Trey is choosing between two exercise routines. In routine #1, he does only running, burning 8.5 calories per minute. In routine #2, he burns 17 calories walking. He then runs at a rate that burns 4.25 calories per minute. For what amounts of time spent running will routine #1 burn more calories then routine #2? Use t for the number of minutes spent running, and solve your inequality for t.

Alex's set of ordered pairs would no longer define a function if any of the following actions were taken:

A set of ordered pairs defines a function if, for every element in the domain (the set of first coordinates), there is exactly one element in the range (the set of second coordinates).

For example, if Alex's set of ordered pairs is {(1,2), (2,3), (3,4)}, it would no longer define a function if a new ordered pair of (2,5) is added to it, as it would mean that there are now two different second coordinates (3,5) for the first coordinate 2. This would violate the rule that every element in the domain must have exactly one corresponding element in the range. Similarly, removing one of the ordered pairs, changing the order of the ordered pair, or changing the domain or range would cause the set to no longer to define a function.

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Answer:

Step-by-step explanation:

First, let us substitute x and y values: -7 = -2(-5) + 4

Next, let us simplify using the substitution property of equality: 14 = -7 (SEE BELOW MORE INFO).

Now, this does not make sense yet because 14 cannot possibly equal -7. Therefore, we must add a b value, therefore leading us to the equation:

14 + b = -7

by simplifying, we can conclude that b = -21

Finally, we can plug in the b-value into our original equation:

y = -2x + 4 - 21

After simplifying, we get y = -2x - 17. When this is graphed, we can see that -2x - 17 intersects (-5, -7).

Answer:

Step-by-step explanation:

The formula for the volume of a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

We know that V = 5,890.625 cm^3, h = 14.5 cm, and l = 25 cm.

Substituting these values into the formula, we get:

5,890.625 = 25w(14.5)

5,890.625 = 362.5w

w = 16.25

Therefore, the width of the rectangular prism is 16.25 cm.

Answer:

It's A

Step-by-step explanation:
well all you have to do is divide like 5,890.625 dvided by 14.5 then divide again by 25 them bam you got 16.25

Answer:

1/9 cup left

Step-by-step explanation:

7/9 - 2/3

Change to a common denominator.

7/9 - 6/9 = 1/9

I hope this helps and please mark me as brainliest!

Answer:

B. $3.56

Step-by-step explanation:

You take $28.48 and divide it by 8

28.48 / 8 = 3.56

/ = divide

Answer:

(−5t−1)(3t−4)

Step-by-step explanation:

Factor −15t2+17t+4

−15t2+17t+4

=(−5t−1)(3t−4)

The factored form of the polynomial is (-3t+ 4) (5t + 1).

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

-15t² + 17t + 4

-15t² + (-3 + 20)t + 4

-15t² - 3t + 20t + 4

-3t(5t + 1) + 4(5t + 1)

(-3t+ 4) (5t + 1)

Thus,

The factored form is (-3t+ 4) (5t + 1)

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Answer:they are both at the same height

Step-by-step explanation: its the same exact number except one is negative and one is positive so if they are the same numbers you should be able to add it and get the number zero.

When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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Answer:

214 cubic feet (rounded to the nearest cubic foot)

Step-by-step explanation:

Step 1  Determine the volume of 1 box

Volume of a box or rectangular prism = dimensions multiplied by each other

Here, the given dimensions are 11 in by 8 in by 12 in

So the volume of one box would be 11 x 8 x 12 = 1056 cubic inches

Step 2 Determine volume of all 350 boxes

Volume of 1 box = 1056

So volume of all 350 boxes = 1056 x 350 = 369600 cubic in

Step 3 Convert cubic in to cubic ft

To convert to cubic feet we divide the amount of cubic inches by 1728 (this is because there are 1728 cubic inches in 1 cubic foot)

369600 / 1728 = 214 cubic feet (to the nearest cubic foot)

214 cubic feet of warehouse space is required for 350 boxes with the dimensions of 11in by 8in by 12in

Answer:

Below

Step-by-step explanation:

1. Linear because it is of the form y = mx + b. The variable x  is of the first degree.

The coefficient of x (1/3)  ( = slope) is positive so it is increasing.

