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Carmen and her dog, Duke walked at a slower rate at 0.625 blocks/min

Carmen and her dog, Duke would take 19.2 minutes to work 12 blocks.

In math, a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate. The word "per" can be further replaced by the symbol "/" in problems.

Carmen/Duke walks 5/8 = 0.625

Terell/Lady walks 8/12 = 0.677

Therefore, from the average time, Carmen and Duke walk slower.

Carmen and Duke will walk 12 blocks in;

= 12/0.625

= 19.2 minutes

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After simplification we got the above expression in the form 3f + 16m -56

The word "simplify" implies to turn something in a simpler form.

In mathematics, simplify an expression means write an expression in such a way that is comparatively less complicated than before. The main purpose of simplify an expression is to make it easy to solve as well as calculation.

3f + 8(2m-7)

we rearrange the expression by removing the parenthesis.

we remove the parenthesis by multiplying the factors.

3f + 8 × 2m - 8 × 7

3f + 16m -56

the above expression has no like terms to add or subtract so it is kept in this form.

Hence, 3f + 16m -56 is the simpler form.

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The width and the length that gives the largest possible areas are 75 meters by 37.5 meters

From the question, we have the following parameters that can be used in our computation:

Number of warehouses = 4

Perimeter of fence = 300 meters

Represent the width with x and the length with y

So, we have the following equations

Area = 4xy

Perimeter = 2(4x + y)

Substitute the known values in the above equation, so, we have the following representation

2(4x + y) = 300

Divide both sides by 2

2x + y = 150

Make y the subject

y = 150 - 2x

Substitute y = 150 - 2x in Area = 4xy

A = 4x(150 - 2x)

This gives

A = 600x - 8x²

Differentiate and set to 0

600 - 16x = 0

So, we have

16x = 600

Divide by 16

x = 37.5

Recall that

y = 150 - 2x

So, we have

y = 150 - 2 x 37.5

Evaluate

y = 75

Hence, the dimensions are 75 meters by 37.5 meters

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Answer:

-3/4

Step-by-step explanation:

y=mx+b is in slope-intercept form, in which m=-3/4 and b=7, describing the slope and y-intercept of a linear equation respectively.

To simplify this expression, you can first simplify the logarithms by using the properties of logarithms and the simplified expression is -0.00195

A logarithm is a mathematical function that is used to determine the power to which a number must be raised in order to produce a certain value. The logarithm of a number "b" to base "a" is represented as loga(b) or logb. The logarithm of b to base a is equal to the exponent to which we must raise a to get b.

[tex]1/2 Log10 25/4 - 2 log10 4/5 + log10 320/125[/tex]

To simplify this expression, you can first simplify the logarithms by using the properties of logarithms.

[tex]1/2 log10 25/4 - 2 log10 4/5 + log10 320/125[/tex]

=[tex]1/2( log10 25 - log10 4) - 2 (log10 4 - log10 5) + (log10 320 - log10 125)[/tex]

= 1/2(1.397940008672037 - 0.6020599913279624) - 2*(-0.6020599913279624 - 0.6989700043360187) + (2.505149978319906 - 2.0969100130080566)

= 0.397940008672037 - 1.204120018655925 - 1.397940008672037 + 0.40825006983185

= -0.2 - 0.2062 + 0.40825

= -0.00195

So the simplified expression is -0.00195

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Complete question is: simplify the given equation:  1/2 Log10 25/4 - 2 log10 4/5 + log10 320/125

A rational function is the algebraic expression y = 2 / x. (Correct choice: A)

Rational functions are algebraic expressions, whose form is described below:

R(x) = P(x) / Q(x)

Where:

Please notice that Q(x) must be a polynomial whose grade is greater than zero.

Polynomials are algebraic expressions of the form:

P(x) = ∑ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., n, ..., m}, where m is the grade of the polynomial.

Therefore, by direct inspection, we conclude that algebraic expression y = 2 / x is a rational expression.

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Answer:

45 cars

Step-by-step explanation:

115+365+(55*5) = 755

755 - 485 =270

270/6 = 45

Answer:

  ∠HAF ≈ 64.90°

Step-by-step explanation:

You want the angle HAF, a base angle in the isosceles triangle formed by the face diagonals of the cuboid with dimensions 6 cm, 6 cm, and 8 cm.

The lengths of the diagonals can be found using the Pythagorean theorem:

  HA² = HD² + DA²

  HA² = 6² +6² = 2·6²

  HA = 6√2 . . . cm

  FA² = FB² +BA²

  FA² = 6² +8² = 36 +64 = 100

  FA = 10 . . . cm

Diagonal FH is the diagonal of a rectangle with the same dimensions as the rectangle whose diagonal is FA:

  FH = FA = 10 . . . cm

The angle A can be found using the law of cosines:

  FH² = FA² +HA² -2·FA·HA·cos(A)

  A = arccos((FA² +HA² -FH²)/(2FA·HA))

  A = arccos((100 +72 -100)/(2·10·6√2)) = arccos(72/(120√2))

  A = arccos(0.3√2) ≈ 64.90°

Angle HAF is about 64.90°.

Answer:

  (a, b, c) = (-3, -2, -4)

Step-by-step explanation:

You want to solve the system of 3 equations in 3 variables shown in the attached figure.

The easiest solution is one provided by a suitable calculator (attached). It tells you ...

The "work" is entering the problem into the calculator.

We notice the sum of 'a' coefficients is zero, so we can add the three equations to get ...

  (4a +5b -6c) +(-3a -2b +7c) +(-a +4b +2c) = (2) +(-15) +(-13)

  7b +3c = -26 . . . . . simplify

Multiplying the third equation by 4 and adding that to the first equation gives ...

  4(-a +4b +2c) +(4a +5b -6c) = 4(-13) +(2)

  21b +2c = -50 . . . . . simplify

Now, we have two equations in two unknowns.

Multiplying the first equation above by 3 and subtracting this last equation eliminates the b term to give ...

  3(7b +3c) -(21b +2c) = 3(-26) -(-50)

  7c = -28 . . . . . simplify

  c = -4 . . . . . . . divide by 7

Using this in the first "ad hoc" equation, we can find b:

  7b +3(-4) = -26

  7b = -14 . . . . . . . . add 12

  b = -2 . . . . . . . . divide by 7

And the values of b and c can go into the last of the original equations to give ...

  -a +4(-2) +2(-4) = -13

  -a = 3 . . . . . add 16

  a = -3 . . . . . multiply by -1

The solution is (a, b, c) = (-3, -2, -4).

__

Additional comment

The given solution is "ad hoc" because we decide how we're going to approach the solution based on the coefficients we see. Here, we are solving by "elimination," performing as little arithmetic as possible.

The third equation suggests we could make a substitution for 'a':

  a = 4b +2c +13

That substitution would give a different set of equations in 'b' and 'c' than the ones shown above.

The second attachment shows a graphical solution to the system. It shows (a, b, c) = (-3, -2, -4). The graphing program requires the use of x and y instead of 'a' and 'b' for the variables.

Four methods of solving the system have been described. Take your pick. The calculator solution was the easiest, requiring each number to be entered once.

Answer:

m=10

Step-by-step explanation:

m/5+9=11 subtract 9

m/5 = 2 multiply 5 by both sides

m = 10

Answer:

13

Step-by-step explanation:

Cuz the factor of y is angle to the 115° is to the Y value

Answer:

Question is not clear

Step-by-step explanation:

Answer:

3.4 seconds

Step-by-step explanation:

Given function:

[tex]h(t)=-4.9t^2+2.45t+48.314[/tex]

where

The ball will strike the ground when its height is zero.

Therefore, to calculate when the ball strikes the ground, substitute h(t) = 0 and solve for t using the quadratic formula.

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]

Therefore:

Substitute these values into the quadratic formula:

[tex]\implies t=\dfrac{-2.45 \pm \sqrt{(2.45)^2-4(-4.9)(48.314)}}{2(-4.9)}[/tex]

[tex]\implies t=\dfrac{-2.45 \pm \sqrt{6.0025+946.9544}}{-9.8}[/tex]

[tex]\implies t=\dfrac{-2.45 \pm \sqrt{952.9569}}{-9.8}[/tex]

[tex]\implies t=\dfrac{-2.45 \pm 30.87}{-9.8}[/tex]

[tex]\implies t=\dfrac{-2.45 + 30.87}{-9.8}=-2.9[/tex]

[tex]\implies t=\dfrac{-2.45 -30.87}{-9.8}=3.4[/tex]

As time cannot be negative, t = 3.4 s only.

Therefore, the ball strikes the ground 3.4 seconds after it is launched.

Answer:

30

Step-by-step explanation:

x + 2x + 3x = 180 (the total angle of a triangle)
6x = 180
x = 180 : 6 = 30

Answer:

x = 30°

2x = 60°

3x = 90°

Step-by-step explanation:

Internal angles of a triangle sum 180°

Then:

x + 2x +3x = 180

6x = 180

x = 180/6

x = 30°

2x = 60°

3x = 90°

When one rectangular tile is 4 cm shorter and 2 cm broader than another rectangular tile, the difference in their perimeters is 2.

