how to solve? …………….

The smaller number is -17, and the quadratic equation that can be used to find it is\(x^2 + x - 272 = 0.\)

The correct answer would be \(x^2 + x - 272 = 0.\)

To find the quadratic equation that can be used to find the smaller number, we can set up the equation using the given information. Let's assume that the smaller number is x.

Since the product of two consecutive integers is 272, we can express this as an equation: x(x + 1) = 272.

Expanding the equation, we have:

\(x^2 + x = 272.\)

To find the quadratic equation, we need to rearrange the equation in the standard form, which is\(ax^2 + bx + c = 0\). In this case, we have:

\(x^2 + x - 272 = 0.\)

Therefore, the correct quadratic equation that can be used to find the smaller number is\(x^2 + x - 272 = 0.\)

This equation can be solved by factoring, completing the square, or using the quadratic formula. Factoring may not be straightforward in this case since 272 does not have obvious factors, so let's use the quadratic formula to find the solutions.

The quadratic formula states that for an equation of the form \(ax^2 + bx + c = 0\), the solutions for x can be found using the formula:

x = (-b ± √\(\sqrt{(b^2 - 4ac)}\)) / (2a).

For the equation\(x^2 + x - 272 = 0,\)we have a = 1, b = 1, and c = -272. Substituting these values into the quadratic formula, we get:

x = (-(1) ± \(\sqrt{((1)^2 - 4(1)(-272))) / (2(1)).}\)

Simplifying further, we have:

x = (-1 ±\(\sqrt{ (1 + 1088)) / 2.}\)

x = (-1 ± \(\sqrt{1089)}\) / 2.

Since we are looking for the smaller number, we take the negative square root:

x = (-1 -\(\sqrt{ 1089}\)) / 2

Calculating the value, we have:

x = (-1 - 33) / 2.

x = -34 / 2.

x = -17.

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Calculation of \$ Z_1Z_2\$ where  \$ Z_1=3+j4\rightarrow 5.00 / 53.13^{\circ} \$ and  \$ Z_2=5-j8\rightarrow 9.43 / -57.99^{\circ} \$:From the given information, we know that, \$ Z_1=5.00 / 53.13^{\circ} \$ and  \$ Z_2=9.43 / -57.99^{\circ} \$.

We need to multiply two complex numbers which are in polar form. If we multiply two complex numbers in polar form, it can be done as follows:\[|Z_1Z_2|=|Z_1|.|Z_2|\]and \[\angle (Z_1Z_2) = \angle (Z_1) + \angle (Z_2)\]Now substituting the given values First, we need to convert the given expression from rectangular to polar form. To convert the rectangular form into polar form, we use the following equation

Now, using De Moivre’s theorem, we can write Calculating \[|z^n|\]:\[\begin{aligned} |z^n| &= |5|^{0.5+j0.7} \\ &= 5^{0.5+j0.7} \\ &= 2.235 \angle 0.962^{\circ} \end{aligned}\]Calculating \[\angle n\theta\]:\[\begin{aligned} \angle n\theta &= \tan^{-1} \left(\frac{0.7}{0.5}\right) + 36.87^{\circ}\\ &= 55.24^{\circ} \end{aligned}\]Therefore,\[(4+j3)^{(0.5+j0.7)} = 2.235 \angle 55.24^{\circ} \]

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Answer:

C

Step-by-step explanation:

don't keep your eyes on the goal cause if you do that something is wrong

The conditional operator creates a compound statement that sets up a condition for something to be true. Therefore, if the condition is met, the statement is true. The parts of the conditional statements are two, the first simple statement in a conditional is called the antecedent  and the second simple statement is called the consequent. So, for two statements A (antecedent) and B (consequent) we will have that:

A → B that means: If A then B

In this problem:

A:  A number is even.

B: The number is divisible by 2.

Thus:

A → B: If a number is even, then the number is divisible by 2.

So, the conclusion of this conditional statement is the consequent, that is,  the number is divisible by 2.

Accordingly, the right answer is D. The number is divisible by 2.

the complete question is

What is the conclusion of the following conditional? A number is divisible by 2 if even.

A. The sum of the digits of the number is divisible by 2.

B. If a number is even, then the number is divisible by 2.

C. The number is even.

D. The number is divisible by 2.

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Answer:

The coefficient of the squared term of the equation is 1/9.

Step-by-step explanation:

We are given that the vertex of the parabola is at (-2, -3). We also know that when the y-value is -2, the x-value is -5. Using this information we want to find the cofficient of the squared term in the parabola's equation.

Since we are given the vertex, we can use the vertex form:

\(\displaystyle y=a(x-h)^2+k\)

Where a is the leading coefficient and (h, k) is the vertex.

Since the vertex is (-2, -3), h = -2 and k = -3:

\(\displaystyle y=a(x-(-2))^2+(-3)\)

Simplify:

\(y=a(x+2)^2-3\)

We are also given that y = -2 when x = -5. Substitute:

\((-2)=a(-5+2)^2-3\)

Solve for a. Simplify:

\(\displaystyle \begin{aligned} -2&=a(-3)^2-3\\ 1&=9a \\a&=\frac{1}{9}\end{aligned}\)

Therefore, our full vertex equation is:

\(\displaystyle y=\frac{1}{9}(x+2)^2-3\)

We can expand:

\(\displaystyle y=\frac{1}{9}(x^2+4x+4)-3\)

Simplify:

\(\displaystyle y=\frac{1}{9}x^2+\frac{4}{9}x-\frac{23}{9}\)

The coefficient of the squared term of the equation is 1/9.

Answer:

x^4n^4

Step-by-step explanation:

Answer:

\(n^{4} x^{4}\)  

I really hope this helps!

Answer:

\(\huge\boxed{V=64cm^3}\)

Step-by-step explanation:

The formula of a surface area of a cube:

\(SA=6a^2\)

The formula of a volume of a cube:

\(V=a^3\)

We have

\(SA=96cm^2\)

Calculate the edge length (a).

\(6a^2=96\)           divide both sides by 6

\(a^2=16\to a=\sqrt{16}\\\\a=4(cm)\)

Calculate the volume of a cube:

\(V=4^3=64(cm^3)\)

Answer:

c

Step-by-step explanation:

S=B+1/2Pl

-b from both sides

s-b=1/2Pl

x2 to both sides

2(S-B)=Pl

divide both sides by l

you get c

Answer:

- A

- D

Step-by-step explanation:

"quotient" means a result obtained by dividing one quantity by another.

Thus, we try all possibilities.

A. \(1600 \div 20 = 80\)

B. \(16000 \div 20 = 800\)

C. \(160 \div 20 = 8\)

D. \(16000 \div 200 = 80\)

E. \(1600 \div 2 = 800\)

Thus, the answers are A, D.

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b=48

1) Solving for b, we'll proceed this way:

b/4 = 12 Multiply both sides by 4, to eliminate the fraction

b= 48

2) So the answer is b=48

Answer: 6.40 = c

Step-by-step explanation:

a^2 + b^2 = c^2

5^2 + 4^2 = c^2

25 + 16 = c^2

41 = c^2

  ____

_/ 41  = c

6.40 = c

For the Following the product function is f(x) = g(x) * h(x) = (9e^{-x} + ln(x)) * 4x^{2.7} and rate of change of function is f'(x) = 43.2x^{1.7}e^{-x} + 10.8x^{1.7}ln(x) - 36e^{-x}

For g(x) = 9e^{-x} + ln(x) and h(x) = 4x^{2.7}, we have:

(a) The product function is: f(x) = g(x) * h(x) = (9e^{-x} + ln(x)) * 4x^{2.7}

(b) The rate-of-change function is:

f'(x) = g'(x) * h(x) + g(x) * h'(x)

where g'(x) and h'(x) are the derivatives of g(x) and h(x), respectively.

Taking derivatives, we have:

g'(x) = -9e^{-x} + 1/x

h'(x) = 10.8x^{1.7}

Substituting into the formula for f'(x), we get:

f'(x) = (-9e^{-x} + 1/x) * 4x^2.7 + (9e^{-x} + ln(x)) * 10.8x^{1.7}

Simplifying, we get:

f'(x) = 43.2x^{1.7}e^{-x} + 10.8x^{1.7}ln(x) - 36e^{-x}

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Answer:

-168

Step-by-step explanation:

because  f(x) = 8 - 10xg(x) = 5x + 4

(fg)(x) = (8 - 10x)(5x + 4)(fg)(x) = 40x + 32 - 50x^2 - 40x(fg)(x) = 32 - 50x^2

(fg)(-2) = 32 - 50(-2)^2(fg)(-2) = 32 - 200(fg)(-2) = -168

Answer:

Step-by-step explanation:

u got it right the first time it is D

Answer:4

Step-by-step explanation:i guess because 4 time 3 if im wrong then 1b time s 12

Answer:

y = -1

Step-by-step explanation:

Any ordinate pair (x, y) represents the input output values of a function to be graphed.

For any input value of x, there will be an output value (y).

If input value for the graph attached is x = 0,

Output value will be represented by the y-value along y-axis as, y = -1

Therefore, y = -1 will be the answer.

The probability of 3 dying of SIDS in this situation is approximately 0.000227. The number of SIDS cases in this hospital is significantly higher than the expected rate.

a. The probability of 3 infants dying of SIDS in this situation can be calculated using the binomial probability formula:
P(X=k) = C(n,k) * p^k * (1-p)^(n-k)
Where:
P(X=k) is the probability of k successes (SIDS cases) in n trials (infants),
C(n,k) is the number of combinations of n items taken k at a time,
p is the probability of SIDS (0.0001),
n = 100 infants,
k = 3 SIDS cases.
P(3 SIDS cases in 100 infants) = C(100,3) * (0.0001)^3 * (1-0.0001)^(100-3)
After calculating, the probability is approximately 0.000227.

b. In this situation, it is alarming that many infants died of SIDS, as the probability of 3 deaths in 100 infants is very low (0.000227), much lower than the prevalence of 0.01%. This indicates that the number of SIDS cases in this hospital is significantly higher than the expected rate.

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Answer:

1.-204.5 2.-557

Step-by-step explanation:

We need to simplify the given expression (200 × 1.07) to find how many cars were sold in July. 200 × 1.07= 214. This means that the dealership sold 214 vehicles in the month of July.

A car dealership sells 200 vehicles in the month of June and then sells1 4 more vehicles in the month of July. This can be modeled by the numerical expression 200 1 4 (200). Simplify the expression to find how many cars were sold in July. The dealership sold cars in July.

As given that in the month of June the car dealership sold 200 vehicles and in the month of July, it sold 14 more vehicles than the June month, we can represent this with the help of the numerical expression,200 + 14 = 214.

Now, we need to simplify the given expression (200 × 1.07) to find how many cars were sold in July. 200 × 1.07= 214.

This means that the dealership sold 214 vehicles in the month of July.

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ΔABC is an equilateral triangle.

All 3 angles must be equal in an equilateral triangle.

\(180/3\)

\(=60\) °

To solve this problem both units must have the same units.

So, let's convert quarts to gallons

1 quart ----------------------- 0.25 gallon

34 quarts -------------------- x

x = (34 x 0.25) / 1

x = 8.5 gallons

8.5 gallons or 34 quarts > 8 gallons

As a result, you'll need 8000 square centimetres of colourful paper to cover the aquarium's base, side faces, and rear face.

What is Rectangle ?

Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles.

The amount of paper required will equal the total of the areas of the aquarium's base, side faces, and back faces.

The area of the base is just the area of an 80cm × 30cm rectangle, which is:

80cm x 30cm = 2400 square centimetres foundation area

The area of each side face is the product of the cuboid's height and breadth, which is

2400 square centimetres = 2 x height x width = 2 x 40cm x 30cm = 2400 square centimetres

Similarly, the back face region is:

Height x length = 40cm x 80cm = 3200 square centimetres for the rear face

As a result, the total amount of paper required is:

Total paper area required = 2400 + 2400 + 3200 = 8000 square centimetres = 2400 + 2400 + 3200 = 2400 + 2400 + 3200 = 2400 + 2400 + 3200 = 2400 + 2400 + 3200 = 2400 + 2

As a result, you'll need 8000 square centimetres of colourful paper to cover the aquarium's base, side faces, and rear face.

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i hope have been useful buddy.

good luck ♥️♥️♥️♥️♥️

Answer:

a

Step-by-step explanation:

the answer is a i took the test

Answer:

C

Step-by-step explanation:

If you look at the constant terms for each of them, ABD is 18, and only C is 14

Answer:

24

Step-by-step explanation:

47= Mean

4 bags represent 16% of samples

16%=4

100= x

X=100 x4/16

100x4=400

400/16= 25

Since the answer ask for a probablity the answer is 24.

Given:

The system of equations is

\(3x-2y=7\)

\(6x-4y=14\)

To find:

The correct statement for the given system of equations.

Solution:

On comparing the given equations and general form of linear equation, i.e., \(ax+by+c=0\), we get

\(a_1=3,b_1=-2,c_1=-7\)

\(a_2=6,b_2=-4,c_2=-14\)

Here,

\(\dfrac{a_1}{a_2}=\dfrac{3}{6}=\dfrac{1}{2}\)

\(\dfrac{b_1}{b_2}=\dfrac{-2}{-4}=\dfrac{1}{2}\)

\(\dfrac{c_1}{c_2}=\dfrac{-7}{-14}=\dfrac{1}{2}\)

Since, \(\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}\), therefore, the two equations are equivalent and the system has infinitely many solutions.

Hence, the correct option is b.

Answer:

I think it 78

Step-by-step explanation:

Area is multiplication