Is the slope the same or different?Is the Y-intercept same or different?Is there infinitely many solutions or not?
Answers
Answer:
Explanation:
Here, we want to answer the questions given
a) To answer this, we have to write the equations in the slope-intercept form:
The slope-intercept form is:
[tex]y\text{ = mx + b}[/tex]m is the slope while b is the y-intercept
The equations would be:
[tex]\begin{gathered} y\text{ = 7x-2} \\ y\text{ = 7x-2} \end{gathered}[/tex]We can see that the equations are same
Since the equations are same, the slope is same which is 7
b) The y-intercept value is same too
c) Since the equations are same, there are infinitely many solutions for the system of equations
Related Questions
what is the area of a triangle with the legth of 8in,12in,6in
Answers
Area is
[tex]A=\frac{1}{2}bh=\frac{1}{2}\times6\times8=\frac{48}{2}=24[/tex]answer: 24 sq in
open up or down, vertex:(0,-4), passes through: (-3,5)
Answers
open up or down, vertex:(0,-4), passes through: (-3,5)
In this problem we have a vertical parabola open upward
the equation in vertex form is equal to
y=a(x-h)^2+k
where (h,k) is the vertex
we have
(h,k)=(0,-4)
substitute
y=a(x)^2-4
Find the value of a
with the point (-3,5)
substitute in the equation
5=a(-3)^2-4
5=9a-4
9a=5+4
9a=9
a=1
therefore
the equation is
y=x^2-4
answer is
f(x)=x^2-4questionSuppose $24,000 is deposited into an account paying 7.25% interest, which is compoundedcontinuouslyHow much money will be in the account after ten years if no withdrawals or additional depositsare made?
Answers
This is a compound interest question and we have been given:
Principal (P) = $24000
Rate (r) = 7.25%
Years (t) = 10
However, we are told this value is compounded continuously. This means that for every infinitesimal time period, the value keeps being compounded.
The formula for finding the compound interest is:
[tex]\text{Amount}=P(1+\frac{r}{n})^{nt}[/tex]But because the compounding period is continuous and therefore, infinitesimal,
[tex]\begin{gathered} Amount=P(1+\frac{r}{n})^{nt} \\ But, \\ n\to\infty \\ \\ \therefore Amount=\lim _{n\to\infty}P(1+\frac{r}{n})^{nt} \end{gathered}[/tex]This is similar to the general formula for Euler's number (e) which is:
[tex]e=\lim _{n\to\infty}(1+\frac{1}{n})^n[/tex]Thus, we can re-write the Amount formula in terms of e:
[tex]\begin{gathered} \text{Amount}=\lim _{n\to\infty}P(1+\frac{r}{n})^{nt} \\ \text{This can be re-written as:} \\ \\ Amount=\lim _{n\to\infty}P(1+\frac{r}{n})^{\frac{n}{r}\times r\times t}\text{ (move P out of the limit because it is a constant)} \\ \\ \text{Amount}=P\lim _{n\to\infty}((1+\frac{r}{n})^{\frac{n}{r}})^{r\times t} \\ \\ \text{Amount}=P(\lim _{n\to\infty}(1+\frac{r}{n})^{\frac{n}{5}})^{rt} \\ \\ \text{but,} \\ e=(\lim _{n\to\infty}(1+\frac{r}{n})^{\frac{n}{r}} \\ \\ \therefore\text{Amount}=Pe^{rt} \end{gathered}[/tex]Therefore, we can find the amount of money in the account after 10 years:
[tex]\begin{gathered} \text{Amount}=Pe^{rt} \\ P=24000 \\ r=7.25\text{ \%=}\frac{7.25}{100}=0.0725 \\ t=10\text{ years} \\ \\ \therefore\text{Amount}=24000\times e^{10\times0.0725} \\ \\ \text{Amount}=24000\times2.06473 \\ \\ \therefore\text{Amount}=49553.546\approx49553.55 \end{gathered}[/tex]Therefore the amount after compounding continuously for 10 years is:
$49553.55
A 6000-seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue
of $168,000?
The number of tickets for sale at $24 should be ?
