The point-slope equation of the line that is perpendicular to y-3=4(x-10) and passes through(-3,7) is:
B. [tex]y-7=\frac{-1}{4} (x+3)\\[/tex]
The slope intercept form is y=mx+b where m is slope.
We have given perpendicular line as:
y-3=4(x-10)
y-3=4x-40
y=4x-37
The slope intercept form of the given line is
y=4x-37
Slope of this line is m=4
Now, as we know the two perpendicular lines have negative reciprocal slope.
Thus the other line have slope [tex]m=-\frac{1}{4}[/tex]
Now. the equation of line passing through point (-3,7) and having slope [tex]\frac{-1}{4}[/tex] is:
[tex]y-7=\frac{-1}{4} (x+3)\\[/tex]
Therefore the correct option is B.
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A pendulum travels 30 inches on its first swing. During each of its subsequent swings, it travels 90 percent of the previous swing.
Answer:
a1= 30 and r=0.9
Step-by-step explanation:
edge
The value of the digit in the hundreds place in the number 653,841 is 1/10 the value of the digit in the thousands place in which number?
The answer is 0.5.
To find the answer, understand the place value system in numbers.
The value of the digit in the hundreds place in the number 653,841 is 1/10 the value of the digit in the thousands place in which number.
To find the answer, we need to understand the place value system. In the number 653,841, the digit in the hundreds place is 8, and the digit in the thousands place is 5. Therefore, 1/10 of the digit in the thousands place is 0.5.
So, the answer is 0.5.
in fifteen minutes greg sailboat went 3/6 miles, gina sailboat went 6/6 miles, and stuart sailboat went 4/6 miles. whose sailboat went the longest distance in fifteen minutes?
Choose the graph that represents the time for which the velocity of the ball will be between –90 and –58 ft/s.
The answer is c because t must be less than 2.5 and more than 1.5.
Find this by separating the inequality into:
-90 < -32t - 10
&
-32t - 10 < -58
Simplify and you get 2.5 and 1.5
Graph (C) represents the time for which the velocity of the ball will be between –90 and –58 ft/s option (C) is correct.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
We have:
The velocity of the ball will be between –90 and –58 ft/s.
Let v be the velocity of the ball:
v lies between -90 and -58
-90 < v < -58
The above expression represents the inequality:
Or
-90 < -32t - 10
t < 2.5
And
-32t - 10 < -58
t > 1.5
The number line will be:
Open the circle on the number 1.5 and open circle at 2.5 and a line was drawn between this point.
Thus, graph (C) represents the time for which the velocity of the ball will be between –90 and –58 ft/s option (C) is correct.
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Find the quadratic function whose zeros are 2 and -2 and has maximum value
NEED HELP ASAP What is the simplified form of the following expression? 4 sqrt 3/2x Assume x>0
Answer:
[tex]\frac{4\sqrt{6x}}{2x}[/tex]
Explanation:
The problem we are given is
[tex]4\sqrt{\frac{3}{2x}}[/tex]
We can write the square root of a fraction as a fraction with a separate radical for the numerator and denominator; this gives us
[tex]4\times \frac{\sqrt{3}}{\sqrt{2x}}[/tex]
We can write the whole number 4 as the fraction 4/1; this gives us
[tex]\frac{4}{1}\times \frac{\sqrt{3}}{\sqrt{2x}}\\\\=\frac{4\sqrt{3}}{\sqrt{2x}}[/tex]
We now need to "rationalize the denominator." This means we need to cancel the square root in the denominator. In order to do this, we multiply both numerator and denominator by √(2x); this is because squaring a square root will cancel it:
[tex]\frac{4\sqrt{3}}{\sqrt{2x}}\times \frac{\sqrt{2x}}{\sqrt{2x}}\\\\=\frac{4\sqrt{3}\times \sqrt{2x}}{2x}[/tex]
When multiplying radicals, we can extend the radical over both factors:
[tex]\frac{4\sqrt{3} \times \sqrt{2x}}{2x}\\\\=\frac{4\sqrt{3\times 2x}}{2x}\\\\=\frac{4\sqrt{6x}}{2x}[/tex]
Answer:
The correct answer is ^4sqrt24x^3/2x or B on edge.
Step-by-step explanation:
Full-time ph.d. students receive an average of $12,837 per year with a standard deviation of $3000. find the probability that the average salary of a group of 16 randomly selected ph.d. students is more than $13,000.
This list shows the age at which 43 U.S. Presidents began their terms. 57 61 50 54 54 54 56 54 61 54 48 49 42 51 61 57 68 65 50 51 60 52 57 51 52 47 56 62 69 58 49 56 55 55 43 64 57 64 46 55 51 55 46 Before you can make a frequency table, you need to decide how to set up the age intervals. What is the BEST way to group these ages into six intervals?
The best way to group these ages into six intervals is from 40-44 to 65-69.
What is a Frequency Distribution Table ?A frequency distribution table gives an idea about the data point or interval and its frequency.
The age of the Presidents given as
57 61 50 54 54 54 56 54 61 54 48 49 42 51 61 57 68 65 50 51 60 52 57 51 52 47 56 62 69 58 49 56 55 55 43 64 57 64 46 55 51 55 46
The smallest number ( age) is 42 and the largest number (age ) is 69
To make 6 intervals in this gap of 27 , each interval should be of length 5
Therefore the intervals will be
40-44
45-49
50-54
55-59
60-64
65-69
This is the best way to group into intervals.
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Final answer:
The best way to group the ages of U.S. Presidents into six intervals for a frequency table is by intervals of five years each, starting at age 42 and ending at age 71, to cover the entire range and maintain equal width for all intervals.
Explanation:
When grouping ages into intervals for a frequency table, it's best to have intervals that are of equal width and cover the entire range of data without overlap. For the ages of U.S. Presidents starting their terms, which range from 42 to 69, we could divide this range into six intervals in a way that makes sense for this data set.
First, find the range by subtracting the youngest age from the oldest: 69 - 42 = 27. Next, divide this range by the number of desired intervals (6), which gives us 4.5. We can round this to 5 to make the intervals more practical. Thus, each age interval will span 5 years. Starting at 42, the six intervals would be: 42-46, 47-51, 52-56, 57-61, 62-66, and 67-71.
This grouping covers all the ages and each interval is of equal width, making it easy to interpret the frequency table.
A university is trying to determine what price to charge for tickets to football games. At a price of $18 per ticket, attendance averages 40,000 people per game. Every decrease of $3 adds 10,000 people to the average number. Every person at the game spends an average of $4.50 on concessions. What price per ticket should be charged in order to maximize revenue? How many people will attend at that price?
Final answer:
To maximize revenue from football game ticket sales and concessions, we create a revenue function based on ticket price adjustments and evaluate changes in quantity demanded. The optimal price and attendance are found by analyzing the combined revenue function, deriving it with respect to the number of price decreases, and finding the maximum value of this function.
Explanation:
To determine the ticket price that should be charged by the university to maximize revenue from football game attendance, we need to analyze the effect of price changes on the quantity demanded. We can create a revenue function based on the given figures and the assumptions that a decrease of $3 in ticket price increases attendance by 10,000 people, and each person spends an average of $4.50 on concessions.
Let x represent the number of $3 decreases in price from the original $18. The ticket price can then be expressed as P = 18 - 3x, and attendance as A = 40000 + 10000x. The revenue from ticket sales is R1 = P × A, which gives us R1 = (18 - 3x) × (40000 + 10000x). The concession revenue per person is $4.50, so total concession revenue is R2 = 4.50 × A, which gives us R2 = 4.50 × (40000 + 10000x).
To maximize total revenue R = R1 + R2, we need to find the maximum of the function R = (18 - 3x) × (40000 + 10000x) + 4.50 × (40000 + 10000x). To find this, we can use calculus to take the derivative of R with respect to x and find the value of x that makes this derivative zero. This will be the critical point which we can then test to confirm it provides a maximum.
^4sqrt6/^5sqrt6 I don't have square root signs
Answer:
6^1/20
Step-by-step explanation:
you multiply the two exponents
Using the zero product property to find the solutions to the equation x^2-9=16
Answer:
x=-5, 5
Step-by-step explanation:
To find the solutions, use inverse operations to rearrange the equation to be equal to 0.
[tex]x^2-9-16=16-16\\x^2-25=0[/tex]
Factor the equation and then set each equal to 0 to solve for x.
[tex]x^2-25=0\\(x+5)(x-5)=0[/tex]
x+5=0
x=-5
x-5=0
x=5
In a line of students ,Jenna is number 8.The teacher says the rule for a number pattern is add4.The first term 7.What number should Jenna say?
8pints compared to 15 cups
Find the fifth term of A n = 2n
Mike drew a quadrilateral with four right angles. What shape could be drawn?
how many miles will you go if you ride your bike for t hours at 9 miles per hour?
Find the slope of the line that passes through (-95, 31) and (-94, 6).
Answer:
The slope of the line that passes through (-95, 31) and (-94, 6) is -25.
Step-by-step explanation:
The equation of a line has the following format:
[tex]y = ax + b[/tex]
In which a is the slope.
Passes through the point (-95, 31).
When [tex]x = -95, y = 31[/tex]
[tex]y = ax + b[/tex]
[tex]31 = -95a + b[/tex]
Passes through the point (-94, 6).
When [tex]x = -94, y = 6[/tex]
[tex]y = ax + b[/tex]
[tex]6 = -94a + b[/tex]
We have to solve the following system:
[tex]31 = -95a + b[/tex]
[tex]6 = -94a + b[/tex]
We want to find a.
From the first equation
[tex]b = 31 + 95a[/tex]
Replacing in the second equation:
[tex]6 = -94a + 31 + 95a[/tex]
[tex]a = -25[/tex]
The slope of the line that passes through (-95, 31) and (-94, 6) is -25.
Cream filled chocolates are $3.59 a pound Billy bought 1/2 pound of vanilla creams what was the cost round your answer
seth made 4 quarts of fruit punch for a birthday party. How many cups of fruit punch did he make
they knew that they could 3 miles in 20 minutes. how far can they ride in 45 minutes?
To find out how far the student can ride in 45 minutes, we calculate the speed of 0.15 miles per minute from the given 3 miles in 20 minutes, then multiply this speed by 45 minutes, resulting in a distance of 6.75 miles.
Explanation:The student has stated that they can travel 3 miles in 20 minutes. To find out how far they can ride in 45 minutes, we need to calculate their riding speed and then apply it to the longer time period.
Step 1: Calculate the riding speed
The speed can be calculated by dividing the distance (3 miles) by the time (20 minutes), which gives us a speed of 0.15 miles per minute.
Step 2: Use the speed to determine the distance in 45 minutes
Now that we know the speed, we can multiply it by the new time period (45 minutes) to find the distance they can ride. That calculation is 0.15 miles/minute × 45 minutes = 6.75 miles.
When we check whether the answer is reasonable, we can notice that 45 minutes is a little more than twice 20 minutes, and since they can ride 3 miles in 20 minutes, it makes sense that they could ride more than twice that distance in 45 minutes, so our answer of 6.75 miles seems reasonable.
They can ride 6.75 miles in 45 minutes.
Explanation:To find how far they can ride in 45 minutes, we can use the concept of average speed.
Given that they can ride 3 miles in 20 minutes, we can calculate their average speed as:
Average Speed = Distance / Time
Average Speed = 3 miles / 20 minutes
Average Speed = 0.15 miles per minute
Now, we can find how far they can ride in 45 minutes:
Distance = Average Speed x Time
Distance = 0.15 miles per minute x 45 minutes
Distance = 6.75 miles
Therefore, they can ride 6.75 miles in 45 minutes.
Given a circle with a diameter of 4, which equation expresses π as the ratio of the circumference of a circle to its diameter?
C /4 = π
Took the test myself, this is the answer.
How to find the area under the standard normal curve between z 1.5 and z 2.5?
We have that for the Question, it can be said that the area under the standard normal curve between z 1.5 and z 2.5 is
P(1.5 &2.5) =0.06
From the question we are told
How to find the area under the standard normal curve between z 1.5 and z 2.5?
Generally the equation for the probability is mathematically given as
P(1.5 &2.5) = P(Z < 2.5) - P(Z < 1.5)
Where
P(Z < 2.5) = 0.99
P(Z < 1.5) = 0.93
From Z Table
Therefore
P(1.5 &2.5) = P(Z < 2.5) - P(Z < 1.5)
P(1.5 &2.5) =0.06
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8 oz of apple juice contains 0.9 milligrams of iron if the RDA for iron is 15 mg what percent of RDA of iron is provided by the apple juice
Use the diagram of the right triangle above and round your answer to the nearest hundredth. If m
Answer choices:
A) 17.32 m
B) 6.83 m
C) 14 m
D) 9.99 m
Answer:
b. 6.93 m.
Step-by-step explanation:
We have been given triangle ABC and we are asked to find the measure of a.
We will use law of sines to solve our given problem.
[tex]\frac{a}{\text{Sin}(A)}=\frac{b}{\text{Sin}(B)}=\frac{c}{\text{Sin}(C)}[/tex], where a, b and c are opposite sides of angle A, B and C respectively.
First of all, we will find the measure of angle B using angle sum property.
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]30^{\circ}+\angle B+90^{\circ}=180^{\circ}[/tex]
[tex]\angle B+120^{\circ}=180^{\circ}[/tex]
[tex]\angle B=180^{\circ}-120^{\circ}[/tex]
[tex]\angle B=60^{\circ}[/tex]
Upon substituting our given values in law of sines we will get,
[tex]\frac{a}{\text{Sin}(30^{\circ})}=\frac{12}{\text{Sin}(60^{\circ})}[/tex]
[tex]\frac{a}{0.5}=\frac{12}{\frac{\sqrt{3}}{2}}[/tex]
[tex]\frac{a}{0.5}=\frac{2*12}{\sqrt{3}}[/tex]
[tex]\frac{a}{0.5}*0.5=\frac{24}{\sqrt{3}}*0.5[/tex]
[tex]a=\frac{12}{\sqrt{3}}[/tex]
[tex]a=6.9282032302755\approx 6.93[/tex]
Therefore, the value of a is 6.93 meters and option 'b' is the correct choice.
Tickets for the movies are $7 for adults and $4 for children. Fourteen people paid a total of $68 for tickets. How many were adults and how many were children?
What is f(2) if the linearization of f(x) at a = 2 is l(x) = 12x + 4?
A polynomial that is written as a product has been ______.
A polynomial that is written as a product has been "factored completely."
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
In the expression Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.
Since we know that factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.
A polynomial which can be written as a product has been "factored completely."
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Write the epxressions for the equivalent capacitance of two capacitors write your answers in terms of c1 and c2
A fourth as much as the product of two thirds and 0.8
A fourth as much as the product of two thirds and 0.8 is ²/₁₅
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem !
First, we will translate this word problem into a mathematical equation.
The product of two thirds and 0.8
[tex]\frac{2}{3} \times 0.8[/tex]
A fourth as much as the product of two thirds and 0.8
[tex]\frac{1}{4} (\frac{2}{3} \times 0.8)[/tex]
[tex]= \frac{1}{4} (\frac{2}{3} \times \frac{4}{5})[/tex]
[tex]= \frac{1}{4} (\frac{2 \times 4}{3 \times 5})[/tex]
[tex]= \frac{1}{4} (\frac{8}{15})[/tex]
[tex]= \frac{1}{4} \times \frac{8}{15}[/tex]
[tex]= \frac{1 \times 8}{4 \times 15}[/tex]
[tex]= \frac{8}{60}[/tex]
[tex]= \frac{8 \div 4}{60 \div 4}[/tex]
[tex]= \boxed {\frac{2}{15}}[/tex]
Learn moreInfinite Number of Solutions : https://brainly.com/question/5450548System of Equations : https://brainly.com/question/1995493System of Linear equations : https://brainly.com/question/3291576Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent
Which multiplication expression that does not belong based on scaling. Explain.
Choose an expression
6 x 2 1/2
6 x 3 3/5
1/2 x 6
2 2/5 x 6