Solve the equation for x.
5x - ( 4x - 1) = 2
1
a.
C.
1
9
bi
b. - 1
d.
1

Answer:

chemical

Step-by-step explanation:

9514 1404 393

Answer:

  22.09 ft²

Step-by-step explanation:

The area of a circle is given by the formula ...

  A = πr² . . . . where r is the radius, half the diameter

The slice, at 45°, is 1/8 of the circle, so the area of the slice is ...

  A = (1/8)π(15 ft/2)² = 225π/32 ft² ≈ 22.09 ft²

Given:

The given equation is:

[tex]-3t^2+24t=h[/tex]

Where, t is the time in seconds and h is the height of the ball above the ground, measured in feet.

To find:

The inequality to model when the height of the ball is at least 36 feet above the ground. Then find time taken by ball to reach at or above 36 feet.

Solution:

We have,

[tex]-3t^2+24t=h[/tex]

The height of the ball is at least 36 feet above the ground. It means [tex]h\geq 36[/tex].

[tex]-3t^2+24t\geq 36[/tex]

[tex]-3t^2+24t-36\geq 0[/tex]

[tex]-3(t^2-8t+12)\geq 0[/tex]

Splitting the middle term, we get

[tex]-3(t^2-6t-2t+12)\geq 0[/tex]

[tex]-3(t(t-6)-2(t-6))\geq 0[/tex]

[tex]-3(t-2)(t-6)\geq 0[/tex]

The critical points are:

[tex]-3(t-2)(t-6)=0[/tex]

[tex]t=2,6[/tex]

These two points divide the number line in 3 intervals [tex](-\infty,2),(2,6),(6,\infty)[/tex].

Intervals      Check point           [tex]-3(t-2)(t-6)\geq 0[/tex]           Result

[tex](-\infty,2)[/tex]               0                       [tex](-)(-)(-)=(-)<0[/tex]         False

[tex](2,6)[/tex]                    4                       [tex](-)(+)(-)=+>0[/tex]            True

[tex](6,\infty)[/tex]                  8                        [tex](-)(+)(+)=(-)<0[/tex]        False

The inequality is true for (2,6) and the sign of inequality is [tex]\geq[/tex]. So, the ball is above 36 feet between 2 to 6 seconds.

[tex]6-2=4[/tex]

Therefore, the required inequality is [tex]-3t^2+24t\geq 36[/tex] and the ball is 36 feet above for 4 seconds.

Answer:

range{-5,4)

Step-by-step explanation:

3(-1)-2= -5

3(2)-2=4

The value of x for the given equation [tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2 will be 2 so option (B) must be correct.

The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.

In another word, a logarithm is a different way to denote any number.

Given the equation

[tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2

We know that,

xlogb = log[tex]b^{x}[/tex]

So,

2[tex]log_{8}[/tex](x) = logx²

For the same base

logA + logB = log(AB)

So,

[tex]log_{8}[/tex](16) + [tex]log_{8}[/tex](x)² = 2

[tex]log_{8}[/tex](16x²) = 2

We know that

[tex]log_{a}[/tex](b) = c ⇒ b = [tex]a^{c}[/tex]

so,

[tex]log_{8}[/tex](16x²) = 2 ⇒ 8² = 16x²

x = 2 hence x = 2 will be correct answer.

For more about logarithm

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The rational function is:

f(x) = x/ (x - 2)(x + 5).

The correct option is D.

As the function approaches a certain value—typically infinity or negative infinity—as the input approaches positive or negative infinity, this is known as a horizontal asymptote.

When the vertical asymptotes are x = 2 and x = -5, this means that the denominator of the rational expression must contain the factors (x - 2) and (x + 5), but not (x - a) or (x + b) for any other values of a and b.

When the horizontal asymptote is x = 0, this means that the degree of the numerator and denominator must be the same, and the leading coefficients must be equal.

