A Vector T Has Initial Point (3.-6) And Terminal Point (4, -2).Write T In The Form T=ai+bj. (2024)

The two true statements are Option B and Option E.

A tangent to a circle is a line that touches the circle at exactly one point and does not lie inside the circle. Tangents to circles are the subject of several theorems and play an important role in many geometric constructions and proofs. A tangent always touches the circle at one point. A circle never intersects at two points. The tangents from the outer points to the circle are of equal length.

Calculation:-

A B is tangent to circle C

A E is tangent to circle C

A G is tangent to circle C

So the length of A F.F G = A E.D E.

and also Length of A G.D E = A E.F G

A straight line that intersects a circle at exactly one point is called a tangent, and the point of intersection is called a tangent. Tangents are always perpendicular to the radius drawn at the point of contact. A line that touches a circle at one point is called a tangent to the circle. The point where the tangent line and the circle intersect is called the tangent point. The tangent line is perpendicular to the radius of the intersecting circle.

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since the line is perpendicular the multiplication of the slopes must be -1, start by writing the perpendicular line in the form y=mx+b

[tex]\begin{gathered} 2x-y=4 \\ y=2x-4 \end{gathered}[/tex]

then solve to find the other slope

[tex]\begin{gathered} (2)\cdot m=-1 \\ m=-\frac{1}{2} \end{gathered}[/tex]

after having the slope use the point to find the y-intercept

[tex]\begin{gathered} 1=-\frac{1}{2}(4)+b \\ 1=-2+b \\ 1+2=b \\ 3=b \end{gathered}[/tex]

write all as a whole equation

[tex]y=-\frac{1}{2}x+3[/tex]

Let's see the child's shoulder height with each part of the statements.

• A child stands in line at the base of the ladder for a piece of playground equipment

The shoulder height is a few feet from the ground (child's original shoulder height). The graph should NOT start at 0. It should start at original shoulder height. The child stands at this position for some time.

• The child then climbs the ladder and plays in the area between the ladder

The climbing part models the height of the shoulder as going above. The graph should be sloping upwards, here.

The playing time in the area between the ladder is the same height of the child. So, a flat graph here.

• "...going down the slide"

This part, he goes down. So, the graph would slope downwards.

Now, looking at the answer choices, we can immediately eliminate 2nd and 3rd choice since they start at 0.

From First and Last choice, the correct answer is the first choice because it shows the "flat" part at the starting which corresponds to the time the child is waiting to go up the ladder.

You have the following equation:

[tex]6x+3y=12[/tex]

To determine both x and y intercepts, proceed as follow:

x-intercept: makes y = 0 and solve for x in the given equation

[tex]\begin{gathered} 6x+3(0)=12 \\ 6x=12 \\ x=\frac{12}{6}=2 \end{gathered}[/tex]

Hence, the xintercept is x = 2

y-intercept: makes x =0 and solve for y:

[tex]\begin{gathered} 6(0)+3y=12 \\ 3y=12 \\ y=\frac{12}{3}=4 \end{gathered}[/tex]

Hence, the y-intercept is y = 4

Area of an equilateral triangle =(√3 /4) *a^2

Where:

a = side length = 18 in

Replacing:

A = (√3 /4) *18^2 = 140.3in 2

Answer:

$6168.39

Explanation:

For a principal, P compounded continuously at a rate of r%, the amount in the account after t years is determined using the formula:

[tex]A(t)=Pe^{rt}[/tex]

Given:

• The starting amount, P = $5,000

,

• Interest Rate, r = 3% = 0.03

,

• Time(t) = 7 years

Substitute these values into the formula:

[tex]\begin{gathered} A(7)=5000\times e^{0.03\times7} \\ =\$6168.39 \end{gathered}[/tex]

Jack will have $6168.39 in his account after 7 years.

analyzing

the first option is not correct since 20 is negative and this would not match the sine function, the graph would be reversed

Second option isnt correct because the amplitude is 1 and the graph will not be as wide as it looks in the graph

The third option has the amplitude because the amplitude is 15+20=35 and on the graph the highest point is 35, now we need to check when x=0 because in the graph when x=0, y=5 so, replace

[tex]\begin{gathered} y=15\sin (\frac{\pi}{4}x+\frac{3\pi}{2})+20 \\ \\ y=15\sin (\frac{\pi}{4}(0)+\frac{3\pi}{2})+20 \\ \\ y=15\sin (\frac{3\pi}{2})+20 \\ \\ y=15(-1)+20 \\ \\ y=-15+20 \\ y=5 \end{gathered}[/tex]

the value is right

then the right option is third

Answer

f(5) = -32

Step-by-step explanation:

