The general form of a linear equation is given by:
y = kx
where k is a constant.
From the given options you can notice that the only equation similar to the previous one is:
y = 1/6 x
Then, the previous equation is the linear equation.
Hello, I could use some help understanding this question please.
To determine the total number of employees, we need to determine first how many are men in the company.
To determine the number of men in the company, we can use the given ratio 7 men is to 5 women and apply direct proportion.
[tex]\frac{7men}{5women}=\frac{?}{135women}[/tex]To solve for the number of men (?), let's apply cross multiplication in the equation above.
[tex]\begin{gathered} \frac{7men\times135women\text{ }}{5women\text{ }}=? \\ \frac{945}{5}=\text{?} \\ 189men=? \end{gathered}[/tex]Hence, there are 189 men in the company.
In total, there are 189 men + 135 women = 324 employees in the company.
What is the solution to the equation?
Hello!
Let's solve:
[tex]\dfrac{2}{5}(15x+40)} =6x+10\\\\\\\text{Multiply the '2/5' into the function inside the parentheses}\\\dfrac{2}{5} *15x + \dfrac{2}{5} *40=6x+10\\\\6x + 16 =6x+10\\\\\\\text{Subtract '6x' from both sides}\\6x + 16-6x=6x+10-6x\\16 = 10[/tex]
Since 16 doesn't equal 10 ==> There are no solution
Hope that helps!
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 1 < x < 5.
2
f(x)
1
77
2
68
3
59
4
50
5
5
41
-
Given:
Function interval
[tex]1\leq x\leq5[/tex][tex]\begin{gathered} x\rightarrow f(x) \\ \\ 1\rightarrow77 \\ \\ 2\rightarrow68 \\ \\ 3\rightarrow59 \\ \\ 4\rightarrow50 \\ \\ 5\rightarrow41 \end{gathered}[/tex]Find-: Average rate of change.
Sol:
The average rate of change is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Choose any two-point.
[tex]\begin{gathered} (x_1,y_1)=(1,77) \\ \\ (x_2,y_2)=(2,68) \end{gathered}[/tex]So average rate of change is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{68-77}{2-1} \\ \\ m=\frac{-9}{1} \\ \\ m=-9 \end{gathered}[/tex]The average rate of change is -9.
exercise after work, Albert (A) went running and Tanisha (T) walked for exercise. Their times and distances are showing in the graph below. How much as Albert running than Tanisha walking in miles per hour? Explain how you found your answer.
In the picture, there are two lines that graph distance versus time, so the slope of the line is teh rate or the speed of Albert or Tanisha.
We need to calculate the slope of each line. We can note that the two lines start in the origin point (0, 0), so:
[tex]\begin{gathered} \text{For Albert, we can s}ee\text{ that the point (10, 1) is in the line, so:} \\ slopeofAlbert=m_A=\frac{1}{10}=0.1\frac{miles}{\min ute} \\ \text{For Tanisha, we can se}e\text{ thet the point (}20,\text{ 1) is in the line. so:} \\ slopeofTanisha=m_T=\frac{1}{20}=0.05\frac{miles}{\min ute} \end{gathered}[/tex]The different between the slopes (speed) is:
[tex]\begin{gathered} m_A-m_T=0.1\frac{miles}{\min ute}-0.05\frac{miles}{\min ute}=0.05\frac{miles}{\min ute} \\ In\text{ miles/hours is:} \\ m_A-m_T=0.05\frac{miles}{\min ute}\cdot\frac{60\text{minutes}}{1\text{hour}}=3\frac{miles}{hour} \end{gathered}[/tex]Albert goes 3 miles/hour faster than Tanisha
How many times larger is (1.008 x 101) than (6 x 10-f)?
0.168
5.95
11.682
16.8
Answer:
11.682 many times larger
Answer:
16.8
Step-by-step explanation:
To find how many times larger (1.008 × 10¹) is than (6 × 10⁻¹), divide the first expression by the second expression:
[tex]\implies \dfrac{1.008 \times 10^1}{6 \times 10^{-1}}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{ab}{cd}=\dfrac{a}{c} \times \dfrac{b}{d}:[/tex]
[tex]\implies \dfrac{1.008}{6} \times \dfrac{10^1}{10^{-1}}[/tex]
Divide the numbers 1.008 and 6:
[tex]\implies 0.168 \times \dfrac{10^1}{10^{-1}}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 0.168 \times 10^{(1-(-1)}[/tex]
Simplify:
[tex]\implies 0.168 \times 10^{2}[/tex]
[tex]\implies 0.168 \times 10 \times 10[/tex]
[tex]\implies 1.68 \times 10[/tex]
[tex]\implies 16.8[/tex]
The length of a rectangular piece of steel in a bridge is 2 meters less than triple the width. The perimeter of the piece of steel is 60 meters. Find the length of the pieceof steel. Find the width of the piece of steel.
Let "x" represent the width of the rectangular steel, then the length, which is 2meters less than triple the width, can be expressed as "3x-2".
The perimeter of the rectangular piece is 60meters.
The formula for the perimeter is the following:
[tex]P=2w+2l[/tex]Replace the formula with the expressions for the width and length and the given perimeter of the piece of steel:
w=x
l=3x-2
P=60
[tex]60=2x+2(3x-2)[/tex]From this expression, you can determine the value of x.
-First, distribute the multiplication on the parentheses term
[tex]\begin{gathered} 60=2x+2\cdot3x-2\cdot2 \\ 60=2x+6x-4 \end{gathered}[/tex]-Second, simplify the like terms and pass "-4" to the left side of the expression by applying the opposite operation "+4" to both sides of it
[tex]\begin{gathered} 60=8x-4 \\ 60+4=8x-4+4 \\ 64=8x \end{gathered}[/tex]-Third, divide both sides by 8 to determine the value of x
[tex]\begin{gathered} \frac{64}{8}=\frac{8x}{8} \\ 8=x \end{gathered}[/tex]The value of x is 8m, which means that the width of the piece of steel is 8m
To determine the length you just have to replace the expression by x=8
[tex]\begin{gathered} l=3x-2 \\ l=3\cdot8-2 \\ l=24-2 \\ l=22 \end{gathered}[/tex]The length is 22m
Jumping makes a frog so tired, each successive jump is 1/3 the distance of the previous hump. If a frog jumps 24 cm on its first jump, how far will the frog travel after four jumps?
Answer:
35 5/9 cm total
Step-by-step explanation:
24 + 8 + 8/3 + 8 / 9 = 35 5/9 cm
The graphs below have the same shape. What is the equation of the blue graph? Gox= ?
Here, we want to deduce the equation of the blue graph
From what we have, we can see that the image of the f(x) was moved 2 units to the right and 1 unit upwards
What this mean is that, we have 1 added to the y value and 2 added to the x value
So, the equation of the blue graph is
[tex]G(x)=(x+2)^2+1[/tex]Convert 120 inches to feet. There are 12 inches in a foot. O A. 1200 feet B. 1440 feet C. 20 feet O D. 10 feet
There are 12 inches in a foot.
To convert 120 inches to feet we can use the next proportion:
[tex]\frac{12\text{ inches}}{120\text{ inches}}=\frac{1\text{ foot}}{x\text{ feet}}[/tex]Solving for x:
x = 1*120/12
x = 10 feet
-9(x-4)=81 i know what im doing im jsur stuck
Solution:
The equation in the question is given below as
[tex]-9(x-4)=81[/tex]Step 1:
Expand the brackets in the qu
Write the statement in if-then form.
Prime numbers only have two factors, 1 and itself.
Answer:
If the wide variety has only two factors, 1 and itself, then it if truth be told is top in a very huge way. If the variety has usually greater than two factors, then it is for all intents and functions composite in a refined way.
Answer:
See below
Step-by-step explanation:
If a number only has factors of one and itself, then the number is a prime number.
sixyt students are competing in a video game challenge. if 2 students comete against each other in every round how many different combinations can be made for the first round of the challenge
Answer:
i believe its 30
Step-by-step explanation:
well i think you would divide sixty by 2 which is thirty.
IM SO SORRY IF IM WRONG- THIS IS JUST WHAT I THINK!
Question is down below Answer choices are the same for each drop down menu.
Given:
The triangles EFG and PQR are given.
To find: The correct answer
Explanation:
a) An angle bisector:
As we know,
An angle bisector is a line or ray that divides an angle into two congruent angles.
Here, The line FJ is the angle bisector for angle F.
Thus, the angle bisector is line FJ.
b) Perpendicular bisector:
As we know,
A perpendicular bisector is a line that bisects another line segment at a right angle, through the intersection point.
Here, the line SL bisects another line segment PQ at a right angle, through the intersection point S.
Thus, the perpendicular bisector is SL.
c) A point is equidistant from the line segment FE and EG:
The point that is equidistant to all sides of a triangle is called the incenter.
Here, H is the point that is equidistant from the line segment FE and EG.
Thus, the point is H only.
d) A point is equidistant from the points P and Q:
The point that is equidistant to all vertices of a triangle is called the circumcenter.
Here, L is the point that is equidistant from the points P and Q.
Thus, the point is L only.
Find θ where θ = sin-1(-.5) where 0 < θ < 2π. Select all the correct choices. Select one or more: a. 11pi/6 b. pi/6 c. 5pi/6 d. 210 degrees e. 30 degrees
The value of inverse trigonometric function θ = sin-1(-.5) is 30°
What is an inverse trigonometric function?
The inverse trigonometric functions perform the opposite operation of the trigonometric functions such as sine, cosine, tangent, cosecant, secant, and cotangent. We know that trigonometric functions are especially applicable to the right angle triangle.
Here, the given inverse trigonometric function is θ = sin⁻¹(0.5)
Now solving the given inverse trigonometric function by consider 0.5 value in terms of sine that is :
0.5 = sine (30°)
Now, substituting back this value in place of 0.5 and solve for θ :
θ = sin⁻¹(0.5)
θ = sin⁻¹(sin(30°))
Now the inverse of sinθ is θ itself
θ = 30°
Therefore, The value of inverse trigonometric function θ = sin-1(-.5) is 30°.
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The bank that the Payans would like to borrow from uses the back-end ratio to determine loan qualification, approving applications if the back-end ratio is less than 36%. So, the Payans have collected some information on what the bank will consider to calculate the ratio, including what they estimate their monthly mortgage payment will be.According to the Payans' back-end ratio calculation, the bank will ______(most likely, not) lend the Payans $250,000 to purchase the home because their back-end ratio is_____(equal to, higher than, lower than) 36%
Approved if back-end ratio is less than 36%
Total income: $10,000
Total expenses:
$1,100 + $150 + $500 + $1,000 + $400 = $3,150
Back-end ratio: (Total expenses) / (Total Income) x 100
= (3150/10000)x100 = 31.5%
According to the Payans' back-end ratio calculation, the bank will most likely lend the Payans $250,000 to purchase the home because their back-end ratio is lower than 36%
2xy + 4 = -2y - x, solve for x
Answer:
x = -2/y -1
Step-by-step explanation:
2xy + 4 = -2y -----> x = -2y -y
Step 1: Divide 2y to all sides. 2xy÷2y + 4÷2y= -2y÷2y. Since we are divinding y with y it cancels out, so it will be -2÷ 2 = -1
Step 2: x + 2y = -1
Step 3: Then subtract 2y and move it to the other side.
x = -2/y -1
Another way of explaining it:
2xy + 4 = -2y
Step 1: Divide 2 to all sides. 2xy÷2 +4÷2 = -2y÷2
Step 2: xy + 2 = -y
Step 3: Subtract the 2 and move it to the other side.
xy + 2 = -y
-2. -2
Step 4: xy = -2 -y
Step 5: Then we divide the y to all sides. xy÷y = -2÷y - y÷y
Step 6: xy÷y = -2 ÷ y -2 ÷y. We're trying to get x by itself.
Step 7: x = -2/y -1. Since we are divinding y with y it cancels out, so it will be
Answer: x = -2/y -1
(Any Further Questions or Confusion Please Let Me Know)
Help me! i need this answer now i am so dead. if i get it worng please help pls
Answer:
x = 4.8
Step-by-step explanation:
Area = Length times width
12 = 2.5x Divide both sides by 2.5
4.8 = x
What is the equation, in slope-intercept form, of the line that passes throughthe point (8, -6) and is perpendicular to y = 4x+7?
From the problem, we are given a point (8, -6) and an equation y = 4x + 7
The equation we are to obtain is perpendicular to y = 4x + 7
In Mathematical terms, it means the slope of the given equation and the one we are to find follow the relation:
[tex]\begin{gathered} m_1\text{ = }\frac{-1}{m_2_{}_{}} \\ \text{where m}_{1\text{ }}\text{represents the slope of the first equation and }m_2\text{ represents the slope of the second equation} \end{gathered}[/tex]slope of the given equation = 4
[tex]\text{Slope of the required equation = }\frac{-1}{4}\text{ = -0.25}[/tex]The required equation passes through a point (8,-6)
The formula for obtaining the equation with a given slope that passes through a point is given as :
[tex]\text{ (y - y}_1)=m(x-x_1)[/tex]By substituting;
[tex]\begin{gathered} (y\text{ - (-6)) = -0.25(x - 8)} \\ y\text{ + 6 = -0.25x + 2} \\ y\text{ = -0.25x -4} \end{gathered}[/tex]The equation in slope-intercept form is y = -0.25x - 4
Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex. (7,2) (-4,0) (-6, -7)
ANSWER:
STEP-BY-STEP EXPLANATION:
[tex]undefined[/tex]At the craft store, Elena bought a bag of purple and blue marbles. She received 19 purple marbles and 6 blue marbles. What percentage of the marbles were purple? were purple?
She received 19 purple and 6 blue marbles, so the total number of marbles is 19 + 6 = 25
Percentage of purple marbles = 100 * 19/25 = 1900/25 = 76%
Percentage of blue marbles = 100 * 6/25 = 600/25 = 24%
Answer:
Percentage of purple marbles = 76%
Percentage of blue marbles = 24%
4x-3
x=2
4(2)-3
The ____ property is used here.
According to the commutative property, the numbers we use can be moved around or swapped around without changing the solution. For addition and multiplication, the principle is true, but not for division or subtraction.
4x-3
Is x=2
4(2)-3
This uses the ___ attribute?
Answer:
(5,-5) commutative property of subtraction property is used.
Example:
It can be commutative if you retain the negative with the 2 and the positive with the 5. Edited: Subtraction is not a commutative operation; for example, 5-2=3 and 2-5=-3. The order of addition or subtraction does not important, though, if you maintain the sign of the integer, as in +5-2=3 and -2+5=3, for example.
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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? a 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 b 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 c 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 d 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 the function f(x) = 4x² + 3x - 5 is [f(x + h) - f(x)]/h = 8x + 4h + 3
How to evaluate the difference quotient?The function is given as
f(x) = 4x² + 3x - 5
Start by calculating the function f(x + h)
So, we have the following
f(x + h) = 4(x + h)² + 3(x + h) - 5
Expand
f(x + h) = 4(x² + 2xh + h²) + 3(x + h) - 5
Open the brackets
f(x + h) = 4x² + 8xh + 4h² + 3x + 3h - 5
The difference quotient is then calculated as
[f(x + h) - f(x)]/h
This gives
[f(x + h) - f(x)]/h = (4x² + 8xh + 4h² + 3x + 3h - 5 - 4x² - 3x + 5)/h
Evaluate the like terms
[f(x + h) - f(x)]/h = (8xh + 4h² + 3h)/h
Evaluate the quotients
[f(x + h) - f(x)]/h = 8x + 4h + 3
Hence, the value of [f(x + h) - f(x)]/h is 8x + 4h + 3
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Complete question
If f(x) = 4x² + 3x - 5, then [f(x + h) - f(x)]/h is equal to which of the following?
ind the point at which the line f ( x ) = − 4 x − 1 intersects the line g ( x ) = − 2 x + 1
Answer:
(-1,3)
Step-by-step explanation:
Where the two lines intersect, they have equal values
-4x-1 = -2x + 1
-2 = 2x
x = -1
Now, you have 'x' ....use this value in either of the equations to find 'y'
-2 (-1) + 1 = y = 3
(-1,3)
2. (05.03 MC)In the figure below, AABC 2 ADEF. Point C is the point of intersection between AG and BF, while point E is the point of intersection between DG and BFДАBFProve AABC AGEC. (10 points)
Prove that Tringle ABC is congruent to tringle GEC
Mason was creating a sundae masterpiece by adding the following chips to his ice cream. He added 1/3 cup of dark chocolate chips, 1/4 cup of milk chocolate chips, 3/4 cup of peanut butter chips, and 1/2 cup of butterscotch chips. At the last minute, he removed all of the milk chocolate chips to save to eat later. Determine how many chips he put on his sundae. Express your answer as a fraction.
Mason added 19/12 cups of chips to his sundae.
How many chips he put on his sundae?We know that Mason has a sundae and he put:
1/3 cup of dark chocolate chips.1/4 cup of milk chocolate chips (latter are removed)3/4 cup of peanut butter chips 1/2 cup of butterscotch chipsTo get the total number of chips, we just need to add these fractions (except the one for the milk chocolate chips, as these are removed).
Then we will get:
Total = 1/3 + 3/4 + 1/2 = 4/12 + 9/12 + 6/12 = 19/12
Where we used the common denominator 12 to add the fractions.
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Many delivery trucks feature a "How Am I Driving?” sticker on the rear bumper, along with a phone number. This sticker allows drivers to report erratic driving by the truck driver or offer a compliment if they like. A dispatcher at the trucking station accepts calls and records information from those who call the phone number. The dispatcher reports that in the past month, 218 calls were received. Of those calls, 178 reported negative driving behaviors by the truck drivers. How might this data-collection method produce bias in obtaining an estimate of all drivers who are satisfied with the company’s truck drivers?
This sample may lead to nonresponse bias because many drivers may not call the phone number.
This sample may lead to undercoverage bias because some drivers will be more likely to be included in the sample.
The sample may lead to response bias because some who call the phone number may not provide a truthful opinion.
This sample may lead to voluntary response bias because drivers can choose to call the phone number and register an opinion.
The way in which this data-collection method produce bias in obtaining an estimate of all drivers who are satisfied with the company’s truck drivers is that: D. This sample may lead to voluntary response bias because drivers can choose to call the phone number and register an opinion.
What is sampling bias?A sampling bias can be defined as a type of bias in which members of an intended population are selected in such a way that some members have a higher or lower sampling probability (chances) than the other members.
This ultimately implies that, a sampling bias would occur when members of an intended population are selected incorrectly and as such resulting in a sample that is not representative of the entire population.
Generally speaking, a voluntary response sample is a data-collection technique (method) that is always biased because it only include individuals who choose to volunteer, unlike a simple random sample.
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a=1.9 in, A=46.5°, C=90°Solve the right triangle. Round side lengths one decimal place.
SOLUTION
Given the following
[tex]a=1.9in,A=46.5^0,C=90^0[/tex]Consider the image below
To solve the right triangle, we need to find the following:
[tex]b=\text{?,c}=\text{?and B=?}[/tex]To find B, we use the sum of angles in a triangle
hence
[tex]\begin{gathered} A^0+B^0+C^0=180^0^{} \\ \text{where A=46.5}^0,C=90^0 \end{gathered}[/tex]Substituting into the equation we have,
[tex]\begin{gathered} 46.5^0+B+90^0=180^0 \\ 136.5+B=180^0 \end{gathered}[/tex]Subtract 136.5 from both sides
[tex]\begin{gathered} 136.5+B-136.5^0=180^0-136.5^0 \\ \text{Then} \\ B=180^0-136.5 \\ B=43.5^0 \end{gathered}[/tex]hence
B = 43.5°
To find b, we use the trigonometry ratio for tangent
From the triangle above
[tex]\begin{gathered} \tan A=\frac{a}{b} \\ \text{Where A=46.5in, a=1.9in, b=?} \end{gathered}[/tex]Substituting into the equation
[tex]\begin{gathered} \tan 46.5=\frac{1.9}{b} \\ \text{Then } \\ b=\frac{1.9}{\tan46.5} \\ \text{Where tan46.5=1.0538} \end{gathered}[/tex]Then
[tex]b=1.8030[/tex]hence
b = 1.8in to 1 decima place
To find c, we also apply trigonometry ratio for sine of an angle
[tex]\begin{gathered} \text{sinA}=\frac{opposite}{\text{hypotenuse}} \\ \text{Where } \\ A=46.5^0,\text{ opposite =1.9in},\text{ hypotenuse =c} \end{gathered}[/tex]Substituting the values into the equation we have,
[tex]\begin{gathered} \sin 46.5=\frac{1.9}{c} \\ Multiply\text{ both sides by c, we have } \\ c\times\sin 46.5=\frac{1.9}{c}\times c \\ \text{Then } \\ c\times\sin 46.5=1.9 \end{gathered}[/tex]Divide both sides by 1.9, we have
[tex]\begin{gathered} c=\frac{1.9}{\sin 46.5}=\frac{1.9}{0.7254} \\ \text{Then} \\ c=2.6193 \end{gathered}[/tex]hence
c = 2.6 in
Therefore, to solve the right triangle, we have
Answer; B = 43.5°, b = 1.8in, c = 2.6 in
6 hours into minute i want answer of this
Answer: 6 hours into minutes is 360
Step-by-step explanation:
plss help me with this i need help
A space shuttle 275 miles above the earth is orbiting the earth once every 4 hours. How far does the shuttle travel in 1 hour? (Assume the radius of the earth is 4,000 miles.) Answer exactly or round to the nearest mile
The space shuttle travels about 6713 miles per hour. Rounded to the nearest mile, this is approximately 6713 miles per hour.
What is a radius ?
In mathematics, the radius is a term used to describe the distance from the center of a circle or a sphere to any point on its surface. It is denoted by the letter "r".
The orbit of the space shuttle is circular, so the distance it travels in one orbit is equal to the circumference of the circle with a radius of 275 + 4000 = 4275 miles (275 miles above the Earth's 4000 mile radius).
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle and π is the mathematical constant pi (approximately 3.14). Therefore, the distance traveled by the shuttle in one orbit is:
C = 2π(4275) ≈ 26851 miles
Since the shuttle orbits once every 4 hours, its average speed is:
distance/time = 26851/4 ≈ 6713 miles per hour
Therefore, the space shuttle travels about 6713 miles per hour. Rounded to the nearest mile, this is approximately 6713 miles per hour.
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