Tristan has 14 nickels and 7 dimes worth of $1. 40.
This is because 1 nickel is worth 5 cents and 1 dime is worth 10 cents.
Let's use the following variables to represent the number of nickels and dimes Tristan has:
n = number of nickels
d = number of dimes
We know that Tristan has $1.40 worth of nickels and dimes. Each nickel is worth $0.05 and each dime is worth $0.10, so we can write an equation based on their values:
0.05n + 0.1d = 1.4
We also know that Tristan has twice as many nickels as dimes:
n = 2d
We can substitute n = 2d into the first equation and solve for d:
0.05(2d) + 0.1d = 1.4
0.1d + 0.1d = 1.4
0.2d = 1.4
d = 7
So Tristan has 7 dimes. Using n = 2d, we can find the number of nickels:
n = 2(7) = 14
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Compound interest. Use the compound interest formula to compute the balance in the following accounts after the stated period of time assuming interest is compounded annually.
$10,000 is invested at an APR of 4% for 10 years
$10,000 is invested at an APR of 2.5% for 20 years
$15,000 is invested at an APR of 3.2% for 25 years
$ 40,000 is invested at an APR of 2.8% for 30 years
compounding more than once a year. Use the appropriate compound interest formula to compute the balance in the following accounts after the stated period of time.
$10,000 is invested for 10 years with an APR of 2% and quarterly compounding
$2000 is invested for 5 years with an APR of 3% and daily compounding
$2000 is invested for 15 years with an APR of 5% and monthly compounding
annual percentage yield (APY) find the annual percentage yield (to the nearest 0.01%) in the following situations.
1. A bank offers an APR of 3.1% compounded daily
2. a bank offers an APR of 3.2% compounded monthly
Maisie has 40 m of railing.
How much more railing does Maisie need
so that she can put railing all the way
around the roof garden?
8 m
9 m
4m
10 m
20 m
8 m
Not drawn accurately
Look at imqhe
Answer:
36
Step-by-step explanation:
see image for explanation
Find the next term of the following sequence.
9, 6, 4, ...
1. 2
2. 8/3
3. 3
Answer:
3
Step-by-step explanation:
You are subtracting 1 less each time, starting at 3:
9 - 3 = 6
6 - 2 = 4
Therefore, you will subtract 1 from 4:
4 - 1 = 3
3 is your answer.
~
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Graph the numbers that are solutions to x−3≤8 and 6x<72 .
can u send a visual picture of the graph?? (94 points)
The graph fοr the sοlutiοns οf the inequalities have been plοtted and attached belοw.
What is an inequality?A relatiοnship in mathematics knοwn as an inequality cοmpares twο numbers οr οther mathematical expressiοns in an unfair manner.
Mοst frequently, size cοmparisοns are dοne between twο numbers οn the number line.
We are given twο inequalities as x - 3 ≤ 8 and 6x < 72.
Nοw, οn sοlving the first inequality, we get⇒ x - 3 ≤ 8⇒ x ≤ 11Similarly, οn sοlving the secοnd inequality, we get⇒ 6x < 72⇒ x < 12
Nοw, οn the graph the sοlutiοns are plοtted and attached belοw. The red pοint represents the secοnd inequality sοlutiοn and the blue represents the first inequality sοlutiοn.
Hence, the graph fοr the sοlutiοns οf the inequalities have been plοtted.
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What is 600 as a percent out 1900? Please show step by step answers I get confused a lot?
Answer:31.58% i think
Step-by-step explanation:
600 of 1900 can be written as:
600/1900
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
600/1900 x 100/100 = 600x100/1900) x1/100= 31.58/100
Therefore, the answer is 31.58%
the perimeter of a rectangular outdoor patio is 106 ft. the length is 9 ft greater than the width. what are the dimensions of the patio?
The perimeter of a rectangular outdoor patio is 106 ft. the length is 9 ft greater than the width. Hence, the dimensions of the patio are 38 ft and 47 ft.
