Solve using the quadratic equation -4x² + 7x + 5 = 0​

Hi! I understand that you want help finding the values of m∆1 and m∆2. To provide a step-by-step explanation, I need more information about the problem, such as the type of triangles, angles, or side lengths involved. Please provide more context or details, and I will be happy to help you.

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Answer:

C. LM ≅ JH

Step-by-step explanation:

The criteria that needs to be satisfied before two right triangles can be said to be congruent to each other is by the Hypotenuse-Leg Theorem are:

1. Both must have a corresponding leg that are congruent to each other.

In the diagram given above, NM is congruent to KH. They are corresponding legs that are congruent.

2. The hypotenuse of one triangle must be equal to that of the other.

We are not given if the hypotenuse of one, LM is congruent to the hypotenuse of the other, JH.

Therefore, the additional information required would be:

LM ≅ JH

Answer:

Since there is 4 quarts in a gallon and 60 minutes in a hour.

60 x 60 = 3600

Multiply: 815  ×  4  =  3260  quarts per hour

So 3260/3600 = 326/360 = 0.905 quarts per second

Step-by-step explanation:

Answer:

D=3x+5, I=4x+8, -1x-3

Step-by-step explanation:

You don't know how many chocolates are in the boxes, so that's x. Always look at "and" and think + something. You know how many extra chocolates there are so you don't need to put the x. Remember, and=plus. Remember the equation is Mx+b.

The two expressions together is 3x+5=4x+8. Move the 4x to the other side with 3x+5 and make it negative. Same for eight. Hopefully that helps.

First you will get 4dz

if the length of the pond is 80 meters and the width is 60 meters, the distance across the pond would be the square root of (80^2 + 60^2) = 100 meters.

To find the distance across the pond indirectly, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In this case, the distance across the pond is the hypotenuse of a right triangle formed by the length and width of the pond.

To find the length of the hypotenuse, you can square the length and width and add them together, then take the square root of the sum. This will give you the distance across the pond. For example, if the length of the pond is 80 meters and the width is 60 meters, the distance across the pond would be the square root of (80^2 + 60^2) = 100 meters.

This method is indirect because you are not directly measuring the distance across the pond. Instead, you are using the length and width to calculate it. However, it is a reliable way to find the distance and has been used for centuries to measure distances that are difficult or impossible to measure directly.

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Answer: 6.25%

Explanation

Given

• 52 playing cards

• both cards are a diamond

Procedure

There are 13 cards of diamonds in a standard deck of cards. Thus our probability of getting one diamond is:

However, they are asking for two cards. Then:

Expressing as a whole percent:

Answer:

$6.35

Step-by-step explanation:

10 quarters =

10 × .25 = $2.50

17 dimes =

17 × .10 = $1.70

40 nickels =

40 × .05 = $2.00

15 pennies =

15 × .01 = $0.15

2.50+1.70+2.00+.15

= 6.35

The total is $6.35.

The speed that an aeroplane is intended to fly at is called its maximum operating speed (VA). With elevations of 12, 15, and 18 degrees, the lift and G-force grow.

 Speed.

It is the rate at which a displacement adapts to its surroundings. A body's speed is a scalar quantity since it is directionless. It is also the rate at which displacement in relation to the environment is shifting in a particular direction.

Here,

The maximum operational speed of an aeroplane is the speed at which it is designed to fly (VA). Elevations of 12, 15, and 18 degrees result in increasing lift and G-force.

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Answer:

  61°

Step-by-step explanation:

As in all parallelograms, adjacent angles are supplementary.

  ∠LMN = 180° -∠MNO

  ∠LMN = 180° -119° = 61°

Answer:

Total of the frequency = The last values of the cumulative frequency (c.f) = 100

Step-by-step explanation:

From the frequency distribution table given in the question, the cumulative frequency (c.f) can be computed by adding each frequency to the sum or total of the preceding frequencies. This makes the last value of the cumulative frequency (c.f) to be equal to the total of the frequency.

Based on this explanation, we have:

mass m (kg)       frequency         mass m (kg)           c.f  

0 < m ≤ 0.1                  2                     m ≤ 0.1                2

0.1 < m ≤ 0.2               7                     m ≤ 0.2               9

0.2 < m ≤ 0.5             32                    m ≤ 0.5              41

0.5 < m ≤ 0.8             46                    m ≤ 0.8              87

0.8 < m ≤ 1                 13                     m ≤ 1                100

From the above, we can observe that:

Total of the frequency = 2 + 7 + 32 + 46 + 13 = 100

The last values of the cumulative frequency (c.f) = 100

Therefore, we have:

Total of the frequency = The last values of the cumulative frequency (c.f) = 100

Answer:

TRUE

Step-by-step explanation:

y-4 = 2(x-1)

here, 4 is representing the y value and 1 is representing the x value.

And the slope is 2.

Answer:

Step-by-step explanation:

a^-4 x 8^14

the solution is C

Answer:  9 Four Wheel and 3 6 Wheel Trucks

Step-by-step explanation:

 Let FW be the four-wheel trucks and SW the six-wheel trucks.

