Which triangle is an obtuse triangle?
A
a triangle with angles that measure 35°, 65°, and 80°
B
a triangle with angles that measure 30°, 40°, and 110°
a triangle with angles that measure 60°, 60°, and 60°
C
a triangle with angles that measure 30°, 60°, and 90°

The amount (present value) that the couple needs to have in this retirement account by the time they retire in 35 years to enable them withdraw $6,000 monthly for 25 years is $777,387.14.

The amount in 35 years' time when the couple retire that they should have can be described as the present value (in 35 years).

Based on the above conclusion, the present value can be determined using an online finance calculator as follows:

With the monthly withdrawal of $6,000 and compounded interest of 8% APR monthly, the future value of the account in 60 years' time will be $0.

N (# of periods) = 300 months (25 years x 12)

I/Y (Interest per year) = 8%

PMT (Periodic Payment) = $-6,000

FV (Future Value) = $0

Results:

Present Value in 35 years (PV) = $777,387.14

Sum of all periodic payments = $-1,800,000 ($-6,000 x 300 months)

Total Interest = $1,022,612.86

Thus, the couple should save up to $777,387.14 in 35 years' time when they retire to achieve their goal.

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The density of the metal is  determined as  6.1 g / cm³.

We have,

The density of the metal is defined as the ratio of the mass per unit volume of the metal.

Mathematically, the formula for density is given as;

ρ = m / V

where;

m is the mass of the metal

V is the volume of the metal

The density of the metal is  calculated as follows;

ρ = ( 0.47 kg x 1000 g/kg ) / ( 77 cm³ )

ρ = 6.1 g / cm³

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Compute the density in g/cm³ of a piece of metal that has a mass of 0.470 kg and a volume of 77 cm³.

X g/cm³

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Answer: The expression (7 − 3) can be simplified as follows:

(7 − 3) = 4

Therefore, the value of the expression (7 − 3) is 4.

Answer:

Step-by-step explanation:

Answer:

x = 1/3; y = -2/3

Step-by-step explanation:

We can solve using substitution by isolating y in the first equation and plug in this y for y in the second equation.  I chose this method because it's very simply to isolate the y and only requires a simple subtraction:

[tex]3x+y=1/3\\y=-3x+1/3\\\\2x-3(-3x+1/3)=8/3\\2x+9x-1=8/3\\11x-1=8/3\\11x=11/3\\x=1/3[/tex]

Now, we can plug in 1/3 for x in any of the two equations.  Let's try the first original equation:

[tex]3(1/3)+y=1/3\\1+y=1/3\\y=-2/3[/tex]

Finally, we can check our answers by plugging in 1/3 for x and -2/3 for y into to both equations and see that we get 1/3 and 8/3 respectively:;

First equation:

[tex]3(1/3)-2/3=1/3\\1-2/3=1/3\\1/3=1/3[/tex]

Second equation:

[tex]2(1/3)-3(-2/3)=8/3\\2/3+2=8/3\\8/3=8/3[/tex]

The equation of the line in point-slope form is y + 3 = 1/4(x + 4).

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The given line passes through the points (-1,1) and (0,-3).

The slope of the line passing through these points can be calculated as:

slope = (y2 - y1) / (x2 - x1)

= (-3 - 1) / (0 - (-1))

= -4 / 1

= -4

Since we are looking for a line that is perpendicular to this line, the slope of the new line will be the negative reciprocal of -4, which is 1/4.

Using the point-slope form of a linear equation, we can write the equation of the new line as:

y - y1 = m(x - x1)

where (x1, y1) is the point (-4,-3) and m is the slope 1/4.

Plugging in the values.

y - (-3) = 1/4(x - (-4))

Simplifying and rearranging.

y + 3 = 1/4(x + 4)

Therefore,

The equation of the line in point-slope form is y + 3 = 1/4(x + 4).

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The five-number summary for the given data set is Min = 90, Q1 = 102, Median (Q2) = 108, Q3 = 128, and Max = 162. These values were found by arranging the data set in order and finding the minimum, maximum, median, and quartiles.

To find the five-number summary for the given data set, we need to find the minimum, maximum, median (Q2), and the first and third quartiles (Q1 and Q3). We can do this by first arranging the data set in order

90, 90, 91, 102, 106, 108, 108, 110, 113, 120, 120, 121, 128, 129, 162

Min = 90 (the smallest value in the data set)

Q1 = 102 (the median of the lower half of the data set)

Median (Q2) = 108 (the middle value of the data set)

Q3 = 128 (the median of the upper half of the data set)

Max = 162 (the largest value in the data set)

Therefore, the five-number summary for the given data set in order is 90, 102, 108, 128, 162.

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Answer:

y = 1.78x + 4.28

Step-by-step explanation:

first isolate y

1.8y = 3.2x + 7.7

now that y is isolated, we can divide out the 1.8

y = 1.78x + 4.28

Answer:

[tex]y=\dfrac{16}{9}x + \dfrac{77}{18}[/tex]

Step-by-step explanation:

To solve for y in this equation, we need to isolate the y term on one side, then multiply by the reciprocal of its coefficient. Remember that any number multiplied by its reciprocal is 1.

3.2x - 1.8y + 7.7 = 0

↓ add 1.8y to both sides

3.2x + 7.7 = 1.8y

↓ represent the decimals as fractions

[tex]\dfrac{16}{5}x + \dfrac{77}{10} = \dfrac{9}{5}y[/tex]

↓ multiply by the reciprocal of y's coefficient: [tex]\frac{5}{9}[/tex]

[tex]\dfrac{5}{9} \cdot \left(\dfrac{16}{5}x + \dfrac{77}{10}\right) = \left(\dfrac{9}{5}y\right) \cdot \dfrac{5}{9}[/tex]

↓ simplify

[tex]\boxed{\dfrac{16}{9}x + \dfrac{77}{18} = y}[/tex]

Using the triangular inequalities we can get:

7/4 < x < 11/2

The image of the triangle is in the image at the end.

A triangle with sides A, B, and C must meet the triangular inequality, it says that the sum of any two sides is larger than the other side.

Now, see the triangle attached at the end, the triangular inequalities say that:

18 + 6x > 2x + 4

18 + 2x + 4 > 6x

6x + 2x + 4 > 18

Now simplify these, for each one we will get:

4x > -14 -----> x > -7/2

22 > 4x -----> 11/2 > x

8x > 14 -----> x > 7/4

Using the second two we can get:

7/4 < x < 11/2

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Car 12 of Train B is also 12 cars away from Car 19 on Train B.

Since each train boasts 31 cars, we can ascertain the total amount of vehicles between Car 19 and Car 12 on Train A:

31 - 19 = 12

Thus, Car 12 on Train A is a dozen units distant from Car 19 on Train A.

Nevertheless, Train B is furthermore moving in an inverring direction and has its exclusive set of automobiles between Car 19 and Car 12. We comprehend that the matching figure of cars must be amongst Car 19 and Car 12 on Train B as with Train A.

In essence, Car 12 of Train B is also 12 cars away from Car 19 on Train B.

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Based on the March expense statement, the proportion of Maria's total expenses that are for her car is D. More than half but less than three-quarters.

The proportion refers to a portion or part of a whole number, value, or expression.

Proportions, which are ratios between two values, are depicted in decimals, fractions, or percentages.

The total expenses for March = $507.59

Auto expenses for March = $290.02

Proportion of auto expenses to the total expenses =0.57 ($290.02 ÷ $507.59)

One-half of $507.59 = 0.50 or $253.795)

Three-quarters of $507.59 = 0.75 or $380.69

Since $290.02 is more than $253.795 but less than $380.69, Option D is correct.

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To draw the histogram we have to find the frequency of the data

Here are the heights of a sample of 15 adults

66,71,76,63,75,77,74,73,64,62,78,80,67,72,68

We have to draw the histogram by taking height on x axis

Let us find the frequency of given heights

62-66 , the frequency is 4

67-71,  the frequency is 3

72-76,  the frequency is 5

77-81 ,  the frequency is 3

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Answer:

Laura's debt has increased by $15, as her account balance has gone from -$30 to -$45. This means that she owes $15 more than what she owed before. A negative account balance indicates that Laura owes money to someone or a company, and the increase in the negative balance implies that her debt has become more significant. It is essential for Laura to keep track of her account and try to improve her financial situation to avoid accumulating debt further.

The Total surface area of the given prism is: 46.3 sq.m

The surface area of the prism is gotten by finding the areas of all surfaces and adding up to get the total surface area. Thus:

We know that formula to find the area of a triangle is:

Area of triangle = ¹/₂*base*height

Area of rectangle = length * width

Thus:

Total surface area = 2(¹/₂* 3 * 3.7) + 2(4 * 3.2) + (3 * 3.2)

Total surface area = 11.1 + 25.6 + 9.6

Total surface area = 46.3 sq.m

Thus, that is the total surface area of the given prism with dimensions

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50 degrees is the value must she enter to construct angle ABX.

The given triangle is ABX

We have to find the value Karla has to enter to construct angle ABX.

By the given figure the angle at B is fifty degrees.

The value of ∠ABX is 50 degrees

Hence, 50 degrees is the value must she enter to construct angle ABX.

