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The lengths of AC and AD using the concept of similar triangles are; AC =  12.5 and AD = 3

We are given that;

∆BDE is a similar triangle to ∆BAC.

This means that their sides are proportional. Thus, we can say that;

BD/BA = BE/BC

Thus;

2/BA = 4/(6 + 4)

BA = 2 × 10/4

BA = 5

Similarly;

BE/BC = DE/AC

4/10 = 5/AC

AC = 5 × 10/4

AC = 25/2

Finally,

AC = 25/2 = 12.5.

Thus;

AD = BA - BD = 5 - 2 = 3.

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15 nm converted into km gives 1·5 × [tex]10^{-11}[/tex] km.

A process involving numerous stages, multiplication or division, especially a conversion factor, can be referred to as Unit Conversion. Additionally, rounding and determining the number of significant digits may be necessary steps in the procedure.

For measuring various properties, including length, weight, capacity, and temperature, many units of conversion are employed. We can change the units of measurement in mathematics to better understand.

Unit conversions are used to represent an amount in a different unit.

We have to convert 15 nm into km.

1 nm = [tex]10^{-12}[/tex] km

15 nm = 15 × [tex]10^{-12}[/tex] km

          = 1·5 × [tex]10^{-11}[/tex] km

Thus, 15 nm converted into km gives 1·5 × [tex]10^{-11}[/tex] km.

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In step 1, y was made the subject of the second equation to get:

y=5x-4

To proceed, the next step is to substitute the expression into the other equation, not the equation we solved for y.

8x+2y=-12

8x+2(5x-4)=-12

8x+10x-8=-12

18x=-12+8

18x=-4

x=-[tex]\frac{4}{18}[/tex]

x=[tex]\frac-{2}{9}[/tex]

answer=  the value of x is -2/9

Answer:

Use a model to find the sum of two fractions with the same denominator

Add fractions with a common denominator without a model

Add fractions with a common denominator that contain a variable

Step-by-step explanation:

j

Domain is the set of values under which a function is defined.

Range is the outcome of all the values of the domain when put in a function.

graphically, the domain is the set of values under which we get some value in the y-axis for a particular function graph .

while the range is the y-coordinate of all the points lying on the graph .

As the graph is not posted by you.

see this graph of the modulus function for instance:

        so,  R is the domain.

        but the range is only positive values of R in y.

        and,

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cos(pi) and cos(-pi) are both equal to -1 because cos is an even function.

For an even function, f(x) = f(-x). Even functions are symmetric about the y-axis.

Symmetricity about y-axis means that for same magnitude of x (like -2 and 2 have the same magnitude that is 2) the value of y will be the same.

Hence, in the case of cos(x), if we give any value as x and then give -x we will get the same result like cos(0.5pi) = cos(-0.5pi)

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Answer:

3 x - y = 6

Step-by-step explanation:

the equation of a line is

ax + by = c

express the slope initially in the form of y=mx+b

b is the y- intercept (the point where it crosses the y axis)

m is basically the slope, to find m, you have to use a specific formula...

m = (y2 – y1) / (x2 – x1)

(x1, y1) (x2, y2) are 2 coordinate points...

(3,3) and (1, -3)

m = -3 -3 divided by 1 - 3 =  -6/-2 =  3

so your formula for now is .. y = 3x + b (you dont know what b is yet)

Now, substitute the points into the equation.

3 = 9 + b.  b = -6

final formula is,

Y=3x -6

u can also rearrange the formula in a standard form:

3x - y = 6

I REALLY HOPE THIS HELPS U!!

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

The equation of the line is

y = x - 10.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The line has,

Slope = 1

Passes through = (-3, -13)

Now,

The equation of a line is given as,

y = mx + c

Put (-3, -13) = (x, y)

-13 = 1 x (-3) + c

-13 = -3 + c

c = -13 + 3

c = -10

Now,

The equation of the line.

y = 1x - 10

y = x - 10

Thus,

The equation of the line is

y = x - 10.

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The sales tax rate for a specific type of wood-frame door priced at $1480 is 25%, or $370.

Percentages are just fractions with a denominator of 100. We use the percent sign (%) beside a number to indicate that it is a percentage. For instance, if you answered 75 questions correctly out of 100 on a test (75/100), you would have received a 75%. A percentage is a relative value that represents one hundredth of a quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given quantity. A percentage is a fraction of a whole expressed as a number between 0 and 100.

Here,

Sale tax=$370

Price of door=$1480

Sales tax percent=370/1480*100

=25%

The rate of sales tax for a particular type of wood-frame door is priced at $1480 is 25% that is $370.

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The percentage of people having a mild allergic reaction is 0.8%.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

As per the given,

16 out of 2000 have a mild allergic reaction.

Percentage of 16 out of 2000 = (16/2000)100 = 0.8%

Hence "The percentage of people having a mild allergic reaction is 0.8%".

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Cost of another 3 panes of class is 7.95

Given, Number of panes of glass bought = 8

Cost of 8 panes of glass = $21.20

Number of broken panes of glass = 3

We must determine the price of three glass panes.

By unitary method, If 8 panes of glass costs $21.20 , then the cost of one pane of glass will be as follows,

Cost of one pane of glass = 21.20/8

                                            = $2.65

Therefore,  cost of  3 panes of glass it would be $2.65×3 = 7.95

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. In essence, this method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple.

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x = -2 and y = -10 is the solution of the equations y = 8x +6 and 10x - 5y = 30.

What is Substitution method to solve equations?

The method of substitution involves three steps: Solve one equation for one of the variables. Substitute (plug-in) this expression into the other equation and solve. Resubstitute the value into the original equation to find the corresponding variable. he substitution method is the algebraic method to solve simultaneous linear equations.

Given Equations :

y = 8x +6

10x - 5y = 30

A) Solve equation [1] for the variable  y

    [1]    y = 8x + 6

B)  Plug this in for variable  y  in equation [2]

  [2]    -5•(8x+6) + 10x = 30

  [2]     - 30x = 60

C)  Solve equation [2] for the variable  x

  [2]    30x = - 60

  [2]    x = - 2

D)  By now we know this much :

   y = 8x+6

   x = -2

E)  Use the  x  value to solve for  y      y = 8(-2)+6 = -10

Solution : {y,x} = {-10,-2}

Hence , x = -2 and y = -10 is the solution of the equations y = 8x +6 and 10x - 5y = 30.

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Answer:

$60.00

Step-by-step explanation:

1/4(40) = 10

40 - 10 = 30

30+ 2 = 32

32 - 8 - 8 = 16

16 - 6 = 10

10 + 50 = 60

The endpoint of each piecewise-defined function is obtained.

The stated function is-

-x + 3 ; x < 2

     3 ; 2 ≤ x < 4

4 - 2x ;   x ≥ 4

For greater clarity, see the graph that is attached.

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The complete question is-

Explain how to graph the given piecewise-defined function. Be sure to specify the type of endpoint each piece of the function will have and why. f(x) = StartLayout enlarged left-brace 1st Row 1st column negative x + 3, 2nd column x less-than 2 2nd row 1st column 3, 2nd column 2 less-than-or-equal-to x less-than 4 3rd Row 1st column 4 minus 2 x, 2nd column x greater-than-or-equal-to 4 EndLayout

Answer:

March 4

Step-by-step explanation:

The fifth Thursday must happen 4 weeks after the first one. That means that the 5th Thursday is 28 days after the first one.

Feb 1 + 28 days = Feb 29

Feb 1, Thursday

Feb 8, Thursday

Feb 15, Thursday

Feb 22, Thursday

Feb 29, Thursday

Mar 1, Friday

Mar 2, Saturday

Mar 3, Sunday

Mar 4, Monday

Answer: March 4

Answer: 1 solution

Step-by-step explanation:

-8(-8x-6)= -2x+7

64x + 48 = -2x +7

66x =  -41

x = -41/66

The statements that are true for functions g(x) = x² and h(x) = -x² are given as follows:

The functions for this problem are defined as follows:

The function h(x) is given by the multiplication of the function g(x) by -1, meaning that it is the reflection over the x-axis of the function g(x).

The two quadratic functions share the same vertex at the origin, meaning that it cannot be affirmed that one function will always be greater than the other for all values of x.

However, considering that the x² function is non-negative in all it's domain, the reflected function -x² will be non-positive at all it's domain, they are equal only at the origin, which is the vertex, all for all remaining non-zero values, g(x) is greater than h(x).

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Compared with randomly paired people, friends are more likely to share the same attitudes and beliefs. this best illustrates the association between similarity and attraction.

What is social Psychology ?

Social psychology is the scientific study of how individuals's thoughts, feelings, and behaviors are affected by the actual or hypothetical presence of other people.

               Social psychology is the study of how individual or group behavior is influenced by the presence and behavior of others.

What is social psychology's primary area of study?

Social psychologists research the ways in which social impact, social perception, and social interaction affect both individual and group behavior.

                   Some social psychologists concentrate their efforts on studying how people behave.

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162.6

+ 4.4

Separate decimals

162 + 4         =  166

0.6 + 0.4       =      1

166 + 1 = 167

162.6

Nearest ten is 160

Hope this helps

The change in Ms Smith's saving account balance each month due to her car payments is of:

-$267.75.

A proportion is a fraction of a total amount, and this fraction is used along with the basic arithmetic operations, especially multiplication and division, to find the desired measures in the context of a problem.

In this problem, the monthly balance change is obtained as follows:

Monthly balance change = Yearly balance change / 12.

(as an year is composed by 12 months).

As stated in the text, the yearly balance change of Ms. Smith's account is given as follows:

-$3,213.

The payments are equal each month, hence the monthly change is of:

Monthly balance change = -3213/12 = -$267.75.

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Answer:

Reflection across the X axis, translate to the right by 7 points

Step-by-step explanation:

A reflection would move ABC to quadrant 3, and the translation of +7 would put point C where point S is.

The vertex form of the equation is in the form of y = a(x-h)^2 + k.

Step 1: Use the formula below to solve for a.

a = -1/4 * (4 - 12) = -1

Step 2: Use the formula below to solve for h.

h = -b/(2a) = 12/(2(-1)) = -6

Step 3: Use the formula below to solve for k.

k = f(h) = -(-6)^2 + 12(-6) - 4 = 36

Therefore, the vertex form of the equation is y = -(x+6)^2 + 36.

A vertex, or particular point, is a place where two or more lines or edges meet in a mathematical object. Angles, polygons, polyhedra, and graphs are where vertices are most frequently seen. Nodes and vertices in a graph are the same thing.

Recall that a parabola's General Form is y = ax2 + bx + c. The x-coordinate of the vertices, which is x = - b/2a, must first be discovered in order to find the vertex from this form. You will use this number to replace x in the parabola equation once you have determined the x-coordinate of the vertex.

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Well said. I 100% know what this is.

Fitness related to endurance and fitness related to skill are the two basic types of physical fitness. Running is most likely the simplest solo sport for fostering both physical and mental fitness.

Jogging, riding, swimming, and brisk walking are among examples. Exercises that build muscle strength are known as resistance training. Using a resistance band and lifting weights are two examples. Walking on uneven ground can be made simpler with balance exercises, which can also assist prevent falls.

Fitness related to endurance and fitness related to skill are the two basic types of physical fitness. Running is most likely the simplest solo sport for fostering both physical and mental fitness.

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Yes, there is evidence that the level of significance is taken at 0.05 or 5% when the p-value is low.

Level of significance: The fixed probability of incorrectly eliminating the null hypothesis when it is actually true is what is meant by the term "level of significance." The probability of type I error is defined as the level of significance, which is set by the researcher using the results of the error. The statistical significance is measured by the level of significance. It specifies whether or not the null hypothesis is thought to be true. It is anticipated to determine whether the outcome is statistically significant enough to reject or prove the null hypothesis wrong.

The significance level is set at 0.05 or 5%. Low p-values indicate that the observed values differ significantly from the population value that was initially hypothesized. If the p-value is as small as possible, it is said to be more significant. Additionally, if the p-value is very low, the outcome would be highly significant. However, since obtaining a p-value below 0.05 is quite uncommon, p-values less than 0.05 are typically considered significant.

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The value of c in the equation 5c = 13.5 - 16.5 - 10c is 0.6.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign

In this case, 5c + 16.5 = 13.5 + 10c

Collect the like terms

5c - 10c = 13.5 - 16.5

- 5c = -3.0

Divide

c = -3.0 / -5

c = 0.6

The value of c is 0.6.

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If abc is 1 degree and 25', the angle ACD is 178° 35'.

An angle is a figure in Euclidean geometry formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are termed dihedral angles. An angle is generated when two straight lines or rays meet at a shared terminus. The common point of contact is called the vertex of an angle.

Here,

∠ACB and ∠ACD are supplementary, so they add up to 180°.

First, convert to degrees (there are 60 minutes in a degree).

∠ACB = 1°25' = 1° + (25/60)° = 1.4167°

Now find the supplementary:

∠ACD = 180° − 1.4167°

∠ACD = 178.5833°

∠ACD = 178° 35'

The value of angle ACD is 178° 35' if abc is 1 degree and 25' .

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Answer:

The answer is 85

Step-by-step explanation:

c/100 = 51/60

(c) × (60) = (51) × (100)

60c = 5100

60c/60 = 5100/60

c = 85

Thus, The value of y is 85

Answer:

[tex] \sf \: c = 85[/tex]

Step-by-step explanation:

Given equation,

[tex] \sf \rightarrow \: \frac{c}{100} = \frac{51}{60} [/tex]

Now the value of c will be,

[tex] \sf \rightarrow \: \frac{c}{100} = \frac{51}{60} [/tex]

[tex] \sf \rightarrow \: c = ( \frac{51}{60} ) \times 100[/tex]

[tex] \sf \rightarrow \: c = \frac{(51 \times 100)}{60} [/tex]

[tex] \sf \rightarrow \: c = \frac{5100}{60} [/tex]

[tex] \sf \rightarrow \boxed{ \sf c = 85}[/tex]

Hence, the value of c is 85.

The measure of the supplementary angle for one of the base angles is 95°.

The supplementary angles are the angles whose sum is given as 180°. The sum of all angles on one side of straight line is also 180°

The measures of angles are given as  (4x + 5)°, (4x + 5)°and  10⁰ respectively.

Since, the sum of the angles of a triangle is 180⁰. The following equation can be written as,

(4x + 5)° + (4x + 5)° + 10⁰ = 180⁰

⇒ 8x = 160°

⇒ x = 20°

Thus, the angles can be written as 4 × 20 + 5 = 85° and 10° respectively.

Now, the measure of the exterior angle can be written as below,

⇒ 180° - 85° = 95°.

Hence, the measure of the exterior angle is given as 95°.

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