State the property of logarithms used to rewrite the expression:
logs 6 - logs 2 = log: 3

It's 36 because f(x)=4 has a y-intercept of 4 and g(x)=2x2-13x+9 has a y-intercept of 9.

Product is a term of muptiplication and 9x4 is 36.

Answer:

720°, 2340°, 180°

Step-by-step explanation:

Look at the attached image of a regular hexagon.  I drew all possible lines from a vertex to other vertices (AC, AD, AE).  Drawing in all those diagonals splits the hexagon into 4 triangles, and adding up the measures of all the triangle angles would account for all the interior angles of the hexagon.

♦  Four triangles have an angle sum of 180° x 4 = 720° (180° in each triangle).

See attached image2 to see what happens in an octagon.  There are six triangles formed, so the total of all interior angle measures is 6 x 180° = 1080°.

What about a 15-sided regular polygon?  How many triangles would be formed by putting in all the diagonals coming from one vertex?  There will be 2 fewer triangles than the number of vertices, 13.

♦  The total of interior angle measures in a 15-gon is 13(180°) = 2340°

♦  A polygon with 3 sides is a single triangle; interior angle sum = 180°

Answer:

10

Step-by-step explanation:

Cake remaiing after eating 1/3 = 1/3 x 5 = 5/3 kg

let x = pieces he divided the cake into

5/3 ÷ x = 1/6

1/ x = 3/5 x 1/6 = 1/10

x = 10

Answer:

fvbbbbb

Step-by-step explanation:

Answer: She ran 7 3/5 miles on the two days

Step-by-step explanation

Miles ran by Deborah on Monday =32/5 miles

Miles ran by Deborah on Tuesday = 41/5 miles'

Total miles ran by Deborah on the two days

=3 2/5 +4 1/5

=7   2+1 /5

=7 3/5 miles

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 6) and (x₂, y₂ ) = (- 1, 8) ← 2 ordered pairs from the table

m = [tex]\frac{8-6}{-1-1}[/tex] = [tex]\frac{2}{-2}[/tex] = - 1 , then

y = - x + c ← is the partial equation

To find c substitute any ordered pair from the table into the partial equation

Using (1, 6 ) , then

6 = - 1 + c ⇒ c = 6 + 1 = 7

y = - x + 7 → B

Answer:

Answer:

1.) [tex]\frac{1}{2}[/tex] ÷ 4 = [tex]\frac{1}{8}[/tex]

2.) [tex]\frac{1}{3}[/tex] ÷ 4 = [tex]\frac{1}{12}[/tex]

3.) [tex]\frac{1}{4}[/tex] ÷ 5 = [tex]\frac{1}{20}[/tex]

4.) [tex]\frac{1}{4}[/tex] ÷ 4 = [tex]\frac{1}{16}[/tex]

5.) 3 ÷ [tex]\frac{1}{4}[/tex] = 12

6.) 4 ÷ [tex]\frac{1}{2}[/tex] = 8

7.) 5 ÷ [tex]\frac{1}{4}[/tex] = 20

8.) 4 ÷ [tex]\frac{1}{4}[/tex] = 16

Hope this helps!

Answer:

Step-by-step explanation:

During a sale at the market​, steaks sold for ​$2 and watermelons sold for ​$1.50. Declan spent ​$10 and bought a total of 6 steaks and watermelons. How many of each did he ​buy?

Let us represent

Steaks = x

Water melons = y

Our system of equations is given as:

x + y = 6.. Equation 1

x = 6 - y

During a sale at the market​, steaks sold for ​$2 and watermelons sold for ​$1.50.

$2× x + 1.5 × y = $10

2x + 1.5y = 10... Equation 2

Substitute

2(6 - y) + 1.5y = 10

12 - 2y + 1.5y = 10

12 - 10 = 2y - 1.5y

2 = 0.5y

y = 2/0.5

y = 4

Answer:

11 marbles

Step-by-step explanation:

Let x = no. of marbles-Alex

3x = no. of marbles-Billie

3x - 9 = no. of marbles-Chris

x + 3x + 3x - 9 = 68

7x - 9 = 68

7x = 77

x = 11

Alex will have 11 marbles out of a total of 68 marbles.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Alex has some marbles. Billie has three times as many marbles are Alex.

Chris has 9 fewer marbles than Billie.

In total, they have 68 marbles.

Let x = no. of marbles-Alex

3x = no. of marbles-Billie

3x - 9 = no. of marbles-Chris

The number of marbles will be calculated as,

x + 3x + 3x - 9 = 68

7x - 9 = 68

7x = 77

x = 11

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Answer:

Step-by-step explanation:

the coefficients of this quadratic are -1, 4 and 4, and so the discriminant b^2 - 4ac works out to 16 - 4(-1)(4), or 0.  Thus this graph has two real, equal roots which are the same point on the graph, the vertex, the maximum of the function.

Letting x = 0, we find that y is 4.  Thus, the y-intercept is (0, 4).  Plot this.

Using the formula x = -b / [2a], we find the axis of symmetry:

   x = -4 / [2*(-1)] = -4 / [-2] = +2

The axis of symmetry is the vertical line x = 2.  

At x = 2, y = -(2)^2 + 4(2) + 4, OR -4 + 8 + 4, or 0.

The vertex and maximum value are (2, 0).  The graph touches the x-axis in only one place.

Draw the axis of symmetry x = 2.  Plot the vertex (2, 0) and the y-intercept.  Reflect the y-intercept about the axis of symmetry to obtain a second point on the graph at the same y-value as (0, 4).

Answer:

Exact Area = 24pi square cm

Approximate Area = 75.36 square cm  (when using pi = 3.14)

Note: "square cm" can be abbreviated to "cm^2" without quotes.

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

Explanation:

Let's find the area of the full circle with radius r = 12

A = pi*r^2

A = pi*12^2

A = 144pi  

This is the exact area of the full circle in terms of pi. To get the approximate area, you would replace pi with something like 3.14 (though you could use more decimal digits in pi to get a more accurate area).

We found the area of the full circle, but we only want a pie slice of it. Each slice is 60 degrees, out of 360 total. So that means we want 60/360 = 1/6 of the full area.

In other words, there are 6 slices because 360/60 = 6, which means we'll divide the area we got by 6

(144pi)/6 = (144/6)pi = 24pi

The exact area of the pie slice is 24pi square cm

If you used the approximation pi = 3.14, then that leads to an approximate answer of 24*pi = 24*3.14 = 75.36 square cm

Answer:

3

Step-by-step explanation:

C(n) = 5n, 0 ≤ n ≤ 10       You would use this equation for finding the cost of 10 shirts. Since 10 is equal to 10.

C(n) = 5n, 0 ≤ n ≤ 10 ← You can ignore the 0 ≤n ≤10 part.

C(10) = 5(10)                 Input the value 10 as x.

C(10) = 50                    Simplified

Next,

C(n) = 4n + 5, n > 10      You would use this equation for finding the cost of 12shirts. Since 12 is greater than 10.

C(n) = 4n + 5, n > 10  ←  You can ignore the n>10 part.

C(12) = 4(12) + 5, n > 10  Input the value of 12 as x.

C(12) = 48 + 5                 Simplify

C(12) = 53    

Finally,

The question is asking you to find the difference between the cost of 12 shirts and the cost of 10 shirts. So the formula would be C(12) - C(10).

C(12) - C(10)

(53) - (50)                       Input the values of C(12) and C(10).

= 3                                  Simplify.

The answer is 3.

Answer:

A = (6,6)

Hope this helps!

Answer:

Consecutive odd numbers will be 11 and 13.

Step-by-step explanation:

Let the two consecutive odd integers are n and (n + 2).

From the given question,

Sum between twice the smallest and the biggest is 35.

Since, smallest number is 'n' and biggest is (n + 2)

Therefore equation will be,

2n + (n + 2) = 35

(2n + n) + 2 = 35

3n + 2 = 35

3n = 33

n = 11

And (n + 2) = 13

Consecutive odd numbers will be,

11, 13

Answer:

first Q . mirror

Second Q. sight and touch

Answer:    Smoothest surface: mirror

senses being used: sight and touch

hope this helps!

Step-by-step explanation:

Answer: C = 12

Step-by-step explanation:

A = x

B = x[tex]\sqrt{3}[/tex]

C = 2x

So then to find A we divide B by [tex]\sqrt{3}[/tex], which makes A =6. But C = 2x, so then C = 2(6), which equals 12. Hope that helps :)

Answer:

[tex]\large \mathbb{ANSWER:-}[/tex]

Sum of the numbers = 3

One number = 6

Other number = 8x

⎇ Equation = 8x + 6 = 3

Other number = ?

[tex]8x + 6 = 3 \\ 8x = 3 - 6 \\ 8x = - 3 \\ x = \frac{ - 3}{8} \\ x = - 0.375 [/tex]

➟ The value of x in fraction form is - 3/8 while in decimal form is - 0.375

[tex]8x = (8 \times \frac{ - 3}{8} ) \\ 8x = - 3[/tex]

⎆ The value of 8 times a number or 8x is - 3.

Answer:

Fraction form of the answer is -3/8. Decimal form is 0.375

Step-by-step explanation:

Change this into a number equation ----->   8x + 6 = 3

Answer:

9k + 36 represents the perimeter of the triangle.

Step-by-step explanation:

Have a nice day!

Answer:

-2/7

Step-by-step explanation:

reciprocal, I'll put it as negative inverse.

so just concert 3.5 to fraction, which is 7/2

then find the negative inverse that's -1÷7/2

answer us -2/7

really hope it's right(...sorry if I'm wrong) and hope you get it.

yeet this is a thicc problem...

6x - 14 + 3(2x-1) = 5 - 2(x-10)

first expand

6x - 14 + 6x -3 = 5 -2x-20

now put constants and variables on either sides of the thingamajig

6x+6x+2x= 5 - 20 + 3 + 14

14x = 2

x = 1/7

i deserve an award for that XD

The value x = 3 makes the given equation true.

Important information:

The given equation can be written as:

[tex]6x-14+6x-3=5-2x+20[/tex]

[tex]12x-17=-2x+25[/tex]

Isolate the variable.

[tex]12x+2x=25+17[/tex]

[tex]14x=42[/tex]

[tex]x=\dfrac{42}{14}[/tex]

[tex]x=3[/tex]

Therefore, the required value of x is 3.

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Answer:

D. 24

Step-by-step explanation:

substitute -4 for x:

f(-4)=20-(-4)

f(-4)=24

Answer:

Option D. {7 + i√71 / 20, 7 – i√71 / 20}

Step-by-step explanation:

10m² – 7m + 3 = 0

Using formula method, the solution to equation can be obtained as follow:

10m² – 7m + 3 = 0

Coefficient of m² (a) = 10

Coefficient of –7m (b) = –7

Constant (c) = 3

m = –b ±√(b² – 4ac) / 2a

= – –7 ±√((–7)² – 4 × 10 × 3) / 2 × 10

= 7 ±√(49 – 120) / 20

= 7 ±√(–71) / 20

Recall:

–17 = –1 × 17

Thus,

7 ±√(–71) / 20 = 7 ±√(–1 × 71) / 20

Recall:

√–1 = i

Thus,

7 ±√(–1 × 71) / 20 = 7 ± i√71 / 20

= 7 + i√71 / 20 or 7 – i√71 / 20

Therefore, the solutions to the equation are:

{7 + i√71 / 20, 7 – i√71 / 20}

Answer:

11

Step-by-step explanation:

[tex] \mathcal{SOLUTION}\begin{cases} \rm \mapsto \: \dfrac{3}{4} (x + 1) + 1 = \dfrac{1}{2} (x - 2) + 5 \\ \rm \mapsto \: \dfrac{3(x + 1)}{4} + 1 = \dfrac{1(x - 2)}{2} + 5 \\ \rm \mapsto \: \dfrac{3x + 1}{4} + 1 = \dfrac{x - 2}{2} + 5 \\ \rm \mapsto \: \dfrac{3x + 1}{4} - \dfrac{x - 2}{2} = 5 - 1 \\ \rm \mapsto \: \dfrac{3x + 1 -(2 x - 4)}{4} = 4 \\ \rm \mapsto \: \dfrac{3x + 1 - 2x + 4}{4} = 4 \\ \rm \mapsto \: x + 5 = 16 \\ \rm \mapsto \: x = 16 - 5 \\ \rm \mapsto \: x = 11\end{cases}[/tex]

Answer:

(x,y) = (7,2)

Step-by-step explanation:

Hope it helps

9514 1404 393

Answer:

  WV = 6

Step-by-step explanation:

The hash marks indicate the corresponding lines are the same length. That is, W is the midpoint of YZ, because YW ≅ WZ. Similarly, V is the midpoint of XY, because XV ≅ VY.

Using this information, it can be shown that ∆YWV ~ ∆YZX. This means corresponding sides have the same ratio.

Because YW is half of YZ, WV is half of ZX.

  YW/YZ = 1/2 = WV/ZX = WV/12

Multiplying by 12 gives the value of WV:

  WV = 12(1/2)

  WV = 6

_____

This is a long way to say that the midsegment (WV) is half the length of the base (ZX) of a triangle.

Answer:

Step-by-step explanation:

Geometric mean = 7.3

Answer:

This is the isosceles right triangle as one of the angles is 45°.

The second leg is same as the first and the hypotenuse is √2 times the leg.

This is the 30°x60°x90° triangle and the ratio of sides is:

Since the hypotenuse is 16, the other sides are:

Geometric mean of two numbers is the square root of their product.

Correct choice is C

Answer:

165 centimeters

Step-by-step explanation:

An example of calculating BMI using the formula: Height = 165 cm (1.65 m), Weight = 68 kg One centimeter is equal to 0.01 meter: 1cm = 0.01m. You are 65 inches tall. 65 * (2.54) = 165.1 cm.

Answer:

165 cm

Step-by-step explanation:

1.65 meters = 1.65 × 100 = 165 centimeters