What triangle congruence theorem could you use to
prove triangle ADE is congruent to triangle CBE?

Answer:

2

Step-by-step explanation:

2

Answer is:

29/2 = 14.5

Step-by-step explanation:

y = -5x² + 2x - 3 and y = -3x - 3.

=> -5x² + 2x - 3 = -3x - 3

=> 5x² - 5x = 0

=> 5x(x - 1) = 0

=> x = 0 or x = 1.

When x = 0, y = -3(0) - 3 = -3.

When x = 1, y = -3(1) - 3 = -6.

The solutions are (0,-3) and (1,-6).

Answer:

one part = 20.5

the other part = 61.5

Step-by-step explanation:

let one part = x

let another part = y

(1) create two equations

i) 82 is separated into 2 parts, x and y. it means x plus y equals to 82

x+y = 82

ii) one part is bigger than the other. if x is the bigger part, it is 3 times bigger than y

x = 3y

(2) use substitution method to find the value of x and y

x+y = 82 -------- (1)

x = 3y ---------- (2)

substitute (2) into (1)

x+y = 82

3y+y = 82

4y = 82

y = 82/4

y = 20.5

substitute y = 20.5 into (2)

x = 3y

x = 3(20.5)

x = 61.5

Answer: x = 15/8

Explanation: I used a calculator on a website.

Answer:

15/8

Step-by-step explanation:

Hope this helps: )

Answer:

81.82%

Step-by-step explanation:

cuz meth

Answer:

81.82

Step-by Step

In order to round to the nearest thousand, you simply have to move the decimal point to the RIGHT. Hope it helps!

                     ~Happy holidays

Answer:

6) b(3a^4-5c³)

7) 3x³yz(2x+5y)

8) 4a²b²c³(2bc-3a)

9) 4xy(2y+7z-1)

10) 2mn(5n²+2m-3n)

Step-by-step explanation:

6) Factor out the b and you get b(3a^4-5c³)

7) Factor out the 3x³yz and you get 3x³yz(2x+5y)

8) Factor out the 4a²b³c³ and you get 4a²b²c³(2bc-3a)

9) Factor out the 4xy and you get 4xy(2y+7z-1)

10) Factor out the 2mn and you get 2mn(5n²+2m-3n)

Answer: True

Step-by-step explanation:

The function is even and negative. A negative function opens down. With this information, the statement is true: the function opens down.

Answer:

True

Step-by-step explanation:

Given a parabola in vertex form

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

• If a > 0 then the graph opens up

• If a < 0 then the graph opens down

Given

f(x) = - (x + 3)² + 2 ← in vertex form

with a = - 1 < 0 then graph opens down is True

Jacob babysat for 4.5 hours 12x4=48 +6(.5)= 4.5 hours

Answer:

The answer is below

Step-by-step explanation:

A) i)

For Anna initially, she has $0 from making 0 envelopes. After making 400 envelopes she has $20. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (400, 20). Using the equation of a line:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{20-0}{400-0}(x-0)\\\\y=\frac{1}{20} x[/tex]

The table is:

x:   200     400       600     800     1000

y:    10        20          30        40       50

ii)

For Jason initially, he has $0 from making 0 envelopes. For every 250 envelopes he has $10. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (250, 10). Using the equation of a line:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{10-0}{250-0}(x-0)\\\\y=\frac{1}{25} x[/tex]

The table is:

x:   200     400       600     800     1000

y:    8         16           24        32       40

The graph is plotted using geogebra online graphing

b) From the table above we can see that Anna makes more stuffing than Jason.

c) Anna has a savings of $100. Hence this can be represented by the points (0, 100) and (250, 10). Using the equation of a line:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-100=\frac{20-0}{400-100}(x-0)\\\\y=\frac{1}{15} x+100[/tex]

We can see from the graph that there is a y intercept at 100. That is the earnings starts from 100.

The equation of a line is given as y = mx + b, where m is the slope and b is the y intercept (initial value)

For the first graph, the slope is 1/20 and the initial value is 0 while for the second graph the slope is 1/15 and the initial value is 100

D) The line pass through (10, 10) and (100, 40), hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{40-10}{100-10}(x-10)\\\\y-10=\frac{1}{3} (x-10)\\\\y=\frac{1}{3}x+\frac{20}{3}[/tex]

Answer:

41.54

Step-by-step explanation:

Answer:

Step-by-step explanation:

$220

5 members

220/5

=44

Answer:

It will take him 3 minutes

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

A Rational Number can be made by dividing two integers

The cordinate plane can be used to plot points and graph lines

Answer:

$26.98

Step-by-step explanation:

1. You have the following information given in the problem above:

- Lou filled the tank with gas that cost ​$3.80 per gallon.

-   Lou​'s car had 5.9 gallons in the 13​-gallon tank.

2. Therefore, if he filled the tank, you can calculate the total amount of money Lou spent, by subtracting 13 gallons and 5.9 gallons and multiplying the result by ​$3.80.

Answer:

26.98

Step-by-step explanation: 5.3 * 3.8 = 26.98

Answer:

  1/5

Step-by-step explanation:

  medium = (1/2)(blue sale) = (1/2)(3/5)(blue) = (1/2)(3/5)(2/3)(all t-shirts)

  medium = 1/5(all t-shirts)

One-fifth of the shop's T-shirts are size medium blue shirts on sale.

Answer:

A. x = -40

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

-3.5(x + 12) = -2x + 18

Step 2: Solve for x

Answer:

The percent error is 99%

Step-by-step explanation

Estimated weight of cat = 10 pounds

Actual weight of cat = 1375 pounds

We need to find the percent of error.

The formula used is: [tex]Percent\:Error=\frac{|Estimated\:value-Actual\:Value|}{Actual\:Value}\times 100[/tex]

Putting values and finding percent of error.

[tex]Percent\:Error=\frac{|Estimated\:value-Actual\:Value|}{Actual\:Value}\times 100\\Percent\:Error=\frac{|10-1375|}{1375}\times 100 \\Percent\:Error=\frac{|-1365|}{1375}\times 100 \\Percent\:Error=\frac{1365}{1375}\times 100\\Percent\:Error=0.99\times 100 \\Percet\:Error=99\%[/tex]

So, the percent error is 99%

Answer:

c=ab/2y

Step-by-step explanation:

y=ab/2c

to get rid of the denominator we divide by 2c.

(y=ab/2c)2c

2cy=ab

now we need to get rid of the 2y from the c to isolate it. in order to do this, we must divide by 2y.

Doing this we get c=ab/2y

9514 1404 393

Answer:

  c = (ab)/(2y)

Step-by-step explanation:

The given equation can be multiplied by c/y to solve for c.

  [tex]y=\dfrac{ab}{2c}\\\\y\cdot\dfrac{c}{y}=\dfrac{ab}{2c}\cdot\dfrac{c}{y}\\\\\boxed{c=\dfrac{ab}{2y}}[/tex]

_____

Comment on the form of the answer

When the answer is written in plain text, the fraction bar no longer serves as a grouping symbol. Hence, parentheses are needed around the denominator:

  c = ab/(2y)

Answer:

Probability of choosing two different types of biscuits is  [tex]\frac{31}{90}[/tex].

Step-by-step explanation:

We have 10 biscuits in a tin.

There are 5 digestive, 3 chocolate, 2 ginger.

Steve takes two biscuits at random.

There are three combinations of biscuits.

P(d, c) + P(c,g)+P(d,g)

Let's find probability of each.

P(d,c)= P(d)* p(c)

         = [tex]\frac{5}{10}*\frac{3}{9}[/tex]

Let's simplify it, we get [tex]\frac{1}{6}[/tex]

Like so, for P(c,g)

P(c,g)= P(c) * P(g)

       =[tex]\frac{3}{10}*\frac{2}{9}[/tex]

Let's multiply and simplify, we get [tex]\frac{1}{15}[/tex].

Now, for p(d,g)

P(d, g)= P(d)* p(g)

        =[tex]\frac{5}{10} *\frac{2}{9}[/tex]

Let's simplify and multiply, we get [tex]\frac{1}{9}[/tex].

Now, add them together

[tex]\frac{1}{6} +\frac{1}{15} +\frac{1}{9}[/tex]

Now, find LCD to make the denominators as same and then add them together.

LCD is 90

So, find equivalent fraction of each which has denominator as 90.

[tex]\frac{15}{90}+\frac{6}{90} +\frac{10}{90}[/tex] = [tex]\frac{31}{90}[/tex]

Answer:

Options (2) and (3)

Step-by-step explanation:

Let, [tex]\sqrt{-8+8i\sqrt{3}}=(a+bi)[/tex]

[tex](\sqrt{-8+8i\sqrt{3}})^2=(a+bi)^2[/tex]

-8 + 8i√3 = a² + b²i² + 2abi

-8 + 8i√3 = a² - b² + 2abi

By comparing both the sides of the equation,

a² - b² = -8 -------(1)

2ab = 8√3

ab = 4√3 ----------(2)

a = [tex]\frac{4\sqrt{3}}{b}[/tex]

By substituting the value of a in equation (1),

[tex](\frac{4\sqrt{3}}{b})^2-b^2=-8[/tex]

[tex]\frac{48}{b^2}-b^2=-8[/tex]

48 - b⁴ = -8b²

b⁴ - 8b² - 48 = 0

b⁴ - 12b² + 4b² - 48 = 0

b²(b² - 12) + 4(b² - 12) = 0

(b² + 4)(b² - 12) = 0

b² + 4 = 0 ⇒ b = ±√-4

                     b = ± 2i

b² - 12 = 0 ⇒ b = ±2√3

Since, a = [tex]\frac{4\sqrt{3}}{b}[/tex]

For b = ±2i,

a = [tex]\frac{4\sqrt{3}}{\pm2i}[/tex]

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

  = [tex]\mp 2i\sqrt{3}[/tex]

But a is real therefore, a ≠ ±2i√3.

For b = ±2√3

a = [tex]\frac{4\sqrt{3}}{\pm 2\sqrt{3}}[/tex]

a = ±2

Therefore, (a + bi) = (2 + 2i√3) and (-2 - 2i√3)

Options (2) and (3) are the correct options.

Answer: b and c

Step-by-step explanation:

Step-by-step explanation:

For this set there are 8 subsets and 7 proper subsets

the subsets are:

{}

{2}

{4}

{6}

{2,4}

{2,6}

{4,6}

{2,4,6}

Answer:

she has 15 boxes of pencils

Step-by-step explanation:

if we have 90 total pencils that need to be split into groups of 6, the way to find how many groups there are is by dividing 90/6, which gives you 15 groups or, in this case, 15 boxes. and you can check your work by multiply the 15 boxes by the 6 pencils in each box, which gives you 90 pencils total, so you're all good!

Answer:

y = -x - 4

General Formulas and Concepts:

Pre-Algebra

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

x + y = -4

Step 2: Rewrite

Find slope-intercept form

Answer:

[tex] \huge \boxed{ \boxed{ \frac{2}{3} }}[/tex]

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

[tex]m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\[/tex]

From the question we have

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

We have the final answer as

[tex] \frac{2}{3} \\ [/tex]

Hope this helps you