Answer:
4/5
Step-by-step explanation:
Multiplying the first equation by n, we have an expression for m:
m/n = 5
m = 5n
Substituting this into the second equation, we have ...
4n/m = 4n/(5n)
4n/m = 4/5
Find the points on the ellipse
5x² + y² = 5
that are farthest away from the point (1, 0).
9514 1400 393
Answer:
(-0.25, ±√4.6875)
Step-by-step explanation:
The square of the distance from a point on the ellipse to the point (1, 0) is ...
d^2 = (x -1)^2 +y^2
Using the equation of the ellipse to write an expression for y^2, we have ...
d^2 = (x -1)^2 +5 -5x^2
d^2 = -4x^2 -2x +6
The expression on the right is that of a downward-opening parabola with ...
a = -4, b = -2, c = 6
The maximum is located at ...
x = -b/(2a) = -(-2)/(2(-4)) = -1/4
The value of y there is ...
y^2 = 5 -5(-1/4)^2 = 4 11/16
y = √4.6875
The points on the ellipse farthest from (1, 0) are (-0.25, ±√4.6875).
5 23 18 8 4
Order of operations
Answer:
no u
Step-by-step explanation:
Answer:
hmm lets see sorry i cant help i wish i could but its been a while
Step-by-step explanation:
The formula for the volume of a sphere is V = 4/3 pie3 . What is the formula solved for r ?
The formula for the radius (r) of a sphere, given the volume (V), is [tex]r = \sqrt[3]{ \frac{3V} {4\pi} }[/tex].
To solve the formula for the volume of a sphere, [tex]V = \frac 43 \pi r^3[/tex], for r, we'll follow these steps:
1. Begin with the formula for the volume of a sphere: [tex]V = \frac 43 \pi r^3[/tex].
2. Multiply both sides of the equation by (3/4) to isolate π[tex]r^3[/tex]:
[tex]\frac34V = \pi r^3[/tex].
3. Divide both sides of the equation by π to obtain the expression for r^3:
[tex]r^3 = \frac34 \frac V\pi[/tex].
4. To solve for r, take the cube root of both sides of the equation:
[tex]r = \sqrt[3]{ \frac{3V} {4\pi} }[/tex].
Therefore, the formula solved for r is [tex]r = \sqrt[3]{ \frac{3V} {4\pi} }[/tex]. This formula allows you to calculate the radius of a sphere when the volume (V) is given.
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Addison is talking $230 of spending money on four day vacation and would like to budget to spend the same amount each day. How much money should Addison spend each day?
Answer:
She should spend $57.5 each day
Answer: $57.5
Step-by-step explanation:
unit rate of 3 1/4 miles in 1 1/4 hours
Answer:
13/5 mi/hr, or 2 3/5 mi/hr
Step-by-step explanation:
Here we want the rate in "miles per hour."
Obtain this as follows:
3 1/4 miles 13/4 mi
------------------- = --------------- = 13/5 mi/hr, or 2 3/5 mi/hr
1 1/4 hours 5/4
Suppose you have a $1,350 charge on a credit card charging 1.5% monthly interest using the adjustable balance method. The minimum payment due in May is $45. How much will you save in interest charges in June by paying $90 instead?
Paying $90 instead of the minimum payment of $45, you would save $1.35 in interest charges in June
To calculate the interest charges in June, we need to understand how the adjustable balance method works. This method calculates interest based on the average daily balance for the billing cycle.
Step 1: Calculate the average daily balance for May. To do this, we need to know the number of days in May and the balance on each day. Let's assume May has 31 days. Since the balance remains constant at $1,350, the average daily balance for May is $1,350.
Step 2: Calculate the interest charges for May. Multiply the average daily balance by the monthly interest rate. In this case, the interest charges for May would be $1,350 * 0.015 = $20.25.
Step 3: Calculate the interest charges for June. Assuming the balance remains the same at $1,350, the average daily balance for June would also be $1,350.
Step 4: Calculate the interest charges for June with a payment of $90. To do this, we need to subtract the payment from the average daily balance for June. In this case, the adjusted balance would be $1,350 - $90 = $1,260.
Step 5: Multiply the adjusted balance by the monthly interest rate to calculate the interest charges for June. In this case, the interest charges for June would be $1,260 * 0.015 = $18.90.
Step 6: Calculate the savings in interest charges. To find the difference in interest charges, subtract the interest charges for June with the $90 payment from the interest charges for June with the minimum payment. In this case, the savings in interest charges would be $20.25 - $18.90 = $1.35.
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Emily was offered a job after college earning a salary of $35,000. She will get a raise
of $2,000 after each year working for the company. Answer the questions below
regarding the relationship between salary and the number of years working at the
company.
, and the
The independent variable, x, represents the
dependent variable is the
depends on the
because the
A function relating these variables is C(x)
So C(4)
meaning 4
Answer:
Step-by-step explanation:
Salary offered to Emily after college = $35000
Rise in her salary = $2000 every year
Let she works for x years in the company,
Salary rise in her salary = $2000x
Total salary after x years = $(35000 + 2000x)
The independent variable x represents NUMBER OF YEARS and dependent variable is the TOTAL SALARY,because the SALARY depends on the NUMBER OF YEARS WORKED.
A function these variables is C(x) = 35000 + 2000x
So, C(4) = 35000 + 2000(4) = 43000, meaning 4 years later Emily will earn a salary $43000.
graph the line with slope -3/4 passing through the point (2,-1)
Answer:
Step-by-step explanation:
Slope of the line:
[tex]m = \frac{y-y1}{x-x1} \\[/tex]
Given:
slope = -3/4
point (x1,y1) = (2, -1)
Substitute and solve
[tex]m = \frac{y-y1}{x-x1} \\-\frac{3}{4} = \frac{y-(-1))}{x-2} \\-3(x-2) = 4(y+1)\\-3x + 6 = 4y + 4 \\Transpose\\4y = -3x + 6 - 4\\4y = -3x + 2 \\y = -3/4x + 2/4\\y = -3/4x + 1/2\\OR\\4y +3x - 2 = 0[/tex]
1/2 is the y-intercept
(0,1/2)
Since we have 2 points already, we can then graph the line.
(2, -1) and (0, 1/2)
who invented the homework?
Answer:
Step-by-step explanation:
Roberto Nevelis
Roberto Nevelis of Venice, Italy, is often credited with having invented homework in 1095—or 1905, depending on your sources. Upon further inspection, however, he seems to be more of an internet myth than an historical personage.
Answer:
Roberto Nevelis
Step-by-step explanation:
Roberto Nevelis of Venice, Italy, is often credited with having invented homework in 1095—or 1905, depending on your sources. Upon further inspection, however, he seems to be more of an internet myth than an historical personage.
Hope this helps :)
12a = 4 what is a HELP ME PLZ
Answer:
a = 1/3
Step-by-step explanation:
a = 4/12
4/12 simplifies to 1/3
What is (x + 1) − (−2x − 5)
Answer:
11x+6
Step-by-step explanation:
Using FOIL
(x+1)-(-2x-5)-original
F-first=(x+2x)=3x
O-outside=(x+5)=5x
I-inside=(1+2x)=3x
L-last=(1+5)=6
11x+6
A jar can hold 3/4 of a pound of flour. Austin empties 1/2 of a pound of flour into the jar. What fraction of the jar is filled? Enter your answer in numerical form. PLEASE HELP!!!
Answer:
2/4 is filled, you have to turn 1/2 into 2/4 by doing (1x2)/(2x2), tha't how my teacher once told me
Please help!!! Brainliest given!!
1. Which of the following polynomial equations are valid identities?
A. m3 - 1 = (m - 1) (1 + m + m2)
B.(n + 3)2 + 2n = 81 +13
A. Only B
B. Only A
C. Neither A nor B
D. Both A and B
2. Select the polynomial that has (x-3) as a factor.
A. p(x)=x^4-2x^3-25
B. p(x)=x^3+3x^2-2x-6
C. p(x)=x^3-2x^2-4x+3
D. p(x)=x^4-20x-23
3. Find the remainder when x^4-2x^3+x^2-5x+3 is divided by x+1
A. 3
B. 8
C. 12
D. -2
Answer:
1: A
2: C
3: I have no clue (Sorry)
Step-by-step explanation:
Answer:
1. A2. C3. CStep-by-step explanation:
1. ................................................
A. m^3 - 1 = (m - 1)( 1 + m + m^2)
When we open parenthesis we get both sides equal. YESB. (n + 3)^2 + 2n = 81 + 13
Left side has variables, right side not. NO2. Polynomial that has (x - 3) as a factor
A. p(x)=x^4-2x^3-25
x^4 - 3x^3 + x^3 - 27 + 2x^3(x-3) + (x - 3)(x^2 + 3x + 9) + 2It can' be factored without remainder. NOB. p(x)=x^3+3x^2-2x-6
x^2(x+3) -2(x+3).It has (x+3) as a factor. NOC. p(x)=x^3-2x^2-4x+3
x^3 - 3x^2 + x^2 - 3x - x +3 =x^2(x - 3) + x(x - 3) - (x - 3)It has a (x - 3) as a factor. YESD. p(x)=x^4-20x-23
x^4 - 27 x + 7 x - 23 =x(x-3)(x+3x + 9) + 7( x - 3) - 2It can' be factored without remainder. NO3. x^4-2x^3+x^2-5x+3 is divided by x+1, find remainder
x^4 + x^3 - 3x^3 - 3x^2 + 4x^2 + 4x - 9x - 9 + 12=x^3 (x + 1) - x^2(x + 1) + 4x(x + 1) - 9(x + 1) + 12The remainder is 12. Option CWrite the following comparison as a ratio reduced to lowest terms.
5 nickels to 40 dimes
A ratio shows us the number of times a number contains another number. The given ratio of nickles to dimes in the reduced form can be written as 1/8.
What is a Ratio?A ratio expresses the number of times one number contains another. For example, if a dish of the fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the lemon to orange ratio is 6:8, while the orange to total fruit ratio is 8:14.
The given ratio of nickles to dimes in the reduced form can be written as shown below.
Nickels / Dimes = 5 /40
Divide both the numerator and the denominator by 5,
Nickels / Dimes = 1/8
Hence, The given ratio of nickles to dimes in the reduced form can be written as 1/8.
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Select all the correct answers.
Which two inequalities can be used to find the solution to this absolute value inequality?
3+2|x-11 <9
2(x - 1) <-3
x-1 <9
X-1 >-9
-2(x - 1) > 3
x-1-3
X-1 <3
Answer: x-1 > -3 and x-1 < 3
Step-by-step explanation:
If you work out the equation, you’ll end up getting -2 and 4, so when you work out the two equations that are the answers you get -2 and 4.
The two inequalities are : x-1 > -3 and x-1 < 3
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
3+2|x-11| <9
On further solving
2|x-11| < 9-3
2|x-11| < 6
x-11< 3
x<14
According to question the inequalities can be used to find the solution to this absolute value inequality.
So, x-1 > -3 and x-1 < 3 ( when negative sign multiply the sign of inequality changes)
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A person leaves home and walks 4 miles west, then 5 miles southwest.
How far from home is she?
miles
In what direction must she walk to head directly home?
degrees North of East
The person is approximately 8.43 miles from home, and they need to walk in the direction of approximately 26.6 degrees east of north to head directly home.
To determine the distance from home, we can use the concept of vector addition. The person walks 4 miles west, which can be represented as a vector (-4, 0) in a coordinate plane. Then, they walk 5 miles southwest, which can be represented as a vector (-3.54, -3.54) since southwest is a combination of west and south. Adding these two vectors together gives us (-7.54, -3.54).
To find the magnitude or distance from home, we use the Pythagorean theorem. The distance is given by sqrt((-7.54)^2 + (-3.54)^2) = 8.43 miles (approximately).
To determine the direction to head directly home, we need to find the angle between the vector (-7.54, -3.54) and the positive x-axis. We can use trigonometry to find this angle. The tangent of the angle is given by the ratio of the y-coordinate to the x-coordinate, which is -3.54 / -7.54. Taking the inverse tangent of this value gives us approximately 26.6 degrees.
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Which expression represents h(x)?
(f. g)(x)
(g + f)(x)
(f- g)(x)
(g - f)(x)
Answer: (f×g)(x)
Step-by-step explanation:
12×-6= -72
3×0= 0
-6×6= -36
So h(x) is equal to (f×g)(x)
An aquarium holds 11.35 cubic feet of water, and is 2.6 feet long and 1.1 feet wide. What is its depth? Round your answer to the nearest whole number.
The depth is
feet.
The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).
To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,
which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).
Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.
Substituting these values into the formula for volume,
we get:11.35 = 2.6 × 1.1 × h
Simplifying this expression:
11.35 = 2.86h
Dividing both sides by 2.6 × 1.1,
we get:h ≈ 3.64 feet (rounded to two decimal places)
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Use the Law of Sines or the Law of Cosines to solve each triangle.
(DRAW TRIANGLES ON YOUR WORKSHEET - IT WILL HELP!)
Round all angle measures to the nearest tenth of a degrees and side lengths to the nearest tenth.
The law of sines and the law of cosines are used to solve triangles. These formulas aid in finding the missing angle or side of a triangle based on the known side lengths and angle measures.A triangle has three sides and three angles. If we know all three sides and all three angles, we can find everything there is to know about that triangle. Unfortunately, this is rare.
We can use the law of sines or the law of cosines to solve a triangle if we know some, but not all, of the side lengths and angle measures.The law of sines, abbreviated L.S., is a formula that relates the side lengths and angles of a triangle. The L.S. formula is as follows:
a/sin A = b/sin B = c/sin C. In this formula, a, b, and c are the lengths of the sides of a triangle, while A, B, and C are the angles opposite those sides. Any two ratios in this formula can be utilized to solve for the third.The law of cosines, abbreviated L.C., is a formula that relates the side lengths and angles of a triangle. The L.C. formula is as follows: a^2 = b^2 + c^2 - 2bc cos A (similarly for the other sides).
