Which graph shows a car traveling at 50 miles per hour?

Answer:

4, 4, and 4.

The three positive numbers that satisfy the given conditions are

x = y = z = 4, and their sum is 12.

Given,

Sum of three numbers is 12.

Let the three positive numbers are x, y, and z.

1. To minimize the sum of their squares as

[tex]f(x, y, z) = x^2 + y^2 + z^2[/tex]

Subject to the constraint: Sum of three numbers is 12.

[tex]g(x, y, z) = x + y + z = 12[/tex]

2. Using Lagrangian function:

[tex]L(x, y, z, \lambda) = f(x, y, z) - \lambda(g(x, y, z) - 12)[/tex]

Substituting the value of f(x, y, z) = [tex]x^2 + y^2 + z^2[/tex] and g(x, y, z) = [tex]x + y + z - 12[/tex]  into Lagrangian function gives

[tex]L(x, y, z, \lambda) = (x^2+y^2+z^2) - \lambda (x+ y+ z - 12)[/tex]

3. Now, take partial derivatives of L with respect to x, y, z, and λ,

[tex]\(\frac{{\partial L}}{{\partial x}}[/tex] = [tex]2x - \lambda\)[/tex]

[tex]\(\frac{{\partial L}}{{\partial y}}[/tex] = [tex]2y - \lambda\)[/tex]

[tex]\(\frac{{\partial L}}{{\partial z}}[/tex] = [tex]2z - \lambda\)[/tex]

[tex]\(\frac{{\partial L}}{{\partial \lambda}}[/tex] = [tex]-(x + y + z - 12)[/tex]

4. Now, set each derivative to zero to find the critical points.

Equation 1:     [tex]\(\frac{{\partial L}}{{\partial x}}[/tex] = [tex]2x - \lambda\)[/tex] =0

Equation 2:     [tex]\(\frac{{\partial L}}{{\partial y}}[/tex] = [tex]2y - \lambda\)[/tex] = 0

Equation 3:     [tex]\(\frac{{\partial L}}{{\partial z}}[/tex] = [tex]2z - \lambda\)[/tex] = 0

Equation 4:     [tex]\(\frac{{\partial L}}{{\partial \lambda}}[/tex] = [tex]-(x + y + z - 12)[/tex] = 0

Solving equations (1), (2), and (3) we get

        x = λ/2

        y = λ/2

         z = λ/2.

5. Substituting the value x = y = z = λ/2 into equation (4) gives

[tex]-(x + y + z - 12) = 0[/tex]

- [tex](\lambda/2 + \lambda/2 + \lambda/2 -12)= 0[/tex]

[tex]-(3\lambda/2 - 12) = 0[/tex]

[tex]3\lambda/2 = 12[/tex]

[tex]\lambda = 8[/tex]

So, x = y = z = λ/2 = 4.

Therefore, the three positive numbers are 4, 4 and 4.

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Answer:

True

m∠T = 40.4°

Step-by-step explanation:

We know all the sides of the triangle but we do not know any of its angles.

To find out if the angle T = 40.4 ° we use the cosine theorem.

According to the cosine theorem:

[tex]c^2=a^2 +b^2-2abcos(\alpha)[/tex]

Where [tex]\alpha[/tex] is the angle between a and b.

In this case:

[tex]\alpha = T\\\\a= 11\\\\b=13\\\\c= 8.5[/tex]

Then we clear α from the formula and verify that it is equal to 40.4 °

[tex]8.5^2 =11^2 + 13^2 -2(11)(13)cos(\alpha)\\\\8.5^2 -11^2 - 13^2= -2(11)(13)cos(\alpha)\\\\-8.5^2 +11^2 + 13^2= 2(11)(13)cos(\alpha)\\\\\frac{-8.5^2 +11^2 + 13^2}{2(11)(13)}=cos(\alpha)\\\\\alpha=arcos(\frac{-8.5^2 +11^2 + 13^2}{2(11)(13)})\\\\\alpha = 40.4\° =T[/tex]

Answer:

simplify -1(3/5)÷(-2/3) = 9/10

=90/100

= .90 and there's your answer

Answer:

12/5 = 2  2/5

Step-by-step explanation:

Convert -1  3/5 into an improper fraction:  -8/5.

