Find two consecutive positive even integers such that the square of the first decreased by 64 equals 3 times the second.

Answer:

a=1

Step-by-step explanation:

-20=-8(a+4)-5(1-5a)

Distribute

-20 = -8a -32 -5 +25a

Combine like terms

-20 =17a -37

Add 37 to each side

-20+37 = 17a-37+37

17 = 17a

Divide by 17

17/17 = 17a/17

1= a

Answer:

You need to use a nested for loop. Use the range() builtin to produce an iterable sequence. The outer for loop should iterate over the number of rows.

Step-by-step explanation:

Use the range() builtin to produce an iterable sequence. The outer for loop should iterate over the number of rows overtime.

Answer:

3/4 75/100 12/16 24/32

Step-by-step explanation:

9/12 is the equivalent of 75% and fractions that express the same proportions.

Answer:

x axis?

Step-by-step explanation:

Answer:

176

Step-by-step explanation:

The f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

To compute f′(a) algebraically for the given value of a, we use the following differentiation rule which is known as the Power Rule.

This states that:If f(x) = xn, where n is any real number, then f′(x) = nxⁿ⁻¹This is valid for any value of x.

Therefore, we can differentiate f(x) = −7x + 5 with respect to x using the power rule as follows:

f(x) = −7x + 5

⇒ f′(x) = d/dx (−7x + 5)

⇒ f′(x) = d/dx (−7x) + d/dx(5)

⇒ f′(x) = −7(d/dx(x)) + 0

⇒ f′(x) = −7⋅1 = −7

Hence, the derivative of f(x) with respect to x is -7.Now, we evaluate f′(a) when a = −6 as follows:f′(x) = −7 evaluated at x = −6⇒ f′(−6) = −7

Therefore, f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

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Answer:

9 birdhouses

Step-by-step explanation:

x = # of birdhouses

22x + 8 = 206

22x = 198

x = 9

Answer:

The answer is 90.

Thank you

Answer:

89.6

Step-by-step explanation:

The formula to convert Celsius to Fahrenheit is given by °F = °C × (9/5) + 32

F = [ C × (9/5) + 32 ]

Given that, C = 32

F = 32 × (9/5) + 32

F = 32 [ 1 + (9/5) ]

F = 32 [ 1 + 1.8 ]

F = 32 × 2.8

F = 89.6

The equation of the parabola that has vertex at the center and focus at the point (6,0) is x = y²/24

We define what a parabola is

 The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

The canonical equation of a parabola is given by

(y - k)² = 4p(x - h)

The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

Since the vertex and the focal axis are on the same axis, we analyze that:

v (0, 0)

f (6, 0) the focus is on the right so the parabola is of the form X = Y².

(y - 0)² = 4p(x - 0)

f = (0 + p, 0)

0 + p = 6

p = 0 + 6

p= 6

(y - 0)² = 4*6(x - 0)

(Y)² = 24(X)

x = y²/24

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It is a graph of a function

Answer:

50,076 square inches

Step-by-step explanation:

When we use a linear function, we have the inequality as 245 + 10x > 569 and the solution is x > 25

We know that the linear function is modeled by: y = mx + b, in which:

a) m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b) b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

Since there are currently 245 glasses (y-intercept), and each set on sale comes with 10 glasses(slope), the number of glasses after x sales is given by: y = 245 + 10x.

She needs at least 569 glasses, hence the inequality is:

y > 569

245 + 10x > 569

Now we need to solve the inequality to find the number of sets needed:

10x > 245

x > 24.5

As the number of sets is an integer number, the solution is:

x > 25

Therefore, when we use a linear function, we have the inequality as 245 + 10x > 569 and the solution is x > 25

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The complete equation so that the statement is true is 3x+9+4x+x= 8x + 1

The equation is given as:

3x+9+4x+x=

Represent the blank with y

So, we have:

3x + 9 + 4x + x = y

Evaluate the like terms

8x + 9 = y

For the equation to have no solution the value of y and 8x + 9 must not be equal.

Take for instance

y = 8x + 1

So, we have:

8x + 9 = 8x + 1

Subtract 8x from both sides

9 = 1

The above equation is false because 1 and 9 are not equal

Hence, the complete equation so that the statement is true is 3x+9+4x+x= 8x + 1

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Complete question

Use the drop-down menus to complete each equation so the statement about its solution is true.

No Solutions

3x+9+4x+x=

A person of interest has been identified by the police, the appropriate location of the person of interest is D(5, -4). Therefore, option D is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let (x, y) be the coordinates of the person of interest. Then, we can set up three equations based on the distances between the person and the three known locations:

√((x-(-2))²+(y-9.9)²)=6

√((x-(-8))²+(-(-4.7))²)=10

√((x -(-12))²+(y-4)²)=9

Squaring both sides of each equation and simplifying, we get:

(x+2)²+(y-9.9)²=36

(x+8)²+(y+4.7)²=100

(x+12)²+(y-4)²=81

Expanding the squared terms and simplifying, we get a system of three linear equations in two variables:

x²+4x+y²-19.8y=4

x²+16x+y²+9.4y=52.59

x²+24x+y²-8y=21

We can solve this system of equations to find the values of x and y that satisfy all three equations.

y = (-11.94 + 6x)/19.8

Substituting this expression for y into the first equation, we get a quadratic equation in x:

x²+4x+((-11.94+6x)/19.8)²-19.8((-11.94+6x)/19.8)-4=0

Simplifying and solving for x, we get:

x=-0.217 or x=5.184

Substituting these values of x into the expression for y, we get:

y=1.283 or y=-3.772

So, x=5 and y=-4

Therefore, option D is the correct answer.

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Step-by-step explanation:

the answer is number A for ur q

The coordinates of the specified vertex after the given sequence of transformations is given by;

Q' = (3, -3).

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Mathematically, a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

By translating the coordinate Q (1, 3) two (2) units to the right, we have the following:

Coordinate Q (1, 3) → Coordinate Q' (1 + 2, 3) = Q (3, 3)

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate would change from positive to negative. Therefore, a reflection over the x-axis is given by this transformation rule:

(x, y)      →       (x, -y)

Coordinate Q' (3, 3) → (3, -3).

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The solution to the nonhomogeneous differential equation y′′+9y=cos(3x)+sin(3x) with initial conditions y(0)=3 and y′(0)=1 is y(x) = c1*cos(3x) + c2*sin(3x) + (1/6)*x*sin(3x) - (1/18)*cos(3x).


Step 1: Find the complementary function, y_h, which is the general solution to the associated homogeneous equation y'' + 9y = 0. The characteristic equation is r^2 + 9 = 0, so r = ±3i. Hence, y_h = c1*cos(3x) + c2*sin(3x).

Step 2: Find a particular solution, y_p, to the nonhomogeneous equation. Assume y_p = A*cos(3x) + B*sin(3x) + C*x*cos(3x) + D*x*sin(3x). Plug this into the nonhomogeneous equation and simplify to determine A, B, C, and D. We get A=-1/18, B=0, C=0, D=1/6.

Step 3: Combine the complementary function and particular solution: y(x) = y_h + y_p = c1*cos(3x) + c2*sin(3x) - (1/18)*cos(3x) + (1/6)*x*sin(3x).

Step 4: Apply initial conditions to find c1 and c2. y(0) = 3 => c1 = 3 + 1/18, y'(0) = 1 => c2 = 1/6. Thus, y(x) = (3+1/18)*cos(3x) + (1/6)*sin(3x) + (1/6)*x*sin(3x) - (1/18)*cos(3x).

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The missing gaps when considering transformation undergone is;

1) Dilation

2) Enlargement.

3) Reduction.

4) Non-rigid transformation.

5) Scale factor of 1/4.

6) Actual length = 80 mm

7) Actual length = 720mm

1) A dilation is what is defined as a transformation in which a figure is enlarged or reduced with respect to a fixed point C, called the center of dilation, and a scale factor k, which is the ratio of the lengths of the corresponding sides of the image and the preimage.

2) When the scale factor is greater than 1, the dilation is called an enlargement.

3) When the scale factor is greater than 0 but less than 1, the dilation is called a reduction.

4) When the shape or size of a figure changes, it is called a non-rigid transformation.

5) To reduce the picture which is 10 inches by 12 inches to a picture which is 2.5 inches by 3 inches, we will multiply by 1/4 which implies a reduction with a scale factor of 1/4.

6) If the magnifying glass shows the image of an object that is 10 times the object's actual size, then we can say that if the object is 8mm, its actual length = 8 * 10 = 80 mm

7) If the magnifying glass shows the image of an object that is 6 times the object's actual size, then we can say that if the object is 120mm, its actual length = 6 * 120 = 720mm

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The two sets of three consecutive integers that meet the criteria, after the calculations are (-1, 0, 1) and (4, 5, 6).

To find three consecutive integers such that four times the sum of all three is two times the product of the larger two, follow these steps:

1. Let the three consecutive integers be x, x+1, and x+2.
2. According to the problem, 4 times the sum of these integers is equal to 2 times the product of the larger two. So, we can write the equation: 4(x + (x+1) + (x+2)) = 2((x+1)(x+2)).
3. Simplify the equation: 4(3x + 3) = 2(x^2 + 3x + 2).
4. Expand the equation: 12x + 12 = 2x^2 + 6x + 4.
5. Move all terms to one side of the equation to form a quadratic equation: 2x^2 - 6x - 8 = 0.
6. Factor the equation: 2(x^2 - 3x - 4) = 0.
7. Solve the quadratic equation: (x-4)(x+1) = 0.
8. Find the integer solutions: x = 4 or x = -1.

So, the two sets of three consecutive integers that meet the criteria are (-1, 0, 1) and (4, 5, 6).

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The test statistic is approximately 7471.77  the F-value, which is the ratio of the between-treatments mean square to the error mean square.

The degrees of freedom for the between-treatments source of variation are 4, and the mean square is calculated by dividing the sum of squares by the degrees of freedom:

Mean square between treatments = 2,073.6 / 4 = 518.4

The degrees of freedom for the error source of variation are 288, and the mean square is calculated by dividing the error sum of squares by the degrees of freedom .Mean square error = 20 / 288 = 0.0694

The F-value is calculated by dividing the mean square between treatments by the mean square error:

F = 518.4 / 0.0694 = 7474.4

The F-value is very large, indicating that the between-treatments variation is much larger than the error variation. To test the null hypothesis, we compare the F-value to the critical F-value at the desired significance level and degrees of freedom.

Since we are not given a significance level, we cannot determine the critical F-value. Therefore, we cannot determine the test statistic or the c

Sum of Squares (SS) = 2,073.6,Degrees of Freedom (def.) = 4

Mean Square (MS) = SS / def. = 2,073.6 / 4 = 518.4,SS = 20

def. = 288,MS = SS / def. = 20 / 288 = 0.0694

To compute the test statistic, we divide the "between treatments" mean square by the error mean square:

Test Statistic = MS (between treatments) / MS (error) = 518.4 / 0.0694 ≈ 7471.77.

The F-value is very large, indicating that the between-treatments variation is much larger than the error variation. To test the null hypothesis, we compare the F-value to the critical F-value at the desired significance level and degrees of freedom.

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Answer:

x = 24

Step-by-step explanation:

if a and b are parallel then

62 and 5x - 2 are same- side interior angles and sum to 180° , that is

5x - 2 + 62 = 180

5x + 60 = 180 ( subtract 60 from both sides )

5x = 120 ( divide both sides by 5 )

x = 24

thus for a to be parallel to b , then x = 24

Answer:

X = 75°

Y = 105°

Z =75

Step-by-step explanation:

Let x be the cost of each notebook. We know that we bought 5 of them, then the total cost of the notebooks is:

We had 21 dollars and we spent 5x on the notebooks, this can be express as:

Finally we know that this is equal to the six dollars we had at the end, then we have the equations:

Solving for x we have:

Therefore each notebook cost $3

Answer:

45-45-90 triangles

30-60-90 triangles

Step-by-step explanation:

45-45-90 triangles

30-60-90 triangles

The required sample size is approximately 386 to be 95% confident that the sample percentage is within 5.8 percentage points of the true population percentage.

To determine the required sample size for desired confidence level and margin of error, we can use the formula for sample size calculation:

\(\[ n = \left(\frac{{Z^2 \cdot p \cdot (1-p)}}{{E^2}}\right) \]\)

Where:

\(\( n \)\) = required sample size

\(\( Z \)\) = Z-score corresponding to the desired confidence level (for 95% confidence, \(( Z = 1.96 \))\)

\(\( p \)\) = estimated proportion (0.5 can be used as a conservative estimate when the true proportion is unknown)

\(\( E \)\) = desired margin of error (5.8 percentage points)

Plugging in the values into the formula:

\(\[ n = \left(\frac{{1.96^2 \cdot 0.5 \cdot (1-0.5)}}{{0.058^2}}\right) \]\)

\(\( n \approx 385.9 \)\)

Since sample size must be a whole number, we round up to the nearest integer.

Therefore, the required sample size is approximately 386 to be 95% confident that the sample percentage is within 5.8 percentage points of the true population percentage.

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Answer:

A) 127.16π m³

Step-by-step explanation:

Volume of a cylinder:

V = πr²h

Given:

r = 3.4

h = 11

Work:

V = πr²h

V = π(3.4²)(11)

V = π(11.56)(11)

V = 127.16π

Answer:

hey bestie, its 127.16

Step-by-step explanation:

3.4 squared is 11.56

and 11.56 times 11 is 127.16