Type the correct answer in the box. Use numerals instead of words.
Consider this expression.



When and , the value of the expression is

Answer:

Step-by-step explanation:

If you plot the focus and the directrix on a coordinate plane, because the parabola wraps itself around the focus away from the directrix, we know that this parabola opens to the left. That means its general form is

[tex]4p(x-h)=-(y-k)^2[/tex] where h and k are the coordinates of the vertex and p is the distance between the vertex and either the focus or the directrix because both distances are the same. Knowing that both distances are the same, it logically follows that the vertex is directly in between the focus and the directrix. So the vertex is at the origin, (0, 0). p is 2 because the vertex is at an x value of 0 and the directrix is at the x value of 2, and because the focus is at an x value of -2. Filling in the equation, then:

[tex]4(2)(x-0)=-(y-0)^2[/tex] which simplifies to

[tex]8x=-y^2[/tex] and, solving for x:

[tex]x=-\frac{1}{8}y^2[/tex]

Answer:

  GH = 16; CH = 12

Step-by-step explanation:

First of all, you need to understand the meaning of "perpendicular bisector." It means that GH is divided into two equal parts by line AC, and that AC makes a right angle to GH.

The right angle is marked.

(a) The length of one of the halves of GH is marked as being 8 units long, so the other half will also be 8 units long. Of course, the length of GH is the sum of its two halves:

  GH = GB +BH = 8 + 8

  GH = 16

__

(b) Triangles CBG and CBH share side CB, so have that length in common. They have equal lengths BG and BH because BC bisects GH. They have a right-angle at B in common, so can be considered congruent by SAS, the fact that two congruent sides have a congruent angle between them.

Since triangles CBG and CBH are congruent, their corresponding sides CG and CH are also congruent. Side CG is marked 12 units long, so CH will be 12 units long, also.

  CH = 12

You could shortcut all of the congruent triangle logic by recognizing that an altitude (CB) is a perpendicular bisector of the base (GH) if and only if the triangle is isosceles. The sides of an isosceles triangle are always congruent, so CG = CH = 12.

__

In part (c), you're supposed to choose possible theorems for demonstrating the congruence of the triangles we described above.

Answer:

[tex]15\sqrt{2}[/tex]      or       21.2132

Step-by-step explanation:

[tex]\sqrt{450}[/tex]

[tex]\sqrt{15^{2} }[/tex]   (root of a product is equal to the product of the roots of each factor)

[tex]\sqrt{15^{2} } \sqrt{2}[/tex]                (simplify)

[tex]15\sqrt{2}[/tex]    or   ≈ 21.2132

Answer:

[tex]15\sqrt{2}[/tex] or 21.213

Step-by-step explanation:

For radical form: think of multiples of 450. Think of a pair that contains one perfect square, particularly the higher, the better . These 2 numbers are 25 and 18. 25 is the perfect square number since the two numbers that multiply to be 25 is 5 and 5.

Now take the perfect square of 25 and put it outside of the radical. The 18 remains inside: [tex]5\sqrt{18}[/tex]

Now, since 18 is a high number that needs to get reduced, do the same for 18 as we did for 450--find two numbers, one of which is a perfect square. These two numbers are 9 and 2.

Now take the perfect square of 9. This is 3. Take it out of the radical so that only the two remains inside. The 3 will now multiply with the 5: [tex]5*3\sqrt{2}[/tex]

Multiply 5 and 3 to get 15. The 15 stays outside the radical. Your answer is:

[tex]15\sqrt{2}[/tex]

[tex]\dfrac{5\cdot10^6}{5\cdot10^4}=10^{6-4}=10^2=100[/tex]

Answer:

100 times more

Step-by-step explanation:

5*10^4 over 5*10^6 is 1/100

Answer:

31° change

Step-by-step explanation:

If we want to find the change between two numbers, we need to imagine it like a number line.

<-------------0------------->

Let's plot -7 and 24 on this number line.

<----------[tex]-7[/tex]--0------------24>

If we want to get from -7 to 0, we increase by 7. To get from 0 to 24, we increase by 24.

So the total change is [tex]7 + 24 = 31[/tex].

Hope this helped!

Answer:

√2=1.414

then :√8 +2√32 +3√128+4√50

√8=√2³ =2√2

2√32=√2^5 = 4*2√2 = 8√2

3√128 = 3√2^6*2=8*3√2 =24√2

4√50 =4√5²*2= 20√2

add results : 2√2+8√2 +24√2+20√2=54√2

x=7-4√3

√x+ 1/√x

√(7-4√3) +1/√(7-4√3) =

(8-4√3)/√(7-4√3)

(8-6.93)/√(7-6.93) = 4 ( after rounded to the nearest whole number)

4 is your answer

Answer:

2/5

Step-by-step explanation:

Good luck!

Answer:

$64

Step-by-step explanation:

She should pay the entire amount which is $17 + $36 + $11 = $64

Answer:

64

Step-by-step explanation:

yezzir

Answer:

20cm

Step-by-step explanation:

If each side of the square = 5 cm, 5 cm times 4 sides = 20 cm.

Answer:

P=20cm

Step-by-step explanation:

To find the perimeter of a square, you just add all the four sides.

Because it says the sides are 5cm, and squares always have the same length, you just:

5+5+5+6=20cm

So, the perimeter of this square is 20cm.

Hope this helps, and have a nice day:)

Well, in this case we can take a as the protagonist.

We can, for example, take the a in the first member of the disequation, the 2 in the second one, changing the signs

so

+ 2 > - a

a > - 2

In fact,

"If 2 > - a, then a > -2."

Answer:

m∠C = 102°

Step-by-step explanation:

The above diagram is a cyclic quadrilateral

Step 1

First we find m∠B

The sum of opposite angles in a cyclic quadrilateral is equal to 180°

m∠D + m∠B = 180°

m∠B = 180° - m∠D

m∠B = 180° - 80°

m∠B = 100°

Step 2

Since we have found m∠B

We can proceed to find the Angle outside to circle

m∠CDA = 2 × m∠B

m∠CDA = 2 × 100°

m∠CDA = 200°

m∠CDA = m∠CD + m∠DA

m∠DA = m∠CDA - m∠CD

m∠DA = 200° - 116°

m∠DA = 84°

Step 3

Find m∠DAB

m∠DAB = m∠DA + m∠AB

m∠DAB = 84° + 120°

m∠DAB = 204°

Step 4

Find m∠C

It you look at the cyclic quadrilateral properly,

m∠DAB is Opposite m∠C

Hence

m∠C = 1/2 × m∠DAB

m∠C = 1/2 × 204

m∠C = 102°

Therefore ,m∠C = 102°

Answer:

4550m ; 4

Step-by-step explanation:

Recall

1 hectometre = 100m

1 decameter = 10m

Distance from shore to center of island = 37hm

Another 85 decameter toward stge se direction

Therefore total metres it will travel in other to get to the treasure :

37 hectometre + 85 decameter

(37 * 100)m + (85 * 10)m

3700m + 850m = 4550m

In kilometers :

1000 meters = 1 kilometers

4550 meters =

(4550 / 1000)meters

= 4.55km

================================================

Explanation:

R is between Q and S and on segment QS, allowing us to say

QR + RS = QS

because of the segment addition postulate.

-------

Use substitution and solve for QR

QR + RS = QS

QR + 11 = 19

QR = 19 - 11 .... subtracting 11 from both sides

QR = 8

Answer:

The answer is below

Step-by-step explanation:

The weights of ice cream cartons produced by a manufacturer are normally distributed with a mean weight of 10 ounces and a standard deviation of 0.5 ounce. (a) What is the probability that a randomly selected carton has a weight greater than 10.21 ounces? (b) You randomly select 25 cartons. What is the probability that their mean weight is greater than 10.21 ounces

Answer:

Given that:

Mean (μ) = 10 ounces, standard deviation (σ) = 0.5 ounces.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score (z) is given by:

[tex]z=\frac{x-\mu}{\sigma} \\\\For\ a\ sample\ size(n):\\\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]

a) For x = 10.21:

[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{10.21-10}{0.5}=0.42[/tex]

From the normal distribution table, probability that a randomly selected carton has a weight greater than 10.21 ounces  = P(x > 10.21) = P(z > 0.42) = 1 - P(z < 0.42) = 1 - 0.6628 = 0.3372

b ) For x = 10.21 and n = 25

[tex]\sqrt{x} \sqrt{x} z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\z=\frac{10.21-10}{0.5/\sqrt{25 } }=2.1[/tex]

From the normal distribution table, probability that a randomly selected carton has a weight greater than 10.21 ounces  = P(x > 10.21) = P(z > 2.1) = 1 - P(z < 2.1) = 1 - 0.9826 = 0.0174

Answer:

1001.66 in²

Step-by-step explanation:

The following data were obtained from the question:

Pi (π) = 3.14

Slant height (l) = 18 in

Diameter (d) = 22 in

Surface Area (SA) =.?

Next, we shall determine the radius of the cone. This can be obtained as follow:

Diameter (d) = 22 in

Radius (r) =.?

Radius = diameter /2

Radius = 22/2

Radius (r) = 11 in.

Finally, we determined the surface area of the cone as follow:

Pi (π) = 3.14

Slant height (l) = 18 in

Radius (r) = 11 in.

Surface Area (SA) =.?

SA = πr² + πrl

SA = (3.14 × 11²)+ (3.14 × 11 × 18)

SA = (3.14 × 121) + 621.72

SA = 379.94 + 621.72

SA = 1001.66 in²

Therefore, the surface area of the cone is 1001.66 in²

Answer:

[tex]\large \boxed{2(x-9)}[/tex]

Step-by-step explanation:

Let the number be x.

The product of 2 and the difference of x and 9.

“product” is multiplication.

“difference” is subtraction.

[tex]2 \times (x-9)[/tex]

The mathematical expression is 2(n - 9) if the product of 2 and the difference of a number and 9.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

The product of 2 and the difference of a number and 9.

Let the number is n; n is the real number.

The difference of a number and 9 = n - 9

The linear expression can be defined as the relation between two variables, if we plot the graph of the linear expression we will get a straight line.

If in the linear expression, one variable is present, then the expression is known as the linear expression in one variable.

The product of 2 and (n - 9)

= 2(n - 9)

Thus, the mathematical expression is 2(n - 9) if the product of 2 and the difference of a number and 9.

Learn more about the expression here:

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Answer:

Step-by-step explanation:

[tex](8,9)=(x1,y1) \\ m=7 \\ y−y1=m(x−x1) \\ y−9=7(x−8)

[/tex]

[tex]y - 9 = 7x - 56 \\ y = 7x - 56 + 9 \\ y = 7x - 47[/tex]

This happens when

1 + a b = 17  ==>  a b = 16

With a and b both positive integers, and 16 = 2^4, we can have

• a = 1 and b = 16

• a = 2 and b = 8

• a = b = 4

and vice versa. So there are 5 possible ordered pairs.

Answer:

a.) For the Junior Varsity Team, mean would be the appropriate measure of center since the data is symmetric or well-proportioned while we should use standard deviation for getting the measure of spread since it also measures the center and how far the values are from the mean.

b.) For the Varsity Team, the median would be the appropriate measure of the center since the data is skewed left and not evenly distributed so median could be used since it does not account for outliers while we use IQR or interquartile range in measuring the spread of data since IQR does not account for the data that is skewed.

For the Junior Varsity Team, the mean would be the appropriate measure of the center since the data is symmetric or well-proportioned .

Median represents the middle value of the given data when arranged in a particular order.

Since the data for the Junior Varsity Team is symmetric or well-proportioned, the mean would be the best way to determine the center, and standard deviation, which also measures the center and how far the values deviate from the mean, should be used to determine the spread.

The median could be utilized for the Varsity Team since the data is not evenly distributed and skewed to the left, and it does not take into account outliers.

We can use the interquartile range (IQR) to quantify the spread of the data because IQR does not take into account the skewed data.

Therefore, the varsity squad competes in intercollegiate or international competitions on behalf of the high school or institution while we should use standard deviation for getting the measure of spread since it also measures the center and how far the values are from the mean.

Learn more about the Varsity team here

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Answer:

1:55 pm

Step-by-step explanation:

So, you arrive at 4: 15 pm in Orlando after a 2 hr and 20 minute flight from Houston.  So, lets start with the easy part: let's subtract the 2 hrs part.  

2 hrs earlier from 4:15 pm is 2:15 pm.

Then, you have to subtract the 20 minutes.  Well, it's quite obvious that if you left at 2:00 pm, that would be a total of 2 hrs and 15 minutes.  Just subtract the 15 minutes from the 2:15 pm.  However, it's 20 minutes, not 15, so you have to still subtract that last five minutes.  

So, 2:00 pm minus 5 minutes would equal 1:55 pm.

Answer:

[tex]1296x^3y^4[/tex]

Step-by-step explanation:

Given the terms:

[tex]144x^3y^2[/tex]

and [tex]81xy^4[/tex]

To find:

Greatest Common Divisor of the two terms or Least Common Multiple (LCM) of two numbers = ?

Solution:

First of all, let us find the HCF (Highest Common Factor) for both the terms.

i.e. the terms which are common to both.

Let us factorize them.

[tex]144x^3y^2 = \underline{3 \times 3} \times 16\times \underline x \times x^{2}\times \underline{y^{2} }[/tex]

[tex]81xy^4= \underline {3\times 3}\times 9 \times \underline{x} \times \underline{y^2}\times y^2[/tex]

Common terms are underlined.

So, HCF of the terms = [tex]9xy^2[/tex]

Now, we know the property that product of two numbers is equal to the product of the numbers themselves.

HCF [tex]\times[/tex] LCM = [tex]144x^3y^2[/tex] [tex]\times[/tex] [tex]81xy^4[/tex]

[tex]LCM = \dfrac{144x^3y^2 \times 81xy^4}{9xy^2}\\\Rightarrow LCM = 144x^3y^2 \times 9x^{1-1}y^{4-2}\\\Rightarrow LCM = 144x^3y^2 \times 9x^{0}y^{2}\\\Rightarrow LCM = \bold{1296x^3y^4 }[/tex]

Answer:

625

Step-by-step explanation:

250 × X = 2

X = 5

250 × 5 = 2

1250 = 2 after this step u divided it by 2

1250 ÷ 2

= 625

Answer:

20%

Step-by-step explanation:

1000×120%=1200

120-100=20

Answer:

Correct answer is a. 2x + 3 y = 9.

Step-by-step explanation:

Let the coordinates of centroid be (h,k)

{h/3 , (-2+k)/3}

h = (2 – 2 + a)/3 = a/3 ---eqn 1

k= ( - 3+ 1 + b )/3 = (-2 + b)/3 -----eqn 2

Where (x,y) are any point on the line 2x+3y=1

3h = a and 3k + 2 = b

From 2x +3y = 1,

Then, 2h +3k = 1, 3k = 1 - 2h -----eqn 3

b = 1 - 2h + 2 = 3 - 2h

also b = 3 - 2a/3

b = (9 -2a)/3

3b = 9 - 2a

3b + 2a = 9

Now (x,y) satisfy the point on the line 2x+3y=9

So the locus is 2x + 3 y = 9.

Answer:

Step-by-step explanation:

Hello,

First term is 2 * 3 * x * x * x

Second term is 2 * 2 * 2 * x * x

Last term is 2 * 2 * x

So we can factorise it as below.

[tex]\boxed{6x^3+8x^2-4x=2x(3x^2+4x-2)}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

The factor should be [tex]2x ( 3x^2 +4x -2 )[/tex]

Given that,

Based on the above information, the calculation is as follows:

[tex] 6x^3+8x^2-4x[/tex]

[tex]2x ( 3x^2 +4x -2 )[/tex]

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Answer:

A dodecahedron has 12 faces

Answer:

Answer is

Step-by-step explanation:

A dodecahedron has 12 faces.

Hope this helps....

Have a nice day!!!!

Answer:

1/r^7 + 1/s^12

Step-by-step explanation:

Since there is a negative exponent, the term becomes a fraction. As we do not know the value of the term, it remains in its variable form with a positive exponent

Answer:

n=   -9

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

5 + n

====   =   -1

4

Multiply both sides by 4

5 + n = - 1 * 4

5 + n = - 4

Subtract 5 from both sides

5-5 + n = - 4 - 5

n = - 9

Congratulations on being able to use latex.

Answer:

The equation which will give the value of x when solved is C. x + 20 = 120

x=100

Step-by-step explanation:

Total distance=120 miles

Distance covered=x miles

Distance remaining=20 miles

The equation is

Total distance=Distance covered + distance remaining

120 miles= x miles + 20 miles

120 miles - 20 miles = x miles

100 miles =x miles

Check:

Total distance=Distance covered + distance remaining

120 miles = 100 miles + 20 miles

120 miles =120 miles

The equation which will give the value of x when solved is C. x+20=120