solve the quadratic equation 2x^2-5x+1=x+4​

to find the interest you simply just multiply the amount by the percentage, so:

$3000 × 3.5%

= $3000÷100×3.5

=$105

Answer:

Kinda vague but here...

Step-by-step explanation:

z*(8-4)
z*(4)
4z

Answer:

   4. 132°

   5. 41°

Step-by-step explanation:

Q4

Q5

mRP

The angle will be twice the m<Q

So

it's

#2

m<ABC

a) The probability that exactly one of them will be a girl = 0.3407

b) The probability that at least one of them will like the football = 0.7672

a) If we select three students then the probability that exactly one of them will be a girl

From the attached two way table we can observe that the total number of girls = 22

the total number of boys = 18

and the total number of students = 40

The possible outcomes for selecting 3 students from 40 would be,

⁴⁰C₃

Using combination formula,

⁴⁰C₃ = 40! / (3! × (40 - 3)!)

      = 9880

If there is exactly one girl then other two must be boys in the set of 3 selected students.

So, the required probability would be,

P = (²²C₁ × ¹⁸C₂) / ⁴⁰C₃

P = (22 × 153)/9880

P = 0.3407

b) The number of students like the football = 15

and the number of students who don't like the football are 40 - 15 = 25

The probability that at least one of them will like the football would be,

P = (¹⁵C₃ × ²⁵C₀ + ¹⁵C₂ × ²⁵C₁ + ¹⁵C₁ × ²⁵C₂) / ⁴⁰C₃

P = ((455 × 1) + (105 × 25) + (15 × 300)) / 9880

P = 0.7672

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On solving the provided question, we can say that - the range \(|x + 1| = 0\) \(x + 1 = 0 = > x = -1\) and \(y = 3\)

Finding the variable's greatest observed value (maximum) and deducting the least observed value will yield the range (minimum). Limits of variation or potential range: a variety of steel costs; several styles; The size or scope of an action or operation: insight. how far a weapon's projectile can or will travel. The number in a list or set between the lowest and maximum is referred to as a range. Line up all the numbers before locating the region. After that, take away (get rid of) the lowest number from the greatest number. The solution provides the list's range.

The regions where the absolute values are zero are known as the vertex points of an absolute value function.

\(|x + 1| = 0\\x + 1 = 0\\x = -1\)

\(y = |-1 + 1| + 3\\y= 0 + 3\\y = 3\)

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Answer:  82 sq. units .

Step-by-step explanation:

Let A (9, −1), B (−1, 7), C(−5, 2), D(5, −6) are the vertices of rectangle.

Then we plot them on graph ( as provided in attachment)

Length = AB \(=\sqrt{(9+1)^2+(-1-7)^2}\) units  [By distance formula : \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)]

\(=\sqrt{(10)^2+(-8)^2}=\sqrt{100+64}=\sqrt{164}=2\sqrt{41}\) units

Width = BC = \(\sqrt{(-1+5)^2+(7-2)^2}\) units

\(=\sqrt{4^2+5^2}\\\\=\sqrt{16+25}\\\\=\sqrt{41}\)

Area = length x width

= \(2\sqrt{41}\times\sqrt{41}=2\times41= 82\text{ sq. units}\)

Hence, the  area of the rectangle is 82 sq. units .

The scale factor used to create the image is given as follows:

k = 1/4.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The equivalent segment lengths for the original figure and the image are given as follows:

Hence the scale factor used to create the image is given as follows:

k = 2/8

k = 1/4.

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Answer:I believe it is -4

Step-by-step explanation:

The domain is all real numbers, and the range is (y ≤ -4.855). (option b)

To sketch the graph of a quadratic equation, you can use a graphing calculator, which is a handy tool that can produce a visual representation of the equation. For instance, let's take the quadratic equation y = -0.5x² + 0.7x - 5.1 and sketch its graph using a graphing calculator.

When we enter this equation into the graphing calculator, we can see a U-shaped curve that is symmetric about the vertical line passing through the vertex. The vertex is the point where the parabola changes direction and is given by the formula x = -b/2a, y = f(x), where f(x) is the value of y at the vertex.

Now let's examine the given options and determine their domain and range based on the graph of the quadratic equation.

all real numbers, R: (y ≤ -4.855)

For this option, we can observe that the parabola opens upward, and the vertex is at (0.7, -5.35).

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Answer: d=18.2

Step-by-step explanation: d=2r=2·9.1=18.2

The distance between the point and the line is 2.1 units

Here, we want to find the distance between the given line and the given point

Firstly, let us write the line in the standard form

That is;

m represents the slope, which is the coefficient of x

The coefficient of x here is 1, and that means the slope of the line is 1

Now, we need the slope of a line perpendicular to this line

A line that is perpendicular to this line will have a slope that is the negative reciprocal of the slope of the given line

This means that the slope of the new line is;

The slope of the line perpendicular to the given line is -1

Using this slope, we need to get the value of the y-intercept of the second line

That can be obtained by substituting the coordiates of the point given

We have this as;

Now, we need to find the point of intersection of the two lines; we can get this by solving both equations simultaneously

The second equation line is given as;

Solving it simultaenously, let us equate the two y;

The point of intersection of the two perpendicular lines is (-7.5,-2.5)

We now proceed to find the distance between the given point and the point of intersection

That is the distance between (-6,-4) and (-7.5,-2.5)

We use the distance formula here;

Answer: x = 50

Step-by-step explanation:

In the given image, the alternate interior angles are equal. Therefore, 80 + x = 180 - 50 (since straight angles measure 180 degrees). Simplifying this equation, we get 130 + x = 180, which gives us x = 50 degrees. Thus, A||B when x = 50 degrees.

Answer:

(0,-3),(1,-1),(2,1)

Step-by-step explanation:

y=2(0)-3

0-3

y=-3

y=2(1)-3

2-3

y= -1

y=2(2)-3

4-3

y=1

Answer:

  m +2m +(2m -6) = 19

Step-by-step explanation:

m = number of books sold on Monday.

2m = number of books sold on Tuesday, twice as many as Monday.

2m -6 = number of books sold on Wednesday, 6 fewer than Tuesday.

The total number of books sold on the three days gives the equation you're looking for:

  m +2m +(2m -6) = 19

_____

Additional comment

Solving this gives ...

  5m = 25 . . . . add 6

  m = 5 . . . . . divide by 5

5, 10, and 4 books were sold on the three days.

Answer:

Step-by-step explanation:

Let's just say this circle has value x.

x increases by 5%, or 0.05 of x.

x + 0.05x = 1.05x

1.05x now increases by 5% again:

1.05x + 0.05(1.05x) = 1.1025x

The total increase is equal to (1.1025-1)*100 = 10.25%

Hope this helps!

the value of the investment when she retires is $26434.92.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Formula:

A = P(1 + {r}/{n})^{n.t}

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

here, we have,

given that,

Leilamade a one-time investment of $12 000.00 in a

registered retirement savings plan (RRSP) at 2.65%, compounded

semi-annually.

She plans to withdraw the money when she retires in 30

years.

So, she get finally is,

using the formula we get,

$26434.92

hence,  the value of the investment when she retires is $26434.92.

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The solution to the equation given by M * M * M = 729 is 9

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

Given the equation:

M.M.M = 729

This gives:

M * M * M = 729

M³ = 729

Taking the cube root of both sides:

∛M³ = ∛729

M = 9

The solution to the equation is 9

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Answer:

She can water 20 plants

Step-by-step explanation:

She has a total of 2 liters in each can, and if she uses 2 full cans, she has a total of 4 liters. 4 liters=4000 milliliters.

To find the amount of plants she can water, we need to divide the amount of water she has by how much it takes to water each plant. So,

\(\frac{4000}{200}\)

\(=\frac{20}{1}\)

\(=20\)

So, she can water 20 plants with two full water cans.

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Answer:

20 plants

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

The quadrilateral PQRS is a parallelogram since opposite sides PQ and SR have the same lengths and slopes.

To determine the correctness of the statements and calculate the lengths and slopes of the given quadrilateral PQRS, let's perform a coordinate proof.

Length and slope of PQ:

The coordinates of points P and Q are P(0, 2) and Q(3, -4), respectively.

Length of PQ: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(3 - 0)² + (-4 - 2)²]

= √[9 + 36]

= √45

= 3√5 (approx.)

Slope of PQ: (y₂ - y₁) / (x₂ - x₁)

= (-4 - 2) / (3 - 0)

= -6 / 3

= -2

Therefore, the length of PQ is approximately 3√5, and its slope is -2.

Length and slope of SR:

The coordinates of points S and R are S(-2, 1) and R(1, -5), respectively.

Length of SR: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(1 - (-2))² + (-5 - 1)²]

= √[9 + 36]

= √45

= 3√5 (approx.)

Slope of SR: (y₂ - y₁) / (x₂ - x₁)

= (-5 - 1) / (1 - (-2))

= -6 / 3

= -2

Therefore, the length of SR is approximately 3√5, and its slope is -2.

Length and slope of SP:

The coordinates of points S and P are S(-2, 1) and P(0, 2), respectively.

Length of SP: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(0 - (-2))² + (2 - 1)²]

= √[4 + 1]

= √5

Slope of SP: (y₂ - y₁) / (x₂ - x₁)

= (2 - 1) / (0 - (-2))

= 1 / 2

Therefore, the length of SP is √5, and its slope is 1/2.

Length and slope of HQ:

The coordinates of points H and Q are H(0, 2) and Q(3, -4), respectively.

Length of HQ: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(3 - 0)² + (-4 - 2)²]

= √[9 + 36]

= √45

= 3√5 (approx.)

Slope of HQ: (y₂ - y₁) / (x₂ - x₁)

= (-4 - 2) / (3 - 0)

= -6 / 3

= -2

Therefore, the length of HQ is approximately 3√5, and its slope is -2.

Based on the calculations, we can conclude that both statements are correct:

The quadrilateral PQRS is a parallelogram since opposite sides PQ and SR have the same lengths and slopes.

The quadrilateral PQRS is not a rectangle since the lengths of the adjacent sides PQ and SP are not equal.

Summary:

Length of PQ is approximately 3√5, and its slope is -2.

Length of SR is approximately 3√5, and its slope is -2.

Length of SP is √5, and its slope is 1/2.

Length of HQ is approximately 3√5, and its slope is -2.

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Answer:

Image result for Two people were standing on a tight rope. Which number sentence represents the distance between the 2 people? •= + HH + "-3" "-2" "-1" 0 1 2 3 4 "-4"

Examples of number sentences include: 32 + 57 = ? 5 x 6 = 10 x ? They will usually comprise of addition, subtraction, multiplication or division – or a combination of all four!

Step-by-step explanation: hope this helps

Answer:

-23

Step-by-step explanation:

The system of inequalities that represent the situation is:

\(y < x\)

\(75x + 120y \leq 3000\)

\(x + y \leq 25\)

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

In the system.

The number of skilled workers is less than the number of student workers, then:

\(y < x\)

Student workers will be paid $75 and skilled  workers will be paid $120.The committee can  spend no more than $3000, then:

\(75x + 120y \leq 3000\)

There is only space for a total of 25 workers, thus:

\(x + y \leq 25\)

The system is:

\(y < x\)

\(75x + 120y \leq 3000\)

\(x + y \leq 25\)

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Answer:  12 possible outcomes in total

Step-by-step explanation:

Answer:

I think the answer is 96%.

Answer:

If their food and beverages cost $25.30 and there is an 8% meals tax, how much is the bill? the bill would be $27.31, after the tip, $32.24, meaning the tip would be $4.93, and that percentage would be %18.05

Step-by-step explanation:

8 percent of 25.30 is 2.01, add that up, 27.31, subtract 27.31 from 32.24, you get 4.93, figure out the percentage and boom, you got your answer

Answer:

193.45

Step-by-step explanation:

The discount price is $69.4428.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A garden store purchased a lawn mower and marked it up 160% from the original cost of $82.67.

So, the Marked up amount

= 160 % of 82.67

= $132. 272

and, then 10% discount

=  10% of 132.272

= 13.2272

so, the discount price = 82.67 - 13.2272 = $69.4428

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Answer: Degenerate

Step-by-step explanation:

This conic section (intersecting lines) is a degenerate

The conic section is degenerate.

The correct option is (e).

Any curve produced by the intersection of a plane and a right circular cone.

As, the given figure shows a degenerate conic is a conic (a second-degree plane curve, defined by a polynomial equation of degree two) that fails to be an irreducible curve.

Hence, the conic section is degenerate.

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Answer:

2 forms

Step-by-step explanation:

hope this helps <3

\( \sf \longrightarrow \: \frac{8}{5} \div 6 \\ \)

\( \sf \longrightarrow \: \frac{5}{8} \times 6 \\ \)

\( \sf \longrightarrow \: \frac{5 \times 6}{8} \\ \)

\( \sf \longrightarrow \: \frac{30}{8} \\ \)

\( \sf \longrightarrow \: \frac{8}{30} \\ \)

\( \sf \longrightarrow \: 0.26 \\ \)

_____________________________

We would expect approximately 132 flowers in the batch to not have eight petals.

If the probability of a flower having eight petals is 0.45, then the probability of a flower not having eight petals is 1 - 0.45 = 0.55.

So, for we to find the expected number of flowers that do not have eight petals in a randomly selected batch of 240 flowers, we have to multiply the total number of flowers (240) by the probability of a flower not having eight petals (0.55):

Expected number of flowers without eight petals = 240 × 0.55

Expected number of flowers without eight petals = 132

Therefore, we would expect approximately 132 flowers in the batch to not have eight petals.

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The difference between the regression equation is Equation 2 is the estimated value of the model in equation 1, to be exact.

Regression analysis evaluates the association between the factors and variable and determines how changes in the independent variable impact the dependent variable. Equation Y is equal to aX plus b, where Y is the dependent variable, an is the slope of the regression equation, x is the independent factor, and b is a constant, is used to represent it.

Regression analysis is one of the most used statistical techniques for determining the relationships between a number of independent and dependent variables.

The two equations are:

y=b0+Bx .........(1)

y=b0+b1x............(2)

The parameter and estimate in the two equations are different.

Equation 1 contains the model that is presumptively present in the data collection. As a result, the parameters or actual values of the regression coefficient make up this model.

Now that these regression coefficients have been determined using the sample data, equation 2 is used to represent the result.

Equation 2 is the estimated value of the model in equation 1, to be exact.

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The central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

what is normal distribution?

A normal distribution is a bell-shaped probability distribution that is symmetrical and characterized by its mean (μ) and standard deviation (σ). It is also known as a Gaussian distribution, after the mathematician Carl Friedrich Gauss.

However, for smaller sample sizes, the distribution of sample means may still resemble the shape of the population distribution.

Here are some more specific descriptions of the distribution of sample means for different population distributions:

1. Rectangular distribution: The distribution of sample means will approach a normal distribution as the sample size increases, with the mean and median at the center of the distribution.

2. Uniform distribution: The distribution of sample means will also approach a normal distribution as the sample size increases, with the mean at the center of the distribution.

3. Normal distribution: The distribution of sample means will be a normal distribution regardless of sample size, with the mean and median at the center of the distribution.

4. Positively skewed distribution: The distribution of sample means will approach a normal distribution as the sample size increases, but the mean will be higher than the median.

5. Nonmodal distribution: The distribution of sample means will approach a normal distribution as the sample size increases, but the exact shape will depend on the specifics of the nonmodal distribution.

6. Multimodal distribution: The distribution of sample means will also approach a normal distribution as the sample size increases, but the exact shape will depend on the specifics of the multimodal distribution.

7. Negatively skewed distribution: The distribution of sample means will approach a normal distribution as the sample size increases, but the mean will be lower than the median.

Therefore, central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

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