2x - 5y = 2
3x + 2y = -16

Answer:

ab=48

Step-by-step explanation:

96/2=48

Hello!

The mean is the average of the terms.

⇒ Mean = Sum of terms / Number of terms

⇒ 130 = 104 + 137 + 154 + 131 + x / 5

⇒ x + 526 = 650

⇒ x = 124

∴ The missing number is 124.

The range for the length of the third side is it must be greater than 10 feet and less than 30 feet.

The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. That sum can equal the length of the third side only in the case of a degenerate triangle, one with collinear vertices.

The length of the third side had to be greater than the difference between the two given sides and less than the sum of the two given sides.

(20 – 10) < S <(20+ 10) ; 10< S < 30

Therefore, the range for the length of the third side is it must be greater than 10 feet and less than 30 feet.

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A triangle is a three-edged polygon with three vertices. Only the law of Sine can be applied to solve the triangle.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

The sum of all three angles can be written as,

118° + 22° + x = 180°

x = 40°

For the sine rule to be applicable, two angles and a side or an angle and two sides are needed. Therefore, the law of Sine can be applied to solve the triangle.

For the cosine rule to be applicable, two sides and an angle between them is needed to be known, hence, the law of cosine can not be applied.

Hence, Only the law of Sine can be applied to solve the triangle.

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Answer:

The inverse is  -1/7(x+4)

Step-by-step explanation:

We have the function

y = -7x-4

To find the inverse, exchange x and y

x = -7y -4

Solve for y

Add 4 to each side

x+4 = -7y -4+4

x+4 = -7y

Divide each side by -7

-1/7(x+4) = -7y/-7

-1/7(x+4) = y

The inverse is  -1/7(x+4)

Answer:

The given relation [tex]$\{(a, b),(c, d),(e, d)\}$[/tex] is a function.

Step-by-step explanation:

A relation [tex]$\{(a, b),(c, d),(e, d)\}$[/tex] is given.

It is required to determine whether the given relation is a function.

To determine whether the given function is a relation, identify the domain and range and then check whether the given relation is a function.

Step 1 of 1

The given relation is {(a, b),(c, d),(e, d)}.

The set of the first components of each ordered pair is called the domain.

From the relation, the domain is {a, c, e}.

The set of the second components of each ordered the range.

From the relation, the range is {b, d, d}.

The given relation is a function. But it is not a one-to-one function.

Answer:

H)

Step-by-step explanation:

First, Length XY is 20 centimeters. Since YZ = 3/5 XY, [tex]\frac{3}5\times20=12[/tex]

YZ = 12 + 20 = 32 cm, hence H)

Hope you have a nice day! (Pls mark brainliest)

The triangle with base 14, sides 12 and 6, will have an area, a = (1/2)(14)(5) = 35 square units. Hence, the 3rd option is the correct choice.

The area of a plane figure is the space occupied within its boundary.

The area of a triangle is given as,

a = (1/2)(b)(h) sq. units, where a is the area of the triangle, b is its base, and h is its height.

In the question, we have been given a triangle with a base of 14, sides 12 and 6, and a height of 5.

We are asked to determine the area of this triangle.

To determine the area of the triangle, we will use the formula:

a = (1/2)(b)(h) sq. units, where a is the area of the triangle, b is its base, and h is its height.

Now, we are given that the base is 14 and the height is 5, thus substituting b = 14, and h = 5, in the above formula, we get:

a = (1/2)(14)(5) sq. units.

or, a = 35 sq. units.

Comparing this with the given options, we can choose the third option.

Thus, the triangle with base 14, sides 12 and 6, will have an area, a = (1/2)(14)(5) = 35 square units. Hence, the 3rd option is the correct choice.

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The domain and the range of the function are all set of real numbers

The function is given as:

f(x) = 4x + 3

The above function is a linear function

Linear functions have a domain and a range of all set of real numbers

Hence, the domain and the range of the function are all set of real numbers

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[tex]x - 3y = 15 \\ x = 15 + 3y[/tex]

[tex](15 + 3y) {}^{2} + y {}^{2} = 25[/tex]

[tex]225 + 90y + 9y {}^{2} + y {}^{2} = 25[/tex]

[tex]10y {}^{2} + 90y + 200 = 0[/tex]

[tex]y {}^{2} + 9y + 20 = 0[/tex]

[tex](y + 4)(y + 5) = 0[/tex]

[tex]y = - 4 \: \: \: \: \: \: y = - 5[/tex]

[tex]for \: y= - 4 \\ x = 15 + 3( - 4) = 15 - 12 = 3[/tex]

[tex]for \: y = - 5 \\ x = 15 + 3( - 5) = 15 - 15 = 0[/tex]

Answer:

a ≈ 4.9

Step-by-step explanation:

using the Cosine Rule in Δ ABC

a² = b² + c² - (2bc cosA )

   = 16² + 18² - (2 × 16 × 18 × cos15° )

   = 256 + 324 - (576cos15° )

   = 580 - 576cos15

   = 23.6267 ( take square root of both sides )

a = [tex]\sqrt{23.6267}[/tex]

   ≈ 4.9 ( to the nearest tenth )

No, we cannot claim that the population mean breaking strength of the newly- manufactured cables is greater than pounds.

Given mean=1900, standard deviation=65, sample size=150, sample mean=1902, level of significance=0.01.

The hypothesis are:

[tex]H_{0}:\\[/tex]μ=1900

[tex]H_{1}:[/tex]μ>1900

We have to use z test as the sample size is large and we know the population standard deviation.

z=(x-μ)/σ/[tex]\sqrt{n}[/tex]

z=(1902-1900)/65/[tex]\sqrt{150}[/tex]

z=0.38

finding the p value:

p value=P(Z>z)

=P(Z>0.38)

=1-P(Z<0.38)

from the z table we get;

P(Z<0.38)=0.6480

Therefore p value=1-0.6480

=0.3520

If the p value is less than 0.01 then we reject the [tex]H_{0}[/tex] otherwise we will reject the null hypothesis.

In this problem we also reject the null hypothesis.

Hence  we cannot claim that the population mean breaking strength of the newly- manufactured cables is greater than pounds.

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Question is incomplete. It should includes:

 mean=1900,

standard deviation=65,

sample size=150,

sample mean=1902,

level of significance=0.01.

The mean score of class B is 82. 92

Class A = 30 pupils

Class B = 26 pupils

Mean score for class A = 70

Mean score of class B = unknown

Total mean score = 76

We have, [tex]\frac{(76 *( 30 + 26) - 70 *30) }{26}[/tex]

Then simply,

Calculate the sum or difference between the classes = [tex]\frac{76 * 56 - 70 * 30}{26}[/tex]

Calculate the product or quotient of the classes = [tex]\frac{4256 - 70 * 30}{26}[/tex]

= [tex]\frac{4256 - 2100}{26}[/tex]

= [tex]\frac{2156}{26}[/tex]

= [tex]\frac{1078}{13}[/tex]

= [tex]82. 92[/tex]

Thus, the mean score of class B is 82. 92

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The equation that can be used to find the proportion to use to solve side LM is 9/13.5 = 14/LM

In order to find the measure of LM, we will take the ratio of the sides of the similar triangles.

Using the equation as shown

DF/EF = LK/LM

DF/LK = EF/LM

Substitute the measure of the sides

9/13.5 = 14/LM

Hence the equation that can be used to find the proportion to use to solve side LM is 9/13.5 = 14/LM

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The larger angle is 55 deg at the larger angle.

We have to know which angles are called Complementary Angles...

if we add two angles and the total will be equal to 90 deg

let's say one angle is x and  another angle is  y

as they are complementary angles from the definition we can write the equation x + y =  90

one angle is 20 deg more  than another one  so from the above condition  we write x = 20 + y

Substitute the value of x  in the first eaquation we get, 20 + y + y =  90

Then,  20 + 2y =  90

subtracting 20 from both sides,

 2y  =  90-20 = 70  

 dividing both sides by 2,

2y/ 2 = 70 / 2

 y  =  35

 So we got one angle is 35 deg

another angle is  35 + 20 = 55 deg.

Our answer is 55 deg the larger angle.

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The length of AL in the triangle is 12cm.

From the information given, angle C = 90° and BAC is given as 2ABC.

In this case, the length of angle BC is given as 24cm. Therefore, the length of AL will be:

= 24/2

= 12..

Therefore, AL = 12cm

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If we want to replace a input and display an output greater than 10⁹ in Susan's calculator, then we want at least 3 consecutive operations.

In accordance with the statement, Susan's calculator performs the following operation by pressing the "cubing" key:

x → x³

If we need to display a number that is greater than 10⁹, then we need to press the "cubing" key as many as needed. By algebra we have the following property for a power:

[tex](x^{m})^{n} = x^{m\cdot n}[/tex]     (1)

Since we have a "cubing" key and we are supposed to make consecutive operation, we derive the following operation:

x → [tex]x^{3^{i}}[/tex], where i is the number of consecutive "cubing" operations.

If we want to replace a input and display an output greater than 10⁹ in Susan's calculator, then we want at least 3 consecutive operations.

The statement presents typing mistakes, correct form is shown below:

Susan's calculator has a key that replaces the number displayed with its cube. If a³, is displayed, how many time must Susan press the "cubing" key to display a number that is greater than 10⁹.

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The statement that proves that that quadrilateral JKLM is a kite is: (Option B) which indicates that:
LM = MJ = 3; a

JK = KL = √17

We know the following:

J = (4,5)

K = (5,1)

L = (1,2)

M = (1, 5)

We must commence by computing the length of the sides of the quadrilateral using:

D = [tex]\sqrt{((x1-x2)^{2} + (y1 -y2)^{2} }[/tex]

JK = [tex]\sqrt{(4-5)^{2} + (5-1)^{2} }[/tex]

= [tex]\sqrt{17}[/tex]

KL = [tex]\sqrt{(5-1)^{2} + (1-2)^{2} }[/tex]

= [tex]\sqrt{17}[/tex]

LM = [tex]\sqrt{(1-1)^{2} + (5-5)^{2} }[/tex]

= [tex]\sqrt{9}[/tex]

= 3

MJ = [tex]\sqrt{(1-4)^{2} + (5-5)^{2} }[/tex]

= [tex]\sqrt{9}[/tex]

= 3

From the above, it is clear that

LM = MJ = 3; and

JK = KL = [tex]\sqrt{17}[/tex]

QED

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Answer: B

Step-by-step explanation:

Answer:

Answer is in the 2nd attachment

Step-by-step explanation:

the first attachment is the work done.

