DIRECTIONS: Use this information to answer Parts A and B. The width of a rectangle is shown. The length is twice the width. Part A 5-1x Write an expression for the perimeter listing each side separately.​

The rate of change of the surface area A(t) of the prism is 136 kilometers per minute.

What does rate of change mean?

An indicator of how one quantity changes in proportion to another is called a rate of change. If x and y are the independent and dependent variables, respectively, then the rate of change is equal to y-to-x conversions. Positive or negative change rates are possible.

Surafce area of a prism is equal to

2(Area of base) + (perimeter of base)(height)

2b^2+4bh

[tex]S=2b^2+4bh[/tex]

[tex]\frac{ds}{dt}=4b\frac{db}{dt} + 4b\frac{db}{dt} + 4h\frac{db}{dt} \\[/tex]

It is given that db/dt= -7 and dh/dt -=10.

At a particular instant b= 4km, h=9 km.

Now we will substitute the values in this formula:

[tex]\frac{ds}{dt}=-4*4*7-4*4*7+ 4*9*10\\\frac{ds}{dt}=136[/tex]

The rate of change of the surface area A(t) of the prism is 136 kilometers per minute.

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The equation has one solution.

A value of x that makes the equation true is 6 which when substituted into the equation and simplified makes the equation turn into x = 0.

A value of x that makes the equation false is 8 which when substituted into the equation and simplified makes the equation turn into x = 2.

From the information provided, we have the following equation:

x - 6 = 6 - x

Rearranging the equation by collecting like terms, we have the following solution:

x + x = 6 + 6

2x = 12

x = 12/2

x = 6

Substituting the value "6" into the equation, we have the following solution;

x - 6 = 6 - 6

x - 6 = 0

Assuming x = 8, we have the following solution;

x - 6 = 8 - 6

x - 6 = 2

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Complete Question:

Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your conclusion.

x - 6 = 6 - x

The equation has _____.

A value of x that makes the equation true is ___ which when substituted into the equation and simplified makes the equation turn into ____.

A value of x that makes the equation false is ___ which when substituted into the equation and simplified makes the equation turn into ___.

Answer:

[tex]x^{2}[/tex]+14x-32 [tex]units^{2}[/tex]

Step-by-step explanation:

a basketball court is a rectangle, therefore its area is length x width.

the length given is (x+16)

the width given is (x-2)

substitute into the rectangular area equation:

length x width = (x+16)(x-2)= [tex]x^{2}[/tex]+14x-32

specific units (e.g. centimetres, meters, feet, etc) were not given so use the term 'units', and because we are dealing with area, use [tex]units^{2}[/tex].

therefore the answer is, [tex]x^{2}[/tex]+14x-32 [tex]units^{2}[/tex].

i hope that helps :)

Answer:

therefore the answer is, [tex]x^{2} +14x-32units^{2}[/tex].

Step-by-step explanation:

The equation of the line that is parallel to the line y = - 5x + c and passes through (-4, -1) will be y = - 5x - 21.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The equation of the line is given below.

y = - 5x + 6

The equation of the line that is parallel to the line y = - 5x + 6 is written as,

y = - 5x + c

The equation passes through (-4, -1), then we have

- 1 = - 5 (-4) + c

- 1 = 20 + c

- 21 = c

The equation of the line that is parallel to the line y = - 5x + c and passes through (-4, -1) will be y = - 5x - 21.

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Answer:

Step-by-step explanation:

Answer:

97611 is the correct answer

Answer:

It means that if the system of equations has an infinite number of solution, then the system is said to be consistent.

Answer:

Given that Figure A and Figure B are similar polygons, the scale factor of Figure A to Figure B = 5/2.

Recall:

Similar Polygons have corresponding side lengths whose ratio are equal. That is, their pairs of corresponding sides are proportional.

The ratio of any of their corresponding side length = scale factor

Given the two pairs of similar polygons, the scale factor of figure A to figure B will be calculated as follows:

A side length of Figure A = 10

Corresponding side length of Figure B = 4

Scale factor of Figure A to Figure B = 10/4 = 5/2

Step-by-step explanation:

The total number of cookies that was made that day given that 55 which is 15% was burnt is 360.

We know that the number of burned cookies is 55, and that this represents 15% of the total production for the day.

We can use this information to set up a proportion to find the total number of cookies made that day.

Burned cookies / Total cookies = 15% / 100%

55 / X = 15/100

To find the total number of cookies made, we can cross-multiply and divide:

X = (55 * 100) / 15

X = 365

So, the bakery made a total of 365 cookies that day.

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Answer:

QS = 12

Step-by-step explanation:

Hello!

We can see that QS is the sum of QR and RS, which is equal to 6x.

We can substitute the given values to solve for x, and then use that to find QS.

The value of x is 2. We can now find QS by substituting 2 for x in 6x.

QS = 12.

Answer: A scale is a ratio of the size of the representation (such as a drawing) to the size of the real-world object being represented. In this case, Patty's drawing uses a scale of 1 inch = 45 feet, and Jamie's drawing uses a scale of 2 inches = 35 feet.

In order to find the side length of Jamie's drawing of one of the side length we need to use a proportion:

Jamie's side length / Patty's side length = Jamie's scale / Patty's scale

So if we know one of the side length of Patty's drawing we can find the side length of Jamie's drawing. Let's assume that the side length of Patty's drawing is x

x / Jamie's side length = 45 / 35

So we can isolate Jamie's side length by multiplying both sides by Jamie's scale of 35ft/2 inches

Jamie's side length = (x*35)/45

This is the length of one side length in Jamie's drawing using the scale of 2 inches = 35 feet. If you don't have the length of one side in patty's drawing you can't find the side length of Jamie's drawing.

Step-by-step explanation:

Therefore , the solution of the given problem of solution of trigonometry d = 33.977 m is the distance from the balloon's base to its apex..

Trigonometry is a discipline of mathematics that examines relationships between triangles' degrees and sides. Trigonometry is used frequently in geometry because every straight-sided form may be broken down into a group of triangles. Trigonometry and other areas of mathematics, particularly calculus, real or complex, infinite series, logarithms, and infinite series, have a staggering amount of interrelationships.

Here,

Angle of elevation to the balloon's peak: = 28°

When the balloon is erect, a right triangle is formed by the horizontal distance to the balloon, l, the height of the balloon, h, and the distance to the top of the balloon, d.

Aside from the hypotenuse

l = The leg next to the provided reference angle

,h = The leg perpendicular to the specified angle,

Trigonometric ratios give us;

Cosx is equal to the product of the hypotenuse and adjacent lengths.

where we obtain;

Cos x equals l/d

=>Cos 28 = 30 m /d

=> d = 30m/Cos 28 ≈ 33.977

Therefore , the solution of the given problem of solution of trigonometry d = 33.977 m is the distance from the balloon's base to its apex.

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Answer: Angle-Side-Angle Theorem

Step-by-step explanation:

The two triangles are shown to have congruent angles. By the Reflexive Property of Congruence, Side PM is shared and congruent between the two.

Because the angles are on either side (left and right) of the shared side, the triangles are congruent by the Angle-Side-Angle Theorem.

On solving the provided question we can say that - the value of the ellipse will be (5+ , root5)

In mathematics, an ellipse is a planar curve that encompasses two focus points and ensures that the sum of the two distances from any point on the curve to the focal points is constant. In doing so, the circle—a particular variety of ellipse with two equal focus points—is generalized. The ellipse, whose eccentricity is less than 1, indicates the area containing the points whose distances from its two foci add up to a certain amount. Running tracks in sporting arenas and 2D egg forms are two straightforward examples of ellipses in daily life.

here we have,

center at (5,-2), one vertex at (2, -2) and a focus at

(5+ √5,-2)

so the answer is (5+ , root5)

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Answer:

Step-by-step explanation:

To find the x-coordinate of the centroid of triangle ABC, we need to take the average of the x-coordinates of the three vertices of the triangle. The x-coordinates of the vertices of triangle ABC are -3, 2, and 4, so the average of these three numbers is (-3 + 2 + 4) / 3 = (3) / 3 = 1.

Therefore, the x-coordinate of the centroid of triangle ABC is 1. The correct answer is (-,1). The given answer (-,5/3) is not the correct x-coordinate of the centroid.

The possible radius and height for Cone B are 3 units and 16 units respectively

The formula for calculating the volume of a cone is expressed mathematically;

Volume = 1/3 πr²h

Given that;

From the information given, we have that;

Now, let the height of cone B be 16 units

Substitute the value into the formula, we have;

48π = 1/ 3 × π × r² × 16

multiply the values, we have

48 = 16r²/3

cross multiply

16r² = 144

Divide both sides by 16

r² = 144/16

r² =9

Find the square root of both sides

r = 3units

Hence, the values are 3 units and 16 units

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For 2 weeks tony will spent time for practice basketball is 10 hours.

Given data :

1st week

= Tuesday = 2 hours

= Wednesday = 1 hour

= Friday = 2 hours

same for 2nd week

so total hours = 1st week + 2nd week

                       =  2 + 1 + 2 + 2 + 1 + 2

                       = 10 hours

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On solving the provided question we can say that by logarithm the statement is true he is short.

The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).

He is tall, or he is short and handsome

It is not true that he is short or not handsome

by logarithm,

the statement is true he is short.

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Factor pair of 32 are (1, 32) ; (2, 16) ; (4, 8)

⇒ Firstly find the factors of 32

How Do You Work Out Factors of 32?

Step 1: Let's start with the whole number 1 and work our way up to the          factors of 32.   32 ÷ 1= 32 
Step 2: Now divide 32 by two.  32 ÷ 2= 16

Step 3: Then we get.   32 ÷ 4= 8

Step 4: Similarly, we calculate all the 32 factors.

32 factors = 1, 2, 4, 8, 16, and 32.

⇒ Secondly, find factor pairs of 32

The two numbers that, when multiplied together, give 32 are the factors of 32 in pairs. The factors of 32 are listed below in pairs.

Products of 32                Factor pair of 32

1 × 32 = 32                              (1, 32)

2 × 16= 32                               (2 ,16)

4 × 8 = 32                                (4, 8)

∴Therefore, factor pair of 32 are (1, 32) ; (2, 16) ; (4, 8)

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When convert it into rectangular form we get x=-1/2 and y=0.

To convert a point in polar coordinates (r, θ) to rectangular coordinates (x, y), you can use the following formulas:

[tex]x = r * cos(θ) \\y = r * sin(θ)[/tex]

Where r is the distance from the origin to the point, and θ is the angle in radians between the positive x-axis and the line connecting the point to the origin.

Alternatively, you can also convert from rectangular to polar coordinates using the following formulas:

[tex]r = sqrt(x^2 + y^2)\\θ = atan2(y, x)[/tex]

Where x, y are the rectangular coordinates and atan2 is a function that computes the angle of a point in a cartesian plane.

In general, it's worth noting that the polar coordinates are often used in some physics and engineering problems, while the rectangular coordinates are often used in computer graphics, analytic geometry and other fields.

The angle of 1's inverse tangent is 45°. This is the outcome of translating to polar coordinates in the form (r,theta).

To convert it into rectangle equation we have

[tex]x=rcos(theta)\\y=rsin(theta)\\r=1\\theta= 3*pi/2\\x= cos(3*pi/2)\\x= -1/2\\y=sin(3*pi/2)\\y=0[/tex]

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The length of ribbon is 48 yards.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Kala got a prepaid debit card with $15.

Price of Ribbon = 24 cents per yard.

After purchase money left $3.48.

So, Price of Ribbon purchased = 15 - 3.48 = $11.52 = 1152 cents

length of ribbon = 1152/ 24

                           = 48 yards

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false

it is a decimal not a fraction

Dalisay hits the target more.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

Kendra hits the target 3 times every 5 misses.

And, Dalisay hits the target 5 times every 7 misses.

Since, Kendra hits the target 3 times every 5 misses.

Hence, In 1 misses Kendra hits the target = 3/5 times

                                                               = 0.6 times

And,  Dalisay hits the target 5 times every 7 misses.

Hence,  In 1 misses Dalisay hits the target = 5/7 times

                                                               = 0.74 times

Thus, Dalisay hits the target more.

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Answer: -18

Step-by-step explanation:

Distribute the -3 to the values inside the parentheses, (x and 8) which equals -3x-24.

Then, use inverse operations by adding 24 on both sides (it will cancel on the left) to get -3x=53

Then divide -3 on both sides to get x by itself

Answer:

-18

Step-by-step explanation:

-3(x+8)=30

by dividing 3 from both sides

-(x+8)=10

by multiplying -1 for both sides

(x+8)= -10

by subtracting 8 from both sides

x = -18

The linear function q(x) = -3x + 1 is graphed and attached

The graph of the linear function is a straight line graph and the table of values used in making the plot is calculated as follows

For x = -20,  q(x) = -3 * -20 + 1 = 61

For x = -10,  q(x) = -3 * -10 + 1 = 31

For x = 0,  q(x) = -3 * 0 + 1 = 1

For x = 10,  q(x) = -3 * 10 + 1 = -29

For x = 20,  q(x) = -3 * 20 + 1 = -59

Table of values

x     y

-20  61

-10    31

0      1

10     -29

20    -59

These points are plotted in the cartesian coordinate by tracing the point of intersection of the x and y and marking it. Then the marked points are joined together to form a straight line

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The expression that represents the price of the video game after the discount is

p - 0.4p
Where p is the original price of the video game.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Price of the video game = p

Discount = 40%

The price of the video game after the discount.

= p - (40% of p)

= p - (40/100)p

= p - 0.4p

Thus,

The expression is p - 0.4p.

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Answer: I don't remember how to solve, but, I figured out the lengths of each side in the shaded region:

11, 11, 7, 7, 4, 4

Step-by-step explanation:

Hope this helps!! :D

Therefore , the solution of this is  the required system of equation is,

y=-x+6 and y=x+10.

A mathematical equation is a formula that links two statements by indicating their equivalence with the equal sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The relationship between two sentences on either side of a letter is expressed mathematically. There is frequently only one variable, which doubles as the symbol. say that 2x - 4 Equals 2.

Here,

(0,6) and the blue line pass through them (-2,8). You may figure out the equation for the blue line as,

=> y-6/x-0 =  8-6 /-2-0

=>y-6/x = 2/-2

=> y-6=-1(x)

y=-x+6

(-2, 8) and the red line pass through them (-3,7). The red line's equation can be calculated as,

y-8/x- (-2) = 8-7 /-2-(-3)

y-8 /x+2 = 1

y-8=x+2

y = x + 10

Thus, the required system of equations is,

y=-x+6 and y=x+10.

Therefore , the solution of this is  the required system of equations is,

y=-x+6 and y=x+10.

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The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The table represents a quadratic function C(t).

 t          C(t)

−2           1

−1           4

0           5

 1           4

2            1

From the table, the coordinate of the vertex will be at (0, 5). Then the equation is given as,

C(t) = a(t - 0)² + 5

C(t) = at² + 5

The equation is passing through the point (1, 4), then we have

4 = a (1²) + 5

4 = a + 5

a = - 1

The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.

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Let n = the number

The solution set is {x | x > 10}. 2. 5 ≥ 7 + y.

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