Find the value of x.
a
x = [?]
x

The half-life of this substance that weighs 32 mg and one year later, the sample weighs 25.5 mg will be 3.053 year.

The duration it takes for a given quantity to fall to half of its initial value is known as the half-life. The phrase can be used to refer to other types of decay, whether or not they are exponential, but it is most frequently used in connection with atoms going through radioactive decay. The amount of time needed for the reactant concentration to drop to half its initial value is known as the half-life of a reaction.

Here,

The initial weight of radioactive substance=32 mg

The final weight of radioactive substance=25.5 mg

Duration=1 year

The formula,

N(t)=N(0)*1/2^(t/t₁/₂)

25.5=32*1/2^(1/t₁/₂)

half-life, t₁/₂ = 3.053 year

The half-life of this substance, which weighs 32 mg, will be 3.053 years when the sample weighs 25.5 mg.

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The distance of each station from the ship is = 250 miles.

acc to our question-

hence,The distance of each station from the ship is = 250 miles.

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The measure of angle 4 is 35 degrees and the measure of angle 5 is 81 degrees

The sum of angles on a straight line is equal to 180 degrees

Then the equation will be

∠3 + 81 +∠4 = 180  degrees

Substitute the value of ∠3 in the equation

64 + 81 + ∠4 = 180  

145 + ∠4 = 180

∠4 = 180 - 145

∠4 = 35 degrees

The sum of interior  angles of the triangle is 180 degrees

∠4 + ∠5 + 64 = 180

Substitute the values in the equation

35 + ∠5 + 64 = 180

∠5 + 99 = 180

∠5 = 180 - 99

∠5 = 81 degrees

Hence, the measure of angle 4 is 35 degrees and the measure of angle 5 is 81 degrees

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Answer:

Step-by-step explanation:

Let the dimensions are width - w, length - l and height - h.

Formula for volume:

Variable expressions for length, height and width:

Equation for the volume of this box:

Substitute the variables:

or

Answer:

Step-by-step explanation:

a) Formula we use,

→ V = l × w × h

b) The variable expressions are,

→ l = (h + 5)

→ w = (h + 2)

→ h = h

c) Forming required equation,

→ V = l × w × h

→ V = (h + 5)(h + 2)(h)

→ 216 = (h + 5)(h + 2)(h)

These are the required answers.

The distance to the top of the building changing when they are 60 feet from the base of the building is 2.19 ft/s.

In the given question we have to find how fast is the distance to the top of the building changing when they are 60 feet from the base of the building.

A family is walking toward their home, which is in an apartment building 123 feet tall.

They are walking at a rate of 5 ft/sec.

So according to the given statement diagram is

In the diagram x represent base and s represent the distance.

Using the Pythagorean theorem to find the value of s.

So the equation should be

[tex]s^2=x^2+(123)^2[/tex]........................(1)

From the question, x=60 feet

Now putting the value

[tex]s^2=(60)^2+(123)^2[/tex]

[tex]s^2[/tex] = 3600+15129

[tex]s^2[/tex] = 18729

s = 136.85

Differentiate equation 1 with respect to t using the power rule then solve the expression for ds/dt

2s ds/dt=2x dx/dt+0

2s ds/dt= 2x dx/dt

Divide by 2s on both side, we get

ds/dt= x/s dx/dt.......................(2)

They are walking at a rate of 5 ft/sec.

So dx/dt=5

Putting the value in the equation 2

ds/dt=60/136.85 ×5

ds/dt=0.438×5

ds/dt=2.19 ft/s

The distance to the top of the building changing when they are 60 feet from the base of the building is 2.19 ft/s.

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Hope this helps you with your question.

Answer:

Step-by-step explanation:

I did it on a graphing app

Answer:

D. 80 degree

Step-by-step explanation:

According to the question:

[tex]\triangle ABC \cong \triangle DEF[/tex]

[tex] \rm m \angle A = (x + 30) \degree \\ \rm m \angle C = 45 \degree \\ \rm m \angle D = 80 \degree[/tex]

From above congruence we can conclude:

[tex] \rm m \angle A = m \angle D[/tex]

[tex] \therefore [/tex]

[tex] \rm m \angle A = 80 \degree[/tex]

If Nita scored 62% of the marks then the maximum marks of the examination was 600  .

In the question ,

it is given that,

the number of marks scored by Nita in the examination = 372 marks

percent of marks scored by Nita in the examination = 62% ,

let the maximum marks of the examination = "x" ,

So , according to the questions

372 = 62% of x

372 = 0.62 * x       ....because 62% = 0.62

x = 372/0.62

x = 600

Therefore , If Nita scored 62% of the marks then the maximum marks of the examination was 600  .

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The required standard equation is given as y(t) = 5.39 sin(4πt + 0.379π).

Given that,

To rewrite y(t)=2×sin 4pi t+5×cos 4pi t in the form y(t)=Asin (wt+Ф).

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here
We know that.
Asin(α + β) = Asinαcosβ + Acosαsinβ,
Comparing it with the given equation,
Asinα = 5  
Acosα = 2
Taking the ratio of the equation,
sinα/cosα = 5/2
tanα = 5/2
α = 0.379π
Now,
Asin0.379π = 5
A = 5 / sin0.379
A = 5.39

Now,
The standard form equation is given as, y(t) = 5.39 sin(4πt + 0.379π) where ω = 4π.

Thus, the required equation is given as y(t) = 5.39 sin(4πt + 0.379π).

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The quadratic form of (x² - 1)² + (x² - 1) - 12 = 0 is (x² + 3)(x² - 4) = 0 and the roots are x = ± i√3 Or x = ± 2.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, (x² - 1)² + (x² - 1) - 12 = 0.

∴ x⁴ - 2x² + 1 + x² - 1 - 12 = 0.

x⁴ - x² - 12 = 0.

x⁴ + 3x² - 4x² - 12 = 0.

x²(x² + 3) - 4(x² + 3) = 0.

(x² + 3)(x² - 4) = 0.

Now (x² + 3) = 0 Or (x² - 4) = 0.

x² = - 3 Or x² = 4.

x = ± √-3 Or x = ± 2.

x = ± i√3 Or x = ± 2.

We can also solve this equation by assuming x² = t and substitute we will get the roots in terms of t and then we'll replace x² again in t.

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Answer:

450 centimeters

Step-by-step explanation:

We know that,

1 meter = 100 centimeters

so 4.5 meters = 4.5*100 centimeters

                      =450 centimeters

Seven huge boxes and two tiny boxes total were bought by the contractor.

A linear equation is defined as an algebraic equation of maximum degree 1 is a linear equation.

According to the question, a builder needs to purchase nails to construct a house.

Both small and large boxes of nails are provided. There are 50 nails in each small box and 350 in each large box.

The contractor purchased 5 more large than tiny boxes, hence it is assumed that he purchased a certain number of little boxes.

He purchased (x+5) huge cartons.

So, 50(x) + 350(x+5) = 2590.

50x + 350x + 1750 = 2590.

400x = 2590 - 1750.

400x = 840.

x = 2.1

The bulk of the boxes he bought is 7.

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Answer:

The correct answer is D.

Step-by-step explanation:

1. You add all 4 of the given closing prices with answer choice D ($56.24)  Getting $271.35

2. Then divide the total of $271.35 by 5. which gives you $54.27.

meaning that your answer is D.

Sorry if this didn't help very much... Would appreciate a 5 star if it did :)

The equivalent fraction for the given fraction -11/-4 is -11/(-4) and -11/-4.

Fraction.

Fraction means a number expressed as a quotient, in which a numerator is divided by a denominator.

Given,

Here we have the fraction -11/-4.

Now, we have to find the equivalent fraction of this fraction.

In order to find the equivalent fraction, we have to identify that the given term is reduceable or not.

If it is reduceable, then we have to simplify it to get the equivalent fraction.

But here the given fraction -11/-4 is not reduceable.

So, the next thing we have to do is to find the sign equivalent value for this one.

In the given fraction both the numerator and the denominator are in negative sign.

So, the equivalent fraction, must have both positive or both negative one.

Therefore, the equivalent fraction are -11/(-4) and -11/-4.

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Step-by-step explanation:

You need to replace x in the equation with x in the table.

Three mathematical terms with no definitions: (1) The terms (ii) and (iii) are correct., (2) The term (ii) is correct., (3) The term (i) and (ii) is correct.

What is parallel and perpendicular lines?

The definition of a parallel line is a pair of lines that never cross and always have the same distance between them. Lines that cross at right angles are referred to as perpendicular lines (90 degrees).

(1) The mathematical term parallel lines explicitly uses the undefined term(s).

The terms (ii) and (iii) are correct.

(2) The mathematical term perpendicular lines explicitly uses the undefined term(s)

The term (ii) is correct.

(3) The mathematical term line segment explicitly uses the undefined term(s).

The term (i) and (ii) is correct.

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Answer:

i dont see image..

Step-by-step explanation:

From the procedure, the simplest form of the radical is  5√7.

A radical can also be called a surd. The surd is an irrational number. We say that it is irrational because it can not be expressed as a terminating decimal.

Now we have to look at the radical √175. We have to think of two numbers that we can multiply to obtain 175 and one of them would be a perfect square.

If we choose the numbers 7 and 25, we can write;

√175 = √7 * √25

Thus we have in the  simplest radical form 5√7.

The expression √5/12 is already in the simplest form.

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Answer:

  (d)  HA

Step-by-step explanation:

You have two right triangles with the hypotenuse and one angle marked as congruent. You want to know the applicable theorem for claiming the triangles are congruent.

When two triangles are known to be right triangles, the known angle is opposite the longest side (hypotenuse), and the two legs are the sides that form that known angle. Hence, some special theorems can be invoked for right triangles:

  LA — leg, angle; equivalent to ASA

  LL — leg, leg; equivalent to SAS

  HA — hypotenuse, angle; equivalent to AAS

  HL — hypotenuse, leg; no equivalent for non-right triangles

The given triangles have the hypotenuse (H) and an acute angle (A) marked, so the HA theorem can be used to prove congruence.

__

Additional comment

The HL condition described above refers two two consecutive sides and the angle not between them (SSA). This set of descriptors will create a unique triangle if and only if the angle is opposite the longest side. In general, that will not be the case, but it is guaranteed to be the case for a right triangle.

The given figure is pentagon, and the perimeter of pentagon is 47 cm.

What is pentagon and its perimeter?

The perimeter of a pentagon is the total length of the pentagon’s boundaries. Therefore, we can find the perimeter by adding the lengths of the five sides of the pentagon.

The length of side with radius = 2rsin(180/n)

Here, n = 5

length of side with r = 8 = 2*8sin(180/5)

=16 sin 32

=16 (0.58779)

=9.4

Perimeter is given as 5(length) = 47 cm.

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The percent sales tax on perchaging new pants is 7%. Percent is very useful for comparing two different things.

What is percent?

It is a figure or ratio stated as a fraction of 100 in mathematics. It is frequently represented by the percent sign, "%".

The formula to calculate the percent sales tax is as follows:

[tex]\textnormal{Percent sales tax}=\frac{\textnormal{Tax amount}}{\textnormal{Price without tax}} \times 100[/tex]

Total price of new pants with tax = $21.40

Price of new pants without tax = $20

The amount of tax on perchanging pants = $21.40 - $20 = $1.40

Now, calculate the percent tax.

[tex]\textnormal{Percent sales tax}=\frac{\textnormal{Tax amount}}{\textnormal{Price without tax}} \times 100\\\textnormal{Percent sales tax}=\frac{\$1.40}{\textnormal\$20}\times 100\\=7\%[/tex]

Hence, the percent sales tax on perchagin new pants is 7%.

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Answer:

Step-by-step explanation:

The rigid transformation of the pre-image ΔABC, that produces the image ΔDEF is option E as follows;

E. [tex]R_{(90^{\circ},\,(0,\, 0))}[/tex]

A rigid transformation is one in which the distances between each pair of points on the pre-image is preserved on the image, such that the pre-image and the image have the same size.

The coordinates of the vertices of ΔABC are;

A(-3, -3), B(-1, -4), C(-3, -4)

The coordinates of the vertices of ΔDEF are; D(-3, 3), E(-4, 1), F(-4, 3)

The formula for the rotation of a point (x, y) 90° clockwise about the origin is presented as follows;

Pre-image point [tex]{}[/tex] (Rotation 90° clockwise)  Image point after rotation

(x, y)            [tex]{}[/tex]                        ⇒               [tex]{}[/tex]           (-y, x)

The points in the image ΔDEF of pre-image triangle ΔABC which corresponds to points on ΔABC are;

Vertex A in triangle ΔABC corresponds to vertex D on triangle ΔDEF

Vertex B in triangle ΔABC corresponds to vertex E on triangle ΔDEF

Vertex C in triangle ΔABC corresponds to vertex F on triangle ΔDEF

The transformation of (x, y) ⇒ (-y, x), (which is the transformation of a 90° clockwise rotation about the origin), on the vertices of ΔABC are;

A(-3, -3)    [tex]\underset \longrightarrow {R_{(90^{\circ}, (0, 0)}}[/tex]  D(-3, 3)

B(-1, -4)    [tex]\underset \longrightarrow {R_{(90^{\circ}, (0, 0)}}[/tex]  D(-4, 1)

C(-3, -4)    [tex]\underset \longrightarrow {R_{(90^{\circ}, (0, 0)}}[/tex]  F(-4, 3)

Therefore, the triangle ΔDEF can be obtained from the triangle ΔABC by a rotation of 90° clockwise about the origin.

The correct option is; E [tex]R_{(90^{\circ}, (0, \,0))}[/tex]

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Answer:

8

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so:

[tex]\frac{A'B'}{12}=\frac{4}{6} \implies A'B'=8[/tex]

The area of the given triangle is 21.33 cm²

This formula is understood for its simple calculation supporting the length of three sides of a triangle, if the length of three sides are a, b, and c, then its semi-perimeter is. s=a+b+c2. Thus, the area is given by,

A=√s(s−a)(s−b)(s−c)

Given a triangle, with lengths 8 cm, 6 cm and 12 cm

Perimeter = 8+6+12 = 26 cm

Semi perimeter = 26/2 = 13 cm

Area = √s(s−a)(s−b)(s−c)

Area = √13(13-8)(13-6)(13-12)

Area = √455

Area =  21.33 cm²

Hence, The area of the given triangle is 21.33 cm²

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Answer: (3,2)

Step-by-step explanation:

[tex]7x-7y=7\\\-4x-7y=-26[/tex]

subtract second equation from the first

[tex]11x=33\\x= 3[/tex]

plug x = 3 back into first equation

[tex]7(3) - 7y = 721 - 7y = 7-7y = -14\\y = -2[/tex]

Answer:

x=3 y=2

Step-by-step explanation:

Answer: D. Y-2 = -7/4(X+9)

Answer:

y - 6 = 8(x + 4)

Step-by-step explanation:

The point-slope form is [tex]y-y_{1}=m(x-x_{1})[/tex], where y1 and x1 are any point on the line and m is the slope.

The formula for slope is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

By plugging in the points we have, we get:  [tex]\frac{22-6}{-2-(-4)}=8=m[/tex]

We can use any of the two pairs of points to represent y1 and x1 so if we choose (-4,6), we get:

[tex]y-6=8(x-(-4))\\y-6=8(x+4)[/tex]

The weighted average of the weighted points on the number line is -0.2.

A weighted average refers to the average of a data set that considers certain numbers as more important. Weighted averages are commonly used in statistical analysis, stock portfolios and teacher grading averages. In order to determine the weighted average of the weight points on the number line:

Hence, the average weight is -0.2.

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The constant of proportionality on this case is 3.2

What is constant of proportionality?

The ratio between any two given values that establishes what is referred to as a proportional relationship is the constant of proportionality.

Main body:

Total amount spent by Mom = $ 72

total gallon bought = 22.5

So constant of proportionality can be found by finding value of 1 gallon of gasoline, which can be found by dividing as follows,

Price of 1 gallon = total spent/ total gasoline bought

                           = 72/22.5

                           = 3.2

Hence constant of  proportionality is 3.2.

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