jonathan went for a jog. every time he stops to tie his shoelaces, his jog lasts 2 1/2 minutes longer. if he stops to tie his shoelaces four times, how much longer does his jog take

Step-by-step explanation:

Supplementary angles equal 180°

1. Let the two angles be x and y

then y = 4x + 10

x + y = 180

x + (4x + 10) = 180

5x + 10 = 180

5x = 180 - 10

5x = 170

x = 170 / 5

x = 34

x = 34y = 146

2. if the two angles are equal then divide 180 by 2 to get 90

3. 180 - x = 3(90 - x)

180 - x = 270 - 3x

2x = 90

x = 45

4. 180 - x = 2x - 12

180 - 12 = 2x + x

168 = 3x

x = 56

Answer:

C

Step-by-step explanation:

The square root of 49 equals 7

This equation can be rewritten as m-5=7

m-5=7

1) add 5 to both sides:

m=12

Nothing else can be done so m=12 is your final answer (c)

7(x + 3 ) = 6 - (-7x - 15)

Apply the distributive rule to remove parentheses.

7x + 21 = 6 + 7x + 15

Right away, you should be able to see that 7x will be cancelled rendering this equation to have no solution.

Answer: NO SOLUTION

The number 0.00052 in standard form can be written as 5.2 × 10⁻⁴ in scientific notation.

Given that:

The number 0.00052 is given in the standard form.

This has to be converted into the scientific notation.

Scientific notation is the notation of writing smaller numbers or larger numbers as the product of an integer from 1 to 10 and the power of 10 is raised to positive or negative power.

Here, the number is very small.

So, the power of 10 is negative.

Here, the integer is 5.2.

The decimal point has to be shifted 4 places to the left.

So, the power of 10 is -4.

Hence, the number can be written as 5.2 × 10⁻⁴.

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Answer:

8,146 x 121

Step-by-step explanation:

This is a problem in which you need to measure your understading of "orders of magnitude."

If the estimated answer is [tex]800000[/tex] that means that we are looking at a multiplication in the "order of" [tex]8*10^5[/tex]

You need to look at the "orders of magnitude" of the things you're multiplying. In the first case, we have [tex]8146*12[/tex] that would be "of the order of" [tex]8*10^3[/tex] times [tex]10^1[/tex]. So the whole multiplication would "of the order of" [tex]8*10^4[/tex] or near [tex]80000[/tex]

The correct answer, 8,146 x 121, is because it's "of the order of" [tex]8*10^3[/tex] times [tex]10^2[/tex] and the gives us the [tex]8*10^5[/tex] we need.

Answer:

Step-by-step explanation:

88

Answer:

Step-by-step explanation:

x(x-2y)-(y-x)2  

Final result :

 -y2

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 x • (x - 2y) -  (y - x)2

Step  2  :

2.1     Evaluate :  (y-x)2   =    y2-2xy+x2  

Final result :

 -y2

Answer: I think the answer is -x + y.

Step-by-step explanation:I think this is the answer because you first start off by distributing all the variables inside the parenthesis by the negative sign which would give you -x+2y-y. After that, you would have to subtract 2y-y because they share the same variable and you must have a SIMPLIFIED ANSWER. So with that said, your overall answer should be -x+y. Hope I'm right in giving you the correct answer!!!!

Answer:

Answer would be B.

Step-by-step explanation:

Answer:

The value of the 8 in the number 38.165.0479 is 8 ones

I am joyus to assist anytime i can :)

[tex]\huge\boxed{600,000 + 80,000 + 700 + 5}[/tex]

To find expanded form, we need to split up the digits. When you do that, you take one digit and cut off everything to the left of it, then make everything to the right zeros.

[tex]600,000 + 80,000 + 0 + 700 + 0 + 5[/tex]

We don't need to keep the zeros.

[tex]\boxed{600,000 + 80,000 + 700 + 5}[/tex]

We can check this by adding the numbers back up to get [tex]680,705[/tex].

[tex]680,000 + 700 + 5[/tex]

[tex]680,700 + 5[/tex]

[tex]680,705[/tex]

Answer:

6

Step-by-step explanation:

32/68- divide by 4 . 32/4=8, 68/4=17

22/28- divide by 2. 22/2=11, 28/2=14

21/49- divide by 7. 21/7=3, 49/7=7

Answers:

32/68=8/17

22/28-11/14

21/49=3/7

Step-by-step explanation:

[tex]\dfrac{32}{68}=\dfrac{32:2}{68:2}=\dfrac{16:2}{34:2}=\dfrac{8}{17}\\\\\\\dfrac{22}{28}=\dfrac{22:2}{28:2}=\dfrac{11}{14}\\\\\\\dfrac{21}{49}=\dfrac{21:7}{49:7}=\dfrac{3}{7}[/tex]

Answer:

x = 8

Step-by-step explanation:

Simplifying

9x + -25 = 5x + 7

Reorder the terms:

-25 + 9x = 5x + 7

Reorder the terms:

-25 + 9x = 7 + 5x

Solving

-25 + 9x = 7 + 5x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5x' to each side of the equation.

-25 + 9x + -5x = 7 + 5x + -5x

Combine like terms: 9x + -5x = 4x

-25 + 4x = 7 + 5x + -5x

Combine like terms: 5x + -5x = 0

-25 + 4x = 7 + 0

-25 + 4x = 7

Add '25' to each side of the equation.

-25 + 25 + 4x = 7 + 25

Combine like terms: -25 + 25 = 0

0 + 4x = 7 + 25

4x = 7 + 25

Combine like terms: 7 + 25 = 32

4x = 32

Divide each side by '4'.

x = 8

Simplifying

x = 8

Answer:

Parallel

Step-by-step explanation:

The two lines y+7x=14 and y+5=-7x are parallel to each other

The two lines y + 7x=14 and y+5=-7x are parallel to each other.

Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness,

thus, are on the same slope.

Since the given parallel line has equation y = 2x + 2, thus its slope is 2 and thus, the slope of the needed line is 2 too.

Given lines is y + 7x=14 and y+5=-7x.

The slope of the given line;

y + 7x=14

y =  -7x + 14

Thus, the slope m = -7.

The slope of the given line;

y+5=-7x

y = -7x - 5

Thus, the slope m = -7.

We can see that the slope are the same.

Thus, The two lines y + 7x=14 and y+5=-7x are parallel to each other.

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Answer: First option.

Step-by-step explanation:

For this exercise it is importnatn to to remember the properties that are shown below:

1) [tex]a^\frac{1}{n}=\sqrt[n]{a}[/tex]

2) [tex](a^m)^n=a^{(mn)}[/tex]

Therefore, given the following expression provided in the exercise:

[tex]\sqrt[3]{4^5}[/tex]

You can apply the properties mentioned before, in order to find an equivalent expression.

Therefore, you get:

[tex]\sqrt[3]{4^5}=(4^5)^{\frac{1}{3}}=4^{\frac{5*1}{3}}=4^{\frac{5}{3}}[/tex]

Then the answer is the first option.

Answer:

[tex]\sqrt[3]{4^5}=(4^5)^{\frac{1}{3}}=4^{\frac{5}{3}}[/tex]

Option 1 and Option 3 is correct

Step-by-step explanation:

Given: [tex] 4^{\frac{5}{3}}=\sqrt[3]{4^5}[/tex]

This is exponent to radical change property.

The fraction exponent write as radical.

[tex]a^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex]

[tex]\sqrt[3]{4^5}=(4^5)^{\frac{1}{3}}=4^{\frac{5}{3}}[/tex]

True

[tex]4^{\frac{8}{3}}\cdot 4^{\frac{7}{3}}=4^{{\frac{8}{3}+\frac{7}{3}}=4^5[/tex]

False

Step-by-step explanation:

It's the DISTRIBUTIVE PROPERTY:

m(a + b) = ma + mb

[tex]m\cdot(a+b)=m\cdot a+m\cdot b=ma+mb[/tex]

Other properties:

Commutative Property:

of addition: a + b = b + a

of multiplication: a · b = b · a

Associative Property:

of addition: (a + b) + c = a + (b + c)

of multiplication: (a · b) · c = a · (b · c)

Answer:

y≤9/8

Step-by-step explanation:

-9≤-8y

1) Divide both sides by -8 (You must flip the sign when dividing by a negative)

y≤9/8

The equation that could be used to solve the graph above is x² - 1 = 0.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

The graph of a quadratic equation y = x² is a parabola that opens upwards.

By observing the graph we conclude that when x = 0, y = - 1 and when

x = ± 1, y = 0.

Now going through the options we conclude that x² - 1 = 0 is the equation that satisfies this criterion.

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The equation that can be solved using the graph is x^2 - 2x + 1 = 0.

The equation that could be solved using the graph above is x2 - 2x + 1 = 0. This is because the graph intersects the x-axis at the point where y=0, and this represents the solutions to the equation.

If we solve the equation x2 - 2x + 1 = 0 using factoring or the quadratic formula, we would find that the solutions are x=1 and x=1. These are the same x-values where the graph intersects the x-axis on the graph provided.

The other equations, x2 + x - 2 = 0, x2 + 2x + 1 = 0, and x2 - 1 = 0, do not have solutions that match the x-values where the graph intersects the x-axis.

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Answer:

[tex]\displaystyle \frac{d}{dt}[t^{\sqrt{11}}] = \sqrt{11}t^{\sqrt{11} - 1}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = t^{\sqrt{11}}[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

Reflect the graph f(x) across the x axis to obtain the graph g(x).

its c

Step-by-step explanation:

following the accepted steps you would first reflect the graph across the y axis due to the negative sign within the function, then you would reflect the result across the x axis due to the negative sign outside of the function. 

In practice however you only need to reflect across the x axis as -(-x)^2 simplifies to -x^2

Answer:

B

Step-by-step explanation:

From any point (x, y) on the parabola the focus and directrix are equidistant.

Using the distance formula

[tex]\sqrt{(x+2)^2+(y-4)^2}[/tex] = | y - 6 |

Squaring both sides

(x + 2)² + (y - 4)² = (y - 6)² ←  distributing

x² + 4x + 4 + y² - 8y + 16 = y² - 12y + 36 ( subtract y² - 12y + 36 from both sides )

x² + 4x + 4 + 4y - 20 = 0 ( subtract x² + 4x + 4 from both sides )

4y - 20 = - x² - 4x - 4 ( add 20 to both sides )

4y = - x² - 4x + 16 ( divide through by 4 )

y = - [tex]\frac{1}{4}[/tex] x² - x + 4, that is

f(x) = - [tex]\frac{1}{4}[/tex] x² - x + 4 → B

Answer:

Option B

Step-by-step explanation:

Given that a parabola has a focus at (−2, 4) and a directrix of y = 6.

We have to find the equation of the parabola in std form

We know that a parabola is a conic section in which all points are equidistant from the focus and vertex.

Let (x,y) be any point on the parabola

Distance of (x,y) from the focus =[tex]\sqrt{(x+2)^2+(y-4)^2}[/tex] ...i

Distance of (x,y) from directrix = difference in y coordinate = [tex]|y[-6|[/tex]...ii

Since i = ii, square and equate both

[tex](x+2)^2+(y-4)^2=(y-6)^2\\x^2+4x+4 -8y+16 = -12y+36\\4y=-x^2-4x+16\\y = \frac{-1}{4} d^2-x+4[/tex]

Hence option B is right.

Answer:

The distributive property lets you multiply a sum by multiplying each addend separately and then add the products. ... Consider the first example, the distributive property lets you "distribute" the 5 to both the 'x' and the '2'.

Step-by-step explanation:

Answer: 4(x-3)=20

4x-4(3)=20

4x-12=20

4x-12+12=20+12

4x=32

4x/4 = 32/4

x=8

Step-by-step explanation:

To “distribute” means to divide something or give a share or part of something.

Answer:

The vertical angles are ∠ WRS and ∠ VRT ⇒ 2nd answer

Step-by-step explanation:

* Lets explain the meaning of the vertical angles

- Vertical angles are the angles opposite to each other when two lines

  are intersected

- The vertical angle are equal in measures

- Look to attached figure which represents the lines

∵ Line TW intersects line SV at R

∴ ∠ WRV and ∠ SRT are vertical angle

∴ ∠ WRS and ∠ VRT are vertical angle

∵ RU is between the rays of angle VRW

∴ RU intersects the lines TW and SV at R

∴ No vertical angles between RU and the other two lines because

  it intersects them its endpoint R

* Now lets look to the answer to chose the right one

- ∠ WRU and ∠ SRT are not vertical angles

- ∠ WRS and ∠ VRT are vertical angles

- ∠ VRU and ∠ TRS are not vertical angles

- ∠ VRT and ∠ SRT are not vertical angles

The pair of angles that are vertical angles is: ∠WRS and ∠VRT.

When two straight lines intersect each other at a point, the opposite angles that are vertical to each other are called vertical angles.

∠WRS and ∠VRT are vertically opposite each other.

Therefore, the pair of angles that are vertical angles is: ∠WRS and ∠VRT.

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Answer:

Given: The total cost of renting a car is determined by the number of days a car is rented, at $75 per day, and the number of miles it is driven, at $0.50 per mile. The company uses the expression [tex]75x +0.50y[/tex] to evaluate the total cost of renting a car.

To check: We need to check what does the variable x represent.

Here, the company uses the expression [tex]75x +0.50y[/tex] to evaluate the total cost of renting a car.

Here 75 represents the rent per day, and 0.50 represents the cost per mile.

As, x is multiplied by 75. So, the variable x represents the number of day one has taken the car.

Answer:

Bedhshshhssjbsbwbsbw

Step-by-step explanation:

Fhdhshhehehehehehehshehs

Answer:

0,0

1,5

2,10

3,15

4,20

5,25

Step-by-step explanation:

x=cups of flour

y=batches of cookies

Answer:

332

Step-by-step explanation:

69-9=60

+23=83

x4=332

Answer:

Step-by-step explanation:

(f o g)(7) = f(g(7))

but  g(7) = 7-4 =3

(f o g)(7) = f(g(7))  =     f(3) =  3² =9

Answer: 30x

Multiply  

−

2

by  

5

.

−

3

x

⋅

−

10

Multiply  

−

10

by  

−

3

.

30

x

Answer:

6[tex]x^{6}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]

Given

(-3x)(-2[tex]x^{5}[/tex])

= - 3 × [tex]x^{1}[/tex] × - 2 ×[tex]x^{5}[/tex]

= (- 3 × - 2) × [tex]x^{(1+5)}[/tex]

= 6[tex]x^{6}[/tex]