Solve for x.

x/2≥−4

x≥−8

x≥−2

x≤−2

x≤−8

Discriminant = b^2 - 4ac

a = 4

b = 16

c = 16

16^2 - 4(4 x 16)

256 - (4x64)

256 - 256 = 0

Therefore it only has one root

The statement is true for linear functions, but not in general for all functions.

The statement is true if f(x) is a linear function.

However, it is not true in general for all functions, so the statement is false.

An example of a linear function where the statement is true would be f(x) = 2x.

If we substitute s + t into the function, we get f(s + t) = 2(s + t) = 2s + 2t.

On the other hand, if we substitute f(s) + f(t) into the function, we get f(s) + f(t) = 2s + 2t.

Therefore, the equality holds and the statement is true for linear functions.

Answer:

  x ≈ 4.1 cm

Step-by-step explanation:

The side (z) opposite the 42° triangle can be found from the relation ...

  z/(3.6 cm) = tan(42°)

  z = (3.6 cm)·tan(42°) ≈ 3.2415 cm

The relationship between z and x is ...

  z/x = cos(38°)

  x = z/cos(38°) ≈ 4.1135 cm

  x ≈ 4.1 cm

Answer:

Here is the answer and proof :)

Step-by-step explanation:

the answer is A my good sir/madam

Answer:

a. 4.85

Step-by-step explanation:

im right

? = a+b

a = 3

(3+b)/3=3/b

b= -4.85 or 1.85

it cant be negive.

so ? = 3+1.85 = 4.85

Answer:

Step-by-step explanation:

1600

The fraction 30/6 can be rewritten as the whole number 5 after performing the division operation 30 ÷ 6.

The problem asks to rewrite 30/6 as a whole number. In mathematics, this implies using the operation of division. Division is one of the four basic operations in math, along with addition, subtraction, and multiplication.

To solve this problem, you need to divide 30 by 6. Perform the division operation as follows: 30 ÷ 6. The result of this operation is 5.

Therefore, the fraction 30/6 can be rewritten as the whole number 5.

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Area is determined by using the formula A=lw  Area= Length x  Width

A= 1 1/4 x 3   convert to an improper fraction

A= 5/4 x 3/1  multiply

A=15/4   divide

A=3 3/4 square feet

Answer: [tex]A=3\dfrac{3}{4}\ ft^2[/tex]

Step-by-step explanation:

Given: The dimensions of the wrapping paper :

[tex]1\text{ and}\dfrac{1}{4}\text{ feet }\text{ by 3 feet}\\\\\text{i.e }1+\dfrac{1}{4}\text{ feet }\text{ by 3 feet}\\\\\text{i.e }\dfrac{5}{4}\text{ feet }\text{ by 3 feet}[/tex]

Now, we know that the area of a rectangle is given by :-

[tex]A=length*width[/tex]

Now, the area of the wrapping paper is given by :-

[tex]A=\dfrac{5}{4}\times3=\dfrac{15}{4}=3\dfrac{3}{4}\ ft^2[/tex]

Answer with Step-by-step explanation:

The volume of cone is given by:

V=[tex]\dfrac{1}{3}\times \pi r^2h[/tex]

Where r is the radius of cone and h is height

r=d/2 where d is the diameter

Hence, here r=5 in.

height is twice its radius ⇒ h=10 in.

V=[tex]\dfrac{1}{3}\times 3.14\times 5^2\times 10[/tex]

V=261.66 in³

Hence, Volume of cone is:

261.66 in³

Answer:

Step-by-step explanation:

6/8

Answer:

The baker made 36 batches of muffins.

Step-by-step explanation:

Let the total amount of flour be x

We know he used 2/5 of the flour for bread, we also know he used 16 pounds for bread.

We can write this as :

[tex]\frac{2}{5}\times x=16[/tex]

Solving this we get;

[tex]2x=80[/tex]

So, x = 40

Means total amount of flour was 40 pounds and he used 16 pounds for bread, so the remaining is for batches of muffins, which is [tex]40-16=24[/tex] pounds

As each batch of muffin uses 2/3 pounds, so 24 pounds of flour will be used to bake :

[tex]\frac{24}{\frac{2}{3} }[/tex]

= [tex]\frac{24\times3}{2} =36[/tex]

Hence, the baker made 36 batches of muffins.

Answer

A

Step-by-step explanation:

Final answer:

To solve the word problem, we define three variables representing the number of first-, second-, and third-place finishers, respectively. We set up three linear equations based on the information provided, and by solving the system, we determined that 10 swimmers finished in first place, 8 in second, and 6 in third.

Explanation:

Setting Up the Equations

Let's denote the number of first-place finishers as x, second-place finishers as y, and third-place finishers as z. According to the information provided:

Total number of individuals placed: x + y + z = 24

Total points earned: 3x + 2y + z = 53

The number of first-place finishers equals the number of second and third-place finishers combined: x = y + z

This is our system of three equations.

Solving the System of Equations

To solve for the number of swimmers in each place, use the substitution or elimination method:

Since x = y + z, substitute x in the first two equations.

You'll get two equations with two variables (y and z).

Solve these equations to find the values of y and z.

Finally, substitute the found y and z back into x = y + z to get the value of x.

By solving this system, we find that 10 swimmers finished in first place, 8 swimmers finished in second, and 6 swimmers finished in third.

The method in which rigid transformations used to justify the SAS congruence theorem is given.

A rigid transformation (also called an isometry) is a transformation of the plane that preserves length. In a rigid transformation the pre-image and image are congruent (have the same shape and sizes).

We are given that;

Theorem is SAS

Now,

The SAS congruence theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. To prove this theorem using rigid transformations, we can start with two distinct triangles that have a pair of corresponding congruent sides and a corresponding congruent included angle23. Then we can use a translation to move one triangle so that its congruent side matches the other triangle’s congruent side. Next, we can use a rotation to align the congruent angles of both triangles. Finally, we can use another translation to move the second congruent side of one triangle to match the second congruent side of the other triangle. By doing these rigid transformations, we have shown that one triangle can be mapped onto the other triangle exactly, which means they are congruent

Therefore, by the transformations the answer will be given above.

Learn more about rigid transformations;

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