Approximate the intervals where each function is increasing and decreasing.

Answer:

[tex]x=-1,\frac{5}{7}[/tex]

Step-by-step explanation:

1) Split the second term in [tex]7{x}^{2}+2x-5[/tex] into two terms.

1 - Multiply the coefficient of the first term by the constant term.

[tex]7\times -5=-35[/tex]

2 - Ask: Which two numbers add up to 2 and multiply to -35?

7 and -5.

3 - Split 2x as the sum of 7x and -5x.

[tex]7x^2+7x-5x-5[/tex]

2)  Factor out common terms in the first two terms, then in the last two terms.

[tex]7x(x+1)-5(x+1)=0[/tex]

3) Factor out the common term x+1.

[tex](x+1)(7x-5)=0[/tex]

4) Solve for x.

1 - Ask: When will (x+1)(7x-5) equal zero?

When x + 1 0 or 7x-5=0

2 - Solve each of the 2 equations above.

[tex]x=-1,\frac{5}{7}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What are the quadratic formulas?}[/tex]

[tex]\bullet\rm{\ \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]

[tex]\bullet\rm{\ ax^2 + bx + c = 0}[/tex]

[tex]\huge\textbf{What are we solving for?}[/tex]

[tex]\rm{7x^2 + 2x - 5 = 0}[/tex]

[tex]\huge\textbf{What do we have to do?}[/tex]

[tex]\rm{7x^2 + 2x - 5 = 0}[/tex]

[tex]\huge\textbf{Factor the LEFT side of the given}\\\\\huge\textbf{equation:}[/tex]

[tex]\rm{(7x - 5)(x + 1) = 0}[/tex]

[tex]\rm{(7x - 5) \times (x + 1) = 0}[/tex]

[tex]\huge\textbf{Set 0 to the factors:}[/tex]

[tex]\rm{7x - 5 = 0\ or\ x + 1 = 0}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{x = \dfrac{5}{7}\ or\ x = -1}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{\mathsf x = \dfrac{5}{7}\ or\ \mathsf{x} = -1}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The slope of diagonal PS is  -1 and the slope of diagonal QR is 1 based on the information about the coordinate plane.

Step 1: Calculate the slope of the diagonals.

The slope of diagonal PS is  -1

The slope of diagonal QR is 1

Step 2: Calculate the midpoint of the diagonals.  

The midpoint of PS is (2,2)

The midpoint of QR is  (2,2)

The diagonals of the square are perpendicular bisectors because the diagonals are perpendicular and share the same midpoint

Learn more about coordinate plane on:

https://brainly.com/question/2644832

#SPJ1

Answer:

1. The slope of diagonal PS is -1.

2. The slope of diagonal QR is 1.

3. The midpoint of PS is (2,2).

4. The midpoint of QR is (2,2).

5. The diagonals of the square are perpendicular bisectors because the diagonals are perpendicular and share the same midpoint.

Step-by-step explanation: I just did it on edge 2023. Hope this helps!

Sample is the 3 selected customers; And population is all customers

According to the statement

we have given that a shopkeeper asks 3 customers to taste the chocolate icecream.

And we have to identify the sample and population.

So, A definition of sample is that a

A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample.

And a Population is defines as the is a discrete group of people, animals or things that can be identified by at least one common characteristic for the purposes of data collection and analysis.

So, according to definition Sample is the 3 selected customers; And population is all customers.

Learn more about Sample here https://brainly.com/question/11073037

#SPJ4

Answer:

He can type 90 words in 3 minutes.

Step-by-step explanation:

We know how many words he can type per minute already. So now, to find how many words he can type in 30 minutes, simply multiply 3 by 30.

[tex]3 \times 30=90[/tex]

So 90 is our answer.

Answer: 15x-2

Step-by-step explanation: ?

Answer:

15x - 10

Step-by-step explanation:

[tex]5(3x-2)=5(3x)+5(-2)=15x-10[/tex]

Hope this helps

Answer:

m = -4

Step-by-step explanation:

We are given that a line intersects the points (-2, 9) and (3, -11).

We want to write the slope of this line.

The slope (m) can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.

Even though we have everything we need to calculate the slope, let's label the values of the points to avoid any confusion & mistakes.

[tex]x_1=-2\\y_1=9\\x_2=3\\y_2=-11[/tex]

Now substitute these values into the formula (remember that the formula has subtraction).

m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{-11-9}{3--2}[/tex]

Simplify.

m=[tex]\frac{-11-9}{3+2}[/tex]

Subtract the values on top.

m=[tex]\frac{-20}{3+2}[/tex]

Now add the values on the bottom together.

m=[tex]\frac{-20}{5}[/tex]

Now divide -20 by 5.

m = -4

The length around the circular edge of the plate is 37.68 inches

The circumference of a circle can be solved as follows:

The ant is standing at the centre of a perfectly circular plate and it walks to the edge of the plate .

The centre of the plate to the edges is 6 inches. Therefore, the radius of the circular plate is 6 inches.

Hence, the distance around the edge of the plate is the circumference of the plate.

Therefore,

circumference of the circular plate = 2πr

circumference of the circular plate = 2 × π × 6

circumference of the circular plate = 12π

circumference of the circular plate = 12 × 3.14

circumference of the circular plate = 37.68 inches

learn more on circle here: brainly.com/question/9330354

#SPJ1

The exponential  equation that matches the coordinate is 3(2)^x while the linear equation is y = 6x

The standard exponential equation is expressed as y= ab^x

where

a is the base

x is the exponent

Given the coordinates (2, 12) and (4, 48)

12 = ab^2

48 = ab^4

Find the ratio

4 = b^2

b = 2

Sice ab^2 = 12

4a = 12

a = 3

The exponential  equation that matches the coordinate is 3(2)^x

For the linear equation

The standard form is y = mx + b

m is the slope = 48-12/4-2
Slope = 12/2

Slope = 6

For the y-intercept

12 = 6(2) + b

b = 0

Hence the required linear equation is. y = 6x

Learn more on exponential and linear equation here: https://brainly.com/question/2456547

#SPJ1

Answer:

y>4x+1

Step-by-step explanation:

We got two simple steps for this question:

1.Find the equation(y=mx+b):

I want to test these two points on my formula:

(0, 1), (–1, –3)

[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{1 - ( - 3)}{0 - ( - 1)} = \frac{4}{1} = 4[/tex]

so we just calculated our m and now it time for b

[tex]y = 4x + b = = = > 1 = 4(0) + b = = = > b = 1[/tex]

So your criterion is y=4x+1

2.

we are looking for ys greater than xs so your answer is gonna be y>4x+1

a. Area of A = 20 ft²

Area of B = 16 ft²

Area of C = 12 ft²

Area of A = 24 ft²

b. The surface area of the triangular prism = 96 ft².

The surface area of the triangular prism given in the diagram = area of A + B + C + D.

a.

Area of A (rectangle) = (length)(width) = (10)(2) = 20 ft²

Area of B (rectangle) = (length)(width) = (8)(2) = 16 ft²

Area of C (rectangle) = (length)(width) = (6)(2) = 12 ft²

Area of A (rectangle) = 1/2(base)(height) = 1/2(6)(8) = 24 ft²

b. The surface area of the triangular prism = 20 + 16 + 12 + 2(24) = 96 ft².

Learn more about the surface area of triangular prism on:

https://brainly.com/question/16147227

#SPJ1

The probability of getting someone in the 22-29 age bracket or someone who agreed to respond is 0.96.

The rate of possible outcomes to the total outcomes is said to be the probability.

P(E) = n(E)/n(S)

E - event and S -sample space

we have,

P(A or B) = P(A) + P(B) - P(A and B)

It is given that,

Pollsters are concerned about declining levels of cooperation among persons contacted in surveys.

The data is listed below:

(Age group)                Response - agreed         Response - refused   Total

18-21                            76                                     14                                 90

22-29                          240                                   23                                263

Total                            316                                    37                                353

So, consider the required events

Age group (22-29) as A and someone who agreed to respond as B

Thus, the probabilities are calculated as below:

P(A) = n(A)/n(S) = 263/353

P(B) = n(B)/n(S) = 316/353

P(A and B) = n(A and B)/n(S) = 240/353

Substituting all these in the formula we get,

P(A or B) = P(A) + P(B) - P(A and B)

               = 263/353 + 316/353 - 240/353

               = 339/353

               = 0.96

Therefore, the required probability is 0.96.

Refer similar probability problem here:

https://brainly.com/question/21329462

#SPJ4

The probability of making a type i error is also α = 0.05 or 5% of error.

For the given question,

A Type I error occurs when a significance test results in the rejection of a true null hypothesis. By one common convention, if the probability value is below 0.05, then the null hypothesis is rejected.

The null hypothesis assumes no cause and effect relationship between the tested item and the stimuli applied during the test. The probability of making a type I error is represented by the alpha level (α), which is the p-value below which you reject the null hypothesis.

Thus, If a hypothesis is tested at the α=0.05 level of significance, then the probability of making a type i error is also α=0.05 or 5% of error.

Hence we can conclude that the probability of making a type i error is also α = 0.05 or 5% of error.

Learn more about type I error here

https://brainly.com/question/13980658

#SPJ4

Answer: Yes, there is

Step-by-step explanation:

Answer:

23/75

Step-by-step explanation:

8/15 + x = 21/25

x = 21/25 - 8/15

now we need to bring both fractions to the same denominator (bottom part), so that we can do the subtraction.

what is the least common multiple (LCM) of 25 and 15 ? that will be the common denominator.

I usually use the prime factor factorization of the involved numbers.

15 : 3, 5 (15 = 3×5, there are no smaller prime factors)

25 : 5, 5 (25 = 5×5, there are no smaller prime factors)

the LCM is the combination of the longest chains of each prime factor :

3×5×5 = 75

so, we bring both fractions to 75 denominators.

how many 1/75th are 1/25 ? as 25×3 = 75, we have 3/3 × 1/25 = 3/75 (= 1/25).

so,

21/25 = 21×3/75 = 63/75

how many 1/75th are 1/15 ? as 15×5 = 75, we have 5/5 × 1/15 = 5/75 (= 1/15).

so,

8/15 = 8×5/75 = 40/75

remember, we have to multiply the numerator and the denominator by the same value to keep the original value of the fraction unchanged.

and now our equation looks like

x = 63/75 - 40/75 = 23/75

Answer:

60 degrees

Step-by-step explanation:

The sum of the interior angles of a triangle are 180.  The bottom triangle give you two of the angle measurements (43 and 35)  Take 180 - 43 -35 = 102.  Angle E is 102.  Vertical angles are congruent so that mean that we can use that to find angle a.  Again, the sum of the interior angles adds up to 180.  180 - 102 - 18 gives us the measurement of angle a (60)

The sum of the lengths of two legs of the 30°-60°-90° right triangle is 6.69 centimeters. Using the ratio of sides for the 30°-60°-90° triangle, the sum is calculated.

The ratio for the 30°-60°-90° triangle is 1:√3:2 or x:x√3:2x

where x corresponds to the length opposite the 30° angle and x√3 is opposite of the 60° angle and 2x is opposite to the 90° angle.

It is given that the triangle is a right triangle with angles 30°-60°-90°

For such a triangle, the ratio of side lengths is x: x[tex]\sqrt{3}[/tex]:2x

we have the length of the hypotenuse is [tex]2\sqrt{6}[/tex]

So, 2x = [tex]2\sqrt{6}[/tex]

⇒ x = [tex]\sqrt{6}[/tex]

So,

the other length of the other leg is x√3 = √6 × √3 = 3 √2

Then, the sum of these two legs = √6 + 3√2 = 6.69 centimeters.

Learn more about the ratio of sides of a 30°-60°-90° triangle here:

https://brainly.com/question/6695000

#SPJ4

Answer:

{x | x > –5}

{x | x > –3}

{x | x > 3}

{x | x > 5}

Step-by-step explanation:

The perimeter of the contest area on the judo mat will be 32 meters.

For a square with a side length of a unit, we get:

Perimeter of the square = 4a unit

The side length of square is 8 m.

Then the perimeter of the contest area on the judo mat will be

P = 4 x 8

P = 32 m

More about the perimeter of the square link is given below.

https://brainly.com/question/11495285

#SPJ2

A significant problem is her sample will not be representative for her survey when she needed a large number of responses for her survey about taste preferences so she chose to do an internet survey.

what is internet survey ?

An Internet survey is a structured questionnaire that your target audience fills out over the internet, typically by filling out a form. The length and format of online surveys can vary. The data is saved in a database, and the survey tool usually includes some level of data analysis in addition to review by a trained expert.

Survey Advantages:

Unlike traditional surveys, internet surveys allow businesses to collect information from a large number of people at a low cost. When you conduct an internet survey, you will have the opportunity to learn:

Who are your customers?

What your users want to achieve?

What information are your users looking for?

Learn more about internet survey here:

https://brainly.com/question/28046490

#SPJ4

The coordinates of triangle RST after it is translated four units right and three units up are (0, 5), (7, 8) and (0, -1)

From the figure, the coordinates of the triangle RST are:

R = (-4, 2)

S = (3, 5)

T = (-4, -4)

The rule of translation is given as:

This is represented as:

(x, y) = (x + 4, y + 3)

So, we have:

R' = (-4 + 4, 2 + 3) = (0, 5)

S' = (3 + 4, 5 + 3) = (7, 8)

T = (-4 + 4, -4 + 3) = (0, -1)

Hence, the coordinates of triangle RST after it is translated four units right and three units up are (0, 5), (7, 8) and (0, -1)

Read more about transformation at:

https://brainly.com/question/8797028

#SPJ1

The measure of angle CKB (m ∠CKB) is 144°

From the question, we are to determine the measure of angle CKB (m ∠CKB)

First, we will determine the value of x

From the given information,

m ∠KAE = 3x

m ∠KCD = 2x

In the diagram,

m ∠KCD = m ∠AKE (Alternate angles)

∴ m ∠AKE = 2x

Also,

m ∠KAE + m ∠AKE + m ∠AEK = 180° (Sum of angles in a triangle)

3x + 2x + 90° = 180°

5x = 180° - 90°

5x = 90°

x = 90°/5

x = 18°

But,

m ∠CKB = 180° - m ∠AKE (Sum of angles on a line segment)

m ∠CKB = 180° - 2x

m ∠CKB = 180° - 2(18°)

m ∠CKB = 180° - 36°

m ∠CKB = 144°

Hence, the measure of angle CKB (m ∠CKB) is 144°

Learn more on Calculating measure of angles here: https://brainly.com/question/18359073

#SPJ1

The triangle drawn on a grid is in the image attached and the complete procedure for the construction of the triangle is summarized in the explanation.

In this question we are asked to draw a triangle on a Cartesian plane. The procedure is summarized below:

Lastly, we present the result of this method in the image attached below.

To learn more on triangles: https://brainly.com/question/2773823

#SPJ1

A distribution of probabilities for random outcomes of bivariate or dichotomous random variables is called (A) binomial probability distribution.

As the description itself says, binomial probability distribution refers to a distribution of probabilities for random outcomes of bivariate or dichotomous random variables.

Therefore, a distribution of probabilities for random outcomes of bivariate or dichotomous random variables is called (A) binomial probability distribution.

Know more about binomial probability distribution here:

https://brainly.com/question/9325204

#SPJ4

Complete question:

A distribution of probabilities for random outcomes of bivariate or dichotomous random variables is called a ______.

Group of answer choices

(A) binomial probability distribution

(B) distribution of expected values

(C) random variable distribution

(D) mathematical expectation

The values of a and b which make the equation true are; a = 3 and b = 4 respectively.

From the question; the expression given is;

[tex]\sqrt{648} = \sqrt{2^{a} * 3^{b} }[/tex]

In essence; we have;

648 = 2^a × 3^b

By expression of of 648 as the product of its lowest factors; we have;

648 = 2 × 2 × 2 × 3 × 3 × 3 × 3.

In which case; we have;

648 = 2³ × 3⁴

Ultimately, the values of a and b which make the equation true are 3 and 4 respectively.

Learn more about indices

brainly.com/question/25969946

#SPJ4

The complete question is -

What values of a and b make the equation true? StartRoot 648 EndRoot = StartRoot 2 Superscript a Baseline times 3 Superscript b Baseline EndRoot a = 3, b = 2 a = 2, b = 3 a = 3, b = 4 a = 4, b = 3

Answer:

49

Step-by-step explanation:

[tex]3^{2} *5+4[/tex]

= [tex]9*5+4[/tex]        Simplify the exponents.

= [tex]45+4[/tex]           Multiplication.

= 49                Addition.

Answer:

49

Step-by-step explanation:

1. Whenever there is an exponent, we solve that first. 3^2 is 9.

2. In an equation, multiplication, and division is first, and since there is no division in the equation, we do the multiplication first. 9 x 5 is 45.

3. We finish by adding 4 to 45, which is 49.

The statement 6.05 can be read as "six and five-hundredths" is true and 11.8 can be read as "eleven and eight tens" is false

6.05

6 = ones

0 = tenths

5 = Hundredth

6.05 = six and five-hundredths

11.8

1 = Tens

1 = Ones

8 = tenths

11.8 = eleven and eight tenths

Learn more about decimal number:

https://brainly.com/question/1827193

#SPJ1

Answer:15000

Step-by-step explanation:50,000 x 0.12=6,000 X 2=12,000

6000 divided by 2= 3,000

12 + 12=24+6=30

The value of the expression 9w + 5x when w= 5 and x =9 is 90

9w + 5x

When

w = 5 and x = 9

9w + 5x

= 9(5) + 5(9)

= 45 + 45

= 90

Complete question:

What is the value of the expression below when w = 5 and x = 9? 9w + 5x

Learn more about algebraic expression:

https://brainly.com/question/4344214

#SPJ1

Answer:

D. (4,0) and (-4,0)

C. there is one discontinuity at x=3

Step-by-step explanation:

Roots can be found by setting f(x)=0:

f(x)=(x^2-16)/(x^2-2x-3)

0=(x^2-16)/(x^2-2x-3), multiply both sides by x^2-2x-3 to get rid of the denominator

0=x^2-16, use difference of squares to factor it

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

x=4,-4

Therefore the roots are (4,0) and (-4,0)

Discontinuities are when f(x) is undefined, and f(x) is undefined when something is divided by 0

Set the denominator equal to 0:

0=x^2-6x+9, use the form a^2 - 2ab + b^2 to factor

0=(x-3)^2

x=3

Therefore, there is a discontinuity at x=3