What is the value of this expression

Answer:

4.5

Step-by-step explanation:

Answer:

f(x) = 1/7 * (x + 7)^2 - 2

axis of symmetry: x = -7

vertex: (-7 | -2)

Step-by-step explanation:

f(x) = 1/7 * (x^2 + 14x + 35)

f(x) = 1/7 * (x^2 + 14x) + 5

f(x) = 1/7 * (x^2 + 14x + 7^2 - 7^2) + 5

f(x) = 1/7 * (x^2 + 14x + 7^2 - 49) + 5

f(x) = 1/7 * (x^2 + 14x + 7^2) + 5 - 7

f(x) = 1/7 * (x + 7)^2 + 5 - 7

f(x) = 1/7 * (x + 7)^2 - 2

The dimensions of the rectangle will be equal to 10 by 4.

A rectangle may be defined as the closed figure having four sides with the interior angles equal to 90°. it has two dimensions the length and the width. The area of a rectangle may be defined as the product of its length and width. According to the question the area of the rectangle is given as 40 square units. Let us assume the length as 'l' units and width as 'b' units. It is given that length is 6 units greater than the width that is l = (b + 6).

Now, the area of the rectangle = l×b

40 = (b + 6)×b

40 = b² + 6b

=> b² + 6b - 40 = 0

=> b = [-6 ± √(36 + 160)]/2

=> b = (-6 ± 14)/2

=>b = 4 units, since width cannot be negative.

Now, length = b + 6 = 10 units.

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Scaled copy of the polygon with scale factor 3 is given below.

A polygon is a closed polygonal chain made up of a finite number of straight line segments and is a type of planar figure in geometry. A polygon is a region that is bounded by a bounding circuit, a bounding plane, or both.

A polygonal circuit's segments are referred to as its edges or sides. A polygon is a geometric object with two dimensions and a finite number of sides. A polygon's sides are made up of segments of straight lines that are joined end to end.

Polygons include shapes like triangles, quadrilaterals, pentagons, and hexagons. The shape's number of sides is indicated by the name. A quadrilateral has four sides, whereas a triangle has three.

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Answer:

y=2X - 6

Step-by-step explanation:

find the slope using the 2 points

m = 8-2/7-3 = 2

substitute 4,2 in the equation y=mx+b and solve for b.

2 = 2x4+b

b=-6

y = 2x - 6

Answer:

Slope intercept formula: y = 2x -6

Point Slope formula y = 2x-6

Step-by-step explanation:

1) Find the slope

2) Choose a point and plug it into the equation y = mx+b

3) Solve for b

4) Plug-in new slope (m) and new y-intercept (b) into equation y = mx+b

Solving:

4 = x1

2 = y1

7 = x2

8 = y2

to find slope with slope formula:

m = y2-y1/x2-x1 = 8-2/7-4 = 6/3 = 2

now plug in,

y = 2x+b

to find b, take any one of the pair

(i will choose (4,2) )

2 = 2(4) + b

now solve for b,

2 = 8+b

b = -6

Slope intercept formula: y = 2x -6

for point slope: y-y1 = m(x-x1)

as we know our slope is 2 and points are (0,-6) where 0 is x1 and -6 is y1

now we plug in,

y-(-6) = 2(x-0)

y+6 = 2x

Point Slope formula y = 2x-6

Hope this helps! Please like!!

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The correct option; Angle BAD is congruent to angle BCA, is requited to show ΔDBA ≅ ΔCBA by side-angle-side congruence theorem.

If all 3 corresponding sides are equal as well as all 3 corresponding angles seem to be equal in measure, two triangles are said to be congruent.

side-angle-side congruence theorem: By SAS rule, two triangles are said to be congruent if any two sides and the angle would include between the sides with one triangle are equivalent to a corresponding two sides and also the angle would include here between sides of the second triangle.

For the given triangles;

ΔDBA and ΔCBA

Side AC = Side AD

Side AB = Side AB  (common)

Thus, to make both triangles congruent the angles falling in between these two triangles must be equal.

Thus,  Angle BAD is congruent to angle BCA,

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The cheaper plan here would be plan A. The equation that is written in terms of the plans on movies is  0 < x < 5

For the plan A, we would have the function to be given as

A = 1x + 18

This is due to thge fact that this plan is said to cost  $18 per month plus $1 per movie watched.

For plan B the function would have to be:

B = 3x + 8

The equation that we would have here would be

1x + 18 <  3x + 8

= x - 3x < 8 - 18

= -2x < -10

x < 5

Hence we would have the equation as 0 < x < 5

Cheaper plan

1x6 + 18  = 24

3x 6+ 8 = 18 + 8 = 26

Plan A id cheaper

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The equation of the line perpendicular to the given line will be equal to 5y = x - 3.

A line may be defined as a straight figure which is drawn and has no end points. The equation of line in slope intercept form may be written as y = mx + c where m is the slope and c is the y intercept. The equation of line passing through a point (x₁, y₂) will be given as (y - y₁) = m(x - x₁). The slope of line perpendicular to a line having slope m is given by -1/m. The equation of line in the question is y = -5x + 1. The slope of the line is -5. The slope of line perpendicular to this line is 1/5. Equation of line passing through (2, -1) and slope 1/5 is given by

(y + 1) = 1/5(x - 2)

5y + 1 = x -2

5y = x - 3 which is the required equation.

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Answer:

the answer is A...

Step-by-step explanation:

Calculate Area (A):

The area formula for a square is denoted below:

A = s2

Taking the square root of both sides, we get:

s = √A

s = √3

s = 1.7320508075689

Answer:

Slope = 1/2 or 0.5

Step-by-step explanation:

Picking two integer points on the line, (any)

(-3, 2) and (-1, 3)

We can find the slope

(3-2)/(-1-(-3)

=1/2

:]

Answer: have you tried m a t h w a y

Step-by-step explanation:

Using fraction, He consumes 1/4 pound of lunch meat each day.

A fraction, expresses a piece of a whole, a fraction, such as one-half, eight-fifths, or three-quarters, specifies the number of components of a respective size.

Given,

He consumes 2 pounds of beef in 8 days.

We need to determine how much meat he consumes each day.

To ascertain:

He consumes 2/4 of a pound of beef in a day.

= 1/4

He thus consumes 1/4 pound or less of lunch meat every day.

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Answer:

$187.5

Step-by-step explanation:

.

Answer:

187.50

Step-by-step explanation:

7.5(25)=187.50

hope this helped

have a good day^^

Answer:

Step-by-step explanation:

Student A:

Mean 80.8

Median: 85.5

The Median is a higher score.

Student B:

Mean 82.7

Median: 79.5

Mean is a higher score

Answer:

Student A's median and Student B's mean would result in the highest grade.

Step-by-step explanation:

How to find the mean:

The mean is the average.

Therefore, you must add all numbers listed, then divide the added numbers by the amount of numbers you added together. Lastly, as instructed round to the nearest whole number.

- Student A : Mean = 81

Step 1 : 25+78+80+82+85+86+88+89+96+99 = 808

Step 2: 808 ÷ 10 = 80.8

Step 3: 80.8 ---> 81

- Student B: Mean = 83

Step 1: 71+77+77+79+79+80+88+89+91+96 = 827

Step 2: 827 ÷ 10 = 82.7

Step 3: 82.7 ---> 83

How to find the median:

The median is the middle number in a sorted list of numbers.

Therefore, you list all of the numbers from least to greatest. Then, you get rid of a number from each side until you finally get to the center number. If there are two numbers left in the center you then find the mean(average) of those numbers.

- Student A: Median = 86

Step 1: Knock off a number from each side until you reach the center number(s)

25, 78, 80, 82, 85, 86, 88, 89, 96, 99 ---> 85, 86

Step 2: Find the mean(average) of the two central numbers

85 + 86 = 171 ---> 171 ÷ 2 = 85.5

Step 3: Round your answer

85.5 ---> 86

- Student B: Median = 80

Step1: Knock off a number from each side until you reach the center number(s)

71, 77, 77, 79, 79, 80, 88, 89, 91, 96 ---> 79, 80

Step 2: Find the mean(average) of the two central numbers

79 + 80 ---> 159 ÷ 2 = 79.5

Step 3: Round your answer

79.5 ---> 80

Tomato sauce will the new can hold is 743[tex]cm^{3[/tex]

let take  us  take,

V = Sh

[tex]S_{1} =S_{2}[/tex]        

[tex]h_{1[/tex] = 12 cm

[tex]h_{2}[/tex]  = 60 cm

[tex]\frac{V_{1} }{V_{2} } = \frac{h_{1} }{h_{2} }[/tex]

[tex]\frac{1487}{v_2} } = \frac{12}{60}[/tex]

= 743[tex]cm^{3[/tex]

Height means the vertical distance, either between the top and bottom of something or between the bottom and the thing above it. height refers to being tall or short as measured vertically.

