Solve for x

2 1/2x - 3/4 ( 2x + 5 ) = 3/8

Please explain step by step on how I get this answer to solve x!

Answer:

See below!

Step-by-step explanation:

Let the two numbers be x and y

x + y = 66 ----------------(1)

2x = y + 15

2x - y = 15 ---------------(2)

Add both equations

x + y + 2x - y = 66 + 15

x + 2x = 66 + 15

3x = 81

Divide both sides by 3

Put x = 27 in Eq. 1

27 + y = 66

Subtract 27 to both sides

y = 66 - 27

[tex]\rule[225]{225}{2}[/tex]

The discontinuity exists irremovable at a given place if the limit will not exist there. On the other hand, if changing a function's value at a particular point of discontinuity results in a linear combination, that location is referred to as the detachable discontinuity.

A graph's vertical asymptote would be a vertical line with the equation x = a, in which the chart tends to positive or negative infinity even as inputs go closer to a.

A vertical line that appears to coincide with such a function's graph but doesn't really cross the curve was known as a vertical asymptote.

Whenever the two-sided limit at c exists but is still not equal to f, the discontinuity is said to be detachable at that point (c). These kinds of discontinuities could be discovered by looking for independent uncertain parameters which are zeros for denominator components that were also numerator components in the provided function.

By finding the solution to the equation n(x) = 0, where n(x) represents the denominator of the function, one can find the vertical assumptote.

Simply locate a vertical line where a section of the curve was parallel as well as very close if you want to determine the constant slope from either the graph of a function.

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The expression that represents the total number of miles Hayden biked is A. 5 × (3 + 3 + 2 1/4)

It is important to note that an expression simply refers to mathematical statements which have at least two terms which are then related by an operator. In this case, they contain either numbers, variables, or both.

In this case, since Hayden rode his bike 5 times and each time he biked a 3 mile path, a 2 mile path, and a 2 1/4 mile path. Then in this situation, the expression will be:

= 5 × (3 + 3 + 2 1/4)

In conclusion, the correct option is A.

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Work Shown:

x = price of the TV before the discount

20% of x = 0.20x = discount, aka amount saved

x - 0.20x = 0.80x = price after discount

0.80x = 240

x = 240/0.80

x = 300

The TV was $300 before the discount.

-------------

Check:

20% of 300 = 0.20*300 = 60 dollars is the amount saved

300-60 = 240 is the price after the discount, which matches the given info. The answer is confirmed.

21⁰

sin0=opp/hyp

sin0=5/14

0=(sin^-1)5/14

0=21⁰

The volume of rectangular prisms is 40656.

Volume is generally defined as the amount of space that a substance or object occupies, or that is enclosed within a container.

The the formula V = Lwh used for calculation of the volume of rectangular prisms.

Where, the L represents the length of the rectangular prism

the W represents the width of the rectangular prism

the H represents the height of the rectangular prism.

The volume is the product of length width and height.

Volume = 44 x 33 x 28 = 40656

Therefore, the volume of rectangular prisms is 40656

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Answer:

34°

Step-by-step explanation:

34° is the the compliment of 56°

complementary angles can add upto 90°

56 + 34 = 90

90° - 56° = 34°

or

56° + x = 90°

-56 -56

x = 34°

Name of the angle = acute angle 34°<90°

0° - 90° = acute angles

90° - 180° = obtuse angles

Answer:

$300

Step-by-step explanation:

S = amount of $$ Shivani currently has

Y = ... Yamini currently has

1. If Shivani gives 60 to Yamini, the amounts with both will be equal:
   S - 60 = Y + 60

2. if Yamini gives 20 to Shivani, the amount with Shivani would become twice the amount left with Yamini: 2(Y-20) = S+20

3. Simplify both equations and solve the system:

   S = Y + 120
   S = 2Y - 60

   Y + 120 = 2Y - 60  ⇒  Y = 180

   S = 180 + 120 = 300

Answer:

Answer is attached as a photo. I will be honest I am not familiar with a calculus problem being set up that way. I am guessing that is what they are looking for...

Step-by-step explanation:

The upper bound of the given function is 20 while the lower bound of the given function is -8.

A certain kind of relationship called a function binds inputs to essentially one output.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

As per the given function,

-2 ≤ f(x) ≤ 5

At the upper bond, f(x) = 5

[tex]\int\limits^{3}_{-1} {f(x)} \, dx[/tex] = [tex]\int\limits^{3}_{-1} {5} \, dx[/tex]

⇒ 5(3 + 1) = 20

At the lower bond f(x) = -2

[tex]\int\limits^{3}_{-1} {f(x)} \, dx=\int\limits^{3}_{-1} {-2} \, dx[/tex]

⇒ -2(3 + 1) = -8

Hence "The upper bound of the given function is 20 while the lower bound of the given function is -8".

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When we have two sides and the angle between them, we have "SAS." Calculate the unknown side using the Law of Cosines, then find the lesser of the other two angles using the Law of Sines, and finally find the final angle by adding the three angles together to make 180 degrees.

The two triangles are congruent if we can demonstrate that two sides and the included angle of one triangle are congruent with two sides and the included angle of another triangle.

Triangles are considered congruent by SAS if their two sides match those of the other triangle's corresponding two sides, and if their included angles are parallel in both triangles.

Hence we get the required answer.

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Answer:

The first option.

Step-by-step explanation:

The graph starts very negative and ends very positive. Not sure how else to explain it.

Answer: [tex]z > -14[/tex]

Step-by-step explanation:

Divide both sides by 2.

Answer:

m = -66

Step-by-step explanation:

-m = -1m

-m = 66  ⇒  -m/-1 = 66/-1  ⇒  m = -66

Answer:

2 hours and 24 minutes

Step-by-step explanation:

If each worker does 100 each hour than 5 workers do 500 in 2 hourse leaving 100 left so then you 2 hours aka 120 minutes divided by 5 = 24 so it all adds to be 2 hours 24 minutes

Answer:

8 cards per chip

Step-by-step explanation:

So 32:4 is the ratio.

Divide by 4 to get 8 cards per chip.

There is no sufficient evidence to support that the population mean is less than 165.

What is mean ?

The average of a set of values is referred to as the mean in statistics and math. The simple arithmetic mean, geometric mean, and harmonic mean are some of the methods that can be used to calculate the mean. The simple arithmetic mean involves adding the numbers together and dividing the result by the number of observations.

From the given data

183, 152, 178 , 157 , 194 , 163 , 144 , 114 , 178 , 152 , 118 , 158

Mean = 157.5833

Standard deviation s = 24.39

  n = 12

Null hypothesis  [tex]H_{0}[/tex] : μ = 165

Alternative Hypothesis [tex]H_{1}[/tex] = μ < 165

Level of significance ∝ = 0.05

degree of freedom (df) = n - 1

                                (df) = 12 - 1

                                (df) = 11

critical value [tex]t_{0.05 , 11}[/tex] = -1.796 (left - tailed)

Test - statistics (t) = ( mean - μ ) / ( s / √n)

                         (t) = -1.053

p - value = 0.1574

p - value > Significance level (∝)

 0.1574 > 0.05

We fail to reject the null hypothesis

Critical value [tex]t_{0.05 , 11}[/tex] = -1.796

                   |[tex]t_{0.05 , 11}[/tex]| = 1.796

|test - statistics| < |critical value|

1.053 < 1.796

We fail to reject the null hypothesis

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The equation that represents how many grams of the compound will remain after 4 hours is A(4) = 380 *(1 - 12.1%)⁴

From the question, we have the following parametersa:

Mass = 380 grams

Rate of decay= 12.1% per hour

These parameters can be represented using the following exponential equation

A(n) = A *(1 - r)ⁿ

Where

n = number of hours = 4

A  = Initial mass = 380

r = rate of decay = 12.1%

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

A(4) = 380 *(1 - 12.1%)⁴

Hence, the equation is A(4) = 380 *(1 - 12.1%)⁴

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Answer: 23/5 = 4 3/5

20/12 = 1 8/12 = 1 2/3

3 3/4 = 15/5

4 7/15 = 67/15

18/8 = 2 2/8 = 2 1/4

45/18 = 2 9/18 = 2 1/2

8 3/10 = 83/10

1 11/12 = 33/12

Step-by-step explanation:

If triangle RST is an acute triangle, then m∠S must be less than 90°.

What is Acute Traingle?

A form of triangle called an acute triangle has acute angles at each of its three internal angles. Triangles with sharp angles are also known as acute triangles. Acute triangles have different side lengths, but their interior angles are always less than 90°.

In light of the foregoing, if triangle RST is an acute triangle,

then,

∠R , ∠S and ∠T, all are less than 90.

