Marcos had $60 in his savings account in January. He continued to add money to his account and by June, the value of the savings account had increased by 50%. How much money is in Marcos's account in June?

9514 1404 393

Answer:

  linear equation in the point-slope form

Step-by-step explanation:

There are many forms an equation for a line may take. Some of the ones commonly seen are ...

  ax +by = c . . . . standard form (a,b,c mutually prime integers; a>0)

  y = mx + b . . . . slope-intercept form (m=slope; b=y-intercept)

  y -k = m(x -h) . . . . point-slope form (m=slope, (h, k)=point)

__

and some additional ones I commonly use are ...

  x/(x-intercept) +y/(y-intercept) = 1

  y = m(x -h) +k . . . . variation of point-slope form (m=slope; (h, k)=point)

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1 . . . . two-point form (points (x1, y1) and (x2, y2))

  bx -ay = bh-ak . . . . line perpendicular to standard form line ax +by = c through point (h, k)

__

If you compare these forms to the equation you're given, you see it matches the "point-slope form" for point (4, 2) and slope 7.

Answer:

68/1000

Step-by-step explanation:

0.68=68/100.68/100×1/10=68/1000

The equation that represents a quadratic relationship is y = 4x^2. Option A.

A quadratic relationship is a mathematical relationship where the variable y is a function of the variable x raised to the power of 2. In other words, it is an equation in which the highest power of the variable is 2.

Let's analyze the given equations:

1. y = 4x^2: This equation represents a quadratic relationship because the variable x is raised to the power of 2. The term 4x^2 indicates that the relationship between x and y is quadratic.

2. y = 4x^4: This equation represents a quartic relationship, not a quadratic relationship. The variable x is raised to the power of 4, which indicates a higher degree relationship than quadratic.

3. y = 4x^3: This equation represents a cubic relationship, not a quadratic relationship. The variable x is raised to the power of 3, indicating a higher degree relationship.

4. y = 4: This equation represents a linear relationship, not a quadratic relationship. It is a constant equation where y is always equal to 4, regardless of the value of x. In a quadratic relationship, the variable x should have a power of 2. Option A.

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Answer:

c below

Step-by-step explanation:

(5, 4), (−2, 3), and (−2, 2) became

(9, 2), (2, 1), and (2, 0).

they got moved 4 units to the right & 2 down

h: The domain

-5 ≤ x ≤ 5

The predicted population in the year 2030 is 10 people

From the question, we have the following parameters that can be used in our computation:

Population function, P(t)= 15е⁻⁰.⁰¹²⁺

Also from the question, we have

The variable t represents the number of years since 2020

This means that the value of t in 2030 is

t = 2030 - 2020

t = 10

So, we have

P(10)= 15е⁻⁰.⁰¹² ˣ ¹⁰

Evaluate the above products

P(10)= 15е⁻⁰.¹²

Evaluate the exponents

P(10)= 13.30

Approximate the above expression

P(10) = 13

This means that the number of people is 13

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The values that go into the blanks are 19200 g, 3700 g, 8455 g, 800 g, 4450 g, 2.765 kg, 77 g, 12.508 kg, 30000 g and 7200 grams

From the question, we have the following parameters that can be used in our computation:

Statements 1 to 10

Evaluating the expressions, we have

Conversion

19 1/5 kg = 19 1/5  * 1000 g

19 1/5 kg = 19200 g

Sum

3.4 kg + 3/10 kg = 3.7 kg

3.4 kg + 3/10 kg = 3700 g

Difference

8.5 kg - 45 g = 8.455 kg

8.5 kg - 45 g = 8455 g

Dictionary and book

Heavier by = 1200 g - 0.4 kg

Heavier by = 800 g

Sum

1/2 kg + 50 g + 3.9 kg = 500 g + 50 g + 3900 g

1/2 kg + 50 g + 3.9 kg = 4450 g

Comparison

3 kg 15 g = ___ more than 1/4 kg

We have

Difference = 3 kg 15 g - 1/4 kg

Difference = 2.765 kg

So:

3 kg 15 g = 2.765 kg more than 1/4 kg

Sum

7/10 kg + 7/100 kg = 77 g

Sum

8 kg 8 g + 4 1/2 kg = 12.508 kg

Mr. Tan and Lisa

We have

Mr. Tan = 75 kg

Lisa = 2/5 of Mr. Tan

So, we have

Lisa = 2/5 of 75 kg

Lisa = 30000 g

Mass of 12 boxes

We have

Mass of 1 box = 0.6 kg

So, we have

Mass of 12 boxes = 0.6 kg * 12

Mass of 12 boxes = 7200 grams

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The quadratic regressiοn equatiοn fοr the given data pοints is y = 5x² - 20x + 7

A secοnd-degree equatiοn οf the fοrm ax² + bx + c = 0 is knοwn as a quadratic equatiοn in mathematics. Here, x is the variable, c is the cοnstant term, and a and b are the cοefficients.

Tο find the quadratic regressiοn equatiοn fοr the given data pοints, we need tο fit a quadratic equatiοn οf the fοrm y = ax² + bx + c tο the data.

We can start by using the three given pοints tο set up a system οf three equatiοns:

\((1,-8): a(1)^2 + b(1) + c = -8\\\\(2,-4): a(2)^2 + b(2) + c = -4\\\\(3,6): a(3)^2 + b(3) + c = 6\)

SimpIifying each equatiοn, we get:

a + b + c = -8 (equatiοn 1)

4a + 2b + c = -4 (equatiοn 2)

9a + 3b + c = 6 (equatiοn 3)

AIternativeIy, we can use technοIοgy such as a caIcuIatοr οr spreadsheet tο sοIve the system.

SοIving the system using technοIοgy, we get:

a = 5

b = -20

c = 7

Therefοre, the quadratic regressiοn equatiοn fοr the given data pοints is:

y = 5x² - 20x + 7

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Answer:

The exact value of the other leg is 10.

Step-by-step explanation:

Finding the exact value of x given a 45 degree angle and a side length of 10 can be done using trigonometry. In a 45-45-90 right triangle, the two legs are congruent and the hypotenuse is equal to the square root of 2 times the length of the legs.

Therefore, if one leg is 10, the hypotenuse is 10 times the square root of 2. To find the length of the other leg, we can use the Pythagorean theorem:

c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the legs of the right triangle.

Substituting known values, we get:

(10√2)^2 = 10^2 + b^2

200 = 100 + b^2

b^2 = 100

b = 10

Therefore, the exact value of the other leg is 10.

"The correct answer is option A." The missing coordinates of point Q are (a, c/2).We are given the coordinates of points P and N as (0, c) and (2a, 0), respectively. We are also given that point Q lies on the same line as points P, Q, and N. We need to find the missing coordinates of point Q.

Since point Q lies on the same line as P, Q, and N, its x-coordinate must be halfway between the x-coordinates of points P and N. That is, the x-coordinate of Q is:

x-coordinate of Q = (x-coordinate of P + x-coordinate of N) / 2

x-coordinate of Q = (0 + 2a) / 2 = a

So, we know that the x-coordinate of point Q is a.

To find the y-coordinate of point Q, we can use the fact that point Q lies on the same line as point P, which has coordinates (0, c). The equation of the line passing through P and N is:

y - c = (0 - c) / (2a - 0) * (x - 0)

Simplifying this equation gives:

y - c = -c/2a * xy = -c/2a * x + c

Substituting x = a in this equation gives:

y = -c/2a * a + cy = -c/2 + cy = c/2

So, we know that the y-coordinate of point Q is c/2.

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Answer:

  ∠DQE = 65°

Step-by-step explanation:

You want to know the measure of Angle DQE in the given figure.

Triangle ADE is inscribed in a semicircle, so is a right triangle. That makes acute angle AED complementary to acute angle EAD. The latter is given as 50°, so ...

  ∠AED = 90° -50° = 40°

We know that tangent line QE is perpendicular to diameter AE, so angle AEQ is a right angle. Segment ED divides that right angle into complementary angles, so ...

  ∠DEA +∠DEQ = 90°

  ∠DEQ = 90° -∠DEA = 90° -40° = 50°

A.pex angle DEQ in isosceles triangle DEQ being 50° means that the base angles QDE and DQE will have measure ...

  ∠DQE = (180° -50°)/2 = 130°/2

  ∠DQE = 65°

__

Alternate solution

Let angles DQE and QDE be represented by x. Then the sum of angles in quadrilateral ADQE is 360°:

  50° +(90+x)° +x° +90° = 360°

  230° +2x = 360° . . . . . . simplify

  x = 130°/2 = 65° . . . . . solve for x

The answer is:  4100x  +  21390

We need to know the number of months Marian wants to save to get the specific value.

In the equation, we will need to calculate the maximum amount of money Marian can spend on the house.

We can calculate the maximum amount of money Marian can spend on a house by multiplying her monthly income by the number of months she would want to save.

Marian earns $4,100.00 per month

Suppose Marian wants  to save for  x months,  then the maximum amount that she can spend on the house is:

4100  *   x    +  21390

The answer is:  4100x  +  21390

We need to know the number of months Marian wants to save to get the specific value.

Hope this helps!

a) She can make 400 milliliters of the fizzy drink.

b) The change does not affect the greatest amount of drink.

We know that the fizzy drink is 7 parts apple juice and 3 parts lemonade. And Kerry thinks that she has 280ml of apple juice and 180 ml lemonade.

If we divide the total amount of apple juice in 7 parts, then each part has:

280ml/7 = 40ml

Then we need 3 parts of 40ml of the lemonade, this is:

3*40ml = 120ml

Then the total amounf of drink fizz that she can make is:

280ml + 120ml = 400ml.

b) Now she has  160 ml of lemonade, but she needs 120 ml of it, so this change does not affect the greatest amount of fizzy drink she can make.

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The simplification of the expression ab³/a⁴b  +  (c²)³ is determined as b²/a³  +  c⁶.

The given expression is simplified as follows;

The given expression is written as;

ab³/a⁴b  +  (c²)³

To simplify the expression given above, we will divide the fraction with the common factor as follows;

From the numerator; ab³, we will factor out "ab"

From denominator; a⁴b, we will factor out "ab"

The resulting expression becomes;

ab³/a⁴b  +  (c²)³

= b²/a³  +  c⁶

Note: for the power of c, we simplify by multiplying 2 and 3 = 6

Thus, the simplification of the expression ab³/a⁴b  +  (c²)³ is determined as b²/a³  +  c⁶.

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The random variable's pdf is f(x) = (3/8) x^2 , x ∈ [0, 2].

Finding the normalizing constant that equals the integral of the pdf over the support of the random variable yields the constant in the pdf (probability density function).

The random variable's support is the interval [0, 2]. The normalizing constant can be calculated as follows:

∫_0^2 x^2 dx = [x^3/3]

_0^2 = (8/3) - (0) = 8/3

So, in the pdf, the constant is 1/(8/3) = 3/8, rounded to the second decimal place.

As a result, the random variable's pdf is:

f(x) = (3/8) x^2 , x ∈ [0, 2].

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Answer:

66

Step-by-step explanation:

the difference of 54 and 32 is 54 - 32 = 22

the difference of 8 and 5 is 8 - 5 = 3

then

22 × 3 = 66

Answer:

45/28

Step-by-step explanation:

6/7+3/4

The least common multiple of 7 and 4 is 28.

Convert 6/7 and 3/4 to fractions with the denominator of 28

24/28+21/28

Since the denominators are now the same, add the numorators to get 45/28

Mass of football = 0.435kg

Mass of football helmet = 2.57kg

To find how much more the mass of the helmet is than the mass of football, we have to find the difference

2.57kg - 0.435kg

For the two similar triangles, the length of side DA = 4 units.

For the two triangles;

ΔABC ≡ ΔADE

The ratios of their side will be equal

Thus,

CB/ED = AB/DA

Put the values of the sides from given diagram.

2/4 = 2/DA

Cancel the common 2 and cross multiplying.

DA = 4 units.

Thus, the length for the side DA is 4 units.

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Please find attached the graph of the straight line equation; y = -2·x + 3/2, which is the same as the graph of the equation; 4·x + 2·y = 3, created with MS Excel

An equation of a straight line is an equation of the form; y = m·x + c

b. 1. The equation of the line is; 4·x + 2·y = 3

The above equation of the line can be expressed in slope-intercept form; y = m·x + c, where; m is the slope of the graph of the equation and c is the y-coordinate of the y-intercept, by making y the subject as follows;

2·y = 3 - 4·x

y = (3 - 4·x)/2

y = 3/2 - 2·x

Therefore; y = -2·x + 3/2

The above equation indicates;

The slope, m = -2

The y-intercept, c = 3/2

The coordinate of the y-intercept is therefore; (0, 3/2)

The point (0, 3/2) is to be plotted on the graph

2. In order to draw the graph, the coordinates of a second point can be found as follows;

The slope of the graph = The ratio of the rise to the run of the graph

Slope = Rise/Run = Δy/Δx

The rise = The number of units a point progresses vertically

The run =  The number of units a point progresses horizontally

Therefore, a slope of -2, indicates;

Slope = Rise/run = Δy/Δx = -2 = -2/1

A rise of -2 units is accompanied by a run of 1 unit

In terms of x and y an increase of 1 unit in the x-value is accompanied in the y-value by a -2 units increase.

Therefore, a second point on the graph is; (0 + 1, ((3/2) - 2)) = (1, -1/2)

3. The line of the graph therefore passes through both (0, 3/2) and (1, -1/2)

Drawing a line through the above two points creates the graph of the equation, 4·x + 2·y = 3

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There are four different types of quadrilaterals: parallelograms, squares, rectangles, and rhombuses.

What is Quadrilateral?

A closed quadrilateral has four sides, four vertices, and four angles. It is a type of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total interior angle of 360 degrees.

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.

An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions.

A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.

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Answer:

= −28.043478261

Step By Step Explanation

Answer From Gauth Math

The ratio of the measurements written as a fraction is 8/9.

A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator.

In order to convert the ratio to fraction, the units of measurements have to be the same. So, pounds would be converted to ounces.

3 x 16 = 48 ounces

48 / 54 = 8/9

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Let's represent the number with the variable "x". According to the given property, we can write the following equation:

3(x + 4) < 7x

Now, let's solve this inequality to find the range of numbers that satisfy the property.

3x + 12 < 7x

Subtract 3x from both sides:

12 < 4x

Divide both sides by 4 (since the coefficient of x is 4):

3 < x

So, the range of numbers that satisfy the given property is x > 3.

Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:

Answer:

The answer is m = 5/3

Step-by-step explanation:

It will take apprοximately 23.29 years fοr the accοunt tο reach $15,000, assuming the given initial investment and interest rate.

A lοgarithm is an inverse οperatiοn tο expοnentiatiοn. It is a mathematical functiοn that helps tο sοlve equatiοns where the variable is in the expοnent. The lοgarithm οf a number tο a certain base is the expοnent tο which the base must be raised tο get that number.

Accοrding tο given infοrmatiοn :

In the given expressiοn, 1,000 • e0.034t, the variable "t" represents the time in years, and "e" is a mathematical cοnstant called Euler's number (apprοximately 2.71828).

The entire expressiοn represents the amοunt οf mοney in an accοunt after "t" years, assuming an initial investment οf $1,000 and a cοntinuοus interest rate οf 3.4% per year (0.034 in decimal fοrm).

Tο find the number οf years it will take fοr the accοunt tο reach $15,000, we can set the expressiοn equal tο 15,000 and sοlve fοr "t".

1,000 • e0.034t = 15,000

Dividing bοth sides by 1,000 gives:

e0.034t = 15

Tο sοlve fοr "t", we can take the natural lοgarithm (ln) οf bοth sides:

ln(e0.034t) = ln(15)

0.034t • ln(e) = ln(15)

Since ln(e) = 1, we can simplify tο:

0.034t = ln(15)

Dividing bοth sides by 0.034 gives:

t = ln(15) / 0.034

Using a calculatοr, we get:

t ≈ 23.29

Therefοre, it will take apprοximately 23.29 years fοr the accοunt tο reach $15,000, assuming the given initial investment and interest rate.

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Answer:

  5 2/5

Step-by-step explanation:

Multiply by (3 3/5)x/(1 1/2):

  x = (2 1/4)(3 3/5)/(1 1/2) = (9/4)(18/5)(2/3) =27/5

  x = 5 2/5

The value of c in the domain of f(x) depends on the specific function f(x) and its domain.

In order to determine which value of c is in the domain of f(x), we need to know the function f(x) and its domain. A domain is the set of all possible input values of a function.

If a value of c is in the domain of f(x), then we can plug it into the function and get a valid output.

In general, a function f(x) can have a restricted domain due to certain conditions or limitations. For example, a square root function cannot have negative values under the radical because that would result in an imaginary number.

Thus, the domain of a square root function is restricted to non-negative values.

In order to find the domain of a function, we need to consider any restrictions on the input values. For example, if we have the function f(x) = 1/x, we cannot plug in x = 0 because that would result in division by zero, which is undefined.

Therefore, the domain of f(x) is all real numbers except 0. We can write this as D(f) = {x : x ≠ 0}.Once we know the domain of f(x), we can check which value of c is in the domain by seeing if it satisfies the condition.

For example, if the domain of f(x) is D(f) = {x : x > 2}, then c = 3 is in the domain because 3 is greater than 2. On the other hand, c = 1 is not in the domain because 1 is less than 2.

Therefore, the value of c in the domain of f(x) depends on the specific function f(x) and its domain.

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Answer:

8.2 mph

Step-by-step explanation:

720 ft/min (60 min/hr / 5280 ft/mi) = 8.1818181818... mi/hr

Answer:

720 multiplied by 60 = 43200

43200 divided by 5280 = 8.18

8.18 rounds to 8.2