work out the length of ab​

Answer:

51

Step-by-step explanation:

1. Approach

One is given the polygon, (ABCDE); the problem asks one to find the area of this polygon. The most logical step to take is to divide this polygon into easier parts, find the area of each part, and then add up the area to find the total area of the figure.

One way to divide this figure up is to draw the line (AC). This will create the triangle (ABC) and rectangle (ACDE).

2. Find the area of (ABC)

The formula to find the area of a triangle is the following:

[tex]A=\frac{b*h}{2}[/tex]

Where (b) is the base of the triangle, and (h) is the height. The base of the triangle (ABC) is (AC), which has a measure of (6) units. The height of the triangle is the distance from the base of the triangle to the vertex opposite the base. This measurement is (3) units. Substitute these values into the formula and solve for the area:

[tex]A=\frac{b*h}{2}[/tex]

Substitute,

[tex]A=\frac{6*3}{2}\\\\A=\frac{18}{2}\\\\A=9[/tex]

3. Find the area of (ACDE)

The formula to find the area of a rectangle is as follows:

[tex]A=b*h[/tex]

The base of the rectangle is the segment (AE), with a measure of (7) units. The height of the rectangle is the segment (AC) with a measurement of (6) units. Substitute these values into the formula and solve for the area:

[tex]A=7*6\\\\A=42[/tex]

4. Find the area of the total figure

To find the area of the total figure, add up the area of the triangle, and the area of the rectangle:

[tex]9+42= 51[/tex]

Answer:

A. log9 3=x

Step-by-step explanation:

The logarithmic form with base 9 is log₉ 3 = x.

The correct option is A.

The equation 9ˣ = 3 can be rewritten in logarithmic form by identifying the base and the result of the exponential operation. In this case, the base is 9, the result is 3, and the exponent is x.

The logarithmic form with base 9 is log₉ 3 = x.

Option A, log₉ 3 = x, is the correct representation of the equation in logarithmic form.

The logarithmic form states that the logarithm of a number (3 in this case) to a specific base (9 in this case) is equal to the exponent (x in this case).

In the equation, 9ˣ = 3, the logarithmic form log₉ 3 = x indicates that the logarithm of 3 with base 9 is equal to x. This means that 3 is the result of raising 9 to the power of x.

Therefore, option A, log₉ 3 = x, is the correct answer representing the equation 9ˣ = 3 in logarithmic form.

To learn more about the logarithms;

brainly.com/question/28346542

#SPJ6

Answer:

1/6 is less than 1/2

Step-by-step explanation:

1/6 is close to 0

8/9 is close to 1

1/6 is less than 1/2

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

Explanation:

10% in decimal form is 0.10

25% in decimal form is 0.25

The jump from 0.10 to 0.25 is "times 2.5" since (0.25)/(0.10) = 2.5

This means that we have 2.5 times as many apples compared to oranges.

If we have 2 oranges, as mentioned in every answer choice, then we must have 2*2.5 = 5 apples.

Based on this, the answer is either A or B.

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

65% turns into 0.65

The jump from 0.10 to 0.65 is 6.5 since (0.65)/(0.10) = 6.5

So we have 6.5 times as many pears as oranges.

If we had 2 oranges, then we have 2*6.5 = 13 pears

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

To summarize, we have:

2 oranges, 5 apples, 13 pears.

The answer is therefore choice A

Answer:

The second decrease is larger at 16 1/6% decrease

Step-by-step explanation:

175 to 150

Take the original price minus the new price divided by the original price

(175 -150) /175 =25/175 = 1/7 =.142857143 = 14.28 % decrease

150 to 125

Take the original price minus the new price divided by the original price

( 150-125)/150 = 25/150 = 1/6 =.16666 = 16 1/6 % decrease

The second decrease is larger at 16 1/6% decrease

Answer:    It's "reflexive" because the equation is equal on both sides

Step-by-step explanation:         The reason it isn't symmetric property, is because the variables are mismatched (it's not the same on both sides.)

Hope this helped!!

Answer:

Below in bold.

Step-by-step explanation:

a. This is the Lowest common multiple of 30 and 40 which is

120 seconds.

b. In 120 seconds Abram had completed 120/40

= 3 laps.

c.  Joshua completed 120/30 = 4 laps.

Answer:

Step-by-step explanation:

A, Lowest common mutiple of 30 and un is 120 seconds

(40x3 = 120, 30x4 = 120)

6.120/40 = 3 laPs Abram did 3 laps.

L. 120/30 = u laPs Jeshya did u laps

Answer:

none of the tables shown

Step-by-step explanation:

Inverse variation is

xy = k where k is the constant

xy = 4

in the top table

-2*2 = -4 so it cannot be the first table

In the middle table

-2 * -8 = 16  so it is not the middle table

In the bottom table

-2 *4 = -8 so it is not the bottom table

There must be a table not shown

Answer: A and C

Step-by-step explanation:

Answer:

Step-by-step explanation:

If we divide 24 by 6, we get 4, which is the other factor of 24 when given the one factor of 6. Same goes here. In order to find out what the other factor of [tex]y^2-10y+24=0[/tex] is when given one factor of y - 4, we simply divide the second degree polynomial by y - 4 to get the quotient. The quotient, then, is the other factor. Synthetic division is the easiest way to do this.

If y - 4 is the factor, then by the Zero Product Property, y - 4 = 0 and y = 4. Setting up synthetic division:

4|   1    -10     24

____________

The rule is to start by bringing down the first term, multiplying it by the number outside, then putting that product up under the next term in line:

4|   1     -10     24

             4          

     1

Then add the column, multiply the sum by the number outside, and put that product up under the next term in line:

4|    1     -10     24

               4    -24

      1      -6

And add the last column and that is the remainder. We get a 0 remainder. That means that y - 4 goes evenly into the polynomial and the other factor we are looking for is found in the numbers under the addition line. These numbers are the leading coefficients of the depressed polynomial, the polynomial that serves as the other factor: 1y - 6.

Therefore, the 2 factors that multiply together to give us [tex]y^2-10y+24=0[/tex] are (y - 4)(y - 6) and we can check ourselves by multiplying this out by FOILing to see if the result is the polynomial we started with. It is, so we're all done!

Answer:

its ( y-6 )

Step-by-step explanation:

well if you use the FOIL method you will get that answer. also i took the test and got a 100 so there u go.

Answer:

$960

Step-by-step explanation:

Let the original amount be = x

Percentage increase is equal to = 12.5%

final amount = original amount + increase

final amount = x + 0.125x

final amount = 1.125x

final amount = 1080 = 1.125x

and then solve for x

[tex]x = \frac{1080}{1.125} \\ \\ x = 960[/tex]

so in the end x is equal to $960

Solve the equation: 1080 = 1.25x

Answer:

151,031

Step-by-step explanation:

If the population of a town is decreasing at 0.8% each year, the new population of the town will be [tex]100\%-0.8\%=99.2\%[/tex] of what it was last year. To find 99.2% of something, multiply it by 0.992. Therefore, we can write the following equation:

[tex]f(x)=157,220\cdot 0.992^x[/tex], where [tex]f(x)[/tex] is the population of the town [tex]x[/tex] years after the town had a population of 157,220.

Substitute [tex]x=5[/tex] into this equation to get the projected population after 5 years:

[tex]f(5)=157,220\cdot 0.992^5, \\f(5)=151031.019048,\\f(5)\approx \boxed{151,031}[/tex]

Therefore, in 5 years, the population should be 151,031.

Answer:

m∠ADC = 90°

5x-5 = 90

x = 19

Step-by-step explanation:

Answer: some parts of your question is missing below is the missing data

Determine if the given vector field F is conservative or not. F = −6e^y, (−6x + 3z + 9)e^y, 3e^y

answer:

F is conservative

F = -6xe^y + ( 33 + 9 ) e^y + C

Step-by-step explanation:

The Potential functions for F so that F = ∇f.

F = -6xe^y + ( 33 + 9 ) e^y + C

attached below is a detailed solution

Answer:

if im not mistaken its 121

Step-by-step explanation:

Answer:

99°

Step-by-step explanation:

The interior angle sum of any 5 sided polygon is 540°.

540-53 = 487 - 137 = 350 - 105 = 245- 146 = 99°

Answer:

add an attachm3nt to make iy clear

Answer:

64 = 2(3x + x)

Step-by-step explanation:

Perimeter of the rectangle = 64 cm

Width of the rectangle = x

Length of the rectangle = 3x

Perimeter of a rectangle = 2(length + width)

The equation is

64 = 2(3x + x)

64 = 6x + 2x

64 = 8x

x = 64/8

x = 8 cm

Width of the rectangle = x = 8 cm

Length of the rectangle = 3x

= 3(8 cm)

= 24 cm

Step-by-step explanation:

the answer is in the image above

Answer:

D. A straight line segment can be drawn between any two points.

Step-by-step explanation:

Euclid of Alexandria was famously known and regarded as the founder of geometry, as well as the father of geometry. He was born in the Mid-fourth century, BC and he specialized in the field of Mathematics. Some of his popular works in the field of Mathematics were Euclid's Elements, Euclidean algorithm and Euclidean geometry.

One of the basic postulate of Euclidean geometry is that a straight line segment can be drawn between any two points.

Others include;

I. All right angles are congruent.

II. All straight line segment is indefinitely extendable in a straight line.

Answer:

f the mean of this set is equal to 20, we can write down the below equation,

20 = (x1 + x2 +x3 + .... + x10)/10

x1 + x2 + x3 + ... x10 = 200

Then we can also write an equation for the mean of the given numbers as below,

Mean  = [(x1+4) + (x2+8) + (x3+12) + .... + (x10+40)]/10

          = (x1 + x2 + x3 + ... + x10 + 4 + 8 + 12 + ... + 40)/10

Then we can use above equation (1) to replace x1 + x2 + x3 + ... + x10 by 200

Mean = (200 + 4 + 8 +12 + 16 + 20 + 24 + 28 + 32 + 36 + 40)/10

        = 420/10

        = 42

If you remember Arithmetic Progressions you can simply add together the above number set.

If you closely look above, you can find that there is an Arithmetic Progression : 4, 8, 12, ... , 40

Here we want the addition of 10 terms. So we can use,

Sn = n/2(a+l)

S10 = 10/2(4+40)

      = 220

Then you can easily get the answer,

Mean = (200 + 220)/10

         = 42

Answer:

Caroline has to pay $8600 taxes

Jennifer has to pay $10320 taxes

Step-by-step explanation:

I guess the question is who has to pay how much taxes, right ?

Caroline earns $49000, and I guess, she belongs to a health fund.

she has to pay $5000 for the first $40000.

and for the remaining $9000 she has to pay $0.40 per dollar.

that means 9000×0.4 = $3600

and no penalties for no health fund.

so altogether $5000 + $3600 = $8600 taxes

Jennifer earns $51000 and did not belong to a health fund.

she has to pay $9000 for the first $50000.

and for the remaining $1000 she had to pay $0.30 part dollar.

that means 1000×0.3 = $300

and 2% of the total income because no health fund

51000×0.02 = $1020

so, altogether $9000+$300+$1020 = $10320 taxes

Answer:

80/3

Step-by-step explanation:

try mathw4y it helps alot.

Answer:

x = 80/3

Step-by-step explanation:

(4x+38) + (2x-18)=180

Combine like terms

6x +20 = 180

Subtract 20 from each side

6x+20 -20 = 180-20

6x = 160

Divide by 6

6x/6 = 160/6

x = 80/3

Answer:

52%

7 more

Step-by-step explanation:

There are 5*5 = 25 boxes in the grid

13 are shaded

13/25 = 13/25 *4/4 = 52/100 = 52% are shaded

We want 80% shaded

80/100

Divide top and bottom by 4

20/25

We need 20 shaded and have 13 shaded

20-13 = 7

We need to shaded 7 more

Answer:

C= 40

D= 75

Alternate interior angle

○●○●○●○●○

Hope it helps...

Have a great day!!!

Answer:

e

Step-by-step explanation:

the graph should look something like this

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

See this attachment