The linear function passes through the point (-1,4) and has a slope of 4. What is the zero of f? Hint: point slope formula.
A: -3
B: 5
C: -2
D: 8

a. The standard deviation of the tuition is  $150.

b. The shape of this distribution is a normal distribution, which is a bell-shaped curve.

(a) The mean tuition is $100 per credit hour * 15 credit hours per semester + $150 lab fee = $1650 per semester.

The standard deviation of the tuition is l:

= ✓(100² + 150²) =

= ✓22500

= $150.

(b) The shape of this distribution is a normal distribution, which is a bell-shaped curve. The mean is the center of the distribution, and the standard deviation is the width of the distribution. The majority of the tuitions will be close to the mean, with fewer and fewer tuitions as you move further away from the mean.

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The angles are formed by a transversal and two parallel lines in the figure. By applying congruent angles and vertical opposite angle property, ∠1 ≅∠3 ≅ ∠5 ≅ ∠7; ∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8. Therefore option B is correct.

Congruent angles are identical to each other and have the same measure. The angles formed by the transversal in corresponding corners are called corresponding angles and they are congruent.

Therefore, ∠1 ≅ ∠5, ∠3 ≅ ∠7----------(1)

At a vertex if two angles are opposite to each other, then they are vertically opposite angles, they are equal and congruent to each other.

Therefore, ∠1 ≅ ∠3, ∠5 ≅ ∠7----------(2)

Combining (1) and (2), we get:

∠1 ≅∠3 ≅ ∠5 ≅ ∠7
Similarly we can find,

∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8.

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1. The product of MG is as follows;

[tex]\left[\begin{array}{ccc}1&k_1+9&4k_2+36 \\2t_1&k_1t_1-17&3k_2-19t_1-11\\t_2+1&k_1-4t_2+5&k_2t_2-8\end{array}\right][/tex]

2. The values are k₁ = -9, k₂ = -9, t₁ = 0 and t₂ = -1 given that G = M⁻¹

Matrix M and matrix G are given as

M = [1, 4, 5; t₁, 3, -1; 1, t₂, 1] and

G = [2, k₁, -19; 1, -4, k₂; -1, 5, 11]

MG becomes

1×2 + 4×1 + 5×-1         1k₁+4×-4+ 5×5       1×-19+4k₂+5×11

t₁×2+3×1+-1×-1             t₁k₁+3×-4+-1×5       t₁×-19+3k₂+-1×11

1×2+t₂×1+1×-1               1k₁+t₂×-4+-1×5        1×-19+t₂k₂+1×11

=

1             k₁+9         4k₂+36

2t₁          k₁t₁-17        3k₂-19t₁-11

t₂+1        k₁-4t₂+5      k₂t₂-8

To solve G = M⁻¹ we know it is an identity matrix

I = | 1 0 0 |

    | 0 1 0 |

    | 0 0 1 |

We can equate the elements of MG and I to find the values of t₁, t₂, k₁, and k₂:

1 = 1,         k₁+9 = 0,       4k₂+36 = 0

2t₁ = 0     k₁t₁-17 = 1        3k₂-19t₁-11 = 0

t₂+1 = 0     k₁-4t₂+5 = 0   k₂t₂-8 = 1

k₁+9 = 0           4k₂+36 = 0            2t₁ = 0          t₂+1 = 0

k₁ = -9                 k₂ = -9                   t₁ = 0           t₂ = -1

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Answer:

The correct answer is D. 56x^2.

The given system of equations has no solution.

Given that a system of equations, 12x + 36y = −3 and −12x − 36y = 0, we need to solve it,

We know for a system of equations =

a₁x + b₁y = c₁ and a₂x + b₂y = c₂

If a₁ / a₂ = b₁ / b₂ = c₁ / c₂ then the system has infinite solutions.

If a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂ then the system has no solutions.

If a₁ / a₂ ≠ b₁ / b₂ then the system has a unique solution.

comparing the coefficients given,

-12/12 = -1

-36/36 = -1

-3/0 = -3

We get here the condition of a₁ / a₂ ≠ b₁ / b₂, which means that the system has no solution.

Hence the given system of equations has no solution.

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The remaining credit after 91 minutes of calls is $16.76.

We are given that;

(24, 22.12) and (63, 17.44)

Now,

To find the slope and the y-intercept of the function. You can write your solution as:

Slope = (y2 - y1) / (x2 - x1) = (17.44 - 22.12) / (63 - 24) = -0.08 y-intercept = y - mx = 22.12 - (-0.08)(24) = 24.04 Equation: y = -0.08x + 24.04

To find the remaining credit after 91 minutes of calls, you need to substitute x = 91 in the equation and simplify. You can write your answer as:

y = -0.08(91) + 24.04 y = -7.28 + 24.04 y = 16.76

Therefore, by the intercept the answer will be $16.76.

