ian's car can go 99 miles on 3 gallons of gas During a drive last​ weekend,Ian used 7 gallons of gas.How far did he drive?Use pencil and paper. Explain how the problem changes if you were given the distance Ian drove last weekend instead of how much gas He used. He drove____ miles.

Answer:

\(W = 9x + 15\)     \(X = 6x + 15\)

Step-by-step explanation:

Given

Shape: Parallelogram

\(U = 9x + 15\)

\(V = 6x + 15\)

Required

Determine W and X

Opposite sides of a parallelogram are equal.

So:

\(U =W\) and \(V = X\)

By substituting values of V and U in the above expressions, we have:

\(9x + 15 = W\)

\(W = 9x + 15\)

\(6x + 15 = X\)

\(X = 6x + 15\)

To determine whether there is a minimum or maximum value to the quadratic function h(t) = -8t² + 4t - 1 and find the minimum or maximum value of h, one has to follow the steps given below. So, the minimum or maximum value of h = -1/2.

Step 1: Write the quadratic function in standard form.

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

h(t) = -8t² + 4t - 1 ... (1)

Step 2: Calculate the axis of symmetry of the parabola.

The axis of symmetry of the parabola is given by x = -b/2a, where a and b are the coefficients of x² and x, respectively. Therefore, the axis of symmetry of the parabola given by h(t) = -8t² + 4t - 1 is given by: t = -b/2a = -4/(2 * (-8)) = 4/16 = 1/4

Step 3: Calculate the vertex of the parabola.

The vertex of the parabola is given by (h, k), where h and k are the coordinates of the vertex. Therefore, the coordinates of the vertex of the parabola given by h(t) = -8t² + 4t - 1 are given by: (1/4, h(1/4))

Substituting t = 1/4 in Equation (1), we have: h(1/4) = -8(1/4)² + 4(1/4) - 1h(1/4) = -8/16 + 4/4 - 1h(1/4) = -1/2 + 1 - 1h(1/4) = -1/2

Therefore, the vertex of the parabola given by h(t) = -8t² + 4t - 1 is given by the point(1/4, -1/2)

Step 4: Determine the nature of the extrema of the functionThe coefficient of the x² term in Equation (1) is -8, which is negative. Therefore, the parabola is downward-facing and the vertex represents a maximum value. Thus, the maximum value of the function h(t) = -8t² + 4t - 1 is given by h(1/4) = -1/2. Answer: Thus, the minimum or maximum value of h = -1/2.

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Using Normal Distribution, If P(-b< z < b) = 0.4972, the value of B has a value of 0.25.

The continuous normal distribution with symmetrical values is the definition of the word "normal distribution." And the numbers are rather close to the mean numbers. A probability distribution that is symmetric around the mean is the normal distribution, sometimes referred to as the Gaussian distribution.

The provided expression, P(-b z b) = 0.4972, may be solved using the normal distribution formula, according to the question.

Consequently, the phrase may be worded as follows:

Z = (b - (-b))/1 = 0.4972

⇒ b = 0.4972/2 = 0.2486 ≅ 0.25

As a result, "b" has a value of 0.25.

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Answer:

B

Step-by-step explanation:

the sum of the 3 angles in a triangle is 180° , so

∠ c + 56° + 38° = 180°

∠ c + 94° = 180° ( subtract 94° from both sides )

∠ c = 86°

Answer: 9 seconds

hope it was helpful (^ = ^)

Step-by-step explanation:

x=number of seconds

100m/6s=150/x

Cross multiply and make x the subject

100m(x)=150m(6s)

x=(150m x 6s)/100m = 9s

therefore it would take the cheetah 9 seconds to run the 150m

Answer: 5

Step-by-step explanation:  You read the graph when x = 2.  Because of the open circle on the graph on point (2,1), that is not an option.  Therefore, the only other option is (2, 5), in which 5 is your answer

The length of side AB is about 5.87 units.

The triangle ABC is a right angle triangle. A right angle triangle is a triangle that has one of its angles as 90 degrees.

Therefore, let's find the length AB in the right triangle.

Using trigonometric ratios,

cos 33 = adjacent / hypotenuse

Therefore,

Adjacent side = AB

hypotenuse side = 7 units

cos 33° = AB / 7

cross multiply

AB = 7 cos 33

AB = 7 × 0.83867056794

AB = 5.87069397562

AB = 5.87 units

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A sequence of instructions that solves a problem is called an algorithm.

The following prices fills the gas cost from top to bottom: Option D

0, $12.40, $24.79, $37.19, $49.58

The practical range of the function is 0 ≤ f(g) ≤ 49.58

Given data

The complete question is attached

f (g) = 2.479 g

f (0), f (5), f (10), f (15), f (20)

The cost of fill up gas, f(g) = 2.479g  

first

f ( 0 ) = $0

second

f ( 5 ) = 2.479 × 5 = $12.40

third

f ( 10 ) = 2.479 × 10 = $24.79

fourth

f ( 15 ) = 2.479 × 15 = $37.19

fifth

f ( 20 ) = 2.479 × 20 = $49.58

The practical range is found by getting an expression that encompass the values gotten. The expression for the range is given as:

0 ≤ f(g) ≤ 49.58

Option D is the correct answer

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Answer:

Undefined

Step-by-step explanation:

The slope of a horizontal line is zero.  The slope of a vertical line is undefined.

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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From the present question, we have the following inequality to solve:

To maintain the inequality unchanged, to every change we make on one of the sides, we MUST make the same on the other. Now, we can verify the simplest way to write the left side of this inequality, as follows:

And for the right side, we can make it become the simplest expression as follows:

From this, we can rewrite the inequality as:

Now, we can subtract both sides with (5y+8), as follows:

From this, we conclude that y can assume any value lower than -2/5. And in interval notation, we write:

Here, we need to find the monthly and the weekly growth rate

The monthly growth rate is 99.33 ounces and the weekly growth rate is 22.9 ounces

Weight at birth = 8 ounces

Weight at one year =75 ounces

1 pound = 16 ounces

75 pounds = 1200 ounces

Additional weight after birth = Weight at one year - Weight at birth

= 1200 ounces - 8 ounces

= 1,192 ounces

There are 12 months in a year

Growth rate per month = Additional weight after birth / 12

= 1,192 / 12

= 99.33 ounces per month

There are 52 weeks in a year

Growth rate per week = Additional weight after birth / 52

= 1,192 / 52

= 22.9 ounces per week

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The meaning of the slope is retained in the case of; "as the time spent swimming increases, the number of calories burnt increases".

The slope of a graph describes how steep the graph is. It can be used to show the relationship between variables.

If we interchange the positions of the dependent and the independent variables, the meaning of the slope is retained in the case of; "as the time spent swimming increases, the number of calories burnt increases".

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Answer: The angles of ΔA'B'C are congruent to the corresponding parts of the original triangle.

Step-by-step explanation:

Given : Triangle ABC was rotated 90 degrees clockwise. Then it underwent a dilation centered at the origin with a scale factor of 4.

A rotation is a rigid transformation that creates congruent images but dilation is not a rigid transformation, it creates similar images but not congruent.

Also, the corresponding angles of similar triangles are congruent.

Therefore, The angles of ΔA'B'C are congruent to the corresponding parts of the original triangle.

The tangent line at that point is:

y = (-3/25)*x + 6/5

so m = -3/25, and b = 6/5

To find the slope at that point, we need to evaluate the derivative at that point.

y = 3/x

The derivative is:

y' = -3/x²

When x = 5, we have:

y' = -3/5² = -3/25

So that is the slope, m.

Now let's find the line.

The line must pass trhough the point (5, 3/5), then:

3/5 = (-3/25)*5 + b

3/5 = -3/5 + b

3/5 + 3/5 = b

6/5 = b

The equation of the line is:

y = (-3/25)*x + 6/5

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Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

6

Step-by-Step Explanation:

if you were to move the bottom triangle to the top, it would make the parallelogram a perfect rectangle.

the area is 60 units^2.

area=length*width

and the one side is 10. 60/10 =6 so 6 units is the answer

Answer: Yes, It's a Function

Step-by-step explanation: The lines dont cross the X-Axis more than once

Answer:

The equation perpendicular to  y = 3x - 2 and passing through  (-9, 0) in the slope-intercept form will be:

Step-by-step explanation:

The slope-intercept form of the line equation

\(y = mx+b\)

where

Given the line

y = 3x - 2

comparing with the slope-intercept form of the line equation

The slope of the line y = 3x - 2 is: m = 3

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:  

slope = m = 3

Thus, the slope of the the new perpendicular line = – 1/m = -1/3 = -1/3

The point-slope form of the line equation is:

\(y-y_1=m\left(x-x_1\right)\)

where

In our case:

now substituting the perpendicular slope m = -1/3 and (-9, 0) in the point-slope form of the line equation

\(y-y_1=m\left(x-x_1\right)\)

\(y-0=-\frac{1}{3}\left(x-\left(-9\right)\right)\)

\(y=-\frac{1}{3}\left(x-\left(-9\right)\right)\)

\(y=-\frac{1}{3}\left(x+9\right)\)

\(\:\:y\:=-\frac{1}{3}x-3\)

Therefore, the equation perpendicular to  y = 3x - 2 and passing through  (-9, 0) in the slope-intercept form will be:

The percent decrease in total principal and interest paid between a 30-year term mortgage and a 15-year mortgage with a principal balance of $484,500.00 and a 6.5% APR is 31.0%. (Option A)

To calculate the  percent decrease, we can use the following formula.

Percent decrease = ( (30-year factor -   15-year factor) / 30-year factor) x 100

Substituting the values from the chart.  

= (($ 6.65 - $8.71) / $6.65) x 100

= ( -$ 2.06 / $6.65) * 100

= -0.309 *  100

Percent decrease ≈ - 30.9 %

Since the question asks for the percent decrease as a positive value, we take the absolute value of the result which is

Percent decrease ≈ 31%

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If Colah Company purchased $2,000,000 of Jackson, Inc., 6% bonds at par on July 1, 2021. The journal entries for the purchase of the Jackson bonds on July 1 is: Debit Available-for-sale securities $2,000,000

Credit Cash $2,000,000.

Journal entry is used by companies to record their day to day business transaction.

July 1 2021

Debit Available-for-sale securities $2,000,000

Credit Cash $2,000,000

December 31 2021

Debit Cash $60,000

Credit Interest income  $60,000

(6% ×$2,000,000 / 2)

December 31 2021

Debit Available-for-sale securities $300,000

Unrealized Gain - Other comprehensive income $300,000

($2,000,000 - $2,300,000)

June 30 2022

Debit Cash $60,000

Credit Interest income  $60,000

(6% ×$2,000,000 / 2)

The entry necessary upon sale of the Jackson bonds on July 1, 2022 is:

July 1 2022

Debit Available-for-sale securities  $2,300,000

Unrealized Gain-Other comprehensive income account $300,000

Credit Cash $1,800,000

Credit Realized Loss on the sale of Available-for-sale securities $200,000  

[$1,800,000 - $2,000,000= $200,000 (Realized Loss)]

2. Table to show the effect of the Jackson bonds on Colah’s net income,

                             2021                   2022                       Total

Net Income       $60 ,000        ($140,000)              ($80,000)

( 60,000 - $200,000= -$140,000)

OCI                       $300,000                                         $300,000

Comprehensive Income $360,000 ($140,000) $220,000

Therefore the  journal entries for the purchase of the Jackson bonds on July 1 is: Debit Available-for-sale securities $2,000,000

Credit Cash $2,000,000.

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1.) Probability of getting 1: 0.12 or 12%.

2.) Probability of getting 2: 0.16 or 16%.

3.) Probability of getting 3: 0.25 or 25%.

4.) Probability of getting 4: 0.18 or 18%.

5.) Probability of getting 5: 0.15 or 15%.

6.) Probability of getting 6: 0.14 or 14%.

To calculate the probability of getting a specific number on a fair die, we divide the number of times that number appears by the total number of rolls. In this case, the die was rolled 100 times, and the results are given as follows:

Number: 1 2 3 4 5 6

Times: 12 16 25 18 15 14

To find the probability of getting each number, we divide the corresponding number of times by the total number of rolls (100):

Probability of getting 1 = 12 / 100 = 0.12.

Probability of getting 2 = 16 / 100 = 0.16.

Probability of getting 3 = 25 / 100 = 0.25.

Probability of getting 4 = 18 / 100 = 0.18.

Probability of getting 5 = 15 / 100 = 0.15.

Probability of getting 6 = 14 / 100 = 0.14.

Therefore, the probabilities of getting each number on a fair die, based on the given results of 100 rolls, are approximately:

1: 0.12 or 12%,

2: 0.16 or 16%,

3: 0.25 or 25%,

4: 0.18 or 18%,

5: 0.15 or 15%,

6: 0.14 or 14%.

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Answer:

Wait lemme think

Step-by-step explanation:

7.7 divided by 1.4 = 5.5. So the flagpole is 5.5 times taller than meter stick

Thus flagpole is 5.5 m tall.

Answer:

Step-by-step explanation:

We need to find the difference in progress:

The first student is 1/12 ahead