Answer:
Step-by-step explanation:
Rewrite this equation in standard form:
x² - 2x + 1 - 1 + y² + 6y + 9 = 0, or
(x - 1)² + (y + 3)² = 1
Compare this to:
(x + h)² + (y + 3)² = r²
We see here that (h, k), the center of the circle, is (1, -3), and the radius of the circle is 1.
Answer:
the center is at (1, -3)
Step-by-step explanation:
The center-radius form of the circle equation is in the format (x – h)2 + (y – k)2 = r2, with the center being at the point (h, k) and the radius being "r".
So we need to write the ecuation x^2 + y^2 - 2x + 6y + 9 = 0 in the format above.
So we have:
x^2 + y^2 - 2x + 6y + 9 = (x^2 -2x + 1) + (y^2 + 6y + 9) - 1
(x^2 -2x + 1) + (y^2 + 6y + 9) - 1 = (x-1)^2 + (y+3)^2 - 1
So now, looking at the equation: (x-1)^2 + (y+3)^2 = 1
We know that h=1 and k=-3. So the center is at (1, -3)
Please help me with this
Answer:
8 ft
Step-by-step explanation:
The area (A) of a triangle = [tex]\frac{1}{2}[/tex] bh
where b is the base and h the perpendicular height
Using b = 20 and h = 12, then
A = 0.5 × 20 × 12 = 120 ft²
Using b = 30 and perpendicular height = h, then
0.5 × 30 × h = 120
15h = 120 ( divide both sides by 15
h = 8
According to lots of Pythagorean theorem,
h=7
I really don’t want to show my work because it took a while to solve this lol but if you want me to show my work just comment
Find the Area of the circle... PLEASE HELP
Answer: Is it 169? i think that wright maybe.
Answer: 530.92916
Step-by-step explanation:
A=πr2=π·132≈530.92916
If a(x) = 3x + 1 and 5(x)=1/x-4, what is the domain of (ba)(x)?
For this case we have the following fusions:
[tex]a (x) = 3x + 1\\b (x) = \frac {1} {x} -4[/tex]
We must find [tex](a * b) (x):[/tex]
By definition:
[tex](a * b) (x) = a (x) * b (x)\\(a * b) (x) = (3x + 1) * (\frac {1} {x} -4)\\(a * b) (x) = \frac {3x} {x} -12x + \frac {1} {x} -4\\(a * b) (x) = 3-12x + \frac {1} {x} -4\\(a * b) (x) = - 12x + \frac {1} {x} -1[/tex]
The domain of the function will be given by all the values for which the function is defined, that is, all real numbers except zero.
Answer:
(-∞, 0) U (0,∞)
in the triangle determine the value of c
Answer: The answer is A: 8.6
Step-by-step explanation: In this case, the side you're trying to figure out is the opposite and the side measurement given is the hypotenuse.
This means that out of the sin, cos, and tan we will be using sin.
Sin(Ф)= opposite/hypotenuse
Plug in the numbers you know: Sin(35)=x/15
Take the 15 to the other side to get x by itself
Then plug into your calculator 15Sin(35)=x
This gives you 8.6
Please help will give brainliest thank you.
Two events are dependent if the outcome of the first event affects the outcome of the second.
The last answer is the correct one.
Convert 90 degrees to radians.
π radians
2π/3radians
π/3 radians
π/2 radians
The answer is the last one . =
π
2
Please help me out!!!
Answer:
y = 30.
Step-by-step explanation:
As they are similar corresponding sides are in the same ratio.
So (y + 20) / 20 = 100/40
(y + 20) / 20 = 5/2
2(y + 20) = 5*20
y + 20 = 50
y = 30 (answer).
A plywood template for a kitchen breakfast bar is cut from a circle.
Answer:
25
Step-by-step explanation:
The radius of the circle, which is the perpendicular bisector of a 48-inch diameter kitchen breakfast bar template, is 30 inches. The correct option is C).
Let's break down the information given in the problem:
PQ is the perpendicular bisector of VW, and Q is the midpoint of VW. This means that PQ passes through the center of the circle.
The length of PQ (perpendicular bisector) is 18 inches.
VW is 48 inches in diameter, which means its radius is half of that, i.e., 48 inches / 2 = 24 inches.
Since PQ is the radius of the circle, and it is also the perpendicular bisector of VW, it divides VW into two equal parts, each measuring 24 inches (as VW has a diameter of 48 inches, and Q is the midpoint).
Now, we have a right-angled triangle, with PQ as the hypotenuse and two legs measuring 18 inches and 24 inches. We can use the Pythagorean theorem to find the length of PQ (the radius of the circle):
PQ² = 18² + 24²
PQ² = 324 + 576
PQ² = 900
PQ = √900
PQ = 30 inches
So, the radius of the circle is 30 inches.
The correct answer is option c) 30 inches.
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WILL GIVE BRAINLIEST
Answer:
(x,y) --> (x, y-5)
Step-by-step explanation:
the y-intercept of f(x) = (0,2)
the y-intercept of g(x) = (0, -3)
-3 - 2 = -5
Find the value of the csc 40° using your calculator.
(A)1.342
(B)0.745
(C)1.556
(D)0.643
The answer is:
C. 1.556.
[tex]csc(40\°)}=1.556[/tex]
Why?To solve the problem using our calculator we need to set it to "Degree" mode in order to avoid miscalculations.
Also, we need to remember that the cosecant (csc) is the inverse function of the sine, so:
[tex]csc(40\°)=\frac{1}{sin(40\°)} =\frac{1}{0.6427}=1.556[/tex]
Hence, the answer is C. 1.556.
Have a nice day!
PLEASE HELP!!:) need help with this question thanks
Answer:
30%
Step-by-step explanation:
24 of (40 +24 +16) = 3/10 of the turkey sandwiches were made with wheat bread. As a percentage, that is ...
3/10 = 30/100 = 30%
Identify the volume of the hemisphere in terms of π. HELP PLEASE!!
Answer:
its D
Step-by-step explanation:
The number 0.9967 represents the area under the standard normal curve below a particular z-score.
What is the z-score?
Enter your answer, as a decimal to the nearest hundredth, in the box.
Answer:
2.72
Step-by-step explanation:
Here, we use a z-score table or calculator to look up the probability and find the corresponding z-score.
P(z < ?) = 0.9967 at z = 2.72.
Using the normal distribution principle, the Zscore which corresponds to the area under the normal curve at P(Z < z) = 0.9967 is 2.716
To obtain the Zscore in this scenario, which is the number of standard deviations from the mean value for a given score ; we make use of Zscore calculator or a normal distribution table ;
Using a normal distribution table;
Zscore at P(Z < z) = 0.9967 is 2.716Therefore, the Zscore value is 2.716
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June has 42 sports books, 85 mystery books, and 69 nature books. She arranged her books equally on 7 shelves. How many books are on each shelf.
Answer:
28
Step-by-step explanation:
Add 42, 85, and 69 together and you get 196 but you need to divide that by 7 and you get 28
Answer:
28
Step-by-step explanation:
We are given that
June has sports books=42
June has mystery books=85
June has nature books=69
Total number of shelves=7
We have to find the number of books are on each shelf.
Total number of books=42+85+69=196
To find the number of books on each shelf we will divide the total number of books by 7.
Number of books on each shelf=[tex]\frac{196}{7}[/tex]
Number of books on each shelf=28
Hence, number of books on each shelf=28
If you multiply a number by five and then subtract negative ten, the difference is negative thirty. What is the number?
Answer:
-8
Step-by-step explanation:
Let n represent the number. The stated relationship is ...
5n -(-10) = -30
5n = -40 . . . . . . . add -10
n = -8
The number is -8.
Final answer:
To solve the equation given in the student's question, convert the operation of subtracting a negative number into addition, subtract 10 from both sides to isolate the term with x, and then divide by 5 to find that the number in question is -8.
Explanation:
The student's question is a linear algebra problem, which can be turned into a simple equation to find the unknown number.
According to the question, we multiply a number by five and then subtract a negative ten to get a difference of negative thirty.
Mathematically, this can be expressed as the equation 5x - (-10) = -30, and we can solve for x. First, we should simplify the equation by turning the subtraction of a negative number into an addition. This makes our equation 5x + 10 = -30.
To find the value of x, we then subtract 10 from both sides of the equation, which gives us 5x = -40.
Finally, we divide both sides by 5 to solve for x, leading us to an answer of x = -8.
Jason and Beth are married and don’t have any kids yet. They are out of debt except for their house, and they have a full emergency fund. But Beth’s car has sputtered its last breath. Fortunately, she’s found a new one for hundreds less than invoice. The payments will be less than a fourth of their combined take- home pay. This fits Dave’s formula, and the payments can be squeezed into their budget. She’ll take $2,000 out of their emergency fund for the down payment. Jason thinks it’s a really bad idea. Why?
Final answer:
Jason thinks it's a bad idea to use the emergency fund for a car down payment as it should be reserved for unforeseen financial emergencies, not planned expenses like a vehicle purchase.
Explanation:
Jason may consider it a bad idea for Beth to use the emergency fund for a down payment on a car because the emergency fund is supposed to be a safety net for unforeseen and critical financial needs, such as sudden medical expenses, job loss, or urgent home repairs.
Depleting the emergency fund for a car purchase, despite the fact that car payments are affordable, puts them at risk should multiple unplanned expenses arise simultaneously.
Financial advisers often recommend keeping 3-6 months of expenses saved for emergencies to maintain financial security. Therefore, it might be better to save up for the down payment separately or consider a less expensive car.
Final answer:
Jason may be concerned about using the emergency fund for a car downpayment since emergency funds are meant for unforeseen and urgent financial needs. Adding new debt could make them vulnerable to financial strain.
Explanation:
The concern Jason may have with Beth taking $2,000 out of their emergency fund for a down payment on a new car is that the emergency fund should be reserved for unforeseen circumstances, such as medical expenses, unexpected home repairs, or job loss. Using it for a car down payment, even if it seems manageable within their budget, could leave them vulnerable if a real emergency arises. Additionally, even though the car payments fit within Dave Ramsey's guidelines of being less than a quarter of their take-home pay, it introduces new debt—which they have worked hard to eliminate, except for their mortgage—and could potentially add financial strain if their income situation changes.
Prove the converse of the Pythagorean theorem using similar triangles. The converse of the Pythagorean theorem states that when the sum of the squares of the links of the legs of the triangle equals the shared length of the hypotenuse, the triangle is a right triangle. Be sure to create and name the appropriate geometric figures. HELPPP
Answer:
Step-by-step explanation:By AA similarity postulate
△ADB∼△ABC∼△BDC
therefore the sides of the triangles are proportional, in particular
ADAB=ABAC ACBC=BCDC
By algebra we have the following equations
AD⋅AC=AB⋅ABAC⋅DC=BC⋅BC
this is the same as
AD⋅AC=AB2AC⋅DC=BC2
"Equals added to equals are equal" allows us to add the equations
AD⋅AC+AC⋅DC=AB2+BC2
By distributive property
AC(AD+DC)=AB2+BC2
but by construction AD+DC=AC.
Substituting we have
AC⋅AC=AB2+BC2
this is equivalent to
AB2+BC2=AC2
which is what we wanted to prove
The Pythagorean theorem uses similar triangles, This is equivalent to AB^2+BC^2=AC^2.
We have given that,
the converse of the Pythagorean theorem using similar triangles.
The converse of the Pythagorean theorem states that when the sum of the squares of the links of the legs of the triangle equals the shared length of the hypotenuse, the triangle is a right triangle.
What is the Pythagorean theorem?
[tex]hypotenuse ^2=side^2+side^2[/tex]
By AA similarity postulate
△ADB∼△ABC∼△BDC
Therefore the sides of the triangles are proportional, in particular
ADAB=ABAC ACBC=BCDC
By algebra, we have the following equations
AD⋅AC=AB⋅ABAC⋅DC=BC⋅BC
This is the same as
AD⋅AC=AB^2AC⋅DC=BC^2
Equals added to equals are equal allows us to add the equations
AD⋅AC+AC⋅DC=AB^2+BC^2
By distributive property
AC(AD+DC)=AB^2+BC^2
but by construction AD+DC=AC.
Substituting we have
AC⋅AC=AB^2+BC^2
This is equivalent to
AB^2+BC^2=AC^2
Hence the proof.
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The Flat Rock auto assembly plant in Detroit, Michigan, produces three different makes of automobiles. In two years, the plant constructed a total of 390,000 cars. If 90,000 more cars were made in the first year than in the second year, how many cars were made in each year?
a. first year: 90,000
second year: 180,000
b. first year: 300,000
second year: 90,000
c. first year: 240,000
second year: 150,000
d. first year: 180,000
second year: 90,000
Answer:
c. first year: 240,000
second year: 150,000
Step-by-step explanation:
We let the number of cars made in the second year be X. Consequently, the number of cars made in the first year would be X+90000 since we are told that 90,000 more cars were made in the first year than in the second year. Furthermore, we are also told that the total number of cars constructed in these two years is 390,000, implying that;
X+X+90000=390000
2X+90000=390000
2X=390000-90000
2X=300000
X=150000; number of cars made in second year
The number made in the first year is thus;
150000+90000 = 240000
Answer:
Option c is correct
So, the cars made in 1st year = x = 240,000
and the cars made in 2nd year = 150,000
Step-by-step explanation:
in this question we have to find the number of cars made in each year by The Flat Rock auto assembly plant.
Given:
the plant constructed a total of 390,000 cars and 90,000 more cars were made in the first year than in the second year
Let cars made in 1st year = x
and cars made in 2nd year = y
then the plant constructed a total of 390,000 will be :
x+ y = 390,000 (i)
and
90,000 more cars were made in the first year than in the second year can be written as:
x=90,000 +y (ii)
Solving equation (i) and (ii) we can find the values of x and y
Putting value of x from eq (ii) into eq(i)
(90,000 + y) + y = 390,000
90,000 +y +y =390,000
2y = 390,000 - 90,000
2y= 300,000
y= 150,000
Putting value of y in equation (ii) we can find the value of x
x= 90,000 + y
x= 90,000 + 150,000
x= 240,000
So, the cars made in 1st year = x = 240,000
and the cars made in 2nd year = 150,000.
Joe ran 3 miles yesterday and wanted to run at least 12 miles this week. Write an inequality that can be used to determine the additional number of days joe must run this week if each run is 3 miles. Then solve the inequality .
Answer:
if you take into consideration the run from yesterday,
Joe needs to run at least three more days
y > = 3
if you don't take into consideration the 3 mile run from yesterday,
The answer is
He needs to run 4 or more days toachieve his goal
y > = 4
Step-by-step explanation:
12 miles as a minimum
that means
let x be the total amount of miles ran
x > = 12
Let y be the number of days in which Joe runs
3*y > = 12
y > = 4
Joe needs to run for at least 3 more days to meet his goal of running at least 12 miles this week, considering that each run is 3 miles.
We can set up an inequality. Joe has already run 3 miles, so we need to find out how many more miles he needs to run. If Joe runs 3 miles each day, the inequality representing the situation is 3d + 3 \\geq 12, where d is the number of additional days Joe must run.
We can solve the inequality as follows:
Subtract 3 from both sides of the inequality: 3d \\geq 9.Divide both sides by 3: d \\geq 3.This means Joe needs to run for at least 3 more days to meet his goal of 12 miles.
The quotient of three divided by the sum of two and four
The sum is the answer to an addition problem. 2+4=6. so, 3÷6=0.5
The quotient of three divided by the sum of two and four will be 0.5.
What is a number system?The number system is a way to represent or express numbers.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
As per the given,
Three divided by the sum of two and four
3/(2 + 4) = 3/6 = 0.5
Hence "The quotient of three divided by the sum of two and four will be 0.5".
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The function [tex]f(x)=3x^3+x^2+2x[/tex] rises as x grows very large.
A. True
B. False
Answer:
A. True
Step-by-step explanation:
The given function is;
[tex]f(x)=3x^3+x^2+2x[/tex]
The leading coefficient of this polynomial function is positive.
The degree of the polynomial is odd.
This implies that, the function will rise on the left and keep rising on the right.
Hence, the end behavior of the function tells us that, the function rises as x-values grow very large.
The correct option is True
Which description means the same as the limit expression? (Image attached)
A. The graph falls on the left side.
B. The graph rises on the left side.
C. The graph falls on the right side.
D. The graph rises on the right side.
Answer:
B. The graph rises on the left side.
Step-by-step explanation:
The limit provided on the image is interpreted as; The limit of the function f(x) as x approaches negative infinity is infinity.
X is approaching negative infinity, this means that along the x-axis we are moving towards the left where the values of x become increasingly negative.
On the other hand, f(x) is approaching positive infinity, meaning that along the y-axis we are moving upwards where the values of y become increasingly positive.
This typically implies that as we move towards the left the graph of f(x) is moving upwards or basically the graph rises on the left side.
Answer:
b. the graph rises on the left side
Given the ordered pair P(1, -3), determine the requested secant, cosecant, or cotangent of angle ?. Cot ? = _____
[tex]\bf P(\stackrel{x}{1},\stackrel{y}{-3})\qquad \qquad cot(\theta )=\cfrac{\stackrel{\stackrel{adjacent}{x}}{1}}{\stackrel{\stackrel{opposite}{y}}{-3}}[/tex]
The value of Cotangent or cot is: [tex]cot \;\theta= \frac{1}{-3}[/tex]
What are Trigonometric ratios?Trigonometric ratios are the ratios of the length of sides of a triangle.
In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent.
Given ordered pair P(1, -3).
As we know that Cotangent is ratio of base : perpendicular i.e.,
adjacent of x: opposite y
So, [tex]cot \;\theta= \frac{1}{-3}[/tex]
Now, Hypotenuse = [tex]\sqrt{base^{2}+perpendicular^{2} }[/tex]
= [tex]\sqrt{1^{2} + (-3)^{2}} =\sqrt{10}[/tex]
and,
[tex]sec\;\theta= \frac{\sqrt{10} }{1} \\cosec\;\theta =\frac{\sqrt{10} }{(-3)}[/tex]
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Which of the following is csc(-166°) equal to?
csc(14°)
-csc(14°)
-csc(-14°)
csc(166°)
Answer:
-csc(14°)
Step-by-step explanation:
The given trigonometric expression is csc(-166°)
-166° is in the third quadrant.
It makes an angle of 14° with the x-axis.
Hence the principal angle for -166° is 14°
In the third quadrant the cosecant function is negative.
This implies that;
csc(-166°) =-csc(14°)
The correct choice is the second option.
Decima is a spanish song form that is a style of poetry. how many lines does it have?
The spanish song Decima has ten lines
Final answer:
A decima is a Spanish form of poetry that consists of ten lines per stanza, with a fixed rhyme pattern of ABBAACCDDC, representing a distinct structure from other forms like sonnets or haikus.
Explanation:
The decima is a form of Spanish poetry. Unlike a sonnet, which typically comprises fourteen lines and may follow various rhyme schemes such as the Shakespearian or Petrarchan forms, the decima is characterized by its ten-line stanzas. These stanzas adhere to a specific rhyme pattern and are traditionally written in eight-syllable lines. Each line in a decima ends with a rhyme following the pattern ABBAACCDDC. The form is quite popular in Spanish literature and folk music, and it is distinct in its total line count from other forms like the sonnet, sestina, and haiku.
What is the 6th value in the sequence with the explicit formula
an= −2n−14?
Answer:
a6 = -26
Step-by-step explanation:
Fill in n=6 and do the arithmetic.
a6 = -2·6 -14 = -12-14 = -26
Solution:
Given, Tn = -2n - 14
To Find : What is the 6th value in the sequence
Solution: Simply Substitute the value of n as 6 .
Tn = -2n-14
Tn = -2(6) -14
Tn = -12 - 14
Tn = -14 - 12
Tn = -26
Therefore -10 is the 6th value in the sequence.
Charles went to a restaurant for dinner and paid a tip of 15% on the total bill amount. He then had an ice cream that cost $13 less than the total restaurant bill excluding the tip.
If he spent $43 in all, how much was the total restaurant bill excluding the tip?
A.
$13.95
B.
$26.05
C.
$48.69
D.
$24.89
Answer:
B. $26.05
Step-by-step explanation:
Since this was a multiple choice question, I used process of elimination. I got rid of A because $13.95 - the ice cream ($13) would be no where near $43. For B, i did ($26.05) + ($26.05 - $13) which equals $39.10 and then i did ($39.10 + ($26.06 x 0.15) and that gave me $43 in all.
All the students in the sixth grade either purchased their lunch or brought their lunch from home on Monday 24% of the students purchased their lunch 190 students brought their lunch from home how many students ante in the sixth grade?
I believe it is 60 but I’m not sure
To rent a carpet cleaner at the hardware store, there is a set fee and an hourly rate. The rental cost, c, can be determined using this equation
when the carpet cleaner is rented for h hours
c = 25 + 3h
Which of these is the hourly rate?
A.3
B.3h
C.25
D.25h
3h
The set cost is 25, because c=25 when h=0. So, this leaves 3h as the hourly rate.
The hourly rate of the carpet cleaning is specified correctly by: Option A: 3
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
c = rental cost of a carpet cleaner
h = number of hours the carpet cleaner is rented.
c = 25 + 3h can be written as:
c = 25 + (3+3+3+...+3) (h times)
That shows that 3 is added h times, which is the number of hours, so for each 1 of h hours, there is one 3 added in the final rental cost. (assuming nothing complex is going to happen)
That shows that the hourly rate is 3.
Thus, the hourly rate of the carpet cleaning is specified correctly by: Option A: 3
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Find a function for the graph below.
Answer:
C
Step-by-step explanation:
From the graph you can see that y changes from -2 to 2, so the range of the function is [tex][-2,2].[/tex]
Since the range of the functions [tex]y=\cos x[/tex] and [tex]y=\sin x[/tex] is [tex][-1,1][/tex] and the range of the functions [tex]y=k\cos x[/tex] and [tex]y=k\sin x[/tex] is [tex][-k,k],[/tex] we can state that the correct option is C: [tex]f(t)=-2\cos 3t.[/tex]
Check the value at t=0:
[tex]f(0)=-2\cos 3\cdot 0=-2\cos 0=-2.[/tex]