Need help on this!!! 6 points!!!

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:

(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:

range{-5,4)

Step-by-step explanation:

3(-1)-2= -5

3(2)-2=4

Answer: (3.5,-2)

Step-by-step explanation:

To solve this problem, all we have to do is plug in y=-2 into either equations from step one to find the coordinate. To make sure we have the right x-coordinate, let's plug in y for both equations.

4x-7y=28        [plug in y=-2]

4x-7(-2)=28    [multiply]

4x+14=28       [subtract both sides by 14]

4x=14              [divide both sides by 4]

x=3.5

------------------------------------------------------------------------------------------------------------

6x-5y=31        [plug in y=-2]

6x-5(-2)=31    [multiply]

6x+10=31       [subtract both sides by 10]

6x=21             [divide both sides by 6]

x=3.5

Now, we know the solution to the system is (3.5,-2).

Answer:

(3.5, -2)

Step-by-step explanation:

Hi there!

We are given a system of equations, and the value for y is already solved (y=-2)

We want to find the value of x

To do that, substitute -2 as y into either one of the equations in the system (the system has the equations 4x-7y=28 and 6x-5y=31) and solve for x

Let's use 4x-7y=28, although picking 6x-5y=31 is completely fine

Substitute -2 as y into the equation

4x-7(-2)=28

Multiply

4x+14=28

Subtract 14 from both sides

4x=14

Divide both sides by 4 and simplify

x=7/2, or 3.5

We found the value of x in the system

Substitute the values of x and y into a point form (x, y)

The solution is (3.5, -2)

Hope this helps!

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:

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:

Its either 2(A+7=5) or 2(A+7) =5

Answer:

- 22.5

Step-by-step explanation:

Substitute x = 3 into f(x) and x = 16 into h(x) , then

[tex]\frac{1}{2}[/tex] g(3) - h(16)

= [tex]\frac{1}{2}[/tex] × - 3(3)² - (2[tex]\sqrt{16}[/tex] + 1)

= [tex]\frac{1}{2}[/tex] × - 3(9) - (2(4) + 1)

= [tex]\frac{1}{2}[/tex] × - 27 - (8 + 1)

= - 13.5 - 9

= - 22.5

Answer:

Step-by-step explanation:

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:

(-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:

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:

m∠DAB+m∠ADC=180

115+ 29 + m∠ADB=180

m∠ADB=180 - 115 -29

= 36°

Answer:

CAUTION HERE !!!!!

if you suggested edits are accurate the solution would be...

[tex]\frac{3p^2 - 5p+9}{6p^2}[/tex]

that is not one of your choices, but is is almost identical to choice "D"

which is different by [tex]6px^2[/tex]  vs   [tex]6p^2[/tex]

which i think is your comment ????  

Step-by-step explanation:

Answer:rrrrrrrr

rrrrrrrrrr

Step-by-step explanation:

rrrrrrrrrrrrrrr

The equation for the scenario is x + x+1 + x+2 = 117 and largest number is 40.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let x be the first number:

The other numbers are:

x+1, x+2

The sum of three consecutive numbers is 117:

x + x+1 + x+2 = 117

3x + 3 = 117

3x = 114

x = 38

x+ 1 = 38+1 = 39

x+2 = 38+2 = 40

Thus, the equation for the scenario is x + x+1 + x+2 = 117 and largest number is 40.

Learn more about the linear equation here:

brainly.com/question/11897796

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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

Answer:

259 ft.

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are isosceles. scalene, equilateral, acute, obtuse and right angled triangle.

A right angled triangle is a triangle in which one of the angles is 90 degrees. Trigonometric ratios show the relationship between the angles of a right angle triangle and its sides.

Let h represent the height of the house above water, hence using trigonometric ratios:

tan(26) = h / 531

h = 531 * tan(26)

h = 259 ft.

Answer:

chemical

Step-by-step explanation:

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

https://brainly.com/question/20785664

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Answer:

a(y_2)_b(y_2) =a_b)(y_2(

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!

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:  -6 only (choice B)

This is because the point (0,-6) is on the blue line. This is the y intercept.

Choice C would be true if you wanted to solve f(x) = 0, instead of f(0) itself.

Answer:

-6

Step-by-step explanation:

f(0) means what is the output when the input is 0

x=0 y= -6

Answer:

p = 1

Step-by-step explanation:

7 = 8 - p

7 + p = 8

p = 8-7

p = 1

Answered by Gauthmath

Answer:

Choice C.

[tex]y + 1 = - 2(x - 2)[/tex]

Step-by-step explanation:

When converting to

[tex]y = mx + b[/tex]

We are left with:

[tex]y = - 2x + 3[/tex]

Which fits both the x-intercept and y-intercept.

Answer:

19: 5

Step-by-step explanation:

Total fruit  is 5+10+4 = 19

fruit: pears

19: 5

Answer:

19:5

Step-by-step explanation:

5+10+4= 19

Pears= 5

Answer:

write question in short form

Step-by-step explanation:

Answer:

180- 110= 70

70+x+90=180

160+x=180

180-160=x

20=x

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.

Mistake in Line 2 : Was in the determining the values for a ,b,c

Mistake in Line 4 : Not taking the square roots of both sides.

Step-by-step explanation:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

First Mistake : Line 2

[tex]a = x \\ b = 6 \\ c = 10[/tex]

Second Mistake : Line 4

[tex]136 = {x}^{2} \\ not \\ 136 = x[/tex]

Correct Solution :

[tex] {x}^{2} + {6}^{2} = {10}^{2} \\ {x}^{2} = {10}^{2} - {6}^{2} \\ {x}^{2} = 100 - 36 \\ [/tex]

[tex] {x}^{2} = 64 \\ \sqrt{ {x}^{2} } = \sqrt{64} \\ x = 6[/tex]