√15, and -√15
1) Considering the equation below, let's solve it:
[tex]\begin{gathered} x^2=15 \\ \sqrt[]{x^2}=\sqrt[]{15} \\ x=\sqrt[]{15},\text{ -}\sqrt[]{15} \end{gathered}[/tex]2) So the answer is √15, and -√15
Since (√15)² = 15 and (-√15)²=15
16.What is the equation of the vertical asymptote for the function f(x) = x-1,x+4(A) x=1(B) x=-1(C) x=4(D) x=-417.
The vertical asymptotes is when the denominator is 0
Hence we have
[tex]\begin{gathered} x+4=0 \\ x=-4 \end{gathered}[/tex]X=-4 is the vertical asymptote
The right option is D
For the polynomial below, -1 is a zero. g(x) = x2-3x² + 25x +29 Express g (x) as a product of linear factors.
Hello there. To solve this question, we'll have to remember some properties about polynomials.
We want to express the following 3rd degree polynomial as a product of linear factors:
[tex]g(x)=x^3-3x^2+25x+29[/tex]Knowing that -1 is a zero.
For this, there are two ways of determining the other roots and hence the linear factors.
Remember that a polynomial is written as a product of linear factors if
[tex]f(x)=a(x-x_1)(x-x_2)\cdots[/tex]Where x1, x2 ... are the roots of the polynomial.
It is also called the canonical form of the polynomial.
First way: divide g(x) by (x - (-1)), that is (x + 1)
We'll use the long division method for polynomials:
At the top of x + 1 in the diagram below, we add the terms that, when multiplied by the bottom expression, gives us a term that can be subtracted from g(x).
We have a x³ factor, so we want to multiply it first by x² in order to cancel out:
Now we have a -4x² factor, so we multiply it by -4x in order to cancel out:
Finally, multiply it by a 29 in order to cancel the first 29x term:
Hence we say that
[tex]x^3-3x^2+25x+29=(x+1)(x^2-4x+29)[/tex]Now, we want to factorize the quadratic expression in the right hand side, writing it as a product of linear factors as well:
As said before, we can take the roots of the expression and write it in canonical form. Since it is a quadratic expression, we have this easier formula to find the roots:
[tex]ax^2+bx+c=0\Rightarrow x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Plugging a = 1, b = -4 and c = 29, we'll get
[tex]\begin{gathered} x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4\cdot1\cdot29}}{2\cdot1} \\ \\ x=\dfrac{4\pm\sqrt{16-116}}{2}=\dfrac{4\pm\sqrt{-100}}{2} \\ \end{gathered}[/tex]Notice the radical is a negative number, hence it cannot be factored in terms of real linear factors.
We say that for an expression
[tex]x^2+\beta x+\gamma[/tex]It is not reducible over R (real numbers) if
[tex]\beta^2-4\gamma<0[/tex]Therefore the final answer is:
[tex](x+1)(x^2-4x+29)[/tex]We could also use the following method to find this answer:
It is called the Horner-Ruffini method, that we dispose the coefficients and the roots in the following manner
Multiply the first coefficient by the root and add it to the second number in the line. Repeat the process until you reach the last number.
Therefore the result of this division is the polynomial:
[tex]x^2-4x+29[/tex]As we found before.
En3. A financial advisor is paid $500 per week plus a 4% commission on all sales over $800. During oneweek, his total sales were $1,330. Find his gross earnings for the week..$541.20$531.20$521.20$551.20
For this problem we know that the salary per week is 500 and he gets a commission of 4% for each sale over 800. During one week the total sales are 1330 and we want to estimate the gross earnings for the week.
Taking in count the info given we can set up the following equation for the total amount recieved:
[tex]A=500+0.04S[/tex]Where A represent the amount recieved and S the sales. For this case S=1330 and replacing we got:
[tex]A=500+0.04\cdot1330=553.2[/tex]i need help asap with these questions please worth 100 of my grades
A line includes the point (7,5)has a slope of 1.What is its equation in slope intercept form?
Given:
Point( 7, 5)
x = 7 and y=5
slope(m) = 1
We need to first find the intercept.
Substitute x=7, y=5 and m=1 into y=mx + b and solve for intercept(b)
5 = 1(7) + b
5 = 7 + b
5 - 7 = b
-2 = b
Now, form the equation by substituting the value of the slope and intercept into y=mx + b
y = x - 2
(3.22x10^3)-(2.96x10^3)
The value of (3.22 - 2.96)×10³ is 0.26×10³.
What is scientific notation?We use scientific notation for writing large numbers in compact form.
Scientific notation is written in base multiplied by 10 raised to some power where 0 ≤base < 10 scientific notation also has an alternative name which is known as engineering notation.
We know when we have numbers in scientific notation with the same exponent value we can do arithmetic operations to the base.
∴ (3.22x10³) - (2.96x10³).
= (3.22 - 2.96)×10³.
= 0.26×10³.
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Find what X equals [tex]2(x + 7) = - 4x + 14[/tex]
To solve the expression: 2(x + 7) = - 4x + 14, just follow these steps:
1. Distribute the product on the left side of the equation:
2(x + 7) = - 4x + 14
2*x + 2*7 = - 4x + 14
2x + 14 = -4x + 14
2. subtract 14 on both sides:
2x + 14 - 14 = -4x + 14 - 14
2x = - 4x
3. Add 4x on both sides:
2x + 4x = -4x + 4x
6x = 0
4. Divide both sides by 6:
6x/6 = 0
x*6/6 = 0
x*1 = 0
x=0
Then x equals 0
What is (a)
5(x+1)+4_4
6
Answer:
x=-1
Step-by-step explanation:
Use the rule to complete the input/output table. Rule: the output is t-3•Input t: 17, 20, 22, 24•output r: On the home work it’s set as a table
Step 1
Write the rule
r = t - 3
Step 2:
Find each output for corresponding input.
When t = 17
r = 17 - 3 = 14
When t = 20
r = 20 - 3 = 17
When t = 22
r = 22 - 3 = 19
When t = 24
r = 24 - 3 = 21
Step 3
Final answer
Hello I am quite confused by this question may you please help me solve and explain this? thank you:)
Given the mean score of a group of people in a quiz, the standard deviation of the scores of the people, and the score of a person, we can easily determine the z-score like this:
[tex]z=\frac{x-μ}{σ}[/tex]Where σ is the standard deviation, μ is the mean score and x is the score. By replacing 78 for μ, 4.2 for σ and 80 for x, we get:
[tex]z=\frac{80-78}{4.2}=0.4762[/tex]Then the z-score equals 0.4762. In this case, the score of 80 is a usual value since it is within one standard deviation of the mean.
Which polynomial is prime?O 3x²+3x²-2x-2O 3x-2x²+3x-4O4x²+2x²+6x +3O4x³+4x²-3x-3
Explanation:
Concept:
If the only factors a polynomial are 1 and itself, then that polynomial is prime.
The first polyonial will be factorised below as
[tex][/tex]Can someone help me with this, please?
Kevin needs to rent tables for his party. There will be 26 people at his party. Each table can seat 4 people. How many tables does Kevin need to order? Write a multiplication and division sentence that will help you answer the question. Use n for the unknown. __ x __ =___ ___÷___=____
Answer:
6.5
Step-by-step explanation:
Well if you do 4 x n=26 26/4=n
Find the slope of the line.
EAT
(3,1
-8-
O A.
(3-1)
O
What is the slope of the line? Select the correct choice below and, if
necessary, fill in the answer box to complete your choice.
The slope of the line is. (Type an integer or a simplified
fraction.)
B. The slope of the line is undefined.
Option A. The slope of the line is zero
How is the slope calculated?
First point = [tex](x_1,y_1)=(-3, -1)[/tex]
Second point = [tex](x_2,y_2)= (3,-1)[/tex]
Slope of the line = m
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\\\m =\frac{-1+1}{3+3} \\\\m = \frac{0}{3} \\\\m= 0[/tex]
Thus the slope of the line is zero.
What is a zero slope?
The slope will be 0 if time passes without any change and is called a zero slope. Here each y point in a horizontal line is identical. This implies that the slope will always be zero because the numerator of the fraction will always equal zero.A vertical line is an undefined slope where the x-points never change as the y-points rise and fall. The zero slope equation, or y = b, is the formula for a line with no slope, also known as a horizontal line.To learn more about zero slope, refer:
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if a (9,18) and b = (1,12) what is the length of ab
To calculate the lenght of AB we'll use the formula for distance between two points.
Remember that the disnatce between points
[tex]\begin{gathered} (x_1,y_1) \\ \text{and} \\ (x_2,y_2) \end{gathered}[/tex]is:
[tex]\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Using this, and the data given,
[tex]\begin{gathered} AB=\sqrt[]{(1_{}-9)^2+(12-18)^2} \\ \rightarrow AB=\sqrt[]{(-8)^2+(-6)^2} \\ \rightarrow AB=10 \end{gathered}[/tex]This way, the lenght of AB is 10 units
The percentage of adult height attained by a girl who is x years old can be modeled byf(x)=61+35 log (x-3)where x represents the girl's age (from 5 to 15) and f(x) represents the percentage of her adult height. Complete parts (a) and (b) below.a. According to the model, what percentage of her adult height has a girl attained at age 12?A girl has attained% of her adult height by age 12.(Do not round until the final answer. Then round to the nearest tenth as needed.)b. Why was a logarithmic function used to model the percentage of adult height attained by a girl from ages 5 to 15, inclusive?O A. Height increases rapidly at a young age, and then increases more slowly.OB. Height increases at a steady rate, regardless of one's age.OC. Height increases rapidly at a young age, stops increasing at a certain age, and then starts decreasing.O D. Height increases rapidly at a young age, and continues to increase even faster as one gets older.
The percentage of her adult height has a girl attained at age 12 is 94.39 %
The percentage of adult height attained by a girl who is x years old can be modeled by
f(x) = 61 + 35 log (x - 3)
where x represents the girl's age and f(x) represents the percentage of her adult height.
The percentage of her adult height a girl attained at age 12
f(12) = 61 + 35 log (12 -3) = 61 + 35 log 9
f(12) = 61 + 35 *0.954 = 94.39
Now, f(12) = 94.39 %
The logarithmic function used to model the percentage of adult height attained by a girl from ages 5 to 15, inclusive, Height increases rapidly at a young age and then increases more slowly.
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Zena's Z-score on the chemistry final was 0.65. If the class mean on the final was 78, the the standard deviation was 12, and the distribution was normal, what was Zena's raw score?
Zena's raw score in the chemistry test is 85.8
How to determine the raw score of the test?From the question, the given parameters are
Mean score of the class = 78Standard deviation of the class = 12z-score of the test = 0.65The z-score of the distribution is calculated using the following z-score formula
z = (raw score - mean value)/standard deviation
Substitute the given parameters in the above equation
So, we have the following equation
0.65 = (Raw score - 78)/12
Cross multiply in the above equation
Raw score - 78 = 7.8
Add 78 to both sides
Raw score = 78 + 7.8
Evaluate
Raw score = 85.8
Hence, the raw score is 85.8
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Hi, can you help me answer this question please, thank you!
We were given the following information:
Sample of men = 80, 45% of the sample owned cats (36 men owned cats)
Sample of women = 80, 55% of the sample owned cats (68.75 women owned cats)
The significance level is 0.025
We will calculate the test statistics as shown below:
[tex]undefined[/tex]Statistics$ 9 45%ХIntFlorinchantemeraldataPositive and negative linear associations from scatter plots80/12so SanThe plot shown below describes the relationship between theaverage income in a city and the average rent for a 1-bedroomapartment in hat city.18001600100Average rent for a 10 dollars per month
Using the given scatter plot, let's describe the relationship between the average income in a city and the average rent for a 1-bedroom apartment in that city.
Here, the average income is represented on the x-axis while the average rent is represented on the y-axis.
Using the scatter plot, we can see that as the average income increases, the average rent also increases.
Since one variable increase as the other increases, and the points show a straight line pattern, we can say the relationship between them is a positive linear association.
Therefore, the relationship between the average income and the average rent for a 1-bedroom apartment in that city is a positive linear association.
ANSWER:
A. Positive linear association.
express (x-3)² as a trinomial in standard form
We will write it as follows:
[tex](x-3)^2=(x-3)(x-3)=x^2-3x-3x+9[/tex][tex]=x^2-6x+9[/tex]A certain group of women has a 0.97% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?
The probability that a randomly selected women does not have red/ green color blindness is 0.9903.
The probability of a woman has red/ green color blindness is,
P (Color blindness) = 0.0097.
The probability that a randomly selected women does not have red/ green color blindness is,
P (No Color blindness) = 1 - P (Color blindness)
= 1 - 0.0097
= 0.9903
Thus, the probability that a randomly selected women does not have red/ green color blindness is 0.9903.
Hence the probability that the women does not have red/green color blindness is 0.9903.
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Joy's investment of $3600 grows to $4800 in 48 weeks. What simple interest did she earn?
Answer:
answer
down
below
8 294 400
Work these out mentally2/5 of 10 mm3/4 of 40 km 5/6 of $12
This can be solved by multiplying.
- 2/5 of 10 mm
[tex]\frac{2}{5}\times10=\frac{20}{5}=4[/tex]Answer: 4 mm
- 3/4 of 40 km
[tex]\frac{3}{4}\times40=\frac{40\times3}{4}=\frac{120}{4}=30[/tex]Answer: 30 km
- 5/6 of $12
[tex]\frac{5}{6}\times12=\frac{5\times12}{6}=\frac{60}{6}=10[/tex]Answer: $10
what is the image point of (-7 6) after a rotation of 270 degrees counterclockwise
270° counterclockwise about the origin. Check the picture below.
Find the area of the shaded region.6005 cmA = [?] cm2Enter a decimal rounded to the nearest tenth.
To determine the area of the shaded region we first need to calculate the area of the whole circle, then we need to calculate the area of the circular sector of 60º, then finally we will calculate the area of the triangle and subtract the area of the triangle from the area of the circular sector, this will be the area of the part that isn't painted. Finally we can subtract the area that isn't painted by the area of the circle to determine the shaded region.
To calculate the area of the circle we will do as follows:
[tex]A_{\text{circle}}=\pi\cdot r^2=\pi\cdot5^2=25\cdot\pi=78.5[/tex]The circular sector can be calculated by the following expression:
[tex]A_{\text{sector}}=\frac{60\cdot\pi\cdot r^2}{360}=\frac{\pi\cdot5^2}{6}=\frac{25\cdot\pi}{6}=13.08[/tex]All of the sides of the triangle are equal, so we can use the following expression:
[tex]A_{\text{triangle}}=\frac{l^2\sqrt[]{3}}{4}=\frac{5\cdot\sqrt[]{3}}{4}=2.163[/tex]Now we will subtract the area of the triangle from the area of the sector to determine the area that isn't shaded.
[tex]A_{\text{blank}}=13.1-2.163=10.937[/tex]To finish we will subtract the area that isn't shaded from the area of the circle.
[tex]A_{\text{shaded}}=78.54-10.937=67.6[/tex]The area of the shaded region is 67.6 cm²
Examine the structure of this question. state if there are infinitely many solutions, no solution, or one solution. If there is one solution, solve the equation and state the solution. If there are infinitely many solutions or no solution, justify why using the structure of the equation.
1) Examining this rational equation. And then solving it.
3/4(x-1) -1/2 =2(1-3x)
3/4x-3/4-1/2=2-6x
2)Combining like terms, let's isolate the x terms on the left side
3/4x+6x -3/4-1/2=2-6x+6x
3)To add these fractions let's calculate the Least Common Multiple of the denominators:
27/4x -5/4=2+0
27/4x -5/4+5/4=2+5/4
27/4x=13/4 Multiplying both sides by four to eliminate the fraction.
27x=13 Dividing both sides by 13 to get the value of x
x =13/27
S={13/27}
2) For those 2 equations there was a single solution for x. We can say that there is one solution to these equations.
Find the cube number
7 12
20
25
27
Answer:
712 = 360944128
20 = 8000
25 = 15625
27 = 19683
Step-by-step explanation:
A cube number is a number that is the product of three numbers which are the same. In other words, if you multiply a number by itself and then by itself again, the result is a cube number.
4 sheets of paper cost's $14 how much will with be for 11 1/2 sheets of paper?
4 sheets of paper cost's $14 how much will with be for 11 1/2 sheets of paper?
we have that
Applying proportion
14/4=x/11 1/2
Convert 11 1/2 to an improper fraction
11 1/2=23/2
substitute
14/4=x/(23/2)
x=(23/2)*(14/4)
x=$40.25
therefore
teh answer is $40.25
point a is to the left of point B on the horizontal number line what could be the valves of point a and point B
Answer:
If point A is to the left of point B, point A is less than B. Therefore, the values of point A and B could be:
A = 7 and B = 9
A = -8 and B = -5
A = -10 and B = 2
Because 7 is less than 9, -8 is less than -5, and -10 is less than 2.
The range of the function f(x)= x^2 + 2x - 8 is all real numbers..
Simplify the expression x^2+2x-8 to obtain the equation as complete square.
[tex]\begin{gathered} x^2+2x-8=x^2+2x+1-1-8 \\ =(x^2+2x+1)-9 \\ =(x+1)^2-9 \end{gathered}[/tex]The value of square terms is 0 or postive, so range of the expression x^2+2x-8 is,
[tex]\lbrack-9,\infty)[/tex]So correct option is B greater than or equal to -9.
