If (1, 2) and (3, 4) lie on the same line, give the slope-intercept equation of the line.

Answer:

Option B is correct.

value of b = -8

Step-by-step explanation:

Given the equation: [tex]x^2+bx+16= 0[/tex]

As per the condition: The only solution for the given equation is, x = 4.

Substitute this value of x =4 in given equation, to solve for b;

[tex](4)^2+b(4)+16= 0[/tex]

Simplify:

[tex]16+4b+16= 0[/tex]

or

[tex]32 + 4b= 0[/tex]  

Subtract 32 on both sides, we get;

32 + 4b -32 = 0-32

Simplify:

4b = -32

Divide both sides by 4 we get;

b = -8

therefore, the value of b = -8

The shadow of the 24-foot tree will be 9.6 feet.

In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.

Given that:-

The shadow of the 24-foot tree will be calculated as follows:-

[tex]\dfrac{40}{16}=\dfrac{24}{x}[/tex]

[tex]x = \dfrac{24\times 16}{40}[/tex]

x = 9.6

Therefore the shadow of the 24-foot tree will be 9.6 feet.

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Final answer:

To find the length of the shadow cast by a 24-foot tree, we use the proportion of a 40-foot tree's height to its 16-foot shadow. The resulting shadow length for the 24-foot tree calculated through cross-multiplication is 9.6 feet.

Explanation:

The length of the shadow cast by a 24-foot tree can be found using a simple proportion based on the shadow cast by a 40-foot tree. Since a 40-foot tree casts a 16-foot shadow, the ratio of the height of the tree to the length of its shadow is 40 to 16. This ratio should be the same for the 24-foot tree. To find the shadow length (x) of the 24-foot tree, we set up the proportion as follows:

40 feet (tree height) / 16 feet (shadow length) = 24 feet (tree height) / x feet (shadow length)

Solving for x gives us:

40 / 16 = 24 / x

40 * x = 24 * 16

x = (24 * 16) / 40

x = 384 / 40

x = 9.6 feet

Therefore, the shadow cast by a 24-foot tree would be 9.6 feet long.

Horizontal lines have a slope of zero because their y-value does not change regardless of the x-value, while vertical lines have an undefined slope because their x-value does not change, leading to division by zero. These lines have different equations compared to diagonal lines because they do not follow the general linear form y = mx + b.

The slope of a line represents its steepness and direction. For a horizontal line, the slope is zero because there is no change in the y-value no matter how much we move along the x-axis. In contrast, a vertical line will have an undefined slope because the run (change in x-value) is zero, and division by zero is not defined in mathematics.

Equations for horizontal and vertical lines differ from those of diagonal lines because they don't fit the general linear equation form y = mx + b, where m represents the slope and b represents the y-intercept. A horizontal line has an equation of the form y = b, indicating that y is constant and does not depend on x, while a vertical line has an equation of the form x = a, indicating that x is constant and does not depend on y.

Graphically, an increase in slope means the line gets steeper, while a decrease in slope means the line is flatter. Horizontal lines are the flattest possible with a slope of zero, while vertical lines are conceptually the steepest with an undefined slope.

Final answer:

The base and height of the triangle are found using the area formula for triangles, with the base being 7 feet more than the height. Using this relationship and the fact that the area is 114 square feet, we solve a quadratic equation to find the height to be 12 feet and the base to be 19 feet.

Explanation:

The student is given that the base of a triangle exceeds the height by 7 feet and that the area of the triangle is 114 square feet. To find the base and height of the triangle, we can use the area of a triangle formula A = (1/2) × base × height. Let's denote the base as b and the height as h. From the given information, b = h + 7.

Substituting the values into the area formula, we get:
114 = (1/2) × (h + 7) × h. Simplifying this, we get 114 = (1/2) × h² + 7/2 × h. Multiplying both sides by 2 to clear the fraction, we obtain 228 = h² + 7h. This is a quadratic equation in the form of h² + 7h - 228 = 0, which we can solve by factoring or using the quadratic formula. Factoring gives us (h + 19)(h - 12) = 0, leading to two potential solutions for h: -19 or 12. Since a height cannot be negative, we discard -19, leaving us with h = 12 feet. Therefore, the base b = h + 7 = 19 feet

The base of the triangle is 19 feet, and the height is 12 feet.

The focus point of the satellite is (-5.5,0).

This is a parabola by the looks of the equation and the fact that it's a satellite dish. The vertex of the equation is (-6,0) and the focus is 2/4, 1/2. 1/2 plus -6 is -5.5. the focus is (-5.5,0).

This refers to the plane curve that is U-shaped and is formed by the intersection of a cone.

Hence, we can see that based on the equation, y^2=2(x+6), we can see that the adjustments made by Samara where the x and y are in inches, the focal point based on the vertex of the equation which is (-6,0) and the focus is 2/4, 1/2.

Therefore, the focal point is 1/2 + -6 which is -5.5.

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Answer:

His acceleration was -1/5 m/s²

Step-by-step explanation:

We can find the acceleration by using the formula to find the final velocity in terms of initial velocity and acceleration and then solving for a. The formula is   V2 = V1 + (a)(t) where V2 is final velocity, V1 is initial velocity and t is time in seconds.

We are going to substitute the values given in the problem:

V2 = 0 m/s

V1 = 6 m/s

t = 4 seconds

[tex]V2=V1+at\\0=6+a4\\0=6+4a\\-6=4a\\-6/4=a\\-1.5=a[/tex]

Therefore, his acceleration was -1.5 m/s²

The correct match is given below:-

2.64 gal-10 liters

0.14 cubic meters -5 cubic feet

5.35 cubic meters- 7 cubic yards

6.34 pints=3 liters

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure. Unit conversion is the process of changing a quantity's measurement between different units, frequently using multiplicative conversion factors.

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units.

The correct match is given below:-

2.64 gal                      ⇒         10 liters

0.14 cubic meters      ⇒          5 cubic feet

5.35 cubic meters     ⇒         7 cubic yards

6.34 pints                   ⇒         3 liters

Hence, the unit conversion is all steps in a multi-step procedure.

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The reflection of points across Y and X axis will be equal to (-5, 9), (5, -9).

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image.

A line, called the line of reflection, will allow an image to reflect through it. Every element inside a figure is thought to reflect another figure when they are all equally spaced apart from one another.

As per the mentioned data in the question,

The given point is (5, 9).

Under the reflection in the y-axis, points are converted as,

(x, y) ⇒ (-x, y)

So,

(5, 9) ⇒ (-5, 9)

Under the reflection in the x-axis, points are converted as,

(x, y) ⇒ (x, -y)

So,

(5, 9) ⇒ (5, -9)

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To solve for 'a' in the equation 5a^2 = 320, first divide both sides of the equation by 5 to get a^2 = 64. Then, take the square root of both sides which provides two possible solutions, a = 8, and a = -8.

The student is asking to solve for 'a' in the algebraic equation 5a2 = 320. To find the solution, we first need to isolate 'a' on one side of the equation. Begin by dividing both sides of the equation by 5:

a2 = 320 / 5

This simplifies to:

a2 = 64

To solve for 'a', we take the square root of both sides:

a = √64

Therefore, the solutions are:

a = 8, a = -8

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Answer: y−9=−14(x+2)

Step-by-step explanation:

See attached image.

The point- slope form is y−9=−14(x+2).

The correct option is (a)

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

given:

(-2, 9)

As,

y- y1= m (x- x1)

y - 9 = -14( x + 2)

y-9 = -14x -28

Hence, the point slope form is y−9=−14(x+2).

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We cannot conclude that rectangle LMNO has side lengths of 3 cm and 4 cm solely based on its area being 12 cm², as the side lengths are not confirmed by the second statement, thus not properly applying the Law of Detachment.

The question involves the use of the Law of Detachment in deductive reasoning within mathematics. The Law of Detachment, also known as modus ponens, is a logical form that states if the following two statements are true: 'If p, then q' and 'p is true', then we can conclude 'q is true'. In the given scenario, the first statement is 'If a rectangle has side lengths 3 cm and 4 cm, then it has an area of 12 cm2'. The second statement is 'Rectangle LMNO has area 12 cm2'.

To use the Law of Detachment, we need the second statement to confirm that rectangle LMNO has side lengths of 3 cm and 4 cm. However, we are only told the area of rectangle LMNO, not its side lengths. Therefore, based on the information given, we cannot properly apply the Law of Detachment because there is no direct statement verifying the specific side lengths of rectangle LMNO. For the Law of Detachment to be used correctly, the second statement must directly assert that LMNO has the side lengths in question.

Given the information provided, we cannot conclude that rectangle LMNO has side lengths of 3 cm and 4 cm just because its area is 12 cm2.

Final answer:

The equations y = 5x + 9 and y - 5x = 3 have the same slope of 5, indicating that their graphs are parallel lines. The difference lies in their y-intercepts; the first line crosses the y-axis at 9 and the second at 3, meaning they are parallel but at different vertical positions.

Explanation:

To compare and contrast the graphs of y = 5x + 9 and y - 5x = 3, we first need to rewrite the equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The first equation is already in this form, with a slope of 5 and a y-intercept of 9. We can rearrange the second equation by adding 5x to both sides to get y = 5x + 3, which has a slope of 5 and a y-intercept of 3.

Both lines have the same slope of 5, which means they are parallel and will never intersect. The difference between them is their y-intercepts; the first line intersects the y-axis at 9, whereas the second line intersects the y-axis at 3. This difference in y-intercepts means that while they have the same steepness and direction, they are located at different vertical positions on the coordinate plane.

The difference of 405,000,000−1.7×108 2.35 2.35×1072.35×107 ​ 2.35×1082.35×108 ​ ​ 2.35×1092.35×109 ​ is -2,397,000,000.

Let's calculate the difference step by step:

1. 405,000,000 - 1.7 × 10^8

To perform this subtraction, we need to subtract the second number from the first:

405,000,000 - 170,000,000 = 235,000,000

2. 235,000,000 - 2.35 × 10^7

Similarly, we subtract the second number from the first:

235,000,000 - 23,500,000 = 211,500,000

3. 211,500,000 - 2.35 × 10^7

Once again, subtract the second number from the first:

211,500,000 - 23,500,000 = 188,000,000

4. 188,000,000 - 2.35 × 10^8

Perform the subtraction:

188,000,000 - 235,000,000 = -47,000,000

5. -47,000,000 - 2.35 × 10^9

Finally, subtract the second number from the first:

-47,000,000 - 2,350,000,000 = -2,397,000,000

So, the difference is -2,397,000,000.

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Answer:

D. Each has a slope of –3, but one has a y-intercept of 3 and the other has a y-intercept of –1, which makes the lines equivalent.

Step-by-step explanation:

If you look at the graph (Firstly), you can see that both lines look similar, which is one big hint to this question. But (secondly), like the other person said, both have equivalent y-intercepts in each problem. I saw an open spot for me to answer this so I took it UuU!

Also Just Realized This Is A Totally Diff Question On My Quiz, So The Question That Goes With This Answer Is "Consider the equations and graph below.

y = negative 3 (x minus 1). Y = negative 3 x minus 1

On a coordinate plane, 2 lines are parallel to each other.

Which explains why this system has no solution?"