Select all the correct answers.
Michael is graphing the parabola represented by this equation.
y = -(x - 3)² - 1
Which features should he include in his graph?

The performance of a thermocouple is displayed in the scatterplot is

Explanatory variable: Temperature

Response variable: Voltage

Given that,

The performance of a thermocouple is displayed in the scatterplot below.

We have to find which of the following choices accurately identifies the explanatory and response variables for the scatterplot.

We know that,

Dots are used to indicate the values for two different numerical variables in a scatter plot (also known as a scatter chart or scatter graph). The positions of each dot on the horizontal and vertical axes represent the values of a single data point. To see how different variables relate to one another, utilize scatter plots.

Explanatory variable: Temperature

Response variable: Voltage

So, we can see the scatterplot in the picture.

Therefore, Explanatory variable: Temperature

Response variable: Voltage when the performance of a thermocouple is displayed in the scatterplot

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Answer:

Explanatory variable: Temperature

Response variable: Voltage

Step-by-step explanation:

Got it right on the test.

Answer:

yellow

Step-by-step explanation:

i can only see one line, and infinitely many points are on it

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Answer:

[tex]5\sqrt{p} ^{11}[/tex]

Answer:

Step-by-step explanation:

The hypotenuses(x) of the triangle whose legs are 12 cm and 16 cm is 20 cm.

As we know that in a right angled triangle there are base, perpendicular and hypotenuse. a hypotenuse is the longest side of a right triangle. In other words, the side opposite to the right angle is called the hypotenuse.

Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

By Pythagoras theorem, hypotenuse (x)  = √(a² + b²)

                                                                        =  √(16² + 12²)

                                                                        = 20 cm

An expression which can be used to determine the total distance in miles that Aisha walked over the 3 days is: C. 3 × 3/4.

In Science, distance can be defined as the amount of ground that is covered (travelled) by a physical object over a particular period of time and speed, irrespective of its direction, starting point or ending point.

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities.

From the information provided, we know that Aisha walked three (3) days in a row and three (3) miles out of four (4) miles. Therefore, a mathematical expression that represents the total distance in miles that she walked over the three (3) days is given by;

Total distance = 3/4 + 3/4 + 3/4

Total distance = 3 × 3/4

Total distance = 9/4 or 2.25 miles.

In conclusion, Aisha walked a total distance of 9/4 miles or 2.25 miles over the three (3) days.

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Option a) The similar triangles are ⇒ ΔADE ≅ ΔABC

Option b) ∠ADE = ∠ABC

According to the figure given in the question,

We can observe that there are two right-angled triangles present and we have to derive the similarities between them

Let one triangle be = ΔADE

Another triangle be = ΔABC

Let us consider the angle arc at point A,

We can conclude that ⇒ ∠BAC = ∠DAE ( according to the property of similar angles )

⇒ ∠ADE = ∠ABC ( by the similar 90° angles )

and both angles are making a total of 180°

So, from the above expressions, we can say that,

⇒ ∠AED = 180° - ∠A - ∠ABC

⇒ ∠ACB = 180° - ∠A - ∠ABC

Hence, ∠AED = ACB ⇒ ΔADE ≅ ΔABC

Therefore,

Option a) The similar triangles are ⇒ ΔADE ≅ ΔABC

Option b) ∠ADE = ∠ABC

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A polynomial function is a mathematical function defined by an expression that is a sum of terms, each of which is a product of a constant and a non-negative integer power of a variable. The term "polynomial" comes from the Greek word "polys," which means "many," and "nomos," which means "terms." Polynomial functions are distinguished by the degree of their highest-degree term, which is the largest exponent of the variable. For example, the polynomial function f(x) = x3 + 2x2 + x - 1 has a degree of 3 because the highest-degree term is x3.

Out of the four given options, only the functions f(x) = x3 + 2x2 + x - 1 and f(x) = x3 +1 are polynomial functions. The other two options, y = -2x3 + 5x – 4 - 4 and f(x) = V2x3 + 5, are not polynomial functions because they contain terms that are not of the form "constant times a non-negative integer power of a variable." The function y = -2x3 + 5x – 4 - 4 contains the term -4, which is not a product of a constant and a non-negative integer power of a variable, and the function f(x) = V2x3 + 5 contains the term V2x3, which is not a product of a constant and a non-negative integer power of a variable. Therefore, the correct answer is A and D.

The best estimate to get the  total number of times to get a "3" will be 24 times.

This is an expression that simply refers to mathematical statements that have at least two terms which are related by an operator and contain either numbers, variables

In this case, Jimm tossed a die several times and he got the number "3" on 8 of the tosses.

Therefore, when there are 64 tosses, the estimate will be:

= 3/8 × 64

= 3 × 8

= 24

The number of times is 24.

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Answer:

Matthew has 24 inches of green ribbon and 3/4 inch of yellow ribbon. How much ribbon does he have in all?

Kiki had 24 marbles. She put 3/4 of the marbles in a jar. How many marbles did she put in the jar?

There were 24 questions on a test. Three-fourths of the questions were science questions. How many questions were science questions?

Aisha baked 24 muffins. She gave 3/4 of the muffins to her friends. How many muffins does she have left?

Step-by-step explanation:

Answer:

Jordan had 18 coins. Two-thirds of the coins were dimes. How many coins were dimes?

Min had 18 quarters. He used 2/3 of the quarters to play arcade games. How many quarters did Min use?

Step - by - step explanation

2/3 × 18

Checking all options

Sarah mixed 18 ounces of orange juice with 23 ounce of pineapple juice. How many ounces of juice did she have in all?

Ounces of orange juice = 18

Ounces of pineapple juice = 23

Total ounces of juice = 18 + 23

= 41 ounces

A container held 18 ounces of water. Two-thirds of the water leaked out of the container. How many ounces of water were left in the container?

Total water in the container = 18

Water leaked out = 2/3

Ounces of water left = 18 - 2/3(18)

= 18 - 36/3

= 18 - 12

= 6

Jordan had 18 coins. Two-thirds of the coins were dimes. How many coins were dimes?

Total Number of coins = 18

Dimes = 2/3 of 18

Number of dimes = 2/3 × 18

= 36 / 3

= 12

Min had 18 quarters. He used 2/3 of the quarters to play arcade games. How many quarters did Min use?

Total quarters = 18

Quarters used for game = 2/3 × 18

= 2/3 × 18

= 36 / 3

= 12

The x-intercept of the function f is greater than the x-intercept of function g is the correct statement.

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

Setting y = 0 will provide the x-value at which the line crosses the x-axis, allowing us to find the x-intercept

Function g(x) is defined as:

g(x)=2+[tex]\sqrt[3]{3x+1}[/tex]

and f(x)=0

To find x-intercept let g(x)=0

So

2+[tex]\sqrt[3]{3x+1}[/tex]=0

[tex]\sqrt[3]{3x+1}[/tex]=-2

Taking cube on both sides we get

3x+1= -8

3x=-9

x=-3

The x-intercept of g(x) + -3, which is less than the x-intercept of function f(x), hence, the correct statement is:

The x-intercept of the function f is greater than the x-intercept of function g.

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the percent increase in enrollment, and round to the nearest percent is 40%

Given that number of students enrolled in 2010= 2000

Given that number of students enrolled in 2018 = 2800

2800is more than 2000 so that means number of students enrollment is increasing.

increase = 2800-2000= 800

Percent increase is given by formula:

% increase = 800/2000*100= 40

which is approx 40%.

Hence final answer is that enrollment increases by 40%

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Answer:

7,2,15

Step-by-step explanation:

In general, to find rational numbers that satisfy a given set of conditions, it is often helpful to first write an equation that relates the numbers to each other.

The three rational numbers are 7, 2 and 15

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

First Number= x

Second Number= x- 5

Third Number = 2x+ 1

so, the product of the three number be 210

x(x-5 )(2x+ 1)= 210

(x² -5x )(2x+ 1)= 210

2x³ + x² - 10x² - 5x= 210

2x³ -9x² -5x -210=0

On solving the equation we get only one real value 7 and other values are imaginary.

Then, the number are

x= 7

2-x-5 = 2

2x+1 = 15

Hence, the three rational numbers are 7, 2 and 15.

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Using the values provided and a derivative of the cone's volume formula, the result is 0.059 feet per minute.

In mathematics, the rate at which a function changes in relation to a variable.

A cone is a three-dimensional geometric structure that has a smooth transition from a flat base that is typically circular to the point at the top, which is also referred to as the apex or vertex.

The formula for cone volume is:

V=πr2h/3

yields the formula for cone volume:

dv/dt = 2r * h/3 * dr/dt dV/dt = 3 r=2 h=12

dr/dt = 0.059 feet per minute.

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x ≥ -26 / (6a - 15)  where a >5/2.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other.

Given a equation, (3ax + 2)/ 3  -  (5x / 2) ≥  -8 where a > 5/2

solving for x in terms of a

ax + 2/3  - 5x/2  ≥ -8

x(6a - 15 )  ≥ -26

x ≥ -26 / (6a - 15)

since a is greater than 5/2 let a be 3 than the value of x ≥ -26/3.

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Answer:

8

Step-by-step explanation:

40:20

x:4

20/4 = 5

40/5 = 8

Answer:

Step-by-step explanation:

same as the last one,  hope you are getting these better now.

minor angle (interior angle)  J is the same as angle  t, b/c of the red marks.

180 = 141 = ∠j

39 = ∠j

t = 39

then find s

180 = 2*t +s

180 = 2*39 +s

180 =78 +s

180-78 = s

102 = s

got it better now?

Answer:

1. Step by step explanation:- Since 120$ is obtained by reducing the price by 30% that is subtracting ORIGINAL COST from its 30%.

In order to obtain the Cost Price we shall add back the 30% to 120$ to obtain the Cost Price -

120+30%*120 = 120+36= 156 $ . (Ignore the currency. Answer remains unaffected )

2. Question is incomplete.

3. 48=2*2*2*2*3

4. Factorization of x^2-2x-35 is

=x^2-7x+5x-35         (-7x+5x= -2x)

=x(x-7)-5(x-7)            (Taking x common from the first () and 5 from the            second bracket)

=(x-5)(x-7)

Factors are 7 and 5.

5. 2.1*10^8

6. For this question it is to be assumed that -

    2x+7=-1

    Now normally solving the equation we get

   2x=-1-7

  => 2x= -8

  => x= -4

7. Multiples of 270 = 3*3*3*2*5

   Multiples of 84 = 2*2*3*7

  Common multiples = 2*3=6

8. First 5 terms can be obtained by putting (1,2,3,4,5) serially in the equation 8n+2

8*1+2=10, 8*2+2= 18, 8*3+2=26 , 8*4+2=34, 8*5+2= 42

Answer:

3/7 ; -7

Step-by-step explanation:

1)

(7-4)/(10-3)

3/7

2) -7 because is the number that multiplies x

The inequality is 7<x<31.

What is inequality ?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The third side of any triangle must be more than the difference between the other two sides.

x>19-12

x>7 (or) 7<x

The third side of any triangle must be less than the sum of the other two sides.

x<19+12

x<31 (or) 31>x

Put them together.

7<x<31 (or) 31>x>7

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The statements which must be true is statement 4 which is  :-

  Point a is not necessarily the center of the circle that passes through points e, f, and g or the center of the circle that passes through points x, y, and z.

3 points uniquely define a circle. so points e,f and g uniquely defines a circle C1 and point x,y and z uniquely defines a circle C2.

The below figure shows the condition that 2 different circle C1 and C2  can have same center , point a and this conditon occurs when they are concentric circle so statement 1,2 is false as in these statement it is told that point a can be center of only one circle but point a can be center of more than 1 circles.

and it is also possible that these 2 different cirlce C1 and C2 can have different center which is 2 different circle ,so statement 3 is also false.

so only statement which must be correct statement is 4 as in this case point a might be center of circle C3 which is neither C1 or C2.

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Answer: C

Step-by-step explanation: because I am amazing

By the age of four, Adam knows that changing one's exterior characteristics  does not change one's gender. Adam has "acquired" or "learned" gender constancy.

Which of the three stages of gender constancy are you?

A child's developing sense of the permanency of being a boy or a girl, which happens in stages: gender identification, gender stability, and gender consistency. Gender constancy is similar to Piaget's concept of physical property conservation in that gender constancy relates to the awareness that gender is an invariant human property that is stable through time and superficial changes in appearance. It starts at the age of six or seven, when a youngster realizes that gender remains consistent across settings (e.g. if a man puts on a dress he is still a man).

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The quadratic function x² + 4x - 5 is factorized to give

(x + 5) (x - 1)

The given quadratic function is x² + 4x - 5

The graph is plotted and the roots of the equation which is the x intercepts that is the points where the graph cuts the x axis is found to be points 1 and -5

Using points 1 and -5 the equation is sort as follows

for 1

x = 1

x - 1 = 0

for -5

x = -5

x + 5 = 0

bringing the solutions together

(x + 5) (x - 1)

The solution is (x + 5) (x - 1)

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Answer:

x= 30

Step-by-step explanation:

Angle E

E + F + G = 180

E + 60 + 90 = 180

E + 150 = 180

E = 180-150

E = 30

Angle E  is congruent to angle X so the measures must be the same

E = X = 30

X = 30

Answer:

[tex]E=30[/tex]

Step-by-step explanation:

[tex]E + F + G = 180\\E + 60 + 90 = 180\\E + 150 = 180 \\E= 180-150 = 30[/tex]

Hope this helps u :)

The conditional relative frequencie of a male preferring pop music to a female preferring pop music is equals to 0.53/0.47 or 0.53 to 0.47. So, correct answer is option(A).

Two-way frequency tables are powerful tools for examining relationships between categorical variables. The entries in the main part of the table are common frequencies. The entries in the "Total" row and "Total" column are limit frequencies. Relative frequencies are used when comparing different classes and classes to the entire data set. The relative frequencies in the body of the table is known as the conditional frequencies. We have a data on the table which decribe the preferred type of music (Rock, Pop and Hip Hop ) a surveyed by females and males as seen above table. We calculated the relative frequencies for each music type so that we should compare the data more reliably. Now, the relative frequency for males who prefer pop music = 10/19

= 0.53

the relative frequency for females who prefer pop music = 9/19 = 0.47

Based on the data collected, males are more likely to prefer pop music than females. The conditional relative frequencie of a male preferring pop music to a female preferring pop music is equals to 0.53/ 0.47 . So, required conditional relative frequency is 0.53/ 0.47 .

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Complete question:

The data on the table decribe the preferred type of muic a urveyed by 9th grader. Rock Pop Hip Hop Total Male 20 17 10 47 Female 16 28 9 53 Total 36 45 9 100 Compare the conditional relative frequencie of a male preferring pop muic to a female preferring pop muic. Round your anwer to two decimal place.

A) 0. 53 to 0. 47

B)0. 37 to 0. 62

C) 0. 36 to 0. 53

D) 0. 17 to 0. 28

Answer:

5000

Step-by-step explanation:

1000+0.8s < 5000

                                  subtract 1000 from both sides of the inequality

0.8s < 4000

                                  divide both sides by 0.8 to get the number of sales (s)

s <5000

Step-by-step explanation:

[tex]y - y1 = m(x - x1[/tex]

[tex]y - - 5 = 4(x - 2)[/tex]

[tex]y + 5 = 4x - 8[/tex]

[tex]y= 4x - 8 - 5[/tex]

[tex]y = 4x - 13[/tex]

[tex]y = 2x - 13 \div 2[/tex]

Net income is the overall increase in wealth over a period and can be calculated by subtracting expenses.

Option D is the correct answer.

Net income is the amount remaining after deducting the expenses from the revenue collected.

We have,

Consider,

Amount collected after production of items = $400

Cost of production of the items = $250

Net income.

= Amount collected - Cost of production

= 400 - 250

= $150

Thus,

Net income is the overall increase in wealth over a period and can be calculated by subtracting expenses.

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if the rate of the current is 5 kilometers per hour, The rate of the boat in still water is 15 km/h.

The rate of the boat in still water is the rate of the boat when the current is not affecting its motion, so we can calculate the rate of the boat in still water by subtracting the rate of the current from the rate of the boat while moving downstream and adding the rate of the current to the rate of the boat while moving upstream. In this case, the rate of the boat while moving upstream is 8 km/h, and the rate of the boat while moving downstream is 20 km/h. Since the rate of the current is 5 km/h, we can subtract 5 km/h from 20 km/h to get the rate of the boat in still water, which is 15 km/h.

Rate of boat in still water = Rate of boat while moving downstream - Rate of current + Rate of boat while moving upstream

= 20 km/h - 5 km/h + 8 km/h

= 15 km/h

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keeping in mind that perpendicular lines have negative reciprocal slopes, and that line "k" has a slope of 1/3, then

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{1}\implies -3}}[/tex]

so for line "j" we're really looking for the equation of a line whose slope is -3 and that it passes through (1 , 4)

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \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-\stackrel{y_1}{4}=\stackrel{m}{- 3}(x-\stackrel{x_1}{1}) \\\\\\ y-4=-3x+3\implies {\Large \begin{array}{llll} y=-3x+7 \end{array}}[/tex]

In the given angles, the values of R=31⁰, x=34⁰, m<S= 38⁰, m<Y = 111⁰

We know that a triangle is a polygon whose sum of angles is equal to 180 degress , with three sides and three vertices.

The given angles are

31⁰,  (x+4)⁰,  (3x+9)⁰

The sum of angles of the triangle

31+x+4+3x+9=180⁰

44+4x=180⁰

Collecting like terms

4x=136

Dividing by 4

x=34⁰

Substituting the value of x=34 in the given angles we have

R= 31⁰,             given

 (x+4)⁰   = 34+4=38⁰,  (3*34+9)⁰=111⁰

In conclusion the values of R= 31⁰, x=34⁰ , m<S=38⁰, m<T=111⁰

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