At the beginning of the day, Hasim counted his money. He gave his brother 1/3 of his money. He spent £12 on a present for his sister. He then counted what he had left, and it was half what he had at the beginning of the day. How much did he give his brother? Show your method.

Answer:

y + 4= -3(x + 1)

y = -3x - 7

Step-by-step explanation:

Step-by-step explanation:

as it is a right angled triangle ,you can use the formula above .

The graph of y=3x^4-16x^3+24x^2+48 is concave down for x values greater than or equal to 0.

The graph of y=3x^4-16x^3+24x^2+48 is an example of a polynomial function. To determine the concavity of a polynomial function, we must first identify the intervals where the function is increasing and decreasing. In this case, the function is increasing for all x values greater than or equal to 0.

Next, we must find the second derivative and determine the intervals where the second derivative is negative. If the second derivative is negative, then the graph is concave down. For this polynomial, the second derivative is y'' = -48x + 48, which is negative for all x values greater than or equal to 0. This means that the graph of y=3x^4-16x^3+24x^2+48 is concave down for all x values greater than or equal to 0.

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Janet should multiply both sides of the equation by the denominator of the fraction to eliminate the fraction on the right side,

To solve this equation, Janet needs to find the value of "y" that makes the equation true. In order to do this, she needs to get all of the terms with "y" on one side of the equation and all of the constants on the other side.

One way to do this would be to multiply both sides of the equation by the denominator of the fraction on the right side. This will eliminate the fraction on the right side and give Janet an equation with only one term on each side. The denominator of the fraction on the right side is (y+1), so Janet should multiply both sides of the equation by (y+1).

This will give her the equation:

(y+1)(y+startfraction y squared minus 5 over y squared minus 1 end fraction) = (y+1)(start fraction y squared + y + 2 over y + 1 end fraction)

Multiplying out the terms on each side will give Janet a polynomial equation in "y" that she can solve using standard techniques.

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Answer:

[tex]\Huge \boxed{\boxed{\bf{-150.69}}}[/tex]

Step-by-step explanation:

To simplify the expression, we can follow the order of operations (also known as PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders, Multiplication/Division, and Addition/Subtraction.

[tex]\Large \boxed{\bf{-15 + (-16 + 9.34/6) \times 3^2 - 5.7}}[/tex]

First, let's simplify the expression inside the parentheses:

Next, let's simplify the exponent:

Now, let's simplify the addition and subtraction within the parentheses:

Next, let's perform the multiplication:

Now, let's perform the addition and subtraction from left to right:

Finally, subtract the two numbers:

Therefore, the simplified expression is -150.69.

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________________________________________________________

The angles of the parallelogram are

The measure of ∠A = 4y° = 108°

The measure of ∠B = ( 3x - 18 )° = 72°

The measure of ∠C = 3z° = 108°

The measure of ∠D = ( 2x + 12 )° = 72°

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as ABCD

where

The measure of ∠A = 4y°

The measure of ∠B = ( 3x - 18 )°

The measure of ∠C = 3z°

The measure of ∠D = ( 2x + 12 )°

From the parallelogram theorem , we get

The measure of ∠B = The measure of ∠D   be equation (1)

And ,

The measure of ∠A = The measure of ∠C   be equation (2)

Substituting the values in the equation , we get

( 3x - 18 )° = ( 2x + 12 )°  

3x - 18 = 2x + 12

Adding 18 on both sides of the equation , we get

3x = 2x + 30

Subtracting 2x on both sides of the equation , we get

x = 30

Substituting the value of x in equation ( 1) , we get

3x - 18 = 3 ( 30 ) - 18

The measure of ∠A = 72°

So , the measure of ∠B = the measure of ∠D = 72°

And ,

The measure of ∠A = The measure of ∠C   be equation (2)

So , 4y° = 3z°

The total internal angle = 360°

So , 4y° + 3z° = 360° - 72° - 72°

4y° + 3z° = 216°   be equation (3)

