The Transformations To The Parent Function Of A Quadratic Equation Are Given Below. Write An Equation (2024)

The right angled triangle has a reference angle labelled 24 degrees.

Also it has the opposite side (the side facing the reference angle) measuring 24.8 units. The adjacent side (the side between the right angle and the reference angle) is labelled w. Therefore we would have the following trigonometric ratio;

[tex]\begin{gathered} \tan \theta=\frac{opp}{adj} \\ \tan 24=\frac{24.8}{w} \\ 0.44522\ldots=\frac{24.8}{w} \\ \text{Cross multiply and you'll have} \\ w=\frac{24.8}{0.44522} \\ \\ w=55.701711\ldots \\ w\approx55.7\text{ (rounded to the nearest tenth)} \end{gathered}[/tex]

Given:

There is a cone given with radius 3 m and slant height 10 m

Required:

We need to find the surface area of given cone

Explanation:

surface area of cone is

[tex]SA=\pi r(l+r)=3.14*3(10+3)\approx122.46\text{ m}^3[/tex]

Final answer:

Surface area of cone is 122.46 cubic meter

Let the unknown be x

1) 4.65 + x =7.88

x = 7.88 - 4.65 = 3.23

The option is yes

2) x + 6.42 = 9.45

x = 9.45 - 6.42 = 3.03

The option is No

3)2.85 + x = 6.08

x = 6.08 -2.85 = 3.23

The option is Yes

4) x + 8.49 = 10.72

x = 10.72 - 8.49 =

Answer

The client would make a call of 400 minutes for the cost of the two plans to be equal

Step-by-step explanation:

Let C be the cost

Let x be the number of minutes of call

For the first plan

The company charge $0.18 for each minute

Let the total cost

C = 0.18 * x

C = 0.18x -------------- equation 1

The second plan

The second plan has a monthly charge of $20 and an additional $0.13 for each minute call

C= 20 + 0.13 * x

C = 20 + 0.13x -------------------- equation 2

To know the number of minutes that will make the cost of the plan equal, then, we need to combine the two equations

0.18x = 20 + 0.13x

Subtract 0.13x from both sides

0.18x - 0.13x = 20 + 0.13x - 0.13x

0.05x = 20

Isolate x by dividing through by 0.05

0.05x / 0.05 = 20/0.05

x = 400 minutes

Hence, the client would make a call of 400 minutes for the cost of the two plans to be equal

Determine the equation of a least square line:

[tex]\bar{y}=a+b\bar{x}[/tex]

where b = slope,

[tex]S_x=5.36,S_y=15.35,\bar{x}=1.75,\bar{y}=9.07[/tex]

[tex]\begin{gathered} b=\frac{SS_{xy}}{SS_x} \\ SS_{xy}=\sqrt[]{(5.36)(15.35)}= \\ S_x=5.36 \\ b=\frac{9.06995}{5.36}=1.69 \end{gathered}[/tex][tex]\begin{gathered} a=y-bx \\ a=9.07-1.69(1.75) \\ a=9.07-2.9237 \\ a=6.1463 \end{gathered}[/tex]

Therefore the equation of the least square line:

[tex]\begin{gathered} \bar{y}=a+b\bar{x} \\ \bar{y}=6.15+1.69x \end{gathered}[/tex]

To solve the exercise, you can first graph the points to see if they have a linear relationship, that is, if all the points are on the same line. So, you have

Since the relationship of the points is linear, then you can take two of the points through which the line passes, find the slope of the line, and then use the formula point-slope.

The formula for the slope is

[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1),(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex]

If for example, you take the points

[tex]\begin{gathered} (x_1,y_1)=(2,9) \\ (x_2,y_2)=(6,-7) \end{gathered}[/tex]

You have

[tex]\begin{gathered} m=\frac{-7-9}{6-2} \\ m=\frac{-16}{4} \\ m=-4 \end{gathered}[/tex]

Now using the formula point-slope, that is,

[tex]y-y_1=m(x-x_1)[/tex]

You have

[tex]\begin{gathered} y-9_{}=-4(x-2_{}) \\ y-9_{}=-4x-4\cdot-2 \\ y-9_{}=-4x+6 \\ \text{ Add 9 }to\text{ both sides of the equation} \\ y-9+9=-4x+6+9 \\ y=-4x+17 \end{gathered}[/tex]

Therefore, the equation representing the values ​​in the table is

[tex]y=-4x+17[/tex]

Ok, so

First of all, remember that the equation of any circumference has the form:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where:

[tex]C(h,k)[/tex]

Is the center, and r is the radius.

In this problem, we got that the center of the circumference is located in the point (7 , -24). We also know that this circumference passes through the origin.

Remember that the radius, is the distance from the center of the circumference, to any point of it. In this case, to find the radius, we have to find the distance between the points (7,-24) and (0,0), using the following formula:

Given two points:

[tex](x_1,y_1);(x_2,y_2)[/tex]

The distance between them is given by:

[tex]D=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

If we replace our values, we got that:

[tex]\begin{gathered} D=\sqrt[]{(0-(-24))^2+(0-7)^2} \\ D=\sqrt[]{(24)^2+(-7)^2} \\ D=\sqrt[]{576+49} \\ D=\sqrt[]{625} \\ D=25 \end{gathered}[/tex]

We got that the distance is 25, so, the radius is 25.

Then, replacing in the general equation of a circumference:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(Our values are):

[tex]\begin{gathered} h=7 \\ k=-24 \\ r=25 \end{gathered}[/tex]

This is;

[tex]\begin{gathered} (x-7)^2+(y-(-24))^2=(25)^2 \\ (x-7)^2+(y+24)^2=625 \end{gathered}[/tex]

Therefore, the correct answer is C. (x−7)^2+(y+24)^2=625

We know that

The initial height is 20 feet above the ground.

The function to model the velocity is

[tex]v(s)=60s[/tex]

Where s represents the distance in feet.

Mathematically, this function has all real numbers as a domain. However, that will no make sense for this situation, because it would use negative numbers for the distance s which does not make sense.

Therefore, the domain, in this case, would be all real numbers greater than or equal to zero, but less than or equal to 20.

The reason for this domain is that the ball will go from 20 feet above the ground to zero feet on the ground.

Using interval notation would be

[tex]D\colon\lbrack0,20\rbrack[/tex]

In the given map, the domain is the Weight.

Thus, all values in the choices that are under the table of the Weight are Domains.

Therefore, the answers (Domains) are: 110, 130, and 140.

The rest of the choices are Ranges.

Arminda,

Operations with negative sign decrease the balance of a bank account

The addition sentence modeled is:

[tex](-4)+(-4)+(-4)=-12[/tex]

In the number line you can see the three segments of four units one after another.

The multiplication sentence is:

[tex]3\cdot(-4)=-12[/tex]

In the picture there are 3 segments of 4 units each one, the negative sign indicates the direction, to the left in this case.

Finally, we can see a division sentence in the number line:

[tex]\frac{(-12)}{(-4)}=3[/tex]

In the picture we can see that the lenght of all segments together is (-12) and there are 3 segments of length (-4) that enter into the (-12).

The perimeter P of a triangle is;

[tex]\text{Side A + Side B + Side C}[/tex]

Let side A be a. side B be b and side C be c;

[tex]\begin{gathered} a=2b \\ c=3+a=3+2b \end{gathered}[/tex][tex]\text{Perimeter P= 93ft}[/tex][tex]\begin{gathered} P=a+b+c \\ 93=2b+b+3+2b \\ 93-3=5b \\ 5b=90 \\ b=\frac{90}{5} \\ b=18ft \end{gathered}[/tex]

Then,

[tex]\begin{gathered} a=2b \\ a=2(18)_{} \\ a=36ft \end{gathered}[/tex]

So,

[tex]\begin{gathered} c=3+a \\ c=3+36 \\ c=39ft \end{gathered}[/tex]

The length of each of the sides is;

[tex]\begin{gathered} a=36ft \\ b=18ft \\ c=39ft \end{gathered}[/tex]

Given data:

The first expression is 1/4 x 36.

The second expression is 5/8 x 36.

The firts expression can be written as,

[tex]\frac{1}{4}\times36=9\ldots\ldots\text{.(I)}[/tex]

The second expression can be written as,

[tex]\begin{gathered} \frac{5}{8}\times36=\frac{5}{2}\times9 \\ =\frac{45}{2} \end{gathered}[/tex]

The 7/8 x 36 can be written as,

[tex]\frac{7}{8}\times36=(\frac{1}{4}\times36)\times\frac{7}{2}[/tex]

Substitute from equation (I).

[tex]\begin{gathered} \frac{7}{8}\times36=9\times\frac{7}{2} \\ =\frac{63}{2} \end{gathered}[/tex]

Thus, the value of firts expression is 9 and second expression is 45/2.

lateral surafce area formular

[tex]\begin{gathered} LA=ph \\ \text{where} \\ p=\text{perimeter of the base} \\ h=\text{height} \end{gathered}[/tex][tex]p=2+2+4+4=12[/tex][tex]h=6[/tex][tex]LA=12\times6=72\operatorname{cm}\text{ squared}[/tex]

He has 5 pennies and 5 nickels in his pocket.

If he pick two coins in a row, we have to compare the probabilities of getting two pennies or one penny and one nickel. We will assume that there is no reposition: the coin that is drawn is not put again in the pocket.

Probability of getting two pennies:

For the first draw, it has p=0.5 (50% of chances) of getting a penny, as there are 10 coins and 5 of them are pennies.

Then, for the second draw there is p=4/9=0.44 chances of getting a penny, as one has already been picked.

Then, the probability of getting two pennies in a row is:

[tex]P(2\text{ pennies})=0.5\cdot0.44=0.22[/tex]

Probability of getting one penny and one nickel:

For the first draw, we can get pennies or nickels. Both of them are valid, so we will have a probability of p=1 for the first draw.

Then, for the second draw, we have to pick the other category: if we had a penny in the first draw, we should get a nickel in the second one and, if we had a nickel in the first draw, we should get a penny in the second draw.

In both cases, there will be 5 coins of the other category out of the 9 remaining coins.

Then, the probability of success in the second draw is p=5/9=0.55.

Then, the probability of getting one nickel and one penny is:

[tex]P(1N\&1P)=1\cdot0.55=0.55[/tex]

Answer: it is more likely that he will pick out one penny and a nickel.

slope = y₂ -y₁ / x₂ - x₁

Let the given points be x₁ = 2 and y₁=3

slope = 3/4

substituting into the formula;

3/4 = y₂ - 3 / x₂ - 2

Which implies;

y₂ - 3 / x₂ - 2 = 3/4

Now let's plug in the point to see whether it satisfy the equation

Let's start with (6,6)

Plugging the above into the equation;

6 - 3 / 6 - 2 = 3/4

It satisfies the equation, hence (6,6) is the second point of the line

Following rules are followed while multiplying the integers,

1. If both the integers being multiplied are either positive, or both are negative, then the product will always be positive.

2. If one of the integers is positive while the other is negative, then the product will always be negative.

Following rules are followed while dividing integers, (the most important thing is to make sure that the denominator is non zero, otherwise the division will take indeterminate form)

1. If both the integers are either negative, or both are positive, then their quotient will always be a positive value.

2. If the integers being divided are of opposite sign, that is, one of them is negative while the other is positive, then the quotient of the two numbers will always be negative.

[tex]\begin{gathered} A^2+B^2=C^2 \\ 7^2+8^2=C^2 \\ 49+64=C^2 \\ C^2=113 \\ C=\sqrt[]{113} \\ \\ C=10.630145 \\ \\ C\approx10.6 \end{gathered}[/tex]

Given,

The weekly income of Marcus is $400 and 3% of sales.

The total sale of the week is $2500.

According to the question,

The income of the Marcus is calculated as,

[tex]\text{Income = salary +3 \% of sales}[/tex]

On substituting the values then,

[tex]\begin{gathered} \text{Income = \$400 +3 \% of \$}2500 \\ \text{Income = \$400 +}\frac{\text{3}}{100}\text{ }\times\text{ \$}2500 \\ \text{Income = \$400 +3 }\times\text{ \$}25 \\ \text{Income = \$400 + \$}75 \\ \text{Income = \$475 } \end{gathered}[/tex]

Hence, his earning for the week is $475.

Identify the values of a, b, and c, by comparing the given equation to the following.

[tex]ax^2+bx+c=0[/tex]

Thus, the value of a, b, and c are as follows.

[tex]\begin{gathered} a=2 \\ b=7 \\ c=5 \end{gathered}[/tex]

Substitute the values into the quadratic formula.

[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-7\pm\sqrt[]{7^2-4(2)(5)}}{2(2)} \end{gathered}[/tex]

Simplify the exponential expression.

[tex]x=\frac{-7\pm\sqrt[]{49^{}-4(2)(5)}}{2(2)}[/tex]

Multiply.

[tex]x=\frac{-7\pm\sqrt[]{49^{}-40}}{4}[/tex]

Subtract.

[tex]x=\frac{-7\pm\sqrt[]{9}}{4}[/tex]

Evaluate the radical expression.

[tex]x=\frac{-7\pm3}{4}[/tex]

Rewrite the equation in two separate equations.

[tex]\begin{gathered} x=\frac{-7+3}{4} \\ \\ x=\frac{-7-3}{4} \end{gathered}[/tex]

Simplify the numerators.

[tex]\begin{gathered} x=\frac{-7+3}{4}=\frac{-4}{4}=-1 \\ \\ x=\frac{-7-3}{4}=-\frac{10}{4}=-\frac{5}{2} \end{gathered}[/tex]

Thus,

[tex]x=-1,-\frac{5}{2}[/tex]

The formula for the surface area of rectangular prism is,

[tex]SA=2(l\cdot b+l\cdot h+b\cdot h)[/tex]

The formula for the suface area of triangula prism is,

[tex]\begin{gathered} SA=2\cdot\frac{1}{2}bh+l\lbrack a+b+c\rbrack \\ =bh+l\lbrack a+b+c\rbrack \end{gathered}[/tex]

The formula for the surface area of cylinder is,

[tex]SA=2\pi rh+2\pi(r)^2[/tex]

The formula for the surface area of cone is,

[tex]SA=\pi rl+\pi(r)^2[/tex]

The formula for the surface area of pyramid is,

[tex]\begin{gathered} SA=4\cdot\frac{1}{2}\cdot b\cdot h+b\cdot b \\ =2bh+b^2 \end{gathered}[/tex]

The formula for the surface area of sphere is,

[tex]SA=4\pi(r)^2[/tex]

From the figure in the question

using ratio of similar triangles

Given the intrustions we have

[tex]\frac{EC}{AE}\text{ = }\frac{BE}{ED}[/tex]

Therefore the correct option is option 4

The correct answer is to represent the negative root by i

Here, we want to use the complex number i to simplify the expression

Mathematically, the complex number i is simply the square root of -1

Thus, we have;

[tex]i\text{ = }\sqrt[]{-1}[/tex]

Answer:

The question is given below as

[tex]\tan(3x)=-\sqrt{3}[/tex]

Step 1:

Take the arctan of both sides

[tex]\begin{gathered} \tan(3x)=-\sqrt{3} \\ 3x=\tan^{-1}-\sqrt{3} \\ \tan^{-1}\sqrt{3}=60^0 \\ tan\text{ is \lparen-ve in the second and fourth quadrant\rparen} \\ hence \\ \theta=180-60^0=120^0 \\ \theta=360-60^0=300^0 \\ \frac{3x}{3}=\frac{120^0}{3},x=\frac{300}{3} \\ x=40^0,x=100 \\ x=\frac{2\pi}{9},x=\frac{5\pi}{9} \end{gathered}[/tex]

Hence,

The values of x are given below as

[tex]x=\frac{2\pi}{9}+\frac{\pi n}{3}[/tex]

where n could be, 1,2,3,4......

1 dollar is equivalent to 107.53 yen based on the exchange rate.

How to solve an equation

An equation is an expression that shows the relationship between two or more numbers and variables.

The exchange rate is given as

1 yen = $0.0093

Therefore the number of yen for one dollar is:

Yen = $1 * (1 yen / $0.0093) = 107.53

1 dollar is 107.53 yen

Find out more on equation at: https://brainly.com/question/2972832

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Given:

Required:

To find the coordinate point of U.

Explanation:

Now from the graph, we can say that the coordinate points of U are

[tex](5,5)[/tex]

Because, the at the point U the x-coordinate is 5 and the y-coordinate is 5.

Final Answer:

[tex](5,5)[/tex]

[tex]\frac{1}{8}\sin ^4(2x)+c[/tex]

Explanation

[tex]\int \sin ^3(2x)\cos (2x)dx[/tex]

Step 1

substitute

Let

[tex]\begin{gathered} u=\sin (2x) \\ \text{hence} \\ du=\cos (2x)\cdot2\cdot dx \\ du=2\cos (2x)dx \\ \text{divide both sides by 2} \\ \frac{du}{2}=\frac{2\cos(2x)}{2}dx \\ \frac{du}{2}=\cos (2x)dx \end{gathered}[/tex]

Step 2

now, replace using the new variable(u)

[tex]\begin{gathered} \int \sin ^3(2x)\cos (2x)dx \\ \int u^3\frac{du}{2} \end{gathered}[/tex]

take out the 1/2 from the integral

[tex]\begin{gathered} \int u^3\frac{du}{2} \\ \int u^3\frac{du}{2}=\frac{1}{2}\int u^3du \\ \frac{1}{2}\int u^3du \end{gathered}[/tex]

finally, solve the simple integral

and rewrite using the original variable( x)

so

[tex]\begin{gathered} \frac{1}{2}\int u^3du \\ \frac{1}{2}(\frac{u^4}{4})+c \end{gathered}[/tex]

rewrite using x

[tex]\begin{gathered} \frac{1}{2}(\frac{u^4}{4})+c \\ \frac{1}{8}(u^4)+c \\ \frac{1}{8}(\sin ^4(2x))+c \\ \frac{1}{8}\sin ^4(2x)+c \end{gathered}[/tex]

therefore, the answer is

[tex]\frac{1}{8}\sin ^4(2x)+c[/tex]

I hope this helps you

Given :

The angle of elevation from her position to the top of a tower is 32°.

The angle of elevation again from a point 50 m closer to the tower and finds it to be 52°.

The following figure represents the given situation :

Let the height of the tower h

And the distance between the tower and the second point = x

So, from the larger triangle :

[tex]\begin{gathered} \tan 32=\frac{h}{x+50} \\ \\ h=(x+50)\cdot\tan 32 \end{gathered}[/tex]

From the smaller triangle :

[tex]\begin{gathered} \tan 52=\frac{h}{x} \\ \\ h=x\cdot\tan 52 \end{gathered}[/tex]

So,

[tex](x+50)\cdot\tan 32=x\tan 52[/tex]

solve for x:

[tex]\begin{gathered} x\cdot\tan 32+50\tan 32=x\cdot\tan 52 \\ 50\cdot\tan 32=x\cdot\tan 52-x\cdot\tan 32 \\ 50\cdot\tan 32=x\cdot(\tan 52-\tan 32) \\ \\ x=\frac{50\cdot\tan 32}{\tan 52-\tan 32}\approx47.7 \end{gathered}[/tex]

so, the height h will be :

[tex]h=x\cdot\tan 52=47.7\cdot\tan 52\approx61m[/tex]

So, the height of the tower​ = 61 m

The equation of the line in Slope-Intercept form is the following:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

In this case, you have the following equation of a line:

[tex]2x+3y=10[/tex]

To write it in Slope-Intercept form, you must solve for "y":

[tex]\begin{gathered} 2x+3y=10 \\ 3y=-2x+10 \\ y=-\frac{2}{3}x+\frac{10}{3} \end{gathered}[/tex]

So you can see that its slope is:

[tex]m_1=-\frac{2}{3}[/tex]

The slopes of perpendicular lines are opposite reciprocals, then you can determine that the slope of the other line is:

[tex]m_2=\frac{3}{2}[/tex]

You can see in the picture that the only equation that has this slope is the one shown

Given the right triangle:

ABC

Where angle B is the right angle.

Let's complete the given statement.

To find where the center of the circ*mscribed cirlce lies, let's first sketch the triangle and the circle.

A circ*mscribed circle is a circle which passes through all the vertices of a triangle.

By applying the converse of Thales theorem, we can see that the point D is center of the cirlce.

The point lies on line segment AC.

Also, the diameter of a circle is a line which passes through the center of the circle and touch the circumference at both ends.

Hence, line AC is the diameter of the circle.

Therefore, the complete statement is:

The center of the circ*mscribed circle of the triangle lies on segment segment AC, which is the diameter of the circle.

ANSWER:

The center of the circ*mscribed circle of the triangle lies on segment segment AC, which is the diameter of the circle.