Split 294x306, which identity is used to solve it?

Answer:

16 pieces

Step-by-step explanation:

(100*100)-(25*25)=16

-7,14,-28,56,-112

an = a1(r)^n-1

a4 = -7(-2)^4-1

a4 = -7(-2)³

a4 = -7(-8)

a4 = 56

an = a1(r)^n-1

a5 = -7(-2)^5-1

a5 = -7(-2)⁴

a5 = -7(16)

a5 = -112

The solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.

To determine which value is included in the solution set for the inequality statement -3(x-4) > 6(x-1), we need to solve the inequality for x.

Starting with the given inequality:

-3(x - 4) > 6(x - 1)

First, distribute -3 and 6 to the terms inside the parentheses:

-3x + 12 > 6x - 6

Next, combine like terms by subtracting 6x from both sides and adding 6 to both sides:

-3x - 6x > -6 - 12

-9x > -18

To isolate x, divide both sides of the inequality by -9. Remember that when dividing by a negative number, we need to reverse the inequality sign:

x < (-18) / (-9)

x < 2

Therefore, the solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.

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Answer:

A,E

Step-by-step explanation:

Operation: Minus

To find how far Sam ran, we need to subtract 2.3 from Dean's distance of 6.8 km.

6.8 km - 2.3 km = 4.5 km

Therefore, Sam ran 4.5 km, since Dean ran 2.3 km fewer than Sam.

Answer:

a and e

Step-by-step explanation:

got it right on homework

The meaning of the absolute value in this problem is given as follows:

The temperature decreased 1.2 degrees.

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.

The number for this problem is -1.2, hence:

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Answer:

The sister is 10 and Mike is 20

Step-by-step explanation:

10 x 2 = 20

10 +20 = 30

Let Mike's sister age be x

Then Mike age ATQ = 2 × age of his sister = 2x

Now According to the Question (ATQ):-

\(Mike \: age + his \: sister \: age = 30 \\ 2x + x = 30 \\ 3x = 30 \\ \cancel{3}x = \cancel{30} ^{ \: \: 10} \\ x = 10\)

So Mike age = 2x = 2×10 = 20

Mike's sister age = x = 10

Just put the value in the equation ATQ :-

\(Mike \: age + his \: sister \: age = 30 \\ 20 + 10 = 30 \\ 30 = 30 \\ LHS = RHS\)

The steps to construct a cumulative frequency distribution table are mentioned above.

Given is to construct a cumulative frequency distribution table.

Since the data is not given, we can write the steps to construct a frequency distribution table. The steps to create a cumulative frequency distribution table are mentioned below -

Therefore, the steps to construct a cumulative frequency distribution table are mentioned above.

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Answer:

Smaller integer = -6

Larger integer = -5

Step-by-step explanation:

Let the two consecutive integers = \(x\) and (\(x+1\))

As per the given statement,

Larger i.e. (\(x+1\)) is 7 greater than twice (\(2\times x\)) the smaller integer.

To find:

The value of integers = ?

Solution:

First of all, let us learn about integers.

The integers are of the form (put in increasing order):

\(-\infty, ...., -3, -2,-1, 0, 1, 2, 3, ...., \infty\)

and -1 > -2

So the consecutive integers are 1 greater than the smaller.

Therefore, the two integers can be \(x, x+1\)

Now, writing the given condition in the form of an equation:

\(x+1=2x+7\\\Rightarrow 1-7=2x-x\\\Rightarrow -6=x\\\Rightarrow \bold{x=-6}\)

So, the smaller integer = -6

Larger integer = -6+1 = -5

Answer:

Hi how are you doing today Jasmine

In triangle UVW, If m∠U = m∠W of a triangles then m∠U = 74.5° when m∠W=31°

A triangle is a three-sided polygon that consists of three edges and three vertices.

The sum of all angles of a triangles should be equal to 180 degrees

Given that the angles opposite UV and VW are congruent.

So ΔUVW is an isosceles triangle.

Which is nothing but m∠U = m∠W

Since the measures of the angles of a triangle have a sum of 180, then

m∠U + m∠W + m∠V = 180

m∠U + m∠U + 31 = 180

Subtract 31 from both sides

2 m∠U = 180-31

2 m∠U =149

Divide both sides by 2

m∠U =74.5°

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Answer:

$3040 profit made

Step-by-step explanation:

$13×95=$1235 cost to make all the shoes they sold

$45×95=$4275 money she made

$4275-$1235=$3040 profit

Answer:

5 horas

Step-by-step explanation:

Answer:

Step-by-step explanation:

( \(4\frac{3}{4}\) + \(3\frac{1}{2}\) + \(6\frac{3}{4}\) + \(4\frac{1}{2}\) + 6 + 5 ) ÷ 6 =

( 4 + 3 + 6 + 4 + 6 + 5 + \(\frac{6}{4}\) + 1 ) ÷ 6 = 30.5 ÷ 6 = \(\frac{61}{2}\) × \(\frac{1}{6}\) = \(\frac{61}{12}\) = \(5\frac{1}{12}\) horas al dia

Answer:

Step-by-step explanation:

Letter B is the correct answer

Initial population is 200, tripled every hour

200 x 3 = 600

First hour 200

Second hour = 600 + 200 = 800

Third hour 800x3 = 2400 + 800 = 3200

and so on.

Answer:

concave up

Step-by-step explanation:

there is no negatives in the equation (in front of x-value)

There are 5319 ways in which each child can choose a flavor for their scoop of ice cream so that each flavor of ice cream is selected by at least two children.

What is inclusion-exclusion principle?

The inclusion-exclusion principle is a counting method that generalises the well-known approach to determining the number of members in the union of two finite sets in the field of combinatorics.

To solve the problem, use the principle of inclusion-exclusion.

First find the total number of ways the six children can choose their ice cream flavors, without any restrictions.

For each child, there are 3 choices of flavors, so the total number of ways is -

3 x 3 x 3 x 3 x 3 x 3 = 3^6 = 729

Next, count the number of ways in which only one flavor is chosen by at least two children.

There are 3 choices of the flavor that will be chosen by two children, and 2 choices of the remaining flavors for the other four children.

The two children who choose the selected flavor can be chosen in 6 choose 2 = 15 ways.

The other four children can choose their flavors independently, so the total number of ways is -

3 x 2 x 2 x 15 x 3 x 3 = 1620

However, the cases are overcounted in which two flavors are each chosen by two children.

There are 3 choices of the first flavor to be chosen by two children, and 2 choices of the second flavor to be chosen by two children.

The two children who choose the first flavor can be chosen in 6 choose 2 = 15 ways, and the two children who choose the second flavor can be chosen in the remaining 4 choose 2 = 6 ways.

The remaining two children must choose the third flavor.

So the total number of ways is -

3 x 2 x 15 x 6 x 1 x 1 = 540

The case has been overcounted in which all six children choose the same flavor.

There are 3 choices of the flavor to be chosen by all six children.

So the total number of ways is -

3

Now apply the principle of inclusion-exclusion to count the number of ways in which each flavor is selected by at least two children.

The total number of ways is -

3^6 - 1620 + 540 - 3 = 5319

Therefore, the number of ways are 5319.

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Answer:

kite

Step-by-step explanation:

The figure is a counterexample for the conditional will be a rectangle. Then the correct option is A.

The quadrilateral has four sides and four angles. The sum of internal angles is 360 degrees.

In the square, the measure of each angle is 90 degrees. And the measure of each side is congruent and the opposite side is parallel to each other.

In the square, the measure of each angle is 90 degrees. And the measure of the opposite side is congruent and the opposite side is parallel to each other.

If a quadrilateral has four right angles, then it is a square.

The figure is a counterexample for the conditional will be a rectangle. Then the correct option is A.

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Answer:

What subject

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf 38}\)

Step-by-step explanation:

= a³ + b (6 + c)

Put a = 2, b = 3 and c = 4

= (2)³ + 3 (6 + 4)

= 8 + 3(10)

= 8 + 30

\(\rule[225]{225}{2}\)

Answer:

Step-by-step explanation:

the requied answer is 38.

according to the question the value of a=2,b=3,c=4.

here,

to find the value of   a³ + b (6 + c)we have to do it in steps:

step 1: solve the bracket (6+4) =10.

step 2:  solve the value of a³ =8.

now put these values ,

=8+3(10)

=38.

Step-by-step explanation:

the area of a parallelogram is

baseline × height = 5 × 3.2 = 16 m²

Explanation

Question 10

We are asked to write the quadratic eqation that has the solutions of x=3 and x =-7

To do so, we will make use of

So we will follow the steps below

substituting the above, we will have

Therefore, the quadratic equation is

Let R be the radius in millions of miles and let t be the time in days. Assume that when t = 0 the radius is 20 million miles and increasing then  R(t) = 20 + 1.6sin(2πt/5.2).

The equation for a sine wave is y = A sin (Bx + C) where A is the amplitude, B is the frequency and C is the phase shift.

In this case, the amplitude is 1.6.

Since the radius changes by a maximum of 1.6 million miles.

The frequency is 2π/5.2 (one full cycle of the sine wave in 5.2 days)

The phase shift is 0, since when t = 0 the radius is increasing.

The equation then becomes R(t) = 20 + 1.6sin(2πt/5.2)

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Value of {4+[−5(2−4)÷2]}⋅(−2)= 104

{4+[−5(2−4)÷2]}⋅(−2)

Following the PEMDAS order of operations

Calculate within parentheses

[−5(2−4)÷2]⋅(−2)=100

(2−4)÷2] = 10

Multiply and divide left to right

Apply rule a.(-b)= -a.b

4(÷2)= -4.2= -8

=2-(-8)

Add and subtract left to right

Apply rule -(-a)= +a

-(-8)= +8

2+8=10

-5.10(-2)

Multiply and divide left to right

-5.10(-2)

-5.10= -50

-50(-2)

Apply rule -a.(-b)= a.b

-50(-2)=50x2= 100

Add and subtract left to right

4+100= 104

Thus, the value is 104

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1) Let's factor this quadratic, by rewriting that coefficient "b" as -4x+2x, this is possible since we have the coefficient a greater than 1 and by doing that we can write coefficients that share divisors with the leading coefficient 2 and the coefficient c = 12

Note that when we find a repetition (x+2) on both factors then we can rewrite as a product.

Complete question :

The computer output and scatter plot output pertaining to the question can be found in the attached picture.

Answer:

Kindly check explanation

Step-by-step explanation:

A.) Relationship between height and fastest serve speed :

According to the scatterplot and Correlation Coefficient (R) value which can be obtauned by getting the square root of R²

R = √27.7%

R = 0.5263 = 52.63% ; this depicts a fairly strong positive correlation or relationship between height and fastest serve speed

B.)

Equation of least square regression line :

From the computer output and scatter plot above :

Recall :

y = mx + c

y =predicted variable (s fastest serve)

m= slope

x = predictor variable (height)

c = intercept

y = 84.98x + 68.81

C.) 27.7% of the variation in fastest speed can be explained by height while the remaining percentage is due to other variables

D.) fastest serve of tennis player with height 1.7m

y = 84.98x + 68.81

y = 84.98(1.7) + 68.81

y = 213.276km/hr

E.)

R = √27.7%

R = 0.5263 = 52.63% ; this depicts a fairly strong positive correlation or relationship between height and fastest serve speed

F.)

Height = 2.06m = x

y = 84.98(2.06) + 68.81

y = 243.8688 km/hr

Residual = Actual - predicted

Actual = 230 ; predicted = 243.8688

Residual = 230 - 243.8688

Residual = −13.8688

Hence, the model overestimated fastest serve speed of a 2.06 m tall player by −13.8688 km/hr

The value of the limit that exists at the given numbers is approximately 0.5.

First of all at x = 3.1, the value of \($$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$\) will be

\($$\lim _{x \rightarrow 3.1} \frac{x^2-3 x}{x^2-9} $$\) = \(\frac{x^2-3 (x) }{x^2-9}$$\) = \(\frac{(3.1)^2-3(3.1)}{(3.1)^2-9}\) = \(\frac{0.31}{0.61}\) ≅ 0.508197

At x = 3.05, the value of \($$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$\) will be

\($$\lim _{x \rightarrow 3.05} \frac{x^2-3 x}{x^2-9} $$\) = \(\frac{x^2-3 (x) }{x^2-9}$$\)  =  \($\frac{(3.05)^2-3(3.05)}{(3.05)^2-9}=\frac{0.1525}{0.3025}$\) ≅  0.504132

At x = 3.01, the value of \($$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$\) will be

\($$\lim _{x \rightarrow 3.01} \frac{x^2-3 x}{x^2-9} $$\) = \(\frac{x^2-3 (x) }{x^2-9}$$\)  = \($\frac{(3.01)^2-3(3.01)}{(3.01)^2-9}=\frac{0.0301}{0.0601}$\) ≅  0.500832

At x =  3.001, the value of \($$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$\) will be

\($$\lim _{x \rightarrow 3.001} \frac{x^2-3 x}{x^2-9} $$\) = \(\frac{x^2-3 (x) }{x^2-9}$$\) =  \($\frac{(3.001)^2-3(3.001)}{(3.001)^2-9} $\)=  \($\frac{3.001 \times 10^{-3}}{6.001 \times 10^{-3}}$\) ≅0.500083

At x =  3.0001, the value of \($$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$\) will be

\($$\lim _{x \rightarrow 3.0001} \frac{x^2-3 x}{x^2-9} $$\) = \(\frac{x^2-3 (x) }{x^2-9}$$\) = \($\frac{(3.0001)^2-3(3.0001)}{(3.0001)^2-9} $\)=  \($\frac{3.001 \times 10^{-4}}{6.001 \times 10^{-4}}$\) ≅ 0.500008

At x = 2.9, the value of \($$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$\) will be

\($$\lim _{x \rightarrow 2.9} \frac{x^2-3 x}{x^2-9} $$\)  = \(\frac{x^2-3 (x) }{x^2-9}$$\) =  \($\frac{(2.9)^2-3(2.9)}{(2.9)^2-9} $\)=  \($\frac{-0.29}{-0.59}$\) = 0.491525

At x = 2.95, the value of \($$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$\) will be

\($$\lim _{x \rightarrow 2.95} \frac{x^2-3 x}{x^2-9} $$\)  = \(\frac{x^2-3 (x) }{x^2-9}$$\) =  \($\frac{(2.95)^2-3(2.95)}{(2.95)^2-9} $\)=  \($\frac{-0.1475}{-0.2975}$\) = 0.495798

At x = 2.99, the value of \($$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$\) will be

\($$\lim _{x \rightarrow 2.99} \frac{x^2-3 x}{x^2-9} $$\)  = \(\frac{x^2-3 (x) }{x^2-9}$$\) =  \($\frac{(2.99)^2-3(2.99)}{(2.99)^2-9} $\)=  \($\frac{-0.0299}{-0.0599}$\) = 0.499165

At x = 2.999, the value of \($$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$\) will be

\($$\lim _{x \rightarrow 2.999} \frac{x^2-3 x}{x^2-9} $$\)  = \(\frac{x^2-3 (x) }{x^2-9}$$\) =  \($\frac{(2.999)^2-3(2.999)}{(2.999)^2-9} $\)=  \($\frac{-2.999 \times 10^{-3}}{-5.999 \times 10^{-3}}$\) = 0.499917

At x = 2.9999, the value of \($$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$\) will be

\($$\lim _{x \rightarrow 2.9999} \frac{x^2-3 x}{x^2-9} $$\)  = \(\frac{x^2-3 (x) }{x^2-9}$$\) =  \($\frac{(2.9999)^2-3(2.9999)}{(2.9999)^2-9} $\)=  \($\frac{-2.999 \times 10^{-4}}{-5.999 \times 10^{-4}}$\) = 0.499992

From above all, we can see that the limit is approximately equal to and tends towards 0.5. So 0.5 will be our answer.

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Your question was incomplete, your most probable question was:
Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).

\($$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9}\),  x = 3.1, 3.05, 3.01, 3.001, 3.0001, 2.9, 2.95, 2.99, 2.999, 2.9999

The correct equation that matches the given graph is y = cos(x) + 1.

To determine the equation that matches the given graph, we can observe the key features and points provided.

The waveform starts from the y-axis at 1 unit: This suggests that the function has a vertical shift of 1 unit upwards.

The waveform passes through (π, -1), (2π, 1), and (3π, -1): This indicates that the function oscillates between the values of -1 and 1 as x increases.

The waveform intercepts the x-axis at π/2, 3π/2, 5π/2, and 7π/2: This suggests that the function has zeros or x-intercepts at these values.

Based on these observations, the function can be represented as a cosine function.

The cosine function with a vertical shift of 1, oscillating between -1 and 1, and having zeros at π/2, 3π/2, 5π/2, and 7π/2 is:

y = cos(x) + 1

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If 30% children travelling by bus is represented by 360 children, then total number of students who attended the school are 1200.

The "Percent" is a way of expressing a fraction or proportion as a number out of 100. It is a unit of measurement used to represent the relative size or amount of something compared to the whole.

If 30% of the children at a particular school travel by bus and this represents 360 children, we use this data to find total number of children who attend the school.

Let "X" be = total number of children at the school.

We know that 30% of X represents 360 children, so we can write an equation:

⇒ 30% of X = 360,

⇒ 30% × X = 360,

⇒ 0.3 × X = 360,            ...because 30% = 0.3,

⇒ X = 360/0.3 = 1200,

Therefore, there are 1200 students who attend the school.

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Answer: (Answer in explanation)

Step-by-step explanation:

(12)B > 180

Her goal is to make more than 180 so if she wants to sell each book for $12 then so if she sells 14 books or above she would get more than $180.

So B could equal anything 16 and above but in my case I chose 24

(12)24 = 288 > 180

So write a equation like mine that equals a number that's greater than 180. Keep in mind each book sells for $12 each. Then solve for B which is how many books she has to sell to get the number greater than 180.

Answer:

\(\displaystyle A=\frac{20}{3}\)

Step-by-step explanation:

\(\displaystyle A=\int^2_{-2}(|x|-(x^2-2))\,dx\\\\A=2\int^2_0(x-(x^2-2))\,dx\\\\A=2\int^2_0(-x^2+x+2)\,dx\\\\A=2\biggr(-\frac{x^3}{3}+\frac{x^2}{2}+2x\biggr)\biggr|^2_0\\\\A=2\biggr(-\frac{2^3}{3}+\frac{2^2}{2}+2(2)\biggr)\\\\A=2\biggr(-\frac{8}{3}+2+4\biggr)\\\\A=2\biggr(-\frac{8}{3}+6\biggr)\\\\A=2\biggr(\frac{10}{3}\biggr)\\\\A=\frac{20}{3}\)

Bounds depend on whether you use -x or +x instead of |x|, but you double regardless. See the attached graph for a visual.