Answers
The number of tickets which should be sold to $24 and $40 are 4500 and 1500 respectively.
Given, A 6000-seat theater has tickets for sale at $24 and $40.
How many tickets should be sold at each price for a sellout performance to generate a total revenue of $168,000 = ?
first, assign variables:
X = # of $24 tickets, Y = # or $40 tickets
write equations based on the data presented:
"6000 seat theater..."
X + Y = 6000 ...equation 1
"total revenue of 168,000"
The revenue from each type of ticket is the cost times the number sold, so:
24X + 40Y = 168,000 .....equation 2
from equation 1:
X = 6000 - Y
substitute this into equation 2: (replace X with 6000-Y)
24 (6000 - Y) + 40Y = 168,000
expand:
144,000 -24Y + 40Y = 168,000
rearrange and simplify:
16Y = 168,000 - 144,000
y = 24000/16
Y = 1500
from equation 1:
X = 6000 - 1500
X = 4500
hence the number of tickets for sale at $24 should be 4500.
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The probability distribution for arandom variable x is given in the table.-105101520Probability.2015051.25115Find the probability that -5 < x < 5
Answers
Answer:
P = 0.30
Explanation:
From the table, we see that:
When: x = -5, Probability = 0.15
When: x = 0, Probability = 0.05
When: x = 5, Probability = 0.1
Therefore, the probability of -5 ≤ x ≤ 5 is obtained by the sum of the probabilities from -5 to 5, we have:
[tex]\begin{gathered} P=0.15+0.05+0.10 \\ P=0.30 \end{gathered}[/tex]Therefore, the probability is 0.30
helppppppppppppppppppppppppppppp
Answers
Answer:
(see attached image)
Step-by-step explanation:
Imagine that there is a line drawn at y=x, when a problem wants you to "show the inverse of a function", imagine that y=x acts as a mirror and you have to make the "reflection" of your given function across that mirror.
the difference between the number c and the quotient of a and b in a mathematical expression.
Answers
Answer:
no difference
step by step explanations
because a/b=c
these means c(b) and a(1)
cb=a this means
cb/b=a/b
b cancle by b
and c=a/b
School: Practice & Problem Solving 7.1.PS-18 Question Help A rectangle and a parallelogram have the same base and the same height. How are their areas related? Provide an example to justify your answer The areas equal. A rectangle has dimensions 5 m by 7 m, so its area is m² A parallelogram with a base of 5 m and a height of 7 m has an area of (Type whole numbers.)
Answers
The image shown below shows the relationship between areas of rectangle and parallelogram
It can be seen that the areas are equal when they have the same sides or dimension
A rectangle has dimensions 5 m by 7 m, so its area is 5m x 7m = 35m²
A parallelogram with a base of 5 m and a height of 7 m has an area of 5m x 7m = 35m²
Rewrite the equation by completing the square. x^{2}-6x-16 = 0
Answers
Answer:
Step-by-step explanation:
x^2 - 6x - 16 = x^2 - 6x + 9 - 9 - 16 = (x - 3)^2 - 25
9Which is the best name for a quadrilateral with vertices at A(5,-2), B(2,2), C(1,-5), and D(-2,-1)?A parallelogramB squarerhombusD rectangle
Answers
Parallelogram. Option A is correct
Explanations:In order to determine the best name for a quadrilateral with the given vertices, we will find the measure of the distance AB, BC, CD, and AD using the distance formula as shown;
[tex]D=\sqrt[]{(x_2-x_1)^2+(y_2-y^{}_1)^2}[/tex]For the measure of AB with coordinates A(5,-2), B(2,2);
[tex]\begin{gathered} AB=\sqrt[]{(5-2)^2+(-2-2^{}_{})^2} \\ AB=\sqrt[]{3^2+(-4)^2} \\ AB=\sqrt[]{9+16} \\ AB=\sqrt[]{25} \\ AB=5 \end{gathered}[/tex]For the measure of BC with coordinates B(2,2) and C(1, -5)
[tex]\begin{gathered} BC=\sqrt[]{(2-1)^2+(2-(-5^{}_{}))^2} \\ BC=\sqrt[]{1^2+7^2} \\ BC=\sqrt[]{50} \\ BC=5\sqrt[]{2} \end{gathered}[/tex]For the measure of CD with coordinates C(1,-5), and D(-2,-1);
[tex]\begin{gathered} CD=\sqrt[]{(1-(-2))^2+(-5-(-1^{}_{}))^2} \\ CD=\sqrt[]{3^2+(-4)^2} \\ CD=\sqrt[]{9+16} \\ CD=\sqrt[]{25} \\ CD=5 \end{gathered}[/tex]For the measure of AD with coordinates A(5, -2), and D(-2,-1);
[tex]\begin{gathered} AD=\sqrt[]{(5-(-2))^2+(-2-(-1^{}_{}))^2} \\ AD=\sqrt[]{(5+2)^2+(-2+1)^2} \\ AD=\sqrt[]{7^2+(-1)^2} \\ AD=\sqrt[]{50} \\ AD=5\sqrt[]{2} \end{gathered}[/tex]For the slopes;
Check if the length AB is perpendicular to AD
[tex]\begin{gathered} m_{AB}=\frac{2+2}{2-5} \\ m_{AB}=-\frac{4}{3} \end{gathered}[/tex]For the slope of AD
[tex]\begin{gathered} m_{AD}=\frac{-1+2}{-2-5} \\ m_{AD}=-\frac{1}{7} \end{gathered}[/tex]Since AB is not perpendicular to AD, hence the quadrilateral is not a rectangle and also not a square or rhombus since all the sides are not equal.
From the given distances, you can see that opposite sides are equal (AB = CD and BC = AD ), hence the best name for a quadrilateral is a parallelogram.
rewrite using a single exponent. 9 4, 9 4
Answers
We need to represent the product of two exponents as one single exponent. To do that we need to calculate their product, when the bases are equal we can conserve the base and add the exponents. We will do this below:
[tex]9^49^4=9^{4+4}=9^8[/tex]For each expression build a rectangle using all of tiles,....
Answers
a.
[tex]\begin{gathered} y^2+xy+2x+2y \\ Factor_{\text{ }}as\colon \\ (y+2)(x+y) \end{gathered}[/tex]i) Sketch each rectangle:
ii) Find its dimensions
iii)
[tex]\begin{gathered} y^2+xy+2y+2x \\ \text{grouping terms:} \\ (y^2+xy)+(2y+2x)=y(y+x)+2(y+x)=(y+x)(2+y) \end{gathered}[/tex]Hello! I need some help with this homework question, please? The question is posted in the image below. Q17
Answers
The function being one-to-one implies that every value of x, has one one vaue of y, and every value of y, has one value of x.
The inverse uses the output(y value) as an input(x value) and spits it out to get the original x value inputted into f.
Using the given point ( 2, -5 ), it implies of f(2) = -5. Since the function is one-to-one, this implies that:
[tex]f^{-1}(-5)=2[/tex][tex]\text{Thus, the point on the graph of f}^{-1}\text{ is }(-5,2\text{ )}[/tex]Hence, the correct option is option B
The equation for a straight line (deterministic model) is y = Bo + B,X.If the line passes through the point ( - 10,3), then x = - 10, y = 3 must satisfy the equation; that is, 3 = Bo + B1(-10).Similarly, if the line passes through the point (11,4), then x = 11, y = 4 must satisfy the equation; that is, 4 = Bo+B1(11).Use these two equations to solve for Bo and By; then find the equation of the line that passes through the points (-10,3) and (11,4)...Find Bo and B,B1 =Bo(Simplify your answers. Type integers or simplified fractions.)
Answers
To find the equation of the line we just need to find the beta constants. In order to do this we have (they provided us with) the following system of equations:
[tex]\begin{cases}3=\beta_0+\beta_1(-10) \\ 4=\beta_0+\beta_1(11)\end{cases}[/tex]Let us subtract the second equation to the first one:
This implies that
[tex]\beta_1=\frac{-1}{-21}=\frac{1}{21}[/tex]Now, let us replace this value we just got into the second equation to find beta_0:
[tex]\begin{gathered} 4=\beta_0+\frac{1}{21}\cdot11, \\ 4=\beta_0+\frac{11}{21}, \\ \beta_0=4-\frac{11}{21}=\frac{4\cdot21}{21}-\frac{11}{21}=\frac{84-11}{21}=\frac{73}{21} \end{gathered}[/tex]At last,
[tex]\beta_1=\frac{1}{21},\beta_0=\frac{73}{21}[/tex]Then, the equation of the line is just
[tex]y=\frac{73}{21}+\frac{1}{21}x[/tex]Janelle says that lines l and m are skew lines. Planes B and A intersect. Plane B is vertical and contains vertical line n. Plane A is horizontal and contains horizontal line m. Line m and n are perpendicular. Line l is on plane A and it is slightly diagonal. Is Janelle correct? Yes, because the lines are not parallel. Yes, because the lines will intersect. No, because the lines are in the same plane. No, because the lines are perpendicular.
Answers
Lines are parallel and on the same plane. The final answer, "No, because the lines are in the same plane," is the proper response.
What is a line that is perpendicular?
Perpendicular lines are those that cross at a perfect right angle. Parallel lines are those that are always the same distance apart from one another.
The question is incomplete.
Please see the accompanying image for a comprehensive explanation of the question.
Line l and line m are the two lines that are depicted in the image.
The skew lines are in different planes and do not overlap, as far as we are aware.
Therefore,
Lines are parallel and on the same plane. The final answer, "No, because the lines are in the same plane," is the proper response.
Learn more about perpendicular lines here;
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All changes saved16. Suppose you invest $7500 at an annual Interest rate of 4.2% compounded continuously. How much will you have in the account after 2 years? Round the solution to the nearest dollar.$8158$17,372$17,373$8157
Answers
We have to use the continuous compound interest formula
[tex]A=P\cdot e^{rt}[/tex]Where P = 7500, r = 0.042, t = 2. Let's replace and solve
[tex]\begin{gathered} A=7500\cdot e^{0.042\cdot2} \\ A\approx8,157 \end{gathered}[/tex]Hence, the answer is $8,157.Here is a list of questions about the students and teachers at a school. Select the questions that are statistical questions.
Answers
As observed, all the questions in the list can be answered on the basis of some data collection and analysis.
So they all can be considered as statistical questions.
Thus, all the questions in the given list are statistical questions.
1.
If you have to answer the question for most popular lunch choice, you have to collect data of the lunch choices by a large portion of the called population. Then the lunch choice corresponding to highest frequency will be considered as the most popular lunch choice. Since the conclusion is data driven, this is a statistical question.
2.
In order to answer the question, you need to collect the information about the name of school each of the called population is admitted to. If all the students are found to be admitted to the same school, then the name of that school would be the answer.
Here also, the conclusion is data driven, so this is also a statistical question.
3.
To answer this question, you have to gather all the teaching staff of the school, and take individual answers to which subject they teach. The number of teachers who answered math will be the answer for this question.
Here also, the conclusion is data driven, so this is also a statistical question.
4.
To answer this question, you have to gather the individual age of each teacher in the school. The age corresponding to the maximum frequency would be the answer to this question.
Here also, the conclusion is data driven, so this is also a statistical question.
5.
To answer this question, you have to collect data about how much sleep each student gets in the school. Then only you can answer this question.
Since the conclusion is data driven, this is a statistical question.
6.
To answer this question, you have to collect data that how many students travel by which mode of transport to travel from home to school. The mode corresponding to highest frequency is the answer to this question.
Here also, the conclusion is data driven, so this is also a statistical question.
Thus, it is seen that all the six questions are statistical questions.
Division Properties of Exponents HW.
Answers
Given the expressions:
[tex]\begin{gathered} \frac{4^5}{4^2} \\ \text{and} \\ \frac{4^2}{4^5} \end{gathered}[/tex]we can use the following property for exponents in quotients:
[tex]\frac{a^n}{a^m}=a^{n-m}[/tex]in this case, we have the following:
[tex]\begin{gathered} \frac{4^5}{4^2}=4^{5-2}=4^3 \\ \text{and} \\ \frac{4^2}{4^5^{}}=4^{2-5}=4^{-3} \end{gathered}[/tex]then, the difference between both expressions is that when they are simplified, they get opposite signs on their exponents.
Write an equation in point slope form for the line given the slope of 4,and a point on the line (1,2)
Answers
[tex]\begin{gathered} \text{ the equation of a line in slope-point form is} \\ y=mx+b,\text{ we know that m=4, and that (1,2) is on the line, so} \\ 2=4(1)+b \\ 2=4+b \\ b=2-4 \\ b=-2 \\ \\ \text{ Thus, the equation has the form} \\ y=4x-2 \\ \end{gathered}[/tex]
Answer:
[tex]y-2=4(x-1)[/tex]
Step-by-step explanation:
Pre-SolvingWe are given that a line has a slope (m) of 4, and that it contains the point (1,2).
We want to write the equation of this line in point-slope form.
Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point, hence the name.
Since we are already given the slope, we can immediately plug it into the formula.
Substitute 4 for m.
[tex]y-y_1=4(x-x_1)[/tex]
Now, let's label the values of (1,2) to avoid confusion while substituting.
[tex]x_1=1\\y_1=2\\[/tex]
Substitute these values into the formula.
[tex]y-2=4(x-1)[/tex]
Topic: point-slope form
See more: https://brainly.com/question/14741996
Evaluate the rational expression for the given x value. Express the answer as a fraction in simplest form.
Answers
Given the expression:
[tex]\frac{x-3}{2x+3}[/tex]We need to find the value of the expression when x = 7
So, we will substitute with x = 7 into the expression as follows:
[tex]\frac{7-3}{2\cdot7+3}=\frac{7-3}{14+3}=\frac{4}{17}[/tex]so, the answer will be 4/17
kindly asking for help to clarify this question and mathematical problem .
Answers
As you can see the options A and B are decreasing, D is constant, therefore, the only increasing relationship is the option C
Find ca^2+b^2=c^2 3^2+2^2=c^29+4=13
Answers
Substituting with a = 3 and b = 2, we get:
[tex]\begin{gathered} 3^2+2^2=c^2 \\ 9+4=c^2 \\ 13=c^2 \\ \sqrt[]{13}=c \\ 3.6\approx c \end{gathered}[/tex]A motor scooter travels 22 mi in the same time that a bicycle covers 8 mi. If the rate of the scooter is 6 mph more than twice the rate of the bicycle, find both rates.The scooter’s rate is ____ mph. (Type an integer or a decimal)
Answers
Let's use the variable x to represent the speed of the scooter and y to represent the speed of the bicycle.
For a same time t, the scooter travels 22 mi and the bicycle travels 8 mi, so we can write the following equation:
[tex]\begin{gathered} distance=speed\cdot time\\ \\ 22=x\cdot t\\ \\ t=\frac{22}{x}\\ \\ 8=y\cdot t\\ \\ t=\frac{8}{y}\\ \\ \frac{22}{x}=\frac{8}{y} \end{gathered}[/tex]Then, if the rate of the scooter is 6 mph more than twice the rate of the bicycle, we have the following equation:
[tex]x=2y+6\\[/tex]Using this value of x in the first equation, let's solve it for y:
[tex]\begin{gathered} \frac{22}{2y+6}=\frac{8}{y}\\ \\ 22y=8(2y+6)\\ \\ 22y=16y+48\\ \\ 6y=48\\ \\ y=8\text{ mph} \end{gathered}[/tex]Now, calculating the value of x, we have:
[tex]\begin{gathered} x=2y+6\\ \\ x=16+6\\ \\ x=22\text{ mph} \end{gathered}[/tex]Therefore the scooter's rate is 22 mph and the bicycle's rate is 8 mph.
What are the first two steps to graph y=4/5x + 3?
Answers
The function y=4/5x + 3 represents a linear equation.
Let's find some points.
Where x=1, then:
[tex]y=\frac{4}{5}x+3[/tex][tex]y=\frac{4}{5}(1)+3[/tex][tex]y=\frac{19}{5}[/tex]We find the point (1,19/5).
Where 19/5 = 3.8
Now, lest find the x-intercept and y-intercept.
To find the x-intercept, set y=0
[tex]0=\frac{4}{5}x+3[/tex]Solve for x:
[tex]-3=\frac{4}{5}x[/tex][tex]5\cdot-3=4x[/tex][tex]-15=4x[/tex]where
[tex]x=-\frac{15}{4}=-3.75[/tex]So, the x-intercept is the point (-15/4, 0)
To find the y-intercept, set x=0. Then:
[tex]y=\frac{4}{5}x+3[/tex][tex]y=\frac{4}{5}(0)+3[/tex][tex]y=3[/tex]So, the y-intercept is the point (0,3)
Use this information to graph the line.
Hence, the graph for y=4/5x + 3 is given by:
Find a function of the form y = A; A * sin(kx) + C or y = A * cos(kx) + C whose graph matches this one:I don’t understand how my answer is wrong
Answers
Recall that the graph of the cosine function is:
Now, notice that the given graph is the above graph but with a midline
[tex]y=1,[/tex]and amplitude equal to 4. The frequency is also different.
Therefore, the equation of the function given in the graph is:
[tex]y=4cos(\frac{\pi}{5}x)+1.[/tex]Answer: [tex]y=4cos(\frac{\pi x}{5})+1.[/tex]1. Which of the following would be considered a statistical question? (1) Who was the highest paid athlete in 2020? (2) How much does a gallon of gasoline cost? (3) How many people voted for president in 2016?(4) What are the different types of maple trees?
Answers
Looking at the sentences, we have that (1), (2) and (3) are questions that require just one specific answer (For (1) it's a name of a person, for (2) it's a value and for (3) it's also a single value).
But in sentence (4), there are more than one type of maple tree, so we can answer with each type of maple tree, stating the percentage of each type for example.
So the sentence that would be considered a statistical question is (4).
A colony of 4,050 bacteria doubles in size every 297 hours. What will the population be 594 hours from now?
Answers
Answer:
About 280,000
Step-by-step explanation:
Answer:
16,200
Step-by-step explanation:
594 ÷ 297 = 2
4,050 × 2 × 2 = 16,200
another way: 4,050 × 2^2 = 16,200
Can you Help me with this i cannot do ir
Answers
To translate f(x) 4 units down we subtract 4 from f(x):
[tex]f(x)-4.[/tex]Now, to reflect f(x)-4 over the x-axis we multiply by -1:
[tex]-1(f(x)-4)=-f(x)+4.[/tex]Answer:
[tex]g(x)=-\sqrt[3]{x-2}+4.[/tex]Find the value of x in this equation.
|2x − 3| − 11 = 0
Answers
Answer:7
Step-by-step explanation:
Answer:
x=−4
x=7
Step-by-step explanation:
1. Combine similar terms and use the equality properties to get the variable on one side of the equals sign and the numbers on the other side. Remember to respect the order of operations.
2. Add 11 to both sides of the equation.
3. Use the absolute value definition.
4. Add 3 to both sides of the equation.
5. Divide both sides by 2.
6. The answer is: x=7
x=−4
Sorry for the bad English, love from Vanuatu!
It takes chuck 24 minutes to type and spell check 14 pages. Find how many pages he can type and spell check in 1.5 hours. Remember to convert 1.5 hours to minutes
Answers
In order to find how many pages can be typed, first let's convert 1.5 hours to minutes:
[tex]\begin{gathered} 1\text{ hour}\to60\text{ minutes} \\ 1.5\text{ hour}\to x\text{ minutes} \\ \\ \frac{1}{1.5}=\frac{60}{x} \\ x=60\cdot1.5 \\ x=90 \end{gathered}[/tex]Then, to find the number of pages, let's do the following rule of three:
[tex]\begin{gathered} 14\text{ pages}\to24\text{ minutes} \\ x\text{ pages}\to90\text{ minutes} \\ \\ \frac{14}{x}=\frac{24}{90} \\ 24x=14\cdot90 \\ x=\frac{14\cdot90}{24}=52.5 \end{gathered}[/tex]Therefore Chuck can type and spell check 52.5 pages in 1.5 hours.
