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Directions: Find the solutions of each quadratic equation
1. x² - 4x = 0

Answer:

A

Step-by-step explanation:

A

Answer:

Q9 -  Option 1---- A -  15.6 Square Units

Q10 --Option --- (B) RECTANGLE

Step-by-step explanation:

Q9 --

we know area of triangle  = 1/2 ab sin theta

Where theta is the angle included between sides A and side B

A  = 5.2

B = 7

theta  = 121 degrees

1/2 * 5.2 * 7 * sin 121 degrees = 15.6 Square Units

Conclusion

The area of the triangle is 15.6 Square Units

Option --- (B) RECTANGLE

Hope this helps!

The correct answer for given dilation will be A and D i.e. Point P is midpoint of AA' and XY⊥AA'.

What precisely is dilation?

Dilation is the process of changing the size of an object or form by shrinking or extending its dimensions based on certain scale variables. For example, a circle with radius 10 unit is decreased to a circle with radius 5 unit. This method is used in photography, arts and crafts, and logo design, among other things. In geometry, there are four basic types of transformations. These are their names:

Properties of Rotation, Translation, Reflection, and Resizing

Dilation properties

The following are some features of shapes that remain constant with dilation changes:

Now,

As The image of A is made on line XY and the image will be A'

then XY⊥AA' because line formed between images is always perpendicular to the plane it is formed on and

P is the midpoint of AA' because we know that AP and A'P are same in a image formation.

Hence,

           Point P is midpoint of AA' and XY⊥AA'.

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To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

The order for the extra materials that are ordered by the man will be between 17.31 ft² and 23.08 ft².

From the information, the man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and wants to order between 15% and 20% extra of the material.

It should be noted that 15% of the material will be:

= 15% × 115.4

= 17.31 ft²

It should be noted that 20% of the material will be:

= 20% × 115.4

= 23.08 ft²

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The diameter of circle is d = 8 cm.

The formula for the area of circle is,

Determine the area of circle.

Option C is correct.

Answer:

w<13

Step-by-step explanation:

Works identically to a normal single-variable equation.
Subtract 7 on both sides in order to isolate w--->w+7-7<20-7
The answer (which cannot be simplified any further) is w<13.

Answer:

w < 1`3

Step-by-step explanation:

Isolate the variable w on one side of the inequality sign.

w+7<20

w<20 - 7

w<13.

The value of x for each radical equation is 243 , 125,8,256 respectively.

The correct question is attached as an image with the answer.

When in an equation the variable is under a radical it is called a Radical Equation.

It is given in the question that

which radical matches to the solution

\(\rm \sqrt[5]{x^4} = 81 \\\\\sqrt[3]{x^4} = 625\\\\\sqrt[3]{x^5} = 32\\\\ \sqrt[4]{x^3}=64\)

\(\rm x^4 = 81^5\\x = 243\)

\(\rm x^4 = 625^3\\x = 125\\\)

\(x^5 = 32^3\\x = 8\\\)

\(\rm x ^3 = 64^4\\x = 256\)

Therefore for each radical the value of x is determined.

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The area of the composite figure is 159.9 cm²

From the question, we are to determine the area of the given composite figure

In the given diagram, the area of the composite figure = Area of triangle + Area of rectangle

First, we will calculate the area of the triangle

Area of triangle = 1/2 × base × height

Thus,

Area of the triangle = 1/2 × 16.4 × 5.5

Area of the triangle = 45.1 cm²

Calculating the area of the rectangle

Area of rectangle = Length × Width

Thus,  

Area of the rectangle = 16.4 × 7

Area of the rectangle = 114.8 cm²

Therefore,

The area of the composite figure = 45.1 cm² + 114.8 cm²

The area of the composite figure = 159.9 cm²

Hence, the area is 159.9 cm²

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Answer:

30 ft

Step-by-step explanation:

10 yards x 3 ft per yard= 10x3=30 ft

False. The equation \(x = x2u + x3v\) describes a line through the origin, not a plane.

The equation \(x = x2u + x3v\) describes a line through the origin, not a plane. This equation can be written as \(x = x2u + x3v\), which is the same as \(ux2 + vx3 - x = 0\). This equation is in the form of \(ax + by + cz = d\), with a = u, b = v, c = -1, and d = 0. Since the coefficients of \(x2, x3\), and x are all non-zero, we can conclude that this equation describes a line, not a plane. To confirm, we can calculate the direction vector for the line. The direction vector is (u, v, -1), which is a single vector and not two or more vectors that would be necessary to describe a plane.

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The probability of randomly picking a school or library-related issue from the ballot is 9/19 or approximately 0.474 (rounded to three decimal places).

To determine the probability of a randomly picked issue being school or library related, you'll need to consider the total number of issues and the number of school and library issues combined.

There are 7 school-related issues, 10 ordinance-related issues, and 2 library-related issues, making a total of 19 issues on the ballot. To find the probability of picking a school or library issue, combine the number of school and library issues: 7 + 2 = 9.

Now, divide the number of school and library issues (9) by the total number of issues (19): 9/19.

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Answer:

the approximate area of corcle is 3848

\(diameter = 70in \\ radius = \frac{70}{2} \\ = 35in \\ area = \pi \: r {}^{2} \\ = \pi \: 35 {}^{2} \\ = 3848.45in {}^{2} \)

Answer:

Kindly refer to the attachment

Answer: where is the answer choices

Step-by-step explanation:

the distance between Dan and jeff is 26 feet

Answer: (-9, 3)

Step-by-step explanation:

This problem works best with substitution.

To do a system of equations with substitution, solve for the first variable in one of the equations, then substitute the result into the other equation.

Since the second equation already gives us what x is (-3y) we can easily substitute this into the first equation. (2x + 7y = 3)

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

\(\left \{ {{2x+7y=3} \atop {x=-3y}} \right.\)

\(2(-3y)+7y=3\)

\(-6y+7y=3\)

Combine the like terms.

\(y=3\)

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

Since we have y, we need to find x now.

Because we already used the first equation to find y, plug y into the SECOND equation.

\(x= -3(3)\\\)

\(x = -9\)

Done!

(-9, 3)

a) The null hypothesis is that there is no difference in the proportion of homeowners using water filters among the three communities. The alternative hypothesis is that at least one community has a different proportion of homeowners using water filters than the other communities.

b) To calculate the expected count for the bottom right cell, we can use the formula:

Expected count = (row total x column total) / grand total

The row total for Community C and the column total for No are both 100, and the grand total is 300. Therefore:

Expected count = (100 x 100) / 300 = 33.33

The expected count of 33.33 for the bottom right cell means that if there were no difference in the proportions of homeowners using water filters among the three communities, we would expect 33.33 of the 100 homeowners in Community C to answer 'No' to the question about water filters.

c) To determine what we can conclude from the Chi-square statistic of 13.22, we need to compare it to the critical value for a Chi-square distribution with (3-1) x (2-1) = 2 degrees of freedom at the desired level of significance. Let's assume a level of significance of 0.05. From a Chi-square distribution table, the critical value with 2 degrees of freedom at 0.05 level of significance is 5.99.

Since 13.22 is greater than 5.99, we can reject the null hypothesis and conclude that there is a significant difference in the proportion of homeowners using water filters among the three communities. However, we cannot determine from this test alone which communities have different proportions of homeowners using water filters. We would need to conduct further tests, such as post-hoc tests, to investigate the specific differences among the communities.

the rate is usually the number in the parentheses in an exponential function, now the tell-tale piece is that, if the rate is less than 1, we have a Decay expression, and if the rate is more than 1, then is Growth.

well, let's see 0.365 is less than 1, so it's Decay.

\(\qquad \textit{Amount for Exponential Decay} \\\\ y=P(1 - r)^t\qquad \begin{cases} y=\textit{current amount}\\ P=\textit{initial amount}\dotfill &3100\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ y = 3100(\stackrel{\stackrel{0.365}{\downarrow }}{1-\frac{r}{100}})^t\qquad \textit{this means that }\qquad 1-\cfrac{r}{100}=0.365 \\\\\\ -\cfrac{r}{100}=-0.635\implies r=(-100)(-0.635)\implies r=\stackrel{\%}{63.5}\)

The Probability that a randomly selected senior is both in the band and on the honor roll is 8/25.

To find the probability that a randomly selected senior is both in the band and on the honor roll, we need to divide the number of seniors who are in both categories by the total number of seniors.

Given:

Total number of seniors = 200

Number of seniors in the band = 32

Number of seniors in the band or on the honor roll = 64

Let's calculate the probability using these values:

Probability = Number of seniors in both categories / Total number of seniors

Probability = 64 / 200

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 8:

Probability = (64 ÷ 8) / (200 ÷ 8)

Probability = 8 / 25

Therefore, the probability that a randomly selected senior is both in the band and on the honor roll is 8/25.

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Answer:

A dog needs 4/3 liters of water 2/5 of a day, Therefore

he'll need 4/3 liters for 5/2 day or

4/3 * 5/2 = 20/6 = 10/3 liters or 3 and 1/3 liters per day

Step-by-step explanation:

An equation that can be used to determine the angle measure, in degrees, of angle DBC is 67 + n = 90.

The measure of n is equal to 23 degrees.

In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).

By substituting the given parameters into the complementary angle formula, the sum of the angles is given by the following mathematical equation;

∠ABD + ∠DBC = 90

∠ABD + n = 90

67 + n = 90.

n = 90 - 67

n = 23°

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

473 books to each class

Step-by-step explanation:

2365÷5=473

Answer:

473

Step-by-step explanation:

Each classroom would receive 473 books.

Answer:

1, 2, and 3

Step-by-step explanation:

a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)

b. The increase in cost between 12 noon and 3 pm is $2.

c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.

The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.

We can represent it as (8am, 9am) U (11am, 12pm).

It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).

And stays constant at : (9am, 10am) U (10am, 11am)

We simply deduct the 12pm's cost from 3pm's cost.

So, we have

Cost increase = $3.5 - $1.5

Evaluate the difference

Cost increase = $2

Hence, the cost increase is $2

When you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

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The equation of the line is y = -11x + 232

The given parameters are:

Slope (m)= -11

Point (x1, y1) = (31, -109)

The linear equation is then calculated as:

y = m(x - x1) + y1

This gives

y = -11(x - 31) - 109

Evaluate the product

y = -11x + 341 - 109

Evaluate the like terms

y = -11x + 232

Hence, the equation of the line is y = -11x + 232

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Answer:

531 1/4 meters cubed

Step-by-step explanation:

Answer:

1 (give brainliest plss)

Step-by-step explanation:

Step-1 : Multiply the coefficient of the first term by the constant 5 • -8 = -40

Step-2 : Find two factors of -40 whose sum equals the coefficient of the middle term, which is -3 .

-40 + 1 = -39

-20 + 2 = -18

-10 + 4 = -6

-8 + 5 = -3 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and 5

5x2 - 8x + 5x - 8

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (5x-8)

Add up the last 2 terms, pulling out common factors :

1 • (5x-8)

Step-5 : Add up the four terms of step 4 :

(x+1) • (5x-8)

Which is the desired factorization

\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the concept of Quadratic Equations.

Degree of a equation represents the highest power of the varible in the equation, For quadratic equation the degree is 2.

Leading Coefficient are the constant numbers that are significantly multiplied with the variables in the equation.

==> 5x^2 - 3x - 8 = 0

==> 5x^2 -8x +5x -8=0

==> x(5x-8) +1(5x-8)=0

==> (5x-8)(x+1) = 0

Answer:

B. The graph would shift 5 units up.

Step-by-step explanation:

Before the change:

Before the change, the function was given by:

\(y = x^2 - 3\)

After the change:

After the change, the function was given by:

\(y = x^2 + 2\)

Considering the function as it was before the change, it can also be written as:

\(y = x^2 - 3 + 5\)

Which means that 5 was added to the function, and when a number n is added to a function, there function is shifted n units up. So the correct answer to this problem is given by option B.