What is the nature of the roots of the quadratic equation 5x^2 4x 1?

Answer: C

Step-by-step explanation:

The HL Theorem states that if the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

In this case, 16 is the hypotenuse (the longest side of a right triangle) and 13 is the leg.

The evaluation of the expression 2ˣ - x² when x = 5 is 7

From the question, we have the following parameters that can be used in our computation:

Expression: 2^x- x^2

Value x = 5

Rewrite the expression as

Expression: 2ˣ - x²

Substitute the known values in the above equation, so, we have the following representation

2ˣ - x² = 2⁵ - 5²

When the exponents are evaluated. we have

2ˣ - x² = 32 - 25

Evaluate the like terms in the equation

So, we have the following representation

2ˣ - x² = 7

Using the above as a guide, we have the following:

The solution is 7

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To simplify the expression 20-10y-7y + 9, we can combine like terms.

Like terms are terms that have the same variables raised to the same exponents. For example, 10y and -7y are like terms because they both have the variable y raised to the exponent 1.

We can start by combining the like terms:

20 - 10y - 7y + 9

= 20 + (-10y - 7y) + 9

= 20 + (-17y) + 9

Next, we can combine the constants:

20 + (-17y) + 9

= (20 + 9) + (-17y)

= 29 + (-17y)

The simplified expression is: 29 + (-17y)

[tex]20-10y-7y + 9[/tex]

Combine Like Terms:

[tex](-10y+-7y)+(20+9)[/tex]

[tex]-17y+29[/tex]

[tex]\fbox{Option E}[/tex]

Answer:

Step-by-step explanation:

1.RS+ST=RT. so 9y+2+2y+7=15y-11

2.11y+9=15y-11

3.15y-11y=11+9

4.4y=20

finally we find the answer is y=5

Answer:

perimeter = 10

area = 6.25

Step-by-step explanation:

Every square has four equal sides. If we know one side is 2.5, then all sides are 2.5.

2.5*4 = 10

To find the area of a square you multiply the height and length. Since all sides of a square are the same, you just multiply 2.5 with itself.

2.5*2.5=6.25

Answer: 2.4

Step-by-step explanation:

we start from the right most digit, that is 8. Since 8 is greater than 5, we add 1 in the number before 8, that is 3. When we add 3 and 1 we get 4. This way, we get our answer 2.4 , which is correct to 2 significant figures.

hope that helps...

On solving the provided question, we can say that - here in number line we jump fron 2 to 7 as we have added +5

A number line is a visual representation of real numbers used in introductory mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. Increments on a number line are separated by equal distances. You can only respond to the numbers on a line in the manner indicated by those numbers. How the number is utilized is determined by the question that goes with it. B: Make a point.

here,

we have +5

so 2+(+5) = 7

we will jump to 7 from 2

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Answer:

4

Step-by-step explanation:

-28 = ±2^2 x ±7
60 = ±2^2 x ±3 x±5
72 = ±2^3 x ±3^2
=> Gcf of -28, 60, 72: 2^2 = 4

Answer: 12

Step-by-step explanation:

Therefore, the highest common factor of 60 and 72 is 12.

:) I know somebody already answered but like..im answering some stuff today, hope this helped by the way!

QUAD ABCD is a rectangular shape whose diagonals meet at point P. AC is 4x-13 and DP is x + 7.

When one set of opposing sides in a quadrilateral are congruent and parallel, the quadrilateral is a parallelogram. ABCD is a parallelogram if — BC — AD and — BC — AD. A quadrilateral becomes a parallelogram if its diagonals are bisected by one another.

In QUAD ABCD, DP equals x + 7 and AC is 4x-13.

4x - 13 is x + 7 + x + 7

4x - 13 = 2x+14

2x-13 = 14.

hence,

The value of x is 13.5.

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Answer: 1:1

Step-by-step explanation:

   We will write a ratio of ponies to goats;

ponies : goats

3 : 3

   Next, 3:3 can be simplified to 1:1. This gives us our fully reduced ratio.

Answer:

-18a^3b^5

Step-by-step explanation:

First do -ab^2*-6ab^2=-6a^2b^4

Then multiply that by 3ab=-18a^3b^5

The answers are given as 1) 165 m 2)3 seconds 3) 9 seconds 4)120 m

A curve is defined as a smoothly- flowing continuous line that has bent. It does not have any sharp turns. The way to identify the curve is that the line bends and changes its direction at least once. Curve of the graph is a pictorial representation of a particular function.

Given :  A object is thrown from the top of the building thus by observing the graph we derive the following information

1) Maximum height = 165 m

2) The object reaches maximum height at t=3 seconds

3) The time it took to reach the ground is 9 seconds

4) The building is 120 m tall

Hence, the answers are  1) 165 m 2)3 seconds 3) 9 seconds 4)120 m

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Answer:

Step-by-step explanation:

Combine multiplied terms into a single fraction

one-third x minus 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1

1 x over 3 end fraction minus 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1

Multiply by 1

1 x over 3 end fraction minus 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1

x over 3 end fraction minus 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1

Multiply the numbers

x over 3 end fraction negative 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1

x over 3 end fraction negative 18 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1

Answer:

  Manuel can make 5 batches of muffins using Recipe 1

Step-by-step explanation:

You want to know the value of b in the equation 2b = 10, where b is the number of batches of muffins Manuel can make using recipe 1.

Divide both sides of the given equation by 2 so solve for the value of b.

  (2b)/2 = (10)/2

  b = 5

Manuel can make 5 batches of muffins using Recipe 1.

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The general formula for logarithms is [tex]log_b(x) = y[/tex].

What is a logarithmic function?

A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x) = log_b(x),[/tex] where b is the base of the logarithm.

The general formula for logarithms is:

[tex]log_b(x) = y[/tex]

This means that b raised to the power of y is equal to x.

Where b is the base of the logarithm, x is the number that we are taking the logarithm of, and y is the result or the logarithm of x to the base b.

Hence, the general formula for logarithms is [tex]log_b(x) = y[/tex].

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The general formula for logarithms is [tex]log_b(x)=y[/tex].

What is a logarithmic function?

A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x)=log_b(x)[/tex] where b is the base of the logarithm.

The general formula for logarithms is:

[tex]log_b(x)=y[/tex]

This means that b raised to the power of y is equal to x.

Where b is the base of the logarithm, x is the number that we are taking the logarithm of, and y is the result or the logarithm of x to the base b.

Hence, the general formula for logarithms is [tex]log_b(x)=y[/tex].

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The measure of the angle ∠6 = 112°

What are parallel lines?

Parallel lines are two or more lines that are always the same distance apart and never meet, no matter how far they are extended. They are coplanar lines that do not intersect or cross each other, and they have the same direction.

As given

a∥e, m∥n, and m∠2 = 112°.

As  m∥n

a is the transversal (A line that cuts across two or more (usually parallel) lines is called transverasl.)

Thus

∠ 2 = ∠3 ( Corresponding angle property )

∠3 = 112°

Also

a∥e and m are transversal.

∠ 3 = ∠6 = 112 ° ( Corresponding angle property )

Hence, the measure of the angle ∠6 = 112°

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The measure of the angle ∠6 = 112°

What are parallel lines?

Parallel lines are two or more lines that are always the same distance apart and never meet, no matter how far they are extended. They are coplanar lines that do not intersect or cross each other, and they have the same direction.

As given

a∥e, m∥n, and m∠2 = 112°.

As  m∥n

a is the transversal (A line that cuts across two or more (usually parallel) lines is called a transversal.)

Thus

∠ 2 = ∠3 ( Corresponding angle property )

∠3 = 112°

Also

a∥e and m are transversal.

∠ 3 = ∠6 = 112 ° ( Corresponding angle property )

Hence, the measure of the angle ∠6 = 112°

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The commission on the sale would be $62.5

To find the commission on a sale, you can use the following formula:

Commission = Sale Amount x Commission Rate

Sale Amount: the total value of the sale

Commission Rate: the percentage or decimal value of the commission rate (e.g. 5% = 0.05)

The commission on a sale can be calculated by multiplying the total sale amount by the commission rate.

In this case, the commission on a 1,250 sale with a commission rate of 5% would be:

= 1,250 x 0.05

= 62.5

So the commission on the sale would be $62.5

It's also worth noting that commission rate is given as a decimal and not a percentage. 5% is 0.05 as decimal.

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The sum of the measures of the four interior angles of a quadrilateral is always 360°

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.

Given is, A quadrilateral is a polygon with four sides. Consider the quadrilateral and the dashed segment

If we draw one diagonal to quadrilateral we will get two triangles i.e. △ABC and △ACD and we know that sum of the angles of a triangle is 180°

Sum of angles of quadrilateral ABCD = sum of angles of △ABC + sum of the angles △ACD

= 180° + 180°

= 360°

If we take examples of a square or a rectangle, we know that they are also a quadrilateral and also their each angle is right angle, i.e. 90°

Therefore, the sum of their interior angles will = 90×4 = 360°

Hence, we can say that the sum of the measures of the four interior angles of a quadrilateral is always 360°

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Answer:

D.

Step-by-step explanation:

They are parallel would be the best explanation. AB and PQ are in a sense the same segment but PQ is AB translated.

Answer:

When solving an inequality:  you can add the same quantity to each side •you can subtract the same quantity from each side you can multiply or divide each side by the same positive quantity If you multiply or divide each side by a negative quantity, the inequality symbol must be reversed.

you can add subtract multiply and divide the quantity to each side

But if you’re doing any of those with a negative quantity, the inequality symbol must be reversed

3 x -8> 29

3 x -8 < 29

Answer:

standard form

= x⁶ + 53x⁵ + 2x⁴ -2

Step-by-step explanation:

the degree is 6.

leading coefficient is 1

this is called a polynomial.

it has 4 terms

Angle 1 and Angle 4 are alternate internal angles, Angle 1 also equals 51.Angles 1 and 2 of the rhombus are bisector by 51 and 2, respectively.

A parallelogram has a unique variation known as a rhombus. A rhombus has opposing sides that are parallel and opposing angles that are equal. A rhombus also has equal-length sides and diagonals that are at right angles to one another. The term "rhombus" can also refer to a diamond or rhombus. A rhombus has equal opposite angles. At a 90° angle, the diagonals split in half. 180 degrees is the sum of adjacent angles.

given

There is a line that passes through the parallel line; the alternate interior angles are 3 and 39.

The alternative interior angles are similar, hence Angle 3 = 39.

Since the upper left triangle is a triangle, angles 3, 4, and the center angle all add up to 180 degrees. The angle in the middle is 90 degrees. hence, we may locate angle 4.

angle 4=51.

Since Angle 1 and Angle 4 are alternate internal angles, Angle 1 also equals 51.Angles 1 and 2 of the rhombus are bisector by 51 and 2, respectively.

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The coordinates of the point P on the directed line segment that partitions the segment into a ratio of 2 to 3 is the ordered pair (3, 0).

In this scenario, we would use line ratio to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 3 to 2.

In Mathematics, line ratio can be used to determine the coordinates of the point P and this is modeled by this mathematical expression:

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Substituting the given parameters into the line ratio formula, we have;

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

P(x, y) = [(2(9) + 3(-1))/(2 + 3)],  [(2(6) + 3(-4))/(2 + 3)]

P(x, y) = [(18 - 3)/(5)],  [(12 - 12)/5]

P(x, y) = [15/5],  [0/5]

P(x, y) = [3, 0]

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Complete Question:

Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-1, -4), B(9, 6); to 3. The coordinates of P are?

Answer:

Step-by-step explanation:

We will check if 5/15 and 1/3 are in proportion or not by cross-multiplication.

5/15 = 1/3

5*3 = 15*1

15 = 15

as the left-hand side is equal to the right side. So, these fractions are in proportion.

Answer:

2n^2-8n-24

Step-by-step explanation:

Uhm i just did this one with one of my classmates like 2-3 months ago so it just came to mind.

Hope this helped tho! :)

A person can rent any of the vehicles shown in the table for a minimum of two to three days before it becomes more expensive for a week.

Algebra state that it is the study of the laws and symbols of mathematics as well as the manipulation of these symbols.

The rent of the small car for a week is $250 and for a day is $100. Then,

The maximum number of days that a car could be rented is,

= 250÷100

= 2.5 days

≅ 3 days

Then, for the medium car is,

= 290÷110

= 2.7 days

≅ 3 days

For the luxury car is,

= 325÷120

= 2.7 days

≅ 3 days

For Small van is,

= 350÷150

= 2.3 days

≅ 2 days

For Large van is,

= 390÷170

= 2.2 days

≅ 2 days

We can conclude from the above calculations that a person can rent a car for 2-3 days before it becomes more expensive for a week.

The complete question is -

For any of the vehicles listed in the table, how many days can you rent the vehicle before it would be less expensive to rent for the week?

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Step-by-step explanation:

2×4=8

8×2/3

8×2=16

16×3=48

ans = 48