Given that

f(x) = - (7 + 5x)

find f(5)

This implies that x = 5

f(5) = - (7 + 5(5)

f(5) = - (7 + 25)

f(5) = -(32)

f(5) =-32

Hence, f(5) = -32

Given the formula

[tex]A=P(1+rt)[/tex]

We want to find the 'P' value given the following information:

[tex]\begin{gathered} A=2242 \\ r=0.06 \\ t=3 \end{gathered}[/tex]

To find 'P', we just need to make the substitutions in the right places. Change 'A' in the equation for our A value(2242), and do the same with the other parameters.

[tex]A=P(1+rt)\Leftrightarrow2242=P(1+0.06\cdot3)[/tex]

Now, we just need to do the calculations

[tex]\begin{gathered} 2242=P(1+0.06\cdot3) \\ 2242=P(1+0.18) \\ 2242=P\cdot1.18 \\ P=\frac{2242}{1.18}=1900 \end{gathered}[/tex]

Our P value is P = $1900.

Let's recall what is the scientific notation:

Scientific notation is the way that scientists easily handle very large numbers or very small numbers.

And now, let's convert this scientific notation to standard form:

9.647 x 10^7

We need to move the decimal point exactly the same quantity of positions to the right, because it's a positive exponent, than the exponent.

In this particular case the exponent is 7, therefore:

96,470,000 is the standard form. The decimal point was after the 9 and moved seven positions to the right.

Answer:

96,470,000 is the standard form

hope this helps

Step-by-step explanation:

One to one function : if no two elements in the domain of f correspond to the same element in the range of f .

The function g and h are one to one function and defined as;

g={(-1,8),(1,3),(6,4),(8,5),(9,-9)}

[tex]h(x)=\frac{x-8}{7}[/tex]

1)

[tex]\begin{gathered} g^{-1}(8) \\ \text{From the defination of function g;} \\ g=\text{ (-1,8)} \\ i\mathrm{}e\text{. it defined as g(-1) = 8} \\ \text{thus, -1=g}^{-1}(8) \\ g^{-1}(8)=-1 \end{gathered}[/tex]

2)

[tex]\begin{gathered} h^{-1}(x) \\ \text{The function h(x) defined as;} \\ h(x)=\frac{x-8}{7} \\ \text{Let h(x)=y} \\ y=\frac{x-8}{7} \\ \text{Solve for x;} \\ 7y=x-8 \\ x=7y+8 \\ h^{-1}(x)=7x+8 \end{gathered}[/tex]

3)

[tex]\begin{gathered} (h\circ h^{-1})(0) \\ (h\circ h^{-1})(x)=h(h^{-1}(x)) \\ (h\circ h^{-1})(x)=h(7x+8) \\ (h\circ h^{-1})(x)=\frac{(7x+8)-8}{7} \\ (h\circ h^{-1})(x)=\frac{7x+8-8}{7} \\ (h\circ h^{-1})(x)=\frac{7x+0}{7} \\ (h\circ h^{-1})(x)=x \\ \text{Substitute x = 0} \\ (h\circ h^{-1})(0)=0 \end{gathered}[/tex]

...

A ray is represented by a symbol of an one-sided arrow over the letters.

Since the ray starts at point B, the arrow will start at B and point towards point A.

So the correct option is 4.

ANSWER:

A. Equivalent

B. Equivalent

C. Not equivalent

D. Not equivalent

E. Not equivalent

F. Not equivalent

STEP-BY-STEP EXPLANATION:

A.

[tex]\begin{gathered} x+y+x+y=2(x+y) \\ 2x+2y=2(x+y) \\ 2(x+y)=2(x+y) \end{gathered}[/tex]

The pair is equivalent

B.

[tex]\begin{gathered} 5x+3x-2y=-2y+8x \\ -2y+8x=-2y+8x \end{gathered}[/tex]

The pair is equivalent

C.

[tex]\begin{gathered} 5(2x-3y)=10x-3y \\ 10x-15y=10x-3y \\ 10x-15y\ne10x-3y \end{gathered}[/tex]

The pair is not equivalent

D.

[tex]\begin{gathered} 4x-5y=5y-4x \\ 4x-5y\ne5y-4x \end{gathered}[/tex]

The pair is not equivalent

E.

[tex]\begin{gathered} 6x-8y=3(2x-4y) \\ 3(2x-\frac{8}{3}y)=3(2x-4y) \\ 3(2x-\frac{8}{3}y)\ne3(2x-4y) \end{gathered}[/tex]

The pair is not equivalent

F.

[tex]\begin{gathered} 9x+2y=11xy \\ 9x+2y\ne11xy \end{gathered}[/tex]

The pair is not equivalent

Step 1

State the expression for an exponential equation

[tex]y=ab^x[/tex]

Step 2

Test option 3 to see if it qualifies to be generated by an exponential equation

[tex]undefined[/tex]

[tex]\frac{12000}{x}\text{ (option 4)}[/tex]Explanation:

Amount needed for the bushels of soybeans = $12000

number of bushels of soybeans = x

Average price is the sum of all the cost divided by the number of units

[tex]\begin{gathered} \text{Average price = }\frac{\text{Total cost of production}}{nu\text{mber of bushels}} \\ \\ \text{Average price = }\frac{12000}{x} \end{gathered}[/tex]

Hence, the average price (in dollars) per bushel of the crop is 12000/x

calculate the supplement of a 112° angle.​

Remember that

If two angles are supplementary, then their sum is equal to 180 degrees'

so

x+112=180

solve for x

x=180-112

x=68 degrees

We have that

[tex]\frac{1}{3}=\frac{3}{9}[/tex]

as 3>2. We get tht

[tex]\frac{3}{9}>\frac{2}{9}[/tex]

so the chloe's family ate more than the Jess's family

To get the inverse of a statement, we take the negation of both the hypothesis and the conclusion.

I.e, if a statement goes thus:

"If a, then b."

The inverse will be "If not a, then not b."

Thus, the inverse of our statement is:

"If it is raining on Saturday then we will not go to the beach"

EXPLANATION

We first can draw the vertex in order to obtain the minimum value:

[tex]\mathrm{The\:vertex\:of\:an\:up-down\:facing\:parabola\:of\:the\:form}\:y=ax^2+bx+c\:\mathrm{is}\:x_v=-\frac{b}{2a}[/tex][tex]\mathrm{The\:parabola\:params\:are:}[/tex][tex]a=1,\:b=-7,\:c=10[/tex][tex]x_v=-\frac{b}{2a}[/tex][tex]x_v=-\frac{\left(-7\right)}{2\cdot \:1}[/tex]

Simplify:

[tex]y_v=-\frac{9}{4}[/tex][tex]\mathrm{Therefore\:the\:parabola\:vertex\:is}[/tex][tex]\left(\frac{7}{2},\:-\frac{9}{4}\right)[/tex]

Now, we need to compute the intercepts:

Plug y=0 into the equation and solve the resulting equation 0=x^2-7x+10:

The x-intercept are the following:

(2,0) and (5,0)

Identifying the y-intercept:

Plug x=0 into the equation and solve the resulting equation y=10 for y:

[tex]y=0^2-7*0+10[/tex]

Computing the power and multiplying terms:

[tex]y=10[/tex]

The y-intercept is at (0,10)

In conclusin, the appropriate option is OPTION B

According to the given graph, the function is not increasing from x = -1 to x = 1.

Remember that not increasing behavior is expressed as a horizontal line.

Hence, the interval is [-1, 1].[tex]-1\leq x\leq1[/tex]

A probability is the number of desired outcomes divided by the number of total outcomes. In the first case,

[tex]\begin{gathered} \#of\text{ desired outcomes = 4} \\ \#\text{ total outcomes = 8} \end{gathered}[/tex]

because there are 4 red zones from a total of 8. Then, we have

[tex]P(\text{red)}=\frac{4}{8}=\frac{1}{2}[/tex]

Similarly, for the green zone, we get

[tex]P(\text{green)}=\frac{3}{8}[/tex]

and for the yellow zone

[tex]P(\text{yellow)}=\frac{1}{8}[/tex]

and finally, for the not yellow zone

[tex]\begin{gathered} P(\text{not yellow)=1-P(yellow)=1-}\frac{1}{8} \\ P(\text{not yellow)=}\frac{7}{8} \end{gathered}[/tex]

Explanation

Part A

To solve the question, we will set up the equation to get the number of times it rebounds is less than 1 foot

[tex]H=10(\frac{14}{15})^n<1[/tex]

To solve for n, we will have to divide both sides by 10

[tex]\frac{10\left(\frac{14}{15}\right)^n}{10}<\frac{1}{10}[/tex][tex]\left(\frac{14}{15}\right)^n<\frac{1}{10}[/tex]

Applying exponents rule

[tex]\begin{gathered} n>\log _{\frac{14}{15}}\left(\frac{1}{10}\right) \\ \\ n>33.3742 \end{gathered}[/tex]

Therefore, the ball must bounce more than 33 times to attain a height of less than 1 foot

Thus, it has to bounce 34 times or more

Part 2

To get the how far it will travel before it comes to rest

We will have to get the sum of the heights as it tends to infinity

[tex]S=\frac{a}{1-r}=\frac{10}{1-\frac{14}{15}}=\frac{10}{\frac{1}{15}}=10\times15=150[/tex]

Thus, the ball will have to travel a distance of 150 feet before it comes to rest

~p means negation of statement p (then the car is black)

~p⇒q means negation of p only if q

Then ~p⇒q means that the car is black only if the car is not red.

The statement that is equivalent to that will be "In order for the car to be black, the car must not be red"

We have the following:

[tex]t=50+35\cdot v[/tex]

t = total, $190

v, number of visits,

replacing:

[tex]\begin{gathered} 190=50+35\cdot v \\ 35v=190-50 \\ v=\frac{140}{35} \\ v=4 \end{gathered}[/tex]

The answer is 4 visits

Given:

A quarterback throws a football with a velocity of 41 mph and a direction of 168°.

The wind on the field is 11 mph with a direction of 339°

So, there are 2 vectors:

[tex]\begin{gathered} v=41\angle168\degree \\ w=11\angle339\degree \end{gathered}[/tex]

We will find the resultant speed as the sum of the vectors v and w

[tex]\begin{gathered} R=v+w=41\angle168\degree+11\angle339\degree \\ \end{gathered}[/tex]

To find the sum of the vectors, convert from the polar form to the rectangular form:

[tex]\begin{gathered} R=(41\cos 168+11\cos 339)i+(41\sin 168+11\sin 339)j \\ R=-29.835i+4.582j \end{gathered}[/tex]

Now, we will convert from the rectangular form to the polar form to express the resultant as magnitude and angle:

[tex]\begin{gathered} |R|=\sqrt[]{(-29.835)^2+(4.582)^2}=30.185 \\ \theta=\tan ^{-1}\frac{4.582}{-29.835}\approx171.268 \end{gathered}[/tex]

So, the answer will be the second option: 30.185, 171°

An inverse function has this form:

[tex]\begin{gathered} y=\frac{k}{x},\text{ where k is a constant of variation.} \\ In\text{ this case is:} \\ g(n)=\frac{k}{n} \end{gathered}[/tex]

We know that g(n) =12 when n=2, so g(2) = 12. Then

[tex]\begin{gathered} g(2)=\frac{k}{2}\text{ = 12} \\ k=12\cdot2 \\ k=24 \end{gathered}[/tex]

So the general expression is

[tex]g(n)=\frac{24}{n}[/tex]

Then to find the value on n when g(n)=3

[tex]\begin{gathered} g(n)=\frac{24}{n}=3 \\ n=\frac{24}{3} \\ n=8 \end{gathered}[/tex]

So the answer is n=8.0

Expressing x> - 4 using interval notation

( -4, ∞ )

We are asked to use oo as ∞

so;

( - 4, oo)

To find:

Select the properties that are true.

Solution:

The square:

All sides are congruent, the square has four right angles, two pair of parallel sides.

The parallelogram:

Two pair of parallel sides.

Rhombus:

the rhombus has all sides are congruent, two pair of parallel sides.

Answer;

SYSTEM. Option B is correct

Explanations;

Linear equations are equations with the highest degree of 1. We can have a linear equation containing 2 or 3 variables or even more.

A typical example of a linear equation having two variables is 2x + y = 3 where x and y are the variables.

When we have two or more of these linear equations taken together, they become a system, hence, they are called SYSTEMS of linear equations.

Examples of two systems of linear equation is;

2x + 3y = 7

x - y = 8

This is a system of two equations containing two-variables

Another example of systems of linear equations containing 3-variables is;

a - b + c = 5

2a + 5b - c = 1

3a - 2b + 3c = 4

REmember that

if two lines are perpendicular, then the product of their slopes is equal to -1

in this problem we have

f (x) = -1/2x +7

the slope is m=-1/2

so

the slope of the perpendicular line is

m=2

therefore

an equation perpendicular to the given line is

y=2x

i need a point to calculate the complete equation of the line