-2(3h-1)=5(2h-3) has how many solutions are there

The distance between the tops of the buildings is 28.5 meters.

To find the distance between the top of the buildings, we can use the concept of similar triangles.

Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).

We can set up a proportion based on the similar triangles formed by the buildings:

a/c = b/x

Substituting the known values:

12/18 = 19/x

To find "x," we can cross-multiply and solve for "x":

12x = 18 * 19

12x = 342

x = 342/12

x = 28.5 m

Therefore, the distance between the tops of the buildings is 28.5 meters.

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Answer:

60 degress

Step-by-step explanation:

5 x 12

Answer:60 degress

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

1 3/5 ÷ 2/5

Change the mixed number to an improper fraction

( 5*1+3)/5 ÷ 2/5

8/5 ÷ 2/5

Copy dot flip

8/5 * 5/2

Rewriting

8/2 * 5/5

4*1

4

The value of ADA is 36

The question could be approached as a quantitative reasoning exercise :

Assigning each alphabet a numeric value corresponding to its position in the English alphabet :

A has a value of 1

B has a value of 2

C has a value of 3

D has a value of 4

ADD could be interpreted as :

ADD = (1 + 4 + 4) = 9

Taking the square of the sum ; 9² = 81

ADD = 81

BAD could be interpreted as :

BAD = (2 + 1 + 4) = 7

Taking the square of the sum ; 7² = 49

CAD could be interpreted as :

CAD = 3 + 1 + 4 = 8

Taking the square of the sum ; 8² = 64

Therefore ;

ADA could be interpreted as :

ADA = 1 + 4 + 1 = 6

Square of the sum ; 6² = 36

Hence, the value of ADA is 36

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The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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Answer:

B

Step-by-step explanation:

any non-zero expression raised to the power of 0 equals 1

The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.

The number of terms in a polynomial helps when performing operations like simplification, factoring, or evaluating expressions.

The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.

In order to determine the number of terms in a polynomial, we count the number of distinct algebraic expressions separated by addition or subtraction operations.

In this polynomial, we have:

Term 1: 18x³ (This is the term with the highest degree, which is 3 in this case, and it includes the coefficient 18.)

Term 2: -2x² (This term has a degree of 2 and a coefficient of -2.)

Term 3: 4x (This term has a degree of 1 and a coefficient of 4.)

Term 4: -1 (This is a constant term with a degree of 0.)

We can see that there are four distinct terms separated by addition and subtraction operations:

18x³, -2x², 4x, and -1.

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Answer:

Each Cat video gets 750 comments

Each dog video gets 450 comments

Hope this helps you!

Answer:

He gets 750 comments on the cat videos and 450 on the dog videos the answer to the second question is yes

Step-by-step explanation:

khan :)

Answer:

a)  $497.70

b)  392.4 square feet

c)  $1,200

Step-by-step explanation:

A regular octagon has 8 sides of equal length.

Given each side of the octagon measures 9 feet in length, and one side does not have a railing, the total length of the railing is 7 times the length of one side:

\(\textsf{Total length of railing}=\sf 7 \times 9\; ft=63\;ft\)

If the railing sells for $7.90 per foot, the total cost of the railing can be calculated by multiplying the total length by the cost per foot:

\(\textsf{Total cost of railing}=\sf 63\;ft \times \dfrac{\$7.90}{ft}=\$497.70\)

Therefore, the cost of the railing is $497.70.

\(\hrulefill\)

To find the area of the regular octagonal gazebo, given the side length and apothem, we can use the area of a regular polygon formula:

\(\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\;s\;a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}\)

Substitute n = 8, s = 9, and a = 10.9 into the formula and solve for A:

\(\begin{aligned}\textsf{Area of the gazebo}&=\sf \dfrac{8 \times 9\:ft \times10.9\:ft}{2}\\\\&=\sf \dfrac{784.8\;ft^2}{2}\\\\&=\sf 392.4\; \sf ft^2\end{aligned}\)

Therefore, the area of the gazebo is 392.4 square feet.

\(\hrulefill\)

To calculate the cost of the gazebo's flooring if it costs $3 square foot, multiply the area of the gazebo found in part (b) by the cost per square foot:

\(\begin{aligned}\textsf{Total cost of flooring}&=\sf 392.4\; ft^2 \times \dfrac{\$3}{ft^2}\\&=\sf \$1177.2\\&=\sf \$1200\; (nearest\;hundred\;dollars)\end{aligned}\)

Therefore, the cost of the gazebo's flooring to the nearest hundred dollars is $1,200.

a. To find the perimeter of the gazebo, we can use the formula P = 8s, where s is the length of one side. Substituting s = 9, we get:

P = 8s = 8(9) = 72 feet

Since one side is open, we only need to find the cost of railing for 7 sides. Multiplying the perimeter by 7, we get:

Cost = 7P($7.90/foot) = 7(72 feet)($7.90/foot) = $4,939.20

Therefore, the cost of the railing is $4,939.20.

b. To find the area of the gazebo, we can use the formula A = (1/2)ap, where a is the apothem and p is the perimeter. Substituting a = 10.9 and p = 72, we get:

A = (1/2)(10.9)(72) = 394.56 square feet

Therefore, the area of the gazebo is 394.56 square feet.

c. To find the cost of the flooring, we need to multiply the area by the cost per square foot. Substituting A = 394.56 and the cost per square foot as $3, we get:

Cost = A($3/square foot) = 394.56($3/square foot) = $1,183.68

Rounding to the nearest hundred dollars, the cost of the flooring is $1,184. Therefore, the cost of the gazebo's flooring is $1,184.

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The Mean Value Theorem states that there exists a point c in the interval (a,b) such that f'(c) equals the function's average rate of change throughout [a,b] if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b).

The Mean Value Theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then at some point c on the interval (a, b), f'(c) must equal the function's average rate of change over [a, b].

There is at least one point on a planar arc between two endpoints where the tangent to the arc is parallel to the secant between its ends.

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The complete question is: Explain why the Mean Value Theorem does not apply to the function on the interval [0,6].

The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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Based on the sample response given, the statements included in the explanation on the horizontal line test are:

The horizontal line test is used to not only find out if a graph has an inverse function, but also if that inverse is also a function itself.

To pass the horizontal line test, the function has to be one-to-one which means that a horizontal line can intersect the graphed function at one point in all places. If this happens, then there is an inverse and the inverse itself is a function.

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a) The initial height of the football at t = 0 is 2 feet.

b) The ball reaches its maximum height at approximately t = 2.05 seconds.

c) The maximum height of the ball is approximately 23.9 feet.

d) It takes approximately 4.579 seconds for the ball to hit the ground.

a) The initial height of the football at time t = 0 can be found by substituting t = 0 into the equation \(5t^2 + 20.5t + 2:h = -5(0)^2 + 20.5(0) + 2 = 0 + 0 + 2 = 2\)

Therefore, the initial height of the football is 2 feet.

b) To find the time at which the ball reaches its maximum height, we can observe the graph of the equation h = \(-5t^2 + 20.5t + 2.\) The maximum height corresponds to the vertex of the parabolic graph. The t-coordinate of the vertex can be calculated using the formula t = -b/2a, where a and b are the coefficients of the quadratic equation.

In this case, a = -5 and b = 20.5. Plugging these values into the formula, we get:

\(t = -20.5 / (2\times (-5)) = -20.5 / -10 = 2.05\)

Therefore, the ball reaches its maximum height at approximately t = 2.05 seconds.

c) The maximum height of the ball can be found by substituting the time t = 2.05 into the equation \(h = -5t^2 + 20.5t + 2:\)

h = -5(2.05)^2 + 20.5(2.05) + 2 ≈ -20.125 + 42.025 + 2 ≈ 23.9

Therefore, the maximum height of the ball is approximately 23.9 feet.

d) To find the time it takes for the ball to hit the ground, we need to determine when the height h becomes zero. We can set the equation \(-5t^2 + 20.5t + 2 = 0\) and solve for t.

This quadratic equation can be solved using factoring, the quadratic formula, or by graphing. The solutions are t ≈ -0.179 and t ≈ 4.579. Since time cannot be negative in this context, the ball takes approximately 4.579 seconds to hit the ground.

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Solution:

2b would be the greatest common factor (GCF) between both 10b^3 and 4b.

Hope this helps!

Answer: The area is going to be 0.8

Step-by-step explanation:  The diameter is 1

You need the radius of the circle which is half the diameter. So the Radius(R) is 0.5.

After you find the radius of the circle to find the area of the circle you use the formula pie (R)^2. You are using 3.14

3.14(0.5)^2= 0.785

you then want to round your answer to the nearest tenth so the 8 turns the 7 into an 8.

So, the Area is 0.785 but after rounding it is 0.8.

Hope that helped :)

The value of sin(θ) = 3√13/13

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.

if cos(θ) = adj/hyp = 2√13/13

then

2√13 = adj, hyp = 13

opp = √ 13²- 2√13)²

= √169- 52

= √117

= √13 × 9

= 3√13

since the θ is in second quadrant, cosine will be negative and sine will be positive

therefore sin(θ) = 3√13/13

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Answer:

b

Step-by-step explanation:

add the three numbers together then minus from the main total

Answer:

B. $899.15

Step-by-step explanation:

The correct solution to the expression 3 + 5^2 is C. 28.

Mathematically, an expression is a combination of variables with numbers, values, or constants.

Mathematical or algebraic expressions use the mathematical operands like addition (+), subtraction (-), division (÷), multiplication (×), exponents (^), etc.

An algebraic expression does not go with the equal symbol (=), unlike an equation.

3 + 5^2

= 3 + 5 x 5

= 3 + 25

= 28

Thus, an evaluation of the algebraic expression 3 + 5^2 gives the solution as Option C.

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Answer: C

Step-by-step explanation:

I just took the quiz and I got it right

Statement describes how to geometrically divide a complex number z by a second complex number w is Option (C) Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.

In mathematics, a complex number is an element of a number system that contains the real numbers and a specific element denoted i, called the imaginary unit

Modulus of the complex number is the distance of the point on the argand plane representing the complex number z from the origin

Given,

Complex number z divides by a second complex number w

To divide a complex number a complex number then multiply the conjugate with the numerator and the denominator of the complex fraction

From the given statements Scale of z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w

Hence, Statement describes how to geometrically divide a complex number z by a second complex number w is Option (C) Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.

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4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.

5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.

In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;

RU ║ ST

Slope of side RU = Slope of side ST

Slope of RU = (y₂ - y₁)/(x₂ - x₁)

Slope of RU = (1 + 3)/(5 + 3)

Slope of RU = 4/8

Slope of RU = 0.5.

Slope of RS = (y₂ - y₁)/(x₂ - x₁)

Slope of RS = (-9 + 3)/(-4 + 3)

Slope of RS = -6/-1

Slope of RS = 6.

Slope of ST = (y₂ - y₁)/(x₂ - x₁)

Slope of ST = (-2 - 1)/(10 - 5)

Slope of ST = -3/5

Slope of ST = -0.6.

Slope of UT = (y₂ - y₁)/(x₂ - x₁)

Slope of UT = (-2 + 9)/(10 + 4)

Slope of UT = 7/14

Slope of UT = 0.5.

Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.

Question 5.

In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance RT = √[(-2 + 3)² + (10 + 3)²]

Distance RT = √170 units.

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance US = √[(5 + 4)² + (1 + 9)²]

Distance US = √181 units.

Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.

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Answer:

The graph will shift 5 units to the left

Answer:

--

Step-by-step explanation:

Show all the options please

Not able to see all options

It would be wiser for the couple to stay in the old apartment and save $1400.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Explanation:

If they stay until the end of the lease, total money that will be paid out is $1000 x 6 = $6000,

If they leave, they'll have to forgo $1000.

If they move to their new apartment, they'll pay $900 x 6 = $5400

total expenditure if they move to the new place at the end of the six months period will be, the $1000 that will not be refunded back to them on the old apartment, plus this new $5600 for six month's rent in this new apartment, and that will be a total of $6400.

It would be wiser for the couple to stay in the old apartment and save $1400.

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Answer:

9 1/8 ribbon would be remaining

Answer:

27

Step-by-step explanation:

The area of this parallelogram is its base times height. 6x4.5 is 27.

Hope this helps! (please mark me brainliest)

Answer:

\(x=1\)

Step-by-step explanation:

Ok, so we start off with \(2^x+2=4\)

Then, we subtract 2 from both sides so that becomes: \(2^x+2-2=4-2\)

After that, we simplify to get: \(2^x=2\)

Finally, the solution becomes: \(x=1\)

Answer:

x=1

Step-by-step explanation:

2^x=4-2

2^x=2

2^x=2^1

x=1

Answer:

\(\displaystyle y=\frac{1}{3}x-6\)

Step-by-step explanation:

Dilation of a Line

Given a line that passes through points A(-3,-4) and B(-6,-5). We'll apply a dilation with a scale factor of 2 centered at the origin by multiplying each coordinate by 2. The points map to:

A'(-6,-8) and B'(-12,-10)

Now we find the equation of the line passing through A' and B'.

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

\(\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)

Substituting:

\(\displaystyle y+8=\frac{-10+8}{-12+6}(x+6)\)

\(\displaystyle y+8=\frac{-2}{-6}(x+6)\)

\(\displaystyle y+8=\frac{1}{3}(x+6)\)

Operating:

\(\displaystyle y=\frac{1}{3}x+\frac{1}{3}*6-8\)

\(\displaystyle y=\frac{1}{3}x+2-8\)

\(\boxed{\displaystyle y=\frac{1}{3}x-6}\)

Answer:

A score of 4.2 on a test with a mean of 2.5 and a standard deviation of 1.2 has the highest relative position.

Step-by-step explanation:

Which score has the highest relative position: a score of 38 on a test with a mean of 30 and a standard deviation of 10, a score of 4.2 on a test with a mean of 2.5 and a standard deviation of 1.2 or a score of 432 on a test with a mean of 396 and a standard deviation of 40.

In order to find the solution, we need to calculate the z score value for each test.

The z score formula: \(z = \dfrac{\bar{x} -\mu}{s}\) where \(\bar{x}\)  is the score, μ is the mean and s is the standard deviation.

Now for test 1:

Put \(\bar{x}=38, \mu=30 \text{ and } s=10\) in the above formula.

\(z = \dfrac{38 -30}{10}\)

\(z = 0.8\)

For test 2:

Put \(\bar{x}=4.2, \mu=2.5 \text{ and } s=1.2\) in the above formula.

\(z = \dfrac{4.2 -2.5}{1.2}\)

\(z \approx 1.417\)

For test 3:

Put \(\bar{x}=432, \mu=396 \text{ and } s=40\) in the above formula.

\(z = \dfrac{432 -396}{40}\)

\(z =0.9\)

Since the z score value of test 2 is greater so a score of 4.2 on a test with a mean of 2.5 and a standard deviation of 1.2 has a highest relative position.