There are 4 identical triangles, each with an area of 4 square units. When put together, they form a square. What is the side length of the square?

Based on the information illustrated, it should be noted that 6 × ✓3 .will be 36.

It should be noted that the information that's illustrated has to do with the square root of numbers. It should be noted that a square root simply means a number that when multiplied by itself will be able to give the original number that's given in the question.

Based on the information, the numbers will be illustrated thus:

6 × ✓36

It should be noted that ✓36 = 6

Therefore, 6 × ✓36

= 6 × 6

= 36

Therefore, the correct option is 36.

Note that the options aren't well written.

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Answer: 34.50

Step-by-step explanation: Since 3 bags cost 17.25 and Marco would buy 6, 3 times 2 is 6 so 17.25 times 2 is 34.50

Answer:

c=d-ab

Step-by-step explanation:

ab+c=d

move over to the other side

change sides change signs

c=d-ab

Answer:

c=d−ab

Subtract ab from both sides of the equation

The counterexample for the conjecture If the perimeter of a rectangle is 40 units, the area must be at least 1 square unit is: A rectangle with length 19.99 units and width 0.01 unit has a perimeter of 40 units and an area of 0.1999 square unit.

The term counterexample refers to an instance or example that makes the statement false. This is used in logic to check if a statement is true or not. Counter example tend to counter the statement being discussed with valid points.

The question wants to show the relationship that may exist between perimeter and area of a rectangle.

The counterexample provided the dimensions that gave the perimeter which is 40 but failed to give area of 1 square unit

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Answer:

1. you can ask directly or indirectly

[tex]32^{\frac{1}{25}}\cdot 2^x ~~ = ~~8^{\frac{1}{4}}\implies (2^5)^{\frac{1}{25}}\cdot 2^x~~ = ~~(2^3)^{\frac{1}{4}}\implies 2^{\frac{5}{25}}\cdot 2^x~~ = ~~2^{\frac{3}{4}} \\\\\\ \stackrel{same~exponent}{\underset{same~base}{2^{\frac{5}{25}+x}~~ = ~~2^{\frac{3}{4}}}}\implies \cfrac{5}{25}+x~~ = ~~\cfrac{3}{4}\implies \cfrac{1}{5}+x~~ = ~~\cfrac{3}{4}[/tex]

[tex]\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{20}}{20\left( \cfrac{1}{5}+x \right)~~ = ~~20\left( \cfrac{3}{4} \right)}\implies 4+20x~~ = ~~15 \\\\\\ 20x=11\implies {\Large \begin{array}{llll} x=\cfrac{11}{20} \end{array}}[/tex]

I don't know what the dropdown menus are, but Mike is half-correct. The opposite of a number is the number with the opposite sign, so the opposite of 5 is -5. But the absolute value of a number is its distance from zero on a number line, and distances can't be negative, so the absolute value of 5 is 5, not -5.

Hello! So...

We are given the following to solve:

[tex]-9+8=?[/tex]

In order to solve this, we simply need to add.

[tex]-9+8=-1[/tex]

Hence, our solution is -1, and would be marked -1 on a number line. Graph is displayed below.

____________________________________

Hope this helps! If so, lmk! Thanks and good luck!

Answer: -4096

Step-by-step explanation: Use the geometric sequence formula to find the 10th term (image attached). So, the 10th term = 8(-2)^9

Note: the common ratio can be found by 2ndterm/1stterm

Answer:

a₁₀ = -4096

Step-by-step explanation:

Geometric sequence

General form of a geometric sequence:

[tex]\boxed{a_n=ar^{n-1}}[/tex]

where:

Given terms of the geometric sequence:

To find the common ratio (r), divide consecutive terms:

[tex]\implies \dfrac{a_3}{a_2}=\dfrac{32}{-16}=-2[/tex]

Substitute the values of a and r into the formula to create an equation for the nth term of the sequence:

[tex]\implies a_n=8(-2)^{n-1}[/tex]

To find the 10th term of the sequence, substitute n = 10 into the equation:

[tex]\begin{aligned}\implies a_{10}&=8(-2)^{10-1}\\&=8(-2)^{9}\\&=8(-512)\\&=-4096\end{aligned}[/tex]

Therefore, the 10th term of the given geometric sequence is -4096.

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Answer:

Step-by-step explanation:

Here, what they're really saying is to find  3 different ways to rearrange the letters A, B, and C. Then, put them together to give the angle a combination of "names"

(1 ABC

(2 BAC

(3 CAB

Hope this helps! :D

Answer:

BC- AB < CA < AB + BC

Step-by-step explanation:

The sides opposite the larger angles are longer than the sides opposite smaller angles.

So, BC (opposite < A) is longer than AB (opposite < C) so,

BC > AB

The other side AC cannot be greater than AB + BC, otherwise the triangle would not exist, so,

AC < AB + BC

Also, CA > BC - AB  

The range for AC is

BC- AB < CA < AB + BC

Hence proved that triangle   AB = 3(3) - 1 = 9 - 1 = 8.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the display style for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle. All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.

Given that,

AB + AC = AC

3y - 1 + 7y = 29

10y = 29 + 1 = 30

y = 30/10 = 3

Therefore, AB = 3(3) - 1 = 9 - 1 = 8.

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Balance of Kevin after 1 quarter will be 1.0055(x)

Compound interest is interest that is calculated using both the starting amount and the interest that has accrued over time.

Interest is considered to be compounded quarterly if it is compounded four times each year.

If interest is compounded four times or quarterly each year, the formula for the amount at time t is as follows.

A = P( ( 1 + (r/4))⁴ⁿ

A = Accumulated amount

P= Principal amount

r = interest rate

n = time

Given that Kevin has x dollars in an account that pays 2.2% interest, compounds quarterly

∴ P = x

r = 2.2% = 2.2/100

To find balance after one quarter , i.e. time n = 1/4 year

⇒ Balance = accumulated amount  =$  x(1 + 2.2/400)¹  = $ 1.0055(x)

Therefore, Balance of Kevin after 1 quarter will be 1.0055(x)

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Answer:

You need at least 101 cans of food in order to meet or surpass the goal.

Step-by-step explanation:

a.

135+89=224

224+c>=325

b.

224-224+x>=325-224

x>=101

You need at least 101 cans of food in order to meet or surpass the goal.

Answer:

The answer is C

Step-by-step explanation:

The increase between the numbers in a arithmetic sequence is always the same, in this case the number always increased by 3.

Here is a another example

3, 5, 7, 9

The difference between the consecutive terms is always 2

Answer: i is just a variable I believe so _ + 7 = 9

So i (<- the variable) would = 2

Answer: G=62, I = 62, H =54

Step-by-step explanation:

3x+26=4x+14

x=12

G=36+26 = 62

180-62-62=54

Answer:

x = 5

Step-by-step explanation:

Comment

The three sides need to add up to 23 (the perimeter is given as 23)

Givens

The sides are

Solution

x + x + 3 + 2x = 23                   Combine

4x + 3 = 23                               Subtract 3 from both sides

4x + 3-3 = 23-3                         Combine

4x = 20                                      Divide  by 4

4x/4 = 20/4

x = 5

The three sides of a triangle is x, x+3 and 2x. If the perimeter is 23 feet. Find the value of x.

In this question we are given

We are asked to calculate the value of x.

To solve this problem first we have to form an equation.

Let us solve this question.

We know that the perimeter of a triangle is the sum of all three sides.

According To Question

x + x + 3 + 2x = 23

→ 2x + 3 + 2x = 23

→ 4x + 3 = 23

→ 4x = 23 - 3

→ 4x = 20

→ x = 20/4 = 5

x = 5

The value of x is 5.

[tex] \rule{70mm}{2pt}[/tex]

Slope of AB = 2; Slope of DC = 2

Slope of AD = -1/2; Slope of BC = -1/2

Both pairs of opposite sides are parallel because they have the same slope, therefore, quadrilateral ABCD is a parallelogram.

A parallelogram is a quadrilateral that has two pairs of opposite sides that have the same lengths and are parallel to each other.

Since the opposite sides of a parallelogram are parallel, therefore, they have the same slope value.

Slope = change in y / change in x.

Find the slope of AB and DC. then AD and BC:

Slope of AB = (-2 - 2)/(-3 -(-1)) = -4/-2

Slope of AB = 2

Slope of DC = (-3 - 1)/(-1 - 1) = -4/-2

Slope of DC = 2

Slope of AD = (-3 -(-2))/(-1 -(-3)) = -1/2

Slope of AD = -1/2

Slope of BC = (2 - 1)/(-1 - 1) = 1/-2

Slope of BC = -1/2

Therefore, since AB and DC have the same slope, they are parallel, so also is AD and BC parallel because they have the same slope, therefore, quadrilateral ABCD is a parallelogram.

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Answer:Your friend is incorrect

x=-2

Step-by-step explanation:

Add 6 to both sides

-6+2x=-10

+6          +6

2x=-4

Then divide each side

2x/2=-4/2

x=-2

Answer: 3x^12

Step-by-step explanation:

66 / 22 = 3

We can add exponents when multiplying them.

-3 + 12 = 9

Answer: 3.3%

Step-by-step explanation:

Principal not given.

SI = PRT/100

CI = P(1+R/100)^T -

SI + CI = 85470

[P×7×2]//100 + P [1+ (7/100)]^2 = 85470

on solving: P = 3,00,000

P = 300000 SI for 2 years = 42000

CI = Rs 43470

The difference= Rs 1470

as percentage to CI = [1470/ 43470] ×100

= 3.38%

The algebraic equation and the original price is:

original price - discount = sales price

x - 27 = 89

x = 116

An algebraic equation is made up of two expressions that are made up of variables or numbers that are connected by an arithmetic operation.  

A discount reduces the price of a good or service. In order to determine the price of a good after the discount has been applied, subtract the amount of the discount from the original price of the item.

original price - discount = sales price

x - 27 = 89

Combine similar terms: x = 89 + 27

Add similar terms together: x = 116

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The equivalent expression for 10⁶ / 10⁴  will be equal to 10²

Given,

Exponents: 10⁶ and 10⁴

We have to find an equivalent expression for 10⁶ / 10⁴

Equivalent expression:

In general, something is considered equal if two of them are the same. Similar to this, analogous expressions in mathematics are those that hold true even when they appear to be different. However, both forms provide the same outcome when the values are plugged into the formula.

Here,

aˣ / aⁿ = x - n

So,

10⁶ / 10⁴ = 6 - 4 = 2

That is,

The equivalent expression for 10⁶ / 10⁴  will be equal to 10²

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Answer:   0.483

Step-by-step explanation: add a zero and a point to the right f it

Answer:

[tex]\textsf{D)} \quad P(n)=0.024n^2-0.3n+4.3[/tex]

Step-by-step explanation:

From inspection of the graph, when the number of coils is 10, the length of the spring is between 0 cm and 20 cm.

Substitute n = 10 into the equation of each given answer option:

[tex]\begin{aligned}\textsf{Option A}: \quad P(10)&=10^2+4.3\\ & =100+4.3\\&=104.3\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Option B}: \quad P(10)&=10^2-0.3(10)+4.3\\ & = 100-3+4.3\\&=97+4.3\\&=101.3\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Option C}: \quad P(10)&=0.24(10^2)+4.3\\&=0.24(100)+4.3\\&=24+4.3\\&=28.3\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Option D}: \quad P(10)&=0.024(10^2)-0.3(10)+4.3\\ & = 0.024(100)-3+4.3\\&=2.4-3+4.3\\&=-0.6+4.3\\&=3.7\end{aligned}[/tex]

Therefore, as 0 < P(10) < 20, the only suitable equation is Option D:

[tex]\boxed{P(n)=0.024n^2-0.3n+4.3}[/tex]

[tex]3 \sqrt{5} - 2 \sqrt{7} + \sqrt{9 \times 5} - \sqrt{4 \times 7} \\ = 3 \sqrt{5} - 2 \sqrt{7} + ( \sqrt{9} \times \sqrt{5} ) - ( \sqrt{4} \times \sqrt{7} ) \\ = 3 \sqrt{5} - 2 \sqrt{7} + 3 \sqrt{5} - 2 \sqrt{7} \\ = 3 \sqrt{5} + 3 \sqrt{5} - 2 \sqrt{7} - 2 \sqrt{7} \\ = 6 \sqrt{5} - 4 \sqrt{7} [/tex]

OPTION C IS THE ANSWER.

Answer:

6√5 - 4√7

Step-by-step explanation:

hope it helps!!

Answer:

its 3 because 4^-n=1/256

We move all terms to the left:

4^-n-(1/256)=0

We add all the numbers together, and all the variables

-n+4^-(+1/256)=0

We add all the numbers together, and all the variables

-1n-(+1/256)=0

We get rid of parentheses

-1n-1/256=0

We multiply all the terms by the denominator

-1n*256-1=0

We multiply elements

-256n-1=0

We move all terms containing n to the left, all other terms to the right

-256n=1

n=1/-256

n=-1/256

Considering the concepts of the diameter and the radius of a circle, it is found that the correct statement is:

The ratio of the lengths of EF and AD is 2:1.

In the context of the circle given in this problem, we have that:

hence:

EF = 2AD, meaning that the ratio is of 2:1.

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