Let's start by setting up the denominator:

denominator = (x - 2)(x + 5)

To satisfy the horizontal asymptote at x = 0, the numerator must also have a factor of x, so we can write:

numerator = kx

where k is a constant to be determined.

To ensure that the rational expression has the desired vertical asymptotes, we need to add any necessary linear or quadratic factors to the numerator.

Since the denominator already has linear factors, we only need to add a quadratic factor.

We can choose any quadratic factor that doesn't affect the horizontal asymptote or the other vertical asymptote.

For example, we can choose:

numerator = kx(x + 7)

Putting it all together, the rational expression is:

f(x) = kx / (x - 2)(x + 5)

To determine the value of k, we can use the fact that the leading coefficients of the numerator and denominator must be equal. The leading term of the numerator is kx², and the leading term of the denominator is x².

Therefore:

k = 1

So the final rational expression is:

f(x) = x / (x - 2)(x + 5)

To learn more about the asymptotes;

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Answer:

-3/5

Step-by-step explanation:

Pythagorean formula :

x^2 + y^2 = r^2

(-8)^2 + (-6)^2 = r^2

64 + 36 = 100

r^2 = 100

r= 10

sin is the y coordinate over the radius :

-6/10

-3/5

Answer:

(x+2)(2x+2) = 130

x=6.58m

Step-by-step explanation:

The shape of the whole figure is a triangle. Hence the area of the whole figure is expressed as:

Area = Length * Width

Given

Length = 2 + x + x = 2+2x

Width = 2 + x

Area = 130m²

Substitute the resultng values into the formula;

(2+2x)(2+x)= 130

(x+2)(2x+2) = 130

Expand the bracket:

[tex]2x^2+2x+4x+4=130\\2x^2+6x+4=130\\[/tex]

Divide through by 2

[tex]x^2+3x+2=65\\x^2+3x=65-2\\x^2+3x = 63[/tex]

Complete the square by adding the square of the half of the coefficient of x to both sides:

[tex](x^2+3x+(\frac{3}{2} )^2)=63+(\frac{3}{2} )^2[/tex]

[tex](x+\frac{3}{2} )^2=63 + \frac{9}{4} \\(x+\frac{3}{2} )^2=\frac{252+9}{4} \\(x+\frac{3}{2} )^2=\frac{261}{4}\\(x+\frac{3}{2} )^2=65.25[/tex]

Take the square root of both sides

[tex]\sqrt{(x+(\frac{3}{2} ))^2} = \sqrt{65.25}\\x+\frac{3}{2}= 8.078\\x=8.078-1.5\\x=6.58m[/tex]

Hence the value of x is 6.58m

Answer:

Lines parallel to this line will have a slope of -1

Step-by-step explanation:

y = -x + 7

This line is in slope intercept form

y = mx+b where m is the slope

The slope is -1

Parallel lines have the same slope

Lines parallel to this line will have a slope of -1

Answer:

-1

Step-by-step explanation:

Parallel lines have the same slope

The equation y = -x + 7 has a slope of -1 meaning that a line parallel to it would also have a slope of -1

Answer:

29

Step-by-step explanation:

all in all it is 180 so 61 + m (which is 90 because it is a right angle)=151

then 180-151=29

Answer:

7

Step-by-step explanation:

Using the definition

n[tex]P_{r}[/tex] = [tex]\frac{n!}{(n-r)!}[/tex]

where n! = n(n - 1)(n - 2)..... 3 × 2 × 1

Then

7[tex]P_{1}[/tex] = [tex]\frac{7!}{(7-1)!}[/tex] = [tex]\frac{7!}{6!}[/tex] ← cancel out the multiples 6 ×5 × 4 × 3 × 2 × 1 , then

7[tex]P_{1}[/tex] = 7

Hello!

a) (t - 2)(t - 2) = (t - 2)² = t² - 4t + 4

b) (3y - 2z)(3y + 2z) = (3y)² - (2z)² = 9y² - 4z²

c) 105 × 98 = 10290

Good luck! :)

Answer:

Step-by-step explanation:

a) Identity : (a- b)² = a²- 2ab +  b²

(t - 2)(t -2) = (t-2)²            {a = t & b =2}

                 = t² -2*t*2 + 2²

                 = t² - 4t + 4

b) (a + b)(a - b) = a² - b²

a = 3y   & y = 2z

(3y - 2z) (3y +2z)  = (3y)² - (2z)²

                             = 3²y² - 2²z²

                              = 9y² - 4z²

c) (x + a)(x + b) =x² + (a+b)x + ab

105 * 98 = (100 + 5) (100 - 2)  {here, x = 100 ; a = 5 ; b = -2}

              = 100² + (5 +(-2) ) *100 + (5)*(-2)

              = 10000 + (3)*100 - 10

              = 10000 + 300 - 10

              = 10290

Answer:

(-2,-2)

Step-by-step explanation:

x^2 + y^2 = 9

A circle has an equation of the form

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

where the center is at ( h,k) and the radius is r

The circle is centered at (0,0) and has a radius 3

The only point entirely within the circle must have points less than 3

(-2,-2)

Answer:

10 digress when converted to nearest digree

Answer:

5

Step-by-step explanation:

because line AB divided the triangle into two equal halves

Answer:

42.78⁹, 137.22⁹.

Step-by-step explanation:

sine Ф=0.6792

Angle Ф in the first quadrant = 42.78 degrees.

The sine is also positive in the second quadrant so the second solutio is

180 - 42.78

= 137.33 degres.

Answer:

AB is longer FD

Step-by-step explanation:

Given

See attachment for triangles ABC and FDE

Required

Compare line segments AB and FD

From the attachment, we have:

[tex]AC = FE[/tex] --- equal line segments

The measure of angles will then be used to compare the line segments;

[tex]\angle C = 72^o[/tex]

[tex]\angle F = 65^o[/tex]

The longer the angle of depression, the shorter the required line segment

[tex]72 > 65[/tex] implies that AB is longer

Answer:

C 3dge

Step-by-step explanation:

Answer:

2/3 kilometers

Step-by-step explanation:

Add the two distances together

4/9 + 2/9 = 6/9

Simplify the fraction by dividing the top and bottom by 3

2/3

Answer:

Step-by-step explanation:

(4/9) + (2/9) = 6/9 = 2/3

Answer:

All of the values in the data are used in calculating the mean.

The sum of the deviations is zero.

There is only one mean for a set of data.

Step-by-step explanation:

Required

True statement about arithmetic mean

(a) False

The mean can be equal to, greater than or less than the median

(b) True

The arithmetic mean is the summation of all data divided by the number of data; hence, all values are included.

(c) True

All mean literally represent the distance of each value from the average; so,  when each value used in calculating the mean is subtracted from the calculated mean, then the end result is 0. i.e.[tex]\sum(x - \bar x) = 0[/tex]

(d) True

The mean value of a distribution is always 1 value. When more values are added to the existing values or some values are removed from the existing values, the mean value will change.

(e) False

Nominal data are not numerical or quantitative data; hence, the mean cannot be calculated.

Answer:

5, 12, 19, 26, 33

Step-by-step explanation:

Using the recursive rule and a₁ = 5 , then

a₂ = a₁ + 7 = 5 + 7 = 12

a₃ = a₂ + 7 = 12 + 7 = 19

a₄ = a₃ + 7 = 19 + 7 = 26

a₅ = a₄ + 7 = 26 + 7 = 33

The first 5 terms are 5, 12, 19, 26, 33

Answer:

the last one: x^3 + 5x^2 - 9x - 45 = 0

Step-by-step explanation:

You can solve all the other ones by simple factoring and/or calculator.

Since the last one has more than 3 terms, it's likely that you'll have to use group factoring to solve it.

Answer:

7 slices

Step-by-step explanation:

1/3 of the bread would be seven slices (21/3), and he would be left with 2/3, half of which is 1/3; another seven slices were eaten. On Wednesday, he will have 7 slices left over.

Answer:

b i think

Step-by-step explanation:

Answer:

Its A

Step-by-step explanation:

I'm very sure

Answer:

C: 2 × 10⁴

Step-by-step explanation:

We are told that the average net primary production in tropical rain forests each year is 8,900 kilocalories per square meter.

Thus;

P_net,average = 8900 Kcal/m²

We are also told that net primary production of a selected portion of a tropical rain forest in a given year is 1.8 × 10^(8) kilocalories.

Thus;

P_net = 1.8 × 10^(8) Kcal

To get the average, the formula is;

P_net,average = P_net/Area

Thus;

Area = P_net/P_net,average

Plugging in the relevant values;

Area = (1.8 × 10^(8))/8900

Area ≈ 2 × 10⁴ m²

Answer:

p = 1

Step-by-step explanation:

7 = 8 - p

7 + p = 8

p = 8-7

p = 1

Answered by Gauthmath

Answer:

[tex]{ \tt{ {x}^{2} - \frac{1}{ {x}^{2} } }} \\ = { \tt{ {(2 + \sqrt{5} )}^{2} - \frac{1}{ {(2 + \sqrt{5}) }^{2} } }} \\ = { \tt{ \frac{(2 + \sqrt{5} ) {}^{4} - 1}{ {(2 + \sqrt{5} )}^{2} } }} \\ = { \tt{ \frac{(9 + 4 \sqrt{5}) {}^{2} }{ {(9 + 4\sqrt{5}) }}}} \\ = { \tt{9 + 4 \sqrt{5} }}[/tex]

Answer:

[tex]8\sqrt{5}[/tex]

Step-by-step explanation:

[tex]x = 2 + \sqrt{5}\\\\ x^{2} = (2+ \sqrt{5})^{2} \\\\ \ \ \ \ = 2^{2}+2* \sqrt{5}*2+( \sqrt{5})^{2}\\\\[/tex]

 [tex]= 4 + 4 \sqrt{5}+5\\\\= 9+4 \sqrt{5}[/tex]

[tex]\frac{1}{x^{2}}=\frac{1}{9+4\sqrt{5}}\\\\=\frac{1*(9-4\sqrt{5}}{(9+4\sqrt{5})(9-4\sqrt{5})}\\\\=\frac{9-4\sqrt{5}}{9^{2}-(4\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-4^{2}(\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-16*5}\\\\=\frac{9-4\sqrt{5}}{81-80}\\\\=\frac{9-4\sqrt{5}}{1}\\\\=9-4\sqrt{5}[/tex]

[tex]x^{2}-\frac{1}{x^{2}}= 9 + 4\sqrt{5} -(9 - 4\sqrt{5})\\\\[/tex]

            [tex]= 9 + 4\sqrt{5} - 9 + 4\sqrt{5}\\\\= 9 - 9 + 4\sqrt{5} + 4\sqrt{5}\\\\= 8\sqrt{5}[/tex]

Answer:

1 = 35p

6 = 35p×6

= 240p

Therefore, 6 bagels cost 240 p

Answer:

180- 110= 70

70+x+90=180

160+x=180

180-160=x

20=x

Answer:

y = -1/4x +2

Step-by-step explanation:

First find the slope using two point

(0,2) and (4,1)

m = (y2-y1)/(x2-x1)

   = (1-2)/(4-0)

   = -1/4

The y intercept is 2

The slope intercept form of a line is

y= mx+b where m is the slope and b is the y intercept

y = -1/4x +2

Answer:

the equation of the line is y = -1/4x +2

Step-by-step explanation:

The first step is to see where the line intercepts on the y-axis, which is 2. The next step is to see what the slope is so because it goes down 1 right 4, you find out that the slope of the line is -1/4.

Hope this helps!