The height of a triangle is 8 centimeters greater than the base. The area of the triangle is 356.5 square centimeters. Find the length of the base and the height of the triangle.

Answer:

  x = 10

Step-by-step explanation:

You want the value of x that satisfies x -(x-1)/3 -(2x-5)/5 +(x+8)/6 = 7.

The least common denominator is 5·6 = 30, so we can eliminate the fractions by multiplying by 30:

  30x -10(x -1) -6(2x -5) +5(x +8) = 7·30

  30x -10x +10 -12x +30 +5x +40 = 210 . . . . . eliminate parentheses

  13x +80 = 210 . . . . . . . . . collect terms

  13x = 130 . . . . . . . . . . subtract 80

  x = 10 . . . . . . . . . . divide by 13

__

Additional comment

Often an equation can be nicely solved by a graphing calculator. We like to write the equation in the form f(x) = 0, and look for the x-intercepts. Those are usually labeled by the calculator. Here that rewrite is accomplished by subtracting 7 from both sides.

The graph of the given function f(x) has two extreme values at the point 'b' and the point 'd'.

Given, The function f(x) is graphed in the figure and we have to find the points on the graph representing the relative extreme values

As, we got the extreme values on the graph of a function when the graph makes a turn and the given function graph is turning at two points.

So, the graph has extreme values at two points i.e. b and d

So, the graph of the given function f(x) has two extreme values at the point 'b' and the point 'd'.

Hence, the graph of the given function f(x) has two extreme values at the point 'b' and the point 'd'.

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Answer:

27

Step-by-step explanation:

I looked at the graph and added 6+6=12 so the bottom is 12 and for the height i added 1+8=9 and then i added another 12 because the bottom is also 12 and divided that by 2 which is 6 so i got 27.

this may not be right but i am hoping that is it!

Have A Great Day!!!

Answer:

72.1

Step-by-step explanation:

It is 10 to the power of 2 because the exponent is 2. The result is a number bigger than the origin or base number because the exponent is positive. We move the decimal two times to the right to arrive at our conclusion:

0.721--> 72.1

therefore, your answer will be 72.1

The trinomial and binomial form of the incomplete algebraic expression is [tex]d^{2}[/tex] -3d + 9/4 and [tex](d-\frac{3}{2}) ^{2}[/tex]

A perfect square is a quadratic expression that factors into two identical binomials.

For example, if you multiply these two identical binomials factors:

(x + 2)(x + 2)

to complete the square in the expression [tex]d^{2}[/tex] -3d, we square the half of the coefficient of d which is -3/2

so the expression becomes,

[tex]d^{2}[/tex] -3d + [tex](\frac{-3}{2}) ^{2}[/tex] = [tex]d^{2}[/tex] -3d +[tex]\frac{9}{4}[/tex]

The Binomial form of the expression [tex]d^{2}[/tex] -3d + [tex](\frac{-3}{2}) ^{2}[/tex]

can be written by take [tex]d^{2}[/tex] term and the constant and putting them in a bracket and squaring

which becomes

[tex](d - \frac{3}{2} )^{2}[/tex]

In conclusion, the trinomial form of the expression is [tex]d^{2}[/tex] -3d +[tex]\frac{9}{4}[/tex] while the Binomial form of the expression is [tex](d - \frac{3}{2} )^{2}[/tex]

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Answer:

[tex]f(x) = 2(x-9)^{2} + 3[/tex]

Step-by-step explanation:

In vertex form, (h, k) represents the vertex.

With the given vertex of (9, 3), h = 9 and k = 3. You can substitute those values into the equation.

In vertex form, a represents vertical stretch or compression.

In this case, since the parent function, x^2 is multiplied by 2, a = 2. You can substitute this into the equation.

You end up with [tex]f(x) = 2(x-9)^{2} + 3[/tex]

Answer:no picture

Step-by-step explanation:

Answer:

Step-by-step explanation:

so there are square root properties that they want you to recognize and respect :P  everyone wants a little respect,  even the square root sign :D

first we can move things under one root sign, like this...

[tex]\sqrt{10}[/tex] * [tex]\sqrt{6}[/tex] = [tex]\sqrt{10 * 6}[/tex]

now we can do that multiplication under the square root sign.

[tex]\sqrt{10 * 6}[/tex] = [tex]\sqrt{60}[/tex]

now we can think about this for a long long time and see that 60 can be split up in other ways besides  10 * 6

for instance 15 * 4  also is  60

so this is equal  [tex]\sqrt{15 * 4}[/tex] = [tex]\sqrt{10 * 6}[/tex] = [tex]\sqrt{60}[/tex]

now just take out the perfect square part

2 * [tex]\sqrt{15}[/tex]

this isn't one of the listed answers but it is a correct answer , for what is being asked.   The teacher got the question wrong :o

When corresponding angles are congruent, the lines are parallel

Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other. The type of angles does not make any difference in the congruence of angles, which means they can be acute, obtuse, exterior, or interior angles. The angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.

Examples of the corresponding angle are any angles which are formed on the opposite side of the transversal. Now, it should be noted that the transversal can intersect either two parallel line or two non-parallel lines. Thus, corresponding angles can be of two types:

Corresponding angles formed by parallel lines and transversals

Corresponding angles formed by non-parallel lines and transversals

Looking at the image, angle I is congruent to each other. Angle II is congruent with each other as well as angle III.

When corresponding angles are congruent, the lines connecting them must be parallel. This is the only valid or correct options in the task.

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The value of the variable x is,  x = 22.

What is variable in equation?

In mathematics, a variable is an alphabet or phrase that denotes an unknowable quantity, unknowable value, or unknowable number. In the case of algebraic expressions or algebra, the variables are employed specifically. A linear equation with x as a variable and 9 and 4 as constants, for instance, is x+9=4.

Consider, the given equation

√(x - 6) + 2 = 6

Subtract 2 on both sides,

√(x - 6) + 2 - 2 = 6 - 2

          √(x - 6) = 4

Taking square on both sides,

[tex](\sqrt{x-6})^2=4^2\\ (x-6)=16[/tex]

     x - 6 = 16

Add 6 on both sides,

x - 6 + 6 = 16 + 6

           x = 22

Hence, the value of the variable x is x = 22.

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Answer:

67

Step-by-step explanation:

a+45=112

  -45.  -45

a=67

Hopes this helps please mark brainliest

Answer:

a = 67

Step-by-step explanation:

Given equation,

→ a + 45 = 112

Now the value of a will be,

→ a + 45 = 112

→ a = 112 - 45

→ [ a = 67 ]

Hence, the value of a is 67.

Using the mathematical operation of subtraction, the cost at Fast BMX is $200 more than the cost at Bike World.

The difference in the cost of bikes can be computed using the mathematical operation of subtraction.

Subtraction operations involve deducting the subtrahend from the minuend to get the result known as the difference.

Bike Stores              Prices

Bike City                   $300

Fast BMX                 $500

Bike World               $300

Awesome Bikes      $400

Difference between Fast BMX and Bike World

= $200 ($500 - $300)

Thus, the cost of bikes is higher at Fast BMX than at Bike World by $200.

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Answer:

120, 60, 180

Step-by-step explanation:

The total profit that the company would make on the trip can be found to be £7,320

The revenue that the company makes would be:

= Number of passengers x Amount that each passenger pays

= 400 x 23

= £9, 200

Each coach takes 50 passengers so the number of coaches needed are:

= 400 passengers / 50 passengers per coach

= 8 coaches

The total cost to the company for the trip is:
= (Number of coaches x Driver cost per coach) + (Number of coaches x Fuel per mile x Distance traveled for each coach)

= ( 8 x 95) + ( 8 x 70p x 200)

= 760 + 112, 000 p

= 760 + 112, 000/ 100 pence per pound

= £ 1,880

The total profit is:

= Revenue - total cost

= 9, 200 - 1, 880

= £7,320

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The true statement is 'Every irrational number can be represented with the help of decimals.'

The correct answer is an option (B)

We know that the rational numbers are of the form p/q (i.e., simple fraction) where p, q are integers with q ≠ 0

And an irrational numbers are real numbers that cannot be represented as simple fractions.

An irrational numbers can be written in decimals.

√3 = 1.7321

We know that every terminating decimal is a rational number (for example, 2.5 = 5/2) but every rational number may not be a terminating decimal (for example, 2/3 = 0.666...)

So, a statement 'Every irrational number can be represented as a fraction.' is false.

A statement 'Every irrational number can be represented with the help of decimals.' is True

A statement 'Every rational number can be represented as a terminating decimal.' is False.

and a statement 'Every rational number can be represented as an integer.' is False.

Therefore, the true statement is 'Every irrational number can be represented with the help of decimals.'

The correct answer is an option (B)

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Answer:

y = -30

(0, -30)

Step-by-step explanation:

f(x) = 2(2x - 3) (5x + 5)

2 = 0, 2x - 3 = 0, 5x + 5 = 0

               +3    +3      -5     -5

          ------------------------------

             2x = 3 ,     5x = -5

            ÷2    ÷2      ÷5    ÷5

         --------------------------------

                x = (3/2),   x = -1

f(x) = 2(2(0) - 3) (5(0) + 5)

        2(0 - 3) (0 + 5)

         2(-3) (5)

             -6 × 5 = -30

f(x) = -30

y = -30

(0, -30)

f(x) = 2(2x - 3) (5x + 5)

        2(2(3/2) - 3) (5(3/2) + 5)

        2(3 - 3) (15/2 + 5)

         2(0) (25/2)

y = 0

((3/2), 0))

f(x) = 2(2x - 3) (5x + 5)

        2(2(-1) - 3) (5(-1) + 5)

         2(-2 - 3) (-5 + 5)

          2(-5) (0)

             -10(0)

y = 0

(-1, 0)

I hope this helps!

The probabilities, using the Poisson distribution, are given as follows:

a) Two earthquakes in a year: 0.0446 = 4.46%.

b) No earthquakes in two consecutive months: 0.3679 = 36.79%.

c) No earthquakes in two consecutive months, given that there were no earthquakes in the previous month: 0.3679 = 36.79%.

The Poisson distribution is used when we only have the mean in a given interval and the mass function is given as follows:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are listed as follows:

For one year, the mean number of earthquakes is given as follows:

[tex]\mu = 6[/tex]

The probability of exactly two earthquakes in a year is obtained as follows:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 2) = \frac{e^{-6}6^{2}}{(2)!} = 0.0446[/tex]

For two months, the mean is given as follows:

[tex]\mu = 2 \times 6 \times \frac{1}{12} = 1[/tex]

For items b and c, the probabilities are the same, P(X = 0), as the events are independent, hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-1}1^{0}}{(0)!} = 0.3679[/tex]

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Answer: I am not sure if you're accustomed to using a z-score and table of probabilities or technology, so I will answer using both!

a) Since you're choosing one person from the population, you will use the mean and standard deviation from the population.  z= (210.9-197.5)/8.6 = 1.56 Using a table of normal probabilities,

P(x>210.9)= 1-P(z<1.56)= 1- 0.9406=0.0594

Using technology: normalcdf(210.9, 1E99, 197.5, 8.6)=0.0596

b) Since you're calculating the population for a sample to occur, you need to get a mean of the sampling distribution and standard deviation of the sampling distribution.

Meanpop=Meansampling dist.=197.5

St. Devsampling dist.= Stdpopulation/√n = 8.6/√15 = 2.22

Using technology, P(X>196.20)= normalcdf( 196.20, 1E99, 197.5, 2.22) = 0.7209

c) You only have to worry about the sample size in a sampling distribution if you either do not know the shape of the distribution of the population or if the distribution of the population is not normally distributed. Since this population is normally distributed (as stated in the given information), then your sample size does not have to be greater than 30.

Hope this helps! I can solve part b using a z-score if you need me to.

Step-by-step explanation:

Amount Invested Annual $7000, Interest Rate of 9%  Accumulated Amount is Double the amount invested in 7.7 years,

What is an interest rate?

An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving. So, if you're a borrower, the interest rate is the amount you are charged for borrowing money, shown as a percentage of the total amount of the loan.

Here, we have

A = P e^(rt) ......(1)

P = Amount Invested = $7000

Interest Rate = 9%

A = Accumulated Amount Double the amount invested = 2P = $14000

t = time in years

from equation (1) , we get

14000 = 7000×e^(0.09)t

2 =  e^(0.09)t

㏑2 = 0.09t

0.6931 = 0.09t

t = 0.6931/0.09

t = 7.7 years

Hence, Amount Invested Annual $7000, Interest Rate of 9%  Accumulated Amount is Double the amount invested in 7.7 years.

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Answer:

each water is $1.25 each coffee is $1.95

Step-by-step explanation:

we know that the difference between $10.85 and $16.70 is 3 cups of coffee

if we subtract $10.85 from $16.70 we get $5.85

$5.85 divided by 3 is $1.95

so each cup of coffee is $1.95

now we subtract the same $5.85 from the price of 4 waters and 3 coffees

$10.85 minus $5.85 equals $5.00

divide that by 4 to get the price of each water bottle and you get $1.25 per water

The required coordinates of vertex A' are (3, 4) in the trapezium ABCD.

Trapezium ABCD is given in the question which has :

The coordinates of vertex A is (2, 6)

Here the scale factor is 2

A = (2, 6)

The scale factor of a dilation is given as

k = 2

The center of dilation is given as

Center = (1, 8)

The rule of the dilation is calculated using as

B' = (k(x - a) + a, k(y - b) + b)

Where

(a, b) = (1, 8)

k = 2

(x, y) =  (2, 6)

So, we have

A' = (2 × (2 - 1) + 1, 2 × (6 - 8) + 8)

A' = (3, 4)

Hence, the required coordinates of vertex A' are (3, 4).

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The question seems to be incomplete the correct question has been attached

Option (C) is the correct one and the only true statement is

The domain of the function f(x) is { -2, -1, 0, 1, 2, 3, 4, 5, 6 }.

Given, a table of values for y = f(x)

x     -2   -1   0   1   2   3   4   5   6

y      7   8   9   10  11  5   6  12  13

We have to find the correct statements,

as the range of the function f(x) is { 4, 8, 9, 10, 11, 5, 6, 12, 13 }

the image of 5 in the function is 6 i.e. f(5) = 6.

The domain of the function f(x) is { -2, -1, 0, 1, 2, 3, 4, 5, 6 }

the image of -1 in the function is 8 i.e. f(-1) = 8.

Hence, only the option (C) is the correct one and the only true statement is

The domain of the function f(x) is { -2, -1, 0, 1, 2, 3, 4, 5, 6 }.

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Answer:

x = 20

Step-by-step explanation:

12x + 11 = 251

12x + 11 - 11 = 251 - 11

12x = 240

12x /12  = 240/12

x=20

The image of (3, 3) after dilation  by a scale factor of 1/3 centered at the origin will have coordinate (1, 1)

Dilation refers to the transformation that increases or reduces the image formed after the transformation

When the scale factor is greater that 1 the transformation will lead to magnification when the scale factor is less than 1 the image formed is compressed.

The transformation rule fir dilation is (x, y) → (kx, ky)

where k is the scale factor = 1/3

(3, 3)  → (1/3 * 3, 1/3 * 3)  → (1, 1)

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Answer:

?????

Step-by-step explanation:

Answer:

70 km/hr

Step-by-step explanation:

Step-by-step explanation:

Rigid motion

Rigid motion – A transformation that preserves distance and angle measure (the shapes are congruent, angles are congruent).

The speed of slower bus is 118 km/hr and speed of faster bus is 133 km/hr

Speed is a scalar quantity that refers to "how fast an object is moving".

Given that, two buses leave a station at the same time and travel in opposite directions, one bus travels 15 km/h faster than the other, the two buses are 1004 kilometres apart after 4 hours,

Speed = distance/ time

Let the speed of the slower bus be v and the faster bus be (v+15)

According to the question,

vt + (v+15)t = 1004

vt + vt + 15t = 1004

t = 4

4v + 4v + 60 = 1004

8v = 944

v = 118

Hence, The speed of slower bus is 118 km/hr and speed of faster bus is 133 km/hr

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The y-intercept (0, 1200) represents the initial cost of the bedroom furniture option (A) is correct.

It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a×

where a is a constant and a>1

The exponential function is of the form:

y = ab×

Plug x = 0 and y = 1200

1200 = a

Plug x = 2, y = 675, and a = 1200

675 = 1200(b)²

b = 0.75

y = 1200(0.75)×

y = 1200

Thus, the y-intercept (0, 1200) represents the initial cost of the bedroom furniture option (A) is correct.

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