The slope of the line represented by the equation; 4/5x - 3 is; 4/5.
What is the slope of the line represented by the equation 4/5x - 3?It follows from the task content that the slope of the line represented by the equation; (4/5)x - 3 is to be determined.
Recall, from line geometry and equation of lines;
The slope-intercept form of the equation of a line, y is given as; y = mx + c.
Where, m is the slope and c is the y-intercept.
Therefore, by comparison of the equation defined as; 4/5x - 3; it follows that the slope of the equation is; 4/5.
Ultimately, the required slope is; 4/5.
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The janitor at a school discovered a leak in a pipe. The janitor found that it was leaking at a rate of 14 fl oz per hour. How fast was the pipe leaking in gallons per day?
Answer:
6.5625 gal per hour
Step-by-step explanation:
Since there are 60 minutes per hour, we need to multiply 14 by 60 to change per minute into per hour. Combining these: 14 fl oz / min x (1 gal / 128 fl oz) x (60 min / hr) = 6.5625 gal per hour. Written as a mixed fraction: 6 9/16 gal per hour.
Which of the following best describes the slope of the line below?
Answer:
D. Negative
Step-by-step explanation:
Always read the graph from left to right
The graph is going down thus it is negative
Answer: Negative.
Step-by-step explanation: The graph of the line falls from left to right which makes it negative.
The hospital is 3.1 miles west of the fire station. What is the length of a straight line between the school and the hospital? Round to the nearest tenth. Enter your answer in the box.
Using the Pythagorean Theorem, it is found that:
A. The straight line distance between the school and the fire station is of 4.62 miles.
B. The distance between the school and the hospital is of 2.08 miles.
Pythagorean TheoremThe Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In the context of this problem, the distance between the school and the fire station is the hypotenuse of a right triangle with sides 4.3 and 1.7, hence:
d² = 4.3² + 1.7²
d = sqrt(4.3² + 1.7²)
d = 4.62 miles.
The hospital is 3.1 miles west of the fire station, hence the distance between the school and the hospital is the hypotenuse of a right triangle of sides 1.7 and 4.3 - 3.1 = 1.2, hence:
d² = 1.2² + 1.7²
d = sqrt(1.2² + 1.7²)
d = 2.08 miles.
Missing informationThe complete problem is given by the image at the end of the answer.
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Part of the graph of the function f(x) = (x + 4)(x - 6) isshown below.Which statements about the function are true? Selecttwo optionsThe vertex of the function is at (1,-25).6The vertex of the function is at (1,-24).The graph is increasing only on the interval -4
The vertex of the function is (1, -25) Correct
Because
f(x) = (x + 4)(x - 6)
Substitution
-25 = (1 + 4)(1 - 6)
Simplification
-25 = (5)(-5)
Result
-25 = -25 As both sides of the equation are equal this option is true
5) The graph is negative on the entire interval - 4 < x < 6 because the graph is below the x-axis
a researcher counted the hours a brand of batteries could power different devices. the data are normally distributed with a mean of 74.674.6 hours and a standard deviation of 9.19.1 hours. what percentage of devices ran on the batteries for fewer than
the data are normally distributed with a mean of 74.674.6 hours and a standard deviation of 9.19.1 hours. So 10.2% of gadgets were powered by batteries for fewer than 63 hours.
Given that,
Data have a mean of 74.6 hours and a standard deviation of 9.1 hours, and they are regularly distributed.
The standard deviation is defined as ?
The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.
[tex]p(X\leq 63) = p(Z\leq 63-74.6/9.1)[/tex]
From standard deviation,
[tex]p(X\leq 63) = p(Z\leq -1.279)= 0.1061[/tex]
a certain percentage of gadgets have battery life of less than 63 hours.
X= 63 hours
Percentage of devices ran on the batteries for fewer than 63 hours = 10.2%
Therefore, 10.2% of electronic devices had battery life of less than 63 hours
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betty and karen have been hired to paint the houses in a new development. working together, the women can paint a house in two-thirds the time that it takes karen working alone. betty takes 4 h to paint a house alone. how long does it take karen to paint a house working alone?
Betty takes 6 hours to paint a house alone, that indicates she can paint 1/6 of the house in 1 hour then Karen working alone will paint a house in 3 hours.
How long does it take paint a house working alone?Since Betty takes 6 hours to paint a house alone, that indicates she can paint 1/6 of the house in 1 hour.
Karen can even paint 1/x in 1 hour
Both of them will paint the house in 3/2 hours.
We then add them together which gives:
1/6 + 1/x = 3/2x
The lowest common multiple is 6x
1x/6x + 6/6x = 9/6x
We then leave out the denominators
1x + 6 = 9
simplifying the above equation, we get
x = 9 - 6
x = 3
Therefore, the value of x = 3.
Karen working alone will paint a house in 3 hours.
The complete question is:
Betty and Karen have been hired to paint the houses in a new development. Working together, the women can paint a house in two-thirds the time that it takes Karen working alone. Betty takes 14 h to paint a house alone. Betty takes 6 h to paint a house alone.
Required:
How long does it take Karen to paint a house working alone?
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Find the area of the region that is inside the square and outside the circle. The circle has a diameter of 8 inches. Round to the nearest tenth.
The area of the region within the square and without the circle is equal to 13.7 square inches.
What is the area of a region generated by a square and a circle?In this problem we find the case of figure generated by a square and an inscribed circle. Then, the area of the region is found by subtracting the area of the circle from the area of the square. Then, the area is:
A = L² - 0.25π · D²
Where:
L - Side length, in inches.D - Diameter, in inches.A - Areas, in square inches.If we know that D = L = 8 in, then the area of the region is:
A = (8 in)² - 0.25π · (8 in)²
A = 64 in² - 50.265 in²
A = 13.735 in²
The area of the region is equal to 13.7 square inches.
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Use the graph to estimate the number of school newspapers distributed in the third month 700250400500
Given the graph, you can identify that x-axis represents the number of the corresponding month, and the y-axis represents the Number of Newspapers distributed (in hundreds).
You know these points:
[tex]\begin{gathered} (2,2) \\ (4,3) \end{gathered}[/tex]Notice that 200 school newspapers were distributed in the second month, and 300 school newspapers were distributed in the fourth month. Therefore, you can conclude that the number of school newspapers that were distributed in the second month must be between 200 and 300. You can set up that, for:
[tex]x=2[/tex]The y-value is:
[tex]y\approx2.5[/tex]Hence, the answer is: Second option.
y =40x^2 find X when y =10,360,1000,4000
Find the measure of
Answer: ∠BDG = 50°
Step-by-step explanation:
We know that a straight line is equal to 180°, meaning that line CDF is 180°.
Next, we know that angle CDB, angle BDG, and angle GDF should all add up to be 180°, since we know CDF is equal to 180°.
Lastly, with all this information in mind, we will set up an equation and solve.
130° + BDG = 180°
∠BDG = 50°
12/-3 Enter your answer as a number, like this: 42
Answer:
-4
Step-by-step explanation:
12/-3=-4
Let x represent the unknown value, then write an algebraic expression for: double a quantity increased by nine
Answer:
2(x + 9)
Explanation:
Let x represent the unknown value.
Double a quantity increased 9 means;
*We'll multiply the quantity by 2
*Increased by signifies addition
*Quantity means we'll put the expression after it in brackets
Let's go ahead and write the required algebraic expression;
[tex]2(x+9)[/tex]A line has a slope of – 1 and includes the points (9,2) and (8,p). What is the value of p?
Answer:
p = 3
Step-by-step explanation:
y = mx + b They gave us the slope of -1. We need to find the y intercept. We will use the x of 9 and the y of 2 to find b. We will plug these numbers in to find b.
y = mx + b
2 = -1(9) + b
2 = -9 + b Add 9 to both sides
11 = b
y = -x +11
Now, plug in 8 for x
y = -1(8) + 11
y = -8 + 11
y = 3
In this case p is 3.
What is the slope of a line perpendicular to the line whose equation is 3x+y=8
Answer:
slope = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
3x + y = 8 ( subtract 3x from both sides )
y = - 3x + 8 ← in slope- intercept form
with slope m = - 3
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]
What is the distance between the points (−7, −3) and (−7, −9) ? Responses
Which expression is equivalent to 2x ^ 2 - 2x + 7 ?
