3(9z+4) > 35z - 4
What is z

Answer:

C

Step-by-step explanation:

The lines cross at (1,4)

A graph of the image of the figure after a reflection across the x-axis is shown below.

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).

This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.

By applying a reflection over or across the x-axis to triangle GLQ, we have;

(x, y)                →      (x, -y)

G (3, 4)             →      (3, -(4)) = G' (3, -4)

L (1, 2)                →     (1, -(2)) = L' (1, -2).

Q (4, -1)              →      (4, -(-1)) = Q' (4, 1)

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The value of f(3) is 0.688.

To find the value of f(3), we need to determine the pattern of decrease and apply it to the given information.

Given that f(0) = 86, we know the starting value of the function. We are also told that for each increase in x by 1, the value of f(x) decreases by 80%. This means that for every unit increase in x, the value of f(x) becomes 80% of its previous value.

Let's calculate the values step by step:

f(0) = 86 (given)

f(1) = 86 - 0.8 * 86 = 17.2

f(2) = 17.2 - 0.8 * 17.2 = 3.44

Now, let's find f(3) by applying the same decrease:

f(3) = 3.44 - 0.8 * 3.44 = 0.688

In summary, starting with f(0) = 86, we applied an 80% decrease for each unit increase in x to calculate the values of f(1) = 17.2, f(2) = 3.44, and f(3) = 0.688. The pattern suggests that the function approaches zero rapidly as x increases.

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TU is parallel to MN.

Given that the slope of a line MN is -3, we need to find a line which is parallel to the MN.
So we know that the parallel lines are having equal slope so the line which is parallel to the MN it must have slope of -3.

Therefore,

Considering the line TU, find the slope = y₂-y₁ / x₂-x₁

= 10-1 / 5-8 = -9/3 = -3

Since, the slope of the line TU is -3 therefore we can say the lines TU and MN are parallel liens.

Hence TU is parallel to MN.

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The value of x is; x = 3.14

Here, we have,

from the given diagram, we get,

there is a right angle triangle.

we have to find the value of x.

we know that,

Let the angle be θ , such that

cos θ = base / hypotenuse

here, we get,

cos 17 = 3/x

so, we have,

0.956 = 3/x

so, x = 3.14

Hence, The value of x is;x = 3.14

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9514 1404 393

Answer:

  153.6 mm³

Step-by-step explanation:

The volume of a prism is given by the formula ...

  V = Bh . . . . . . where B is the area of the base, and h is the height

The area of the triangular base is given by the formula ...

  A = 1/2bh . . . . where b and h are the base and height of the triangle

For a right triangle, the lengths of the legs can be used for the base and height.

The base area is ...

  A = (1/2)(6 mm)(8 mm) = 24 mm²

Then the volume is ...

  V = (24 mm²)(6.4 mm) = 153.6 mm³

Answer:

Reason 2

Step-by-step explanation:

The reason should be transitive property( if a=b and b=c then a=c) not reflective property.

Given:

1. A= {1,2,3} and B= {4,5,6}

2. A= {a,b,c,d} and B = {11,55,66}

Required:

Find the union of events A and B.

Explanation:

The union of two sets A and B is the set of elements in which elements of both A and B.

1.

2.

Final answer:

1.

2.

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

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

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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Answer:

1,100

Step-by-step explanation:Well first find the principal first Multiply the rate 0.02 by the time 1 year this gives us 0.02 then divide the interest ($22) by 0.02 then you get $1,100

Answer:

not 1,100 its 1100

Step-by-step explanation:

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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Answer:

a.35

Step-by-step explanation:

10 + 20/2 equals 20

20/2+5 equals 15

20+15 equals 35

Answer:

x = 56°

Step-by-step explanation:

The triangle given has two equal sides, therefore, it is an isosceles triangle. And isosceles triangle has two equal base angles which are opposite to each of the equal sides.

Therefore:

2(62°) + x = 180° (sum of triangle)

Solve for x

124° + x = 180°

x = 180° - 124°

x = 56°

Answer:

5

Step-by-step explanation:

3×9×X=135

27×X=135 divide 27 from both sides

missing side is 5

We must add the relevant components of each of the three vectors, X1, X2, and X3, in order to resultant vector the final vector XR, which has the components (1, -5)m.

R = A + B. Equation 2 To create the resultant vector, opposing vectors are subtracted from one another. R is the resulting vector in this case, and the column B is directed in the opposite direction to a vector A.

We must add the relevant components of each of the three vectors, X1, X2, and X3, in order to resultant vector the final vector XR, which has the components (1, -5)m.

To find the resultant vector, we need to add the corresponding components of the three given vectors. So, we have:

XR = X1 + X2 + X3

XR = (-2,0) m + (0,-5) m + (3,0) m

XR = (-2+0+3, 0+(-5)+0) m

XR = (1, -5) m

Therefore, the resultant vector XR is (1, -5) meters.

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Complete question -

Add the following three vectors to find the resultant vector, XR:

X1 = (-2,0)m, X2= (0,-5,)m, x3 = (3,0)m

Step-by-step explanation:

a) If the given set of vectors does not span \(\mathbb{R}^{3}\) , it means the number of linearly independent vectors are less than 3. So by adding one or more linearly independent vectors with respect to existing vectors, we can convert the set to basis and basis always spans vector space.

eg. \(S= \left \{ (1,0,0)^{T},(1,2,0)^{T} \right \}\) this set does not span \(\mathbb{R}^{3}\) . Since it has only two vectors and both vectors are linearly independent, so adding one linearly independent vector with respect to the vectors of S viz. (0,0,1)^{T} can span whole \(\mathbb{R}^{3} \).

b) It is not possible. Since if a set of vectors is linearly dependent then after adding linearly independent vectors it will also linearly dependent i.e. addition of a linearly independent vector does not effect on the set.

Answer:(

(0,-4) (2,-3)

Step-by-step explanation:

y=1/2x-4

Answer:

Step-by-step explanation:

a.) When you have the following equation \(a(x-h)^2+z\) To find the vertex you take the h value, change its sign (to positive in this case) and that will give you the x value. To find the y-value just take the z. This gives us (15,-100)

b.) The axis of symmetry is just the x value of the vertex which is 15

c.) I'm not too sure what this means but can tell you that it's concave up because there's no way x can be negative

d.)Because the a value is positive that means that the graph is concave up which means that it has a minimum. The minimum is just the y value of the vertex which is just -100

e.) I'm going to write this in interval notation. The domain is all the possible x values of the graph which is all real numbers or (-∞,∞). The range is all the possible y values. We know that the minimum is -100 which means all the possible y values are [-100,∞)

f.) This is obviously a parabola and because the graph is concave up and has a negative minimum there must be 2 x intercepts.

Answer:

D

Step-by-step explanation:

quotient of a and b:   a ÷ b

multiplied:  ×

difference of t and s:  t - s

Therefore:  (a ÷ b) × (t - s)

Answer:

D. (a/b) x (t-s)

Step-by-step explanation:

Given :-

The quotient of a and b multiplied by the difference of t and s.

Solving :-

Quotient of a and b = a/b

Difference of t and s = t - s

Multiplied together :-

(a/b) x (t-s)

Solution :-

D. (a/b) x (t-s)

Answer:

( x - 1) ( 2x + 3)

Step-by-step explanation:

It's actually the other way round.

2x^2- + x - 3

( 2x^2 - 2x) + (3x-3)

2x ( x-1 ) + 3( x-1)

( x -  1)(2x+3)

Its the other way around

HOPE IT HELPED

Answer:

y=3x+6

Step-by-step explanation:

the equation of a line in

slope-intercept form

is.

xy=mx+b

The domain of the exponential function is all real numbers.

The domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.

For the exponential function y = 2ˣ + 6, the domain includes all real numbers.

This is because there are no restrictions on the input values that can be plugged into the function.

We can take any real number x, substitute it into the expression 2ˣ, and then add 6 to get a corresponding output value y.

Hence,  the domain of the exponential function is all real numbers.

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Answer:

\(d=17.69\ \text{inches}\)

Step-by-step explanation:

Given that,

The length of a television, l = 13 inches

Width of the television, b = 12 cm

We ned to find the diagonal of the television. Let the diagonal be d. We can find it using Pythagoras theorem,

\(d^2=l^2+b^2\\\\d=\sqrt{13^2+12^2} \\\\d=17.69\ \text{inches}\)

So, the diagonal of the television is \(17.69\ \text{inches}\).

Answer:

Step-by-step explanation:

Please, share the instructions that come with each problem.  Thanks.

2a -a + 1 = can be simplified to a + 1.

x + y + x + 2 = cannot be simplified.

2(x + 4) + 2x =

3x + 2(x - 2) =​ can be expanded and then simplified:  

   3x + 2x - 4 = 5x - 4

Answer:

3 beause when you dividend it -5.6+4(3) .

Answer:

Step-by-step explanation:

The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000,  3,983 rounded to the nearest thousand is 4,000,  13,560 rounded is 14,000.

7,000 + 4,000+ 14,000 = 25,000

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Distance traveled after toll payment is 1.2 miles on highway 40.

The distance may be calculated using a curved route. Displacement measurements can only be made along straight lines. Distance is path-dependent, meaning it varies depending on the direction followed. Displacement simply depends on the body's beginning and ending positions; it is independent of the route.

Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.

The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance traveled between them are not the same. The entire length of the journey taken between two points is known as the distance traveled. Travel distance is not a vector.

Distance traveled before toll payment =3/5 miles on highway 40

Distance traveled after toll payment =2*3/5  = 6/5 =

1.2 miles on highway 40.

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(a) The amplitude of the function is 2.

(b) The amplitude of the function is 3.

Amplitude is interval between the resting position and the maximum migration of the wave.

Formula for amplitude of the function is:

y = A sin (ωt + Ф) or y = A cos (ωt + Ф), where A represent the amplitude.

Given:

(a) y = 2 cos [3(Ф + 45)]

Formula for amplitude is:

y = A cos (ωt + Ф)

(b) y = 3 sin [2(Ф - 90)]

Formula for amplitude is

y = A sin (ωt + Ф)

After compare amplitude with equation than we get amplitudes are 2 and 3.

Therefore, the amplitude of the following function are 2 and 3 respectively.

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Therefore, the probability that a woman will give birth to two boys is only one in three, whereas the probability that a man will do so is one in two.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here,

The woman may have at least one boy in the three following ways: 1) older boy, younger girl; 2) older girl younger boy; 3) older boy, younger boy.

But the man's children may be distributed in only two ways: 1) older boy, younger girl; or 2) older boy, younger boy.

So the chances are only 1 out of 3 that the woman has two boys, but the chances are 1 out of 2 that the man has two boys.

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