In this formula, a, b, and c are the lengths of the sides of a triangle, while A, B, and C are the angles opposite those sides. This formula may be used to solve for one of the missing side lengths or one of the missing angles of the triangle if we know the length of two sides and the angle between them.
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Solve for x.
n(17+x) = 34x-r
Answer:
The value of X will be (17N + r)/ (34-N).
N(17 + x) = 34x -r
17N + Nx = 34x - r
Collect the x together.
17N/N + 34x -r
Therefore the answer will be
(17N +r) / (34-N).
Step-by-step explanation:
I hope i helped you : )
Solve the formula for converting temperature from degrees Celsius to
degrees Fahrenheit for C.
F = 9/5C +32
O A. C = 9/5(F +32)
O B. C = 9/5F + 32
O C. C = 5/9F-32
O D. C = 5/9(F-32)
Answer:
C. C=9/5F+32
Step-by-step explanation:
divided by 5 then multiply by 9 then add 32
Sasha is dividing 1/4 pound of peanuts into 5 plastic bags. What fraction of a pound of peanuts will be in each plastic bag?
Answer:
1/20
Step-by-step explanation:
(1/4)/5= (1/4)/(5/1)
You cross multiply and you get 1/20
The grocery store is having a sale on cereal. A box of cereal normally costs $4.56. Today, it is on sale for 25% off. If you buy 4 boxes of cereal, how much money will you have to pay at the register? There is no sales tax on the cereal.
Answer:
13.68
Step-by-step explanation:
if you do 4.56*4 you get 18.24 and 18.24 minus 25 percents is 13.68
The model represents an equation.
х
What is the solution for this equation?
Answer:
dividend
Step-by-step explanation:
783389$98_;8282(4((_
E = IR to solve for R
Answer:
R = E/I
Step-by-step explanation:
Step 1: Write equation
E = IR
Step 2: Divide both sides by I
E/I = R
Step 3: Rewrite
R = E/I
please help it's due at midnight tonight.
Answer:
See attached
Step-by-step explanation:
The first one
-3 ≤ x < 6x = [-3, 6)The second one
-3x > 24 + 6-3x > 30x < -10x = ( -oo, -10)Put the following equation of a line into slope intercept form, simplifying all fractions 4x+3y=-3
Answer:
[tex]y=-\frac 4 3 x+1[/tex]
Step-by-step explanation:
Slope intercept form comes in this format: y= mx+b.
Let's convert it.
[tex]4x+3y=3\\3y=-4x+3\\y=-\frac 4 3 x+1[/tex]
In conclusion the answer is y = -4/3x+1
Alex purchased a phone card for $30. He has used t minutes of access time
at 10 cents per minute. To write an algebraic expression to represent how
many dollars Alex has left on his card, fill in the boxes
Answer:
30- 0.1t
Hope it helps!
Geometric definition of circle: a circle is the set of all points (x,y) in a plane (________) that are equidistant (_________) from a fixed point called the focus which also is the center of the circle
A circle is defined geometrically as the set of all points (x, y) in a two-dimensional plane that are equidistant from a fixed point called the center of the circle.
In other words, for any point (x, y) on the circle, the distance between that point and the center is constant.
To elaborate, let's consider a circle with center (h, k) and radius r. Any point (x, y) lying on the circle satisfies the equation of distance as follows:
√((x - h)² + (y - k)²) = r
This equation represents the Pythagorean theorem applied to the right triangle formed by the distance between the point (x, y) and the center (h, k), with the hypotenuse being the radius r. Since all points on the circle have the same distance from the center, this equation holds true for any point on the circle.
The constant distance, or radius, is the key characteristic of a circle. It determines the size of the circle and is defined as the distance from the center to any point on the circumference. The radius is typically denoted by the lowercase letter "r" and can be used to calculate various properties of the circle, such as its area and circumference.
In summary, a circle is the set of all points in a plane that are equidistant from a fixed point called the center. The distance between any point on the circle and the center is constant, and this distance is defined as the radius of the circle. The geometric definition provides a clear understanding of the fundamental properties and characteristics of a circle.
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Each morning librarians place 560 books on a book shelf in the school library. Each student that visits library that day takes exactly 3 books from this shelf. Let s be the number of students which visit library on a particular day. Let b be the number of books left on the shelf at the end of that day.
a.How does the number of books left on the shelf depend on number of students visiting library? Find formula for the function b(s).
b.There are 150 students studying in this school. Use this information to find the domain of the function b(s).
Answer:
A. The function is -3s+560 Step-by-step explanation:
