What is the unit rate of the number of miles driven per number of hours of driving?


25 miles per hour
30 miles per hour
35 miles per hour
40 miles per hour

Answer:

see below

Step-by-step explanation:

  y = x^2 - 6x + 14        'complete the square for 'x'  

       x^2 - 6x + 9    - 9   + 14

 y =  (x-3)^2 + 5           vertex from     vertex = (3,5)

                            since the coefficient of ^2 is positive it is a bowl shaped parabola and the vertex is a MINUMUM

    vertex  

2x-5+5>7+5

2x>12

2x partido de 2 > 12 partido de 2 :

x>6

The solution to the system of equations 2x + y = 30 and 2x + 6y = 72 is (10.8, 8.4)

An equation is an expression showing the relationship between numbers and variables.

Given the equations:

2x + y = 30     (1)

x + 3y = 36; multiplying by 2 gives:

2x + 6y = 72     (2)

To solve by elimination method, subtract equation 2 from 1, hence:

-5y = -42

Dividing by -5:

y = 8.4

Put y = 8.4 in equation 2:

2x + 6(8.4) = 72

2x = 21.6

x = 10.8

The solution is (10.8, 8.4)

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The experimental probability that Jason will roll a 2 is 3/14.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Given that, Jason rolls the die 14 times.

From the given table,

Number of favorable outcomes = 3

Total number of outcomes = 14

So, the probability = 3/14

Therefore, the experimental probability that Jason will roll a 2 is 3/14.

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Answer:

A. 250

B. 67.5

127.5x100/51

100x7.02/10.4

Answer:

The  bird flies  35 degrees north for about 3 to 4 miles

Answer:

Step-by-step explanation:

tan35 = x/2

tan35(2) = .9476 miles, due northeast.

you have two sides and a angle, i used tan to find the opposing side of the turn of the street, which was angled at 35 degrees.

Answer: X ≥ 5 or X ≥ 2

Step-by-step explanation:

Add 3 to both sides for the first equation

x ≥ 5

and subtract 5 from both sides for the second one

x ≥ 2

ANSWER

EXPLANATION

To find the number of square feet the window requires, we have to find the area of the shape.

The shape given is a kite, and the area of a kite is:

where p and q are the diagonal lengths.

From the question given:

Therefore, the area of the kite is:

That is the number of square feet of glass that the window requires.

The coordinates of point J of parallelogram GBJF are (2, 0), and the correct answer is (A) (2, 0).

What is parallelogram?

A parallelogram is a quadrilateral (a 4-sided polygon) with opposite sides parallel to each other.

We know that the diagonals of a parallelogram bisect each other. Since GBJF is a parallelogram, the diagonals must bisect each other.

Let O be the mid point for diagonals GJ and BF

Using the midpoint formula and the information that O is the midpoint of diagonals GJ and BF, we can find the coordinates of point J.

The midpoint formula states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by:

((x1 + x2)/2, (y1 + y2)/2)

Using this formula, we can find the midpoint of GJ and BF:

Midpoint of GJ = ((-4 + xJ)/2, (1 + yJ)/2)

Midpoint of BF = ((-2 + xJ)/2, (3 + 0)/2)

Since O is the midpoint of these two points, we can set the two formulas equal to each other and solve for xJ and yJ:

((-4 + xJ)/2, (1 + yJ)/2) = ((-2 + xJ)/2, 3/2)

Simplifying, we get:

-4 + xJ = -2 + xJ

1 + yJ = 3

Solving for xJ and yJ, we get:

xJ = 2

yJ = 0

Therefore, the coordinates of point J are (2, 0), and the correct answer is (A) (2, 0).

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The coordinates of p which divides the line AB in ratio 3:1 is (3.75, 3.5).

The section formula provides the coordinates of a point that, either internally or externally, divides the line connecting two locations in a ratio.

P ( x , y ) = ( c ⋅ m + a ⋅ n m + n , d ⋅ m + b ⋅ n m + n ) .

Ratio of line = 3:2

m and n represents the ratios 3:2

let the coordinates of p(x, y).

using Section formula

= [ (3(4) + 1(3) / (3+1), 3(3) + 1(5) / 3+ 1]

= (15/ 4, 14/4)

= (3.75, 3.5)

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i dont have time to do it right now but here is the percent error equation!

The number in an expanded form is 700,000 + 182 + 0.009

The number is given as:

seven hundred thousand one hundred eighty-two and nine thousandths

Next, we split the numbers:

seven hundred thousand = 700,000

one hundred eighty-two = 182

and nine thousandths = 0.009

Next, we add the numbers

700,000 + 182 + 0.009

Hence, the number in an expanded form is 700,000 + 182 + 0.009

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Step-by-step explanation:

\(305x + 30 - 80 \\ 305x - 50 \\ 305x = 50 \\ x = \frac{305}{50} \\ x = \frac{61}{10} \)

Given dimensions of the room:

Length: \(\displaystyle\sf 12.5 \,m\)

Width: \(\displaystyle\sf 9 \,m\)

Height: \(\displaystyle\sf 7 \,m\)

Area of each wall:

\(\displaystyle\sf Area_1 = 12.5 \times 7 = 87.5 \,m^2\)

\(\displaystyle\sf Area_2 = 12.5 \times 7 = 87.5 \,m^2\)

\(\displaystyle\sf Area_3 = 9 \times 7 = 63 \,m^2\)

\(\displaystyle\sf Area_4 = 9 \times 7 = 63 \,m^2\)

Area of each door:

\(\displaystyle\sf Area_{\text{door}} = 2.5 \times 1.2 = 3 \,m^2\)

Area of each window:

\(\displaystyle\sf Area_{\text{window}} = 1.5 \times 1 = 1.5 \,m^2\)

Total area occupied by doors:

\(\displaystyle\sf Total_{\text{doors}} = 2 \times Area_{\text{door}} = 2 \times 3 = 6 \,m^2\)

Total area occupied by windows:

\(\displaystyle\sf Total_{\text{windows}} = 4 \times Area_{\text{window}} = 4 \times 1.5 = 6 \,m^2\)

Total wall area excluding doors and windows:

\(\displaystyle\sf Total_{\text{wall\,area}} = (Area_1 + Area_2 + Area_3 + Area_4) - Total_{\text{doors}} - Total_{\text{windows}}\)

\(\displaystyle\sf = (87.5 + 87.5 + 63 + 63) - 6 - 6\)

\(\displaystyle\sf = 275 - 6 - 6\)

\(\displaystyle\sf = 263 \,m^2\)

Cost of painting the walls:

\(\displaystyle\sf Cost_{\text{painting}} = Total_{\text{wall\,area}} \times 3.50\)

\(\displaystyle\sf = 263 \times 3.50\)

\(\displaystyle\sf = 920.50 \,Rs\)

Therefore, the cost of painting the walls of the room at Rs. 3.50 per square meter is Rs. 920.50.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The perimeter and area of a rectangle are (5,6) and (6,5).

The perimeter method for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width. when you are given the size of a square form, you may simply plug within the values of L and W into the formula that allows you to clear up for the fringe.

A perimeter is a closed course that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional period. The perimeter of a circle or an ellipse is known as its circumference. Calculating the perimeter has several practical programs.

The perimeter P of a rectangle is given by means of the method, P=2l+2w, in which l is the period and w is the width of the rectangle. The place A of a rectangle is given with the aid of the components, A=lw, wherein l is the length and w is the width.

The perimeter of the rectangle:

P=2l+2w=22

divide 2 into both sides

l+w=11 -------------> (1)

w=11-l

Area of the rectangle:

l*w=30

l(11-l)=30

11l-l^2-30=0

l^2-11l+30=0

By factor method,

(l-5)(l-6)=0

l=5,6.

Substitute this value in w,

l=5 implies w=6

l=6 implies w=5

There we have two solutions.

The length and breadth of the rectangle is

(5,6) and (6,5).

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Answer:

Since f(-1) = 0 and f(-2) = 0, we can set up two equations:

(-1)³ + p(-1)² - q(-1) - 4 = 0

(-2)³ + p(-2)² - q(-2) - 4 = 0

Simplifying each equation, we get:

-1 + p - q - 4 = 0

-8 + 4p - 2q - 4 = 0

Simplifying further, we get:

p - q = 5

2p - q = 6

Solving for p and q, we can add the two equations together to eliminate q:

p - q + 2p - q = 5 + 6

3p - 2q = 11

Then, we can substitute the value of q from the first equation into this equation to solve for p:

3p - 2(q + 5) = 11

3p - 2q - 10 = 11

3p - 2q = 21

3p - 2(5 + p) = 21

p - 10 = 7

p = 17

Substituting this value of p into either equation for q, we get:

q = p - 5 = 12

Therefore, the coefficients are p = 17 and q = 12. To factor the expression, we can use synthetic division or long division. Using synthetic division, we get:

-1 | 1 17 -12 -4

|__ -1 -16 28

1 1 12

This gives us the factorization:

f(x) = (x + 1)(x² + x + 12)

To find the solutions, we can use the quadratic formula on the quadratic factor:

x = (-1 ± sqrt(1 - 4(1)(12))) / 2(1)

x = (-1 ± sqrt(1 - 48)) / 2

x = (-1 ± sqrt(-47)) / 2

x1 = (-1 + i(sqrt(47))) / 2

x2 = (-1 - i(sqrt(47))) / 2

Therefore, the solutions are x1 = (-1 + i(sqrt(47))) / 2, x2 = (-1 - i(sqrt(47))) / 2, and x3 = -1.

Step-by-step explanation:

give me thanks for more! your welcome bud!

The graph of the function f(x) = 5(2)^x is an upward-sloping exponential curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing the x-axis.

The function f(x) = 5(2)^x represents exponential growth. Let's analyze its graph.

As x increases, the value of 2^x grows exponentially. Multiplying it by 5 further amplifies the growth. Here are a few key points to consider:

When x = 0, 2^0 = 1, so f(0) = 5(1) = 5. This is the y-intercept of the graph, meaning the function passes through the point (0, 5).

As x increases, 2^x grows rapidly. For positive values of x, the function will increase quickly. As x approaches positive infinity, 2^x grows without bound, resulting in the function also growing without bound.

For negative values of x, 2^x approaches zero. However, the function is multiplied by 5, so it will not reach zero. Instead, it will approach y = 0, but the graph will never touch or cross the x-axis.

The function is always positive since 2^x is positive for any value of x, and multiplying by 5 does not change the sign.

Based on these observations, we can conclude that the graph of f(x) = 5(2)^x will be an exponential growth curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing or touching the x-axis.

The graph will have a smooth curve that rises steeply as x increases. The rate of growth will be determined by the base, in this case, 2. The larger the base, the steeper the curve. The function will approach but never reach the x-axis as x approaches negative infinity.

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Answer:

To study and get work done and to understand the material

Step-by-step explanation:

Answer:

6x2-10x-4

Step-by-step explanation:

hx=(2x-4)(3x+1)

hx=2x(3x+1)-4(3x+1)

hx=6x2+2x-12x-4

hx=6x2-10x-4

Answer:3.5? i’m not sure sorry

hope that kinndaaaa helps if xxo

Step-by-step explanation:

The representation of (7/2)i in complex number will be 0 + (7/2)i thus option (C) will be correct.

Complex numbers are helpful in finding the square root of negative numbers.

If we solve x² + 1 = 0 ⇒ x = √(-1) which is called as iota(i).

The general form of a complex number is a + ib where the first part a called real and the ib is called imaginary.

The complex number is written as a + ib where a is said to be the real part while bi is the imaginary part.

As per the given (7/2)i here real part is missing thus, put a = 0

0 + (7/2)i will be the correct.

Hence "The representation of (7/2)i in complex number will be 0 + (7/2)i".

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The limit of the given function as x approaches 1 is 0.

To find the limit of the given function as x approaches 1, we need to evaluate the expression by substituting x = 1. Let's break it down step by step:

1. Begin by substituting x = 1 into the numerator:

\(\[12\sin\left(\frac{\pi}{2}\cdot 1\right)\ln(1) = 12\sin\left(\frac{\pi}{2}\right)\ln(1) = 12(1)\cdot 0 = 0\]\)

2. Now, substitute x = 1 into the denominator:

(1³ + 5)(1 - 1) = 6(0) = 0

3. Finally, divide the numerator by the denominator:

0/0

The result is an indeterminate form of 0/0, which means further analysis is required to determine the limit. To evaluate this limit, we can apply L'Hôpital's rule, which states that if we have an indeterminate form 0/0, we can take the derivative of the numerator and denominator and then evaluate the limit again. Applying L'Hôpital's rule:

4. Take the derivative of the numerator:

\(\[\frac{d}{dx}\left(12\sin\left(\frac{\pi}{2}x\right)\ln(x)\right) = 12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{x} + \frac{\sin\left(\frac{\pi}{2}x\right)\ln(x)}{x}\right)\]\)

5. Take the derivative of the denominator:

\(\[\frac{d}{dx}\left((x^3 + 5)(x - 1)\right) = \frac{d}{dx}\left(x^4 - x^3 + 5x - 5\right) = 4x^3 - 3x^2 + 5\]\)

6. Substitute x = 1 into the derivatives:

Numerator: \(\[12\left(\cos\left(\frac{\pi}{2}\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{1} + \sin\left(\frac{\pi}{2}\right) \cdot \frac{\ln(1)}{1}\right) = 0\]\)

Denominator: 4(1)³ - 3(1)² + 5 = 4 - 3 + 5 = 6

7. Now, reevaluate the limit using the derivatives:

lim as x approaches 1 of \(\[\frac{{12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{{-1}}{{x}} + \sin\left(\frac{\pi}{2}x\right) \cdot \frac{{\ln(x)}}{{x}}\right)}}{{4x^3 - 3x^2 + 5}}\]\)

= 0 / 6

= 0

Therefore, the limit of the given function as x approaches 1 is 0.

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Answer:

The answer is "np(1+p)".

Step-by-step explanation:

\(N_1\) = Number of n tossed heads  

According to \(N_1\), Y = amount of \(N_1\) tossing heads

So, \(N_1\)~ Bin(n, p) and \(N_2\) | \(N_1\) ~ Bin(\(N_1\), p)

\(E(N_1+N_2) & = E\Big[N_1+N_2\vert N_1\Big]\\ &\)

                   \(= E(N_1)+E\Big[N_2\vert N_1\Big]\\\\ & = E(N_1) + E(N_1\,p)\\\\ & = np + np.p \\\\ =np+np^2\\\\ =np(1+p)\)

Answer:

12 packets

Step-by-step explanation:

96 ÷ 8 = 12 packets

Answer: it’s 12

Step-by-step explanation:

The expressiοn (x+1)(x+2) has the greatest vaIue οf 30 when x=4.

An aIgebraic expressiοn is a mathematicaI phrase that cοntains variabIes, cοnstants, and mathematicaI οperatiοns. It may aIsο incIude expοnents and/οr rοοts. AIgebraic expressiοns are used tο represent quantities and reIatiοnships between quantities in mathematicaI situatiοns, οften in the cοntext οf prοbIem-sοIving.

Tο evaIuate the expressiοn (x+1)(x+2) when x=4, we simpIy substitute 4 intο the expressiοn, which gives us (4+1)(4+2).

SοIving this expressiοn, we first perfοrm the additiοns inside the parentheses tο get (5)(6).

Then, we muItipIy the twο numbers tο get 30.

when x=4, the expressiοn (x+1)(x+2) evaIuates tο 30, which is its greatest vaIue. This is because the quadratic expressiοn x² + 3x + 2 increases as x increases, and it reaches its maximum vaIue when x=4.

Therefοre, the expressiοn (x+1)(x+2) has the greatest vaIue οf 30 when x=4.

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Answer:

exponent

Step-by-step explanation:

To get log2(4)=2

so 2 to the power of 2 is 4

4 is the number between brackets in log

another example

log2(8)=3

2 to the power of 3 is 8