Answer with explanation: A hiker has increased his distanced covered by 10% each day since the start, the total distance covered at the end of the 7th day is 75.897mile:
(A) The number of miles on the first day:
[tex]\begin{gathered} \text{let x be the distance covered on first day:} \\ x,1.1x,1.21x,1.331x,\ldots. \\ \text{ This is a Geomatric sequence:} \\ S_n=\frac{a(r^n-1)}{r-1} \\ a=x \\ r=\frac{1.1x}{x}=1.1 \\ r=1.1 \\ n=7 \\ S_n=\frac{x((1.1)^7-1)}{1.1-1}\Rightarrow(0) \end{gathered}[/tex]Substituting the total miles covered on the 7th day in equation(0) gives:
[tex]\begin{gathered} 75.897=\frac{x((1.1)^7-1)}{1.1-1} \\ 7.5897=0.9487171x \\ x=7.9999612107761101807904590314647 \\ x\approx7.9999mi \end{gathered}[/tex]Therefore on the first day, the hiker covered about 7.99 miles:
(B) The equation for the S:
[tex]\begin{gathered} S_n=\frac{a(r^n-1)}{r-1} \\ S_n=\frac{7.99((1.1)^n-1)}{1.1-1}\Rightarrow(1) \end{gathered}[/tex]The equation (1) gives the number of miles hiked on the nth day.
(C) miles covered on 10th day:
The number of miles covered on the 10th day is calculated using the equation(1) as follows:
[tex]\begin{gathered} S_n=\frac{7.99((1.1)^n-1)}{1.1-1}\Rightarrow n=10 \\ S_{10}=\frac{7.99((1.1)^{10}-1)}{1.1-1} \\ S_{10}=127.340mi \end{gathered}[/tex]The number of miles covered on the 10th day is 127.340miles.
About the formula used:
[tex]\begin{gathered} S_n=\frac{a-ar^n}{1-r}\Rightarrow\text{ Your formula} \\ \text{Multiply by:} \\ \frac{(-1)}{(-1)} \\ \therefore\Rightarrow \\ S_n=\frac{(-1)}{(-1)}\times\frac{(a-ar^n)}{(1-r)}=\frac{(-1)\cdot(a-ar^n)}{(-1)\cdot(1-r)}=\frac{-a+ar^n}{-1+r}=\frac{ar^n-a}{r-1} \\ S_n=\frac{ar^n-a}{r-1}=\frac{a(r^n-1)}{r-1} \\ S_n=\frac{a(r^n-1)}{r-1}\Rightarrow\text{ My formula} \end{gathered}[/tex]In conclusion, the formula used is the same as the one that was required to be used.
Find the value of x in the given right triangle. 12. x = [?] 62° х Enter your answer as a decimal rounded to the nearest tenth. Enter
EXPLANATION
Let's see the facts:
We can use the Law of Cosines to calculate the unknown value:
[tex]\cos \alpha\text{ = }\frac{\text{Adjacent cathetus}}{\text{Hypothenuse}}[/tex]Replacing terms:
[tex]\cos 62\text{ = }\frac{x}{12}[/tex]Isolating x:
[tex]x\text{ = 12}\cdot\cos 62\text{ = 6}[/tex]Answer is x=6.
NO LINKS!! Please help me with this probability 1c
Answer: Choice A) [tex]\boldsymbol{78.67\% \ \pm \ 9.46\%}[/tex]
======================================================
Explanation:
phat = 59/75 = 0.7867 = 78.67% approximately is the sample proportion
n = 75 is the sample size
Your teacher doesn't mention a confidence level, so I'll assume it's the default 95%.
Let's compute the margin of error at 95% confidence
E = z*sqrt(phat*(1-phat)/n)
E = 1.96*sqrt(0.7867*(1-0.7867)/75)
E = 0.0927 approximately
E = 9.27% approximately
Unfortunately the margin of error 9.27% isn't listed among the four answer choices, but let's change the z = 1.96 to z = 2 instead.
Recalculate the margin of error.
E = z*sqrt(phat*(1-phat)/n)
E = 2*sqrt(0.7867*(1-0.7867)/75)
E = 0.0946 approximately
E = 9.46% approximately
This margin of error is listed among the four answer choices.
------------------
We found that
phat = 78.67% approximatelyE = 9.46% approximatelyThe confidence interval in the format [tex]\text{phat} \ \pm \ \text{E}[/tex] is approximately [tex]78.67\% \ \pm \ 9.46\%[/tex] which points us to choice A as the answer.
Answer:
[tex]\textsf{a)} \quad 78.67\% \pm 9.46\%[/tex]
or d) None of the answers are correct. (Please see notes below).
Step-by-step explanation:
P-hat is the probability that a given outcome will occur given a specified sample size.
[tex]\boxed{\begin{minipage}{7.5 cm}\underline{P-hat formula}\\\\$\hat{p}=\dfrac{X}{n}$\\\\where:\\\phantom{ww}$\bullet$ $\hat{p}$ is the probability. \\ \phantom{ww}$\bullet$ $X$ is the number of occurrences of an event. \\ \phantom{ww}$\bullet$ $n$ is the sample size.\\\end{minipage}}[/tex]
Given:
X = 59n = 75Substitute the given values into the formula to find p-hat:
[tex]\implies \hat{p}=\dfrac{59}{75} =0.78666666...[/tex]
The critical value for a 95% confidence level using normal distribution is:
[tex]z=1.9600\;\;\sf (4\;d.p.)[/tex]
[tex]\boxed{\begin{minipage}{5.2 cm}\underline{Margin of error}\\\\$ME=z \cdot \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$\\\\where:\\\phantom{ww}$\bullet$ $z$ is the critical value. \\ \phantom{ww}$\bullet$ $\hat{p}$ is the sample proportion. \\ \phantom{ww}$\bullet$ $n$ is the sample size.\\\end{minipage}}[/tex]
Substitute the given values into the margin of error formula:
[tex]\implies ME=1.9600 \cdot \sqrt{\dfrac{\dfrac{59}{75}\left(1-\dfrac{59}{75}\right)}{75}}[/tex]
[tex]\implies ME=0.092715036...[/tex]
Therefore, an estimate of the proportion of young-adult novels that include a love triangle (including a margin of error) is:
[tex]\implies \hat{p}\pm ME[/tex]
[tex]\implies 0.7867\pm 0.0927[/tex]
[tex]\implies 78.67\% \pm 9.27\%[/tex]
This result if not given in the list of answer options. However, the final result depends on the accuracy of the z-score and p-hat used in the calculations.
If we round the critical value to the nearest integer then:
[tex]\implies z=2[/tex]
Substitute the rounded z-value into the margin of error formula:
[tex]\implies ME=2\cdot \sqrt{\dfrac{\dfrac{59}{75}\left(1-\dfrac{59}{75}\right)}{75}}[/tex]
[tex]\implies ME=0.094607180...[/tex]
Therefore, an estimate of the proportion of young-adult novels that include a love triangle (including a margin of error) using z = 2 is:
[tex]\implies 78.67\% \pm 9.46\%[/tex]
Note: It is likely that this question required the critical value to be rounded to the nearest integer, however please note that this is not normal practice as it produces a different result, as evidenced above.
Simplify these thing below please. I am stuck again... Thank you
[tex]9\sqrt{56 x^7 y^{12}}\qquad \begin{cases} 56=7\cdot 2\cdot 2\cdot 2\\ \qquad 7\cdot 2^2 \cdot 2\\ \qquad 2^2\cdot 14\\ x^7=x^{(3)(2)+1}\\ \qquad (x^3)^2\cdot x^1\\ y^{12}=y^{(6)(2)}\\ \qquad (y^6)^2 \end{cases}\hspace{5em} \begin{array}{llll} 9\sqrt{2^2(14)(x^3)^2 x (y^6)^2} \\\\\\ 9(2)(x^3)(y^6)\sqrt{14x} \\\\\\ {\Large \begin{array}{llll} 18x^3y^6\sqrt{14x} \end{array}} \end{array}[/tex]
Answer:
[tex]\textsf{1.} \quad 18\;x^3\;y^{6}\sqrt{14x}[/tex]
[tex]\textsf{2.} \quad -8\sqrt{2}[/tex]
Step-by-step explanation:
Question 1Given expression:
[tex]9\sqrt{56x^7y^{12}}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies 9\sqrt{56}\sqrt{x^7}\sqrt{y^{12}}[/tex]
Rewrite 56 as 4·14:
[tex]\implies 9\sqrt{4 \cdot 14}\sqrt{x^7}\sqrt{y^{12}}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies 9\sqrt{4}\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]
Rewrite 4 as 2²:
[tex]\implies 9\sqrt{2^2}\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]
Simplify:
[tex]\implies 9\cdot 2\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]
[tex]\implies 18\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt{a}=a^{\frac{1}{2}}:[/tex]
[tex]\implies 18\sqrt{14}\;(x^7)^{\frac{1}{2}}\;(y^{12})^{\frac{1}{2}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 18\sqrt{14}\;x^{\frac{7}{2}}\;y^{\frac{12}{2}}[/tex]
[tex]\implies 18\sqrt{14}\;x^{\frac{7}{2}}\;y^6[/tex]
Rewrite ⁷/₂ as 3 + ¹/₂
[tex]\implies 18\sqrt{14}\;x^{(3+\frac{1}{2})}\;y^{6}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}= a^b \cdot a^c:[/tex]
[tex]\implies 18\sqrt{14}\;x^3 \; x^{\frac{1}{2}}\;y^{6}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{2}}=\sqrt{a}:[/tex]
[tex]\implies 18\sqrt{14}\;x^3 \; \sqrt{x}\;y^{6}[/tex]
Rearrange:
[tex]\implies 18\;x^3\;y^{6}\sqrt{14x}[/tex]
Question 2Given expression:
[tex]7\sqrt{32}-6\sqrt{72}[/tex]
Rewrite 32 as 16·2 and 72 as 36·2:
[tex]\implies 7\sqrt{16 \cdot 2}-6\sqrt{36 \cdot 2}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies 7\sqrt{16}\sqrt{2}-6\sqrt{36}\sqrt{2}[/tex]
Rewrite 16 as 4² and 36 as 6²:
[tex]\implies 7\sqrt{4^2}\sqrt{2}-6\sqrt{6^2}\sqrt{2}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]
[tex]\implies 7 \cdot 4\sqrt{2}-6\cdot 6\sqrt{2}[/tex]
Simplify:
[tex]\implies 28\sqrt{2}-36\sqrt{2}[/tex]
[tex]\implies -8\sqrt{2}[/tex]
This graph shows the height in inches, `h`, of a bamboo plant `t` months after it has been planted.
Write an equation that describes the relationship between `t` and `h`.
Drag the movable point to trace along the line if that helps you with your thinking.
The graph that shows the relationship between the height of the bamboo and months planted is given as h = 5t + 10
How to solve an equation?Given that the graph shows the relationship between the height (h) of a bamboo plant after months it has been planted.
Let us assume that h is plotted on the vertical axis and months (t) is planted on the horizontal axis.
If the graph passes through the points (0, 0) and (2, 10), hence:
h - 10 = [(10 - 0)/(2 - 0)](t - 0)
h - 10 = 5(t)
h = 5t + 10
The graph is given as h = 5t + 10
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QUESTION 9 1 POINTSimplify: ( 12 + 1/2 m)÷ 0, where + #0.4 2If the given expression is undefined enter Ø as your answer.Provide your answer below:Content attribution
Given
[tex](\frac{1}{4}+\frac{1}{2}m)\div0[/tex]Find
Simplify
Explanation
[tex]\begin{gathered} (\frac{1}{4}+\frac{1}{2}m)\div0 \\ \\ (\frac{1+2m}{4})\div0 \end{gathered}[/tex]as we know , any number divided by zero is infinity because division by zero is undefined and infinity does not really exist.
so , the solution is undefined.
Final Answer
Hence , the solution is undefined. so , the answer is
[tex]\emptyset[/tex]What’s the correct answer answer asap for brainlist
Answer:
B. radio stations stopped advertising
Answer:
As televisions became more affordable and advertisers flocked to the new medium, radio stations had to quickly adapt to the changing field. Stations stopped using live in-studio performances, instead playing less expensive recordings.
Step-by-step explanation:
In the 1950s, television surpassed radio as the most popular broadcast medium, and commercial radio programming shifted to narrower formats of news, talk, sports and music. Religious broadcasters, listener-supported public radio and college stations provide their own distinctive formats.
Describe two different ways to translate a figure that result in the same image. Justify your answer.
The ways to translate the figure include:
It doesn't change its orientation.
It also doesn't change its size or shape.
How to illustrate the information?When a geometric figure glides up, down, left, or right on the coordinate plane, this is referred to as translation. The figure changes its location but not its orientation. It also retains its size and shape. When you translate a figure, you slide it left or right, up or down.
When you translate a figure, you slide it left or right, up or down. This indicates that the coordinates for the figure's vertices will vary on the coordinate plane. To graph a, make the same modification at each point. The variations in coordinates of a reflection can be used to identify it.
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Which of the expressions are equivalent to the one below? Check all thatapply.5•(3 + 7)A. 5•(7+3)B. 5.3 + 5.7C. (5.3) +7D. (3+7)5
Concept
To solve the question you will use the associative property.
a . ( b + c ) = a . b + a . c
The expressions that is equivalent to 5 .(3 + 7) = 5 . 3 + 5 . 7 , ( 3 + 7 ) 5 , 5 . (
Fi
please help asap !!!!
What is the solution of the equation [tex]\frac{2}{3}(x-1) -\frac{1}{5} (2x-3)=1[/tex] ?
x=4
How is the given equation solved?
[tex]\frac{2}{3}(x-1) -\frac{1}{5} (2x-3)=1\\\\\frac{2}{3} x-\frac{2}{3} -\frac{2}{5} x+\frac{3}{5}=1\\\\\frac{2}{3} x-\frac{2}{5}x =1+\frac{2}{3}- \frac{3}{5}\\\\\text{Taking LCM},\\\\\frac{10x-6x}{15} =\frac{15+10-9}{15} \\\\4x= 16\\\\x=4[/tex]
What is solving an equation?
Finding an equation's solutions, or the values that satisfy the condition given by the equation, is known as solving an equation in mathematics.Solutions often consist of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.To learn more about equation solving, refer:
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Simplify the expression.
the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
The value of the expression after simplify will be,
''negative 43 over 24 times j plus negative 1 over 12.''
Option D is true.
What is mathematical expression?
Expression in math is defined as the collection of the numbers, variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is;
''The expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths.''
Now, We can write the expression in mathematical form as;
⇒ (- 1/8 j + 2/3) - (5/3 j + 9/12)
Solve the expression as;
⇒ - 1/8 j + 2/3 - 5/3 j - 9/12
⇒ - 1/8 j - 5/3 j + 2/3 - 9/12
⇒ j (-1/8 - 5/3) + 2/3 - 3/4
⇒ j (- 3 - 40)/24 + (8 - 9)/12
⇒ j (-43/24) + (- 1/12 )
This can be written as;
''negative 43 over 24 times j plus negative 1 over 12''
Therefore, The value of the expression after simplify will be,
''negative 43 over 24 times j plus negative 1 over 12.''
Option D is true.
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Kylie shoots an arrow during an archery lesson at camp. The height of the arrow can be modeled by the equation ℎ = −8t(2t−6), where ℎ is the height in feet of the arrow and t is the time in seconds. How long is the arrow in the air?
The arrow will be in the air for 3 seconds after 3 seconds the arrow hit the target.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
The equation:
h = −8t(2t−6)
To find the total number of seconds the arrow will be in the air:
Plug h = 0
−8t(2t−6) = 0
t(2t−6) = 0
t = 0 or t = 6/2
t = 0 or t = 3 seconds
Thus, the arrow will be in the air for 3 seconds after 3 seconds the arrow hit the target.
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For each calculation choose the correct answer written in standard form.
a) (7 × 10⁵ ) × (3× 10²)
A 21 × 10¹⁰
B 21 ×10⁷
C 2.1 × 10¹¹
D 2.1 × 10⁸
b) ( 2 × 10⁵) ÷ ( 4 × 10² )
A 2 × 10 ³
B 5 × 10²
C 0.5 × 10³
D 2 × 10²
Answer:
A car travels at average speed of 4m/s and covers a distance of 2.4km calculate the time take help me
Answer this for me please Number 2 have 3 more answer choices Which are 16:57D - the number of centimeters in x inches E- the height of a swinging pendulum as a function of timeF- the height of a ball tossed in the air as a function of time
1)
Consider P to be at the same vertical distance between the maximum and minimum height the blades can reach. Therefore, at t=0, P has to be at h=0 (the maximum height is 1 and the minimum one is -1).
Then, since the fan blades rotate counterclockwise, after t=0, h has to increase until it reaches a value of 1.
Finally, a revolution is completed after 1 second; therefore, at t=1, the h has to be equal to 0 (the same height as at t=0).
Thus, the graph that models the function is option D.2)
Approximately, every year the Earth reaches its maximum distance from the sun and its minimum distance once a year, and that is a cycle that repeats almost without alteration. Furthermore, since the position of the Earth around the sun is given by an ellipse, the position of the Earth around the Sun can be expressed using trigonometric functions (because of polar coordinates).
Similarly, a rotating wheel will reach its maximum and minimum height eventually; therefore, it can be modeled using trigonometric functions which are periodic.
Finally, as for the area of a sheet of paper. Notice that the more we fold it, the less its area becomes, it does not reach its maximum anymore.
Given x inches, the number of centimeters is 2.54x, this is not a periodic function.
Due to the effects of gravity, the height of a pendulum can be expressed using a periodic function given that no energy is lost.
The trajectory of a tossed ball is given by a parabola, unless one tosses the ball again at the same initial height, option F cannot be modeled using a periodic function.
The answers to part 2 are A, B, and E.Write the sentence as an inequality. The sum of 3 times a number n and 8 is at most 16. 0 3n + 8 > 16 o 31 -8 < 16 O 3 + 8n
ANSWER
[tex]3n\text{ + 8 }\leq\text{ 16}[/tex]EXPLANATION
We want to write the sentence as an inequality.
We have:
The sum of 3 times a number n and 8 is at most 16.
3 times a number n is 3 * n i.e. 3n
Adding that to 8 would yield:
3n + 8
That is at most 16.
This means that it is less than or equal to 16.
That is:
[tex]3n\text{ + 8 }\leq\text{ 16}[/tex]factored form of y=x2-x-12
The factored form of y = x² - x + 12 will be (x + 3)(x - 4).
What is factor?It should be noted that a factor simply means the number than can be multiplied by another number to get the original number. The factored form is when a quadratic expression is a product of two factors, each of which is a linear expression. By expanding, or multiplying out the factors, an equation in factored form can be restated in standard form.
This will be illustrated as:
x² - x - 12
x² - 4x + 3x - 12.
x(x - 4) + 3(x - 4)
(x + 3)(x - 4)
The factored form is (x + 3)(x - 4).
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For a standard normal distribution, find:P(z > 1.74)
Solution
Using Z score calculator
P(x>Z) = 0.04093
I need help on this Homework question and also please give the steps on what lead to the answer.
The function is given by:
[tex]f(x)=x(x^2+7)(x^2-8)[/tex]The three quantities are zero then it follows:
[tex]\begin{gathered} x=0;x^2+7=0;x^2-8=0 \\ x=0;x^2=-7;x^2=8 \\ x=0,x=\pm\sqrt[]{7}i;x=\pm2\sqrt[]{2} \end{gathered}[/tex]Option D is correct.
Find 3 ratios that are equivalent to the given ratio. 30:42 Find three ratios that are equivalent to the given ratio. DA. 60:84 B. 5:126 DC. 60:7 D 90:7 DE. 60:126 OF 90:126 O G. 5:84 OH 5:7
The The 3 ratios are;
A=60: 84
F=90:126
H=5:7
How many degrees mustFigure A be rotatedcounterclockwise aroundthe origin in order to lineup with Figure B?АBA. 90B. 180C. 270D. 360
The answer is A 90 degrees
B
Find the slope for each line then determine if they are parallel, perpendicular, and neither.
Points on lines E & F;
Line E: (-1,-4) (5, -3) & Line F: (14, 3) (15,-3)
O Perpendicular
O Not Enough Information
O Parallel
ONeither
I need questions 10 , 13 , 15 , and 16 solved with steps and graph
The graphic solutions for the expressions are given as follows:
10. x = 2.667 and x = 8.
13. x = 8.
15. x < -1 or x > 8.
16. x > 3.
Item 10In item 10, we are going to solve an equation graphically, hence we have to find the points of intersection of the two curves given by:
y = |x - 4|.y = 0.5x.From the first graph given at the end of the answer, the x-coordinates of these points are given as follows:
x = 2.667 and x = 8.
Item 13Now we have to find the point of intersection of these two equations:
y = 0.75x.y = 2x - 10.They have only one intersection point, at x = 8, which is the solution to the system.
Item 15The inequality is:
x² - 7x- 8 > 0.
Hence we have to find the intervals for which the function x² - 7x - 8 is above the x-axis, and from the third graph, these intervals are described as follows:
x < -1 or x > 8.
Item 16The inequality is:
x - 5 > -2x + 4.
Combining the like terms, it can be written as;
3x > 9
x > 3.
The interval for which the increasing line is above the decreasing line is x > 3, and is shown in the fourth graph.
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The functions f(x) and g(x) are shown on the graph.
f(x) = |x|
What is g(x)?
10
f(x) = x
-5
107
-5
-10
g(x) = ?
~XAX
K
Answer:
what graph?
Step-by-step explanation:
By the knowledge on absolute values, functional theory and rigid transformations and given that the function f(x) = |x|, the function g(x) = f(x - 4) is equal to |x - 4|.
What is absolute value?In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. Namely, {\displaystyle |x|=x} if x is a positive number, and {\displaystyle |x|=-x} if x is negative, and {\displaystyle |0|=0}.
here, we have,
According to the image attached herein,
the function f(x) is an absolute value and the function g(x) results from translating f(x) in +x direction, representing a kind of rigid transformation as Pythagorean distance at every point of the function is conserved.
There, we can define the function g(x) as follows:
g(x) = f(x - k), for k > 0 (1)
By the knowledge on absolute values, functional theory and rigid transformations
and given that
the function f(x) = |x|, the function g(x) = f(x - 4) is equal to |x - 4|.
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The table lists several points that form a line on a coordinate plane. x y 4 6 12 8 16 9 28 12 Based on the information in the table, what are the y-intercept and slope of the line described by these points?
A.y-intercept: = 2; slope: m = 4
B.y-intercept: = –20; slope: m =14
C.y-intercept: = 5; slope: m = 4
D.y-intercept: = 5; slope: m =14
Slope is 1/4 (0.25) while y-intercept is 5.
Here, we are interested in getting the y intercept and slope of the line joining the given points.
We can get the slope by using any two points
Let’s say (4,6) and (12,8)
Mathematically; slope
= (y2-y1)/(x2-x1) = (8-6)/(12-4) = 2/8 = 1/4 = 0.25
To get the y-intercept, we proceed
kindly recall that the equation of a straight line is;
y = mx + c
where m is the slope and c is the y-intercept
Let’s take any of the points (28,12)
Thus:
12 = 0.25(28) + c
12 = 7 + c
c = 12-7
c = 5
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Express Your Answer As A Polynomial In Standard Form.
f(x)= x-7
g(x)= 3x^2-7x-10
Find (f o g)(x)
Look at photo
According to the solving the Polynomial Standard Form of the given equation is :
3x^2-7x-17.
What is Polynomial Standard Form?When expressing a polynomial in its standard form, the greatest degree of terms are written first, followed by the next degree, and so on. When x is the variable and ai are coefficients, the polynomial has the conventional form f(x) = anxn + an-1xn-1 + an-2xn-2 +... + a1x + a0.
