Test Prep What fraction is represented by the point on the number line?

Answer:

k = - 4

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 ) , then the product of the roots is [tex]\frac{c}{a}[/tex]

3x² + 5x + 3k = 0 ← is in standard form

with a = 3 and c = 3k , then

[tex]\frac{c}{a}[/tex] = - 4 , that is

[tex]\frac{3k}{3}[/tex] = - 4 ( multiply both sides by 3 to clear the fraction )

3k = - 12 ( divide both sides by 3 )

k = - 4

Answer:

Step-by-step explanation:

x+y+z=27

x+y=17

z=?

since x+y=17

then

17+z=27

z=27-17

z=10

The given supply curve is: Qs = 6700 + 75P

To find how many AirPods Apple would produce at a price of $185, we can substitute P = $185 in the equation and find the corresponding quantity (Qs).

Qs = 6700 + 75P Qs = 6700 + 75($185) Qs = 6700 + 13875 Qs = 20575

Therefore, at a price of $185, Apple would produce 20,575 AirPods according to the given supply curve.

Answer:

130 degrees

Step-by-step explanation:

DE+DA=130

Answer:

Step-by-step explanation:

Your ability to borrow money at lower rates improves as your credit score increases. Option D.

Your ability to borrow money at lower rates improves as your credit score increases.

A higher credit score indicates to lenders that you have a strong credit history, responsible financial behavior, and a lower risk of defaulting on loans.

Lenders view borrowers with higher credit scores as more reliable and trustworthy, making them more likely to offer lower interest rates and better loan terms.

While saving more and earning more can indirectly contribute to improving your credit score by positively impacting your financial stability and ability to manage debt, they are not direct factors that lenders consider when determining interest rates.

More on credit scores can be found here: https://brainly.com/question/19435264

#SPJ9

The trigonometric ratios are expressed as;

sin θ = 3/5

cos θ = 4/5

tan θ = 3/4

To determine the trigonometric ratios, we need to know the six identities.

These trigonometric identities are listed thus;

From the information given, we have that;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

We have that;

The hypotenuse is labeled as 5.

The adjacent leg is 4

The angle opposite the side labeled 3 is theta

Now, substitute the value to determine the ratios for each identity, we have that;

sin θ = 3/5

cos θ = 4/5

tan θ = 3/4

Learn more about trigonometric identities at: https://brainly.com/question/7331447

#SPJ1

Step-by-step explanation:

(540×45) + ( 540×55)

(24300) +(29700)

54000

Answer:

540*45+540*55=540*45=24300 540*55=29700=24300+29700=54000

Step-by-step explanation:

by solving the the first bracket to get the answer then the other one, after getting the both answer, then add it together

The value of y from the given right angled triangle is 9.2 cm.

Given that, a right angled triangle has 8.2 cm, y cm and 12.3 cm.

Let, hypotenuse = 12.3 cm, perpendicular = 8.2 cm and base = y cm.

By using Pythagoras theorem, we get

8.2²+y²=12.3²

67.24+y²=151.29

y²=151.29-67.24

y²=84.05

y=9.2 cm

Therefore, the value of y from the given right angled triangle is 9.2 cm.

To learn more about the Pythagoras theorem visit:

brainly.com/question/21926466.

#SPJ1

The volume of the rectangular prism in this problem is given as follows:

99 ft³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem can be divided into two prisms, with dimensions given as follows:

Hence the volume of the prism is given as follows:

V = 3 x 5 x 1 + 6 x 2 x 7

V = 99 ft³.

A similar problem about the volume of rectangular prisms is presented at brainly.com/question/22070273

#SPJ1

In 20 days was the whole job done.

Let efficiency of each worker is 1 unit / day .

So, Total work = 10 x 1 x 15 = 150 units .

Now, in first 5 days 6 worker completes

= 5 x 6 x 1 = 30 units .

and, in next 3 days 8 workers completes

= 3 x 8 x 1 = 24 units .

Now, 4 more workers joined then total workers are = 12 workers .

So, amount of work left = 150 - 30 - 24 = 96 unit

Thus, the time taken by 12 workers to complete remaining work

= 96/12

= 8 days .

So, the Whole job was done in = 5 + 3 + 12 = 20 days

Learn more about Work done problem here:

https://brainly.com/question/32738245

#SPJ1

The question attaches here seems to incomplete the complete question is

10 workers can finish the job in 15 days. For the first 5 days, only 6 workers worked on the job. Then for the next 3 days 2 more workers joined them. To finish the job, 4 more workers joined them. After how many days was the whole job done?

14. The measure of angle ABC is 90⁰.

15. The measure of angle CED is 43⁰.

16. The measure of angle BDE is 47.5⁰.

17. The measure of angle CBD is 43⁰.

18. The measure of arc AD is 94⁰.

19. The measure of angle BCE is 47.5⁰.

20. The measure of angle ABD is 47⁰.

21.  The measure of arc ABC is 180⁰.

The measure of the missing angles is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

The measure of angle ABC is calculated as follows;

m∠ABC = 90⁰ (since line AC is the diameter)

The measure of angle CED is calculated as follows;

m∠CED = ¹/₂ (arc CD) (interior angle of intersecting secants)

m∠CED = ¹/₂ (86⁰) = 43⁰

The measure of angle BDE is calculated as follows;

m∠BDE= ¹/₂ (arc BE) (interior angle of intersecting secants)

m∠BDE = ¹/₂ (95⁰) = 47.5⁰

The measure of angle CBD is calculated as follows;

m∠CBD = ¹/₂ (arc CD) (interior angle of intersecting secants)

m∠CBD = ¹/₂ (86⁰) = 43⁰

The measure of arc AD is calculated as follows;

arc ABC = 180 (sum of angles in a semi circle)

arc ADC = 180 (sum of angles in a semi circle)

arc ADC = arc AD + arc CD

180 = AD + 86

AD = 94⁰

The measure of angle BCE is calculated as follows;

m∠BCE= ¹/₂ (arc BE) (interior angle of intersecting secants)

m∠BCE = ¹/₂ (95⁰) = 47.5⁰

The measure of angle ABD is calculated as follows;

m∠ABD = ¹/₂ (arc AD) (interior angle of intersecting secants)

m∠ABD = ¹/₂ (94⁰) = 47⁰

Learn more about chord angles here: brainly.com/question/23732231

#SPJ1

The legs of the big triangle are 14 units and the legs of the small triangle are 7√2 units

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

The right triangles

The right triangles are special triangles with acute angles of 45 degrees

This means that the relationship between the legs and the hypotenuse of the triangles is

Hypotenuse = Leg√2

Leg = Hypotenuse/√2

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

Leg = 14√2/√2

Leg = 14

i.e. the legs of the big triangle are 14 units

Leg = 14/√2

Leg = 7√2

i.e. the legs of the small triangle are 7√2 units

See attachment for the triangles

Read more about right triangles at

https://brainly.com/question/2437195

#SPJ1

Answer:

Step-by-step explanation:

The value of a in the triangle, given that in the triangle ABC, b = 2, c = 6, and A = 35° is 7.7 (option A)

We can obtain the value of a in the triangle ABC as shown in the attached photo by using the cosine rule as illustrated below:

Cosine rule states as follow:

a² = b² + c² + 2bc Cos A

Inputting the given parameters, we can obtain the value of a as follow:

a² = 2² + 6² + (2 × 2 × 6 × Cos 35)

Clear the bracket

a² = 4 + 36 + 19.66

a² = 59.66

Take the square root of both sides

a = √59.66

a = 7.7

Thus, we can conclude from the above calculation that the value of a is 7.7 (option A)

Learn more about cosine rule:

https://brainly.com/question/22390660

#SPJ1

The approximation of [tex]\sqrt{44}[/tex], to the hundredths place, is given as follows:

[tex]\sqrt{44} = 6.63[/tex]

The estimate of a non-exact square root of x is done finding two numbers, as follows:

For this problem, we want to estimate the root to the hundredth's place, hence the number that we must compare is:

44 x 10^4 = 440000.

(as each 10² is equivalent to the square root of a decimal digit).

Then the numbers are:

Hence the square root is approximated as follows:

663/100 = 6.63.

More can be learned about the estimation of the square root of a number at brainly.com/question/28734995

#SPJ1

Answer:

A. Because it would simplify this equation.

The solution of the system of equations is (-2, 2).

Here we want to find the solution of the system of equations:

x + 2y = 2

y = -2x- 2

To solve this, we can replace the second equation into the first one, then we will get:

x + 2*(-2x - 2) = 2

Now we can solve that for x:

x - 4x - 4 = 2

-3x = 2 + 4

-3x = 6

x = 6/-3 = -2

Thus, the value of y is:

y = -2*-2 - 2

y = 4 - 2 = 2

The solution of the system is (-2, 2)

Learn more about systems of equations at:

https://brainly.com/question/13729904

#SPJ1

Complete question:

"Which is the solution of the system of equations?

x + 2y = 2

y = -2x- 2"

Answer:18

Step-by-step explanation:

Answer:

(b) 20

Step-by-step explanation:

We are trying to solve a-13 = ____ for when a=33.

Substitute 33 for a.

33-13 = 20

the answer is b) 20

16800 cubic inches of concrete is needed to make the stairs

Rectangular prism is a three dimensional shape which consist of six faces. The two faces are at the top and bottom and the other faces are lateral faces.

The given stairs can be divided into 3 rectangular prisms as shown in the image attached.

Volume of a concrete needed = Volume of A + Volume of B + Volume of C

Volume of a rectangular prism = l × w × h

where l is the length, w is the width and h is the height

For A:

l = 40, w = 10 in and h = 7 + 7 + 7 = 21 in  

For B:

l = 40, w = 10 in and h = 7 + 7 = 14 in

For C:

l = 40, w = 10 in and h = 7 in

Volume of a concrete needed = (40 * 10 * 21) * (40 * 10 * 14) + (40 * 10 * 7)

Volume of a concrete needed = 8400 + 5600 + 2800

Volume of a concrete needed = 16800 in³

Learn more about Rectangular Prisms on:

brainly.com/question/21308574

#SPJ1

The missing reason in the proof is "mZDEC = 90°" or "Angle DEC is a      right angle."

The missing reason in the proof is the statement "mZDEC = 90°". This statement implies that the angle DEC is a right angle, which is a crucial piece of information in proving that ABCD is a square.

In a square, all angles are right angles, so if we can establish that an angle in the figure is 90°, we can conclude that the figure is a square. In this case, the angle DEC being 90° is the key piece of evidence that supports the claim that ABCD is a square.

The statement "mZDEC = 90°" indicates that the measure of angle DEC is 90 degrees. This is significant because it confirms that one of the angles in the figure is a right angle, meeting the definition of a square.

For such more questions on Right angle:

https://brainly.com/question/30366726

#SPJ11

The set of 3 lengths that make a right triangle is {8, 15, 17}

Remember that for any right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longer side.

So if the 3 sides are A, B, and C, such that:

A < B < C

We will have:

A² + B² = C²

Now you only need to try sets of 3 values in that equation, if we use: 8, 15, and 17 we will have:

8² + 15² = 17²

289 = 289

That equationis true, thus, these 3 lengths make a right triangle.

Learn more about right triangles at:

https://brainly.com/question/2217700

#SPJ1

The coordinates of vertex D in the parallelogram are (-7, -10).

We have,

To find the coordinates of vertex D of the parallelogram, we need to use the properties of a parallelogram.

One of these properties states that opposite sides of a parallelogram are parallel and have equal lengths.

Given that A = (8, 2), B = (6, -4), and C = (-5, -4), we can find the coordinates of D as follows:

Find the vector representing one of the sides of the parallelogram.

We can use the vector AB.

Vector AB = (x-coordinate of B - x-coordinate of A, y-coordinate of B - y-coordinate of A)

= (6 - 8, -4 - 2)

= (-2, -6)

Add this vector to point C to find the coordinates of D.

Coordinates of D = (x-coordinate of C + x-coordinate of AB, y-coordinate of C + y-coordinate of AB)

= (-5 - 2, -4 - 6)

= (-7, -10)

Therefore,

The coordinates of vertex D are (-7, -10).

Learn more about parallelograms here:

https://brainly.com/question/1563728

#SPJ1

Approximately 7 employees took a break longer than 49 minutes.

We have,

In a box-and-whisker plot, the box represents the interquartile range (IQR), which includes the middle 50% of the data.

The line within the box represents the median.

The "whiskers" extend to the minimum and maximum values, excluding any outliers.

Given the information provided:

Median = 41

Q1 = 37

Q3 = 49

Largest = 55

Smallest = 35

Since Q3 represents the upper quartile and corresponds to the boundary for the upper 25% of the data, we can conclude that 25% of the employees took a break longer than 49 minutes.

Now,

The number of employees who took a break longer than 49 minutes can be estimated by calculating 25% of the total number of employees:

25% of 27 employees

= (25/100) x 27

= 6.75

Since we cannot have a fractional number of employees, we round up to the nearest whole number.

Therefore,

Approximately 7 employees took a break longer than 49 minutes.

Learn more about the interquartile range here:

https://brainly.com/question/29204101

#SPJ1

Cos = 20/27 = 0.7407

so

angle that stream makes with the road = 42.2

answer

42 (Round only your final answer to the nearest degree)

The classification , symmetry , maximum r-values and the zeroes of the function are solved

Given data ,

a)

Let the function be represented as A

Now , the value of A is

r² = 25 sin( 2θ )

The equation represents a cardioid

It is symmetric about the polar axis.

The maximum values of r occur at θ = (π/4) + kπ/2, and the maximum value of r is 5.

The equation has zeroes at θ = kπ/2, and the corresponding values of r are given by r = 0

b)

The equation represents a limaçon.

It is symmetric about the polar axis.

The maximum value of r is 7.

The equation has zeroes at θ = arccos(1/3) + 2kπ or θ = -arccos(1/3) + 2kπ, and the corresponding values of r can be found by substituting into the equation r = 4 - 3cos(θ).

c)

The equation represents an Archimedean spiral.

It does not possess any symmetry.

There is no maximum r value.

The equation has a zero at θ = 1/2.

Hence , the zeroes of the function are solved

To learn more about symmetry of functions click :

https://brainly.com/question/29292066

#SPJ1

The sum of the number 199 + 61 by vertical table will be 260.

Since, Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Use the table to add 199 + 61 vertically. Then we have

                                Hundreds          Tens          Ones

Regrouping                    1                       1            

First addend                  1                      9               9

Second addend            0                      6               1

Sum                              2                      6               0

Thus, The sum of the number 199 + 61 by the vertical table will be 260.

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ1

The table to add 199+61 vertically is shown below.

To add 199 and 61 vertically, we'll set up the addition table as follows:

 1  9  9

+   6  1

_________

Let's start by adding the digits in the rightmost column, which is the ones place:

9 + 1 = 10

We write down 0 in the bottom row and carry over the 1 to the top row:    1  9  9

+   6  1

_________

   0

Now, let's add the digits in the next column (the tens place), including the carry-over:

1 + 9 + 1 = 11

We write down 1 in the bottom row and carry over the 1 to the top row:

   1  9  9

+   6  1

_________

  1  1

Finally, let's add the digits in the leftmost column (the hundreds place), including the carry-over:

1 + 1 = 2

We write down 2 in the bottom row:

   1  9  9

+   6  1

_________

  2  1

Learn more about Addition here:

https://brainly.com/question/29560851

#SPJ1

The values of the composite functions are

(1) (f + g)(x) = 4x² + 2x - 2

(2) (fg)(x) = 8x³ - 4x² - 2x + 1

(3) (fⁿ)(x) = (4x² - 1)ⁿ

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

f(x) = 4x² - 1

g(x) = 2x - 1

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

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

(f + g)(x) = 4x² - 1 + 2x - 1

Evaluate the like terms

(f + g)(x) = 4x² + 2x - 2

(fg)(x) = f(x) * g(x)

(fg)(x) = (4x² - 1) * (2x - 1)

Evaluate the products

(fg)(x) = 8x³ - 4x² - 2x + 1

(fⁿ)(x) = (f(x))ⁿ

So, we have

(fⁿ)(x) = (4x² - 1)ⁿ

Read more about composite functions at

https://brainly.com/question/10687170

#SPJ1

It is possible for a sample to follow a normal distribution, depending on the nature of the data being accumulated.

The regular distribution is a bell-shaped curve that is symmetric across the mean, and it's far typically used to model various natural phenomena and measurements in fields such as information, engineering, and social sciences.

If the data being gathered is continuous and the sample length is large sufficient, it is regularly assumed that the pattern follows a normal distribution.

This assumption is based at the critical limit Theorem, which states that the sampling distribution of the suggest of any independent, random variable will tend toward a ordinary distribution because the sample size increases.

But, it's far critical to notice that not all samples will observe a ordinary distribution, and in a few cases, different distributions may be greater suitable for the records being amassed.

It's far consequently essential to analyze the information and evaluate the assumptions being made before using the regular distribution as a model.

Learn more about normal distribution:-

https://brainly.com/question/23418254

#SPJ1

Note that the substance(s) that Jacob and Natalie should use to make a cold pack that will do the BEST job of keeping food cool is " Sample 1, because it absorbs the most energy" (option A)

In physics, energy is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light.

Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed

Learn more about energy at:

https://brainly.com/question/13881533

#SPJ1

Full Question:

Although part of your question is missing, you might be referring to this full question:

People use self-warming and self-cooling devices for many purposes such as keeping drinks cold or food warm. Medical professionals also use these types of devices to store medicines and other substances that need to stay colder than room temperature. These cooling and warming devices use a chemical reaction to produce their chilling and warming effects. Compounds combine in endothermic (heat absorbing) or exothermic (heat releasing) reactions within these devices to help them keep items cool or warm.

Jacob and Natalie are asked by their science teacher to design a warming or cooling device. They decide to design a cold pack that can be used to help keep food cool. Jacob

and Natalie read about different substances that can be used inside cold packs and learn that most cold packs use endothermic reactions to cool objects. They find the table below while researching.

Which sample uses the substance(s) that Jacob and Natalie should use to make a cold pack that will do the BEST job of keeping food cool?

answer choices

Sample 1, because it absorbs the most energy

Sample 2, because it absorbs the most energy

Sample 3, because it absorbs the least energy

Sample 4, because it absorbs the least energy