evaluate the exponent

(-6) EE -3

Answer:

The jogging rate of Matthew is 5 mph.

Step-by-step explanation:

Let the jogging rate of Matthew be x mph.

It is given that his jogging rate was 25 mph slower than the rate when he was riding. So, the riding rate is (x+25) mph.

The distance between Matthew and his friend's house is 12 miles.

[tex]Speed=\frac{Distance}{Time}[/tex]

[tex]Time=\frac{Distance}{Speed}[/tex]

The time taken by Matthew in jogging is [tex]\frac{12}{x}[/tex] and the time taken by Matthew in riding is [tex]\frac{12}{x+25}[/tex].

It took him 2 hours longer to jog there than ride back.

[tex]\frac{12}{x}=\frac{12}{x+25}+2[/tex]

[tex]\frac{12}{x}-\frac{12}{x+25}=2[/tex]

[tex]\frac{12(x+25)-12x}{x(x+25)}=2[/tex]

[tex]12x+300-12x=2x(x+25)[/tex]

[tex]300=2x^2+50x[/tex]

[tex]0=2x^2+50x-300[/tex]

[tex]0=x^2+25x-150[/tex]

[tex]0=x^2+30x-5x-150[/tex]

[tex]0=(x+30)(x-5)[/tex]

Equate each factor equal to 0.

[tex]x=5,-30[/tex]

The speed cannot be negative, therefore the jogging rate of Matthew is 5 mph.

Answer:

the answer is D

Step-by-step explanation:

Answer:

[tex]d =30g[/tex]

Step-by-step explanation:

Sam drives his car at a constant speed. He travels a distance (d) of 15 miles with 1/2 of a gallon of gas (g)

Distance d= 15

Gallons of gas (g)= 1/2

Equation is d= rg

Now plug in the values

15 = r* 1/2

Now we divide by 1/2 on both sides

[tex]r=\frac{15}{\frac{1}{2}}=15 * \frac{2}{1}= 30[/tex]

r=30

Now we replace the value of 'r' in the equation d=rg

[tex]d = 30g[/tex]

Answer:

Math

Step-by-step explanation:

Answer:

D. 51%

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

If ΔGJI and ΔPKH are similar, then ∡G≅∡P, ∡J≅∡K and ∡I≅∡H.

We have m∡G + m∡P = 50°, therefore m∡G = m∡P = 50° : 2 = 25°.

m∡I = 48° therefore m∡H = 48°.

We know, the sum of the measures of the angles of a triangle is equal 180°.

Therefore we have the equation:

m∡G + m∡J + m∡I = 180°

25° + m∡J + 48° =180°

73° + m∡J = 180°      subtract 73° from both sides

m∡J = 107° → m∡K = 107°.

The measures of all the angles of these triangles are: [tex]\rm 25^\circ,\;48^\circ\;and \; 107^\circ[/tex] and this can be determined by using the properties of the triangle.

Given :

Given that triangle GJI and triangle PKH are similar therefore:

[tex]\rm \angle G = \angle P[/tex]

[tex]\rm \angle J = \angle K[/tex]

[tex]\rm \angle I = \angle H[/tex]

The sum of the interior angles of the triangle is [tex]180^\circ[/tex].

[tex]\rm \angle G + \angle I + \angle J = 180^\circ[/tex]

[tex]\rm 25^\circ + 48^\circ + \angle J = 180^\circ[/tex]

[tex]\rm 73^\circ + \angle J = 180^\circ[/tex]

[tex]\rm \angle J = 107^\circ = \angle K[/tex]

The measures of all the angles of these triangles are: [tex]\rm 25^\circ,\;48^\circ\;and \; 107^\circ[/tex].

For more information, refer to the link given below:

https://brainly.com/question/10652623

Answer:

∠RQP

Step-by-step explanation:

The correct answer is option (D).

Inequality shows relation between two expression which are not equal to each others.

The graph shows an open circle at -6,

which implies that -6 is not a solution to the inequality.

The shaded arrow on all values shows that values are smaller than -6 and  x < -6 is the inequality that represented on the line graph.

The required inequality is x < -6.

To know more about Inequality on:

https://brainly.com/question/20383699

#SPJ

Hello from MrBillDoesMath!

Answer:

Sum = -119,962                    ( I hope!)

Discussion:

Let's determine the pattern.

first term:  -3

2nd term:  (-3) * (-6) = 18                     (multiply first term by -6)

3rd  term:  (18) * (-6) = -108                 (multiply 2nd term by -6)

4th term :  (-108)*(-6) = 648                ( etc)

5th term :  (648)*(-6) =  -3888            (etc)

6th term :  (-3888)*(-6) = 23328         (etc)

7th term:   (23328)*(-6) =  -139967     (etc)

Sum = -119,962

A simpler way to do this is to use the formula for the sum of a geometric series to n terms. The series is

-3  Sum ( -6)^n                n = 0, 1, 2, 3, 4, 5, 6

Regards,  

MrB

P.S.  I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!

Answer:

The number (x) is 127.1

Step-by-step explanation:

4% of a number (x) is equal to;

31% of 16.4

i.e 0.04x = 5.084

x = [tex]\frac{5.084}{0.04}[/tex] = 127.1

The number (x) is 127.1

Answer:

x = 127.1

Step-by-step explanation:

Let x be the unknown number.

It is given that 4% of the number is 31% of 16.4

4% of x  = 31% of 16.4

[tex]x\times \dfrac{4}{100}=16.4\times \dfrac{31}{100}[/tex]

[tex]\dfrac{4x}{100}=\dfrac{508.4}{100}[/tex]

Multiply both sides by 100.

[tex]\dfrac{4x}{100}\times 100=\dfrac{508.4}{100}\times 100[/tex]

[tex]4x=508.4[/tex]

Divide both sides by 4.

[tex]x=\dfrac{508.4}{4}[/tex]

[tex]x=127.1[/tex]

Therefore, the unknown number is 127.1.

Answer:

ax²+ bx + c = 0

Step-by-step explanation

Multiplying (x+4) and (x−1) together (called Expanding) gets x2 + 3x − 4 :

expand vs factor quadratic

So (x+4) and (x−1) are factors of x2 + 3x − 4

Just to be sure, let us check:

(x+4)(x−1)  = x(x−1) + 4(x−1)

 = x2 − x + 4x − 4

 = x2 + 3x − 4 yes

Yes, (x+4) and (x−1) are definitely factors of x2 + 3x − 4

To factorise a quadratic equation, express it in the standard form ax² + bx + c = 0, identify coefficients a, b, and c, and then apply the quadratic formula.

To factorise quadratics in their simplest form, you need to express them in the standard quadratic form, which is ax² + bx + c = 0. For example, if you are given the equation x² + 4x - 21 = 0, you should identify a = 1, b = 4, and c = -21. Then you can apply the quadratic formula:

'x' equals minus ‘b’, plus-or-minus the square root of ‘b’ squared minus four ‘a’ ‘c’, all over two 'a' (x = [tex]\frac{-b \pm \sqrt{b^2- 4ac} }{2a}[/tex])

If you are given an equation like 3x +3 + x² + x = 24, first rearrange it into the standard quadratic form by combining like terms. Use the quadratic formula if you cannot factor the quadratic easily.

Keep in mind that the quadratic formula can only be used if the equation is a true quadratic with powers confined to the second, first, and zeroth (constant term). If other powers or roots are present, then alternative methods must be used.

[tex]\left\{\begin{array}{ccc}y=5x-7\\-6x-4y=-24&\text{divide both sides by (-2)}\end{array}\right\\\left\{\begin{array}{ccc}y=5x-7&(*)\\3x+2y=12&(**)\end{array}\right\\\\\text{substitute }\ (*)\ \text{to}\ (**):\\\\3x+2(5x-7)=12\qquad\text{use distributive property}\\\\3x+(2)(5x)+(2)(-7)=12\\\\3x+10x-14=12\qquad\text{add 14 to both sides}\\\\13x=26\qquad\text{divide oth sides by 13}\\\\\boxed{x=2}\\\\\text{Put the vaalue of x to}\ (*):\\\\y=5(2)-7\\\\y=10-7\\\\\boxed{y=3}\\\\Answer:\ \boxed{x=2\ and\ y=3\to(2,\ 3)}[/tex]

Answer:

51.544 L  in our tank

Step-by-step explanation:

We have a 13.6 gallon tank

Our conversion factor is 3.79 L = 1 gallon.  We want liters on top since that is where we want to end up

3.79 L /1 gallon is what we want to use

13.6 * 3.79L/1 gallon = 51.544 L  in our tank

Answer:

18 = diameter

Step-by-step explanation:

Answer:

The money earned by Drea was [tex]\$225[/tex]

The money earned by Sajini was [tex]\$200[/tex]

Step-by-step explanation:

Let

x------> money earned by Drea

y------> money earned by Sajini

we know that

[tex]x+y=425[/tex] -----> equation A

[tex]x=y+25[/tex] ----> equation B

substitute equation B in equation A

[tex](y+25)+y=425[/tex]

solve for y

[tex]2y=425-25[/tex]

[tex]y=400/2=\$200[/tex]

Find the value of x

[tex]x=y+25[/tex] ----> [tex]x=200+25=\$225[/tex]

using a graphing tool

solve the system of equations

Remember that the solution of the system of equations is the intersection point both graphs

The intersection point is [tex](225,200)[/tex]

see the attached figure

Answer:

Drea: $225

Sajini: $200

Step-by-step explanation:

D + S = 425

D = S + 25

S + 25 + S = 425

2S = 400

S = 200

D = 200 + 25 = 225

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]4x+y>1[/tex] -----> inequality A

The solution of the inequality A is the shaded area above the dashed line

The equation of the dashed line is [tex]4x+y=1[/tex]

The slope of the dashed line is negative

The y-intercept of the dashed line is the point [tex](0,1)[/tex]

The x-intercept of the dashed line is the point [tex](0.25,0)[/tex]

[tex]y\leq \frac{3}{2}x+2[/tex] -----> inequality B  

The solution of the inequality B is the shaded area below the solid line

The equation of the solid line is [tex]y=\frac{3}{2}x+2[/tex]

The slope of the solid line is positive

The y-intercept of the solid line is the point [tex](0,2)[/tex]

The x-intercept of the solid line is the point [tex](-1.33,0)[/tex]

using a graphing tool

The graph in the attached figure

Answer: 27-c =x

Step-by-step explanation:

We'll use c to represent the amount taken away (subtracted) and x to represent the amount left (the answer).

We begin with 27 balloon, and take away c amount to make x.

27-c =x

The number of balloons left after c balloons have popped from an initial number of 27 balloons can be represented by the mathematical expression 27 - c.

In order to determine the number of balloons that were left after some of them had popped, we can use a simple mathematical expression. If there were initially 27 balloons and c balloons popped, then the number of balloons left would be the initial number of balloons minus the number popped.

Mathematically, this can be represented by the expression: 27 - c.

The variable c is used to represent the number of balloons that popped during the party. By subtracting this from the total number of balloons, we're left with the number of balloons that survived the party.

https://brainly.com/question/30350742

#SPJ3

Answer: The Perimeter is 90 meters

Step-by-step explanation:

Area = 126

Width = 3

Length = L

3 x L = 126

3 x L / 3 = 126/3

L = 42

Check:

3 x 42 = 126

126 = 126

Perimeter = L2 + W2

P = 42 x 2 + 3 x 2

P = 84 + 6

P = 90

Answer: Try checking B

Step-by-step explanation:

Answer: lower right hand corner

In this corner is an expression that has "pi" in it that doesn't cancel out like it does in the upper left hand corner. The number pi is irrational because it cannot be written as a fraction of two whole numbers. We can sorta get close when we say 22/7 = 3.14129 but the more accurate version of pi is pi = 3.14159; however we cannot get an exact match.

Answer:

the answer is 16

Step-by-step explanation:

25-9=16 pens

Answer:25-9= 16 pens

Step-by-step explanation:

Answer:

[tex]S_{10}[/tex] = - 30

Step-by-step explanation:

For a given arithmetic sequence the n th term formula is

[tex]t_{n}[/tex] = [tex]t_{1}[/tex] + (n - 1)d

where d is the common difference and [tex]t_{1}[/tex] the first term

We have to find d and [tex]t_{1}[/tex]

from the given information we can write 2 equations and solve for d and [tex]t_{1}[/tex]

[tex]t_{6}[/tex] = [tex]t_{1}[/tex] + 5d = - 4 → (1)

[tex]t_{10}[/tex] = [tex]t_{1}[/tex] + 9d = - 12 → (2)

subtract (1) from (2) term by term

4d = - 8 ⇒ d = - 2

substitute d = - 2 in (1)

[tex]t_{1}[/tex] - 10 = - 4 ⇒ [tex]t_{1}[/tex] = - 4 + 10 = 6

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex][2[tex]t_{1}[/tex] + (n - 1)d ], hence

[tex]S_{10}[/tex] = 5[(2 × 6) + (9 × - 2) ] = 5(12 - 18) = 5 × - 6 = - 30

Choice C for problem 6 is correct. The two angles (65 and 25) add to 90 degrees, proving they are complementary angles.

===========================================

The answer to problem 7 is also choice C and here's why

To find the midpoint, we add up the x coordinates and divide by 2. The two points A(-5,3) and B(3,3) have x coordinates of -5 and 3 respectively. They add to -5+3 = -2 which cuts in half to get -1. This means C has to be the answer as it's the only choice with x = -1 as an x coordinate.

Let's keep going to find the y coordinate of the midpoint. The points A(-5,3) and B(3,3) have y coordinates of y = 3 and y = 3, they add to 3+3 = 6 which cuts in half to get 3. The midpoint has the same y coordinate as the other two points

So that is why the midpoint is (-1,3)

To find the diagonal of a door frame, use the Pythagorean theorem. Substitute the door's height and width into the formula, then find the square root of the sum. Round your answer to the nearest tenth.

To find the length of the diagonal of the door frame, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the long side, or in this case, the diagonal) is equal to the sum of the squares of the other two sides (height and width of the door).

So, the formula becomes: Diagonal = √((Height)^2 + (Width)^2)

Substitute the given values of the height and width into the equation: Diagonal = √((80 inches)^2 + (36 inches)^2) = √(6400 + 1296) = √7696

The square root of 7696 is about 87.7 inches. So, the length of the diagonal of the door frame, rounded to the nearest tenth, is 87.7 inches.

https://brainly.com/question/28361847

#SPJ12

To calculate the length of the diagonal of the door frame, use the Pythagorean theorem by squaring the width and height, adding the squared values, and then taking the square root. The length of the diagonal is approximately 87.9 inches.

To calculate the length of the diagonal of the door frame, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the width and the height of the door frame form the legs of the right triangle, and the diagonal is the hypotenuse. Using the Pythagorean theorem, we can calculate the length of the diagonal as follows:

Therefore, the length of the diagonal of the door frame is approximately 87.9 inches, rounded to the nearest 10th.

https://brainly.com/question/28361847

#SPJ12

Answer:

Step-by-step explanation:

It is given that the perimeter of the regular hexagon is 48 inch. Thus,

Perimeter of the regular hexagon = 48

⇒[tex]Sum of all the sides=48[/tex]

⇒[tex]6x=48[/tex]

⇒[tex]x=8inch[/tex]

Thus, the side of the regular hexagon is 8 inch.

Now, [tex]area of the regular hexagon=\frac{3\sqrt{3}}{2}(x)^2[/tex]

⇒[tex]A=\frac{3\sqrt{3}}{2}(8)^2[/tex]

⇒[tex]A=\frac{3\sqrt{3}}{2}(64)[/tex]

⇒[tex]A=96\sqrt{3}[/tex]

⇒[tex]A=166.03 sq inches[/tex]

Thus, the area of the regular hexagon is 166.03 sq inches.

The area of the regular hexagon that's given will be 166.03 inches².

From the information, it was stated that the regular hexagon has a perimeter of 48 inches.

Therefore, the length of each side will be:

= 48/6

= 8 inches

The area of a regular hexagon calculated as:

= 3✓3/2 × x²

= 3✓3/2 × 8²

= 96✓3

= 166.03

In conclusion, the area is 166.03 inches².

Learn more about hexagon on:

https://brainly.com/question/3812956

Answer:

The correct answer is for the given expression is -43.

Step-by-step explanation:

We are given the following expression and we are supposed to evaluate it:

[tex](-2)^2 + (-42) + (18 - 23)[/tex]

Solving the terms inside the brackets first, following the order of operations to solve a mathematical expression to get:

= 4 + (-42) + (-5)

Further adding and subtracting the terms to get:

= 4 - 42 - 5

= -38 - 5

= -43

Answer:

-17

Step-by-step explanation:

Evaluate the expression: (–2)^2 + (–4^2) + (18 – 23) = -17

Answer:

It's 3/2p!

Step-by-step explanation:

Because Helen do the same number of exercises on 2 days, the time to do and the average rate are  inversely proportional!

So, if on Monday, Helen's average rate is p then on the next day, her average rate is:

p × 3 ÷ 2 = [tex]\frac{3p}{2}[/tex]

=3/2p

Brainliest?

Answer:

y = (x + 9)² + 9

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

given a parabola in standard form : ax² + bx + c : a ≠ 0

the the x-coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

y = x² + 18x + 90 is in standard form

with a = 1, b= 18 and c = 90

[tex]x_{vertex}[/tex] = - [tex]\frac{18}{2}[/tex] = - 9

to find the corresponding y-coordinate substitute x = - 9 into the equation

y = (- 9)² + 18(- 9) + 90 = 81 - 162 + 90 = 9

⇒ y = (x + 9)² + 9 ← in vertex form

Answer:

3 weeks, $45

Step-by-step explanation:

So we can make an equation!

55+5x=100-10x

So solving for x,

X=3

Final answer:

After solving the equations, Mindy and Sean will have the same amount of money, which is $70, after 3 weeks.

Explanation:

The question is about finding after how many weeks Mindy and Sean would have the same amount of money and how much that amount would be. Let's denote the number of weeks as w. For Mindy, who starts with $55 and saves $5 per week, her amount of money as a function of weeks is 55 + 5w. For Sean, who starts with $100 and spends $10 every week, his amount of money as a function of weeks is 100 - 10w.

To find out after how many weeks they would have the same amount of money, set the two expressions equal to each other:

55 + 5w = 100 - 10w

Add 10w to both sides and subtract 55 from both sides to solve for w:

15w = 45

Therefore, w = 45 / 15 = 3

To find out how much money they would have, substitute w = 3 into one of the original equations:

Mindy: 55 + 5(3) = 70

So, after 3 weeks, both Mindy and Sean will have $70

Option B. 12/ 125  is the answer.

Explanation

Total umber of sour ball candies = 50

Number of lemon candies = 12

Hence the probability to get a lemon candy is = 12/50

Number of cherry sour balls = 20

So, the probability to get a cherry sour ball = 20/50

So, to get the joint probability for a random selection to either get a lemon or cherry candy, we will multiply both the probabilities.

[tex]\frac{12}{50}*\frac{20}{50}[/tex]

= [tex]\frac{12}{125}[/tex]

Answer: A swimming pool that is 5/10 full.