1/2= 3.
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when conducting an evaluation of child welfare supervision practices in one state, the researchers surveyed those involved in an intervention designed to improve supervision. the supervisors in the sample represented what type of sample?
the supervisors in the sample represented a purposeful sample as "The participants in an intervention aimed at enhancing supervision were surveyed by the researchers as part of their analysis of child welfare supervision practices in one state. The sample's supervisors represented a carefully chosen sample."
What is purposeful sample?The participants in an intervention aimed at enhancing supervision were surveyed by the researchers as part of their analysis of child welfare supervision practices in one state. The sample's supervisors represented a carefully chosen sample. A group of non-probability sampling techniques known as "purposive sampling" involve choosing units for your sample based on their possession of specific qualities. In other words, purposive sampling selects units "on purpose." Purposive sampling, also referred to as purposive and selective sampling, is a sampling strategy used by qualitative researchers to identify participants who can offer in-depth and detailed information about the phenomenon under study.
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Kuta Software Infinite Algebra 1. Solving Systems of Equations by Substitution. Solve each system by substitution. 1) y=6x-11. -2x-3y=-7. -2x-3(60x-11)=-7
the solution to the system of equations is x = 2 and y = 1.
To solve the system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation.
Given the system of equations:
1) y = 6x - 11
2) -2x - 3y = -7
Step 1: Solve equation (1) for y.
y = 6x - 11
Step 2: Substitute the value of y from equation (1) into equation (2).
-2x - 3(6x - 11) = -7
Step 3: Simplify and solve for x.
-2x - 18x + 33 = -7
-20x + 33 = -7
-20x = -7 - 33
-20x = -40
x = (-40)/(-20)
x = 2
Step 4: Substitute the value of x into equation (1) to find y.
y = 6(2) - 11
y = 12 - 11
y = 1
Therefore, the solution to the system of equations is x = 2 and y = 1.
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The solution to the system of equations y = 6x - 11 and -2x - 3y = -7 is x = 2 and y = 1. This is achieved by substituting y into the second equation, simplifying, and solving for x, then substituting x back into the first equation to solve for y.
Explanation:To solve the system of equations y = 6x - 11 and -2x - 3y = -7 by substitution, we start by substituting the equation y = 6x - 11 into the second equation in place of y, giving us -2x - 3(6x - 11) = -7. Next, simplify the equation by distributing the -3 inside the parentheses to get -2x - 18x + 33 = -7. Combine like terms to get -20x + 33 = -7. Subtract 33 from both sides to obtain -20x = -40, and finally, divide by -20 to find x = 2.
Once we find the solution for x, we substitute it back into the first equation y = 6x - 11. Substituting 2 in place of x gives y = 6*2 - 11, which simplifies to y = 1.
Therefore, the solution to the system of equations is x = 2 and y = 1.
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A piecewise function g(x) is represented by the graph.
Which functions represent a piece of the function? Select three options.
The piecewise functions that are represented by the graph are; g(x) = −2, x < −2; g(x) = −2x + 6, x ≥ 1; g(x) = x/2 + 1, –2 ≤ x < 1
How to Interpret a Piecewise Function graph?From the attached graph of the piecewise function, we can access each option as follows;
A) g(x) = −2x, −2 < x < 0
This is not represented by the graph because g(x) = −2x has negative slope which means it goes downward. There's also no y-intercept in g(x) = −2x.
B) g(x) = −2, x < −2;
This is represented by the graph because g(x) = −2 is a horizontal line which is only on the left side of x = -2.
C) g(x) = x − 2, −2 < x < 1;
This is not represented by the graph because g(x) = x − 2 has y-intercept at y = -2 and slope of 1 which means that graph of g(x)= x - 2 must be going upward and crossing at y = -2.
D) g(x) = −2x + 6, x ≥ 1
This is represented by the graph because g(x) = −2x+6 satisfies the graph which is going downward.
E) g(x) = x/2 + 1, –2 ≤ x < 1
This is represented by the graph because g(x) = (x/2) + 1 satisfies the graph which is going downward.
The options are;
g(x) = −2x, −2 < x < 0
g(x) = −2, x < −2
g(x) = x − 2, −2 < x < 1
g(x) = −2x + 6, x ≥ 1
g(x) = x/2+ 1, –2 ≤ x < 1
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suppose f : rn → rm is a linear map. what is the derivative of f ?
If f: rn → rm is a linear map, then its derivative is simply the map itself. This is because a linear map is a function that preserves vector addition and scalar multiplication.
In other words, if we take two vectors in the domain and add them together, and then apply the linear map, it is the same as applying the linear map to each vector separately and then adding the results. Similarly, if we multiply a vector in the domain by a scalar and then apply the linear map, it is the same as multiplying the result of applying the linear map to the original vector by the same scalar.
Formally, we can express this idea using the concept of a Jacobian matrix. The Jacobian matrix of a function describes the rate at which the function changes near a particular point. For a linear map, the Jacobian matrix is simply the matrix that represents the map. This means that the derivative of f is the matrix A such that f(x) = Ax for all x in rn.
To see why this makes sense, consider the simplest case of a linear map from R1 to R1, given by f(x) = ax, where a is a constant. The derivative of this function is f'(x) = a, which is just the constant coefficient of the linear map. More generally, the derivative of a linear map f: rn → rm is the matrix A such that f(x) = Ax for all x in rn.
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AB is a straight line. XYZ is an isosceles triangle. A What is the value of angle m? A 120° B 95° C 60° D 85° E 75°
AB is a straight line ⇒ m(∡BXA) = 180°
m(∡BXA) = m(∡BXY) + m(∡YXA) ⇔
⇔ 180° = 60° + m(∡YXA) ⇔
⇔ 60° + m(∡YXA) = 180° ⇔
⇔ m(∡YXA) = 180° - 60° ⇒ m(∡YXA) = 120°
∆XYZ is an isosceles triangle and has an angle of 90° ⇒ m(∡ZXY) = m(∡XYZ) = 45°, because a triangle has 180°
m = m(∡AXZ) ⇒ m(∡AXZ) = ?
m(∡BXA) = m(∡BXY) + m(∡YXZ) + m(∡AXZ) ⇔
⇔ 180° = 60° + 45° + m(∡AXZ) ⇔
⇔ 105° + m(∡AXZ) = 180° ⇔
⇔ m(∡AXZ) = 180° - 105° ⇒ m(∡AXZ) = 75° ⇔
⇔ m = 75°
Good luck! :)
this is my question.please help QUICK
Answer:
sry i dont know sorry please
A pack of six pencils costs 5 times as much as a single pencil. A single pencil costs 9 cents. How much does the pack of six pencils cost?
Answer:
im sorry I dont know
Which ones are equivalent
Answer:
(12+3x)x
Step-by-step explanation:
the other 3 can be simplified into 15x, but (12+3x)x = 12x+3x^2
0.2(x + 1) + 0.5x = –0.3(x – 4)
equation of the circle centered at the origin and passing through the point equation of the circle centered at the origin and passing through the point (-4,0)
The equation of the circle centered at the origin and passing through the point (-4,0) is \(x^2+y^2=16\).
Equation of a circle
A circle may also be defined as a special kind of ellipse in which the two foci are coincident, the eccentricity is 0, and the semi-major and semi-minor axes are equal.
We know that,
Equation of the circle passing through the origin is given by:-
\(x^2+y^2=r^2\)
Where,
r is the radius of the circle, and
(x,y) are the coordinates of each point of the circle.
Hence, we can write,
The radius of the circle will be :-
\(\sqrt{(0-(-4))^2+(0-0)^2} =\sqrt{ 4^2+0^2} =\sqrt{16}=4 units\)
Hence, r = 4 units.
Hence, the equation of the circle is given by:-
\(x^2+y^2=16\)
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PLEASE HELP!!
Danielle needs your help! She is practicing operations with polynomials, but she keeps making mistakes! Find the error(s) that Danielle made for each problem. Help Danielle understand her
mistake by explaining the error(s) and then correctly performing the operation.
The correct result is 3x^2 - 6 - x^3.
What is Danielle's mistake?A polynomial is an expression that contains values that is raised to a given power. The rules of algebra are applied when we are dealing with polynomials of any degree. There are several kinds of polynomials depending on the order to which the term is raised in the expression.
An expression is cubic when the terms are raised to power 2 and the expression is quadratic when the terms are raised to power 2 and so on.
In this case, we have the expressions; x^3 - 2x^2 and x^2 -6. We are expected to subtract x^3 - 2x^2 from x^2 -6.
The mistake of Danielle was that x^2 -6 was subtracted from x^3 - 2x^2 rather than x^3 - 2x^2 from x^2 -6.
The correct work is;
x^2 - 6 - (x^3 - 2x^2)
x^2 - 6 - x^3 + 2x^2
3x^2 - 6 - x^3
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Find the lengths of the diagonals of rectangle $wxyz$ . $wy=6x-7$ $xz=3x+2$ the length of each diagonal is units.
The lengths of the diagonals of rectangle WXYZ are 15 units and 11 units.In a rectangle, the diagonals are congruent, meaning they have the same length.
To find the lengths of the diagonals, we need to determine the value of x.
Given that WY = 6x - 7 and XZ = 3x + 2, we can equate these expressions to find the value of x. Setting 6x - 7 equal to 3x + 2, we can solve for x:
6x - 7 = 3x + 2
3x = 9
x = 3
Now that we know the value of x, we can substitute it back into the expressions for WY and XZ to find the lengths of the diagonals.
For WY:
WY = 6(3) - 7
WY = 11 units
For XZ:
XZ = 3(3) + 2
XZ = 11 units
Therefore, the lengths of the diagonals of rectangle WXYZ are 15 units and 11 units.
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a ramp measures 6 feet long. if the ramp is 12 inches tall, what is the horizontal distance it covers? i'll give brainliest to whoever answers first/correctly!
we know that
1 ft--------> is equals to 12 in
the ramp is 12 inches tall----------> 1 ft tall
A ramp measures------------------> 6 ft long
applying the Pythagorean theorem
c²=a²+b²
where
c-----> 6 ft long
a----> horizontal distance
b-----> 1 ft tall
a²=c²-b²------> a²=6²-1²-----> a²=35------> a=√35------> a=5.92 ft
the answer is
5.92 ft
Answer:
6.08 or so
Step-by-step explanation:
The height is 1 foot, while the length is 6 feet.
You can use the Pythagorean Theorum to solve this, as you plug in the values.
The theorum states that A squared plus B squared = C squared, where A is the length, and B is the width. (It doesn't matter if A is the width and B is the length either.)
So if we plug in the values:
1 squared plus 6 squared = C squared.
1 + 36 = 37
Since it is C squared, we can find the square root of 37, which is something like 6.0827625302982196889996842452021.
So usually we round to the hundredths place, so we can use 6.08.
a. write a rule for the congruence mapping that will move a figure 5 units to the right and 3 units up. b. write a rule for congruence mapping that reflects a figure across the y-axis.c. why are these mappings called congruence mappings?
Given:
Two different congruency mapping
To find:
a) a rule for the congruence mapping that will move a figure 5 units to the right and 3 units up
b) a rule for congruence mapping that reflects a figure across the y-axis
\(\begin{gathered} a)\text{ Translation rule to the right:} \\ f(x\text{ -d\rparen: \lparen x, y\rparen }\rightarrow\text{ \lparen x+d, y\rparen} \\ Translation\text{ rule up:} \\ f(x)\text{ + b: \lparen x, y\rparen }\rightarrow\text{ \lparen x, y + b\rparen} \\ \\ 5\text{ units to the right and 3 units up:} \\ (x,\text{ y\rparen }\rightarrow\text{ \lparen x + 5, y + 3\rparen} \end{gathered}\)\(\begin{gathered} b)\text{ reflection across the y-axis} \\ The\text{ x coordinate will be negated while the x coordinate will remain constant} \\ (x,\text{ y\rparen }\rightarrow\text{ \lparen-x, y\rparen} \end{gathered}\)\(\begin{gathered} c)\text{ The mappings are called congruence mapping because the shapes and size remain the same } \\ \text{but the }position\text{ changes.} \\ As\text{ a result the corresponding angles and sides will be equal} \end{gathered}\)david is asked to tell the researcher what he sees in a series of inkblots. he is completing a
David is completing a Rorschach test, which is a type of projective psychological assessment. The test consists of a series of inkblots presented to the participant, and their responses are analyzed by the researcher to gain insights into their personality, thought processes, and emotional functioning.
The Rorschach test is a widely used tool in clinical psychology and has been subject to much controversy and debate over its validity and usefulness in assessment.
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at a particular restaurant, each pizza roll has 65 and each chicken wing
at a particular restaurant, each pizza roll has 65 and each chicken wing is 11 pizza rolls and 6 chicken wings.
What is calories?Calories are units of energy that a food or drink provides. You can usually find calorie counts listed on food items, and wearables like the best fitness trackers allow you monitor how many calories you're burning by doing different activities. Certain foods, such as fatty, fried, or processed foods, tend to have more calories. Other foods, such as fresh fruit and vegetables, tend to have fewer calories. However, some healthy fruits and vegetables can be high in calories, while low-calorie foods, such as diet soda, don’t provide any nutritional value. We need calories to give us enough energy to move around, stay warm, grow, work, think, and play. Even our blood circulation and digestion need the energy gained from calories in order to function well.
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A new process for producing silicon wafers for integrated circuits is supposed to reduce the proportion of defectives to 8%. A sample of 200 wafers will be tested. Let X represent the number of defectives in the sample. Let p represent the population proportion of defectives produced by the new process. A test will be made of H0 : p ≥ 0.08 versus H1 : p < 0.08. Assume the true value of p is actually 0.04.
a. It is decided to reject H0 if X ≤ 16. Use the normal approximation to the binomial to find the level of this test. Round the answer to four decimal places.
The level of the test is approximately 0.0143.
What is the approximate level of the hypothesis testing for the given scenario of "H0: p ≥ 0.08 versus H1: p < 0.08"?The given hypothesis test involves testing the null hypothesis H0: p ≥ 0.08 against the alternative hypothesis H1: p < 0.08. The null hypothesis assumes that the population proportion of defectives produced by the new process is greater than or equal to 8%, while the alternative hypothesis suggests it is less than 8%.
To determine the level of the test, we need to find the probability of observing a sample result as extreme as or more extreme than the one specified in the alternative hypothesis, assuming the null hypothesis is true. In this case, the test statistic X, representing the number of defectives in the sample of 200 wafers, follows a binomial distribution with parameters n = 200 and p = 0.08 (under the null hypothesis).
To approximate the binomial distribution with a normal distribution, we can use the mean and standard deviation of the binomial distribution. The mean (μ) is given by μ = np, and the standard deviation (σ) is given by σ = √(np(1-p)).
Using the true value of p as 0.04, we can calculate the mean and standard deviation as follows:
μ = 200 * 0.04 = 8
σ = √(200 * 0.04 * 0.96) ≈ 3.0984
Now, we can standardize the test statistic to a standard normal distribution using the z-score formula: z = (X - μ) / σ.
For the specified rejection region X ≤ 16, the corresponding z-score is:
z = (16 - 8) / 3.0984 ≈ 2.5819
Finally, we find the probability associated with this z-score by looking up the corresponding value in the standard normal distribution table or using a statistical calculator. The level of the test is the probability of observing a value less than or equal to this z-score, which is approximately 0.0143.
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use the vectors in the figure below to graph the following vector
Given:
The given vector is w.
Required:
We need to draw 3w.
Explanation:
Use the Pythagorean theorem to find the magnitude AB.
Let the origin be (0,0).
Point A is (0,4) and point B is (3,0).
The magnitude of AB is (3-0,0-4)
\(w=(3,-4)\)Multiply the equation by 3 to find 3w.
\(3\cdot w=3\cdot(3,-4)\)\(3w=(3\cdot3,3\cdot(-4))\)\(3w=(9,-12)\)Consider any point on the graph and take it as the origin (0,0) and mark (9,-12) and joint them as follows.
Final answer:
Given the following program, write a C (user-defined) function that returns the sum of the following series x+2mx2+3mx3+4mx4+⋯+nmxn
The function in C (user-defined) that returns the sum of the given series is shown below:```cint series_sum(int x, int m, int n){ int i, j = 1, sum = 0, term = 0; for(i = x; i <= n; i++){ term = j * m * i; sum += term; j++; } return sum;}```.
Here, `x`, `m`, and `n` are the integer inputs of the function, and `j` is a variable whose value gets incremented by 1 in each iteration of the for loop. The for loop runs from the `xth` term to the `nth` term of the series and calculates the `ith` term of the series as `j*m*i` and adds it to the variable `sum`. Finally, the variable `sum` is returned as the output of the function.
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On thursday, what fraction of the time from 8:00 a.m. to 2:15 p.m. is gerald scheduled to be in class?
Gerald is scheduled to be in class for 45/93 of the time from 8:00 a.m. to 2:15 p.m. on Thursday.
To determine the fraction of time Gerald is scheduled to be in class, calculation of the duration of his class and divide it by the total duration from 8:00 a.m. to 2:15 p.m.
Step 1: Calculate the duration of Gerald's class:
The class starts at 8:30 a.m. and ends at 12:00 p.m. To find the duration, we subtract the start time from the end time:
12:00 p.m. - 8:30 a.m. = 3 hours and 30 minutes.
Step 2: Calculate the total duration from 8:00 a.m. to 2:15 p.m.:
To find the duration, we subtract the start time from the end time:
2:15 p.m. - 8:00 a.m. = 6 hours and 15 minutes.
Step 3: Calculate the fraction of time Gerald is scheduled to be in class:
To find the fraction, we divide the duration of Gerald's class by the total duration:
3 hours and 30 minutes / 6 hours and 15 minutes = 210 minutes / 375 minutes.
To simplify the fraction, divide both the numerator and denominator by their greatest common divisor, which is 15:
210 minutes ÷ 15 / 375 minutes ÷ 15 = 14 / 25.
Therefore, Gerald is scheduled to be in class for 14/25 of the time from 8:00 a.m. to 2:15 p.m. on Thursday.
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III Question 4 of 10 ( point) Question Attempt: 1 of Unlimited Susan makes house calls. For each, she is paid a base amount and makes additional money for each hour she works, The graph below shows her pay in dollars) versus the number of hours worked. Use the graph to answer the questions.
Answer:
a) $30
b) 30
Step-by-step explanation:
a) Her starting pay is $60. After an hour it goes up to $90. 90-60=30.
b) Every hour, the pay goes up 30. Slope is calculated as the change in y divided by the change in x. That means 30/1, or just 30 is the slope.
A support wire is attached to the top of an antenna. The support wire connects
to the ground 15 feet from the bottom of the antenna. The support wire and the
ground meet at an angle with measure 70°, as shown.
Antenna
70°
15 ft-
To the nearest foot, what is the height of the antenna?
The antenna is
feet tall.
Answer:
Step-by-step explanation:
The antenna height is 41.23 feet if the support wire is attached to the top of the antenna.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
A support wire is attached to the top of an antenna. The support wire connects to the ground 15 feet from the bottom of the antenna.
Let x be the height of the antenna.
We can find the length of the antenna using the trigonometric ratios:
As we know, the trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
Applying tan ratio in the right angle triangle:
tan70 = x/15
x =15tan70
x = 41.212 feet ≈ 41.23 feet
Thus, the height of the antenna is 41.23 feet if the support wire is attached to the top of the antenna.
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LeashTYPE 1TYPE 273DogLadder20 ft19.5 ftThe end of a dog's leash is attachedDon placed a ladder againstto the top of a 5-foot-tall fence post,the side of his house asas shown in the diagram below. Theshown in the diagramdog is 7 feet away from the base ofbelow. Write an equation tothe fence post. How long is thefind the distance, x, fromleash, to the nearest tenth of a foot.the foot of the ladder to thebase of the house.WHAT IS THE DIRERENCESolve the equation for x,BETWEEN TYPE 1 AND TYPE 2?round to the nearesthundredth of a foot.BREAKOUTROOMSх
Type 1
this is a right triangle, the we can apply pythagoras
\(a^2+b^2=h^2\)where a and b are sides and h the hypotenuse on this case L(leash)
replacing
\(5^2+7^2=L^2\)simplify
\(\begin{gathered} 25+49=L^2 \\ 74=L^2 \end{gathered}\)now solve for L
\(L=\sqrt[]{74}\approx8.6\)The leash is 8.6ft
Type 2
we have a right triangle too
on this case the missing number is a side, not hypotenuse
remember pythagoras
\(a^2+b^2=h^2\)and replace for this case
\(x^2+19.5^2=20^2\)simplify
\(\begin{gathered} x^2+380.25=400 \\ \end{gathered}\)and solve for x
\(\begin{gathered} x^2=19.75 \\ x=\sqrt[]{19.75}\approx4.44 \\ \end{gathered}\)then le length of the side x is 4.44ft
Yo can somebody please help me with this math problem
Answer:
what is the problem it doesn't show anything
Given g(x) = -
—x – 2, find g(-3).
Answer:
1
Step-by-step explanation:
negative times negative is positive so that would make it 3-2 which is 1.