From equation (2) , we get

2 ( 4y° ) = 216°

Divide by 2 on both sides of the equation , we get

( 4y ) ° = 108°

So , y = 27

And , ( 3z )° = 108°

So , z = 36

And , The measure of ∠A = The measure of ∠C = 108°

Hence , the measures of the angles of the parallelogram are 108° , 72° ,  108° and 72°

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Answer:

y = -4x + 9

Step-by-step explanation:

y = mx + b

First, we will find 'm', aka slope,

([tex]y_{2}[/tex] - [tex]y_{1}[/tex] ) / ([tex]x_{2}[/tex] - [tex]x_{1}[/tex]) = m

(-7 -7)/ (4 - (-3)) = m

-14/ 7 = m

∴ m = -2

Then we can substitute m = -2 and point 1 in to find 'b', aka y-intercept,

7 = -2 (-3) + b

7 = 6 + b

7 - 6 = b

∴ b = 1

Hence the equation is,

y = -2x + 1

Answer:

.3 x 500 = 150 = answer

Step-by-step explanation:

multiply the numbers

The equation of the sphere with center (6, 4, 9) that just touches the xy-plane is (x - 6)^2 + (y - 4)^2 + (z - 9)^2 = 0.

To find the equation of the sphere with center (6, 4, 9) that just touches the xy-plane, we can first find the equation of the xy-plane and then use the point-normal form of the equation of a sphere to find the desired equation.

The equation of the xy-plane is z = 0. Now, we can use the point-normal form of the equation of a sphere, which is

(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2,

where (h, k, l) is the center of the sphere and r is the radius of the sphere. Since the sphere is just touching the xy-plane, the z-coordinate of the center is equal to 0, so the equation of the sphere can be written as (x - 6)^2 + (y - 4)^2 + (z - 0)^2 = r^2.

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Answer:

Step-by-step explanation:

Statistical models can help people make informed decisions by providing them with the likelihood of success so that they can make decisions that are informed and are knowledgeable of the outcomes.

Answer:

I am not sure I hope this helps!

Selling price- $500.00

Rate of discount- 20%

Discount- $100.00 (20% of $500.00)

Sale price- $400.00 ($500.00 - $100.00)

100 meters was he under the sea at the end of the 10 minutes. This can be solved using the concept of multiplication.

Along with addition, subtraction, and division, multiplication is one of the four fundamental mathematical operations. Multiply in arithmetic refers to the continuous addition of equal-sized groups.

Multiplication in mathematics is the addition of equal groups. The number of items there in group expands while we multiply. An example of a multiplication issue would be the product and the two components. The components in the multiplication problem 8 x 9 = 72 are the numbers 8 and 9, while the result is the number 72.

At the end of 10 minutes, the deep-sea diver would have been at a depth of 100 meters under the sea.

This is because 10 meters per minute multiplied by 10 minutes

=  100 meters.

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Step-by-step explanation:

y1(1) = 1 = A + B

y2(1) = e = C + D

Answer:

Add 3 to both sides

Divide -9 from each side

Step-by-step explanation:

-9d - 3 = -12

      +3 = +3

-9d = -9

then, divide each side by -9 and you have your answer

Hope that helps!

Answer:

Add 3 to both sides

Divide both sides by -9

Step-by-step explanation:

-9d -3 = -12

-9d - 3 + 3 = -1 + 3  Add 3 to both sides

-9d = -9  Divide both sides by -9

[tex]\frac{-9d}{-9}[/tex] = [tex]\frac{-9}{-9}[/tex]

d = 1

Answer:

Simplify the following:

(10 x)^(-3)

Multiply each exponent in 10 x by -3:

1/(10^3 x^3)

10^3 = 1000:

Answer: 1/(1000 x^3)

Step-by-step explanation:

The relationships between the angles x and y are given as follows:

Alternate interior angles. and Alternate exterior angles.

Vertical angles are angles that are on the opposite by the same vertex, and in item 1, the vertex is the intersection of the upper parallel line with the transversal, hence angles x and y are vertical angles.

Alternate Interior angles;

These are the angles that are on the inner side of the two parallel lines but on opposite sides relative to the transversal, therefore, on item 2 x and y are alternative interior angles.

The Corresponding angles are angles that are on the same position relative to the transversal line, but relative to different parallel lines, thus on item x and y are corresponding angles.

Alternate Exterior angles;

There are angles that are on the opposite sides of the transversal line, and one above the upper parallel line and the other below the lower parallel line, shows that angles x and y are alternate exterior angles in item 4.

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The commutative property of addition states that when two numbers are added together, the sum is the same regardless of the order in which the numbers are added. This means that for any two numbers a and b, a + b = b + a.

The commutative property of addition states that for any two numbers a and b, a + b = b + a. This means that when two numbers are added together, the sum is the same regardless of the order in which the numbers are added. For example, in the expression 3 4i + 5 6i, the sum is the same whether we add 3 4i and 5 6i or 5 6i and 3 4i. Thus, the commutative property of addition is demonstrated.

3 4i + 5 6i = 8 10i

5 6i + 3 4i = 8 10i

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In expression 3 + 4i + 5 + 6i = 3 + 5 + 4i + 6i the Commutative property of addition is used.

Consider the given mathematical expression,

3 + 4i + 5 + 6i = 3 + 5 + 4i + 6i

We can observe that the position of 4i and 5 is switched.

We know that the Commutative property of addition.

For any two numbers a, b the commutative property of addition:

a + b = b + a

So for numbers 4i and 5, by the Commutative property of addition,

4i + 5 = 5 + 4i                     ............(1)

3 + 4i + 5 + 6i

= 3 + (4i + 5) + 6i

= 3 + (5 + 4i) + 6i                .................(from (1))

= 3 + 5 + 4i + 6i

Therefore, 3 + 4i + 5 + 6i = 3 + 4i + 5 + 6i, by Commutative property of addition.

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Answer:

x = 17.6

Step-by-step explanation:

This is a right triangle.

To find the value of x, the length of the hypotenuse, we write the following equation using Pythagoras theorem:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] {12}^{2} + {13}^{2} = {x}^{2} [/tex]

[tex]144 + 169 = {x}^{2} [/tex]

[tex]313 = {x}^{2} [/tex]

x = 17.6 approximately

The probability that Marta makes at least 2 of the 3 free throws is 0.73.

1. Marta makes all three free throws :

Probability of making one free throw = 0.90 (90%)

Chance of converting all three free throws =  [tex]\(0.90 \times 0.90 \times 0.90\)[/tex]

2. Marta makes two free throws and misses one

Probability of making one free throw = 0.90 (90%)

Missing one free throw has a probability = 1 - 0.90

                                                              = 0.10 (10%)

Probability of making two free throws and missing one

[tex]=\(0.90 \times 0.90 \times 0.10 + 0.90 \times 0.10 \times 0.90 + 0.10 \times 0.90 \times 0.90\)[/tex]

3. Marta makes one free throw and misses two (OXO, OOX, XOO):

Probability of making one free throw = 0.90 (90%)

Missing one free throw has a probability = 1 - 0.90

                                                              = 0.10 (10%)

Probability of making one free throw and missing two

= [tex]\(0.90 \times 0.10 \times 0.10 + 0.10 \times 0.90 \times 0.10 + 0.10 \times 0.10 \times 0.90\)[/tex]

Now, add the probabilities of all these scenario

[tex]\[\text{Probability of making at least 2 free throws} \\= \text{Probability of making all three} \\+ \text{Probability of making two and missing one} \\+ \text{Probability of making one and missing two}\][/tex]

= 0.729

Thus, the probability is 0.73.