According to the given data:f(x)= x-7
g(x)= 3x^2-7x-10
f(x)= x-7 by substituting in the value of g into f.
f(3x^2-7x-10) = (3x^2-7x-10)-7
= 3x^2-7x-17
According to the solving the slandered form of the given equation is :
3x^2-7x-17
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Write an equation in point-slope form for the line that satisfies the given set of conditions.
slope of 0, passes through (0, -10)
y + 5x = 0 is the line's equation in point-slope form.
Given is a line with a slope of 0 and a point at (0, -10) on it. We must determine the line's point slope form equation.
What shape does a line's point slope take?The line's point-slope shape is ( y -[tex]Y_{1}[/tex] ) = m ( x - [tex]X_{1}[/tex] ).
According to the query, slope (m) = 0 and
the line is going through ( [tex]X_{1}[/tex] , [tex]Y_{1}[/tex] ) = ( 0 , -10 )
∴ ( y - [tex]Y_{1}[/tex] ) = m ( x - [tex]X_{1}[/tex] )
y + 10 = 0 ( x - 0 )
y + 10 = 0
y + 5x = 0
As a result, the equation for the line in point-slope form will be
y + 5x = 0.
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What does the leading term of −5x^4+4x^3−6x^2+8 tell you?
A radar unit is used to measure speeds of a car on a motorway. Speeds are normal distributed with a mean of 90 km an hour and a standard deviation of 10 km an hour. What is the probability that a car picked at random is traveling out more than 100 km an hour
let x is the random variable that represents the speed of car.
[tex]\begin{gathered} \mu(\operatorname{mean})=90 \\ \sigma=10 \end{gathered}[/tex]probability that x is higher than 100 :
[tex]P(x>100)[/tex]for x=100:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{100-90}{10} \\ z=1 \end{gathered}[/tex]so,
[tex]p(x>100)=p(z=1)[/tex]probability =total area - area of the left of (z=1)
[tex]\begin{gathered} \text{probability}=1-0.8413 \\ p(x>100)=0.1587 \end{gathered}[/tex]and the area of the left of z=1 is 0.8413 (from normal distribution)
If f(x)=rootx-3 and g(x)=1-x^2, then what do you notice about the domaine of (f•g)(x)
The domain will be x ≥ 3 for f(x)=√x-3 and g(x)=1-x².
In case a function f gives a way to effectively create a single value y utilizing for that reason a value for x at that point that chosen x-value is said to have a place to the domain of f. there are some conditions to be checked such as denominators cannot equal 0, radicands of even roots can't have a negative value, logarithms can as it was being taken of positive values. Since we are given that f[tex]\sqrt{x-3}[/tex] and g(x)=1-x², for g(x) since it's a polynomial function its domain had to be real numbers, whereas for f(x) is all positive and real numbers.
for the given condition (f•g)(x)
=> (f•g)(x)= f(x)*g(x)
=> (f•g)(x) = √(x-3) * (1 - x²)
=>(f•g)(x) = √(x-3)-x²(√x-3)
So the domain for (f•g)(x) will be all positive real numbers x≥3 x ∈ [3,∞)
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7.02 is what percent of 67.5?
312% of what is 39?
Use the given conditions to write an equation for the line in point-slope form and general form. Passing through (8,-4) and perpendicular to the line whose equation is x-6y-5=0
Answer:
y + 4 = -6 (x - 8)
Step-by-step explanation:
Change the equation to the slope intercept form for a line
x - 6y 5 = 0 Add 5 to both sides
x - 6y = 5 Subtract x from both sides
-6y = -x + 5 Divide both sides by -6
y = [tex]\frac{1}{6}[/tex] c - [tex]\frac{5}{-6}[/tex] Your slope is [tex]\frac{1}{6}[/tex]
A perpendicular slope is the opposite reciprocal of [tex]\frac{1}{6}[/tex], that would be -6
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex]) Plug is -4 for [tex]y_{1}[/tex] and 8 for [tex]y_{1}[/tex]
y - -4) -6(x-8)
y + 4= -6 (x -8)