The expression below represents the perimeter, in feet, of Manual’s garden. 15 + 2x + 7 + 15 + 2x + 7 Use exactly two terms to write an equivalent expression to represent the perimeter, in feet, of Manual’s garden. The area, measured in square feet, of Manual’s garden is found by calculating 15(2x + 7). Manual incorrectly says the area can also be found using the expression 30x + 7. Describe the error in Manual’s expression. Also, find the difference, in square feet, between the actual area of Manual’s garden and the area found using his expression as a part of your explanation. Manual’s friend Sasha designs a square garden. Each side measures 3x + 5 in length. The perimeter of Sasha’s garden is how much larger than the perimeter of Manual’s garden?​

[tex]\\ \rm\Rrightarrow \sqrt{x²-10x+25}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{x²-5x-5x+25}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{x(x-5)-5(x-5)}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{(x-5)(x-5)}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{(x-5)^2}[/tex]

[tex]\\ \rm\Rrightarrow\pm (x-5)[/tex]

Solution set(for x-5)

for 5-x

Answer:

First, simplify the expression under the square root sign by factoring:

[tex]\implies x^2-10x+25[/tex]

[tex]\implies x^2-5x-5x+25[/tex]

[tex]\implies x(x-5)-5(x-5)[/tex]

[tex]\implies (x-5)(x-5)[/tex]

[tex]\implies (x-5)^2[/tex]

Therefore:

[tex]\implies \sqrt{x^2-10x+25}=\sqrt{(x-5)^2}[/tex]

[tex]\implies \sqrt{x^2-10x+25}=\pm(x-5)[/tex]

[tex]\implies \sqrt{x^2-10x+25}=|x-5|[/tex]

As the domain is -5 ≤ x < 5, then:

[tex]\implies y=-x+5[/tex]

and the range is 0 < y ≤ 10

Answer:

the region of the graph where the shaded regions of the graph of each inequality overlap, or where the regions intersect

Step-by-step explanation:

Answer:

m = [tex]\frac{1}{2}[/tex] , c = [tex]\frac{5}{2}[/tex]

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 )

given

y + 2x = 4 ( subtract 2x from both sides )

y = - 2x + 4 ← in slope- intercept form

with slope m = - 2

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex] , then

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute (3, 4 ) into the partial equation

4 = [tex]\frac{3}{2}[/tex] + c ⇒ c = 4 - [tex]\frac{3}{2}[/tex] = [tex]\frac{5}{2}[/tex]

y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{5}{2}[/tex] ← equation of line

with m = [tex]\frac{1}{2}[/tex] and c = [tex]\frac{5}{2}[/tex]

Answer:

6x+8

Step-by-step explanation:

2(3x+4)= 2(3x) + 2(4) = 6x+8

Answer:

Step-by-step explanation:

Minimum: 2

Quartile Q1: 4.5

Median: 10

Quartile Q3: 15

Maximum: 19

Answer:

The mass of salt!

Step-by-step explanation:

The responding variable is the part of an experiment that a scientists measures and observes closely for a change or a response

The provided graph is not a function because  it touches the graph more than one point.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have given a graph of a function.

We can check the whether the given graph is a function or not by drawing a vertical line if the vertical line touches the graph more than two points then the graph is not a function.

The given graph is not a function because it touches the graph more than one point.

Thus, the provided graph is not a function because  it touches the graph more than one point.

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Answer:

0 pars

Step-by-step explanation:

3-3=0

Answer:

If we square both sides then we get

x2-8x+16 = (x-4)2

Now if we expand the right side of the equation we get

x2-8x+16 = (x-4)(x-4)

x2-8x+16 = x2-8x+16

So no matter what x is, the right side will be equal to the left side.

However, if we look at the original equation on the left side, √(x2-8x+16) , the value under the square root symbol has to be greater than or equal to zero (otherwise we get an imaginary number and you might not be working with those yet)

Step-by-step explanation:

So in order for √(x2-8x+16) to be greater than or equal to zero, x has to be greater than or equal to 4. If x is less than 4 you get a negative number. If x is greater than 4, you'll get the same answer on both sides no matter what x is

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{2} - 8x + 16} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{2} - 4x - 4x + 16} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{} (x - 4) - 4(x - 4)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ (x - 4)(x - 4)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ (x - 4) {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: x - 4[/tex]

Now, it's given that ~

[tex]\qquad \sf  \dashrightarrow \:x \geqslant 4[/tex]

plug the value of x as 4 :

[tex]\qquad \sf  \dashrightarrow \:4 - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \:0[/tex]

So, we can infer that :

Value of the required expression lies in :

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{2} - 8x + 16} \geqslant 0[/tex]

it's value is always greater than pr equal to 0, satisfying the given condition ~

1inch = 2.5cm

∆ 30cm

5cm =2inch

Answer:

(-1, -5)

(0, -2)

(-3, -11)

Step-by-step explanation:

y = 3x - 2.

→ 3×(-2)-2=-8 ≠0 ⇒(-2, 0) doesn’t correspond to input-output pairs for the function

→ 3×(-1)-2=-5 ⇒(-1, -5) corresponds to input-output pairs for the function

→ 3×(0)-2=-2 ⇒(0, -2) corresponds to input-output pairs for the function

→ 3×(2)-2=4≠3 ⇒(2, 3) doesn’t correspond to input-output pairs for the function

→ 3×(-3)-2=-11 ⇒(-3, -11) corresponds to input-output pairs for the function

The value of the function at the right endpoint of the rectangle is 5 +6k/n.

In the question above;

Th width of the interval is said to be  (5 -2) = 3.

So, the width of one of n parts of it = 3/n

To solve for the differences that exist between the left end point of the interval and the value of  x at the right end of the k-th rectangle, one can say that:

 k·(3/n) = 3k/n

Note that the value of x at shows the point of  difference added to the interval's left end and thus it will be:  2 + 3k/n

Therefore, the value of the function for the value of x will be:

 f(2 +3k/n) = 2(2 +3k/n) +1  = (4 +6k/n) +1

 = 5 +6k/n

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Answer:

37.2mm

Step-by-step explanation:

A = ½bh

h = (2A)/b

h = (2(39.06))/2.1

h = 78.12/2.1

h = 37.2mm

Answer: F

Step-by-step explanation:

Answer:

3,600

Explanation:

There's nine thousand numbers here, 4,500 of which are even, you will need to subtract mutiples of five from this number, making it even smaller.

subtract the non-even five's (exactly half of the 1800 hundred fives that fit in our little original number, (900!) ) 4,500-900= 3,600. Which should be your answer. :D

Step-by-step explanation:

Answer:

1.7.

Step-by-step explanation:

2x^3 + 9x^2 - 2x + 8 = 40

Substituting values for x in the range 1 to 2:

when x = (1.1):

f(1.1) = 2(1.1)^3 + 9(1.1)^2 - 2(1.1) + 8 = 19.32.

x = 1.3:

f(1.3) = 25.004

F(1.5) = 32

F(1.6) = 36.032

F(1.7) = 40.436   which is just greater than 40.

So the root is between 1.6 and 1.7.

f(1.65) = 38.19

Therefore the root is > 1.65 and < 1.7

and to  1 DP it is 1.7.

Answer:

= -6

Step-by-step explanation:

-12/2

= -6

Answer:

14.167

Step-by-step explanation:

assuming you meant 5+13

Answer:

SolutioN :

[tex] \bf \: \star ( - 3x^{2} + 4x) + (2 {x}^{2} - x - 11)[/tex]

[tex] \longrightarrow \bf \: - 3 {x}^{2} + 4x + 2 {x}^{2} - x - 11[/tex]

[tex] \longrightarrow \bf \: - 3 {x}^{2} + 2 {x}^{2} + 4x - x - 11[/tex]

[tex] \longrightarrow \boxed{\bf \: - {x}^{2} + 3x - 11}[/tex]

-------------HappY Learning <3 ----------

Given expression:

[tex](-3x^2+4x)+(2x^2-x-11)[/tex]

To simplify the expression, it is needed to open the parentheses.

[tex]\implies (-3x^2+4x)+(2x^2-x-11)[/tex]

[tex]\implies -3x^2+4x+2x^2-x-11[/tex]

To further simplify the expression, let us combine like terms.

[tex]\implies -3x^2+4x+2x^2-x-11[/tex]

[tex]\implies x^{2} (-3 + 2)+x(4-1)-11[/tex]

Now, simplify the expression as needed.

[tex]\implies x^{2} (-3 + 2)+x(4-1)-11[/tex]

[tex]\implies x^{2} (-1)+x(3)-11[/tex]

Finally, open the parentheses to get the simplified form

[tex]\implies x^{2} (-1)+x(3)-11[/tex]

[tex]\implies \boxed{\bold{-x^{2} +3x-11}}[/tex]

[tex]\text{Therefore, the simplified expression is} \ \boxed{-x^{2} +3x-11}[/tex]

Answer:

bottom left

Step-by-step explanation:

when divideing/mult by neg number, sign flips.

The equivalent expression of [tex]\frac{(2mn)^4}{6m^{-3}n^{-2}}[/tex] is [tex]\frac{(2mn)^4}{6m^{-3}n^{-2}}[/tex]

The expression is given as:

[tex]\frac{(2mn)^4}{6m^{-3}n^{-2}}[/tex]

Evaluate the expression on the numerator

[tex]\frac{16m^4n^4}{6m^{-3}n^{-2}}[/tex]

Divide 16 by 6

[tex]\frac{8m^4n^4}{3m^{-3}n^{-2}}[/tex]

Apply the law of indices

[tex]\frac{8m^7n^6}{3}[/tex]

Hence, the equivalent expression of [tex]\frac{(2mn)^4}{6m^{-3}n^{-2}}[/tex] is [tex]\frac{(2mn)^4}{6m^{-3}n^{-2}}[/tex]

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Answer:

-3125

Hope this helps!!

Answer:

  6.1 km

Step-by-step explanation:

The Pythagorean theorem tells you the relationship between the lengths of the sides of a right triangle.

  c² = a² +b² . . . . a, b are the short sides; c is the hypotenuse

__

The geometry of this problem can be modeled by a right triangle with legs 3.7 km and 4.9 km. The distance of interest is the hypotenuse of the triangle.

  c² = 3.7² +4.9² = 13.69 +24.01 = 37.70

  c = √37.70 ≈ 6.1

The straight-line distance is about 6.1 km.

To find the point of symmetry:

  ⇒ must find where the distance between the original point and the

   line of symmetry and reflected point and the line of symmetry are

   equally distant from each other

Based on that knowledge:

 ⇒ the image appears to be entirely reflected horizontally

    ⇒ when the line of symmetry is the y-axis

        ⇒ A, A' equal distant from line of symmetry

        ⇒ B, B' equal distant from line of symmetry

        ⇒ C, C' equal distant from line of symmetry

Answer: y- axis

Hope that helps!

The formula is given by

Or

Where

Answer:

Count the tally marks to determine the frequency of each class. The relative frequency of a data class is the percentage of data elements in that class. The relative frequency can be calculated using the formula fi=fn f i = f n , where f is the absolute frequency and n is the sum of all frequencies

Answer:

it 288

Step-by-step explanation:

if u multiply 24x12 it gives you 288 hope this help you

The smallest possible number that is divisible by 45 when the blanked place of the number is filled is 345285.

The divisible rule of 9 and 5 are:

Two digits of the 6-digit number are missing.

[tex]X = 345 * 8*[/tex]

The smallest possible number from this is divisible by 45. The factors of 45 are 9 and 5.

[tex]45=9\times5[/tex]

Thus, the 6-digit number which is divisible by 45, must be divisible by 9 and 5.  

To be divisible with 5, the number has 0 or 5 in last. So the numbers can be,

[tex]X = 345 * 85\\X=345 * 80[/tex]

For first number, when the blank is filled with number 2 to make sum 9 and for second the blank number should be 7. Thus, the numbers,

[tex]X = 345 285\\X=3457 80[/tex]

Thus, the smallest possible number that is divisible by 45 when the blanked place of the number is filled is 345285.

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Answer:

See below

Step-by-step explanation:

each term is the sum of the two before it

2 3 5 8 13 21 34

Answer:

true

Step-by-step explanation:

yas