A triangle that is equilateral and has all three interior angles equal and less than 90 degrees, or angles that are all 60 degrees, is an example of an acute triangle.

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Answer:

Great than 10, but less than 100

Step-by-step explanation:

Make 700% a decimal by dividing by 100

700/100 = 7

7 = 5 = 35

700% of 5 is 35.

Answer:Greater than 10 but less than 100

Step-by-step explanation

700% of 5 = 35

35 is greater than 10

but less than 100

hope this helps

The 7 names of triangles:

Scalene, Isosceles, Equilateral, Equiangular triangle, Acute triangle,

Right triangle, Obtuse triangle

What are triangles?

Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed by a point where the three sides are joined end to end. The triangle's three angles add up to a total of 180 degrees.

Equiangular triangle: All angles are equal.

Acute triangle . . . all three angles are less than 90°

Right triangle . . . one angle is 90°

Obtuse triangle . . . one angle is greater than 90°

Equilateral triangle . . . all three sides are the same length

Isosceles triangle . . . two sides are the same length

Scalene triangle . . . all three sides are different lengths

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Answer:

33,000

Step-by-step explanation:

0.33 x 10^5 is 33,000

Using translation concepts, it is found that the correct option is:

D. It is the graph of  translated 3 units up and 7 units to the right.

The parent function is:

[tex]f(x)=y=1nx[/tex]

Shifting a function a units to the right is equivalent to finding f(x - a), thus:

[tex]f(x-7)=1n(x-7)[/tex]

Shifting a function a units up is equivalent to finding f(x) + a, thus:

[tex]f(x-7)+3=1n(x-7)+3[/tex]

Which means that the function was shifted 7 units to the right and 3 up, thus, option D is correct.

The number of sugar cups will be equal to 7.5 cups.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that the ratio of flour to sugar is 2 cups to 3 cups. The number of cops for flour is 5.

The number of sugar cups will be calculated as,

F / S = 2 / 3

5 / S = 2 / 3

S = ( 5 x 3 ) / 2

S = 7.5 cups

Therefore, the number of sugar cups will be equal to 7.5 cups.

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Graph of the system of inequality is a solid line and a portion of area is shaded which satisfy the condition of the inequality.

What is inequality?

When left hand side is not exactly equal to the right hand side of an equation then it is known as inequality. For system of inequality, there are four types of inequalities <, >, [tex]\le[/tex], and [tex]\ge[/tex].

Using following steps anyone can graph the inequality:

1. Get y alone on one side of a linear inequality in two variables (like x and y) before graphing it. Then, take into account the associated equation that was created by switching the inequality sign for an equality sign. This equation has a line as its graph.

2. The graph is a dashed line if the inequality is strict ( < or >). The graph is a solid line if the inequality is not strict ([tex]\le[/tex] or [tex]\ge[/tex] ).

3. The last step is to choose a point that is not on either line (typically (0, 0) is the simplest) and determine whether or not these coordinates fulfil the inequality. If so, shade the portion of the half-plane that contains that point. If not, shade the opposite half-plane.

Hence, the graph of the system of inequality is a solid line and a portion of area is shaded which satisfy the condition of the inequality.

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The example of a complex fraction is the fraction that consisting fraction on the numerator or denominator or both, that is 4 / (1/6)

The simple fraction consist of both numerator and denominator as whole number. The term on the top is the numerator and the term on the bottom is called the denominator

The complex fraction is defined as the fraction that consisting fraction on the numerator or denominator or both

The example of the complex fractions are

4 / (1/6)

Here the numerator is the 4 and it is a whole number. The denominator is 1/6 that is a fraction

Therefore, the example of a complex fraction is 4 / (1/6)

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Answer:

$531.25

Step-by-step explanation:

The total length of fence required is given by the perimeter of a square:

[tex]P=2l+2w\\l=25ft\\w=25ft\\P=2(25ft)+2(25ft)\\P=50ft[/tex]

Since the price is per 8 foot unit of fencing:

[tex]\frac{50ft}{8ft}=6.25units[/tex]

Each unit will cost $85:

Total cost = 6.25 units($85)

Total cost =$531.25

This answer could also be found by calculating the cost per foot of the fencing: [tex]\frac{85 dollars}{8ft}=10.625\frac{dollars}{foot}[/tex]

Since 50 feet are needed: 50 ft (10.625 [tex]\frac{dollars}{foot}[/tex])=$531.25

Answer:

depends on how long u need it for

Step-by-step explanation: