Answer:
The rate of change in Erinn's hourly wage per year is [tex]1.25\$\ hour/year[/tex]
Step-by-step explanation:
we have that
x ----> the time in years that she worked at a company
y ----> represent the hourly wage
[tex]-5x+4y=32[/tex] ----> linear equation that represent the situation
Solve for y
[tex]4y=5x+32[/tex]
[tex]y=(5/4)x+32/4[/tex]
[tex]y=1.25x+8[/tex]
The slope m of the linear equation is
[tex]m=1.25\$\ hour/year[/tex]
The rate of change in Erinn's hourly wage per year is equal to the slope of the linear equation
so
The rate of change in Erinn's hourly wage per year is [tex]1.25\$\ hour/year[/tex]
Justin and Desiree each wrote a ratio comparing the numbers of students and tables in their classroom. There are 6 tables in the room with 4 students at each table.
Justin states that the ratio is 4:1.
Desiree insists the ratio is 24:6.
They both ask Luke to tell them which ratio is correct. Which statement below would be the best answer for Luke?
Answer:
Desiree and Justin have the same ratio, Justin's is just simplified.
Step-by-step explanation:
Take Desiree's ratio and divide both sides by 5
24:6
24/6 : 6/6
4:1
This is the same ratio as Justin
Both ratio's are the same
Answer:
Both are correct
Step-by-step explanation:
is a line best fit appropriate for the data? explain why or why not
30 points!
Answer:
no
Step-by-step explanation:
a line is better for a more constant and organized data. this data is unorganized and is scattered. this would be best for this type of dara
Which scenario could be represented by the algebraic expression n/12?
Answer:
Step-by-step explanation:
A pie weighs n pounds. How much would one serving weigh if the entire pie were to be shared equally among 12 people?
Which ratio can be used to solve for y in the triangle below?
Option (1) will be the answer.
Sine rule in a triangle,sine rule defines the ratio of the sine of the angles and lengths of the opposite sides of a triangle.sine rule in a triangle ABC is defined by,[tex]\frac{\text{sinA}}{a}= \frac{\text{sinB}}{b}= \frac{\text{sinC}}{c}[/tex]
Where [tex]a,b,c[/tex] are the opposite sides of ∠A, ∠B and ∠C.
Given in the question,
Two angles 75° and 40°Measure of opposite sides of the angles are 25 mm and 'y' respectively.Apply sine rule in the triangle given in the picture,
[tex]\frac{\text{sin(40)}^\circ}{y}= \frac{\text{sin(75)}^\circ}{25}[/tex]
Therefore, expression given in option (1) will be the answer.
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1) For the triangle shown, find the value of x.
A) 4
B) 6
C) 8
D) 10
E) None of the above
2) For the triangle shown, find the value of y.
A) 8
B) 8√2
C) 8√3
D) 16√3
E) None of the above
The value of x in the triangle is 8 and the value of y is [tex]8\sqrt2[/tex]
How to determine the value of x in the triangle
From the question, we have the following parameters that can be used in our computation:
The triangle
Using the Pythagoras theorem, we have:
[tex]x^2 = 10^2 - 8^2[/tex]
This gives
[tex]x^2 = 36[/tex]
take the square root of both sides
x = 8
How to determine the value of y in the triangle
Using the Pythagoras theorem on the second triangle, we have
[tex]y^2 = 8^2 + 8^2[/tex]
This gives
[tex]y^2 = 2(8^2)[/tex]
take the square root of both sides
[tex]y = 8\sqrt2[/tex]
Hence, the value of x is 8 and the value of y is [tex]8\sqrt2[/tex]
You invested $5000 between two accounts paying 4% and 9% annual interest, respectively. If the total interest earned for the
year was $350, how much was invested at each rate?
$
was invested at 4% and
was invested at 9%.
Answer:
Part 1) The amount invested at 4% was $2,000
Part 2) The amount invested at 9% was $3,000
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
Let
x------> the amount invested at 4%
5,000-x ----> the amount invested at 9%
in this problem we have
[tex]t=1\ year\\ P=\$5,000\\I=\$350\\r1=0.04\\r2=0.09[/tex]
substitute in the formula above
[tex]350=x(0.04*1)+(5,000-x)(0.09*1)[/tex]
[tex]350=0.04x+450-0.09x[/tex]
[tex]0.05x=450-350[/tex]
[tex]0.05x=100[/tex]
[tex]x=2,000[/tex]
so
[tex]5,000-x=5,000-2,000=3,000[/tex]
therefore
The amount invested at 4% was $2,000
The amount invested at 9% was $3,000
A walking path across a park is represented by the equation y= -4x - 6 . A new path will be built perpendicular to this path. The path will intersect at the point (-4 , 10) . Identify the equation that represents the new path .
Answer:
y=1/4 x +11
Step-by-step explanation:
So this is a word problem but it isn't too bad to figure what they want: They are looking for a line that is perpendicular to y=-4x-6 and goes through (-4,10).
So we are looking for an equation whose slope is the opposite reciprocal of the given equation's slope.
The given equation has a slope of -4
The opposite reciprocal of -4 is 1/4 so that is the slope of our new line.
So we know our equation is in the form of y=1/4 x+b
Now we are given that this line should go through (-4,10) so plug it in to find b.
10=1/4 * (-4)+b
10=-1+b
11=b
So the equation is y=1/4 x+11
Answer: [tex]y=\frac{1}{4}x+11[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Given the equation of the line [tex]y= -4x - 6[/tex], you can identify that the slope is:
[tex]m=-4[/tex]
By definition, the slopes of perpendicular lines are negative reciprocals, then the slope of equation of the line that represents the new path which will be built perpendicular to other path, is:
[tex]m=\frac{1}{4}[/tex]
Knowing that the path will intersect at the point (-4 ,10), you need to substitute the slope and this point into [tex]y=mx+b[/tex] and solve for "b":
[tex]10=\frac{1}{4}(-4)+b\\\\10+1=b\\\\b=11[/tex]
Therefore, the equation that represents the new path is:
[tex]y=\frac{1}{4}x+11[/tex]
If f(x)=x^4-x^3+x^2 and g(x)=-x^2, where x =/= 0, what is (f/g)(x)?
Answer:
- x² + x - 1
Step-by-step explanation:
(f / g)(x)
= [tex]\frac{x^4-x^3+x^2}{- x^2}[/tex]
divide each term on the numerator by - x²
= [tex]\frac{x^4}{- x^2}[/tex] - [tex]\frac{x^3}{-x^2}[/tex] + [tex]\frac{x^2}{-x^2}[/tex]
= - [tex]x^{4-2}[/tex] + [tex]x^{3-2}[/tex] - [tex]x^{2-2}[/tex]
= - x² + x - [tex]x^{0}[/tex] = - x² + x - 1
There are 36 squares in the model.What is the result of 36 divided by 3
Answer:
The result of 36 divided by 3 is 12
Answer:
12 is the answer
Step-by-step explanation:
Type in the correct answer. What is the slope of line m?
Answer:
[tex]-\dfrac{1}{2}[/tex]
Step-by-step explanation:
In the given graph of straight line to find the slope of the line.
First we choose two points on line and then using formula to find the slope.
Formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Point on line from graph: (2,-1) and (-2,1)
[tex]x_1\rightarrow 2[/tex]
[tex]y_1\rightarrow -1[/tex]
[tex]x_2\rightarrow -2[/tex]
[tex]y_2\rightarrow 1[/tex]
Substitute the points into formula
[tex]m=\dfrac{1+1}{-2-2}[/tex]
[tex]m=-\dfrac{1}{2}[/tex]
Hence, The slope of the line is [tex]-\dfrac{1}{2}[/tex]
The slope (m) of the line passing through the points (-2, 1) and (2, -1) is -1/2.
The slope of a line is a measure of its steepness or incline. It determines how much the line rises or falls for each unit of horizontal change. Mathematically, the slope is defined as the ratio of the vertical change (the difference in y-coordinates) to the horizontal change (the difference in x-coordinates) between any two points on the line.
The slope is typically denoted by the letter "m" and can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two distinct points on the line.
The slope can be positive, negative, zero, or undefined. A positive slope indicates that the line is upward-sloping from left to right, a negative slope indicates a downward-sloping line, a zero slope indicates a horizontal line and an undefined slope indicates a vertical line. The magnitude of the slope represents the steepness of the line.
To find the slope (m) of a line passing through two points (x1, y1) and (x2, y2), you can use the formula:
m = (y2 - y1) / (x2 - x1)
In this case, the points are (-2, 1) and (2, -1). Let's substitute the values into the formula:
m = (-1 - 1) / (2 - (-2))
= (-2) / (2 + 2)
= (-2) / 4
= -1/2
Therefore, the slope (m) of the line passing through the points (-2, 1) and (2, -1) is -1/2.
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x^2+y^2=25 find the distance of point (x,y) from origin
Answer:
5
Step-by-step explanation:
The radius is 5.
All I do was think of the center-radius form a circle
(x-h)^2+(y-k)^2=r^2
x^2 + y^2 =25
(x-0)^2+(y-0)^2=5^2
The center is (0,0) and the radius is 5.
So a point on the circle (x,y) has a distance of 5 from the center
and the center's case here is (0,0).
Which of the following functions will produce the graph shown below?
ANSWER
The answer is B.
[tex]y = \frac{ {x}^{2} - 1}{ {x}^{2} + 2x - 3 } [/tex]
EXPLANATION
The graph represents a rational function.
This rational function has a hole at x=1 and a vertical asymptote at x=-3.
This implies that the denominator of the rational function in factored form is
[tex](x + 3)(x - 1)[/tex]
When we expand this, we get:
[tex] {x}^{2} + 2x - 3[/tex]
This tells us that the answer must be option B.
This graph also has a horizontal asymptote at y=1.
The numerator must therefore have leading term that is quadratic with the coefficient being unity or 1.
Therefore the function is actually
[tex]y = \frac{ {x}^{2} - 1}{ {x}^{2} + 2x - 3 } [/tex]
Give a reason to justify the equation. 3 • (10 • 12) = (3 • 10) • 12
The equation 3 • (10 • 12) = (3 • 10) • 12 is justified by the associative property of multiplication, stating that the grouping of numbers in multiplication does not change the outcome.
Explanation:The equation 3 • (10 • 12) = (3 • 10) • 12 can be justified using the property of associative property of multiplication. This property states that when three or more numbers are multiplied, the way in which the numbers are grouped does not change the product. In simpler terms, no matter how we place the parentheses in a multiplication equation, the result will always be the same.
For example, let's take three numbers, a, b, and c. The associative property of multiplication tells us that (a • b) • c = a • (b • c). Applying this to the given equation, 3 • (10 • 12) is the same as (3 • 10) • 12 because, according to the property, the grouping of numbers does not affect the outcome. This demonstrates why the original equation holds true.
each machine ch the bottling plant can fill several gallons of milk every 15 seconds . this sequence describes the number of gallons of milk each machine at the bottling plant can fill over time 12,24,36,48,80
Answer:
A-B-D-B
Step-by-step explanation:
f(x) = x5 – 8x4 + 16x3?
The graph touches, but does not cross, the x–axis at x =
The graph of the function crosses the x–axis at x =
.
URGENT
The true statement is the graph of the function crosses the x-axis at x = x = 0, 1.34 and 7.97
The function is given as:
[tex]\mathbf{f(x) = x^5 - 8x^4 + 16x^3}[/tex]
See attachment for the graph of [tex]\mathbf{f(x) = x^5 - 8x^4 + 16x^3}[/tex]
From the attachment, we have the following highlights
The graph crosses the x-axis at all points it touches the x-axis,The graph of the function crosses the x-axis at x = x = 0, 1.34 and 7.97Hence, the true statement is (b) above
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Please answer ASAP. You begin with 1/2 scoop of ice cream. Since you're hungry, you ask the vendor for 2/7 more scoops of ice cream. Then, you eat 5/8 scoops. How many scoops of ice cream are left on your cone? I will mark Brainliest for first correct answer.
Answer:
9/56
Step-by-step explanation:
[tex] \frac{1}{2} + \frac{2 }{7} - \frac{5}{8 } = \frac{9}{56} [/tex]
What is the result of the following division?
For this case we must indicate the result of the following expression:
[tex]\frac {2x ^ 3-3x + 5} {x + 3}[/tex]
We must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend until it reaches the remainder.
It must be fulfilled that:
Dividend = Quotient * Divider + Remainder
Answer:
See the attached image
Option A
Answer: Choice A
Step-by-step explanation:
Find Percent increase or Percent Decrease
Question
The price of a share of one stock rose from $12.50 to $50. Find the percent increase
Provide your answer below:
The increase in price of the stock is $37.50. To find the percent increase, divide the increase (37.50) by the original price (12.50) and multiply by 100, giving a percent increase of 300%.
Explanation:The question requires us to find the percent increase in the price of a stock. First, to find the increase, we subtract the initial price from the final price. We get $50 - $12.50 = $37.50. This is the increase in price. To find the percentage increase, we divide this increase by the initial price and multiply by 100 to convert it into percent. Therefore, the percentage increase = ($37.50 / $12.50) x 100 = 300%. Therefore, there is a 300% increase in the stock price.
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the national flag of scotland has a white diagonal on a blue backround Tracy is sewing a scottish flag she knows that the length of one diagonal will be 15 feet and the flag will be 9 feet high to the nearest foot how long will the scottish flag be
The answer is 12
a² = c² - b²
a² = 15² - 9²
a² = 225 - 81
a² = 144
a = √144
a = 12
Answer:
12 ft
Step-by-step explanation:
The diagonal divides the flag into 2 right triangles.
Using Pythagoras' identity on the right triangle.
The square on the hypotenuse (diagonal ) is equal to the sum of the squares on the other 2 sides.
let x be the length, then
x² + 9² = 15²
x² + 81 = 225 ( subtract 81 from both sides )
x² = 144 ( take the square root of both sides )
x = [tex]\sqrt{144}[/tex] = 12
The length of the flag is 12 ft
Fourteen is 20% of what
Answer: 14 is 20% of 70
If AC = 15 centimeters, and BC = 12 centimeters, which does AB equal?
a. 6
b. 8
c. 9
d. 10
The formula W = Fd shows the relationship between work, force, and distance. Solve this formula for distance.
Answer:
[tex]d = \frac{W}{F}[/tex]
Step-by-step explanation:
To do this, we must isolate the variable d.
W = Fd
To isolate d, we must divide the variable F from both sides.
W ÷ F = Fd ÷ F
W ÷ F = d
Now that we have isolated the variable d, we have successfully solved this formula for distance.
[tex]d = \frac{W}{F}[/tex]
Answer:
d = W/F.
Step-by-step explanation:
You simply divide both sides by F:
W / F = Fd / F
W/F = d.
what is the equation of the line that is perpendicular to and has the same y intercept as the given line
Answer:
y=5x+1
Step-by-step explanation:
step 1
Find the slope of the given line
we have
(0,1) and (5,0)
m=(0-1)/(5-0)
m=-1/5
step 2
Find the slope of the perpendicular line to the given line
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1
m1*m2=-1
m1=-1/5
substitute
(-1/5)*m2=-1
m2=5
step 3
Find the equation of the line with slope m=5 and y-intercept (0,1)
The equation of the line into slope intercept form is equal to
y=mx+b
we have
m=5
b=1
substitute
y=5x+1
Answer:
C
Step-by-step explanation:
Line AB contains points A (3, −2) and B (1, 8). The slope of line AB is
−5
negative 1 over 5
1 over 5
5
Answer:
-5
Step-by-step explanation:
We have two points. We can find the slope m using
m = (y2-y1)/ (x2-x1)
= (8--2)/ (1-3)
(8+2)/(1-3)
10/-2
-5
The slope is -5
Answer:
-5
Step-by-step explanation:
Which of the following are reciprocal functions? sin x and cos x tan x and cot x cot x and csc x csc x and sec x
Answer:
1). sin x and csc x
2). cos x and sec x
3).tan x and cot x
Step-by-step explanation:
Points to remember
Trigonometric ratios
Sin θ = Opposite side/Hypotenuse
Cos θ = Adjacent side/Hypotenuse
Tan θ = Opposite side/Adjacent side
Csc θ = Hypotenuse /Opposite side
Sec θ = Hypotenuse /Adjacent side
Cot θ = Adjacent side/Opposite side
To find the correct answers
From the above points we get reciprocal of functions are,
1). sin x and csc x
2). cos x and sec x
3).tan x and cotx
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! WILL MARK BRAINLIEST TO BEST DETAILED ANSWER
Minnie is doing a survey to find the time her classmates spend playing musical instruments. She asks the following question: Which student spends the most time playing musical instruments? Part A: Describe the data you would expect her to collect from this question. (5 points) Part B: Explain whether this is a statistical question. If this is not a statistical question, then modify the question to make it statistical. (5 points)
A. You would just get a lot of names back from people, thinking they have the most time playing instruments.
B. This question is not a statistically accurate question if you would like statistical answers back.
Statistical question definition:
A statistical question is one that can be answered by collecting data and where there will be variability in that data. For example, there will likely be variability in the data collected to answer the question,
The question to ask to get statistical answers back would be: How many hours do you play the instrument a day?
Each student would answer and you would see who has the most hours.
Final answer:
Minnie should collect quantitative data on the hours spent playing instruments by her classmates to determine who spends the most time. The original survey question is not statistical because it does not allow for analysis of a group trend, but changing the question to inquire about the typical number of hours spent by students each week would make it statistical.
Explanation:
Part A: Expected Data Collection
The data Minnie would expect to collect from her survey question would consist of quantitative information. Specifically, she should gather the number of hours each classmate spends playing musical instruments per week. This data allows her to determine which student spends the most time practicing.
Part B: Statistical Question Analysis
The question, "Which student spends the most time playing musical instruments?" is not a statistical question because it seeks a singular answer rather than understanding a trend, variation, or distribution within a group. To make it statistical, the question could be modified to: "How many hours do students typically spend playing musical instruments each week?" This revised question allows for the collection, analysis, and interpretation of data, which can lead to conclusions about the musical habits of Minnie's classmates.
Which equation is equivalent to y - 6 = -12(x+4)?
Answer:
The answer is y = -12x - 42
Step-by-step explanation:
First distribute -12 into the paranthesis.
y - 6 = -12x - 48
Then add 6 to both sides.
y = -12x - 42
That's your final answer. I hope this helps love! :)
Answer:
[tex]x = \frac{ - 1}{12} y + \frac{ - 7}{2} \\ c. \: y = - 12x - 42[/tex]
Step-by-step explanation:
[tex] 1. \: - 12x - 48 = y - 6 \\ 2. \: - 12x = y + 42 \\ 3. \: \frac{12x}{ - 12} = \frac{y + 42}{ - 12} \\ x = \frac{ - 1}{12} y + \frac{ - 7}{2} [/tex]
PLEASE HELP ME!! THIS IS FOR MY MATH FINALS! RESPOND ASAP!!
While Raj was in Italy he heard the weather forecaster say it was going to be 14C that day. Raj wasn’t sure if that was hot or cold, so he converted the temperature to degrees Fahrenheit. What is the temperature in degrees Fahrenheit?
Use the formula, F=9/5C+32, where F is the number of degrees in Fahrenheit and C is the number of degrees in Celsius. Round your answer to the nearest whole number.
A) 25C
B) 40C
C) 57C
D) 83C
Answer:
The answer is 57 degrees Fahrenheit
Step-by-step explanation:
The temperature in degrees Fahrenheit is 57.2°F
What is formula for temperature in Fahrenheit?The Fahrenheit temperature scale is used in the United States; the Celsius, or centigrade, scale is employed in most other countries and for scientific purposes worldwide.
The conversion formula for a temperature that is expressed on the Celsius (°C) scale to its Fahrenheit (°F) representation is:
°F = (9/5 × °C) + 32.
Given:
temperature= 14 C
using formula,
F=9/5C+32,
F= 9/5 * 14+32
F= 126/5+32
F= 25.2+32
F= 57.2
Hence, the temperature in degrees Fahrenheit is 57.2°F.
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On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distance
from the y-axis to the same point. What is sin theta?
Check the picture below.
since the vertical distance, namely the y-coordinate, is twice as much as the horizontal, then if the horizontal is "x", the vertical one must be 2x.
let's find the hypotenuse first.
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{x}\\ b=\stackrel{opposite}{2x}\\ \end{cases} \\\\\\ c=\sqrt{x^2+(2x)^2}\implies c=\sqrt{x^2+4x^2}\implies c=\sqrt{5x^2}\implies c=x\sqrt{5} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{2~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }}{\stackrel{hypotenuse}{~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \sqrt{5}}}\implies \stackrel{\textit{and rationalizing the denominator}~\hfill }{\cfrac{2}{\sqrt{5}}\cdot \cfrac{\sqrt{5}}{\sqrt{5}}\implies \cfrac{2\sqrt{5}}{(\sqrt{5})^2}\implies \cfrac{2\sqrt{5}}{5}}[/tex]
The value of Sin θ for a given circle and given condition is (2√5)/5.
What is Circle?
A circle is the set of all points in the plane that are a fixed distance (the radius) from a fixed point (the center). Any interval joining a point on the circle to the center is called a radius.
Here, let the horizontal side be x.
vertical side be y
then as per the given condition
Vertical distance = 2 X horizontal distance
y = 2x
By Pythagoras Theorem,
r = [tex]\sqrt{x^2+y^2}[/tex]
1 = [tex]\sqrt{x^2+(2x)^2}[/tex]
1 = x² + 4x²
5x² = 1
x² = 1/5
x = 1/√5
then, y = 2/√5
Now, Sin θ = perp. / Hypo.
Sin θ = y/1
Sin θ = 2/√5
or Sin θ = (2√5)/5
Thus, the value of Sin θ for a given circle and given condition is (2√5)/5.
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What is this functie
f(x) = 2x + 5