Use operation to 56 48 32 to get GCF and explain ​

Step-by-step explanation:

Completing the square is a useful technique for solving quadratic equations. It is a more powerful technique than factorisation because it can be applied to equations that do not factorise.

When completing the square, an expression like,

ax2 + bx + c is written in the form (Ax + B)2 + C.

We will begin with the simple example where a = 1. In this case we will write expressions in the form

x2 + bx + c as (x + B)2 + C

If we expand (x + B)2 + C we get x2 + 2Bx + B2 + C.

Comparing this with x2 + bx + c shows that

b = 2B and c = B2 + C

which gives B =

b

2

and C = c – B2

To find the value of "p" from the polynomial x^2 + 3x + p, if one of the zeroes of the polynomial is 2, we can use the fact that if 2 is a zero of the polynomial, then (x - 2) is a factor of the polynomial.

So, let's divide the polynomial x^2 + 3x + p by (x - 2) using polynomial long division:

___________________

(x - 2) | x^2 + 3x + p

- (x^2 - 2x)

_______________

5x + p

- (5x - 10)

_______________

p + 10

The remainder of the division is p + 10.

Now, since 2 is a zero of the polynomial, the remainder of the division should be zero. Therefore, we can equate the remainder to zero:

p + 10 = 0

Solving for "p", we subtract 10 from both sides:

p = -10

So, the value of "p" is -10.

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♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

The time needed between injections of a drug is determined using an exponential function [tex]\(D(h) = 40e^{-0.15h}\)[/tex]. By setting the function equal to 9 solving for h. We obtain [tex]\(h = \frac{\ln\left(\frac{9}{40}\right)}{-0.15}\)[/tex].

To find the time needed between injections, we set the exponential function equal to 9 and solve for h:

[tex]\[9 = 40e^{-0.15h}\][/tex]

To isolate the exponential term, we divide both sides by 40:

[tex]\[e^{-0.15h} = \frac{9}{40}\][/tex]

Taking the natural logarithm of both sides, we can solve for \(h\):

[tex]\[\ln(e^{-0.15h}) = \ln\left(\frac{9}{40}\right)\][/tex]

Using the property of logarithms, the natural logarithm and exponential cancel out:

[tex]\[-0.15h = \ln\left(\frac{9}{40}\right)\][/tex]

Now, we can solve for \(h\) by dividing both sides by -0.15:

[tex]\[h = \frac{\ln\left(\frac{9}{40}\right)}{-0.15}\][/tex]

Using a calculator, we can evaluate the right side of the equation to get the value of \(h\). This value represents the time needed between injections, rounded to the nearest tenth of an hour.

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Answer:

x^4+64 = x^2 -4x+8 * x^2 +4x+8

Step-by-step explanation:

x₁ = - 4 + 3√2

x₂ = - 4 - 3√2

Hi !

2x² + 16x - 11 = - 7

2x² + 16x - 11 + 7 = 0

2x² + 16x - 4 = 0 | : 2

x² + 8x - 2 = 0

a = 1 ; b = 8 ; c = - 2

x = (- b ± √b² - 4ac)/2a

x = (-8 ± √8² - 4×1×-2)/2×1

x = 2(-4 ± √3√2)/2

x = - 4 ± 3√2

x₁ = - 4 + 3√2

x₂ = - 4 - 3√2

Good luck !

Answer:

is A: A=B

Step-by-step explanation:

The answer to the equation is [tex]x=2.2[/tex]

First, you must subtract 0.33 on both sides.

[tex]-0.45x=-0.99[/tex]

Then, you must divide -0.45 on both sides.

[tex]x=2.2[/tex]

Your answer is [tex]x=2.2[/tex]

Answer:

a) 64

b)11664

Step-by-step explanation:

Se tiene que seguir la jerarquía de operaciones y la ley de los signos. Primero resuelve lo que esta dentro de paréntesis. ejm:

a) 8+ (5+3)=

   8+(8)=

   8(8)=    (multiplicamos)

    64

Answer:

B

Step-by-step explanation:

Since 64.25 is for five dozen roses, we need to know what 1 dozen is. First we have to divide 64.25/5. That is equal to 12.85.

Boom! Theres your answer

Step-by-step explanation:

perimeter of rectangle = 2( l+w)

=2(7x+1+x-3)

=2(8x-2)

=16x-4

4 = 16x

4/16=x

1/4=x

answer is 16x-4

but you can write the value of x also

Step-by-step explanation:

Let width of the rectangle be y

Length of rectangle = 3y + 12.1

Perimeter = 2(L + y) = 122.6

2 (4y + 12.1 ) = 122.6

8y + 24.2 = 122.6

y = 98.4 / 8

y (width) = 12.3

Length = 49

Answer:

z = 0

Step-by-step explanation:

Step 1: Write equation

9z - 5 - 4z = -5

Step 2: Solve for z

Step 3: Check

Plug in x to verify it's a solution.

9(0) - 5 - 4(0) = -5

0 - 5 - 0 = -5

-5 = -5

Answer:

z=0

Step-by-step explanation:

First, let's combine like terms (9z and -4z). When we add these two values, we get 5z. This leaves the left side to be 5z-5 and that is equal to -5. To get z by itself, we have to add 5 on both sides. This equals 5z=0. Then, we divide by 5 on both sides since the inverse operation of multiplication is division. This leaves z=0.

Answer:

70

Step-by-step explanation:

20 km times 3 plus 10 km

Answer:

•y=m(35+0.75)

•15(0.20×)

Answer:

C. -1

Step-by-step explanation:

im not sure, but it's the one that makes sense to me, hope this helps!

Answer:

sorry but this is very confusing but i'll try for the sake of it.

Step-by-step explanation:

M+T=Y

The demand function for good X is Qx = m - 3Px + 2Py, where Qx is the quantity demanded of X, m is income, Px is the price of X, and Py is the price of a related good Y. The equation shows that the demand for X is inversely related to its price and directly related to the price of Y. Income, price of X, and price of Y collectively affect the overall demand for X.


The demand function for good X is given by Qx = m - 3Px + 2Py, where Qx represents the quantity demanded of good X, m is the income, Px is the price of good X, and Py is the price of a related good Y. In this equation, the income and prices are assumed to be positive.

To determine the demand for good X, we can analyze the equation. The coefficient -3 in front of Px indicates that the demand for good X is inversely related to its price. As the price of X increases, the quantity demanded of X decreases, assuming other factors remain constant. On the other hand, the coefficient 2 in front of Py indicates that the demand for good X is directly related to the price of the related good Y. If the price of Y increases, the quantity demanded of X also increases, assuming other factors remain constant.

Furthermore, the term (m - 3Px + 2Py) represents the overall effect of income, price of X, and price of Y on the quantity demanded of X. If income (m) increases, the quantity demanded of X increases. If the price of X (Px) increases, the quantity demanded of X decreases. If the price of Y (Py) increases, the quantity demanded of X increases.

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Answer:

f(0) = -2

Step-by-step explanation:

f(x) = 3x – 2

Let x=0

f(0) = 3*0 – 2

     = 0-2

    = -2

Answer:

f(0)= -2

Step-by-step explanation:

f(0)= 3(0)-2

3x0 is 0

f(0)= -2

The sequence that models the amount of the radioactive substance left after each year is a geometric sequence with a recursive formula of An+1 = (2/3) * An.

The recursive formula for the sequence that models the amount of the radioactive substance left after each year can be derived from the given information that the substance decreases by one third each year. Let's denote the amount of substance after n years as An.

The recursive formula can be written as:

A1 = g (the starting amount)

An+1 = (2/3) * An (each year, the amount decreases by one third)

To determine whether the sequence is arithmetic or geometric, we need to check if the common difference or common ratio between consecutive terms is constant.

In this case, the sequence is geometric because the ratio between consecutive terms, An+1/An, is constant. It is equal to 2/3, indicating that each term is obtained by multiplying the previous term by the same ratio.

Therefore, the sequence that models the amount of the radioactive substance left after each year is a geometric sequence with a recursive formula of An+1 = (2/3) * An.

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Using properties of logarithms, the expression 1/4log(x) + 1/2log(y) can be rewritten as log(√(x)*√(y)).

To rewrite the given expression 1/4log(x) + 1/2log(y) as the logarithm of a single quantity, we can use the properties of logarithms.

First, we can rewrite the coefficients as exponents inside the logarithm:

1/4log(x) + 1/2log(y) = log(x^(1/4)) + log(y^(1/2))

Next, we can combine the logarithms using the property log(a) + log(b) = log(ab):

log(x^(1/4)) + log(y^(1/2)) = log(x^(1/4) * y^(1/2))

Since the exponents have a common denominator, we can simplify the expression further:

log(x^(1/4) * y^(1/2)) = log((√(x))^2 * √(y))

Finally, we can simplify the expression inside the logarithm by recognizing that (√(x))^2 is equal to x:

log((√(x))^2 * √(y)) = log(√(x) * √(y))

Therefore, the given expression 1/4log(x) + 1/2log(y) can be rewritten as log(√(x)*√(y)).

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Answer:

x ≥ 25/9

Step-by-step explanation:

7x + 6 ≥ 31 - 2x

7x ≥ 25 - 2x

9x ≥ 25

x ≥ 25/9

this is the Answer:

18

Answer:

12

Step-by-step explanation:

6 * 5 is 30 6*2 is 12

Answer:

12

Step-by-step explanation:

Blue : green

5           2

We have 30 blue shoes

5*6 = 30

So multiply each term by 6

Blue : green

5 *6      2*6

30           12

There are 12 green shoes

Step-by-step explanation:

The t statistic, t = 1.808, is calculated using the sample statistics from the high school (sample 1) and college (sample 2) groups. In order to determine if high school students carry more books than college students, we need to perform a hypothesis test.

Let's set up the hypotheses:

Null hypothesis (H0): The mean number of books carried by high school students is equal to the mean number of books carried by college students.

Alternative hypothesis (Ha): The mean number of books carried by high school students is greater than the mean number of books carried by college students.

Next, we'll perform a one-tailed independent samples t-test to compare the means of the two groups using the given t statistic, degrees of freedom (df), and alpha level (α).

Given the t statistic of 1.808 and the degrees of freedom (df) calculated as df = n1 + n2 - 2 = 17 + 17 - 2 = 32, we can consult a t-distribution table or use statistical software to find the critical value corresponding to our desired alpha level.

Finally, by comparing the calculated t statistic to the critical value, we can determine whether to reject or fail to reject the null hypothesis. If the calculated t statistic is greater than the critical value, we reject the null hypothesis and conclude that high school students carry more books than college students. Otherwise, if the calculated t statistic is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that high school students carry more books than college students.

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Answer:invalid

Step-by-step explanation:

Answer:

I would say Invalid

Step-by-step explanation:

Because if a coffee is hot it is strong and if a coffee is cold it would be strong still. (sorry if incorrect!)

The predicted number of situps a person who watches 12 hours of TV can do, based on the regression results, is approximately 15.8.

To predict the number of situps a person who watches 12 hours of TV can do, we can utilize the regression equation obtained from the given results: y = ax + b.  

a = -0.978

b = 27.735

x (hours of TV watched) = 12

Substituting the values into the equation, we can calculate the predicted value of y (number of situps):

y = (-0.978) [tex]\times[/tex] 12 + 27.735

y = -11.736 + 27.735

y = 15.999

Rounding to one decimal place, the predicted number of situps a person who watches 12 hours of TV can do is approximately 16.0.

It is important to note that the regression equation is based on the data and assumptions used to derive it.

Therefore, the prediction should be considered an estimate and may not perfectly represent the actual number of situps a person can do.

Additionally, other factors not accounted for in the regression, such as individual fitness level or health conditions, could influence the actual number of situps performed.

Regression analysis allows us to examine relationships between variables and make predictions based on the obtained model.

However, it is always prudent to interpret the results with caution and consider other factors that may impact the accuracy of the predictions.

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Answer:

$775

Step-by-step explanation:

When you take the $49,000 he spend and the $5,000 in taxes he spent $54,000. when he makes a down payment for $7,500 that means he has to pay $46,500 off in the next five years making equel payment each month. Since there are 60 months in 5 years if we divide $46,500 by 60 we get our answer $775 a month in payments

Answer:

$775

Step-by-step explanation:

Answer:

162.5

Step-by-step explanation:

130/200 = x/250

200x = 32500

x = 162.5

In these tasks, we are exploring the relationship between volume, scale factor, and dilations. We are given different volumes of dilated objects and need to find the corresponding scale factor. Additionally, we encounter a problem involving surface area and another problem related to angles and side lengths. By applying the concept of dilations and their effects on volume, surface area, and side lengths, we can find the scale factors and solve the given problems.

In Task #1, we have a solid with an initial volume of 10 cubic units that is dilated to obtain a solid with a volume of 40 cubic units. To find the scale factor, we can divide the final volume by the initial volume: 40 / 10 = 4. Therefore, the scale factor used in the dilation is 4.
In Task #2, a superhero action figure has a volume of 1500 cm³, which is dilated to create a store display with a volume of 45,000 cm³. To find the scale factor, we divide the final volume by the initial volume: 45,000 / 1500 = 30. Therefore, the approximate scale factor of the dilation is 30.
For the practice problems listed, they involve finding scale factors, volumes, surface areas, and areas of dilated objects using given information and applying the relevant formulas and concepts. By understanding the relationships between volumes, scale factors, and dilations, we can solve these problems effectively.

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a. The probability that the customer ordered dessert is approximately 0.1732. b. The probability that the customer came for lunch or ordered dessert is approximately 0.4252.

(a) The total number of customers who ordered dessert is 7 + 15 = 22. The total number of customers is 127. So the probability that the customer ordered dessert is:

P(dessert) = 22/127

P(dessert) ≈ 0.1732

(b) The number of customers who came for lunch or ordered dessert is 7 + 32 + 15 = 54. The total number of customers is 127. So the probability that the customer came for lunch or ordered dessert is:

P(lunch or dessert) = 54/127

P(lunch or dessert) ≈ 0.4252

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