Find the critical point for f(x)=x^2-2x+4 and determine their nature.
Select one:
O a. (3, 1) minimum point
O b. (1, 3) minimum point
O c. (1, 3) maximum point
O d. (3, 1) maximum point

Answer:

-12

Step-by-step explanation:

Order of operations:

PEMDAS

First, do parenthesis, 2 x 2.2 = 4.4 then do -7.6 - 4.4 = -12

The way to write this expression in mathematics is A'∩B

In order to get the right way to write this expression we have to break it down in two parts.

First we are told that some of the elements are not in A.

This is represented as A'.

Then we are told that they are in the set B. Hence we have it written as B.

Then the expression  not in set A but are in set B would be written as

A'∩B.

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The missing reason in Step 8 is substitution

When a triangle is not a right triangle and when either the lengths of two sides and the measurement of the included angle are known (SAS) or the lengths of the three sides are known (SSS), the Law of Cosines is used to discover the remaining pieces of the triangle.

According to the law of cosine, if a, b, and c are any triangle's three sides, then a² = b² + c² - 2bcosa

The x in statement 5 of the preceding proof is changed to c cos A from statement 6 in statement 8 of the proof.

Option C, from the list of alternatives, is the one that best explains statement 8.

Hence  missing reason in Step 8 is substitution

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Answer: OPTION C

Step-by-step explanation:

EDGE22

Answer:

Step-by-step explanation:

1 ft/s = 0.681818 mph

355.7 * 0.681818 = 242.5226626

355.7 ft/s = 242.5226626 mph

Answer:

x = - 5/2

Step-by-step explanation:

Using the law of indices

. a^-n = 1/a^n

. (a^4)^5 = a^5×4 = a^20

Note : When two base are equal , we equate the Exponents.

3^4x-5 = (1/27)^2x+10

= 3^4x-5 = (27^-1)^2x+10

= 3^4x-5 = (3^-3)^2x+10

= 3^4x-5 = 3^ -3(2x+10)

= 3^4x-5 = 3^ -6x-30

The two base are 3 so we equate the exponents.

= 4x - 5 = -6x - 30

= 4x + 6x = -30+5

= 10x = -25

= 10x/10 = -25/10

x = -25/10

x = - 5/2

X is -5/2

Answer:

let the no. of students who failed the examination be X

therefore, no. of students passed = 5x

total no. of students = 582

5x + X = 582

6x = 582

x = 97

no. of students failed the examination = 97

no. of students passed = 97*5 = 485

Answer:

Longer side is 75 feet, shorter side is 50 feet.

Step-by-step explanation:

Let l be the length of the longer side and w be the length of the shorter side.

2l + 2w = 250, which simplifies to

l + w = 125. Solving for w, we have

w = 125 - l.

lw = l(125-l) = 3750

[tex] {l}^{2} - 125l - 3750 = 0[/tex]

[tex]( l - 50)(l - 75) = 0[/tex]

l = 75, w = 50

The bagel shop will earn $9625 in 12 months.

Scatter plot are graphs that identifies relation between x and y variables.

The scatter points are given in the graph and we have to determine the equation that best fits the data .

the points in the scatter plot is

(3,4) and (8,6)

The slope of the equation

y = mx +c is given by

m =(y2 - y1)/(x2-x1)

m = (9-4)/(11-3)

m = 5/8 = 0.625

The equation is

y= 0.625x +2.125

for 12 months

y = 9.625 thousand = 9625 thousand in 12 months

Therefore the bagel shop will earn $9625 in 12 months.

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Answer:

$9,625 is the answer, and $9,300 is the rounded answer

Step-by-step explanation:

general formula: y=ax-b

required form: p=am-b

choose two dots: (11,9), (3,4)

find the slope: 9-4/11-3=5/8 -> p=5/8

put it into an equation: f(11)=6&7/8-b=9, f(3)=1&7/8-b=4

finding the y-intercept: -9+6&7/8=2&1/8, -4+1&7/8=2&1/8 -> b=2&1/8

forming a whole equation: p=5/8m+2&1/8

predict the profit in December: p=7&4/8+2&1/8=9&5/8

the bagel shop will earn $9,625 in December

round them to the nearest tenth:  p=0.6m+2.1

predict the profit in December: p=7.2+2.1=9.3 -> $9,300

Triangle ABC and DEC are said to congruent since all their sides and angles are equal.

The angle for triangle ABC lies in angle B

The angle for triangle DEC lies in angle E

From the diagram, angles B and E are alternate angles and alternate angles are equal.

A corresponds to D

B corresponds to E

The measure of their angles are also equal

Note, congruent triangles are triangles with three corresponding sides and angles

Therefore, triangle ABC and DEC are said to congruent since all their sides and angles are equal.

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Answer:

The slope of the line passing through is -6.

Answer:

Step-by-step explanation:

The expression (a²b¹c)² × (6a³b) × (2c³)³ × (4ab¹) × (2c³) is equivalent to the expression 384a⁸b⁴c¹⁴.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

⇒ (a²b¹c)² × (6a³b) × (2c³)³ × (4ab¹) × (2c³)

By simplifying, we have

⇒ a⁴b²c² × 6a³b × 8c⁹ × 4ab¹ × 2c³

⇒ 384a⁸b⁴c¹⁴

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Answer:

1/1

Step-by-step explanation:

As the question is halfing by 2

So

2 divide 2 equals 1

Answer:

1

Step-by-step explanation:

it's fractions of divided half. next one will be number 1

Answer:

G. 0.45

Step-by-step explanation:

To find expected value, you simply multiply the value of each outcome (the numbers in the left column) by its probability

(the numbers in the right column) and then add them all together.

0(0.7) + 1(0.2) + 2(0.05) + 3(0.05)

0 + 0.2 + 0.1 + 0.15 = 0.3 + 0.15 = 0.45

The expected value is 0.45. Thus, the correct option is G.

In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

The expected value is calculated as,

E(x) = 0 x 0.70 + 1 x 0.20 + 2 x 0.05 + 3 x 0.05

E(x) = 0 + 0.20 + 0.10 + 0.15

E(x) = 0.45

Thus, the correct option is G.

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The expression that can be used to find the difference of the polynomials is (4m - 5) + ( -6m + 7 - 2n). D

Given the expression:

(4m - 5) - (6m - 7 + 2n)

Note that  - * - = +

+ * - = -

So in finding the difference, we have

(4m - 5) - ( 6m + 7 - 2n )

It could as be written as

(4m - 5) + ( -6m + 7 - 2n)

Therefore, the expression that can be used to find the difference of the polynomials is (4m - 5) + ( -6m + 7 - 2n) . D

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There will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have a circle and a parabola:

As we know the standard form of a circle:

[tex]\rm (x-h)^2 +(y-k)^2=r^2[/tex]

The standard form of the parabola:

[tex]\rm y = a(x-h)^2+k[/tex]  

If we plug the value of y from the parabola equation in the circle equation, we get a quartic equation(4th order equation)

The solution of the quartic equation will be 4.

Thus, there will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.

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Inequalities help us to compare two unequal expressions. There exists no solution to the given set of inequalities.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The given Inequalities can be solved as,

5 - x > 7

-x > 7 - 5

-x > 2

x < -2

2x + 3 ≥ 13

2x ≥ 10

x ≥ 5

As per the solution of the two inequalities, the value of x should be less than -2 but at the same time, it should be more than or equal to 5, which is impossible. Thus, there is no solution for the given inequalities.

This can be confirmed by graphing the two inequalities, as shown below. Since there is no area in common between the two inequalities, there exists no solution to the given set of inequalities.

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========================================================

Explanation:

The range of x values is [tex]-1 \le x \le 1[/tex] which means x = -1 is the smallest and x = 1 is the largest possible.

Similarly the smallest y value is y = -1 and the largest is y = 1.

----------

Plug in the smallest x and y value to get

f(x,y) = x+5y

f(-1,-1) = -1+5(-1)

f(-1,-1) = -6

Therefore, the absolute min is -6

----------

Now plug in the largest x and y values

f(x,y) = x+5y

f(1,1) = 1+5(1)

f(1,1) = 6

The absolute max is 6

Answer:

y = -2x

Step-by-step explanation:

It passes through -5, 10 and 5, -10

gradient = Δy/Δx

gradient = -10 - 10 / 5 -- 5

gradient = -20 / 10

gradient = -2

let's use -5, 10 for y = mx + b

10 = -2(-5) + b

10 = 10 + b

b = 10 - 10

b = 0.

the equation of the line is just y = -2x

Answer:

[tex] - 5.4z {}^{2} + 6.6z[/tex]

Step-by-step explanation:

Given:

[tex]-3z(1.8z-2.2)[/tex]

Solution:

Applying Distributive property,we obtain

Simplifying using PEMDAS:

Done!

Answer:A

Step-by-step explanation:

Answer:

[tex]\text{length of \textit{CA}} \ = \ 12.0 \ \ \ (\text{nearest tenth})[/tex]

Step-by-step explanation:

Radian measure is the ratio of the length of a circular arc to its radius.

A radian is the measurement of the central angle which subtends an arc whose length is equal to the length of the radius of the circle.

In the case of the unit circle, as shown in the figure below, one radian is the angle of the sector with a radius of 1 and circular arclength of 1.

Following this definition, the magnitude, in radians, of one complete revolution of a unit circle is the circumference of the unit circle divided by its radius, [tex]\displaystyle\frac{2\pi}{1}[/tex] or [tex]2\pi[/tex]. Thus, [tex]2\pi[/tex] radians is equal to [tex]360^{\circ}[/tex] degrees. Alternatively, one radian is equal to [tex]\displaystyle\frac{180^{\circ}}{\pi} \ \approx \ 57.296^{\circ} \ \ \ (3 \ d.p.)[/tex].

Since radian measure is defined as the ratio of the arc length of a sector to its radius, hence

                                                        [tex]\displaystyle\frac{s}{r} \ = \ \theta \\\\ s \ = \ r\theta[/tex]

where [tex]s[/tex] is the arclength, [tex]r[/tex] is the radius, and [tex]\theta[/tex] is the central angle, in radians.

Therefore, the length of CA is

                                           [tex]\displaystyle\frac{s}{\theta} \ = \ r \\ \\ r \ = \ \displaystyle\frac{26}{124^{\circ} \ \times \ \displaystyle\frac{\pi}{180^{\circ}} \ \text{rad}} \\ \\ r = \displaystyle\frac{26 \ \times \ 45}{31 \ \times \ 3.14} \\ \\ r\ = \ 12.0 \ \ \ \ \left(\text{nearest tenth}\right)[/tex]

Answer:

(3, 2)

Step-by-step explanation:

To be considered part of a solution set for the inequality provided, a given point must lie within the shaded region that is graphed. Since we want to find the point that is not included in the solution set for the inequality, we need to find the point that does not lie in the shaded region.

Let's test each point to see which doesn't lie in the region. Refer to the image below if you're having trouble graphing the points:

Hope this helps!

Answer:

6.3 *30= 189; so 4 cotton swabs

Answer:

h(-1) is -1, h(-0.5) is 0 and h(1) is 1.

Step-by-step explanation:

functions :- an expression, rule or law that defines relationship between one variable and another variable. When a certain condition is fulfilled, then the result is corresponding to that condition.

In the function it is given that when x∈(-2,-1] then we get -1. Now here x=-1 satisfies the given condition. So, the answer will be -1.

In the function it is given that when x∈(-1,0] then we get 0. Now here x=-0.5 lies in the range (-1,0]. So, the answer is 0.

In the function it is given that when x∈(0,1] then we get 1. Clearly, x=1 satisfies this range of values. So, we get 1.

Hence, the Answer is h(-1) = -1, h(-0.5) = 0 and h(1) = 1.

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Answer:

B

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= x + 8 - 4x - 3 ← collect like terms

= - 3x + 5

Answer:

[tex]\huge\boxed{\sf (f + g)(x) = -3x + 5}[/tex]

Step-by-step explanation:

Add both functions

(f + g)(x) = x + 8 + (-4x - 3)

(f + g)(x) = x + 8 - 4x - 3

(f + g)(x) = x - 4x + 8 - 3

(f + g)(x) = -3x + 5

[tex]\rule[225]{225}{2}[/tex]

Answer:  Choice (C)  0> -s> -r

==========================================================

Explanation:

Let's consider an example. Pick any two positive numbers for r and s, where r is larger than s. I'll go with these:

We see that r > s is true since 5 > 2 is true

Also both are larger than 0 so we can say r > 0 and s > 0

This all combines into r > s > 0 being the case.

If we negate each number, then -r > -s would no longer be true. Use a number line to see that -5 is to the left of -2, so -5 > -2 is not true. Instead it would be -5 < -2

You can think of it like floors on a skyscraper. Positive numbers are above ground, while negative numbers are below ground in the basement levels. See the diagram below.

So -r > -s must be -r < -s instead. Both are smaller than 0

-r < 0 and -s < 0

This combines to -r < -s < 0

Flip everything and swap the outer sides to get 0 > -s > -r which leads us to choice C as the final answer

Answer:

32. {-4, 1, 2, 12}

33. {2, 6, 9, 31, 65}

34. No

Step-by-step explanation:

32. The domain of a relation is the set that contains all the x-coordinates of all the ordered pairs of the relation.

domain = {-4, 1, 2, 12}

33. The range of a relation is the set that contains all the y-coordinates of all the ordered pairs of the relation.

range = {2, 6, 9, 31, 65}

34. No since the same number, 2, appears twice as an x-coordinate. In a function, no two ordered pairs can have the same x-coordinate.

Answer:

x=5 y=0

Step-by-step explanation:

cancel out the 4y's and then add the x's together. also add the 5s together. 2x = 10, x = 5, and plug it in, and 5 cancels out, leaving y by itself.

The expression represents the probability of getting exactly 3 heads is,

[tex]C(n,r)(0.5)^3(0.5)^6[/tex]

We have given

Aron flips a penny 9 times.

We have to determine

Which expression represents the probability of getting exactly 3 heads

The binomial distribution is determined as the probability of mass or discrete random variable which yields exactly some values.

The binomial probability formula shown has variables that represent:

[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]

Where n is the total number of trials (here, we flip penny 9 times, hence n = 9).

r is the number we want to find (here, we want the probability of 3 heads, so r = 3).

p is the probability of success (here, success means getting heads.

So, in a coin flip the probability of heads is always 1/2, so p = 1/2).

Therefore, The expression represents the probability of getting exactly 3 heads is;

[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]

[tex]=C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex]

Hence, the expression represents the probability of getting exactly 3 heads is [tex]C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex].

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The probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

Given the probability of a child being girl is 0.5, therefore, the probability of a child being boy is 0.5. Now, the probability of at least 3 girls out of 5 is,

Probability (x≥3)

= ⁵C₃ (0.5)³(0.5)² + ⁵C₄ (0.5)⁴(0.5)¹ + ⁵C₅(0.5)⁵(0.5)⁰

= 0.5

Probability (x≤3)

= ⁵C₃ (0.5)³(0.5)² + ⁵C₂(0.5)²(0.5)³ + ⁵C₁(0.5)¹(0.5)⁴ + ⁵C₀(0.5)⁰(0.5)⁵

= 0.8125

Hence, the probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.

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