Next, divide -8/5 by (-2/3).  Equivalently, invert (-2/3), obtaining (-3/2), and multiply:

(-8/5)(-3/2) = 24/10 = 12/5 = 2  2/5

Step-by-step explanation:

20°

Half of 40°

x=20° answer

Answer:

x = 20°

Step-by-step explanation:

The inscribed angle x is half the central angle subtended by the same arc on the circle, hence

x = 0.5 × 40 = 20°

Answer:

x^4 + 4x^3 + 6x^2 + 7x +2

Step-by-step explanation:

Answer: The answer is D.

Step-by-step explanation: Considering that the dots represent people, all you have to do is count the dots. Graph D is the only plot that has three in both 6 and 8.

Hope this helps & Good Luck,

Melodii

The answer is D

The last chart that has three dots on the numbers 8 and 6

To find 3 people that sleep for 8 hrs, there should be 3 dots on top of the number 8...

And to find 3 people that sleep ofor 6 hrs, there should be 3 dots on top of the number 6 too

Hope this helped,

have a blessed day :-)

Answer: Last option

(42÷2) +5

Step-by-step explanation:

We know that Mr. Roberts drove 42 miles on Monday.

On Tuesday Mr. Roberts drove half of what he drove on Monday plus 5 miles.

If we want to know how many miles Mr. Roberts drove on Tuesday then we should divide 42÷2 to find half of 42.

[tex]\frac{42}{2} = 21[/tex]

Then we know that in addition to the 21 miles he drove 5 more miles. Then we add 21 +5 = 26 miles.

So the expression that gives us the number of miles that Mr. Roberts drove on Tuesday is:

(42÷2) +5

The answer is D trust me

Answer:

m<ADB = 25 degrees

Step-by-step explanation:

<ADB has two different intercepted arcs: AB and the unlabeled one that has a measure of 20. To find the actual measure of the angle, we must find the difference between these arcs and divide by 2.

70-20 = 50

50/2 = 25

Applying the angle of intersecting secants theorem, the measure of angle ADB in the diagram is: A. m∠ADB = 25°

When two secants meet at a point outside a circle, the measure of angle formed at that point is half the positive difference of the intercepted arcs, based on the angle of intersecting secants theorem.

m∠ADB = 1/2(70 - 20)

m∠ADB = 1/2(50)

m∠ADB = 25°

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Answer:

see explanation

Step-by-step explanation:

36

Since triangle is isosceles then AB = BC

Equate the 2 sides, that is

4x - 21 = 2x - 7 ( subtract 2x from both sides )

2x - 21 = - 7 ( add 21 to both sides )

2x = 14 ( divide both sides by 2 )

x = 7, hence

AB = 2x - 7 = (2 × 7) - 7 = 14 - 7 = 7

BC = 4x - 21 = (4 × 7) - 21 = 28 - 21 = 7

AC = x - 3 = 7 - 3 = 4

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

37

Since the triangle is equilateral then all 3 sides are equal.

Equate any 2 sides and solve for x

6x + 1 = 3x + 10 ( subtract 3x from both sides )

3x + 1 = 10 ( subtract 1 from both sides )

3x = 9 ( divide both sides by 3 )

x = 3

HF = 6x + 1 = (6 × 3) + 1 = 18 + 1 = 19 = FG = HG

ANSWER

[tex]y ={x}^{2} + 2[/tex]

EXPLANATION

The equation of a parabola that has vertex at (h,k) is given by:

[tex]y = a {(x - h)}^{2} + k[/tex]

If the given parabola has vertex at (0,2), then h=0 and k=2.

Considering the possible answers, we must have a=1.

We substitute the values in to the formula to get:

[tex]y =1 {(x - 0)}^{2} + 2[/tex]

[tex]y ={x }^{2} + 2[/tex]

The first option is correct.

Answer:

At 1.5 seconds and 2.5 seconds

Step-by-step explanation:

Because this is parabolic motion, the object will reach the height of 68 feet when it's going up AND when it's coming down.  In order to find out those times, you set the h on the left side of the equation equal to 68, because h stands for height.

[tex]68=-16t^2+64t+8[/tex]

Set that equal to 0 and factor to solve for t:

[tex]-16t^2+64t-60=0[/tex]

Using the quadratic formula, we get t = 1.5 and t = 2.5

the answer is........ B

For this case we must factor the following expression:

[tex]x^{12}y{18}+1[/tex]

We rewrite [tex]x^{12}y^{18}[/tex]as [tex](x ^ 4y ^ 6) ^ 3:[/tex]

[tex](x ^ 4y ^ 6) ^ 3 + 1[/tex]

Being both perfect cube terms, it is factored by applying the cube sum formula:

[tex]a ^ 3 + b ^ 3 = (a + b) (a ^ 2-ab + b ^ 2)[/tex]

Where:

[tex]a = x ^ 4y ^ 6\\b = 1[/tex]

So:

[tex](x ^ 4y ^ 6 + 1) ((x ^ 4y ^ 6) ^ 2-x ^ 4y ^ 6 + 1 ^ 2) =\\(x ^ 4y ^ 6 + 1) (x ^ {8} y ^ {12} -x ^ 4y ^ 6 + 1)[/tex]

Answer:

Option B

The intersecting secants theorem says

[tex]PQ\cdot PR=PS\cdot PT[/tex]

[tex]\implies8(8+x)=4(24+4)[/tex]

[tex]\implies64+8x=112[/tex]

[tex]\implies8x=48[/tex]

[tex]\implies x=6[/tex]

It's clear from the image that [tex]PT=28[/tex], so the first option is correct.

###

Same as in the first problem; the intersecting theorems says

[tex]NM\cdot NL=NO\cdot NP[/tex]

[tex]\implies5(5+x)=3(3+17)[/tex]

[tex]\implies25+5x=60[/tex]

[tex]\implies5x=35[/tex]

[tex]\implies x=7[/tex]

so the third option is correct.

Answer:

x = 6; PR = 14; PT = 28

Step-by-step explanation:

ur welcome

Answer:

1.

A) Graph the points (length is x, weight is y)

B) Find slope and substitute 75 for x value

c) the relationship between length and weight is... (define the slope)

d)

2.

a) draw line through (0,40) and (6,70)

b) First find the slope and put it into y=mx+b (i guess you know this). then put slope into slope int. form and yeah.

c) just put x as 18 and solve for y, monthly revenue.

Step-by-step explanation:

I was too lazy so i just gave instructions in the answer. Follow them and you should be fine. Good Night.

Answer:

The 7 basic units of measurement in the metric system are:

- second (s), measuring time

- meter (m), measuring length/distance

- kilogram (kg), measuring the mass/weight

- ampere (A), measuring electric current

- kelvin (K), for temperature.  kelvin uses the Celsius scale, but kelvin is the measure in the metric system for temperature because it starts at the absolute 0 (-273° C).

- mole (mol), the amount of a substance, used mostly in chemistry

and

- candela (cd), to measure light intensity

Final answer:

The 7 basic units of measurement in the metric system include meter, kilogram, second, ampere, kelvin, mole, and candela, serving as the foundation for scientific measurements.

Explanation:

The metric system, also known as the International System of Units (SI), is comprised of 7 basic units of measurement. These units form the foundation of the metric system and all other units are derived from these. The SI system is advantageous because it's based on powers of 10, making conversions between units straightforward.

The 7 Basic SI Units are:

Units such as millimeter, centimeter, and kilometer are derived from the basic unit of length, the meter, emphasizing the metric system's coherence and simplicity.

Answer:

[tex]\large\boxed{_6P_2=30}[/tex]

Step-by-step explanation:

[tex]_nP_k=\dfrac{n!}{(n-k)!}\\\\n!=1\cdot2\cdot3\cdot...\cdot n\\======================\\\\_6P_2=\dfrac{6!}{(6-2)!}=\dfrac{6!}{4!}=\dfrac{4!\cdot5\cdot6}{4!}\\\\\text{cancel}\ 4!\\\\=5\cdot6=30[/tex]

Answer:

PARABOLA

Step-by-step explanation:

The graph of a quadratic function is a PARABOLA.

