Triangles ABC and EDC are similar.
ACE and BCD are straight lines.
Angle BAC = angle DEC
Angle CBA= angle CDE
AB = = 6 cm, BC = 2.5 cm, CD = 7.5 cm and CE = 10.5 cm.

y = x²-5

f(x) = x² - 5

f(-4) = (-4)² - 5

f(-4) = 16 - 5

f(-4) = 11

give me brainliest pls hehe

The solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.

Part A:

Given:

To find an equation,

Where x is number of monthly minutes.

and y is total monthly of splint plan.

So, equation is:

\(\rightarrow \text{y} =\text{mx} +\text{b}\)

For the first case:

\(\rightarrow\bold{173 = 380x + b}\)

Second case:

\(\rightarrow\bold{249= 570x + b}\)

Solve for x:

\(\rightarrow{173 - 380\text{x}=249- 570\text{x}\)

\(\rightarrow{-207=-321\)

\(\rightarrow \text{x} =\dfrac{321}{207}\)

\(\rightarrow \text{x} =\dfrac{107}{69}\)

\(\rightarrow \text{x} \thickapprox1.55\)

For value of b

\(\rightarrow 173 = 380(1.55) + \text{b}\)

\(\rightarrow 173 - 589 = \text{b}\)

\(\rightarrow -416 = \text{b}\)

Part B:

\(\rightarrow \text{y} = 942(1.55) - 416\)

\(\rightarrow \text{y} = 1460.1 - 416\)

\(\rightarrow \text{y} \thickapprox1044\)

Therefore, the solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

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Answer:

  (x, y) ⇒ (-x√3/2 +y/2, -x/2 -y√3/2)

Step-by-step explanation:

The rule for CCW rotation through an angle α is ...

  (x, y) ⇒ (x·cos(α) -y·sin(α), x·sin(α) +y·cos(α))

So, for α = 210°, the rule becomes ...

  (x, y) ⇒ (-x√3/2 +y/2, -x/2 -y√3/2)

The value of x in the pentagon JKLMN is 7.2.

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

The pentagons ABCDE and JKLMN are similar.

when two figures have the same shape but their sizes are different, then such figures are called similar figures.

We need to find the value of x.

1/1.8=4/x

Apply cross multiplication

x=4×1.8

x=7.2

Hence, the value of x in the pentagon JKLMN is 7.2.

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Ms. Banacka purchased a total of 25 items and spent $95.

Since each package of water balloons costs $3.25 and each water gun cost $4.50, we can calculate the total cost of the water balloons and water guns together.

Total cost of water balloons = 3.25 x number of packages of water balloons purchased

Total cost of water guns = 4.50 x number of water guns purchased

Total cost of all items = number of packages of water balloons x 3.25 + number of water guns x 4.50

Since the total cost of all items is $95 and the total cost of the water balloons is 3.25 x number of packages of water balloons purchased, we can set up the following equation:

3.25 x number of packages of water balloons purchased + number of water guns x 4.50 = 95

To solve this equation, we can first calculate the total cost of the water guns by subtracting the total cost of all items ($95) from the total cost of the water balloons (3.25 x number of packages of water balloons purchased):

number of water guns x 4.50 = 95 - 3.25 x number of packages of water balloons purchased

Now we can solve for number of water guns:

number of water guns = (95 - 3.25 x number of packages of water balloons purchased) / 4.50

We know that the total number of items purchased is 25, so the number of water guns must be equal to 25 minus the number of packages of water balloons purchased:

number of water guns = 25 - number of packages of water balloons purchased

Substituting this expression for number of water guns in our original equation gives us

3.25 x number of packages of water balloons purchased + (25 - number of packages of water balloons purchased) x 4.50 = 95

Now we can solve for number of packages of water balloons purchased:

number of packages of water balloons purchased = (95 - 25 x 4.50) / (3.25 - 4.50)

Simplifying, we get

number of packages of water balloons purchased = 16

Therefore, Ms. Banacka purchased 16 packages of water balloons.

The solutions to the inequalities are given as follows:

The first inequality is given as follows:

\(2^{x^2 - 5x - 4} < 4\)

We have that 4 = 2², hence:

\(2^{x^2 - 5x - 4} < 2^2\)

As the exponential function is increasing over it's entire domain, the inequality can be represented as follows:

x² - 5x - 4 < 2

x² - 5x - 6 < 0.

The quadratic equation x² - 5x - 6 is concave up, hence it's negative between it's roots, obtained as follows:

(x - 2)(x - 3) = 0.

Applying the Factor Theorem:

Hence the solution to the inequality is of:

2 < x < 3.

The second inequality is given as follows:

\(\log_{0.3}{(x^2 + 3)} \geq \log_{0.3}{4x}\)

The logarithm function is also increasing over it's entire domain, hence the inequality is simplified as follows:

x² + 3 ≥ 4x

x² - 4x + 3 ≥ 0.

Another concave up quadratic equation, which is non-negative to the left of the smallest root and to the right of the highest root.

The roots are obtained by factoring as follows:>

(x - 3)(x - 1) = 0.

Hence:

Then the solution is given as follows:

x ≤ 1 or x ≥ 3.

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The value of the function when x = 2 is 33.25.

A function with the formula f(x) = abˣ is an exponential function. A and b are constants, and b is a positive real integer that is greater than zero. The basis b determines how much the function increases or decreases, and x is the exponent or power that raises the base. The function shows exponential growth if b is bigger than 1, whereas the function shows exponential decline if b is between 0 and 1. Many phenomena, including population expansion, compound interest, radioactive decay, and the spread of infectious illnesses, are modelled using exponential functions.

The given function is \(f(x) = 3 +7e^{0.58x}\).

Substitute the value of x = 2 we have:

\(f(2) = 3 + 7(2.72)^{0.58(2)}= 3 + 7(2.72)^{1.16}\)

= 3 + 7(4.464)

= 33.25

Hence, the value of the function when x = 2 is 33.25.

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Step-by-step explanation:

lo que tú puso es muy falso

Answer:

4/x = 200

x = 4/200

x = 2/100

x = 0.02

so the correct option is C. 0.02

Step-by-step explanation:

brainliest plz

Answer:

7

Step-by-step explanation:

The calculated volume of the prism is 702 cubic cm

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

The trapezoidal prism (see attachment)

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (8 + 10) * 6

Evaluate the sum of 8 and 10

Base area = 1/2 * 18 * 6

Evaluate the products of 1/2, 18 and 6

Base area = 54

Also, we have

Height = 13

So, the volume is calculated as

volume = 13 * 54

Evaluate

volume = 702

Hence, the volume of the prism is 702 cubic cm

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Answer: \(\frac{5}{(x+1)(x+5)}\)

Step-by-step explanation:

\(\frac{5}{x+5} - \frac{5x}{x^2+6x+5}\)=

\(\frac{5}{x+5} - \frac{5x}{(x+1)(x+5)}\)=

\(\frac{5(x+1)}{(x+1)(x+5)} - \frac{5x}{(x+1)(x+5)}\)=

\(\frac{5(x+1)-5x}{(x+1)(x+5)}\)=

\(\frac{5x+5-5x}{(x+1)(x+5)}\)=\(\frac{5}{(x+1)(x+5)}\)

Answer:

A. Relation

B. Relation

C. Function

D. Function

E. Relation

The sector angle are 140.4° for bus, 43.2° for bike, 90° for walk and 86.4° for car.

A pie chart is a type of graph where a circle is divided into certain sectors where each sector shows a proportion of the whole.

We have to show the given data in a pie chart where each sector represents a proportion of a type of transportation.

39 students uses bus for transportation.

12 students uses bike for transportation.

25 students walk for transportation.

24 students uses car for transportation.

Total number of students = 39 + 12 + 25 + 24 = 100

Total sector angle of a circle = 360°

Sector angle for bus = (39 / 100) × 360 = 140.4°

Sector angle for bike = (12 / 100) × 360 = 43.2°

Sector angle for walk = (25 / 100) × 360 = 90°

Sector angle for car = (24 / 100) × 360 = 86.4°

Hence the sector angle for each mode of transportation is 140.4° for bus, 43.2° for bike, 90° for walk and 86.4° for car.

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The required radius of the circular pond is 12 meters.

The area of the circle is given by the pie times square of the radius.

Area of circle = πr²

Here,
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius of the circle.

Given that the area of the circular pond is 144π square meters, we can set up the equation:

144π = πr²

Dividing both sides by π, we get:

144 = r²

Taking the square root of both sides, we get:

r = 12

Therefore, the radius of the circular pond is 12 meters.

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Answer:

x^2+9x+20.25=5.25

Step-by-step explanation:

a^2+ba+c; x^2+9x+15=0; x^2+9x+15-15=0-15; x^2+9x=-15; then you you take (1/2b)^2 and add it to both sides, 4.5^2=20.25; x^2+9x+20.25=-15+20.25; x^2+9x+20.25=5.25

Answer: We can set up the following pair of simultaneous equations:

a + c = 6.70 (equation 1) (the total amount of money they have is ₹6.70)

a = c + 1.70 (equation 2) (Alan has ₹1.70 more than Conner)

We can substitute equation 2 into equation 1 to eliminate a:

(c + 1.70) + c = 6.70

Simplifying and solving for c:

2c + 1.70 = 6.70

2c = 5.00

c = 2.50

So Connor has ₹2.50.

We can substitute this value into equation 2 to find the value of a:

a = c + 1.70

a = 2.50 + 1.70

a = 4.20

Therefore, Alan has ₹4.20.

The total income and expenditure of Agri-small business limited in September is R 299596 and expenditure is R 193236.

We have to find the total income and expenditure in September.

The equation for insurance is mathematically given as :

Insurance = 42% of the balance

Insurance=0.42*0.64A

Insurance=0.2688A.

Total expenditure after all other expenditures = 0.64A-0.2688A

Total expenditures after all other expenditures = 0.3712A.

Total expenditures after all other expenditures is as 111210 (106360 +4850)

Equating both the equation and value:

111210 = 3712 A

A = 299596

Thus The total income is 299596.

Therefore the calculation of expense is given as:

Expense=0.25A+0.11A+0.2688A+4850

Expense=0.6288A+4850

=0.6288*299596+4850

=193236

The expense is 193236.

Hence, the total income and expenditure in September are "Income is R 299596 and expenditure is R 193236.

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Answer:

80 degrees

Step-by-step explanation:

Triangle has 180 add the 2 you already have and subtract from 180

2. The transformations are given as follows:

3. The transformations are given as follows:

For item 2, the transformations in this problem are given as follows:

For item 3, the transformations are given as follows:

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The value of x, considering the vertical angles in this problem, is given as follows:

x = 11.

Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.

The vertical angles for this problem are given as follows:

As the vertical angles are congruent, the value of x is obtained as follows:

2x - 4 = x + 7

x = 11.

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Answer:

See below for explanation

Step-by-step explanation:

The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:

\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)

As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).

Hence, the area function for our cross-sections are:

\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)

Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:

\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)

Therefore, this explanation confirms that the correct volume is 24!

Answer: 45

Step-by-step explanation:

\(f(-5)=2(-5)^{2} -5\)

\(f(-5)= 2(25) -5\)

\(f(-5) = 50-5\)

\(f(-5) = 45\)

Answer:

Sample space is the collection of all possible events.

So, sample space of tossing two coins, S=(H,T),(T,T),(T,H),(H,H)

Step-by-step explanation:

Second choice.

Which is 1591.1 cm^2.

Answer:

f(x)=x-5/3x

Step-by-step explanation: