What is the slope of the line through (-1,8)(−1,8)left parenthesis, minus, 1, comma, 8, right parenthesis and (3,-4)(3,−4)left parenthesis, 3, comma, minus, 4, right parenthesis?
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The  values of for which the rocket's height is 29 meters are 0.75 and -0.67.

The rocket's height h (in meters) after t seconds is given by the following.

h=57t-5t^2

Then the equation after the height is 29 meters was given will be

[tex]h=57t-5t^2[/tex]

29=57t-5t^2

then we will have  [tex]57t-5t^2-29=0[/tex]

Then this is a quadratic equation, which can be solved, to find t, then after using the quadratic formular the values of t are:

0.75 and -0.67

Then we can chose 0.75 seconds

Therefore, from the question, we can see that after the quadratic equation has been performed  0.75 and -0.67 serves as the values for the height of 29 metres.

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The inverse of the function f(x) = y = 2x² - 8 is [tex]y=\pm\sqrt{\frac{x+8}{2} }[/tex].

A function's inverse is a function that reverses the action of a function, say [tex]f[/tex]. If the inverse of f exists, it is denoted by f ⁻¹ and exists only if f is a bijective function.

The domain of a relation's inverse corresponds to the original relation's range. In other words, the inverse's x values are the relation's y values.

Consider the function,

f(x) = y = 2x² - 8

Swapping x and y, to find the inverse.

x = 2y² - 8

Adding 8 on both sides of the equation.

x + 8 = 2y² - 8 + 8

2y² = x + 8

Dividing each side of the equation by 2.

y² = ( x + 8 )/ 2

Taking the square root of the equation.

[tex]\sqrt{y^{2}}=\pm\sqrt{\frac{x+8}{2} }[/tex]

[tex]y=\pm\sqrt{\frac{x+8}{2} }[/tex]

The inverse of the function f(x) = y = 2x² - 8 is [tex]y=\pm\sqrt{\frac{x+8}{2} }[/tex].

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We conclude that the percent error in Terry's reading is 8.3 percent.

If you did a reading on a value V, and your reading is another value V', the percent error in your reading is given by the formula:

P = 100%*|V - V'|/V

In this case, Terry's reading of the volume of the liquid is V' = 33.0, while the actual value is V = 36.0

Replacing that in the formula for the percent error we get:

P = 100%*|36.0 - 33.0|/36.0 = (3.0/36.0)*100% = 8.3%

We conclude that the percent error in Terry's reading is 8.3 percent.

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Step-by-step explanation:

It sounds like you need to find your slope. The equation is y2-y1/x2-x1

Say you have two points, and those two points make a line.

Say those points are (0,0), and (5,5).

To find the slope, we need which is equal to x2-x1/y2-y1 (the two coordinates for the points) which in this case, equals one. That means the constant rate of going up is, 1 each time it moves to the left once.

I hope this answers your problems. If you don't understand anything, I can try to help in the comments!

The distance, in miles, from Pine Gap to Turkey Trot is 48 miles.

Here, we are given that on a road map, the distance from Pine Gap to Turkey Trot is 2 inches. The scale of the maps shows that 1 inch is equal to 24 miles.

This simply means that 1 inch on the map is equal to 24 miles in reality. Usually maps use a scale factor to compare the distances as the map is a condensed version of the actual geographical area. Here, the scale factor is 1 inch : 24 yards.

Thus, a distance of 2 inches on the map will be equal to 24 × 2 = 48 miles.

Therefore, the distance, in miles, from Pine Gap to Turkey Trot is 48 miles.

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Answer:

An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio

so the answer would be √13

Step-by-step explanation:

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Answer:

c

Step-by-step explanation:

an irrational number is a number that cannot be written as a number or a fraction

Answer:

Add 2 to both sides.

1/4x=2x-7

Multiply both sides by 4

x=8x-28

-8x from each side.

-7x=-28

divide both sides by -7

X=4

Answer:  x=4

1. Multiply both sides by 4 to get rid of the denominator, which gives you x-8 = 8x-36
2. Subtract 8x from both sides, which gives you x - 8 - 8x= -36

3. Add 8 to both sides, which gives you x - 8x = -36 + 8

4. Simplify, -7x = -28

5. Divide both sides by -7, x = -28/-7

6. the negative signs cancel and you just get 4

Answer:

1 and 1.50 or 1 and 2, but most likely the first one.

Step-by-step explanation:

Each issue will cost £3.5 if a yearly subscription to a monthly magazine costs £42.00.

Given, a yearly subscription to a monthly magazine costs £42.00 i.e., 12 months to a monthly magazine costs £42.00.

one month will cost £42.00 divide by 12 and let it be x.

we simply calculate the value of x by dividing £42.00 by 12.

x = 42.00/12

x = 3.5

x = £3.5

Therefore, each issue will cost £3.5 if a yearly subscription to a monthly magazine costs £42.00.

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log 150 = log 50 + log 3

∴ log 150 = 2.176

As the base is not mentioned, we will take the base as 10. We will apply the product rule of logarithms to this equation.

log (150) can also be written as log (50×3).

Therefore, log (150) = log 50 + log 3

We know, log 3 = 0.477log 150 = log 50 + 0.477

Now, we can write log 50 as log (100/2). We will use the quotient rule of logarithms.log 50 = log 100 - log 2

We know, log 100 = 2 and log 2 = 0.301∴ log 50 = 2 - 0.301

log 50 = 1.699 Substituting the value of log 50 = 1.699 in the main equation, log 150 = log 50 + log 3log 150 = 1.699 + 0.477log 150 = 2.176

Therefore, the final answer to the question log 150 = 2.176

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By evaluating the equation we found  3 pairs we can write the table:

x = -7, 0, 7

y = 2, -2, -6

Which represents our equation.

We want to get a table of the form:

x: x₁, x₂, x₃, ...

y: y₁, y₂, y₃, ...

To get that, we need to evaluate the given equation in some different values of x, so let's do that.

if we take x = 0, then we get:

y = -(4/7)*0 - 2 = -2

So we have the pair (0, -2)

If x = 7, then:

y = (-4/7)*7 - 2 = -4 - 2 = -6

So we have the pair (7, -6)

If x = -7 then:

y = (-4/7)*-7 - 2 = 4 - 2 = 2

So we have the pair (-7, 2)

So now that we have 3 pairs we can write the table:

x = -7, 0, 7

y = 2, -2, -6

Which represents our equation.

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Answer:

p = 8

Step-by-step explanation:

3 + 1 + p = 12

Rearrange the equation so that you have integers on one side and algebra on the other.

3 + 1 + p = 12

p = 12 - 3 - 1

p = 8

The actual area of the bedroom is bigger than the actual area of the kitchen.

The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The area of a rectangle is determined by its dimensions. A rectangle's area is essentially equal to the product of its length and breadth.

In the drawing, the kitchen is in the shape of a rectangle with dimensions of 12 cm × 27 cm.

Therefore, the area of the rectangle will be:

Area = Length × Breadth

Area = 12 cm × 27 cm

Area = 324 cm²

Now, the actual area of the bedroom is 300,000 cm².

Then the difference between the area,

difference = bedroom - kitchen

difference = 300,000 - 324 cm²

difference = 299676 cm²

Therefore, the area of the bedroom is bigger than the area of the kitchen.

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x = -4 is the extraneous solution of the equation.

The equation is

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

To find the extraneous solution first we need to find the value of x.

So we need to square on both sides of the equation

[tex](\sqrt{5- x})^{2}[/tex] = [tex](x + 1)^{2}[/tex]

5 - x = [tex]x^{2}[/tex] +2x + 1

[tex]x^{2}[/tex] + 3x - 4= 0

[tex]x^{2}[/tex] + 4x - x - 4 = 0

x( x + 4 ) - 1 ( x + 4) = 0

( x + 4)( x - 1) =0

x = -4, 1

Now put both the value of x in the solution in the equation.

x = -4

[tex]\sqrt{5 - (-4)}[/tex] = -4 + 1

[tex]\sqrt{9}[/tex] = -3

3≠ -3

Now put

x = 1

[tex]\sqrt{5 -1}[/tex] = 1 +1

[tex]\sqrt{4}[/tex] = 2

2 = 2

Therefore we get that x = -4 is the extraneous solution of the equation and x = 1 is the solution of the equation.

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The value of x for log₉3=x is 1/2 or 0.5.

An exponent is a logarithm. You may convert any exponential expression to logarithmic form. As an illustration, if 8 = 23, the base is 2, the exponent is 3, and the outcome is 8. This may be represented as 3 = log2 8 in logarithmic notation.

The equation y=logb(x+h)+k shifts the logarithmic function, y=logbx, by k units vertically and h units horizontally.

The equation given is -

log₉3=x

It can be expressed in the form -

3 = 9ˣ

3 = 3²ˣ

As base is same,

1 = 2x

x = 1/2 = 0.5

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The number of parallel sides that the translated figure will have is 2 pairs of parallel sides.

We are given the properties of the figure as;

Number of Parallel sides = Two Pairs

Number of Right Angles = 4

Now, a rectangle is the figure that has two pairs of opposite sides parallel, and four right angles. A square could also have this same properties.

Now, if the figure is translated by 4 units down, according to transformation, that does not change the dimension of the figure and as such it retains same number of parallel sides.

Thus, the number of parallel sides that the translated figure will have is 2 pairs of parallel sides.

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The relationship between area and cost is 3/4 means 4 times area gets 3 times cost.

Given the cost to rent an apartment is proportional to the number of square feet in the apartment.

Given the cost of an 800 sqft apartment per month = 600$

By using the given information we can define the relationship between area and cost as below

For 800 sqft = 600 $

for 1 sqft = x

It can be written as

800/1 = 600/x

By cross multiplicating the terms on both sides we get

800 * x = 600

x = 600/800

x = 3/4

The relationship between area and cost is 3/4 means 4 times area gets 3 times cost.

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The stemplot gives a correct comparison of eastern and western states’ expenditures as The eastern states have, on average, a higher per-pupil expenditure than the western states.

The Eastern States have expenditure per pupil which are higher in number and in quantity. For instance, they have per-pupil expenditure of $153, $154, $155, and $156. They also have $191, and $190.

When compared to the western states therefore, the eastern states seem to on average, spend more per-pupil.

Options for this question include:

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The solutions for this quadratic equation is

x = 0 , -2/3

What is quadratic equation ?

A quadratic equation is also known as quadratic function. The quadratic function has the form of equation as  ax²+ bx + c, where a, b, and c are the numbers not equal to zero. In mathematics, the quadratic function, the quadratic polynomials , 2nd degree polynomial is a polynomial function with one or more that one variables in which the highest term is of the second degree.

according to question given,

9 x²+6 x=0

take the 3x as common factor, equation is

3x ( 3x + 2) = 0

now, evaluating this expression

3x = 0  , say equation 1

and, 3x +2 =0  say equation 2

from equation 1 , x = 0

and, from equation 2

3x + 2 =0

x = -2 / 3

Thus final solutions for this equation is

x = 0 , -2/3

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Answer:

(-a)(-b)

-a ×-b

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Explanation:

Multiply both sides by 2 to clear out the fraction

11 - (1/2)y = 3 + 6x

2* ( 11 - (1/2)y ) = 2*(3 + 6x)

2*11 - 2*(1/2)y = 2*3 + 2*6

22 - y = 6 + 12x

Then let's solve for y

22 - y = 6 + 12x

-y = 6 + 12x-22

-y = 12x-16

y = -(12x-16)

y = -12x+16  is the answer

The final answer is in slope intercept form y = mx+b

m = -12 = slope

b = 16 = y intercept

Drawn using the same scale, the shape of the normal curve H will be more spread out than the shape of the normal curve G.

Normal curve, or Gaussian distribution, is a curve that describes data form a variable that has infinite, or very large, number of possible values distributed among the population. It has a symmetric shape, and the distribution rises in the middle, and goes down to the left and to the right. The mean is equal to the mode and median and is located at the middle or top of the curve.

If two normal curves have the same mean, but different standard deviations, then the curve with the larger standard deviation will have a more spread out shape than the other.

If Normal curve H has a standard deviation of 10 and normal curve G has 5, but both has the same mean, then Normal curve H has a more spread out shape than the curve of normal curve G.

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Answer:

Centena de mil, sorry, hundred thousand

Step-by-step explanation:

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If ∆ABC and ∆FDE are congruent, then the correct statement among options is ∠C ≅ ∠E.

Congruent figures refers to the figures that can be superimposed on each other. This states that the angles and sides are similar for both the figures being compared. We are given that two triangles are congruent. Same will be true for their sides as well.

Thus, we can interpret that similar angles in the mentioned two triangles will be -

∠A ≅ ∠F

∠B ≅ ∠D

∠C ≅ ∠E

Similarly, the similar sides for both triangles will be -

AB ≅ FD

BC ≅ DE

AC ≅ FE

Therefore, in the congruent triangles ABC and FDE, ∠C and ∠E are congruent.

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The algebraic expression 6x(3y + 4z) can be simplified as 18xy + 24xz

the algebraic expression given in the question is a linear equation in three variables that are x , y and z and the simplification of this algebraic expression would also contain all the three variables

To solve this question we have to use the algebraic of  distributive property of addition over multiplication

so, using the above property and substituting the values given in the question we get

6x(3y +4z) = 6x(3y) + 6x(4z)

                  = 18 xy + 24 xz

Hence, The algebraic expression 6x(3y + 4z) can be simplified as 18xy + 24xz

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