3 quick algebra 1 questions for 50 points!

Only answer if you know the answer, quick shout-out to Mr.Royal, tysm for the help!

The solution to the expression x/3 - 3/4 = 5/12 is given as x = 7/2

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the equation:

x/3 - 3/4 = 5/12

Hence:

x/3 = 5/12 + 3/4

x/3 = 7/6

x = 7/2

The solution to the expression x/3 - 3/4 = 5/12 is given as x = 7/2

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Answer:15000

Step-by-step explanation:50,000 x 0.12=6,000 X 2=12,000

6000 divided by 2= 3,000

12 + 12=24+6=30

The factored expression of the polynomial is (4 - x)(5 + x)

The polynomial expression is given as;

20 - x - x^2

Expand the expression

20 - 5x + 4x - x^2

Factorize the expression

5(4 - x) + x(4 - x)

Factor out 4 - x

(4 - x)(5 + x)

Hence, the factored expression of the polynomial is (4 - x)(5 + x)

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The weighted mean grade for the semester is 8.22

It is calculated by dividing the total number of values in a set of data, such as measurements or numbers, by the total number of values.

No. of credits for Spanish, History and English = 6

No. of credits for Statistics = 8

Grade points for A = 4

Grade points for B = 3

Grade points for C = 2

Weighted mean = (6 * 2 + 6 * 3 + 8 * 4 + 6 * 2) / 9

Weighted mean = (12  + 18 + 32 + 12) / 9

Weighted mean = 74 / 9 = 8.22

Hence, the weighted mean grade for the semester is 8.22.

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Answer:

Step-by-step explanation:

 5x² - 6x - 2 = 0

a = Coefficient of x² = 5

b = coefficient of x = -6

c = constant = -2

Discriminant = D = b² - 4ac

                           = (-6)² - 4 * 5 * (-2)

                           = 36 +  40

                           = 76  > 0

So, the quadratic equation has two distinct real roots.

[tex]\sf \boxed{\bf x = \dfrac{-b \± \sqrt{D}}{2a}}\\\\[/tex]

     [tex]\sf = \dfrac{-[-6] \± \sqrt{76}}{2*5}\\\\= \dfrac{6 \±8.7}{10}\\\\=\dfrac{6+8.7}{10} \ ; \ or \ x =\dfrac{6-8.7}{10}\\\\=\dfrac{14.7}{10} \ ; \ or \ x = \dfrac{-2.7}{10}[/tex]

x = 1.47  or x = -0.27

Answer: x = 1.5 or (-0.3)

b) x² + 3x = 40

x² + 3x - 40= 0

We can solve the quadratic equation using factor method.

Sum = 3

Product = -40

Factors = 8 , (-5)

 When we add, 8 + (-5) = 3 , we get 5and when we multiply 8 *(-5) = -40, we get -(-40).

Rewrite the middle term of the quadratic equation using the factors.

 x² + 8x - 5x - 40 = 0

x(x + 8) - 5(x + 8)= 0

 (x + 8) (x - 5)    = 0

 x + 8 = 0   or x - 5 = 0

     x = -8   or       x = 5

Answer : x = -8 , 5

The quotient of the synthetic division is x^3 + 3x^2 + 4

The bottom row of synthetic division given as:

1 3 0 4 0

The last digit represents the remainder, while the other represents the quotient.

So, we have:

Quotient = 1 3 0 4

Introduce the variables

Quotient = 1x^3 + 3x^2 + 0x + 4

Evaluate

Quotient = x^3 + 3x^2 + 4

Hence, the quotient of the synthetic division is x^3 + 3x^2 + 4

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Answer:

A. x=5 is a solution, but x=3 is not

Step-by-step explanation:

When x=5, 11-5<7, 6<7, this is a solution

When x=3, 11-3<3l, 8<7, this is not a solution

Probability that a card selected at random is purple = 7/25

Number of red cards, N(red) = 12

Number of blue cards, N(blue) = 17

Number of purple cards, N(purple) = 14

Number of yellow cards, N(yellow) = 7

Total number of cards, N(total) = 12 + 17 + 14 + 7

N(total) = 50

Probability that a card selected at random will be purple

P(purple) = N(purple) / N(total)

P(purple) = 14/50

Reduce to the lowest fraction

P(purple) = 7/25

Therefore, probability that a card selected at random is purple = 7/25

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Complete Question

There are 12 red cards, 17 blue cards, 14 purple cards, and 7 yellow cards in a hat. If a card is selected at random, what is the probability that the card is purple

The curve passes through the point (3, 3), so [tex]y=3[/tex] when [tex]x=3[/tex]. Then

[tex]y = ax^2 + bx \implies 3 = 9a + 3b \implies 3a + b = 1[/tex]

The tangent line to the curve at (3, 3) has gradient [tex]\frac{dy}{dx}[/tex] at [tex]x=3[/tex]. Compute the derivative.

[tex]y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b[/tex]

Then when [tex]x=3[/tex], the gradient is 4, so

[tex]2ax + b = 4 \implies 6a+b=4[/tex]

Solve for [tex]a[/tex] and [tex]b[/tex]. Eliminating [tex]b[/tex], we find

[tex](6a+b) - (3a+b) = 4-1 \implies 3a = 3 \implies \boxed{a=1}[/tex]

and it follows that

[tex]3 + b = 1 \implies \boxed{b = -2}[/tex]

Using the domain concept, the only value of x that is not on the domain of [tex]f(x) = \frac{1}{3x + 5}[/tex] is given as follows:

[tex]x = -\frac{5}{3}[/tex]

The domain of a function is the set that contains all possible input values for the function. For a rational function, for example, the zeros of the denominator are excluded from the domain. Another example is an even root, where the inside term has to be positive.

The rational function for this problem is given by the function f(x) presented below:

[tex]f(x) = \frac{1}{3x + 5}[/tex]

The denominator is 3x + 5, hence the restriction in the domain of f(x) is given as follows:

3x + 5 = 0

3x = -5

[tex]x = -\frac{5}{3}[/tex]

The solution to the equation above is the only value of x that is not part of the domain of f(x).

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Answer:

  18 cans

Step-by-step explanation:

The number of cans of paint will be the least integer greater than or equal to the number required to cover the area of the trapezoid.

The area of the wall is given by the formula ...

  A = 1/2(b1 +b2)h

where b1 and b2 are the bases, and h is the height.

We are given the values b1=20 ft, b2=24 ft, h=16 ft, so the area is found to be ...

  A = 1/2(20 ft +24 ft)(16 ft) = 352 ft² . . . . . area of the wall

Each can of paint covers 20 ft², so n cans of paint will cover 20n square feet. We want to find the minimum integer value of n that satisfies ...

  20n ≥ 352

  n ≥ 17.6 . . . . . . . . . divide by 20

The next larger integer is 18.

The painter will need to buy 18 cans of paint.

Answer:

98

Step-by-step explanation:

96+100=196

196÷2=98

Answer:

97.

Step-by-step explanation:

86 96 100 98

Place them in order:

86 96 98 100

The median is the middle value of an ascending sequence of numbers.

As there is an even number of values the median is the mean of the 2 middle ones:

So here it is (96 + 98) / 2

= 97.

The probability of catching a bass in the lake is given by:

Probability = probability 1 × probability 2

Since the forest ranger caught a fish from his prior fishing experience, we can infer that he has a probability of catching a bass in a lake:

Probability 1 = Number of fish caught/Number of tries

By using a special type of bait, he should calculate the probability of catching a fish as follows:

Probability 2 = Number of fish caught/Number of tries

Therefore, the probability of catching a bass in the lake is given by:

Probability = probability 1 × probability 2

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Answer:

Step-by-step explanation:

AC=DC. (Given in figure)

AB=BD. (Given in figure

BC=BC. (Common)

that means triangle BAC is congruent to triangle BDC by SSS criterion.

Answer:

B. (3x - 9) (x + 3i)

Step-by-step explanation:

[tex]\bf 3 {x}^{2} = + 27[/tex]

Therefore, B is your answer!!!!

Answer:

d. 64

Step-by-step explanation:

x^1/2 = 8

Square each side

(x^1/2 )^2=( 8)^2

x = 64

Answer:

80

Step-by-step explanation:

To find the mean we add up all the numbers and then divide that number by the amount of numbers we added up.

So in this case we added up 65, 70, 75, 80, 85, 90 & 95. This gives us 560. Now we divide 560 by 7 as that is the amount of numbers we added up. This gives us 80 which means the answer is 80.

I hope this helped! :)

Answer:

Horizontal reflection

Step-by-step explanation:

a math chart that was labeled had these pattern examples with the the translation and transformation.

Answer:60g

Step-by-step explanation:

Hope this the answer

[tex]a(0) = 1 \: \: \: \: \: \: b(0) = 2 \: \: \: \: \: c(0) = 3 \\ a(1) = b(0) + c(0) = 2 + 3 = 5 \\ b(1) = a(0) + c(0) = 1 + 3 = 4 \\ c(1) = a(0) + b(0) = 1 + 2 = 3 \\ \\ a(2) = b(1) + c(1) = 4 + 3 = 7 \\ b(2) = a(1) + c(1) = 5 + 3 = 8 \\ c(2) = a(1) + b(1) = 5 + 4 = 9[/tex]

[tex]a(3) = b(2) + c(2) = 8 + 9 = 17\\ b(3) = a(2) + c(2) =7 + 9 = 16 \\ c(3) = a(2) + b(2) = 7 + 8 = 15 \\ \\ a(4) = b(3) + c(3) = 16 + 15 = 31 \\ b(4) = a(3) + c(3) = 17 + 15 = 32 \\ c(4) = a(3) + b(3) = 17 + 16 = 33[/tex]

[tex]a(5) = 32 + 33 = 65 \\ b(5) = 31 + 33 = 64 \\ c(5) =31 + 32 = 63 \\ \\ a(6) = 64 + 63 = 127 \\ b(6) = 65 + 63 = 128 \\ c(6) = 65 + 64 = 129 \\ [/tex]

[tex]a(7) = 128 + 129 = 257 \\ b(7) = 127 + 129 = 256 \\c (7) = 127 + 128 = 255 \\ \\ a(8) = 256 + 255 = 511 \\ b(8) = 257 + 255 = 512 \\ c(8) = 257 + 256 = 513[/tex]

[tex]a(9) = 512 + 513 = 1025 \\ b(9) = 511 + 513 = 1024 \\ c(9) = 511 + 512 = 1023 \\ \\ a(10) = 1024 + 1023 = 2047 \\ b(10) = 1025 + 1023 = 2048 \\ c(10) = 1025 + 1024 = 2049[/tex]

[tex]a(n) + b(n) + c(n) = \\ 2(a(n - 1) + b(n - 1) + c(n - 1)) \\ 6 \times 2 {}^{n } [/tex]

[tex]6 \times 2 {}^{n} > 100 \: 000 \\ 2 {}^{n} > \frac{100 \: 000}{6} \\ n > log {}^{2} ( \frac{100 \: 000}{6} ) \\ n > 14.02468 \\ n = 15[/tex]

Answer:

13%

15%

41%

31%

Step-by-step explanation:

To find the percentage one amount is out of another amount, divide the smaller amount by the bigger amount. You will end up with a decimal (0.xy where x is the 10% place and y is the 1% place).

For example: to find the percentage that 39 is out of 300 students, we divide 39 by 300. This gives us the decimal 0.13. Written as a percentage, that is 13%.

We can do this for all of them.

Here is the math for each one:

39 ÷ 300 = 0.13 → 13%

45 ÷ 300 = 0.15 → 15%

123 ÷ 300 = 0.41 → 41%

93 ÷ 300 = 0.31 → 31%

Once you have all these decimals, you might choose to check your work by adding them up. They should at up to 1.00, or 100%. In this case, they do, so we know these answers are correct.

I hope this helps. Please let me know if you have questions.

Using linear functions, it is found that over a range of x < 10000 she will make more from the Comfort over Style job than she will from the Heels for Fashion Slaves job

A linear function is modeled by:

y = mx + b

In which:

Considering the fixed salary as the intercept and the earning per shoe sold the slope, the functions for her salaries at each situation is:

He will make more from the Comfort over Style job than she will from the Heels for Fashion Slaves job when:

C(x) > H(x)

52000 + 3.25x > 37000 + 4.75x

1.5x < 15000

x < 15000/1.5

x < 10000

The range is x < 10000.

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The mean of the scores to the nearest 10th digit will be 74.9.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean.

Then the mean is given as,

Mean = (Total score) / (total student)

The total score will be

Total score = 65 x 8 + 70 x 7 + 75 x 3 + 80 x 8 + 85 x 3 + 90 x 2 + 95 x 2

Total score = 520 + 490 + 225 + 640 + 225 + 180 + 190

Total score = 2470

The total number of students will be

Total student = 8 + 7 + 3 + 8 + 3 + 2 + 2

Total student = 33

Then the mean will be

Mean = 2470 / 33

Mean = 74.85 ≈ 74.9

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The volume of the cylinder is 301.593 cubic centimeter.

Volume exists as a scalar quantity representing the amount of three-dimensional space enclosed by a sealed surface. For example, the space that a substance or 3D shape inhabits or contains. The volume stands often quantified numerically utilizing the SI-derived unit, the cubic meter.

A cylinder contains traditionally been a three-dimensional solid, one of the most essential curvilinear geometric shapes. Geometrically, it has been regarded as a prism with a circle as its base.

The dimensions of the cylinder is given as - 8 cm and 12 cm .

The formula of the volume of the cylinder is given as -

V = π * (8) * (12)

Thus the volume is = 96π ≈ 301.593 cubic centimeter.

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Answer:

Domain: ( Positive infinity, Negative Infinity)

Range: (-3, Positive Infinity )

Step-by-step explanation:

we conclude that the sequence has 8 terms.

Here we have the geometric sequence:

2/81, 4/27, 8/9, ..., 6912

Notice that each term is equal to 6 times the previous term, such that:

2/81*6 = 4/27

4/27*6 = 8/9

Then the n-th term is equal to:

[tex]a_n = a_1*r^{n-1}[/tex]

Where in this case:

[tex]a_1 = 2/81\\\\r = 6[/tex]

Now we need to find the value of n such that:

[tex](2/81)*6^{n-1} = 6912\\\\6^n = 6*6812*(81/2) = 1,679,616[/tex]

If we apply the natural logarithm to both sides, then:

[tex]n*ln(6) = ln(1,679,616)\\n = ln(1,679,616)/ln(6) = 8[/tex]

Then we conclude that the sequence has 8 terms.

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Answer:

Step-by-step explanation:

A parallel line will have the same slope, m, as the reference line given by the form y=mx+b.  b is the y-intercept, the value of y when x=0.

The reference line of y = -(1/2)x + (3/7) has a slope of -(1/2).

The parallel line will have the same slope, so we can write:

y - -(1/2)x + b

We need a value of b that forces the line to go through point (-1,0).  Enter that point in the equation and solve for b:

y - -(1/2)x + b

0 - -(1/2)(-1) + b

b = -(1/2)

The equation of the line parallel to y = -(1/2)x + (3/7) and going through (-1,0) is

  y=-(1/2)x - (1/2)

Answer:

I don't think the answer is in the options.