-
4. Which shows the solution to the
inequality? 6(x-2) +21 <39

Answer:

Step-by-step explanation:

The line rises to the left so the slope is negative.

The slope m = -24/12 = -2.

Using the point-slope formula and taking the point (12, 0) on the line:

y - y1 = m(x - x1)   where m = -1, x1 = 12 and y = 0:

y - 0 = -2(x - 12)

y = -2x + 24   <------- this is the required equation.

Answer:

Blank 1 : -2

Blank 2 : 24

Step-by-step explanation:

The first blank denotes the rate of change, or the slope of the graph.

Slope = y₂ - y₁ / x₂ - x₁

The second blank denotes the value of variable K when the value of variable J is 0, or rather the y-intercept of the graph.

The y-intercept is clearly (0, 24)

No

Step-by-step explanation:

For a triangle to have a right angle the square sums of the legs have to equal the square of the hypotenuse.

In this case 9 is the hypotenuse which is the longest side in a triangle. 5 and 7 are the two smaller sides which make them the legs.

Putting this set of numbers into the pythagorean theorem is the way to solve this.

5²+7² should equal 9² if the triangle is a right triangle.

Solve the squares: 25+49=81

This would add up to be 74 and that is not equal to 81, so by this statement we can conclude that 5, 7, and 9 do not make a right triangle.

Answer:

7/32

Step-by-step explanation:

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

To find a fraction between 1/4 and 1/5:

1. Make common denominators with both fractions. The larger the common denominator, the more you will find.

2. Choose any fraction between 1/4 and 1/5. That fraction will be in between 1/4 and 1/5.

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

[tex]\dfrac{1}{4}\ \text{and }\dfrac{1}{5} \ \rightarrow \ \dfrac{1 \times 40}{4 \times 40} \ \text{and} \ \dfrac{1 \times 32}{5 \times 32} \ \rightarrow \ \dfrac{40}{160} \ \text{and} \ \dfrac{32}{160}[/tex]

Now, you may choose any fraction between 40/160 and 32/160.

My chosen fraction is 35/160, which when simplified, gives 7/32.

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

Answer:

[tex]\dfrac{9}{40}[/tex]

Step-by-step explanation:

Subtract 1/5 from 1/4, divide by 2, then add to 1/5:

[tex]\implies \dfrac{\frac14-\frac15}{2}+\dfrac15[/tex]

[tex]\implies \dfrac{\frac{5}{20}-\frac{4}{20}}{2}+\dfrac15[/tex]

[tex]\implies \dfrac{\frac{1}{20}}{2}+\dfrac15[/tex]

[tex]\implies \dfrac{1}{20} \times \dfrac12+\dfrac15[/tex]

[tex]\implies \dfrac{1}{40}+\dfrac15[/tex]

[tex]\implies \dfrac{1}{40}+\dfrac{8}{40}[/tex]

[tex]\implies \dfrac{9}{40}[/tex]

The equation that relates the number of campers this year to the number of campers last year is c = 440 / 1.10

The number of campers last year is 400.

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentages are used to measure frequency.

The number of campers last year = number of campers this year / (1 + percentage increase)

440 / 1.1 = 400

To learn more about percentages, please check: https://brainly.com/question/25764815

Answer:

90

Step-by-step explanation:

Measure of one arc = 90°

-> Measure of other arc = 360°- 90° = 270°

x° = 1/2 (270° - 90°)

-> x° = 1/2 * 180°

-> x° = 90°

-> x° = 90°

-> x = 90

Using the slope concept, it is found that the angle measurement has to be within 1.2º of 30º.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem, considering the horizontal distance and the actual angle, the following equation is applied to find the actual height:

[tex]\tan{30^\circ} = \frac{h}{25}[/tex]

[tex]h = 25\tan{30^\circ}[/tex]

h = 14.43.

For an error of 5%, the bounds of h are as follows:

[tex]h_{min} = 0.95 \times 14.43 = 13.71[/tex]

[tex]h_{max} = 1.05 \times 14.43 = 15.15[/tex]

Hence, the angles will be given by:

[tex]\tan^{\alpha} = \frac{13.71}{25}[/tex]

[tex]\alpha = \tan^{-1}{\left(\frac{13.71}{25}\right)}[/tex]

[tex]\alpha = 28.8[/tex]

[tex]\tan^{\alpha} = \frac{15.15}{25}[/tex]

[tex]\alpha = \tan^{-1}{\left(\frac{15.15}{25}\right)}[/tex]

[tex]\alpha = 31.2[/tex]

Hence the angle measurement has to be within 1.2º of 30º.

More can be learned about the slope concept at https://brainly.com/question/18090623

Answer:

90 if I am wrong sorry I have a hard time with math

Answer:

22.5

Step-by-step explanation:

By the angle bisectors theorem,

30/32 = x/24

x=24(30/32) =22.5

Answer:

Step 2-3

Step-by-step explanation:

I don't know what's wrong with step 2 but in step 3 the student added the exponent instead of multiplying.

That automatically makes every other step done afterwards wrong but it's not 3-4 because the math is right it's just that step 3 messed up step 4 laws of exponent wise.

7+7+5+5=24

So therefore the permeter is 24

Answer:

Low

Step-by-step explanation:

Low because it only overlaps twice.

Answer:

5 or 5/8

Step-by-step explanation:

To go from 10/16 to a bottom number/denominator of 8, you have to divide by 2.

Whatever you do to the top, you also do to the bottom, so you would divide 10, the numberator, by 2 to find the missing value.

10/2 is 5.

There is your answer.

Using the binomial distribution, it is found that:

3.1 There is a 0.5033 = 50.33% probability that he makes at most one sale.

3.2 There is a 0.8322 = 83.22% probability that he makes at least one sale.

3.3. There is a 0.4404 = 44.04% probability that he makes two or three sales.

3.4. There is a 0.0011 = 0.11% probability that he makes six sales.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

Item 1:

The probability that he makes at most one sale is:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{8,0}.(0.2)^{0}.(0.8)^{8} = 0.1678[/tex]

[tex]P(X = 1) = C_{8,1}.(0.2)^{1}.(0.8)^{7} = 0.3355[/tex]

Then:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1678 + 0.3355 = 0.5033[/tex]

There is a 0.5033 = 50.33% probability that he makes at most one sale.

Item 2:

The probability that he makes at least one sale is:

P(X > 1) = 1 - P(X = 0) = 1 - 0.1678 = 0.8322.

There is a 0.8322 = 83.22% probability that he makes at least one sale.

Item 3:

The probability that he makes two or three sales is given by:

[tex]P(2 \leq X \leq 3) = P(X = 2) + P(X = 3)[/tex]

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{8,2}.(0.2)^{2}.(0.8)^{6} = 0.2936[/tex]

[tex]P(X = 3) = C_{8,1}.(0.2)^{3}.(0.8)^{5} = 0.1468[/tex]

Then:

[tex]P(2 \leq X \leq 3) = P(X = 2) + P(X = 3) = 0.2936 + 0.1468 = 0.4404[/tex]

There is a 0.4404 = 44.04% probability that he makes two or three sales.

Item 4:

The probability that he makes six sales is P(X = 6), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 6) = C_{8,6}.(0.2)^{6}.(0.8)^{2} = 0.0011[/tex]

There is a 0.0011 = 0.11% probability that he makes six sales.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

Answer:

7/2(a+b)

Step-by-step explanation:

To add fractions you need to find the LCM (least common multiplier) and then combine.

least common multiplier of a+b, 2(a+b) : 2(a + b)

Adjust fractions based of LCM

2/2(a + b) + 5/2(a +b)

2+5/2 (a + b) =

7/2 (a + b)

I hope this makes sense! :)

Answer:

<DFE

Step-by-step explanation:

Verticle angles are when they are directly apart and equal. So,

Answer:

Step-by-step explanation:

Firsly ,we notice that the base of the prism is a regular pentagon

regular means the five sides of the pentagon are equal in measure .

_______

Formula :

Area of a regular pentagon B = 1/2 × p × a;

where p is the perimeter of the pentagon

          a is the apothem of the pentagon

_______________________________

then p = 5×6 = 30 ft

a = 4.1 ft. (Given)

therefore ,

B = 1/2    ×  p  ×   a

   = (1÷2) × 30 × 4.1 = 61.5 ft²

height of the prism h = 12 ft  (given)

Volume V = B × h = 61.5 × 12 = 738.ft³

Since the surface area of this cylinder is [tex]432\pi \;yd^2[/tex], its diameter is equal to 12 yards.

Mathematically, the surface area (SA) of a cylinder is given by this formula:

[tex]S.A = 2\pi rh + 2\pi r^2[/tex]

Where:

Given the following data:

Substituting the given parameters into the formula, we have;

[tex]432\pi = 2\pi r(5r) + 2\pi r^2\\\\432\pi = 2\pi 5r^2 + 2\pi r^2\\\\216=5r^2+r^2\\\\216=6r^2\\\\r^2=36\\\\r=\sqrt{36}[/tex]

r = 6 yards.

For the diameter:

Diamter = 2 x radius

Diamter = 2 x 6

Diameter = 12 yards.

Read more on surface area here: brainly.com/question/21367171

Answer:

24

Step-by-step explanation:

So, Dersan's path is a right triangle. You have to find the last side. You can use the triples or 6^2+8^2=c^2 but I'll use a triple.

3,4,5.

The last side is 10.

6+8+10=24

hope this helped!

the first 400 digits of pi

3.1415926535897932384626433832795028841971

6939937510582097494459230781640628620899

8628034825342117067982148086513282306647

0938446095505822317253594081284811174502

8410270193852110555964462294895493038196

4428810975665933446128475648233786783165

2712019091456485669234603486104543266482

1339360726024914127372458700660631558817

4881520920962829254091715364367892590360

0113305305488204665213841469519415116094

Answer:

12.058

Step-by-step explanation:

You steal one "count" from the 8, and move it to the 7 so you have 12.0587, instead of 12.0578. Then, you are able to take off the 7 from the back.

Answer:

Length: 24 cm

Width: 8 cm

Explanation:

Let Width be "w"

Then Length is "3w"

=================

Perimeter of rectangle = 2(length+width)

===================================

So, width is 8 cm

Length: 3w ⇒ 3(8) ⇒ 24 cm

Answer:

Step-by-step explanation:

Given

Solving

The distance between Vega 3 and the Mars (MV) illustrates cosine function, and the distance is 29.1 million light years or 142.8 million light years

From the question, we have the following parameters

See attachment for the illustration of the given parameters.

The distance between Vega 3 and the Mars (MV) is then calculated using the following cosine function

VS² = MS²+ MV² - 2 * MS * MV * cos(Ф)

This gives

4489 = 8649+ MV² -  171.96MV

Subtract 8649 from both sides

MV² -  171.96MV = -4160

Rewrite as:

MV² -  171.96MV + 4160 = 0

Using a graphing tool, we have:

MV = 29.1 and MV = 142.8

Hence, the distance between Vega 3 and the Mars is 29.1 million light years or 142.8 million light years

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Answer:

non renewable you can't renew what you already bought and renewable you can renew what you bought

Answer:

yes

Step-by-step explanation:

Answer:

1000

Step-by-step explanation:

Let's round!

96.8 can be rounded to 100

9.74 can be rounded to 10

100*10=1000

Hope this helps!

The estimated value of the given product is 970. The given product is (96.8×9.74). This is obtained by using the rounding-off method.

The given product is (96.8×9.74)

Here the first decimal number in the product is 96.8

Since the digit after the decimal point 8 is nearer to the value of 10, it is rounded to 97. I.e., 96.8≅97

And the second decimal number is 9.74

Since the digit after the decimal 7is nearer to the value of 10, it is rounded to 10. I.e., 9.74≅10

So, the product is  97×10=970

Thus, 96.8×9.74≅970 (approx.)

Therefore, the estimated value is 970.

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Answer:

47

Step-by-step explanation:

49x - 2

==> plug in x = 1

49(1) - 2

==> multiply 49 and 1

49 - 2

==> subtract 2 from 49

= 47

Answer:

47

Step-by-step explanation:

49x means 49×x

So substituting 1 into the equation gives us :

(49×1)-2

49-2

47

Therefore our answer is 47.

Answer:

First problem:  max when x = 4

Second problem:  min when x = 1

Step-by-step explanation:

The graph of f(x) = –|x – 4| – 5 is a translation of that of g(x) = -|x|.  The vertex of the latter is (0, 0).  First this must be translated 4 units to the right and then the resulting graph 5 units downward.  The vertex of this translation is (4, -5).  Since this graph opens downward, this (4, -5) is the maximum function value, that is, when x = 4.

The graph of f(x) = x2 – 2x +­ 1, or (better yet) f(x) = x^2 – 2x +­ 1, or

f(x) = (x - 1)^2 + 0, is that of a parabola that opens upward and has its minimum at x = 1, or (1, 0).

Answer:

Hope the pictures will help you.

The solution to the system of equations is x = -2 and y = 5.

Given the parameters:

7y - 5x = 45

x = 8 - 2y

To solve the system of equations, substitute the expression for x from the second equation into the first equation.

7y - 5x = 45

Plug in x = 8 - 2y:

7y - 5( 8 - 2y) = 45

7y - 40 + 10y = 45

Collect and add like terms:

7y + 10y = 45 + 40

17y = 85

y = 85/17

y = 5

Plug the value of y into the second equation and solve for x:

x = 8 - 2y

Plug in y = 5:

x = 8 - 2( 5 )

x = 8 - 10

x = -2

Therefore, the value of x is -2 and y is 5.

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Answer:

i dont know what youre trying to answer but if your trying to answer how much money can you get if you get all of the marbles you get $9

just blue- $1.50

just orange- $1.50

just black- $3

just green- $3

red=$0