The equation 2x(x + 8) = 110 represents the area of a rectangle.
Solve the equation. What are the approximate dimensions of the rectangle? Express your answers as decimals rounded to the nearest tenth.

6 integers that satisfy the given condition are 10,11,12,13,14,15.

Inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size

we have the number X

Of which the square root is greater than 3 and less than 4

so,

[tex]3 < \sqrt{X} < 4[/tex]

on squaring both sides

[tex]3^2 < (\sqrt{X})^{2} < 4^2[/tex]

[tex]9 < X < 16[/tex]

so the integer that satisfies the condition is 10,11,12,13,14,15.

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Answer:

6

Step-by-step explanation:

Because 4 > √x > 3, we know that 16 > x > 9. Thus, the integers from 10 to 15 inclusive satisfy this inequality, which means 6 integers satisfy the condition in the problem.

Answer:

x=y/3 + 2/3

Step-by-step explanation:

Is this what you wanted?

Answer:

x < 10 - 2y

Step-by-step explanation:

a. The system of inequalities that best represent how much of the agricultural products of soybeans and corn the river barge can carry is

b. option A

c. The river barge can safely ship the agricultural products

information gotten from the question include

Corn weighs about 60 pounds per bushel

soybeans weigh about 90 pounds per bushel

A river barge can safely carry up to 4,500,000 pounds of cargo.

Let x = bushels of corn and y = bushels of soybeans.

a. From the statement, it can be deduced that the equation is

A. 60x + 90y ≤ 4,500,000, x ≥ 0, y ≥ 0

b. some interpretation on inequality

from the interpretation

the correct option is A (graph attached)

c. 60 * 24000 + 90 * 24000

= 3,600,000

The value is ≤ 4,500,000 hence the river barge can carry it

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Answer:

Step-by-step explanation:

Slope-intercept form is y=mx+b where m is your slope and b is your y-intercept.

To find your equation with what you are given, you have to plug in your values.

(-5, 6) = (x, y) so plug -5 in where there is x and 6 in where there is y

then your slope, m, is 2 so plug 2 in where there is m.

so it should look like

6=2(-5)+b, now you are solving for b.

  6    = -10+b

+10      +10

___________

16     =  b           Then take the values and plug back into the slope intercept formula, y=mx+b.

Plug 16 in for b and 2 in for m (m represents slope and they told us the slope =2)

*you no longer need the y and x values because you only use those to solve for m or b, in this case b, so leave y and x in your equations*

y=2x+16

The POINT of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.

Hence, The POINT of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.

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Answer:

$210 in bank

Step-by-step explanation:

Kelly earned 300 dollars and put 70% of it into the bank. How much did she put into the bank?​

70% = 0.7

300 * 0.7 = $210 in bank

Answer: when the value on each side of the equal sign is the same

Step-by-step explanation: for example, 9=9 is a true equation. 5+4 = 9 is a true equation

The vertices of a parallelogram are given, according to which the area of the parallelogram will be equal to 58 units.

The perimeter of a shape is its boundary's length, regarded as a whole. A form's circumference can be calculated by adding the lengths of all of its sides and edges. Utilizing linear length units like centimeters, millimeters, yards, and feet, it is determined.

The total of all a parallelogram's sides is its perimeter.

Firstly, solve for vertices AB:

AB = √(17- 1)² + (1 - 1)² = 16

Then,

BC = √(22 - 17)² + (13 - 1)² = 13

Then,

CD = √(6 - 22)² + (13 - 13)² = 16

Lastly,

AD = √(6 - 1)² + (13 - 1)² = 13

Add all the values,

P = 16 + 13 + 16 + 13

P = 58 units.

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fi r e re r er e r er e re r e r er e re

The time taken by peregrine falcon dove at its maximum speed to cover half a mile is 9 sec.

For the given question;

The maximum speed of peregrine falcon dove is 200 mph.

Time of travel  = 0.5 miles.

The relation of distance and speed is;

speed = distance/time

200 mph = 0.5 miles / time

Time = 0.5 miles / 200 mph

Time = 0.5 × 60 × 60  miles / 200 m/ sec

Time = 9 sec

Thus, time taken by peregrine falcon dove at its maximum speed to cover half a mile is 9 sec.

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If the amount after 4 years is 844.13. Then the rate of the compound interest will be 3%.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Hannah contributes £750 and following 4 years has £844.13. Then the compound interest rate is given as,

844.13 = 750 (1 + r)⁴

(1 + r)⁴ = 1.1255

1 + r = 1.02999

r = 0.0299

r = 2.99%

r ≈ 3%

If the amount after 4 years is 844.13. Then the rate of the compound interest will be 3%.

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Answer:

Length = 4x - 5

Step-by-step explanation:

A = length x width

When a bowling ball is propelled with a force of 22. 0 N and accelerates at a rate of 5. 5 [tex]ms^{-2}[/tex], its mass is 4. 0 kg.

Newton's Second Law of Motion states that force is the result of mass times acceleration.

[tex]F=m*a[/tex]

[tex]m = F / a[/tex]

A force of 22.0 Newtons (  [tex]kgms^{-2}[/tex] ) and an acceleration of 5.5 meters per second squared were used to drive the bowling ball.

F = 22.0 [tex]kgms^{-2}[/tex] and

a = 5.5 [tex]ms^{-2}[/tex]

Put the values in the formula as replacements.

M = 22 [tex]kgms^{-2}[/tex]/ 5.5 [tex]ms^{-2}[/tex]

Meters per second squared (m/s2) units cancel each other out.

M = 22 kg / 5.5

   = 4 kg

The bowling ball weighs 4 kilogram.

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The length of side GF from the similar triangles shown is GF = √10 units

A mathematical phrase known as an equation demonstrates the connection between two or more variables and numbers.

If a pair of triangles share the same shape, all of their angles are equal, and their ratio of comparable sides is proportionate, then they are said to be similar.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." Standard form, slope-intercept form, and point-slope form are the three primary types of linear equations.

In a similar triangle, DE = GF, Hence:

GF/DF = GH/DE

GF / 5 = 2 / GF

GF² = 10

GF = √10

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The equation of the line that passes through the points (-2,-6) and (1,2) is y = 8x/3-2/3.

According to the question,

We have the following information:

Points through which line is passing =  (-2,-6) and (1,2)

Now, we have the following values:

x1 = -2, y1 = -6

x2 = 1 and y2 = 2

We know that the following formula is used to find the slope of the line:

m = (y2-y1)/(x2-x1)

m = (2+6)/(1+2)

m = 8/3

Now, the following formula is used to find the equation of the line:

y-y1 = m(x-x1)

y+6 = 8/3(x+2)

y+6 = 8x/3+16/3

Subtracting 6 from both sides:

y = 8x/3+16/3-6

y = 8x/3-2/3

Hence, the equation of the line that passes through the points (-2,-6) and (1,2) is y = 8x/3-2/3.

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The number of views in the four weeks round to the whole number is 48.

Here it is given that the initial number of views for a reader board was 25 and it gets increased at the rate of 18% per week.

We have to find the number of views in the fourth week.

On the first week the increase = 25 + 25× 18%

                                                   = 25 + 25 × 18/100

                                                   = 25 + 4.5

                                                   = 29.5

The second week increase = 29.5 + 29.5 × 18%

                                              = 29.5 + 5.31

                                                = 34.81

The third week increase = 34.81 + 34.81 × 18%

                                         = 34.81 + 6.2658

                                         = 41.0758

The fourth week increase = 41.0758 + 41.0758 × 18%

                                           = 41.0758 + 7.393644

                                            = 48.469444

Therefore the number of views in the four weeks is 48.

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Answer:

20

Step-by-step explanation:

do parenthesis first

1/5(3+2+ 5)² =

1/5(10)² =

then exponent

1/5(10)² =

1/5(100) =

20

Answer

Step-By-Step-Explanation

2 mangoes=eleven lassis

×6                   ×6

12 mangoes=66 lassis

Answer=66 lassis

Step-by-step explanation:

ABC and CDE are similar triangles.

similar shapes means that both shapes have the same angles. and : that there is one scaling factor for all lines of one of the shapes to calculate the lengths of the lines of the other shape.

we see that all the other sides of ABC are scaled 2:1 to the corresponding sides of CDE. that means the sides of ABC are twice a long as the sides of CDE.

the same scaling factor has to apply to AB vs. DE.

therefore,

11x - 25 = 2(4x + 1) = 8x + 2

3x = 27

x = 9

DE = 4x + 1 = 4×9 + 1 = 36 + 1 = 37

A 90% confidence interval for the average speed of all drivers on interstate 94 is (73.69, 76.31)

Given that,

Imagine asking a sample of 16 people how quickly they travel on Interstate 94. You determine the average speed to be 75 mph and the variance to be 9 mph after gathering your sample.

Solution is as given below :

90% Confidence Interval for μ is

μ = X ± tₐ/2 (n-1) 5/[tex]\sqrt{n}[/tex]

μ = 75  ± (1.75) * 3/[tex]\sqrt{16}[/tex]

μ = (73.69, 76.31)

Consequently, a 90% confidence interval for the interstate 94 average speed of all drivers is μ = (73.69, 76.31)

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A cosine function has an amplitude of 1/3, period of π/3, horizontal shift of -2π, and vertical shift of -3, x=π, then the value y is -2.8889

The general cosine function is given by

f(x)= A cos (B x -C) +D

where A= 1/3 is the amplitude,

period =  2π /B

π/3 =2π/B

B= 2/3

C= -2π is the horizontal shift and  D= -3s a downward vertical shift.

If we substitute all these values into the formula we obtain;

f(x)= 1/3 cos (2/3 x +2π ) -3

if x= π then we have to calculate y

y= 1/3*0.3333 -3

y= -2.8889

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The values satisfies the linear equation y = −47x−2 is (0, -2).

For the given question.

The linear equation is given as;

y = −47x −2

Check the result by putting the values from option.

For : −7 −6

Put x = -7

y = −47(-7) −2

y = 799 -2

y = 498 (incorrect)

For: 0 −2

Put x = 0

y = −47x −2

y = −47(0) −2

y = -2 (correct)

Thus, the values satisfies the linear equation y = −47x−2 is (0, -2).

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Answer:

SAS

Step-by-step explanation:

By applying the Side Angle Side Postulate (SAS), you can be sure that your two triangles are congruent.

For given line segments RS = TR

In this question, we have been given two line segments QS and TU intersected at point R.

Also, we have been given QS = TU, QR = RU

We need to prove, RS = TR

We can observe that,

QS = QR + RS

and UT = UR + RT

QS = TU                               ................(Given)

QR + RS = UR + RT

QR + RS = QR + RT              .............(Given QR = RU )

QR + RS - QR = QR + RT - QR     .............(subtraction property of equality)

RS = TR

Hence proved.

Therefore, for given line segments RS = TR

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Step-by-step explanation:

x/y = y/z = z/x

x = y²/z = zy/x and y = z²/x

x = y²/z

putting this into the 3rd part of the original equation :

z/x = z/ y²/z = z²/y²

now using the y identity of the second part there :

y = z²/x

z²/y² = z² / z⁴/x² = x²/z² (= z/x per previous equation)

so,

x²/z² = z/x

x³/z³ = 1

x/z = 1

x = z

then

y/z = y/x = z/x (= 1)

and therefore,

y/x = z/x meaning

y = z (and therefore = x)

so,

x = y = z

The probability that exactly one insect will die is 142.611.

The subject of a random event is covered in the mathematical field of probability. For instance, if a coin is flung into the air, it could land on its Head or Tail. Probability is equal to the number of favorable outcomes (Total number of outcomes) P = n (E) / n (S) (S) E is the event, P is the probability, and S is the sample area.

Given,

P( an insect will die) = 0.60

q = 1 - p

q = 1 - 0.60

q = 0.40

Sample size,

n = 9

Binomial distribution:

P(X) = ⁿCₓ pˣ qⁿ⁻ˣ

Probability that exactly one insect will die = P(X = 1)

= ⁹C₁ × 0.6¹ × 0.4⁸

= 362880 × 0.6 × 0.000655

= 142.611

The probability that exactly one insect will die is 142.611.

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The total cost of painting is $564.

What is surface area of cuboid ?

  A cuboid is a three-dimensional figure enclosed by six rectangular planes, each of which has a different size in terms of length, breadth, and height. Anything in the shape of a rectangle, such as a box, brick, or other object, may be a cuboid if you look about. When viewed from any of the ends, a cuboid (3-dimensional) can be seen to be made up of different-sized rectangles (2-dimensional). A cuboid's area is its surface because it is a solid with three dimensions. Since a cuboid's faces are rectangular, its area may be determined using the formula for the area of a rectangle.

Total Surface Area of a Cuboid (TSA) = 2 (lw + wh + lh) square units

We have been given that a community hall is in the shape of a cuboid. The hall is 40m long 15m high and 3m wide.

The paint will be required for 4 walls and ceiling.

Let us find area of walls and ceiling.

Area of walls and ceiling = 2( 40*15) + 2(3*15) + (40*3)

=> Area of walls and ceiling = 2(600)+2(45)+120

=> Area of walls and ceiling = 1200+90+120

=> Area of walls and ceiling = 1410 [tex]m^2[/tex]

Therefore, the area of walls and ceiling is 1410 square meters.

Here Cost for 10 litre of paint is $10 and 10 litre paint covers 25 square meter.

Then total cost of paint = 10*[tex]\frac{1410}{25}[/tex] = 10*56.4 = $564.

Hence cost of paint is $564.

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