12 less than a number is equal to the product of 7 and that number. Convert into an
equation and find the number?

Answer:

A. The tree provides shelter for the ants, and the ants help the tree to stay alive

Answer and explanation:

To construct a circle, draw a line that represents the diameter of the circle. Bisect the line so that it is a perpendicular bisector of the diameter of the circle. Place your compass at the bisection point/midpoint and draw an arc or better still the whole circle.

Theorem: the perpendicular bisector of a chord passes through the center of a circle.

Note: a diameter of a circle is a chord that passes through the center of a circle.

Given:

Initial number of participants = 128

During each round, half of the players are eliminated.

To find:

The number of players remain after 5 rounds.

Solution:

It is given that, the initial number of participants is 128 and during each round, half of the players are eliminated.

If half of the players are eliminated, then half of the players are remained.

So, the initial value is 128 and the decay factor is [tex]\dfrac{1}{2}[/tex].

The general exponential decay model is:

[tex]y=a(b)^x[/tex]

Where, a is the initial value and b is the decay factor.

Putting [tex]a=128[/tex] and [tex]b=\dfrac{1}{2}[/tex] in the above model, we get

[tex]y=128\left(\dfrac{1}{2}\right)^x[/tex]

Here, y is the number of remaining players after x rounds.

Substituting [tex]x=5[/tex], we get

[tex]y=128\left(\dfrac{1}{2}\right)^5[/tex]

[tex]y=128\left(\dfrac{1}{32}\right)[/tex]

[tex]y=4[/tex]

Therefore, the required model is [tex]y=128\left(\dfrac{1}{2}\right)^x[/tex] and the number of players remain after 5 rounds is 4.

Answer:

450 jumping jacks

Step-by-step explanation:

f(10) = 45 (10)

45 * 10 is just 450 :)

Answer:

450.

Step-by-step explanation:

f(10) = 45 * 10 = 450 jumping jacks.

No, The third line does not necessarily be a transversal.

What is Equation of line?

The equation of line with slope 'm' and y intercept at point 'b' is given as;

⇒ y = mx + b

Given that;

Two lines intersected by a third line.

Since, When two lines are parallel to each other and two lines intersected by a third line then, third lines are transversal.

So, Here it is not given two lines are parallel.

Thus, Third line is not necessarily a transversal.

Hence, The third line does not necessarily be a transversal.

Learn more about the transversal visit:

https://brainly.com/question/2141319

#SPJ2

9514 1404 393

Answer:

  A.  (0, -3)

Step-by-step explanation:

Graphing the given points shows you the y-intercept is between them. The x-coordinate of the y-intercept is always 0, so the only viable answer choice is ...

  (0, -3)

Answer:

A. [tex]UPC = 0-03700-80049-9[/tex]

Step-by-step explanation:

Given

[tex]ID = 037000[/tex]

[tex]Item\ Number = 80049[/tex]

Required

The valid UPC

First, the UPC is represented as:

UPC = ID followed by item number followed by the checksum

So, we have:

[tex]upc = 0-03700-80049-X[/tex]

To calculate X (the checksum)

Add up digits at odd positions

[tex]Odd = (0 + 7 + 0) + (8 + 0 + 9)[/tex]

[tex]Odd = 24\\[/tex]

Multiply by 3

[tex]Product = Odd * 3[/tex]

[tex]Product = 24 * 3[/tex]

[tex]Product = 72[/tex]

Add up digits at even positions

[tex]Even = (3 + 0 + 0) + (0 + 4)[/tex]

[tex]Even = 7[/tex]

Add the product and the sum of even

[tex]Result = Product + Even[/tex]

[tex]Result = 72+7[/tex]

[tex]Result = 79\\[/tex]

The last digit of the UPC is 9.

