Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent. Photo attached.

Answer: "7 is a solution to the original equation. The value –1 is an extraneous solution."

Step-by-step explanation:

The equation [tex]x=\sqrt{6x+7}[/tex] can be solved by squaring both sides:

[tex]x^2 = 6x + 7\\\\x^2 - 6x - 7 = 0\\\\(x-7)(x+1) = 0[/tex]

We can see that -1 and 7 are solutions, but make sure they are not extraneous by substituting them in the original equation:

[tex]1 = \sqrt{-1}\\ 7 = \sqrt{49}[/tex]

The square root of 49 equals 7, but the square root of -1 is an imaginary number.

The correct choice is "7 is a solution to the original equation. The value –1 is an extraneous solution."

Answer: "7 is a solution to the original equation. The value –1 is an extraneous solution."

Step-by-step explanation:

Answer:

119

Step-by-step explanation:

it will be the same as 8 because they are adjacent..

Answer:

Step-by-step explanation:

Answer:

Solve for the (number or thing that changes), so you need to (separate far from others)/get x by itself

-2x - 4 + 5x = 8 First I want to combine like terms (-2x and 5x)

-4 + 3x = 8 (Add 4 on both sides)

3x = 12 Then divide 3 into both sides to get x by itself

x = 4

Combine like terms (add the 5x to the -2x to get 3x). Move the -4 to the other side to get 3x= 12. Divide both sides by 3 to get x=4. Apply the addition property of (a state where all things are equal), Apply the division property of (a state where all things are equal) to divide both sides by 3, Finally, check the solution by substituting 4 into the original equation.

*PLEASE MAKE TEXT INTO OWN WORDS IF POSSIBLE

Answer:7.939

Step-by-step explanation:

Answer:

0.25

Step-by-step explanation:

25% can be written as the decimal 0.25. The word 'percent' means 'per 100. ' So, 25 percent is the same as 25 out of 100.

Answer:

[tex]25\% = \frac{25}{100 } \\ \\ 25\% = 0.25[/tex]

Answer:

the length and width . Round to the nearest tenth are 8.8 inches and 3.8 inches respectively.

Step-by-step explanation:

The area A of a rectangle is the product of the length L and width W. This may be expressed mathematically as

A = L * W

As such, given that the length is 5 inches more than the width,

L = W + 5

33 = W(W + 5)

W² + 5W  - 33 = 0

Using the formula method which states that

s = -b±√(b²-4ac)/2a

W = -5 ± √5² - 4(1)(-33)/2

= -5 ± 12.53/2

= 7.53/2 (since length cannot be negative)

= 3.755 inches

L = 3.755 + 5

= 8.755 inches

Answer: total net sales = $7950

Step-by-step explanation:

The formula for determining total net sales is expressed as

total net sales = Gross sales - (sales returns + allowances + discount)

Gross sales means total sales.

From the information given,

Gross sales = $9000

Discounts = $900

Returns = $150

Allowances = 0(this is because it was not given)

Therefore,

total net sales = 9000 - (900 + 150)

= 9000 - 1050

total net sales = $7950

Answer:

7950

Step-by-step explanation:

Answer:

2.4 inches per hour

Step-by-step explanation:

A total of 13.2 inches of snow fell during a snowstorm that lasted 5.5 hours and the same amount of snow fell each hour of the storm.

This means that there was a constant rate of snow fall.

To find how many inches of snow fell each hour, we divide the amount of snow fall by the amount of time that the snowstorm lasted.

That is:

[tex]R = \frac{13.2}{5.5}[/tex]

R = 2.4 inches per hour

This means that 2.4 inches of snow fell each hour during the snowstorm.

Answer:

2.4 inches

I did the quiz

Answer:

There would be 859 bacteria after 13 hours.

Step-by-step explanation:

The population of bacteria after t hours is given by the following equation:

[tex]P(t) = P(0)e^{rt}[/tex]

In which P(0) is the initial population and r is the growth rate.

The number of bacteria is able to double every 24 hours.

This means that [tex]P(24) = 2P(0)[/tex]. So

[tex]P(t) = P(0)e^{rt}[/tex]

[tex]2P(0) = P(0)e^{24r}[/tex]

[tex]e^{24r} = 2[/tex]

[tex]\ln{e^{24r}} = \ln{2}[/tex]

[tex]24r = \ln{2}[/tex]

[tex]r = \frac{\ln{2}}{24}[/tex]

[tex]r = 0.0289[/tex]

590 bacteria are placed in a petri dish.

This means that P(0) = 590. So

[tex]P(t) = P(0)e^{rt}[/tex]

[tex]P(t) = 590e^{0.0289t}[/tex]

How many bacteria would there be after 13 hours, to the nearest whole number?

This is P(13).

[tex]P(t) = 590e^{0.0289t}[/tex]

[tex]P(13) = 590e^{0.0289*13} = 859[/tex]

There would be 859 bacteria after 13 hours.

Answer:

Subtract 4 from both sides

Step-by-step explanation:

Ap ex

Answer:

The last option.

Step-by-step explanation:

Answer:

132 square centimeters

Step-by-step explanation:

The surface area of a rectangular prism can be calculated with the formula [tex]2lh+2lw+2hw[/tex] where l represents length, h represents height, and w represents width. In this case, the equation is [tex]2\cdot 2\cdot 8 + 2\cdot 2\cdot 5 + 2\cdot 8\cdot 5=132[/tex] square centimeters. Hope this helps!

Answer:

23p

Step-by-step explanation:

Pens : Cost

8       :  £1.84

divide each by 8

1 pen = £0.23 = 23p

Answer:

You have to invest $5,020.71  to have $6,000 in 4 years 3 months at 4 1\5% annual interest, compounded monthly.

Step-by-step explanation:

Let the principal be x

Amount = $6000

Time = 4 years 3 months = [tex]4 years +\frac{3}{12} years = 4.25 years[/tex]

Rate of interest = [tex]4 \frac{1}{5}\% = \frac{21}{5}\%[/tex]

No. of compounds per year = 12

Formula:[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

[tex]6000=P(1+\frac{21}{500 \times 12})^{12 \times 4.25}[/tex]

[tex]\frac{6000}{(1+\frac{21}{500 \times 12})^{12 \times 4.25}}[/tex]=P

P=$5,020.71

Hence You have to invest $5,020.71  to have $6,000 in 4 years 3 months at 4 1\5% annual interest, compounded monthly.

Answer:

The length of a leg of the isosceles triangle is 50√(2

Step-by-step explanation:

Since it is an isosceles right triangle, the length of the adjacent and the opposite is the same value which is let’s say x.

Mathematically; the square of the hypotenuse equals the square of the adjacent plus the square of the opposite according to Pythagoras.

Thus;

100^2 = x^2 + x^2

10000 = 2x^2

divide the through by 2, we have;

x^2 = 10,000/2

x^2 = 5,000

x = √5,000

x = √2,500 * 2

x = 50√2

Answer:no

Step-by-step explanation:

Answer:

C. x [tex]\geq[/tex] 0

Step-by-step explanation:

The answer is C, x is greater than or equal to zero, because that is the only answer that makes sense.

A) x can also be equal to 0, so this answer is wrong

B) x can't be -2, and it definitely can't be less than -2, so that's wrong.

D) Again, x can't be -2, or -1. It can't be any negative number because 4 * (a negative number) would put a negative sign under the square root. You can't take square roots of negative numbers.

Hope this is correct and that it helps you!

Final answer:

The correct equation representing the relationship between x and y values is y = -2x + 12. This is found by recognizing the pattern in the table and using the slope-intercept form to find the slope and y-intercept. Thus, option A is correct.

Explanation:

The student is asking to determine which equation represents the relationship between the x values and the y values in the given table. To find the correct equation, we examine the pattern of changes in the x and y values.

The y values decrease by 2 as the x values increase by 1, indicating a slope of -2.

Starting with the x value of 1, which corresponds to a y value of 10, we apply the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

We find that the y-intercept, b, must be 12 to satisfy the equation when x is 1 (10 = -2(1) + b).

Thus, we can conclude that the equation representing the relationship between x and the y values is y = -2x + 12, which is option A.

This type of equation is a linear equation and the slope-intercept form is particularly useful for quickly identifying the slope and y-intercept of the line represented by the equation.

Answer: about 630.57 rotations per mile.

Step-by-step explanation: There are 1760 yards in one mile. 36 inches per yard. Convert miles to inches: 1760×36=63360

Figure the circumference of the tire: C=π×32 3.14×32=100.48=C

Divide the length of the mile by the circumference of the tire:. 63360/100.48 = 630.57 approximately.

Answer:

5

Step-by-step explanation:

A negative plus a negative equals a positive so the equation would be 4 1/3 + 2/3 and the sum is 5.

Hopes this helps :)

Answer:

the answer is A because it has 2 sides of parallel line

Step-by-step explanation:

The correct shape which is always a parallelogram is,

⇒ A rectangle because it has 2 pairs of parallel sides.

We have to given that,

To find shape which is always a parallelogram

Since, A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Hence, We can say that;

Rectangle shape is always a parallelogram.

Thus, The correct shape which is always a parallelogram is,

⇒ A rectangle because it has 2 pairs of parallel sides.

Learn more about the rectangle visit:

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Answer:

y = 5 * (1/2)^x

Step-by-step explanation:

This is an exponential function

y =ab^x

where a is the initial value ( where x = 0)

a = 5

y = 5 * b^x

Pick a point to determine b

(1,2.5)

2.5 = 5 * b^1

2.5 = 5 *b

Divide each side by 5

2.5/5 = b

b = 1/2

y = 5 * (1/2)^x

Answer:

The answer is A

Step-by-step explanation:

hope this helps

Answer:

182

Step-by-step explanation:

You can start by realizing that 14 is 7*2, and that that is already a common multiple, meaning that you can forget about 7 entirely. Now, because 13 is prime, the least common multiple of 13 and 14 will just be 13*14=182. Hope this helps!

Answer:

182

Step-by-step explanation:

The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.

Answer:

Only II. is written in standard form

Step-by-step explanation:

The three polynomials given are:

I. [tex]15x^4 - 6x + 3x^2 - 1[/tex]

II. [tex]12x^3 + 8x + 4[/tex]

III. [tex]285 + 8x^2 + 10%[/tex]

A polynomial is said to be in standard form when the variables are written in terms of descending powers i.e. the term with the highest power first, followed by the next and so on.

Examining the three polynomials I, II and III, there is only one which follows this rule and that is:

II. [tex]12x^3 + 8x + 4[/tex]

The term with the highest power (3) came first, followed by the term with the next degree of power (1) and the last term with degree of power as 0.

Hence, only II. is written in standard form.

Only the second polynomial, 12x3 + 8x + 4, is in standard form because its terms are arranged in descending order of degrees. The first polynomial is not in standard form due to the incorrect order of terms by degree. The third expression contains a percentage sign (%) and wasn't written in order of descending degree, hence it doesn't qualify as a polynomial in standard form.

In mathematics, a polynomial is said to be in standard form when its terms are written in descending order by degree. The degree of a term is the exponent used in the term. Let's evaluate each option:

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Answer:

80 represents the monthly fees and 50 represents the fixed one-time fee to store the bike at the train station.

The number 80 represents the monthly train pass cost, while 50 represents the one-time bike storage fee. Multiply the monthly fee by the number of months and add the bike storage fee to get total cost c for m months.

The number 50 is the initial, one-time cost to store Felipe's bike at the train station. To calculate the total commuting cost c for Felipe for m months, you multiply the number of months m by the monthly train pass cost, and then add the one-time bike storage fee.

Answer:

A

Step-by-step explanation:

-2(5x)+(-2)(-3/4) = -10x +6/4

-2(5x-3/4) = the same

Answer:

6.4

Step-by-step explanation:

A^2+B^2=C^2

(5*5)+(4*4)=C^2

25+16=[tex]C^{2}[/tex]

41=[tex]C^{2}[/tex]

[tex]\sqrt{41}[/tex]=[tex]\sqrt{C^{2} }[/tex]

c= 6.4

Answer:

x=34

Step-by-step explanation:

3x-12=90

3x-12+12=90+12

3x=102

3x/3 = 102/

x=34

Answer:

Step-by-step explanation:

From the picture we have

AD = CD = BC = AB

it's enough to say that this quadrangle is a rhombus.

The diagonals in each rhombus are perpendicular and divide to half.

Therefore we have the equation:

3x - 12 = 90            add 12 to both sides

3x - 12 + 12 = 90 + 12

3x = 102          divide both sides by 3

3x : 3 = 102 : 3

x = 34

Answer:

2.5%

Step-by-step explanation:

Simple Interest formula  :   V = P + P*r*t

I = Prt

$150 = $2000*r * 3

r = $150 / ($2000*3) =  5/200 = 0.025  = 2.5%