Solving a quadratic equation, the correct option is given by:
Yes, they intersect at the coordinates (0, 8) and (6, 26).
What is a quadratic function?A quadratic function is given according to the following rule:
y = ax² + bx + c
The solutions are:
x1 = (-b + sqrt(Delta))/2a
x2 = (-b - sqrt(Delta))/2a
In which:
Delta = b² - 4ac
The equation for this system if:
-x² + 9x + 8 = 3x + 8
x² - 6x = 0
x(x - 6) = 0
Then:
x = 0 -> y = 3 x 0 + 8 = 8.x - 6 = 0 -> x = 6, y = 3 x 6 + 8 = 26.Which means that the correct option is:
Yes, they intersect at the coordinates (0, 8) and (6, 26).
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What is the equation of the line that is perpendicular to the line defined by the equation 2y=3x+2 and goes through the point (3,2)
The equation of the perpendicular line is [tex]y=-\frac{2}{3}x+4[/tex]
Equation of perpendicular linesThe equation is defined by 2y = 3x + 2
Rewrite the equation in the form y = mx + c
[tex]y=\frac{3}{2}x + 1[/tex]
The slope, m = 3/2
The y-intercept, c = 1
The equation perpendicular to the given line will be of the form:
[tex]y-y_1=\frac{-1}{m}(x-x_1 )[/tex]
Substitute [tex]x_1=3, y_1=2, and m=\frac{3}{2}[/tex] into the equation above
[tex]y-2=\frac{-2}{3} (x-3)\\\\y-2=-\frac{2}{3}x+2\\\\y=-\frac{2}{3}x+4[/tex]
Therefore, the equation of the perpendicular line is [tex]y=-\frac{2}{3}x+4[/tex]
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A customer's stock value seems to be rising exponentially. The equation for
the linearized regression line that models this situation is log(y) = 0.30x +0.296,
where × represents number of weeks. Which of the following is the best
approximation of the number of weeks that will pass before the value of the
stock reaches $600?
Considering the given regression equation, the number of weeks that will pass before the value of the stock reaches $600 is of:
B. 8.3.
What is the regression equation?The value of the stock y after x weeks is given as follows:
log(y) = 0.3x + 0.296.
We have to solve for x when y = 600, hence:
log(600) = 0.3x + 0.296
0.3x = 2.7782 - 0.296
x = (2.7782 - 0.296)/0.3
x = 8.3 weeks.
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which equation is represented by the graph below a. y=1/8ex b.y=1/2ex c.y=2ex. d.y=8ex
(02.05 LC)
Which of the following statements best describes the effect of replacing the graph of f(x) with the graph of f(x) + 4?
The graph shifts 4 units up.
The graph shifts 4 units down.
The graph shifts 4 units left.
The graph shifts 4 units right.
Answer:
1st option
Step-by-step explanation:
given the graph of f(x) then the graph of f(x) ± c is a vertical translation of f(x)
• if - c then a shift down of c units
• if + c then a shift up of c units
then for f(x) + 4 is a shift up of 4 units
Chandra invests $75 every month at 4.8%/a compounded monthly for 8 years. What is the total amount of
Chandra's investments after 8 years?
The total amount of Chandra's investments after 8 years exists at $110.03 Compound interest.
How to estimate the total amount of Chandra's investments after 8 years?The formula for calculating the compound interest exists described as;
[tex]A = P(1+r/n)^{nt[/tex]
where, P is the amount invested = $75
r be the rate. = 0.048
t be the time = 8 years
n = 12 (monthly)
Substitute, the values in the above equation, then we get
[tex]$A = 75(1+0.048/12)^{96[/tex]
A = 75(1.467)
A = 110.03
Hence the total amount of Chandra's investments after 8 years is $110.03 Compound interest.
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Select linear or nonlinear to correctly classify each function. Function Linear Nonlinear 72=x3+y Linear – 72= x 3 +y Nonlinear – 72= x 3 +y y+1=5(x−9) Linear – y+1=5( x−9 ) Nonlinear – y+1=5( x−9 ) 7y + 2x = 12 Linear – 7y + 2x = 12 Nonlinear – 7y + 2x = 12 4y = 24 Linear – 4y = 24 Nonlinear – 4y = 24
The linear functions are: y + 1 = 5(x - 9), -y + 1 = 5(x − 9), 7y + 2x = 12, -7y + 2x = 12, 4y = 24, and -4y = 24
How to classify the functions?As a general rule, linear functions take any of the following forms:
y = mx + b
Ax + By = C
y - y1 = m(x - x1)
Any equation that take a different form is not a linear function
Using the above as a guide, the linear functions are:
y + 1 = 5(x - 9), -y + 1 = 5(x − 9), 7y + 2x = 12, -7y + 2x = 12, 4y = 24, and -4y = 24
Other functions are nonlinear
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Find the area of a triangle with legs that are: 16 m, 12 m, and 8 m.
Answer: 46.48 m²
Step-by-step explanation:
this question was answered already, go search it up
Christine has scored 73, 85, 70, and 63 on her previous four tests. What score does she need on her next test so that her average (mean) is 73?
Answer:
74
Step-by-step explanation:
(73 + 85 + 70 + 63 + x)/5 = 73.
You find the average by adding all of the test scores and dividing that number by the number of tests. We had four test, so will will take that total, plus some mystery number (let's call it x), we divide that total by 5 because now there are 5 tests and not 4. We already know what we want the average to be, we want the average to be 73. We now have:
(291 + x)/5 = 73 Multiply both sides by 5
291 + x =365 Subtract 291 from both sides to get
x = 74
Answer: 74
Step-by-step explanation:
The mean is the average of all the values, which we find by finding the sum of each value and dividing by the total number of data points.
With 5 data points, we can use this equation to find, x, or the data point needed to obtain a mean of 73:
[tex]\frac{73+85+70+63+x}{5}=73\\ 291+x=365\\x=74[/tex]
find w + y + y + z
someone pls help
Answer:
300
Step-by-step explanation:
30+30+w+x+y+z = 360 (all angles round a point add up to 360)
Simplifying :
60 + w+x+y+z = 360
Subtracting 60 from both sides :
w+x+y+z = 300
Hope this helped and brainliest ?
Sum of entire angle=360°
so
30+x+y+x+w+30=360w+x+y+z=360-60w+x+y+z=300What kind of multi step do I have to do to prove a is parallel to b and m parallel to n.
The proof that line n is perpendicular to both a and b is proved below using definition of right angle and perpendicular transversal theorem.
How to prove Perpendicular and Parallel Lines?
We are given that;
Line a is parallel to line b
Line m is parallel to line n.
A) We want to prove that line a is perpendicular to n.
From the image, we see that there is a right angle sign on the opposite side of ∠1 facing m.
Now, we know that by definition of a right angle that ∠1 will also be a right angle.
Since angle 1 is a right angle, then we can say the line transversal a is perpendicular to line m.
B) We want to prove that line b is perpendicular to n.
The definition of the perpendicular transversal theorem, states that if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.
Thus, b will be perpendicular to n.
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What is the equation of the rational function g(x) and its corresponding slant asymptote?
Rational function with one piece increasing from the left in quadrant 3 and passing through the point negative 3 comma 0 and going to the right asymptotic to the line x equals 2 and another piece increasing from the left in quadrant 3 asymptotic to the line x equals 2 and passing through the point 3 comma 0 and going to the right
g of x is equal to the quantity x squared minus 9 end quantity over the quantity x plus 2 end quantity with a slant asymptote at y = x + 2
g of x is equal to the quantity x squared minus 9 end quantity over the quantity x minus 2 end quantity with a slant asymptote at y = x + 2
g of x is equal to the quantity x squared minus 9 end quantity over the quantity x plus 2 end quantity with a slant asymptote at y = x – 2
g of x is equal to the quantity x squared minus 9 end quantity over the quantity x minus 2 end quantity with a slant asymptote at y = x – 2
The solution to the Questions are
The alternate hypothesis demonstrates that there are two possible outcomes for the test.Decision rule: If z > 2.05 or z<-2.05, reject H0z=2.59The two-tailed nature of the test is shown by the alternative hypothesis.The result of the test yields the following P-value: 0.0096What is the alternate hypothesis?(a)
The alternate hypothesis demonstrates that there are two possible outcomes for the test.
(b)
Here we have
[tex]n_{1}=40,\\\\ \bar{x}_{1}=102,\sigma_{1}=5,n_{2}=50,\bar{x}_{2}=99,\sigma_{2}=6[/tex]
(b)
Here the test is two-tailed. So for [tex]\alpha =0.04[/tex], the critical values of the z-test are -2.05 and 2.05.
Decision rule: If z > 2.05 or z<-2.05, reject H0
(c)
Test statistics will be
[tex]z=\frac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{\sigma^{2}_{1}}{n_{1}}+\frac{\sigma^{2}_{2}}{n_{2}}}} \\\\\\z=\frac{(102-99)-(0)}{\sqrt{\frac{5^{2}}{40}+\frac{6^{2}}{50}}}[/tex]
z=2.59
(d)
The two-tailed nature of the test is shown by the alternative hypothesis.
(e)
The result of the test yields the following P-value: 0.0096
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The function f and g are given by [tex]f(x)=x^2[/tex] and [tex]g(x)=-^1_2 x+5[/tex].
Let R be the region bounded by the x-axis and the graphs f and g as shown at the bottom. Also, I only need you to answer part b, I've already finished part a.
a) Describe how you would find the area of R.
[tex]R=18 \frac{2}{3}[/tex]
b) The region R is the base of a solid. For each y, where
0 < y < 4, the cross-section of the solid taken perpendicular to the y-axis is a rectangle whose base lies in R and whose height is 3y. Explain how you would write an expression that gives the volume of the solid.
As you've pointed out, R is a different region that I originally thought. The area of R can be computed using either
[tex]\displaystyle \int_0^2 x^2 \, dx + \int_2^{10} -\frac x2 + 5 \, dx[/tex]
or
[tex]\displaystyle \int_0^4 (10-2y)-\sqrt y \, dy[/tex]
Either way, you've gotten the correct area for part (a).
For part (b), we can use part of the integral with respect to [tex]y[/tex] above. The horizontal distance between the curves [tex]y=x^2[/tex] and [tex]y=-\frac x2+5[/tex] is obtained by first solving for [tex]x[/tex],
[tex]y=x^2 \implies x=\sqrt y[/tex]
[tex]y=-\dfrac x2+5 \implies x = 10-2y[/tex]
so the length of each cross section is [tex]10-2y-\sqrt y[/tex].
The height of each cross section is [tex]3y[/tex].
Then the volume of the solid is
[tex]\displaystyle \int_0^4 3y \left(10-2y-\sqrt y\right) \, dy = \boxed{\int_0^4 -6y^2 + 30y - 3y^{3/2} \, dy}[/tex]
The instructions don't say to evaluate, but if you're looking for practice the volume ends up being 368/5, or 73 3/5.
Given the similar hexagon-based prisms pictured below, if prism 2 has a surface area of 256 cm, what is the surface area prism 1? Hint : the ratio of surface areas is the scale factor squared.
Using the hint that the ratio of surface areas is the scale factor squared, the surface area of prism 1 is 36 square cm
How to determine the surface area prism 1 using the hint that the ratio of surface areas is the scale factor squared?From the figure, we have the following parameters
Prism 1 = 3 cm
Prism 2 = 8 cm
Calculate the scale ratio of dilation from prism 2 to prism 1 using the following equation
Scale ratio = Prism 1/Prism 2
Substitute the known values in the above equation
Scale ratio = 3m/8m
This gives
Scale ratio = 0.375
The surface area of prism 1 is then calculated using the following equation
Area of prism 2 = Scale ratio^2 * Area of prism 1
Substitute the known values in the above equation
Area of prism 2 = 0.375^2 * 256 square cm
Evaluate the product
Area of prism 2 = 36 square cm
Hence, the surface area of prism 1 is 36 square cm
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A truack Cars a load of 50 boxes 50 men are 20kg boxes and the rest and 25 ка Boxes. Is the Total weight of all Boxes is 1175 kg. How many of each type are there? X = 50kg Y=20kg 2= 25kg then sum of that is 1175 kg
The number of boxes with 20kg = 15
The number of boxes with 25 kg = 35.
How to estimate the value of X and Y?
To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.
Total weight of all boxes = 1175kg
Total number of boxes = 50
X + Y = 50........................(1)
20X + 25Y = 1175 .............(2)
(1) [tex]\times[/tex] 20
20 (X + Y = 50)
20X + 20Y = 1000 .............(3)
Subtracting (3) from (2), we get
20X + 25Y = 1175 -
20X + 20Y = 1000
--------------------
5Y = 175
Y = 175/5
Y = 35
Substitute the value of y in (1), then we get
X + Y = 50
X + 35 = 50
X = 50 - 35
X = 15
The value of X = 15 and Y = 35
Number of boxes with 20kg = 15
Number of boxes with 25 kg = 35.
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Please help me with this problem literally so desperate right now.
Answer: 13 inches by 2 inches
Step-by-step explanation:
26 can be made by:
1 x 26
2 x 13
There are only 2 possibilities for the dimensions.
2 x 3 + 7 is 13, which fits the requirements.
Which means, the length is 13 and the width is 2.
(giving brainlyst) Question 2(Multiple Choice Worth 2 points) (13.03 LC) Which statement best describes the expression (5 x 3-12) x 87 O Subtract the product of 5 and 3 from the product of 12 and 8. O Multiply the difference of 12 and 8 by the product of 5 and 3. O Multiply the difference of 5 and 3 by 8, then subtract 12. O Subtract 12 from the product of 5 and 3, then multiply by 8. k
Answer:
See below
Step-by-step explanation:
Using PEDMAS:
O Subtract 12 from the product of 5 and 3, then multiply by 87
simplify (2+3)2 + 8/2
Answer
[tex]2 \times 2 + 6 \times 2 + \frac{8}{2 } [/tex]
[tex]4 + 12 + 4[/tex]
[tex]16 + 4[/tex]
[tex]20[/tex]
Which of the following points is in the solution set of y < x2 - 2x - 8?
The solution set of the given inequality has a domain of (-∞, ∞) and the vertex(h,k) = (1, -9)
What is the solution set for inequality?The solution set for inequality is the set of all solutions for which the inequality is defined. It can also be represented in an interval notation.
Given that:
y < x² - 2x - 8By rewriting the equation in the parabola standard form 4p(y-k) = (x - h)², we have:
[tex]\mathbf{4\times \dfrac{1}{4}(y-(-9)) = (x-1)^2}[/tex]
Therefore, the parabola properties are:
The solution set of the domain is (-∞, ∞)Vertex(h,k) = (1, -9) Focal length |p| = 1/4Learn more about the solution set of inequality here:
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do you have a picture of what the graph would look like?
The attached graph represents the piecewise function.
How to determine the graph of the equation?The piecewise function is given as:
f(x) = 3x - 5, x ≤ -1
= -2x + 3, -1 < x < 4
= 2, x ≥ 4
To plot the graph, we simply plot the equations together with their domains
i.e.
3x - 5 with the domain of x ≤ -1, -2x + 3 with the domain of -1 < x < 4 and 2 with the domain of x ≥ 4
See attachment for the graph of the function
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Calculate the probability for the following situation, then select the correct answer:
You are tossing a coin, then rolling a die, then drawing a card from a deck of cards. What is the probability that you will get: a head AND an odd number on the die AND a card greater than 6 (assume the ace is equal to 1) from the deck?
The probability is P = 0.135
How to find the probability?
First, we need to find the individual probabilities, that are given by the quotient between the number of outcomes that meet the condition and the total number of outcomes.
P(head) = 1/2P(odd number) = 3/6 (there are 3 odd numbers on the dice)P(card greater than 6) = 28/52 (28 cards with numbers larger than 6).The joint probability is given by the product between the individual probabilities, so we get:
P = (1/2)*(3/6)*(28/52) = 0.135
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Using the data in the table, which statement is true?
The true statement is mean > median
How to determine the true statement?The mean is the average value.
So, we have
Mean = Sum/Count
This gives
Mean = (8 * 1 + 10 * 3 + 14 * 2)/(1 + 3 + 2)
Evaluate
Mean = 11
The mode is the measure with the highest frequency.
So, we have
Mode = 10
The median is the middle element
So, we have
Median = 10
The mean (11) is greater than the mode and the median
Hence, the true statement is mean > median
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Suppose we want to choose colors, without replacement, from the colors red, blue, green, and purple.
(a) How many ways can this be done, if the order of the choices is relevant?
(b) How many ways can this be done, if the order of the choices is not relevant?
The number of ways when the choice is not relevant is 4
How to determine the number of ways?The number of colors are:
Colors, n = 4
The color to choose are:
r = 3
Relevant choice
When the choice is relevant, we have:
[tex]Ways = ^nP_r[/tex]
This gives
[tex]Ways = ^4P_3[/tex]
Evaluate
Ways = 24
Hence, the number of ways when the choice is relevant is 24
Not relevant choice
When the choice is not relevant, we have:
[tex]Ways = ^nC_r[/tex]
This gives
[tex]Ways = ^4C_3[/tex]
Evaluate
Ways = 4
Hence, the number of ways when the choice is not relevant is 4
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x+11=35 solve on algebraic equation
Answer:
x = 24
Step-by-step explanation:
x + 11 = 35
x = 35 - 11
x = 24
x+11=35
Subtract 11 on both sides.
x=35−11Subtract 11 from 35 to get 24.
x=24 === Answerил
-
10: Find the x-and y-intercepts of the graph of the function f(x) = x^4 − 1
Solution :
Find the x-and y-intercepts of the graph of the function f(x) = x^4 − 1
Answer: The given equation is
f(x) = x^{4} - 1
x- and y-intercept of the graph of the function f(x) = x^4 - 1 is
x-intercept(s): (1,0), (−1,0)
y-intercept(s): (0, −1)
A graph of the above point is attached
Step-by-step explanation:
Given equation, f(x) = x^{4} - 1
let's assume the above equation with respect to y to find intercept i.e
y = x^{4} - 1 .........................(i)
Now, for the x-intercept put y = 0 in eq.(i)
So, we get,
0 = x^4 - 1
x^4 = 1
x = -1, +1
from above we get the x-intercept (1,0), (−1,0)
Now, for the y-intercept put x = 0 in eq.(i)
So, we get
y = 0^4 - 1
y = -1
from above we get the y-intercept (0, -1)
Therefore, from all above
x- and y-intercept of the given equation f(x) = x^4 - 1 isx-intercept(s): (1,0), (−1,0)
y-intercept(s): (0, −1)
Graph of the given equation f(x) = x^4 - 1 with intercept is
Factor f(x) =3x^2+23x^2-35x+9 into linear factors given that -9 is a zero of f(x).
Using the Factor Theorem, the function factored into linear factors is given as follows:
[tex]3x^2 + 23x^2 - 35x + 9 = 3(x + 9)(x - 1)\left(x - \frac{1}{3}\right)[/tex]
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
-9 is a zero of f(x), hence [tex]x_1 = -9[/tex] and:
3x³ + 23x² - 35x + 9 = (x + 9)(ax² + bx + c)
ax³ + (b + 9a)x² + (9b + c)x + 9c = 3x³ + 23x² - 35x + 9
The coefficients are given as follows:
a = 3.9c = 9 -> c = 1.b + 9a = 23 -> b = -4.Hence:
3x³ + 23x² - 35x + 9 = (x + 9)(3x² - 4x + 1)
[tex]3x^2 + 23x^2 - 35x + 9 = 3(x + 9)(x - 1)\left(x - \frac{1}{3}\right)[/tex]
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This table shows how many students from two high schools attended a
football game
Attended the game
Total
Did not attend
the game
90
Westville
60
150
North Beach
110
90
200
Total
170
180
350
A student is randomly selected.
What is the probability that a student attended the game, given that the
student is from North Beach? Round your answer to two decimal places,
O A. 0.57
B. 0.48
C. 0.55
OD. 0.65
The probability that a student attended the game, given that the student is from North Beach is 0.65.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that a student attended the game, given that the student is from North Beach = number of North beach students that attended the game / total number of students who attended the game
110 / 170 = 0.65
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Todd and his friends are painting 5 equal sections of a wall. The wall is 10 feet tall, but its length is unknown.
Each section will be a different color, so they need to know the area of each section
1. Write an expression for the total area of the wall. Explain how you came up with your expression
The expression for the total area of the wall is 10x.
What is area of rectangle?
Let l be length and b be breadth of the rectangle.
Then the area is the product of length and breadth of the rectangle.
That is area = l* b
We can find the expression for the total area of the wall as shown below:
Let the total length of the wall be x.
Height=10 ft
Total area = Height*Length
Putting the value of length and breadth in the above formula.
Total area = 10*x
Total area = 10x
Hence, the expression for the total area of the wall is 10x.
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A stairway rises 6 feet 4 inches over a horizontal distance of 8 feet 6 inches. What is the diagonal length of the stairway
Answer:
10.6 ft
Step-by-step explanation:
to find the diagonal length of the stairway we can use the pythagorean theorem or a^2 + b^2 = c^2
6'4" is also 6 1/3' or 19/3'
8'6" is also 8 1/2' or 17/2'
now square them both
361/9 + 289/4
make them have the same denominator
1444/36 + 2601/36
add them
4045/36
take the square root
10.6000524 is your answer
10.6 ft
1 On a trip, a family drove 270 kilometers in 3 hours. a Find how many kilometers were traveled in one hour. Express this as a rate per hour. it rate
Answer:
90 kilo per hour
Step-by-step explanation:
hope that helps!!
The table shows the multiplication of two linear expressions.
A 2-column table with 5 rows. First column is labeled Reason with entries Given, Step 1, Step 2, Step 3, Step 4. Second column is labeled Step with entries three-fourths x (negative 8 x + 6), (three-fourths x) (negative 8 x) + (three-fourths x) (6), three-fourths times (negative 8) times x times x + three-fourths times 6 times x, (three-fourths times (negative 8)) times (x times x) + (three-fourths times 6) times x, negative 6 x squared + 9 over 2 x.
What is the mathematical reasoning for Step 3?
associative property
commutative property
distributive property
simplify
The mathematical reasoning for Step 3 is a distributive property.
What is distributive property?It should be noted that the distributive property is the multiplication of the sum of two to more addends by a number that will give same result.
In this case, the mathematical reasoning for Step 3 is a distributive property.
Therefore, the correct option is C.
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Answer: C. Distributive Property