Please help me solve this problem, and someone please clearly explain to me how to solve it.

1.) Use the value of the discriminant to determine if the given trinomials has 2 real solutions, 1 real solution, or no real solutions.
a. x2 − 4x − 7 = 0
b. 4r2 + 11r − 3 = 0
c. 3m2 + 7 = 0
d. t2 + 2t + 1 = 0​

Answer:

- 2, 64, 0

Step-by-step explanation:

f(- 3) ← x < 0 ⇒ f(- 3) = - 3 + 1 = - 2

f(8) ← x > 0 ⇒ f(8) = 8² = 64

f(0) → x = 0

f(0) = 0² = 0

Answer:

x^(-5)+4x+1

given f(x)=4x+1 and g(x)=x^(-5)

Step-by-step explanation:

f(x)=4x+1

g(x)=x^(-5)

(f+g)(x) means you are just going to do f(x)+g(x)

or (4x+1)+(x^(-5))

There are absolutely no like terms so it can't be simplified. We can use commutative and associative property to rearrange the expression.

x^(-5)+4x+1

ANSWER

[tex](f + g)(x) = \frac{4{x}^{6} \: + {x}^{5} + 1 }{ {x}^{5} } [/tex]

EXPLANATION

The given functions are:

[tex]f(x) = 4x + 1[/tex]

and

[tex]g(x) = {x}^{ - 5} [/tex]

We now want to find

[tex](f + g)(x)[/tex]

We use this property of Algebraic functions.

[tex](f + g)(x) = f(x) + g(x)[/tex]

We substitute the functions to get:

[tex](f + g)(x) = 4x + 1 + {x}^{ - 5} [/tex]

Writing as a positive index, we get:

[tex](f + g)(x) = 4x + 1 + \frac{1}{ {x}^{5} } [/tex]

The property we used to obtain the positive index is

[tex] {a}^{ - n} = \frac{1}{ {a}^{n}} [/tex]

We now collect LCD to get:

[tex](f + g)(x) = \frac{4x \cdot {x}^{5} \: + {x}^{5} + 1 }{ {x}^{5} } [/tex]

This simplifies to:

[tex](f + g)(x) = \frac{4{x}^{6} \: + {x}^{5} + 1 }{ {x}^{5} } [/tex]

Answer:

-8

Step-by-step explanation: I worked it out and I got -8 on a graphing calculator.

Answer: 13.2

Step-by-step explanation: First, turn the percent into a decimal by dividing it by 100.

22/100 = 0.22

Multiply the decimal by 60.

0.22 x 60 = 13.2

Final answer:

The expression 5÷7a is equivalent to 5a/7 when rewritten in simplest algebraic form. It represents multiplying 5 by the reciprocal of 7a. None of the provided answer options match this expression. Option. A

Explanation:

The expression 5÷7a can be rewritten as 5÷7 × a or 5/7a. This is because division by a number is the same as multiplying by its reciprocal. Thus, we take the reciprocal of 7a to be (1/7)a or a/7, multiply it by 5, giving us 5a/7. This is how we denote division within algebraic expressions and simplifies the equation.

If the question is looking for an equivalent single-term expression, none of the given options (5×7b, 7÷5b, 7×1/5c, 35d, 5×1/7) are correct, as they are all different in terms of algebraic structure and value. However, if you're looking for an equivalent expression in the simplest algebraic form, the equivalent expression for 5÷7a is simply 5a/7.

Answer:

SD(σ)=2.91548

Step-by-step explanation:

Definition:

Standard deviation (SD) measures the volatility or variability across a set of data. It is the measure of the spread of numbers in a data set from its mean value and can be represented using the sigma symbol (σ)

To find out SD you must know the value of Mean and Variance.

Mean=sum of values / N (number of values in set)

Mean=7+5+10+11+12/5

Mean=45/5

Mean=9

Variance=((n1- Mean)2 + ... nn- Mean)2) / N-1 (number of values in set - 1)

Variance=((7-9)^2 +(5-9)^2+(10-9)^2+(11-9)^2+(12-9)^2))/5-1

Variance=((-2)^2+(-4)^2+(1)^2+(2)^2+(3)^2)/4

Variance=(4+16+1+4+9)/4

Variance=34/4

Variance=8.5

Standard Deviation(σ)=√Variance

σ = √8.5

By taking the square root of √8.5 we get;

σ = 2.91548

Thus the value of Standard Deviation(σ)=2.91548....

Answer: f(g(x))=x and g(f(x)) = x

              f⁻¹(x) = g(x) YES ARE INVERSES

              f⁻¹(x) ≠ g(x) NOT INVERSES

Step-by-step explanation:

Inverse is when you swap the x's and y's and then solve for y.

If f⁻¹(x) = g(x), then they are inverses of each other.

Similarly, if g⁻¹(x) = f(x), they are inverses of each other.

NOTE: You can also use composition to determine if they are inverses  -->    If (fog)(x) = x, then they are inverses of each other.

[tex]f(x) = \dfrac{1}{x+4}-9\\\\\\\text{Swap the x's and y's. NOTE: f(x) is y}\\x=\dfrac{1}{y+4}-9\\\\\\\text{Add 9 to both sides}\\x+9=\dfrac{1}{y+4}\\\\\\\text{Flip the fractions}\\\dfrac{1}{x+9}=y+4\\\\\\\text{Subtract 4 from both sides}\\\dfrac{1}{x+9}-4=y\\\\\\\boxed{f^{-1}(x)=g(x)\text{ so f(x) and g(x) are inverses of each other}}[/tex]

[tex]f(x) = 3x+27\\\\\\\text{Swap the x's and y's NOTE f(x) is y}\\x=3y+27\\\\\\\text{Subtract 27 from both sides}\\x-27=3y\\\\\\\text{Divide everything by 3}\\\dfrac{1}{3}x-\dfrac{27}{3}=y\\\\\\\text{Simplify}\\\dfrac{1}{3}x-9=y\\\\\\\boxed{f^{-1}(x)\neq g(x)\text{ so f(x) and g(x) are NOT inverses of each other}}[/tex]

[tex]\bf x= \begin{cases} 6\\ 4 \end{cases}\implies \begin{cases} x=6\implies &x-6=0\\ x=4\implies &x-4=0 \end{cases} \\\\\\ (x-6)(x-4)=\stackrel{y}{0}\implies \stackrel{\mathbb{F~O~I~L}}{x^2-10x+24}=0\implies \stackrel{\textit{adding a common factor of 5}}{5(x^2-10x+24)=0} \\\\\\ 5x^2-50x+120=0\implies 5x^2-50x+120=y[/tex]

now, the common factor of 5 simply makes the parabola steeper, but the roots are the same, whilst the vertex of it changes

Final answer:

To write a quadratic equation given the roots and the leading coefficient, use the formula ax² + bx + c = 0, where the roots are the values of x when the equation equals zero, and the leading coefficient determines the value of a.

Explanation:

To write a quadratic equation given the roots and the leading coefficient, you can use the formula ax² + bx + c = 0. The roots of the quadratic equation are the values of x when the equation equals zero. The leading coefficient determines the value of a in the equation. In this case, the roots are 6 and 4, and the leading coefficient is 5.

Using the formula, we get: 5x² - (6+4)x + (6)(4) = 0.
Simplifying, we have 5x² - 10x + 24 = 0. This is the quadratic equation with the given roots and leading coefficient.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x^2+y^2=36\\x+y=6&\text{subtract y from both sides}\end{array}\right\\\left\{\begin{array}{ccc}x^2+y^2=36&(1)\\x=6-y&(2)\end{array}\right\qquad\text{substitute (2) to (1):}\\\\(6-y)^2+y^2=36\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\6^2-(2)(6)(y)+y^2+y^2=36\\36-12y+2y^2=36\qquad\text{subtract 36 from both sides}\\2y^2-12y=0\qquad\text{distributive}\\2y(y-6)=0\iff2y=0\ \vee\ y-6=0\\\\2y=0\qquad\text{divide both sides by 2}\\y=0\\\\y-6=0\qquad\text{add 6 to both sides}\\y=6[/tex]

[tex]\text{put the values of y to (2):}\\\\for\ y=0:\\x=6-0=6\\\\for\ y=6\\x=6-6=0[/tex]

Answer:

The answer is C. Angle with greatest measure

Step-by-step explanation:

In any triangle, there are two property that they always fulfill:

A classical example is in a right triangle: We know that the hypotenuse is the longest side, and also we know that the greatest angle is the right angle.