The area of the composite shape is 136 square cm

The area of the composite function is expressed as;

Area = area of triangle + area of rectangle

Area of the composite shape = (1/2* 4 * 5) + (7*18)

Area of the composite shape = 10 + 126

Area of the composite shape = 136 square cm

Hence the area of the composite shape is 136 square cm

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Answer:

(-5,7) (5,-7)

Step-by-step explanation:

When you are told to lable, show or name the points that lie on a horizontal line, it basically means that; when a line is drawn, it passes through the selected points without changing the direction when joined together (horizontally).

From the above problem, (-5,7) and (5,-7) lie in the same horizontal line.

For (7,-5) and (-7,5) lie in the same vertical line.

Thereforeour, the answer is (-5,7) (5,-7).

The simplification that represents ∛7=[tex]7^{1/3}[/tex] is [tex](7^{1/3} )^{3} =7^{1/3} .7^{1/3} .7^{1/3} =7^{1/3+1/3+1/3} =7^{1}=7[/tex]

The simplification that accurately explains the statement ∛7 = [tex]7^{1/3}[/tex] is as follows;

Therefore, the simplification is as follows

[tex](7^{1/3} )^{3} =7^{1/3} .7^{1/3} .7^{1/3} =7^{1/3+1/3+1/3} =7^{1}=7[/tex]

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The sample space is a combination of these two dice as we have shown in the attachment

This is the defined to be the set of all of the possible outcomes that can exist or be possible in a random experiment.

The question has two dice. These dice are made up of numbers from 1 to 6  each.

Die A = {1,2,3,4,5,6}

Die b = {1,2,3,4,5,6}

The sample space would be pairs of two of these two dices. The total number in the sample space would be 36.

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The graph that shows y=3⌈x⌉ + 1 from the given options is the Third graph as shown attached.

The third graph shows the function and this can be tested as follows:

When x = 2, y = 7:

y = 3x + 1

= 3 x 3 + 1

= 7

When x = 3, y = 10:

y = 3 x 3 +1

= 10

When x = 1, y = 4

y = 3 x 1 + 1

= 4

This shows that the line on the third graph is well represented by the function, y=3⌈x⌉+1.

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The interval on the number line is (-∞, 2) U [3, ∞)

From the number line, we have the following inequalities

x < 2 and x ≥ 3

In inequalities, < and > are represented by brackets i.e. ( and )

While ≤ and ≥ are represented by square brackets i.e. [ and ]

So, we have:

x < 2 and x ≥ 3 = 2) and [3

The intervals must be closed and opened with infinity symbols.

So, we have:

x < 2 and x ≥ 3 = (-∞, 2) and [3, ∞)

Replace and with U

x < 2 and x ≥ 3 = (-∞, 2) U [3, ∞)

Hence, the interval on the number line is (-∞, 2) U [3, ∞)

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Step-by-step explanation:

the area is

(x² + 17x + 72) m²

it is the result of the usual

length × width

calculation.

length = x + g

width = x + h

length × width = x² + gx + hx + ab = x² + (g+h)x + gh =

= x² + 17x + 72

g + h = 17

gh = 72

just by looking at it that gives us 9 and 8 as g and h.

FYI - formally to calculate them we can say

g = 17 - h

(17 - h)h = 72

17h - h² = 72

h² - 17h + 72 = 0

the solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = h

a = 1

b = -17

c = 72

h = (17 ± sqrt(17² - 4×1×72))/(2×1) =

= (17 ± sqrt(289 - 288))/2 = (17 ± 1)/2

h1 = (17 + 1)/2 = 18/2 = 9

h2 = (17 - 1)/2 = 16/2 = 8

as we can see

g = 17 - h

if we say h = 9, then g = 8.

if we say h = 8, then g = 9.

so, these are our solutions.

we simply pick that length is longer than width, so, g = 9, h = 8.

the area including the walkway is then

(length + 3)(width + 3) =

= (x + 9 + 3)(x + 8 + 3) = (x + 12)(x + 11) m²

and the dimensions incl. the walkway are

length = x + 9 + 3 = x + 12

width = x + 8 + 3 = x + 11

Answer:

If compounding = rs 11547.36

If not compounding = rs 11484

For the function f(x) = -3|x - 2| - 1, we have that:

The x-intercept of a function is the value of x when y = f(x) = 0, hence:

0 = -3|x - 2| - 1

-3|x - 2| = 1

|x - 2| = -1/3

The absolute value cannot be negative, hence the function has no x-intercepts.

The x-intercept of a function is the value of y = f(x) when x = 0, hence:

f(0) = -3|0 - 2| - 1 = -6 - 1 = -7.

The y-intercept is of y = -7.

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