A solar panel has an area of x2 + 13x + 42. Find the possible dimensions of the solar panel.

In the first case the equation has only one unique solution and in the second case the equation has many solutions.

We are given the equation a|x + b| + c = d and we need to determine the solution of this equation when a > 0 and c = d. The equation contains absolute value symbol which always gives a positive value. The equation can be written as

a|x + b| + c = d

a|x + b| = d - c, since c = d then we can write equation as

a|x + b| = 0, Now, a > 0

=> |x + b| = 0

=> x = -b that is only one unique solution.

Now, in second case a < 0 and c > d then

a|x + b| = d - c

If c > d, then the left-hand side of the equation becomes negative and also a < 0 so the right-hand side also becomes negative. So, the equation will have many solutions in this case.

Learn more about Equation at:

brainly.com/question/27893282

#SPJ9

EXPLANATION

Since we have four given scenarios, the only viable option is the third one because It's the only statement where we take a sample (1000 individuals of 1883 participants).

The common difference in the given arithmetic sequence is 8.

So, formula for common differences:

Now, insert terms in the formula as follows:

Therefore, the common difference in the given arithmetic sequence is 8.

Know more about arithmetic sequence here:

https://brainly.com/question/6561461

#SPJ9

1 and 3

1 * 12 = 12

2 * 12 = 24

so 1 is true

7 * 5.14 = 36

9 * 5.14 = 46.26

so 2 is not true

7 * 4 = 28

2 * 4 = 8

so 3 is true

Here, we want to get the value of x

We can get this by isolating x

We start by bringing like terms together

Answer:

[tex]t = 18.9[/tex]

Information given :

We know that:

- Element X is a radioactive isotope such that every 20 years, its mass decreases by half

- the initial mass of a sample of Element X is 770 grams

And we must find how long it would be until the mass of the sample reached 400 grams

Step-by-step explanation:

To find it, we need to use the following formula:-

[tex]A(t) = A(0)(0.5)^{\frac{t}{20} }[/tex]

- A(0) is the initial amount

From given information, A(0) = 770 grams

Now, replacing the value in t :

[tex]A(t) = (770)(0.5)^{\frac{t}{20} }[/tex]

Then, we must solve for t :-

[tex]400 = 770(0.5)^{\frac{t}{20} } \\\frac{400}{700}= (0.5)^{\frac{t}{20} } \\\\ 0.51948 = (0.5)^{\frac{t}{20} } \\\\log(0.51948) = log((0.5)^{\frac{t}{20} }) \\\\\\log(0.519,48) = \frac{t}{20} log (0.5)\\t=\frac{20*log(0.519,48)}{log(0.5)} \\t=\frac{20(-0.284431}{-0.301029} \\giving\\t=18.9[/tex]

Hope this helps you out and if does so just mark me as brainliest as this answer took a lot of time to plot down so that it acts as a fuel to your learning,

Stay positive,

a fellow comrade,

Cheers !

The cost of the watch which sold at 130% of its cost and sale price is $39 is equal to $30.

As given in the question,

Sale price of the watch for which dealer sold = $39

Let $'x' be the cost of the watch with which dealer purchase

A dealer sold a watch 130% of its cost

Required expression to show the given condition of a dealer is given by:

   130% of x = $39

⇒ (130 /100) × x = $39

⇒ x = ( 39 × 100 ) / 130

⇒ x = $30

Therefore, the cost of the watch which sold at 130% of its cost and sale price is $39 is equal to $30.

Learn more about cost here

brainly.com/question/13945982

#SPJ1

Answer:

  17%

Step-by-step explanation:

You want the percentage represented by a tip of $10.34 on a dinner bill of $61.66.

A percentage is a fraction that has been multiplied by 100%:

  10.34/61.66 × 100%

  ≈ 0.168 × 100%

  ≈ 17%

The tip was about 17% of the original bill.

If there are 189 children, then there are 189 divided 7 = 27 groups of 7 children.

As mentioned in the problem, for every 7 children, there are 2 caretakers therefore, there are a total of 2 x 27 = 54 caretakers in the local daycare.

So, in total, there are 189 children + 54 caretakers = 243 people in the daycare facility.

Answer:

−1≤x<3

Step-by-step explanation:

−4≤3x−1<8

−4≤3x−1and3x−1<8

3x−1≥−4and3x−1+1<8+1

3x≥−3and3x<9

x≥−1andx<3

−1≤x<3

Answer:

When making homemade ice cream in a hand-cranked freezer, the tub containing the ice cream mix is surrounded by a brine (water/salt) solution. To freeze the ice cream mix rapidly so that smooth and creamy ice cream results, the brine solution should combine crushed ice and rock salt in a ratio of 5 to 1.

Data:

Students: 180

Half male.

Male students: 180/2=90

Male teachers: 2

Ratio of male teachers to male students:

You can write the ratio in three different forms:

he Solution:

iven in the question that if

We are required to give a counterexample to the given conditional statement above.

Solving each of the equations above, we get

So, the counterexample to the given conditional statement is x = 4.

To solve the given system of equation by graphing you only have to graph both lines. The solution is the intersection between the lines.

According to this, the intersection of the two lines is (-2, -2). It means that the solution is (-2, -2).

The three sides of the triangle will be 82, 63, and 41 feet.

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees. The perimeter of the triangle is the sum of all three sides of the triangle.

That a flower bed is in the shape of a triangle with one side twice the length of the shortest​ side, and the third side 22 feet more than the length of the shortest side.

Let the three sides of the triangle be A, B, and C. Here A is the longest side B is the shortest side and C is the third side.

Perimeter = A + B + C

A = 2B and C = 22 + B

Put the values in the equation as solve:-

Perimeter = A + B + C

186 = 2B + B + 22 + B

186 = 4B + 22

4B = 186 - 22

4B = 164

B = 164 / 4

B = 41 feet

Longest side = 2B = 2 x 41 = 82 feet

Shirtest side = B = 41 feet

Third side = 22 + B = 22 + 41 = 63 feet

Therefore, the three sides of the triangle will be 82, 63, and 41 feet.

To know more about triangles follow

https://brainly.com/question/24382052

#SPJ1

Answer:

[tex]\frac{-5}{2}[/tex]

Step-by-step explanation:

There are two blue dots on the graph.  It does not matter which dot you startr at.  Let's start at the bottom, right dot.  How many space up and to the left you do you have to move to get to the second dot?

You need to move 5 dots straight up.  Up is a positive direction.  Then you have to move 2 spaces left.  Left is a negative direction, so your slope will be negative.

- [tex]\frac{5}{2}[/tex]            [tex]\frac{-5}{2}[/tex]           [tex]\frac{5}{-2}[/tex]   All of these mean the same thing.

Answer:  3 ≥ W > -5

Step-by-step explanation:

Just look at the way the question is asked, that is the best I can explain. Sorry.

To carry out the vertical analysis of an income statement, set the Revenue as the base figure to 100% for each line item.

Vertical analysis of a financial statement compares each line item on the financial statement as a percentage of a base figure.

The base figure is the revenue in the income statement or the total assets in the balance sheet.

The formula for vertical analysis is given as a financial statement line item divided by the total base figure X 100.

Examples of vertical analysis can be shown with AT$T and Verizon below:

                                                       AT&T        Percent

Revenue                                     $132,447        100%

Cost of Services (Expenses)         60,611        45.8% ($60,611/$132,447 x 100)

Selling & Marketing Expense      39,697       30.0%  

Depreciation & other expenses 20,393        15.4%

Operating Income                       $11,746         8.9%

                                                     Verizon      Percent

Revenue                                     $127,079       100%

Cost of Services (Expenses)         49,931        39.3% ($49,931/$127,079 x 100)

Selling & Marketing Expense        41,016       32.3%

Depreciation & other expenses   16,523       13.0%

Operating Income                      $19,599       15.4%

Thus, we have performed the vertical analysis of AT$T and Verizon above.

Learn more about the vertical analysis at https://brainly.com/question/14115729

#SPJ1

Income Statements of AT&T and Verizon (in millions) are:

                                                       AT&T         Verizon

Revenue                                     $132,447     $127,079

Cost of Services (Expenses)         60,611          49,931

Selling & Marketing Expense      39,697          41,016

Depreciation & other expenses 20,393          16,523

Operating Income                       $11,746       $19,599

Answer:

19

Step-by-step explanation:

-3(-7)-2

21-2

19

it need to be at least 20 chqracters so ignore this the answer is at the top

Numerical variables are the subject of quantitative data. Qualitative data can be represented by a name, symbol, or number code and are measures of "types."

Numerical variables are the subject of quantitative data. Qualitative data can be represented by a name, symbol, or number code and are measures of "types." Data concerning categorical variables make up qualitative data.

Quantitative Variables with values obtained through measurement or counting. Variables that exists not measurement variables are referred to as qualitative variables. Their values are not determined by counting or measuring. Values that are used to identify people in a table are called designators. While qualitative research focuses on words and meanings, quantitative research deals with figures and statistics.

To learn more about quantitative variables refer to:

https://brainly.com/question/14037311

#SPJ13

The maturity value is the sum of the interest and the principal. The formula for calculating interest is expressed as

I = PRT

where

I is the interest after time t

P is the principal or initial amount

R is the interest rate

T is the time in years

From the information given,

P = 10800

R = 8/100 = 0.08

T = 8 months

We would convert 8 months to years. Recall,

12 months = 1 yr

8 months = 8/12 = 0.67

Thus,

t = 0.67 yr

By substituting these values into the formula, we have

I = 10800 x 0.08 x 0.67

I = 578.88

Thus,

Maturity value = 10800 + 578.88

Maturity value = $11378.88

If  the interest rates suddenly rise by 2 percent,  the percentage change in the price of these bonds are : 19.73%, 16.56%.

Using this formula to find the current price of a bond

P=C×1-1(1+YTM)^n/YTM +F /(1+YTM)^n

Where:

P =Current price of a bond

C = Coupon payment,

YTM = Yield to maturity

n = Time to maturity

F =Face value of a bond

The Faulk Corp. bond

C = Coupon rate / number  of payments per year × face value = 4% / 2×$1,000 = $20

n = 13 years = 36 half-year periods

YTM = 7% annually = 7% / 2 = 3.5% semiannually

F = $1,000

hence,

P=20× 1- 1/(1+0.035)^26/0.035 +1,000/ (1+0.035)^36

P=20× 1- 1/(1.035)^36/0.035 +1,000/ (1.035)^36

P= $405.81 + $289.83

P=$695.61

Assuming the annual YTM rises by 2%, the semiannual YTM = 9% / 2 = 4.5%.

Price of the Faulk Corp. bond:

P=20× 1- 1/(1+0.045)^36/0.045 +1,000/ (1+0.045)^36

P=20× 1- 1/(1.045)^36/0.045 +1,000/ (1.045)^36

P= $353.32 +$205.03

P=$558.38

Percentage change:

Percentage change = $558.38 - $695.61/$695.61×100%

Percentage change =19.73%

Gonas Company bond:

C =Coupon rate / number of payments per year× face value = 10% / 2 × $1,000 = $50

n = 18 years = 36 half-year periods,

YTM = 7% annually = 7% / 2 = 3.5% semiannually

F = $1,000

P=50× 1- 1/(1+0.035)^26/0.035 +1,000/ (1+0.035)^36

P=50× 1- 1/(1.035)^36/0.035 +1,000/ (1.035)^36

P= $1,014.52 + $289.83

P=$1,304.35

Assuming the annual YTM rises by 2%, the semiannual YTM = 9% / 2 = 4.5%, bond :

P=50× 1- 1/(1+0.045)^36/0.045 +1,000/ (1+0.045)^36

P=50× 1- 1/(1.045)^36/0.045 +1,000/ (1.045)^36

P= $883.30 +$205.03

P=$1,088.33

Percentage change:

Percentage change = $1,088.33 - $1,304.35/$1,304.35×100%

Percentage change =16.56%

Therefore the percentage change in the price of these bonds are : 19.73%, 16.56%.

Learn more about percentage change here: https://brainly.com/question/11360390

#SPJ1

1) As we were told of the half-life formula along with the data, we can write out the following to get the remains after 170 years:

2) So, according to this model we can tell there will be left approximately

the probability of having exactly 2 boys in 3 births AND having exactly 2 girls in 3 births is 3/8.

the possible outcomes are

BBB,BBG,BGB,GBB,BGG,GBG,GGB,GGG

wherein 3 meet the requirement. There are 8 possible outcomes, all equally likely (if we assume each gender is equally likely). Hence the choice is 3/8.

We can also think about it in at least one more way: You identified all the possible ways to get 2 boys and one girl. Since the events are disjoint, we can add up the probabilities

P(2 boys, 1 girl)=P(BBG)+P(BGB)+P(GBB)

          =[tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex]+ [tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex] + [tex]\frac{1}{2} X\frac{1}{2} X \frac{1}{2}[/tex]

          = 3/8.      

To learn more about : Probability

Ref : https://brainly.com/question/9325204

#SPJ13                          

The one digit numbers that when added to 746 gives a digit in the ones place of the sum which is less than the ones digit in 746 are;

4, 5, 6, 7, 8, or 9

Place values is the value a digit in a number posseses based on its position in the number

The given parameters of the number are;

The number of digits in the number = 1

The ones digit of the sum of the number and 746 is less than the ones digit in 746, which is 6

Therefore;

The value of the number when added to 746 can be expressed as 7xy

Where;

y < 6

The process of adding two numbers involves the addition of the numbers based on their place values such that the ones digit part of the result is placed as the output while the 1 in a result that is 10 or more is added to the next higher place value number to the left of the added digits

Therefore, to have a value of the digit in the ones place less than 6, we can have;

746 + 0 = 746

746 + 1 = 747

746 + 2 = 748

746 + 3 = 749

The possible one digit numbers that gives a sum with a ones digit less than 6 when added to 746 therefore includes; 4, 5, 6, 7, 8, and 9

Learn more about addition and subtraction using place values here:

https://brainly.com/question/25137147

https://brainly.com/question/776078

https://brainly.com/question/750450

#SPJ1

Answer:

-5x1/2= -2.5 14x1/8= 1.75

Step-by-step explanation:

-2.5+1.75=-0.75

Answer:

-3/4

Step-by-step explanation:

Plug in values of x and y into expression:

[tex]-5(\frac{1}{2})+14(\frac{1}{8})=[/tex]

[tex]-\frac{5}{2} +\frac{14}{8}=[/tex]

Find common denominator:

[tex]-\frac{5*4}{2*4} +\frac{14}{8}=[/tex]

[tex]-\frac{20}{8} +\frac{14}{8}=\frac{14}{8}-\frac{20}{8}=[/tex]

Solve numerator:

[tex]14-20=-6[/tex]

So,

[tex]=-\frac{6}{8}=-\frac{3}{4}[/tex]

Let's begin by listing out the given information: