A=1/2h(B+b); A=45, B=4, b=5

Step-by-step explanation:

the option that you've chose.

it's the correct answer!

have a good day :)

Answer:

The answer is D. number 4.

Answer:

The measure of B is 56 degrees.

Rhetorical algebra has never really gone away, as evidenced by a 19th century school notebook that includes a rule for computing the area of a triangle using algebraic operations.


The quote highlights the fact that algebraic methods for solving problems have been around for centuries and continue to be used in modern mathematics. The rule provided demonstrates the use of algebraic operations such as addition, subtraction, multiplication, and the square root function to arrive at a solution for the area of a triangle. This underscores the enduring importance of algebra in mathematical problem-solving and the relevance of historical approaches to modern mathematical education.

The inclusion of a rule for computing the area of a triangle in a 19th century school notebook is evidence that rhetorical algebra has never really gone away. Rhetorical algebra refers to the use of words and symbols to express mathematical ideas and solve problems, and has been an important tool in mathematics for centuries.

The rule provided for computing the area of a triangle involves several algebraic operations, including addition, subtraction, multiplication, and the square root function. The process involves taking half the sum of the three sides of the triangle, subtracting each side severally, multiplying the half sum and the three remainders continually together, and taking the square root of the last product to arrive at the area of the triangle. This rule demonstrates the use of rhetorical algebra to solve a geometric problem, and underscores the enduring importance of algebra in mathematical problem-solving.

Furthermore, the inclusion of this rule in a 19th century school notebook highlights the relevance of historical approaches to modern mathematical education. While the specific methods used in rhetorical algebra may have evolved over time, the underlying principles and problem-solving strategies remain relevant to this day. As such, the study of rhetorical algebra can provide valuable insights into the development of mathematical thought and the historical context in which mathematical ideas have been developed and applied.

In conclusion, the inclusion of a rule for computing the area of a triangle in a 19th century school notebook serves as a reminder of the enduring importance of rhetorical algebra in mathematical problem-solving. This example highlights the use of algebraic operations such as addition, subtraction, multiplication, and the square root function to arrive at a solution for a geometric problem, and underscores the relevance of historical approaches to modern mathematical education.

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Answer:  The correct answer is x=−3 or x=5

Step-by-step explanation:

Solve for x^2−2x=15 using the quadratic equation

Step 1) Subtract 15 from both sides

x2−2x−15=15−15

x2−2x−15=0

For this equation: a=1, b=-2, c=-15

1x2+−2x+−15=0

Step 2) Use quadratic formula with a=1, b=-2, c=-15

x= (−b±√b2−4ac)/2a

x= (−(−2)±√(−2)2−4(1)(−15))/2(1)

x= (2±√64)/2

x=5 or x=−3

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Speed is the rate of distance over time.

The speed of the boat is 13mph south-west

Given

\(v_1 = 12mph\) --- west

\(v_2 = 5mph\) -- south

The speed is illustrated with the attached image

Because both speeds act at a diagonal, the speed (v) of the boat is calculated using Pythagoras theorem as follows:

\(v^2 = 12^2 + 5^2\)

\(v^2 = 144 + 25\)

\(v^2 = 169\)

Take square root

\(v = \sqrt{169\)

\(v = 13\)

Hence, the speed of the boat is 13mph south-west

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A. To transform triangle XYZ to AX'Y'Z', following sequence of transformations is applied: Translation, Rotation, Dilation.

Transformations of a triangle are changes made to the position, size, or orientation of the triangle in a coordinate plane.

There are four types of transformations that can be applied to a triangle.

A. To transform triangle XYZ to AX'Y'Z', the following sequence of transformations can be applied:

Translation: Translate triangle XYZ so that point X coincides with point X'. This can be done by moving the entire triangle 6 units to the left and 8 units up.

Rotation: Rotate the translated triangle around point X' by an angle of 135 degrees in the counterclockwise direction. This can be done by applying a rotation matrix:

[ cos(135)  -sin(135)   0 ]   [ x ]

[ sin(135)   cos(135)   0 ] * [ y ]

[    0          0       1 ]   [ 1 ]

Dilation: Dilate the rotated triangle with center X' by a scale factor of 1/2. This can be done by multiplying the coordinates of each point by 1/2 with respect to point X'.

B. No, a dilation alone is not enough to show similarity of two figures. Similarity of two figures requires that the figures have the same shape but not necessarily the same size. In addition to dilation, the figures could be subject to other transformations such as translation, rotation, and reflection. Therefore, to show similarity between two figures, it is necessary to demonstrate that the corresponding angles of the figures are congruent and that the corresponding sides are proportional.

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5 x 6 = 30

9 x 6 = 54

54 + 30 = 84

you would be intaking 84 grams of fat

Answer:

  56.3 units

Step-by-step explanation:

You want the side opposite a 102° angle in a triangle with a side of length 27 opposite a 28° angle.

The law of sines tells you side lengths are proportional to the sine of the opposite angle.

  b/sin(102°) = 27/sin(28°)

  b = 27(sin(102°)/sin(28°)) ≈ 56.3

The length of side b is about 56.3 units.

__

Additional comment

The side labeled b is not the "hypotenuse" in this triangle. The term "hypotenuse" is reserved for the long side of a right triangle.

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The system of linear equation for the graph are: y = -1/3x + 3 and y = 3x - 7.

A system of linear equation is a combination of two linear equation. Each linear equation is made of algebraic equation that consists of variables, constant, and arithmetic operation.

To determine the linear equation on the graph, we need to find two points on the each line on the graph and determine the slope-intercept form.

For the first decreasing line to the left, we have the two points

(0, 3)(9,0)

Using the slope intercept form y = mx + b. The linear equation for the first line is: y = -1/3x + 3

For the second increasing line to the right, the two points are:

(3,2)(0,-7)

The linear equation for the second line is:

y = 3x - 7

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Answer:

6.5 Meters per second

Step-by-step explanation:

if the bird flew 65 meters in 10 seconds, just divide 65 ÷ 10 = 6.5.

which if you were to add 6.5 ten times you would get 65.

Answer:

  18

Step-by-step explanation:

Triangles FEG and DEG are congruent by SAS, so DG = FG.

  a+6 = 3a

  6 = 2a

  3 = a

  3a = 3·3 = 9 = FG = DG

DF = 9+9 = 18

Answer:

AB = 25 units

Step-by-step explanation:

In right triangle ACB, \( CD\perp AB\)

Therefore, by geometric mean property:

\(CD^{2} ={AD\times DB} \\ \\ {10}^{2} = AD\times 5 \\ \\ 100 = 5AD \\ \\ AD = \frac{100}{5} \\ \\ AD = 20\)

AB = AD + DB

AB = 20 + 5

AB = 25 units

Answer:

x = 9

y = 9√2

Step-by-step explanation:

We can use the properties of an isosceles right triangle (45-45-90) to solve for x and y.

The legs of an isosceles triangle are congruent, so x = 9.

The hypotenuse of an isosceles right triangle is equal to one of the legs multiplied by the square root of 2. Therefore,

y = 9 · √2 = 9√2

Answer:

x = 9 , y = 9\(\sqrt{2}\)

Step-by-step explanation:

the triangle is a 90- 45- 45 , isosceles right triangle, with congruent legs

then x = 9

using Pythagoras' identity in the right triangle

y² = 9² + 9² = 81 + 81 = 162 ( take square root of both sides )

y = \(\sqrt{162}\) = \(\sqrt{81(2)}\) = \(\sqrt{81}\) × \(\sqrt{2}\) = 9\(\sqrt{2}\)

Answer:

false i think

Step-by-step explanation:

Answer: true

Step-by-step explanation:

Answer:

3a^2 + 28b^2 - 5ab

Step-by-step explanation:

here's your solution

=> to subtract (12x^2 + 15ab - 29b^2) from

( 15a^2 + 10ab + 8b^2)

=> (15a^2 + 10ab + 8b^2) - (12a^2 + 15ab - 20b^2)

=> 15a^2 + 10ab + 8b^2 - 12a^2 - 15ab + 20b^2

=> 15a^2 - 12a^2 + 8b^2 + 20b^2 + 10ab - 15ab

=> 3a^2 + 28b^2 - 5ab

hope it helps

Answer:

20 mins

Step-by-step explanation:

2003 17 2005 20

Answer:

mark can buy 6 packs of pens

Step-by-step explanation:

Mark has $30 and he wants to buy 3 notebooks. Each notebook is $5 ,so 5×3=15 witch leaves only 15 dollars left because that's half of 30 . Then you take your 15 dollars you have left and divide by 2.50 . This will give you 6 . that's how many packs of pens Mark can buy .

Answer:

Spencer

Step-by-step explanation:

The points are (3,-1) and (5,4) to find slope, you subtract the two y and x points  and divide or put it into a fraction.

The equation for the numerator would be 4-(-1). The negatives cancel out, so the equation is actually 4+1, which is 5.

The equation for the denominator is 5-3, which is 2.

The slope would be 5/2, and Spencer did that work, so Spencer is correct.

The slope will be 5/2, and Spencer did that work, so Spencer is correct.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

Given the points;

(3,-1) and (5,4)

x1 = 3 ; x2 = 5 ; y1 = - 1 ; y2 = 4

Spencer is right because, the slope of a line is obtained thus ;

Slope = change in y / change in x

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

Slope = (4 - (-1)) / (5 - 3)

Slope = (4 + 1) / 2

Slope = 5 / 2

Hence, slope = 2.5

The slope will be 5/2, and Spencer did that work, so Spencer is correct.

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The function that describes the fund that was raised is 0.05³ - 30x - 12425

The revenue is  R (z) = 0.05x³ + 75

the cost = C(z) = 30x + 12,500.

Please note that the equation for revenue missed a sign in the question so I made use of the plus sign

We would have revenue - cost

Hence ( 0.05x³ + 75) - (30x + 12,500)

We would open the bracket

0.05x³ + 75 -30x -12500

We would take the like term to

0.05³ - 30x -12500 + 75

0.05³ - 30x - 12425

The function that describes the fund that was raised is 0.05³ - 30x - 12425

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Answer: F(x)=0.05x^3-30x-12,575

Step-by-step explanation:

Correct on test.

Answer:

1

Step-by-step explanation:

Answer:

i think like the 2nd one im not sure i cant see the lines

Step-by-step explanation:

Step-by-step explanation:

100x4=400miles

400miles in February

OR

300x4=1200 miles

1200 miles in February

I don't know what is the correct one tho

Answer:

Step-by-step explanation:

1200 miles

Answer: slope =1/2  y intercept (0,6)

Step-by-step explanation: use the slope and y intercept form y=mx + b

The expression of the league fee is an algebraic expression

The expression that represents the league fee is 14x

The expression is given as:

14x + 20(2y + ) 5z + 10

The expression is not properly stated;

Only the league fee can be deducted from the given expression.

From the question, we understand that there are 14 players in total

i.e you (1) and (13) others

This means that the total league fee for the 14 players is:

Total = 14 * League fee for each player.

One of the terms of the expression is 14x.

So, we have:

14 * League fee for each player. = 14x

Hence, the expression that represents the league fee is 14x

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Answer:  Let's assume the number of pretzels sold is represented by the variable "P," and the number of hot dogs sold is represented by the variable "H."

Based on the information given in the problem, we can create a system of equations:

The total sales equation: $3P + $2H = $195

The relationship between the number of pretzels and hot dogs: H = P + 15

Now, let's evaluate each answer choice by substituting the values into the equations and checking if they satisfy the system:

A. 33 pretzels, 48 hot dogs:

$3(33) + $2(48) = $99 + $96 = $195 (satisfies the total sales equation)

48 = 33 + 15 (satisfies the relationship equation)

So, option A is a possible combination.

B. 15 pretzels, 30 hot dogs:

$3(15) + $2(30) = $45 + $60 = $105 (does not satisfy the total sales equation)

30 ≠ 15 + 15 (does not satisfy the relationship equation)

Therefore, option B is not a possible combination.

C. 35 pretzels, 45 hot dogs:

$3(35) + $2(45) = $105 + $90 = $195 (satisfies the total sales equation)

45 = 35 + 15 (does not satisfy the relationship equation)

Thus, option C is not a possible combination.

D. 31 pretzels, 51 hot dogs:

$3(31) + $2(51) = $93 + $102 = $195 (satisfies the total sales equation)

51 = 31 + 15 (satisfies the relationship equation)

Therefore, option D is a possible combination.

Based on the evaluation, the possible amounts of pretzels and hot dogs that Joanie sold today are:

A. 33 pretzels, 48 hot dogs

D. 31 pretzels, 51 hot dogs

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

2 |  1   5   - 14

          2     14

  -----------------------

     1    7      0 ← remainder = 0

     Quotient is 1x + 7 = x + 7 → D

A graph of the system of inequalities is shown in the image attached below.

The region that represents the combinations of balloons and streamers that Tamara can purchase is the shaded region that contains the point (1, 3).

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of packages of balloons and number of streamer rolls respectively, and then translate the word problem into algebraic equation as follows:

Since one package of balloons costs $4.50 and streamers are $1.50 per roll, and Tamara wants to spend no more than $15 on decorations, a linear inequality to describe this situation is given by:

4.50x + 1.50y ≤ 15.

Additionally, Tamara knows she will be buying at least 2 rolls of streamers;

y ≥ 2

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