The length of the unknown leg is

Answer: y = (1/7) x - 2

Step-by-step explanation:

The slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept.

The slope of an equation is the change in y over the change in x.

We can see from the image that every time the line increases by 1 in the rise (y), it increases by 7 in the run (x).

Therefore, the slope is 1/7.

The y-intercept of a line is the point at which it intercepts the y-axis.

From the image, we can see that it intersects at the point (0,-2)

Therefore, the slope-intercept form is y = (1/7) x - 2

Take two points

Slope:-

[tex]\\ \sf\longmapsto \dfrac{-1}{-7}=\dfrac{1}{7}=m[/tex]

Equation in point slope form

[tex]\\ \sf\longmapsto y+3=1/7(x)[/tex]

[tex]\\ \sf\longmapsto y=1/7x-3[/tex]

Using a geometric sequence, it is found that the missing terms of the table are, respectively, given by:

[tex]243, 1, \frac{1}{81}[/tex]

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

From the table, we get that the common ratio is of [tex]q = \frac{1}{3}[/tex], hence each term is the previous divided by 3, or the next multiplied by 3. Hence, the missing terms are given by:

[tex]3 \times 81 = 243[/tex]

[tex]3 \times \frac{1}{3} = 1[/tex]

[tex]\frac{1}{27} \times \frac{1}{3} = \frac{1}{81}[/tex]

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Answer:

[tex] \huge \boxed{c = 4 \sqrt{2} }[/tex]

Step-by-step explanation:

Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x

Using Pythagoras theorem we have

c² = a² + b²

where

c is the hypotenuse

So from the question we have

[tex] {c}^{2} = {4}^{2} + {4}^{2} \\ c = \sqrt{16 + 16} \\ c = \sqrt{32} \: \: \: \: \: \: \: \: \: \\ \\ \\ c = 4 \sqrt{2} \: \: \: \: \: \: \: \: [/tex]

Hope this helps you

Answer:

d

Step-by-step explanation:

-5 is the least because it is the furthest from zero, -0.5 is greater than -5 because it is closer to zero, zero is zero, 1.25 is less than 1.5

Answer:

X = 6

Step-by-step explanation:

Since the two angles are equal, in order to solve for X, you set the two equal:

40° = (4 + 6x)°

-4      -4

36° = 6x

36°/6 = 6x/6

6 = X

X = 6

Hope this helps!

I left the work too ;)

Function that models the situation is  f(x) = 1/2(x-6)²+2.

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

Given parabola is of concave upward type.

So, the parabola will be of form f(x)=p(x-q)²+r....(1)

As vertices of parabola are (6,2)

So, we can put q=6 and r =2 in (1)

So, (1) becomes f(x) = p(x-6)²+2.....(2)

The y-intercept of the parabola is 20

This means, (2) becomes 20 = p(0-6)²+2

i.e. p = 1/2

So, function will be f(x) = 1/2(x-6)²+2

Therefore, function that models the situation is  f(x) = 1/2(x-6)²+2.

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Answer:

55

Step-by-step explanation:

I'm assuming n is the term #..

[tex]f(4) = 3(4)^2+7[/tex]

f(4) = 3 * 16 + 7

f(4) = 48 + 7

f(4) = 55

Answer:

The sequence is the ratio of 4:8, or 16:32. This is because the sequence needs to be divided into 2 different factors in order for it to match. The sequence is...

add 4, add 8, add 16, continue on.

The formula is...

4 * x = sequence

In this case, x is the increasing factor. I substituted it due to the fact that it's a constantly increasing number, not just a straight-up number we can declare.

Answer:

4

Step-by-step explanation:

Given,

[tex]6+log\frac{3}{2} (\frac{1}{3\sqrt{2} } \sqrt{4-\frac{1}{3\sqrt{2} }\sqrt{4-\frac{1}{3\sqrt{2} } ...} }[/tex]

Let,

[tex]x= \sqrt{4-\frac{1}{3\sqrt{2} }\sqrt{4-\frac{1}{3\sqrt{2} }\\[/tex]

By this we get

[tex]x=\sqrt{4-\frac{1}{3\sqrt{2} }(x) } }[/tex]

On squaring both sides,

[tex]x^{2} =4-\frac{1}{3\sqrt{2} }(x) } }\\\\x^{2} -4+\frac{x}{3\sqrt{2} } =0\\\\3\sqrt{2} x^{2} -12\sqrt{2} +x=0\\\\x=\frac{-1+\sqrt{1-(-12\sqrt{2})*(3\sqrt{2})*4 } }{2*3\sqrt{2} } \\\\x=\frac{-1+\sqrt{289} }{6\sqrt{2} } \\\\x=\frac{-1+17}{6\sqrt{2} } \\\\x=\frac{8}{3\sqrt{2} }[/tex]

Now,

[tex]6+log\frac{3}{2} [\frac{1}{3\sqrt{2} } *\frac{8}{3\sqrt{2} } ]+log\frac{3}{2} *[\frac{8}{9*2} ]\\\\6+log\frac{3}{2}(\frac{4}{9} )\\\\6-log\frac{3}{2}(\frac{9}{4} )\\\\6-log\frac{3}{2} (\frac{3}{2})^2 \\\\6-2=4[/tex]

[tex]\sqrt{4 - \dfrac1{3\sqrt2} \sqrt{4 - \dfrac1{3\sqrt2} \sqrt{4 - \dfrac1{3\sqrt2} \sqrt{\cdots}}}}[/tex]

Starting from the identity

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

take the positive square root on both sides.

[tex]x - y = \sqrt{x^2 - 2xy + y^2}[/tex]

Note that we must have [tex]x\ge y[/tex]. Rewrite the radicand and substitute [tex]x-y[/tex].

[tex]x - y = \sqrt{x^2 - xy - y (x - y)} \\\\ ~~~~ = \sqrt{x^2 - xy - y \sqrt{x^2 - xy - y (x - y)}} \\\\ ~~~~ = \sqrt{x^2 - xy - y \sqrt{x^2 - xy - y \sqrt{x^2 - xy - y (x - y)}}} \\\\ ~~~~ \vdots \\\\ ~~~~ = \sqrt{x^2 - xy - y \sqrt{x^2 - xy - y \sqrt{x^2 - xy - y \sqrt{\cdots}}}}[/tex]

Let [tex]y=\frac1{3\sqrt2}[/tex]. Solve for [tex]x[/tex].

[tex]x^2 - \dfrac x{3\sqrt2} = 4 \\\\ x^2 - \dfrac x{3\sqrt2} + \dfrac1{72} = \dfrac{289}{72} \\\\ \left(x - \dfrac1{6\sqrt2}\right)^2 = \dfrac{289}{72} \\\\ x - \dfrac1{6\sqrt2} = \pm \dfrac{17}{6\sqrt2} \\\\ x = \dfrac{18}{6\sqrt2} \text{ or } x = -\dfrac{16}{6\sqrt2} \\\\ x = \dfrac3{\sqrt2} \text{ or } x = -\dfrac8{3\sqrt2}[/tex]

Take the positive solution to ensure [tex]x>y[/tex]. Then the infinitely nested root expression in the logarithm converges to

[tex]x - y = \dfrac3{\sqrt2} - \dfrac1{3\sqrt2} = \dfrac{4\sqrt2}3[/tex]

and the overall expression has a value of

[tex]6 + \log_{\frac32} \left(\dfrac1{3\sqrt2} \times \dfrac{4\sqrt2}3\right) = 6 + \log_{\frac32} \left(\dfrac49\right) \\\\ ~~~~ = 6 + \log_{\frac32} \left(\dfrac23\right)^2 \\\\ ~~~~ = 6 - 2 \log_{\frac32} \left(\dfrac32\right) \\\\ ~~~~ = 6 - 2 = \boxed{4}[/tex]

Answer:

1=false 2=false 3=true 4=true 5=false 6=false

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

1/2 + 6/6

= (1*3)/(2*3) + 6/6

= 3/6 + 6/6

= 9/6

= 3/2

So the fraction 1/2 make the equation true.

Let's check

[tex]\\ \rm\Rrightarrow 6/6+1/2[/tex]

[tex]\\ \rm\Rrightarrow 1+1/2[/tex]

[tex]\\ \rm\Rrightarrow 2+1/2[/tex]

[tex]\\ \rm\Rrightarrow 3/2[/tex]

Yes true

Answer:

In standard from, the value will be 8.234 * 10^17

Step-by-step explanation:

The answer shown on the screen of the calculator after multiplying is;

8,234 E14

This is same as;

8,234 * 10^14

In the stands from, this will be;

8.234 * 10^3 * 10^14 = 8.234 * 10^17

Answer:

4.2 team members per day

Step-by-step explanation:

5 + 4 + 2 + 7 + 3 = 21

21/5 = 4.2

An average is the arithmetic mean of a set of observations. The average number of team members who reached their goal per day is 4.2.

An average is the arithmetic mean of a set of observations. it is given by the formula,

[tex]\rm Average=\dfrac{\text{Sum of All the workers of reached their goal}}{\text{Number of working days}}[/tex]

As it is given that the Number of team members that reach their goal on the weekdays Monday, Tuesday, Wednesday, Thursday, and Friday are 5, 4, 2, 7, and 3 respectively. Therefore, the average number of team members who reached their goal per day can be written as,

[tex]\rm Average=\dfrac{\text{Sum of All the workers of reached their goal}}{\text{Number of working days}}\\\\\\Average = \dfrac{5+4+2+7+3}{5} = \dfrac{21}{5}=4.2[/tex]

Thus, the average number of team members who reached their goal per day is 4.2.

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78 sit ups in 2 minutes

so

= 78 : 2 sits in 1 minute = 39 sits up per minute

x 5 = 195 sit ups in 5 minutes

Answer:  39 situps per time

Step-by-step explanation:

Answer:

[scale]=[drawing]/[real]-----------> [real]=[drawing]/[scale]

scale=3 cm/ 4 m------> 0.75 cm/m

the dimensions of backyard in the drawing are 9 cm x 6 cm

step 1

find the real dimensions of backyard

for 9 cm

[real]=[drawing]/[scale]

[real]=[9]/[0.75]----------> 12 m

for 6 cm

[real]=[drawing]/[scale]

[real]=[6]/[0.75]----------> 8 m

so

the real dimensions of backyard are 8 m x 12 m

[the area of the real backyard ]=8*12--------> 96 m²

the answer is 96 m²

A biased sample is best described by:

C. The sample does not accurately represent the population.

It is a common statistics practice, when we want to study something from a population, we find a sample, which is a group of members of this population. The sample has to be representative of the population, that is, it has to involve all of it's groups. If it does not involve all the groups, it is not an accurate representation of the population, and is called biased, hence option C is correct.

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Answer:

7

Step-by-step explanation:

y2-y1/x2-x1=  14-0/5-3  14/2=7

Answer: 4/15

For fraction multiplication, multiply the numerators and then multiply the denominators

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 12 and 45 using

GCF(12,45) = 3

Therefore: it's 4/15

Hope this helps (>'-'<)

Answer: 14

Step-by-step explanation:

Answer:

1.5 inches

Step-by-step explanation:

18 divided by 12 = 1.5

Answer:

C. All numbers are rational numbers

Step-by-step explanation:

In mathematics, any number that can be stated in fraction form or ratios is said to be a rational number. This simply means that some numbers cannot be written in fraction form and so all numbers are not rational numbers.

Examples of rational numbers include terminating decimals, integers, repeating decimals and the fractions.  

The other non-rational numbers are called irrational numbers, as they cannot be written in fraction form.

Answer:

[tex]\frac{1}{a^{7} }[/tex]

Step-by-step explanation:

Use this rule:

[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

So, this gives you

[tex]a^{-13+6}[/tex]

This equates to:

[tex]a^{-7}[/tex]

However, we cant leave the exponent negative, so we use this formula:

[tex]a^{-b}=\frac{1}{a^b}[/tex]

So, the answer is:

[tex]\frac{1}{a^{7} }[/tex]

Answer:

There is no denominator a^-7

The power is positive 1/a^7

Step-by-step explanation:

Remark

We are not told what the restrictions on the power are. Here are the possibilities.

So I will give the answer to both conditions. You will have to choose.

There is no denominator

That means that The powers are subtracted

Multiply numerator and denominator by a+6

a^- 13 * a^6

=========

a^-6 * a^6

To start a^(-6 + 6) = a^0 which = 1. That is not written, so you are left with a^ (-13 + 6) = a ^ -7

The answer must have a positive power.

Multiply the numerator and denominator by a^13.

numerator

a^-13 * a^13

a^(-13 + 13)

a^0

1

So we are left with 1 in the numerator.

a^-6 * a^13

a^(-6 + 13)

a^7

Answer: what is left is  1/a^7

Answer:

the answer is D.all of the above

Step-by-step explanation:

The ozone layer helps to sustain terrestrial life by absorbing incoming UV radiation.

Option A is the correct answer.

The ozone layer is a layer of gas in the Earth's stratosphere that helps to protect the planet from the harmful effects of ultraviolet (UV) radiation from the sun.

We have,

UV radiation can cause damage to living organisms, such as skin cancer, cataracts, and other health problems.

The ozone layer absorbs much of this radiation, preventing it from reaching the Earth's surface and thus helping to sustain terrestrial life.

Option B is incorrect because the ozone layer is located in the stratosphere, above the troposphere.

Option C is incorrect because while the ozone layer can play a role in maintaining the Earth's temperature, its primary function is to absorb UV radiation.

Option D is incorrect.

Thus,

The ozone layer helps to sustain terrestrial life by absorbing incoming UV radiation.

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#SPJ5

Answer: D: x/2 = 45; x = 90

Step-by-step explanation:

half of a number is 45:

x/2 = 45

.: x = 90

Your answer is D

Answer:

D

Step-by-step explanation:

Answer:

y=-7

Step-by-step explanation:

Simple enough. Slope of zero means that x does not have to be determined. So if you just put the y coordinate in a slope of zero, you should get your answer.

The equation of line is y = -7.

Equation of line is,

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

Where m is slope.

Given that, slope is 0.

Equation of line become, [tex]y=0*x+c=c[/tex]

And Line passes through the point (5, -7)

Substitute these point,

       [tex]c=-7[/tex]

Hence, equation of line is, [tex]y=-7[/tex]

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Step-by-step explanation:

cost of 1 kg of jam = x

cost of 1 kg of butter = y

3x + 2y = 29 .....1

6x + 3y = 54 .....2

.....1 × 2 both sides of equation

6x + 4y = 58 .....3

.....3 - ......2

y = 4

replace y = 4 in 1......

3x + 8 = 29

x = 7

Answer:

first pic- 1. slope is -2/3, y-inter is 1, y=-2/3x+1

2.slopeis 3/-2, y-inter is -1, y=3/-2x+(-1)

Answer:

second pic- 1. slope is -3/-2, y-inter is 0, y=-3/-2x+0

2. slope is 1/2, y-inter is -1, y=1/2x+(-1)

Answer:

  see attached for a graph

Step-by-step explanation:

It looks like you want to plot a graph of the function. For a piecewise function like this one, the effort is divided into pieces. The "or equal to" part of the comparison symbol tells you the end value is included in that interval.

__

For the piece between x=-8 and x=-6, you can find the y-values by evaluating the function for those x-values.

For x = -8: y = -1/2(-8) = 4.

For x = -6: y = -1/2(-6) = 3.

So, the left piece can be plotted by drawing a line segment between points (-8, 4) and (-6, 3).

__

For the piece between x=-6 and x=1, you can do the same thing:

For x=-6: y = -(-6) -3) = 6-3 = 3

For x=1: y = -(1) -3 = -4

So, the right piece can be plotted by drawing a line segment between points (-6, 3) and (1, -4). We notice that (-6, 3) is already the end point of the first piece, so the function is continuous at x=-6. (Sometimes there is a discontinuity between pieces. Not here.)

You can also plot the right piece by recognizing it is a line with a y-intercept of -3 and a slope of -1. That is, point (0, -3) will be on that line, and it will have a "rise" of -1 for each "run" of 1 (to the right).

__

A graph is shown. We have made the pieces different colors, so you can see what they are. And we have plotted a filled dot at (-6, 3) to indicate that point is part of the function definition. (The dot is unnecessary.)

Answer:

45

Step-by-step explanation:

this is correct this is correct