Factor completely.
-3x^2 +17x -20

Answer:

x=74

Step-by-step explanation:

We know this triangle is an isosceles, because there are two angles that are congruent and one angle that isn't, because x=x.

All angles in a triangle add up to 180, so to find the value of x, we can use this equation: 180=32+x+x

We can simplify by combining the x's:

180=32+2x

Then subtract 32 to isolate the variable

148=2x

And divide by 2

The answer would be 74.

After 24 days, there will be approximately 25 atoms of I13153 remaining. The nuclear process that occurs during the decay is the transformation of I13153 into Xe13154.

The half-life of I13153 is nearly 8 days, which means that after each 8-day period, half of the atoms will decay into Xe13154. Starting with a sample of 200 atoms of I13153, we can calculate the number of remaining atoms after 24 days. Since the half-life is 8 days, the number of remaining atoms after each 8-day period is halved. After the first 8 days, there will be 100 atoms of I13153 remaining.

After the second 8 days, there will be 50 atoms remaining. And after the third 8 days, there will be 25 atoms of I13153 remaining. The nuclear process that occurs during the decay of I13153 is radioactive decay. Specifically, it undergoes beta decay, where a neutron in the nucleus of I13153 is converted into a proton, resulting in the formation of Xe13154. This process releases radiation and transforms the original isotope into a different element.

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Answer:

60

Step-by-step explanation:

y =  k/x ( as y is inversely proportional to x)

yx = k

--> k = yx

k = (6)(10)

k = 60

Enjoy it. I hope it will help you.

Let \(\(a\)\) and \(\(b\)\) be integers such that \(\(ab = 4\)\). We want to prove that \(\((a - b)^3 - 9(a - b) = 0\).\)

Starting with the left side of the equation, we have:

\(\((a - b)^3 - 9(a - b)\)\)

Using the identity \(\((x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\)\), we can expand the cube of the binomial \((a - b)\):

\(\(a^3 - 3a^2b + 3ab^2 - b^3 - 9(a - b)\)\)

Rearranging the terms, we have:

\(\(a^3 - b^3 - 3a^2b + 3ab^2 - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\(a^3 - b^3 - 3a^2(4) + 3a(4^2) - 9a + 9b\)\)

Simplifying further, we get:

\(\(a^3 - b^3 - 12a^2 + 48a - 9a + 9b\)\)

Now, notice that \(\(a^3 - b^3\)\) can be factored as \(\((a - b)(a^2 + ab + b^2)\):\)

\(\((a - b)(a^2 + ab + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Simplifying further, we get:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\)

Now, we can observe that \(\(a^2 + 4 + b^2\)\) is always greater than or equal to \(\(0\)\) since it involves the sum of squares, which is non-negative.

Therefore, \(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\) will be equal to \(\(0\)\) if and only if \(\(a - b = 0\)\) since the expression \(\((a - b)(a^2 + 4 + b^2)\)\) will be equal to \(\(0\)\) only when \(\(a - b = 0\).\)

Hence, we have proved that if \(\(ab = 4\)\), then \(\((a - b)^3 - 9(a - b) = 0\).\)

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Answer:

Step-by-step explanation:

its 100%

Answer:

I got 936 cm² as an answer

I hope it right

I hope it helps

The total surface area of the given triangular prism is 936 cm².

Triangular prism is a three dimensional object which has three rectangular sides and two triangular bases.

So it has three side faces and two base faces.

Triangular prism has two triangular sides and three rectangular sides.

Area of one triangular side = 1/2 bh, where b is the base and h is the height.

Area of two triangular sides = 2 × 1/2 b h = b h

                                                                    = 24 × 18

                                                                    = 432 cm²

Area of a rectangular side = l b, where l is length and b is breadth.

Area of one rectangular side = 30 × 7 = 210 cm²

Area of second rectangular side = 24 × 7 = 168 cm²

Area of third rectangular side = 18 × 7 = 126 cm²

Total surface area = 432 cm² + 210 cm² + 168 cm² + 126 cm²

                               = 936 cm²

Hence the total surface area of the triangular prism is 936 cm².

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Answer:

128500

Step-by-step explanation:

This is an arithmetic sequence with a common difference of 3500

The formula for an arithmetic sequence is

an = a1+d(n-1)  where a1 is the first term and d is the common difference

an = 48000+ 3500(n-1)

We want n = 24

a24 = 48000+3500(24-1)

       = 48000+3500(23)

       =48000+80500

       =128500

The value of the the function h(x) at x = 4 is given as follows:

8.7.

The quadratic regression equations for each table are given as follows:

The function for the first item is defined as follows:

h(x) = 50/(5.5 + 8e^(-0.9x)).

At x = 4, the value assumed by the function is obtained replacing the lone instance of x by 4, hence:

h(4) = 50/(5.5 + 8e^(-0.9(4))).

Then a calculator is used to obtain the exact value due to the exponential, hence:

h(4) = 8.7.

The regression equations are obtained inserting the points of each table into a quadratic regression calculator.

For the first table, the points are given as follows:

(16, 15), (18, 15.6), (20, 15.7), (21, 15), (23, 13.1), (26, 8.9), (27, 6.6).

Hence the equation is of:

y = -0.127x² + 4.699x - 27.777.

For the second table, the points are given as follows:

(3, 330), (4, 276), (5, 263), (6, 86), (7, 174), (8, 198), (9, 553).

Hence the equation is of:

y = 32.86x² - 379.14x + 1229.14.

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Answer:

d) PU Q = {The English alphabet}​

Step-by-step explanation:

because U means Union of all P and Q

The surface area of revolution of y = √1-a² around the x-axis between

z = 0 and 2π is

π[(2 - a) √(a² + 1) + a² sin⁻¹(1 - 2a)] square units.

The length of this element can be determined by the Pythagorean Theorem:

L² = Δx² + Δy²L

= √(Δx² + Δy²)

Now, taking the limit as Δx approaches 0 and forming a sum over all the elements of the curve, we can obtain the length of the entire curve:

y = √1 - x²dy/dx

= -x / √1 - x²

(by implicit differentiation)

Δs = √1 + (dy/dx)²Δx

= √1 + (x² / (1 - x²)) Δx

∴ ds/dx = √1 + (x² / (1 - x²))S

= ∫ds = ∫(√1 + (x² / (1 - x²))) dx

Solving the above integral by using trigonometric substitution,we get

S = ½π units.

Therefore, the length of the curve y = √1-x² between x = 0 and x = 1 is π/2.

9. Surface area of revolution of y = √1-a² around the x-axis between z = 0 and 2π (part of a sphere)The curve is rotated around the x-axis.

We can find the surface area of the curve by using the formula:

S = 2π ∫yds

Solving for ds, we obtain

ds = √(1 + (dy/dx)²) dxds/dx

= √(1 + (dy/dx)²)

Substitute y = √(1 - a²), dy/dx

= -x / √(1 - x²), and z = 2π to obtain:

S = 2π ∫yds

= 2π ∫√(1 + (dy/dx)²) dx

= 2π ∫√(1 + (x² / (1 - x²))²) dx

By using the trigonometric substitution x = tanθ, we can simplify the above equation.

S = π[(2 - a) √(a² + 1) + a² sin⁻¹(1 - 2a)] square units

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Answer:

22 cents per ounce

Step-by-step explanation:

Answer:

93 if rounding from 89.5 to 90 counts, if not then 95

Step-by-step explanation:

The first thing you do is add 92+94+79=265

then divide by 3 265/3=88 1/3

so his score has tp be higher than an 88 so lets try 90

92+94+79+90=355: 355/4=88.75

so higher lets try 94

94+94+92+79=359

359/4=89.75

Answer:

Center of circle: (1, -2)

Radius: √6

Step-by-step explanation:

First, we need to isolate the constant:

\(4x^2 + 4y^2 - 8x + 16y = 4\)

Then, we can divide the whole equation by 4:

\(x^2+y^2-2x+4y=1\)

Then, we can complete the square(reminder: (a+b)^2 = a^2 + 2ab + b^2)

\((x^2-2x)+(y^2+4y)=1\\(x^2-2x+1)+(y^2+4y)=1+1\\(x^2-2x+1)+(y^2+4y+4)=1+1+4\\(x-1)^2+(y+2)^2=6\)

Now that we got the standard equation of the circle, we can find the center and radius by using the equation \((x-h)^2+(y-k)^2=r^2\), where (h, k) is the coordinate of the center, and r is the radius.

Therefore, the center of the circle is (1, -2), and the radius of the circle is √6.

The center of the circle is (1,-2) and the radius is \(\sqrt{6}\).

Important information:

The standard equation of the circle is:

\((x-h)^2+(y-k)^2=r^2\)            ...(i)

Where, \((h,k)\) is center and \(r\) is the radius.

The given equation can be written as:

\(4(x^2+y^2-2x+4y-1)=0\)

\((x^2-2x)+(y^2+4y)=1\)

Add square of half of coefficients of \(x\) and \(y\).

\(\left(x^2-2x+1^2\right)+(y^2+4y+2^2)=1+1^2+2^2\)

\((x-1)^2+(y+2)^2=1+1+4\)

\((x-1)^2+(y+2)^2=6\)

\((x-1)^2+(y+2)^2=(\sqrt{6})^2\)           ...(ii)

On comparing (i) and (ii), we get

\(h=1\)

\(k=-2\)

\(r=\sqrt{6}\)

Therefore, the center of the circle is (1,-2) and the radius is \(\sqrt{6}\).

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Answer:

12 inches

Step-by-step explanation:

Even integers are multiple of 2 and differ by 2.

Thus,

as quadrilaterals have 4 sides

let the length of those sides be

2x , 2x + 2 , 2x+4, 2x+6

given that their sum is 36 inches

thus

lets take sum of assumed sides

2x + 2x + 2 + 2x+4 +  2x+6 = 36

=> 8x + 12 = 36

=> 8x = 36 - 12 = 24

=> x = 24/8 = 3

Thus,

sides are

2x = 2*3 = 6

2x + 2 = 6 +2 = 8

2x + 4 = 6 + 4 = 10

2x + 6 = 6 + 6 = 12

Thus,

length of longest side is 12 inches.

Answer:

Step-by-step explanation:

a) Length = 20 m, Width = 10 m

2x * x = 200

x * x = 100, x = 10, 2x = 20

b) 60 m

Find Perimeter

20 x 2 + 10 x 2 = 40 + 20 = 60

c) 22.4 meters

Find diagonal using Pythagorean Theorem

10 x 10 + 20 x 20 = x * x

100 + 400 = x * x

x * x = 500

x = \(\sqrt{500}\), rounded to 22.4

We need to know about test statistic to solve the problem. The formula we will need to calculate test statistic is  (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Test statistic is a number calculated by a statistical test. It describes how far the observed data is from the null hypothesis of no relationship between variables or no difference among sample groups. The test statistic can be calculated using the sample mean, the population mean and population standard deviation.

test statistic= (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Therefore the formula to calculate the test statistic will be (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

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The number of complete days that 4 packs of treats will last, we need to determine the total number of packs each day and divide it into the total number of packs Mrs. Mills has bought.

Let's call the number of days the treats will last "d".

Then, the number of packs Fluff eats in "d" days is d * (1/6 of a pack per day) = (1/6)d.

Similarly, the number of packs Tigger eats in "d" days is d * (1/5 of a pack per day) = (1/5)d.

The total number of packs they eat in "d" days is (1/6)d + (1/5)d = (11/30)d.

Since Mrs. Mills has bought 4 packs, we have 4 = (11/30)d.

Finally, solving for "d", we have d = (30/11) * 4 = 120/11 days.

Since "d" must be a whole number, we round down to get 10 complete days that the 4 packs of treats will last.

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The total number of packs they eat in "d" days is (1/6)d + (1/5)d = (11/30)d.

Since Mrs. Mills has bought 4 packs, we have 4 = (11/30)d.

Finally, solving for "d", we have d = (30/11) * 4 = 120/11 days.

Brand₂ has the highest impact on the price of a smartphone, increasing the price by $80 for each unit increase in that variable.

Regression analysis is a statistical method that helps us understand the relationship between two or more variables.

Based on the regression equation, we can determine which brand increases the price of a smartphone the most. The regression equation is as follows:

Price = 1100 + 50 (Brand₁) + 80 (Brand₂) + 30 (Brand₃) + 20 (Battery Life) + 10 (Camera Resolution)

In this equation, the intercept (1100) represents the average price of a smartphone with all other variables set to zero. The coefficients for each variable represent the change in the price of a smartphone for a one-unit increase in that variable, holding all other variables constant.

Brand₁ and Brand₂ have a lower impact on the price, increasing it by $50 and $30, respectively, for each unit increase in those variables. Battery life and camera resolution have the smallest impact on the price, increasing it by $20 and $10, respectively, for each unit increase in those variables.

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Complete Question:

Can brand, battery life, and camera resolution affect a smartphone's price? Use α= o.05 to perform a regression analysis for the Smartphones01BC dataset and answer the following questions. Solve this problem using Excel and Mega Stat, and write your complete answers in the Response Box so I know that you can interpret the output.

Based on your regression equation, which brand increases the price of a smartphone the most? Use the statistics from your output to explain your answer.

The answer to the inequality of an equation  9x - 2y< -9 is x<(2/9)y-1

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality in mathematics.

Inequalities in mathematics specify the connection between two non-equal quantities. Not equal is what inequality means. Typically, we use the "not equal symbol ()" to denote an inequality between two numbers. However, a variety of inequalities are employed to compare the values, whether they are less than or more than.

The two expressions that make up an equation or an inequality are connected in a mathematical statement. The equal sign (=) in an equation denotes the equality of the two expressions.

Given,

9x-2y<-9

(9x-2y)+9<-9+9

9x-2y+9<0

(9x-2y+9)+(2y-9)<2y-9

9x-2y+9+2y-9<2y-9

9x-2y+2y+9-9<2y-9

9x<2y-9

(9x/9)<(2y-9)/9

x<(2/9)y-(9/9)

x<(2/9)y-(3²/3²)

x<(2/9)y-1

Therefore, the answer to 9x - 2y< -9 is x<(2/9)y-1

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Answer:

70

Step-by-step explanation:

The cutoff score so that only 5% of the population has a higher score is 124.7.

If 5% of the population has a higher score, then the probability of selecting these is 0.05.

Find the z-score that corresponds to the probability in the z-table. (see attached images)

probability = 1 - 0.05 = 0.95

z-score = 1.647

Using the formula for the z-score below, determine the cutoff score.

z-score = (x – μ) / σ

where x = individual data value = cutoff score

μ = mean = 100

σ = standard deviation = 15

1.647 = (x - 100) / 15

1.647(15) = x - 100

x = 24.705 + 100

x = 124.705

cutoff score = 125

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Answer:

First box, fourth box, sixth box

Step-by-step explanation:

Positive in division means either both numbers are positive or negative

The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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Answer:

A. 147

Step-by-step explanation:

Answer:

I think it’s 90% if u round up it should be 91%

Step-by-step explanation:

If it’s wrong I’m REALLY sorry

Answer:

47.619047619047

Step-by-step explanation:

63-33= 30

\( \frac{30}{63} \times 100 = 47.619047619047\)

you are welcome

Answer:

it is 2 minus six

2-6

Step-by-step explanation:

hdgeheksdiddh

Answer:

-27/64

Step-by-step explanation:

Exact form

-27/64

Decimal Form

-0.421875

Answer:

The answer is ≈3 to the nearest whole number

Step-by-step explanation:

using SOH CAH TOA

BCA

sin0=opp/hyp

sin0=7.9/11

0=sin‐¹(7.9/11)

0=46 to the nearest degree

<A=<D

so,<EDF=46°

tan0=adj/hyp

tan46=x/3.3

x=tan46×3.3

x=3 to the nearest whole number

Answer:

no. of consecutive integers--- X, X+1, X+2.

there sum is 60

X+X+1+X+2=60

3X+3=60

X+1=20

X=19

integers are=19, 20, 21