What is the equation of the parabola with focus (1, -3) and directrix y = 22
A. y - 4x^2 +8x-21
B. y=2/3×^2-4/3×+7/6
C. y =-1/10×^2+1/5×-3/5
D. y=-3×^2+2x-2​

Answer:

4.12 kg

Step-by-step explanation:

Regular cakes:

1 dozen normal sponge cakes: 264 g plain flour

Vegetarian cakes:

1 dozen cakes: 264 g plain flour

4 eggs are replaced by 4 * 30 g of flour = 120 g flour

total flour for 1 dozen vegetarian cakes = 264 g + 120 g = 384 g

Proportion for regular cakes:

12 cakes to 264 g flour = 100 cakes to x grams flour

12/264 = 100/x

12x = 26400

x = 2200

2200 g flour for 100 regular cakes

Proportion for vegetarian cakes:

12 cakes to 384 g flour = 60 cakes to y grams flour

12/384 = 60/y

12y = 384 * 60

12y = 23040

y = 1920

1920 g flour for 60 vegetarian cakes

Total flour needed:

2200 g + 1920 g = 4120 g

4120 g * 1 kg/(1000 g) = 4.12 kg

Answer: 4.12 kg

Answer:

The answer is 20

Step-by-step explanation:

(Edge2020)

Answer:

Its A on edge

Step-by-step explanation:

i took the test. good luck guys!

Answer:

[tex]\boxed{3}[/tex]

Step-by-step explanation:

We can use ratios to solve since the sides are proportional.

[tex]\frac{18}{x} =\frac{48}{8}[/tex]

Cross multiply.

[tex]48x=18 \times 8[/tex]

Divide both sides by 48.

[tex]\frac{48x}{48} = \frac{18 \times 8}{48}[/tex]

[tex]x=3[/tex]

The value of x in the given triangle is 3.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Given are two similar triangles,

Therefore, they have the same ratio of corresponding sides

18/48 = x/8

x = 3

Hence, The value of x in the given triangle is 3.

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Circumference of the cylinder :

C = 2 x pi x r

C = 2 x 3.14 x 25 = 157 cm

Multiply the circumference by number of wraps:

157 x 50 = 7,850 cm long ( 78.5 meters)

Answer:

Step-by-step explanation:

Given two lines y=(3a+2)x-2 and 2y=(a-4)x+2, Since both lines are parallel to each other, this means that the slope of both lines are the same

Let's get the slope of both equation. For the first equation;

y=(3a+2)x-2

We can see that the equation is written in this form y = mx+c where m is the slope of the line. On comparison, the slope of the given line is 3a+2

Similarly for the second line;

2y=(a-4)x+2

Re-writing in the standard format we will have;

y = (a-4)x/2+2/2

y = (a-4)x/2 + 1

The slope of the second line is (a-4)/2

On equating the slope of both lines to get the value of 'a' we will have;

3a+2 = (a-4)/2

Cross multiplying

2(3a+2) = a-4

6a+4 = a-4

Collecting like terms;

6a-a = -4-4

5a = -8

a = -8/5

Hence the value of a is -8/5

Answer:

[tex]\frac{-89}{40}[/tex]

As a Proper Fraction: -2[tex]\frac{9}{40}[/tex]

Step-by-step explanation:

So i assume the fraction sits like this:

[tex]\frac{-5}{8}[/tex] + [tex]\frac{-8}{5}[/tex]

This essentially becomes:

[tex]\frac{-5}{8}[/tex]  -  [tex]\frac{8}{5}[/tex]

Now multiply the denominators for a LCM (Lowest common denominator)

8*5 = 40

And now multiply the top parts with the respective denominator (-5 * 5) and (8 * 8)

So Now you get

[tex]\frac{-25}{40}[/tex] -  [tex]\frac{64}{40}[/tex]

and now that u have same denominators, just subtract -25 - 64  and get -89

Final Simplified answer: [tex]\frac{-89}{40}[/tex]

As a Proper Fraction: -2[tex]\frac{9}{40}[/tex]

37.62202 sq units

First, calculate the areas of the separate triangles:

ABD = 20.19968 sq units

ACD = 17.46234 sq units

then add them to get 37.62202 sq units

Answer:

30.51 units^2

Step-by-step explanation:

Well to find the area of a triangle without height we use the following formula,

[tex]A = \sqrt{S(S-a)(S-b)(S-c)}[/tex]

To find S we use the following formula,

[tex]S = \frac{1}{2} (a+b+c)[/tex]

So a b and c are the sides of a triangle, we'll start with the left triangle.

S = 1/2(7 + 5.22 + 7.4)

S = 1/2(19.62)

S = 9.81

Now we can plug in 9.81 for S,

[tex]A = \sqrt{9.81(9.81-a)(9.81-b)(9.81-c)}[/tex]

[tex]A = \sqrt{9.81(9.81-7)(9.81-5.22)(9.81-7.4)}[/tex]

[tex]A = \sqrt{9.81(2.81)(4.59)(2.41)}[/tex]

[tex]A = \sqrt{9.81(31.083939)}[/tex]

[tex]A = \sqrt{304.93344159}[/tex]

[tex]A = 17.46234353086664[/tex]

But we can just simplify that to the nearest hundredth place which is,

17.46.

Now for the next triangle,

[tex]S = \frac{1}{2} (6.36 + 6.85 + 7.4)[/tex]

[tex]S = \frac{1}{2} (20.61)[/tex]

[tex]S = 10.305[/tex]

Plug in 10.305 for S,

[tex]A = \sqrt{10.305(10.305-6.36)(10.305-6.85)(10.305-7.4)}[/tex]

[tex]A = \sqrt{10.305(3.945)(3.455)(2.905)}[/tex]

[tex]A = \sqrt{10.305(16.534975)}[/tex]

[tex]A = \sqrt{170.392917375}[/tex]

A = 13.053463807549

We can round it to the nearest hundredth,

A = 13.05

So we just add 17.46 + 13.05

= 30.51 units^2

Thus,

the area of the figure is 30.51 units^2.

Hope this helps :)

Answer:

5

Step-by-step explanation:

We know that we have to add all numbers then divide it by how many numbers there are. So, 10 + 6 + 9 + 2 + 0 + 3 = 30.  30/6 = 5.  

Answer:

Step-by-step explanation:

[tex] \frac{x - 1}{x + 5} \times \frac{x + 1}{x - 5} [/tex]

To multiply the fraction, multiply the numerators and denominators separately

[tex] \frac{(x - 1) \times (x + 1)}{(x + 5) \times (x - 5)} [/tex]

Using [tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex] simplify the product

[tex] = \frac{ {x}^{2} - 1 }{ {x}^{2} - 25 } [/tex]

Hope this helps..

Best regards!!

Answer:

AC2  =  AB2 + BC2     --->     AC2  =  122 + 52     --->   AC  =  13

AD / AB  =  AB / AC     --->     AD / 12  =  12 / 13     --->     AD  =  144/13

DC  =  AC - AD     --->   DC  =  13 - 144/13     --->     DC  =  25/13

AD / DB  =  DB / DC     --->   DB2  =  AD · DC     --->     DB2  =  (144/13) · (25/13)  --->     DB  =  60/13

DB is the geometric mean of AD and DC.

Step-by-step explanation:

Answer:

1) rectangle

2) rectangle

Step-by-step explanation:

Any cross section of a rectangular prism is a rectangle.

Hope it helps <3

Answer:

since the top of the ladder is making the angle, the of the ladder's base from the building is our opposite and the ladder is the hypotnuse,

sin (32)=opp/hyp, 0.52=opp/25, opp=13 ft

Answer:

[tex]a_{n} = a + 2(n-1)[/tex]

Step-by-step explanation:

[tex]a_{5}= a_{1} + 4d \\4 = -4 +4d\\8= 4d\\d= 2\\\\Therefore \\a_{n} = a_{1} + 2(n-1)[/tex]

Answer:

2.09 seconds.

Step-by-step explanation:

We are given...

y = 70 feet

v0 = 0 feet/second

a = 32 feet/second^2

We need to find t using the following equation...

y = v0 * t + (1/2) * a * t^2

70 = 0 * t + (1/2) * 32 * t^2

70 = (1/2) * 32 * t^2

70 = 16t^2

16t^2 = 70

t^2 = 4.375

t = sqrt(4.375)

t = 2.091650066

So, it will take the toy about 2.09 seconds to hit the ground.

Hope this helps!

Answer:

0.99379

Step-by-step explanation:

The first thing to do here is to calculate the z-score

mathematically;

z-score = x-mean/SD/√(n)

From the question x = 9.5 ,

mean = 9, SD = 2 and n = 100

Plugging the values we have;

z-score = (9.5-9)/2/√(100) = 0.5/2/10 = 0.5/0.2 = 2.5

So the probability we want to calculate is;

P(z<2.5)

We use the standard table for this

and that equals 0.99379

Answer:

The central angle for the cheese sector would be 108 degrees.

Step-by-step explanation:

We know that a pi chart takes the form of a circle so the total angle measure is 360 degrees.

Now we want to find out what ratio of the pie chart that cheese takes up and apply it to the total degree measure.

30 of 100 students voted for cheese:

so the ratio would be 30/100 or 3/10

Now apply that to the total angle measure:

3/10*360 degrees= 108 degrees.

Answer:

[tex]\large \boxed{\sf \ \ \ -4x^2+8x-8 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex](f-g)(x)=f(x)-g(x)\\\\=3x-1 - (4x^2-5x+7)\\\\=3x-1-4x^2+5x-7\\\\=-4x^2+8x-8[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

[tex]Length = 25cm[/tex]

Step-by-step explanation:

Given

Brass Shape: Square

[tex]Density = 4.2g/cm^3[/tex]

[tex]Mass = 1.05kg[/tex]

[tex]Height = 4mm[/tex]

Required

Determine the length of the plate

First, we need to calculate the Volume of the Brass using

[tex]Density = \frac{Mass}{Volume}[/tex]

Make Volume the subject of formula

[tex]Volume = \frac{Mass}{Density}[/tex]

Substitute 1.05kg for Mass and 4.2g/cm³ for Density

[tex]Volume = \frac{1,05\ kg}{4.2\ g/cm^3}[/tex]

Convert 1.05 kg to grams

[tex]Volume = \frac{1.05 * 1000\ kg}{4.2\ g/cm^3}[/tex]

[tex]Volume = \frac{1050 \ kg}{4.2\ g/cm^3}[/tex]

[tex]Volume = \frac{1050 \ kg}{4.2\ g/cm^3}[/tex]

[tex]Volume = 250cm^3[/tex]

Next is to determine the Area of the brass;

[tex]Volume = Height * Area[/tex]

Substitute 250cm³ for Volume and 4mm for Height

[tex]250cm^3 = 4mm * Area[/tex]

Convert mm to cm

[tex]250cm^3 = 4 * 0.1cm * Area[/tex]

[tex]250cm^3 = 0.4cm * Area[/tex]

Divide both sides by 0.4cm

[tex]\frac{250cm^3}{0.4cm} = \frac{0.4cm * Area}{0.4cm}[/tex]

[tex]\frac{250cm^3}{0.4cm} =Area[/tex]

[tex]625cm^2 = Area[/tex]

[tex]Area = 625cm^2[/tex]

Lastly, we'll calculate the length of the brass

Since the brass is square based;

[tex]Area = Length^2[/tex]

Substitute 625cm² for Area

[tex]625cm^2 = Length^2[/tex]

Take square root of both sides

[tex]\sqrt{625cm^2} = Length[/tex]

[tex]25cm = Length[/tex]

[tex]Length = 25cm[/tex]

Hence, the length of the square brass is 25cm

Answer:

Step-by-step explanation:

PEMDAS - Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

We have to do operations by the Order of Operations(PEMDAS)

Parentheses:

           Addition/Subtraction:

            (7 - 1)

             (6)

16/4 + 56 - 6

Multiplication/Division

4 + 56 - 6

Addition/Subtraction

60 - 6

Answer:

(x - 2)(x + 2)

Step-by-step explanation:

(x - 2)(x + 2) = x² - (2)² [Since (a - b)(a + b) = a² - b²]

                   = x² - 4

There are two terms in this expression. Therefore, the give term is a binomial.

(2x - 1)(x + 4) = 2x(x + 4) - 1(x + 4) [Distributive property]

                    = 2x² + 8x - x - 4

                    = 2x² + 7x - 4

There are three terms in this polynomial. Therefore, the given polynomial is a trinomial.

(x + 4)(x + 1) = x(x + 1) + 4(x + 1)

                   = x² + x + 4x + 4

                   = x² + 5x + 4

This polynomial is having 3 terms therefore, it's a trinomial.

(m - 4)(m + 1) = m(m + 1) - 4(m + 1)

                     = m² + m - 4m - 4

                     = m² - 3m - 4

Therefore, this polynomial is a trinomial.

Since (x - 2)(x + 2) is a binomial, so this expression doesn't belong to this group.

Answer:

its D

Step-by-step explanation:

The approximate sum is 134.83

The correct option is (D).

What is series?

A series in math is simply the sum of the various numbers or elements of the sequence.

For example, to make a series from the sequence of the first five positive integers 1, 2, 3, 4, 5 we will simply add them up. Therefore 1 + 2 + 3 + 4 + 5 is a series.

A series in math is the sum of the terms in a sequence. The series and the sequence given in this example are almost identical. What differentiates the two is the addition of the + sign. Changing the comma to a plus sign changes the sequence into a series.

Suppose a person wanted to increase their level of fitness. The person decides to walk for 15 minutes the first day and increases the time spent walking by 5 minutes each day for the first week. The sequence that shows this example is

15, 20, 25, 30, 35, 40, 45

series used to find the answer is

15+20+25+30+35+40+45

Given:

[tex]\sum[/tex] (k =1 to 8) 5* (4/3)^(k-1)

So,

Putting values k=1 to 8 one by one then

= 5 + 20/3 + 80/9+0320/27+......+81920/2187

=294875/2187

=134.83

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Answer: 35.9

Step-by-step explanation:

The tree is approximately 35.979 feet tall, computed using the sine rule.

The sine rule in a triangle can be shown as this.

A triangle ABC, with the values of the side BC = a, CA = b, and AB = b, follows the rule by:

(Sin A)/a = (sin B)/b = (sin C)/c.

In the question, we are informed about Tasha who is willing to measure the height of a tree, which grows at an angle of 85° with respect to the ground. Also, we are informed that when Tasha is 80 feet away from the base of the tree, then the angle from the ground to the top of the tree is 25°.

We are asked to find the height of the tree.

We first draw a triangle using the given details, AB being the tree, and C being the point where Tasha is.

We know ∠A = 180° - (∠B + ∠C) {By angle sum property of triangles)

or, ∠A = 180° - (85° + 25°) = 180° - 110° = 70°.

Now, by sine rule, we can say that:

(Sin A)/a = (sin B)/b = (sin C)/c.

or, (Sin 70°)/80 = (sin 85°)/b = (sin 25°)/c,

or, 0.93969262078/80 = 0.42261826174/c {We ignored the middle term as we only need the height of the tree, that is, c}

or, c = 0.42261826174*80/0.93969262078/80

or, c = 35.9792768309.

Therefore, the tree is approximately 35.979 feet tall, computed using the sine rule.

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Answer: 64% of the variability in weight can be explained by the relationship with height.

Step-by-step explanation:

Here, r= 0.80

[tex]\Rightarrow\ r^2= (0.80)^2=0.64[/tex]

That means 64% of the variability in weight can be explained by the relationship with height.

The variability in weight is 64 % , explained by the relationship with height.

Correlation coefficients are always values between -1 and 1, where -1 shows a perfect, linear negative correlation, and 1 shows a perfect, linear positive correlation.

The correlation coefficient is measure the strength of the linear relationship between two variables in a correlation analysis.

Correlation coefficient is represented by r.

Given that, the correlation between height and weight for adults is 0.80.

                   [tex]r=0.8[/tex]

The variability in weight is, = [tex]r^{2}=(0.8)^{2} =0.64[/tex]

Thus, the variability in weight is 64 % , explained by the relationship with height.

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Answer:

Step-by-step explanation:

Using the formula for calculating the energy used up during the process;

Energy used up = Amount of CO₂ created.

Energy used up in the process = Power * Time.

Given Parameters:

Power = 3,030Watts

Converting to Kilowatts, power = 3030/1000 kW

Power (in kW) = 3.03kW

Time taken = 34 minutes

Converting to hour;

Since 60 minutes = 1hr

34minutes = (34/60)hr

34minutes = (17/30)hr

Required:

Energy used up = 3.03 * 17/30

Energy used up = 51.51/30

Energy used up = 1.717 kW/hr

Hence, amount of CO₂ created in kW/hr is 1.7 kW/hr to 1 decimal place.

Step-by-step explanation:

a. z = 5.5

25 ^( 5.5 - 4 ) = 125

25 ^ (1.5) = 125

125 = 125

z = 5.5

PlZzzzz follow me

Answer:

5

Step-by-step explanation:

Find the z-scores.

z = (x − μ) / σ

z₁ = (92 − 82) / 5

z₁ = 2

z₁ = (97 − 82) / 5

z₂ = 3

Find the probability:

P(92 < X < 97)

P(2 < Z < 3)

P(Z < 3) − P(Z < 2)

0.9987 − 0.9772

0.0215

Find the number of tests:

0.0215 (241) ≈ 5

Answer:

False

Step-by-step explanation:

It was proved with advanced algebra that a doubled cube could never be constructed with a straightedge and compass

Answer:

False

Step-by-step explanation:

A tessellation refest to a shape that is repeated over and over again covering a plane without any gaps or overlaps. The statement is false given that regular tessellations use only one polygon. Semi-regular tessellations are created with more than one type of regular polygon.

Answer:

B.3

Step-by-step explanation:

to get the scale factor divide a side from the bigger triangle by the equivalent in the small one

15/5 = 3

Answer:

x > 29

Step-by-step explanation:

−x<−29

Divide each side by -1, remembering to flip the inequality

x > 29

Answer:

Step-by-step explanation:

-x < -29   change the signs

x > 29