Mrs. Perky bought 2 3/4 gallons of blue paint. Each gallon of blue paint cost $19.50. Mrs. Perky also bought 1 1/3 gallons of orange paint. Each gallon of orange paint cost $16

To find the domain of the expression 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)), we need to consider the values of x for which the expression is defined.

First, we need to consider the square root term, sqrt(5x^2-8x). The square root of a number is only defined for nonnegative values, so we need to find the values of x for which 5x^2-8x is nonnegative. We can do this by setting 5x^2-8x equal to 0 and solving for x:

5x^2-8x=0

5x(x-8)=0

We can see that x=0 and x=8 are the solutions to this equation. Since the square root of a negative number is not defined, the expression 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)) is only defined for x values that are greater than or equal to 0 and less than or equal to 8. This means that the domain of the expression is x ∈ [0, 8].

To solve the equation 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)), we can start by isolating one of the exponential terms on one side of the equation. Let's isolate the term 2^(sqrt(5x^2-8x)):

24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x))

22^(2sqrt(5x^2-8x)+1)=332^(sqrt(5x^2-8x))

2^(2sqrt(5x^2-8x)+1)=16.52^(sqrt(5x^2-8x))

2sqrt(5x^2-8x)+1=4.5+sqrt(5x^2-8x)

sqrt(5x^2-8x)=3.5

5x^2-8x=12.25

5x^2-8x-12.25=0

We can use the quadratic formula to solve this equation for x:

x = (-(-8) ± sqrt((-8)^2 - 45(-12.25))) / (2*5)

x = (8 ± sqrt(64 + 97)) / 10

x = (8 ± sqrt(161)) / 10

x = (8 ± sqrt(289)) / 10

x = (8 ± 17) / 10

x = -9/10 or 25/10

Since x must be greater than or equal to 0 and less than or equal to 8, the only solution that is within the domain of the expression is x=25/10, or x=2.5.

Therefore, the solution to the equation 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)) is x=2.5.

what do you mean by domain of a function?

The domain of a function is the set of all input values for which the function is defined. In other words, it is the set of all values that can be plugged into the function as an argument, or input, and produce a valid output

For example, consider the function f(x) = x^2. The domain of this function is all real numbers, since the function is defined for any value of x. However, some functions may not be defined for certain values of x. For example, the function g(x) = 1/x is not defined for x=0 because division by zero is not allowed. In this case, the domain of the function g(x) would be all real numbers except for x=0.

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Answer: [tex]y=-\frac{4}{3}x+2[/tex]

Step-by-step explanation:

The slope of [tex]AB[/tex] is [tex]-4/3[/tex]. Thus, the slope of [tex]CD[/tex] is also [tex]-4/3[/tex].

Thus, the equation of [tex]CD[/tex] can be found as follows:

[tex]y-10=-\frac{4}{3}(x+6)\\\\y-10=-\frac{4}{3}x-8\\\\y=-\frac{4}{3}x+2[/tex]

Answer:

third option

Step-by-step explanation:

sinX = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{YZ}{XY}[/tex] = [tex]\frac{3}{\sqrt{34} }[/tex]

tanY = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{XZ}{YZ}[/tex] = [tex]\frac{5}{3}[/tex]

Answer:

A circle is formed.

Step-by-step explanation:

When a plane, parallel to the base of a cone, slices a cone, a circle is formed

and for proof:

When the truck cost 60,000 it depreciate in value 4000 per year, the model is 60000 - 4000x

Equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario

In this case, the truck cost 60,000 it depreciate in value 4000 per year.

Let the number of years be x.

The linear model in the representation will be:

60000 - 4000(x)

= 60000 - 4000x

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Answer:

asa

Step-by-step explanation:

there Is angle

there is side

there is angle but not shown

The point estimate proportion that they would seriously consider purchasing an electric-powered vehicle is 0.468.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

let y be 2326 said that they would seriously consider purchasing an electric-powered vehicle and x be the sample of 4972 car owners.

∴ The point estimate proportions is y = px.

2326 = 4972p.

p = 2326/4972.

p = 0.468.

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Answer: 28055

Step-by-step explanation:

You will able to deposit  X=7000.182500⁴⁷⁴⁵/182537⁴⁷⁴⁵now under the scenario Below.

A minimum deposit or initial  deposit is the lowest minimum  amount of the  money required to open an object account with all the  financial institution, such as the bank or the brokerage firm.

Based on the given scenario the formulate is-

X×(1+7.4%÷ 365)¹³×365 = 70000

Now we have to solve the equation -

X×(1+0.074/365)¹³×365=70000

Convert the number

X× 1+ (74/365000)¹³×365=70000

Now reduce

X×(1+37/182500)¹³×365=70000

Now we have to calculate=

X× (1+ 37/182500)⁴⁷⁴⁵=70000

We have to transfer the edition

X× (1+ 37/182500)⁴⁷⁴⁵=70000

Devide both side

X= 70000/ ( 182537/182500)⁴⁷⁴⁵

By Calculation we can get

X= 70000×182500^4745/182537⁴⁷⁴⁵

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The global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint is correct. Statement C.

The critical value is the value of x for which the double derivative of the function f(x) becomes zero.

When double derivative becomes zero, the graph of the function is neither increasing nor decreasing and hence, the the function attains either

a maxima or a minima.

Hence, he global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint.

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Answer:

50

Step-by-step

One of the interior angles of the triangle, angle y is equal to 67° and the exterior angle x is equal to 113°.

The interior angles of a triangle have a total sum of 180°.

Considering the triangle with interior angles: y, 51°, and 62° we have that;

y + 51° + 62° = 180°

y + 113° = 180°

y + 113° - 113° = 180° - 113° {subtract 113° from both sides}

y = 67°

the exterior angle x and the angle y lie on a straight line, so they sum up to 180°.

x + 67° = 180°

x + 67° - 67° = 180° - 67° {subtract 67° from both sides}

x = 113°

Therefore, the interior angle y = 67° and the exterior angle x = 113°.

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In linear equation ,The correct order from least time to greatest time is: Andy, Beth, Cindy.

Describe a linear equation using an example.

An equation with only one variable is referred to as a linear equation in one variable.

                   It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.

Consider the provided information,

Andy walked [tex]2\frac{3}{4}[/tex]  mi at a constant speed of [tex]2\frac{1}{2}[/tex] mi/h.

As we know

       Time = distance/speed

           = [tex]\frac{2\frac{3}{4} }{2\frac{1}{2} }[/tex]

            =  [tex]\frac{11/4}{5/2}[/tex]

           = 11/40

Therefore, Andy takes 1.1 hours.

Beth walked 1 1/2 mi at a constant speed of 1 1/8 mi/h .

  time = [tex]\frac{1 1/2}{ 1 1/8}[/tex]

           = 3/2/ 9/8

           = 4/3

Therefore, Beth takes 1.33 hours.

Cindy walked for 1 h and 24 min at a constant speed of 1[tex]\frac{1}{4}[/tex] mi/h.

   1  hour 24 min   =  1 + 24/60   = 1.4 hours

    Therefore Cindy takes 1.4 hours.

Andy spent least time i.e 1.1 hours and Cindy spent greatest time i.e 1.4 hours.

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Answer:

clap

Step-by-step explanation:

since the rhythm repeats every 5, then you will be clapping on the fifty first beat.  on the 6th beat in the rhythm, its a clap, so since 50/5 is 10 then the next will be clap

The Inequality expression that shows the above situation is x ≥ 75.

The word "inequality" describes the state of being unequal, In Inequalities like in equations, we compare two values but not with the equal signs here we use signs like Not equal, less than, less than or equal to; greater than or greater than or equal to, etc.

Here we have,

The minimum amount required to open a new checking account is $ 75        

Let us assume that we used $ x dollars to open a bank account

By the given data,

The amount is a minimum of $ 75  

=> x ≥ 75      [ x is less than or equal to $ 75 ]

Therefore,

The Inequality expression that shows the above situation is x ≥ 75.  

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1. We can prove these triangles are congruent through J. SSS.

2. A triangle with 3 congruent angles is called an equilateral triangle.

If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent. These triangles can be moved, rotated, flipped, and turned to look exactly the same. They coincide if they are repositioned.

SSS rule states that two triangles are congruent if all three sides of one triangle are equivalent to the corresponding three sides of the other triangle.

An equilateral triangle has all three sides and angles equal.

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Answer: y=−2x+16

Step-by-step explanation:

The second inequality, y < (3/2)x² + 9x -21/2, is less than the quadratic function with zero -7 and 1 and includes the point (2, 27/2).

The equation of the form ax² + bx +c is known as a quadratic equation.

Given that, the zeros of the quadratic function are -7 and 1 and include the point (2,27/2).

Substitute x = 1 into the given inequality to check whether any of them becomes less than 0 or not:

From the first inequality:

y < -3/2 + 9 + 21/2

y < 18

From the second inequality:

y < 3/2 + 9 -21/2

y < 0

Since the inequality is less than 0, it is also less than the quadratic function at x = 1.

Similarly, checking the third inequality also gives y < 0, but the fourth doesn't.

Now, from the second and the third inequality, check which one is less than 27/2 for x = 2:

From the second inequality:

y < 6 + 18 -21/2

y < 27/2

From the third inequality:

y < -6-9+21/2

y < -27/2

Since the second inequality, y < (3/2)x² + 9x -21/2, is less than 0 at x =1 and less than 27/2 at x=2, it is also less than the quadratic function whose zeros are -7 and 1 and includes the point (2,27/2).

Hence, the second inequality, y < (3/2)x² + 9x -21/2, is less than the quadratic function with zero -7 and 1 and includes the point (2, 27/2).

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Answer:

it’s B took the test

Step-by-step explanation:

The largest 15-year term policy he can buy without spending more than $800 per annum is $148,699.

What is insurance?

An agreement to pay compensation to another party in the event of a specific loss, damage, or injury is known as insurance, and it is a way to protect against financial loss. It is a type of risk management that is mostly applied to protect against the risk of a potential or unforeseen loss.

The terms "insurer," "insurance company," "insurance carrier," and "underwriter" all refer to organizations that offer insurance.

Given: Justin, age 52, wants to pay no more than $800 a year in life insurance. If the annual life insurance premium rate (per $1000 of face value) is $5.38.

Annual life insurance premium rate = $5.38 per $1000 of the face value.

Largest 15-year term policy possible

= [tex]\frac{800}{5.38}*1000 = 148,698. 885 = 148, 699[/tex]

Therefore, the largest 15-year term policy he can buy without spending more than $800 per annum is $148,699.

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Answer: 24. The remainder is 7

Step-by-step explanation:

2.1m/s is the tip of his shadow moving when he is 15 m from the pole

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

x is the distance from the man to the pole, and y is the distance from the tip of the man's shadow to the pole. i assume the man and pole are standing straight up, which means the 2 triangles are similar.

(y-x)/y=2/6

(y-x)/y=1/3

Apply cross multiplication

3(y-x)=y

3y-3x=y

2y=3x

y=3/2x

differentiate both sides with respect to t or time.

dy/dt=3/2dx/dt

By given dx/dt=1.4m/s

dy/dt=3/2×1.4

dy/dt=2.1m/s

Hence, 2.1m/s is the tip of his shadow moving when he is 15 m from the pole

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The length of side DE of the rectangle ABCD is 11/5 units .

What is rectangle?

In euclidean plane geometry, a rectangle may be a quadrilateral with four right angles. It also can be outlined as: an angular quadrilateral, since angular means all of its angles square measure equal; or a tetragon containing a right angle.

Main body:

given:

AE = 4x+8       -----------(1)

CE = 7x - 3      -----------(2)

as we know diagonal of rectangle bisect each other , which means AE = CE

using the property , we get

4x+ 8 = 7x -3

taking like terms to one side,

7x - 4x = 8+3

3x = 11

x = 11/3

put the value of x in any equation,

AE = 4(11/3) +8

AE = 44/3 +24/3

AE = 68/3

as AE = DE

Hence the value of DE is 68/3 units.

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Answer:Yes

Step-by-step explanation:It changes the answer,

Answer:

Step-by-step explanation:

nope

Example:

5+(6+3)                   (+)  (+) = +

5+9= 14

The two column proof is written as follows

Statement                                                           Reason

line UT ≅ line GH                                     given

line UV ≅ line GH                                     given

< U ≅ < G                                                  given

Δ TUV  ≅  Δ BEC                                     Congruent triangles by SAS

< F ≅ < V                                                  CPCTC theorem

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

Side -  Side - Side = SSS

Side - Angle - Side = SAS

Angle - Side - Angle = ASA

Angle - Angle - Side = AAS

Hypotenuse and one leg = HL

The problem requires the prove by Side - Angle - Side = SAS to ensure that the the triangles are congruent

The SAS have it that the two sides of the triangles being compared should be equal and the included angles are equal

The given sides and the included angle are

line UT ≅ line GH    Side

< U ≅ < G                  included angel

line UV ≅ line GH    Side

< F ≅ < V                  CPCTC theorem

According to the CPCTC theorem, whenever two triangles are congruent, then each of their corresponding parts are also congruent. In other words, if two or more triangles are congruent, then their corresponding sides and angles are also congruent or equivalent in size.

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a) The percentage reduction in the price of the television each time is as follows:

b) The absolute change after the two reductions amounting to $100 is that the price of the television is now $380.

c) The overall percentage decrease in the price of the television is 20.83%.

The percentage is the ratio.

The percentage is computed as the quotient of the smaller value (numerator) over the larger value (denominator), between two values.

Percentages are depicted using the percentage sign (%) to show that the value is expressed over 100.

Price of the television = $480

First price reduction = $50

New price after the first price reduction = $430 ($480 - $50)

Percentage reduction in price = 10.42% ($50/$480 x 100)

Second price reduction = $50

New price after the second price reduction = $380 ($430 - $50)

Percentage reduction in price = 11.63% ($50/$430 x 100)

Overall percentage decrease = 20.83% ($100/$480 x 100)

Thus, overall, the price of this television decreased by 20.83 percent.

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Answer:

Step-by-step explanation:

oh wow

a) The velocity of the particle is described by v(t) = - 3 · t² + 12 · t - 9.

b) The particle is at rest when t = 1 s. and t = 3 s.

c) The particle changes its direction when t = 1 s. and t = 3 s.

d) The particle is moving right when 0 s < t < 1 s and t > 3 s and left when 1 s < t < 3 s.

e) The acceleration of the particle is described by a(t) = a(t) = - 6 · t + 12.

f) The velocity increases at t = 1 s.

g) The particle has a total distance of 54 meters.

In the statement we find the function of a particle that describes its position (y), measured in meters, in time (t), in seconds. Herein we shall analyze the function to determine all important features.

a) The velocity of the particle (v), in meters per second, is the first derivative of the function position:

v(t) = - 3 · t² + 12 · t - 9

b) The particle is at rest when v(t) = 0. Now we proceed to determine the roots of the resulting polynomial:

- 3 · t² + 12 · t - 9 = 0

t = 3 s. or t = 1 s.

c) The particle changes its direction when v(t) = 0. Then, this change happens in t = 1 s and t = 3 s.

d) The particle is moving right when v(t) > 0, then:

(t - 1) · (t - 3) > 0

There are two possible intervals: (i) 0 s < t < 1 s, (ii) t > 3 s. The particle is moving left when 1 s < t < 3 s.

e) The acceleration is the second derivative of function position, thus:

a(t) = - 6 · t + 12

f) The velocity increases when a(t) > 0. Then, the acceleration at t = 1 s is:

a(1) = - 6 · 1 + 12

a(1) = 6

The velocity is increasing at t = 1 s.

g) The total distance (s), in meters, traveled is determined by the following expression:

s = |x(1) - x(0)| + |x(3) - x(1)| + |x(6) - x(3)|

s = |7 - 11| + |11 - 7| + |- 43 - 11|

s = |- 4| + |4| + |- 54|

s = 54

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