how to solve 2x^2-3x-1=0

f(x) + 3, translates f(x) 3 units up

In this case, the function is y = 2x² - 2.

Applying the above rule, we get:

y = 2x² - 2 + 3

y = 2x² + 1

Answer:

0.25meters

As 100cm=1metre

so, 25cm=25/100meter

=0.25metre

Step-by-step explanation:

If you like my answer than please mark me brainliest

The answer is 0.25 meters

Answer:

A = 530.929158457

Answer:

Area = 706.8583471

Explanation:

The used law to measure the surface area of the sphere is

\(area \: = 4\pi \: {r}^{2} \)

Where (r) is the radius. The radius is half the diameter, so it will be half 13 which is equal to 7.5. By using this law:

\(4\pi \: {7.5}^{2} = 706.8583471\)

Answer:

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

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - \(\frac{1}{3}\) x + 5 ← is in slope- intercept form

with slope m = - \(\frac{1}{3}\)

• Parallel lines have equal slopes , then

y = - \(\frac{1}{3}\) x + c ← is the partial equation

to find c substitute (9, - 1 ) into the partial equation

- 1 = - \(\frac{1}{3}\) (9) + c = - 3 + c ( add 3 to both sides )

2 = c

y = - \(\frac{1}{3}\) x + 2 ← equation of parallel line

Answer:

The problem statement suggests that the series of donations is arithmetic, as each student's donation increases by one as their number increases. Therefore, we can apply the formula for the sum of an arithmetic series to solve this problem.

In an arithmetic series, the sum S of n terms is given by:

S = n/2 * (a + l)

where:

- n is the number of terms (which represents the number of students in this case),

- a is the first term (in this case, the first student's number, which would be 1), and

- l is the last term (in this case, the last student's number, which we don't know yet).

Given that S = Rs. 13225, we have:

13225 = n/2 * (1 + l)

Since this is an arithmetic series starting from 1, the last term, l, is equal to n. Thus, we can substitute l with n:

13225 = n/2 * (1 + n)

Multiplying through by 2 to clear the fraction gives:

26450 = n * (1 + n)

Rearranging to a quadratic equation gives:

n^2 + n - 26450 = 0

This is a quadratic equation in the form of ax^2 + bx + c = 0. To solve for n, we can use the quadratic formula, n = [-b ± sqrt(b^2 - 4ac)] / (2a). But since n cannot be negative in this context (as it represents the number of students), we will only consider the positive root.

Applying the quadratic formula, we find that the positive root is approximately 162.5. However, the number of students must be a whole number. Therefore, the number of students is 163, because the 163rd student did not donate fully as per their number, and that's why the total amount doesn't reach the full sum for 163 students.

So, there were 163 students who donated money to the fund.

Answer:

Step-by-step explanation:

Short answer 2/3 if you need more just text bcak I will be happy to explain

Answer:

\(\huge\boxed{\frac{1}{15} }\)

Step-by-step explanation:

\(\sf= \frac{2}{6} * \frac{1}{5} \\\\=\frac{2*1}{6*5} \\\\=\frac{2}{30} \\\\= \frac{1}{15} \\\\\rule[225]{225}{2}\)

Hope this helped!

Answer:

C

Step-by-step explanation:

\(\frac{2}{6}*\frac{1}{5}=\frac{1}{3}*\frac{1}{5} = \frac{1}{15}\)

Answer: B

Step-by-step explanation:

e2020

Answer:

Step-by-step explanation

First, let's remember the equation for point-slope form and how to find the 'm' value:

\(y-y1 = m (x-x1)\\m = rise/run\\m = \frac{-4-(8)}{-1-(0)} = 12\)

Now plug your m value and (x1, y1) into point-slope form:

\(y - 8 = 12(x-0)\\reduce\\y=12x+8\)

Answer:

The center mass of the lamina =   \({\begin {pmatrix} 0, \dfrac{1755}{146 \pi } \end {pmatrix}\)

Step-by-step explanation:

Let take a look at the boundary of the lamina that comprises of the semicircles \(y = \sqrt{1-x^2}\) and \(y = \sqrt{64-x^2}\)

We are also informed that the density at any point is proportional to its distance from the origin.

Thus, the main task required is to find the center mass of the lamina.

In as much as the density is proportional to the distance from the origin;

Then;

\(\rho (x,y) = k \sqrt{x^2 + y^2} = kr\)

Thus; the mass of the lamina is determined as:

\(m = \iint \limits _ D \rho (x,y) \ dA= \int ^{\pi}_{0}\int ^{8}_{1} kr.r dr d \theta\)

\(m = \int ^{\pi}_{0}\int ^{8}_{1} kr^2 dr d \theta\)

\(m = k \int ^{\pi}_{0} \begin {bmatrix} \int \limits ^8_1 r^2 dr \end {bmatrix} d \theta\)

\(m = k \int ^{\pi}_{0} \begin {bmatrix} \int \limits\dfrac{r^3}{3} \end {bmatrix} ^8_1d \theta\)

\(m = k \int ^{\pi}_{0} \begin {bmatrix} \dfrac{512}{3}- \dfrac{1}{3} \end {bmatrix} d \theta\)

\(m = \dfrac{511 \ k}{3} \int \limits ^{\pi}_{0} \ d \theta\)

\(m = \dfrac{511 \ k}{3} \bigg (\theta \bigg ) ^{\pi}_{0}\)

\(m = \dfrac{511 \ k \pi}{3}\)

Now, about the y-axis, the moment of the entire lamina can be computed as:

\(M_y = \iint \limits _D x\rho (x,y) \ dA = \int \limits^{\pi}_{0} \int \limits ^{8}_{1} r cos \theta kr .r \ dr \ d \theta\)

\(M_y = k \int \limits ^{\pi}_{0} \int ^{8}_{1} \ cos \theta . r^3 \ dr \ d \theta\)

\(M_y = k \begin {bmatrix} \int \limits ^{\pi}_{0} cos \theta d \theta \end {bmatrix} \begin {bmatrix} \int \limits ^8_1 r^3 dr \end {bmatrix}\)

\(M_y = k (sin \ \theta )^{\pi}_{0} \begin {bmatrix} \dfrac{r^4}{4} \end {bmatrix}^8_1\)

\(M_y = k(sin \pi - sin 0 ) \bigg ( \dfrac{8^4}{4}- \dfrac{1^4}{4} \bigg)\)

\(M_y = 0\)

Similarly; about the x-axis, the moment of the entire lamina can be computed as:

\(M_x = \iint \limits _D y \rho (x,y) \ dA = \int \limits^{\pi}_{0} \int \limits ^{8}_{1} r sin \theta kr .r \ dr \ d \theta\)

\(M_x = k \int \limits ^{\pi}_{0} \int ^{8}_{1} \ sin \theta . r^3 \ dr \ d \theta\)

\(M_x = k \begin {bmatrix} \int \limits ^{\pi}_{0} sin \theta d \theta \end {bmatrix} \begin {bmatrix} \int \limits ^8_1 r^3 dr \end {bmatrix}\)

\(M_x= k (- cos \ \theta )^{\pi}_{0} \begin {bmatrix} \dfrac{r^4}{4} \end {bmatrix}^8_1\)

\(M_x = k(-cos \pi +cos 0 ) \bigg ( \dfrac{8^4}{4}- \dfrac{1^4}{4} \bigg)\)

\(M_x = \dfrac{4095}{2}k\)

Hence,  The center mass of the lamina is:

\(( \overline x, \overline y) = \bigg ( \dfrac{M_y}{m}, \dfrac{M_x}{m} \bigg )\)

\(( \overline x, \overline y) = \begin {pmatrix} \dfrac{0}{\dfrac{511 \ k \pi}{3}}, \dfrac{\dfrac{4095 \ k}{2}}{\dfrac{511 \ k \pi}{3}} \end {pmatrix}\)

\(( \overline x, \overline y) = \begin {pmatrix} 0, \dfrac{1755}{146 \pi } \end {pmatrix}\)

Let x and y represent the cost of one box of popcorn and one soft drink respectively.

Given;

Ms. Torres purchased two boxes of popcorn and three soft drinks for $6.05.

Also, Mr. Russo purchased three boxes of popcorn and five soft drinks for $9.50.

From the question we have generated a system of simultaneos equation.

we now need to solve the simultaneous equation to get the value of x and y.

Let's solve by elimination.

Firstly multiply equation 1 through by 3 and equation 2 by 2.

This is to have equal coefficient of x for the two equations, to make elimination possible.

Now we have equation 3 and 4.

Let us subtract equation 3 from 4.

We can now substitute the value of y into equation1 to get x

The coordinates of vertex A' are (1, 1)

The coordinates of vertex B' are (2, 3).

The coordinates of vertex C' are (2, 1).

In Geometry, a reflection over or across the x-axis is represented or modeled by the following transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate (x-value) while the sign of the y-coordinate (y-value) changes from positive to negative or negative to positive as the case may be.

In this exercise, you are required to apply a reflection over the x-axis, a rotation of 90° clockwise about the origin, and finally reflected across the line y = x as shown in the transformation table below;

Original vertex   Reflection (x-axis)   Rotated 90° clockwise   Line y = x

A (1, 1)           →             (1, -1)          →              (-1, -1)           →             (1, 1)

B (2, 3)          →            (2, -3)        →              (-3, -2)         →             (2, 3)

C (2, 1)          →            (2, -1)         →              (-1, -2)         →              (2, 1)

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Answer:

Step-by-step explanation:

Volume

V = w h l

V = 2*15*13

V = 390 ft^3

-------------------------

Surface area

SA = b*h

SA = 15*13

SA = 195

-------------------------

b) Surface area

C) Volume

The value of the expression represented by |M × N| is 64

from the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

M = 8 i.e.  {m, a, t, h, e, i, c, s}.

N = 8 i.e. {n, e, v, r, t, h, l, s}.

So, we have

|M × N| = 8 * 8

Evaluate

|M × N| = 64

Hence, the value of |M × N| is 64

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Answer:

Perimeter:\(4x+10\) feet
Area:\(x^{2}+5x+6\) feet

Step-by-step explanation:

The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=\(x^{2}+2x+3x+6=x^{2}+5x+6\)

Answer:

(-4,3)

Step-by-step explanation:

the coordinate (4,-3) is just at the 4th quadrant in which the value of x is positive and the value of y is negative

the quadrant (4,3) is on the first quadrant and the value expressed with the letter A

the coordinate (-4,-3) is a coordinate on the quadrant in which both values are negative

The function that grows at the fastest rate for increasing values of x is f(x) = 4×2ˣ.

We can see this by comparing the growth rates of the three functions for larger and larger values of x.

As x gets larger, the exponential function f(x) grows much faster than the other two functions, which are both polynomial functions.

if we plug in x = 10, we get:

f(10) = 4×2¹⁰ = 4×1024 = 4096

h(10) = 9×10² + 25 = 925

g(10) = 15×10 + 6 = 156

As we can see, f(10) is much larger than h(10) and g(10), indicating that f(x) grows at a much faster rate than the other two functions.

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A probability value equal to or smaller than 0.05 would indicate that Gaurav's null hypothesis should be rejected at the 5% significance level.

In hypothesis testing, the significance level, denoted as alpha (α), is the predetermined threshold used to determine whether to reject the null hypothesis.

Gaurav has specified a 5% significance level, which means he wants to control the probability of making a Type I error (rejecting the null hypothesis when it is true) at 5% or less.

If Gaurav were to conduct a test and calculate the p-value, he would compare it to the significance level of 0.05.

The p-value is the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.

If the p-value is less than or equal to the significance level (p ≤ α), it indicates that the observed difference is unlikely to occur by chance alone under the assumption of the null hypothesis.

Gaurav would reject the null hypothesis and conclude that there is a significant difference between the average amount of medication his patients are taking and the national average.

Conversely, if the p-value is greater than the significance level (p > α), it suggests that the observed difference could reasonably occur by chance, and Gaurav would fail to reject the null hypothesis.

This would imply that there is no significant difference between the average medication amounts of Gaurav's patients and the national average.

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Answer:

57.8 degrees

Step-by-step explanation:

Complementary angles are angles that add up to 90 degrees so you take 32.3 and figure what plus 32.3 equals 90

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expressionns.

Given the algebraic expressions,

\(\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2\)

Substituting 2 for x in the first expression gives:

(1/2 × 2) + 4

1 + 4

5

Substituting 2 for x in the second expression gives:

2 + 6 - (1/2 ×2) - 2

8 - 1 - 2

8 - 3

5

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

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Answer:

https://www.calculatorsoup.com/calculators/algebra/quadratic-formula-calculator.php try this website, it shows a step by step solution, and is a calculator for your problem <3

Step-by-step explanation:

Therefore, we can conclude that the price of the antique clock increased by 2% from its original selling price.

In mathematics, an expression is a combination of numbers, variables, and operations that represents a value or a set of values. Expressions can be simple, such as a single number or variable, or complex, such as a combination of variables and operations.

Here,

The expression 1.2(0.85c) represents the selling price of the antique clock at a later date, which is obtained by multiplying the original selling price c by 0.85 and then multiplying the result by 1.2.

To understand what happened to the price of the antique clock, we can simplify the expression as follows:

1.2(0.85c) = 1.02c

So the selling price at a later date is 1.02 times the original selling price c. This means that the price of the antique clock increased by 2% (since 1.02 is 102% of 1).

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Answer:

Step-by-step explanation:

Let's denote the volume of the cube as V and the length of each edge as x. Given that the volume of a cube is V = x^3, we can find the rate at which the length of each edge is changing.

We're given that the rate of change of the volume is dV/dt = 56 in³/sec. We want to find the rate of change of the length of each edge, which is dx/dt, when the length of each edge is 6 inches.

First, we differentiate the volume equation with respect to time t:

V = x^3

dV/dt = d(x^3)/dt

Using the chain rule:

dV/dt = 3x^2 * (dx/dt)

Now, we know that dV/dt = 56 in³/sec and x = 6 in. Plugging these values into the equation, we get:

56 = 3 * (6)^2 * (dx/dt)

Solving for dx/dt:

56 = 108 * (dx/dt)

dx/dt = 56 / 108

dx/dt ≈ 0.5185 in/sec (rounded to four decimal places)

So, the rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.

Answer:

I believe it’s option c!

Step-by-step explanation:

Correct me if I’m wrong!

Answer:

Yes, you subtract 5 every time

The value of ''a'' will be 1

What is Matrix?

A set of numbers arranged in rows and columns so as to form a rectangular array, is called Matrix.

Given that;

1,2 and 3 are the eigen values of matrix A.

Now,

We know that;

The product of eigen values of a matrix is equal to the determinant of that matrix.

So, We find the determinant of matrix as;

\(A = \left[\begin{array}{ccc}2&0&1\\0&2&0\\a&0&2\end{array}\right]\)

Hence, We get;

| A | = 2 (4 - 0) - 0 (0 - 0) + 1 (0 - 2a)

| A | = 8 - 2a

And, The product of eigen values = 1 x 2 x 3 = 6

Hence, We get;

| A | = 8 - 2a

6 = 8 - 2a

2a = 8 - 6

2a = 2

a = 1

Thus, The value of ''a'' will be 1

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Answer:

1) 1/7

2) 1/3

3) 1/4

Step-by-step explanation:

1) Since there are 7 days in a week it can be expressed as the fraction 1/7

2) Since there are 3 feet in a yard it can be expressed as the fraction 1/3

3) Since there are 4 quarts in a gallon it can be expressed as the fraction 1/4

Answer:

y=-5/3x+10

-5/3

(0,10)

Step-by-step explanation:

5x+3y=30

-5x. -5x

3y=-5x+30

÷3. ÷3

y=-5/3x+10

the number by the x is the slope and the constant

is the y intercept. in a y intercept the x=0 and they y=the constant which is 10 in this case making it (0,10)