Height is a way of measuring someone or something from the bottom to the top or from the head to the feet. In other words, height indicates how tall someone or something is. We can compare how tall we will be when we grow up. We often compare the average height of men and women in different countries.

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Answer:

Angle LMN = 180 - 142

= 38° (sum of angles on a straight line=180)

x = 180 - 90 - 38

= 52° (sum of angles in triangle=180)

Answer:

k=3/10

Step-by-step explanation:

8y=12x+6 >>>>(÷8) both sides

y= (3/2)x+(3/4)

if x=0, y=3/4

4y=k(3x+10) >>> plug in (0, 3/4)

4(3/4)= k(0+10)

3= 10k >>> (÷10) both sides

k=3/10

The difference between the areas of the posters is 56 in².

There are different quadrilaterals, for example: square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example,  in a square, all angles are 90° and all sides present the same value.

The area of a square is given by: A= a², where  a=the length of the side.

         A=(13 in)²

         A= 169 in²

         A=(15 in)²

         A= 225 in²

Therefore, the difference in square inches between the area of Latrice's poster and the area of Nura's poster is 225 - 169=56 in²

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The number of milligrams of medication medication left after 6 hours is; 50 milligrams.

The number of milligrams of medication medication left after 7 hours is; 35.36 milligrams.

The number of milligrams of medication medication left after 8 hours is; 25 milligrams.

It follows from the task content that the amount of medications left in the patient's body be determined in each case.

Recall the formula for the amount of substance remaining for half life situations is as follows;

A = N (1/2)^(t/half-life)

Since half life = 2 hours and N = 400 milligrams;

Hence;

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Answer:

15

Step-by-step explanation:

Supposing:

Coloured marbles = x

Glass marbles = y

According to Question

x = 3y

As,

x + y = 60

3y + y = 60 (putting value of x = 3y)

4y = 60

y = 60/4

y = 15

Hence, Leo has 15 Clear-glass marbles

Answer:

see explanation

Step-by-step explanation:

each term inside the parenthesis is raised to the exponent outsie, that is

(2xy)³

= 2³ × x³ × y³ ← 2³ = 2 × 2 × 2 = 4 × 2 = 8

= 8x³y³

The probability that the shorts of the basketball team will be of a different color than the jersey is 2/3.

Probability can be found using the following formula;

probability = number of favorable outcomes or events ÷ total number of outcomes or events

In order to calculate the probability that the shorts will be of a different color than the jersey, we first determine the total number of combinations that are possible;

1- Black-Black

2- Black-White

3- Black-Gold

4- Gold-Black

5- Gold-White

6- Gold-Gold

Hence there are a total of 6 possible combinations of shorts and jerseys out of which 2 are the same and 4 are different.

Therefore the probability that the shorts will be of a different color can be calculated as follows;

probability = number of favorable outcomes or events ÷ total number of outcomes or events

probability = 4 ÷ 6

probability = 2/3

Hence, 2/3 is the probability that the shorts will be of a different color than the jersey.

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The answer is

x = 7, -7, √2, -√2

Add the two equations to get

x2 + y2 = 74

Eliminate y from the first by solving for y and using that result:

(x2 − 14) = x√74 - x2

square both sides, then condense:

x4 − 51x2 + 98 = 0

These ready factors:

(x−7)(x+7)(x−√2)(x+√2)=0

I'll let you handle it from there, but keep in mind that if we square all sides, we might find roots that need to be pulled out afterward.

Therefore,

x = 7, -7, √2, -√2

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The exponential function y = 60(1.2)7 yields the number of patents in 1998.

The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis. Let y be the number of nanotechnology-related patents issued in the US in year x following 1991.

There were 60 patents on nanotechnology in 1991, and since then there has been a factor of 1.2 increase.

y = 60(1.2)ˣ

y = 60 in 1998 (7 years ago) (1.2)⁷

The exponential function is used to calculate the number of patents in 1998.

y=60(1.2)⁷

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To paint the circular table top Beth need to buy 2 cans of paint .

In the question ,

it is given that ,

the radius of the circular table top is = 3 feet

So , the area of the circular table top is = π*r² = π*(3)²

= 9π

= 28.26

also given that

area covered by 1 small can of paint = 15 sq. feet

So , the number of cans needed to paint the table top is = (area of table top)/(area covered by 1 small can of paint)

On substituting the values , we get

number of cans needed to paint the table top is = 28.26/15

= 1.884

≈ 2

Therefore , To paint the circular table top Beth need to buy 2 cans of paint  .

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Answer:

(2x + 5)/(x + 4) = 1

and

6x - 19 = 3x - 10

Step-by-step explanation

Linear euqations are the equation for the straight line. When graphed both equations will be straight lines.

Hope this helps you!

Kelly gets 38.59 miles per gallon of gasoline

Miles drove by Kelly = 238 miles

Gasoline used by the car = 6 1/6 gallons

Gasoline used in the car in improper fraction = 37/6 gallons

Average fuel economy: Average fuel economy of a car gives the distance covered by the car in one gallon of gasoline. This is an important factor to consider while buying or using a car as it is a major source of expenditure for the car.

To calculate miles per gallon we use the following formula:

Miles per gallon = Miles driven/ Gasoline used in the car

= 238/(37/6)

= 238*6/37

= 38.59

Miles per gallon = 38.59

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Answer:

Hope the picture will help you

Answer:

2.718

Step-by-step explanation:

let x = .027^2/3

x=.027^.67

applying natural log on both sides

lnx = ln.027^.67

lnx = .67ln.027

lnx = 2.42004

applying antilog on both sides

x = e^2.42004

x = 2.718

thus, .027^2/3 = 2.718

The height of the cone to the nearest tenth of a centimeter is 17.40 cm.

From the given information provided in the question, we can solve this problem by following a few steps.

The surface area of a right pyramid is 258 cm² according to the question.

The surface area of the cone is equal to the surface area of the right pyramid. Therefore the surface area of the cone is also 258 cm².

The surface area of a cone is denoted as ( πrh + πr² ).

Where h is denoted as the height and, r is denoted as the radius of the cone which is 4 cm.

Hence the surface area of the cone is,

SA = (π× 4× h+ π× 4² ) cm²

Now, we can generate an equation, as both represent the value of the surface area of the cone.

(π× 4× h+ π× 4² ) = 258

Or, (12.56h + 39.44) = 258             [ The value of π is 3.14 ]

Or, 12.56h = 258 - 39.44                [ subtracting 39.44 from both sides ]

Or, 12.56h = 218.56

Or, h = 218.56/12.56                       [ dividing both sides by 12.56]

Or, h = 17.40

Now, we can conclude that the height of the cone is 17.40 cm.

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The speed for maximum car mileage will be 48 mph. The maximum gas mileage will be 29.5 mpg.

We are provided with an equation for mileage of car as

m(x) =  -0.028x² + 2.688x  -35.012

here , variable 'x' is the speed of the car.

Now

for the maximum speed of the car we have to first take the derivative of m(x) and then for the boundary value condition by  putting the derivative equal to zero.

comparing to the equation  ax² + bx + c , if the value of

'a' is positive, then we have minimum value at 1st derivative = 0

'a' is negative we have maximum value .

in this case a = -0.028 ( -ve) so we will have a maxima at 1st derivative.

so, dm/dx = -0.056x + 2.688

putting the 1st derivative = 0 , we have

x = 48

therefore , car gets maximum gas mileage at speed of 48 mph.

Also , putting this value in equation (1) we will get max. mileage.

so max. mileage = -0.028 (48)² + 2.688 x 48 - 35.012

                           = -64.512 + 129.024 - 35.012

                           = 29.5

so the maximum gas mileage will be 29.5 mpg .

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