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a) There are no values of x for which h'(x) is undefined.

b) The critical numbers of h(x) = sin²(x) + cos(x) in the domain 0 < x < 2π are x = kπ, x = π/3 + 2πn, and x = 5π/3 + 2πn, where k and n are integers.

a) To find the values of c for which h'(c) = 0 or is undefined, we first need to find the derivative of h(x):

h'(x) = 2sin(x)cos(x) - sin(x)

Now we can set h'(x) equal to 0 and solve for x:

2sin(x)cos(x) - sin(x) = 0

sin(x)(2cos(x) - 1) = 0

This equation is satisfied when sin(x) = 0 or 2cos(x) - 1 = 0. The first equation has solutions x = kπ, where k is an integer. The second equation has solutions x = π/3 + 2πn or x = 5π/3 + 2πn, where n is an integer.

Next, we need to check if there are any values of x for which h'(x) is undefined. Since h'(x) is a combination of sin(x) and cos(x), it is defined for all values of x in the given domain.

b) The critical numbers of h(x) are the values of x at which h'(x) = 0 or h'(x) is undefined. From part (a), we have the solutions x = kπ, x = π/3 + 2πn, and x = 5π/3 + 2πn, where k and n are integers. These are the critical numbers of h(x) in the given domain.

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Answer: 1. 15 2. 13 3. 17 4. 29

Step-by-step explanation:

12^2 + 9^2 = 15^2, 5^2 + 12^2 = 13^2, 8^2 + 15^2 = 17^2, 20^2 + 21^2 = 29^2.

The height of the school is given as follows:

34 ft.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The height of the school for this problem is given as follows:

h = x + 10 ft.

In which segment x is one of the sides of a right triangle, in which the other side is of 7 ft and the hypotenuse is of 25 ft, hence:

x² + 7² = 25²

x = sqrt(25² - 7²)

x = 24 ft.

Hence the height of the school is of:

24 ft + 10 ft = 34 ft.

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The transformed equation of the given function is y = x²+5.

Given that a transformed graph of the function y = x², we need to find the equation of the transformed graph,

We see that the y-intercept is (0, 5) so the graph has been translated 5 units up.

Therefore the equation can be written as y = x²+5.

Hence, the transformed equation of the given function is y = x²+5.

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The final value of the given amount compounded is $1518.69

Compound interest is the interest earned on the principal and the interest previously accumulated. It is given by

[tex]A=P(1+r/n)^n^t[/tex]

where P = Principal, r = annual rate of interest, n = number of times interest is compounded per year & t = time in years.

The given principal is $800 for 11 years & annual interest rate is 6%.

To find the amount compounded annually at 6% for 11 years substituting the given values in the above formula i.e.

Amount =  [tex]800(1+0.06)^1^1[/tex]

Amount = $1518.69

Hence, the Amount is equal to $1518.69.

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The number of schools that can get the book is obtained using the formula

s = 56 ÷ 7

Information form the problem

schools across

To find the number of schools, s; that will get the book we use the formula

s = number of books / how many books each school will get

substituting into the formula

s = 56 / 7

s = 56 ÷ 7

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Answer:

it is 17.5

Step-by-step explanation:

you add 6.2 and 11.3 equal 17.5

Answer:

≈ 681.38 ft^2 when pi≈ 3.14

Step-by-step explanation:

2(3.14)(6.2^2)+(3.14)(12.4)(11.3)

241.4032+439.9768≈ 681.38

Answer:

third quadrant

its position with respect to reference planes will be behind Vertical Plane and below the Horizontal Plane.

The given figure shows different positions and their respective views

The vertex of f(x) is ( 1, - 108) and vertex of g(x) is (1, 36).

For the given functions are;

f(x) = 3(x + 7)(x - 5)

g(x)= x²  + 2x + 35

Now proceed,

f(x) = 3(x + 7)(x - 5)

     = 3x² - 15x + 21x - 105

     =  3x² - 6x - 105

     = 3(x² - 2x ) - 105

     = 3(x² - 2x + 1 - 1 ) - 105

     = 3(x² - 2x + 1 ) - 108

     = 3(x- 1)² - 108

Since for a function p(x) = a(x-h)²+k the vertex be (h, k)

Therefore vertex of f(x) be ( 1, - 108)

Now proceed

g(x) = x²  + 2x + 35

      = x²  + 2x - 1 + 1 + 35

      = (x-1)² + 36

Similarly vertex of g(x) is (1, 36)

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Answer: It's kind of hard to answer a question you don't have all the parts too. :(

Step-by-step explanation:

Answer:

Step-by-step explanation:

To calculate the rate of return when 35 shares of Stock A, purchased for $20/share, are sold for $815, you can use the following formula1:

Rate of Return = (Proceeds - Cost - Commission) / Cost

where Proceeds is the amount received from selling the shares, Cost is the amount paid for the shares, and Commission is the commission paid on the sale1. Plugging in the values, we get:

Rate of Return = (815 - (35 * 20) - 6) / (35 * 20) = 0.2875

Multiplying by 100 to convert to a percentage, we get a rate of return of 28.75%1.