Answer:
(x² -5x +13) + (x² +3x -6)
Step-by-step explanation:
(x² -5x +13) + (x² +3x -6)
x² -5x +13 + x² +3x -6
|x² + x²| |-5x + 3x| |+13 -6|
2x² -2x +7
Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. if beth places the swings at point d, how could she prove that point d is equidistant from the jungle gym and monkey bars? if segment ad ≅ segment cd, then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent. if segment ad ≅ segment cd, then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. if m∠acd = 90° then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent. if m∠acd = 90° then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
The angle bisector theorem states that a triangle's opposite side is divided into two halves by an angle bisector that is proportional to the triangle's other two sides.
A point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects, therefore if mACD = 90°, point D is equidistant from points A and B.
Any point on the perpendicular bisector is simply equal distance from both endpoints of the line segment on which it is drawn, according to the perpendicular bisector theorem.
The answer is that point is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it makes up. Therefore, if a pillar is stationed at the middle of a bridge at an angle, all the points on the pillar will be equidistant from the end points of the bridge intersects.
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A Large bag contains 7/12 pound of nails. How many 1/4 pound bags can be filled with this amount of nails?
The number of 1/4 pound bags that can be filled with this amount of nails is 2 1/3 bags.
How to calculate the fraction?The large bag contains 7/12 pound of nails.
We also want to fill them into 1/4 pounds of bags. The number of bags needed will be calculated through division. This will be:
= Amount in large bags / Smaller bags
= 7/12 ÷ 1/4
= 7/12 × 4/1
= 28/12
= 2 1/3
Therefore, 2 1/3 1/4 bags are required
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pulse rates of adult females are normally distributed with a mean of 74.0 beats per minute (bpm) and a standard deviation of 12.5 bpm. what is the percentage of adult females with pulse rates between 49.0 bpm and 86.5 bpm? what percentage of adult females have pulse rates below 90 bpm?
The percentage of adult females with pulse rates between 49.0 bpm and 86.5 bpm - 81.86%
The percentage of adult females have pulse rates below 90 bpm - 89.97%
a)
X ~ N ( µ = 74 , σ = 12.5 )
P ( 49 < X < 86.5 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 49 - 74 ) / 12.5
Z = -2
Z = ( 86.5 - 74 ) / 12.5
Z = 1
P ( -2 < Z < 1 )
P ( 49 < X < 86.5 ) = P ( Z < 1 ) - P ( Z < -2 )
P ( 49 < X < 86.5 ) = 0.8413 - 0.0228
P ( 49 < X < 86.5 ) = 0.8186 ≈ 81.86%
b)
X ~ N ( µ = 74 , σ = 12.5 )
P ( X < 90 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 90 - 74 ) / 12.5
Z = 1.28
P ( ( X - µ ) / σ ) < ( 90 - 74 ) / 12.5 )
P ( X < 90 ) = P ( Z < 1.28 )
P ( X < 90 ) = 0.8997 ≈ 89.97%
What is pulse rate ?
The pulse rate, or the number of times the heart beats each minute, is gauged by the pulse rate. The arteries enlarge and constrict with the flow of blood as the heart pumps blood through them. An elevated heart rate, or tachycardia, can occur for any reason. Exercise-induced or stress-related heart rate increases are two possible causes (sinus tachycardia). Sinus tachycardia is not seen as an illness but rather a symptom. Another factor contributing to tachycardia is an unsteady heartbeat (arrhythmia).
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Which transformations do not result in mapping (-k, k) to
(k, - k) ?
A) Reflection in the line y = x
B) Reflection in the line y = -x
C) Reflection in the y -axis, followed by a reflection in the x-axis
D)Translation k units right, followed by a reflection in the y-axis
The function translation / transformation rules:
f (x − b) moves the function b units to the right.−f (x) reflects the function in the x-axis (that exists, upside-down).What are the types of transformations on a graph?Function transformations specify how a function is moved on a graph and how its shape is altered. Translation, dilatation, and reflection are the three main categories of function transformations.
The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. In particular, the change of algebraic equations is a typical kind of algebraic problem.
The function translation / transformation rules:
f (x) + b moves the function b units upward.f (x) − b moves the function b units downward.f (x + b) moves the function b units to the left.f (x − b) moves the function b units to the right.−f (x) reflects the function in the x-axis (that exists, upside-down).To learn more about transformations refer to:
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What is the exchange rate? Show your work.
1 US dollar = _________ euro.
The current exchange rate is 1 US dollar = 1 euro.
What is an exchange rate?The exchange rate of a currency is the worth of one currency in respect to another, or the rate at which one currency will be exchanged for another.
The foreign exchange market, commonly known as Forex or FX, is a global decentralized market for currency trading that determines the exchange rates of such currencies.
A currency exchange rate is the rate at which one currency can be exchanged for another. In other words, the exchange rate is the price of one currency in terms of another.
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The difference between the two numbers is -1. Their sum is -27. Find the numbers. Let x represent the first number and y represent the second number. first number x = second number y =
Taking into account the definition of a system of linear equations, the first number is x= -14 and the second number y= -13.
System of linear equationsA system of linear equations is a set of linear equations (that is, a system of equations in which each equation is of the first degree) in which two or more unknowns are related.
Systems of linear equations have as a solution set all ordered pairs (x, y) that satisfy the equation, where x and y are real numbers. That is, solving a system of equations consists of finding the values of the unknowns, with which, when replaced in the equations, they must give the proposed solution.
This caseIn this case, a system of linear equations must be proposed taking into account that
"x" is the first number."y" is the second number.You know:
The difference between the two numbers is -1. Their sum is -27.The system of equations to be solved is
x-y= -1
x+y= -27
It is decided to solve the system of equations using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable "x" from the first equation:
x= -1 +y
Replacing this expression in the second equation:
-1 +y +y= -27
Solving:
y +y= -27 +1
2y= -26
y= (-26)÷2
y= -13
Remembering that x=-1 +y, you get
x= -1 -13
x= -14
Finally, the numbers are -13 and -14.
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The values of the first and second numbers are - 13 and - 14 respectively.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let us assume that the two numbers are x and y.
Given, The difference between the two numbers is -1.
∴ x - y = - 1...(i)
And, Their sum is - 27 which is,
x + y = - 27...(ii)
Now, if we add eqn (i) to eqn (ii)
x + y = - 27
+ x - y = -1
---------------------
2x = - 28
+ y and - y get canceled and we get
∴ 2x = 26.
x = - 13.
Now, substitute the value of x in any of the eqn(i). we get y = - 14.
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If a = 3 and b = -5- 2i, then find the value of the a³b in fully simplified form.
The value of a³b for the value of a=3 and b=-5-2i is -135-54i for the given complex number that defines "Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number called “iota”."
What is complex numbers?Complex numbers are those that are expressed as a+ib, where a and b are real numbers and I is a fictitious number called a "iota." I has the value (√-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im). In the 19th century, the term "complex numbers"—which denotes that they have both real and imaginary components—became widely used. Occasionally, the term "imaginary number" is used to describe a complex number that is not real or, more commonly, a number whose real part is zero (a.k.a "pure imaginary").
Here,
The value of a³b
=3³(-5-2i)
=27(-5-2i)
=-135-54i
For the given complex number that defines "Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and I is an imaginary number called "iota," the value of a³b is -135-54i.
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Mr. Webster sells vacation rentals and
earns a 3.5% commission on every
vacation rental he sells. How much
commission would he earn on a vacation
rental that sold for $4,200?
Answer:
$134.50
Step-by-step explanation:
4200 x .035 = 134.50
3.5% Percent means per 100
3.5/100 when you divide by 100, you move the decimal two places to the left.
The commission amount is $147
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Mr. Webster sells vacation rentals and earns a 3.5% commission on every vacation rental he sells.
He sold $4200.
So, 3.5% of commission:
4200 x 3.5 / 100
= 147
Therefore, the commission is $147.
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If f (x) = 4x2 + 3x − 5, then the quantity f of the quantity x plus h end quantity minus f of x end quantity all over h is equal to which of the following?
4 times the quantity x plus h end quantity squared plus 3 times the quantity x plus h end quantity minus 5 minus 4 times x squared plus 3 times x minus 5 all over h
4 times the quantity x squared plus 2 times x times h plus h squared end quantity plus 3 times the quantity x plus h end quantity minus 5 minus the quantity 4 times x squared plus 3 times x minus 5 end quantity all over h
the quantity 4 times x plus 4 times h end quantity squared plus the quantity 3 times x plus 3 times h end quantity minus 5 minus the quantity 4 times x squared plus 3 times x minus 5 end quantity all over h
4 times the quantity x plus h end quantity squared plus 3 times x minus 5 minus 4 times x squared minus 3 times x plus 5 all over h
The difference quotient of f(x) is:[ f(x + h) - f(x)]/h = 8x + 4h + 3
How to get the difference quotient?Here we have the function:f(x) =4x^2 +3x - 5
And we want to get the difference quotient that can be written as:
[f(x + h) - f(x)]/h
Replacing the function we get:
[f(x + h) - f(x)]/h = [4*(x + h)^2 + 3*(x + h) - 5 - 4*x^2 - 3x + 5]/h
Solving further (open the brackets), we have
[f(x + h) - f(x)]/h = [4x^2 + 8*x*h + 4h^2 + 3x + 3h -5 - 4x^2 - 3x + 5]/h
Evaluate the like terms
So, we have
[f(x + h) - f(x)]/h = [8*x*h + 4h^2 + 3h]/h
Evaluate the quotients
[f(x + h) - f(x)]/h = 8x + 4h + 3
That is the difference quotient.
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classify in as many ways possible
The figure above is a rectangle
The classifications of a rectangle are:
1. A rectangle has 4 sides and angles, therefore, it is a quadrilateral.
2. Each interior angle is a right-angle, that is 90⁰
3. The sum of the interior angles equals 360
4. The opposite sides are parallel
5. The opposite sides are equal
6. The diagonals bisect each other
7. The diagonals have the same length
Evaluate the function for the following values:
f(1) =
f(2)=
f(3) =
Answer: [tex]f(1)=1, f(2)=0, f(3)=2[/tex]
Step-by-step explanation:
[tex]0 \leq 0 \leq 1 \implies f(1)=1^2 =1\\\\1 < 1 \leq 2 \implies f(2)=-2+2=0\\\\2 < 3 \leq 3 \implies f(3)=3^2 -3(3)+2=2[/tex]
A construction crew has just built a new road. They built the road at a rate of 18.75 kilometers per week. They worked for 3 weeks. How many kilometers of road did they build?
Answer:
6.25 weeks
Step-by-step explanation:
Take 18.75 ÷ 3. The construction crew finishes 3 km per week. You should receive 6.25 by solving the equation. So, this is the answer.
2/3×4/5 in fraction bar
Answer:
8/15
Step-by-step explanation:
Multiply the numerators:
2*4 = 8
Multiply the denominators:
3*5 = 15
Now we have 8/15.
This cannot be simplified, so this is our final answer.
[tex]\frac{2}{3} \times\frac{4}{5}[/tex]
Multiply numerator by numerator and denominator by denominator:
[tex]2*4=8\\3*5=15[/tex]
[tex]\frac{8}{15}[/tex] would be your final answer.
Use point-slope form to write the equation of a line that passes through the point (-12,15) with slope -1.
The equation that passes through (-12, 15 with a slope of -1 in point slope form is y - 15 = - 1(x + 12)
How to represent equation in point slope form?Linear equation can be represented in different form such as point slope form, slope intercept form and standard form.
Therefore, let's represent the line that passes through (-12, 15) with a slope of -1 in point slope form.
Hence,
y - y₁ = m(x - x₁)
where
m = slopey₁ and x₁ are the coordinates of the point.Therefore,
m = slope = -1
using (-12, 15)
Hence,
y - 15 = - 1(x - (-12))
Therefore,
y - 15 = - 1(x + 12)
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