The length of a rectangle is 7cm more than twice the width. When just the width is tripled, the perimeter of the resulting rectangle is 74cm. What are the original dimensions of the rectangle?

The distance between the two circles is 5.

The distance between two circles is the difference between the sum of their radii and the distance between their centers. In the given diagram, the radius of the circles centered at $A$ and $B$ is 2, and the distance between their centers is the length of $\overline{AB}$, which is 5. Therefore, the distance between the two circles is 5 - (2 + 2) = 5.

The distance between the two circles is 5.

The distance between two circles is the difference between the sum of their radii and the distance between their centers.

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Answer:

-2, 4

-1, -2

0, 0

1, 2

2, 4

Step-by-step explanation:

X. Y

-2 = 4

-1 = 2

0 = 0

1 = -2

2 = -4

Answer:

A

Step-by-step explanation:

A triangular prism has two rectangles on each side, then two triangles on the other sides. I hope this helps! :)

The solution to the system of equations is x = 4 and y = 2.

We would use the elimination method to solve the system of equations:

Let's eliminate the variable y by adding equations 1 and 2:

4x + 8y = 24

2x + y = 19

.

.

.,

6x + 9y = 43

Now we can eliminate the variable x by subtracting equation 3 from the above equation:

6x + 9y = 43

3x + y = 15

.

.

.

3x + 8y = 28

We now have an equation with one variable: 3x + 8y = 28. We can solve for x by dividing both sides by 3:

x = (28 - 8y) / 3

Now we can substitute this expression for x into one of the original equations and solve for y. Let's use equation 4:

4x + 2y = 12

Substituting x = (28 - 8y) / 3:

4((28 - 8y) / 3) + 2y = 12

If we simplify:

Finally, we can use this value of y to find x by plugging it into the expression we found earlier:

x = (28 - 8(2)) / 3

x = (28 - 16) / 3

x = 12 / 3

x = 4.

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Answer:

Step-by-step explanation:

line given is x-y+1= 0

you can rewrite it in slope intercept y=mx+b where m is the slope, and b is the y-intercept where the line meets the y-axis

x-y+1 =0 subtract x and 1 from both sides of the equation

-y = -x-1 multiply both sides by -1

y = x+1 so the slope of this line is 1 and the y-intercept is 1

If you draw this line you can see that there are actually 2 lines that form 45° angles with y=x+1 and pass through (-1, 2), one is vertical x= -1 and one horizontal y =2

The given algebraic equation can be written in many ways as shown.

The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables.

Solution:-

-5x-15+25x-30

it can be written as

-5(x+3-5x+6)

20x-45

5(4x-9)

and also

-5(9-4x)

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Find the equation that is equivalent to [tex]-5x-15+25x-30[/tex].

First, complete arithmetic operations on linear equations [tex]-5x-15+25x-30[/tex]

*Remember : how to complete arithmetic operations on linear equations, grouping terms with the same variable and then adding them up

[tex]-5x-15+25x-30 = -5x+25x-15-30=20x-45[/tex]

Then, find the common factors of [tex]20x[/tex] and [tex]-45[/tex].

Both have the same factor is [tex]-5[/tex].

Use the distributive property to find the equation that is equivalent.

[tex]20x-45=-5(\frac{20x}{-5}-\frac{45}{-5} )=-5(-4x-(-9))=-5(-4x+9)[/tex]

So, [tex]-5x-15+25x-30[/tex] equivalent to [tex]-5(-4x+9)[/tex]

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Answer:

two hundred fifty and six hundred elensths (i dont remember the end)

Step-by-step explanation:

Answer:

12.5%

Step-by-step explanation:

He scored [tex]168-147=21[/tex] points in the playoff game.

This is equal to [tex]\frac{21}{168}(100)=12.5\%[/tex].

Answer:

The answer is x=-6, x=8

Step-by-step explanation:

I recommend using the quadratic formula to solve this problem.

x^2=a

-2x=b

-48=c

Plug it into the quadratic formula.