I have attached an image that shows the properties of the triangles.

Finally, the answer is C. Angle with the greatest measure.

Answer:

Angle with the greatest measure.

Step-by-step explanation:

Answer:

Lol I just took this text couple weeks ago. The answer is (1,1) Solve the system of equations by substitution.

3/8x + 1/3y = 17/24

x + 7y = 8

x = -7y + 8 and substituting it to the first equation

3/8x + 1/3y = 17/24

3/8(-7y + 8 )+ 1/3y = 17/24

Solving for the value of y = 1

And substituting y =1 to the second equation

X= 1

(1, 1)

Answer:

1,1

Step-by-step explanation:

Answer:

$4,500

Step-by-step explanation:

Given:

Price Bought: $3,900

Transportation: $200

Repair: 900

Total amount spent = 3,900 + 200 + 900 = $5,000

10% of amount spent = 10% x 5,000 = 0.1 x 5000 = $500 (= amount loss)

TV was sold at a 10% loss,

selling price = $5,000 - $500 = $4,500

Answer:

Rs.4500

Step-by-step explanation:

1.total cost of TV=3900+200+900

                           =5000

2. loss=10/100*5000

           =500

selling price of TV=5000-500

                              =Rs.4500

Final answer:

To calculate the perimeter of a square with a side length of 5/7 units, multiply the side length by 4 since all sides of a square are equal. The perimeter is 20/7 units.

Explanation:

The question asks, "What is the perimeter of a square with a side length of 5/7 units?" To find the perimeter of a square, we use the formula P = 4a, where P represents the perimeter and a is the length of one side of the square. Since all sides of a square are equal in length, if the side length is 5/7 units, the perimeter would be 4 times 5/7 units.

Performing the multiplication:

P = 4 × (5/7) units

P = (4 × 5) / 7 units

P = 20/7 units

Therefore, the perimeter of the square is 20/7 units.

it is 82.4

i hope you have a good day now

Final answer:

The volume of a sphere with a radius of 2.7 inches is calculated using the formula V = (4/3)πr³. After substituting the radius into the formula and calculating, the volume is approximately 82.5 cubic inches when rounded to the nearest tenth. None of the options provided match this value exactly.

Explanation:

To calculate the volume of a sphere with a radius of 2.7 inches, we use the formula for the volume of a sphere, which is V = (4/3)πr³. Plugging the radius into the formula gives:

V = (4/3)π(2.7 in)³

To find the volume, we perform the following calculations:

Calculate the radius cubed (2.7 in)³ = 19.683 in³.

Multiply by π (approximately 3.14159): 19.683 in³ × 3.14159 ≈ 61.8982 in³.

Multiply by 4/3: ≈ (4/3) × 61.8982 in³ ≈ 82.5309 in³.

Finally, round the volume to the nearest tenth: 82.5309 in³ rounds to 82.5 in³, which is not one of the options given. However, if we round to the nearest whole number, then 82.5 in³ would be rounded to 83 in³, which is also not one of the options. This indicates there may have been a mistake in the calculations or options provided.

None of the options given precisely match the calculated volume when rounded to the nearest tenth. However, the calculation we did indicates that the volume is approximately 82.5 cubic inches when we round to one decimal place. There may be an issue with the provided options or expected precision, so it's advisable to double-check the calculations and verify the choices provided for the answer.

Answer:

# The growth value of the function is 1/3 ⇒ 2nd

# f(x) shows exponential decay ⇒ 3rd

# The function is a stretched of the function [tex]f(x)=(\frac{1}{3}) ^{x}[/tex] ⇒ 4th

Step-by-step explanation:

* Lets explain the exponential function

- The form of the exponential function is f(x) = a b^x, where a ≠ 0,

  b > 0 , b ≠ 1, and x is any real number

- a is the initial value of f(x) ⇒ (when x = 0)

- b is the growth factor

- The exponent is x

- If the growth factor (b) is in between 1 and 0 then it is exponential

 decay

* Lets solve the problem

∵ [tex]f(x)=3(\frac{1}{3})^{x}[/tex]

- Lets find the initial value

∵ At the initial position x = 0

∴ [tex]f(0)=3(\frac{1}{3})^{0}=3(1)=3[/tex]

* The initial of f(x) is 3

∵ b = 1/3

∵ b is the growth factor of the function

* The growth value of the function is 1/3

∵ b = 1/3

∵ 0 < b < 1

∴ The function is exponential decay

* f(x) shows exponential decay

- A vertical stretching is the stretching of the graph away from the x-axis

- If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched

∵ [tex]f(x)=(\frac{1}{3})^{x}[/tex]

∵ Its parent function is [tex]f(x)=3(\frac{1}{3})^{x}[/tex]

∴ k = 3

∵ k > 1

∴ the function is stretched vertically

* The function is a stretched of the function [tex]f(x)=(\frac{1}{3})^{x}[/tex]

∴ The true statements are:

# The growth value of the function is 1/3

# f(x) shows exponential decay

# The function is a stretched of the function [tex]f(x)=(\frac{1}{3})^{x}[/tex]

You must remember that a polynomial is written like so...

ax^2 + bx + c

In this case...

a = 1

b = 3

c = -10

To factor you must find two numbers who both add up to b (3) AND multiply to c (-10)

-2 + 5 = 3

-2 * 5 = -10

so...

(x - 2)(x + 5)

To find the zero you must set each factor equal to zero and solve for for x like so...

x - 2 = 0

x = 2

x + 5 = 0

x = -5

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

x= -5 and x= 2

Step-by-step explanation:

[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})~\hspace{10em} slope = m\implies \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-4)=\cfrac{3}{5}(x-2)\implies y+4=\cfrac{3}{5}(x-2) \\\\\\ y+4=\cfrac{3}{5}x-\cfrac{6}{5}\implies y=\cfrac{3}{5}x-\cfrac{6}{5}-4\implies y=\cfrac{3}{5}x-\cfrac{26}{5}[/tex]

For this case we have the following expressions:

[tex]x \leq-2\\x \geq0[/tex]

So:

[tex]x \leq-2[/tex] Indicates all values less than or equal to -2.

That is, from -∞ to -2.

[tex]x \geq0[/tex] Indicates all values greater than or equal to 0.

That is, from 0 to ∞.

The "or" means that they do not intersect. So, the correct graph is option A.

Answer:

Option A

Answer:

Option A

Step-by-step explanation:

Edg 2020

Replace f(x) with y:

y = 5x-6

Swith the variables:

x = 5y -6

Now solve for y:

add 6 to each side:

x +6 = 5y

Divide both sides by 5:

y = (x+6)/5

Now replace y with the inverse function f^-1 (x):

f^-1(x) = (x+6)/5

Answer:

See below attachment

Step-by-step explanation:

A p E x

Answer

I assume you're talking about 6-7, so on the left lines, you already did it, you just regularly subtract the numbers, and then on the right lines, you round the first problem to the nearest ten, remember five and up, round up, so for question 6 the new number model would be 90-40=50. since 93 rounds down to 90 and 38 rounds up to 40. continue to do that and write the entire model AND answer on the line to the right. hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

Estimate means put your calculator in a drawer or under a pillow. You are not going to use it.

The question means round to the nearest 10 (as it says)

One

93 rounds to 90   (93 is only 3  away from 90)

38 rounds to 40   (38 is very close to 40. You are only 2 away).

90 - 40 = 50

If you answer 55, you should get it wrong. That's not estimating.

Two

67 rounds to 70

49 rounds to 50

70 - 50 = 20        18 is just too exact.

Three

75 is very nasty. My call would be that you can call it 70 or 80. It all depends on what you have been told about 5s. On Brainly, I think you round up. So 75 become 80

27 rounds to 30

80 - 30 = 50  

The last one is all yours.

Answer:

C. 3x^2 -13x + 7

Step-by-step explanation:

Lets start in the ones place:

    +3

 - (-4)

_______

    +7

Now go to the tens place:

   -5x

  -(8x)

________

  -13x

Lastly, go to the hundreds place:

   6x^2

  -(3x^2)

_________

   3x^2

So, the correct answer is "3x^2 -13x + 7", which is C.

I hope this helps! :)

Answer:

C) 3x squared - 13x + 7

Step-by-step explanation:

To subtract this problem you need to combine like terms

6x squared - 3x squared = 3x squared

-5x - 8x = -13

3 - -4 = 7

Since you combined the like terms put it back into an expression

3x squared - 13x + 7

Since the 13 is negative it becomes a subtraction sign in this expression.

The 7 is positive so it becomes an addition sign.

Answer:

(f+g)(x) = [tex]\sqrt{5x+7}+\sqrt{5x-7}[/tex]

Step-by-step explanation:

f(x) = [tex]\sqrt{5x+7}[/tex]

and g(x) = [tex]\sqrt{5x-7}[/tex]

We need to find (f+g)(x)

(f+g)(x) = f(x) + g(x)

(f+g)(x) = [tex]\sqrt{5x+7}+\sqrt{5x-7}[/tex]

It can't be further solved so,

(f+g)(x) = [tex]\sqrt{5x+7}+\sqrt{5x-7}[/tex]

Answer:

6a^3 + 22a^2 - 6a - 10

Step-by-step explanation:

(3a + 5)(2a^2 + 4a - 2)

distribute 3a

6a^3 + 12a^2 - 6a

distribute 5

10a^2 + 20a - 10

combine like terms/simpify

6a^3 + 22a^2 - 6a - 10

Answer:

6a^3 + 22a^2 +14a-10

Step-by-step explanation:

Hi, to solve this you have to apply the distributive porperty:

So:

[tex](3a +5)x ( 2a^{2} +4a -2)\\6a ^{3} +12a^{2} -6a + 10a^{2} +20a^{2} -10\\\\[/tex]

Then, combine like terms and solve using addition or subtraction:

[tex]6a^{3} +12a^{2} +10a^{2} +20a-6a-10\\6a^{3} +22a^{2} +12a-10[/tex]

In conclusion the product is 6a^3 + 22a^2 +14a-10.

Feel free to ask for more if it´s necessary or if you did not understand something.

Answer:

≈ 35 ft²

Step-by-step explanation:

The area (A) of a regular pentagon is

A = [tex]\frac{1}{2}[/tex] × perimeter × apothem

perimeter = 5 × 4.5 = 22.5 ft, thus

A = 0.5 × 22.5 × 3.1 = 34.875 ≈ 35 ft²

The area of a regular pentagon with an apothem of 3.1ft and a side length of 4.5ft is 35 ft².

A pentagon is considered to be irregular when all five sides are not equal in length. However, sometimes two or three sides of a pentagon might have equal sides but it is still considered as irregular.

The area (A) of a regular pentagon is

A =  perimeter × apothem

perimeter = 5 × 4.5 = 22.5 ft, thus

A = 0.5 × 22.5 × 3.1 = 34.875 ≈ 35 ft²

A regular pentagon has all equal sides and angles. In a regular pentagon, its interior angles are 108 degrees and its exterior angles are 72 degrees.

The angles of a pentagon add up to 540 degrees. In an irregular pentagon, pentagon sides and angles can be different sizes.

To learn more about pentagon, refer

https://brainly.com/question/11512679

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For this case we must find the product of [tex](3x + 5) (x + 4)[/tex]

By definition, the distributive property states that:

[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]

Then, according to the expression we have:

[tex]3x ^ 2 + 12x + 5x + 20 =\\3x ^ 2 + 17x + 20[/tex]

Answer:

[tex]3x ^ 2 + 17x + 20[/tex]

Option C

Answer:

C

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

3x(x + 4) + 5(x + 4) ← distribute both parenthesis

= 3x² + 12x + 5x + 20 ← collect like terms

= 3x² + 17x + 20

The Measure of angle c is 144 because line segment mn is a transversal and angles a and b are corresponding angles. option B) is correct choice.

Corresponding angles are angles that are in the same position relative to the transversal and on opposite sides of it. In this case, angles a and b are both alternate interior angles, so they are corresponding angles.

Alternate interior angles are angles that are on opposite sides of the transversal and inside the parallel lines.

Since corresponding angles are congruent, we know that the measure of angle a is equal to the measure of angle b. We are also given that the measure of angle a is 100 degrees. Therefore, the measure of angle b is also 100 degrees.

The sum of the measures of the angles in a triangle is 180 degrees. Therefore, the measure of angle c is equal to 180 degrees - 100 degrees - 100 degrees = 144 degrees.

The other options are incorrect:

Option A: The measure of angle c cannot be 36 degrees because angle b and angle c are vertical angles, and vertical angles are always congruent.

Option B: The measure of angle c cannot be 144 degrees because of the properties of the exterior angles of a triangle. The exterior angle of a triangle is equal to the sum of the two remote interior angles, and the two remote interior angles in this case are angles a and b, which have a combined measure of 200 degrees. Therefore, the measure of angle c must be less than 144 degrees.

Option C: The measure of angle c cannot be 44 degrees because line segment MO is not a transversal. A transversal is a line that intersects two parallel lines. In this case, line segment NO is the transversal.

Option D: The measure of angle c cannot be 100 degrees because angles m and c are not alternate interior angles. Alternate interior angles are angles that are on opposite sides of the transversal and inside the parallel lines. In this case, angle m is an alternate interior angle, but angle c is an exterior angle.

Therefore, the best answer is The measure of angle c is 144 because line segment mn is a transversal and angles a and b are corresponding angles. option B) is correct choice.

For more such questions on Measure of angle

https://brainly.com/question/30846319

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Answer:

−x^2+7x−5

Step-by-step explanation:

---- times this by 1 (3x^2+4x−3) −(4x^2-3x+2) ---- times this by - 1

3x^2+4x−3−4x^2+3x−2

3x^2+4x−3−4x^2+3x−2 - collect like terms

(3x^2+−4x^2)+(4x+3x)+(−3+−2) - solve it

(3x^2+−4x^2)= −x^2

(4x+3x) = 7x

(−3+−2) = −5

−x^2 + 7x−5

On simplifying the given equation  [tex](3x^2+4x-3)-(4x^2-3x+2)[/tex] we get [tex]-x^2+7x-5[/tex]

Given: [tex](3x^2+4x-3)-(4x^2-3x+2)[/tex]

To find: simplify

We have been given an equation and for solving it we first need to open the parenthesis

[tex]3x^2+4x-3-4x^2+3x-2[/tex]

Now we will group terms on which addition or subtraction can be performed

[tex]3x^2-4x^2 +4x+3x-3-2\\= -x^2+7x-5[/tex]

Answer:

a number subtracted by four equals twelve and five tenths

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

Possible outcomes in a fair sided die 1,2,3,4,5,6 = 6 possible outcomes

Odd numbers = 1,3,5 = 3 odd numbers

Probability of rolling an odd number = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

Total number of rolls = 64

expected number of odd number rolls in 64 roll,

= [tex]\frac{1}{2}[/tex] x 64 = 32

Y=3x+8

Step-by-step explanation:

The slope is 3

Slope Intercept form is Y=Mx=b

We want to write the given equation in the form y = mx + b.

y-5 = 3(x+1)

y - 5 = 3x + 3

y = 3x + 3 + 5

y = 3x + 8

Done!