We are given the following equation of a circle.
[tex]\mleft(x-1\mright)^2+(y+3)^2=4[/tex]The standard form of the equation of a circle is given by
[tex](x-h)^2+(y-k)^2=r^2[/tex]Comparing the given equation with the standard form we see that
[tex]\begin{gathered} h=1 \\ k=-3 \\ r^2=4 \\ r=\sqrt[]{4} \\ r=2 \end{gathered}[/tex]Therefore, the center of the circle is
[tex]C=(h,k)=(1,-3)[/tex]Therefore, the radius of the circle is
[tex]r=2[/tex]May I please get help with this. For I have tried multiple times but still can’t get the right answer or the triangle after dilation?
Solution:
Given the triangle ABC as shown below:
To draw the image,
step 1: Determine the coordinates of the vertices of the triangle.
In the above graph,
[tex]\begin{gathered} A(6,7) \\ B(9,9) \\ C(8,6) \end{gathered}[/tex]step 2: Evaluate the new coordinates A'B'C' of the triangle after a dilation centered at the origin with a scale factor of 2.
After a dilation centered at the origin with a scale factor of 2, the iniatial coordinates of the vertices of the triangle are multiplid by 2.
Thus,
[tex]\begin{gathered} A(6,7)\to A^{\prime}(12,14) \\ B(9,9)\to B^{\prime}(18,18) \\ C(8,6)\to C^{\prime}(16,12) \end{gathered}[/tex]step 3: Draw the triangle A'B'C'.
The image of the triangle A'B'C' is as shown below:
(b) The area of a rectangular window is 3740 cmcm?If the length of the window is 68 cm, what is its width?Width of the windoow
Step 1
The area of a rectangle = Length x width
Step 2
Parameters given include
Area of rectangular window= 3740 square cm
Length of window = 68cm
Step 3
Substitute and solve
[tex]\begin{gathered} 3740\text{ = 68 x width} \\ \text{width = }\frac{3740}{68}\text{ = 55cm} \end{gathered}[/tex]Therefore, the width of the window = 55 cm
Which formula can be used to find the sum of the mesures of all the interior angles of a regular polygon with n sides?
A. S = (n-2)180 degrees
B. S = (n+2)180 degrees
C. S = (n-2)90 degrees
D. S = (n+2)90 degrees
Answer:180(n – 2),
Step-by-step explanation:
The mean height of women in a country (ages 20-29) is 63.6 inches. A random sample of 70 women in this age group are selected. What is the probability that the mean height for the sample is greater than 64 inches?Assuming sigma= 2.53 inches
We have a mean of 63.6 inches and a standard deviation of 2.53 inches. We want to find the probability for our random sample to have a greater mean than 64 inches. We can do that by finding the probability of getting women higher than 64 inches in the original group. To do that, we're going to use a z-table.
First, let's convert 64 inches to a z-score:
[tex]\begin{gathered} z(64)=\frac{64-\mu}{\sigma/\sqrt[]{n}}=\frac{64-63.6}{2.53/\sqrt[]{70}}=\frac{0.4\sqrt[]{70}}{2.53}=1.32278265065\ldots \\ z(64)\approx1.32 \end{gathered}[/tex]Using a right z-table, we have
This z-table gives us the area between the middle of the bell curve and our desired value.
This means, the probability of getting a sample higher than our value, will be 0.5 minus the probability given by the z-table.
[tex]0.5-0.4066=0.0934[/tex]Then, we have our result.
[tex]P(\bar{x}>64)=0.0934[/tex]Samuel and Kathleen deposit $700.00 into a savings account which earns 4% interestcompounded monthly. They want to use the money in the account to go on a trip in 2 years.How much will they be able to spend?
To find how much they will be able to spend, we have to use the compoud interest formula, so:
[tex]\text{Amount}=700000\cdot(1+0.04)^{24}[/tex][tex]Amount=1794312.92[/tex]Can someone show me how to do this one correctly?
ANSWER:
Juwan has 19 dimes and 6 quarters in his pocket.
STEP-BY-STEP EXPLANATION:
From the statement we can establish the following system of equations:
Taking into account that one dime is 10 cents and a quarter is 25 cents.
Let x be the number of dimes
Let y be the number of quarters
[tex]\begin{gathered} x+y=25\rightarrow x=25-y\text{ (1)} \\ 10x+25y=340\text{ (2)} \end{gathered}[/tex]We solve the system of equations by means of the substitution method, we substitute equation (1) in (2):
[tex]\begin{gathered} 10\cdot(25-y)+25y=340 \\ 250-10y+25y=340 \\ 15y=340-250 \\ y=\frac{90}{15} \\ y=6 \\ \\ \text{therefore, for x:} \\ x=25-6 \\ x=19 \end{gathered}[/tex]Therefore they are 19 dimes and 6 quarters
The table below shows the relationship between the number of hours a student studied and theirgrade on a certain test.
It is necessary to adjust the given points of the graph to a line. The general form of the equation of a line is given by:
y = mx + b
where m is the slope of the line and b is the y-intercept of the line.
To calculate the slope m, use the following formula:
[tex]undefined[/tex]Find the slope of the line in the graph below using: rise m= 0 6 -2)
Given data:
The given graph of the line.
The slope of the line passing through (4, 0) and (12, 2) is,
[tex]\begin{gathered} m=\frac{2-0}{12-4} \\ =\frac{2}{8} \\ =\frac{1}{4} \end{gathered}[/tex]Thus, the solpe of the line is 1/4.
Step-by-step explanation:
Given data:
The given graph of the line.
The slope of the line passing through (4, 0) and (12, 2) is,
\begin{gathered}\begin{gathered} m=\frac{2-0}{12-4} \\ =\frac{2}{8} \\ =\frac{1}{4} \end{gathered}\end{gathered}
m=
12−4
2−0
=
8
2
=
4
1
Thus, the solpe of the line is 1/4.
Solve. Your answer should be in simplest form. 2/5 (−3/7)
Answer:
2/5 (-3/7) = -6/35 ≅ -0.1714286
Step-by-step explanation:
and that’s how you do it
Add: 2/5 + 3/7 = 2 · 7/5 · 7 + 3 · 5/7 · 5 = 14/35 + 15/35 = 14 + 15/35 = 29/35.
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(5, 7) = 35. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 7 = 35. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - two fifths plus three sevenths is twenty-nine thirty-fifths.
Which measurement is closest to the area of the triangle in square centimeters? A 63 cm2 B 42.75 cm2 С 35.5 cm2 D 31.5 cm2
The measurement shows that the base of the triangle is approximately 7 cm
while the height is approximately 9cm
The area of the triangle is given by
[tex]\text{Area = }\frac{1}{2}\text{ x base x height}[/tex][tex]\begin{gathered} \text{Area =}\frac{1}{2}\text{ x 7 x 9} \\ \text{Area = }\frac{63}{2}cm^2 \\ \\ \text{Area = 31.5cm}^2 \end{gathered}[/tex]Option D is the closest to the answer
is A square with a perimeter of 38 units is graphed on a coordinate grid. The square dilated by a scale factor of 0.8 with the origin as the center of dilation. If (x,y) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square? 0 (0.8x, 0.8y) 0 (x + 38, y + 38) O (x + 0.8, y + 0.8) O (38x, 38y)
Answer:
(0.8x, 0.8y)
Step-by-step explanation:
in a dilation with the origin as the center all point coordinates are multiplied by the scaling factor.
identify the rate, base and portion.What percent of 126 is 44.1
In this problem, we have that
Base=126 (represents the 100%)
Portion=44.1
Find out the percentage
100/126=x/44.1
solve for x
x=(100/126)*44.1
x=35%
The percentage is 35%
what are the coordinates of the focus of the conic section shown below (y+2)^2/16-(x-3)^2/9=1
Given the function of the conic section:
[tex]\mleft(y+2\mright)^2/16-\mleft(x-3\mright)^2/9=1[/tex]This conic section is a hyperbola.
Use this form below to determine the values used to find vertices and asymptotes of the hyperbola:
[tex]\frac{(x-h)^2}{a^2}\text{ - }\frac{(y-k)^2}{b^2}\text{ = }1[/tex]Match the values in this hyperbola to those of the standard form.
The variable h represents the x-offset from the origin b, k represents the y-offset from origin a.
We get,
a = 4
b = 3
k = 3
h = -2
A. The first focus of a hyperbola can be found by adding the distance of the center to a focus or c to h.
But first, let's determine the value of c. We will be using the formula below:
[tex]\sqrt[]{a^2+b^2}[/tex]Let's now determine the value of c.
[tex]\sqrt[]{a^2+b^2}\text{ = }\sqrt[]{4^2+3^2}\text{ = }\sqrt[]{16\text{ + 9}}\text{ = }\sqrt[]{25}[/tex][tex]\text{ c = 5}[/tex]Let's now determine the coordinates of the first foci:
[tex]\text{Coordinates of 1st Foci: (}h\text{ + c, k) = (-2 + 5, 3) = 3,3}[/tex]B. The second focus of a hyperbola can be found by subtracting c from h.
[tex]\text{ Coordinates of 2nd Foci: (h - c, k) = (-2 - 5, 3) = -7,3}[/tex]Therefore, the conic section has two focus and their coordinates are 3,3 and -7,3.
In other forms, the foci of the hyperbola is:
[tex]\text{ }(h\text{ }\pm\text{ }\sqrt[]{a^2+b^2},\text{ k) or (-2 }\pm\text{ 5, 3)}[/tex]Therefore, the answer is letter B.
Answer :It's A lol
Step-by-step explanation:
A choir concert platform consists of 6 rows. The number of performers increases by 2 witheach successive row. How many performers are there in all if the back row has 36performers?A 48B 84C 186D 372
In this problem, we have the sequence
inverse sequence
36,34,32,30,28,26
The sum is equal to
S=36+34+32+30+28+26
S=186
The answer is option CIn this problem, we have the sequence
inverse sequence
36,34,32,30,28,26
The sum is equal to
S=36+34+32+30+28+26
S=186
The answer is option CState if the given binomial is a factor of the given polynomial.Question #9
We can use the Factor Theorem to state if the given binomial is a factor of the given polynomial.
The factor theorem states that when f(c)=0 that means the remainder is zero and (x-c) must be a factor of the polynomial.
The given polynomial is:
[tex]k^3+8k^2+6k-12[/tex]Then if (k+2) is a factor of the polynomial, k+2=0, k=-2, f(-2) must be equal to 0.
Let's check:
[tex]\begin{gathered} f(k)=k^3+8k^2+6k-12 \\ f(-2)=(-2)^3+8(-2)^2+6(-2)-12 \\ f(-2)=-8+8\cdot4-12-12 \\ f(-2)=-8+32-24 \\ f(-2)=32-32 \\ f(-2)=0 \end{gathered}[/tex]Thus, (k+2) is a factor of the given polynomial.
The cost of a laptop computer decreased from $600 to $480. By what percentage did the cost of the computer decrease?
Initial value= $600
new value = $ 480
[tex]\begin{gathered} =\frac{600-480}{480}\times100 \\ =\text{ }\frac{120}{480}\times100 \\ =\text{ 25\%} \end{gathered}[/tex]25% decrease is the answer
Write an expression to show how much Gretchen paid for drama,action, and comedy videos if she paid $4 for each at a sale. Evaluate the expressionGretchen’s video purchasesMystery 6Action 3Comedy 5Drama 2Romance 2
Let d the number of drama videos, c the number of comedy videos and a the number of action videos.
If the cost per video (independently of the genre) is $4, then, for the total cost of the videos Gretchen payed, you can write:
total = 4d + 4c + 4a
Now, based on the given table, you have:
d = 2
c = 5
a = 3
By replacing the previous values into the expression for total, and by simplifying, you obtain:
total = 4(2) + 4(5) + 4(3)
total = 8 + 20 + 12
total = 40
Hence, Gretchen payed $40 for the videos
what is 6!3! over 2!5!
Answer:
16
Step-by-step explanation:
6!3!
-------
2!5!
(1 × 2 × 3 × 4 × 5 × 6)(1 × 2 × 3)
--------------------------------------------
(1 × 2)(1 × 2 × 3 × 4 × 5)
(720)(6)
-------------------
(2)(120)
4320
------------ = 18
240
I hope this helps!
I need your help know
Given the following data
Base area of the cone = 6cm
Height of the cone = 9 cm
The volume of a cone is given as
[tex]\begin{gathered} V\text{ = }\frac{1}{3}\cdot\text{ }\pi\cdot r^2\cdot\text{ h} \\ \text{where }\pi\text{ = 3.14},\text{ r = 6cm , and h = 9cm} \\ V\text{ = }\frac{1}{3}\cdot\text{ 3.14 }\cdot6^2\cdot\text{ 9} \\ V\text{ = }\frac{1}{3}\text{ x 3.14 x 36 x 9} \\ V\text{ = }\frac{3.14\text{ x 36 x 9}}{3} \\ V\text{ = }\frac{1017.36}{3} \\ V=339.1cm^3 \end{gathered}[/tex]Graph the line y = 5x – 1, then name the slope and y-intercept by looking at the graph.
Answer:
m = 5
y-intercept = (0, -1)
Step-by-step explanation:
y = mx + b
y = 5x - 1
m = 5
y-intercept = b = (0, -1)
Point 1: (0, -1)
Point 2: (1, 4)
Point 3: (-1, -6)
I hope this helps!
What is the remainder when 5x3 + 2x2 - 7 is divided by x + 9?-93,7503,800-3,490
Explanation
Given the expression
[tex]5x^3+2x^2-7[/tex]The remainder when it is divided by x+9 can be seen below;
[tex]r=5(-9)^3+2(-9)^2-7=-3645+162-7=-3490[/tex]Answer: -3490
At a school on Monday, 3 out of every 4 students were wearing shirts. There were 600 students present in school on Monday. How many of the students were wearing shirts? A. 599, because 600 - (4 - 3) = 599 B. 450, because C. 50, because 600 - (4 x 3) = 50 600 - Student D. 800, because 450 4= Students 3=sludents 4 600 600 800 so
3 out of 4 students mean
3/4th students were wearing shirts.
Total students = 600
So,
3/4th of 600 students were wearing shirt.
Let us calcualte (3/4)th of 600:
[tex]\begin{gathered} \frac{3}{4}\times600 \\ =\frac{3\times600}{4} \\ =\frac{1800}{4} \\ =450 \end{gathered}[/tex]Answer450 students
Inside. Make sure you don’t enter any spaces in your answers. This answer needs to be rounded to the nearest hundredth.
ANSWER
c = 14.14
EXPLANATION
To find the length of side AB, which is the hypotenuse of the right triangle ABC, we have to apply the Pythagorean Theorem,
[tex]AB^2=AC^2+BC^2[/tex]Replace the known values and solve for c,
[tex]c^2=10^2+10^2=100+100=200\Rightarrow c=\sqrt{200}\approx14.14[/tex]Hence, the value of c is 14.14, rounded to the nearest hundredth.
Dave and his brother. Theo, are selling cookies by the pound at the school bake sale Dave sold 14 84 pounds of cookies and Theo sold 21.45 pounds of cookies How many pounds did they sell altogether? A 35 29 OB 36 39 C36 25 0 D. 36 29
For tis problem we have that Dave sold 14.84 pounds of cookies and Theo sold 21.45 pounds of cookies.
If we want to find the total of pounds that they sold together we just need to add the two values and we have:
[tex]14.84+21.45=36.29\text{pounds}[/tex]The reason is because 0.84+0.45=1.29
14+21=35. And finally 35+1.29=36.29
And the best answer for this case would be D. 36.29
Find the solutions to the following quadratic equation negative 3X squared plus 4X plus one equals zero (-3x^2 + 4x + 1 = 0)
Answer:
Explanation:
Given:
[tex]-3x^2+4x+1=0[/tex]To find:
the value of x using the quadratic formula
The quadratic formula is given as:
[tex]$$x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$$[/tex]where a = -3, b = 4, c = 1
[tex]\begin{gathered} x\text{ = }\frac{-4\pm\sqrt{(4)^2-4(-3)(1)}}{2(-3)} \\ \\ x\text{ = }\frac{-4\pm\sqrt{16+12}}{-6} \\ \\ x\text{ = }\frac{-4\pm\sqrt{28}}{-6} \end{gathered}[/tex][tex]undefined[/tex]What value n makes the eauqation n x 3/4 = 3/16
Answer:
N = 1/4
Step-by-step explanation:
Okay, so 1/4 is equal to N.
3/4 x1/4=3/16
What is the sign of mlio Choose 1 answer: Positive Negative Neither positive nor negative the sum is zero.
The sign will be positive.
hi I need on this. $6000 invested at 5.5% interest, compounded annually. how how would i have in 6years?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
principal = $6000
rate (interest) = 5.5%
time = 6 years
Step 02:
compound interest:
n = annually
n = 1
r = 5.5 % = 5.5 / 100 = 0.055
A = amount
[tex]A\text{ = P \lparen1 + r/n\rparen}^{nt}[/tex][tex]A\text{ = 6000 * \lparen1 + }\frac{0.055}{1})\placeholder{⬚}^{1*6}[/tex][tex]A\text{ = 6000 * \lparen1.3877\rparen = 8273.06}[/tex]The answer is:
$8273.06
3.2 Similar FiguresIf ASRT - ACBD, find the value of x.Show all work.Hint: Don't let your eyes deceive you pay attention tothe similarity statement.
Find the ratio of corresponding sides:
SRT to CBD =
70/50 = 1.4
SR / 60 = 1.4
SR = 60 x 1.4
SR = 84
84= 11x-4
Solve for x:
84+4 = 11x
88= 11x
88/11 = x
8=x
3-35. Fisher thinks that any two lines must have a point of intersection. Is he correct? If so, explain how youknow. If not, produce a counterexample. That is, find two lines that do not have a point of intersection and explainhow you know
Any two lines must have a point of intersection, with ONLY ONE exception : when the lines are parallel. That means they have exactly the same inclination or Slope.
As an example of two lines that hasnt point of intersection they are
y = 5x + 16
y = 5x + 11
We know both lines have no point of intersection because
both have the same slope or inclination m. By comparation with slope intercept equation
y = mx + b
then we see both have same inclination, and b is 11 in one line and 16 in the other line. This means both lines are parallel with one line going over the other line, without touching it in any point.