1. Triangles

B = 4in, H = 5in
B = 6ft, H= 10ft
B = 12m, H = 15m
Application: Sandy is making tablecloths in the shape of triangles. She needs to make two triangle tablecloths for one table. The triangles have base of 2 ft and a height of 4 ft. What is the total area of the triangle tablecloths for one table?
2. Parallelogram (H = height) and (B = base)

H = 9in, B = 6in
H = 5 ft, B = 2ft
H = 7yds, B = 3yds
Application: If a parallelogram has a base of 13 mm and an area of 78 mm2 what is the height?
Hint: Use the formula. Substitute the given values and then solve as an equation.

3. Rectangle (L = length) and (w = width)

rect. DKIF with L = 8 ft and w = 6 ft
rect. AOPU with L = 13 ft and w = 5 ft
Application: Charles is paining the den. Two walls are 9 ft high and 15 ft long. The other two walls are 8 ft high and 10 ft long. Charles bought one gallon of paint that will cover 440 square feet of wall space. Does he have enough paint? Explain.
4. Rhombus ( d1 = diagonal 1) (d2 = diagonal 2)

rhombus with d1 = 12 yds and d2 = 12 yds
rhombus with d1 = 10 ft and d2 = 25 ft
rhombus with d1 = 16 in and d2 = 22 in
Application: a rhombus as an area of 72 ft and the product of the diagonals is 144. What is the length of each diagonal?
5. Trapezoid ( b1 = base 1) (b2 = base 2) (H = height)

b1 = 6 ft, b2 = 7 ft, H = 10 ft
b1 = 5 yds, b2 = 8 yds, H = 4 yds
c. b1 = 9 in, b2 = 11 in, H = 13 in
d. Application: The two bases of a trapezoid = 16 km and its area = 32 km2. What is its height?

Answer:

answer A

Step-by-step explanation:

Hello,

\((fog)(x)=f(g(x))=f(2x-1)=3(2x-1)+14=6x-3+14=6x+11\)

so the correct answer is A.

hope this helps

Answer:

A.  6x + 11.

Step-by-step explanation:

(f o g)(x)

We replace the x in f(c) by g(x) and simplify:

= 3(2x - 1) + 14

= 6x - 3 + 14

= 6x + 11.

Answer:

\(56\) cents

Step-by-step explanation:

If \(18\) inches of wire cost \(72\) cents, then each inch of wire will cost \(\frac{72}{18}=4\) cents. Therefore, 14 inches of wire will cost \(14*4=56\) cents. Hope this helps!

Answer:

56 cents

Step-by-step explanation: 72 cents divided by 18= 4 so for one inch of wire it cost 4 cents       Then 14 inches times 4= 56  I think thats

the answer

Answer:

45cm^2

Step-by-step explanation:

multiply 5 and 9 and thats the answer you end up with basically

Answer:

y=-4/3x+3

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

360 - (130 + 80) = 150

Answer:

150

Step-by-step explanation:

130+80= 210

360-210= 150

so it is 150

a^2 + b^2 =c^2

1^2 + 2^2 = 1+4 = 5

so no it doesn't make a right triangle

Given: X-3(x+2)=4X-3(x+2)=4

Find: the solution of the given equation

Explanation:

on solving equation (1) and (2) , we get

Answer:

x = -5

Step-by-step explanation:

    x - 3(x + 2)= 4

    x - 3x - 3*2 = 4     {Distributive property}

   x - 3x  - 6    = 4

Combine like terms in LHS,

         -2x - 6  = 4

Add 6 to both sides,

               -2x = 4 + 6

               -2x = 10

Divide both sides by (-2)

                   x = 10 ÷ (-2)

                   \(\sf \boxed{x= -5}\)

Answer:

∠1=66⁰

∠2=24⁰

∠3=24⁰

∠4=90⁰

Step-by-step explanation:

∠2=∠ADB=24 (ΔADB is isosceles, so ∠ADB=∠ABD)

∠4 =90 (right angle)

∠3=24 (BD bisects ∠ABC, so ∠2=∠3)

∠1+∠2+90=180 (angles in triangle add to 180)

∠1=66

RQ ⊕ ST | Given

RS = RQ + ST | Definition of ⊕ (circle plus)

RS > RQ | Addition property of inequality

RS > TQ | Transitive property of inequality

To prove the statement RS > TQ, we can use a two-column proof format. Let's go step by step:

Given: RQ ⊕ ST

This is the given information, stating that RQ is in direct relation with ST.

