Which is a polar form of the following parametric equations?x=5cos² thetay = 5 cos theta sin theta
Answers
ANSWER
[tex]r(\theta)=5cos\theta[/tex]EXPLANATION
Given;
[tex]\begin{gathered} x=5cos^2\theta \\ y=5cos\theta\:sin\theta \end{gathered}[/tex]Convert from polar form to parametric form.
[tex]\begin{gathered} x(\theta)=r(\theta)cos\theta \\ y(\theta)=r(\theta)sin\theta \end{gathered}[/tex]Here;
[tex]\begin{gathered} x(\theta)=5(cos\theta)^2=5cos\theta\times cos\theta \\ y(\theta)=5cos\theta s\imaginaryI n\theta=5cos\theta sin\theta \\ \Rightarrow r(\theta)=5cos\theta \end{gathered}[/tex]Related Questions
Factor the polynomial completely.
5x2 + 3x - 14
Group of answer choices
(x - 7)(5x + 2)
(x - 2)(5x + 7)
prime polynomial
(x + 2)(5x - 7)
Answers
[tex]5 {x}^{2} + 10x - 7x - 14 \\ = (5 {x}^{2} + 10x) - (7x + 14) \\ = 5x(x + 2) - 7(x + 2) \\ = (x + 2)(5x - 7)[/tex]
LAST OPTION IS THE ANSWER.
11.) A system of two linear equations can have no solution, onesolution, or infinitely many solutions. Draw graphs or write aparagraph explaining how a graph of the two equations wouldappear for each of these possibilities,Ihp
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The solution of a system of two linear equations interprets the point of intersection of the two lines geometrically
When the two lines intersect each other at a point, then the system of two linear equations has a unique solution.
If two linear equations in the given system represent two lines parallel to each other, then the system becomes inconsistent and in that case, it has no solution.
If the system is dependent i.e. there is only one linear equation in two variables, then every point on the line is the solution of the equation.
So, in that case, it has infinitely many solutions.
Given m||n, find the value of x and y 35 need help please
Answers
Answer:
x = 35
Step-by-step explanation:
x and 35° are alternate angles and are congruent , then
x = 35
Taylor's dad lifted 80°g of weight how much more did Taylor's dad left than Davin record your answering grams
Answers
The weight that Taylor's dad lifted higher will be 30g.
What is weight?It should be noted that weight simply means the mass that a body contains.
From the information, Taylor's dad lifted 80g of weight and Davin's dad lifted 50g of weight.
The weight that Taylor's dad lifted more than Davin's dad will be:
= Weight of Taylor's dad - Weight of Davin's dad
= 80 - 50
= 30g
The difference is 30g.
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Taylor's dad lifted 80g of weight and Davin's dad lifted 50g of weight. How much more did Taylor's dad lift than Davin?
If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?48O y - 3 (2)O y = 4g (2)(48)(B)O y--(48)(6)
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The phrase y varies directly as x can be understood that y gets bigger when x gets bigger as well, this can be written as,
[tex]\frac{y_1}{x_1}=\frac{y_2}{x_2}[/tex]then, using the point (6,48) find the value when x is 2,
[tex]\frac{48}{6}=\frac{y_2}{2}[/tex]clear for y2,
[tex]y_2=\frac{48}{6}(2)[/tex]Answer:
[tex]y_=\frac{48}{6}(2)[/tex]Jaime opens an account with a $400 deposit that earns 7% simple interest annually. She makes no other deposits or withdrawls. This situation can be modeled by {blank} function that grows {blank} each year After 4 years, she earned {blank}. Fill in the blanks.
Answers
This situation can be modeled by a linear function that grows at a constant rate each year After 4 years, she earned $112.
What is the interest after four years?Simple interest is the amount of interest that is earned on amount that is deposited or invested. The simple interest earned is a function of the amount invested, interest rate and the duration of the investment.
An amount that earns a simple interest grows linearly and can be modelled using a linear function. A linear function is a function that increases at a constant rate and when it is drawn on graph, it is a straight line.
