Answers
use the definition of sec and write it in terms of cos
[tex]r=4\cdot\frac{1}{\cos \theta}[/tex]multiply both sides by cos
[tex]r\cos \theta=4[/tex]then we know that r*cos is equal to x in the cartesian
[tex]x=4[/tex]Related Questions
two functions are given below: f(x) and h(x) state the axis of symmetry for each function and explain how to find it f(x)=3(x+4)^2+1
Answers
The axis of symmetry for each function are x = -4 and x =1
How to determine the axis of symmetry for each function?The functions are given as
f(x) and h(x)
As a general rule of functions;
The axis of symmetry for a function is the x-coordinate of the vertex of the function
In f(x), we have
f(x)=3(x+4)² + 1
The vertex of this function is
(x, y) = (-4, 1)
So, the axis is x = -4
For function h(x), we have
The vertex of this function is
(x, y) = (1, -3)
So, the axis is x = 1
Hence, the axis of symmetry are x = -4 and x =1
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Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form. (2 points)
A) f(x) = (x − 8)2
B) f(x) = (x − 4)2 − 13
C) f(x) = (x − 4)2 + 3
D) f(x) = (x − 4)2 + 16
Answers
By using the completing the square method, f(x) = x² − 8x + 3 in vertex form is: B. f(x) = (x − 4)² − 13.
The vertex form of a quadratic equation.In this exercise, you're required to rewrite the given function in vertex form by using the completing the square method. Mathematically, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
f(x) = x² − 8x + 3
f(x) = x² − 8x + (8/2)² - 13
f(x) = x² − 8x + (4)² - 13
f(x) = x² − 8x + 16 - 13
f(x) = (x² − 8x + 16) - 13
f(x) = (x − 4)² − 13
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A cab company charges a flat rate of $2 plus an additional $0.50 for every mile traveled. Use this information for Items 12 and 13. 12. a. Write an expression that can be used to determine the total cab fare for a distance of m miles. b. When Sara arrived at your destination, her cab fare was $7.50. Write an equation to represent this situation. How many miles did Sara travel?
Answers
The cost for each travel on this cab company can be expressed as a sum of the fixed fee and the price per mile multiplied by the distance in miles of the travel. Therefore:
[tex]c(m)=2+0.5\cdot m[/tex]If Sarah paid $7.5 for her cab, then c(m)=7.5 and we can use this value on the expression above to solve for "m". We have:
[tex]\begin{gathered} 7.5=2+0.5\cdot m \\ 0.5\cdot m=7.5-2 \\ 0.5\cdot m=5.5 \\ m=\frac{5.5}{0.5}=11 \end{gathered}[/tex]She traveled 11 miles.
What does 10 represent in 10/6
Answers
10/6
This is a fraction, in a fraction the bottom number represents the denominator and the top number represents the numerator.
So, in this case, 10 represents the numerator.
Solve the system of equations. If the system has no solution say that it's inconsistent. [tex]\begin{gathered}x + 5y = 2 \\ 3x + 15y = 6\end{gathered}[/tex]
Answers
Answer:
Explanation: Given the system of equations:
[tex]\begin{gathered} x+5y=2 \\ 3x+15y=6 \end{gathered}[/tex]will send image. select the expression. that is not equivalent to 10 + 10p
Answers
We have that
[tex]\begin{gathered} 5(10\text{ + p +p) = 5(10 + 2p)} \\ =\text{ 50 + 10p }\ne\text{ 10 + 10 p} \end{gathered}[/tex]So the answer is the first one.
the ratio of men to woman working for a company is 5 to 4. if there is 225 employees total how many women work for the company
Answers
Given:
The ratio of men to women = 5: 4
Total number of employees = 225
The total ratio is:
[tex]\begin{gathered} =\text{ 5 + 4} \\ =\text{ 9} \end{gathered}[/tex]The number of women is the ratio of women to the total ratio times the number of employees
[tex]\begin{gathered} =\frac{4}{9}\times225 \\ =\text{ 100} \end{gathered}[/tex]Answer:
100 women
The initial directions are in the pic below. I’m sending 2 pics now. And the other 2 soon. For a total of 4.
Answers
Recall that the rule of transformation of a point reflected over the y-axis is as follows:
[tex](x,y)\rightarrow(-x,y).[/tex]Therefore, the transformed coordinates of the vertices of the triangle are:
[tex]\begin{gathered} N(4,6)\rightarrow N^{\prime}(-4,6), \\ P(1,6)\rightarrow P^{\prime}(-1,6), \\ Q(3,4)\rightarrow Q^{\prime}(-3,4)\text{.} \end{gathered}[/tex]Therefore, the image of the triangle is the triangle with the above vertices.
Answer:
What is the area of the shaded region if the radius of the circle is 6 in.
Answers
Then, the area of 1/4 of the circle is:
[tex]\begin{gathered} A=\text{ }\frac{\theta}{360}\text{ x }\pi r^2 \\ A=\text{ }\frac{90}{360}\text{ x }\pi r^2 \\ A\text{ = }\frac{1}{4}\pi\text{ 6}^2 \\ A=\text{ 9}\pi \\ \\ \end{gathered}[/tex]The area of the triangle is:
[tex]\begin{gathered} A=\text{ }\frac{b\text{ x h }}{2} \\ A\text{ = }\frac{6\text{ x 6}}{2} \\ A=\text{ 18in}^2 \end{gathered}[/tex]The area of the shaded region is the area of 1/4 of the circle minus the area of the triangle:
[tex]\begin{gathered} A\text{ = 9}\pi\text{ - 18 in}^2 \\ A=\text{ 28.27in}^2\text{ - 18in}^2 \\ A=\text{ 10.27in}^2 \end{gathered}[/tex]What’s the correct Answer answer asap for brainlist please
Answers
Answer:
A. accuracy
Step-by-step explanation:
precise means to be accurate
Hello hope all is well can you tell me what am doing wrong for number 6
Answers
We have the next data
70,89,75,36,80
First we will calculate the mean
(70+89+75+36+80)/5=70
mean=70
Then we will calculate the Median
36,70,75,80,89
median =75
Then we will calculate the mode because any value is repeated all the values given are the mode
mode:70,89,75,36,80
Range
89-36=53
Range =53
which number is 5 more than 8009998
Answers
A number which is 5 more than 8009998 is 8010003
In this question we need to find a number which is 5 more than 8009998.
Let x be a number which is 5 more than 8009998.
We get the required number by adding 5 to 8009998.
so, we write it down as:
x = 8009998 + 5
x = 8010003
Therefore, a number which is 5 more than 8009998 is 8010003
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13. slove for x so the [tex]f(x) = 5[/tex]
Answers
Solution
We have the following function given:
f(x) = -3x+5
And we need to do the following:
5= -3x+5
And if we subtract 5 in both sides we got:
0 =-3x
Dividing both sides by -3 we got:
[tex]\frac{0}{-3}=\frac{-3x}{-3}[/tex]And finally we got:
x= 0
Problem 17
17) f(-2)= 3
18) f(0)= 3
19) f(1)= 0
20) f(-1)= 5.2
Write an addition equation and a subtraction equation
to represent the problem using? for the unknown. Then solve.
There are 30 actors in a school play. There are 10 actors from second grade. The rest are from third grade. How many actors are from third grade?
a. Equations:
b. Solve:
Answers
The Equation is 10 + x= 30 and 20 actors are from third grade.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
There are 30 actors in a school play.
There are 10 actors from second grade.
The rest are from third grade.
let the actors in third grade is x.
Equation is:
Actors from second grade + Actors from third grade = Total actors
10 + x= 30
Now, solving
Subtract 10 from both side
10 +x - 10 = 30 - 10
x = 20
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In 2001, Rodney Hampton earned $75,200 as a self-employed worker. He also earned $41,350 as an employee. How much FICA tax did he pay for both earnings? Note:Self-employed tax rate is 15.3% and the employee tax rate is 7.65%.$14,668.88$14,577.25$14,324.09$14,225.50None of these choices are correct.
Answers
Step 1: Rodney Hampton earned $75,200 as a self-employed worker
% tax rate for self employed = 15.3%
[tex]\begin{gathered} =15.3\text{ \% of \$75200} \\ =\frac{15.3}{100}\text{ x \$75200} \\ =11505.6 \\ =\text{ \$11505.6} \end{gathered}[/tex]Step 2: Rodney Hampton earned $41,350 as a employee worker
%tax rate for employee = 7.65%
[tex]\begin{gathered} =\text{ 7.65\% of \$41350} \\ =\text{ }\frac{7.65}{100}\text{ x \$41350} \\ =\text{ 3163.3} \\ =\text{ \$3163.3} \end{gathered}[/tex]Step 3: FICA tax paid for both earnings = $11505.6 + $3163.3
= $14668.875
=$14668.88
Hence FICA tax paid for both earnings = $14668.88
Find the measure of the indicated angle to the nearest degreeQuestion 15
Answers
Question 15.
Given:
Length of side opposite the indicated angle = 12 units
Length of side adjacent the hypotenuse = 24 units
Let's find the measure of the indicated angle.
Here, we have a right triangle.
To find the measure of the indicated angle, apply the trigonometric ratio formula for sine:
[tex]sin\theta=\frac{opposite\text{ side}}{hypotenuse}[/tex]Where:
θ is the indicated angle.
Thus, we have:
[tex]\begin{gathered} sin\theta=\frac{12}{24} \\ \\ sin\theta=\frac{1}{2} \end{gathered}[/tex]Take the sine inverse of both sides:
[tex]\begin{gathered} \theta=sin^{-1}(\frac{1}{2}) \\ \\ \theta=30^o \end{gathered}[/tex]Therefore, the measure of the indicated angle us 30 degrees.
• ANSWER:
30°
Suppose A is true, B is true, and C is true. Find the truth values of the indicated statement.
Answers
Solution:
If A is true, B is true, and C is true, then:
[tex]A\lor(B\wedge C)=\text{ T }\lor(T\wedge T)\text{ = T}\lor(T)\text{ = T }\lor\text{ T = T}[/tex]we can conclude that the correct answer is:
TRUE
0 Rick has been losing weight at a constant rate since he began his new fitness plan. The table below shows Rick's weight for the first four weeks, 2 3 I 220.2 218.6 221.8 223.4 Weight (lbs) a) Write an equation to represent this sequence. b) Find Rick's weight after 16 weeks. ter your answer(s) here
Answers
To make the equation lets us find the rate of change of the weight
The form of the equation is y = m x + b
where:
m is the rate of change (slope)
b is the y-intercept (value y when x = 0)
To find m use two-point from the table
(1, 223.4) , (2, 221.8)
[tex]m=\frac{221.8-223.4}{2-1}=-\frac{8}{5}=-1.6[/tex]Substitute it in the form of the equation
[tex]y=-1.6x+b[/tex]To find b use any point in the table
(1, 223.4)
x = 1 , y = 223.4
[tex]\begin{gathered} 223.4=-1.6(1)+b \\ 223.4=-1.6+b \end{gathered}[/tex]Add 1.6 for both sides to find b
[tex]\begin{gathered} 223.4+1.6=-1.6+1.6+b \\ 225=b \end{gathered}[/tex]Substitute value b in the equation
[tex]y=-1.6x+225[/tex]The equation of the sequence is y = -1.6 x + 225
to find his weight after 16 weeks substitute x by 16
[tex]\begin{gathered} y=-1.6(16)+225 \\ y=-25.6+225 \\ y=199.4 \end{gathered}[/tex]His weight after 16 weeks is 199.4 Ibs
Laverne created a painting with an area of 72 square inches and a length of 9 inches. They create a second painting with an area of 56 square inches. It has the same width as the first painting. What is the length of the second painting?
Answers
Answer: 7
Step-by-step explanation:
As our first step, we can divide 72 by 9 to discover the width of the first AND second painting. 72÷9=8
Now that we have discovered the width of the second painting, we will now solve the mathematical expression 56÷8.
Because 56 divided by 8 equals 7, the length of the second painting is 7 inches.
Find the volume of a cone with a height of 10cm and diameter of 6cm. Round to the nearest tenth. Use 3.14 for .
Answers
We can find the volume of a cone using the formula
[tex]V=\frac{\pi r^2h}{3}[/tex]Where
h = height
r = radius
Remember that
[tex]d=2r\Rightarrow r=\frac{d}{2}[/tex]Therefore, let's find out the radius first, the problem says that the diameter is 6cm, then
[tex]r=\frac{6}{2}=3\text{ cm}[/tex]The radius is 3cm and the height is 10cm, let's use it in our formula:
[tex]\begin{gathered} V=\frac{\pi\cdot(3)^2\cdot10}{3} \\ \\ V=30\pi \end{gathered}[/tex]The problem also say to use = 3.14, then the volume is
[tex]\begin{gathered} V=30\cdot3.14 \\ V=94.2 \end{gathered}[/tex]Therefore, the volume is
[tex]V=94.2\text{ cm}^3[/tex]
White the inequality shows by the shaded region in the graph with the boundary line y=x/3-5
Answers
From the given figure
Since the line is a dashed line, then
The sign of inequality does not have equal (< OR > )
Since the shading area is down the line, then
The sign of inequality should be smaller than (<)
Then the inequality is
[tex]y<\frac{x}{3}-5[/tex]Match each expression to the equivalents value. 4. i^121 A. 15. i^240 B. -16. i^90 C. -i7. i^43 D. i
Answers
Let's find the value of each expression.
[tex]undefined[/tex]Herb Garrett has an 80% methyl alcohol solution. He wishes to make a gallon of windshield washer solution by mixing his methyl alcohol solution with water. If 128 ounces or a gallon of windshield washer fluid contain 6% methyl alcohol, how much of the 80% methyl alcohol solution and how much water must be mixed? Express your answer in ounces.
Answers
First, calculate the total volume of alcohol in the gallon of windshield washer solution by calculating what is 6% of a gallon equal to. Since a gallon is equal to 128 ounces, then:
[tex]undefined[/tex]The bar graph below shows the number of students at Lindsay's school who were born in various states.Oregon?ColoradoStateUtah -Arizona -New Mexico04812 16 20 24 28 32Number of StudentsThe number of students who were born in Oregon is the same as the number of students from Utah and NewMexico combined.Umantudante at Lindsay's school were born in Oregon?We
Answers
Since the number of students who were born in Oregon is the same as the number of students from Utah and New Mexico, add the amount of students from Utah and New Mexico to find the number of students who were born in Oregon.
18 students were born in Utah, and 12 students were born in New Mexico.
Since 18+12=30, then, 30 students were born in Utah and New Mexico combined.
Therefore, the amount of students who were born in Oregon, is:
[tex]30[/tex]This is very hard for me I need to know how to do it
Answers
The zeros of a function are the values of x that make the function be equal to zero.
When graphing a quadratic equation, the graph is a parabola, and the zeros of the function are the x-intercepts of the graph, which are the points where the graph intersects the x-axis.
So, if the zeros of this function are x = -8 and x = 2, that means the parabola crosses the x-axis at x = -8 and x = 2.
Therefore the correct option is the first one.
Consumption and savings if real domestic output is $370 billion and planned investment is $15 billion
Answers
The consumption is 355 billion .
Given,
In the question:
Consumption and savings if real domestic output is $370 billion and planned investment is $15 billion.
Now, According to the question:
Based on the given condition,
Formulate;
Aggregate expenditure (consumption)= Output - Savings= Investment
370 - 15
Calculate the sum or difference
= 355billion
Hence, The consumption is 355 billion .
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Remmy establishes a loan for an $8000 vacation package to Transylvania. The vacation company charges 5.5% simple interest rate. Remy plans to pay back the loan over 1.5 years.How much interest will Remmy pay?
Answers
Remmy will pay $660 interest.
Step - by - Step Explanation
What to find? The amount of interest to be paid.
Given Parameters:
• Principal (P) = $8000
,• Rate of interest(R) = 5.5
,• Time(t in years) = 1.5
The formula for calculating simple interest is given below:
[tex]S.I=\frac{P\times R\times T}{100}[/tex]Where P is the principal.
R represents the rate.
T is the time given in years.
S.I is the simple interest.
Substitute the values into the formula and simplify.
[tex]S.I=\frac{8000\times5.5\times1.5}{100}[/tex][tex]S.I=\frac{80\cancel{00}\times5.5\times1.5}{1\cancel{00}}[/tex][tex]=80\times5.5\times1.5[/tex]= 660
Hen
Determine if the triangles are similar, if similar state how
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Triangle YXZ
Triangle AXB
Similar Triangles = ?
Step 02:
Similar Triangles
AB || YZ
The Side-Splitter Theorem:
AB || YZ ===> XY/ YA = XZ / ZB
The answer is:
The triangles are similar, by the Side-Splitter Theorem.
18. The table below gives the population of a town (in thousands) from the year 2000 to the year 2008. Year '00 '01 '02 03 04 '05 06 '07 '08 Population 87 84 83 80 77 76 78 81 85 (thousands) What was the average rate of change of population: a. between 2002 and 2004? b. between 2002 and 2006?
Answers
a . Average rate of change between 2002 and 2004 can be calculated below
[tex]\begin{gathered} average\text{ rate of change=}\frac{chang\text{e in y}}{\text{change in x}} \\ average\text{ rate of change = }\frac{77-83}{2004-2002} \\ average\text{ rate of change}=\frac{-6}{2}=-3(thousand) \end{gathered}[/tex]b. Average rate of change between 2002 and 2006 is
[tex]\begin{gathered} \text{average rate of change = }\frac{78-83}{2006-2002} \\ average\text{ rate of change}=\frac{-5}{4}=-\frac{5}{4}(thousand) \end{gathered}[/tex]a rectangle width is 3 1/2 inches and the lenght is 4 3/4 inches. What is the area of the rectangle?
Answers
The area of the rectangle with length [tex]4 \frac{3}{4}[/tex] inches and width [tex]3 \frac{1}{2}[/tex] inches will be;
⇒ [tex]16 \frac{5}{8}[/tex] inches²
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The length of the rectangle = [tex]4 \frac{3}{4}[/tex] inches
= 19 / 4 inches
The width of the rectangle = [tex]3 \frac{1}{2}[/tex] inches
= 7 / 2 inches.
Since, We know that;
The area of the rectangle = Length x Width
Substitute all the values , we get;
The area of the rectangle = Length x Width
The area of the rectangle = 19 / 4 x 7 / 2
= 133 / 8 inches²
= [tex]16 \frac{5}{8}[/tex] inches²
Therefore,
The area of the rectangle with length [tex]4 \frac{3}{4}[/tex] inches and width [tex]3 \frac{1}{2}[/tex] inches will be;
⇒ [tex]16 \frac{5}{8}[/tex] inches²
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