RS = RQ + ST

According to the definition of the ⊕ symbol (circle plus), the length of RS is equal to the sum of the lengths of RQ and ST.

RS > RQ

Since ST is positive and nonzero, adding it to RQ will result in RS being greater than RQ. Therefore, RS is greater than RQ.

RS > TQ

By the transitive property of inequality, if RS is greater than RQ, and RQ is greater than TQ (as proven in step 1), then RS must also be greater than TQ. Hence, RS > TQ.

Therefore, based on the given information and the logical deductions, we have proved that RS > TQ.

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The point (3, 2) is feasible for the constraint 2x1 + 6x2 ≤ 30. (False)

To determine if a point is feasible for a constraint, we need to substitute the values of the point into the constraint equation and check if the resulting inequality holds true.

In this case, the constraint is 2x1 + 6x2 ≤ 30. Substituting x1 = 3 and x2 = 2 into the equation, we get 2(3) + 6(2) = 6 + 12 = 18. Since 18 is not less than or equal to 30, the inequality is not satisfied.

Therefore, the point (3, 2) is not feasible for the given constraint. Feasible points satisfy the constraint, while infeasible points do not. In this case, any point that lies below the line represented by the constraint equation would be feasible, while points above the line would be infeasible.

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a)the HCF of 12xy and 3x is \(2 \times 3 \times x\), which simplifies to 6x. b)  the HCF of 54xyz and 12x²12 is 2xy. c)  the HCF of 21x²y²z and 7.xyz is xyz. d) the HCF of 3a²b³c³, 9a³b³c³, and 18a²b²c² is 3a²b²c². d) the HCF of 6abc, 7ab³c, and 8abc³ is abc.

a) To find the highest common factor (HCF) of 12xy and 3x, we need to determine the highest power of each common factor that appears in both terms. Here, the common factors are 2, 3, and x. The highest power of 2 in both terms is 1 (from 12xy), the highest power of 3 is 1 (from 3x), and the highest power of x is 1. Therefore, the HCF of 12xy and 3x is\(2 \times 3 \times x\) which simplifies to 6x.

b) The common factors in 54xyz and 12x²12 are 2, 3, x, and y. The highest power of 2 in both terms is 1, the highest power of 3 is 0 (as it appears in only one term), the highest power of x is 1, and the highest power of y is 1. Therefore, the HCF of 54xyz and 12x²12 is 2xy.

c) The common factors in 21x²y²z and 7.xyz are 7, x, y, and z. The highest power of 7 in both terms is 0 (as it appears in only one term), the highest power of x is 1, the highest power of y is 1, and the highest power of z is 1. Therefore, the HCF of 21x²y²z and 7.xyz is xyz.

d) To find the HCF of 3a²b³c³, 9a³b³c³, and 18a²b²c², we consider the common factors and their highest powers. The common factors are 3, a, b, and c. The highest power of 3 in all terms is 1, the highest power of a is 2, the highest power of b is 2, and the highest power of c is 2. Therefore, the HCF of 3a²b³c³, 9a³b³c³, and 18a²b²c² is 3a²b²c².

e) The common factors in 6abc, 7ab³c, and 8abc³ are a, b, and c. The highest power of a in all terms is 1, the highest power of b is 1, and the highest power of c is 1. Therefore, the HCF of 6abc, 7ab³c, and 8abc³ is abc.

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The required return for a stock with a beta of 2.20, a risk-free rate of 2%, and a market risk premium of 6% is 14.39%.  The correct option is c.

To calculate the required return, we can use the Capital Asset Pricing Model (CAPM), which relates the expected return of a stock to its beta, the risk-free rate, and the market risk premium. The formula for CAPM is as follows:

Required Return = Risk-Free Rate + (Beta × Market Risk Premium)

In this case, the risk-free rate is 2% and the market risk premium is 6%. The beta of the stock is given as 2.20. Plugging these values into the formula, we get:

Required Return = 2% + (2.20 × 6%) = 2% + 13.2% = 15.2%

Therefore, the correct answer is option C: 14.39%.

The CAPM is a widely used model in finance to estimate the required return on an investment. It takes into account the risk-free rate, which represents the return on a risk-free investment such as government bonds, and the market risk premium, which represents the additional return investors expect to receive for taking on the risk of investing in the overall market.

The beta of a stock measures its sensitivity to market movements, and multiplying it by the market risk premium gives us an estimate of the stock's additional required return. By summing this additional return with the risk-free rate, we obtain the required return for the stock.

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Best-of-breed software architecture is the use of the best software in each software category, but can have potential downsides. BIS infrastructure security risk assessment is concerned with identifying threats, evaluating their severity, and determining the necessary security measures. COBIT is a widely used framework for BIS infrastructures.

Best-of-breed software architecture is the use of the best software in each software category, rather than relying on a single software solution. However, it can have potential downsides such as excessive software licensing costs, difficulty sharing data across applications, and difficulty providing end-to-end support for business processes. BIS infrastructure security risk assessment is concerned with identifying threats to business operations, evaluating their severity, and determining the adequacy of current security measures to mitigate them. COBIT is a widely used risk assessment framework for BIS infrastructures. Risk assessments are conducted to determine the necessary security improvements for BIS infrastructures.

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Answer:

Step-by-step explanation:

- 25x + 15y = 750

- (30, 0) are coordinates of x-intercept. If there is no pool-cleaning job student has to do 30 lawn-mowing.  

- (0, 50) are coordinates of y-intercept. If there is no lawn-mowing job student has to do 50 pool-cleanings.

- ( 15 , 25 ) mean 15 lawn-mowing and 25 pool-cleanings

$25(15) + $15(25) = $750

$375 + $375 = $750

Answer:

If you round it to nearest tenth it will be 50

Step-by-step explanation:

14x3.14=49

Answer: 7313

Step-by-step explanation:

Answer:

The probability of rolling a dice six time until a 7 is first seen is 0.059

Step-by-step explanation:

The probability of getting a seven is equal to \(\frac{1}{10}\)

The dice need to be rolled only six times.

This means that for the first 5 times the dice showed values other than 7 and in the last roll it displays 7

Hence the probability of rolling a dice six time until a 7 is first seen is

\((\frac{9}{10})^5 * (\frac{1}{10})^1\)

\(= \frac{9^5}{10^6} \\= 5.90\) % or 0.059

To describe y as the sum of two orthogonal vectors, x1 in the span{u} and x2 orthogonal to u , we follow two steps procedure:

1.First, find a vector x1 in the span{u} that is the projection of y onto u. To do this, use the formula:
  x1 = (y • u / ||u||^2) * u, where • represents the dot product and || || represents the magnitude of the vector.

2.Next, find the vector x2 that is orthogonal to u. Since y can be represented as the sum of x1 and x2, you can find x2 by subtracting x1 from y:
  x2 = y - x1

3.Now, you have y as the sum of two orthogonal vectors x1 and x2, with x1 in the span{u} and x2 orthogonal to u.

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The stratified sample ensures that the opinions of employees from both locations are represented.

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Answer:

32 in

Step-by-step explanation:

Volume= 1/2 a•c•h

=1/2•4•4•4

= 32 in

Answer:

8.6 meters

Step-by-step explanation:

a² + b² = c²    means        leg² + leg² = hypotenuse ²

5² + 7² = hypotenuse²

25 + 49 = hypotenuse²

74 = hypotenuse ²

\(\sqrt{74}\) = hypotenuse

8.6 = hypotenuse

The FV is $107 for the simple interest.

The formula to calculate simple interest is given as:

I = P × R × T

Where,I is the simple interest, P is the principal or initial amount, R is the rate of interest per annum, T is the time duration.

Formula to find FV:

FV = P + I = P + (P × R × T)

where,P is the principal amount, R is the rate of interest, T is the time duration, FV is the future value.

Given that P = $100, R = 7%, and T = 1 year, we can find the FV of the investment:

FV = 100 + (100 × 7% × 1) = 100 + 7 = $107

Therefore, the FV of $100 invested at 7% for one year (simple interest) is $107.

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Based on the graph of line R, the values of slope (m) and y-intercept (c) are 5 and -2 respectively.

In order to determine the slope (m) and y-intercept (c) of this line, we would select four (4) points on the graph through which line R passes through to represent a solution.

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the graph of line R, we have the following points:

Point (x, y) = (0, -2)

Point (x, y) = (1, 3)

Substituting the given points into the formula, we have;

Slope, m = (3 + 2)/(1 - 0)

Slope, m = 5/1

Slope, m = 5

In Mathematics, the y-intercept of any graph generally occurs at the point where the value of "x" is equal to zero (x = 0). Therefore, the y-intercept (c) of this line is given by:

y-intercept (c) = -2.

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The required measure of x in segment ED = 6x - 4 is 4.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
Consider the similar triangles ABE and ACD,
Since the side of a similar triangle are always proportional to each other,
AB/AC = AE/AD

42+35 / 42 = 24 + 6x - 4 / 24
77 / 42 = 20 + 6x / 24
x = 4

Thus, the required measure of x in segment ED = 6x - 4 is 4.

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The area of the composite figure is 242in² as per the given information in the figure.

Rectangulus, a combination of the Latin words rectus (as an adjective, right, appropriate), and angulus, is where we get the word rectangle (angle).

A crossed rectangle is a crossed (self-intersecting) quadrilateral made up of two opposing sides and the two diagonals of a rectangle[4] (therefore only two sides are parallel). It is a specific case of an antiparallelogram with angles that are not all equal and right angles, even though opposite angles are. Other geometries, including spherical, elliptic, and hyperbolic,  with opposite sides of equal length and equal angles that are not right angles.

Area =Area of the down rectangle+ Area of the up rectangle+2×Area of the triangle

Area= (7×24)+(4×13)+2×(1/2)×b×4

Let, 13+2x=24

Here, x=b

So, 2b=11

b=11/2

Area= 168+52+4(11/2)

Area=168+52+22

Area=242in²

Therefore, the area of the composite figure is 242in².

So, option C is correct.

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Answer:

I = 17deg, II = 73deg

Step-by-step explanation:

Let's say first angle is x, and then respectively, the second angle is 4*x + 5.

Their sum is 90 degrees, so:

x + (4*x+5) = 90

5x + 5 = 90

5x = 85 | :5

x = 17 degrees ==> first angle

4*x+5 = 73 degrees ==> second angle

Answer:

40%

Step-by-step explanation:

Discount = 40%

10% = 0.245

40% = 0.98

$2.45 - $0.98 = $1.47

Answer:

322

Step-by-step explanation:

40a + b

40(8) + 2

320 + 2

322

A scatter plot is a data visualization technique in data analysis that uses a graph to show the relationship between two variables. It is used to display the relationship between two variables in a two-dimensional graph, with one variable on the x-axis and the other variable on the y-axis.

Scatter plots are used to explore the relationship between two variables, identify any patterns, and detect outliers. Scatter plots can also be used to compare the trends between groups of data, such as the relationship between different age groups and salary, or the relationship between different countries and GDP.

Scatter plots can provide insights into which variables are most important when predicting a response variable. Scatter plots are a powerful tool for understanding relationships between variables and can be used in a wide variety of data analysis tasks.

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