What’s a converse in mathematics

Answer:

a = 2

b = 0

c = 3

Step-by-step explanation:

if I understand correctly the problem should look like

2x⁴ + 2x³ + 5x² + 3x + 3 = (x² + x + 1)(ax² + bx + c)

let's calculate the right side

ax⁴ + ax³ + ax² + bx³ + bx² + bx + cx² + cx + c

as there is only one term of x⁴, we know a = 2

as there is only one term without any x, we know c = 3

now we get

2x⁴ + 2x³ + 2x² + bx³ + bx² + bx + 3x² + 3x + 3

remember, that is equal to

2x⁴ + 2x³ + 5x² + 3x + 3

after subtracting 2x⁴ and 3 from both sides we get

2x³ + 5x² + 3x = 2x³ + 2x² + bx³ + bx² + bx + 3x² + 3x

we subtract 2x³ and 3x from both sides and get

5x² = 2x² + bx³ + bx² + bx + 3x² = 5x² + bx³ + bx² + bx

we subtract 5x² from both sides and get

0 = bx³ + bx² + bx

=> b must be 0 to make this true for all values of x

Answer:

Decreasing linear

Step-by-step explanation:

An arithmetic sequence decreases by a set amount every time through subtraction, so that means it's linear

Answer:

Step-by-step explanation:

x=[tex]\sqrt{100+16}[/tex]

x=[tex]\sqrt{116}[/tex]

x=2[tex]\sqrt{29[/tex]

Answer:

[tex] x = \blue{2\sqrt{29}} [/tex]

Step-by-step explanation:

[tex] a^2 + b^2 = x^2 [/tex]

[tex] 4^2 + 10^2 = x^2 [/tex]

[tex] 16 + 100 = x^2 [/tex]

[tex] x^2 = 116 [/tex]

[tex] x = \sqrt{116} [/tex]

[tex] x = \sqrt{4 \times 29} [/tex]

[tex] x = \blue{2\sqrt{29}} [/tex]

Answer:

TU ≈ 12.96

Step-by-step explanation:

Using the Altitude on Hypotenuse theorem

(leg of outer triangle)² = (part of hypotenuse below it) × (whole hypotenuse)

TU² = UV × SU = 6 × 28 = 168 ( take square root of both sides )

TU = [tex]\sqrt{168}[/tex] ≈ 12.96 ( to the nearest hundredth )

Answer: AOB

This is because angle AOB on top adds with BOC down below to get the largest angle AOC. See the diagram below.

Answer:

2703

explanation:

12×189=2268

2268+435=2703

Darrel earned 1503 dollars that week.

Suppose we are given how many no. are there from 224 to 358.

To find do the following (358 - 224 + 1) = 135 numbers.

According to the question Darrel receives a weekly salary of 435 dollars. In addition, 12 dollars is paid for every item sold in excess of 100 items.

Here excess of 100 items means after 100 which is 101.

He sold 189 items so his addition earning is for (189 - 101 + 1) = 89 items.

Given for each item he is paid 12 dollars.

∴ For 89 items he is paid (89 × 12) dollars which is

= 1068 dollars.

So in that week Darrel earns total of (435 + 1068) dollars.

= 1503 dollars.

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Answer:

20

Step-by-step explanation:

Answer: [tex]\dfrac{35}{6}\ \text{days},\ 35\ \text{days}[/tex]

Step-by-step explanation:

Given

Andrew can paint  times faster than the other

Suppose the other person take 6x days

So, andrew takes only x days to paint alone

When they work together, it took them 5 days i.e.

[tex]\Rightarrow \dfrac{1}{x}+\dfrac{1}{6x}=\dfrac{1}{5}\\\\\Rightarrow \dfrac{6+1}{6x}=\dfrac{1}{5}\\\\\Rightarrow x=\dfrac{35}{6}\ \text{days}[/tex]

So, time taken by the to finish individually is given by

[tex]\Rightarrow \text{Andrew= }\dfrac{35}{6}\ \text{days}\\\\\Rightarrow \text{Other Person}=6\times \dfrac{35}{6}\\\\\Rightarrow \text{Other Person}=35\ \text{days}[/tex]

Answer: The slope of the line is -2

Step-by-step explanation:

We can use the formula [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] to solve to for this

[tex]\frac{-9--1}{-1--5} \\\frac{-8}{4} \\-2[/tex]

The question given is incomplete, find the possible version in the comment below.

Answer:

9765625 ways

Step-by-step explanation:

To solve questions of this kind, we can apply the product rule ;

We have 10 different questions, each with 5 alternative options, even though there is only one correct answer, the number of answers that can be chosen (either correct or incorrect) is 5 ;

Therefore, we have 5 possible choices for each question :

Question 1 = 5 ; question 2 = 5,....

This can be written as :

5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 = 5^10 = 9765625 ways

Answer:

x = 71.5 in

Step-by-step explanation:

Remember the SOHCAHTOA rule

Soh...

Sine = Opposite / Hypotenuse

...cah...

Cosine = Adjacent / Hypotenuse

...toa

Tangent = Opposite / Adjacent

In this case, we use: CAH.

cos(52) = 44/x

x = 44/cos(52)

x = 71.5 inches

Answer:

Step-by-step explanation:

Use the slope formula here along with the fact that the slope is equal to 1:

[tex]1=\frac{-6-1}{x-4}[/tex] and

[tex]1=\frac{-7}{x-4}[/tex]  and cross multiply to get x - 4 = -7 so

x = -3

Answer: 28 hours

Step-by-step explanation:

1. Write original equation: 7.15x=3.40x+105

2. Combine like terms to isolate x: 3.75x=105

3. Divide both sides by same amount to find x: x=28

They would have to work 28 hours to earn the same amount of money.

Answer:

Completa la tabla para la expresión en que y= 2x – 1

y = 2x – 1

y = 2(1) – 1

y = 2 – 1 = 1 ahora hagan lo mismo con los otros valores de x en la tabla notación científica las siguientes cantidades, observa el ejemplo

Answer:

[tex]{ \tt{ - \frac{3}{8} + \frac{1}{6} }} \\ { \bf{l.c.m \: of \: 8 \: and \: 6 = 24}} \\ { \tt{formular = \frac{(l.c.m \times denominator \div numerator)}{l.c.m} }} \ \\ \\ = \frac{(24 \times 8 \div - 3) + (24 \times6 \div 1)}{24} \\ = - \frac{5}{24} [/tex]

We know that :

⊕  Sum of the interior angles in a Pentagon should be equal to 540°

⇒  x° + (2x)° + (2x)° + 90° + 90° = 540°

⇒  (5x)° = 540° - 180°

⇒  (5x)° = 360°

[tex]\sf{\implies x^{\circ} = \dfrac{360^{\circ}}{5}}[/tex]

⇒ x° = 72°

Answer:

Wouldn't it be B?

Step-by-step explanation:

When you have a radical like -[tex]\sqrt{25}[/tex], it would be -5 because the negative is added after the radical is simplified. When the negative is in the inside like your [tex]\sqrt{-25}[/tex], then you can ignore the negative temporarily and simplify to get 5. Then you add an imaginary number.

So it would be 5i?

5si = good

Answer:

120

Step-by-step explanation:

i dont know the exact reason but the formula to problems like this is the actual number which is 5 in this sitaution and then multiply the numbers below it. For the equation i did 5x4x3x2x1 and i got 120

Answer:

x = 2, BD = 13

Step-by-step explanation:

Given 2 intersecting chords , then

The product of the parts of one chord is equal to the product of the parts of the other chord, that is

4(5x - 1) = 6 × 6 = 36 ( divide both sides by 4 )

5x - 1 = 9 ( add 1 to both sides )

5x = 10 ( divide both sides by 5 )

x = 2

Then

BD = 5x - 1 + 4 = 5(2) + 3 = 10 + 3 = 13

Answer:

The function represents the height of the water in the bucket

Step-by-step explanation:

Given

[tex]f(t) = -t^2 + 4t[/tex]

Required

State what the function represents

From the question, we understand that t represents the time spent while the function illustrates the water level in the bucket.

This implies that f(t) calculates the height of the water in the bucket, given the value of time (t)

Answer:

Step-by-step explanation:

Answer:

they are congruent im pretty sure

Step-by-step explanation:

looks like they are congruent by SAS

The horizontal distance from Jayden to the bridge will be equal to 845.17 feets.

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

Given that:-

The angle of elevation of 42⁰

The bridge stands 761 feet above

Here the horizontal distance will be calculated as:-

[tex]x= \dfrac{761}{tan42}=845.187\ feet\\[/tex]

Therefore the horizontal distance from Jayden to the bridge will be equal to 845.17 feet.

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Explanation:

Both legs are the same length, as indicated by the tickmark.

Use the pythagorean theorem to solve for x

[tex]a^2+b^2 = c^2\\\\( \sqrt{10} )^2 + ( \sqrt{10} )^2 = x^2\\\\10 + 10 = x^2\\\\x^2 = 20\\\\x = \sqrt{20}\\\\x = \sqrt{4*5}\\\\x = \sqrt{4}*\sqrt{5}\\\\x = 2\sqrt{5}\\\\[/tex]

Answer:

$3100

Step-by-step explanation:

Just do 0.025*14000=350. Then add it to $2750

Step-by-step explanation:

i dont know i guess we'll never know

Answer:

The current temperature = 34.2°C

Step-by-step explanation:

Initial temperature = 46.8°C

After 20 minutes temperature reduced by 12.6°C

Therefore, the current temperature is = 46.8°C - 12.6°C = 34.2°C