Answer please with proofs and statements

The equation of the graphed line is written as: y = 2x + 2.

The equation of a graphed line can be determined by calculating the slope of the line, m = rise/run, and determining the y-intercept value, b, which is the point at which the line intersects the y-axis.

Using two points on the graphed line in the diagram attached below, (-4, -6) and (2, 6):

Slope (m) = change in y / change in x = (-6 - 6) /(-4 - 2)

Slope (m) = -12/-6

Slope (m) = 2

The line cuts the y-axis at y = 2. The y-intercept of the line, b = 2.

Wrote the equation of the graphed line by substituting m = 2 and b = 2 into y = mx + b:

y = 2x + 2.

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Answer:

1221

Step-by-step explanation:

if you do 156 times 6 and add that to 95 times 3, you get 1221

Answer:

$1,221

Step-by-step explanation:

156 x 6 = 936

95 x 3 = 285

936 + 285 = $1,221

Answer:

8°

Step-by-step explanation:

For the acute angles in a right triangle,

[tex]sin(90-\theta)=cos\theta[/tex]

Given expression is:

[tex]cos(7x)=sin(4x+2)\\sin(90-7x)=sin(4x+2)\\90-7x=4x+2\\88=11x\\x=8^o[/tex]

To check our answer, determine the measures of the other angles in a right triangle.

[tex]A1=90^o\\A2=8^o\\A3=90-8=82^o[/tex]

The smallest angle is 8°

Answer:

enlargement

Step-by-step explanation:

observe from the figure [tex]OK=x<x+5=7=OK'[/tex]

since [tex]OK<OK'[/tex], then the dilation is an enlargement.

Answer:

Step-by-step explanation:

defsfvbrfdv

The reasonable measurement is D.)the distance from New York to California is 2,250 miles

Measurement:

Measurement is the process of comparison of an unknown quantity with a known or standard quantity.

Given,

Mr. Customs is correcting the class’s math homework on customary units. Here we need to find which of the following measurements is reasonable.

By looking at the given options,

A) a pencil is 12 feet long - This one is wrong because the measuring unit of pencil is cm.

B) the back porch is 12 inches wide - For this one we have to use the feet or meter scale.

C) the 3rd hole in the golf course is is 123 miles long - Here this one we have to use either cm or mm.

Therefore, option (D) the distance from New York to California is 2,250 miles is a reasonable statement.

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Answer:

Step-by-step explanation:

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. Each of these equations on their own could have infinite possible solutions.

The solution for the equation are a.  x = 5/3 or 2

b. x= 43/7 or 6

c. x =114/5 or 23

d. x =114/5 or 23

What is simplified fraction?

Simplified fraction are fraction in there lowest value or reduced form.

a. 25=x15

Divide both sides by 15

25/ 15 = 15x/15

X = 25/ 15 = 5/3

Therefore, the value of x is 5/3 or 2.

b. 43=x7

Divide both sides by 7

43/7 = 7x/7

x= 43/7 = 6.14

Therefore, the value of x is x= 43/7 or 6

c. 75=28x

Divide both sides by 28

75/28 =28x/28

x = 75/28 =2.67

Therefore, the value of x is x=  75/28 or 3

d. 114=5x

Divide both sides by 5

114/5 = 5x/5

x =114/5 =22.8

Therefore, the value of x is x =114/5 or 23

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The remainder for the given polynomial is 9

A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division (No division operation by a variable). It is a function that only uses non-negative integer powers or positive integer exponents of a variable

Given f(x) = 4x^6+ x^4+4

Now f(x-1) = 0

X= 1

Substitute the x value in the function

f(x) = 4x^6+ x^4+4

f(x) = 4(1)^6+ (1)^4+4

f(x) = 4+ 1+ 4

f(x) = 9

Therefore the remainder for the given polynomial is 9

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The answer to the Exponent is [tex]w^{64}[/tex]

What does the term Exponent means?

A quantity that represents the degree of power to which a particular number or expression is to be increased, commonly displayed as a raised symbol next to the number or word is termed as exponent.

Solution:

According to the rule of Exponent

[tex](a^{b} )^{c} = a^{b*c}[/tex]

Using the same rule;

[tex](w^{8})^{8} = w^{8*8}[/tex]

[tex]w^{64}[/tex]

So, the correct answer is w^64

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Answer:

Step-by-step explanation:

this seems tough, but,  remember the formulas  ,  point slope  and how to find M ( slope)  and this gets much easier.

let's use the point-slope formula to get the  slope-intercept formula

from my memory,  which you can also memorize

y-y1=m(x-x1)   (point-slope formula)

we are given the slope m = -2

and we're given a point  P(x1,y1)  as  ( -1,-4)

plug this info into our plug and play formula  :P

y-(-4) = (-2)(x-(-1))    : note all the careful attention to minus signs

y+4 = (-2)(x+1)

y+4 = -2x -2

y = -2x -2 -4

y =-2x-6   (slope-intercept formula  y = mx +b)

y= -2x + (-6)

I'll use Desmos to quickly graph this for you, see attached graph

All the real numbers x which satisfy the given inequality x²<4 , in  interval form is (-2, 2).

As given in the question,

Given inequality is given by :

x²< 4

Simplify the given inequality  x² < 4 to get all the real numbers x we have,

x² < 4

⇒ x² - 4 < 0

⇒ x² - 2² < 0

Apply a² - b² = ( a - b ) ( a + b ) we get,

⇒ ( x - 2 ) ( x + 2 ) < 0

⇒ x ∈ ( -2 , 2 ) as less than symbol represent open interval.

Therefore, all the real numbers x which satisfy the given inequality x²<4 , in  interval form is (-2, 2).

The complete question is :

Find all real numbers x such that x^2 < 4. Give your answer in interval notation.

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[tex]\boldsymbol{\sf{\sqrt{3^2+27}+2^3+\sqrt[3]{64} }}[/tex]

Calculate 3 to the power of 2.

[tex]\boldsymbol{\sf{\sqrt{9+27}+2^3+\sqrt[3]{64} }}[/tex]

Add 9 and 27.

[tex]\boldsymbol{\sf{\sqrt{36}+2^3+\sqrt[3]{64} }}[/tex]

Find the square root of 36.

[tex]\boldsymbol{\sf{6+2^3+\sqrt[3]{64} }}[/tex]

Calculate 2 to the power of 3.

[tex]\boldsymbol{\sf{6+8+\sqrt[3]{64} }}[/tex]

Add 6 and 8.

[tex]\boldsymbol{\sf{14+\sqrt[3]{64} }}[/tex]

Calculate [tex]\sqrt[3]{64}[/tex]

[tex]\boldsymbol{\sf{14+4=18}}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ 18}[/tex]

[tex] \: \: \: \: \: \: \: \bold{\sqrt{9 + 27} + 2 {}^{3} + \sqrt[3]{64} }[/tex]

To solve this problem, the first thing we have to do is simplify 3² to 9, since it multiplies 2 times 3 to give us 9.

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \bold{ \sqrt{36} + {2}^{3} + \sqrt[3]{64} }[/tex]

Then we must add 9 + 27 to give us a result of 36.

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{6 + {2}^{3} + \sqrt[3]{64} }[/tex]

Now we must multiply again but this time we are going to multiply 2 times 6 since 6 × 6 is equal to 36.

[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{6 + 8 \: + \sqrt[3]{64} }[/tex]

Now we must again multiply 3 times 2 to give us 8.

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{6 + 8 + 4}[/tex]

Then we must add 6 + 8 + 4.

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{14 + 4}[/tex]

Before finishing we know that we got 14, now we must add 14 + 4 to give us a result of 18.

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{18}[/tex]

Rpt: The result is 18.

Option-A is correct, when the The exponential term is (3⁴)⁻¹ which is in the division.

Given that,

The exponential term is (3⁴)⁻¹

We have to find the the exponential term which is correct from the option.

The multiplicative inverse of the base raised to a power with the opposite sign of the given power is a negative exponent. In plain English, we write the number's reciprocal and solve it just like positive exponents. For instance, (3/2)² can be used to represent (2/3)⁻². We are aware that an exponent indicates the degree of multiplication a number has undergone.

Take the term,

(3⁴)⁻¹

1/3⁴

Therefore, Option-A is correct, when the The exponential term is (3⁴)⁻¹ which is in the division.

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The percentage of jerseys that were medium-sized jerseys is 35.71%

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

Total number of jerseys the football team has = 28 jerseys

Total number of jerseys that were medium sized = 10

So ,

Percentage of jerseys that were medium sized =
( Total number of jerseys that were medium sized / Total number of jerseys ) x 100

Percentage of jerseys that were medium sized = ( 10 / 28 ) x 100

= ( 5 / 14 ) x 100

= 7.14285 x 5

= 35.71 %

Therefore , the percentage of jerseys that were medium sized = 35.71%

Hence , the percentage of jerseys that were medium-sized jerseys is 35.71%

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Both the length and width of the rectangle are approximately 31.62 m each.

The Area of a rectangle is calculated by multiplying the length by the width.

A = L x W

We have given that area of rectangle is 1,000 m²

1000 = W× L => W = 1000/L ---(1)

The circumference of rectangle is twice the sum of the dimensions. That is,

P = 2L + 2(1000/L)

Now, it is provided that perimeter is minimum so, we differentiate perimeter with respect to L then put first order derivative equal to zero.

dP/dL = 2 + 2000(-1/L²) = 0

=> 2-2000/L²=0

=>2000/L²=2

=> L²=2000/2

=> L²= 1000

=> L= 31.622

putting value of L in (1) we get , W= 31.622m

Therefore the length and width of the rectangle are both approximately 31.622m .

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Answer:

6,10,500,000

Step-by-step explanation:

Answer:

610500000 is the answer! I hope this helps!

The coordinates of the point on the directed line segment that partitions the segment into a ratio of 5 to 3 are [-3.5, -2].

In this exercise, line ratio would be used to determine the coordinates of the point on the directed line segment that partitions the segment into a ratio of 5 to 3.

Mathematically, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical expression:

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Given the following parameters:

Substituting the given parameters into the line ratio formula, we have;

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

P(x, y) = [(5(-2) + 3(-6))/(5 + 3)],  [(5(-8) + 3(8))/(5 + 3)]

P(x, y) = [(-10 + (-18))/(5 + 3)],  [(-40 + 3(8))/(5 + 3)]

P(x, y) = [(-10 - 18)/(8)],  [(-40 + 24)/(8)]

P(x, y) = [(-28)/(8)],  [(-16)/(8)]

P(x, y) = [-3.5, -2]

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Answer:

Your answer would be B!!

Step-by-step explanation:

If you need me to show how to work it let me know!!

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{5}}x-1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{5}{-2}\implies \cfrac{5}{2}}}[/tex]

so we're really looking for the equation of a line whose slope is 5/2 and it passes through (-2 , 14)

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{14})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{14}=\stackrel{m}{ \cfrac{5}{2}}(x-\stackrel{x_1}{(-2)}) \implies y -14= \cfrac{5}{2} (x +2) \\\\\\ y-14=\cfrac{5}{2}x+5\implies {\Large \begin{array}{llll} y=\cfrac{5}{2}x+19 \end{array}}[/tex]

Answer: 20 dollar because every 20% is 4$ therefore 100% is 20$

Answer:

It will take 5 lunges to cover the path.

Step-by-step explanation:

Path length = 110

1 lunge = 22 yards

110/22 = 5

5 lunges = 22x5 = 110 yards

I think is is 22

because it is asking how many times can .6m go into 13.2m of ribbon? If you start with 20x.6 you will get 12. Then you add on another one and get 12.6. Finally add one more to get 13.2m ribbon which would make the answer 22. You can also divide 13.2m divided by .6m and get 22.

Hopefully this helped you guys. If you guys want more answers please give me those 5 Stars and Give me a thanks to show you appreciation.

Over all the Answer is 22

Have a great day (:

The closed right circular cylindrical can of the smallest surface area whose volume is 250π cm³ has a radius of 5cm and a height of 10 cm.

Let r and h be the radius and height of the cylinder respectively.

Volume, V= πr²h

Given,

Volume = 250 π

Now, we can solve by:

⇒ 250 π = πr²h

⇒ r²h=250

⇒ h= 250/r²

We know that,

Surface area, A = 2πr²+2πrh

⇒ A = 2πr²+ 2πr(250/r²)

⇒ A = 2πr²+ (500π/r)

Differentiating the above equation,

dA / dr = 4πr+500π(-1/r²)

For A to be maximum or minimum, dA/dr = 0

⇒ 4πr-500(π/r²) = 0

⇒ 4πr - 500π / r² = 0

⇒ 4πr³ -500π/ r² = 0

⇒ π (4r³ -500) = 0

⇒ 4r³ - 500 = 0

⇒ r = ∛125

⇒ r = 5

Putting value of r = 5, we get,

h = 250/(5)² = 10

By second derivative test,

d²A/dr² = 4π-500π(-2/r³)

At r= 5,

d²A/dr² = 4π+1000(π/r³) > 0 .

Therefore, It is a local minimum.

Ans: Radius = 5 and Height = 10

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Answer: 6a^3b^3

Step-by-step explanation:

Answer:

6a³b³

Step-by-step explanation:

-0.6a^2b*(-10ab^2) =

= -0.6 × (-10) × a² × a × b × b²

= 6a³b³

Answer:

X intercept: (-3/4 , 0)

Y intercept: (0 , 3/7)

Step-by-step explanation: The x intercept is a coordinate whenever y is 0. The y intercept is a coordinate whenever x is 0. So to find the x intercept you put 0 in place of Y and you solve for x. So you get x=-3/4.

You do the same thing to find Y, but you put 0 instead of x and you get y=3/7.

Reasoning is not accurate because we cannot take 79.4 and 0.815 has cluster estimates of 8.

Given:

A student estimated the sum 7.95 + 8.11 + 78.5 + 8.05 + 79.4 + 0.815 as: All the numbers begin with a 7 or 8, so use cluster estimation. 8 + 8 + 80 + 8 + 80 + 0.8 = 184.8  

7.95 + 8.11 + 78.5 + 8.05 + 79.4 + 0.815

8 + 8 + 80 + 8 + 80+ 0.8 = 184.8  

Cluster estimation is  used to estimate sums and products when the numbers being  added or multiplied cluster near/ close in value to a single number.

Here 79.4 does not cluster around 8

And 0.815 does not cluster around 8  

Therefore reasoning is not accurate because we cannot take 79.4 and 0.815 has cluster estimates of 8.

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The probability that the same letter is obtained in all trials is given as follows:

P(all P or all Q) = 1/8.

The probability of an event in an experiment is obtained as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

In this problem, the trials are given as follows:

Only two out of the 16 trials resulted in the same four letters being chosen, hence the probability is:

P(all P or all Q) = 2/16 = 1/8.

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Answer:

Co-interior angles or Consecutive interior angles are the two angles that are on the same side of the transversal. Co-interior angles are the interior angles and it sums up to 180 degrees. It means that the sum of two interior angles, which are on the same side of transversal is supplementary. Co-interior angles resemble like in “C” shape and both the angles are not equal to each other. The co-interior angle is also known as the consecutive interior angles or the same side interior angles.Co-interior Angles

Co-interior Angle Theorem and Proof

Statement:

If the transversal intersects the two parallel lines, each pair of co-interior angles sums up to 180 degrees (supplementary angles).

Proof:

Co-interior Angles Proof

Let us consider the image given above:

In the figure, angles 3 and 5 are the co interior angles and angles 4 and 6 are the co-interior angles.

To prove: ∠3 and ∠5 are supplementary and ∠4 and ∠6 are supplementary.

Given that, a and b are parallel to each other and t is the transversal.

By the definition of linear pair,

∠1 and ∠3 form the linear pair.

Similarly, ∠2 and ∠4 form the linear pair.

By using the supplement postulate,

∠1 and ∠3 are supplementary

(i.e.) ∠1 + ∠3 = 180

Similarly,

∠2 and ∠4 are supplementary

(i.e.) ∠2 + ∠4 = 180

By using the corresponding angles theorem, we can write

∠1 ≅∠5 and ∠2 ≅ ∠6

Thus, by using the substitution property, we can say,

∠3 and ∠5 are supplementary and ∠4 and ∠6 are supplementary.

Hence, the co-interior angle theorem (consecutive interior angle) is proved.

The converse of this theorem is “if a transversal intersects two lines, such that the pair of co-interior angles are supplementary, then the two lines are parallel”.

There are 7 possible positive integers that satisfy the inequality.

In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.

We can find the positive values of x in the given inequality.

2x + 8 < 22

2x < 22 - 8

2x < 14

x < 7

The solution shows that x < 7

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