Question 5 (2 points) Find the intersection point of the two lines: [x, y, z) = (-2, 3, -3] + f[1,-1, 2] and [x, y, z) = [2, 7,5] + u[1, 3, 2]. Format answer (x,y,z) A

Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.

Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.

How do equations work?

A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.

Equation symbols (=) are used to represent equations.

A finance charge is what?

The interest and other fees levied on credit cards are included in a finance charge.

Typically, the finance charge is based on a stated APR (annual percentage rate).

The month's billing cycle lasts for 28 days.

Balance at current starting = x.

APR = 24%, or annual percentage rate.

The monthly percentage rate (MPR) equals 2% (24% divided by 12).

The final day's purchase cost $1,400.

$51 is the total finance fee for the month.

($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.

$50 ($51 - $1) serves as the initial balance's finance charge.

The starting balance at this time is x = $2,500 ($50 x 2%).

Current Beginning Balance Equation: x = 51 - 1 0.02

($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.

Finance charge savings from buying on the last day equals $27 ($28 - $1).

By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.

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Answer:

slope = 5

Step-by-step explanation:

The equation of a lin in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x + 3 ← is in slope- intercept form

with slope m = 5

Parallel lines have equal slopes , then

The slope of a line parallel to y = 5x + 3 is 5

Answer:

HI! If this helps plz brainlist

Step-by-step explanation:

Rewrite 8 x 3 8 x 3 as (2x)3 ( 2 x ) 3 . Rewrite 27 as 33 . Since both terms are perfect cubes, factor using the difference of cubes formula, a3−b3=(a−b)(a2+ab+b2) a 3 - b 3 = ( a - b ) ( a 2 + a b + b 2 ) where a=2x a = 2 x and b=3 . Simplify.

Answer: 28 because 16+12=28

Answer:yes the ratios are the same

Step-by-step explanation: when found to common denominator they are equal 16x3 equals 48 and 12x4 equals 48

The inequality \($uv^2 \leq (uv)^2$\) holds for any vectors u and v in \(R^2\). Equality holds when the vectors u and v are collinear or when one of them is the zero vector.

To prove the inequality \($uv^2 \leq (uv)^2$\), we can start by expressing the dot product of u and v in terms of their components. Let u = (\(u_1, u_2\)) and v = (\(v_1, v_2\)).

Then, the dot product of u and v is given by\(uv = u_1 v_1 + u_2 v_2\).

Now, consider the squared length of the projection of u onto v.

This can be calculated as \((uv)^2\) / \(||v||^2\), where ||v|| represents the length of vector v.

Since ||v||^2 = vv, we have \((uv)^2\) /\(||v||^2\) = \((uv)^2\) / (\($v \cdot v$\)).

On the other hand, the squared length of vector u can be expressed as \(u\cdot u = u1^2 + u2^2\).

Now, we can compare the two expressions: \(uv^2\) and \((uv)^2\) / (vv).

By substituting the expression for uv, we get \(uv^2\) = \((u_1 v_1 + u_2 v_2)^2\), and by substituting the expressions for \(||v||^2\) and uu, we get \((uv)^2\) / (vv) = (\(u_1^2 v_1^2 + u_2^2 v_2^2\)) / (\(v_1^2 + v_2^2\)).

It can be shown that \((u_1 v_1 + u_2 v_2)^2 \geq (u_1^2 v_1^2 + u_2^2 v_2^2)\) for any real numbers \(u_1, u_2, v_1, v_2\). Therefore, \(uv^2\) ≤ \((uv)^2\) / \((vv)\), which implies \(uv^2\) ≤ \((uv)^2\).

Equality holds in the inequality \($uv^2 \leq (uv)^2$\) when the vectors u and v are collinear or when one of them is the zero vector.

Geometrically, this inequality represents the fact that the squared length of the projection of vector u onto vector v is always less than or equal to the squared length of the projection of u onto v.

When the vectors are collinear, their projections coincide and the inequality becomes an equality. Similarly, when one of the vectors is the zero vector, its projection onto any other vector is zero, resulting in equality as well.

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Answer:

72

Step-by-step explanation:

A person can read 24 pages in 1/3 hour.  There are 3 * 1/3 hours in 1 hour.

So, the person can read 24 * 3 = 72 pages in one hour.

Answer:

59/12

Step-by-step explanation:

2 1/4=9/4

9/4+8/3=27/12+32/12=59/12

Answer:

x=19.5cm

Step-by-step explanation:

15÷10= 1.5

13x1.5

=19.5cm

Answer:

The slope is 30, and the y-intercept is 75.

Step-by-step explanation:

Use two points from the table, and find the equation of a line given two points.

Point 1: (1, 105)

Point 2: (3, 165)

y = mx + b

slope = m = (y_1 - y_1)/(x_2 - x_1)

m = (165 - 105)/(3 - 1) = 60/2 = 30

y = 30x + b

Use point (1, 105) for x and y.

105 = 30(1) + b

105 = 30 + b

b = 75

y = 30x + 75

The slope is 30, and the y-intercept is 75.

Answer:

(-inf,6]

Step-by-step explanation:

The width of the rectangular prism will be 3 units.

Given that:

Length, L = 7 units

Height, H = 5 ¹/₅ units

Volume, V = 109 ¹/₅ cubic units

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as,

V = L x W x H

Then the width of the prism is calculated as,

109 ¹/₅ = 7 x W x 5 ¹/₅

W = 3 units

The width of the rectangular prism will be 3 units.

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The difference between the circumference of circle X and circumference of circle Y is 5π cm.

This is the distance round a circle.

The circumference of circle X is calculated as follows;

\(C_X = \pi d\\\\ C_X = 15\pi \ cm\)

The circumference of circle Y is calculated as follows;

\(C_Y = \pi d\\\\ C_Y = 20 \pi \ cm\)

The difference between the circumference of circle X and circumference of circle Y is calculated as follows;

\(C_Y - C_X = 20\pi - 15 \pi = 5\pi \ cm \\\\ \)

Thus, the difference between the circumference of circle X and circumference of circle Y is 5π cm.

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Using the formula for the circumference, it is found that the difference between the circumference of circle X and the circumference of circle Y is of 31.4 centimeters.

\(C = 2\pi r\)

The diameter of circle X is 15 centimeters, hence \(r = 15\) and:

\(C_X = 2\pi(15) = 30\pi\)

The diameter of circle Y is 20 centimeters, hence \(r = 20\) and:

\(C_Y = 2\pi(20) = 40\pi\)

Then, the difference, in centimeters, is of:

\(d = C_X - C_Y = 40\pi - 30\pi = 10\pi = 31.4\)

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Answer:

-12.7125

Step-by-step explanation:

The equivalent expression to the model equation is:

\(P(t) = 300\cdot16^{t}\)

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).

To find the equivalent expression for the model equation \(P(t) = 300\cdot2^{4t}\),  we can rewrite the given option. That is:

\(P(t) = 300\cdot16^{t}\)

\(P(t) = 300\cdot(2^{4}) ^{t}\)    (Remember: 2⁴ = 16)

\(P(t) = 300\cdot2^{4} ^{t}\)

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Answer:

B 7feet

Step-by-step explanation:

Side a = 24

Side b = 25

Side c = 7

Angle ∠A = 73.74° = 73°44'23" = 1.287 rad

Angle ∠B = 90° = 1.5708 rad = π/2

Angle ∠C = 16.26° = 16°15'37" = 0.28379 rad

C=16.26°B=90°A=73.74°b=25a=24c=7

Area = 84

Perimeter p = 56

Semiperimeter s = 28

Height ha = 7

Height hb = 6.72

Height hc = 24

Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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The value of m so that the condition satisfies is -2, the correct option is A.

We are given that;

y=f(x) is continuous

Now,

To find the numbers c that satisfy the conclusion of the Mean Value Theorem, we need to solve the equation:

f’© = [f(2) - f(0)] / (2 - 0)

f’(x) = 8x - 2

f(2) = 4(2)^2 - 2(2) + 3 = 23

f(0) = 4(0)^2 - 2(0) + 3 = 3

f’© = (23 - 3) / (2 - 0)

f’© = 10

8m - 2 = 10

8m = 12

m = 12/8

m = -2

Therefore, by the given function the answer will be -2.

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Answer:

J

Step-by-step explanation:

Since it says 30 each month, each being the keyword, we now can see what our x is. It states that the INITIAL payment, initial is only in the beginning so we now know what our b is, 50. Following the y=mx+b format we plug it in. y=30m+50      

Answer:

G ( i like ur pfp btw)

Given function, `f(x) = x³ - 9x² - 48x + 50`.To find the local maximum and minimum and justify your answer using the first derivative test Find the first derivative of the function f(x).\(f(x) = x³ - 9x² - 48x + 50\)

Differentiate both sides of the equation with respect to x.\(f^\prime(x) = 3x² - 18x - 48\)Step 2: Equate \(f^\prime(x) = 0\) to find the critical points.3x² - 18x - 48 = 03(x² - 6x - 16) = 0x² - 6x - 16 = 0x = 3 ± √(9 + 64) = 3 ± √73Critical points = {3 + √73, 3 - √73}

Determine the sign of \(f^\prime(x)\) in each interval and apply the first derivative test.Intervals:

\((-\infty, 3 - \sqrt{73})\)\((3 - \sqrt{73}, 3 + \sqrt{73})\)\((3 + \sqrt{73},

\infty)\)Test points: 2, 4, 5, 10Sign of \(f^\prime(x)\):

\(f^\prime(2) = 3(2)² - 18(2) - 48 = -45 < 0\)\(f^\prime(4) = 3(4)² - 18(4) - 48 = -6 < 0\)\(f^\prime(5) = 3(5)² - 18

(5) - 48 = 27 > 0\)\(f^\prime(10) = 3(10)² - 18(10) - 48 = 132 > 0\)

First Derivative Since the sign of \(f^\prime(x)\) changes from negative to positive at x = 5, this means that there is a local minimum at x = 5. Since the sign of \(f^\prime(x)\) changes from positive to negative at x = 3, this means that there is a local maximum at x = 3.To find the local maximum and minimum and justify your answer using the second derivative:

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The acceleration of the particle at t = 36 seconds is 11/8 meters/s2

Acceleration (a) is the change in velocity (Δv) over the change in time (Δt), represented by the equation a = Δv/Δt

using the second derivative of a and to find the time at 36 seconds is

a(36)=v'(36)=\(\frac{v(40)-v(32)}{40-32} \\\)

=7-(-4)÷8

a(36)=11/8 meters/s^2

The Trapezoidal Rule:

This is a rule that defines the area under the curves by dividing the total area into smaller trapezoids rather than using rectangles.

The formula for the trapezoidal rule:

T n = 1 2 Δ x ( f ( x 0 ) + 2 f ( x 1 ) + 2 f ( x 2 ) + ⋯ + 2 f ( x n − 1 ) + f ( x n ) )

∫v(t) dt is the particle’s change in position in meters from time

t = 20 seconds to time 40 t = seconds.

\(\int\limits {v(t)} \, dx =\frac{v(20)+v(25)}{2}*5+\frac{v(25)+v(32)}{2} *7+\frac{v(32)+v(40)}{y} *8 \\\\=\frac{-18*5}{2} +\frac{-12*7}{2} +\frac{24}{2} \\\\=\frac{-90}{2} +\frac{-84}{2} +\frac{24}{2} \\\\=-45-42+12\\=-75\)

∫v(t) dt=-75meters.

For 0 ≤t≤40, must the particle change direction in any of the subintervals indicated by the data in the table

since v(t) is differentiable, v(t) is continuous.

Particle changes direction is v(t) changes sign.

The particle must change direction in (8,20) and (32,40)

v(8)=5>0 and v(20)=-10<0 for this v(t) changes sign for same C for8<C<20.

v(32)=-4<0 and v(4)=7>0 for this v(t) changes sign for some d for 32<d<40

the above is true due to the Intermediate Value theorem.

since v(t) changes sign in (8,20) and in (32,40)

The particle changes sign in (8,20) and in (32,40)

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Answer:

a) The horizontal asymptote is y = 0

The y-intercept is (0, 9)

b) The horizontal asymptote is y = 0

The y-intercept is (0, 5)

c) The horizontal asymptote is y = 3

The y-intercept is (0, 4)

d) The horizontal asymptote is y = 3

The y-intercept is (0, 4)

e) The horizontal asymptote is y = -1

The y-intercept is (0, 7)

The x-intercept is (-3, 0)

f) The asymptote is y = 2

The y-intercept is (0, 6)

Step-by-step explanation:

a) f(x) = \(3^{x + 2}\)

The asymptote is given as x → -∞, f(x) = \(3^{x + 2}\) → 0

∴ The horizontal asymptote is f(x) = y = 0

The y-intercept is given when x = 0, we get;

f(x) = \(3^{0 + 2}\) = 9

The y-intercept is f(x) = (0, 9)

b) f(x) = \(5^{1 - x}\)

The asymptote is fx) = 0 as x → ∞

The asymptote is y = 0

Similar to question (1) above, the y-intercept is f(x) = \(5^{1 - 0}\) = 5

The y-intercept is (0, 5)

c) f(x) = 3ˣ + 3

The asymptote is 3ˣ → 0 and f(x) → 3 as x → ∞

The asymptote is y = 3

The y-intercept is f(x) = 3⁰ + 3= 4

The y-intercept is (0, 4)

d) f(x) = 6⁻ˣ + 3

The asymptote is 6⁻ˣ → 0 and f(x) → 3 as x → ∞

The horizontal asymptote is y = 3

The y-intercept is f(x) = 6⁻⁰ + 3 = 4

The y-intercept is (0, 4)

e) f(x) = \(2^{x + 3}\) - 1

The asymptote is \(2^{x + 3}\)  → 0 and f(x) → -1 as x → -∞

The horizontal asymptote is y = -1

The y-intercept is f(x) =  \(2^{0 + 3}\) - 1 = 7

The y-intercept is (0, 7)

When f(x) = 0, \(2^{x + 3}\) - 1 = 0

\(2^{x + 3}\) = 1

x + 3 = 0, x = -3

The x-intercept is (-3, 0)

f) \(f(x) = \left (\dfrac{1}{2} \right)^{x - 2} + 2\)

The asymptote is \(\left (\dfrac{1}{2} \right)^{x - 2}\) → 0 and f(x) → 2 as x → ∞

The asymptote is y = 2

The y-intercept is f(x) = \(f(0) = \left (\dfrac{1}{2} \right)^{0 - 2} + 2 = 6\)

The y-intercept is (0, 6)

The correct option is (D). Approximately 77.3% of new machine set ups are completed in less than 25 minutes.

Given a local manufacturing plant, employees must complete new machine set ups within 30 minutes.

The new machine set-up times can be described by a normal model with a mean of 22 minutes and a standard deviation of four minutes. The typical worker needs five minutes to adjust to their surroundings before beginning their duties.

To find the percentage of new machine set ups completed in less than 25 minutes, we need to calculate the z-score. For this, we will use the formula:

z = (X - μ) / σ

where X = 25 minutes, μ = 22 minutes, and σ = 4 minutes

z = (25 - 22) / 4z = 0.75

We can now look up the percentage of the area under the normal distribution curve that corresponds to z = 0.75. Using a standard normal distribution table, we find that the area to the left of z = 0.75 is approximately 0.7734.

So, the percentage of new machine set ups completed in less than 25 minutes is approximately 77.34%.

Therefore, the correct option is (D).Approximately 77.3% of new machine set ups are completed in less than 25 minutes.

