Compare the function f(x)=3x-1/2 to the function shown in the graph. Which statements are correct?

Answer: $605.25

Step-by-step explanation:

100% - 25% = 75%

807 times 0.75 = $605.25

The sale price is $ 605.25

Answer:

  A:) T(t) = 305(230/305)^(t/10) +70

  B:) T(20) ≈ 243.4 °F

Step-by-step explanation:

You have a pie removed from a 375° oven to a room temperature of 70° that has cooled to 300° after 10 minutes. You want to know its temperature after 20 minutes.

Newton's law of cooling tells you the rate of change of an object's temperature is proportional to the difference between the object's temperature and that of its surroundings. The differential equation describing this has an exponential function as its solution. That exponential function can be written as ...

  temperature = (initial temperature difference)·(cooling factor)^(time/(cooling time)) + (final temperature)

Here, the initial temperature difference between the pie and room temperature is ...

  initial temperature difference = 375° -70° = 305°

The final temperature is the room temperature:

  final temperature = 70°

The cooling factor is the multiplier applied to the temperature difference in the time period "cooling time". Here, the pie is at 300°, a temperature difference of 300° -70° = 230° after a cooling time of 10 minutes. The cooling factor is ...

  cooling factor = 230/305

These values let us write the equation as ...

  T(t) = 305(230/305)^(t/10) +70

The temperature after 20 minutes is found using this equation:

  T(20) = 305(230/305)^(20/10) +70 = 305(46/61)^2 +70 = 243 27/61

  T(20) ≈ 243.4 . . . . degrees F

__

Additional comment

The cooling factor can be expressed as a value that lets the exponent be t. Often, it is written as (e^k), where ...

  k = 1/10·ln(230/305) ≈ -0.0282232

Then the equation is ...

  T(t) = 305·e^(-0.0282232t) +70

It could also be written as ...

  T(t) = 305(0.972171^t) +70

where 0.972171 = (46/61)^(1/10).

The correct option is a) online by $0.04.

The better deal is online, by $0.04 will save per diaper.

How do I solve for x in a equation?

Apply arithmetic operations to both sides of the equation to bring the variable to one side and all other values to the other side in order to find the value of x. To determine the outcome, simplify the values.

Cost of 56 diapers at Babies-R-Us = $28

Cost of 1 diaper at Babies-R-Us = [tex]\frac{28}{56}[/tex]

                                                    =  0.5

Cost of 112 diapers online = $52

Cost of 1 diaper online = [tex]\frac{52}{112}[/tex]

                                      = 0.46

So, the cost of diapers online is cheaper than that at Babies-R-Us.

Difference between 1 diaper in both case = $0.5- $0.46= $0.04

Online deal is better than and you will save by $0.04 per diaper.

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Answer:

Step-by-step explanation:

it is an isosceles right triangle, we divide it in two parts and we have two  right triangles, with the Pythagorean theorem we find the hypotenuse and add it to the other side to get the perimeter (SEE FIGURE)

BC and AC = √(8²+6²)

BC and AC = √(64+36)

BC and AC = √100

BC and AC = 10 units

now we add the sides and find the perimeter

16 + 10 + 10 =

36 units

AC:PC.= 3/5, as  Line l ∥ AB and passes through point M to intersect diagonal AC and leg BC at points P and N.

A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides.

The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.

A trapezoid is a closed, four-sided, two-dimensional figure that has both a perimeter and an area.

The bases of the trapezoid are the two sides of the shape that are parallel to one another. The legs or lateral sides of a trapezoid are the non-parallel sides. The altitude is the shortest distance between two parallel sides.

According to our question-

Consider about the triangles ACB and PCN.

These triangles contain

Since angle C is the common angle and the transversal BC cuts two parallel lines PN and AB, angles ABC and PCN are congruent as equivalent angles by virtue of the reflexive property.

In light of the AA Similarity Theorem, triangles ACB and PCN are comparable.

Similar triangles have matching sides that are proportionate, thus

3/8 / 5/8= 3/5

Hence, Due to the fact that Line l AB and goes via point M to intersect Leg BC and the diagonal AC at points P and N, AC:PC.= 3/5.

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Using the scale factor, the length of the new figures are as 21 inches, 21 inches and 36 inches.

Bill drew a scale drawing of the figure using a scale factor of 3.

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.

The length of the drawing are 7 inches , 7 inches and 12 inches . The length of the new figure can be found as follows.

using the scale factor

length 1 = 7 × 3  = 21 inches

length 2 = 7 × 3  = 21 inches

length 3 =  12 × 3  = 36 inches

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Answer:

q=82

Step-by-step explanation:

The line is equal to 180 degrees, and we have three angles and two have numbers, so this will be easy.

Add 58+40 to get 98, now subtract 98 from 180.

180-98=82

A sector is a part of a circle that is bounded by an arc and two radii. Thus the area of the lawn is Option D. 589.

A circle is a figure that is bounded by curved lines called circumference. Some parts of a circle are radius, sector, diameter, chord, circumference, arc etc.

A sector can be defined as a part of a circle which is bounded by two radii and an arc.

The area of a sector can be determined by;

Area of a sector = (θ/360) *r²

where: θ is the measure of the internal angle of the sector        

   r is the radius of the sector

In the given question, it can be observed that the area of the lawn that receives water from the sprinkler has the shape of a sector.

So that:

Area of the lawn = (300/360)*22/7 * 15²

                   = 589.2857

Area of the lawn = 589²

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To turn $900 into $900 over the course of two and a half years at the rate of 3.5%, we can use the following formula:

Copy code

investment = (900 * (1 + 0.035)) ^ (2.5 / 1)

In this formula, investment represents the amount of money you need to invest, 900 represents the final amount you want to end up with, 0.035 represents the interest rate of 3.5%, 2.5 represents the number of years you want to invest for, and 1 represents the number of times per year that the interest is compounded.

Plugging in the values from the problem into the formula, we get:

Copy code

investment = (900 * (1 + 0.035)) ^ (2.5 / 1)

investment = ($900 * 1.035) ^ (2.5 / 1)

investment = $931.75 ^ 2.5

investment = $1434.24

Therefore, to turn $900 into $900 over the course of two and a half years at the rate of 3.5%, you will need to invest $1434.24.

Answer:

NO

Step-by-step explanation:

You need x on one side of the equation.

3+4x ≤ 2(1+2x)

3+4x ≤ 2+4x

  -4x       -4x

3 ≤ 2

Since there is no x value there is no solution

The new coordinate of point (5,-4) after dilation by a scale factor of 33 centered at the origin is (165,-132)(165,132)

You must specify the extent of the shape's enlargement when describing one.

The scale factor is the ratio of two dimensions such that one figure is large and another is small.

Given the coordinate (5,-4),(5,-4)

If we apply a scale factor by 33 on any general coordinate (x,y)

Then,

x → 33x and y → 33y

Similarly

5 → 33(5) = 165

-4 → 33(-4) = -132

So the new coordinate will be (165,-132)(165,-132)

Same step apply once more for (5,-4) the coordinate of other is same

Hence "The new coordinate of point (5,-4)(5,-4) after dilation by a scale factor of 33 centered at the origin is (165,-132),(165,-132)

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The graph of the absolute function g(x) = -|x + 3| - 4 has vertex at (-3, -4) and touches the y -intercept at (0, -7)

The graph of an absolute value function is called an absolute value graph. The absolute value graph depicts the distance of a number from the origin. The graph of the absolute value function is symmetric about the y -axis. The graph of the absolute value function makes a right angle at the origin.

In this problem the function given is

g(x) = -|x + 3| - 4

To graph this function, we can use a graphing calculator which will enable us to plot all points accurately.

The graph touches the y -axis at (0, -7)

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Therefore , the height of the given square pyramid is 12 cm.

The area occupied within an object's three-dimensional bounds is referred to as its volume. The object's capacity is another name for it.

Here,

To calculate a square pyramid's volume in terms of h, use the formula h = [tex]\frac{3V}{s^{2} }[/tex]

With V = 400 and s = 10 cm, a square pyramid's height is 12 cm.

The equation for calculating the volume of a square pyramid is:

=> 1/3 [tex]s^{2}[/tex]h =V

=> h = [tex]\frac{3V}{s^{2} }[/tex]

Therefore we can rewrite the formula in terms of h you need to:

=> h = [tex]\frac{3V}{s^{2} }[/tex]

You must substitute these numbers into the following formula to determine the height of a square pyramid with volume V = 400 and side lengths s = 10 cm:

=> h = 3 * 400 / [tex]10^{2}[/tex]

=> 3* 400/100

=> 3*4

=> 12

Therefore , the height of the given square pyramid  is 12 cm.

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Answer:sd

Step-by-step explanation:

By using the property of isosceles triangle, it can be proved that-

∆CDL is an isosceles triangle

What is isosceles triangle?

At first, it is important to know about triangle.

A triangle is a two dimensional three sided figure. A triangle has three sides and three interior angles.

A triangle whose any two sides are equal are called isosceles triangle.

JK || AB [Given]

[tex]\angle 1 \cong \angle 3[/tex] and [tex]\angle 2 \cong \angle 4[/tex] [Corrosponding angle]

[tex]\angle 1 \cong \angle 2[/tex] [Given]

[tex]\angle 3 \cong \angle 4[/tex] [Transitive property of congruence]

CL [tex]\cong[/tex] DL [Converse of isosceles triangle theorem]

∆CDL is an isosceles triangle [Def. of isosceles triangle]

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The required simplified value of the given expression is 120.

Given that the expression as;

(50 + 30) + 40.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here, we have;

= (50 + 30) + 40

Now, using associative property, in parenthesis 50 + 30 become 80.

= 80 + 40

Then using associative property, 80 + 40 become 120

= 120

Thus, the simplified value is 120.

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The region with the most rainfall is Beaumont, and the region with the least is El Paso.

How can I find the locations with the most and least rainfall?

Making sure to utilize the same units is the first step. Let's convert everything to meters as a result.

Austin equals 0.8687 m

Beaumont = 1.534 meters.

Galveston = 1,095 meters

El Paso equals 0.246 m

Del Rio equals 0.4953 m

South Padre=0.655 meters

Based on this, El Paso has the least amount of rainfall, while Beaumont has the most.

How are the two locations connected?

These locations have a ratio of 1.5 to 0.2, or 1.5/ 2 = 0.7. According to this ratio, the amount of rainfall in these locations varies by 0.7 meters.

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1.4  is the value of r in the equation given.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. For solving equations The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.

In the given equation,

10r -1.5 = 12.5

Simplifying using PEMDAS

add 1.5 on both sides

10r = 14

divide by 10 into both sides

r = 14/10 = 1.4

Therefore, The value of r in the given equation is 1.4.

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Answer:

x < 3 or x ≥ 11

Step-by-step explanation:

(-∞, 3) or [11, ∞)

Step-by-step explanation:

subtract 4 from each side

2x < 6 .     or .         3x  ≥ 33

x < 3 or x ≥ 11

make sure you have an OPEN DOT at 3 pointing to negative infinity and a CLOSED DOT at 11 pointing to positive infinity.  

The required Polynomial equation is − 5x²+ 19x + 4.  

Factorization is the process of determining the factors of a given value or algebraic statement. The numbers or the algebraic expressions that are multiplied to create the original number or original expressions are known as factors.

If p(x) is polynomial, with factors (x + a) and (x - a) then p(x) will equal to product of (x + a) and (x - a) => p(x) = (x + a)(x - a)

Here we have

The factorization of a polynomial is −1(x − 4)(5x+1)

To find the Polynomial we need to multiply given factors as given below

=> −1(x − 4)(5x+1)

=> −1 [ (x − 4)(5x+1)]  

=> −1 [ 5x²−20x + x −4 ]     [ add like terms ]

=>  − 5x²+ 19x + 4       [ Multiply with  − 1 ]

Therefore,

The required Polynomial equation is − 5x²+ 19x + 4.    

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The mse will be 16 in the given case as mse is the square of standard error.

What is regression analysis ?

Regression analysis is a group of statistical procedures used in statistical modelling to determine the relationships between a dependent variable (often referred to as the "outcome" or "response" variable, or a "label" in machine learning jargon), and one or more independent variables (often referred to as "predictors," "covariates," "explanatory variables," or "features").

Given, the standard error = 4

We know that standard error is the square root of mse ( mean squared error ).

So, mse = (standard error)^2

              = 4^2

              = 16.

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Therefore, percentage of those who opened the email ,  clicked a link is  28.57%

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Here,

Let the amount of people  receiving your email is x

The amount of people receiving your email opened it is 7%

7/100 * x = 0.07x

The amount of people receiving your email clicked a link is 2%

So,

2/100 * x = 0.02x

Therefore,

percent of those who opened the email ,  clicked a link is

=> 0.02x/0.07x * 100

=> 2/7*100 = 28.57%

Therefore, percentage of those who opened the email ,  clicked a link is  28.57%

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To rotate a triangle 180° about the origin counterclockwise, we can take each vertex of the triangle and reflect it across the origin. This will produce a new set of coordinates for each vertex that is the same distance from the origin as the original, but on the opposite side of the origin.

For example, the vertex F has coordinates (6, 3). If we reflect this point across the origin, we get the new point (-6, -3). Similarly, the vertex G has coordinates (3, 4), which become (-3, -4) when reflected across the origin, and the vertex H has coordinates (1, 7), which become (-1, -7) when reflected across the origin.

Therefore, the coordinates of each vertex of the triangle after rotating it 180° about the origin counterclockwise are as follows:

Note: When rotating a point about the origin, the direction of rotation (clockwise or counterclockwise) is important. If we had rotated the triangle 180° about the origin clockwise instead of counterclockwise, the new coordinates of each vertex would have been the same as the original, since the triangle would be reflected across the origin and end up in the same position as it started.

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The required area of the polygons is given as 100 ft², 9 ft², 16 ft², and 64 ft².

Given that,
The dimensions of this polygon are shown in feet (ft). 10ft/3ft/4 ft/8 ft. The area, in square feet, of the polygon is to be determined.

A polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,

Examples of polygons, equilateral triangles, squares, pentagons etc

Here,
Assumed that all the polygons are square,
The area of the square is given as (side)².
1,
Side = 10 ft
Area of the square = [10 ft]² = 100 ft²

Similarly,
For side 3 areas is 9 ft²,

For side 4 areas is 16 ft²,

For side 8 areas is 64 ft²,

Thus, the required area of the polygons is given as 100 ft², 9 ft², 16 ft², and 64 ft².

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Answer:

Based on my estimates, Thy answer shall be the letter known as C

Answer:

5 y (2 y^4 + 6 y^2 - 3)

Step-by-step explanation:

The given input is 10y^5+30y^3-15y

10y^5+30y^3-15y has factors i.e 5 y (2 y^4 + 6 y^2 - 3)

By verifying each polynomial factor we get the GCF i.e common factor of the polynomial is 5 y (2 y^4 + 6 y^2 - 3) and simplified as 10 y^5 + 30 y^3 - 15 y

The value of [tex]\sqrt{x}(\pi-\sqrt{x} \cdot 17) x^2[/tex] is [tex]\pi x^2 \sqrt{x}-17 x^3[/tex]

[tex]$$\begin{aligned}& \sqrt{x}(\pi-\sqrt{x} \cdot 17) x^2 \\& =x^2 \sqrt{x}(\pi-17 \sqrt{x})\end{aligned}$$[/tex]

Apply the distributive law: [tex]$\quad a(b-c)=a b-a c$[/tex]

[tex]$$\begin{aligned}& a=\sqrt{x} x^2, b=\pi, c=\sqrt{x} \cdot 17 \\& =\sqrt{x} x^2 \pi-\sqrt{x} x^2 \sqrt{x} \cdot 17 \\& =\pi x^2 \sqrt{x}-17 x^2 \sqrt{x} \sqrt{x} \\& 17 x^2 \sqrt{x} \sqrt{x}=17 x^3 \\& =\pi x^2 \sqrt{x}-17 x^3\end{aligned}$$[/tex]

What is distributive law?

The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true. For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication.

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Yes subtracting a number is the same as adding its inverse. We have to find the additive inverse of a function.

The additive inverse of a number is the number which when we add to the number results zero.

Complex numbers are made up of both real and fictitious numbers. A + iB, where A is the real number and B is the imaginary number, is a complex number.

The additive inverse of A + iB should now be a value that, when added to a given complex number, produces the result zero. It will therefore be -(A + iB).

Suppose we have to find additive inverse of 5.

Let the additive inverse of 5 be x.

So,5+x=0

x=-5

So the additive inverse of 5 is -5.

Hence to find additive inverse of a positive number we have to just put a negative mark and for a negative number we have put positive mark in front of the number.

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