Find the length of side x in simplest radical form with a rational denominator.
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Answer:

Slope - 21 Intercept - 15

The equation of the function h(x) is h(x) = 21x + 15, slope = 21, and y-intercept = 15.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The equation of the function f(x) is:

f(x) = -7x + 9

add 2 to the input off to create a new function g:

f(x + 2) = g(x) = -7(x + 2) + 9 = -7x - 5

g(x) = -7x - 5

Multiply the output of function g by -3 to create function h:

h(x) = -3g(x)

h(x) = -3(-7x - 5)

h(x) = 21x + 15

The slope = 21 and

y-intercept = 15

Thus, the equation of the function h(x) is h(x) = 21x + 15, slope = 21, and y-intercept = 15.

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Step-by-step explanation:

what to find then??.........

Answer:

The order of operations is Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.

Step-by-step explanation:

The order of operations is PEMDAS.

P: Parenthesis

E: Exponents

M: Multiplication

D: Division

A: Addition

S: Subtraction

An easy way to remember PEMDAS is, please excuse my dear aunt sally.

Hope this helps!

If not, I am sorry.

hmmm let's find hmmm say angle who knows, ∡C, using the law of cosines.

\(\textit{Law of Cosines}\\\\ \cfrac{a^2+b^2-c^2}{2ab}=\cos(C)\implies \cos^{-1}\left(\cfrac{a^2+b^2-c^2}{2ab}\right)=\measuredangle C \\\\[-0.35em] ~\dotfill\\\\ \cos^{-1}\left(\cfrac{18^2+14^2-12^2}{2(18)(14)}\right)=\measuredangle C \implies \cos^{-1}\left(\cfrac{ 376 }{ 504 }\right)=\measuredangle C \\\\\\ \cos^{-1}\left(\cfrac{ 47 }{ 63 }\right)=\measuredangle C\implies \cos^{-1}(0.7460317) \approx \measuredangle C \implies 41.75^o \approx \measuredangle C\)

well then, let's now us the law of sines to get hmm say ∡A

\(\textit{Law of Sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin( A )}{18}\approx\cfrac{\sin( 41.75^o )}{12}\implies 12\sin(A)\approx18\sin(41.75^o) \implies \sin(A)\approx\cfrac{18\sin(41.75^o)}{12} \\\\\\ A\approx\sin^{-1}\left( ~~ \cfrac{18\sin( 41.75^o)}{12} ~~\right)\implies A\approx 87.22^o\)

well, if we subtract ∡C and ∡A from the triangle's interior angle sum, we'll get that ∡B ≈ 51.03°.

Answer:

The given question requirement is to find the the measure of the minor arc \(m\widehat{AB}\)

An arc is said to be minor when represented as \(m\widehat{AB}\) and an arc is termed a major arc, when it presented as \(m\widehat{ACB}\)

From the given diagram, the measure of the minor arc \(m\widehat{AB}\) is given as the measure of the angle, m∠CAB which is equal to 38°

Therefore, the measure of the minor arc \(m\widehat{AB}\) = m∠CAB = 38°

The measure of the minor arc \(m\widehat{AB}\) is 38°

Step-by-step explanation:

The measure of the arc of the circular basin of the fountain that will be in the photograph is; 111°

Now, To answer this question, we need to understand the angle of intersecting secant theorem which state that;

If two lines intersect outside a circle, then the measure of the angle formed by the two lines is half of the positive difference of the measures of the intercepted arcs.

Thus;

θ = 1/2 (x₂ - x₁)

Where:

x₂ is large angle

x₁ is small angle

θ is measure of the Angle formed by the two lines

Now, we are given θ = 69°

Now the measure of the arc of the circular basin will be the smaller angle x₁.

However, the sum of the large and small angle is 360° and so large angle is 360 - x₁.

Thus;

69 = 1/2(360 - x - x)

2 × 69 = 360 - 2x

138 = 360 - 2x

360 - 138 = 2x

2x = 222

x = 222/2

x = 111°

Thus, The measure of the arc of the circular basin of the fountain that will be in the photograph is; 111°

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Answer:

70% of the juice boxes are left.

Step-by-step explanation:

10 is the total number of juice boxes which means that 10 is 100%

If there are 10 total juice boxes and Sam drank 3, there are 7 juice boxes left. Sam drank 30% of the juice boxes which means that there is 70% of the juice boxes left.

Hope this helps!

True: The line has a slope of zero.

False: The line can be represented by the equation x = 11. However, the line can be represented by the equation y = -4.

False: Austin draws a vertical line. Instead, Austin draws a horizontal line.

Mathematically, the standard form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

In Mathematics, a condition that must be met in order for two lines to be perpendicular is given by this mathematical expression:

m₁ × m₂ = -1

Since the line on Austin's graph is perpendicular to the y-axis, we can logically deduce that its slope (m) is equal to zero because there is no change in the y-value on the y-axis.

At point (11, -4), the equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-4) = 0(x - 11)

y + 4 = 0

y = -4

Therefore, this line can be represented by the equation y = -4 Austin should draw a horizontal line as shown in the image attached below.

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Complete Question:

Austin graphs a line perpendicular to the y-axis passing through the point (11, -4), Mark a-c as true or false. If false, rewrite the statement correctly.

a. ____ The line has a slope of zero.

b. ____ The line can be represented by the equation x = 11.

c. ___ Austin draws a vertical line.

Answer:16

Step-by-step explanation:

Answer:

This team can form 400 pretzels in one hour

Step-by-step explanation:

How many pretzels in 9 minutes?

5(12)=60

Solve as proportion

60 pretzels = 9 minutes

x    pretzels = 60 minutes

60(60)=9x

3600=9x

Divide both sides by 9

x= 400 pretzels

This team can form 400 pretzels in 1 hour

Answer:

this team can form 30 pretzels in 1 hour

Step-by-step explanation:

60 minutes are in a hour, and 60 divided by 9 is 6.6. So that means you would have to use 6. So 9 x 6 equals 54. Now do 5 x 6 and that would equal 30.

The error term is a random variable with an expected value of zero.2. The error term is normally distributed

The assumptions underlying the simple linear regression model `y = Bo + B1x + e` are: 1.

The variance of the error term e is constant across all values of x.Thus, the assumptions that are underlying the simple linear regression model `y = Bo + B1x + e` are the second and the third options, which are "The error term is normally distributed." and "The variance of the error term e is constant across all values of x." respectively.

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Answer:

B: 4

Step-by-step explanation:

The graph shows that there is 4 units between the numbers 30-36.

Hope this helps!

Answer:

\(x=7\)

Step-by-step explanation:

So we have the equation:

\(7x-27=3x-5+x-1\)

Combine like terms:

\(7x-27=4x-6\)

Subtract 4x from both sides:

\(3x-27=-6\)

Add 27 to both sides:

\(3x=21\)

Divide both sides by 3:

\(x=7\)

So, the value of x is 7.

And we're done!

Steps to solve:

7x - 27 = 3x - 5 + x - 1

~Combine like terms

7x - 27 = 4x - 6

~Add 27 to both sides

7x = 4x + 21

~Subtract 4x to both sides

3x = 21

~Divide 3 to both sides

x = 7

Best of Luck!

The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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The probability for each k value is from 15 to 25 and sum them up to get the final probability.

The situation you described is not a geometric distribution. Instead, it follows a binomial distribution. A binomial distribution is appropriate here because we have a fixed number of trials (25 coin flips), each trial has two outcomes (heads or tails), and the probability of success (getting heads) remains constant throughout the trials.

To calculate the probability of getting 15 or more heads in 25 coin flips, you can use the binomial formula:

\(P(X = k) = C(n, k) * p^k * (1-p)^{(n-k)}\)

where n is the number of trials (25), k is the number of successful outcomes (15 or more), p is the probability of success (0.5 for a fair coin), and C(n, k) represents the number of combinations of n items taken k at a time.

You'll need to calculate the probability for each k value from 15 to 25 and sum them up to get the final probability.

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Answer:

\( {m}^{2} \)

Step-by-step explanation:

\( \frac{ \sqrt{ {m}^{3} } \times {m}^{ \frac{2}{3} } }{ {m}^{ \frac{1}{6} } } \\ \\ = \frac{ { {m}^{ \frac{3}{2} } } \times {m}^{ \frac{2}{3} } }{ {m}^{ \frac{1}{6} } } \\ \\ = \frac{ {m}^{ \frac{3}{2} + \frac{2}{3} } }{ {m}^{ \frac{1}{6} } } \\ \\ = \frac{ {m}^{ \frac{3}{2} + \frac{2}{3} } }{ {m}^{ \frac{1}{6} } } \\ \\ = \frac{ {m}^{ \frac{9 + 4}{2 \times 3} }}{ {m}^{ \frac{1}{6} } } \\ \\ = \frac{ {m}^{ \frac{13}{6} }}{ {m}^{ \frac{1}{6} } } \\ \\ = {m}^{ \frac{13}{6} - \frac{1}{6} } \\ \\ = {m}^{ \frac{12}{6} } \\ \\ = {m}^{2} \)

The directional derivative of h at (2, 2, 2) in the direction of the vector v is 24sqrt(2).

To find the directional derivative of the function h(r, s, t) = ln(3r^6s^9t) at the point (2, 2, 2) in the direction of the vector v = 8i + 24j + 12k, we need to first find the gradient of h at that point:

∇h(2, 2, 2) = (∂h/∂r, ∂h/∂s, ∂h/∂t)|_(2,2,2)
= (18/2, 54/2, 36/2)
= (9, 27, 18)

Next, we normalize the vector v to get a unit vector u in the direction of v:

||v|| = sqrt(8^2 + 24^2 + 12^2) = sqrt(800) = 20sqrt(2)
u = (1/||v||) v = (1/20sqrt(2))(8i + 24j + 12k) = (1/sqrt(50))(i + 3j + k)

The directional derivative of h in the direction of v is then given by the dot product of the gradient of h at (2, 2, 2) and the unit vector u:

D_v h(2, 2, 2) = ∇h(2, 2, 2) · u
= (9, 27, 18) · (1/sqrt(50))(i + 3j + k)
= (9/sqrt(50)) + (81/sqrt(50)) + (18/sqrt(50))
= (108/sqrt(50))
= 24sqr

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Answer:

To find out by how much the price was reduced, we can use the following equation:

price reduction = original price * reduction percentage

We know that the price reduction is £264 and the reduction percentage is 17.5%, so we can plug those values into the equation to get:

price reduction = £264 / 17.5%

To solve this equation, we need to express the percentage as a decimal. We can do this by dividing the percentage by 100:

price reduction = £264 / (17.5 / 100)

This simplifies to:

price reduction = £264 / 0.175

Solving this equation gives us a price reduction of £1512.

So, the original price was reduced by £1512.

Step-by-step explanation:

Answer:

f=6 and s=18

Step-by-step explanation:

Let's solve your system by substitution.

s+f=24;s=3f

Rewrite equations:

s=3f;f+s=24

Step: Solves=3ffor s:

s=3f

Step: Substitute3fforsinf+s=24:

f+s=24

f+3f=24

4f=24(Simplify both sides of the equation)

4f

4

=

24

4

(Divide both sides by 4)

f=6

Step: Substitute6forfins=3f:

s=3f

s=(3)(6)

s=18(Simplify both sides of the equation)

Answer:

f=6 and s=18

Answer:

sometimes is called the cost or wholesale price

Answer: 3

Step-by-step explanation:

Because if you look on the graph and count up to 80 the inequality says greater than and therefore 3 dots are greater than 80.

Answer:

Step-by-step explanation:

The answer is 3. Please see picture attached below.

To check our answer, we can verify that the number of quarters is 1.7 times the number of dimes, which would be 102. And the total value of her dimes and quarters would be:  $31.50

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let's start by using algebra to solve the problem.

Let x be the number of dimes that Carol has saved.

According to the problem, there are 70% more quarters than dimes. We can express the number of quarters in terms of x as 1.7x, since 1.7 times the number of dimes is equal to the number of quarters.

We also know that the combined value of her quarters and dimes is $31.50. We can express this as an equation:

0.10x + 0.25(1.7x) = 31.50

Simplifying and solving for x, we get:

0.10x + 0.425x = 31.50

0.525x = 31.50

x = 60

Therefore, Carol has 60 dimes.

Therefore, To check our answer, we can verify that the number of quarters is 1.7 times the number of dimes, which would be 102. And the total value of her dimes and quarters would be:

60 * $0.10 (dimes) + 102 * $0.25 (quarters) = $31.50

which matches the information given in the problem.

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Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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Answer:

x=4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

0.75x+3=6(x−3)

0.75x+3=(6)(x)+(6)(−3)(Distribute)

0.75x+3=6x+−18

0.75x+3=6x−18

Step 2: Subtract 6x from both sides.

0.75x+3−6x=6x−18−6x

−5.25x+3=−18

Step 3: Subtract 3 from both sides.

−5.25x+3−3=−18−3

−5.25x=−21

Step 4: Divide both sides by -5.25.

−5.25x/-5.25    =    -21/-5.25

Answer: x=4

The value of x from the given equation is 4.

The given equation is 0.75x + 3 = 6 (x - 3).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation can be solve for x as follows:

0.75x + 3 = 6x - 18

⇒ 6x-0.75x = 3+18

⇒ 5.25x=21

⇒ x=21/5.25

⇒ x=4

Therefore, the value of x from the given equation is 4.

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Answer:

5

Step-by-step explanation:

slopes of the parallel lines are always same this line has slope five

because equation in y intercept form is y=mx+b

where m is the slope.

so the slope of the new line will be five

Answer: The numbers on a distance of 3.2 units from −4 on a number line are -7.2 and - 0.8 .

Step-by-step explanation:

The numbers on a number line are from - infinity to + infinity whose center is at 0.Om left sides of 0 , there are negative integers and on the right side there are positive integers.

So, The numbers on a distance of 3.2 units from −4 on a number line are

-4 - 3.2 and -4+3.2

= - (4+3.2)  and - (4-3.2)

= -7.2 and - 0.8

Hence, the numbers on a distance of 3.2 units from −4 on a number line are -7.2 and - 0.8 .

Answer:

−7.2 and −0.8

Step-by-step explanation:

Have a blessed day

Answer:

I took 97000 and doubled it to get the doubling at 8 hours. For the 3 hours I took 3/8 of the doubled number. Then added doubled population and 3/8. 266,750.00 Not 100% on this one. I would double check.

The population of bacteria in the culture after 11 hours, to the nearest whole number, will be 327,375.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, A culture of bacteria has an initial population of 97000 bacteria and doubles every 8 hours.

The given formula is,

Pt = P2á ,

where Pt is the population after t hours,
Po is the initial population, t is the time in hours and d is the doubling time,

The population of bacteria in the culture after 11 hours is obtained as,

= 97000 +97000 × 2 + 97000 × 3/8

=327,375

Thus, the population of bacteria in the culture after 11 hours, to the nearest whole number, will be 630,500.

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A)The probability of exactly four buses arriving in the next 2 hours is\($P(X=4)=e^{\wedge}(-2)\left(2^{\wedge} 4 / 4 !\right)=0.090$\) ≈ 0.090.

B) The probability of at least two buses arriving in the next 2 hours is =0.865

C)  The probability of no buses arriving in the next 2 hours is =0.135

d) The probability that it will be between 30 and 90 minutes before the next bus arrives is ,0.185

a) Let \($X$\) be the number of buses that arrive in a 2-hour period. Since the time between arrivals of buses follows an exponential distribution with a mean of 60 minutes, the arrival rate λ is given by\($\lambda=1 / 60$\) 0 buses per minute.

Therefore, the number of buses that arrive in a 2-hour period is a Poisson distribution with parameter \(\mu=\lambda t=(1 / 60) \times 120=2$.\). Thus, X has a Poisson distribution with parameter μ = 2.

The probability of exactly four buses arriving in the next 2 hours is\($P(X=4)=e^{\wedge}(-2)\left(2^{\wedge} 4 / 4 !\right)=0.090$\) ≈ 0.090.

b) The probability of at least two buses arriving in the next 2 hours is

\($P(X \geq 2)=1-P(X=0)-P(X=1)=1-e^{\wedge}(-2)\left(2^{\wedge} 0 / 0 !\right)-e^{\wedge}(-2)\left(2^{\wedge} 1 / 1 !\right)=0.865$.\)

c) The probability of no buses arriving in the next 2 hours is

\(P(X=0)=$ $e^{\wedge}(-2)\left(2^{\wedge} 0 / 0 !\right)=0.135$\)

d) Let Y be the time between the first and second bus arrivals. Then Y follows an exponential distribution with a mean of 60 minutes. We want to find the probability that \($30 \leq Y \leq 90$\).

This is equivalent to finding \(P(Y \leq$ $90)-P(Y \leq 30)$,\), which is equal to F(90) - F(30), where F is the cumulative distribution function of the exponential distribution with \($\lambda=1 / 60$\)

Therefore, the probability that it will be between 30 and 90 minutes before the next bus arrives is\(F(90)-F(30)=\left(1-e^{\wedge}(-90 / 60)\right)-(1$ $\left.e^{\wedge}(-30 / 60)\right)=e^{\wedge}(-1.5)-e^{\wedge}(-0.5)=0.185$\)

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