Complete this item.


Identify ∠1 and ∠ 2. Select all that apply of the following terms: acute, right, obtuse, adjacent, vertical, complementary, supplementary.

Answer:

Undefined? Or 5?

Step-by-step explanation:

The two column method can be used to prove that BD is congruent to CE BD ≅ CE as follows;

Statement \({}\)                                            Reasons

1. ΔABC is an isosceles triangle \({}\)       1. Given

2. AB and AC are legs of ΔABC \({}\)       2. Given

3. BD ⊥ DC   \({}\)       \({}\)       \({}\)       \({}\)       \({}\)         3. Given

CE ⊥ BE

4. ∠BDC = 90° and ∠CEB = 90° \({}\)      4. Definition of perpendicular lines

5. ∠BDC = ∠CEB  \({}\)       \({}\)       \({}\)       \({}\)       5. Substitution property

6. ∠BDC ≅ ∠CEB  \({}\)       \({}\)       \({}\)       \({}\)      6. Definition of congruency

7. ∠ABC ≅ ∠ACB \({}\)       \({}\)       \({}\)       \({}\)  7. Base angles of an isosceles triangle

8. \(\overline{BC}\) ≅ \(\overline{BC}\)  \({}\)       \({}\)       \({}\)       \({}\)       \({}\)       8. Reflexive property of congruency

9. ΔBCE ≅ ΔCBD  \({}\)       \({}\)       \({}\)       \({}\)      9. SAA congruency postulate

10. BD ≅CE \({}\)       \({}\)       \({}\)       \({}\)       \({}\)       \({}\)  10. CPCTC

Two figures are congruent if they have the same size and shape.

The properties, postulates, and theorem used in the prove that BD ≅ CE are as follows;

Perpendicular lines;

Perpendicular lines are lines that form 90° angles where they intersect.

Substitution property

The substitution property of equality states that if one quantity a = b, then b can be substituted for a in equations and expression, such that the value of the expressions and equations remain the same.

Definition of congruency

Congruent figures are figures that have the same shape and size

Base angles of an isosceles triangles

The base angles of an isosceles triangle are congruent

Reflexive property

The reflexive property of congruency states that a figure is congruent to itself

SAA congruency postulate

The Side-Angle-Angle, SAA congruency postulate states that if two angles and  the non included side of one triangle are congruent to two angles and the non included side of the other triangle, then the two triangles are congruent.

CPCTC

Corresponding Parts of Congruent Triangles are Congruent, CPCTC states that the corresponding parts of congruent triangles are also congruent.

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To calculate the probability of drawing a king or a diamond from a standard deck of 52 cards, we first need to determine the number of favorable outcomes and the total number of possible outcomes.

The number of favorable outcomes is the number of cards that are either kings or diamonds. In a standard deck, there are 4 kings (one king in each suit) and 13 diamonds. However, we need to subtract one king of diamonds from the count since it was already counted as a king. So, the total number of favorable outcomes is 4 (kings) + 13 (diamonds) - 1 (king of diamonds) = 16.

The total number of possible outcomes is simply the total number of cards in the deck, which is 52. Therefore, the probability of drawing a king or a diamond from the deck is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:

Probability = Favorable outcomes / Total outcomes
Probability = 16 / 52
Probability = 4 / 13
Hence, the probability of drawing a king or a diamond from a standard deck of 52 cards is 4/13 or approximately 0.3077.

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The sum of the factors is:x + y = 16 + (-3) = 13The sum of the factors is 13.

To solve this problem, we need to use factoring of algebraic expressions. We are given that two factors of -48 have a difference of 19, and the factor with a greater absolute value is positive. We are to find the sum of the factors.The first step to solving this problem is to write -48 as a product of two factors that differ by 19. Let x be the greater of these factors, and let y be the other factor. Then we have:x - y = 19xy = -48

We need to solve these equations to find the values of x and y. We can solve the second equation for y by dividing both sides by x: y = -48/x. We can then substitute this expression for y into the first equation: x - (-48/x) = 19x + 48/x = 19Multiplying both sides of this equation by x gives us a quadratic equation: x² + 48 = 19xRearranging this equation, we get: x² - 19x + 48 = 0We can solve this quadratic equation using factoring. We need to find two numbers that multiply to 48 and add up to -19. These numbers are -3 and -16. Therefore, we can write: x² - 19x + 48 = (x - 3)(x - 16)Setting each factor equal to zero gives us the possible values of x: x - 3 = 0 or x - 16 = 0x = 3 or x = 16Since we know that the factor with the greater absolute value is positive, we have:x = 16 and y = -48/x = -3

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The volume of the box at x = 1 will be 15 cubic units.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

Noah finds an expression for V(x) that gives the volume of an open-top box in cubic inches in terms of the length x in inches of the cutout squares used to make it. This is the graph Noah gets if he allows x to take on any value between -1 and 5.

From the graph, the volume of the box at x = 1 will be 15 cubic units.

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Answer:

Part 2

A. 10

B. 20

C. 15.4

Part 3

A. 96

B.96

C.24

D. 12

Step-by-step explanation:

I am not sure of the last part but I hope the first to help you

for the area of a triangle it is b*h*1/2 and for a rectangle it is bh

Assuming Delia works 5 days a week:

Since she works from 8:00 to 16:30, she works 8.5 hours a day. However, she takes one hour off for lunch, so in reality she works 7.5 hours a day.

Since we're assuming she works 5 days a week, she works

hours a week. If her hourly wage is $4.80, then she earns

so she earns $180 per week. Option c. is the correct answer.

Answer:

should be 110

Step-by-step explanation:

if you use PEMDAS you first add what is in () so you add 3+52 which is 55 now do 4 X (55) divided by 2 no you go from left to right and multiply 4 x 55 which gives you 220 and now you divide 220/2 and you get 110 hope that helps give me BRAINLIEST !!!

Hey there!

Just do PEMDAS

• Parentheses

• Exponent

• Multiplication

• Division

• Addition

• Subtraction

To remember the PEMDAS formula you could say “Please Excuse My Dear Aunt Sally”

Anyway

Solving for your equation….

4 × (3 + 52) ÷ 2

= 4 × 55 ÷ 2

= 220 ÷ 2

= 110

Therefore, your answer is: 110

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

Step-by-step explanation:

The equation of a line with slope of m and y-intercept of b is: y = mx + b

b = 2 and line contains the point (4, -9), so:

-9 = m×4 + 2          {subtract 2 from both sides}

-11 = 4m                   {divide booth sides by 4

m = -¹¹/₄

The two sides are equal and for that reason DE = CE as shown below :

AD = BC, DF = GC

E = A(F) and E = BG,  therefore A(F) = BF

Now we all know that a rectangle has four edges which are A, B, C, D.

when we divide the bottom line, which is the line from point C to D into three parts we will have ( DF, FG, and GC )

From the question we know that DF = GC

E is the intersection of A(F) and BG

we can now Prove that DE = CE.

since D and C are point included in E and since this is a rectangle

AD = BC, DF = GC

E = A(F) and E = BG,  therefore A(F) = BF

DE = CE

We can conclude by saying that in a rectangle two sides are equal and for that reason DE = CE

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well 6 bagels cost $7.50  and you bought 11 bagel with a $20 dollar bill

so answer that

Answer:

46

Step-by-step explanation:

230÷10=23

23×2=46

answer 46

Answer:

5/15 = 1/3

Step-by-step explanation:

Answer: 1/3 km

Step-by-step explanation:

5 can go into both 5 and 15, which would simplify to 1/3 :)

Part A: 1. The best expected payoff is $3630.

2. The expected value of perfect information (EVPI) is $2470.

Part B: 1. $3176, 2. $2784, 3. $4702, 4. $1072, 5. 43.4%.

1. The best expected payoff and the corresponding decision using the Expected Monetary Value (EMV) approach is:

The expected payoff for each decision can be calculated by multiplying the payoff for each market potential scenario by its corresponding probability and summing them up.

For the small store:

EMV(small) = (0.4 * 4500) + (0.3 * 4800) + (0.3 * 0) = 1800 + 1440 + 0 = $3240

For the regular store:

EMV(regular) = (0.4 * 5700) + (0.3 * 5500) + (0.3 * (-1000)) = 2280 + 1650 - 300 = $3630

For the large store:

EMV(large) = (0.4 * 6100) + (0.3 * 3500) + (0.3 * (-300)) = 2440 + 1050 - 90 = $3400

The highest expected payoff is $3630, which corresponds to the regular store. Therefore, the decision with the best expected payoff is to open a regular store.

2. The expected value of perfect information (EVPI) is the maximum possible improvement in expected payoff that could be achieved with perfect information. It can be calculated by finding the difference between the expected payoff under perfect information and the expected payoff under the current situation.

To calculate EVPI, we need to consider the maximum expected payoff under perfect information. This means we assume we know the market potential with certainty and choose the store type accordingly.

Under perfect information, the decision will be:

EVPI = Max(Payoff under perfect information) - EMV(current situation)

= Max($6100, $5500, $4800) - EMV(current situation)

= $6100 - $3630

= $2470

Therefore, the expected value of perfect information (EVPI) is $2470.

Part B:

To calculate the expected value of the optimal decision with ALBION's report, we need to consider the probabilities and payoffs associated with each scenario.

1. If ALBION gives a favorable report:

The probability of high market potential is 0.52, and the payoff for opening a large store is $6100.

The probability of low market potential is 0.08, and the payoff for opening a small store is $4800.

Expected value with a favorable report:

EV(favorable) = (0.52 * 6100) + (0.08 * 4800) = $3176

2. If ALBION gives an unfavorable report:

The probability of high market potential is 0.16, and the payoff for opening a large store is $6100.

The probability of low market potential is 0.48, and the payoff for opening a small store is $4800.

Expected value with an unfavorable report:

EV(unfavorable) = (0.16 * 6100) + (0.48 * 4800) = $2784

3. The expected value with sample information (EVwSI) provided by ALBION can be calculated by weighting the expected values of the optimal decisions with the probabilities of receiving a favorable or unfavorable report.

EVwSI = (0.45 * EV(favorable)) + (0.55 * EV(unfavorable))

= (0.45 * $3176) + (0.55 * $2784)

= $3170.80 + $1531.20

= $4702

4. The expected value of the sample information (EVSI) provided by ALBION is the difference between the expected value with sample information and the expected value without any information.

EVSI = EVwSI - EMV(current situation)

= $4702 - $3630

= $1072

5. The efficiency of the sample information is the ratio of the expected value of the sample information to the expected value of perfect information (EVSI/EVPI), multiplied by 100 to express it as a percentage.

Efficiency of the sample information:

Efficiency = (EVSI / EVPI) * 100

= ($1072 / $2470) * 100

≈ 43.4%

Therefore, the efficiency of the sample information provided by ALBION is approximately 43.4%.

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We need to know about the relation between roots of a quadratic equation for solving the question. The quadratic equation with roots 3/4 and 1/2 is \(8x^{2} -10x+3=0\)

Quadratic equation is an equation with the highest order of variable being 2. Roots of a quadratic equation are the values that satisfy the equation.Since quadratic equation has the highest order as 2, the equation has two roots. Roots of a quadratic equation can be real and unique, real and equal or imaginary. The roots of a quadratic equation can be used to get the quadratic equation itself.

Let there be a quadratic equation:

\(ax^{2} +bx+c=0\\x^{2} +\frac{b}{a} x+\frac{c}{a} =0\)

Let the roots of the quadratic equation be α and β, then

α+β=-b/a

αβ=c/a

In this question we know the two roots are 3/4 and 1/2. So we can derive the quadratic equation from them

\(\frac{3}{4} +\frac{1}{2} =\frac{-b}{a} \\\frac{-b}{a} =\frac{5}{4}\)

\(\frac{3}{4}\)×\(\frac{1}{2} =\frac{c}{a}\)

\(\frac{c}{a} =\frac{3}{8}\)

The quadratic equation is:

\(x^{2} -\frac{5}{4} x+\frac{3}{8} =0\\8x^{2} -10x+3=0\)

Therefore we found the quadratic equation with roots 3/4 and 1/2 to be \(8x^{2} -10x+3=0\)

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its the red one

i learnt it in school

Answer

Matilda needs to sell 1376$ worth of coffee

The value of x is 16.

The value of y is 1.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

x - 2y = 14 ____(1)

x = 14 + 2y _____(2)

x + 3y = 9 _____(3)

Putting (2) in (3) we get,

14 + 2y + 3y = 9

14 + 5y = 19

5y = 19 - 14

5y = 5

y = 1

Now,

y = 1 in (2)

x = 14 + 2 x 1

x = 14 + 2

x = 16

Thus,

The value of x and y is 16 and 1.

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Answer:

Oblique rectangular prism

Answer:

x = -4.5

Step-by-step explanation:

Given:

0.1x + 0.008 = 0.06x − 0.172

Collect like terms

0.1x - 0.06x = -0.172 - 0.008

0.04x = - 0.18

x = -0.18/0.04

x = -4.5

Check:

0.1x + 0.008 = 0.06x − 0.172

0.1(-4.5) + 0.008 = 0.06(-4.5) - 0.172

- 0.45 + 0.008 = -0.27 - 0.172

-0.442 = -0.442

Answer:

(-2, 12)

Step-by-step explanation:

7x + 2 = 8x + 4

2 = x + 4

x = -2

The first derivatives for the given functions are:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For  \(y = 100200x + 7x,\) the first derivative is dy/dx = 100207.

For \(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

To find the first derivative for each of the given functions, we'll use the power rule, constant rule, and chain rule as needed.

For the function\(y = 3x^2 + 5x + 10:\)

Taking the derivative term by term:

\(d/dx (3x^2) = 6x\)

d/dx (5x) = 5

d/dx (10) = 0

Therefore, the first derivative is:

dy/dx = 6x + 5

For the function y = 100200x + 7x:

Taking the derivative term by term:

d/dx (100200x) = 100200

d/dx (7x) = 7

Therefore, the first derivative is:

dy/dx = 100200 + 7 = 100207

For the function \(y = ln(9x^4):\)

Using the chain rule, the derivative of ln(u) is du/dx divided by u:

dy/dx = (1/u) \(\times\) du/dx

Let's differentiate the function using the chain rule:

\(u = 9x^4\)

\(du/dx = d/dx (9x^4) = 36x^3\)

Now, substitute the values back into the derivative formula:

\(dy/dx = (1/u) \times du/dx = (1/(9x^4)) \times (36x^3) = 36x^3 / (9x^4) = 4/x\)

Therefore, the first derivative is:

dy/dx = 4/x

To summarize:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For y = 100200x + 7x, the first derivative is dy/dx = 100207.

For\(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

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Answer:

2.645751311064591 (2.65 rounded to nearest hundredth)

Step-by-step explanation:

you take 7 and you try and find the closest number down to the furthest numbers. Or if you are using a calculator, you put 7, then you press the 2√x

Answer:

54 MINUETS

Step-by-step explanation:

IM RIGHT;}

Answer:

Current Bond price = $1155.5116

Step-by-step explanation:

We are given;

Face value; F = $1,000

Coupon payment;C = (7.3% x 1,000)/2 = 36.5 (divided by 2 because of semi annual payments)

Yield to maturity(YTM); r = 5.6%/2 = 2.8% = 0.028 (divided by 2 because of semi annual payments)

Time period;n = 13 x 2 = 26 years (multiplied by 2 because of semi annual payments)

Formula for bond price is;

Bond price = [C × [((1 + r)ⁿ - 1)/(r(r + 1)ⁿ)] + [F/(1 + r)ⁿ]

Plugging in the relevant values, we have;

Bond price = [36.5 × [((1 + 0.028)^(26) - 1)/(0.028(0.028 + 1)^(26))] + [1000/(1 + 0.028)^(26)]

Bond price = (36.5 × 18.2954) + (487.7295)

Bond price = $1155.5116

The height of the pennant is 30 inches. To find the height of the pennant, we'll use the formula for the area of a triangle: Area = (1/2) * base * height.

Given that the area is 180 square inches and the base length is z inches, we have: 180 = (1/2) * z * height. Now, we are told that the height is 6 inches longer than twice the base length. Therefore, we can write: height = 2z + 6. Substituting this value into the equation for the area, we have: 180 = (1/2) * z * (2z + 6). Simplifying this equation, we get: 180 = z * (z + 3). Now, we can solve for z by rearranging the equation and solving the quadratic equation: z^2 + 3z - 180 = 0.

Using factoring, quadratic formula, or other methods, we find that z = 12 or z = -15. Since we are dealing with lengths, we'll discard the negative solution. So, the base length of the pennant is 12 inches. To find the height, we substitute z = 12 into the expression for the height: height = 2z + 6; height = 2(12) + 6; height = 24 + 6; height = 30. Therefore, the height of the pennant is 30 inches.

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Answer:

89 m²

Step-by-step explanation:

Area of rectangle = 8 x 13 = 104

Area of triangle = (5 x 6) / 2 = 15

104 - 15 = 89 m²

To classify a quadrilateral by its sides, we need to calculate the distance between each pair of its vertices.

The distance between Q and R is the square root of ((1-(-2))^2 + (5-(-1))^2) = square root of (3^2 + 6^2) = square root of (9+36) = square root of 45 = 6.7

The distance between R and T is the square root of ((-8-1)^2 + (-4-5)^2) = square root of (9+81) = square root of 90 = 9.5

The distance between Q and T is the square root of ((-8+2)^2 + (-4+1)^2) = square root of (10+5) = square root of 15 = 3.87

If the quadrilateral is a rectangle, two sides of it have to be equal, so in this case, AQRT is not a rectangle.

If the quadrilateral is a rhombus, all four sides have to be equal, so in this case, AQRT is not a rhombus.

If the quadrilateral is a square, all four sides have to be equal, so in this case, AQRT is not a square.

If the quadrilateral is a trapezoid, two adjacent sides are parallel, so in this case, AQRT is not a trapezoid.

If the quadrilateral is a parallelogram, two pairs of opposite sides are parallel, so in this case, AQRT is not a parallelogram.

If the quadrilateral is a kite, two pairs of sides have the same length, so in this case, AQRT is not a kite.

So the only possible classification is that AQRT is a general quadrilateral.

so we have:

QR = 6.7

RT = 9.5

QT = 3.87