[tex]5x^{2} - 15x-4=0[/tex]

completing the square

Answer:

Rs216.98

Step-by-step explanation:

If Rs230 is including the 6% tax then 230 = 106%

230 / 106 = 1% = 2.1698

2.1698 X 100 = 100% = 216.98

The original price of a packet of biscuits will be Rs216.98.

The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the original price of a packet of biscuits bought for Rs230 including 6% tax.

The original price will be calculated as below:-

If Rs230 is including the 6% tax then 230 will be equal to 106 percent as below:-

230 = 106%

Then 1 percent will be equal to the ratio of 230 and 106 as below,

1% = 230 / 106= 2.1698

Divide 230 by 106 and to calculate the original price multiply by 100.

2.1698 X 100 = 100% = Rs216.98

Therefore, the original price of a packet of biscuits will be Rs216.98.

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Answer: choice B

Step-by-step explanation:

just took the quiz

omm its B. G(x)=(x+8)^2

just took the test

Answer:

20 cm^2.

Step-by-step explanation:

If the scale factor is 2 each of the sides of the figure will be increased by a factor 2.

So each side will have a length of 2 * 1 = 2 centimeters.

It will consist of 5 squares of dimension 2*2 =  an area of 4 cm^2

So the area of the new cross  is 5*4 = 20 cm^2.

We can also calculate the area directly by multiplying  by 2^2 ( the scale factor)squared.)

The original area = 5 so the area of the enlarged figure = 5 * 2^2 = 20 cm^2.

Answer: 50 grams of fat

Step-by-step explanation:

From the question, we are informed that one serving of pretzels contains 1.5 grams of fat which is 3% of the daily amount recommended for a 2,000 calorie diet.

This means that we are expected to find the grams of fat for 100%. Since one serving of pretzels contains 1.5 grams of fat which is 3%, this means 1% will contain (1.5/3) = 0.5 grams of fat.

Therefore the grams of fat that are recommended will be:

= 100 × 0.5

= 50 grams of fat

Answer:

50 grams of fat

1.5 / 3 = 0.5

0.5 x 100 = 50

Step-by-step explanation:

Answer:

Value of y = 3

Step-by-step explanation:

Given:

y-2<2 ........Eq1

3y+10>16.........Eq2

Find:

Value of y

Computation:

y-2<2

Add 2 both side,

y-2+2<2+2

y < 4

So y = (0,1,2,3)

Put y = 3 in both equation:

y-2<2

3-2<2

1<2

3y+10>16

3(3) + 10 >16

19>16

Both equation get satisfies by y = 3

So, Value of y is 3

Answer:

x = 12

m(∠B) = 45°

Step-by-step explanation:

Given question is incomplete; find the complete question in the attachment.

In the figure attached two lines 'l' and 'm' are the parallel lines and line 'n' is a transverse.

Angles A and B are the "Alternate exterior angles" which will equal in measure.

m(∠A) = m(∠B)

(5x - 15) = (2x + 21)

5x - 2x = 15 + 21

3x = 36

x = 12

Since, m(∠B) = (2x + 21)

                     = (2×12) + 21

                     = 24 + 21

                     = 45°

Therefore, x = 12 and measure of angle B will be 45°.

Answer:

He needs just 13 pages

That is round up to not more than 20 pages will be the smallest

Step-by-step explanation:

Vincent wants to put 75 photograph in an album.

And a full page holds 6 photo graphs.

If 6 photographes is one page

Then 75 photographes =( 75*1)/6

75 photographes = 75/6

75 photographes= 12.5

12.5 pages will hold 75 photographes but nothing like 12.5 pages.

To the nearest page = 13 pages

x = 4 is the answer because the y coordinate is zero and at x axis it intersects at 4..

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Answer:

x=5 is the answer

Step-by-step explanation:

hope this helped

Answer:

We can call the supplementary angle of x as (180 - x)°. Since the lines are parallel, 61° and (180 - x)° are congruent because they are alternate interior angles. We can write:

61 = 180 - x

-119 = -x

x = 119°

Answer:

0.89.

Step-by-step explanation:

So, we are given the following data or parameters or information which is going to aid in the solution to this question or problem. So, the data or parameters are;

(1). "probability 0.7 of having no claims, 0.2 of having exactly one claim, and 0.1 of having exactly two claims."

(2). " distributed on the interval [0,60] and are independent."

(3). "The insurer covers 100% of each claim."

So, taking (1) above we will have;

(Total probability= 0.7 + 0.2 + 0.1 = 0.1)

A = { (0.7 × 0)^2 + (0.2 × 1)^2 + ( 0.1 × 2)^2 =( 0.4) +( 0.4) = 0.8.

0.8 + total probability = 0.8 + 0.1 = 0.9.

So, from the question, we are to "Calculate the probability that the total benefit paid to the policyholder is 48 or less."

Hence, P< 48/A = P < 48/0.9 = P < 53.33.

Thus, 53.33/60 = 0.89.

Answer:

A

Step-by-step explanation:

To determine if a point lies on the curve, substitute the x- coordinate into the equation. If the value obtained is equal to the y- coordinate then the point lies on the curve, that is

A

y = ([tex]\frac{3}{2}[/tex] )² = [tex]\frac{9}{4}[/tex] ≠ [tex]\frac{9}{2}[/tex] ← not on line

B

y = (- 1)² = 1 ← lies on line

C

y = 4² = 16 ← lies on line

D

y = ([tex]\frac{1}{2}[/tex] )² = [tex]\frac{1}{4}[/tex] ← lies on line

Answer:  A,B,D,C

Step-by-step explanation:

Hi, to answer this question we have to analyze each expression:

Assuming x is the number of years, we have to calculate each equation for x =1:

A = 110 (0.70)^X = 110 (0.70)^1= 77

B = 140 (1.07)^X= 140 (1.07)^1 = 149.8

C =430 (1.90)^x=430 (1.90)^1= 817

D = 310 (1.14)^x= 310 (1.14)^1= 353.4

Comparing the sales:

77(A) < 149.8 (B) <353.4 (D) < 817(C)

So, the correct option is:

A,B,D,C

Distance from Y to Z is 10.4 km and Z to X is 20 km

Distance is a numerical measurement of how far apart objects or points are.

A triangle is a polygon with three edges and three vertices.

From the given data plot the graph,

Then,

∠XYZ=∠YZX=75 degrees

Therefore XY=XZ=20 km

[tex]YZ^{2}=20^{2} +20^{2} -2(20)(20)cos30[/tex]

YZ=10.4 km

Hence, Distance from Y to Z is 10.4 km and Z to X is 20 km

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Answer:

Step-by-step explanation:

Answer:

The answer is "[tex]2^3 \times 3^2 \times 5 \times 7\\\\[/tex]"

Step-by-step explanation:

Given:

2520

Prime factor=?

Prime factor of 2520 is:

[tex]= 2 \times 2 \times 2\times 3\times 3 \times 5 \times 7\\\\= 2^3 \times 3^2 \times 5 \times 7\\\\[/tex]

Answer:

37.57 + 1.95x

Step-by-step explanation:

The cost of the shoes is a constant, and we don't know how many socks she bought, but we know that for every pair of socks she bought, they cost would be 1.95. Since we haven't been given the total cost of the purchase, meaning how much the total was, this will be an expression. We will multiply an x against the amount (1.95), which will calculate the price for how many socks were purchased. This means the answer will be 37.57 + 1.95x.

I will clarify a little bit more on why the other answers are incorrect. The first option is 37.57x + 1.95. This is incorrect because the question is not asking how many shoes were bought, but it is questioning how many socks were bought. Option number two states 37.57x + 1.95x. This means that the number of socks and shoes are both unknown, and the question does not state that. Also, another point to make would be that we could also add these variables together, and we do not want that. Option number three states 37.57 + 1.95 + x. X cannot be a separate variable, because by stating that, it means that there would be one more object that was bought that is unknown. I hope this helps you understand my explanation a bit more.

Have a great day, and best of luck for your math problem!

Answer:

5.5

Step-by-step explanation:

Picture Proof

Answer: 5.5 : ) ~ Hope you have a great day!

Answer:

[tex]Area = 336\ m^2[/tex]

Step-by-step explanation:

If the ratio of the sides is 13:14:15, we can say that the length of each side is 13x, 14x and 15x.

Then, if the perimeter is 84 m, we have:

[tex]P = 13x + 14x + 15x = 84[/tex]

[tex]42x = 84[/tex]

[tex]x = 2[/tex]

The length of each side is:

[tex]13x = 26\ m[/tex]

[tex]14x = 28\ m[/tex]

[tex]15x = 30\ m[/tex]

Now, to find the area of the field, we can use the following formula:

[tex]Area = \sqrt{p(p-a)(p-b)(p-c)}[/tex]

Where a, b and c are the sides and p is the semi perimeter:

[tex]p = P/2 = 42\ m[/tex]

So we have that:

[tex]Area = \sqrt{42(42-26)(42-28)(42-30)}[/tex]

[tex]Area = 336\ m^2[/tex]

Answer:

P = 5.4641b cm.

Step-by-step explanation:

If the triangle ABC is isosceles and m∠BAC = 120°, we have that:

[tex]mACB = mABC = (180-120)/2 = 30\°[/tex]

Then, in triangle ABH, we have:

[tex]mABH + mBHA + mHAB = 180\°[/tex]

[tex]30\° + 90\° + mHAB = 180\°[/tex]

[tex]mHAB = 60\°[/tex]

If m∠BAC is 120°, we have:

[tex]mHAB + mHAC = 120\°[/tex]

[tex]m∠HAC = 60\°[/tex]

Now we can find the length of AH using the sine relation of angle m∠HAC:

[tex]sin(mHAC) = DH / AH[/tex]

[tex]0.866 = b / AH[/tex]

[tex]AH = b / 0.866 = 1.1547b[/tex]

Now, to find the length of HB and AB, we can use the tangent and cosine relation of the angle m∠HAB:

[tex]tan(mHAB) = HB / AH[/tex]

[tex]1.7321 = HB / 1.1547b[/tex]

[tex]HB = 1.7321 * 1.1547b = 2b[/tex]

[tex]cos(mHAB) = AH / AB[/tex]

[tex]0.5 = 1.1547b / AB[/tex]

[tex]AB = 1.1547b / 0.5 = 2.3094b[/tex]

So the perimeter of triangle ABH is:

[tex]P(ABH) = AB + HB + AH[/tex]

[tex]P(ABH) = 2.3094b + 2b + 1.1547b[/tex]

[tex]P(ABH) = 5.4641b[/tex]

The relation of a and b can be calculated using the tangent relation of the angle m∠HAC:

[tex]tan(mHAC) = DH / AD[/tex]

[tex]1.7321 = b / a[/tex]

[tex]b = 1.7321a[/tex]

Answer:

a: 3

b. 6973568802

Step-by-step explanation:

a₁ = 6 , r = 3 , a₂₀ =?

Result:

a₂₀ = 6973568802

Explanation:

To find a₂₀ we use the formula

aₙ = a₁ · r ^ⁿ⁻¹

In this example we have a₁ = 6 , r = 3 , n = 20. After substituting these values to above

formula, we obtain:

aₙ = a₁ · r ^ⁿ⁻¹

a₂₀ = 6 · 3 ^²⁰⁻¹

a₂₀ = 6 · 1162261467

a₂₀ = 6973568802

Answer:

4 is the answer to your question

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

(y2-y1) / (x2-x1)

(10-2) / (3-(-1))

8/(3+1)

8/4

2

Answer:

2

Step-by-step explanation:

(x¹, y¹) (x², y²) = (-1,2) (3,10)

Slope = (y²-y¹) ÷ (x²-x¹)

= (10 - 2) ÷ (3 -(-1))

= 8 ÷ 4

= 2

Answer:

[tex]Vol=883.6875\,\, cm^3\\[/tex]

Step-by-step explanation:

Recall that the volume of a whole sphere is given by the formula:

[tex]Vol_{sphere}=\frac{4}{3} \pi\,R^3[/tex]

then, the volume of a semi-sphere would be half of the formula above:

[tex]Vol=\frac{2}{3}\, \pi\,R^3[/tex]

Now, the radius R is given by half of the semi-sphere diameter: 15/2 = 7.5 cm.

which makes our calculation:

[tex]Vol=\frac{2}{3}\, \pi\,R^3=\frac{2}{3}\, \pi\,(7.5\,cm)^3=883.6875\,\, cm^3\\[/tex]

Answer:

√63 can be written as

√ 9 × 7 = √ 9 × √7 = 3 × √ 7

= 3√7

Hope this helps you

Answer: [tex]3\sqrt{7}[/tex]

Step-by-step explanation:

Separate [tex]\sqrt{63}[/tex] into [tex]\sqrt{7}[/tex] and [tex]\sqrt{9}[/tex].  Then simplify [tex]\sqrt{9}[/tex] into 3.  Thus, the simplified version of [tex]\sqrt{63}[/tex] is [tex]3\sqrt{7}[/tex]

Answer:

[tex]62.4$ cm^2[/tex]

Step-by-step explanation:

The net of the triangular pyramid is attached below.

Since each of the faces is an equilateral triangle of side 6cm, the base of the pyramid will also be an equilateral triangle of side lengths 6cm .

In the equilateral triangles

Therefore, the surface area of the pyramid formed from the net shown

= 4 X Area of One Triangular Face

[tex]=4 (\frac12 \times bh)\\=4 (\frac12 \times 6\times 5.2)\\=4(15.6)\\=62.4$ cm^2[/tex]

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▹ Answer

[tex]\frac{3}{10}[/tex]

▹ Step-by-Step Explanation

2 + 1 = 3

Written as → [tex]\frac{3}{10}[/tex]

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

Step-by-step explanation:

Total pencils that Lisa had = 10 pencils

Total pencils that Lisa had given to Anna and Ben:

=2+1

= 3

Now,

Fraction of her pencils that she gave away:

[tex] \frac{3}{10} [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

Option D is correct.

A voluntary response error was made in this design. This type of sampling only targets those who are passionate about a specific act and call in to vote; it is not a good representation of the population.

Step-by-step explanation:

When humans are given the choice whether to participate in a survey like in this question, most often than not, the survey becomes biased.

This is because only the people or set of people who feel strongly the most about the subject matter of the poll will participate in the survey. This favours the group that disagrees as this group, if given the choice to express their opinion, will most likely be the set of people that will readily express their discontent.

Discontent is more visibly and strongly expressed in humans.

In order to remove this bias, people should have been chosen at random and their responses recorded.

Hope this Helps!!!

Answer:

0.667

Step-by-step explanation:

According to Bayes theorem:

Since there are three cards, the probability that the side is green = 1/3

For the first card, if one side is green, the probability that the other side is also green = 1 (both sides are green)

For the second card, if one side is green, the probability that the other side is also green = 0 (both sides are red)

For the third card, if one side is green, the probability that the other side is also green = 1/2 (one side is green and the other side is red)

[tex]P(G_k/A)=\frac{P(G_k)P(A/G_k)}{\Sigma_{i=1\ to\ m} P(G_i)P(A/G_i)} \\P(B_1/A)=\frac{P(G_1)P(A/G_1)}{P(G_1)P(A/G_1)+P(G_2)P(A/B_2)+P(G_3)P(A/G_3)}\\ P(B_1/A)=\frac{1/3*1}{(1/3*1)+(1/3*0)+(1/3*1/2)=\frac{1/3}{1/2} }=0.667[/tex]

Answer:

A,and C

Step-by-step explanation:

A and C have the same level precision , they have three significant digit

Answer:

[tex]\boxed{20(r + 3t)}[/tex]

Step-by-step explanation:

[tex]20r + 60t[/tex]

Factor out 20 from the expression.

[tex]20(r) + 20(3t)[/tex]

Take 20 as common.

[tex]20(r + 3t)[/tex]