Answer must be simplified

Step-by-step explanation:

1. 22+5x+3=90

2.3+5x+82=180

3. 89=6x+5

4. 4x+3= 43

you can solve them luv

The triangles which are similar or congruent discussed below.

If the triangles are similar then the corresponding side ratios are equal.

1. 6/9 = 2/3

9/13.5= 2/3

8/12= 2/3

Thus, the triangle are similar.

2. The second case is neither similar or congruent.

3. The pair has one right angle common and one side measure 6 unit.

So, the triangle are neither similar or congruent.

4. The triangles have two angles equal.

so, the triangle are similar.

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Step-by-step explanation:

Hey there!

According to the question;

Mass of an object (m) = 630 kg

Volume of an object (v) = 7m³

We know that;

\(density = \frac{mass(kg) \: }{volume( {m}^{3} )} \)

or, density = (630/7) kg/m³

Therefore, density of the substance is 90kg/m².

Hope it helps!

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Plug in the values of the variables:-

\(\sf{4x-2y}\)

\(\sf{4(7)-2(-3)}\)

\(\sf{28+6}\)

\(\sf{34}\)

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

Answer:

34

Step-by-step explanation:

We have to find the value of the expression ( 4x - 2y ).

Also, given that,

x = 7

y = -3

So, to find the value of the given expression, you have to replace x and y with 7 & -3 respectively.

Let us solve it now.

4x - 2y

4 × 7 - 2 × -3

28 + 6

34

Answer:

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Step-by-step explanation:

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Answer: 14

Step-by-step explanation:

Answer:

Approximately 3.81 seconds

Step-by-step explanation:

d = 3t + 5t²

d = 84

84 = 3t + 5t²

3t + 5t² - 84 = 0

5t² + 3t - 84 = 0

5(t² + 3/5t - 84/5) = 0

5(((t + 3/10)² - 9/100) - 84/5) = 0

5((t + 3/10)² - 9/100 - 84/5) = 0

5((t + 3/10)² - 9/100 - 1680/100) = 0

5((t + 3/10)² - 1689/100) = 0

5(t + 3/10)² - 1689/20 = 0

5(t + 3/10)² = 1689/20

(t + 3/10)² = 1689/100

t + 3/10 = ±√(1689)/10

t = -3/10 ± √(1689)/10

t = -3/10 ± ≈41.1/10

t = -3/10 ± ≈4.11

t ≈ -0.3 ± 4.11

t [can only be positive] ≈ 4.11 - 0.3

t ≈ 3.81

9514 1404 393

Answer:

  (a, B, C) ≈ (9.15, 29.2°, 102.8°)

Step-by-step explanation:

The given angle lies between the given sides, so the law of sines cannot be used. The third side is ...

  a² = b² +c² -2bc·cos(A) ≈ 83.6452

  a ≈ √83.6452 ≈ 9.146

__

Then angle B is found from the law of sines. We want to find the smaller angle, so we can tell if the triangle is acute or obtuse.

  sin(B)/b = sin(A)/a

  B = arcsin(b/a·sin(A)) ≈ arcsin(0.48753)

  B ≈ 29.2°

  C = 180° -48° -29.2° = 102.8°

The solution to the triangle is (a, B, C) = (9.1, 29.2°, 102.8°).

The solutions of the present given equation is x=5 or x=-1.

The answer of an equation is the set of all values that, whilst substituted for unknowns, make an equation true. For equations having one unknown, raised to a power, essential regulations of algebra, inclusive of the additive belongings and the multiplicative belongings, are used to decide its solutions.

A technique to an equation is a range of that may be plugged in for the variable to make a real wide variety announcement. 3(2)+5=11 , which says 6+5=11 ; that is true! So 2 is a answer. In fact, 2 is the ONLY technique to 3x+5=11. An equation is a mathematical announcement this is made from expressions related through an same sign. For example, 3x – 5 = sixteen is an equation. Solving this equation, we get the price of the variable x as x = 7.

Using the Equation we derive the roots:

\((x-3)^{2} + 2(x-3) - 8 = 0\\(x^{2} +9-6x)+2x-6-8=0\\(x^{2} -4x-5)=0\\\\\\\\\\\)

\(x^{2} -5x+1x-5=0\\x(x-5)+1(x-5)=0\\(x+1)(x-5)=0\\x+1=0\\ or\\ x-5=0\\\ then \\x= -1 \\or \\\ x = 5\)

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Correct Question:

what are the solutions of the equation \((x-3)^{2} * 2(x-3) - 8 = 0\)

The equivalent fractions for the mixed numbers, with the same denominator, are given as follows:

32/12 and 27/12.

The mixed numbers in the context of this problem are given as follows:

The fractions that represent each number are given as follows:

The least common factor of 3 and 4 is given as follows:

3 x 4 = 12.

Hence the equivalent fractions are given as follows:

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Anya's current age is 30 years and Cole current age is 27 years

Let x represent Anya current age and y represent Cole current age.

Anya is three years older than her brother, Cole. Hence:

x = y + 3

x - y = 3   (1)

In 11 years, the sum of their ages will be 79. Hence:

(x + 11) + (y + 11) = 79

x + y = 57    (2)

Solving equations 1 and 2 simultaneously gives:

x = 30, y = 27

Anya's current age is 30 years and Cole current age is 27 years

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Answer:

Do PRT: 5009.31

Step-by-step explanation:

Princable: 5000

Rate: 2.5

Time: 10

Answer:

Answer:

$16800

Step-by-step explanation:

16000 * 1.05 = 16800

Answer:

800

Step-by-step explanation:

$16,000 x 0.05= $800

Answer:

12

Step-by-step explanation:

I took away 1/3 ig sheeeeeeeeeeeeeeeeeee

The ordered pairs that represents a function y in terms of x are  {(-2, -3),(1, 3),(1, 6) (9, 8}, (12, 11)) and {(-3, -5), (3, 2), (6, 5), (7, 9), (10, 16)}

A set of ordered equation represents a linear function if the domain of the coordinates are not repeated.

For instance, the ordered pairs that is a function are the coordinates that do not have any repeated y-coordinates.

From the given linear functions, the ordered pairs that represents a function y in terms of x are  {(-2, -3),(1, 3),(1, 6) (9, 8}, (12, 11)) and {(-3, -5), (3, 2), (6, 5), (7, 9), (10, 16)}

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A) The variable is n, which represents the number of the figure in the pattern.

B) Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                      1

2                      3

3                      6

4                     10

5                     15

6                     21

7                    28

8                    36

C) The equation to represent the nth term of the sequence is n(n+1)/2.

D) If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12.

E) It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

Here is a more detailed explanation of how to answer each question:

A) Identify and label the variable

The variable is n, which represents the number of the figure in the pattern. For example, the first figure is figure 1, the second figure is figure 2, and so on.

B) Make a table for up to 8-figure patterns

Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                        1

2                        3

3                        6

4                        10

5                        15

6                        21

7                        28

8                        36

C) Write an equation to represent the nth term of the sequence

The equation to represent the nth term of the sequence is n(n+1)/2. This equation can be derived by looking at the table of values. For example, the number of Cheerios in the first figure is 1, which is equal to 1(1+1)/2. The number of Cheerios in the second figure is 3, which is equal to 2(2+1)/2. And so on.

D) If the pattern continues, what figure number will have 20 whole Cheerios in it?

If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12. This can be found by solving the equation n(n+1)/2 = 20. The solution is n = 12.

E) Is it reasonable to think this pattern would continue forever? If not, explain.

It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?

Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

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There were 18 time trials recorded during the experiment.

To determine the number of time trials recorded during the experiment, we count the total number of dots on the dot plot.

According to the given information, we have:

- Two dots over 15

- Three dots over 17

- Two dots over 19

- Two dots over 20

- One dot over 21

- Four dots over 23

- One dot over 24

- Three dots over 25

By adding up these counts, we get:

2 + 3 + 2 + 2 + 1 + 4 + 1 + 3 = 18

Therefore, there were 18 time trials recorded during the experiment.

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Answer:

C: 144

Step-by-step explanation:

3 in. × 3 in. = 9

9 in. × 16 in. = 144 in.

The length of v to the nearest 10th of an inch is 2.0 inches.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

We can use the Law of Sines,

Which states that for any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides of the triangle opposite the angles A, B, and C.

Now,

a = UV = u = 3.4 inches

A = ∠TUV

  = 180° - m∠U - m∠V

  = 180° - 144° - 35°

  = 1°

B = ∠UTV

   = m∠U

   = 144°

C = ∠TVU

  = m∠V

  = 35°

Using the Law of Sines,

v/sin(C) = u/sin(B)

Substituting in the values.

v/sin(35°) = 3.4/sin(144°)

Solving for v.

v = (3.4 × sin(35°)) / sin(144°)

v = 1.97 inches

Therefore,

The length of v to the nearest 10th of an inch is 2.0 inches.

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Answer:

The measure of CD is 46

Step-by-step explanation:

From the midpoint theorem, we have,

FG = (1/2)CD

so,

\(13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2\)

Now,

\(CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46\)

Answer:

7

Step-by-step explanation:

The cardinality of B and (A ⋂ C) will be n(B) = 3 and n(A ⋂ C) = 1.

In mathematics, cardinality refers to the size or number of elements in a set. It is a concept used to compare the sizes of sets, regardless of their specific elements. For instance, the cardinality of the set {1, 2, 3} is 3, while the cardinality of the set {2, 4, 6, 8, 10} is 5. Cardinality is typically denoted using vertical bars, such that |S| represents the cardinality of set S.

Now,

The symbol "n(S)" represents the cardinality

Given sets:

A = {1, 2, 3, 4, 5}

B = {1, 3, 5}

C = {4, 6}

To find the cardinality of the sets:

n(B) = 3

Set B has three elements: 1, 3, and 5.

n(A ⋂ C) = 1

The intersection of sets A and C is the set of elements that are in both A and C. Since A and C only have one element in common (the number 4), the cardinality of the intersection set A ⋂ C is 1. Therefore, n(A ⋂ C) = 1.

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Answer:

She bought more of the solid ribbon.

Step-by-step explanation:

Let's look for the LCD

The common denominator is 72

So we have 63/72 and 64/72

Thus, 63/72 < 64/72.

Emma bought solid ribbons more as 8/9 is greater than 7.8.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Emma bought 7/8 yards of striped ribbon and 8/9 yards of solid ribbon.

Now, The LCM of the denominators 8 and 9 is 72.

So, (7×9)/(8×9) and (8×8)/(9×8).

63/72 and 64/72.

As the numerator of the solid ribbon is greater the fraction 8/9 is greater.

So, She bought more solid ribbons.

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Answer:

volume = 33965.39

Step-by-step explanation:

Attached below is a detailed solution of the problem and the required sketch

volume of this solid is calculated integrating about the axis of : 5,3

Y = In x = x = e^y

the shaded region in the sketch represent the region where the rotating takes place.

Answer:1 carrot cost .75 cents and a mango cost 1.40

Step-by-step explanation:

12 carrots + 10 mangoes = 23$

4 carrots + 5 mangoes = 10$

I know to get from 5 mangoes to 10 mangoes you have to multiply twice. so it wil come up to 20 dollars

8 carrots + 10 mangoes = 20$

divide by 2

that will leave 4 carrots and 3 dollars.

4/3 = .75

17 dollars is left

so 10 carrots is equal to 14 dollars

14/10 = 1.4 dollars