Hence, the UPC is:

[tex]UPC = 0-03700-80049-9[/tex]

Answer:

[tex] \rm\displaystyle( {a}^{2} + {b}^{2} - 22)( {a}^{2} + {b}^{2} + 4)[/tex]

Step-by-step explanation:

we would like to factor the following:

[tex] \rm\displaystyle ( {a}^{2} + {b}^{2} {)}^{2} - 18( {a}^{2} + {b}^{2} ) - 88[/tex]

let a²+b²=x

thus substitute:

[tex] \rm\displaystyle x {}^{2} - 18x- 88[/tex]

rewrite the middle term as 4x-22x:

[tex] \rm\displaystyle x^{2} + 4x - 22x - 88[/tex]

factor out x:

[tex] \rm\displaystyle x( x^{} + 4)- 22x - 88[/tex]

factor out -22:

[tex] \rm\displaystyle x( x^{} + 4)- 22(x + 4)[/tex]

group:

[tex] \rm\displaystyle( x- 22)(x + 4)[/tex]

substitute back:

[tex] \rm\displaystyle( {a}^{2} + {b}^{2} - 22)( {a}^{2} + {b}^{2} + 4)[/tex]

and we are done!

[tex]\longrightarrow{\green{- 9 {x}^{2} + 14x + 16}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] \sqrt{49} + [ \sqrt{81} - x \: (9x - 14) ] \\ \\ = \sqrt{7 \times 7} + [ \sqrt{9 \times 9} - 9 {x}^{2} + 14x] \\ \\ = \sqrt{( {7})^{2} } + [ \sqrt{ ({9})^{2} } - 9 {x}^{2} + 14x ] \\ \\ (∵ \sqrt{ ({x})^{2} } = x ) \\ \\ = 7 + (9 - 9 {x}^{2} + 14x) \\ \\ = 7 + 9 - 9 {x}^{2} + 14x \\ \\ = - 9 {x}^{2} + 14x + 16[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]

It only has one x intercept

Step-by-step explanation: when you graph it there is only one point where the line meets the x intercept

Answer:

A: [tex]f(x)=(4x+5)(x-3)[/tex]

B: [tex](-\frac{5}{4} , 0)[/tex] and [tex](3, 0)[/tex]

C: They are parallel, which means they have no endpoint.

Answer:

B

Step-by-step explanation:

They are alternate interior angles so that means they are equal

4x - 30 = 2x

2x = 30

x = 15

[tex]\longrightarrow{\green{A.\:2 \: ( x + 3)(x + 3) }}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]2 {x}^{2} + 12x + 18[/tex]

Taking 2 as common factor, we have

[tex] = 2 \: ( {x}^{2} + 6x + 9) \\ = 2 \: ( {x}^{2} + 3x + 3x + 9)[/tex]

Next, we take [tex]x[/tex] as common from first two terms and 3 from last two terms,

[tex] = 2 \: [x(x + 3) + 3(x + 3)][/tex]

Taking the factor [tex](x+3)[/tex] as common,

[tex] = 2 \: ( x + 3)(x + 3)[/tex]

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]

Answer:

Correct to 1dp

127.3 cm = 127.0 cm

86.5 cm = 87.0 cm

Upper limits:

127.0 cm = 127.05 cm

87.0 cm = 87.05 cm

Lower Limits:

127.0 cm = 126.95 cm

87.0 cm = 86.95 cm

upper limit of perimeter of rectangle:

P = 2(l+w)

= 2(127.05 + 87.05)

= 2(214.1)

= 428.2 cm

lower limit of perimeter of rectangle:

P = 2(l+w)

= 2(126.95 + 86.95)

= 2(213.9)

= 427.8 cm

therefore;

[tex]427.8 cm \leqslant perimeter < 428.2cm[/tex]

The upperbound and the lowerbound for the perimeter of the rectangle are;

Upper bound perimeter = 428.2 cm

Lower bound perimeter = 427.8 cm

To get the upper bound and Lower limits for the length and width, we need to first approximate them to 1 decimal place to get;

Length; 127.3 cm ≈ 127 cm

Width; 86.5 cm ≈ 87 cm

Thus;

Upper limit of length = 127.05 cm

Lower limit of length = 126.95 cm

Upper limit of width = 87.05 cm

Lower limit of width = 86.95 cm

Formula for perimeter of rectangle is;

P = 2(length × width)

Thus;

Upper bound perimeter = 2(127.05 + 87.05)

Upper bound perimeter = 428.2 cm

Lower bound perimeter = 2(126.95 + 86.95)

Lower bound perimeter = 427.8 cm

Read more on perimeter of rectangle at; https://brainly.com/question/17297081

Answer:

Step-by-step explanation:

Decreased students = 1050 - 798 = 252

Decreased percentage = (decreased students ÷ number of last year students) * 100

= [tex]\frac{252}{1050}*100[/tex]

= 24%

Answer:

24%

Step-by-step explanation:

% change = [tex]\frac{difference}{original amount}[/tex] x 100

; 1050 - 798 = 252

% change = [tex]\frac{252}{1050}[/tex] x 100

% change = 0.24 x 100

% change = 24

the percentage decrease in the number of students enrolled is 24%

Step-by-step explanation:

everything can be found in the picture

Answer:

2*(-3)= -6

Step-by-step explanation:

I do not see how "a*b=2a-3b" would change the fact 2 times negative 3 is -6

Answer:

Option 4

Step-by-step explanation:

2x² + 32 = 0

2x² = -32

x² = -16

sqrt(-16) got no real solution. (no real number multiplied by itself will be negative)

Answer:

There are two simple, compelling reasons to use a heart-rate monitor: to train and race at the best pace for you. The table below shows you how to find your perfect paces for: (1) the three most important workouts in any training program; and (2) the four most popular road-race distances.

Step-by-step explanation:

Hope this helps :)

Answer:

Step-by-step explanation:

when it touch the ground,y=0

-16x²+232x+134=0

-16(x²-29/2 x+(-29/4)²-(-29/4)²)=-134

-16(x-29/4)²-16(-861/16)=-134

-16(x-29/4)²+861=-134

-16(x-29/4)²=-134-861

(x-29/4)²=-995/-16=995/16

x-29/4=±√995/4

rejecting negative sign

x=29/4+√995/4=(29+√995)/4≈15.14 second

Answer:

i think the answer is Options B, C and E holds.

Step-by-step explanation:

this makes options B and C a choice:

Given the expression: 12x+18xy-24y

Factors of 12x=1,2,3,4,6,12 and x

Factors of 18xy=1,2,3,6,9,18,x and y.

Factors of 24y=1,2,3,4,6,8,12,24 and y.

next for E this is why its a choice:

12x+18xy-24y=6(2x+3xy-4y)

Answer:

bce

Step-by-step explanation:

Answer:

a = 120 cm²

Step-by-step explanation:

n = number of sides

edge length

40/n

divide the polygon into n congruent triangles

a = (1/2)(edge * apothem) * number of triangles

a = (1/2)(40/n)(6) * n

n cancels out

a = (1/2)(40)(6)

a = 120 cm²

Answer:

x = 3.24, x = -1.24

Step-by-step explanation:

The standard form for a quadratic equation is [tex]ax^2+bx+c=0[/tex]. For your equation a = 1, b = -2, c = -4. The quadratic formula you will be using is [tex]x=\frac{-b\pm \sqrt{b^{2} -4ac} }{2a}[/tex].

Plug in a = 1, b = -2, and c = -4 into the formula.

[tex]=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:1\cdot \left(-4\right)}}{2\cdot \:1}[/tex]

We'll do the top part first:

[tex]\sqrt{\left(-2\right)^2-4\cdot \:1\cdot \left(-4\right)}[/tex]

Apply rule [tex]- (-a) = a[/tex]

[tex]=\sqrt{\left(-2\right)^2+4\cdot \:1\cdot \:4}[/tex]

Apply exponent rule [tex](-a)^{n} =a^n[/tex] if [tex]n[/tex] is even

[tex](-2)^2=2^2[/tex]

[tex]=\sqrt{2^2+4\cdot \:1\cdot \:4}[/tex]

Multiply the numbers

[tex]=\sqrt{2^2+16}[/tex]

[tex]2^2=4[/tex]

[tex]=\sqrt{4+16}[/tex]

Add

[tex]=\sqrt{20}[/tex]

The prime factorization of 20 is [tex]2^2*5[/tex]

20 divides by 2. 20 = 10 * 2

[tex]=2*10[/tex]

10 divides by 2. 10 = 5 * 2

[tex]=2* \:2*5[/tex]

2 & 5 are prime numbers so you don't need to factor them anymore

[tex]=2*2*5[/tex]

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

[tex]=\sqrt{2^2\cdot \:5}[/tex]

Apply radical rule [tex]\sqrt[n]{ab} =\sqrt[n]{a} \sqrt[n]{b}[/tex]

[tex]=\sqrt{5}\sqrt{2^2}[/tex]

Apply radical rule [tex]\sqrt[n]{a^{n} } =a[/tex]; [tex]\sqrt{2^2} =2[/tex]

[tex]=2\sqrt{5}[/tex]

[tex]=\frac{-\left(-2\right)\pm \:2\sqrt{5}}{2\cdot \:1}[/tex]

Because of the [tex]\pm[/tex] you have to separate the solutions so that one is positive and the other is negative.

[tex]x=\frac{-\left(-2\right)+2\sqrt{5}}{2\cdot \:1},\:x=\frac{-\left(-2\right)-2\sqrt{5}}{2\cdot \:1}[/tex]

Positive x:

[tex]\frac{-\left(-2\right)+2\sqrt{5}}{2\cdot \:1}[/tex]

Apply rule [tex]-(-a)=a[/tex]

[tex]=\frac{2+2\sqrt{5}}{2\cdot \:1}[/tex]

Multiply

[tex]=\frac{2+2\sqrt{5}}{2}[/tex]

Factor [tex]2+2\sqrt{5}[/tex] and rewrite it as [tex]=2\cdot \:1+2\sqrt{5}[/tex]. Factor out 2 because it is the common term. [tex]=2\left(1+\sqrt{5}\right)[/tex].

[tex]=\frac{2\left(1+\sqrt{5}\right)}{2}[/tex]

Divide 2 by 2

[tex]x=1+\sqrt{5}[/tex] or [tex]x=3.24[/tex] (You'll probably have to use a calculator for the square root of 5)

^Repeating the process of positive x for negative x in order to get [tex]x=1-\sqrt{5}[/tex] or [tex]x=-1.24[/tex]

Answer:

15.25%

Step-by-step explanation:

The actual amount in a 12-ounce container of a certain brand of orange juice is normally distributed with mean μ = 12.34 ounces and standard deviation σ = 0.04 ounce. What percentage of the juice bottles contain between 12.24 and 12.30 ounces of orange juice?

We solve using the z score formula

z-score is is z = (x-μ)/σ,

where x is the raw score

μ is the population mean = μ = 12.34 ounces

σ is the population standard deviation = σ = 0.04 ounce

For x = 12.24

z = 12.24 - 12.34/0.04

z = -2.5

Probability value from Z-Table:

P(x = 12.24) = 0.0062097

For x = 12.30

z= 12.30 - 12.34/0.04

z = -1

Probability value from Z-Table:

P(x = 12.30) = 0.15866

Hence, the probability of the juice bottles contain between 12.24 and 12.30 ounces of orange juice

P(x = 12.30) - P(x = 12.24)

= 0.15866 - 0.0062097

= 0.1524503

Therefore, the percentage of the juice bottles contain between 12.24 and 12.30 ounces of orange juice is calculated as:

= 0.1524503 × 100

= 15.24503%

= 15.25%

Answer:

tan angle = x/5.

Step-by-step explanation:

If I understand your description,

tan angle at bottom of ramp = 1.2/3.

Then tan angle = x/5.

Check my thinking.

Answer:

y -4 = 1/6(x-24)

y = 1/6x -2

Step-by-step explanation:

We can point slope form

y-y1 = m(x-x1)  where m is the slope and (x1,y1) is a point on the line

y -4 = 1/6(x-24)

Or we can write slope intercept form

y = mx+b where m is the slope and b is the y intercept

Substituting the points

4 = 1/6(24)+b

4 = 6+b

4-6 = b

-2 =b

y = 1/6x -2

Answer:

[tex]y = mx + c \\ 4 = (\frac{1}{6} \times 24) + c \\ 4 = 4 + c \\ c = 0 \\ y = \frac{1}{6} x[/tex]

Answer:

The answer is the third one, x - 7 < 4

Step-by-step explanation: