1 What is the slope of the graph of y = 12x – 19?

Answer:

1.5 inches

Step-by-step explanation:

(10+2x)(14+2x) = 221

4x² + 48x - 81 = 0

4x² + 54x - 6x - 81 = 0

2x(2x + 27) - 3(2x + 27) = 0

(2x + 27)(2x - 3) = 0

x = -27/2, 3/2

x = 3/2 or 1½ or 1.5 inches

The width of the picture frame is [tex]\\ x_{2} &=1,5 \end{aligned}$[/tex].

Given:

A painting with dimensions 10 inches by 14 inches is placed in a picture frame (of constant width), increasing its area to 221 square inches.

From the above explanation, we get the equation

[tex]4 x^{2}+2 \cdot 10 x+2 \cdot 14 x+10 \cdot 14 &=221[/tex]

[tex]\\ 4 x^{2}+48 x+140 &=221[/tex]

By using the quadratic formula, we get

[tex]\\ 4 x^{2}+48 x-81 &=0[/tex]

Solve with the quadratic equation formula

For a quadratic equation of the form [tex]$a x^{2}+b x+c=0$[/tex] the solutions are

[tex]\\ x &=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

[tex]\\ x &=\frac{-48 \pm \sqrt{48^{2}-4 \cdot 48 \cdot(-81)}}{2 \cdot 4}[/tex]

[tex]\\ x &=\frac{-48 \pm \sqrt{3600}}{8}[/tex]

[tex]\\ {\left[x_{1}\right.} &=-13,5][/tex]

[tex]\\ x_{2} &=1,5 \end{aligned}$[/tex]

Therefore, the width of the picture frame is [tex]\\ x_{2} &=1,5 \end{aligned}$[/tex].

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Answer:

a.) equivilent to;     4 x 7x - 4 x 6         and         28x-24

b.) equivilent to;     8y + 13y          and            21y

Step-by-step explanation:

A.)

4(7x-6)     First you have to multiply everything in the parenthesis by 4 because of distribution

7x x 4 - 6 x 4                That is why it is equivilent to the  4 x 7x - 4 x 6  awnser

28x - 24                    That is the end result by simplifiying and show why it is equivient to 28x-24

B.)

8y+6y+7y                 Simplify the like terms

8y+13y                   6+7 is 13 so that is why it is eauals to 8y+13y

21y                       if you continue adding you see why it equals 21y

Solution:

The slope intercept form of equation is given as:

y = mx + c ------ eqn 1

Where,

m is the slope of line

c is the y intercept

From given,

slope = m = 3

y intercept = c = 5

Substitute m = 3 and c = 5 in eqn 1

y = 3x + 5

3x - y = -5

Thus the equation of line is found

Answer

[tex]\angle \ LMN=49\textdegree[/tex]

Step-by-step explanation:

The diagonals of kite KLMN meet at 90°

Since, LK and KN are congruent,[tex]\angle KLM[/tex] and[tex]\angle KNM[/tex] form a set of opposite congruent angles. Congruent angles are equal.

All interior angles of a kite add up to 180°, therefore:-

[tex]\angle LMN=360\textdegree - 2\times106\textdegree-99\textdegree\\=49\textdegree[/tex]

Answer:

∠LMN = 49°

Step-by-step explanation:

Given that

∠LKN = 99°

∠MNK = 106°.

Because, the lengths of LK and KN are congruent.

LK=KN because congruent lines are equal

Hence, ∠MNK=∠MLK = 106°

Adding all angles together, we have

∠MNK + ∠MLK + ∠LKN + ∠LMN = 360°

By substituton;

We have

106° + 106° + 99° + ∠LMN = 360°

311° + ∠LMN = 360°

Collect like terms

∠LMN = 360° - 311°

∠LMN = 49°

Answer:

Step-by-step explanation:

0.103 <= You want to round the number to two decimal places, we will use the  3 to see if it should be rounded up, or stay the same

3 is less than or not equal to 5, so therefore it should be rounded down

0.10 <= Your answer should be like this, or 0.1 if you don't want to add the 0 (because they are the same thing)

I hope this helps! Make sure to give me the brainliest answer , because it is greatly appreciated. Thank You!

The cost of the phone, without tax is,

⇒ $150

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

We have to given that;

Desmond paid 8.5% sales tax when he bought a new phone.

And, The sales tax was $12.75.

Now,

Let the cost of the phone, without tax = x

Hence, We can formulate;

⇒ 8.5% of x = 12.75

⇒ 8.5/100 × x = 12.75

Multiply by 100;

⇒ 8.5x = 12.75 × 100

⇒ 8.5x = 1275

Divide by 8.5 both side;

⇒ x = 1275/8.5

⇒ x = 150

Therefore, We get;

The cost of the phone, without tax is,

⇒ $150

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To find the cost of the phone without tax, convert the tax rate to a decimal and then divide the amount of sales tax paid by this decimal. The calculation shows that the phone cost $150.00 before tax.

Desmond paid an 8.5% sales tax on a new phone and the amount of tax was $12.75. To find the cost of the phone without tax, we can divide the amount of sales tax paid by the tax rate expressed as a decimal.

Let's do the calculation:

$12.75 \/ 0.085 = $150.00

Therefore, the cost of the phone before the addition of sales tax was $150.00.

Answer:

the answer is 36xy squared

Answer:If we are traveling in a car around a corner and we drive over something slippery on the road (like oil, ice, water or loose gravel) and our car starts to skid, it will continue in a direction tangent to the curve.

Step-by-step explanation:

Tangent lines are essential in real-life scenarios like physics for analyzing motion, such as object velocity and acceleration, enabling accurate predictions in various fields.

**Tangent lines** are crucial in various real-life scenarios. For instance, in **physics**, when analyzing the motion of an object along a curved path, the tangent line at a specific point helps determine the object's instantaneous velocity or acceleration. This is vital in understanding how objects move in the real world.

A practical example is when studying the trajectory of a ball thrown into the air. By using the **tangent line** at different points of its path, we can calculate the ball's velocity or acceleration at those instances, assisting in sports analytics, engineering designs, or even space exploration calculations.

Understanding **tangent lines** is essential in fields like **engineering** and **physics** as it allows for precise calculations and predictions based on the behavior of curved functions and their instantaneous rates of change.

Answer: It's B

Step-by-step explanation: Got 100% on the quiz

Answer:

x= 45

y= 18.5 (3 s.f.)

Step-by-step explanation:

Since the quadrilateral has 4 equal sides, it is a square and hence the 4 angles are right angles.

I have drawn the 2 triangles of the square separately for better understanding.

Please see the attached pictures for full solution.

Answer:

x = 2

Step-by-step explanation:

Step 1:  Convert words into an expression

What is the value of x in the equation 13 x minus 2 (8 + 5 x) = 12 minus 11 x?

13x - 2(8 + 5x) = 12 - 11x

Step 2:  Distribute

13x - 2(8 + 5x) = 12 - 11x

13x - 16 - 10x = 12 - 11x

Step 3:  Solve for x

13x - 16 - 10x + 11x + 16 = 12 - 11x + 11x + 16

14x / 14 = 28 / 14

x = 2

Answer:  x = 2

Answer:

x=2

Step-by-step explanation:

Just took the test

Answer:

15 hours

Step-by-step explanation:

To solve this you start by setting up the proportion: [tex]\frac{3}{x} \\\\[/tex] = [tex]\frac{20}{100}[/tex]. This is because we want to know if 3 hours is 20 percent, then how much is 100 percent.

Next we cross multiply to get 300 = 20x

Now we can divide both sides by 20 to get 15.

To check the work we can multiply 15 by .2 and we get 3, so we know it's correct.

Answer:

15 hours to do the entire project

Step-by-step explanation:

20% is the same as 1/5.

"percent" means "per 100", so 20% means 20/100 which reduces to 1/5.

20% of an art project took 3 hours. That means that 1/5 of the art project took 3 hours. The entire project then takes 5 times as much time.

5 * 3 hours = 15 hours

It takes 15 hours to do the entire project.

15 - 3 = 12

It takes 12 more hours after 20% was done.

He needs to drink 3 cups MORE to meet his daily requirement.

Step-by-step explanation:

Here, as given in the question:

The total need for water = half a gallon = 0.5 gallon

1 gallon  = 128 oz

So, 0.5 gallon = 128/2  = 64 oz

Now, the capacity of 1 cup = 3.5 oz

The number of cups already drank by the person = 15 cups

So, the total amount of water already taken by him

= 15 cups x Capacity of 1 cup

= 15 x (3.5 oz)  = 52.5 oz

So, the amount of water left to be drink by him

= Total Need - Already covered

= 64 oz - 52 . 5 oz  =  11.5 oz

Now, as 1 cup = 3.5 oz

So, 11.5 oz  has [tex]( \frac{11.5}{3.5} )[/tex]cups  = 3.28 cup≈ 3 cups

Hence, he needs to drink 3 cups MORE to meet his daily requirement.

Final answer:

Abby has already consumed 52.5 oz of water by drinking 15 small cups at 3.5 oz each. Since the recommended daily intake is 64 oz, she needs to drink an additional 11.5 oz to meet the daily hydration recommendation.

Explanation:

The question pertains to calculating the amount of water a person needs to drink to meet the recommended daily hydration level. In this case, the student needs to find out how much more water Abby should drink after having consumed 15 cups of 3.5 oz each.

First, we calculate the total amount of water Abby has already consumed -

Therefore, Abby needs to drink an additional 11.5 ounces of water to meet the daily recommendation of half a gallon.

Answer:

1(18 + 6)/4

Step-by-step explanation:

1(18 + 6)/4

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Final answer:

The numerical expression for 1/4 of the sum of 18 and 6 is calculated by adding 18 and 6 to get 24, then multiplying by 1/4 to get 6.

Explanation:

The numerical expression for 1/4 of the sum of 18 and 6 is found by first adding 18 and 6 to get their sum, which is 24. Then, to find 1/4 of this sum, you multiply 24 by 1/4. The calculation step-by-step is as follows:

Therefore, the numerical expression for 1/4 of the sum of 18 and 6 is 6.

Step-by-step explanation:

[tex] \because \: time \times speed = distance \\ \therefore \: 4(t + 3) \times 10(t + 3) = 810 \\ \therefore \: 4(t + 3)^{2} = 81 \\ \therefore \: \{2(t + 3) \}^{2} = {9}^{2} \\ \therefore \: \{2(t + 3) \} = {9} \\ \therefore \: t + 3 = \frac{9}{2} \\ \therefore \: t = \frac{9}{2} - 3 \\ \therefore \: t = \frac{9 - 6}{2} \\ \therefore \: t = \frac{3}{2} \\ \therefore \: t = 1.5 \: hrs \\ [/tex]

[tex] \because \: time \times speed = distance \\ \therefore \: 4(t + 3) \times 10(t + 3) = 810 \\ \therefore \: 4(t + 3)^{2} = 81 \\ \therefore \: \{2(t + 3) \}^{2} = {9}^{2} \\ \therefore \: \{2(t + 3) \} = {9} \\ \therefore \: t + 3 = \frac{9}{2} \\ \therefore \: t = \frac{9}{2} - 3 \\ \therefore \: t = \frac{9 - 6}{2} \\ \therefore \: t = \frac{3}{2} \\ \therefore \: t = 1.5 \: hrs \\ speed \: of \: car = 10(t + 3) \\ \hspace{60 pt} = 10(1.5 + 3) \\ \hspace{60 pt}= 10 \times 4.5 \\ \red{ \boxed{ \bold{ \therefore \: speed \: of \: car = 45 \:km/ h}}} \\ [/tex]

Answer:

square area is 100 in

triangle area is 12

so your full area of the figure would be 112 i believe

Step-by-step explanation:

Hope this helps have a wonderful day

The options A, B and C are geometric sequences whereas option D is not.

Step-by-step explanation:

Step 1:

For a series to be a geometric sequence, the numbers in the series must be of a common multiplying ratio. So multiplying a constant value with any number will give the value of the next number.

The multiplying constant can be determined by;

[tex]\frac{2^{nd} term}{1^{st} term} = \frac{3^{rd} term}{2^{nd} term} = \frac{4^{th} term}{3^{rd} term} =[/tex]  The common multiplying ratio.

Step 2:

For option A, we determine the multiplying ratio,

[tex]\frac{2^{nd} term}{1^{st} term} = \frac{10}{5} =2,[/tex]  [tex]\frac{3^{rd} term}{2^{nd} term} = \frac{20}{10} =2, and[/tex] [tex]\frac{4^{th} term}{3^{rd} term} = \frac{40}{20} =2.[/tex]

Since there is a common multiplying ratio of 2, option A is a geometric series.

Step 3:

For option B, we determine the multiplying ratio,

[tex]\frac{2^{nd} term}{1^{st} term} = \frac{5}{10} =0.5,[/tex]  [tex]\frac{3^{rd} term}{2^{nd} term} = \frac{2.5}{5} =0.5, and[/tex] [tex]\frac{4^{th} term}{3^{rd} term} = \frac{2.5}{1.25} =0.5.[/tex]

Since there is a common multiplying ratio of 0.5, option B is also a geometric series.

Step 4:

For option C, we determine the multiplying ratio,

[tex]\frac{2^{nd} term}{1^{st} term} = \frac{3}{1} =3,[/tex]  [tex]\frac{3^{rd} term}{2^{nd} term} = \frac{9}{3} =3, and[/tex] [tex]\frac{4^{th} term}{3^{rd} term} = \frac{27}{9} =3.[/tex]

Since there is a common multiplying ratio of 3, option C is a geometric series.

Step 5:

For option D, we determine the multiplying ratio,

[tex]\frac{2^{nd} term}{1^{st} term} = \frac{6}{3} =2,[/tex]  [tex]\frac{3^{rd} term}{2^{nd} term} = \frac{9}{6} =1.5, and[/tex] [tex]\frac{4^{th} term}{3^{rd} term} = \frac{12}{9} =1.33.[/tex]

Since there is no common multiplying ratio, option D is not a geometric series.

Answer: C & D

Step-by-step explanation:

The fish is 2.25 ft above the water surface.

Step-by-step explanation:

⇒ y = -16(0.375)² + 12 × 0.375 = -2.25 + 4.5 = 2.25 ft

The given equation is:
x + 15 = 22
To determine what operation is being used, we look at the equation and identify the mathematical symbols. The symbol "+" represents the addition operation. This indicates that the number 15 is being added to the variable x.
Therefore, the operation being used in the equation is addition.

16x²-49=

(4x)²-7²=

(4x-7)(4x+7)

Here I have used the expression:

a²-b²=(a-b)(a+b)

Answer:

(4x-7)(4x+7)

Step-by-step explanation:

16x² - 49

realize that 16 = 4² and 49 = 7²

Substituting these values into the expression,

16x² - 49

= 4²x² - 7²

= (4x)² - 7²

recall the algebra property :  a² - b² = (a+b)(a-b)

Applying this to our expression:

(4x)² - 7²

= (4x-7)(4x+7)     Answer

Answer:

b

Step-by-step explanation:

when you have the l-10l  it means the distance from 0  and the distance from 0 from -10 is 10

The length of image of AB after the dilation is 18 cm

Solution:

Given data:

Length of AB = 9 cm

Scale factor (k) = 2

Length of image of AB = ?

By the definition of scale factor,

[tex]$k=\frac{\text { Length of Dilated image AB }}{\text { Length of original image } \mathrm{AB}}$[/tex]

[tex]$2=\frac{\text { Length of Dilated image AB }}{9}[/tex]

Do cross multiplication, we get

2 × 9 = Length of dilated image of AB

18 = Length of dilated image of AB

Hence the length of image of AB after the dilation is 18 cm.

Answer: Brownies that are $1.58 for a 6-pack

Step-by-step explanation:

Well, since 6 times 2 is 12, why don’t you just add $1.58 again, right? So if you do you get $3.16. So Brownies that are $1.58 for a 6-pack are better.

Answer:

Step-by-step explanation:

First you divide 1.58 and 6 to find how much one brownie is.

So that would be roughly $0.26.

Now you divide 3.99 and 12 which is roughly $0.33.

So you now have to see which one has a smaller cost. Which is $0.26. SO it would be the 6-pack.

Another way to figure is out to multiply 0.26 and 12, and 0.33 and 6.

0.33 x 6=1.98

0.26 x 12=3.12

So that makes it more clear that the 6 pack is a better buy!

The equation that represents the relationship between step number and the number of dots is [tex]y=5^n[/tex].

Solution:

Let the number of dots be y.

Step number 0: Number of dots = 1

y = 1

Using exponential rule: [tex]a^0=1[/tex]

[tex]y=5^0[/tex]

Step number 1: Number of dots = 5

y = 5

[tex]y=5^1[/tex]

Step number 2: Number of dots = 25

y = 25

[tex]y=5^2[/tex]

Step number 3: Number of dots = 125

y = 125

[tex]y=5^3[/tex]

Note that in step number 0 the power is 0, 1st step power of 5 is 1, 2nd step power of 5 is 2 and the third step power of 5 is 3.

If the process goes on up to n steps, then power of 5 is n.

∴ Step number n:

[tex]y=5^n[/tex]

Number of dots = [tex]5^n[/tex].

Hence the equation that represents the relationship between step number and the number of dots is [tex]y=5^n[/tex].

Answer: is where that one dot is at home n the y-axis

Step-by-step explanation:

Step-by-step explanation:

Line is passing through the points (6, 2) & (0, 4)

Therefore slope

[tex]m = \frac{2 - 4}{6 - 0} = \frac{ - 2}{6} = - \frac{1}{3} \\ [/tex]

The best prediction is that around 4 students (40% of 10 students) will receive historical fiction novels during Miss Nestor's class free reading time.

Miss Nestor is randomly passing out books to her students for free reading time. With a mix of 10 mysteries, 8 historical fiction novels, and 2 biographies in her basket, and 10 students in the class, we can make a prediction. Assuming each genre of book has an equal chance of being selected and each student gets one book, the probability of getting a historical fiction novel is the number of historical fiction novels divided by the total number of books. That's 8 historical fiction novels divided by (10 mysteries + 8 historical fiction novels + 2 biographies), which equals 8/20 or 40%. Therefore, if we predict using probability, around 40% of the students, which equals 4 students (40% of 10 students), will receive historical fiction novels for free reading time.

the best prediction of the number of students who will receive historical fiction novels for free reading time is 4.

To predict the number of students who will receive historical fiction novels, we can use the concept of probability.

First, let's find the probability that a student randomly selects a historical fiction novel from the basket.

The total number of books in the basket is 10 + 8 + 2 = 20

The probability of selecting a historical fiction novel is the ratio of the number of historical fiction novels to the total number of books:

[tex]\[ P(\text{historical fiction}) = \frac{8}{20} = \frac{2}{5} \][/tex]

Now, if there are 10 students in the class, the expected number of students who will receive historical fiction novels can be found by multiplying the probability by the total number of students:

Expected number of students receiving historical fiction = P(historical fiction) * Total number of students

[tex]\[ = \frac{2}{5} \times 10 \][/tex]

= 4

So, the best prediction of the number of students who will receive historical fiction novels for free reading time is 4.

A total of 168 non-commercial vehicles and 60 commercial vehicles use the country's highways during September.

Step-by-step explanation:

Step 1:

Assume the number of non-commercial vehicles to be x and the number of commercial vehicles to be y.

It is given that for every 14 non-commercial vehicles there will be 5 commercial vehicles. So a ratio can be formed as follows;

[tex]\frac{x}{14}[/tex] = [tex]\frac{y}{5}[/tex], cross multiplying, we get [tex]5 x=14 y[/tex], take this as equation 1.

Step 2:

It is also given that there were 108 more non-commercial vehicles than commercial vehicles. So

[tex]x=y+108[/tex], take this as equation 2.

If we solve equations 1 and 2, we will get the values of x and y.

Step 3;

Substitute equation 2 in equation 1.

[tex]5(y+108)=14 y[/tex],

[tex]5y+540 = 14y[/tex],

[tex]y = \frac{540}{9} = 60[/tex].

Substitute [tex]y = 60[/tex] in equation 2.

[tex]x=60+108 = 168[/tex].

So x = 168 and y = 60.

So a total of 168 non-commercial vehicles and 60 commercial vehicles use the country's highways during September.

Answer:

48.

Step-by-step explanation:

Perimeter is 2l+2w

current perimeter is 16

16x3=48