(4x-5x)(x-3) use foil to multiply the binomial

ANSWER

[tex]( {y - 8)}^{2} = - 28(x + 5)[/tex]

EXPLANATION

The given parabola has directrix x=2.

This implies that, the parabola is opens in the direction of the negative x-axis because it must open in a negative direction to the directrix.

The equation of such parabola is of the form:

[tex]( {y - k)}^{2} = 4p(x - h)[/tex]

where (h,k)=(-5,8) is the vertex.

[tex] |p| = | - 2 - 5| = 7[/tex]

[tex]p = \pm7[/tex]

But the parabola opens to the left.

p=-7

The equation now becomes

[tex]( {y - 8)}^{2} = 4( - 7)(x - - 5)[/tex]

[tex]( {y - 8)}^{2} = - 28(x + 5)[/tex]

Answer:

  C)  f(x) = tan^-1(x)

Step-by-step explanation:

The question is equivalent to asking which trig function passes the horizontal line test over the domain (-90°, 90°). Both the sine function and the tangent function are defined on that domain and pass the horizontal line test.

The inverse sine function has a range of [-90°, 90°] (with square brackets, signifying the end points are part of the range). The inverse tangent function does not have a range that includes ±90°, so is a better match for the range in the question.

By dividing the total amount of £1890 by 1.125, we find that the original price the Jones family thought they would be paying for their holiday was £1680, before the 12.5% surcharge was added.

The Jones family encountered a last-minute surcharge on their holiday package with Shark Tours, which affected the total cost they paid. Given a 12.5% surcharge applied to their original cost, we can calculate the initial price by considering the final amount (£1890) to be 112.5% (100% + 12.5%) of the original price. To find the original price, we divide the total amount by 112.5% (or 1.125 as a decimal).

Original price = Total amount paid / Surcharge rate

We then have:

Original price = £1890 / 1.125

Original price = £1680

Therefore, the Jones family originally thought they would be paying £1680 for their holiday before the surcharge was added.

Answer:

option B

Step-by-step explanation:

Use a compass to draw a circle centered at B with a radius that is length of AB.

then  draw a circle centered at A with a radius that is length of AB

join the point of intersection of two circles through straight lines to point A and point B.

!

Answer with explanation:

Given a circle having center A, and radius equal to AB.

   One side of equilateral Triangle = AB

We have to draw two sides which have length equal to AB.

Draw a circle having center B and radius equal to AB.The Circle will pass through center A and cuts the Original circle at P.Join AP and BP.This is the equilateral triangle that we are interested in.

The Next in the construction of an equilateral triangle is:

Option B:→ Use a Compass to draw a circle centered at B with a radius that is equal to AB.

Answer:

20

Step-by-step explanation:

area of a rectangle is determined by length times width so 5 units lies between -7 and -2; and 4 units lie between -5 and -1

The area of the rectangle with given vertices is calculated as the product of the lengths of two adjacent sides, resulting in 20 square units.

To find the area of the rectangle with vertices at A(-7,-5), B(-2,-5), C(-2,-1), and D(-7,-1), you can calculate the lengths of adjacent sides and multiply them together. The length of side AB is the difference in the x-coordinates of A and B, which is |-2 - (-7)| = 5. Similarly, the length of side AD is the difference in the y-coordinates of A and D, which is |-1 - (-5)| = 4.

Therefore, the area of the rectangle is 5 units times 4 units, which equals 20 square units.

Answer:

btw way you all this means

Step-by-step explanation:

Two books cost 125 MDL together. Knowing that the price has risen by 10% and the other by 20%, after the cost of the cars costs 143.5 lei together with the initial price of each book

Answer:

8

Step-by-step explanation:

We want to evaluate the function f(x) = 3(log to the base 2 of x) + (log to the base 2 of 1/x) at x = 16.

Note that 2^4 = 16, so (log to the base 2 of 16) is 4.

Also note that 1/16 = 1/(2^4), so (log to the base 2 of 1/(2^4 is -4.

In summary, f(x) = 3(log to the base 2 of x) + (log to the base 2 of 1/x) at x = 16 is equal to 3(4) -4, or 8.

Answer:

A(50) = 10,000 . . . . . square feet

Step-by-step explanation:

Put 50 where w is in the function definition and do the arithmetic

A(50) = 250·50 -50^2 = 12500 -2500 = 10,000 . . . . square feet

Answer:

42 suitcases screened = x

Step-by-step explanation:

7/24 = x/144

7(144) = 24x

1,008 = 24x

42 = x

The most reasonable prediction for the number of suitcases should be 44.

The airport security randomly selected 24 suitcases from in the security like. Of these bags, they screened 7 suitcases.

Here we assume that no of suitcases be x

So,

[tex]7\div 24 = x\div 144[/tex]

7(144) = 24x

1,008 = 24x

42 = x

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Answer:

49.1%

Step-by-step explanation:

From the table, the number of male voters who are registered Democrats is given as 600. Moreover, the total number of male voters is given as 1222. Therefore, the probability that a randomly chosen male voter is a registered Democrat will be calculated as;

number of male voters who are registered Democrats /  total number of male voters

600/1222 = 0.491

As a percentage this becomes;

0.491 * 100 = 49.1%

Answer:

Answer is A

Step-by-step explanation:

Answer:

225/756

Step-by-step explanation:

275+256+225

=756

We want to know what are the odds of selecting a seventh grader which is:

225/756

Answer:

818.4 in²

Step-by-step explanation:

shaded region = area of sector - area of triangle

area of sector = area of circle × fraction of circle

A = π × 27.8² × [tex]\frac{150}{360}[/tex] ≈ 1011.65 in²

area of triangle = 0.5 × 27.8 × 27.8 × sin150° ≈ 193.21 in²

shaded region = 1011.65 - 193.21 ≈ 818.4 in²

ANSWER

The points (1,2) and (7,2) lie on the given curve.

EXPLANATION

The given parametric equations are:

[tex]x = 3t + 4[/tex]

and

[tex]y = 2 {t}^{2} [/tex]

We make t the subject in the first equation to obtain:

[tex]t = \frac{x - 4}{3} [/tex]

We substitute this into the second equation to get:

[tex]y =2{(\frac{x - 4}{3} )}^{2} [/tex]

When x=1,

[tex]y = 2 {(\frac{1 - 4}{3} )}^{2} = 2[/tex]

When x=2

[tex]y =2{(\frac{2- 4}{3} )}^{2} = \frac{8}{9} [/tex]

When x=7,

[tex]y =2{(\frac{7 - 4}{3} )}^{2} = 2[/tex]

Therefore the points (1,2) and (7,2) lie on the given curve.

The points are on a plane curve described by the following set of parametric equations are:(1,2), (7,2).

Given:

x= 3t+4 and y= 2t²

Hence:

x=3t +4 = t=(x-4)/3

y=2t² =y=2[(x-4)/3]

y=2[(x-4)/3]²

When x=1

y=2(1-4/3)²

y=2(-3/3)²

y=2(1)

y=2

When x=7

y=2(7-4/3)²

y=2(3/3)²

y=2(1)

y=2

Therefore the points are on a plane curve described by the following set of parametric equations are:(1,2), (7,2).

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Answer:

i need a picture of the graph but im pretty sure its graph B

Step-by-step explanation:

Answer:

11.

Step-by-step explanation:

Basically without calculus we have the answer. As ABC is a equilateral triangle we have that then medians cut each side at the half. So, as you can see in the picture, BD=x is a half of BC and ABC is equilateral so BC=AC=22. Then, BD=22/2=11.

Answer:

[tex]\large\boxed{(x-5)^2+(y+7)^2=36}[/tex]

Step-by-step explanation:

The equation of a circle in standard form:

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

(h, k) - center

r - radius

We hace the center at (5, -7) → h = 5 and k = -7.

The radius is equal to the distance petween the center and other point on the circumference of a circle.

The formula of a distance between two points:

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

Substitute the coordinates of the points (5, -7) and (5, -1):

[tex]d=\sqrt{(5-5)^2+(-1-(-7))^2}=\sqrt{0^2+6^2}=\sqrt{36}=6[/tex]

Therefore the equation of a circle is:

[tex](x-5)^2+(y-(-7))^2=6^2\\\\(x-5)^2+(y+7)^2=36[/tex]

Answer:

294.5 m²

Step-by-step explanation:

shaded region = area of major sector + area of triangle

central angle of major sector = 360° - 130° = 230°

area of sector = area of circle × fraction of circle

A = π × 11.1² × [tex]\frac{230}{360}[/tex]

   = [tex]\frac{x11.1^2(230)\pi }{360}[/tex] ≈ 247.3 m²

area of triangle = 0.5 × 11.1 × 11.1 × sin130° ≈ 47.2 m²

shaded area = 247.3 + 47.2 ≈ 294.5 m²

Answer:

294.5 m^2 to the nearest tenth.

Step-by-step explanation:

First work out the area of the blue sector (not including the triangle):

The measure of the large arc =  360 - 130 = 230 degrees and the area of the Whole circle is π(11.1)^2 so, by proportion:

Area of the large sector = 230/360 * π(11.1)^2

= 247.30 m^2.

The area of the triangle = 1/2 * 11.1^2 sin 130 = 47.19 m^2.

So the area of the whole shaded region is 247.30 + 47.19

=  294.49 m^2 (answer)

Answer:

No hardly any difference

Step-by-step explanation:

Because they had about the same number of (ML) drank by the dogs and cats regardless of color

Answer:

C

Step-by-step explanation:

Answer: C) 110

Step-by-step explanation:

Answer:

C:  (4, 8)

Step-by-step explanation:

Rewrite the given equation x² - 8x = -y² + 16y - 44 in std. form:

                                              x² - 8x + 16 - 16 + y² - 16y + 64 =  64 - 44,  or

                                                 (x - 4)²  + (y - 8)² = 64 - 44 + 16

         Comparing this to            (x - h)² + (y - k)² = 6²

we see that h = 4 and k = 8.  The radius is 6.  The center is at (4, 8) (Answer C).

Choice D, because you would have to divide 3 1/2 by 2 to find the answer

the rest are either subtraction or multiplication

Answer:

Option D  is best modeled with a division expression

Step-by-step explanation:

A)  How much does it cost to buy 3 and 1/2 pounds of apples at $2 per pound?

Cost of 1 pound = $2

Cost of 3 and 1/2 pounds  = [tex]2 \times 3.5[/tex]

B) B. How many apples are needed for 2 pies if the recipe uses 3 and 1/2 apples per pie?

1 pie requires 3.5 apples

So, 2 pies requires apples = [tex]3.5 \times 2[/tex]

C)  How many more apples are needed if a recipe uses 3 and 1/2 apples and you only have 2 apples?

Recipe requires 3.5 apples

You have 2 apples

More apples required = 3.5 - 2

D) . How many apples are in each pie if a total of 3 and 1/2 apples were used to bake 2 pies?

Apples required in 2 pies = 3.5

Apples required in 1 pie = [tex]\frac{3.5}{2}[/tex]

Hence Option D  is best modeled with a division expression

Answer:

  (-1, 1), (-1, 2), (0, 1)

Step-by-step explanation:

It appears as though letter designations have become confused. If not, your question answers itself, as a, b, c are given and you're asking for a, b, and c.

___

Reflecting the given points across the line y=-x transforms them like this:

  (x, y) ⇒ (-y, -x)

That is, you swap the coordinates and negate them both. The result will be as shown above and in the attachment.

The vertices of the reflected triangle ABC are A'(-1, 1), B'(-1, 2), and C'(0, -1).

Reflection of points involves transforming each point across a specified line or axis, resulting in a mirrored image. This geometric operation is fundamental in mathematics and is commonly used in various applications. To find the vertices of the reflected triangle ABC, we need to reflect each vertex across the line y=-x.

For vertex A (-1, 1), the reflection is (-1, 1).

Similarly, for vertex B (-2, 1), the reflection is (-1, 2).

And for vertex C (-1, 0), the reflection is (0, -1).

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Answer:

Step-by-step explanation:

First, i would add 15 until you get to 60, or divide.

15 / 60 = 4

Then multiply 30 by 4:  30 X 4 =120.

120 is the awnser.

Answer:

Your answer should be 56

Marlena can choose 3 out of 8 essay questions in 56 different ways.

The question asked by the student is related to combinations in mathematics. Marlena must choose 3 out of 8 essay questions on her writing test. To determine how many ways Marlena can choose 3 questions, we use the formula for combinations:

C(n, k) = n! / [k! * (n - k)!]

Where n is the total number of items to choose from (in this case, 8 questions), and k is the number of items to choose (3 questions). The symbol '!' represents a factorial, which is the product of all positive integers up to that number. So we calculate as follows:

This simplifies to:

C(8, 3) = (8*7*6) / (3*2*1) = 56

Therefore, Marlena has 56 different ways to choose 3 out of the 8 essay questions.

Answer:

Option B. Area = 30 Perimeter = 22.31

Step-by-step explanation:

step 1

Find the measure of the sides of the pentagon

Observing the graph

AE= 5 units

ED ----> Applying Pythagoras theorem

ED²=2²+3²=13

ED=√13 units

DC=3 units

BC=4 units

AB ---->Applying Pythagoras theorem

AB²=3²+6²=13

AB=√45 units

step 2

Find the perimeter

P=AE+ED+DC+BC+AB

substitute

P=5+√13 +3+4+√45=22.31 units

step 3

Find the area

The area of the figure is equal to the area of two trapezoids

so

A=(1/2)(2+5)(6)+(1/2)(6+3)(2)=21+9=30 units²

Final answer:

To find the total cost of a CD with a 20% discount and 8% sales tax, calculate the discount on the original price, subtract it to find the discounted price, then add the sales tax to this discounted price. The total cost comes out to $12.10.

Explanation:

Calculating the Total Cost of a CD Including Discount and Sales Tax

Firstly, to determine the sale price of the CD that usually sells for $14.00 with a 20% discount, we apply the discount percentage to the original price. We convert 20% to its decimal form, which is 0.20, and multiply by $14.00 to find the amount discounted: $14.00 × 0.20 = $2.80. Subtracting this discount from the original price, $14.00 - $2.80, gives us the discounted price of the CD, which is $11.20.

Next, to calculate the total cost including a sales tax of 8%, we first convert the tax rate to its decimal form, 0.08, and multiply it by the discounted price: $11.20 ×0.08 = $0.896. Rounding to the nearest cent, the sales tax is approximately $0.90. Adding the sales tax to the discounted price, $11.20 + $0.90, gives us the total cost of the CD, which is $12.10.

Therefore, the total price of the CD, including the 20% discount and the 8% sales tax, is $12.10.

Answer:

D.

Step-by-step explanation:

Use the equation m=y2-y1/x2-x1 to get the equation of both lines. Then, substitute numbers in to get the y-intercept. For example, for line A, you get y=4x+8. This is because 12-0/1--2 = 12/3 or 4. Then, do 12=4(1)+b. 12-4 = 8, so b equals 8. Do the same for the other line. Then, use the substitution method. This is where you take both equations and combine them without using y. For example, -2x+12=4x+8. You add 2x to 4x and get 6x. Then, you subtract 8 from 12 and get 4. We get x=4/6, which simplifies into 2/3. Then, you substitude that into one of the equations. 2/3 times 4 is 8/3 and add 8 to it. Multiply 8 by 3 to get that amount in thirds. You will get 8/3 plus 24/3 to get 32/3 as your y-value.

To find where two lines intersect, you set their equations equal to each other to solve for x, then substitute x into one equation to solve for y. The point of intersection in the example is (0.67, 4.34).

To find the point where Line A intersects with Line B, you first need to write out the equations for both lines. Assuming you know the slope and y-intercept of each line, an equation for a line takes the form y = mx + b, where m is the slope and b is the y-intercept. For example, if Line A is y = 2x + 3 and Line B is y = -x + 5, you would set the two equations equal to each other, like this: 2x + 3 = -x + 5. Solving for x, you'd get x = 0.67. Then, you would substitute x into either line's equation for y (I'll use Line A): y = 2(0.67) + 3 = 4.34. So, the point of intersection would be (0.67, 4.34).

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For this case we must rewrite the following expression:

[tex]x ^ {\frac {9} {7}}[/tex]

By definition of properties of powers and radicals we have to:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, the expression can be rewritten as:

[tex]x ^ {\frac {9} {7}} = \sqrt [7] {x ^ 9}[/tex]

If we want to simplify:

[tex]\sqrt [7] {x ^ 9} = \sqrt [7] {x ^ 7 * x ^ 2} = x \sqrt [7] {x ^ 2}[/tex]

ANswer:

[tex]x ^ {\frac {9} {7}} = \sqrt [7] {x ^ 9} = x \sqrt [7] {x ^ 2}[/tex]

Answer:

The amplitude is 3 and the downward vertical translation is 4 ⇒ 3rd answer

Step-by-step explanation:

* Lets revise some facts about the cosine function

- The Amplitude of cos(x) is the height from the center line to the

 peak (or to the trough). Or we can measure the height from

 highest to lowest points and divide that by 2.

- The Vertical Shift is how far the function is shifted vertically from

  the usual position.

* Now lets solve the question

∵ y = cos(Ф)

- There is a change in amplitude, it becomes a

- There is a vertical translation by b units

∴ y = a cos(Ф) + d

* Now lets look to the graph to find a and d

- From the graph:

∵ The highest value is -1

∵ The lowest value is -7

∴ The amplitude a = (-1 - -7)/2 = (-1 + 7)/2 = 6/2 = 3

∵ The highest value of y = cos(Ф) is 1

∵ The amplitude is 3

∴ The highest value of y = acos(Ф) = 3

∵ The highest value of y = acos(Ф) + d is -1

∴ d = 3 - (-1) = 4 ⇒ means downward vertical translation by 4

∴ y = 3 cos(Ф) - 4

* The amplitude is 3 and the downward vertical translation is 4