4 sides, 4 corners, and 4 right angles make up the 2D shape of a rectangle. A rectangle's diagonal sides are equal in length, with one pair being longer than the other. A rectangle would be referred to as a square if all of its sides were the same size.

given

Allowing for a rectangular card that is x cm long and y cm broad

The perimeter of another rectangular tile is 2 cm broader and 4 cm shorter.

L+B = L+B -2 = 2(L + B)

= 2(L-4 + B+2) = 2(L + B)

= L+B = L+B -2

Therefore, when one rectangular tile is 4 cm shorter and 2 cm broader than another rectangular tile, the difference in their perimeters is 2.

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Answer:

Step-by-step explanation:

-1 +2=1

2+2=4

5+1=6

Using the given function and the ordered pairs, we observed that Mr. Poppen pays more initially, to join the club

From the question, we are to determine who pays more initially to join the club between Mr. Poppen and Mrs. Zagorski  

From the given information,

"Mr. Poppen joins a fitness club which has a cost represented by the function y = 10x + 70"

The initial amount paid by Mr. Poppen is the value of y when x is 0

y = 10x + 70

y = 10(0) + 70

y = 0 + 70

y = 70

From the given ordered pairs

(0, 50)

(1, 60)

(2, 70)

(3, 80)

We can conclude that the initial amount paid by Mrs. Zagorski is 50

Hence, Mr. Poppen pays more initially

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Answer:

Corresponding Parts of Congruent Triangles are Congruent.

ASA

Step-by-step explanation:

We know that <YPC and angle <YPX are congruent angles.  They are both 90°.

Side YP is congruent to YP, so these sides are congruent in both triangles.

<XYP and <YPZ are congruent, because the perpendicular bisector cuts <XYZ in two equal parts.

ASA (Angle, Side, Angle)

Answer:

17.5 miles

Step-by-step explanation:

right!!

Answer:

D

Step-by-step explanation:

8x+12y-2y+3x=11x+10y

Answer:

answer D

Step-by-step explanation:

8x+12y-2y+3x

11x+ 10y

A system of equations to model this scenario is given as follows -

x + y = 320

7x + 10y = 2900

        {m} - slope                 {c} - intercept along the y - axis.

Given is that on one day at a local minigolf course, there were 320 customers who paid a total of $2,900. The cost for a child is $7 per game and the cost for an adult is $10 per game.

Let {x} represents the number of children and {y} represents the number of adults who played that day. We can write the given system of equations as -

x + y = 320

7x + 10y = 2900

Therefore, a system of equations to model this scenario is

x + y = 320

7x + 10y = 2900

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Answer:

2 1/3

Step-by-step explanation:

Seperate equation

(3 1/2) - 1

( 3 - 1 ) + 1/2

2 and 1/3

Answer:

  57

Step-by-step explanation:

You want a positive number that gives a product of 1995 when it is multiplied by each of its digits.

The prime factors of 1995 are 3, 5, 7, 19. The product of 3 and 19 gives 57, so multiplying 57 by 5 and 7 will result in the product 1995.

The original number is 57.

<95141404393>

Precipitation (inches), 2.08, 1.98, 2.64, 3.29; Snowfall (inches), 17.6, 14.2, 11.7, 3.4; The Ithaca Climate Page.

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Answer: 109 it says 109 in the corner of b and d

Using an inverse trigonometric function, we will find that the solution is:

θ = 1.047

Here we want to solve the equation:

1 - cos(θ) = 1/2

Such that θ ∈  [0,2pi)

Now let's return to our equation:

1 - cos(θ) = 1/2

1 - 1/2 = cos(θ)

1/2 = cos(θ)

Now we could apply the inverse cosine function to both sides, then we will get:

Acos(1/2) = Acos(cos(θ))

1.047 = θ

That is the solution.

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Answer:

  y = 2x -3

Step-by-step explanation:

You want the equation of the line through the points (-1, -5) and (2, 1).

The slope of the line is given by ...

  m = (y2 -y1)/(x2 -x1)

  m = (1 -(-5))/(2 -(-1)) = 6/3 = 2

The y-intercept of the line can be found from ...

  b = y -mx

  y = -5 -2(-1) = -3

The slope-intercept form of the equation of a line is ...

  y = mx +b . . . . . . . line with slope m and y-intercept b

Using our found values, the equation is ...

  y = 2x -3 . . . . . . . . line with slope 2 and y-intercept -3