What two numbers go there

To solve the equation 4x² - x - 3 = 0 by completing the square, we can rewrite it in the form (2x - 1)² - 4 = 0. The solutions are x = (1 ± √13)/4.

To solve the equation 4x² - x - 3 = 0 by completing the square, we follow these steps:

1. Move the constant term to the other side of the equation:

4x² - x = 3

2. Divide the coefficient of x² by 2 and square the result:

(1/2)² = 1/4

3. Add and subtract the value obtained in step 2 inside the parentheses on the left side of the equation:

4x² - x + 1/4 - 1/4 = 3

4. Rewrite the left side as a perfect square trinomial:

(2x - 1/2)² - 1/4 = 3

5. Simplify the equation:

(2x - 1/2)² = 3 + 1/4

(2x - 1/2)² = 13/4

6. Take the square root of both sides and solve for x:

2x - 1/2 = ±√(13/4)

2x - 1/2 = ±(√13/2)

7. Solve for x:

2x = 1/2 ± √13/2

x = (1 ± √13)/4

Therefore, the solutions to the equation 4x² - x - 3 = 0 are x = (1 ± √13)/4.

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Answer:

Step-by-step explanation:

IKRRRRRRRRRR

Math is hard because it can take alot of processes to solve problems.  Theres alot of unique stuff, so it takes alot more practice than other subjects.  To get better at math, you gotta practice.

Answer:

See below

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step one:

given data

the cost of the laptop= $800

initial payment= $200

monthly payment = $60

let the number of months be x

the expression for the situation is the function for the equation of line

y=mx+c

Step two:

the expression for the situation is

800=200+60x

solve for x

800-200=60x

400=60x

divide both sides by 60

x=400/60

x=6.7

Approximately 7 months

Laplace transforms are an essential mathematical tool used to solve differential equations. These transforms transform differential equations to algebraic equations that can be solved easily.

To solve the differential equations given in the question, we will use Laplace transforms. So let's start:Solution:a) y" – y = t y(0) = 1, y'(0) = 1First, we take the Laplace transform of the given differential equation.L{y" - y} = L{ty}

Taking the Laplace transform of both sides gives:L{y"} - L{y} = L{ty}Using the formula, L{y"} = s²Y(s) - s*y(0) - y'(0), and L{y} = Y(s) then we get:s²Y(s) - s - 1 = (1/s²) + (1/s³)Rearranging the above equation, we get:Y(s) = [1/(s²*(s² + 1))] + [1/(s³*(s² + 1))]Now, we apply the inverse Laplace transform to find the solution.y(t) = (t/2)sin(t) + (cos(t)/2)

The solution of the differential equation y" – y = t, with initial conditions y(0) = 1, y'(0) = 1 is y(t) = (t/2)sin(t) + (cos(t)/2).

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The level of measurement used in the classification is ordinal.

Ordinal levels of measurement group variables into categories like nominal scales, but also convey the order of the variables. For example, rate pain on a scale of 1 to 5, or classify income as high, medium, or low.

An ordinal scale is a second-level measure that indicates the ranking and order of data without actually specifying the degree of variation among the data. The order measurement level is his second of the four measurement scales. "Ordinal" means "order".

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Answer:

is it about your future profession or your dream

Step-by-step explanation:

Sandy's $8.50 been on the deli counter.

Answer:

75 geese

Step-by-step explanation:

Lets first calculate how many birds and turkeys there are to subtract from the 180 chickens.

1/3 x 180 = 60

1/4 x 180 = 45

The amount of chickens and turkeys combined is:

60 + 45

105

180 - 105 = 75

75 remaining

The center of the circle is (6,7) and the radius of the circle is 1.414 units

The diameter with endpoints = (5, 8) and (7, 6)

The mid point of the diameter = The center of the circle

The center of the circle = \((\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)

Substitute the values in the equation

The center of the circle = ( (5+7)/2 , (6+8)/2 )

= (12/2 , 14/2)

= (6, 7)

The radius of the circle = The distance between (6, 7) and (7, 6)

The distance between two points = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The distance between (6, 7) and (7, 6) = \(\sqrt{(7-6)^2+(6-7)^2}\)

= \(\sqrt{1^2+(-1)^2}\)

= \(\sqrt{1+1}\)

= \(\sqrt{2}\)

= 1.414 units

Hence, the center of the circle is (6,7) and the radius of the circle is 1.414 units

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Based on the information provided, Jameela, who lives in poverty and has a diet mainly consisting of legumes, whole-grain breads and rice, fruits, and a few vegetables, is most at risk of nutrient deficiencies.

Jameela's limited access to a varied and balanced diet puts her at risk of nutrient deficiencies. While legumes, whole-grain breads, rice, fruits, and vegetables can provide essential nutrients, it is important to have a diverse range of food sources to ensure an adequate intake of all necessary vitamins, minerals, and other nutrients.

The heavy veils worn by Jameela may further contribute to her risk of nutrient deficiencies. The veils may limit her approach to sunlight, which is an important source of vitamin D synthesis in the body. Vitamin D is crucial for bone health and overall immune function. If Jameela does not have alternative sources of vitamin D in her diet or through supplements, she may be at risk of deficiency.

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Answer:

x = 8

The measure of angle A = 30°

Step-by-step explanation:

angle A and B are supplementary and their sum is 180°

6x - 18 + 14x + 38 = 180° add like terms

20x + 20 = 180

20x = 180 - 20

20x = 160 divide both sides by 20

x = 8 and the measure of angle A

6x - 18 ➡ 6 × 8 - 18 = 30°

Answer:

Range is the answer you get when you subtract the lowest number in a set of numbers from the highest number in the same set.

Step-by-step explanation:

Example

What is the range of 2,6,10,5,7 and 9

lowest number=2

highest number=10

range=10-2

range=8

Answer:

Range is the difference between the highest number in the group and the lowest number so you subtract the highest number from the lowest to get the range.

Step-by-step explanation:

The number of mangoes = 48

The number of grapefruit = 12

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A box of fruit has four times as many oranges as grapefruit.

And, Total number of fruit = 60 pieces

Now,

Let number of grapefruit = x

Then, Number of Mangoes = 4x

So, We can formulate;

⇒ x + 4x = 60

Solve for x as;

⇒ 5x = 60

⇒ x = 12

Thus, Number of grapefruit = x

                                          = 12

Then, Number of Mangoes = 4x

                                          = 4 × 12

                                          = 48

Therefore, The number of mangoes = 48

The number of grapefruit = 12

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Step-by-step explanation:

for triangle HLM

180-2x

180-(3x+6)

H

2x=3x-10

x=10°

180-36=144°

36-20=16°

H=2x

H= 180-144-16= 20°

Answer: 12x-17

PR>PQ => QR = PR-PQ

15x - 11 - (3x + 6) = 15x - 11 - 3x - 6 = 12x - 17

Answer:

15/100*1800=15*1800/100=15*18=270

Step-by-step explanation:

1800-270=1530 therefore answer is 1530

Answer:

c and d are monomial because they have only one term

An equation highlighting the discount: y = (65 - 7)x

A simpler equation: y = 58x

Answer:

0.84134

Step-by-step explanation:

Given that:

Mean = 3.4 hours

Standard deviation (s) = 2.6 hours

Percentage of students that spend less than 6 hours doing homework

P(x < 6)

Using the relation to obtain the standardized score (Z) :

Z = (x - m) / s

Z = (6 - 3.4) / 2.6

Z = 2.6 / 2.6

Z = 1

p(Z < 1) = 0.84134 ( Z probability calculator)

The percentage of the students at Happy High spends an average of less than 6 hours per week doing homework is 0.84134

Answer:

Median: \(\frac{173+176}{2}= 174.5\). Mode: \(141\). Mean: \(\approx179.8\)

Step-by-step explanation:

The median is the value separating the higher half from the lower half of a data sample. The sample size is 22; hence, the median the average between the 11th and 12th values, 173 and 176, respectively.

The mode is the value that appears most often in a set of data values. In this case, there is only one value that appeared twice in this data set, which is 141.

The mean, or average, is just the sum of the values divided by the sample size, N. \(\frac{x_1+x_2+x_3+...x_N}{N}\), so you add the values up and divide by 22.

Let's create a vector F(x, y, z) with at least two variables in its components:

F(x, y, z) = (xy + 2z)i + (yz + 3x)j + (xz + y)k

Now, let's find the gradient, divergence, and curl of this vector:

1. Gradient (∇F):

The gradient of a vector is given by the partial derivatives of its components with respect to each variable. For our vector F(x, y, z), the gradient is:

∇F = (∂F/∂x)i + (∂F/∂y)j + (∂F/∂z)k

Calculating the partial derivatives:

∂F/∂x = yj + zk

∂F/∂y = xi + zk

∂F/∂z = 2i + xj

Therefore, the gradient ∇F is:

∇F = (yj + zk)i + (xi + zk)j + (2i + xj)k

2. Divergence (div F):

The divergence of a vector is the dot product of the gradient with the del operator (∇). For our vector F(x, y, z), the divergence is:

div F = ∇ · F

Calculating the dot product:

div F = (∂F/∂x) + (∂F/∂y) + (∂F/∂z)

Substituting the partial derivatives:

div F = y + x + 2

Therefore, the divergence of F is:

div F = y + x + 2

3. Curl (curl F):

The curl of a vector is given by the cross product of the gradient with the del operator (∇). For our vector F(x, y, z), the curl is:

curl F = ∇ × F

Calculating the cross product:

curl F = (∂F/∂y - ∂F/∂z)i - (∂F/∂x - ∂F/∂z)j + (∂F/∂x - ∂F/∂y)k

Substituting the partial derivatives:

curl F = (z - 3x) i - (z - 2y) j + (y - x) k

Therefore, the curl of F is:

curl F = (z - 3x)i - (z - 2y)j + (y - x)k

That's it! We have calculated the gradient (∇F), divergence (div F), and curl (curl F) of the given vector F(x, y, z) by finding the partial derivatives, performing dot and cross products, and simplifying the results.

Answer:

second table

Step-by-step explanation:

Out of the 8 options on the spinner, 2 of them are 0's, 1 of them is a 1, 2 of them are 2's and 3 of them are 3's so the probability of spinning a 0, 1, 2 or 3 is 2/8, 1/8, 2/8 or 3/8 which becomes 0.25, 0.125, 0.25 or 0.375 respectively. Therefore, the answer is the second table.

Answer:

x=40

Step-by-step explanation:

Looking at this problem, we can see that 3x+9=129

Subtract 9 on both sides:

3x=120

Divide by 3 on both sides:

x=40

Matrix diagrams show optionality and cardinality of the erds they document is a false statement.

Matrix diagrams are graphical representations that display the relationships between two or more sets of items. They are commonly used in various fields, including project management, decision-making, and process improvement.

While matrix diagrams can be used to depict relationships and interactions between different elements, such as processes, functions, or components, they do not specifically show optionality and cardinality as defined in Entity-Relationship Diagrams (ERDs).

Optionality and cardinality are concepts typically associated with ERDs, which are used in database design to illustrate the relationships between entities. Optionality refers to the participation or existence of entities in a relationship (e.g., mandatory or optional participation), while cardinality specifies the number of instances of one entity that can be associated with another entity [e.g., one-to-one, one-to-many, many-to-many relationships].

Matrix diagrams, on the other hand, are not specifically designed to represent these concepts and focus more on visualizing the relationships between items rather than expressing optionality and cardinality.

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Answer:

x > 1/6.

Step-by-step explanation:

–2(8x – 4) < 2x + 5

-16x + 8 < 2x + 5

-18x < -3

x > 1/6.

The solution to the inequality expression is x > 1/6

Given the inequality expression

–2(8x – 4) < 2x + 5

Expand the parenthesis

-16x + 8 < 2x + 5

Subtract 5 from both sides

-16x + 8 - 5 < 2x + 5 - 5

-16x + 3 < 2x

-16x - 2x < -3

-18x < -3

Divide both sides by -18

-18x/-18 > -3/-18

x > 1/6

Hence the solution to the inequality expression is x > 1/6

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The lengths of the sides of the triangles can be found by using the

distance formula and the included angle is congruent to itself.

The correct response:

The given points are;

P(-5, -1), R(-3, 1), O(1, 5), V(4, -7) and E(-2, -3)

Required:

The option that proves that ΔPOV ~ ΔPRE

Solution;

By the Distance (between coordinate points) Formula, we have;

PO = \(\sqrt{(1 - (-5))^2 + (5 - (-1))^2}\) = 6·√2

PV = \(\sqrt{(4 - (-5))^2) + (-7 - (-1))^2}\) = 3·√13

PR = \(\sqrt{(-3 - (-5))^2 + (1 - (-1))^2}\) = 2·√2

PE = \(\sqrt{(-2 - (-5))^2 + (-3 - (-1))^2}\) = \(\mathbf{\sqrt{13}}\)

\(\dfrac{PO}{PR} = \dfrac{PV}{PE} = \mathbf{\dfrac{3 \cdot \sqrt{13} }{\sqrt{13} }} = 3\)

∠P ≅ ∠P, y reflexive property

Therefore, given that the ratio of two corresponding sides in triangles ΔPOV and ΔPRE are equal, and the included angles, ∠P, between the corresponding sides are equal, ΔPOV is similar to ΔPRE, by Side-Angle-Side, SAS, Similarity.

The correct option is therefore;

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Answer:

your answer is D

Step-by-step explanation:

I looked at the answer above and figured it out.
By the Distance Formula,PO=6/2–√, PR=2/2–√, PV=3/13−−√, and PE=13−−√. Since, PO/PR=PV/PE=3/1=3, and ∠P≅∠P by the Reflexive Property, △POV∼△PRE by SAS ∼.

the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

Here we have the quadratic equation:

f(x) = (x + 3)*(x + 5)

The first claim is: "The y-intercept is at (15, 0)."

This is clearly false, as the y-intercept is at x = 0, and in that point we have x = 15.

The second claim is:

"The x-intercepts are at (–3, 0) and (5, 0)"

This is false, in the factored equation we can see that the x-intercepts are x =-3 and x = -5.

Third claim:

"The vertex is at (-4, -1)"

The middle value between the zeros is:

(-3 + (-5))/2 = -4

Evaluating the function in x = -4 we get the y-value of the vertex:

f(-4) = (-4 + 3)*(-4 + 5) = -1*1 = -1

So the vertex is at (-4, -1), this claim is true.

The fourth claim is:

"The midpoint between the x-intercepts is at (4, 0)."

Which is false, we already saw that the midpoint between the x-intercepts is at x = -4

Then the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

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