As a single logarithm, 2log2 6- log29+ 1/3log2 27 = log2 12.

Rewrite 1/4 to have 8 as the denominator: 1/4 = 2/8

Now add the two days together:

2/8 + 3/8 = 5/8

Answer: 5/8

The total amount collected over the life of the bond is $7,500.

A bond is a debt instrument that entitles its holder to regular interest payments. At the end of the life of the bond, the bondholder receives the amount invested back.

Total earnings = interest + amount invested

(20 x 0.025 x 5000) = $2500

Amount invested = $5000

= 2500 + 5000 = $7,500

To learn more about interest, please check: https://brainly.com/question/26164549

#SPJ1

Answer:
56

Step-by-step explanation:

with Usain Bolt getting the the first place there is only 9 other contestants that can get the two other available medal position. When the second place is taken, there will be 8 remaining contestants for a third place therefore you do 9 multiplied by 8 to get 56 differrent combinations of contestants for the third or second place medal

The amount of force it takes to push Jeff’s race car will be 1875 Newtons.

Force is explained as the multiplication of mass and acceleration. Its unit is N. It is the external agent which helps to change the shape and size of an object.

The formula of force will be

F = ma

Where m is the mass of the body and a is the acceleration of the body.

Then the amount of force it takes to push Jeff’s race car if the mass of the race car is 750 kg and the acceleration is 2.5 meters per square second.

Then we have

F = 750 x 2.5

F = 1875 Newton

To learn more about the force refer to the link;

https://brainly.com/question/26115859

#SPJ1

Answer:

Step-by-step explanation:

x + 3 = -x - 1

2x + 3 = -1

2x = -4

x = -2

y = -2 + 3

y = 1

(-2, 1)

answer is A

Answer:

30 mm, 2.5cm,20cm and 1m

Based on the SAS congruence criterion, the statement that best describes Angie's statement is:

Two triangles having two pairs of congruent sides and a pair of congruent angles do not necessarily meet the SAS congruence criterion, therefore Angie is incorrect.

The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.

An included angle is found between two sides that are under consideration.

See image attached below that demonstrates two triangles that are congruent by the SAS Congruence Theorem.

Thus, two triangles having two pairs of corresponding sides and one pair of corresponding angles that are congruent to each other is not enough justification for proving that the two triangles are congruent based on the SAS Congruence Theorem.

The one pair of corresponding angles that are congruent MUST be "INCLUDED ANGLES".

Therefore, based on the SAS congruence criterion, the statement that best describes Angie's statement is:

Two triangles having two pairs of congruent sides and a pair of congruent angles do not necessarily meet the SAS congruence criterion, therefore Angie is incorrect.

Learn more about congruency at

brainly.com/question/14418374

#SPJ1

Answer:

0 ≤ y ≤ 8

Step-by-step explanation:

DOMAIN is x values of a function/graph

RANGE is the y-values that a function can have .....

     this one goes from 0 to 8 inclusive

The slope of the cubic polynomial and it's y-intercept are respectively; f(1) = -4 and f(0) = -6

We are given the equation;

f(x) = 2x³ - 6

Now, because the highest power of x is 3, it means that this is a cubic polynomial and not linear because it has a degree of 3

Thus, let us differentiate to get the slope;

f'(x) = 6x² - 6

At f'(x) = 0; x = 1

Thus, slope is;

f(1) = 2(1)³ - 6

f(1) = -4

y-intercept is f(x) at x = 0. Thus;

f(0) = 2(0³) - 6

f(0) = -6

Read more about slope of equation at; https://brainly.com/question/1884491

#SPJ1

Let's start with the given arc and its angle.

The angle YWX is going to be half the arc length.

YWX = 1/2 (226) = 113

Angles VWX and YWX form a linear pair (or are supplementary angles), which means that their sum is 180 degrees.

(15x - 8) + 113 = 180

15x + 105 = 180

15x = 75

x = 5

Hope this helps!

see the attached figure

A(4,8)  B(0,7)  C(4,3)

the line of reflection is x=5

the reflection is (x,y)-------------------> (10-x,y)

therefore

A(4,8)-----------------> A1(10-4,8)------> A1(6,8)

B(0,7)-----------------> B1(10-0,7)------> B1(10,7)

C(4,3)-----------------> C1(10-4,3)------> C1(6,3)

Answer:

90°

Step-by-step explanation:

This is important to remember, the three interior angles will always have a sun of 180.

knowing this it’s pretty basic math

a + b + c = 180

33 + 57 + c = 180

90 + c = 180

[subtract 90 from each side (90 cancels out)]
c = 90°

…

Check
- > 33 + 57 + 90 = 180

33 + 147 + = 180

180 = 180

Check!

The proof of the given statements is shown below:

A line segment which touches a circle specified to only one point is called a tangent to that circle.

1. given

2. A line is a tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency.

3. Since the tangent is perpendicular to radius i.e., EFC is right angle then,

   angle EFC =90

4.  Sum of interior angles of a triangle is 180°.

5. proved above: angle EFC= 90

6. FEC + ECF= 180-90=90

7. As proved above

  FEC + ECF=90, its shows that angle FEC and ECF are complementary angle.

Learn more about tangent here:

brainly.com/question/19064965

#SPJ1

Answer:

30 & 60°

Step-by-step explanation:

2x + X + 90 = 180

3x = 90

X = 30°

so the accute angles are 30° and 60°

Answer:

c.9.5

Step-by-step explanation:

im awesome so so very

Answer:

28815.3333333

Step-by-step explanation:

Answer:

3260

Step-by-step explanation:

Answer:

Discus, Hurdles, Long jump, and 100m

Step-by-step explanation:

Answer:

A) -7 is the least

Step-by-step explanation:

A)  (-5) + (-2) = (-7)

If two numbers have same sign, add and the result will have the common sign.

b) (-5) ÷ (-2) = 2.5

In division negative number divided by another negative number will give a positive number.

c) (-5)*(-2) = 10

In multiplication multiplication of two negative numbers will give a positive number.

d) = -5

In these (-7) is the least integer

Answer:

4/5

Step-by-step explanation:

Answer:

=4/5 or 0.8 as decimal

Step-by-step explanation:

8/10

Factor the number: 8=2· 4

2x4

Factor the number: 10 = 2· 5

2x4/2×5

Cancel the common factor: 2

=4/5

or (decimal 0.8)

Answer:

8.382 cm

Step-by-step explanation:

1in = 2.54 cm

3.30 x 2.54 = 8.382 cm

Step-by-step explanation:

Given:
40 houses,

500 liters of waters everyday for common utilities

Unknown amount of water per house which we will call x.

4500 max liters for the gated community

Solve:

4500=40x+500

subtract 500 from both sides

4000=40x

divide by 40

100=x

Check:

40(100)+500=4500

4000+500=450

correct

Answer:

100 liters of water can be used by each house.

Answer:

32x^10y

Explanation -

You want to use distributive property. Take 2x^5 and the Exponent 2y^5

It should look like this

Answer:

let M point x1, Y1 and f point X2,y2 then we know the formula of distance root (x2-x1)^2+(y2-y1)^2 then you will found the distance

Answer:

a.i.

[tex]mab = \frac{ya - yb}{ xa - xb} = \frac{8 - 4}{9 - 12} = \frac{4}{ -3} [/tex]

a.ii.

[tex]mc = mab = \frac{4}{ - 3} \\ (y - y1) = m(x - x1) \\ y - ( - 2) = \frac{4}{ - 3}(x - 4) \\ y + 2 = \frac{4}{ - 3}x + \frac{16}{3} \\ y = \frac{4}{ - 3} x + \frac{16}{ 3} - 2 \\ y = \frac{4}{ - 3}x + \frac{10}{3} [/tex]

Answer:

Step-by-step explanation:

Equation

-6(1-4v) = 3v-8(-6-6v)                  Use the distributive property to get rid of the brackets.

Solution

-6 + 24v = 3v +48 +48v              Combine

-6 + 24v = 51v + 48                     Subtract 24v from both sides

-6 +24v-24v =51v-24v +48         Combine.

-6 = 27v + 48                              Subtract 48 from both sides.

-6-48 = 27v+48-48                     Combine

-54 = 27v                                    Divide by 27

-54/27=27v/27

-2 = v

Answer

v=-2

Answer:

m∠A = 49°

Step-by-step explanation:

According to Angle Sum Property,

m∠A