Which of the following is the minimum value of the equation y = 2x2 + 5?


5


0


−5


2

Step-by-step explanation:

a) Use sine law:

[tex]\dfrac{g}{\sin 60} = \dfrac{17\:m}{\sin 49}[/tex]

Solving for g,

[tex]g = \left(\dfrac{\sin 60}{\sin 49}\right)(17\:m)=19.5\:m[/tex]

b) Use the cosine law here:

[tex]q^2 = (11\:\text{cm})^2 + (16\:\text{cm})^2 \\ - 2(11\:\text{cm})(16\:\text{cm})\cos 29[/tex]

Solving for q,

[tex]q = 8.3\:\text{cm}[/tex]

Answer:

D = [4, 10]

Step-by-step explanation:

Since the line starts when x = 4, the domain begins there. And since the line ends when x=10, the domain ends there.

Answer:

Solution given:

f(x)=x²

g(x)=x+5

h(x)=4x-6

now

23:

(fog)(x)=f(g(x))=f(x+5)=(x+5)²=x²+10x+25

24:

(gof)(x)=g(f(x))=g(x²)=x²+5

25:

(foh)(x)=f(h(x))=f(4x-6)=(4x-6)²=16x²-48x+36

26:

(hof)(x)=h(f(x))=h(x²)=4x²-6

27;

(goh)(x)=g(h(x))=g(4x-6)=4x-6+5=4x-1

28:

(hog)(x)=h(g(x))=h(x+5)=4(x+5)-6=4x+20-6=4x-14

Answer:

[tex]{ \tt{f(x) = 2 {x}^{2} + 3x - 3 }} \\ { \tt{g(x) = - {x}^{2} }} \\ f(x) + 2 \times g(x) : \\ 0 {x}^{2} + 3x - 3 = 0 \\ x = 1 [/tex]

point's (1, 0)

Answer:

39.7

Step-by-step explanation:

Answer:

Cost to pave the road = $4257

Step-by-step explanation:

Area of the pavement = Area of the outer circle - Area of the internal circle

Area of the outer circle = πr²

                                       = π(55)²

                                       = 3025π square feet

Area of the inner circle = π(33)²

                                       = 1089π square feet

Area of the pavement = 3025π - 1089π

                                     = 1936π

                                     = 6082.12 square feet

Cost of pavement = $0.70 per square feet

Therefore, cost of 6082.12 square feet = 6082.12 × 0.70

                                                                 = 4257.49

                                                                 ≈ $4257

Cost to pave the road = $4257                                    

Answer: [tex]y=\sqrt[3]{\frac{x}{10} }[/tex]

Step-by-step explanation:

[tex]f(x)=10x^{3}\\y=10x^{3}[/tex]

switch the x and y:

[tex]x=10y^{3}[/tex]

Now solve for y:

[tex]x=10y^{3} \\\frac{x}{10} =y^{3} \\\sqrt[3]{\frac{x}{10} } =y\\[/tex]

Therefore, the inverse of that function is: [tex]y=\sqrt[3]{\frac{x}{10} }[/tex]

Using translation concepts, the vertex of k(x) is 6 units below the vertex of f(x) = x² for:

D. f(x) = x² and k(x) = x² - 6.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

We want to shift the vertex 6 units down, hence the transformation is y -> y - 6, so the correct pair is:

D. f(x) = x² and k(x) = x² - 6.

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Answer:

Step-by-step explanation:

The mean the the average of 5 numbers. If the next score is x, then the mean is:

Solve it for x:

It is given that,

The mean is the average of 5 numbers.

Then if the,

Next score is x the mean will be.

We can solve now,

→ (85 +78 +77 + 69 + x)/5 = 80

→ (309 + x)/5 = 80

→ 309 + x = 80 × 5

→ 309 + x = 400

→ x = 400 - 309

→ x = 91

Hence, the next score is 91.

FINAL ANSWER:

1

Step-by-step explanation:

[tex]\frac{2}{3} +\frac{1}{3}[/tex]

the denominators are the same so all we need to do is add.

[tex]\frac{2}{3} + \frac{1}{3} =\frac{3}{3}[/tex]

[tex]\frac{3}{3} =[/tex] 1 whole

final answer: 1

hope this answer helps you :)

have a great day and may God Bless You!

Answer:

B. <4

D. <5

Step-by-step explanation:

Exterior angle is the angle found outside the triangle. In the diagram given, angle 5 and angle 4 are located outside of the triangle, therefore, the exterior angles in the diagram given are <4 and <5.

Answer:

Given that m∠abc=70° and m∠bcd=110°. Is it possible (consider all cases): Line AB intersects line CD?

Step-by-step explanation:

#CarryOnLearning

Answer:

Let June's sweets be 5x.

Then Gavyn's sweets will be 5x.

And Alex's sweets will be 3x.

5x = 3x + 22

2x = 22

x = 11

So June has 5 x 11 = 55 sweets

Gavyn has 5 x 11 = 55 sweets

And Alex have 3 x 11 = 33 sweets

Total

= 55 + 55 + 33

= 143 sweets

Answer:

Step-by-step explanation:

Please can you re-write your question, the question is incomplete and difficult to understand.

Thanks.

Answer:

a) it is a discrete random variable

b) It is a continuous random variable

c) It is not a random variable

d) It is a discrete random variable

e)  It is a discrete random variable

f) It is a continuous random variable

Step-by-step explanation:

Explanation,

Continuous Random Variable  

A continuous variable is one that can take on an uncountable set of values.

It may take any values within an interval.

It can take infinite values within an interval.

They are obtained by measuring rather than counting.

Discrete Random Variable  

These can only take a discrete value and cannot be expressed in the form of decimals.

They are obtained by counting rather than measuring.

a). it is a discrete random variable  ⇒ as a number of people is a discrete count, which takes values such as 0 or 1 or 2.

b). The exact time it takes to evaluate 27+72 ⇒ Since, Time is measured and thus it is a continuous random variable.

c). The gender of college students ⇒ Gender is categorical data. It is neither continuous nor discrete.

d).  The number of hits to a website in a day ⇒ Since the number of people cannot be expressed as decimals, thus it is a discrete random variable

e). The number of bald eagles in a country ⇒ Since the number of people cannot be expressed as decimals, thus it is a discrete random variable

f).  The distance a baseball travels in the air after being hit  ⇒ Distance is measured and thus it is a continuous random variable.

Answer:

(a) 1 - (15 C 6) / (30 C 6)

(b)  (5 C 2) x (10 C 2) x (15 C 2) / (30 C 2)

Step-by-step explanation:

Number of  nickels = 5

Number of dimes = 10

Number of quarters = 15

(a) The probability of getting 6 quarters  

= (15 C 6) / (30 C 6)

So, the probability of not getting 6 quarters = 1 - (15 C 6) / (30 C 6)

(b) Probability of getting 2 nickels , 2 dimes and 2 quarters

= (5 C 2) x (10 C 2) x (15 C 2) / (30 C 2)

Answer:

27%

Step-by-step explanation:

The approximate value of the relative frequency of students with green eyes from the given sample population is; 27%

From the given table, the number of students with Blonde hair = 78

Number of students with blonde hair and green eyes = 21

Now, relative frequency is defined as the ratio of the number of outcomes in which a specified event occurs to the total number of trials, in an actual experiment.

Thus, in this question;

Relative frequency of students with green eyes = 21/78 = 2.7 = 27%

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x = 100° (using definition of vertical angles)

Given:

Consider the below figure attached with this question.

The table represents a proportional relationship.

To find:

The missing value from the table.

Solution:

If y is proportional to x, then

[tex]y\propto x[/tex]

[tex]y=kx[/tex]                 ...(i)

Where, k is a constant of proportionality.

The relationship passes through the point (-3,-1). Substituting [tex]x=-3,y=-1[/tex] in (i), we get

[tex]-1=k(-3)[/tex]

[tex]\dfrac{-1}{-3}=k[/tex]

[tex]\dfrac{1}{3}=k[/tex]

Putting [tex]k=\dfrac{1}{3}[/tex] in (i), we get

[tex]y=\dfrac{1}{3}x[/tex]           ...(ii)

We need to find the y-value for [tex]x=-12[/tex].

Substituting [tex]x=-12[/tex] in (ii), we get

[tex]y=\dfrac{1}{3}(-12)[/tex]

[tex]y=-4[/tex]

Therefore, the missing value in the table is -4. Hence, option D is correct.

Angle QNM is =x by alternate angle reason (QU is parallel to MP)

X = 69

Answer:

Step-by-step explanation: as the formula to find volume is L*W*H

so v=lwh

=   5*30*14

= 2100cm^3

Answer:

///////

Step-by-step explanation:

Answer:

The level of significance is the

b. maximum allowable probability of Type I error.

Step-by-step explanation:

The significance level provides the maximum probability of rejecting the null hypothesis when it is true.  It is the same as a type I error (also known as false-positive).  This error occurs when a researcher or investigator rejects a true null hypothesis that is supposed to be accepted.  It is the opposite of a type II error (false-negative), which occurs when the researcher fails to reject a false null hypothesis.

Hello!

1) -3x - 4 = 23

-3x = 23 + 4

-3x = 27

x = 27 : (-3)

x = -9

2) x/2 - 12 = -4

x - 24 = -8

x = -8 + 24

x = 16

3) 6a + (-1) = 10

6a - 1 = 10

6a = 10 + 1

6a = 11

a = 11 : 6

a = 11/6

4) -(x + 2) = 12

x + 2 = -12

x = -12 - 2

x = -14

5) 7a + 12 = 10

7a = 10 - 12

7a = -2

a = -2 : 7

a = -2/7

6) -4(a + 2) = 12

a + 2 = -3

a = -3 - 2

a = -5

Good luck! :)

Answer:

[tex] {3}^{2} \div 48 - 6 \\ 9 \div 48 - 6 \\ = - 5.8125[/tex]

Answer:

Step-by-step explanation:

If the tank holds 2500 liters and there are already 750 liters in there, he only needs to buy 1750 liters.

If he is saving 6%, he is still spending 94%, so

.94(58.4) = 54.896 (what he'll be paying per liter after the 6% comes off, then

54.896(1750) = $96,068

Answer:

Use calculation for the population  standard deviation

Step-by-step explanation:

We are given that the data data set represents the ages of all 6 of Nancy's grandchildren

11,8,5,6,3,9

We have to determine which standard deviation would used for calculation of  the given data set.

Sample standard deviation :If the data values represent the data collected from   subset of  population .Then the sample standard deviation should be used.

Population standard deviation:

If the data values represents the data collected from entire population, then population standard deviation should be used.

We can see that the given data collected from entire population.

Therefore, we would use  calculation for population standard deviation of given data set.

Explanation:

The coefficients -24 and 8 divide to -24/8 = -3. Based on this alone, the answer is between choices B and C.

The m terms divide to [tex]\frac{m^5}{m^{-7}} = m^{5-(-7)} = m^{5+7} = m^{12}[/tex]

Notice how I subtracted the exponents. The general rule is [tex]\frac{a^b}{a^{c}} = a^{b-c}[/tex]

Since we get m^12, this points us to choice C as the final answer

For the sake of completeness, here's what the n terms divide to

[tex]\frac{n^4}{n^{-2}} = n^{4-(-2)} = n^{4+2} = n^{6}[/tex]

Answer:

7

Step-by-step explanation:

28-3(7)

The 7th term of the given sequence 28 - 3n is 7.

A sequence is an ordered list of elements with a specific pattern.

According to the given question.

We have a sequence 28 - 3n.

So, for finding the value 7th term of the sequence substitute n = 7 in

28 - 3n.

Therefore, the 7th term of the given sequence

= 28 - 3(7)

= 28 - 21

= 7

Hence, the 7th term of the given sequence 28 - 3n is 7.

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Step-by-step explanation:

she gives each of her children $25 each,if Raul spends $15 then he would have $10 left.

Division then subtraction can be used to solve the problem.

An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.

Given

she gives each of her children $25 each,if Raul spends $15 then he would have $10 left.

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