The system of equations has two solutions, these are:
(-0.89, 2.33) and (1.4, 9.2)
How to solve the system of equations?Here we have the following system of equations:
y = 3x + 5
y = 4x² + x
We can see that y is already isolated in both equations, so we can write the equation:
3x + 5 = y = 4x² + x
3x + 5 = 4x² + x
now we can solve this for x, this is just a quadratic equation:
3x + 5 - 4x² - x = 0
-4x² + 2x + 5 = 0
Using the quadratic formula, we can see that the two solutions are:
[tex]x = \frac{-2 \pm \sqrt{2^2 - 4*(-4)*5} }{2*-4} \\\\x = \frac{-2 \pm 9.17}{-8}[/tex]
So the solutions are:
x = (-2 +9.17)/-8 = -0.89
x = (-2 - 9.17)/-8 = 1.4
Evaluating the linear equation in these values, we get:
y = 3*(-0.89) +5 = 2.33
y = 3*(1.4) + 5 = 9.2
So the solutions of the system are:
(-0.89, 2.33) and (1.4, 9.2)
Learn more about systems of equations
https://brainly.com/question/13729904
#SPJ1
For this exponential function,
what is the output value (y),
when the input value (x) is 3?
y = 5.2x
(3, [?])
Enter
Answer:
40
Step-by-step explanation:
5*(2^3)=40
Givin f(x) = 1/x+5 and g(x)=x-2. What are the restrictions of the domain of f(g(x))?
OX≠ -5
OX≠ -3
OX≠ 2
OThere are no restrictions
Answer:
Step-by-step explanation:
x cannot be -3 or 2
Step-by-step explanation:
f(g(x)) = 1 / (( x-2) +5)
= 1/ (x+3)
g(x) cannot have x=2
The domain is restricted where
f(x) has an restriction that x cannot be 5
so g(x) cannot be -5
-5 = x-2
Add 2 to each side
-5+2 = x
-3
The product of -2 and a number is at most 10.
Find the possible numbers.
On<-5
Ons-5
Onz-5
On>-5
Answer:
n ≥ -5
Step-by-step explanation:
-2n ≤ 10
Divide both sides by -2. Remember to flip ≤ to ≥.
-2n/(-2) ≥ 10/(-2)
n ≥ -5
write and solve a real world problem in which you find the commission
A car salesman earns a 3% commission on sales. If he sells a car for $27,990, how much commission will he earn?
($27,990)*(0.03) = $839.70
The Jones family will pay their insurance broker a commission of $1,750.00.
Commission is an amount of money paid to an employee or company as an incentive to sell more. A straight commission is a percentage of sales.
To know more about Commission
Refer this link:
https://brainly.com/question/957886
#SPJ1
A house has decreased in value by 35% since it was purchased. If the current value is $78,000, what was the value when it was purchased?
Answer: The value of the house when it was purchased was 120,000
Step-by-step explanation:
1) Set up the equation. Let x be the house.
x-x*35%= 78,000
First, the house decreases 35% of the cost of the original house. It now costs 78,000.
2) Solve the equation.
x-x*0.35 = 78,000
x-0.35x=78,000
0.65x = 78,000
x= 120,000
What are three pairs of corresponding angles?
Wilbur landed his plane.
The plane's elevation relative to the ground
(in meters) as a function of time (in seconds)
is graphed.
How high was the plane after 1000 seconds?
At 1000 seconds the graph shows the height of 3500 meter.
what is graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
Following the creation of a research question, data is continuously gathered through observation. The information is subsequently arranged, condensed, categorised, and visually portrayed.
In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.
Usually, data that varies over time is represented with a line graph.
Given:
The graph gives the relation between Elevation and Time.
As, if at 400 seconds the height is 6500 meters.
and, at 800 seconds the height is 4500 meters.
Thus, at 1000 seconds the graph shows the height of 3500 meter.
Learn more about graph here:
https://brainly.com/question/17267403
#SPJ1
PLEASE HELP ME ILL LITERALLY AND I PROMISE ON GOD TO RATE YOU 5 STARS AND GIVE U POINTS
Answer:
1. 12hrs
2. 2hrs
Step-by-step explanation:
4:00pm is 2 hrs from 6:00pm
5:00am is 12hrs from 5:00pm
find the area of the circle. Use 3.14 for pie. Do not round your answer.
Answer: A = 452.16 ft²
Step-by-step explanation:
This gives us the formula to solve for the area.
A = πr²
The radius (r) is the same as the diameter divided by 2.
24 ft / 2 = 12 ft
We will input these given values and solve.
A = πr²
A = (3.14)(12)²
A = 452.16 ft²
Answer:
452.16 ft²
Step-by-step explanation:
To find the radius, you divide the diameter (24) by 2, which equals 12. The area of a circle formula is πr². To find area, you do 12² * 3.14. That equals 144 * 3.14, which equals 452.16.
If triangle LMN has an obtuse angle at vertex M, which statements could be true? Check all that apply.
Triangle LMN is an obtuse angle then, the angle at vertex L is acute, the angle at vertex N is acute.
The triangle LMN is an obtuse angle at the vertex M. So by the definition of obtuse angle triangle LMN is an obtuse angle.
As ∠M is an obtuse angle
So 90° < m∠M < 180°
By the property of a triangle,
m∠L + m∠M + m∠N = 180°
m∠M = 180° - (m∠L + m∠N)
90° < 180° - (m∠L + m∠N) < 180°
90° - 180° < -(m∠L + m∠N) < 0
-90° < -(m∠L + m∠N) < 0
90° >(m∠L + m∠N) > 0
90° > m∠L and 90° > m∠N
Therefore both angles L and N are acute angles.
To know more about the obtuse angle refer to the link given below:
https://brainly.com/question/3250447
#SPJ1
Answer:
1, 2 and 5
Step-by-step explanation:
see picture
describe five occupations you want to do, and how you prepare for your dream job. And list the average salary, and then, combine your family cost per month, make a reasonable saving plan.
architecture, invest money so that I can pay fr fees
find the area under the standard normal distribution curve to the right of . use a ti-83 plus/ti-84 plus calculator and round the answer to at least four decimal places.
using calculator
Area right to the right of the 2=2.12
P(Z > 2.12)
• P(Z < -2.12)
= 0.0170
Learn more about Standard normal distribution curve:
brainly.com/question/22923352
#SPJ4
Please help and provide an explanation for why the answer is f(x) = -1/3x - 4
What is the equation of the line that passes through Point (-6, -2) and has a Slope of -1/3.
y=-1/3-4
Step-by-step explanation:
point slope form!
y-y=m(x-x)
with the point (-6,-2) and the slope (-1/3) replace the 2nd variables of each variable and replace m with the slope
y-(-2)=-1/3(x-(-6))
then solve that normally
y-(-2)=-1/3(x-(-6))
y+2=-1/3x -2
y=-1/3x-4
I didnt use officially math symbols but i hope you can still read it!
Find all of the numbers less than100 that have at least 2 and at least one 5 in their prime factorization
Answer: [tex]10, 20, 30, 40, 50, 60, 70, 80, 90[/tex]
Step-by-step explanation:
If the numbers have at least one 2 and at least one 5, then they are multiples of 10 (since [tex]10=2 \times 5[/tex]).
So, these numbers are [tex]10, 20, 30, 40, 50, 60, 70, 80, 90[/tex].
How do I solve number 4 and 5 to get the correct answer?
Answer:
4. (d)
5. (b)
Step-by-step explanation:
You want to apply the secant and chord rules to the circles given in the diagram.
The secant rule is "the product of distances from the point of intersection of secants to the two points of intersection of the secant with the circle is the same for both secants." A tangent can be considered to be a secant that has both points of intersection with the circle in the same place.
The chord rule is similar to the secant rule: "The product of distances from the point of intersection of the chords to their intersection with the circle is the same for both chords."
4.The diagram shows a tangent of length 12, so the product of distances to the two points of intersection with the circle is 12(12).
The secant has length 8 to the near point of intersection, and (x+8) to the far point of intersection. That product is the same as for the tangent:
8(x +8) = 12(12) . . . . . . matches choice D
5.One chord has lengths of 14 and x, so the product of those is 14x.
The other chord has lengths of 12 and 21, so the product of those is 12(21).
The product is the same for both chords, meaning ...
14x = 12(21) . . . . . . matches choice B
__
Additional comment
We have purposely tried to write the rules in "parallel" fashion, because we find them easier to remember that way. Considering a tangent to be a secant with the points of intersection with the circle merged means the same rule can be used for all three cases:
intersecting secants, a tangent intersecting a secant, and intersecting chords.a $52 video game is adversited for 20% of it sales tax is 6%
Answer:
39 dollars
Step-by-step explanation: 20 perrcent of 52
What is the US GDP for the first quarter and second quarter of 2020? What is the personal consumption expenditures for the first quarter and second quarter of 2020?
The US GDP for the first quarter of 2020 was 21.54 trillion dollars, and the US GDP for the second quarter of 2020 was 19.49 trillion dollars.
The personal consumption expenditures for the first quarter of 2020 are 13.02 trillion dollars.
the personal consumption expenditures for the second quarter of 2020 are 11.82 trillion dollars.
What are the personal consumption expenditures?
Personal consumption expenditures are the price that citizens of the US pay for goods and services. This is a crucial index that indicates inflation or deflation and consumer behavior over some time.
To know more about personal consumption expenditures and GDP visit,
https://brainly.com/question/15682765?referrer=searchResults
#SPJ9
Price-club sells a 12-ounce package of spaghetti noodles for $3.44 and Shop Mart sells a 2 1/2-pound box of spaghetti noodles for $8.35.
The unit price per ounce at Price-Club is $ and the unit price per ounce at
Shop Mart is $
0.28 0.21
0.30 0.20
0.29 0.19
The unit price per ounce at Price-Club is $0.29 per ounce and the unit price per ounce at Shop Mart is $0.21 per ounce.
What is the unit price?The unit price can be determined by dividing the total cost by the total ounce that is purchased.
Division is the process of putting a number into equal groups using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. The result of the division process is known as the quotient. Other mathematical operations include addition, subtraction and multiplication.
Unit price = total cost / total ounce sold
Unit price of Price-Club = $3.44 / 12 = $0.29 per ounce
In order to determine the unit price of Shop Mart, pounds have to be converted to ounces
1 pound = 16 ounces
To convert 2 1/2 pounds to ounces, multiply 2 1/2 by 16. Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
16 x 2 1/2
16 x 5/2 = 40 ounces
Unit price of Shop Mart = $8.35 ÷ 40 = $0.21 per ounce
To learn more about division, please check: https://brainly.com/question/13281206
#SPJ1
Choose two statements that are true for this expression
7th grade students were asked to choose their
favorite color. The table shows the fraction of
students that choose each color. What DECIMAL
shows the difference between the most and least
favorite colors?
Color
Fraction
Red Yellow Blue Green
5/18
1/6
4/9
1/9
Answer:
Step-by-step explanation:
Use the intersect method to solve the equation. x^2 - 3x = x^2 -1
The coordinate that represent the solution of the equation -
x² - 3x = x² - 1 is (0.333, -0.8889).
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given is the following equation -
x² - 3x = x² - 1
In order to solve it using intersect method, we will plot the graphs of both functions and find the point of intersection of graphs of both the equations.
Assume -
f(x) = x² - 3x
g(x) = x² - 1
Now, the point of intersection of both the graphs will be the solution to the equation given by -
f(x) = g(x)
It can be seen from the graph that, both the graphs intersect at the coordinate (0.333, -0.8889). This coordinate will be the solution set of the equation -
f(x) = g(x)
Therefore, the coordinate that represent the solution of the equation -
x² - 3x = x² - 1 is (0.333, -0.8889).
To solve more questions on solving equation by graphs , visit the link below-
https://brainly.com/question/16604883
#SPJ2
Part 1
Tell whether the sequence is arithmetic. If it is, identify the common difference.
-1,4,9,14
PLEASE HURRY
Answer:
It is arithmetic, the common difference is 5
Step-by-step explanation:
What an arithmetic sequence has to have is a common difference meaning you are adding or subtracting the same number each time, in this case you are adding 5 every time so it is arithmetic
ANSWER QUICK I WILL GIVE BRAINLIEST!
Solve k over negative 1.8 is less than negative 4.9 for k.
k < −8.82
k > 8.82
k < −6.7
k > −6.7
Answer:
k<-8.82
Step-by-step explanation:
k/1.8<-4.9
k<-8.82
Answer:k<-8.82
Step-by-step explanation:
Write 41% as a fraction in simplest form.
Answer:
[tex]\frac{41}{100}[/tex]
Step-by-step explanation:
It cannot be simplified.
Ex: 50% can be simplified to [tex]\frac{1}{2}[/tex]
1/16 - ( -7/16)
Write your answer as a fraction in simplest form.
You take a $4,500 loan to pay for a trip
to the Amazon rainforest to photograph
wild animals. If the loan's interest rate is
8% for 1 year, what is the interest for the
first payment?
A $12.58
C $30.00
Vincent Fal
B $26.00
D $80.99
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (4500)(0.08)(1) \implies I = 360~\hfill \underset{monthly~payment}{\stackrel{360 ~~ \div ~~ 12}{\text{\LARGE 30}}}[/tex]
c.
PRT/100
4500×8×1/100=360
per month=360÷12
=30
A store has two types of animal feed available. Type A contains 3 pounds of oats and 3 pounds of corn per bag. Type B contains 1 pound of oats and 7 pounds of
corn per bag. A farmer wants to combine the two types so that the resulting mixture has at least 18 pounds of oats and at least 54 pounds of corn. The store
only has 11 bags of type A feed and 12 bags of type B feed in stock. Type A costs $4 per bag, and type B costs $1 per bag. How many bags of each type should
the farmer buy to minimize her cost?
Note that the ALEKS graphing calculator can be used to make computations easier.
Type A feed:
Type B feed:
bag(s)
bag(s)
The farmer will purchase five bags of kind A and six bags of type B.
Per bag, Type A includes 9 pounds of oats and 3 pounds of maize.
Per bag, Type B includes 2 pounds of oats and 10 pounds of maize.
The farmer is looking for a blend that comprises at least 57 pounds of oats and 75 pounds of maize.
Allow the farmer to mix type A feed = x pounds.
and feed type B = y pounds
(9x + 2y) pounds of oats when blended
Corn amount when combined: (3x + 10y) pounds
Oats equation: 9x + 2y = 57 ———— (1)
Corn equation: 3x + 10y = 75 ————- (2)
Subtract equation (2) from equation (2) by multiplying it by three (1)
3(3x + 10y) - (9x + 2y) = 75×3 - 57
9x + 30y - 9x - 2y = 225 - 57
28y = 168
y = 6 bags
derived from the equation (1)
9x + 2×6 = 57
9x + 12 = 57
9x = 57 - 12
9x = 45
x = 5 bags
Because the business has 15 bags of each sort, each bag costs $4.
As a result, the cost of 5 bags of type A and 6 bags of type B is = (54) + (64)
= 20 + 24
= $44
The farmer intends to buy five bags of kind A and six bags of type B.
Learn more about mathematical expressions at
https://brainly.com/question/14070584
#SPJ1
question is in the picture
Create three probability application problems of your own. Solve your problems. Explain your answers.
In the above question, we need to from 3 probability questions and then give solutions for them
Example 1 : A coin is tossed three times. What is the probability of getting at least one head?
Solution : A coin is tossed 3 times then
Sample space = [HHH, HHT, HTH, THH, TTH, THT, HTT, TTT]
Total number of ways = 2 × 2 × 2 = 8
Favorable Cases = 7
P (A) = 7/8
OR
Probability (of getting at least one head) = 1 – P (no head)⇒ 1 – (1/8) = 7/8
Example 2 : Three red and four black balls are contained in a bag. Randomly, one ball gets taken out of the bag. Determine the probability that the drawn ball is
(i) black
(ii) not black
Solution :
Total number of balls in the bag are = 3 + 4 = 7 balls
Number of favorable outcomes or number of black balls in the bag = 4
(i) Probability getting black balls = [tex]\frac{number of favorable outcomes}{number of total outcomes}[/tex]
P(black ball) = [tex]\frac{4}{7}[/tex]
(ii) Probability getting no black balls = 1 - P(black ball)
= 1 - [tex]\frac{4}{7}[/tex]
= [tex]\frac{3}{7}[/tex]
Example 3 : Given two dice, what is the likelihood of receiving the number 7?
Mathematical probability - There are 36 ways in all, or 6 times 6. Favorable scenarios are (1, 6) (6, 1) (2, 5) (5, 2) (3, 4) (4, 3), etc., in six different ways. P (A) = 6/36 = 1/6
To learn more about, probability here
https://brainly.com/question/11034287
#SPJ1
Find the values of a,b and c that would make the statements true.
1) (ax+2)(5x+b)=10x^2+bx+c
The values of a, b and c are a = 2, b = -10 and c = -20
How to determine the values of the variables?The equation is given as
(ax + 2)(5x + b) = 10x^2 + bx + c
Open the brackets
So, we have
5ax^2 + 10x + abx + 2b = 10x^2 + bx + c
By comparing the above equation.
We have the following set of equations
5a = 10
10 + ab = b
2b = c
By solving the equations, we have
a = 2
Substitute a = 2 in 10 + ab = b
10 + 2b = b
So, we have
b = -10
Substitute b = -10 in 2b = c
2(-10) = c
Evaluate
c = -20
Hence, the values of the variables are a = 2, b = -10 and c = -20
Read more about quadratic equations at
https://brainly.com/question/1214333
#SPJ1