Math
82°F
Algebra 1 CC.20 Checkpoint: Quadratic equations NXG
2
x² - y + x = 16
y = 3x + 2
3x² - y + 32 = 22x
y = 2x - 16
Language arts
Decide whether each system of equations has two real solutions, exactly one real solution, or
no real solutions.
y = -x² + 6x + 12
y = -x +3

Siama and Wills used different methods to find the differences between (5x + 6x) and (2x - 1) but they both arrived at the same answer.

I prefer Wills method because it is easier and less complicated.

Wills method:

(5x + 6x) - (2x - 1)

Subtract both 2x and -1

5x + 6x - 2x - - 1

5x + 4x + 1

In conclusion, Wills method is preferred when both methods are compared.

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The period of the function is 4π, and the amplitude is 2.

Given data ,

Let the function be represented as f ( x ) = y

Now , the value of f ( x ) is

y = 2sin ( 1/2 )x

To find the period and amplitude of the function y = 2sin((1/2)x), we can use the standard form of a sine function: y = Asin(Bx).

In this case, the amplitude (A) is 2.

The amplitude represents the maximum displacement from the midpoint of the sinusoidal function.

To find the period, we can use the formula:

Period = (2π) / |B|.

B = 1/2.

Period = (2π) / |1/2|

P = (2π) / (1/2) = 2π * 2/1 = 4π

Hence , the period of the function is 4π, and the amplitude is 2.

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Answer:

look at explanation

Step-by-step explanation:

it's a 50/50 chance

Answer: 43.75 miles per day.

Step-by-step explanation: All you have to do is divide 350 by 8, when you divide you basically just split the number evenly 8 times, which is what 350 divided by 8 is. He will have to drive 43.75 miles a day.

Answer: -5/4

Step-by-step explanation:

Answer:f=60a(60)

hope this helps bye

The value of x from given parallel lines is 2.

In the given figure, three lines are parallel and two lines are passing through.

When three or more parallel lines are cut by two transversals, the line segments formed are proportional.

That is, 2x/x = (x+4)/(4x-5)

2/1 = (x+4)/(4x-5)

2(4x-5)=1(x+4)

8x-10=x+4

8x-x=4+10

7x=14

x=2

Therefore, the value of x from given parallel lines is 2.

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The number of fluid ounces of iced tea does the bottle hold is 25.

Given that, a bottle holds 750 milliliters of iced tea.

1 fluid ounce has 30 milliliters.

Here, the number of fluid ounces = Total quantity of iced tea/Quantity of fluid in a fluid ounce

= 750/30

= 25

Therefore, the number of fluid ounces of iced tea does the bottle hold is 25.

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The radius of the sphere is 2cm

The circumference of the sphere is about 12.56 cm

cm²

The volume of the sphere is about 33. 5cm³

From the information given, we have that;

We have that the largest cross sectional area of the sphere takes the value

πr²

The circumference of the sphere = 2πr

Equate the expressions;

2πr = πr²

in the ratio of 4: 1

2πr = 4πr²

Divide the values

r =2cm

Substitute the value to determine the circumference of the sphere, we get;

Circumference = 2 × 3.14 × 2

Multiply the values, we get

Circumference = 12.56 cm

The volume of the sphere is represented as;

=4/3 ×  3.14 × (2)³

Multiply the values, we have;

=4/3 × 3.14 ×8

Multiply the values, we get;

= 33. 5cm³

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Answer:

2ab(b + 4 - 3a)

Step-by-step explanation:

a^2b + 2ab^2 + 8ab - 7a^2b

= 2ab^2 + 8ab + a^2b - 7a^2b

= 2ab^2 + 8ab - 6a^2b

= 2(ab^2 + 4ab - 3a^2b)

= 2a(b^2 + 4b - 3ab)

= 2ab(b + 4 - 3a)

No, there are x values which map to more than 1 y-value.

Given that Matthew examines the relation as shown in the below.

{(4, -11), (3,1), (0,1), (2,6), (3, -1)}

We need to check whether the relation is a function or not,

So, we know that,

A relation can map inputs to multiple outputs. It is a function when it maps each input to exactly one output. The set of all functions is a subset of the set of all relations.

If any x values are repeated, and the corresponding y values are different, then we have a relation and not a function.

Here we can see that the y values are repeated, so it is not a function.

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Answer: Bryan drove the fastest.

Step-by-step explanation: To find out who drove the fastest, we need to calculate the speed of each person. Speed is given by the formula distance/time.

For Doug:

Speed = 28 miles / 2.3 hours = 12.17 miles/hour

For Primo:

Speed = 34 miles / 2.1 hours = 16.19 miles/hour

For Camillo:

Speed = 57 miles / 1.4 hours = 40.71 miles/hour

For Bryan:

Speed = 49 miles / 1.2 hours = 40.83 miles/hour

The length of the ladder is 4.72 meters and its angle of elevation is 30.4 degrees.

Using the Pythagorean theorem:

Length of the ladder = √(height² + horizontal distance²)

= √(2.35² + 4.10²)

= √(5.5225 + 16.81)

= √22.3325

≈ 4.72 meters

To calculate the angle of elevation (θ), we can use the trigonometric function sine:

sin(θ) = height / length of the ladder

θ = arcsin(height / length of the ladder)

θ = arcsin(2.35 / 4.72)

θ ≈ 30.4 degrees

Therefore, the length of the ladder is 4.72 meters and its angle of elevation is 30.4 degrees.

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The Translation of given question is:

A ladder is being constructed that starts at 4.10 m and reaches a height of 2.35 m. Calculate the length of the ladder and its angle of elevation.

The number of square inches or area of gift wrap that the makeup artist will need is 10.8π square inches.

Given that,

A makeup artist purchased some lipsticks and wants to wrap them individually with gift wrap.

Radius of each lipstick = 0.6 inch

Height of the lipstick = 2.4 inches

Now,

Area of the each lipstick = 2πrh + 2πr², where r is the radius and h is the height.

Area = 2π (0.6) (2.4) + 2π (0.6)²

        = 2.88π + 0.72π

        = 3.6π

Area of the wrap for 3 lipsticks = 3 × 3.6π = 10.8π square inches.

Hence the area is 10.8π square inches.

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Answer:

[tex]\Huge \bold{\boxed{\boxed{\text{5\%}}}}[/tex]

Step-by-step explanation:

To calculate the margin of error for the survey, we need to use the formula:

[tex]\large \text{Margin of error} = \large \text{$\frac{\text{Range of values}}{2}$}[/tex]

The range of values is the difference between the upper and lower bounds of the interval. In this case, the lower bound is 22% and the upper bound is 32%, so the range of values is:

[tex]\large \text{Range of values = 32\% - 22\% = 10\%}[/tex]

Substituting this value into the formula, we get:

[tex]\large \text{Margin of error = $\frac{10\%}{2}$ = 5\%}[/tex]

Therefore, the margin of error on the survey is 5%.

The height d as shown in the right angled triangle is 4.95.

Height is the vertical distance between two points.

To calculate the height d as shown in the right angled triangle, we use the formula below

Formula:

From the diagram in the question,

Given:

Substitute these values into equation 1

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The perimeter of the tri9angle MNO is P = 58 units.

The perimeter of the triangle is equal to the sum of the lengths of the sides, we know that:

OM = 23

NM = 18.4

To find the missing side we can use the similar triangle that we have next to it.

We can see that that OM is correspondent to LJ

Then if the scale factor between the triangles is K, we can write:

18.4  = 10*K

18.4/10 = K = 1.84

Now, NO is correspondent to KL, then:

NO = 1.84*9

NO = 16.6

Then the perimeter is:

P = 16.6 + 23 + 18.4

P = 58 units.

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The expression that is equivalent to the given variables above would be =y¹²/5. That is option A.

To determine the expression that is equivalent to the given variable above, the following steps needs to be taken as follows;

That is:

= 9x⁵y¹⁶/45x⁵y⁴

Divide the whole numbers using 9 for both the numerator and denominator.

= x⁵y¹⁶/5x⁵y⁴

To solve for x':

= X(5-5 = 0)

To solve for y':

= y(16-4= 12)

Therefore the equivalent = =y¹²/5

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The value of variables a and b are,

a = - 4,

b = - 2

WE have to given that;

Function is,

⇒ f (x) = x³ - 12x² + 48x - 62

Now, We can simplify for change the function in the form of

f (x) = (x + a)³ + b as;

⇒ f (x) = x³ - 12x² + 48x - 62

⇒ f (x) = x³ - 12x² + 48x - 62 - 2 + 2

⇒ f (x) = (x - 4)³ + 2

Hence, We get;

By comparing we get;

a = - 4,

b = - 2

Thus, The value of variables a and b are,

a = - 4,

b = - 2

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The perimeter of the shaded figure is 21.42 units.

Given that, radius of two congruent circles is 3 units.

Dimensions of rectangle are length=6 units and width=3 units.

The formula to find the arc length of a circle is θ/360° ×2πr.

Here, arc length = 90°/360° ×2×3.14×3

= 0.25×2×3.14×3

= 4.71

Arc length of two congruent circles = 2×4.71

= 9.42 units

Perimeter = 9.42+6+6

= 21.42 units

Therefore, the perimeter of the shaded figure is 21.42 units.

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The third root of 11 lies between the whole numbers 2 and 3.

The estimate of a non-exact root of x is done finding two numbers, as follows:

The number for this problem is given as follows:

Cubic root of 11.

For the parameters, we have that:

Hence the third root of 11 lies between 2 and 3, as 2³ < 11 < 3³.

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The number of additional copies you could ship by ordering 128 instead of 127 copies is 0 copies.

We have,

To determine the number of additional copies you could ship if you ordered 128 copies instead of 127 copies, we need to compare the costs of ordering each quantity using the given function C(n).

For n = 127:

C(127) = $6.91 x 127 = $878.57

For n = 128:

C(128) = $5.16 x 128 = $660.48

By subtracting the cost of ordering 127 copies from the cost of ordering 128 copies, we can determine the cost difference:

Cost difference = C(128) - C(127)

= $660.48 - $878.57

= -$218.09

Since the cost difference is negative, it means that ordering 128 copies is cheaper than ordering 127 copies.

However, the question asks for the number of additional copies, so we need to consider the whole number of copies.

Rounding down to the nearest whole copy, the number of additional copies you could ship by ordering 128 instead of 127 copies is 0 copies.

Thus,

The number of additional copies you could ship by ordering 128 instead of 127 copies is 0 copies.

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Answer: $275

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

3√5/√11 = 2.02

3√55/11 = 2.02

so,

3√5/√11 = 3√55/11

Answer:

130° and 310°

Step-by-step explanation:

the bearing of A from B is the measure of the clockwise angle from a north line at B to A

the angle at B and A are same- side interior angles and sum to 180°

angle at B = 180° - 50° = 130°

the bearing of A from B is then 130°

the bearing of B from A is the measure of the clockwise angle from the north line at A to B

the complete angle about A = 360° then clockwise angle from north line at A to B is

360° - 50° = 310°

the bearing of B from A is 310°

Answer:

Step-by-step explanation:

[tex]log_{4}2x = 5 \\2x = 4^5\\2x = 2^{10}\\x = \frac{2^{10}}{2}\\ x = 2^9\\x = 512[/tex]

Mistake is in step - 3 .

Answer:

Step-by-step explanation:

he correct answer for the domain of function p(x) is:

Domain: [1, ∞)

This means that x can take any value greater than or equal to 1, including 1 itself. The square root function (√x) is defined for non-negative real numbers, so x must be greater than or equal to 0. In this case, since we have √x - 1 in the function, x must be greater than or equal to 1 to avoid a negative value under the square root. Additionally, there are no other restrictions on the domain, so any value of x greater than or equal to 1 is allowed.

The solution is, After decreasing £16870 by 3% we get, £16363.90.

Here, we have,

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

First, find the percentage of £16870 by 3%

%value = 3% * 16870

           = (3 / 100) * 16870

           = 506.1

Now, just minus with actual value

New value = actual value - %value

We know, actual value = £16870 and %value = 506.1

so, New value = 16870 - 506.1

we get, New value = £16363.90

Therefore, After decreasing £16870 by 3% we get, £16363.90

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complete question:

Decrease £16870 by 3%

Give your answer rounded to 2 DP.

Answer:

(d) -12

Step-by-step explanation:

3a = _____

a = -4

3(-4) = ___

3(-4) = -12

The answer is (d) -12

Borrowing $50,000 for 30 years at 11% instead of 10% would result in an extra cost of approximately $44.63 per month.

To estimate the extra cost per month of borrowing $50,000 for 30 years at 11% instead of 10%, you can follow these steps:

Calculate the monthly payment for each interest rate:

The formula to calculate the monthly payment for a fixed-rate loan is:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M is the monthly payment,

P is the principal amount (loan amount),

r is the monthly interest rate (annual interest rate divided by 12),

n is the total number of monthly payments (number of years multiplied by 12).

Let's calculate the monthly payment at 10% interest rate first:

P = $50,000

r = 10% / 100 / 12 = 0.0083333 (monthly interest rate)

n = 30 years * 12 = 360 (total number of monthly payments)

M1 = $50,000 * (0.0083333 * (1 + 0.0083333)^360) / ((1 + 0.0083333)^360 - 1)

Calculate the monthly payment at 11% interest rate using the same formula:

P = $50,000

r = 11% / 100 / 12 = 0.0091667 (monthly interest rate)

n = 30 years * 12 = 360 (total number of monthly payments)

M2 = $50,000 * (0.0091667 * (1 + 0.0091667)^360) / ((1 + 0.0091667)^360 - 1)

Calculate the difference in monthly payments:

Extra cost per month = M2 - M1

Now let's perform the calculations:

M1 ≈ $446.92 (monthly payment at 10% interest rate)

M2 ≈ $491.55 (monthly payment at 11% interest rate)

Extra cost per month = $491.55 - $446.92 ≈ $44.63

Therefore, borrowing $50,000 for 30 years at 11% instead of 10% would result in an extra cost of approximately $44.63 per month.

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