Simple interest = amount deposited x time x interest rate
$400 x 0.07 x 4 = $112
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For the attached blue bird, find the quadratic equation written in vertex form
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The vertex form of a quadratic equation is expressed as
y = a(x - h)^2 + k
where
h and k are the x and y x and y coordinates of the vertex of the parabola.
a is the leading coefficent
From the information on the graph,
h = 13
k = 13
By substituting these values into the formula,
y = a(x - 13)^2 + 13
On the graph, when x = 26, y = 0
Substituting these values into the equation, we have
0 = a(26 - 13)^2 + 13
0 = a * 13^2 + 13
0 = 169a + 13
169a = - 13
a = - 13/169
a = - 1/13
By substituting a = - 1/13, h = 13 and k = 13 into the verte form equation, the quadratic equation written in vertex form is
y = - 1/13(x - 13)^2 + 13
do jalapenos come from northeast region
Answers
Answer: Jalapeño peppers are a top crop of Mexico and the Southwestern United States, but our Northeast region can produce some of the best jalapeños out there
Step-by-step explanation:
The majority of the U.S. commercial jalapeño supply is grown in New Mexico, Texas, and California
Answer:
No, but they can come from there.
Step-by-step explanation:
4(x - 2)³6 = √x+4Which statement explains why the solution to the equation is= 4?OA. The x-value of 4 is a x-intercept for both f (x) = (x2)³6and g(x)O B.The x-value of 4 produces the same y-value in both f(x)OC.The x-value of 4 is undefined for both f(x)O D.The x-value of 4 is defined on the graphs of both f (x)===Reset(x-(2)³6and g(x)2)³ - 6and g(x)= √x+4.= √x+4.=Next(22)³6and g(x)=√x+4= √x+4.
Answers
Notice that:
[tex]\begin{gathered} (4-2)^3-6=(2)^3-6=8-6=2, \\ \sqrt[3]{4+4}=\sqrt[3]{8}=2. \end{gathered}[/tex]Therefore, the value x=4 is a solution because it produces the same value for both sides of the equation.
Answer: Option B.
HARVEY HAS KEPT A RECORD OF ALL THE FISH HE CAUGHT IN WILLOW GROVE LAKE. HE HAS CAUGHT, 126 BASS 42 CATFISH 72 BLUE GILL WHAT IS THE EMPIRICAL PROBABILITY THAT THE NEXT FISH HE CATCHES WILL BE A CATFISH?
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Given that Harvey caught:
• 126 bass.
,• 42 catfish.
,• 72 blue gill
You need to remember that, by definition, an Empirical Probability can be calculated by dividing the number of times the event occurs by the total number of trials.
In this case, you know that he caught 42 catfish. Therefore, you can identify that:
[tex]Number\text{ }of\text{ }times\text{ }the\text{ }event\text{ }occurs=42[/tex]You can also determine that:
[tex]Total\text{ }number\text{ }of\text{ }trials=126+42+72=240[/tex]Therefore, you can determine that the Empirical Probability that the next fish Harvey catches will be a catfish is:
[tex]P(E)=\frac{42}{240}=\frac{7}{40}=0.175[/tex]Hence, the answer is:
[tex]P(E)=0.175[/tex]at a local gym you can either pay $90 for money pass then pay for dollars each time you go to the gym or you can pay $13 each time you go with no monthly pass fee what is the cost where the two options are the same?
Answers
Option A
$90 + $4 each time
Option B
$13 each time
Procedure
Equations
[tex]\begin{gathered} (1)\to C=90+4t \\ (2)\to C=13t_{} \\ \\ 90+4t=13t \\ 13t-4t=90 \\ 9t=90 \\ t=\frac{90}{9} \\ t=10 \end{gathered}[/tex]The cost would be
[tex]\begin{gathered} C=90+4\cdot10 \\ C=90+40 \\ C=130 \end{gathered}[/tex]The answer would be $130
Solve the equation for all real solutions. --d2 - 12d + 4 = -6d?
Answers
the real solutions for the equation d² - 12 d + 4 = 6 is d = 6 ± √38.
The equation given is:
d² - 12 d + 4 = 6
Subtract 6 from both the sides:
d² - 12 d + 4 - 6 = 6 - 6
d² - 12 d - 2 = 0
solve for the real solutions:
D = b² - 4ac
D = (-12)² - 4(-2)(1)
D = 144 + 8
D = 152
d = 12 ±√152 / 2 (1)
d = 6 ± √38
Therefore, we get that, the real solutions for the equation d² - 12 d + 4 = 6 is d = 6 ± √38.
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HELP PLEASEEEEEEEEEEE!! ILL MARK BRAINLIEST
Answers
The answer is follows,
[tex]-3^5[/tex] = -243
[tex](-3)^5[/tex] = -243
[tex]\left(-3^5\right)[/tex] = -243
[tex]-\left(-3\right)^5[/tex] = 243
An exponent is a number or letter written above and to the right of the base of a mathematical expression.
What is meant by exponent?The number of times a number is multiplied by itself is referred to as its exponent. For instance, 2 to the third (written as 23) means: 2 x 2 x 2 = 8. An exponent is a number that is superscripted over another number. In other words, it denotes that the base has been raised to a certain level of power. Other names for the exponent include index and power. If m is a positive number and n is its exponent, the expression mn denotes that m has been multiplied by itself n times. Power is defined in mathematics as a base number raised to the exponent, where the base number is the factor multiplied by itself and the exponent is the number of times the same base number is multiplied.To learn more about exponent, refer to:
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Select all the equations that have the same solution as 2x – 5 = 15. A: 2x = 10 B: 2x = 20 C: 2(x – 5) = 15 D: 2x – 20 = 0 E: 4x – 10 = 30 F: 15 = 5 – 2x
Answers
The equation that has same solution as that of equation 2x - 5 = 15 is 2x = 10.
What is an equation?
An equation in mathematics is used to equate two expressions using a equals sign. For example -
x = 4y
3x = 7y
Given is the following equation -
2x - 5 = 15
The solution of the equation will be the value of [x] for which the LHS equals to RHS. On solving -
2x - 5 = 15
2x = 10
x = 5
Only equation [A] has the same solution as that of equation -
2x - 5 = 15
Equation [A] is -
2x = 10
x = 5
Therefore, the equation that has same solution as that of equation 2x - 5 = 15 is 2x = 10.
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Please just answer part B And please explain every step and how its simplified so I can understand better.
Answers
Given that
We have to find the inverse of a function and the function is
[tex]g(x)=2^{x-1}[/tex]Explanation -
The steps to find the solution are -
(1). First, we will consider the function equal to y as
[tex]\begin{gathered} g(x)=y \\ x=g^{-1}(y)----------(i) \\ y=2^{x-1} \end{gathered}[/tex](2). Now from this, we will find the value of x in terms of y.
And we will take the base of the log as 2 because the x is in the power of 2. As an exponential function.
As
[tex]\begin{gathered} y=\frac{2^x}{2} \\ Taking\text{ the }\log_2\text{ on both sides we have} \\ \log_2y=\log_2(\frac{2^x}{2}) \\ \log_2y=\log_22^x-\log_22 \\ \\ Using\text{ the formulae of log,} \\ \begin{equation*} \log_a(\frac{b}{c})=\log_ab-\log_ac \end{equation*} \\ \log_aa^p=p\times\log_aa \\ and\text{ }\log_aa=1 \\ \\ Now,\text{ } \\ \log_2y=\log_22^x-1 \\ \log_2y=x\log_22-1 \\ \log_2y=x-1 \\ x=\log_2y+1 \end{gathered}[/tex](3). Now from eq (i) we have
[tex]g^{-1}(y)=\log_2y+1[/tex](4). At last, we will replace y with x. Then,
[tex]g^{-1}(x)=\log_2x+1[/tex]Final answer -
The final answer is [tex]g^{-1}(x)=\log_2x+1[/tex]Find each angle measure in the figure. (x + 30) and The angle measures are Use the equation to justify your answer. x + (x +30) + 2x =
Answers
Answer:
37.5, 75 and 67.5 degrees
Explanation:
The sum of angle in the given triangle is 180 degrees
Hence;
x + x + 30 + 2x = 180
4x + 30 = 180
4x = 180 - 30
4x = 150
x = 150/4
x = 37.5 degrees
Get angle 2x
2x = 2(37.5)
2x = 75 degrees
Get angle x + 30
x + 30 = 37.5 + 30
x = 30 = 67.5 degrees
Hence the angles of the triangle are 37.5, 75 and 67.5 degrees
solve for x5(x-2)^2+4=9
Answers
the square root of 1 has 2 solutions: 1 and -1, then:
[tex]\begin{gathered} x_1-2=1 \\ x_1=1+2 \\ x_1=3 \\ or \\ x_2-2=-1 \\ x_2=-1+2 \\ x_2=1 \end{gathered}[/tex]i need help with this. please someone i’m begging lol
Answers
The inverse of the given equation is given by f⁻¹(x) = (x+8)²/49 - 8
What is an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Equations are used to describe geometric shapes in Cartesian geometry. Since the investigated equations, such as implicit equations or parametric equations, have an unlimited number of solutions, the goal has changed. Now, one utilizes equations to analyze the attributes of figures rather than explicitly providing the solutions or counting them, which is impossible. The fundamental concept of algebraic geometry, a significant branch of mathematics, is presented here. Equations involving one or more functions and their derivatives are known as differential equations. By identifying a derivative-free formulation for the function, they may be resolved. Processes involving rates are modeled using differential equations.
given equation,
f(x) = 7√(x+8) - 8
y = 7√(x+8) - 8 (replace f(x) with y)
x = 7√(y+8) - 8 (interchange x and y)
y = (x+8)²/49 - 8 (solve for y)
f⁻¹(x) = (x+8)²/49 - 8 (replace y with f(x))
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what number 14 is 70 percent of
Answers
Answer:
20
Step-by-step explanation:
70% of x = 14
0.7x = 14
x = 14/0.7
x = 20
find the domain of the graphed function. A) x ≥ - 4 B) - 4 ≤ x ≤ 4 C) x is all real numbers D) - 4 ≤ x ≤ 2
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Given data:
The given graph.
The domain is the value of x, for the given function domain is,
[tex]-4\leq x\leq2[/tex]Thus, the domain is
Write the following comparison as a ratio reduced to lowest terms.223 inches to 19 feet
Answers
Given:
223 inches to 19 feet.
Required:
To write the given comparison as a ratio reduced to lowest terms.
Explanation:
1 feet = 12 inches
19 feet = 228 inches.
So, we get 223 inches to 228 inches and now have to simplify
This is the same as
[tex]\begin{gathered} =\frac{223}{228} \\ \end{gathered}[/tex]Final Answer:
[tex]\frac{223}{228}[/tex]Basil N. Thyme is putting in a triangular herb garden with sides of 2 yards, 3 yards and 4 yards. He needs to know the area of his garden so he would know how many herb plants to germinate in his greenhouse.. What is the area of his herb garden to the nearest square foot? (convert yards to feet.)
Answers
26.14 ft²
1) Considering that triangular herb:
2) Let's calculate the area of that triangle using the Heron formula so that we can not need to find the height:
2.1) Calculate the Perimeter:
2P = 2+3+4
2P = 9 yd
2 yards = 6 ft
3 yd = 9ft
4 yd = 12 ft
Converting into feet
9 yards = 27 feet
And the Semi perimeter (half the perimeter):
P = 9/2
27/2
Now we can plug that into Heron's Formula:
[tex]\begin{gathered} A=\sqrt[]{p(p-a)(p-b)(p-c)} \\ A=\sqrt[]{\frac{27}{2}(\frac{27}{2}-6))(\frac{27}{2}-9)(\frac{9}{2}-12)} \\ A=\frac{27\sqrt[]{15}}{4}\approx26.14 \end{gathered}[/tex]3)
So the area of that triangular garden is approximately 26.14 ft²
1/3 |2x+3|-1 is less than or equal to 8
Answers
Adding 1 to both sides gives
[tex]\frac{1}{3}|2x+3|\leq9[/tex]and then multiplying both sides by 3 gives
[tex]|2x+3|\leq27[/tex]At this point, this absolute value inequality can be decomposed into two separate inequalities
[tex]\begin{gathered} -(2x+3)<27 \\ (2x+3)<27 \end{gathered}[/tex]We first solve the first inequality.
Multiplying both sides by -1 reverses the sign of the inequality and gives
[tex]2x+3>-27[/tex]subtracting -3 from both sides we get
[tex]2x>-30[/tex]and finally dividing both sides by 2 gives
[tex]x>-15.[/tex]That is the first solution, the second solution is given by the second inequality 2x+ 3 <27.
Subtracting 3 from both sides and then dividing the equation by 2 gives
[tex]x<12[/tex]Hence, the solution to our inequality is
[tex]-15
What can be concluded from the graph shown here?
Answers
The correct option regarding the skewness of the given distribution is:
The data is clumped to the right.
How to find the skewness of the distribution?To find the skewness of the distribution, we need to look at the mean and the median of the distribution.
The mean is the sum of all the observations in the distribution divided by the number of observations. The graph shows the number of times that each observation appears, hence the mean is found as follows:
Mean = (1 x 2 + 2 x 5 + 3 x 8 + 4 x 2 + 5 x 12 + 6 x 7 + 7 x 13 + 8 x 3 + 9 x 5 + 10 x 11)/(2 + 5 + 8 + 2 + 12 + 7 + 13 + 3 + 5 + 11) = 6.12.
The median is the middle term of the distribution. There are 68 terms in the distribution, hence the median is the observation in which the count reaches 34. Then:
Observation 1: Count 2.Observation 2: Count 2 + 5 = 7.Observation 3: Count 7 + 8 = 15.Observation 4: Count 15 + 2 = 17.Observation 5: Count 17 + 12 = 29.Observation 6: Count 29 + 7 = 36 > 34.Hence the median is of 6, which is less than the mean. Since the median is less than the mean, the data is right skewed, that is, clumped to the right.
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What is the area of a square with a side length of 12 units? What is the area of a square with a side length of 2.5 units?
Answers
Explanation: hope it helps :)
You want to build a deck in your back yard. The deck will be 14 feet long and 12 feet wide. If you will put railing along all four sides of the deck, how many feet of railing are needed?A) 26 feetB) 38 feetC) 52 feetD) 104 feet
Answers
C) 52 feet
Explanation:
Since the deck will be 14 feet by 12 feet and it has four sides, we can deduce that it's a rectangle.
Therefore all you need to do is sum up all the sides together
14 + 14 + 12 + 12 => 14 * 2 + 12 * 2 = 52 feet
Turica has 4 different pen colors: Red, purple, blue, and green. She has 8 pens of each color. She selects a pen at random.What is the probability she will select a green pen?A: 1/2B: 1/3C: 1/4D: 1/32
Answers
Brand A has a recognition value worth 43$ billion more than brand B. If the total value of these two brands is 107$ billion, find the value of each of the brands.
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The value of Brand A is $75 billion and Brand B is $32 billion.
What is an expression?An expression is used to illustrate the relationship between the variables.
Let brand B value = x
Brand A has a recognition value worth 43$ billion more than brand B. This will be x + 45
The total value of these two brands is 107$ billion.
The expression to find the value is for each brand will be:
x + x + 43 = 107
2x + 43 = 107
Collect like terms
2x = 107 - 43
2x = 64
Divide
x = 64/2
x = 32
Brand B is $32 billion
Brand A = x + 43 = 32 + 43 = $75 billion.
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Forearm lengths of men, measured from the elbow to the middle fingertip, are normallydistributed with a mean 18.8 inches and a standard deviation 1.1 inches.If 1 man is randomly selected, what is the probability that his forearm length is below 17
Answers
Solution
Part A
What are the parameters?
The parameters are
[tex]\begin{gathered} \operatorname{mean}\text{ = }\mu=18.8 \\ \text{Standard Deviation = }\sigma=1.1 \end{gathered}[/tex]We want to find
[tex]p(\mu<17)[/tex]Part B
Find the z score
The formula to use is given by
[tex]z=\frac{\bar{X}-\mu}{\sigma}[/tex][tex]\begin{gathered} z=\frac{\bar{X}-\mu}{\sigma} \\ z=\frac{17-18.8}{1.1} \\ z=\frac{-1.8}{1.1} \\ z=-1.6363636363 \\ z=-1.64 \end{gathered}[/tex]The construction of the standard normal curve is shown below
Part C
We use the standard normal table (from statistical table)
Thus, From statistical table
[tex]p(z<-1.64)=0.05[/tex]
A trail mix recipe calls for the following ratios: 21.25 % raisins, 5/9 peanuts, 0.14 chocolate chips, and the rest is made up of chex mix. Approximately what percent is made up of chex mix?
Answers
Answer:
11.2%Step-by-step explanation:
Given ratios21.25% raisins,5/9 peanuts,0.14 chocolate chips,x - chex mixSolutionConvert every ratio into percentage and then find the missing value
Peanuts
5/9 = 5/9*100% = 55.55%Chocolate chips
0.12 = 0.12*100% = 12%Chec mix
x = 100% - (21.25% + 55.55% + 12%) = 100% - 88.8% = 11.2%