The graph of a quadratic function is called a parabola.

A parabola is a U-shaped curve that is symmetric about a vertical line called the axis of symmetry. The vertex of the parabola is the point that is highest or lowest on the curve.

The number a determines the shape of the parabola. If a is positive, the parabola opens upward. If a is negative, the parabola opens downward. The number h determines the horizontal shift of the parabola. The number k determines the vertical shift of the parabola.

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Answer:

$59.27

Step-by-step explanation:

It is exponential decrease.

After each year goes by its worth 100 - 0.13 = 0.87 of the previous value.

The equation of decrease  is V = 90(0.87)^t   where t = the number of years.

So after 3 years it is worth  90(0.87)^3

= $59.27.

George's earnings from typing forty-five regular pages are $67.50. To calculate his total earnings, the charge per page for thirty-six technical papers is needed, which is not provided in the question.

To calculate how much George will earn for typing papers, we must know the charge per page for both regular and technical papers. For regular term papers, the charge has been provided: $1.50 per page. However, the charge for technical papers has not been specified. Thus, additional information is needed: the rate George charges per page for technical papers. Without this rate, we cannot accurately calculate his total earnings.

Given that George types forty-five regular pages, his earnings from regular papers can be calculated as:
45 pages *$1.50 per page = $67.50

As for the technical papers, we must have the rate per page to calculate his earnings from the thirty-six technical pages he typed. Once we have this rate, it would be a similar calculation to the one done for regular papers.

Answer:

We have to determine the time it takes for carbon 14 to decay to 15% of its original amount.

The half life of carbon 14 is 5,730 years

elapsed time = half life * log (beginning amount / ending amount) / log 2

elapsed time = 5,730 * log (100 / 15) / log 2

elapsed time = 5,730 * 0.82390874094 / 0.30102999566

elapsed time = 5,730 * 2.7369655942

elapsed time = 15,683 years

= 15,700 years

Step-by-step explanation:

Solving the exponential equation, it is found that the painting is 15,679 years old.

The amount of carbon-14 after t years is modeled by the following equation:

[tex]A(t) = A(0)e^{-0.000121t}[/tex]

It retains 15% of the original amount, thus:

[tex]A(t) = 0.15A(0)[/tex]

Solving for t, we find the age.

[tex]0.15A(0) = A(0)e^{-0.000121t}[/tex]

[tex]e^{-0.000121t} = 0.15[/tex]

[tex]\ln{e^{-0.000121t}} = \ln{0.15}[/tex]

[tex]-0.000121t = \ln{0.15}[/tex]

[tex]t = -\frac{\ln{0.15}}{0.000121}[/tex]

[tex]t = 15679[/tex]

The painting is 15,679 years old.

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Answer:

The quotient contains a terminating decimal and The quotient is a whole number less than 11.

Step-by-step explanation:

To answer this one, it's mandatory to remember that quotient, is the outcome of a ratio: a number (r) over another (s) (different than 0). In this case:[tex]\frac{81}{918}[/tex]. So q is equal to =0.08823529411.

Analyzing the number: 0.08823529411

This is not a repeating decimal, but it is a terminating decimal for it has an end.

The quotient is also a whole number less than 11.

The Whole Set of numbers is made up of the following numbers W ={0,1,2,...} and 0 < 11. Therefore it is true.

The quotient of 81 divided by 918 is a decimal that contains repeating digits.

The question asks about the quotient of the division problem 81 divided by 918. To find out the nature of the quotient, we can perform the division. The result of this division is not a whole number since 81 cannot evenly divide 918. Therefore, we will be looking at a decimal result. When we carry out the division, we notice that the decimal will not terminate shortly; thus, we can infer that the pattern of digits will start to repeat at some point. This tells us that the quotient contains a repeating decimal. Therefore, the correct answer is that the quotient contains a repeating decimal. It is not a whole number, nor is it terminating, and the quotient will be less than 1 since 81 is less than 918.

Check the picture below.

let's recall that the point of tangency  with the radius chord is always a right-angle.

Answer:

x = 9

Step-by-step explanation:

The angle formed by the tangent BC and the radius AB is right at B

Thus ΔABC is right with AC as the hypotenuse

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, hence

AC² = AB² + BC² ← substitute given values

(x + 6)² = x² + 12² ← expand squared parenthesis on left side

x² + 12x + 36 = x² + 144 ( subtract x² from both sides )

12x + 36 = 144 ( subtract 36 from both sides )

12x = 108 ( divide both sides by 12 )

x = 9

A parabola is U shaped.

Answer:

C

The answer is c

Hope it helps

Answer:

Step-by-step explanation:

find the value of x and y

Answer:

Step-by-step explanation:

THE ANSWER IS C.

3x-14=58

3x-14+14= 58+14

3x= 72

Divide by 3 for 3x=72

x= 24

check answer by using substitution method

3x-14=58

3(24)-14=58

72-18=58

58=58

Answer is C.(x=24)

Answer:  The correct option is (A) 58.

Step-by-step explanation:  We are given to find the length of JK in the given figure.

From the figure, we note that

JKLM is a parallelogram. So, the opposite sides of JKLM will be parallel and congruent.

Also, JK = 3x - 14  and  LM = 58.

Since JK and LM are the opposite sides of the parallelogram JKLM , so we must have

[tex]JK=LM\\\\\Rightarrow 3x-14=58\\\\\Rightarrow 3x=58+14\\\\\Rightarrow 3x=72\\\\\Rightarrow x=\dfrac{72}{3}\\\\\Rightarrow x=24.[/tex]

Therefore, the length of JK is given by

[tex]JK=3x-14=3\times24-14=72-14=58.[/tex]

Thus, the length of JK is 58 units.

Option (A) is CORRECT.

Answer:

William's age is 18 years old and Monica's age is 6 years old

Step-by-step explanation:

Let

x ----> William's age

y ----> Monica's age

we know that

x=3y ----> equation A

(x+6)=2(y+6) ----> equation B

Substitute equation A in equation B and solve for y

(3y+6)=2(y+6)

3y+6=2y+12

3y-2y=12-6

y=6 years

Find the value of x

x=3(6)=18 years

therefore

William's age is 18 years old

Monica's age is 6 years old

Answer:

109 degrees is the answer

Answer:

96°

Step-by-step explanation:

The given quadrilateral is inscribed in a circle, so its opposite angles are supplementary, which means that the sum of their measures is 180∘.

The measures of the opposite angles in the quadrilateral are given as      (6m + 1 3)∘ and (4m + 7)∘.

Equate the sum of the given measures to 180∘.

6m + 13 + 4m + 7 = 180

Combine like terms.

10m + 20 = 180

Subtract 20 from both sides.

10m = 160

Divide both sides by 10.

m = 16

Substitute 16 for m into the expression given for the measure of angle M and simplify.

6m = 6(16)

=96∘

Therefore, m∠M = 96∘.

Answer:

  0.5588

Step-by-step explanation:

The CDF of an exponential function with mean μ is ...

  CDF(x) = 1 - e^(-x/μ)

Then the probability that graduation will occur in 4.5 years or less is ...

  P(x<4.5) = 1 - e^(-4.5/5.5) ≈ 0.558767 ≈ 0.5588

Answer:

±0.04

Step-by-step explanation:

From the Empirical Rule, we can estimate the range as being 6 standard deviations wide.  Therefore, the standard deviation is:

σ = (0.40 - 0.28) / 6

σ = 0.02

The margin of error is ±2σ, so:

ME = ±0.04

Answer:

a x = 14.3 units

Step-by-step explanation:

The Pythagorean theorem is

a^2 +b^2 = c^2  where a and b are the sides and c is the hypotenuse

x^2 + 14^2 = 20^2

x^2 +196 = 400

Subtract 196 from each side

x^2+196-196 = 400-196

x^2 =204

Take the square root of each side

sqrt(x^2) = sqrt(204)

x =14.28285686

To the nearest tenth

x = 14.3 units