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The solution to the equation  [tex]2log_a(x) - log_a(x-1) = log_a(x-2)[/tex]  is

x = 2/3.

To solve the equation [tex]2log_a(x) - log_a(x-1) = log_a(x-2)[/tex] for x, We can employ algebraic manipulation and logarithmic characteristics.

Apply logarithmic properties.

Using the logarithmic property[tex]log_a(b) - log_a(c) = log_a(b/c),[/tex] we can rewrite the equation as:

[tex]log_a(x^2) - log_a(x-1) = log_a(x-2).[/tex]

Combine the logarithms.

Applying the logarithmic property [tex]log_a(b) - log_a(c) = log_a(b/c),[/tex] we can combine the logarithms on the left-hand side:

[tex]log_a[(x^2)/(x-1)] = log_a(x-2).[/tex]

Take the logarithms out.

We can do away with the logarithms because the base of the equation is the same.

[tex](x^2)/(x-1) = x-2.[/tex]

Streamline the equation.

We can eliminate the denominator and simplify the equation by multiplying both sides by (x-1):

[tex]x^2 = (x-2)(x-1).[/tex]

Expand and simplify.

Expanding the right-hand side, we have:

[tex]x^2 = x^2 - 3x + 2[/tex]

Rearrange the equation.

Rearranging the equation, we get:

0 = -3x + 2.

Do the x math.

We must isolate x on one side of the equation in order to find its value. Taking 2 away from both sides:

3x = 2.

Finally, divide both sides by 3:

x = 2/3.

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The height of the kite off the ground is approximately 17.87 feet rounded to two decimal places.

To solve the problem can use similar triangles.

Let's draw a diagram:

     A

      |\

      | \

   h |   \   x

      |      \

      |____\

       d   B

Point A represents the kite, point B represents the tip of the kite's shadow on the ground and point D represents the point directly below the spool of string on the ground.

The height of the kite represented by h.

The length of the string is 42.9 feet so the distance from point A to point D is also 42.9 feet.

The distance from point B to point D is 16.5 feet.

These two lengths to find the length of segment AB:

AB/AD = BD/AD

AB/42.9 = 16.5/42.9

AB = 16.5

So AB is 16.5 feet.

Now we can use the similar triangles to find h.

We have:

h/x = AB/AD

h/x = 16.5/42.9

h = x × 16.5/42.9

We need to find x.

The spool of string is 3.4 feet above the ground and we know that the kite is directly above the spool when it is at its highest point in the sky.

So the height of the kite above the ground is the same as the height of the spool above the ground plus the length of string that has been let out:

x = 3.4 + 42.9

= 46.3

Now we can substitute this value of x into the previous equation to find h:

h = 46.3 × 16.5/42.9

= 17.87

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The amount Sam needs to pay in each installment is $141.1

From the question, we have the following parameters that can be used in our computation:

Cost of refrigerator = 1058

Down payment = 211.40

Number of equal installments = 6

Using the above as a guide, we have the following:

Each installment = (Cost of refrigerator - Down payment)/Number of equal installments

substitute the known values in the above equation, so, we have the following representation

Each installment = (1058 - 211.40)/6

Evaluate

Each installment = 141.1

Hence, the amount in each installment is $141.1

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Answer:Therefore, the dimensions of the rectangle are 14 ft by 4 ft.

Let's use variables to represent the length and width of the rectangle. We know from the problem that:Length = 3 times the width + 2

Area = 40 ft²We can use the formula for the area of a rectangle to set up an equation:Area = length x widthSubstituting in the values we have:40 = (3w + 2)wExpanding the brackets and simplifying:40 = 3w² + 2wRearranging into a quadratic equation form:3w² + 2w - 40 = 0We can solve for w using the quadratic formula:w = (-2 ± sqrt(2² - 4(3)(-40))) / (2 x 3)

w = (-2 ± sqrt(484)) / 6

w = (-2 ± 22) / 6The two possible solutions are w = 4 and w = -6.67. Since width cannot be negative, we take the positive solution: w = 4 ft.To find the length, we can use the formula we established earlier:Length = 3w + 2

Length = 3(4) + 2

Length = 14 ft

Answer:

16 in

Step-by-step explanation:

50 ft x 12 in/ft = 600 in

Scale factor:  2 : 600 = 1 : 300

x = length of island on the map

400 ft = 4800 in

1/300 = x/4800

x = 4800/300 = 16 in

[tex]w^2 - 6w + 4[/tex] is a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.

The profit earned by selling w pear trees is 2w + 10

To find the difference in profit, we need to subtract the profit earned by selling w pear trees from the profit earned by selling w apple trees:

[tex](w^2 - 4w + 14) - (2w + 10)[/tex]

Simplifying the expression:

[tex]w^2 - 6w + 4[/tex]

Therefore, the polynomial that represents how much more profit is earned by selling w apple trees than w pear trees is [tex]w^2 - 6w + 4[/tex].

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1) Note that the population mean is 153.

2) there are 36 possible random samples of size two that can be selected from a population of nine.

1) Population Mean = (172 + 148 + 156 + 170 + 161 + 138 + 142 + 156 + 134) / 9

= 1377 / 9

Population Mean = 153

2) To get the number of possible random samples, we must use Combination whose equation is given as

nCr = n! / (r! (n-r)!)

nC2 = 9! / (2!(9-2)!)

= 9! / (2! 7!)

= (9 x 8 x 7!) / (2!7!)

= (9 x 8) / 2

= 36

Thus, the number of random samples that can be selected form a population of 9 is 36.

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To achieve a 1 in row 1, column 1, divide row 1 by 4 in the given matrix, resulting in the updated matrix. This row operation preserves the system of linear equations represented by the matrix.

To get a 1 in row 1, column 1 of the given matrix, you can perform the following valid row operation:

R1 = (1/4) * R1

This operation scales row 1 by a factor of 1/4, resulting in the new matrix:

1 , -3/4 , -43/4

3 , -2 , -30

By dividing each element in row 1 by 4, the value in row 1, column 1 becomes 1. This row operation maintains the equivalence of the system of linear equations represented by the matrix.

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The equation of the quadratic function C(t) is given as follows:

C(t) = t² + 3.

The quadratic function of vertex(h,k) is given by the rule presented as follows:

y = a(x - h)² + k

In which:

The vertex is the turning point of the function, where it changes from decreasing to increasing, or vice versa, hence:

(0,3).

Then:

y = at² + 3.

When x = 1, y = 4, hence the leading coefficient a is obtained as follows:

4 = a(1)² + 3

a = 1.

Hence the function is given as follows:

y = t² + 3.

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The correct statements are:

If "positive" end behaviour:

The arrows point in the same direction.

The right arrow is up.

The graph hits the y-axis.

If "negative" end behaviour:

The arrows point in opposite directions.

The right arrow is down.

The graph hits the X-axis.

In mathematics, a graph is a visual representation of a set of data, which consists of points, called vertices or nodes, and lines connecting them, called edges or arcs.

Graphs are often used to represent mathematical functions, data sets, or relationships between objects, and they can be used to model real-world phenomena.

Graphs can be drawn on a coordinate plane or in a more abstract form, and they can be used to analyze and understand complex systems and relationships.

The correct statements are:

If "positive" end behaviour:

The arrows point in the same direction.

The right arrow is up.

The graph hits the y-axis.

If "negative" end behaviour:

The arrows point in opposite directions.

The right arrow is down.

The graph hits the X-axis.

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The equation of h(x) in vertex form is given as follows:

h(x) = (x + 2)² - 3.

The quadratic function of vertex(h,k) is given by the rule presented as follows:

y = a(x - h)² + k

In which:

The vertex is the turning point of the function, where it changes from decreasing to increasing, or vice versa, hence it's coordinates are given as follows:

(-2,-3).

Then the equation is:

h(x) = a(x + 2)² - 3.

When x = 0, h(x) = 1, hence the leading coefficient a is obtained as follows:

1 = a(2)² - 3

4a = 4

a = 1.

Hence the equation is:

h(x) = (x + 2)² - 3.

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The horizontal transformations are defined as follows:

cos(ax).

They are classified as follows:

The vertical transformations are defined as follows:

acos(x).

They are classified as follows:

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Answer:

  80°

Step-by-step explanation:

You want the sum of angles 1 and 2 in the attached figure where line m ║ line n.

Vertical angles are congruent. This means angle 1 is 60°, and the unnumbered angle in triangle ABC at vertex A is 20°.

Where a transversal crosses parallel lines, alternate interior angles are congruent. This means angle 2 is congruent with the unnumbered interior angle at A, which we know is 20°.

Angle 1 is 60° and angle 2 is 20°. Their sum is ...

  ∠1 +∠2 = 60° +20° = 80°

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Answer:

Step-by-step explanation:

What is the Formula for Calculating the Square Root of a Number? The square root of any number can be expressed using the formula: √y = y½. In other words, if a number has 1/2 as its exponent, it means we need to find the square root of the number.

In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number.

The square root of a number "a" is denoted by the symbol "√a" or "a^(1/2)." For example, the square root of 9 is 3 because 3 * 3 = 9.

The error E = ± 4.04 %

Sample data = ( p ).

success p = success percentage = 40 %

confidence interval CI = 98%

sample size n = 800

margin of error E:

The margin of error "E" for estimation of population proportion ( p ) is given by:

E = z - critical √(p(1-p)/n)

P ( Z < Z-critical ) = a/

a = 1 - CI

P ( Z < Z-critical ) = (1 - 0.98) / 2

P ( Z < Z-critical ) = 0.01

Z-critical = 2.33

The error E = ± 4.04 %

Thus, the correct answer is E=± 4.04 %

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The parent function for the quadratic equation is y = x²

From the question, we have the following parameters that can be used in our computation:

The graph

From the graph, we have the following points

vertex = (0, 0)

Points = (±1, 1) and (±2, 4)

The equation for the quadratic function is represented as

y = a(x - h)² + k

Where vertex = (h, k)

So, we have

y = a(x - 0)² + 0

Evaluate

y = ax²

Using the points, we have

a(1)² = 1

Evaluate

a = 1

So, we have

y = x²

Hence, the parent function for the quadratic equation is y = x²

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The value of the limit of the function f(x) = x² - 2 is 7.

The value of the limit of the function f(x) = -3x + 15 is -6.

We have,

To evaluate the limit as x approaches 3, we need to find the limit of function f(x) as x approaches 3 from both sides of 3.

First, let's evaluate the limit from the left side of 3:

lim x → 3⁻ f(x) = lim x → 3⁻ (x^2 - 2)

Substituting x = 3 - h (where h approaches zero) gives:

lim h → 0⁺ [(3 - h)^2 - 2]

= lim h → 0⁺ [9 - 6h + h^2 - 2]

= lim h → 0⁺ [h^2 - 6h + 7]

= 7

(since the limit of a quadratic function as h approaches zero is the constant term)

Next, let's evaluate the limit from the right side of 3:

lim x → 3⁺ f(x)

= lim x → 3⁺ (-3x + 15)

= -6

Since the limit from the left side is not equal to the limit from the right side, the limit of f(x) as x approaches 3 does not exist.

Thus,

The value of the limit of the function f(x) = x² - 2 is 7.

The value of the limit of the function f(x) = -3x + 15 is -6.

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The trigonometric value equation is solved and sin ( 0 )° + cos ( 0 )° = 1

Given data ,

Let the trigonometric relation be represented as A

Now , the value of A is

sin ( 0 )° - cos ( 0 )° = 1

From the trigonometric relation , we get

sin 0 = 0

cos 0 = 1

So , the equation is

sin ( 0 )° + cos ( 0 )° = 1

Hence , the equation is solved

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The area of the sector is approximately 9.25 ft².

We have,

The formula for the area of a sector.

A = (θ/360°) × πr²

where A is the area of the sector, θ is the central angle in degrees, and r is the radius.

Substituting the given values.

A = (40°/360°) × 3.14 × (16.7 ft)²

A = 0.1111 × 3.14 × 278.89 ft²

A = 9.2465 ft²

Rounding to the nearest hundredth.

A ≈ 9.25 ft²

Therefore,

The area of the sector is approximately 9.25 ft².

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An equation that can be used to find the value of x include the following: 110° + 7x = 180°.

In Mathematics and Geometry, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the sum of the given angles are supplementary angles:

110 + 7x = 180°

7x = 180° - 110°

7x = 70°

x = 70°/7

x = 10°

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The statement thet complete the proof of the congruent triangles is (a) SAS criterion

From the question, we have the following parameters that can be used in our computation:

The incomplete proof

In the proof, we have

AD ≅ BC --- side length

DC ≅ DC --- side length

∠ADC ≅ ∠BCD -- angle

This means that the triangles are congruent by the SAS theorem

The SAS theorem is defined by "If two sides in one triangle are congruent to two sides in another triangle and the included angle in both are congruent, then the two triangles are congruent"

This means that they are congruent by the SAS congruent

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Answer: A. SAS criterion.

Step-by-step explanation: Angle : ∠ADC ≅ ∠BCD                                         Side length : AD ≅ BC                                                                                       Side length : DC ≅ DC                                                                                                

Because of this △ADC ≅ △BCD by SAS criterion.

From matrix property it can be showed that A=B.

Given,

If A,B and x are matrices with x≠0 and AX=BX

Now,

X must be non-singular matrix because

A[tex]XX^{-1}[/tex]=B[tex]XX^{-1}[/tex]

AI = BI

= I( identity matrix )

⇒A = B

Hence Proved, A = B .

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