The quadratic function will be x²+ 2x,Carolina will need to have at least 272 square feet available in her yard.
What is quadratic function?A quadratic function is a polynomial function of degree two, which means it is a function that can be expressed as an equation with the second-degree degree of the highest exponent of the unknown variable. It is typically expressed as ax² + bx + c, where a, b and c are constants, and x is an unknown variable. Quadratic functions can be used to model many real-world situations, such as the height of a projectile in motion or the area of a circle.
a. The area of the pool and the deck can be represented by a quadratic function, A = f(x) = x² + 2x, where x is the width of the pool in feet.
b. For the 16-ft wide pool, the area of the pool and the deck will be A = f(16) = 16² + 2(16) = 272 ft². Therefore, Carolina will need to have at least 272 square feet available in her yard.
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1. A young man rents an apartment for $850 / month. His
sister buys a house with a $20,000 down payment and
monthly mortgage payments of $1,150. Determine who spends
more over the 30-year period that her mortgage lasts,
assuming that both living situations remain the same. Who is in
a better position as far as having a financial asset?
a) The sister spends more (making total payments of $414,000) over the 30-year period than the young man, who spends $306,000.
b) Assuming both living situations are the same, the sister is in a better position as far as having a financial asset is concerned.
How the numbers are determined:The numbers are determined using the mathematical operations of multiplication and subtraction.
The monthly rent for an apartment = $850
The total payments for 30 years = $306,000 (30 x 12 x $850)
Sister's Payment for a Mortgaged House:
Down payment = $20,000
Monthly mortgage payments = $1,150
The total payments for 30 years = $414,000 ($1,150 x 360)
The difference in total payments = $108,000 ($414,000 - $306,000)
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What are like terms examples?
Step-by-step explanation:
Examples of like terms in math are x, 4x, -2x, and 7x. These are like terms because they all contain the same variable, x. The terms 8y2, y2, and -2y2 are like terms as well. These all contain the same variable, y, raised to the second power.
Plsss help
Find the exact are of the shaded region. Point I marks the center of the circle.
The area of the shaded region that is the segment of the circle is equal to 4.6 ft² to the nearest tenth.
How to calculate the area of the circle segmentTo calculate the area of a segment of a circle, you need to know the radius of the circle, the central angle of the segment (in radians or degrees), and possibly the height of the segment (the distance from the chord of the segment to the center of the circle).
The formula for the area of a segment of a circle is:
A = θ/360° × πr² - 1/2 × r² × sinθ
where A is the area of the segment, r is the radius of the circle, and θ is the central angle of the segment in degrees.
From the question;
the central angle = 90°
radius r = 4ft
Area of the segment = 90°/360° × π4² - 1/2 × 4² × sin90°
Area of the segment = 1/4 × π × 4 × 4 - 1/2 × 4 × 4 × 1 {sin90° = 1}
Area of the segment = 4π × 8
Area of the segment = 4.5714
Therefore, the exact area of the shaded region that is the segment of the circle is equal to 4.6 ft² to the nearest tenth
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If the hypotenuse of a right triangle is 35 cm and the radius of the inscribed circle is 4 cm, find the area of the triangle.
Answer: Let the legs of the right triangle be a and b. We know that the radius of the inscribed circle is 4 cm, which means that the inradius is also 4 cm. The inradius is given by:
r = (a + b - c)/2
where c is the hypotenuse, so we can substitute the given values to get:
4 = (a + b - 35)/2
Multiplying both sides by 2, we get:
8 = a + b - 35
Adding 35 to both sides, we get:
a + b = 43
We also know that the area of the triangle is given by:
A = (ab)/2
where a and b are the legs of the triangle. We can use the Pythagorean theorem to relate the legs to the hypotenuse:
a^2 + b^2 = c^2
Substituting the given value for the hypotenuse, we get:
a^2 + b^2 = 35^2
Simplifying, we get:
a^2 + b^2 = 1225
Now we can use the equation for the sum of the legs to solve for one of the legs in terms of the other:
a + b = 43
b = 43 - a
Substituting this expression for b into the equation for the area, we get:
A = (a(43 - a))/2
Simplifying, we get:
A = (43a - a^2)/2
To find the maximum value of the area, we can take the derivative of A with respect to a and set it equal to 0:
dA/da = 43/2 - a = 0
Solving for a, we get:
a = 43/2
Substituting this value into the equation for the area, we get:
A = (43/2)(43/2 - 43/2)/2 = 0
This means that the area of the triangle is 0 when one of the legs has a length of 0, which is not possible. Therefore, the maximum area occurs when the legs have equal lengths, which means that the right triangle is an isosceles right triangle. In this case, we have:
a = b = (35/sqrt(2)) cm
Substituting these values into the equation for the area, we get:
A = (ab)/2 = ((35/sqrt(2))^2)/2 = 612.5 cm^2
Therefore, the area of the right triangle is 612.5 square centimeters.
Step-by-step explanation:
Suppose we want to compute x ≡ a^b (mod pq) for primes p and q, utilizing the Chinese Remainder Theorem and Fermat's Little Theorem. Select the true statements. The Chinese Remainder Theorem guarantees a unique solution to any system of modular equations. Fermat's Little Theorem allows us to conclude that ap^−1≡1(mod p) for any integer a and any prime p. By CRT,x=(a^b mod p) (q^−1 mod p) q + (ab mod p)(p^−1 mod q) p
By CRT,x=(a^b mod q)(q^−1 mod p) q + (a^b mod q)(p^−1 mod q) p
Ifb≥p, then a^b−p+1≡a^b (mod p)
If b ≡ c (mod p), then a^b≡a^c (mod p)
The true statements are: The Chinese Remainder Theorem guarantees a unique solution to any system of modular equations.
Fermat's Little Theorem allows us to conclude that ap^−1≡1(mod p) for any integer a and any prime p.
The first formula given in the question for computing x using CRT is also true.
Statement 3, "If b≥p, then a^b−p+1≡a^b (mod p)", is not necessarily true. Fermat's Little Theorem states that if p is prime and a is not divisible by p, then a^(p-1) ≡ 1 (mod p). However, this does not extend to arbitrary exponents b.
Statement 4, "If b ≡ c (mod p), then a^b≡a^c (mod p)" is true by Fermat's Little Theorem, which implies that a^(p-1) ≡ 1 (mod p), we can write b = kp + c for some integer k, then
a^b = a^(kp+c) = (a^p)^k * a^c ≡ a^c (mod p)
since a^p ≡ a^(p-1) * a ≡ 1 * a ≡ a (mod p) by Fermat's Little Theorem.
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What is the discount for a retail price of $892 and a discount rate of 12%
Determine the height of a picture when the total height of the picture with the frame is 38.5 cm.
A graph of the relationship modeled by the equation is shown in the image attached below.
If the graph continues, the point (28, 24) will not be on the graph.
The height of a picture when the total height of the picture with the frame is 38.5 cm would be 34.5 cm.
How to graph the relationship modeled by the equation?In this scenario, the total height of a picture in its frame (in centimeters) would be plotted on the y-axis of the graph while the height of the picture (in centimeters) would be plotted on the x-axis of the graph.
Based on the ordered pair (28, 24), we would determine if it lies on the graph of the equation:
y = x + 4
24 = 28 + 4
24 = 32 (False).
When the total height of the picture with the frame is 38.5 cm, the height of a picture can be calculated as follows;
y = x + 4
38.5 = x + 4
x = 38.5 - 4
x = 34.5 cm.
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Complete Question:
The equation y = x + 4 models the total height of a picture in its frame, y, in centimeters with respect to the height of the picture, x, in centimeters.
a. Graph the relationship modeled by the equation. Be sure to label the axes.
b. If the graph continues, will the point (28, 24) be on the graph?
c. Determine the height of a picture when the total height of the picture with the frame is 38.5 cm.
A triangle has angles of −3,2+8, 3−17. Solve for g and find the measures of the
angles
The measures of the angles of the triangle are:
Angle 1: −3 degrees
Angle 2: 10 degrees
Angle 3: −14 degrees
To solve for g and find the measures of the angles of the triangle, we need to use the fact that the sum of the angles in a triangle is 180 degrees. This means that:
−3 + (2+8) + (3−17) = 180
Simplifying the equation, we get:
−3 + 10 + (−14) = 180
−7 = 180
To solve for g, we need to isolate it on one side of the equation. To do this, we can add 7 to both sides of the equation:
g = 180 + 7
g = 187
Now, we can plug g back into the original equation to find the measures of the angles:
−3 + (2+8) + (3−17) = 187
−3 + 10 + (−14) = 187
−7 = 187
Therefore, the measures of the angles of the triangle are:
Angle 1: −3 degrees
Angle 2: 10 degrees
Angle 3: −14 degrees
I hope this helps! Let me know if you have any further questions.
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Chris is 6 feet tall and he casts a shadow that is 5 feet longHe measures that the shadow cast by the school building is 30 feet longHow tall is the school building?
The school building is 36ft tall.
What is Pythagoras theorem?The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.
Chris is 6 feet tall and he casts a shadow that is 5 feet long
He measures that the shadow cast by the school building is 30 feet long
We can say the ratios will be same 6/h = 5/30
h =6 × 6 = 36 ft
Hence the school building is 36ft tall.
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Planes X and Y intersect at a right angle. Line A B and Line C G lie in plane X and do not intersect. Line R S lies in plane Y.
Vertical plane x intersects horizontal plane y. Line R S is horizontal on plane y. Lines A B and C G are vertical and beside each other on plane x. A right angle is indicated between the lines on the y plane and x plane. Lines A B and D G are parallel.
Which statements are true? Select three options.
The following statements are true:
Line AB and line CG are parallel.
Line CG and line RS are perpendicular.
Line segment CG lies in plane X.
What is a line segment?
A line segment is a section of a straight line that is enclosed by two clearly defined endpoints and contains every point on the line located within. The Euclidean distance between two ends of a line segment determines its length.
Here, we have
Given: Planes X and Y intersect at a right angle. Line A B and Line C G lie in plane X and do not intersect. Line R S lies in plane Y.
A) Line AB and Line CG are parallel: As both lines, AB and CG lie in plane X. Thus both are parallel and option A is the correct option.
B) Line AB and Line RS are parallel: As a line, AB lies in plane X and line RS lies in plane Y. Thus both are perpendicular and not parallel. Option B is the incorrect option.
C)Line CG and Line RS are perpendiculars: As line CG lies in plane x and line RS lies in plane Y. Thus both are perpendicular. Option C is the correct option.
D) Line AB and Line RS must intersect: line RS passes from the middle of plane Y and line AB passes from the left of plane X center. Thus they do not intersect each other. Option D is the incorrect option.
E) Line segment CG lies in plane X: As shown in the diagram, line CG lies in plane X. Thus option E is the correct option.
F) Line segment RS lies in plane X: As shown in the diagram, and the line lies RS in plane Y. Thus option F is the incorrect option.
Hence, The following statements are true:
Line AB and line CG are parallel.
Line CG and line RS are perpendicular.
Line segment CG lies in plane X.
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1. find the square roots of (a) 2i; (b) 1−√3i and express them in rectangular coordinates.
a) The square root of complex number, 2i is equals to the ±( 1 + i).
b) The square root of complex number, (1 - √3i) is equals to the ±1/√2(√3 - 1). The rectangular coordinates plane of both present in above figure.
Square root of a number is defined as a value which on multiplication by itself, results the original number. If p is the square root of q then it is denoted as p=√q. We have to determine the square root of complex numbers and express them in rectangular coordinates. For a nonzero complex number z, its square roots are √z =√r exp( i(2πk + θ)/2), k = 0,1
(a) The magnitude of 2i is r =√(2² + 0) = 2, and the principal argument is θ = π/2. So, (2i)½ = r½ exp(i (2πk + π/2)/2) , k = 0, 1
For first root, substuting, k = 0
=> (2i)½ = 2½ exp(i (2π×0 + π/2)/2)
=> (2i)½ = √2 exp(i (π/2)/2)
=> (2i)½ = √2 exp(i π/4) = √2(cos(π/4) + i sin(π/4)
=> (2i)½ = √2( 1/√2 + i(1 /√2)) = 1 + i
For second root substuting, k = 1
=> (2i)½ = 2½ exp(i (2π×1 + π/2)/2)
=> (2i)½ = √2 exp(i (5π/2)/2)
=> (2i)½ = √2 exp(i (5π/4) = √2( cos(5π/4) + i sin(5π/4)
=> (2i)½ = √2(- 1/√2 + i(-1 /√2)) = - (1 + i)
Hence, square root of 2i is ±( 1 + i).
b) 1 -√3i
The magnitude and principal argument of 1 −√3i are respectively, r = √(1² + (√3)²) = 2 and θ = tan⁻¹ ( -√3/1) = - π/3. Similar to part(a), square root of (1 - √3i) is written as (1 - √3i)½ = r½ exp(i (2πk - π/3)/2), k= 0, 1
For first root , k = 0
(1 - √3i)½ = √2 exp(i (2π×0 - π/3)/2)
=> (1 - √3i)½ = √2 exp(i (- π/6) )
=> (1 - √3i)½ = √2( cos(-π/6) - i sin(π/6))
=> (1 - √3i)½ = √2( cos(π/6) - i sin(π/6))
=> (1 - √3i)½ = √2( √3/2 - i (1/2)) = 1/√2(√3 - 1)
For second root, k = 1
(1 - √3i)½ = √2 exp(i (2π×1 - π/3)/2)
=> (1 - √3i)½ = √2 exp(i (5π/3)/2)
=> (1 - √3i)½ = √2 exp(i (5π/6))
=> (1 - √3i)½ = √2 (cos(5π/6) + i sin(5π/6))
=> (1 - √3i)½ = √2 (- √3/2 + i(1/2) ) = - 1/√2(√3 - i)
so, (√1- √3i ) is ± 1/√2(√3 - 1). Hence, we got all required square roots.
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Complete question:
1. Find the square roots of (a) 2i; (b) 1 - √3i and express them in rectangular coordinates.
I need help someone!! Please helpPP
Answer:
60
Step-by-step explanation:
Your weight on planets different is affected by gravity 50 £ 55 pounds on Mars the same ways only to 24 pounds on the moon what percent of an object earth weight is it weight on mars and
on the moon
Answer:
Assuming the weight of the object on Earth is 100 pounds, its weight on Mars would be:
(50 / 100) x 100 = 50 pounds
So the weight of the object on Mars is 50% of its weight on Earth.
Similarly, the weight of the object on the moon would be:
(24 / 100) x 100 = 24 pounds
So the weight of the object on the moon is 24% of its weight on Earth.
1) h(n) = 32¹; Find h(0)
2n
The function h(0) when evaluated is 3
How to evaluate the functionFrom the question, we have the following parameters that can be used in our computation:
h(n) = 3(2)^n
Given that
h(0)
This means that
n = 0
Substitute the known values in the above equation, so, we have the following representation
h(0) = 3(2)^0
Evaluate
h(0) = 3
Hence, the value is 3
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which of the following methods can enid use to test her claim? choose the two correct answers. responses she could calculate the ratio change in calories burned to change in miles jogged for two data point and compare the results to the same ratio with two other data points. she could calculate the ratio change in calories burned to change in miles jogged for two data point and compare the results to the same ratio with two other data points. she could plot the data on a coordinate plane and see if a straight line starting at (0, 0) passes through all the data points. she could plot the data on a coordinate plane and see if a straight line starting at (0, 0) passes through all the data points. she could put the data in a table and check to see that the difference between the number of calories burned changes by the same amount for each row. she could put the data in a table and check to see that the difference between the number of calories burned changes by the same amount for each row. she could calculate the ratio between the number of calories burned for each pair of jogs and see if the ratio is always the same.
She should figure out how many calories she burned compared to how many miles she ran, which is the proper statement.
What is a ratio?When two amounts are quantitatively related, it is possible to see how many times one value contains or is contained by the other. for instance, "There are now two computers for every student."
Given here: The table containing data calories vs miles run.
Calculating the ratio between each pair of data in a table allows you to determine whether a proportional relationship is there. The table depicts a proportionate relationship if all of those ratios are the same.
Thus calculating the ratio for each pair of entries we get
1) ratio=118/1.2
=295:3a or unit rate 98.33 calories per mile
2) 190/2= 95:1 or unit rate 95 calories per mile
3) 226/2.4=565:6 or unit rate94.1
clearly, the ratios are different.
Hence, the table containing the data doesn't form a proportional relationship.
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I need help on these two
The prepositional phrase would be B. of the bees.
The prepositional phrase would be C. he took shelter.
What is a prepositional phrase ?A prepositional phrase is a group of words that includes a preposition (such as "in," "on," "at," "by," "with," etc.) and a noun or pronoun object, along with any associated modifiers.
Prepositional phrases can be used in a variety of ways, including to describe location, time, possession, and other relationships between words in a sentence. In the given statements, the prepositional phrases would be "of the bees" and " he took shelter. "
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(8.8 x 109) + (2.2 × 10³)
Answer: 3159.2
Step-by-step explanation:
8.8 times 109= 959.2
2.2 times 10 cubed= 2200
2200+959.2= 3159.2
Answer:
3159.2
Step-by-step explanation:
You have to do it step by step. You have to do the first parentheses, then the next, then add it together. Here's how you would do it:
[tex](8.8 * 109)+(2.2 * 10^{3}[/tex]You have to figure out the end result of the square root, then figure out the parentheses.
[tex]959.2 + 2200[/tex]This is the end result of all the parentheses. All you have to do now is add the two numbers to get the end number.
[tex]3159.2[/tex]This is the final result of the equation.
I need alottttt of hellp
The expressions that have 3 as the greatest common factor are b + 3 + 6c, 27n + 66p, and 36 - 9j + 6k.
Thus,
b + 3 + 6c - Yes
-30 - 24z - No
27n + 66p - Yes
36 - 9j + 6k - Yes
Determining the greatest common factorFrom the question, we are to determine if 3 is the greatest common factor of the given expressions
b + 3 + 6c
3(b + 1 + 2c)
The greatest common factor is 3
-30 - 24z
6(-5 -4z)
The greatest common factor is not 3. The greatest common factor is 6
27n + 66p
3(9n + 22p)
The greatest common factor is 3
36 - 9j + 6k
3(12 - 3j + 2k)
Thus, The greatest common factor is 3
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The radius of a circle is 6 inches. What is the area of a sector bounded by a central angle measuring 120°
Knowing that a circle has a radius of 6 inches, the area of a sector with a central angle of 120º is 12π square inches.
The area of a sector can be found using the formula:
Area of sector = (Central angle/360°) × π × r²
Where "central angle" is the angle of the sector in degrees and "r" is the radius of the circle.
In this case, the central angle is 120° and the radius is 6 inches. Plugging these values into the formula, we get:
Area of sector = (120°/360°) × π × 6²
Area of sector = (1/3) × π × 36
Area of sector = 12π square inches
Therefore, the area of the sector bounded by a central angle measuring 120° in a circle with a radius of 6 inches is 12π square inches.
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how many ounces to a milliliter
Answer:
1 fluid oz = 29.5735 milliliters
Step-by-step explanation:
What are units?A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.
Converting these units:
1oz = 29.5735ml1ml = 0.033814ozTherefore, for every 1 fluid ounce, it is equivalent to 29.5735 milliliters.
What is the equation of the line that passes through the point (−4, 8)
and has a slope of zero?
Answer:
y=8
Step-by-step explanation:
Slope-intercept form
y=mx+b
Plug in values
y=0x+b
8=0(-4)+b
b=8
substitute
y=8
When can a correlation coefficient based on an observational study be used to support a claim of cause and effect? A. Never B. When the correlation coefficient is close to -1 or +1. C. When the correlation coefficient is equal to -1 or +1. D. When the scatterplot of the data has little vertical variation.
Option A. Never. A correlation coefficient is a measure of the strength and direction of the linear relationship between two variables.
However, a strong correlation between two variables does not necessarily mean that one causes the other. This is because there may be other factors, known as confounding variables, that affect both variables simultaneously. Therefore, it is not appropriate to use a correlation coefficient to establish a causal relationship between two variables. In order to establish causality, more rigorous methods such as randomized controlled trials must be used, which attempt to isolate the effect of one variable on another while holding other factors constant.
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Carrie spent half of her allowance playing mini golf. She then earned $12 more babysitting. What is her weekly allowance if she has $24 left?
Answer: her allowance is $24
Step-by-step explanation:
A town is designing a rectangular park that will be 600 feet by 1000 feet. A rectangular area of the park for swing sets will be 25 feet by 100 feet. On a scale drawing of the park the swing set area is 0. 5 inch by 2 inches. What is the dimensions of the park on the scale drawing?
The dimensions of the park on the scale drawing are 2 inches by 0.5 inches
The dimensions of the park on the scale drawing can be determined by using the scale factor between the actual dimensions and the scale drawing dimensions. The scale factor can be found by dividing the actual dimensions by the scale drawing dimensions.
Scale factor for length = Actual length / Scale drawing length = 1000 feet / 2 inches = 500 feet per inch
Scale factor for width = Actual width / Scale drawing width = 600 feet / 0.5 inches = 1200 feet per inch
Now, we can use the scale factor to determine the dimensions of the park on the scale drawing.
Length of park on scale drawing = Actual length / Scale factor for length = 1000 feet / 500 feet per inch = 2 inches
Width of park on scale drawing = Actual width / Scale factor for width = 600 feet / 1200 feet per inch = 0.5 inches
Therefore, on the scale drawing, the park measures 2 inches by 0.5 inches.
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What is the area of the circle in the figure below ?
Answer:
100[tex]\pi[/tex]
Step-by-step explanation:
A = [tex]\pi r^{2}[/tex]
The diameter is 20,. The radius is 1/2 of the diameter.
A = [tex]\pi 10^{2}[/tex]
A = [tex]\pi 100[/tex]
Answer:
Step-by-step explanation: That is actually the hidden number that is on the other side of the circle so it says how or what numbers is on the hidden circle so good luck finding the number
Eva deposits $2,000 in a savings account with an interest rate of 5% compounded continuously. She decides not to deposit or withdraw any money after the initial deposit. She uses the formula A = Petto represent her account balance, A, after t years, where r is the rate of interest and P is the beginning balance, or principal. How long will it take for Eva's initial deposit to double?
It take 20 years for Eva's initial deposit to double?.
What is Simple interest?A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
Eva deposits $2,000 in a savings account with an interest rate of 5% compounded continuously.
Here, Principal amount = $2000
Amount = $4000
Interest rate = 5%
Now, We know that;
⇒ Interest = PRT
Substitute all the values, we get;
⇒ 2000 = 2000 × 0.05 × T
⇒ T = 1/0.05
⇒ T = 100/5
⇒ T = 20 years
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Suppose a population of honey bees in Ephraim, UT has an initial population of 3600 and 12 years later the population reaches 25000. Use an explicit exponential model to find the rate of growth and common ratio for the honey bee population.
Express the rate of growth as a percentage. Round to the nearest tenth.
r=______%
Express the common ratio as a decimal. Round to the nearest thousandth.
1+r =_______
1) The rate of growth for the honey bee population is approximately 10.1%, rounded to the nearest tenth.
2) The common ratio is approximately 1.101, rounded to the nearest thousandth.
We can use the formula for an explicit exponential model:
N = N0 × (1 + r)^t
where N0 is the initial population, r is the rate of growth (expressed as a decimal), t is the time elapsed (in years), and N is the final population.
We can use the given information to write two equations:
N0 = 3600
N = 25000
t = 12
Substituting these values into the formula, we get:
25000 = 3600 × (1 + r)^12
Solving for (1 + r), we get:
(1 + r)^12 = 25000/3600
(1 + r) = (25000/3600)^(1/12)
(1 + r) ≈ 1.101
r ≈ (1.101 - 1) × 100% ≈ 10.1%
Therefore, the rate of growth for the honey bee population is approximately 10.1%, rounded to the nearest tenth.
2) The common ratio is 1 + r, so
1 + r ≈ 1.101
Rounding to the nearest thousandth, we get:
1 + r ≈ 1.101
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Your checking account has a constant balance of $500. Let the function m represent the balance of your savings account after t years. The table shows the total balance of the accounts over time.
This equation can be used to predict the balance of the savings account after t years.
What is equation?Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.
We can graph the data in a line graph to visualize the relationship between the two variables. The graph will have time (t) represented on the x-axis and the balance of the savings account (m) represented on the y-axis. The graph will demonstrate that the total balance of the two accounts increases over time.
The equation that models this data can be found by using the slope-intercept form, y = mx + b. Here, y represents the balance of the savings account (m), x represents the time (t), m is the slope of the line, and b is the y-intercept. To find the equation, we can first find the slope, which is the change in y divided by the change in x. This is (2,800 - 500) / (3 - 0) = 2,300 / 3 = 766.67. The y-intercept is the balance of the savings account when t = 0, which is 500. We can now write the equation as m = 766.67x + 500. This equation can be used to predict the balance of the savings account after t years.
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there is one line on the graph and its asking what is in the solution set?
Answer: you
Step-by-step explanation:
Use an algebraic method (substitution or elimination) to solve the system of equations. Show your work.
PLEASE HELP!!!!
4X − 2Y = 16
2X + 3Y = 32
Answer:
X=7
Y=6
Step-by-step explanation:
Divide the 1st equation by 2.
2x+3y=32
2x-y=8
When you subtract those 2 numbers, you get that 4y=24.
Y=6
32-6*3=14=2x
X=7
