if you form a triangle from three given side lengths, will you always get one triangle or more than one triangle?

The solution of a compound inequality is the common region or intersection region of two inequalities.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

A sentence having two inequality statements connected by the words 'or' Or 'and' is referred to as a compound inequality. The conjunction "and" denotes the simultaneous truth of both statements in the compound sentence.

For example, if in a compound inequality we get x > 3 and x > 5 so the final conclusion is x > 5.

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Answer: x = 1

Step-by-step explanation:

The population of the state is 23.1 million

The population of the state will reach 28.3 million in 13.5 years

What is population ?

Any whole group that shares at least one trait is referred to be a population. People do not make up all populations. Populations can include, but are not limited to, individuals, animals, organizations, structures, buildings, cars, farms, objects, or occasions.

The population state is:

A = 23.1*e^(0.0153*t)

In millions.

Where t represents the number of years after 2000.

a) For the population at the year 2000, we need to evaluate the function at t = 0 (2000 is 0 years after 2000).

A(0) = 23.1*e^(0.0153*0) = 23.1

The population at year 2000 was 23.1 millions.

b) Now we want to solve:

A(t) = 28.3 = 23.1*e^(0.0153*t)

        28.3/23.1 = e^(0.0153*t)

        1.23 = e^(0.0153*t)

Now we can apply the natural logarithm to both sides:

ln(1.23) = ln( e^(0.0153*t) )

ln(1.23) = 0.0153*t

ln(1.23)/0.0153 = t = 13.5

So 13.5 years after 2000 the population will be 28.3 million.

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The simplest form of the given expression is 3x³+4x²+6x

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical operation, and extraction of roots.

Main body:

according to question ,

6x³+2x²+3x -(3x³-2x²-3x)

we need to simplify the given equation.

firstly opening the bracket and taking care of sign,

⇒6x³+2x²+3x -3x³ +2x² +3x

taking like terms seperately,

⇒6x³ -3x³ +2x²+2x²+3x+3x

⇒3x³+4x²+6x

Hence the simplest form of the given expression is 3x³+4x²+6x

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What is the maximum height of the ball 182.25 feet

How many seconds does it take until the ball hits the ground 6 seconds

The maximum height will occur at the vertex v(h', k)

h' = -b/2a

From the equation h = − 16 t^2 + 84 t + 72

a = -16

b = 84

h' = -84/(2 * -16)

h' = t = 2.625

k = h = − 16 t^2 + 84 t + 72 at t = 2.625

= − 16 * 2.625^2 + 84 * 2.625 + 72

= 182.25 feet

The ball hits the ground when h = 0

0 = − 16 t^2 + 84 t + 72

solving the quadratic equation gives

t = 6 OR -3/4

Use the positive value

t = 6 seconds

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Answer:

The answer is in the picture

Step-by-step explanation:

The explanation is in the picture

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

Equation

[tex]20 + 4(3x-5)+2x=28[/tex]

Expand the brackets

[tex]20 + 12x- 20 + 2x=28[/tex]

Combine like terms

[tex]14x=28[/tex]

Solve

[tex]x=2[/tex]

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Answer:

1:25

$0.04 or 4 cents per can

Step-by-step explanation:

The ratio of dollars to can is 2:50 = 1:25.

$1/25 = $0.04

She gets $0.04 or 4 cents per can

The expression for the exact number of inches in 1 centimeter is 2.54/2.54 cm = 1/2.54 in and the number of inches is 0.39

From the question, we have the following parameters that can be used in our computation:

1 inch = 2.54 centimeters and 1 centimeter = 0.39 inch.

To calculate the number of inches expression, we make use of the following equation

1 inch = 2.54 centimeters

Divide both sides of the equation by 2.54

So, we have the following representation

1/2.54 inch = 2.54/2.54 centimeters

Rewrite the expression as

2.54/2.54 centimeters = 1/2.54 inch

So, we have

2.54/2.54 cm = 1/2.54 in

So, the expression is 2.54/2.54 cm = 1/2.54 in

In (a), we have'

Expression: 2.54/2.54 cm = 1/2.54 in

This implies that

2.54/2.54 cm = 1/2.54 in

Evaluate the quotients

1 cm = 0.39 in

Hence, the value is 0.39 inches

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Step-by-step explanation:

w=x

l=2x

p=2(l+w)

p=2(2x+x)

p=6x

The degree of the remainder is less than the degree of the divisor, we have found the complete remainder. Therefore, the quotient is 4x² + 8x + 6, and the remainder is -16x² -16x.

What is the quotient?

The number we obtain when we divide one number by another is the quotient. For example, in 8 ÷ 4 = 2; here, the result of the division is 2, so it is the quotient. 8 is the dividend and 4 is the divisor.

To find the quotient and remainder when dividing 8x³ +16x² + 12x+13 by 2x+2, we can use polynomial long division.

First, we divide the leading coefficient of the dividend (8x³) by the leading coefficient of the divisor (2x). This gives us a quotient of 4x². We then multiply the divisor (2x+2) by this quotient and subtract it from the dividend to get the first term of the remainder:

8x³ +16x² + 12x + 13

(2x+2)(4x²)

8x³ - 8x³ -8x² -8x² +12x+13

This leaves us with 12x+13 as the first term of the remainder.

Next, we bring down the next term of the dividend (16x²) and divide it by the leading coefficient of the divisor (2x). This gives us a quotient of 8x. We then multiply the divisor (2x+2) by this quotient and subtract it from the dividend to get the next term of the remainder:

12x+13

(2x+2)(8x)

12x+13 - 16x² - 16x

-4x² -4x

This leaves us with -4x² -4x as the next term of the remainder.

Finally, we bring down the last term of the dividend (12x) and divide it by the leading coefficient of the divisor (2x). This gives us a quotient of 6. We then multiply the divisor (2x+2) by this quotient and subtract it from the dividend to get the final term of the remainder:

-4x² -4x

(2x+2)(6)

-4x² -4x -12x -12

-16x² -16x

This leaves us with -16x² -16x as the final term of the remainder.

Hence, the degree of the remainder is less than the degree of the divisor, we have found the complete remainder. Therefore, the quotient is 4x² + 8x + 6, and the remainder is -16x² -16x.

We can write the result of the division as:

(8x³ + 16x² + 12x + 13) ÷ (2x+2) = (4x² + 8x + 6) + (-16x² -16x)/(2x+2)

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a) The equation is 10p + 80 = 180 and p = 10.

b) The three angles are 90°, 37°, 53°.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given that, the angles of the triangles are 53°, 2p + 17°, and 8p + 10°.

The sum of all angles of a triangle is  53° + 2p + 17° + 8p + 10° = 80 + 10p

The sum of all angles of a triangle is 180°.

Therefore,

80 + 10p = 180

Subtract 80 from both sides:

10p = 100

divide both sides by 10:

p = 10.

Putting p = 10 in 2p + 17°, and 8p + 10°:

2p + 17° = 20° + 17° = 37°

8p + 10° = 80° + 10° = 90°

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Answer:

25.5 inches.

Step-by-step explanation:

To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, we have a right triangle with legs of length 19 inches and 17 inches. The length of the hypotenuse is the square root of the sum of the squares of the other two sides. We can calculate this as follows:

hypotenuse = sqrt(19^2 + 17^2)

hypotenuse = sqrt(361 + 289)

hypotenuse = sqrt(650)

hypotenuse = 25.495097568 inches

Rounding to the nearest tenth, the length of the hypotenuse is 25.5 inches.

Tell me if it helped :)

Answer:

Step-by-step explanation:

there is no answer it just a bunch of f,h,y and t this is not math this is something

Answer:

Si...

En una progresión geométrica se conocen a1 = 64 y r = 0,75

The value of r is 45 and the value of s is 29

From the question, we are to solve the parallelogram for the missing variables.

The missing variables are r and s

Since opposite angles of a parallelogram are equal, we can write that

(r - 10)° = (3r - 100)°

Solve for r

r - 10 = 3r - 100

-10 + 100 = 3r - r

90 = 2r

r = 90/2

r = 45

Also,

We can write that

(5s)° = (4r - 35)°

Substitute the value of r and solve for s

5s = 4(45) - 35

5s = 180 - 35

5s = 145

s = 145/5

s = 29

Hence, r = 45, s = 29

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Answer:

C. 0.33 hour

Step-by-step explanation:

15 miles = 1 hr

5 miles = x hr

cross multiply

5 = 15x

x = 5/15

x = 0.333 hr

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Answer:

Therefore, the value of k is 1.

Step-by-step explanation:

Vertical angles are pairs of angles that are opposite each other and are formed by two intersecting lines. If one angle measures 160°, the other angle must measure 180° - 160° = 20°. Therefore, if the other angle measures (3k + 61)°, we can set up the equation 20 = 3k + 61. Solving for k, we get k = -41. However, since the value of k must be a positive integer, the only possible value of k is k = 1. Therefore, the value of k is 1.

Answer:

k = 33

Step-by-step explanation:

The equation has no solution if the blank is filled with 5y, so option c is correct.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions printed on the left and right sides have an equal relationship.

Given equation:

5y + 9 = _

Use the hit and trial method and put the value zero,

5y + 9 = 0

y = -9 / 5

So the equation has a solution,

Again put

5y + 9 = 5y

9 = 0, which is not possible

Therefore, the equation has no solution if we fill the blank with 5y.

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The p-value for the hypothesis test in this problem is given as follows:

0.0258.

The first step in obtaining the p-value of the test is verifying the hypothesis that are test, to classify the test.

At the null hypothesis, it is tested if the mean carrier data speed is of 12 Mbps, that is:

[tex]H_0: \mu = 12[/tex]

At the alternative hypothesis, it is tested if the mean carrier data speed is different of 12 Mbps, that is:

[tex]H_1: \mu \neq 12[/tex]

Then we have a two-tailed test, as we are testing if the mean is different of a value, and the parameters are given as follows:

Using a t-distribution calculator with these parameters, the p-value for the test is given as follows:

0.0258.

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Answer:

It is rounded to 3 sig figs already

Step-by-step explanation:

Answer:

he answer is B

Step-by-step explanation:

Total angle is 180°

angle a=59°angle b=180°-59°=121°

On solving the provided question, we got that the number of months is proportional to the number of years

When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.

We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.

Here,

12/1 = 12

24/2 = 12

36/3 = 12

48/4 = 12

So, They are proportional to each other.

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"In a relation r, for every instance of a, that value of a uniquely determines the value of b then a primary dependency exists in the relation.

Relation:

In math relation means the relationship between sets of values of ordered pairs.

Given,

Here we need to find if for every valid instance of a, that value of a uniquely determines the value of b in the relation.

As per the definition of relation, for every relation has two set of data ad each of the element in one set is uniquely refers the other one's element.

Here we have to identify the type of relation between a an b.

Here we have given that the relation a uniquely determines the value in b.

So, this type primarily refers the dependency of the relation.

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The answer for the first shape would be 24cm^2.

The answer for the second shape would be 20cm^2.

The answer for the third shape would be 30cm^2. "30".

What are Shapes?

A shape in geometry can be characterized as an object's form, outline, outer border, or outer surface.

The first shape seems to be scaling up. From 3cm to 12cm. So for this you need to multiply. Using the formula that I gave you last time.

3cm times ___ = 12cm. 4 fits in there,

therefore 6cm^2 times 4 = 24cm^2.

The answer for the first one would be 24cm^2. "24" in the blank.

The second shape seems to be scaling down. From 16cm to 8cm. So for this you need to divide.

16cm divided by ___ = 8cm. 2 fits in there,

therefore 40cm^2 divided 2 = 20cm^2.

The answer for the second one would be 20cm^2. "20" in the blank.

The third shape seems to be scaling up.

From 3cm to 4.5cm.

So for this you need to multiply. 3cm times ___ = 4.5cm.

Now since we're dealing with decimals, not whole numbers this time you can't really use guess and check as efficiently. So you do the opposite operation, which in this case the opposite of multiplication is division.

You take 3cm (the original shape's number) and divide it into 4.5cm. So 4.5cm divided by 3cm = 1.5. 1.5 fits in there,

therefore 20cm^2 times 1.5 = 30cm^2.

The answer for the third one would be 30cm^2. "30" in the blank.

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Answer:

Andre walks more steps

Step-by-step explanation:

Step-by-step explanation:

dawn step rate=8400/60=140step/he

dawn step=140×240=33600 steps

teddl step=142 ×240 =34080

The measure of x = 64°

The opposing angles created by the intersection of two lines are known as vertical angles or vertically opposed angles. A pair of angles that are vertically opposed to one another are always equal.

Here we have

Three lines are intersected and formed a triangle  

Let's assume that the triangle formed is ΔABC

In ΔABC,  ∠C = 34°  

Since Vertical opposite angles are equal

=> ∠B = 30°  

As we know the sum of angles in a triangle = 180°

=> ∠A + ∠B + ∠C = 180°

=> ∠A = 180° -  30° - 34°  

=> ∠A = 116

From the line CL [ observe the given picture ]  

=> ∠A + x = 180°

=> 116° + x = 180°

=> x = 180° - 116°

=> x = 64°  

Therefore,

The measure of x = 64°

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