2. This is non-linear because the variable x is an exponent.

3. Because  its of the second degree (x^2) - it is non-linear.

The square root of 76.8 is 8.76.

Square root of 76.8 is 8.746.

Given,

\(\sqrt{76.8}\)

Now,

Simplifying the square root :

If square root of x is to be calculated then,

\(\sqrt{x}\) = \(x^{1/2}\)

Similarly,

\(\sqrt{76.8}\) = \(76.8^{1/2}\)

= 8.746

Thus the square root of 76.8 is 8.746.

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Answer:

To calculate the book value of the building, we need to calculate the annual depreciation amount and multiply it by the number of years elapsed since the building was completed.

The annual depreciation amount is calculated as: $1 million / 50 years = $20,000

In 2014, the book value of the building was: $1 million - ($20,000 * (2014 - 2010)) = $1 million - ($20,000 * 4) = $960,000

In 2022, the book value of the building will be: $1 million - ($20,000 * (2022 - 2010)) = $1 million - ($20,000 * 12) = $680,000

Triangles ΔICR and ΔISU are congruent by SAS rule of congruency, therefore; ∠CIR ≅ ∠SIU by CPCTC

Two triangles, ΔABC and ΔXYZ are said to be congruent by the Side-Angle-Side, SAS congruency rule, if the two sides and an included angle of triangle ΔABC, are congruent to two sides and an included angle of triangle ΔXYZ.

The specified measurements are;

∠1 ≅ ∠4

CU = RS

IC = IS

IC ≅ IS (Definition of congruency)

The congruency of the sides IC and IS indicates that the triangle ΔICS is an isosceles triangle

Therefore, ∠2 ≅ ∠3 by the properties of the base angles of an isosceles triangle

CU - RU = RS - RU (subtraction property)

RU ≅ RU, (reflexive property of congruency)

CU - RU = CR

RS - RU = SU

CR = SU (Substitution property)

CR ≅ SU (Definition of congruency)

ΔICR is congruent to ΔISU by Side-Angle-Side, SAS, rule of congruency.

∠CIR ≅ ∠SIU by Corresponding Parts of Congruent Triangles are Congruent, CPCTC

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Answer:

x - y = 4

Step-by-step explanation:

Hope this helped! :)

Answer:

Step-by-step explanation:

This problem is on the mensuration of solid shapes, an oblique cylinder.

the expression for the volume of an oblique cylinder is given as

\(volume= \pi r^2h\)

Given data

radius r= 5

height h= 12, and

slant length of 13.

Substituting the given data into the expression we can solve for the volume below

\(volume= \pi* 5^2*12\\\ volume= \pi*25*12\\\ volume= \pi*300\\\ volume= 300\pi\)

Answer:

300

Step-by-step explanation:

All you have to do is solve this by using substitution or elimination. or in this case, because we don’t have a second equation, we would solve the x-intercept and y-intercept

X=-12

Y=-9

The value of x in the rectangle is 6

The given parameters are

Perimeter = 62

From the figure, we have

Length = 2x

Width = x + 13

The perimeter is calculated as:

P =2 * (L + W)

This gives

2 * (2x + x + 13) = 62

So, we have

2 * (3x + 13) = 62

Divide by 2

3x + 13 = 31

Subtract by 13

3x = 18

Divide by 3

x = 6

Hence, the value of x in the rectangle is 6

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Least time required to reach the point Q as per the distance and the speed rate is equal to 2 hours.

As given in the question,

Nearest point on the coast is 2 miles far away

rate of the row = 1mile per hour

Walk at the rate of 3 miles per hour

Let 'x' hours be the least time to reach point Q.

Time = distance / speed

Time taken to reach the point Q = [√ 1 + ( 3 - x)² ]/ 3

Time taken to reach the coast = (√ 4 + x² ) / 1

Total  time taken 't' = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

To find least time dt/dx = 0

t  = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

⇒dt/dx = [ x / √ 4 + x² ] + ( 3 - x) / √( 10 -6x + x² )

⇒x / √ 4 + x² = ( x - 3) / √( 10 -6x + x² )

Squaring both the side we get,

x² / (4 + x²) = ( x - 3)² / ( 10 -6x + x² )

⇒3x² -24x +36 =0

⇒ x² -8x + 12 = 0

⇒ x = 2 or 6 hours

Therefore , the least time taken to reach the point Q is equal to 2 hours.

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Answer:

The answer is A.

Step-by-step explanation:

You have to multiply by converting the second fraction into upside down :

\( \frac{4x + 1}{6x} \div \frac{x}{3x - 1} \)

\( = \frac{4x + 1}{6x} \times \frac{3x - 1}{x} \)

\( = \frac{(4x + 1)(3x - 1)}{x(6x)} \)

\( = \frac{12 {x}^{2} - 4x + 3x - 1}{6 {x}^{2} } \)

\( = \frac{12 {x}^{2} - x - 1 }{6 {x}^{2} } \)

The required answer is the domain is time (t) and the range is a distance (d) i.e. Option 2.

What are domain and range?

The value range that can be plugged into a function is known as its domain. In a function like f, this set represents the x values f(x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

From the given question, and the above definition of domain and range,

the time (t) acts as an x-values or input value and the distance (d) acts as a y-value or output value

Hence, the domain is time (t) and the range is a distance (d) i.e. Option 2.

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Gross Domestic Product (GDP) is a monetary measure of the value of all final goods and services produced within a region over a specific time frame, typically annually.

To compute the number of times larger Canada's GDP was than that of Palau in 2017, we must first convert both figures into the same currency.

Using the 2017 average exchange rate, we will convert the GDP of both nations from Canadian dollars and Palauan dollars to US dollars, which is the world's primary currency.  

Then we can compare these two figures. Let us assume that $1 CAD = 0.770838 USD and $1 PWD = 0.1200 USD:GDP of Canada in US dollars in 2017 = $1.653 trillion CAD x 0.770838 USD/CAD = $1.274 trillion USDGDP of Palau in US dollars in 2017 = $291.5 million PWD x 0.1200 USD/PWD = $34.98 million USDTo get the ratio between the two values, we will divide the GDP of Canada by the GDP of Palau:$1.274 trillion USD / $34.98 million USD = 36.4 (rounded to one decimal place)

Therefore, the gross domestic product of Canada in 2017 was 36.4 times higher than the gross domestic product of Palau in the same year.

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The graph of the trigonometry function g(x) = 4 cos πx is plotted and attached,

The graph is made by picking some x values say 0, 0.5, 1, 1.5, 2 .... and solve for the output y.

For x = 0, y = 4 cos π * 0 = 4

For x = 0.5, y = 4 cos π * 0.5 = 0

For x = 1, y = 4 cos π * 1 = -4

For x = 1.5, y = 4 cos π * 1.5 = 0

For x = 2, y = 4 cos π * 2 = 4

Table of value

x     y

0     4

0.5  0

1      -4

1.5    0

2      4

The graph is plotted by tracing each x and y value and joining the intercepts to form a curve

It can be deduced that the amplitude of the graph is 4 and it completes a revolution in 2 units

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Answer:

It would take 40 times to match the amount of money

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Answer:

-5 is the answer

Hope it will be helpfull....

The function is continuous in the domain x ≥ 3/4

Here we have a root function:

f(x) = ⁴√(4x - 3)

This is an even degree root function, so we have problems when the argument is negative.

Then the allowed values (where the function is defined, and thus, continuous) are:

4x - 3 ≥ 0

4x ≥ 3

x ≥ 3/4

There the function is continuous.

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