Given that the perimeter of a rectangular outdoor patio is 106 ft. The length is 9 ft greater than the width. Now we need to find the dimensions of the patio.
Step 1: Let's consider the width of the patio be x feet.
The length of the patio is given as 9 ft greater than the width.
So the length of the patio will be (x + 9) feet.
Step 2: The perimeter of a rectangle is given by P = 2(l + w).
So the perimeter of the patio is given as 106 ft.
Thus,2(l + w) = 1062(x + x + 9)
= 1062(2x + 9)
= 1062x + 1821
= 106x = 106 - 182x
= -76 (not possible)
Therefore, x = 38 ftSo the width of the patio is 38 ft The length of the patio is 38 + 9 = 47 ft
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Which statement is true about this quadratic equation?
The correct statement regarding the quadratic equation is given as follows:
C. There are two complex solutions.
How to obtain the number of solutions of the quadratic function?A quadratic equation is modeled by the general equation presented as follows:
y = ax² + bx + c
The discriminant of the quadratic function is given by the equation as follows:
Δ = b² - 4ac.
The numeric value of the coefficient and the number of solutions of the quadratic equation are related as follows:
Δ > 0: two real solutions.Δ = 0: one real solution.Δ < 0: two complex solutions.The coefficients of the function for this problem are given as follows:
a = -2, b = 9, c = -12.
Hence the discriminant is given as follows:
Δ = 9² - 4(-2)(-12)
Δ = -15.
Negative discriminant, hence there are two complex solutions.
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The quadratic equation has two real solutions
Which statement is true about this quadratic equation?Here we have the quadratic equation:
y = -2x^2 + 9x - 12
We want to study the solutions of the equations, so we need to look at the discriminant:
Generally for a*x^2 + b*x + c = 0 the discriminant is b^2 - 4ac
Here it is:
D = 9^2 - 4*-12*-2 = 33
A positive determinant means that there are 2 real solutions so the correct option is A.
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Please help I’ll give brainliest!!
(1). A cyclist starts a journey from town A. He rides 10km north, then 5km east and finally 10km on a bearing of 045°. a) How far east is the cyclist's destination from town A? b). How far north is the cyclist's destination from town A? c). Find the distance and bearing of the cyclist's destination from town A (Correct your answers to the nearest km and degree)
The required answers are a) 17.1 km b) 7.1 km, c) 18.6 km away from town A on a bearing of 293°.
How to find the distance and angle?To solve this problem, we can use vector addition to find the displacement vector from town A to the cyclist's destination.
a) To find how far east the cyclist's destination is from town A, we need to find the east component of the displacement vector. We can break down the displacement vector into its north and east components using trigonometry:
[tex]$$\text{East displacement} = 5\text{ km} + 10\text{ km}\cos(45^\circ) = 5\text{ km} + 10\text{ km}\frac{\sqrt{2}}{2} = 10\text{ km} + 5\sqrt{2}\text{ km} \approx 17.1\text{ km}$$[/tex]
So the cyclist's destination is approximately 17.1 km east of town A.
b) Similarly, to find how far north the cyclist's destination is from town A, we need to find the north component of the displacement vector:
[tex]$$\text{North displacement} = 10\text{ km}\sin(45^\circ) = 10\text{ km}\frac{\sqrt{2}}{2} = 5\sqrt{2}\text{ km} \approx 7.1\text{ km}$$[/tex]
So the cyclist's destination is approximately 7.1 km north of town A.
c) To find the distance and bearing of the cyclist's destination from town A, we can use the Pythagorean theorem and trigonometry. The displacement vector is the hypotenuse of a right triangle with legs of length 17.1 km and 7.1 km, so its length is:
[tex]$$\text{Displacement} = \sqrt{(17.1\text{ km})^2 + (7.1\text{ km})^2} \approx 18.6\text{ km}$$[/tex]
To find the bearing of the displacement vector, we can use the inverse tangent function:
[tex]$$\text{Bearing} = \tan^{-1}\left(\frac{\text{East displacement}}{\text{North displacement}}\right) \approx 67^\circ$$[/tex]
However, this angle is measured clockwise from north, so we need to subtract it from 360° to get the bearing measured counterclockwise from north:
[tex]$$\text{Bearing} = 360^\circ - 67^\circ = 293^\circ$$[/tex]
So the cyclist's destination is approximately 18.6 km away from town A on a bearing of 293°.
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through: (-4,-3), parallel to y=2x+4
Whts this in slope int form
Answer:
y=2(x+4)-3
Step-by-step explanation:
To make it parallel to y=2x+4, the slope needs to be the same
Point-slope form is: y=m(x-x1)+y1
In this case,
m = 2
x1 = -4
y1 = -3
So when put into point-slope form, it is y=2(x+4)-3
Given the function h(x)=-2√x, which statement is true about h(x)?
O The function is decreasing on the interval (0,0).
O The function is decreasing on the interval (-∞, 0).
O The function is increasing on the interval (0, ∞).
O The function is increasing on the interval (-∞, 0).
Answer:
The statement "The function is decreasing on the interval (0, ∞)" is true about h(x).
To see why, let's take the derivative of h(x) and examine its sign:
h(x) = -2√x
h'(x) = -2/(2√x) = -1/√x
Since √x is always positive, h'(x) is negative for all x > 0. This means that h(x) is decreasing on the interval (0, ∞).
Therefore, the correct answer is: The function is decreasing on the interval (0, ∞).
The ratio of dogs to cats is 2:3. If there are 520 dogs, determine how many cats are there?
If the ratio of dogs to cats is 2:3 and there are 520 dogs, the number of cats is 780.
What is the ratio?The ratio refers to the relative size of one quantity or value compared to another quantity or value.
Ratios are proportionate values stated in ratio form using (:), in percentages or fractions.
The ratio of dogs to cats = 2:3
The sum of ratios = 5
The number of dogs based on this ratio = 520 dogs
The total number of dogs and cats based on the above ratio and the number of dogs = 1,300 (520/2 x 5)
The ratio of cats to dogs = 3:2 or 3/5
The number of cats = 780 (1,300 x 3/5)
Thus, using the ratio of dogs to cat, with the number of dogs as 520, there are 780 cats.
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can anyone explain this?
Two sides of a rectangle differ by 3.5cm find the dimensions of the rectangle if it's perimeter is 67cm.solve by matrix inversion method.
Using matrix inversion method and perimeter of rectangle, the dimension of the rectangle are 16cm and 7cm
What is the dimension of the rectangleLet the length of the rectangle be l and the width be w. We know that l - w = 3.5 and 2l + 2w = 67. We can rewrite these equations as a system of linear equations in matrix form:
[tex]$$\begin{bmatrix}1 & -1 \ 2 & 2\end{bmatrix} \begin{bmatrix}l \ w\end{bmatrix} = \begin{bmatrix}3.5 \ 67/2\end{bmatrix}$$[/tex]
We can solve for [tex]$\begin{bmatrix}l \ w\end{bmatrix}$[/tex] by multiplying both sides of the equation by the inverse of the coefficient matrix:
[tex]$$\begin{bmatrix}l \ w\end{bmatrix} = \begin{bmatrix}1 & -1 \ 2 & 2\end{bmatrix}^{-1} \begin{bmatrix}3.5 \ 67/2\end{bmatrix}$$[/tex]
To find the inverse of the coefficient matrix, we can use the following formula:
[tex]$$\begin{bmatrix}a & b \ c & d\end{bmatrix}^{-1} = \frac{1}{ad-bc} \begin{bmatrix}d & -b \ -c & a\end{bmatrix}$$[/tex]
Plugging in the values for our matrix, we get:
[tex]$$\begin{bmatrix}1 & -1 \ 2 & 2\end{bmatrix}^{-1} = \frac{1}{1 \cdot 2 - (-1) \cdot 2} \begin{bmatrix}2 & 1 \ -2 & 1\end{bmatrix} = \begin{bmatrix}1/2 & 1/4 \ -1/2 & 1/4\end{bmatrix}$$[/tex]
Now we can substitute this matrix and the vector on the right-hand side of the equation into our formula to obtain the solution:
[tex]$$\begin{bmatrix}l \ w\end{bmatrix} = \begin{bmatrix}1/2 & 1/4 \ -1/2 & 1/4\end{bmatrix} \begin{bmatrix}3.5 \ 67/2\end{bmatrix} = \begin{bmatrix}16 \ 7\end{bmatrix}$$[/tex]
Therefore, the dimensions of the rectangle are 16 cm by 7 cm.
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PROBLEM SOLVING WITH TREND LINES
2. 75
2. 50
Part I: The scatter plot at the left shows the
cost of gas per gallon during certain years.
Use the scatter plot to answer questions 1-5.
2. 25
2. 00
2017-1970 = ?
1. 75
1. 50
PRICE OF GAS PER GALLON ($)
1. 25
Y=0. 05(?) +0. 25
1. 00
. 75
. 50
. 25
5
10
15 20 25 30 35 40 45 50
YEARS (SINCE 1970)
The trend line equation y = 0.05x + 0.25 can be used to accurately predict the cost of gas per gallon for any year since 1970.
The equation of the trend line in the scatter plot is given by y = 0.05x + 0.25, where x is the number of years since 1970 and y is the price of gas per gallon in dollars. This equation can be used to calculate the price of gas in a given year since 1970. For example, if we want to calculate the price of gas in 2017, we can plug in x = 47 (the number of years since 1970) into the equation to get y = 0.05(47) + 0.25 = 2.85. This means that in 2017, the price of gas per gallon was approximately 2.85 dollars. This equation can be used to accurately predict the cost of gas for any given year since 1970.
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A new cylindrical can with a diameter of 7 cm is being designed by a local company. The surface area of the can is 130 square centimeters. What is the height of the can? Estimate using 3 14 for x, and
round to the nearest hundredth. Apply the formula for surface area of a cylinder SA= 2B+ Ph.
Answer:
see below
Step-by-step explanation:
[tex]SA = 2\pi r \ \ (h+r)[/tex]
[tex]130=2(3.14)(7\div2)(h+(7\div2))[/tex]
[tex]130\div(2(3.14)(7\div2)) = h+(7\div2)[/tex]
[tex]5.91=h+(7\div2)[/tex]
[tex]h = 5.91-3.5[/tex]
Answer Below:
[tex]\bold{x=2.41}[/tex]Which of the japanese islands do you think became the center of power in japan
The Japanese island that became the center of power in Japan is Honshu.
Honshu is the largest and most populous island in Japan and has historically been the center of political, economic, and cultural power in Japan. It is home to Tokyo, the capital city of Japan, as well as many other major cities such as Osaka, Kyoto, and Yokohama. Honshu's central location and natural resources have made it a strategic location for political power throughout Japan's history, including during the feudal period when various powerful clans vied for control. Honshu's position as the economic and cultural hub of Japan has also helped solidify its status as the center of power, as it has been a center for education, trade, and innovation for centuries.
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Please help!! Thanks
Answer:
[tex]\boxed{\mathtt{Area \approx 104.7m^{2}}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find the area of 1/3 of a circle.}[/tex]
[tex]\textsf{Let's review the formula needed to find the area of a \underline{whole} circle.}[/tex]
[tex]\large\underline{\textsf{Formula:}}[/tex]
[tex]\mathtt{Area = \pi (radius)^{2}.}[/tex]
[tex]\textsf{We should know that a circle is 360}^{\circ}. \ \textsf{We are given 120}^{\circ} \textsf{of a circle.}[/tex]
[tex]\textsf{The area of \underline{1/3} of a Circle is the area of a whole circle \underline{divided by 3.}}[/tex]
[tex]\textsf{Let's begin solving for the area.}[/tex]
[tex]\large\underline{\textsf{Substitute:}}[/tex]
[tex]\mathtt{Area = \pi (10)^{2}}[/tex]
[tex]\large\underline{\textsf{Evaluate:}}[/tex]
[tex]\mathtt{Area = 100\pi }[/tex]
[tex]\large\underline{\textsf{Divide by 3:}}[/tex]
[tex]\mathtt{\frac{Area}{3} = \frac{100\pi }{3}} [/tex]
[tex]\boxed{\mathtt{Area \approx 104.7m^{2}}}[/tex]
What is
4y+6x=18
3y-2x=33
Answer:
x = -3 and y = 9
Step-by-step explanation:
Solving system of linear equations by elimination method:4y + 6x = 18 -----------------(I)
3y - 2x = 33 -----------------(II)
Multiply equation (II) by 3.
(I) 4y + 6x = 18
(II)*3 9y - 6x = 99 {Now add the equations}
13y = 117
Divide both sides by 13,
y = 117 ÷ 13
[tex]\boxed{\bf y = 9}[/tex]
Substitute y = 9 in equation (I) and obtain the value of 'x',
4*9 + 6x = 18
36 + 6x = 18
Subtract 36 from both sides,
6x = 18 - 36
6x = -18
Divide both sides by 6
x = -18 ÷ 6
[tex]\boxed{\bf x = -3}[/tex]
[tex] \\ 4y + 6x = 18 \\ \\ 6x= 18 - 4y \\ = x = 3 - \frac{2}{3 }y \\ x = - \frac{2}{3} y+ 3[/tex]
To find the roots of a quadratic equation, ax^2+ bx + c, where a, b, and c are real numbers, Jan uses the quadratic formula. Jan finds that a quadratic equation has 2 distinct roots, but neither are real numbers.
A. Write an inequality using the variables a, b, and c that must always be true for Jan's quadratic equation.
The expression 3+√-4 s a solution of the quadratic equation x^2- 6x +13=0.
B. What is 3+ √-4 written as a complex number?
The inequality will be and [tex]3 + √-4[/tex] will be written as [tex]3 +2i[/tex] as complex number.
What are complex numbers?
In mathematics, a complex number is a number of the form a + bi, where a and b are real numbers and i is the imaginary unit (√-1). Complex numbers are an extension of the real numbers, which include all the numbers that can be represented on a number line.
The real part of a complex number a + bi is the real number a, and the imaginary part is the real number bi.
A. Since Jan found that both roots of the quadratic equation are not real numbers, this means that the discriminant b² - 4ac is negative. Therefore, the inequality that must always be true for Jan's quadratic equation is:
[tex]b² - 4ac < 0[/tex]
B. The expression [tex]3+√-4[/tex] can be written as [tex]3 + 2i,[/tex] where i is the imaginary unit (√-1). This is because √-4 is equal to 2i, so [tex]3+√-4[/tex] can be written as [tex]3 + 2i.[/tex] Therefore, [tex]3+√-4[/tex] written as a complex number is 3 + 2i.
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An insurance company keeps statistics on reported damage to passenger cars. The number of reported injuries for a driver during a year is linked to how long the driver has held a driving licence. The insurance company uses the statistics to set up a probability distribution for two stochastic variables ???? and ???? , for drivers who have held a driving license for up to 3 years.
???? is the number of reported injuries for a driver during a year.
???? is the number of years the driver has held a driving license (???? = 0 means the driver has held a driving license for less than one year).
a)
(i) What is the probability that a random driver has held a license for 2 years and reports 1 injury?
(ii) What is the probability that a random driver has had a driver's license for 1 year and reports 1 injury or has had a driver's license for 2 years and reports 2 injuries?
b) Set up the marginal probability distributions of ???? and ????. What is the probability that a random driver reports 0 injuries? What is the probability that a random driver has had a driver's license for 3 years?
c) If a random driver has not reported any injuries, what is the probability that he has had a driving license for 3 years?
d) Find the expected values ????(????) and ????(????), and the variances ????????????(????) and ????????????(????).
e) Calculate the covariance between ???? and ???? . Calculate the correlation coefficient and give an interpretation of this, related to the task text.
The probability that a random driver reports 0 injuries is 0.25, and the probability that a random driver has had a driver's license for 3 years is 0.25.
a) (i) The probability that a random driver has held a license for 2 years and reports 1 injury is 0.125.
(ii) The probability that a random driver has had a driver's license for 1 year and reports 1 injury or has had a driver's license for 2 years and reports 2 injuries is 0.3125.
b) The marginal probability distributions of ???? and ???? are given in the table below:
????
???? = 0
???? = 1
???? = 2
???? = 3
???? = 0
0.25
0.125
0.0625
0.03125
???? = 1
0.25
0.25
0.125
0.0625
???? = 2
0.25
0.25
0.25
0.125
???? = 3
0.25
0.25
0.25
0.25
The probability that a random driver reports 0 injuries is 0.25, and the probability that a random driver has had a driver's license for 3 years is 0.25.
c) If a random driver has not reported any injuries, the probability that he has had a driving license for 3 years is 0.25.
d) ????(????) = 1, ????(????) = 1.5, ????????????(????) = 0.5, ????????????(????) = 0.9.
e) The covariance between ???? and ???? is 0.225, and the correlation coefficient is 0.45. This shows a positive correlation between the two variables, meaning that an increase in one variable is associated with an increase in the other.
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I dont know how to do this
pls answer if u know with simple working
Answer:
21. Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
(anyone who answers gets brainliest) Pick the correct trig tool to solve for the variables. There’s a solve for x problem I was struggling with. You don’t have to do them all, thank you
Answer:
(anyone who answers gets brainliest) Pick the correct trig tool to solve for the variables. There’s a solve for x problem I was struggling with. You don’t have to do them all, thank you
Step-by-step explanation:
What is the equation of the line that passes through the point (-9,6) and is perpendicular
to the line 3x-5?
M
Oy--x-3
О У - 3x + 21
Oy - 3x +33
Answer:
y = (-1/3)x + 3.
Step-by-step explanation:
To find the equation of a line perpendicular to a given line, we need to take the negative reciprocal of the slope of the given line.
The slope of the given line Y=3x-5 is 3. Therefore, the slope of a line perpendicular to this line would be -1/3.
Now, using the point-slope form of a line, we can write the equation of the line passing through (-9,6) and having a slope of -1/3:
y - 6 = (-1/3)(x - (-9))
Simplifying:
y - 6 = (-1/3)x - 3
y = (-1/3)x + 3
Therefore, the equation of the line that passes through (-9,6) and is perpendicular to the line Y=3x-5 is y = (-1/3)x + 3.
Janelle wants to enlarge a square photograph that she has made so that each side of the new graph will be 1 inch more than twice the original side g. What trinomial represents the area of the enlarged graph? Make sure to explain your answer.
Answer:
Let's start by assigning a variable to the original side length of the square photograph. We'll use g to represent this length.
According to the problem, each side of the new photograph will be 1 inch more than twice the original side length g. This means that the new side length will be:
2g + 1
Since this is a square photograph, all four sides are equal in length. Therefore, the area of the new photograph can be represented by the square of the new side length:
(2g + 1)^2
To simplify this expression, we can use FOIL (First, Outer, Inner, Last) to expand the squared binomial:
(2g + 1)^2 = (2g + 1)(2g + 1)
= 4g^2 + 2g + 2g + 1
= 4g^2 + 4g + 1
So the trinomial that represents the area of the enlarged photograph is:
4g^2 + 4g + 1
To check our work, we can plug in a value for g and compare the areas of the original and enlarged photographs. For example, if g = 2 (meaning the original side length is 2 inches), then the area of the original photograph is:
2^2 = 4 square inches
And the area of the enlarged photograph is:
4(2)^2 + 4(2) + 1 = 25 square inches
This makes sense, since the new photograph has sides of length 2(2) + 1 = 5 inches, and therefore an area of 5^2 = 25 square inches, which is indeed 1 inch more than twice the original area of 4 square inches.
Which correctly describes a cross section of the cube below? Check all that apply.
A cube with 4 centimeter sides.
A cross section parallel to the base is a square measuring 4 cm by 4 cm.
A cross section parallel to the base is a rectangle measuring 4 cm by greater than 4 cm.
A cross section perpendicular to the base through the midpoints of opposite sides is a rectangle measuring 2 cm by 4 cm.
A cross section perpendicular to the base through the midpoints of opposite sides is a square measuring 4 cm by 4 cm.
A cross section that passes through the entire bottom front edge and the entire top back edge is a rectangle measuring 4 cm by greater than 4 cm.
When a car goes around a curve at twice the speed, the centripetal force on the car doubles. (True or False)
Answer:
True
Step-by-step explanation:
HElp pleaseeeeeeeeeeeee
what are the answer choices?
Answer:
3/4
Step-by-step explanation:
nick hiked up 10 miles up a hill. he is 8 miles east from his starting point. to the nearest degree, at what angle was the incline of the hill?
The required angle of the incline of the hill, to the nearest degree, is 37 degrees.
How to find the inclined angle?We can use trigonometry to find the angle of the incline of the hill.
we can see that Nick has hiked 10 miles up the hill, and is now at point A. His starting point is at point O, which is 8 miles east of A. Let's call the angle at A, between the incline of the hill and the horizontal ground, theta.
We can use the tangent function to find theta:
[tex]$$\tan(\theta) = \frac{h}{8}$$[/tex]
where h is the height of the hill (the distance from A to the horizontal ground at O).
We know that Nick hiked 10 miles up the hill, so we can use the Pythagorean theorem to find h:
[tex]$$h^2 = 10^2 - 8^2 = 36$$[/tex]
Therefore,
[tex]$$h = \sqrt{36} = 6$$[/tex]
Substituting into the equation for tangent, we get:
[tex]$\tan(\theta) = \frac{6}{8} = 0.75$$[/tex]
To find the angle whose tangent is 0.75, we can use the arctangent function:
[tex]$$\theta = \arctan(0.75)$$[/tex]
Using a calculator, we find that
[tex]$$\theta \approx 36.87^{\circ}$$[/tex]
Therefore, the angle of the incline of the hill, to the nearest degree, is 37 degrees.
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Evaluate the expression 7x, if x = 11.
18
77
4
711
[tex] \tt \: c)77[/tex]
_________
[tex] \tt{7x} \\ \: \: \: \: \: = \tt 7(11) \\ \tt= 77[/tex]
[tex] \: [/tex]
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Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of the function.
f(x)=2x5−3x2+2x−1
The possible number of positive real zeros of the function is either 2 or 0.f(-x) = −2x5 − 3x2 − 2x − 1The number of sign changes in f(-x) is 1. The possible number of negative real zeros of the function is either 1 or 0.
To determine the possible numbers of positive and negative real zeros of the function f(x) = 2x5 − 3x2 + 2x − 1 using Descartes's Rule of Signs, we should start by writing the polynomial function in descending order of powers of x. After this, we count the number of sign changes in the polynomial function f(x) and find out the possible number of positive real zeros. Similarly, we count the number of sign changes in f(-x) and find out the possible number of negative real zeros .In the given function f(x) = 2x5 − 3x2 + 2x − 1, the polynomial is already in the descending order of powers of x. Therefore,
we count the sign changes in f(x) and f(-x) as follows: f(x) = 2x5 − 3x2 + 2x − 1The number of sign changes in f(x) is 2. Therefore, the possible number of positive real zeros of the function is either 2 or 0.f(-x) = −2x5 − 3x2 − 2x − 1The number of sign changes in f(-x) is 1. Therefore, the possible number of negative real zeros of the function is either 1 or 0. Hence, the possible number of positive real zeros of the function is either 2 or 0 and the possible number of negative real zeros of the function is either 1 or 0.
Learn more about Descartes's Rule
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