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The coffee shop charge for her purchase $46.

The slope of the line and a point on the line can be used to create the equation of a line. To better comprehend how the equation for a line is formed, let's learn more about the line's slope and the necessary point on the line. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis.

The slope intercept form of equation is

y= mx+ b

As, we know the slope intercept form

y= mx + b

Now, we have the points (0, 26) and (4, 52)

So, the y- intercept is 26.

and, slope= (52- 26)/ (4- 0)

                 = 26/4

                 = 6.5

So, coffee shop charge for her purchase is

= 6.5 x 3 +26

= 46

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Answer:

4 different rays that can be formed from 3 collinear points.

Step-by-step explanation:

A ray is a part of a line that starts at a single point (called the endpoint) and extends infinitely in one direction.

A ray is named using its endpoint first, and then any other point on the ray, with an arrow on top, pointing in the direction of the ray. For example, the ray starting at point A and extending in the direction of point B is denoted as \(\overrightarrow{AB}\).

Collinear points are points that lie on the same straight line. Three or more points are said to be collinear if there exists a single straight line that passes through all of them.

Let the three collinear points be A, B and C (see attachment).

Each point can be the endpoint of a ray.

As point A if the left-most point, we can form one ray with point A as the endpoint. As this ray extends in the direction of points B and C, we can use either point B or point C as the directional point when naming the ray:

\(\overrightarrow{AB}\;\;\left(\text{or}\;\;\overrightarrow{AC}\right)\)

As point C if the right-most point, we can form one ray with point C as the endpoint. As this ray extends in the direction of points A and B, we can use either point A or point B as the directional point when naming the ray:

\(\overrightarrow{CB}\;\;\left(\text{or}\;\;\overrightarrow{CA}\right)\)

Finally, if we use point B as the endpoint of the ray, we can form two rays. As point B is between points A and C, we have one ray in the direction of point A, and the other ray in the direction of point C:

\(\overrightarrow{BA}\;\;\text{and}\;\;\overrightarrow{BC}\)

Therefore, there are 4 different rays that can be formed from 3 collinear points.

Q = amount of quarters

D = amount of dimes

so we know that a quarter is just 25cents, so if we had Q quarters, that's a total of 25*Q or 25Q cents total.

likewise, a dime is 10cents so if we had D dimes that's 10*D or 10D cents.

no matter whatever 10D and 25Q are, we know their sum is $5.50 or 550 cents, 10D + 25Q = 550.

Since Tara has more Q than D, actually she has 8 more, so whatever D is, we know that Q = D + 8.

\(\begin{cases} 10D+25Q=550\\\\ Q=D+8 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 1st equation}}{10D~~ + ~~25(D+8)~~ = ~~550}\implies 10D+25D+200=550 \\\\\\ 35D+200=550\implies 35D=350\implies D=\cfrac{350}{35}\implies \boxed{D=10} \\\\\\ \stackrel{\textit{since we know that}}{Q=D+8}\implies \boxed{Q=18}\)

Answer:

I believe Laila saved $9.

Step-by-step explanation:

63/7=9

Divide

63/7 = 9

She saved $9

The correct answer is (a). The conclusion that the frequency of mothers' smoking is not related in any way to the incidence of influenza in their babies is a common correlation error.

The correct answer is (a) Conclusion: The frequency of mothers' smoking is not related in any way to the incidence of influenza in their babies. This conclusion makes a common correlation error by assuming that there is no relationship between smoking during pregnancy and the incidence of influenza in babies, just because there is a very low linear correlation coefficient.

It is important to note that correlation does not imply causation, and a low correlation coefficient does not necessarily mean that there is no relationship between the two variables. Therefore, this conclusion is invalid and incorrect.

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Answer:

30.5 ft squared

Step-by-step explanation:

First, find the area and shape. If it is a square then you want to divide by four since all sides are equal. So divide 122 by 4 and you get the answer.

Answer:

18

Step-by-step explanation:

6*6/2 = 18

Answer: what is X and y?

Step-by-step explanation: