Twelve times a number is - 72. Find the
Number.

Answer:

(x + 4)^2 + (y + 7)^2 = 36

Step-by-step explanation:

The given information describes a circle with its center at (-4, -7) and tangent to the vertical line x = 2. To determine the radius of the circle, we need to find the distance between the center and the tangent line.

The distance between a point (x1, y1) and a line Ax + By + C = 0 is given by:

d = |Ax1 + By1 + C| / sqrt(A^2 + B^2)

In this case, the equation of the line is x = 2, which can be written as 1x + 0y - 2 = 0. Therefore, A = 1, B = 0, and C = -2. The center of the circle is (-4, -7), so x1 = -4 and y1 = -7. Substituting these values into the formula, we get:

d = |1*(-4) + 0*(-7) - 2| / sqrt(1^2 + 0^2)

d = |-6| / sqrt(1)

d = 6

Therefore, the radius of the circle is 6 units. The equation of a circle with center (h,k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

Substituting the values we have found, we get:

(x + 4)^2 + (y + 7)^2 = 36

This is the equation of the circle that satisfies the given conditions.

Answer:

yes quadrilateral is a polygon

Step-by-step explanation:

because quadrilateral is a four sided figure

For the given figure,   x = 23°  and      y = 129°

Parallel lines:

                        Parallel lines are lines that always stay the same distance apart and never meet.

Transversal line :

                             A transversal is a line that crosses two or more other lines.

given,

     ∠TLN = (3x - 18)°

    ∠MZQ = (5x + 14)°

    ∠NLM = y°

Now,

         ∠MZP + ∠MZQ = 180°  (Linear Pair)

        ∠MZP  = 180° - ∠MZQ  ...........(I)

again,

          ∠NLM + ∠TLN  =180°  ...........(II)      (Linear Pair)

  As,         ∠TLN = ∠MZP  (Corresponding Angle)

             (3x - 18)° =  180° - ∠MZQ  

           (3x - 18)° = 180° - (5x + 14)°

         3x + 5x  = 180° - 14° + 18°

           8x = 184°

           x = 184 / 8

          x = 23°

      From (II),

      ∠NLM + ∠TLN  =180°

    y° + 3x - 18° = 180°

 y = 180 - 3x + 18

     = 180 - 3* 23 + 18

      = 180 - 69 +18

     y = 129°

For the given figure,

                                     x = 23°  and      y = 129°

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Answer:

o 1)

\(Y= 6x + 11 \\ \\ 6x = Y - 11 \\ \\ x = \frac{Y - 11}{6} \\ \\ x = \frac{Y}{6} - \frac{11}{6} \)

___o__o__

o 2)

\(A = \frac{1}{2} bh \\ \\ bh = A \div \frac{1}{2} \\ \\ bh = A \times 2 \\ \\ bh = 2A\)

\(b = \frac{2A}{h} \)

\(h = \frac{2A}{b} \)

Answer: C) triangles ABC is not similar to  the triangle DEF because angles B and D re not congruent.

Step-by-step explanation:

...as it say...

Answer:

$5.98 credit

Step-by-step explanation:

the slope OR "m" in y=mx in this equation is given to be: -0.16

To find the answer you know that the calling time (x) is 37 minutes, therefore you multiply 3 by -0.16 to find the credit after 37 mins

y=mx

y=(0.16)(37)

y=5.92

To establish trust with Martina, the nurse should show respect, use non-verbal communication, incorporate play, involve the parent, and individualize the approach.

To establish a trusting relationship with Martina, the nurse can employ several approaches:

Respect and empathy: The nurse should approach Martina with genuine respect and empathy, recognizing her unique needs and individuality. This can be conveyed through a calm and patient demeanor.

Non-verbal communication: Since Martina may not be responsive to verbal cues, the nurse can utilize non-verbal communication to establish connection and trust. This can include maintaining eye contact, using gentle touch, and respecting Martina's personal space.

Play and familiar objects: Given Martina's engagement with the blue stuffed dog, the nurse can incorporate play into their interactions. Bringing familiar objects or toys that Martina finds comforting can help create a sense of familiarity and security.

Parental involvement: Involving Martina's mother in the care process can be beneficial. The nurse can communicate with the mother, seek her input, and involve her in the administration of medications. This helps build trust not only with Martina but also with her caregiver.

Individualized approach: Recognizing Martina's autistic disorder, the nurse should tailor their approach to her specific needs. Understanding her sensory sensitivities and preferences can help create a safe and comfortable environment.

By implementing these strategies, the nurse can foster trust and a positive therapeutic relationship with Martina, promoting her overall well-being and care.

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Complete Question:

What approach would help the nurse establish a trusting relationship with Martina, a 3-year-old with bronchitis and autistic disorder, who is intensely occupied with a blue stuffed dog and does not seem responsive to the nurse's presence in the room, while the mother is also present?

The functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

a) To find two functions f and g such that (fog)(x) = 1/(x + 2), we need to determine how the composition of the two functions f and g produces the given expression.

Let's start by assuming g(x) = x + a, where a is a constant. This means that g(x) adds the constant a to the input x.

Next, let's determine the function f(x) such that (fog)(x) results in the desired expression. We have:

(fog)(x) = f(g(x)) = f(x + a)

b) To simplify the expression 1/(x + 2) and make it match f(g(x)), we can consider f(x) = 1/x.

Substituting the expressions for f(x) and g(x) into (fog)(x), we have:

(fog)(x) = f(g(x)) = f(x + a) = 1/(x + a)

Comparing this with the desired expression 1/(x + 2), we see that a = 2. Therefore, the functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

Using these functions, we can verify the composition (fog)(x):

(fog)(x) = f(g(x)) = f(x + 2) = 1/(x + 2)

Thus, (fog)(x) = 1/(x + 2), which matches the desired expression.

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There is insufficient evidence that more than 15% of all such bottles are contaminated.

So, we do not reject the null hypothesis.

Part A

Here, we have to use z test for population proportion.

The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: p = 0.15

Alternative hypothesis: Ha: p > 0.15

The test statistic formula is given as below:

Z = (P – p) / √(pq/n)

Where, P = sample proportion, p = population proportion, q = 1 – p, n = sample size

For the given data we have

Alpha = 0.05

Number of items of interest = x = 16

Sample size = n = 91

Sample proportion = 16/91 = 0.175824

Standard error = √(pq/n) = √(0.15*0.85/91) = 0.0374

Z = (0.175824 – 0.15) / 0.0374

Z = 0.6899

P-value = 0.2451

P-value >α

So, we do not reject the null hypothesis

There is insufficient evidence that more than 15% of all such bottles are contaminated.

Part b

Here, z test is appropriate.

Because two conditions are satisfied as below:

np = 91*0.15 = 13.65 > 5

nq = 91*0.85 = 77.35 > 5

Hence we get the required answer.

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Answer:

31 is n

Step-by-step explanation:

75=13+2n

75-13=62

62=2n

62/2=31

31=n

Answer:

Let the required number be "n"

According to the above problem,

\(2n + 13 = 75 \\ 2n = 75 - 13 \\ 2n = 62 \\ n = \frac{62}{2} \\ \boxed{n = 31 }\)

Therefore,

Answer:

18 square units

Step-by-step explanation:

The parallelogram has been plotted in the attached figure

The area of a parallelogram is b x h

where b is one side and h is the vertical distance between the two bases

In the figure, we see that base = AB is parallel to the y-axis

This means the y-coordinates of A and B are the same and the distance is obtained by taking the absolute difference between the x-coordinates of A and B

b = |x1 - 2| = |6 - 0| = 6

The height h is a perpendicular line from point D(1, 3) to the base which touches the base at point E

Since this line is horizontal to the x-axis in the figure, the y coordinates of the endpoints of the line are the same i.e y1 =3 and y2 = 3

Therefore h = absolute difference between the x coordinates
= |1-4| = 3

Given b = 6, h = 3

area = 6x 3 = 18 square units

Answer:

5870.23

The digit 3

Step-by-step explanation:

Answer:

$75.00

Step-by-step explanation:

The option "On a coordinate plane, a curve starts in quadrant 4 and curves up into quadrant 1" is the correct alternative.

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x. We can write -

\($y =log_{e} x\)

We have logarithmic function as -

\($y =log_{e} x\)

Refer to the graph of the logarithmic function attached. It can be seen that on a coordinate plane, a curve starts in quadrant 4 and curves up into quadrant 1.

Therefore, the option "On a coordinate plane, a curve starts in quadrant 4 and curves up into quadrant 1" is the correct alternative.

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A zero has the same meaning as the vertex.

The point where two lines meet forming an angle or set of angles is referred to as a vertex. This can also be called a point of origin especially when considering the axis of a Cartesian coordinate.

The vertex can be taken as zero since it is referred to as the point of origin. This is different to the axis of symmetry; as the axis of symmetry is one that splits a given plotted points i.e. a graph into two equal parts.

Thus, a zero has the same meaning as the vertex.

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Using the Pythagorean Theorem, the rate at which the distance between the vehicles is changing at t = 10 minutes is of -20 km/hour.

The Pythagorean Theorem relates the length of the legs \(l_1\) and \(l_2\) of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the equation given below:

\(h^2 = l_1^2 + l_2^2\)

In the context of this problem, the distances of the cars from Sioux Falls, considering the initial distances and the velocities, are given as follows:

The distance after t hours is the hypotenuse of a right triangle in which the legs are the functions, hence:

D²(t) = P²(t) + T²(t).

Hence the rate of change of the distance after t hours is:

2D'(t) = 2P'(t) + 2T'(t)

Simplifying by 2:

D'(t) = P'(t) + T'(t).

Applying the exponent rules, the derivatives are given as follows:

Hence the constant rate is:

D'(t) = -160 + 140 = -20 km/hour.

Meaning that the police car is getting 20 km closer to the truck each hour.

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As he rolls the dough, if length is increasing at a rate of 0.5 cm/sec, the rate at which the radius is changing when the radius is 1cm and the length is 5cm will be -0.05 cm/sec using the concept of increasing or decreasing functions.

As per the question statement, if dough is in form of a cylinder and its length is increasing at a rate of 0.5 cm/sec, we have to find the rate at which the radius is changing when the radius is 1cm and the length is 5cm.

Volume V = πr^2h, where 'r' is the radius and 'h' is the length

dV/dt = πr^2*(dh/dt) + h*2πr*(dr/dt) [Derivation wrt 't']

dV/dt = 0, as quantity of dough is same.

so at r = 1cm and h = 5cm

0 = π(1^2)*(0.5) + 5*2π*1(dr/dt)

5*2π*1(dr/dt) = -π(1^2)*(0.5)

10π*(dr/dt) = -π*0.5

(dr/dt) =  -0.05 cm/sec

Hence, as he rolls the dough, if length is increasing at a rate of 0.5 cm/sec, the rate at which the radius is changing when the radius is 1cm and the length is 5cm will be -0.05 cm/sec using the concept of increasing or decreasing functions.

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Answer:

m = 5

Step-by-step explanation:

A quadratic function is in the form \(ax^{2} +bx+c\).

To factor an equation, you are looking for two numbers that multiply to c (are factors of c), and add to b. In this case, c = -15, and b = 2.

The factors of -15 include 1, 3, 5, 15, -1, -3, -5, and -15.

After looking through the possible combinations, we can come to the conclusion that the only factors that multiply to -15 and add to 2 are 5 and -3, as 5 x -3 = -15, and 5 + -3 = 2.

You can now plug these numbers into the factored form (x + factor1)(x + factor2).

This then becomes (x + -3)(x + 5) or (x - 3)(x + 5).

Therefore, m = 5.

Answer:

y = 3.2

Step-by-step explanation:

Simplifying

5y + -6 = 10

Reorder the terms:

-6 + 5y = 10

Solving

-6 + 5y = 10

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '6' to each side of the equation.

-6 + 6 + 5y = 10 + 6

Combine like terms: -6 + 6 = 0

0 + 5y = 10 + 6

5y = 10 + 6

Combine like terms: 10 + 6 = 16

5y = 16

Divide each side by '5'.

y = 3.2

Simplifying

y = 3.2

It will take Adrian 16 full months to save enough money for the electric keyboard.

- Price of the keyboard (with tax) at Macelli's: $2,400
- Adrian's monthly savings: $150
We need to find how long it will take Adrian to save for the keyboard. To do this, we'll divide the total cost of the keyboard by his monthly savings and round up to the nearest full month.
Step 1: Divide the total cost by monthly savings.
Time (in months) = (Total Cost) / (Monthly Savings) = ($2,400) / ($150)
Step 2: Calculate the result.
Time (in months) = 16
So, it will take Adrian 16 full months to save enough money for the electric keyboard.

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Answer:

121 is the perfect square between 100 and 144.

Answer:

---------------------------

There are two triangular faces with base of 16 cm and height of 15 cm and three rectangular faces.

Find the sum of areas of all five faces:

Answer:

0.29

Step-by-step explanation:

Answer:

it's 0.29 because we move the decimal point 2 spaces to the left

Given statement solution is :-  For the third week of April, Patricia's:

Regular pay amount is $476.

Overtime pay is $231.45.

Gross pay is $707.45.

To calculate Patricia's pay for the third week of April, we'll need to determine her regular pay, overtime pay, and gross pay.

Regular Pay:

Patricia worked 53 hours, but only 40 hours are considered regular hours. Therefore, the regular pay is calculated as follows:

Regular Pay = Regular Hours x Hourly Rate

Regular Pay = 40 hours x $11.90/hour

Regular Pay = $476

Overtime Pay:

Since Patricia worked 53 hours in total and 40 of those are regular hours, the remaining 13 hours are considered overtime hours. Overtime pay is calculated by multiplying the overtime hours by 1.5 times the hourly rate.

Overtime Pay = Overtime Hours x (Hourly Rate x 1.5)

Overtime Pay = 13 hours x ($11.90/hour x 1.5)

Overtime Pay = 13 hours x $17.85/hour

Overtime Pay = $231.45

Gross Pay:

Gross Pay is the sum of Regular Pay and Overtime Pay.

Gross Pay = Regular Pay + Overtime Pay

Gross Pay = $476 + $231.45

Gross Pay = $707.45

Therefore, for the third week of April, Patricia's:

Regular pay amount is $476.

Overtime pay is $231.45.

Gross pay is $707.45.

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Answer:

Three types of ratios that are equivalent to 8.2

Step-by-step explanation:

S. No. Ratios. Formulas

1. Current Current Assets/

ratio Current Liabilities

2. Quick Liquid Assets/ Current

ratio Liabilities

3. Absolute Absolute Liquid Assets/

liquid Current Liabilities

ratio

Please mark as brainliest

Answer: Hi I will solve this right quick.

Step-by-step explanation:

The equation is \(\frac{4}{9} x^{2} y x(x^{2} -3xy+y^{2} )\)

The answer is this

\(\frac{4y (x^{2} - 3xy +y2) x^{3} }{9}\)

Answer:

\(\dfrac{4}{9}x^{5}y-\dfrac{4}{3}x^{4}y^{2}+\dfrac{4}{9}x^{3}y^{3}\)

Step-by-step explanation:

Given expression:

\(\dfrac{4}{9}x^2yx(x^2-3xy+y^2)\)

Distribute:

\(\implies \dfrac{4}{9}x^2yxx^2-\dfrac{4}{9}x^2yx3xy+\dfrac{4}{9}x^2yxy^2\)

Re-order each term to collect like variables:

\(\implies \dfrac{4}{9}x^2x^2xy-\dfrac{4 \cdot 3}{9}x^2xxyy+\dfrac{4}{9}x^2xy^2y\)

\(\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:\)

(Remembering that a = a¹)

\(\implies \dfrac{4}{9}x^{2+2+1}y-\dfrac{12}{9}x^{2+1+1}y^{1+1}+\dfrac{4}{9}x^{2+1}y^{2+1}\)

\(\implies \dfrac{4}{9}x^{5}y-\dfrac{12}{9}x^{4}y^{2}+\dfrac{4}{9}x^{3}y^{3}\)

Reduce 12/9 to 4/3:

\(\implies \dfrac{4}{9}x^{5}y-\dfrac{4}{3}x^{4}y^{2}+\dfrac{4}{9}x^{3}y^{3}\)

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9514 1404 393

Answer:

  13/8

Step-by-step explanation:

Put the numbers in the formula and do the arithmetic.

  \(\dfrac{4\dfrac{2}{3}-\left(-1\dfrac{5}{6}\right)}{-7\dfrac{3}{4}-(-11.75)}=\dfrac{6.5}{4}=\boxed{\dfrac{13}{8}}\)