Total wheels is 4*FW + 6*SW and is equal to 54 wheels

We know that FW = 3*SW, so substitute that into the above equation:

4*3*SW + 6*SW  = 54

12*SW +6*SW = 54

18*SW = 54

SW = 3

Therefore FW = 3*3 = 9

FW  4 x 9  = 36 wheels

SW  6 x 3  =  18 wheels

     Total   =   54 wheels  

The value of a in the equation is 5.

The expression can be solved below using the law on indices.

Therefore,

\(a^{x} X a^{y} = a^{x+y}\)

Therefore,

\(\frac{x^{a^{2}} }{x^{ab} } = x^{10}\)

a - b = 2

let's find a.

\(\frac{x^{a^{2}} }{x^{ab} } = x^{10}\)

cross multiply

\(x^{ab} X x^{10} = x^{a^{2} }\)

Using law of indices,

ab + 10 = a²

Therefore,

a²  - ab = 10

a(a - b) = 10

2a = 10

a = 10 / 2

a = 5

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Zero represents the sea level in this situation. It is the point where the dolphin and seagull would meet if they were in the same location.

Sea level is the average level of the ocean's surface. It is the point where the water meets the air and the point of reference for measuring depths and heights. In this scenario, the dolphin is located 25 feet below sea level, while the seagull is located 25 feet above sea level. This means that they are 50 feet apart from each other in terms of elevation, but they are both referenced from the same point - sea level.

Therefore, zero represents the level of the sea, which is the starting point for measuring heights and depths. It is the point of equilibrium where the forces of gravity and buoyancy balance each other out. Understanding the significance of zero in this situation is important for accurately interpreting and measuring the locations of the dolphin and seagull relative to the sea level.

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The difference between the circumference of the outer circle with a radius of 2 meters and the circumference of the inner circle with a radius of 18 meters can be calculated by subtracting the circumference of the inner circle from the circumference of the outer circle, both expressed in terms of π.

The circumference of a circle can be calculated using the formula C = 2πr, where C represents the circumference and r represents the radius of the circle. In this case, we have an outer circle with a radius of 2 meters and an inner circle with a radius of 18 meters.

The circumference of the outer circle is given by:

C_outer = 2π(2) = 4π meters

The circumference of the inner circle is given by:

C_inner = 2π(18) = 36π meters

To find the difference between the circumferences, we subtract the circumference of the inner circle from the circumference of the outer circle:

Difference = C_outer - C_inner = 4π - 36π = -32π

Therefore, the difference between the circumferences of the outer and inner circles is -32π meters.

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The work required to move the object from A to B in the force field is 64 units. The force field F = (x, 4) is not conservative.

To find the work required to move an object in a force field from point A to point B, we can integrate the dot product of the force vector and the displacement vector along the path.

Given the force field F = (x, 4) and the points A(0, 0) and B(4, 2), we can calculate the work as follows:

Determine the displacement vector from A to B:

Δr = B - A = (4, 2) - (0, 0) = (4, 2)

Calculate the dot product of the force vector and the displacement vector:

W = ∫F · dr = ∫(x, 4) · (4, 2) dr

Integrate with respect to x:

W = ∫(4x + 8) dx = 2x^2 + 8x + C

Evaluate the integral limits from x = 0 to x = 4:

W = [2x^2 + 8x]₀^₄ = 2(4)^2 + 8(4) - (2(0)^2 + 8(0))

= 32 + 32 - 0 = 64

Therefore, the work required to move the object from A to B in the force field is 64 units.

To determine if the force field is conservative, we need to check if the curl of the force vector is zero. Taking the curl of F = (x, 4):

∇ × F = (∂Fz/∂y - ∂Fy/∂z, ∂Fx/∂z - ∂Fz/∂x, ∂Fy/∂x - ∂Fx/∂y)

= (0 - 0, 0 - 1, 1 - 4)

= (0, -1, -3)

Since the curl of the force vector is not zero, the force field F = (x, 4) is not conservative.

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When given the value of 5/4 hours then in minutes this is equal to 75 minutes.

In every hour, there are 60 minutes. If you want to covert hours to minutes therefore, you multiply the number of hours by 60 minutes.

When given the number of hours as 5/4 hours, in minutes this becomes:

= Number of hours x 60 minutes per hour

= 5/4 x 60 minutes per hour

= 300 / 4 minutes

= 75 minutes

In conclusion, the number of minutes in 5/4 hours is equal to 75 minutes.

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The limit provided indeed represents the derivative of the function f(x) = (2x - 8) at the point a = 3, and its value is 2.

Consider the function f(x) = (2x - 8). The limit you provided can be rewritten as:
lim (x→3) [(f(x) - f(3))/(x - 3)]
This expression is actually the definition of the derivative of f(x) at a point a. In this case, a = 3. The expression represents the slope of the tangent line to the curve of the function f(x) at the point (3, f(3)). So, this limit represents the derivative of f(x) = (2x - 8) at a = 3.
To confirm this, let's find the derivative of f(x) using the power rule:
f'(x) = d(2x - 8)/dx = 2
Now, evaluate the derivative at a = 3:
f'(3) = 2
So, the limit provided indeed represents the derivative of the function f(x) = (2x - 8) at the point a = 3, and its value is 2.

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Answer:

y = -2

Step-by-step explanation:

using slope formula, you can create the following proportion:

y-(-1) = 1

-5-(-1)    4

cross-multiply:

4(y+1) = -4

4y + 4 = -4

4y = -8

y = -2

The given set {00, -6, 2} is not a basis of R³ because it does not span R³ and is not linearly independent.

The correct statement for the given set is: "Not a basis of R³." The set {00, -6, 2} is not a basis of R³ because it fails to meet the criteria of being linearly independent and spanning R³.

To determine if the set {1, 2, 3} is equal to the span of {1, 7 + 0², 7 - 2² + 0³}, we need to analyze the linear combinations that can be formed. By expanding the expression {1, 7 + 0², 7 - 2² + 0³}, we get {1, 7, 7 - 4}, which simplifies to {1, 7, 3}.

Since both sets {1, 2, 3} and {1, 7, 3} contain the same vectors, their spans will be equal. Therefore, the statement "Span{1, 2, 3} = Span{1, 7 + 0², 7 - 2² + 0³}" is true.

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The store manager can use f∘g function to find the final price of a bicycle.

Let the buying price be Y,

Store is offering sale on the item given by function,

f(x) = x - 30

And offering an additional discount given by function,

g(x) = x - 0.1x = 0.9x

So final price be written as;

0.9x - 30    [ 10% off and 30$ discount ]

Then 0.9x - 30 = f∘g ( operations of functions of functions ).

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

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Answer:

12) You should "Never drop trash on the ground"

13) I believe "Everyone should be aware about littering"

14) I believed "that everyone should know littering is bad "

15) Do you think "Littering is bad?"

16) I can't stand "when people do not care about littering " 

17) It is important "to be aware about littering and the effect it has on the world"

Step-by-step explanation:

The statement given "regression equations are usually used to predict values of unavailable data. if the data do not closely model a particular type of function, then that type of function is not appropriate to use in statistical regression. the more closely data fit a model, the more predicted values will be." is true because regression equations are indeed employed for predicting values of unavailable data.

Regression equations are commonly utilized to make predictions for unavailable data. When the data does not closely conform to a specific type of function, that function is deemed inappropriate for statistical regression. The accuracy of predicted values is contingent on the degree of resemblance between the data and the chosen model. Hence, a strong fit between the data and the model enhances the reliability of predicted values, ensuring that regression analysis is effectively applied for making accurate predictions.

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The derivative of the function y(x) = ln(cosh(x) + √(cosh²(x) – 1)) can be found as follows:

1. Start with the function y(x) = ln(cosh(x) + √(cosh²(x) – 1)).

2. Take the derivative of the inner function, cosh(x), which is sinh(x). The derivative of cosh(x) with respect to x is sinh(x).


3. Now, differentiate the expression inside the natural logarithm. Using the chain rule, we have:

Dy/dx = 1 / (cosh(x) + √(cosh²(x) – 1)) * (sinh(x) + (1/2) * (2 * cosh(x) * sinh(x)) / √(cosh²(x) – 1))

4. Simplify the expression:

Dy/dx = (sinh(x) + cosh(x) * sinh(x)) / (cosh(x) + √(cosh²(x) – 1))

Further simplification may be possible, but this is the complete derivative of y(x) with respect to x.


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Answer:

\(a_n = 2^{(n\, -\, 1)}\)

Step-by-step explanation:

The general form for a geometric sequence is:

\(a_n = a_1 \cdot r^{(n\, -\, 1)}\)

where \(a_n\) is the \(n\)th term in the sequence, \(a_1\) is the 1st term, and \(r\) in the common ratio between any two consecutive terms.

In this sequence:

\(1, 2, 4, ...\)

we can identify the common ratio as:

\(r= \dfrac{2}{1} = \dfrac{4}{2} = 2\)

We are also given that the first term is:

\(a_1 = 1\)

Hence, we can plug these values into the general form for a geometric sequence to get the explicit formula for the given sequence:

\(a_n = 1 \cdot 2^{(n\, -\, 1)}\)

\(\boxed{a_n = 2^{(n\, -\, 1)}}\)

The required area of the polygons is given as 100 ft², 9 ft², 16 ft², and 64 ft².

Given that,
The dimensions of this polygon are shown in feet (ft). 10ft/3ft/4 ft/8 ft. The area, in square feet, of the polygon is to be determined.

A polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,

Examples of polygons, equilateral triangles, squares, pentagons etc

Here,
Assumed that all the polygons are square,
The area of the square is given as (side)².
1,
Side = 10 ft
Area of the square = [10 ft]² = 100 ft²

Similarly,
For side 3 areas is 9 ft²,

For side 4 areas is 16 ft²,

For side 8 areas is 64 ft²,

Thus, the required area of the polygons is given as 100 ft², 9 ft², 16 ft², and 64 ft².

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