Help me solve it please
((3*3)²)²

The equation K = 4a + 9ab solved for a is a = K /(4 + 9b). (Option D)

In mathematics, an equation refers to a formula that expresses the equality of two mathematical expressions by connecting them with the equals sign =.

The given equation is K = 4a + 9ab.

In order to solve for a, the a variable must be isolated at one side of the equation and the other variables must be collected on the other sides.

On the right-hand side, as both terms contain the variable a, hence factoring it,

K = a(4 + 9b)

Dividing both sides by (4 + 9b) to isolate a,

a = K /(4 + 9b)

Note: The question is incomplete. The complete question probably is: Solve the equation for a in K = 4a + 9ab. A) a = K(4 + 9b) B) a = 4(K + 9b) C) a = (4 + 9b)/K D) K /(4 + 9b)

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The coordinates of the square be

A (0, 0)

B (a, 0)

C (a, a)

D (0, a)

slope of line AC = 1

Slope is the rate of change of the line AC this is solved by taking the ratio of change in y to change in x

A (0, 0) and C (a, a)

= (0 - a) / (0 - a)

= -a / -a

= 1

Slope of line BD = -1

the product of the slopes

= 1 * -1

= -1

therefore the diagonals of the ABCD are perpendicular since the product of the slope is -1

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Answer:

A D F

Step-by-step explanation:

The parent functions with a domain of all real values of x are the linear function, the absolute value function, the square root function, and the cube root function.

The linear function is defined by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. The domain of this function is all real values of x.

The absolute value function is defined by the equation y = |x|, where |x| is the absolute value of x. The domain of this function is all real values of x.

The square root function is defined by the equation y = √x, where √x is the square root of x. The domain of this function is all nonnegative real values of x.

The cube root function is defined by the equation y = ∛x, where ∛x is the cube root of x. The domain of this function is all nonnegative real values of x.

Therefore, the correct answers are A, D, and F. The reciprocal function, the cubic function, and the quadratic function do not have a domain of all real values of x.

Answer:

0.75 or 75%

Step-by-step explanation:

I know that 2/4 is 0.5 or 50% and 1/4 is 0.25 or 25% so it goes by 25. One more than 2/4 is 3/4, which is what you are trying to find, so it would be 0.75, or 75%.

The value of tanA is always less than 1.

What is a number's tan of?

Tangent is the ratio of the side opposite the angle we know or want to know over the side next to that angle, and is sometimes abbreviated as T-A-N.

Describe tan angle A.

The trigonometric ratio between the opposite and adjacent sides of a right triangle that contains an angle is its tangent.

                     Tangent is the mathematical term for the length of the leg that faces the angle and is often abbreviated as "tan." For instance, in the triangle above, tan(A) = 68 or 34 and tan(B) = 86 or 43.

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Theoretical centre-to-centre distance (C)=3.25 which is the distance between the centers of the pinion and gear

Given data:

No. of teeth on the pinion(TP)=17.

Diametral pitch(pd)=8 teeth/in.

The rotational speed of the pinion(NP)=1120 rev/min or 1120 rpm.

The rotational speed of the gear(NG)=544 rev/min or 544 rpm.

To calculate:

No. of teeth on gear(TG) & theoretical centre-to-centre distance(C).

We know that;

Diametral pitch(pd)=No. of teeth in the gear/Diameter of the gear

For pinion,

pd=TP/DP

Pittiong the values in above eq.

8 teeth/in =17/DP =>DP=17/8 in.

or DP=2.125 in.

Gear ratio(G)=(NP/NG)=(TG/TP)=(DG/DP)

(NP/NG)=(TG/TP)

1120/544 =TG/17 =>TG=35

therefore No. of teeth the gear(TG)=35 {Ans}

Also from gear ratio formula,

(NP/NG)=(DG/DP)

1120/544=DG/2.125

DG=4.375 in.

In figure I have drawn a rough diagram of the pinion and gear arrangement which will help you to understand how to calculate the centre-to-centre distance(C)

From fig.,

centre to centre distance,C=rP+rG {Where rP and rG are the radii of pinion and gear respectively}

C=(DP+DG)/2 {\large \because Diameter =2*radius}

C=(2.125+4.375)/2 in. =3.25 in.

therefore Theoretical centre to centre distance (C)=3.25

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If right triangle ABC with right angle ACB and altitude CD then

ΔABC ~ ΔACD

ΔABC ~ ΔCBD

ΔACD ~ ΔCBD

What is Angle-Angle Similarity (AA~) Theorem?

If two angles of one triangle and two corresponding angles of another triangle are congruent, then the triangles are similar.

According to the given question:

A right triangle is given with its altitude drawn from the right angle to its hypotenuse.

Consider the triangled ABC and ACD

By the reflexive property of angle congruence, it follows that:

∠A ≅ ∠A

Since the angles B and D are right angles, from the right angles congruence theorem, it also follows that:

∠C ≅ ∠D

Hence, by the Angle-Angle Similarity (AA~) Theorem, it follows that triangles ABC and ACD are similar. Similarly triangle ABC is similar to triangle CBD

Consider triangles ACD and CBD:

Triangles ABC and ACD are similar. Also triangle ABC is similar to triangle CBD

Therefore, Triangle CBD is similar to triangle ACD as both of them are similar to triangle ABC.

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Answer:

4 1/2 ft

Step-by-step explanation:

18 = 4s

Divide both sides by 4.

18/4 = 4s/4

9/2 = s

4 1/2 = s

The side of the table is 4 1/2 ft.

The expected value for the number of subjects who are vaccinated and are diseased is  56.7

Since we are given the information that a new vaccination is being used in a laboratory experiment to investigate whether it is effective. there are 273 subjects in the study.  We can calculate this by taking the total number of subjects who are vaccinated (119) and multiplying it by the proportion of subjects who are diseased

(47/273).  119 x (47/273) = 56.7

which is  the expected value for the number of subjects who are vaccinated and are diseased

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60% of Julio's number was Bill"s number

percentage, a relative value indicating hundredth parts of any quantity.

Given,

bill and julio each thought of a whole number between 1 and 20.

Bill"s number was 15

Julio's number was 6

We need to find what percent of Julio's number was Bill"s number

Original number minus new number by original number

(15-61)/15

9/15

0.6

Now we have multiply with 100 as it is a hundredth part.

0.6×100=60

Hence, 60% of Julio's number was Bill"s number

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The sample mean is less than 26.92 hours per week .

What is  standard deviation?

Your dataset's average level of variability is represented by the standard deviation. In general, it reveals how far away from the mean each value is.

                  A low standard deviation denotes that values are grouped closely to the mean, while a high standard deviation denotes that values are typically spread widely from the mean.

Let X~ Normal (26, 4/√16) distribution ie Normal (26, 1) distribution

We want,

P(X<a) = 0.82

Using standard normal approximation,

P(z< (a-26)/1) = 0.82

Using standard normal distribution tables, we get

(a-26)/1 = 0.915

(Since P(z<0.915) = 0.82)

So, a= 26+0.915= 26.915

So the required value is 26.92 (rounded to two decimals)

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Answer:

From 1846 to 1847 there was a 30% decrease and from 1847 to 1848 it increased by 51.4%

Step-by-step explanation:

How it decreased by 30%

V2-V1/V1x100

V2=3.5 V1=5

=(3.5−5)|5|×100
=−1.55×100

=−0.3×100

=−30%change

=30%decrease
How it increased by 51.4%
V2-V1/V1x100
V2=5.3 V1=3.5

=(5.3−3.5)|3.5|×100

=1.83.5×100

=0.514286×100

=51.4286%change

=51.4%increase

For the given line y = 1/2x - 4,

Consider a line with the equation ax+by+c=0

It is given that, the equation of a line is given as y = 1/2x - 4.

The slope of the given line is m = 1/2; (since it is in the form of y=mx+c)

Then, the slope of the line parallel to the given line is m = 0.

And the equation of the parallel line passing through the point (-4, 2) is

a(x - x1) + b(y - y1) = 0; where a = 1; b = -2 (y = 1/2x-4 ⇒ 2y = x - 8)

⇒ 1(x + 4) - 2(y - 2) = 0

⇒ x + 4 -2y + 4 = 0

⇒ x - 2y +8 = 0

So, the point on the parallel line is (0, 4).

The slope of the line perpendicular to the given line is m = -1/1/2 = -2.

And the equation of the perpendicular line passing through the point (-4, 2) is

b(x - x1) - a(y - y1) = 0; where a = 1; b = -2;

⇒ -2(x + 4) - 1(y - 2) = 0

⇒ -2x - 8 - y +2 = 0

⇒ y = -2x - 6

So, the point on the perpendicular line is (-2, -2).

All of these are shown in the graph below:

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Answer: 85%

Step-by-step explanation:

Since percentages are numbers/ratios expressed as a fraction of 100, 85/100 becomes 85%

The domain of the graph is {1, 2, 3, 4}

"All the values" that are input into a function are referred to as the domain of a function. The set of all potential inputs for a function is its domain.

Given:

As, we know domain of a function is the set of all possible inputs for the function.

from the Graph, we can find the coordinates ( 1, 10), (2, 20), (3, 40) and ( 4, 80)

So, the domain of the graph is {1, 2, 3, 4}

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The value of the condensed logarithm is, log(dq^8).

What is logarithm?

The opposite of exponentiation in mathematics is the logarithm. The exponent to which b must be raised in order to produce a number x is therefore the logarithm of a number x to the base b. For instance, since 1000 = 10^3, log10 of 1000 is 3, or [tex]log_1_0[/tex] = 3.

Given: log d + 8 log q.

We have to condense the given logarithm

Frist to simplify 8 log q by moving 8 inside the logarithm.

⇒ log(q)^8

⇒ log d + log(q^8)

Applying the product rule of logarithm

log(a) + log(b) = log(ab)

⇒ log d + log (q^8) = log(dq^8)

Hence, the condensed logarithm form of the given logarithm is, log(dq^8).

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Answer:

y = x + 17

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - x - 18 ← is in slope- intercept form

with slope m = - 1

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-1}[/tex] = 1 , then

y = x + c ← is the partial equation of the perpendicular line

to find c substitute (- 6, 11 ) into the partial equation

11 = - 6 + c ⇒ c = 11 + 6 = 17

y = x + 17 ← equation of perpendicular line

Answer:

24 days

Step-by-step explanation:

you have to divide the balance by the spending money, so £48.00, divided by £2.00 will equal 24 meaning, Claudia can last 24 days without adding money to her account

Answer: The first pair of equations, i.e., −3.2x=0.64 and x/4 =−0.05, have exactly the same solution. In both of these equations, the value of x comes out as -0.2.

Step-by-step explanation: Simplifying the first set of equations, we get:[tex]-3.2x=0.64[/tex]

[tex]x=0.64/-3.2[/tex]

x=-0.2

 [tex]x/4=-0.05[/tex]

[tex]x=-0.05*4[/tex]

x=-0.2

Simplifying the second set of equations, we get:

[tex]3/8x=1[/tex]

[tex]x=8/3[/tex]

x=2.66

[tex]1/3x=1/8[/tex]

[tex]x=1/8*3[/tex]

x=0.375

Simplifying the third set of equations, we get:

[tex]x/3.2=1.8[/tex]

[tex]x=1.8*3.2[/tex]

x=5.76

[tex]1.8x=3.2[/tex]

[tex]x=3.2/1.8[/tex]

x=1.77

Simplifying the fourth set of equations, we get:

[tex]-3/4x=5/2[/tex]

[tex]x=5/2*-4/3[/tex]

x=-3.33

[tex]5/2x=-3/4[/tex]

[tex]x=-3/4*2/5[/tex]

x=-0.3

Therefore, the first pair of equations, i.e., −3.2x=0.64 and x/4 =−0.05 have exactly the same solution.

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The required graph of the inequality has been shown and the solution is; 8 Nickels  and 12 dimes.

Inequality can be defined as the relation of the equation possessing the symbol of ( ≤, ≥, <, >).

Let the number of nickels be x and let the number of dimes be y,

We are told that Addison has x dimes and y nickels, having a minimum of 20 coins worth at most $1.60 combined. Thus, we can generate the equations as;

x + y = 20

x = 20 - y - - - - (1)

0.05x + 0.10y ≤ 1.60 - - - -(2)

We are also told that no less than 4 of the coins are dimes. Thus;

x ≥ 4

From the graph, one solution is given as 8 Nickels and 12 dimes.

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In a probability histogram, there is a correspondence between area and probability. Hence, option D is the right answer.

An histogram shows the variation in a variable over time. There are a certain number of samples in each category: this is called the frequency distribution. The number of children born according to their birth gender, such as males or females.

Probability histogram

A probability histogram is a histogram with probabilities on the y-axis and all the possible values on the x-axis. They represent chance. The area above a class interval represents the chance of that class interval.

A probability distribution shows the probabilities related to all possible outcomes of an event.

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The complete question is-

Fill in the blank.

In a probability histogram, there is a correspondence between--------------

A. volume and probability

B. area and volume

C. variation and area

D. area and probability

Answer:

A

Step-by-step explanation:

diameter

The another name for the chord that passes through the center of the circle is the diameter.

The correct option is (A).

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.

As per the given data:

We have to find out the alternate name for a chord that passes through the center of a circle out of the given options.

Diameter:

It's a chord that passes through the center and touches the ends of the circumference of the circle.

Hence, this is correct.

Circumference:

It's the length of the boundary of a circle, hence this cannot be a chord.

This is incorrect.

Center:

It's a point and a chord is a line, hence this cannot be true.

Radius:

A radius is not a chord, as it does not touch the endpoints on the circumference of the circle.

The another name for the chord that passes through the center of the circle is the diameter.

Hence, The another name for the chord that passes through the center of the circle is the diameter.

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Answer:

Liter

Step-by-step explanation:

Milliliters are used for much smaller amounts of liquid.

Length of the curve is e² - 1 .

What is function?

In arithmetic, a function from a group X to a group Y assigns to every part of X precisely one part of Y. The set X is termed the domain of the function and therefore the set Y is termed the codomain of the function

Main body:

A parametric curve is a function expressed in components form, such that

x=f(t) , y=g(t). The length of a parametric curve on the interval a ≤ t ≤ b is given by the definite integral :

L =  [tex]\int\limits^a_b {\sqrt{(\frac{dx}{dt} )^2 + (\frac{dy}{dt} )^2} } \, dt[/tex]

Let's begin by getting the first derivative of the components of the function with respect to the variable t.

x = e^t - t  

dx / dt = e^t−1

y = 4 e^t/2

dy /dt = 2 e^t/2

Substitute the derivatives into the following definite integral which computes the length of the parametric curve on the interval

[a,b]=[0,2].

L =[tex]\int\limits^a_b {\sqrt{(\frac{dx}{dt} )^2 + (\frac{dy}{dt} )^2} } \, dt[/tex]

L=  [tex]\int\limits^2_0 {\sqrt{(e^{t}-1 )^2 + (2e^{t/2} } )^2} } \, dt[/tex]

L =[tex]\int\limits^2_0 {e^{t} -1} \, dt[/tex]

Evaluate the solution at the limits of integration to get the length.

L = (e² - 1 )- (e⁰ - 1)

L = e² - 1 - 1 + 1

L= e² - 1

Hence , length of the curve is e² - 1 .

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Answer:

Step-by-step explanation:

You want the net and total surface area for the triangular prism shown.

The net diagram is attached. It consists of three rectangles with triangles attached to the ends of the widest rectangle. Of course, these parts can be arranged in any order you find convenient, as long as the common edges match the original prism.

The net shows the area can be computed as the sum of a rectangle 9 cm high and 5+6+5 = 16 cm wide, together with two triangles of base 6 cm and height 4 cm.

  A = (9 cm)(16 cm) +2(1/2)(6 cm)(4 cm)

  = 144 cm² +24 cm²

  = 168 cm²

The total surface area of the prism is 168 cm².

__

Additional comment

The formulas for the area of a rectangle and triangle are ...

  A = LW . . . . . area of a rectangle of length L and width W

  A = 1/2bh . . . . area of a triangle of base b and height h

Answer:

step 4 ,step 2, step 1 , step 3 , step 5