The given system is
[tex]\mleft\{\begin{aligned}y-2x^2=4x+1 \\ y=14x-7\end{aligned}\mright.[/tex]Let's replace the second equation with the first one.
[tex]14x-7-2x^2=4x+1[/tex]Now, we solve the quadratic equation.
[tex]\begin{gathered} 14x-7-2x^2-4x-1=0 \\ -2x^2+10x-8=0 \\ -2(x^2-5x+4)=0 \\ x^2-5x+4=0 \end{gathered}[/tex]Then, we have to find two numbers whose product is 4 and whose sum is 5. Those numbers are 4 and 1.
[tex]\begin{gathered} (x-4)(x-1)=0 \\ x_1=4 \\ x_2=1 \end{gathered}[/tex]We use these values to find y.
[tex]\begin{gathered} y_1=14\cdot4-7=49 \\ y_2=14\cdot1-7=7 \end{gathered}[/tex]Hence, the solutions to the given system are (4,49) and (1,7).Why are there two possible solutions to the equation, X2 = 100?
Answer:
100 is perfect square
Step-by-step explanation:
in x² =100, we have x×x=100 and x could be ±10 since both 10² and (-10)² is equal to 100
Write the equation of the line in y=mx+b form using the following two points:
(-2,-1) and (-1,-2)
Enter you equation here: type your answer....
10 points
Answer: The slope-intercept form for a line with the coordinates of (-2,-1) and (-1,-2) is:
y= -1.00x + -3.00
(results are in decimal form, rounded to the nearest 100th)
i hope i helped it is for if it was for like slope intercept form
Step-by-step explanation:
Which inequality is equivalent to 22 ≤x-9?
(A) 13sx
(B) 13zx
(C) 31sx
(D) 31zx
Answer:
31 ≤ x
Step-by-step explanation:
22 ≤ x - 9;
22 + 9 ≤ x - 9 + 9;
31 ≤ x
you are playing a game of hide - and - seek with two friends . while one of your friends counts , you and your other friend are given a chance to hide in one of five possible hiding spots . you are each allowed to pick a hiding spot , and are permitted to share a hiding spot . your friend finishes counting and checks one of the five hiding spots . assuming that everyone's decisions are made uniformly at random , what are the chances that your friend does not find anyone in the first spot that they check ?
The probability the friend finds no one in the first spot is 60%.
What is probability?Probability is the chance or likelihood that an expected event occurs when there are many possible outcomes or events.
For instance, the probability that when the counting friend goes to the hiding spot, they can or cannot find a friend there.
The two friends can only hide in 2 spots, leaving 3 spots with nobody.
The number of hiding spots = 5
The number of friends hiding = 2
The number of counting friends = 1
The number of spots they can hide = 2 out of 5
The probability of finding a person in a hiding spot = 2/5 or 40%
The probability of not finding a person in a hiding spot = 3/5 (1 - 2/5) or 60% (1 - 40%).
The chances that your friend finds anyone in the first spot are 60%.
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101x^2+231x-334=-2 find the A,B,C
The roots of the equation is 1 and 3.28
The given equation is a quadratic
To find the roots of a quadratic equation, the formula is
[tex]\frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]
The equation is 101x^2+231x-334=-2 we need to find the A,B,C
101x^2+231x-332 = 0
here a is 101, b is 231, and c is -332
[tex]\frac{-b + \sqrt{b^{2} - 4ac } }{2a}\\\frac{-231 + \sqrt{231^{2} - 4(101)(-332) } }{2(101)}\\\frac{-231 + \sqrt{53361 + 134128 } }{202}\\\frac{-231 + \sqrt{187489 } }{202}\\\\\frac{-231 + \sqrt{187489 } }{202}\\\\\frac{-231 + 433 }{202}\\\\=\frac{202}{202}\\\\ 1[/tex]
[tex]\frac{-b - \sqrt{b^{2} - 4ac } }{2a}\\\frac{-231 - \sqrt{231^{2} - 4(101)(-332) } }{2(101)}\\\frac{-231 - \sqrt{53361 + 134128 } }{202}\\\frac{-231 - \sqrt{187489 } }{202}\\\\\frac{-231 - \sqrt{187489 } }{202}\\\\\frac{-231 -433 }{202}\\\\=\frac{664}{202}\\\\ 3.28[/tex]
Therefore, the roots of the equation is 1 and 3.28
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Does anyone know why this is wrong??
[tex]=-10x^4-4x^3+6x^2[/tex]
Susie has a part-time job at the video store. She makes between $41.89 and $47.91 a day. Which is a reasonable amount of money that Susie makes for working 7 days?
The amount of money that Susie makes for 7 working days will be;
⇒ $314.3
What is mean by Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Susie has a part-time job at the video store and she makes between $41.89 and $47.91 a day.
Now,
The amount of money for a day = ($41.89 + $47.91) / 2
The amount of money for a day = $89.8 / 2
The amount of money for a day = $44.9
Thus, The amount of money that Susie makes for 7 working days is;
= 7 x $44.9
= $314.3
Hence,
The amount of money that Susie makes for 7 working days will be;
⇒ $314.3
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i really need help can anyone help solve the attatched question
PLEASE HELP!!!!!!!!!!!!
The stem-and-leaf plot shows kilometers walked by participants in a charity benefit walk. Use it to answer the questions.
A stem and leaf plot shows the number of kilometers walked for charity.
The plot is titled 'Kilometers Walked for Charity.' The numbers 12, 13, 14, 15, 16, and 17 are in a vertical column to the left of a vertical line.
· On the same line as 12 but on the right of the vertical line are the numbers 3, 3, 6, 7, 9, and 9.
· On the same line as 13 but on the right of the vertical line are the numbers 1, 1, 4, 5, and 5.
· On the same line as 14 but on the right of the vertical line are the numbers 0, 0, 2, 3, 3, 8, 8, and 9.
· On the same line as 15 but on the right of the vertical line are the numbers 2, 2, 2, 2, 2, 3, 5, 5, and 7.
· On the same line as 16 but on the right of the vertical line are the numbers 4, 5, 5, 9, and 9.
· On the same line as 17 but on the right of the vertical line are the numbers 3 and 5.
The key to the stem and leaf plot identifies that 12 vertical line 3 means 12.3.
a. How many people participated in the walk?
b. How many of the walkers traveled more than 14 kilometers?
Answer:
35 participants for A
22 participants traveled more than 14 km for B.
Step-by-step explanation:
which integers represent each situation? a) a debt of $10b) 6 degrees below 0 c) deposit of $25 someone please help fast
An integer that represent the debt of $10 can be express below
[tex]-\text{ \$10}[/tex]An integer that represent 6 degree below 0 is expressed below
[tex]0-6=\text{ -6 degre}e[/tex]An integer that represent a deposit of $25 can be express below
[tex]+\text{ \$25= \$25}[/tex]please help thank you
Answer:
%25 of customers ordered ice tea.
Step-by-step explanation:
To find percentage = Part/Whole x 100
35/140 x 100 = 0.25 x 100 = %25
If y varies directly with x, write an equation for the direct variation. Then find each value.1. If x= -12 when y= -3 find x when y= -6
Since y varies directly with x then
[tex]\begin{gathered} \frac{y}{x}=k \\ \text{Where k }is\text{ the constant of proportionality} \end{gathered}[/tex]So,
[tex]\frac{y}{x}=\frac{-3}{-12}=\frac{3}{12}=\frac{1\cdot3}{4\cdot3}=\frac{1}{4}[/tex]Then, 1/4 is the constant of proportionality. So that,
[tex]\begin{gathered} \frac{y}{x}=\frac{1}{4} \\ \frac{-6}{x}=\frac{1}{4} \\ -\frac{6}{x}\cdot x=\frac{1}{4}\cdot x \\ -6=\frac{x}{4} \\ 4\cdot-6=\frac{x}{4}\cdot4 \\ -24=x \end{gathered}[/tex]Divide write the answer as a fraction in simplest form 7/8 divided by 6 =
Answer:
[tex]\frac{7}{48}[/tex]Explanation: We have been given a fraction 7/8 and we need to divide it by 6 and write it in simplest terms.
Dividing and simplifying gives us following:
[tex]\frac{7}{8}\text{ Divied 6}\rightarrow\frac{7}{8}\times\frac{1}{6}=\frac{7}{48}=\frac{7}{48}[/tex]There are two spinners. one spinner has three equally sized sectors that are numbered 1, 2, and 4. the second spinner has four equally sized sectors that are labeled a, b, c, and d. each spinner is spun once. how many outcomes do not show c? responses 4 4, 6 6, 7 7, 9
The number of outcomes that do not show c is calculated to be 9 if each spinner is spun once.
The three possible outcomes of the first spinner are 1,2 and 4 and the possible outcomes of the second spinner are a,b,c and d; so if the two spinners are spun together, the possible outcome will be:
a1, a2, a4
b1, b2, b4
c1, c2, c4
d1, d2, d4
Therefore, there are a total of 12 possible outcomes, and 3 out of these possible outcomes show c. Now the outcomes that do not show c can be calculated by subtraction as follows;
Outcome not showing c = Total outcomes - Outcomes showing c
Outcome not showing c = 12 - 3
Outcome not showing c = 9
Therefore, 9 outcomes do not show c if each spinner is spun once.
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Answer: 6
Step-by-step explanation:
14. Consider this system of equations.y = -2x2 + 9y = 4x + 3What values of x are solutions to the system of equations?A.x = -9 and x = 7B.x= -7 and x = 9C.x = -3 and x = 1D.x = -1 and x = 3
SOLUTION:
Step 1:
In this question, we are given the following:
Consider this system of equations:
[tex]\begin{gathered} y=-2x^2\text{ +9} \\ y\text{ = 4x + 3} \end{gathered}[/tex]Step 2:
The details of the solution are as follows:
CONCLUSION:
The values of x that are the solutions to the system of equations are:
[tex]x\text{ =- 3 and x = 1 -- OPTION C}[/tex]
(07.02 HC)
Barbara draws pens randomly from a box containing 5 pens of the same shape and size. There is 1 green pen, 3 red pens, and 1 blue pen. She draws 1 red pen and then
another red pen without replacing the first one. Find the probability of drawing 1 red pen followed by another red pen, and show the equation used.
Answer: She already got rid of two red pens, so there's one red pen left.
5-1=4-1=3. 1 red 1 blue 1 green. 100/3=33.3333333… so her chance of getting another red pen is 33.3333333333333333333333% and a 66.66666666666666666666% chance of not.
Step-by-step explanation
A guy wire runs from the top of a cell tower to a metal stake in the ground. Hannah
places a 6-foot tall pole to support the guy wire. After placing the pole, Hannah
measures the distance from the stake to the pole to be 1 ft. She then measures the
distance from the pole to the tower to be 12 ft. Find the length of the guy wire, to the
nearest foot.
The length of the guy wire, to the nearest foot is 1548 ft.
What is the Pythagoras theorem?The right-angled triangle's relationship between its three sides is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The square of a triangle's hypotenuse is equal to the sum of its other two sides' squares, according to the Pythagoras theorem. The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized
After sketching the information given, we have two similar right triangles, ΔABE and ΔCDE.
CD = 6 ft
DE = 1 ft
BD = 12 ft
Since ΔABE ~ ΔCDE, therefore,
AB/CD = BE/DE (proportional sides)
Plug in the values
AB/6 = (12 + 1)/2
AB/6 = 13/2
Cross multiply
AB = 13(3)
AB = 39 ft
AE = √(AB² + BE²)
AE = √(39² + 12²)
AE = 1548 ft (nearest foot)
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Answer: The length of the guy wire, to the nearest foot is 1548 ft.
Step-by-step explanation:
Tom surveyed 150 students at his school to find out each student's favorite color. His results are shown in the circle graph above. Candace asked 15 of her friends from the same school to choose their favorite color, and 5 people chose yellow. According to Tom's survey, how many of Candace's friends would have been expected to choose yellow?
We have that in Tom's survey he obtained that 20% of the students like the yellow color (see graph above).
Then, in Candance's (small) survey, she asked 15 friends. According to Tom's survey, Candance should have obtained that 20% of her friends like the yellow color.
Therefore, we need to find 20% of 15 (friends) to find the expected number of friends that Candance should have had using the results of Tom's survey. Then, we have:
[tex]\frac{20}{100}\cdot15=\frac{300}{100}=3[/tex]Hence, according to Tom's survey, Candance's friends would have been expected to be 3 to choose (of her 15 friends) yellow (3 is 20% of 15).
5x^2-25=100 solve by taking square root
Answer:
x=5,−5
Step-by-step explanation:
type the correct answer in each box. use numerals instead of words if neasary
This is given point in the fourth quadrant.
In this point, the adjacent is
[tex]\frac{5}{13}[/tex]The opposite is y.
Find hypotenuse h using the pythagorean theorem:
[tex]\begin{gathered} h^2=(\frac{5}{13})^2+y^2 \\ h=\sqrt[]{\frac{25}{169}+y^2} \end{gathered}[/tex][tex]\sec (\theta)[/tex]is equal to hypotenuse by adjacent.
[tex]\cot (\theta)[/tex]is equal to adjacent by opposite.
In the fourth quadrant,
[tex]\sec \theta[/tex]is positive , and
[tex]\cot \theta[/tex]is negative.
So,
[tex]\begin{gathered} \sec \theta=\frac{h}{\frac{5}{13}} \\ =\frac{13\sqrt[]{\frac{25}{169}+y^2}}{5} \\ \cot \theta=\frac{\frac{5}{13}}{-y} \\ =-\frac{5}{13y} \end{gathered}[/tex](03.03)
The point R is halfway between the integers on the number line below and represents the number ____. (Use the hyphen for negative numbers and write the answer as a decimal, such as -6.4). please help
The point R represents the number -2.5 on the number line
How to determine the location of the point R?From the question, we understand that the point R is halfway between the integers on the number line
This means that
Point R = 1/2 * (a + b)
Where variables a and b represent the boundaries of the integers
In this case, we have
a =-2
b = -3
Substitute a =-2 and b = -3 in the equation Point R = 1/2 * (a + b)
So, we have
Point R = 1/2 * (-2 - 3)
Evaluate the difference
Point R = 1/2 * -5
Evaluate the product
Point R = -2.5
Hence, the location of R on the number line is -2.5
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What is the equation of a line that passes though the pointe (8, -3) and has a slope of 1/4?
Answer:
y = (1/4)x - 5
Step-by-step explanation:
We'll look for an equation having the form y=mx+b, where m is the slope and b is the y-intercept, the value of y when x=0.
We are told the slope, m, is (1/4):
y = (1/4)x+ b
We need to find a value of b such that it forces the line to go through point (8,-3). Enter that point in the equation:
y = (1/4)x + b
-3 = (1/4)(8) + b for (8,-3)
-3 = 2 + b
b = -5
The equation is y = (1/4)x - 5
See attached graph.
The cost to rent a paddle boat at the country park is $8 per hour plus a non-refundable deposit of $10. The cost can be modeled by the function f(h) = 8h + 10, where h represents the number of hours the boat is rented. Describe the graph g(h) as it relates to f(h) if the non-refundable deposit increases to %15. PLEASEE HELPP!!
The relationship between the graph of f(h) and graph of g(h)
Both graphs have same slope of 8The y intercept of f(h) = 10The y intercept of g(h) = 11.5both graphs are straight line graph representing linear functions.What is a graph ?A graph is a pictorial representation of information
How to find the increment in the non refundable depositThe difference in the two graphs is the part of the non refundable deposit which will affect the intercept.
In f(h) = 8h + 10, the non refundable deposit 10 and the increment is 15%
The increment is solved below
solving the percentage increased
15% of $10 = 0.15 * 10 = $1.5
adding to the initial deposit
10 + 1.5 = 11.5
g(h) = 8h + 11.5
The graph of g(h) will have same slope as graph of f(h) which is 8
The y intercept of the graph if g(h) will be 11.5 while that of the graph of f(h) is 10
both graphs will form parallel lines
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I just need a little help
Which table represents a function?
Answer:
A would be the correct answer because to find a function when you draw a line on the graph, the line cannot cross each other. Even if the line is verticle, it is still crossing each other.
Step-by-step explanation:
the scale of topographical of map is 1:50000.what is the area of a dam which is represented on the map by an area of 3.5 centimeter square
The scale of a topographical map is 1:50000. This means that 1 cm on the map is 50 000 cm on reality.
[tex]1\operatorname{cm}\rightarrow50000\operatorname{cm}[/tex]Now, we can take the
Find the mean for n = 200 and p = 0.24 when the conditions for the binomial distribution are met.
The mean value of expected value for a binomial distribution is given by the next formula:
[tex]\mu_x=n\cdot p[/tex]Where n is the number of trials and p is the probability of success. So, using the given data:
[tex]\begin{gathered} \mu_x=200\cdot0.24 \\ \mu_x=48 \end{gathered}[/tex]So the expected value or mean is 48
-3(0.5+3p)=-6(p-5.9) show work
help
Answer:
p=12.3
Step-by-step explanation:
-1.5-9p= -6p+35.4
36.9=3p
p=12.3
i need this asap pleasee 44 points
Answer:
Step-by-step explanation:
i think its the 3rd one
Please answer only if you know the answer.
Step-by-step explanation:
The slope-intercept form of the equation of a line that passes through (5, -4) and has a slope of 3/4 is y = (3/4)x - 31/4.
What is the slope-intercept form?
The slope-intercept form of a line is y=mx + c.
Where, x and y are coordinates. m = slope and c = y intercept.
Given, slope (m) = 3/4
Substituting the values of (x, y) as (5, -4) and m = 3/4, we get:
-4 = (3/4) × 5 + c
⇒ c = -4 - (3/4) × 5 = -4 - 15/4 = -31/4
Now, putting the value of c in the standard equation:
y = (3/4)x - 31/4
⇒ 4y = 3x - 31
⇒ 3x - 4y = 31
Answer is Option C
f(x)=4x+2; Find f(8)
We have:
[tex]f(x)=4x+2[/tex]And want to find f(8), for this we simply replace x with 8 and operate:
[tex]f(8)=4(8)+2\Rightarrow f(8)=34[/tex]