Determine if the sentence is true. Select all that apply. □ 2 + 5 = 19 − 12 □ -.+ /. = 2 − 1 − 1 □ 5 − 4 − 3 − 2 − 1 = 30 − 34 − 1 □ 2 � + 8 = 2� − 8 □ 2 x + 5 − 4x = 3 x − 2 − 5x + 16

Answer:

Step-by-step explanation:

You want the maximum possible number of solutions to the equation

  ||ax -b| +c| = d

The values of 'a' and 'b' represent a vertical scale factor and a horizontal shift, so don't really contribute to the number of possible solutions. That means we can consider only the equation ...

  ||x| +c| = d

Positive c

We know |x| is always positive, and may have the same value for two different values of x. For positive 'c', the outside absolute value function does nothing, so the equation is effectively ...

  |x| = d-c

For d < c, there can be no solutions. For d = c, there will be one solution, and for d > c, there will be two solutions.

Negative c

When 'c' is negative, then sum |x| +c may have either sign. This gives rise to another pair of possible solutions, for a total of four solutions.

The attached graph shows the two cases. The red graph shows the left side expression with c > 0; the purple graph shows the left side expression with c < 0. The orange horizontal line represents a value of 'd'. The number of intersection points with that horizontal line is the number of possible solutions to the given equation.

For c > 0, there are two possible solutions.

For c < 0, there are four possible solutions.

Using proportions, it is found that:

a) You need 15 tablespoons of brown sugar.

b) You need 8 tablespoons of baking soda.

c) You need 10 cups of brown sugar.

d) You need 24 cups of baking soda.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for ratio problems.

For this problem, the recipe uses a 2:5 ratio of baking soda to brown sugar, hence:

Hence, for item a, the amount is:

5/2 x 6 = 30/2 = 15.

You need 15 tablespoons of brown sugar.

For item b, the amount is:

2/5 x 20 = 40/5 = 8.

You need 8 tablespoons of baking soda.

For item c, the amount is:

5/2 x 4 = 20/2 = 10.

You need 10 cups of brown sugar.

For item d, the amount is:

2/5 x 60 = 120/5 = 24.

You need 24 cups of baking soda.

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Answer:the number is 15

if i am correct give me brainliest

Step-by-step explanation:because 5-15=10 the number is 15

Answer: jus subtract untill u find x

Step-by-step explanation:

whether u do to one side do to the other

Answer:

55%

Step-by-step explanation:

She has ridden 22 out of 40 miles

22/40 is 0.55

0.55 = 55%

She has eight more miles or 45% left to go.

The solution of the inequality is 1<x<2.

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations.

According to the given statement;

2 < 3x - 1 < 5

or, 2 + 1 < 3x - 1 + 1 < 5 + 1

or, 3 < 3x < 6

Divide the whole by 3, we get

or, 3/3 < (3/3)x < 6/3

or, 1 < x < 2

hence, the solution of the inequality is 1<x<2.

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A geometric sequence with first term 16 and common ratio 0.5, with 10 terms, satisfies the requirements for this problem, and the first four terms are:

16, 8, 4, 2.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

For this problem, we have that:

Each term is the previous term multiplied by 0.5, hence the first four terms are:

16, 8, 4, 2.

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Answer:

  x = √65

Step-by-step explanation:

You are given a right triangle with leg lengths 4 and 7, and you are asked for the length of the hypotenuse, x.

The Pythagorean theorem relates the lengths of the sides of a right triangle. It tells you the square of the hypotenuse (x²) is the sum of the squares of the other two sides.

  x² = 4² +7² . . . . . . . . . Pythagorean relation

  x² = 16 +49 = 65 . . . evaluate the expression

  x = √65 . . . . . . . . . . take the square root

Using the Pythagorean Theorem, the distance between Pole X and Pole Z is of 15.3 m.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

The first part of the distance is the hypotenuse of a right triangle of sides 0.5 and 2.5, tracing a right triangle at the top of pole X and tracing it to segment Y, hence:

df² = 0.5² + 2.5²

df = sqrt(0.5² + 2.5²)

df = 2.55m.

For the second part, we apply equivalent triangles, as we can also trace a right triangle at the top of segment Y to segment Z, hence:

0.5/2.5 = df/ds

1/5 = 2.55/ds

ds = 2.55 x 5 = 12.75m

Then the total distance is:

2.55 + 12.75 = 15.3 m.

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The statement is false and the changes to make the statement true are:

The statement is given as:

The common difference for the geometric sequence given by 1, -1, -3, -5, -7… is 2.

The above statement is false because of the following reasons:

Hence, the statement is false and the changes to make the statement true are:

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Answer:

The first one is a function of x. The graph with a straight line up and down (vertical).

Step-by-step explanation:

Answer:

sin 11pi/3 = - root3/2

cos 11pi/3 = 1/2

tan 11pi/3 = - root3

csc11pi/3 =-2root3/3

sec11pi/3= 2

cot11pi/3 = -root3/3

see image

Step-by-step explanation:

This is a question that you should use the Unit Circle to find the answers. Unit Circle looks like a horrible math nightmare pizza, but it is really a great big giant Answer Key. It has all the trig answers on it.

First, change 11pi/3 to an angle that IS on the Unit Circle. See image for three ways to change 11pi/3 to an equivalent (on the UnitCircle) angle 5pi/3.

Then, since the Unit circle is the Answer Key. Use the x and y given, in the form (x, y) to find all 6 trig values.

Memorize for this type of question:

sin = y (they both have that long i sound)

cos = x

tan = y/x

csc (flip over sin) = 1/y

sec = 1/x (flip cos)

cot = x/y (flip tan)

Also, to make things hairier, you have to know how to rationalize the denominator. This just means you canNOT leave a sqrt symbol on the bottom of a fraction.

And unfortunately, if you never learned how to manipulate a fraction over a fraction, you will have to do that too. Use Keep-Change-Flip. That makes it super do-able. See image.

Answer: X = 21/6

Step-by-step explanation:

The angle is a 90 degree angle.

that means we know 21x+6=90

21x = 90-6

21x=84

x = 84/24

x = 21/6

x = 21/6

Answer:

I'm pretty sure it's 5:4 or 5/4. I think this because there are 5 peaches and four oranges.

Answer:

Step-by-step explanation:

Answer:

first translate triangle FDE down 5 units

second reflect it over the y axis

The image

Step-by-step explanation:

Answer: -2

Step-by-step explanation:

[tex]g(x) = g(-2) = -(-2)-4=2-4=-2[/tex]

Answer:

34.972 ≈ 35

0.948 ≈ 1

Hope this helps :)

Step-by-step explanation:

To round to the nearest whole number look at the tenths place (the place right after the decimal). If the number is 1,2,3,4 then round down or keep the number the same. If the number is 5,6,7,8,9 then round up.

The five rational number between -5/6 and 5/6 are [tex]\frac{-4}{6} ,\ \frac{-3}{6} ,\ \frac{-2}{6} , \ \frac{-1}{6} ,\ \frac{1}{6}[/tex]

We have given two rational numbers [tex]\frac{-5}{6}[/tex] and [tex]\frac{5}{6}[/tex] .

For finding rational number make the denominator of given numbers same.

As the denominator of given numbers is already same so , we don't need to multiply .

Thus , five rational numbers are

 [tex]\frac{-4}{6} ,\ \frac{-3}{6} ,\ \frac{-2}{6} , \ \frac{-1}{6} ,\ \frac{1}{6}[/tex]

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The vertex of the function is (1, 0), the maximum is y = 0 and it has no minimum

The function is given as:

y = -2/3|x - 1|

The above function is an absolute value function

An absolute value function is represented as:

y = a|x - h| + k

Where the vertex is

Vertex = (h, k)

By comparing y = a|x - h| + k and y = -2/3|x - 1|, we have

(h, k) = (1, 0) --- vertex

a = -2/3

Because a = -2/3 is negative, then the vertex is a maximum

Hence, the vertex of the function is (1, 0), the maximum is y = 0 and it has no minimum

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Answer:

100

Step-by-step explanation:

The average rate of change of the given function f over the intervals-

f(x) = x²/8 ; x=a=1

the average rate of change of f(x) over the time interval [a, a + h] is

rc= [f(a +h) - f(a) ] / [(a +h)-a] = [(a +h)²/8 - a²/8] /h = 1/h [ (a²/8 +a*h/4+ h²/8) - a²/8]

= a /4+ h/8

then

rc= a/4+ h/8

for x=a=1 and h=1

rc= 1/4 + 1/8 = 0.375

for a=1 and h=0.1

rc= 1/4 + 0.1/8 = 0.2625

for a=1 and h=0.01

rc= 1 /4+ 0.01/8 = 0.25125

for a=1 and h=0.001

rc= 1/4 + 0.001/8 = 0.250125

for a=1 and h=0.0001

rc= 1 /4+ 0.0001/8 = 0.2500125

when h goes smaller , the average rate of change gets closer to the instantaneous rate of change of f(x) in x=a=1 (the derivative of f in a=1) , that is

f'(x) = x

then

f'(a) = a

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Answer:

It will be. - 4/10 only that

We get that the value of (f + g​)(x​) is 11 x - 1.

Function: a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

We are given the two functions:

f(x) = 4 x + 3

g(x) = 7 x - 4

We need to find:

(f + g​)(x​)

We know that this is equal to

= f(x) +g(x)

Substituting the values, we get that:

= 4 x + 3 + 7x - 4

Combining the like terms, we get that:

= 11 x - 1

Therefore, we get that the value of  (f + g​)(x​) is 11 x - 1.

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There are 53 classes in South Beach middle school

South beach middle school has 1,272 students

The students are divided into equal classes of 24 students each

Therefore the number of classes can be calculated by dividing the total population of the students in the school by 24

= 1272/24

= 58

Hence there are 58 classes in the school

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