What is the measure of angle ABC in the circle shown in the picture?

Answer:

Shifts it up c units.

Step-by-step explanation:

The '+ c'  will move the whole graph upwards c units.

By translation of axis, the effect of c on the graph of y=f(x) for the function y=f(x)+c is it shifts up the curve by c units.

The translation of axis on any curve y = f(x) is the shifting of the graph by a definite unit from the original equation or curve.

If the curve is given as y = f(x) ± a, then for +a , it shifts the curve on the graph upwards on y axis by a units and for -a, it shifts the curve on the graph downwards on y axis by a units.

The given function is y = f(x) and thus for the graph y = f(x) + c, from the principle of translation of axis, it shifts the curve upwards on y-axis by c units.

Therefore, by translation of axis, the effect of c on the graph of y=f(x) for the function y=f(x)+c is it shifts up the curve by c units.

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Answer:

Motorcyclist: 2 hours

Bus: 2.5 hours

Truck: 3 hours

Bicyclist: 7.5 hours

Step-by-step explanation:

If N || P and P bisects M then, line N must be perpendicular to line M (N ⊥ M) (option A).

How to determine the relationship between line N and line P?

From the given diagram we are told that line N is parallel to line P and line P is perpendicular to line M.

So line P bisect line M and it is also perpendicular to line M, we can deduce the following;

line N is perpendicular to line M

So based on the information given to us, we can only deduce the relationship between M, N and P.

Hence N must be parallel to P, then line P must be perpendicualr to line M and line N and line M must be perpendicular to each other.

For this case we must solve the following equation by completing squares:

[tex]x ^ 2 + 6x-6 = 0[/tex]

We add 6 to both sides of the equation:

[tex]x ^ 2 + 6x = 6[/tex]

We divide the middle term by 2, and square it:

[tex](\frac {6} {2}) ^ 2[/tex]

And we add it to both sides of the equation:

[tex]x ^ 2 + 6x + (\frac {6} {2}) ^ 2 = 6 + (\frac {6} {2}) ^ 2\\x ^ 2 + 6x + (3) ^ 2 = 6 + 9[/tex]

We rewrite the left part of the equation:

[tex](x + 3) ^ 2 = 15[/tex]

We apply root to both sides:

[tex]x + 3 = \pm \sqrt {15}[/tex]

We have two solutions:

[tex]x_ {1} = \sqrt {15} -3\\x_ {2} = - \sqrt {15} -3[/tex]

Answer:

[tex]x_ {1} = \sqrt {15} -3\\x_ {2} = - \sqrt {15} -3[/tex]

Answer:

[tex]x=-3\±\sqrt{15}[/tex]

Step-by-step explanation:

We have the following equation

[tex]x^2+6x-6=0[/tex]

To use the method of completing squares you must take the coefficient of x and divide it by 2 and square the result.

[tex](\frac{6}{2})^2=9[/tex]

Now add 9 on both sides of equality

[tex](x^2+6x+ 9)-6=9[/tex]

Factor the term in parentheses

[tex](x+3)^2-6=9[/tex]

Add 6 on both sides of the equation

[tex](x+3)^2-6+6=9+6[/tex]

[tex](x+3)^2=15[/tex]

Take square root on both sides of the equation

[tex]\sqrt{(x+3)^2}=\±\sqrt{15}[/tex]

[tex]x+3=\±\sqrt{15}[/tex]

Subtract 3 from both sides of the equation.

[tex]x+3-3=-3\±\sqrt{15}[/tex]

[tex]x=-3\±\sqrt{15}[/tex]

Step-by-step explanation:

If we graph elevation vs time, the rate of change is the slope of the line.

At t = 0, h = -90.

At t = 15, h = -20.

m = (-20 − (-90)) / (15 − 0)

m = 70/15

m = 4.67

The closest answer is B.  The elevator traveled upward at a rate of 4 feet per second.

Answer:

Point S is the endpoint of a ray.

Step-by-step explanation:

A ray is a line with a single endpoint (or point of origin) that extends infinitely in one direction. Point S is the endpoint for rays SR, SU, and ST.

The ray's endpoint is Point S.

Given is a figure of an angle S being divided into two angles by the ray SU,

We need to find the endpoint of the ray,

So,

A ray's endpoint is the singular location where the ray comes to an end.

A ray is a line that emanates from an initial point known as the endpoint or origin and travels endlessly in one direction.

A ray, as opposed to a line segment, has no set length and travels in one direction indefinitely.

A ray's terminus, which is also its beginning point, is typically identified as a single point in space.

A ray is a line that has a single terminus (or point of origin) and travels in a single direction indefinitely.

The intersection of rays SR, SU, and ST is at point S.

Hence the ray's endpoint is Point S.

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Answer:

y=-2x+13

Step-by-step explanation:

Slope-intercept form of a line is y=mx+b where m is slope and b is y-intercept.

The slope of y=-2x-2 is -2 since m=-2.

A line that is parallel to the given line is going to have the same slope.

So we already know the equation we are looking for should be in the form y=-2x+b.

We just to need to find b.

We can use the given point on our line do that.

5=-2(4)+b

5=-8+b

8+5=b

13=b

So the equation is y=-2x+13.

Answer:

y = -2x+13

Step-by-step explanation:

The slope of the original line is -2 so you take that and plug it in with the points (4,5) in point slope form to get y-5 = -2(x-4), then you simplify to get      y-5 = -2x+8 then y = -2x+13

Answer:

[tex]32\ hair\ ties[/tex]

Step-by-step explanation:

we know that

To make one hair ties is needed 3 3/8 inches of elastic

so

using proportion

Find out how many hair ties can you make with 9 feet of elastic

Remember that

[tex]1\ ft=12\ in[/tex]

Convert 9 ft to inches

[tex]9\ ft=9*12=108\ in[/tex]

Convert mixed number to an improper fraction

[tex]3\frac{3}{8}\ in=\frac{3*8+3}{8}=\frac{27}{8}\ in[/tex]

using proportion

[tex]\frac{1}{(27/8)}=\frac{x}{108}\\\\x=108*8/27\\\\x=32\ hair\ ties[/tex]

Answer:

(13/2,   -27/2)

Step-by-step explanation:

The midpoint is found by using

midpoint = (x1+x2)/2,  (y1+y2)/2

               = (15+-2)/2,  (-9+-18)/2

                 =13/2,   -27/2

[tex]h(k)=k^2-k\\\\h(10)=(10)^2-10=90[/tex]

Answer:

Step-by-step explanation:

The roots are very clear on the graph. I have left them unlabeled so that you can put the two points in.

The points are (-4,0) and (-2,0)

The graph was done on desmos which you can look up. The box in the upper left corner was filled with

y = x^2 + 6x + 8

Answer:

20 percent

Step-by-step explanation:

To find the percentage that were children, we take the number of children over the total and multiply by 100%

There are 240 children and 1200 total people

240/1200 * 100%

.2*100%

20%

Answer:

20 Percent.

Step-by-step explanation:

240:1200*100 =

(240*100):1200 =

24000:1200 = 20

Answer: x = -8

Step-by-step explanation:

First you change 1/4 to 2/8. Then you want to get all of your x values on one side. So, +5/8x to each side turning your equation into 7/8x+2= -5. Then -2 from each side. 7/8x= -7. Finally get your variable by itself. Divide each side by 7/8 or multiple each side by its reciprocal (8/7)  

Answer:

8.6%

Step-by-step explanation:

To find the percent change, you will need to compute the positive difference and then divide the difference by the original (the older amount).

So the positive difference will be obtain by doing larger minus smaller:

 6300

- 5800

-----------

   500

The older amount was 5800.

So 500/5800 is the answer as a un-reduced fraction.

I'm going to reduce it by dividing top and bottom by 100:

500/5800  = 5/58

5/58 is the answer as a reduced fraction.

5 divided by 58 gives=0.086206897  in the calculator .

Approximately 0.0862 is the answer as a decimal.

To convert this to a percentage, multiply it by a 100:

8.62%

Rounded to the nearest tenths is 8.6%

-------------

So 5800+5800(.0862) should be pretty close to 6300 (not exactly though since we rounded).

5800+5800(.0862)=6299.96 using the calculator.

Answer:

B

Step-by-step explanation:

Given

24 + 15 ← factor out 3 from each term

= 3(8 + 5)

As a check

24 + 15 = 39 and

3(8 + 5) = 3 × 13 = 39

Hence 24 + 15 = 3(8 + 5) → B

F(x) = -3x + 3  

replace x in the equation with -1:

F(-1) = -3(-1) + 3

Simplify:

f(-1) = 3+3

f(-1) = 6

Answer:

[tex]\boxed{OY = 6.35 m} \\\boxed{AY=19.05 m}[/tex]

Step-by-step explanation:

The centroid of a triangle always cuts a triangle perfectly at 2/3.

What I mean by this is that the line that touches the tip of the triangle and touches the median of the base is cut into one third and its other part is cut into two thirds of the whole segment. This segment is AY.

Knowing this, I can tell that OY is 1/3 of the length of AO, which is given to be 12.7 m.

To find OY, make an equation where AO and OY add up to AY.

The variable x represents the length of AY, and 1/3x represents the length of OY (because it is one-third of AY).

Solve the equation by subtracting 1/3x from both sides.

Divide both sides by 2/3.

Now we know the length of AY (x). To find the length of OY substitute this value of x into 1/3x, which represents OY.

[tex]\frac{1}{3} (19.05)[/tex]

This gives us 6.35, which is the length of OY.

The final answers are:

Answer: Second option.

Step-by-step explanation:

Given a Quadratic equation in the form:

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

It can be solve with the Quadratic formula. This is:

[tex]x=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]

In this case, given the Quadratic equation:

[tex]3x^2=20-7x[/tex]

You can rewrite it in the form [tex]ax^2+bx+c=0[/tex]:

- Subtract 20 from both sides of the equation:

[tex]3x^2-20=20-7x-20\\\\3x^2-20=-7x[/tex]

- Add [tex]7x[/tex] to both sides of the equation:

[tex]3x^2-20+7x=-7x+7x\\\\3x^2+7x-20=0[/tex]

Therefore, you can identify that:

[tex]a=3\\b=7\\c=-20[/tex]

Answer:

option B. a=3, b=7, c=-20

I just took the test :)

Step-by-step explanation:

Answer:

0.0203 meters

Step-by-step explanation:

If a coral reef grew 20.3 mm taller, it grew 0.0203 meters taller.

20.3 mm = 0.0203 meters

The coral reef grew by 20.3 millimeters last week, which is equivalent to 0.0203 meters. This is calculated by dividing the millimeters by 1000, as there are 1000 millimeters in a meter.

The amount of growth in the coral reef's height can be converted from millimeters to meters by using the conversion ratio of 1 meter being equal to 1000 millimeters. So, to find out how much the coral reef grew in meters, we would take the growth in millimeters (20.3 mm) and divide by 1000.

The calculation would be like this: 20.3 mm / 1000 = 0.0203 meters.

So, the coral reef grew by 0.0203 meters last week.

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[tex]\dfrac{6!}{2!2!}-1=\dfrac{3\cdot4\cdot5\cdot6}{2}-1=180-1=179[/tex]

The number of passwords she can create is an illustration of permutations.

The number of ways to create the password is 179

The password is given as: ELLIE9

The number of characters in the password is:

[tex]n = 6[/tex]

L and E are repeated twice.

So, we have

[tex]L = 2[/tex]

[tex]E = 2[/tex]

The number of new passwords to create is then calculated as:

[tex]Passwords = \frac{n!}{L!E!} - 1[/tex] --- 1 represents the current password

This gives

[tex]Passwords = \frac{6!}{2!2!} - 1[/tex]

Expand

[tex]Passwords = \frac{6 \times 5 \times 4 \times 3 \times 2!}{2! \times 2 \times 1} - 1[/tex]

[tex]Passwords = \frac{6 \times 5 \times 4 \times 3 }{2 \times 1} - 1[/tex]

Simplify

[tex]Passwords = 180 - 1[/tex]

Subtract

[tex]Passwords = 179[/tex]

Hence, the number of ways to create the password is 179

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Answer:

d

Step-by-step explanation:

3×3×3 is 27 so that's the answer

Answer:

B. 55°

Step-by-step explanation:

Note that the total angle measurements of a triangle is = 180°.

Add all the measurements together:

40 + y + 30 + y = 180

Simplify. Combine like terms:

(40 + 30) + (y + y) = 180

70 + 2y = 180

Isolate the y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First subtract, then divide.

Subtract 70 from both sides:

70 (-70) + 2y = 180 (-70)

2y = 180 - 70

2y = 110

Divide 2 from both sides:

(2y)/2 = (110)/2

y = 110/2

y = 55

B. 55° is your answer.

~

Answer: The answer is B, 55 degrees.

Step-by-step explanation:

You substitute 55 into y, making it 55+85, +55, +40, making it 180 degrees. Since all sides in a triangle add up to 180, B is your correct answer.

Hope that helps!

Answer:

(3,9)

Step-by-step explanation:

This is a quadratic equation.

A quadratic in standard form is [tex]y=ax^2+bx+c[/tex].

If we compare [tex]y=ax^2+bx+c[/tex] to [tex]y=6x-x^2[/tex], we see there [tex]c=0,b=6,a=-1[/tex].

Now to find the vertex, we first find the x-coordinate of the vertex which is:

[tex]\frac{-b}{2a}[/tex].

So now plug in our values:

[tex]\frac{-6}{2(-1)}=\frac{-6}{-2}=3[/tex]

So the corresponding y-coordinate can be found by the equation that relates x to y:  [tex]y=6x-x^2[/tex].

So we are plugging in 3 where we see x:  [tex]y=6(3)-3^2=18-9=9[/tex].

So the vertex is (3,9).

Answer:

(0,3)

Step-by-step explanation:

The x-intercept is the point in the graph where x=0.  On the graph you can see that when x=0, y=3.  Therefore our coordinate is (0,3)

Our coordinate pair in the graph is (0,3)

The x-intercept of a line occurs where the line intersects the x-axis, meaning the y-coordinate is zero. In the provided graph, when x equals zero, the corresponding y-value is three. Thus, the coordinate pair (0,3) represents the point where the line intersects the x-axis. This result indicates that when x equals zero, the line crosses the y-axis at a height of three units.

To find the x-intercept, one sets y equal to zero and solves for x. In this case, when y equals zero, there is no such point on the line, so the x-intercept does not exist. Therefore, the coordinate (0,3) accurately identifies the x-intercept of the given line, demonstrating the point where it intersects the x-axis on the graph.

[tex]\bf \cfrac{\sqrt{12x^8}}{\sqrt{3x^2}}~~ \begin{cases} 12=&2\cdot 2\cdot 3\\ &2^2\cdot 3\\ x^8=&x^{4\cdot 2}\\ &(x^4)^2 \end{cases}\implies \cfrac{\sqrt{2^2\cdot 3(x^4)^2}}{\sqrt{3x^2}}\implies \cfrac{2\stackrel{x^2}{~~\begin{matrix} x^4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} ~~\begin{matrix} \sqrt{3} \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ ~~\begin{matrix} \sqrt{3} \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 2x^2[/tex]

Answer:

2x^3 (C on edge)

Step-by-step explanation:

Answer:

The slope is -3/2.

Step-by-step explanation:

Hint: slope formula:

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{rise}{run}[/tex]

[tex]\displaystyle \frac{0-(-6)}{(-4)-0}=\frac{6}{-4}=\frac{6\div2}{-4\div2}=\frac{3}{-2}=-\frac{3}{2}[/tex]

[tex]\Large \textnormal{Therefore, the slope is -3/2.}[/tex]

Answer:

y=(-3/2)x+-6

or

y=(-3/2)x-6

Step-by-step explanation:

We are going to use slope-intercept form to find the equation for this line.

y=mx+b is slope-intercept form where m is the slope and b is the y-intercept.

y-intercept means where it crosses the y-axis; the x will be 0 here.  Look the question gives us the y-intercept which is -6.

So we already know b which is -6.

y=mx+-6  

Instead of finding the slope using the slope formula which you could.

I'm going to plug in the point (-4,0) into y=mx+-6 to find m.

So replace x with -4 and y with 0 giving you:

0=m(-4)+-6

0=-4m-6

Add 6 on both sides:

6=-4m

Divide both sides by -4:

6/-4=m

Reduce the fraction:

-3/2=m

The slope is -3/2.

Again you could use the slope formula which says [tex]m=\frac{y_2-y_1}{x_2-x_1} \text{ where } (x_1,y_1) \text{ and } (x_2,y_2) \text{ are points on the line}[/tex].

This is the same thing as lining the points up vertically and subtracting the points vertically then putting 2nd difference over first difference.  Like this:

(  0   , -6)

-( -4  ,   0)

---------------

  4        -6

The slope is -6/4 which is what we got doing it the other way.  

So the equation with m=-3/2 and b=-6 in y=mx+b form is

y=(-3/2)x+-6

or

y=(-3/2)x-6

let's say the amount purchased was "x", so then that's the 100%.

if we know that 400 is the 1¼% and "x" is the 100%, what is "x"?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 400&1\frac{1}{4} \end{array}\implies \cfrac{x}{400}=\cfrac{100}{1\frac{1}{4}}\implies \cfrac{x}{400}=\cfrac{100}{\frac{1\cdot 4+1}{4}}\implies \cfrac{x}{400}=\cfrac{\frac{100}{1}}{\frac{5}{4}} \\\\\\ \cfrac{x}{400}=\cfrac{\stackrel{20}{~~\begin{matrix} 100 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{1}\cdot \cfrac{4}{~~\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{x}{400}=80\implies x=32000[/tex]

-4^2= 16

anytime you have a negative number squared it results in the positive version

ex. -4×-4 equals -16, except it should be positive instead of negative.

now 16+-10×-6

-10×-6=60

16+60=76

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Answer:

Step-by-step explanation:

[tex](-12.7y-3.1x)+5.9y-(4.2y+x)\\\\=-12.7y-3.1x+5.9y-4.2y-x\qquad\text{combine like terms}\\\\=(-12.7y+5.9y-4.2y)+(-3.1x-x)\\\\=-11y-4.1x[/tex]

The simplest form of given expression is  [tex]-11y-4.1x[/tex].

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given expression

[tex](-12.7y-3.1x)+5.9y-(4.2y+x)[/tex]

= [tex]-12.7y-3.1x+5.9y-4.2y-x[/tex]

Combine like terms

= [tex](-12.7y+5.9y-4.2y)+(-3.1x-x)[/tex]

= [tex]-11y-4.1x[/tex]

The simplest form of given expression is  [tex]-11y-4.1x[/tex].

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Answer:

13

Step-by-step explanation:

The magnitude of a vector < a, b > is

[tex]\sqrt{a^2+b^2}[/tex]

Given < - 12, 5 > then the length of the side is

[tex]\sqrt{(-12)^2+5^2}[/tex]

= [tex]\sqrt{144+25}[/tex]

= [tex]\sqrt{169}[/tex] = 13

Final answer:

The length of the triangle side represented by the vector 〈-12,5〉 is calculated using the Pythagorean theorem and is found to be 13 units.

Explanation:

The student has asked about finding the length of the side of a triangle given a vector from one vertex to another. The vector given is 〈-12,5〉. The length of this side can be calculated using the Pythagorean Theorem for the magnitude of a vector, which states that the magnitude is the square root of the sum of the squares of the vector's components. The formula for the magnitude (or length) of a vector 〉 a, b 〉 is √(a² + b²).

For the vector 〈-12,5〉, the calculation would be:

Which simplifies to:

Therefore, the length of the side of the triangle is 13 units.