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Answer:

hard question

Step-by-step explanation:

An equivalent fraction with a rational denominator can multiply the original fraction by a fraction with a rational denominator.

To produce an equivalent fraction with a rational denominator, you can multiply the original fraction by a fraction with a rational denominator. For example, if the original fraction is [tex]$\frac{3}{5}$[/tex] , you can multiply it by [tex]$\frac{2}{2}$[/tex]  to get the equivalent fraction [tex]$\frac{3 \cdot 2}{5 \cdot 2} = \frac{6}{10}$[/tex]  . The denominator of this equivalent fraction, 10, is a rational number.

In general, to produce an equivalent fraction with a rational denominator, you can multiply the original fraction by a fraction with a rational denominator. The specific fraction you choose will depend on the desired denominator.

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Multiplying [tex]\frac{3}{\sqrt{17}-\sqrt{2} }[/tex] by  [tex]\frac{\sqrt{17}+\sqrt{2}}{5}[/tex] will produce an equivalent fraction with a rational denominator.

Consider given  expression [tex]\frac{3}{\sqrt{17}-\sqrt{2} }[/tex]

First we rationalize a denominator of  fraction [tex]\frac{3}{\sqrt{17}-\sqrt{2} }[/tex]

To rationalize the denominator, multiply and divide the expression by [tex]{\sqrt{17}+\sqrt{2} }[/tex]

So given fraction would be,  

[tex]\frac{3}{\sqrt{17}-\sqrt{2} }\\\\= \frac{3\times (\sqrt{17}+\sqrt{2})}{(\sqrt{17}-\sqrt{2})\times (\sqrt{17}+\sqrt{2}) }\\\\= \frac{3\times (\sqrt{17}+\sqrt{2})}{(\sqrt{17}^2-\sqrt{2}^2) }\\\\ = \frac{3\times (\sqrt{17}+\sqrt{2})}{(17-2) }\\\\= \frac{3\times (\sqrt{17}+\sqrt{2})}{15 }\\\\= \frac{3\times (\sqrt{17}+\sqrt{2})}{3\times 5 }\\\\= \frac{\sqrt{17}+\sqrt{2}}{5 }[/tex]

Therefore, the required fraction is:  [tex]\frac{\sqrt{17}+\sqrt{2}}{5}[/tex]

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A complete question is:

Multiplying 3/sqrt 17 - sqrt 2 by which fraction will produce an equivalent fraction with a rational denominator

The midpoint of the line segment is (4, -3).

The slope of the line segment is -2/5.

The equation of the perpendicular bisector is y = 5/2x - 13.

To find the equation of the perpendicular bisector of a line segment, we need to determine two things:

The midpoint of the line segment and the slope of the perpendicular bisector.

Midpoint:

The midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by the formula:

[(x₁ + x₂) / 2, (y₁ + y₂) / 2]

Using the endpoints (-1, -1) and (9, -5), we can find the midpoint:

x = (-1 + 9) / 2 = 4

y = (-1 - 5) / 2 = -3

Slope:

The slope of the line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Using the endpoints (-1, -1) and (9, -5), we can find the slope:

m = (-5 - (-1)) / (9 - (-1))

= (-5 + 1) / (9 + 1)

= -4 / 10

= -2 / 5

Perpendicular Bisector:

The slope of the perpendicular bisector will be the negative reciprocal of the slope of the line segment.

The slope of the perpendicular bisector will be 5/2.

Using the midpoint (4, -3) and the slope 5/2, we can find the equation of the perpendicular bisector using the point-slope form:

y - y₁ = m(x - x₁)

Plugging in the values, we have:

y - (-3) = 5/2(x - 4)

y + 3 = 5/2(x - 4)

y + 3 = 5/2x - 10

y = 5/2x - 10 - 3

y = 5/2x - 13

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A linear function which has the greatest y-intercept include the following: D. y = 3x + 4

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Based on the information provided regarding the equations and graphs, the y-intercept are as follows:

Therefore, y = 3x + 4 is a linear function with the greatest y-intercept.

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Complete Question:

Which linear function has the greatest y-intercept?

y = 6x + 1

On a coordinate plane, a line goes through points (0, 2) and (5, 0).

On a coordinate plane, a line goes through points (1, 2) and (0, negative 3).

y = 3x + 4

The required area of the rectangular floor and square yards needed are given as 270 ft² and 30 respectively.

A rectangle is a type of parallelogram having equal diagonals.

All the interior angles of a rectangle are equal to the right angle.

The diagonals of a rectangle do not bisect each other.

The dimensions of the floor are given as 15 feet and  18 feet respectively.

(a) The carpet required is equivalent to the area of the floor given as,

Area of floor = 15 × 18

⇒ 270 ft²

(b) Since, 1 feet = 3 yard

⇒ 1 square feet = 9 square yard.

Then, the number of square yards required is given as,

⇒ 270 ÷ 9 = 30

Hence, the area of the floor and number of square yards are 270 ft² and 30 respectively.

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Answer:

(0, 1)

Step-by-step explanation:

Basically, substitute the x and y coordinates into the inequality and check whether the solution tallies with the inequality given.

y < 6x + 2 is the equation provided.

For (-1, 0) , when x = -1 , y = 0 , 0 < 6(-1) + 2     -> 0 < -4 (False)

For (1, 8) , when x = 1, y = 8, 8 < 6(1) + 2      ->  8 < 8 (False)

For (0, 1) , when x = 0, y = 1, 1 < 6(0) + 2      ->  1 < 2 (True)

For (2, 15) , when x = 2, y = 15, 15 < 6(2) + 2      ->  15 < 14 (False)

Hence, the only coordinate that satisfies the inequality is (0, 1)

Answer:

Step-by-step explanation:

1.4

Answer:

1 2/5

Step-by-step explanation:

simplified: 1.4

The value of a and b are 9 and 14 when the two triangle ΔJHK congruent to ΔTRS.

Given that,

We have two triangle. ΔJHK congruent to ΔTRS

We must evaluate what a and b are worth.

We know that,

In the picture we have two triangle

ΔJHK has ∠H = 51° and ∠K = 7b-15

ΔTRS has ∠S= 83° and ∠T = 6a-3

When all three corresponding sides are the same length and all three corresponding angles are the same size, two triangles are said to be congruent.

We have ∠ H ≅ ∠ T,

∠ J ≅ ∠ R and

∠ K ≅ ∠ S.

So,

∠ H ≅ ∠ T,

51°=6a-3

6a=51+3

6a =54

a=9

∠ K ≅ ∠ S.

7b-15=83

7b=83+15

7b=98

b=14

Therefore, The value of a and b are 9 and 14 when the two triangle ΔJHK congruent to ΔTRS.

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the values or root of x and y. are

• x = 9

• y = 6√2

The right triangles are all similar, so the ratios of hypotenuse to short side are the same:

27/x = x/3

x^2 = 81 . . . . . multiply by 3x

x = 9 . . . . . . . . take the square root

Then y can be found from the Pythagorean theorem:

x^2 = y^2 + 3^2

81 - 9 = y^2 = 72 . . . . . subtract 9

y = √72 = 6√2 . . . . . . .take the square root

The values of x and y are 9 and 6√2, respectively.

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Answer:

y=37

Step-by-step explanation:

-8 + (y+3) =32

-8+y+3=32

-5+5+y=32+5

y=37

The required length of LM and LK are given as 4.709 cm and 3.151 cm respectively.

These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.

Here,
Let LM = x and LK = y

Applying trig operators,

(1)

tan48 = 3.5 / y
y = 3.5 / tan48
y =  3.151 cm

(2)

sin48 = 3.5 / x
x = 3.5/sin 48
x = 4.709 cm

Thus, the required length of LM and LK are given as 4.709 cm and 3.151 cm respectively.

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