Which of the following equations has infinitely many real solutions?
A) 4x + 1 = x-1
B) 4(x-5)=4x+20
C) 4(x-5) =4x-20
D) 4x+ 1 = 4x-1

Which of the following equations has exactly one solution?
A) x + 1= x + 1
B) 7x= 7x
C) x + 1 = x + 2
D) 7x= 7

Which of the following equations has no real solutions?
A) 14x-6=14x-6
B) 4(x+8) = 4( x+4)
C) 4x-8 =4x -28
D) 8(x-6) =8x-48

The answer is [tex]x^2 + 2xy + y^2 - x - y - 12[/tex]

The square root of 15 is approximately 3.872983346. However, when rounded to the nearest hundredth, it is 3.87.

The question is asking for the square root of 15 rounded to the nearest hundredth. The square root of any number is the value that, when multiplied by itself, gives the original number. It's generally represented with the symbol √.

In the case of 15, if you type in your calculator the square root of 15, you get an answer of approximately 3.872983346. However, the student question asks for this value rounded to the nearest hundredth. Thus, you would round this to 3.87. So, the square root of 15 rounded to the nearest hundredth is 3.87.

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Final answer:

The square root of 15 is approximately 3.87 when rounded to the nearest hundredth, following the rules of rounding where you round down if the third decimal is less than 5.

Explanation:

The question asks for the square root of 15 rounded to the nearest hundredth. To find this, we calculate the square root using a calculator, which gives us an approximate value. We then apply the rules of rounding: if the digit after the hundredths place is 5 or higher, we round up, and if it is lower than 5, we round down. This ensures that our answer is as close as possible to the actual square root without exceeding two decimal places.

Performing the calculation, we find that the square root of 15 is approximately 3.87298. Since the third decimal place (after the hundredth) is '2', which is less than 5, we round down. Therefore, the square root of 15 rounded to the nearest hundredth is 3.87.

Answer:

[tex]y - 3 = - \frac{1}{2}(x + 2)[/tex]

Explanation:

I chose the coordinate of [-2, 3], and according to the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY careful inserting this coordinate into the formula with their CORRECT signs:

I am joyous to assist you anytime.

** It does not matter which coordinate you choose, as long as it falls on the line.

Answer:

$13.75

Step-by-step explanation:

First figure out how much she paid, by taking the change from the $50

50 - 8.75 = 41.25

She paid $41.25 dollars on three tee-shirts.

Now take how much she spent and divide it on the number of items (tee-shirts) to figure how much each one cost.

41.25 divided by 3 = 13.75

$13.75

Each Tee-shirt cost $13.75

Final answer:

To find the cost of each shirt, subtract the change given from the total amount paid and then divide by the number of shirts purchased.

Explanation:

In this scenario, Maria paid $50.00 for three shirts and received $8.75 in change. To find the cost of each shirt, we subtract the change from the total amount she gave. $50.00 - $8.75 = $41.25. Since she bought three shirts, we divide $41.25 by 3 to find the cost of each shirt. The cost of each shirt is $13.75.

[tex]\bf \lim\limits_{x\to \infty}~-4x^9-3x^3+2x-11 \\\\\\ \lim\limits_{x\to \infty}~-4x^9~~+~~\lim\limits_{x\to \infty}~-3x^3~~+~~\lim\limits_{x\to \infty}~2x~~+~~\lim\limits_{x\to \infty}~-11[/tex]

for any positive value of "x" as it races off towards ∞, our first limit  of -4x⁹ will give us a rather large negative value, our second limit of -3x³ will also give us a large negative value and both will combine to produce an even larger negative value.

our third limit of 2x will give us a positive value, however a much smaller than its previous siblings, and our last limit is just a fixed of -11, not moving at all.

since the negative values are moving faster than the positive ones, and thus overwhelming the positive ones, the limit will increasingly be racing towards -∞.

The limit of the function, [tex]\lim_{n \to \infty} f(x)= -4x^2 - 3x^3+2x - 11[/tex] is - ∞.

Here, given function is,

f(x)=−4x^9−3x^3+2x−11

We have to find the value of [tex]\lim_{n \to \infty} f(x)= -4x^2 - 3x^3+2x - 11[/tex].

What is limit of function?

Limit of function means the value towards which a function moves when the value of independent variable moves to infinity.

Now,

[tex]\lim_{n \to \infty} f(x)= -4x^2 - 3x^3+2x - 11[/tex]

[tex]\lim_{n \to \infty} f(x)= \lim_{n \to \infty} (-4x^2) - \lim_{n \to \infty} (3x^3) + \lim_{n \to \infty} 2x - \lim_{n \to \infty} 11[/tex]

[tex]\lim_{n \to \infty} f(x)= -[/tex]∞

Here, limit of [tex]-4x^{2}[/tex] is -∞,  limit of [tex]-3x^{3}[/tex] is -∞ and limit of 2x is ∞.

For any positive value of x as it races off towards ∞ but here we find the limits as, -∞.

Since the negative values are moving faster than positive.

Hence, the limit will be towards  -∞.

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Answer:

B

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y ), thus

N(- 4, 3 ) → N'(4, 3 ) → B

Answer:

B. (4, 3)

Step-by-step explanation:

Since N is four units to the left of the y-axis, reflecting it would make it four units to the right of the y-axis, so you would base this off of the y-coordinate.

I am joyous to assist you anytime.

Hey!

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[tex]\large\boxed{The~plant~grew~2\frac{1}{2}~feet!}[/tex]

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Steps To Solve:

~Find common denominators

6/7 = 54/63

2/9 = 14/63

~Turn into improper fractions

1 54/63 = 117/63

4 14/63 = 266/63

~Subtract.

266/63 - 117/63 = 149/63

~Turn into mixed number

149/63 = 2 23/63

~Round

2 23/63 ≈ 2 1/2

Answer:

2 1/2

Step-by-step explanation:

because 4 2/9 － 1 6/7 equal to 2 half which equal to 2 1/2

Answer:

35° and 55°

Step-by-step explanation:

The sum of the angles of a right rectagle is 180°, with a right angle of 90°.

The tell us that A = 2B-15, so:

180° = 90° + A + B

180° = 90° + 2B - 15 + B

180° - 90° + 15 = 2B + B

105° = 3B

B = 105°/3 = 35°

Now, let's find A:

A = 180° - 90° - 35° = 55°

Using the properties of a right triangle and setting up an equation based on the relationship between the two small angles, we find that the angles measure 35 degrees and 55 degrees, respectively.

To solve the problem involving the angles of a right triangle, we recall that the sum of the angles in any triangle is 180 degrees. In a right triangle, one angle is always 90 degrees, which leaves a total of 90 degrees to be shared between the other two angles.

If we let x represent the measure of one of the small angles, then the problem tells us that the other angle is 2x - 15 degrees.

Therefore, we can set up the following equation to solve for x:

x + (2x - 15) + 90 = 180

Combining like terms gives us:

3x - 15 + 90 = 180

3x + 75 = 180

Now, we subtract 75 from both sides of the equation:

3x = 105

Finally, we divide by 3 to find the measure of x:

x = 35

Having found that one of the small angles measures 35 degrees, we can now find the other small angle:

2x - 15 = 2(35) - 15

= 70 - 15

= 55 degrees.

So, the two small angles of the right triangle are 35 degrees and 55 degrees.

Answer:

Step-by-step explanation:

[tex]f(x) = 3(x + 3) - 3[/tex]

[tex]f(x) = 3x + 9 - 3[/tex]

[tex]f(x) = 3x + 6[/tex]

Answer:

5

Step-by-step explanation:

[tex]\text{Hello there!}\\\\\text{We are simplifying the fraction:}\,\frac{9}{45}\\\\\text{Both 9 and 45 is divisible by 9, so we'll divide both sides by 9}\\\\\text{Divide:}\\\\\frac{9\div9}{45\div9}=\frac{1}{5}\\\\\boxed{\text{Answer:}\frac{1}{5}}}[/tex]

Answer:

146 in

12ft 2in

Step-by-step explanation:

4ft 9 = 4*12+9=48+9=57

3ft 10 = 3*12+10=36+10=46

3ft 7 = 3*12+7=36+7=43

57+46+43=146

146/12 = 12ft remainder 2

12ft 2in

Answer:

5 <-11

Step-by-step explanation:

5 is greater than -11

6

5

4

3

2

1

0

-1

-2

-3

-5

-6

-7

-8

-9

-10

-11

The inequalities created from the number pair 5 and -11 are '5 > -11' and '-11 < 5'. These represent that 5 is greater than -11 and that -11 is less than 5.

To write two inequalities using the number pairs 5 and -11 with the symbols < and >, we consider the numeric value and sign of the numbers. We know that any positive number is always greater than a negative number. This gives us the first inequality: 5 > -11

Now, if we want to write an inequality using <, then we swap the order of numbers. Thus: -11 < 5

These statements tell us that 5 is greater than -11 and -11 is less than 5, which demonstrates how to use < and > inequalities with numbers.

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Answer:

70°

Step-by-step explanation:

If in the quadrilateral ABCD diagonal BD is an angle bisector for angles B and D, then

Consider triangles ABD and CBD. In these triangles,

Hence, triangles ABD and CBD are congruent by ASA postulate.

So, AD ≅ DC.

Now, consider triangle ADC. This is an isosceles triangle, because AD ≅ DC. In this triangle, m∠ADC = m∠ADB + m∠BDC = 20° + 20° = 40°. AC is the base. Angles DAC and DCA are congruent as adjacent angles to the base AC, so

m∠DAC = 1/2 (180° - 40°) = 70°

Answer:

m∠DAC = 70°

m∠ACB = 30°

Step-by-step explanation:

Answer:

y = 10

Step-by-step explanation:

Given

10 - y = y - 10 ( subtract y from both sides )

10 - 2y = - 10 ( subtract 10 from both sides )

- 2y = - 20 ( divide both sides by - 2 )

y = 10

Answer 15 20 10 2.5 7.5

Answer:

A,shift the graph of y =x2 right 15 units

Step-by-step explanation:

The new equation is subtracting 15 from the value of x.

When you subtract a number from x, the graph moves to the right by the number you subtract.

x-15, shifts the graph right 15 units.

The answer is: Shift the graph of y = x2 right 15 units.

Answer:

500,000

Expanded forms can be written like a sentence or stacked for readability as they are here.

Expanded Notation Form:

 500,000  

+ 0  

+ 0  

+ 0  

+ 0  

+ 0  

Expanded Factors Form:

 5 × 100,000  

+ 0 × 10,000  

+ 0 × 1,000  

+ 0 × 100  

+ 0 × 10  

+ 0 × 1  

Expanded Exponential Form:

5 × 105

+ 0 × 104

+ 0 × 103

+ 0 × 102

+ 0 × 101

+ 0 × 100

Word Form:

five hundred thousand

Step-by-step explanation:

Answers above..

Answer:

Share sold by Stock A = 4000, Stock B = 1000 and Stock C = 5000

Step-by-step explanation:

Total sold sold = 10000

i.e. [tex]A + B + C = 10000[/tex] ....(1)

Shares sold by stock A = 4 × Shares sold by stock B

i.e. [tex]A = 4B[/tex] ....(2)

Shares sold by stock C = Shares sold by stock A + Shares sold by stock B

i.e. [tex]C = A + B[/tex] ....(3)

substituting value of [tex]A[/tex] from (2) in (3) we get

[tex]C = 4B + B = 5B[/tex] ....(4)

substituting value of [tex]A[/tex] and [tex]C[/tex] from (2) and (4) in (1) we get

[tex]4B + B + 5B = 10000\\10B = 10000\\B = 1000[/tex]

[tex]A = 4B = 4*1000 = 4000[/tex]

[tex]C = 5B = 5*1000 = 5000[/tex]

Answer:

x = ± [tex]\sqrt{\frac{ab+2}{3} }[/tex]

Step-by-step explanation:

Given

3x²  - 2 = ab ( isolate the x² term by adding 2 to both sides )

3x² = ab + 2 ( divide both sides by 3 )

x² = [tex]\sqrt{\frac{ab+2}{3} }[/tex] ( take the square root of both sides )

x = ± [tex]\sqrt{\frac{ab+2}{3} }[/tex]

Answer:

x =  √ [(ab + 2)/ 3]

Step-by-step explanation:

3x^2 - 2 = ab

3x^2 = ab + 2

x^2 = (ab + 2)/ 3

x =  √ [(ab + 2)/ 3]

Final answer:

1 kilogram is 10^9 times greater than 1 microgram because 1 kg equals 1000 grams, and there are 10⁶ micrograms in a gram, equating to 10⁹ µg/kg.So,option A.10⁹ is correct.

Explanation:

To determine how many times greater 1 kilogram is than 1 microgram, we need to understand the metric prefixes and their corresponding values. Knowing that 'micro' denotes 10⁻⁶, we can establish that 1 microgram (µg) equals 10⁻⁶grams (g). Since 1 kilogram (kg) equals 1000 grams, we then convert kilograms to micrograms by multiplying by 10⁶:

1 kg = 1000 g x 10⁶ µg/g = 10⁹ µg.

Thus, 1 kilogram is 10⁹ times greater than 1 microgram, which corresponds to option A.

Graph the following points:

(-2, -3)

(-1, -2)

(0, -1)

(1, cuberoot{2} -2}

(7, 0)

Answer:

666 divided by 6 is 111. So, they would need 111 vans.

Only the graph A represents the proportional relationship between the variables.

Given that :

For every 4 defense cards ; there are 2 offense cards :

Defense cards = y

Offense cards = x

For proportional relationship :

y α x

y = kx

k = y/x

k = constant of proportionality

k = 4/2

k = 2

y = 2x

The value of y when x = 4

The value of y when x = 4 When ; x = 4

The value of y when x = 4 When ; x = 4 y = 2×4 = 8

Only graph A gives the proportional value of y when x = 4

Hence, Graph A represents the proportional relationship between defense and offense.

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Final answer:

The correct graph would show a straight line through the origin with a slope of ½, reflecting the 2:1 ratio of defense to offense sports game cards Chad owns.

Explanation:

The subject of this question is Mathematics, and it pertains to the concept of ratios and proportional relationships, which is typically taught at the Middle School level. To determine which graph represents the proportional relationship between Chad's defense and offense sports game cards, we must consider that for every 4 defense cards, he owns 2 offense cards. This establishes a constant ratio of defense to offense cards of 2:1.

A graph that accurately represents this relationship would be a straight line through the origin (0,0) that has a slope of ½, because for every 2 units increased in the defense (x-axis), there should be a 1 unit increase in the offense (y-axis). This is because the graph of a proportional relationship is always a straight line that passes through the origin, and the slope of the line reflects the ratio of the quantities compared.

Answer:

the answer is A.

Step-by-step explanation:

The values of the system of equations y=[tex]x^{2}[/tex]-3x+6, y=2x+6 is (0,6),(5,16).

Equation is relationship between two or more variables that are expressed in equal to form.Equations of two variables look like ax+by=c.It may be linear equation, quadratic equation,cubic equation.

We have been given two equations as y=[tex]x^{2}[/tex]-3x+6 and y=2x+6 and we are required to solve the equations for the value of x.

Putting the value of y from second equation in first equation.

2x+6=[tex]x^{2}[/tex]-3x+6

Cancellng 6 from both sides.

[tex]x^{2}[/tex]-5x=0

x(x-5)=0

x=0,x-5=0

x=0,x=5

Putting the values of x in second equation to get the value of y.

y=2x+6

y=2(5)+6

=10+6

y=16

y=2x+6

y=2*0+6

=6

Points will be (0,6),(5,16).

Hence the values of the system of equations y=[tex]x^{2}[/tex]-3x+6, y=2x+6 is (0,6),(5,16).

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Answer:

-2

*Remember- negative ×/÷ positive= negative. Negative ×/÷ negative=positive.

Explanation:

22÷ -11 (The parenthesis arn't really necessary)

I hope I was helpful! :D

Answer: The Statement is true

Step-by-step explanation: the lines in the graph are constantly parallel to each other, showing that when one increases, so does the other

Answer:

The given statement is true.

Step-by-step explanation:

We are given the following graph in the picture:

On the x-axis years are shown from 1959 to 2005.

The y axis shows the poverty rate and the number of people in poverty.

The blue strips in the graph are the recession time.

Now, for each blue strip, we could see the line for poverty rate and the number of people in poverty increases. There is an upward trend in the line in the blue strip.

In other words we could say that the slope increases for all the blue strips which actually represents that the number of people in poverty increases in recession.

Thus, the given statement is true.

Answer:

1.6, 1 4/5 (1.8), 1.82

Step-by-step explanation:

Answer:

1.6;1 4/5;1.82

Answer:

Both pet stores are an equal distance away from the book store.

East and West are opposites and she has to go 7 in each direction (from the bookstore) to reach each pet store

Answer:

If your asking us to just combine like terms it would be -3b^2-2b^2+1.4b+4c+c

but if your asking us to answer the question it would be -5b^2+1.4b+5c

Hope I helped :)