New equation:[tex]\frac{2+-\sqrt{(-2)^2-4(1)(-48)}}{2(1)}[/tex]

Simplify

Equation: [tex]\frac{2+-\sqrt{4+192}}{2}[/tex]

Add 4 and 192.

Equation: [tex]\frac{2+-\sqrt{196}}{2}[/tex]

Do the square root of 196.

Equation: [tex]\frac{2+-14}{2}[/tex]

Make into two different equations.

Equation 1: [tex]\frac{2+14}{2}[/tex]

Equation 2: [tex]\frac{2-14}{2}[/tex]

Solve the two equations and you will get -6 and 8.  Hope this helps!

[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]

[tex] \large \boxed{\mathbb{ANSWER \: WITH \: EXPLANATION} \downarrow}[/tex]

[tex] \sf \: x ^ { 2 } - 2 x - 48 = 0[/tex]

All equations of the form ax² + bx + c = 0 can be solved using the quadratic formula: [tex]\sf \frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex]. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

[tex] \sf \: x^{2}-2x-48=0 [/tex]

This equation is in standard form: ax² + bx + c = 0 Substitute 1 for a, -2 for b and -48 for c in the quadratic formula.

[tex] \sf \: x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-48\right)}}{2} \\ [/tex]

Square -2.

[tex] \sf \: x=\frac{-\left(-2\right)±\sqrt{4-4\left(-48\right)}}{2} \\ [/tex]

Multiply -4 times -48.

[tex] \sf \: x=\frac{-\left(-2\right)±\sqrt{4+192}}{2} \\ [/tex]

Add 4 to 192.

[tex] \sf \: x=\frac{-\left(-2\right)±\sqrt{196}}{2} \\ [/tex]

Take the square root of 196.

[tex] \sf \: x=\frac{-\left(-2\right)±14}{2} \\ [/tex]

The opposite of -2 is 2.

[tex] \sf \: x=\frac{2±14}{2} \\ [/tex]

Now solve the equation [tex]\sf\:x=\frac{2±14}{2}[/tex] when ± is plus. Add 2 to 14.

[tex] \sf \: x=\frac{16}{2} \\ [/tex]

Divide 16 by 2.

[tex] \boxed{ \boxed{ \bf \: x=8 }}[/tex]

Now solve the equation [tex]\sf\:x=\frac{2±14}{2} [/tex] when ± is minus. Subtract 14 from 2.

[tex] \sf \: x=\frac{-12}{2} \\ [/tex]

Divide -12 by 2.

[tex] \boxed{\boxed{ \bf \: x=-6 }}[/tex]

The equation is now solved.

[tex] \underline{ \bf \: x=8 }\\ \underline{ \bf \: x=-6 }[/tex]

So x = 2.1 is the only possible value of x that makes the equation true.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

The equation is given as follows:

-3x + 6.3 = 0

To find the value of x, we need to isolate x on one side of the equation. We can do this by adding 3x to both sides:

-3x + 3x + 6.3 = 0 + 3x

6.3 = 3x

Now we can divide both sides by 3:

x = 6.3/3

x = 2.1

So x = 2.1 is the only possible value of x that makes the equation true.

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Answer:

Roots x = -1 and x =5

k(x) = (x + 1)(x - 5)

m(x) = 1/2(x + 1 )(2x - 10)

Roots x = 1 and x = -5

n(x) = (3x + 15)(x - 1)

f(x) = (x - 1)(x + 5)

q(x) = (2x - 2)(3x + 15)

Neither

h(x) = 1/2(x + 1)(2x - 20)

Step-by-step explanation:

We have given that ,the quadratic functions shown are written in factored form. The roots of a quadratic function will make the factors equal to 0.

1. Write root as factor changing the sign and put each factor in paranthesis

2.Multiply paire of roots together using box to find the multiplication

3.Make sure that each factor multiplied by every other factor.

The function has roots x = -1 and x =5

[tex]k(x) = (x + 1)(x - 5)\\\\k(x)=x^2-5x+x-5\\k(x)=x^2-4x-5\\[/tex]

[tex]m(x) = 1/2(x + 1 )(2x - 10)\\m(x)=1/2(2x^2-10x+2x-10)\\m(x)=1/2(2x^2-8x-10)\\m(x)=x^2-4x-5[/tex]

The function k(x) and m(x) has root x=-5 and x=5

The function has roots x = 1 and x = -5

[tex]n(x) = (3x + 15)(x - 1)\\n(x)=3x^2-3x+15x-15\\n(x)=3x^2+12x-15\\n(x)=1/3(x^2+4x-5)[/tex]

[tex]f(x) = (x - 1)(x + 5)\\f(x)=x^2+5x-x-5\\f(x)=x^2+4x-5[/tex]

[tex]q(x) = (2x - 2)(3x + 15)\\q(x)=6x^2+30x-6x-30\\q(x)=6x^2+24x-30\\q(x)=1/6(x^2+4x-5)[/tex]

The function n(x),q(x) and f(x) has roots x=1 and x=-5

h(x) = 1/2(x + 1)(2x - 20)

h(x) has no roots from roots at x=−1 and x=5, and x=1 and x=−5.

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Answer:

yes

Step-by-step explanation:

The word linear is used for a straight line. A linear function is a function of a straight line, which means that the degree of a linear function must be 0 or 1 . In this case, The degree of f(x)=2x−3 f ( x ) = 2 x - 3 is 1 , which makes the function a linear function.

Answer:

-x + 5

Step-by-step explanation:

x - (-3) + 8 - 2x - 6 = x - 2x + 3 + 8 - 6 = -x + 5

Answer:

[tex] \sf \: -x + 5 [/tex]

Step-by-step explanation:

Given expression,

→ x - (-3) + 8 - 2x - 6

Let's simplify the expression,

→ x - (-3) + 8 - 2x - 6

→ x + 3 + 8 - 2x - 6

→ (x - 2x) + (3 + 8 - 6)

→ (-x) + (5)

→ -x + 5

Hence, the answer is -x + 5.

Answer: 1/2

Step-by-step explanation:

The question is asking you to find how many centimeters in the scale drawing equal 1 foot on the actual building. The answer will be 1/2 because 1 centimeter is equal to 2 feet in reality. But since we want to know the answer of how many centimeters is in 1 foot, we will divide that in half, to get an answer of 1/2 centimeter, or A.

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Answer:

∠T≈44.1

Step-by-step explanation:

Please see the attached image.

Relative to ∠T, we know the adjacent side and the hypotenuse, 28 and 39 respectively.

We can use a trig function to solve for ∠T. When given the adjacent side and hypotenuse, we can use cosine.

The cosine of an angle is the adjacent side to that angle over the hypotenuse.

cos(T)=28/39

T=[tex]cos^-1[/tex](28/39)

T≈44.1

Answer:

I think the third option

Step-by-step explanation:

Have a nice day! Hope this helps! Owa Owa!!!!

Convert from number format to standard form as a decimal multiplied by a power of 10.

step 1

convert 1.5806*10rais to 4

Convert to decimal notation

1.5806*10^4

The exponent is 4, making it 10 to the power of 4. As the exponent is positive, the solution is a number greater than the origin or base number. To find our answer, we move the decimal to the right 4 time(s)

1.5806 ->15806

step 2

final result

15806

Simplify the expression

1.581*10^4

Simplify exponents and square roots

1.581*10^4

10 ^4 = 10 × 10 × 10 × 10 = 10,000

1.581*10000

Perform any multiplication or division, from left to right:

1.581*10000

15806

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Answer:

  25%

Step-by-step explanation:

Of the 12 girls and 16 boys in Mr. Johnson's class, 3 girls and 4 boys wear glasses. You want to know the percentage of students in the class who wear glasses.

The percentage is the fraction multiplied by 100%. The fraction is the ratio of glasses-wearers to total students.

  percentage = (girls w/ glasses + boys w/ glasses)/(girls + boys)×100%

  percentage = (3 +4)/(12+16) × 100% = 7/28 × 100% = 25%

25% of the students in Mr. Johnson's class wear glasses.

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C. The system has no solution.

Answer:

5

Step-by-step explanation:

4x-3=17

+3 on both sides = 4x=20

divide 20 by 4 and your answer is 5

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{4x - 3 = 17}[/tex]

[tex]\text{ADD 3 to BOTH SIDES}[/tex]

[tex]\mathsf{4x - 3 + 3 = 17 + 3}[/tex]

[tex]\text{SIMPLIFY IT}[/tex]

[tex]\mathsf{4x = 17 + 3}[/tex]

[tex]\mathsf{4x = 20}[/tex]

[tex]\text{DIVIDE 4 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{4x}{4} = \dfrac{20}{4}}[/tex]

[tex]\text{SIMPLIFY IT}[/tex]

[tex]\mathsf{x = \dfrac{20}{4}}[/tex]

[tex]\mathsf{x = 5}[/tex]

[tex]{\huge\text{Therefore, your answer should be:}[/tex][tex]\huge\boxed{\mathsf{x = 5}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The correct graph which represents the equation y = 1/2x - 1 is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ y = 1/2x - 1

Now, After draw the equation we get;

Graph of a line passing through the points (-2, - 2) and (0, - 1).

Thus, The correct statement is,

⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.

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The given set of ordered pairs does not satisfy a linear function.

A linear function is one that, when plotted, forms a straight line. Therefore, non-linear functions are all non-linear functions. We can discern if a function is linear or non-linear from its input/output table or equation, but graphing may be the quickest way to do it.

Given:

The given set of ordered pairs is:

{(3, 2), (4, 3), (5, 4), (6, 5)}

To find:

Whether the given set of ordered pairs satisfies a linear function or not.

Explanation:

The slope of a linear function is:

m = (y₂ - y₁)/ (x₂ -x₁)

The slope of the linear function passes through the points  and  is:

m₁ = (3-1)/(3-1)

m₁ = 2/2

m₁ = 1

The slope of the linear function passes through the points  and  is:

m₂ = (9-3)/(5-3)

m₂ = 6/2

m₂ = 3

Therefore m₁ ≠ m₂ therefore the given set of ordered pairs does not satisfy a linear function.

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Answer:

Step-by-step explanation: Because all three angles of the triangle must equal to 180 degrees, the two smaller angles of the right triangle must be 45 degrees. This is because a right angle always is 90 degrees and because you know that the other two angles are the same, and it must all equal to 180, the angles must be 45 degrees, 45 degrees, and 90 degrees.

Angle 1: (right angle) 90 degrees

Angle 2: 45 degrees

Angle 3: 45 degrees

Answer:

Positive

Step-by-step explanation:

Positive / positive = positive

positive / negative = negative

negative / negative = positive

negative/ positive = negative

Sign of -4 divided by -8 we get positive expression.

Here we have to find the sing of expression,

When -4 divided by -8

Since we know that,

Dividing two fractions is equivalent to multiplying the first fraction by its reciprocal. The first step in splitting fractions is to get the reciprocal of the second fraction (reverse the numerator and denominator). Then, multiply the numerators.

We can write it,

-4 divided by -8  = -4/-8

                            = (4/8)x(-1/-1)

                            =  1/2    its a positive number.

Hence,

-4 divided by -8  = 1/2

Hence we get positive expression.  

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Answer:

the one that is not equivalent to the others would be 116-34

Step-by-step explanation:

because its 116 and the others dont have anything to do with 116 :)

Answer: The statement that is not equivalent should be D. |16-34

Answer:

I believe you're using a tool that I'm not gonna say because Brainly doesn't allow such sins, haha. I bet the name of the tool you're using starts with a K, correct?

Anyways, I don't think you can add values such as a, h, k. The only values you're allowed to add are x and y :(

Step-by-step explanation:

Answer:

y=4x+1

Step-by-step explanation:

i hope this helps :)