y= -2x - 7x - y = -8
Answers
Given the system of equations:
[tex]\begin{gathered} y=-2x-7\rightarrow(1) \\ x-y=-8\rightarrow(2) \end{gathered}[/tex]we will find the solution to the system by graphing
To draw the lines, we need to know two points on each line
so, substitute with two values of x and calculate the corresponding value of y
For line (1): y = -2x - 7
[tex]\begin{gathered} x=0\rightarrow y=-2\cdot0-7=-7 \\ x=1\rightarrow y=-2\cdot1-7=-9 \end{gathered}[/tex]so, line (1) passes through the points ( 0, -7) and ( 1, -9)
For line (2): x - y = -8
y = x + 8
[tex]\begin{gathered} x=0\rightarrow y=8 \\ x=1\rightarrow y=1+8=9 \end{gathered}[/tex]So, line 2 passes through the points ( 0, 8) and ( 1, 9)
The graph of the line will be as shown in the following picture
As shown in the figure:
Line (1) is the blue line
Line (2) is the red line
The point of intersection = ( -5, 3)
So, the solution is point ( -5, 3)
Related Questions
Freya counted then number of cars that came to a complete stop at stop sign. of the 25 cars, 13 cars came to a complete stop. if Freya observes the next 75 cars that reach the stop sign, how many cars can she expect to come to a complete stop?
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The expected value can be calculated with the formula
[tex]E(x)=x\cdot p(x)[/tex]Where p represents the probability, and x represents the new event.
Basically, we just have to find the probability of the 13 cars
[tex]p(x)=\frac{13}{25}=0.52[/tex]Then, we multiply by the numbers of cars x = 75.
[tex]E(75)=75\cdot0.52=39[/tex]Hence, the right answer is 39. The expected value is 39.What is the difference between the inverse function of quadratic and exponential
Answers
Answer:
Quadratic functions are those where their rate of change changes at a constant rate. Exponential functions are those where their rate of change is proportional to itself.
Step-by-step explanation:
An example of a quadratic function would be the shape that a ball makes when you throw it. Gravity causes a constant acceleration, the ball slows down as it is moving up, and then it speeds up as it comes down.
An example of an exponential function would be the population of a bacterium as long as there is enough space and nutrients or how your money grows with compound interest in a bank.
pls help the hw is due today
Answers
Answer: the slope for the line is
y= -2x-4
Part A. 150% of what number is 156 Part B. 4.4 is 5.5% of what number
Answers
EXPLANATION
Since 150% represents a percentage bigger than 156, the appropiate relationship would be as follows:
[tex]Part\text{=}\frac{\text{Percentage}}{100}\cdot\text{Whole}[/tex]Where the whole number is 156 and the percentage is 150%:
[tex]\text{Part}=\frac{150}{100}\cdot156[/tex][tex]\text{Part}=1.5\cdot156=234[/tex]In conclusion, the solution is 234
determine the orderd pair (8,-3)is a solytion to the linear pair
Answers
To answer this question, we need to evaluate if the ordered pair forms an identity with both equations. We need to substitute the values for x = 8, and y = -3 in both equations:
[tex]\frac{x}{2}+5y=-11\Rightarrow\frac{8}{2}+5(-3)=-11\Rightarrow4-15=-11\Rightarrow-11=-11[/tex]These values result in an equality in this equation. We need to evaluate the other equation:
[tex]6x-\frac{y}{6}=40\Rightarrow6\cdot(8)-(\frac{-3}{6})=40\Rightarrow48+\frac{1}{2}=\frac{97}{2}\ne-11[/tex]In this case, the values do not result in an equality in one of both equations.
Therefore, we have that the correct answer is the option B:
No, the proposed solution does not result in an equality in one of the two equations.
3.8% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive? 0.475 0.038 0.525 0.905
Answers
ANSWER:
0.475
STEP-BY-STEP EXPLANATION:
The probability of a person has disease given the test is positive:
P (disease) = 3.8% = 0.038
P (positive | disease) = 93.9% = 0.939
P (positive | no disease) = 4.1% = 0.041
P (no disease) = 100% - 3.8% = 96.2% = 0.962
The probability that the person has the disease given that the test result is positive is calculated as follows:
[tex]\begin{gathered} \text{ P\lparen infected \mid test positive\rparen }=\frac{\text{ P\lparen positive \mid infected\rparen }\times\text{ \rbrack P \lparen infected\rparen}}{\text{ P \lparen positive\rparen}} \\ \\ \text{ P \lparen positive \mid infected\rparen }=\text{ P \lparen positive \mid disease\rparen = 0.939} \\ \\ \text{ P \lparen infected\rparen = P \lparen disease\rparen = 0.038} \\ \\ \text{ P \lparen positive\rparen = P \lparen positive \mid infected\rparen }\times\text{ P \lparen infected\rparen }+\text{ P \lparen positive \mid no infected\rparen}\times\text{ P \lparen no infected\rparen } \\ \\ \text{ P \lparen positive \mid infected\rparen =P \lparen positive \mid no disease\rparen = 0.041} \\ \\ \text{ P \lparen no infected\rparen = P \lparen no disease\rparen = 0.962} \\ \\ \text{ We replacing:} \\ \\ \text{ P \lparen positive\rparen = }0.038\cdot0.939+0.041\cdot0.962=0.075124 \\ \\ \text{ P\lparen infected \mid test positive\rparen }=\frac{0.038\cdot0.939}{0.075124} \\ \\ \text{ P\lparen infected \mid test positive\rparen = }\:0.47497=0.475 \end{gathered}[/tex]The correct answer is the first option: 0.475
Find all solutions of the equation in the interval [0,2pi). csc =7/4 If there is more than one solution, separate them with commas.Do not round any intermediate computations. Give your answer(s) in radians, and round your answer(s) to the nearest hundredth
Answers
Since the cosecant is the inverse of the sine, we can write the following:
[tex]\begin{gathered} \csc (\theta)=\frac{7}{4} \\ \sin (\theta)=\frac{1}{\csc(\theta)}=\frac{1}{\frac{7}{4}}=\frac{4}{7} \end{gathered}[/tex]Then, using a calculator, we can calculate the angle that has a sine of 4/7:
[tex]\begin{gathered} \theta=\sin ^{-1}(\frac{4}{7})_{} \\ \theta=34.85\degree \end{gathered}[/tex]There is one more angle between 0 and 2π that has the same value of 4/7 for the sine, and it's the supplementary angle to the one we found:
[tex]\theta_2=180-\theta_1=180-34.85=145.15\degree[/tex]Therefore the answers are 34.85° and 145.15°.
Converting to radians, we have:
[tex]\begin{gathered} 34.85\cdot\frac{\pi}{180}=0.61 \\ 145.15\cdot\frac{\pi}{180}=2.53 \end{gathered}[/tex]So the final answer is 0.61 and 2.53.
Calculate the value of each expression.
1) (-5)
/
4
2) (-5)-(-/-)
3)-20
4)-20
(-20)
(4)
5)
Answers
Answer:
1) -15/4 or -3.75
2) 15/4 or 3.75
3) 5
4) -5
5) -5
Step-by-step explanation:
Can the three segments below form a triangle? Explain how you will change the length of one or two of these segments to form each kind of triangle. If no changes needed enter the original length or state that no changes needed. scalene triangleAB=… BC=…. AC=… equilateral triangleAB = … BC = … AC = …isosceles triangleAB = … BC = … AC = …
Answers
ANSWERS
• They cannot form a triangle
,• Scalene triangle: ,AB = 7
,• Equilateral triangle: ,BC = 5, AC = 5
,• Isosceles triangle: ,AB = 8
EXPLANATION
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side,
[tex]\begin{gathered} 14+8>5\Rightarrow true \\ 14+5>8\Rightarrow true \\ 5+8>14\Rightarrow false \end{gathered}[/tex]Hence, these side lengths cannot form a triangle.
To form a scalene triangle one of the shortest sides must be larger, for example, AB should be 7, instead of 5. Other combinations are possible as well.
To form an equilateral triangle all sides must have the same length, for example, AB = BC = AC = 5
To form an isosceles triangle, two of the sides must have the same length, while the third side has a different length, for example, AB = 8
To form all three kinds of triangles, the first rule must be valid as well.
What type of number is - Choose all answers that apply:AWhole numberBIntegerRationalDIrratio
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It is whole, integer, rational
Find x rounded to the nearest whole degree. Be sure to round correctly!
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answer: 36°
In a class of students, the following data table summarizes the gender of the studentsand whether they have an A in the class. What is the probability that a student whohas an A is a female?Female MaleHas an A24Does not have an A176
Answers
We are asked to find the probability that a student is female given that they have an A.
Since this is the case, we limit ourselves to observing the row "Has an A".
In said row, there is a total of 6 students who have an A. Out of those 6, 2 are female.
Thus, P(Female|A) = 2/6 = 1/3 = 33.33%.
The figure below shows a striaght line AB intersected by another straight line t: Write a paragraph to prove that the measure of angle 1 is equal to the measure of angle 3. (10 points)
Answers
Angles 1 and 3 are vertical angles, that is, are pairs of opposite angles made by intersecting lines. If 2 angles are vertical then they are congruent, in other words, they have the same measure.
The distance from the earth to Pluto is 4.67x10^9 mi, If a new flying machine can travel 1.92x10^5 miles per year, how many years would it take to reach Pluto? Write your answer in standard form, rounded to the nearest year.
Answers
24333 years
Explanationto solve this we need to use the time formula ,it says
[tex]time=\frac{distance}{speed}[/tex]Step 1
a)given
[tex]\begin{gathered} distance=4.67*10^9\text{ miles} \\ speed=1.92*10^5\text{ }\frac{miles}{year} \end{gathered}[/tex]b) now, replace in the formula and calculate
[tex]\begin{gathered} time=\frac{distance}{speed} \\ time=\frac{4.67*10^9}{1.92*10^5}=2.43*10^{9-5}=2.43*10^4 \\ time=2.43*10^4\approx24333\text{ years} \end{gathered}[/tex]therefore, the answer is
24333 years
I hope this helps you
May I get help, I know I have to multiply the possibilities, but I keep getting stuck
Answers
First we obtain each probability
The land has no oil
is a 45% chance that the land has oli , then the chance that the land has not oil is 55%
55% can be represented like 0.55
then the probability to the land has no oil is 0.55
The test shows that there is no oil
Kit claims to have an 80% of idicating oil, then the percent that there is no oil is 20%
20% can be represented like 0.2
the tne probability to shows that theere is no oil is 0.2
Finally
Multiply the probabilities to find the probability that say the land has no oil and the test shows that there is no oil
[tex]0.55\times0.2=0.11[/tex]then irhg toption is B
use the data below make a frequency table take a picture of you frequency table and attach it to your answer marathon time
Answers
A frequency table is a table that shows how many times each number appears.
Looking at this set of numbers, we can see that each number appears only one time.
So we can create the following frequency table:
[tex]\begin{gathered} \text{value | frequency} \\ 135\text{ | 1} \\ 211\text{ | 1} \\ 220\text{ | 1} \\ 180\text{ | 1} \\ 175\text{ | 1} \\ 161\text{ | 1} \\ 246\text{ | 1} \\ 201\text{ | 1} \\ 192\text{ | 1} \\ 167\text{ | 1} \\ 235\text{ | 1} \\ 208\text{ | 1} \end{gathered}[/tex]Here is another riddle:•The sum of two numbers is less than 2.•If you subtract the second number from the first, the difference is greater than 1.What are the two numbers? Explain or show how you know.
Answers
Let the two numbers be A and B
Their sum is less than 2
Thus,
[tex]A+B<2[/tex]When the second number is subtracted from the first number, the difference is greater than 1.
Thus,
[tex]A-B>1[/tex]help meeeeeeeeee pleaseee !!!!!
Answers
The addition of the given functions f(x) and g(x) is equal to the expression x^2+ 3x + 5
Composite function.Function composition is an operation that takes two functions, f and g, and creates a function, h, that is equal to g and f, such that h(x) = g.
Given the following functions
f(x) = x^2 + 5
g(x) = 3x
We are to determine the sum of both functions as shown;
(f+g)(x) = f(x) + g(x)
Substitute the given functions into the formula
(f+g)(x) = x^2+5 + 3x
Write the expression in standard form;
(f+g)(x) = x^2+ 3x + 5
Hence the sum of the functions f(x) and g(x) is equivalent to x^2+ 3x + 5
Learn more on sum of functions here: https://brainly.com/question/17431959
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I have to create a graph but I need some help and clarification
Answers
To complete the table you evaluate the equation by the given value of x to find the corresponding value of y:
[tex]y=x+4[/tex][tex]\begin{gathered} x=4 \\ \\ y=4+4 \\ y=8 \\ \\ (4,8) \end{gathered}[/tex][tex]\begin{gathered} x=8 \\ \\ y=8+4 \\ y=12 \\ \\ (8,12) \end{gathered}[/tex][tex]\begin{gathered} x=12 \\ \\ y=12+4 \\ y=16 \\ \\ (12,16) \end{gathered}[/tex][tex]\begin{gathered} x=16 \\ \\ y=16+4 \\ y=20 \\ \\ (16,20) \end{gathered}[/tex]To put those (x,y) points in the plane;
the frist coordinate x is the number of units you move to the left (if x is negative) or to the right (if x is positive)
the second coordinate y is the number of units you move down (if y is negative) or up (if y is positive)
Then, using the points (0,4), (4,8), (8,12), (12,16) and (16,20) you get the next graph for y=x+4:
Differentiate. f(x) = (x3 - 3)2/3 2x f'(x) 3 x 8 х f'(x) 3 | 23-8 2x2 f'(x) 3 S x2 f'(x) 3 8
Answers
1) Let's calculate the derivative of f(x) = (x³-8) ^(2/3)
Let's start applying the power rule :
[tex]undefined[/tex]A local dairy has three machines to fill half-gallon milk cartons. The machines can fill the daily quota in 3 hrs, 14 hrs, and 10.5 hrs, respectively. Find how long it takes to fill the daily quota if all three machines are running.
Answers
Answer
It will take 2 hours to fill the daily quota if all the machines are running.
Explanation
To find how long it takes to fill the daily quota if all the machines are running, we use the relation below:
Rate of machine 1 + Rate of machine 2 + Rate of machine 3 = Total rate of the machines
[tex]\begin{gathered} \Rightarrow\frac{1}{3}+\frac{1}{14}+\frac{1}{10.5}=\frac{1}{x} \\ \text{Where x is the }time\text{ it takes to fill the daily quota} \\ \frac{1}{3}+\frac{1}{14}+\frac{2}{21}=\frac{1}{x} \\ \text{Multiply all through by 42x} \\ 42x(\frac{1}{3})+42x(\frac{1}{14})+42x(\frac{2}{21})=42x(\frac{1}{x}) \\ 14x+3x+4x=42 \\ 21x=42 \\ x=\frac{42}{21} \\ x=2 \\ \text{Therefore it will take 2 hours to fill the daily quota} \end{gathered}[/tex]Consider the following equation: - 6x – 8y =—2A) Write the above equation in the form y = mx + b. Enter the values of m and b in theappropriate boxes below as integers or reduced fractions in the form A/B.)Answer: y =+Preview m: ; Preview b:B) Use your answer in part (A) to find the ordered pair that lies on this line when x = – 40.Answer: (-40,Enter your answer as an integer or a reduced fraction in the form A/B.
Answers
we have the equation
-6x-8y=-2
step 1
Isolate the variable y
Adds 6x both sides
-6x-8y+6x=-2+6x
simplify
-8y=6x-2
Divide both sides by -8
-8y/8=(6x-2)/-8
y=-(6/8)x+(2/8)
simplify
y=-(3/4)x+(1/4)therefore
m=-3/4b=1/4Part b
For x=-40
substitute in the equation above
y=-(3/4)(-40)+(1/4)
y=30+1/4
y=121/4
therefore
the answer part b is
(-40,121/4)Given: Circle PB52°РMAD =mBD =mBAC =:: 52°.: 90°:: 128°:: 142°.: 232°:: 308°
Answers
From the circle given, it can be observed that AC is the diameter of the circle and it divides the circle into two equal parts. The total angle in a semi-circle is 180°. It then follows that
[tex]arcAD+arcDC=arcAC[/tex][tex]\begin{gathered} \text{note that} \\ arcAC=180^0(\text{angle of a semicircle)} \\ arcDC=90^0(\text{given)} \end{gathered}[/tex][tex]\begin{gathered} \text{Therefore,} \\ arcAD+arcDC=arcAC \\ arcAD+90^0=180^0 \\ arcAD=180^0-90^0 \\ arcAD=90^0 \end{gathered}[/tex][tex]\begin{gathered} \text{From the circle, it can be seen that:} \\ arcBD=arcBA+arcAD \\ \text{note that } \\ arcBA=52^0(\text{given)} \\ arcAD=90^0(\text{calculated earlier)} \end{gathered}[/tex][tex]\begin{gathered} \text{Therefore,} \\ arcBD=52^0+90^0 \\ arcBD=142^0 \end{gathered}[/tex][tex]\begin{gathered} \text{From the given circle, it can be seen that} \\ arcBA+arcAD+arcDC=arc\text{BAC} \end{gathered}[/tex][tex]\begin{gathered} \text{Therefore,} \\ 52^0+90^0+90^0=\text{arcBAC} \\ 232^0=\text{arcBAC} \end{gathered}[/tex]Hence, arcAD = 90°, arc BD = 142°, and arc BAC = 232°
Convert 145 to base 4
Answers
Answer:
Converting 145 to base 4 will give;
[tex]2101_4[/tex]Explanation:
We want to convert;
[tex]145_{ten}\text{ to base 4}[/tex]Converting, we have;
[tex]\begin{gathered} 145\text{ }\div\text{ 4 } \\ 36\text{ }\div\text{ 4 R 1} \\ 9\text{ }\div\text{ 4 R 0} \\ 2\text{ }\div\text{ 4 R 1} \\ 0\text{ R 2} \end{gathered}[/tex]Therefore, converting 145 to base 4 will give;
[tex]2101_4[/tex]A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, thenthe unit cost is given by the function C(x) = 0.5x? - 260x +53,298. How many cars must be made to minimize the unit cost?Do not round your answer.
Answers
Okey, here we have the following function:
[tex]C(x)=0.5x^2-260x+53298[/tex]Considering that "a" is a positive coefficient, then it achieves the minimum at:
[tex]x=-\frac{b}{2a}[/tex][tex]\begin{gathered} x=-\frac{(-260)}{2(0.5)} \\ =\frac{260}{1} \\ =260 \end{gathered}[/tex]Now, let's find the minimal value of the quadratic function, so we are going to replace x=260, in the function C(x):
[tex]\begin{gathered} C(260)=0.5(260)^2-260(260)+53298 \\ C(260)=0.5(67600)-67600+53298 \\ =33800-67600+53298 \\ =19498 \end{gathered}[/tex]Finally we obtain that the number of cars is 19498.
Consider the following expression-x + 8x2 - 9x?Step 2 of 2: Determine the degree and the leading coefficient of the polynomial.
Answers
Solution
For this case we have the following polynomial:
[tex]-x+8x^2-9x[/tex]For this case the higher degree is 2 then the answer is:
Degree= 2
Leading Coefficient of the polynomial: 8
What is 3 +4.3+45?A4늘OB.B. 7O. 8○ D. 12
Answers
solution
[tex]3+4\frac{1}{3}=7\frac{1}{3}[/tex]answer: B
The local appliance store is advertising a 17% off sale on a new flat-screen TV. If the saleprice is $664, what was the original price of the flat-screen TV? Use X in the equation
Answers
Let's assume X is the original price of the flat-screen TV
The store is advertising a 17% off sale in that price, so the real sale price should be less than the original price
To calculate a % discount, we proceed as follows:
Compute the discount:
discount = 17% of X
Recall a percentage can be expressed as the number divided by 100, that is:
discount = 17 / 100 * X = 0.17X
Now we have the discount, we calculate the actual or sale price, which is the original price minus the discount:
sale price = original price - discount
sale price = X - 0.17X
We apply simple algebra to simplify the expression, just subtracting 1-0.17=0.83
sale price = 0.83X
We know the sale price is $664, thus:
0.83X = 664
Finally, we solve for X
[tex]X=\frac{664}{0.83}=800[/tex]This means that the original price of the TV was $800. Let's verify our result
what us the area of the triangle if the perimeter is 16
Answers
We are asked to find the area of the given triangle.
Recall that the area of a triangle is given by
[tex]A=\frac{1}{2}\cdot b\cdot h[/tex]Where b is the base and h is the height of the triangle.
Let us find the base and height from the given figure.
As you can see,
base = 6
height = 4
[tex]\begin{gathered} A=\frac{1}{2}\cdot b\cdot h \\ A=\frac{1}{2}\cdot6\cdot4 \\ A=\frac{1}{2}\cdot24 \\ A=12 \end{gathered}[/tex]Therefore, the area of the triangle is 12 square units.
For each value of v, determine whether it is a solution to -96= -8(v +7)
Answers
Everything else is no
