Find the gradient of the curve
y = 5x − 10/x^2
at the point where the curve crosses the x-axis

Answer:

But the 2lbs.

Step-by-step explanation:

Divide $9.19 by 2 and you get 4.595 which would be the cheapest option out of the 3 because the 1lb is $7.05 and the 3lb is $5.13.

You're welcome.

Answer:

0.16 square inches

Step-by-step explanation:

We know that 1 centimeter of length is equal to 0.39 that is 0.4 inches approximately. This implies 1 square centimeter = 0.16 square inches

The side AC corresponds to the side AC in the other triangle and the length of BC is 15 units

For two triangles to be similar, the corresponding sides of the triangles must be in proportion

Having said  that

The side AC corresponds to the side AC in the other triangle

The length BC is calculated as

BC/9 = 25/15

Express as products

So, we have

BC = 9 * 25/15

Evaluate the products

BC = 15

Hence, the length of BC is 15 units

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Answer: 7.9

Step-by-step explanation:

\(P=2000, r=0.09, n=2\\\\4000=2000\left(1+\frac{0.09}{2} \right)^{2t}\\\\4000=2000(1.045)^{2t}\\\\2=1.045^{2t}\\\\\log_{1.045} 2=2t\\\\t=\frac{\log_{1.045} 2}{2}\\\\t \approx 7.9\)

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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Answer:

\(\displaystyle d = 15\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Point (-6, 6)

Point (3, -6)

Step 2: Identify

(-6, 6) → x₁ = -6, y₁ = 6

(3, -6) → x₂ = 3, y₂ = -6

Step 3: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

2.cms

Step-by-step explanation:

Answer:

(5, -10)

Step-by-step explanation:

the solution is where both points meet

The possible rectangle's length and width are A) 1 cm and 15 cm and C) 3 cm and 5 cm

The given parameters are

Area = 15 square cm

The area is given as

Area = 15 square cm

The formula of area is

Area = Length x Width

Using the above formula, we have:

A) 1 cm and 15 cm ⇒ 15 square cm

B) 2 cm and 7 cm ⇒ 14 square cm

C) 3 cm and 5 cm ⇒ 15 square cm

D) 4 cm and 4 cm ⇒ 16 square cm

Hence, the possible rectangle's length and width are A) 1 cm and 15 cm and C) 3 cm and 5 cm

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Possible question

The area of a rectangle is 15 square cm

Which of the following could be the rectangle's length and width?

(Area = length x width)

Choose all answers that apply:

A) 1 cm and 15 cm

B) 2 cm and 7 cm

C) 3 cm and 5 cm

D) 4 cm and 4 cm

The center of the hanger represents an equal sign, since both sides of the hanger are equal.

Given different coloured triangles and shapes, we can assign a variable to each of them.

Let one green triangle be equal to \(a\).

Let one blue square be equal to \(b\)

Let one red circle be equal to \(c\).

Let one yellow pentagon be equal to \(d\).

On the left side of the hanger/equation, there are 3 green triangles. This means that one of our terms in our equation will be \(3a\).

Under the triangles on the left side is 1 blue square. This means that the next term could be \(1b\), or just \(b\).

Next is 2 red circles ⇒ \(2c\)

And finally are 3 yellow pentagons ⇒ \(3d\)

To sum up the left side as an expression, we can write all the terms we have just written as a sum:

\(3a+b+2c+3d\)

Now, after doing the same procedure for the right side of the hanger, we get:

\(2a+3b+c+2d\)

For now, we only have two expressions representing the two sides of the hanger:

Left: \(3a+b+2c+3d\)

Right: \(2a+3b+c+2d\)

To turn these into an equation, we must have an equal sign.

Remember that both sides of the hanger are equal. Knowing this, we can state the following:

Left side = Right side

\(3a+b+2c+3d = 2a+3b+c+2d\)

\(3a+b+2c+3d = 2a+3b+c+2d\)

Answer:

1.53

Step-by-step explanation:

1

36

(

85

)

+

(

35

36

)

(

−

4

)

=

E

V

85

36

−

140

36

=

E

V

−

55

36

=

E

V

E

V

≈

−

$

1.53

Answer: the fraction is 4over 12

Step-by-step explanation:

first you multiply the top and bottom number then u divide the number by the bottom.

Answer:

1/2

Step-by-step explanation:

If you were to multiply 1/2 by -50 you would get -25, which is greater than -50.

The same goes for 1/5, if you were to multiply 1/5 by -50, you would get -10.

Another example is 1/10 times -50, that would be -5.

The number of square inches of cardboard that are needed to make one

the container is 18.

We have,

The volume of the triangular prism.

= Area of the triangle x height

Now,

Height = 6 in

And,

To find the area of a triangle, we can use Heron's formula.

A = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.

Let's calculate the area using Heron's formula:

s = (3.2 + 3.2 + 2) / 2 = 4.2

A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))

A = √(4.2 x 1 x 1 x 2.2)

A = √(9.24)

A ≈ 3.04 square inches

Now,

The volume of the triangular prism.

= Area of the triangle x height

= 3.04 x 6

= 18.24 in²

Now,

Area of one cardboard.

= 1² in²

= 1 in²

Now,

The number of square inches of cardboard that are needed to make one

container.

= The volume of the triangular prism / Area of one cardboard

= 18.24 in² / 1 in²

= 18.24

= 18

Therefore,

The number of square inches of cardboard that are needed to make one

the container is 18.

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Answer:

x\(\leq\)3

Step-by-step explanation:

hope this helps

Answer:

-6 <x< 3 or x<3, x<-6

Step-by-step explanation:

-18 < 4x +6 < 18

-18-6 <4x< 18-6

-24 <4x< 12

-24/4 <x< 12/4

-6 <x< 3

hope this help you

The area on the graph that is not shaded is the region of feasibility. The shape is a triangle and the vertices of the feasible region are: (5,1.5), (.75,.75), (1.5,.5)

The system of inequalities below, We need to determine the shape of the feasible region and find the vertices of the feasible region

x+y<=2

3x+y>=3

x+3y>=3

x>=0

y>=0

Now, we would graph with the following inequalities

x+y>=2

3x+y<=3

x+3y<=3

x<=0

y<=0

Therefore, the area on the graph that is not shaded is the region of feasibility and the shape is a triangle, the vertices of the feasible region are: (5,1.5) (0.75, 0.75), (1.5,.5).

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To solve the equation 7(x + 3) = 7(x + 5), we can start by simplifying both sides of the equation:

7x + 21 = 7x + 35

Subtracting 7x from both sides, we get:

21 = 35

This is a contradiction, as 21 is not equal to 35. Therefore, the equation has no solution.

However, the problem states that the equation has an infinite number of solutions. This can only happen if the missing number is a factor that appears on both sides of the equation, and therefore cancels out when we simplify the equation.

Looking at the equation, we can see that both sides have a factor of 7, which cancels out when we simplify the equation. Therefore, the missing number must be the factor that was torn off, which is 7 multiplied by the difference between the two numbers inside the parentheses:

7(5 - 3) = 14

Therefore, the missing number is 14, which corresponds to answer option B.

\(b\) and \(27^{\circ}\) are vertical angles, therefore \(b=27^{\circ}\).

The sum of the interior angles of a triangle is \(180^{\circ}\), therefore:

\(90^{\circ}+27^{\circ}+c=180^{\circ}\\c=63^{\circ}\)

The limiting value of the population is 1000000, and it will take approximately 49.92 months for the population to be equal to one-half of this limiting value. The correct option is A.

To find the limiting value of the population and the time it will take the population to be equal to one-half of this limiting value, we need to solve the initial-value problem:

dp/dt = 0.1P(1 - P/1000000), P(0) = 10000

To find the limiting value of the population, we need to find the value of P as t approaches infinity. We can do this by finding the equilibrium solutions of the differential equation. An equilibrium solution is a constant population size that does not change over time. It is found by setting dp/dt = 0, and solving for P.

In this case, we have:

dp/dt = 0.1P(1 - P/1000000) = 0

Solving for P, we get:

P = 0 or P = 1000000

The population size cannot be zero, so the limiting value of the population is P = 1000000.

To find the time it will take the population to be equal to one-half of this limiting value, we need to solve for the value of t when P = 500000. Unfortunately, there is no algebraic solution for this equation, so we need to use numerical methods to estimate the value of t.

One way to do this is to use a numerical solver to solve the initial-value problem. Here, we can use a computer software or a graphing calculator to solve the differential equation and find the value of P for different values of t, until we find the time at which P = 500000.

Using a graphing calculator or a computer software, we can solve the differential equation to get:

P(t) = 1000000/(1 + 999e^(-0.1t))

Using this formula, we can find the time it takes for P to reach 500000 by solving for t when P = 500000:

500000 = 1000000/(1 + 999e^(-0.1t))

1 + 999e^(-0.1t) = 2

e^(-0.1t) = 1/999

-0.1t = ln(1/999)

t = -10 ln(1/999) ≈ 49.92

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Complete question is:

A model for the population P(t) in a suburb of a large city is given by the initial-value problem dp = 0.1 P(1 - P/1000,000), P(O) = 10,000 where t is measured in months. The limiting value of the population and the time will take the population be equal to one-half of this limiting value respectively are

a. 1000,000, 49.92

b. 500,000, 58

C. 1000,000 42

d. 1000,000 46

a. The secant slope through (-2,4) and (0,0) is -2.

b. The secant slope through (-1.5,2.25) and (-0.5,0.25) is -2.

The estimated slope of the tangent line to f(x) = x^2 at x = -1 is approximately -2.

To estimate the slope of the tangent line to the function f(x) = x^2 at x = -1, we can find the slopes of the secant lines through different pairs of points.

a. (-2,4) and (0,0):

The coordinates of the two points are (-2, 4) and (0, 0). We can calculate the slope of the secant line passing through these points using the formula:

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

Plugging in the values, we get:

msec = (0 - 4) / (0 - (-2))

= -4 / 2

= -2

So, the slope of the secant line passing through (-2, 4) and (0, 0) is -2.

b. (-1.5, 2.25) and (-0.5, 0.25):

The coordinates of the two points are (-1.5, 2.25) and (-0.5, 0.25). Using the slope formula, we can calculate the slope of the secant line passing through these points:

msec = (0.25 - 2.25) / (-0.5 - (-1.5))

= (-2) / (1)

= -2

So, the slope of the secant line passing through (-1.5, 2.25) and (-0.5, 0.25) is -2.

By finding the slopes of the secant lines, we have estimated the rate of change of the function f(x) = x^2 at x = -1. The slope of the tangent line at this point will be very close to these secant slopes, particularly as the two points used to calculate the secant lines get closer together.

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Impossible

Hope this helps! :)

Answer:

Impossible

Step-by-step explanation:

Based on the Inequality Theorem, in any triangle, the sum of any two sides will be larger than the length of the thrid side. If the side lengths do not follow this rule, then that means that you can not create a triangle with such side lengths. In our case, the sum of two sides with lengths 1 and 8 is 1 + 8 = 9 and 9 is not greater than the length of the third side which is also 9. Therefore, it is impossible to build a triangle with such lengths.

The value οf v=3√2 and  w=√3/√2.

If a triangle has a straight angle (90 degrees), the hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides, accοrding tο the Pythagοras theοrem.

Keep in mind that BC² = AB² + AC²in the triangle ABC signifies this. This equatiοn uses the variables base AB, height AC, and hypοtenuse BC. It is impοrtant tο nοte that the hypοtenuse, οr lοngest side, οf a right-angled triangle is.

Here fοr sin(30)= v/3√2

1/2 = v / 3√2

v = 3√2

cοs(30)= w/3√2

w=3√2*√3/2

w=√3/√2

Hence the value οf v=3√2 and  w=√3/√2.

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Answer:

-1/2

Step-by-step explanation:

Answer:

-9/8.

Step-by-step explanation:

-3/2 * 3/4

= -3*3 / 2*4

= -9/8.

Answer:

A

Step-by-step explanation:

With function transformation, added/subtracted numbers outside of the x always mean the function is being translated up/down. In this case, since the 2 is being replaced with a 4, the new function is 2 units higher than the previous function.

The ratio of the new volume to the old volume will be 3:1, the correct option is D.

We are given that;

The measurements= 9 cm*5 cm*3 cm

Now,

To find the volume of a rectangular prism, we can use the formula V = lwh, where l is the length, w is the width, and h is the height. Using the given dimensions, we get:

V = lwh V = 9 * 5 * 3 V = 135 cm^3

To find the new volume after tripling the width, we can use the same formula but replace w with 3w. We get:

V’ = l * 3w * h V’ = 9 * 3 * 5 * 3 V’ = 405 cm^3

To find the ratio of the new volume to the old volume, we can divide V’ by V and simplify. We get:

V’ / V = (405 cm^3) / (135 cm^3) V’ / V = 3

To write the ratio in the form of a fraction, we can use 1 as the denominator of V. We get:

V’ / V = 3 / 1

Using these steps, I found that the ratio of the new volume to the old volume will be 3:1.

Therefore, by the given rectangular prism the answer will be 3:1.

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Answer:

61.3°

Step-by-step explanation:

For angle x, 12 is the adjacent leg. 25 is the hypotenuse.

The trig ratio that relates the adjacent leg and the hypotenuse is the cosine.

cos A = adj/hyp

cos x = 12/25

x = cos^-1 12/25

x = 61.3°

Answer:

$9000

Step-by-step explanation:

36000:4=$9000

Answer:

$20

Step-by-step explanation:

First we will change the ratio so that we are finding how much money Siti receives to the total amount of money.

\(4:3 \rightarrow 4:(3+4)=4:7\)

Now we can solve for how much money Siti receives using a proportion.

\(\frac{4}{7} = \frac{\mbox{money Siti receives}}{35}\)

We can see that the denominator increases 5 times, so the numerator must increase 5 times too. This means Siti receives $20.

Answer:

Hope this helps!!!

Step-by-step explanation:

6(2−3)

Answer:

6(2n - 3)

Step-by-step explanation:

The probability of Miguel selecting a tile number less than 3 from each bag -1 is 1/5 and bag-2 is 2/5.

The given tiles in bag-1 = {2, 4, 5, 8, 9}

Total number of tiles in bag-1 = 5

The number of tiles less than number 3 in the bag - 1 = 1

The probability of Miguel selecting a tile number less than 3 =

number of tiles less than 3 / total number of tiles = 1/3

The given tiles in bag-2 = {0, 1, 3, 6, 7}

Total number of tiles in bag-2 = 5

The number of tiles less than number 3 in the bag-2 = 2

The probability of Miguel selecting a tile number less than 3 =

number of tiles less than 3 / total number of tiles = 2/3

From the above analysis, we solved the problem.

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Answer:

to solve the equation you first need to bring it to factors and by doing that you first need to let the equation equal 0 hence you need to minus 2 on both sides of the equation therefore

x^2 + 10x + 25 - 2 =2 - 2

therefore

x^2 + 10x +23 = 0

now since the equation cannot be factored, we use the formula.

x= \(\frac{-b +- \sqrt{b^{2}-4ac } }{2a}\)

where

a=1

b=10

c=23

note we use the coefficients only.

therefore x = \(\frac{-10 -+ \sqrt{10^{2}-4(1)(23) } }{2(1)}\)

=\(\frac{-10-+\sqrt{100-92} }{2}\)

=\(\frac{-10-+\sqrt{8} }{2}\)

then we form two equations according to negative and positive symbols

x=\(\frac{-10+\sqrt{8} }{2} or x =\frac{-10-\sqrt{8} }{2}\)

therefore x = \(-5+\sqrt{2}\)   or x=\(-5-\sqrt{2}\)