Two sides of a triangle are
shown. Find the range of
values of the third side.
8, 5
< X <

Answer:

X=0

Y=4

Step-by-step explanation:

4X+2y-8=0

2y=4x+8

y=2x+4

Substituting y in the equation

4x+2(2x+4)-8=0

4x+4x+8-8=0

8x=0

X=0

Substituting in equation y=2x+4

y=2(0)+4

Y=4

The approximate cost of 5-hour trip if the price of fuel is R78 per liter by finding the average speed is R3000.68.

To find the the total distance travelled by the car in 5 hours at an average speed of 100 km/h is:

Distance = Speed x Time

Distance = 100 km/h x 5 h

Distance = 500 km

The total amount of fuel consumed during the trip is:

Fuel consumed = Distance / Fuel efficiency

Fuel consumed = 500 km / 13 km/l

Fuel consumed = 38.46 liters (rounded to two decimal places)

The cost of the fuel consumed during the trip is:

Cost of fuel = Fuel consumed x Price per liter

Cost of fuel = 38.46 liters x R78/liter

Cost of fuel = R3000.68 (rounded to two decimal places)

Therefore, the approximate cost of the 5-hour trip is R3000.68, assuming that the only cost incurred is for the fuel consumed during the trip.

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Angle A is 27 degrees, angle B is 75 degrees then the angle C is 78 degrees.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Let the triangle be ABC.

The angle A is 27 degrees.

The angle B is 75 degrees,

We need to find the angle of C

From Angle sum property the sum of three angles is 180 degrees.

∠A+∠B+∠C=180

27+75+∠C=180

102+∠C=180

∠C=78 degrees.

Hence, angle A is 27 degrees, angle B is 75 degrees then the angle C is 78 degrees.

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Complete Question below:

In Triangle ABC, angle A is 27 degrees, angle B is 75 degrees then the angle C?.

Factoring polynomials with a leading coefficient greater than 1 is to use the factoring by grouping technique or quadratic formula.

Factoring a polynomial with a leading coefficient greater than 1 can be more challenging than factoring a polynomial with a leading coefficient of 1. However, there are several methods and techniques that can be used to factor such polynomials.

One common method for factoring polynomials with a leading coefficient greater than 1 is to use the factoring by grouping technique. This involves grouping the terms of the polynomial in pairs and factoring out the greatest common factor of each pair.

The resulting expressions can then be further factored or combined to obtain the final factorization of the polynomial.

Another method for factoring polynomials with a leading coefficient greater than 1 is to use the quadratic formula, which can be used to find the roots of a quadratic polynomial. Once the roots are found, the polynomial can be factored as a product of linear factors.

In some cases, it may also be helpful to use a combination of these techniques, along with other algebraic manipulations, such as completing the square or long division.

Overall, factoring a polynomial with a leading coefficient greater than 1 may require more patience and creativity than factoring a polynomial with a leading coefficient of 1, but with practice and persistence, it is possible to develop the skills and techniques needed to factor such polynomials efficiently and accurately.

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first one is a

Step-by-step explanation:

There is no real solution to the given equation s = 4 + sqrt(s+2) with value of s = 2, s = 7, s = 2 or s = 7.

To solve the equation:

s = 4 + sqrt(s+2)

We can start by isolating the square root term on one side:

s - 4 = sqrt(s+2)

Then, we can square both sides to eliminate the square root:

(s - 4)^2 = s + 2

Expanding the left side:

s^2 - 8s + 16 = s + 2

Bringing all terms to one side:

s^2 - 9s + 14 = 0

We can solve for s using the quadratic formula:

s = (9 ± sqrt(9^2 - 4(1)(14))) / 2(1)

s = (9 ± sqrt(49)) / 2

s = (9 ± 7) / 2

So the two possible solutions are:

s = 8/2 = 4

s = 2/2 = 1

However, we need to check if these solutions satisfy the original equation.

If we plug s=4 into the equation, we get:

4 = 4 + sqrt(4+2)

4 = 4 + sqrt(6)

This is not true, since the right-hand side is greater than the left-hand side.

If we plug s=1 into the equation, we get:

1 = 4 + sqrt(1+2)

1 = 4 + sqrt(3)

This is also not true.

Therefore, there is no real solution to the equation s = 4 + sqrt(s+2).

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Answer:

B

Step-by-step explanation:

The mentioned  scenario can be calculated using the distance equation, the number of seconds in which explosion would occur is 1.125 seconds.

The distance covered by the object is equal to the  product of the speed of object and the time required for it.

Distance = Time x speed

Firework A :

D = 360xt - - - (1)

Firework B:

D = 280x(0.25) + 280xt

D= 70 + 280xt - - - (2)

Equate equation (1) and (2) :

360t = 280t + 70

Collect like terms

360t - 280t = 70

80t = 70

t = 70/80

t = 0.875 seconds

0.875 + 0.25 = 1.125 seconds

Hence, the fireworks will explode after 1.125 seconds of launching Firework B.

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Answer:

Below

Step-by-step explanation:

1 + 19/10 + 8/100   = 1   +  1.9    + .08   =  2.98

The required measurement of the ingredient has been shown below for half a batch of cookies.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
When making 1/2 a batch of the cookie recipe, you will need to halve the amount of each ingredient.

Here is the list of ingredients for half a batch:

1 7/8 cups flour

5/8 cup brown sugar

1 egg

1/8 teaspoon salt

1/6 teaspoon baking soda

5/8 cup butter

3/4 cup white sugar

Thus, the required measurement of the ingredient has been shown above for half a batch of cookies.

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We can order the bonds from slowest-growing to fastest-growing as:

First bond: fixed growth rate of $50 per year

Third bond: growth rate of 4% per year, compounded continuously

Second bond: growth rate of 6% per year, compounded annually

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To order the bonds from slowest growing to fastest growing, we need to compare their growth rates.

The first bond grows at a fixed rate of $50 per year, regardless of how long it is held.

So its growth rate is constant and does not change with time.

The second bond is worth $500 and grows at a fixed annual rate of 6%, so its value after one year will be:

Value after one year
= $500 + 0.06 x $500

= $530

After two years, its value will be:

Value after two years.

= $530 + 0.06 x $530

= $561.80

We can see that the second bond's growth rate is increasing over time since the increase in value each year is calculated as a percentage of the new value.

The third bond is worth $100 and grows at an annual rate of 4% that is applied continuously.

The formula for the value of a continuously compounded bond after t years  = $100 x e^(0.04t)

where e is the mathematical constant approximately equal to 2.718.

After one year,

The value of the third bond.

= $100 x e^(0.04 x 1) = $104.08

After two years,

Value after two years

= $100 x e^(0.04 x 2)

= $108.24

We can see that the growth rate of the third bond is also increasing over time because the interest is being compounded continuously.

Now,

We can order the bonds from slowest-growing to fastest-growing as:

First bond: fixed growth rate of $50 per year

Third bond: growth rate of 4% per year, compounded continuously

Second bond: growth rate of 6% per year, compounded annually

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Answer:

11 glasses

Step-by-step explanation:

There are 200 ml glasses and we have 2.21 liter of bottels. So first of all covert liter into ml so we get 2210 ml of coca cola.now divide 2210 by 200 so we get 11 glasses

We can see here that with the information given, one can prove that this quadrilateral is a parallelogram. Thus, it is yes>

A polygon with four sides and four vertices (corners) is called a quadrilateral. Its internal angles add up to 360 degrees.

Squares, rectangles, parallelograms, trapezoids, and rhombuses are all examples of quadrilaterals.

We can see that looking at the quadrilateral, we can deduce that it is parallelogram. This is because the opposites sides are equal. Also, their opposite angles are equal.

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Answer:

89

Step-by-step explanation:

903 - 814 =

= (900 + 3) - (800 + 14) =

= 900 + 3 - 800 - 14 = 100 - 11 =

= 89

Answer:

3y(y + 4)

Explanation:

[tex]3y^{2} + 12y\\3(y^{2} + 4y)\\3y(y + 4)\\[/tex]

Answer:

5

Step-by-step explanation:

  2 1/2

+ 2 1/2

1/2 and 1/2 makes a whole which is 1

so if you have 4 and and a whole which is 5

They can also be turned into decimals. 1/2 as a decimal is .5

so 2.5 plus 2.5 = 5

The table to explain the equation will be:

x (minutes) y (altitude, in feet) Worked-out equation

0                          300                 -10x + 300 = 300

5                              250                   -10x + 300 = 250

8                         220                         -10x + 300 = 220

10                         200                   -10x + 300 = 200    

30                     0                         -10x + 300 = -0

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario

I used the equation y = -10x + 300 to find the altitude of the airplane for each x value.

The altitude after 5 minutes is 250 feet and 0 after 30 minutes.

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Answer:

5x + y = 17

Step-by-step explanation:

y -2 = -5(x -3)

y-2 = -5x + 15  Add 5x to both sides

5x + y - 2 = 5x - 5x + 15

5x + y - 2 = 15   Add 2 to both sides

5x + y + 2 - 2 = 15 + 2

5x + y = 17

Answer:

51 stamps

Step-by-step explanation:

since salman's amount is going from 5 to 45 its being multiplied by nine. to keep the ratio true, you need to multiply the other two numbers by 9 too. Nathan then has 12 stamps and Gordon has 63. 63-12=51

The area of a four-sided regular pyramid, given the base edge and the side edge is 340 cm ² .

The area of a four-sided regular pyramid can be found by the formula :

= Area of base + 1 / 2 x perimeter of base x side edge

Area of base :

= 10 x 10

= 100 cm ²

Perimeter of base ;

= 10 + 10 + 10 + 10

= 40 cm

The area of the four-sided regular pyramid is;

= 100 + ( 1 / 2 x 40 x 12 )

= 340 cm ²

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Answer:

Both data sets represent multiplicative relationships. In Table A, y is 2.5 times x, and in Table B, y is 3 times X

Step-by-step explanation:

Self-explanatory

Every value of y in Table A is 2.5 times  x value

and

every value of y in table B is 3 times x value

a = 1st zero or root of the quadratic

b = 2nd zero or root of the quadratic

[tex]x^2-8x+k=0\implies (x-a)(x-b)=0\implies x= \begin{cases} a\\ b \end{cases} \\\\[-0.35em] ~\dotfill\\\\ -ax-bx=-8x\implies -a-b=-8\implies -b=a-8\implies b=8-a \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{3a+4b=29}\qquad \implies \qquad \stackrel{\textit{substituting from above}}{3a+4(8-a)~~ = ~~29}\implies 3a+32-4a=29 \\\\\\ -a+32=29\implies 32=a+29\implies \boxed{3=a}\hspace{5em}\stackrel{ 8~~ - ~~3 }{\boxed{b=5}}[/tex]

[tex]~\dotfill\\\\ (x-3)(x-5)=0\implies x^2-8x+\stackrel{ \textit{\LARGE k} }{15}=0[/tex]

Answer:

24 cars are green

Step-by-step explanation:

We know

Amir notices that 3 out of every 50 cars that pass by his window are green.

So, the ratio is 3:47

To get from 50 to 400, we time 8.

If he observes 400 cars, what is the best estimate of how many will be green?

We take

3 x 8 = 24 cars are green

So, there will be 24 cars that are green.

A polygon with a sum of interior angles of 3960 has 22 sides.

The sum of the interior angles of a polygon can be calculated using the formula:

(n-2) * 180

where n is the number of sides of the polygon. This formula is derived from the fact that the total degree measure of a polygon is equal to the sum of the degree measures of its interior angles. In a polygon with n sides, there are n angles, each measuring 180 degrees. So the total degree measure of a polygon with n sides is n * 180.

Now, if we subtract the degree measures of two angles, we are left with the sum of the degree measures of the remaining n-2 angles. This is why the formula for the sum of the interior angles of a polygon is given as (n-2) * 180.

To find the number of sides of a polygon given its sum of interior angles, we can rearrange the formula as follows:

n = (Sum of interior angles / 180) + 2

So, if the sum of the interior angles is given as 3960, we can plug that into the formula:

n = (3960 / 180) + 2

n = 22

Therefore, a polygon with a sum of interior angles of 3960 has 22 sides.

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How many sides does a polygon have if the sum of the interior angles is 3960?

Answer:

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

b)  y + 2 = 4(x+ 1)

c) y = -(x - 3)

d) y = -5x

Step-by-step explanation:

You did not say which form, so I put them in the point-slope form of a line that follows the pattern:

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(a)

given m = 3 , then

y = 3x + c ← is the partial equation

to find c substitute (1, 4 ) into the partial equation

4 = 3(1) + c = 3 + c ( subtract 3 from both sides )

1 = c

y = 3x + 1 ← equation of line

(b)

given m = 4 , then

y = 4x + c ← is the partial equation

to find c substitute (- 1, - 2 ) into the partial equation

- 2 = 4(- 1) + c = - 4 + c ( add 4 to both sides )

2 = c

y = 4x + 2 ← equation of line

(c)

given m = - 1 , then

y = - x + c ← is the partial equation

to find c substitute (3, 0 ) into the partial equation

0 = - 3 + c ( add 3 to both sides )

3 = c

y = - x + 3 ← equation of line

(d)

given m = - 5 , then

y = - 5x + c ← is the partial equation

to find c substitute (0, 0 ) into the partial equation

0 = - 5(0) + c = 0 + c ⇒ c = 0

y = - 5x ← equation of line

Answer:

Top box is 2

Middle box is 10

Bottom box is 18

Step-by-step explanation:

[tex]\frac{6}{9}[/tex] = [tex]\frac{x}{3}[/tex]

9 ÷ 3 = 3

6 ÷ 3 = 2

x = 2

[tex]\frac{6}{9}[/tex] = [tex]\frac{x}{15}[/tex]

9 x [tex]\frac{15}{9}[/tex] = 15

6 x [tex]\frac{15}{9}[/tex]  = 10

x = 10

[tex]\frac{6}{9}[/tex] = [tex]\frac{12}{x}[/tex]

6 x 2 = 12

9 x 2 = 18

x = 18

The cost of one plum in pence is 9p. The cost of 1 lime in pence is 12p.

Comparing the cost plum is cheaper.

The cost of 1 plum can be found by dividing the total cost of 7 plums by 7:

63 p / 7 = 9 p

Therefore, the cost of 1 plum is 9 p.

The cost of 1 lime can be found by dividing the total cost of 5 limes by 5:

60 p / 5 = 12 p

Therefore, the cost of 1 lime is 12 p.

Comparing the costs of 1 plum and 1 lime, we see that 1 plum costs 9 p and 1 lime costs 12 p. Therefore, the plum is cheaper per item.

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____The given question is incomplete, the complete question is given below:

A grocery shop sells plums and limes. 7 plums cost 63 p. 5  limes cost 60p a) Work out the cost of  1 plum, in pence (p).

b) Work out the cost of 1 lime, in pence (p).

c) Which type of fruit is cheaper per item?

The equation -13x+12-(-13x+12)-13x+12 = -13x+12   is equivalent to the given expression that is -13x+12.

10x^2 - 23x + 12 = (5x - 3)(2x - 4) = 0

So the solutions to the equation are x = 3/5 or x = 2.

Therefore, this expression is not equivalent to -23x + 12 for all values of x.

10x^2 - 7x - 12 = 0 can be factored as (2x - 3)(5x + 4) = 0.

So the solutions to the equation are x = 3/2 or x = -4/5.

Therefore, this expression is not equivalent to -7x - 12 for all values of x.

-13x+12-(-13x+12)-13x+12  = -13x+12

-13x+12  = -13x+12

This expression is equivalent to -13x+12 .

7x^2 - 23x - 77 = (7x + 11)(x - 7) = 0

So the solutions to the equation are x = -11/7 or x = 7.

Therefore, this expression is not equivalent to -23x - 7 for all value x.

The given expressions of each case are not equivalent to the given equations for all values of x, except −13x+12-(-13x+12)-13x+12  = -13x+12 which is equivalent to -13x+12 .

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______The given question is incorrect, the correct question is given below:

An expression is given on equation

Which expression is equivalent to the given expression of each case

?

A

10x2−23x+1210x^2-23x+1210x = −23x+12

B

10x2−7x−1210x^2-7x-1210x = −7x−12

C

−13x+12-(-13x+12)-13x+12 = -13x+12

D

7x2−23x−77x^2-23x-77x = −23x−7

Answer:

75%

Step-by-step explanation:

If you have a calculator, you can divide 39/52. If not,

39/52 = x/100

52x = 3900

x = 75

75/100 = 75%

a) Probability that all four are the same suit = 0.0106 b) Probability that all four are red =0.055 c) Probability each has a different suit = 0.105

Total number of cards =52

No. of cards for each suit =13

Total types of four suit =4 (heart, spades, diamonds, clubs)

Total numbers of ways = [tex]^{52}C_4[/tex] =270,725 ways

a) number of ways choosing four cards of the same suit

= [tex]^{13}C_4+^{13}C_4+^{13}C_4+^{13}C_4[/tex]

= [tex]4 \times ^{13}C_4\\[/tex]

= [tex]4 \times \frac{13!}{4!(13-4)!}[/tex]

=2860 ways

Probability that all four are the same suit is 2860/270,725 = 0.0106

b) Number of ways all four cards are red

=[tex]^{26}C_4[/tex]

= 4,950 ways

Probability that all four are red = 4950/270,725 =0.055

c)  Number of ways each card has a different suit

=[tex]^{13}C_1\times^{13}C_1\times^{13}C_1\times^{13}C_1[/tex]

= 28,561 ways

Probability each has a different suit is 28561/270725 = 0.105

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The boat travels a distance of [tex](1/2k) ln(61/42)^2[/tex] in the first 2 minutes after its motor quits.

We can solve this problem using separation of variables. The differential equation that models the velocity of the boat is:

[tex]dv/dt = -kv^2[/tex]

To do this, we first need to separate the variables and integrate both sides:

[tex]1/v^2 dv = -k dt[/tex]

Integrating both sides, we get:

-1/v = kt + C

where C is the constant of integration. To find C, we can use the initial condition that the boat is moving at 83 ft/s when the motor quits:

-1/83 = k(1) + C

C = -1/83 + k

Now we can substitute C back into our equation:

-1/v = kt - 1/83 + k

Solving for v, we get:

v = 1 / (k(t - 1/83 + 1))

Now we can integrate v over the time interval [1, 121] to find the distance traveled by the boat:

d = ∫[1,121] v dt

Substituting v into the integral, we get:

d = ∫[1,121] 1 / (k(t - 1/83 + 1)) dt

We can simplify the integral by using the substitution u = t - 1/83 + 1:

d = ∫[84/83, 122/83] 1 / (ku) du

Now we can integrate this expression to get:

d = ln(u) / k |[84/83, 122/83]

d = ln(122/83) / k - ln(84/83) / k

d = (1/k) ln(122/83) - (1/k) ln(84/83)

We can simplify this expression using the fact that C = -1/83 + k:

d = (1/k) ln(122/83 / 84/83)

d = (1/k) ln(61/42)

Finally, we can plug in the initial condition k > 0 to get the distance traveled by the boat:

d = [tex](1/k) ln(61/42) = (1/2k) ln(61/42)^2[/tex]

d = [tex](1/2k) ln(61/42)^2[/tex]

Since we are not given the value of k, we cannot compute the exact numerical value of the distance traveled.

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