Given the equations $3x+y=17,5y+z=14$ and $3x+5z=41$, what is the value of the sum $x+y+z$?
Thanks

A base must be raised to a certain exponent or power, or logarithm, in order to produce a given number. If bx = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n. For instance, 23 = 8; consequently, 3 is the base-2 logarithm of 8 or 3 = log2 8.

When measuring the relative change of a value rather than its absolute difference, logarithmic scales are helpful. Moreover, logarithmic scales are used to compress large-scale scientific data because the logarithmic function log(x) grows very slowly for large x.

\(log_{2} 2=1\\log_{4}4=1\\ log_{100}100=1\\log10=1\)

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Answer:

negative

Step-by-step explanation:it goes down

Answer:

A-the slope is negative

Step-by-step explanation:

right on plato/edmentum

Answer:

1

Step-by-step explanation:

\(v = whl\)

1 = 5/4 x 4/3 x 3/5

The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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Actual area of bedroom is bigger than the kitchen as per the given measurements and scale.

As per the given question,

Given drawing scale is:

1 : 30

Shape of the kitchen is rectangle with measurements = 12cm by 27cm

Using scale :

Length = 12cm

Actual length = 12 × 30

                      = 360cm

Width = 27cm

Actual width = 27 × 30

                     = 810 cm

Actual area of kitchen = 360 × 810

                                     = 291,600 cm²

Actual area of bedroom = 300,000cm²

300,000 > 291,600

Actual area of bedroom > Actual area of kitchen

Therefore, actual area of bedroom is bigger than the actual area pf kitchen.

The complete question is:

A drawing has a scale of 1:30 On the drawing, a kitchen is a rectangle measuring 12 cm by 27 cm A bedroom has an actual area of 300 000 cm² Which has the bigger actual area, the kitchen or the bedroom? You must show your working.​

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Answer:

So, the correct answer is (30.104, 32.896).

Step-by-step explanation:

To find the 95% confidence interval for the mean number of pounds of trash per person per week, we can use the following formula:

CI = X + Zα/2 * (σ/√n)

σ = population standard deviation = 7.8 pounds

n = sample size = 120

Plugging in the values, we get:

CI = 31.5 ± 1.96 \times(7.8/√120)

CI = 31.5 ± 1.96 \times 0.711

CI = 31.5 ± 1.39

Therefore, the 95% confidence interval for the mean number of pounds of trash per person per week is (30.11, 32.89).

So, the correct answer is (30.104, 32.896).

So the maximum number of edges in an undirected graph with 100 vertices is 4950.

In an undirected graph, each edge connects two vertices, and as such, it is counted twice, once for each vertex it connects. Therefore, the total number of edges in the graph is the sum of the degrees of all vertices, divided by 2.

In a complete graph with n vertices, every vertex is connected to every other vertex, except itself, and so the degree of each vertex is n-1 (it is connected to n-1 other vertices). Therefore, the total number of edges in the graph is:

n * (n-1) / 2

Substituting n = 100, we get:

100 * 99 / 2 = 4950

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The function with a greater stretch factor is the function graphed and the value is 3 times greater

The function with a greater stretch factor is the function which has a greater number multiplying the function

The given equation is a(x) = 1/3 x³ while the function graphed is b(x) = x³+ 2

The stretch factor is determined by the coefficients which are

a(x): 1/3 and b(x): 1

comparing this numbers

= b(x) / a(x)

= 1 / 1/3

= 3

this shows that b(x) which is 1 is greater by 3 times.

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Answer:

201495

Step-by-step explanation:

You can reverse this by multiplying 101 by 1995 which will give you that.

not good at explaining, am sorry.

Answer:

7

Step-by-step explanation:

5  right, 2 down

5+2=7

Answer:

Step-by-step explanation:

For the first line, you are copying the dimensions from the figure to the blanks. The dimensions on the figure are (4a +1), and (8), both in centimeters. When you have filled in that line, it will read ...

  2((4a +1) +8) cm

__

For the second line, you must collect terms and use the distributive property to eliminate parentheses from the above expression.

  2((4a +1) +8) cm = 2(4a +9) cm = 2(4a) +2(9) cm

  = 8a +18 cm

__

The third line simply sets this expression equal to the given perimeter, 42:

  8a +18 = 42

_____

Additional comment

To solve this equation, you can subtract 18 from both sides:

  8a +18 -18 = 42 -18

  8a = 24 . . . . . . . . . . . simplify

Then divide both sides by 8.

  8a/8 = 24/8

  a = 3

Finally, the length of the rectangle is ...

  4a +1 = 4(3) +1 = 12 +1 = 13

The rectangle is 13 cm long and 8 cm high. Its perimeter is ...

  2(13 +8) = 2(21) = 42 . . . cm

The correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are given below.Option A. V = -(0.25)x - 4 Option B. V = − (0.25)x+4

A function can be defined as a special relation where each input has exactly one output. The set of values that a function takes as input is known as the domain of the function. The set of all output values that are obtained by evaluating a function is known as the range of the function.

From the given options, only option A and option B are the functions that satisfy the condition.Both of the options are linear equations and graph of linear equation is always a straight line. By solving both of the given options, we will get the range as (-∞, 4) and domain as (-∞, 0).Hence, the correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are option A and option B.

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Answer:

can i see the numbers

Step-by-step explanation:

there is no picture

The end behavior of the function f(x) is: continues downward to the left and upward to the right.

Consider the function,

f(x) = (x + 1)(x - 2)(x + 3)

The zeros are when f(x) = 0

f(x) = 0

(x + 1)(x - 2)(x + 3) = 0

Therefore,

(x + 1) = 0

So, x = -1

(x - 2) = 0

So, x = 2

(x + 3) = 0

So, x = -3

Therefore, the zeros are at x = - 1, x = 2 and x = - 3

To expand the function, we multiply the brackets:

f(x) = (x + 1)(x - 2)(x + 3)

f(x) = ( x + 1 )( x² + x - 6 )

f(x) = x³ + 2x² - 5x - 6

As the leading coefficient (the coefficient of x³) is positive, the end behavior of the function is:

f(x ) → + ∞, as x → + ∞

f(x ) → - ∞, as x → - ∞

Therefore, the end behavior is "continues downward to the left and upward to the right".

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Answer:

B

Step-by-step explanation:

(x+5)^2

x^2+10x+25

(y+3)^2

y^2+6y+9

then it would be

x^2+10x+34+y^2+6y

subtract 34-36 since ur moving 36 to the left

where u get -2

so ur final equation would be x^2+y^2+10x+6y-2=0

Answer:

3x - 1 = 6x - 7

x = 2

Explanation and Check part below

Hope this helps :)

Step-by-step explanation:

1. To solve it, first get the variable on same side.

3x - 1 = 6x - 7

- 3x - 3x

- 1 = 3x - 7

2. Isolate the variable by doing the inverse operation which is in this case addition (adding 7).

- 1 = 3x - 7

+ 7 + 7

6 = 3x

3. Isolate variable by doing the inverse operation which is in this case division (dividing by 3).

6 = 3x

3 3

2 = x

OR

x = 2

Check:

1. Substitute x with 2 and solve.

3(2) - 1 = 6(2) - 7

6 - 1 = 12 - 7

5 = 5

True statement.

Answer:

f(10)=290

Step-by-step explanation:

Function Evaluation

Given a function f(x) as an explicit expression, finding f(x=a) implies substituting the value of x by a in every instance it occurs.

We are given the function:

\(f(x)=3x^2-x\)

It's required to find f(10). We replace the x for 10:

\(f(10)=3*10^2-10\)

Operating:

\(f(10)=3*100-10\)

\(f(10)=300-10\)

\(f(10)=290\)

Thus, f(10)=290

Answer:

20t+4

Step-by-step explanation:

20t=?t

4=?

Answer:

here

Step-by-step explanation:

Answer:

The answer would be A. (3,0)

Answer:

12

Step-by-step explanation:

7 + 13 + (-8)

Keep in mind, adding a negative number is like subtracting that number.

7 + 13 - 8

= 20 - 8

= 12

Answer:

Step-by-step explanation:

AFR = VFN (opposite angle rule)

7x + 33 = 9x + 7

33 - 7 = 9x - 7x

26 = 2x

x = 26 : 2

x = 13°

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

check

7 * 13 + 33 = 9 * 13 + 7   (remember PEMDAS)

91 + 33 = 117 + 7

124 = 124

the answer is good

This question is incomplete

Complete Question

At Tom's workplace, the thermometer is reading 86 degrees Fahrenheit. When the temperature goes over 32 degrees Celsius, Tom must have an extra break. He uses the formula below to calculate the temperature in °C.

C=(F−32)5/9

Will Tom get an extra break? YES ? NO ?

Answer:

No

Step-by-step explanation:

We are given the formula

°C=(F−32)5/9

F = 86°F

°C = (86 - 32) × 5/9

°C = 54 × 5/9

°C = 6 × 5

°C = 30°C

The rule says: When the temperature goes over 32 degrees Celsius, Tom must have an extra break.

From the question, the temperature does not go above 30°C , hence, Tom doesn't get an extra break.

The provided assertion indicates that (A) is 41° (b) is -17.16 (a) is 5.41

Having three sides, three angles, and three points, a triangular is a closed, two-dimensional object. A hexagon also includes a triangular.

The total of a triangle's three sides is.

We know that a right angle is , and we are given another angle that is , so that means that angle  is:

A + 49 +90 = 180

A + 139 = 180

A = 180 - 139

A = 41°

To find side length b, we can use the sin function:

sin(49) = b/18

18 ×-0.53 = b

b = -17.16

To find side length a, we can use the cos function:

cos(49) = a/18

18 × 0.300 = a

a = 5.41

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Answer: NO

Step-by-step explanation: if the two lines intersect none of the points should be parrelle.

Answer:

No

Step-by-step explanation:

Parrallel means nothing touches it and it is at the same angle as the second line. You already say they touch so No.

Answer:

12  cm

Step-by-step explanation:

In a trapezoid, the length of the mid segment is half of the sum of the lengths of  the parallel sides.

XY = (AB + DC)/2

    = (15 + 9)/2

    = 24/2

  = 12 cm

Answer:

The correlation coefficient is approximately -0.9949

Step-by-step explanation:

The given data is presented as follows;

\(\begin{array}{lcl}x&&y\\-10&&2\\-8&&-3\\-1&&-15\\-4&&-10\\-6&&-6\\-7&&-5\\-5&&-8\\-3&&-13\\-2&&-14\\-9&&-1\end{array}\)

The correlation coefficient, r is given as follows;

\(r = \dfrac{\sum(x_i - \overline x) \cdot (y_i - \overline y)}{\sqrt{\sum (x_i- \overline x)^2\times \sum (y_i- \overline y)^2 } }\)

From MS Excel, we have;

∑(\(x_i - \overline x\))·(\(y_i - \overline y\)) = -155.5

∑(\(x_i - \overline x\))² = 82.5

∑(\(y_i - \overline y\))² = 296.1

Therefore, r = -155.5/(√(82.5 × 296.1)) ≈ -0.9949

The correlation coefficient, r ≈ -0.9949

The dimensions of pool 25.5m width, 76.5m length.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure.

let x=  Width

formula of area of rectangle = Length x Width

Given;

\(\begin{aligned}&(3 x+2)(x+2)=3 x^{2} +208 \\&3x^{2} +8 x+4=3x^{2} +208\end{aligned}\)

We can substrate \(3x^{2}\) and 4 from both sides.

8x = 204

x = 25.5m width, 76.5m length.

(25.5)(76.5) = 1950.75 \(m^{2}\)

(27.5)(78.5) = 2158.75 \(m^{2}\)

The difference is 208\(m^{2}\)

The dimensions of pool 25.5m width, 76.5m length .

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The height of the lamppost is 110 in (optionC)

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

To find the height;

Tan 70 = h/ 40

h = tan70 × 40

h = 2.75 × 40

h = 110 in

therefore the height of the lamppost is 110 in

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Answer:

im not good with math sorry :(

Step-by-step explanation: