10.
Which graph shows the following system of equations and its solution?














ows the following system of equations and its solution?

Answer:

  (x +3)^2 +(y -2)^2 = 16

Step-by-step explanation:

Complete the squares.

  (x^2 +6x) +(y^2 -4y) -3 = 0

  (x^2 +6x +9) +(y^2 -4x +4) = 16 . . . . add 9+4+3 = 16

  (x +3)^2 +(y -2)^2 = 16

_____

Additional comment

The square (x +a)^2 is (x^2 +2ax + a^2). When you have (x^2 +2ax), you complete the square by adding the square of half the x-coefficient.

Answer: neither

Step-by-step explanation:

To get rid of the fractions, we pick a useful number and multiply both sides of the equation by that number. The number is useful if multiplying eliminates all fractions.

The lengths of the segments x and y in the right triangles are x = 6√2 and y = 12√2

The given shape is the right-angled triangle

Such that

We have angles = 30 degrees and 45 degrees

The measure of y can be calculated using the following sine ratio

sin(45) = y/24

Make y the subject

So, we have

y = 24 * sin(45)

When evaluated, we have

y = 12√2

The length x is calculated as

sin(30) = x/y

So, we have

x = y * sin(30)

This gives

x = 12√2 * 1/2

Evaluate

x = 6√2

Hence, the value of x in the triangle is 6√2

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The correct value of 2f(a-1) is 2a^2 - 12a + 10.

To find the value of 2f(a-1), we need to substitute (a-1) into the function f(x) and then multiply the result by 2.

Given: f(x) = x^2 - 4x

Substituting (a-1) into the function:

f(a-1) = (a-1)^2 - 4(a-1)

Expanding and simplifying:

f(a-1) = (a^2 - 2a + 1) - (4a - 4)

f(a-1) = a^2 - 2a + 1 - 4a + 4

f(a-1) = a^2 - 6a + 5

Now, we multiply the result by 2:

2f(a-1) = 2(a^2 - 6a + 5)

Expanding:

2f(a-1) = 2a^2 - 12a + 10

Therefore, the value of 2f(a-1) is 2a^2 - 12a + 10.

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After answering the presented question, we can conclude that As a equation result, the pizza's temperature after 5 minutes is 320°F.

In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). The argument \("2x + 3 = 9," f\)or example, states that the sentence "2x Plus 3" equals the value "9." The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. In the equation\("x^2 + 2x - 3 = 0,"\)the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.

Let T(t) be the temperature of the pizza at time t, where t is in minutes. Then,

(a) Applying the Newton's Law of Cooling calculation, we get:

(T(0) - 80) / (400 - 80) = k (where k is the proportionality constant) (where k is the proportionality constant)

When we solve for k, we get:

k = (T(0) - 80) / 320

(T(3) - 80) / (400 - 80) = (T(0) - 80) / 320

T(0) = 400 - 320 * (T(3) - 80) / 320 = 400 - (T(3) - 80) = 320 + 80 = 400°F

(T(5) - 80) / (400 - 80) = (T(0) - 80) / 320

(T(5) - 80) / 320 = (400 - 80) / 320

T(5) - 80 = 3 * (400 - 80) / 4

T(5) = 3 * 320 / 4 + 80 = 240 + 80 = 320°F

As a result, the pizza's temperature after 5 minutes is 320°F.

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The total bill with the tip amount is $29.50

In this question, we have the following parameters

Tip amount = $4.50

Tip = 18% of the total bill

This means that

Total bill = Tip/18%

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

Total bill = $4.50/18%

Evaluate the quotient

Total bill = $25

The bill inclusive of the tip is then calculated as

Overall bill = Total bill + Tip amount

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

Overall bill = 25 + 4.50

Evaluate

Overall bill = 29.50

Hence, the total is $29.50

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Answer:

Perimeter of ΔABC =32.31 units

Area of the triangle ABC = 47.81 sq. unit

Step-by-step explanation:

In triangle ABC

\(\angle A = 60^{\circ}\\\angle C = 45^{\circ}\)

Angle sum property of triangle : The sum of the measures of the all angles of triangle is 180°

\(\angle A + \angle B + \angle C = 180^{\circ}\\60 + \angle B + 45 = 180\\\angle B + 105 = 180\\\angle B = 75^{\circ}\)

Now we are supposed to find the perimeter and the area of the ΔABC

We will use the sine rule to find the lengths of sides BC and AC

Sine rule : \(\frac{Sin A}{BC}=\frac{Sin B}{AC}=\frac{Sin C}{AB}\)

\(\frac{Sin 60}{BC}=\frac{Sin 75}{AC}=\frac{Sin 45}{9}\\BC \times sin(45) = 9 \times sin(60)\\ BC = 11.02\)

\(AC \times sin(45) = 9 \times sin(75)\)

AC = 12.29

Perimeter of ΔABC = AB + BC + AC

Perimeter of ΔABC = 9 + 11.02 + 12.29 =32.31 units

Area by using the sine rule:

Area of the triangle ABC =\(\frac{1}{2} (AB)(BC) sin B\)

Area of the triangle ABC =\(\frac{1}{2} (9)(11) sin(75)\)

 Area of the triangle ABC = 47.81 sq. unit

1. It is false that when non-Standard unit used is small few unit's are

needed .

2. Objects with different shapes can have the same volume. True

3. Length, width and height and multiplied to find volume of a rectangular prism. True

4. It is false that volume is measured in square unit.

5. It is true that Volume is a measure of the amount of space inside an object.

6. The formula for volume of a rectangular prism is V = l × w × h. True

7. It is true that Standard units give a consistent and accurate measure of a container.

8. It is false that Non-Standard units cannot be used to measure volume.

9. Volume is measured in cubic units. True

Volume can be defined as the amount of space inside and object. the object can be in different form such as cone, rectangular prism, cylinder and many other shapes. Even though shapes are different, It is possible for different shapes or objects to have the same volume when measure.

Measurement of volume can be through standard measurement and non standard measurements such as a cup of rice. However, for consistency and the sake of accuracy, it is advisable to always use standard measurements of volume where possible to avoid error that may occur in non standard measurement. The acceptable and recognized unit of volume is cubic meter (\(m^3\)).

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Answer:

Step-by-step explanation:

25.24

Answer: The two numbers that multiply to -65 and add to -8 are -13 and 5.

Steps: Here are the steps to find two numbers that multiply to -65 and add to -8:

Write down the equation x * y = -65 where x and y are the two numbers you’re looking for.

Write down the equation x + y = -8.

Solve for one of the variables in one of the equations. For example, solving for x in the second equation gives us x = -8 - y.

Substitute this expression for x into the first equation: (-8 - y) * y = -65.

Solve this quadratic equation for y: -y^2 - 8y + 65 = 0.

Use the quadratic formula to find the values of y: y = (-(-8) +/- sqrt((-8)^2 - 4 * (-1) * 65)) / (2 * (-1)).

This gives us two possible values for y: -13 and 5.

Substitute these values back into one of the original equations to find the corresponding values of x. For example, when y = -13, we have x = -8 - (-13) = 5. When y = 5, we have x = -8 - 5 = -13.

So, the two numbers that multiply to -65 and add to -8 are -13 and 5.

The answer is 11.

Answer:

0.090909

Step-by-step explanation:

I used a calculator

Answer:

The probability of getting a cookie with no more than 3 chips is 0.0424.

Step-by-step explanation:

Let X number of chocolate chips apiece of cookie.

The mean number of chocolate chips apiece is λ = 8.

The random variable X follows a Poisson distribution with parameter λ = 8.

Compute the probability of getting a cookie with no more than 3 chips as follows:

\(P(X\leq 3)=\sum\limits^{3}_{x=0}{\frac{e^{-8}(8)^{x}}{x!}}\)

                \(=0.00034+0.00268+0.01073+0.02863\\=0.04238\\\approx 0.0424\)

Thus, the probability of getting a cookie with no more than 3 chips is 0.0424.

The number of miles that Jose will have left after resting will be 1 1/8 miles.

Total distance to be covered = 2 3/4 miles

Distance traveled = 1 5/8 miles

Therefore, in order to get the distance that's left for Jose to complete his journey, we've to subtract the distance traveled from the total distance and this will be:

= 2 3/4 - 1 5/8

= 2 6/8 - 1 5/8

= 1 1/8

Therefore, he has 1 1/8 miles left to travel.

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ANSWER : FALSE

EXPLANATION : The sum of two complementary angles is 90°. Adding the measure of two right angles (right angles is a 90° angle) is equal to 180°.

Therefore, adding the two pairs of complementary angles is not equal to the sum of two right angles.

Answer:

$150

Explanation:

The simple interest can be calculated using the following equation

I = Prt

Where P is the principal, r is the rate as a decimal and t is the number of years.

So, replacing P = $4000, r = 5% = 0.05 and t = 3/4 years, we get:

I = ($4000)(0.05)(3/4)

I = $150

Therefore, the simple interest is $150

Answer:

60

Step-by-step explanation:

If he gave 15 grapes to his friends and he has 45 left, add 15+45 to get 60.

Initially, Takehiko has 60 grapes before sharing their grapes to his friends.

Given that,
Takehiko brought grapes to school. He gave 15 of his grapes to his friends. If he is left with 45 grapes, how many did he bring to school is to be determined

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
He gave  grapes to his friends and left with grapes, So
The total grapes he had  =  45 + 15 = 60

Thus, Initially, Takehiko has 60 grapes before sharing their grapes with his friends.

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Ants

Step-by-step explanation:

Length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

The area of Rectangle is length times of width

Given that, a rancher has 200 feet of fencing to enclose two adjacent rectangular corrals of the same dimensions.

Here, the dimensions of the rectangles are the same.

The width of the two rectangles is W=2W+2W=4W

The length of the two rectangles is L=L+L+L=3L

Because the adjacent side has a common length.

3L+4W=200

3L=200-4W

Divide both sides by 3

L=(200-4W)/3

Let us form an equation using the area of rectangle formula:

A=2LW

=2(200-4W)/3.W

A=400-8W²/3

Let us differentiate to get the area to be maximized dA/dW=0

1/3×(400-8W²)=0

1/3(400-16W)=0

400-16W=0

400=16W

Divide both sides by 16

W=25

The width is 25 feet.

Substitute W value in equation to get L value:

L=200-4×25/3

=200-100/3

=100/3

=33.33

The length is 33.33 feet.

Now let us find the maximum area

A=2LW

=2×33.33×25

=1666.66

Hence, length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

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Answer:

38.0

Step-by-step explanation:

first you divide then times

Part (a)

Answer: Constant of proportionality = 5/8

Reason:

The general template equation is y = kx where k is the constant of proportionality. It is the slope of the line.

The direct proportion line must pass through the origin. In other words, the y intercept must be zero.

=====================================

Part (b)

Answer: Not Proportional

Reason:

The y intercept isn't zero.

Plug x = 0 into the equation to find y = 1 is the y intercept. This graph does not pass through the origin.

Answer:

87.3%

Step-by-step explanation:

you got 3 candy bars. The cost for each is $0.89

So, 3 x 0.89= $2.67

Gave $5 and the difference between $2,67 is 2.33

5-2.67=2.33

The change was 2.33 and the cost was 2.67 so the % tip was

2.33/2.67= 0.873=87.3%

Answer:

Approximately 87.02% tip was left.

Step-by-step explanation:

The total cost of the three candy bars is 3 x $0.89 = $2.67.

so the total amount spent is $2.67.

You gave the cashier $5 and told them to keep the change, which is $5 - $2.67 = $2.33.

Therefore, the tip you left is $2.33.

To calculate the percentage tip:

(total cost of the three candy bars/the tip you left) x 100

which is equal to:

($2.33 / $2.67) x 100% ≈ 87.20%

So you left approximately an 87.20% tip.

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The Rule that best describes the dilation that was applied to Triangle 1 to create Triangle 2 is

B. (x, y) → (5x, 5y)

Dilation in geometry refers to a transformation that changes the size of a figure while maintaining its shape and proportionality. it is a type of transformation that expands or contracts a shape by a certain scale factor.

In this case it was a magnification or expansion by a factor of 5

This is seen by comparing the values in the table

(2 * 5, -2 * 5) results to  (10, -10)

(3 * 5, -6 * 5) results to  (15, -30)

(5 * 5, -4 * 5) results to  (25, -20)

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Answer:

This question is not complete. Let me explain the concept of combination and permutation.

Step-by-step explanation:

The general formula for factorial is n! = n×(n - 1)×(n - 2)×...×2×1

0! = 1

Example 1:

How many different words can we make using the letters D, S, K and Z?

Solution:

We have 4 letters here.

Therefore, to get the possibility of the numbers, we will use:

4! = 4 x 3 x 2 x 1 = 24. We have 24 different words that can be made with the letters.

Permutation

The general formula for permutation is n P r = n! / (n - r)!

Example 2:

Find 5 \(P_{3}\)

Solution: This will give 5!/(5-3)! = (5 x 4 x 3 x 2 x 1) / 2!

= 120 / 2 x 1 = 120 / 2 = 60

Combinations

The general formula for combination is n C r = n! / [ (n - r)! r! ]

Example 3:

Find 4\(C_{3}\)

Solution: 4\(C_{3}\) will give 4!/(4-3)!3! = (4 x 3 x 2 x 1) / 1!3!

= 24 / 1(3 x 2 x 1) = 24 / 6 = 4

Example 4: In Nigeria, the car number plate is formed by 4 digits from the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 followed by 3 letters from the alphabet. How many number plates will be formed if neither the digits nor the letters are repeated?

Solution: Note that we have 26 letters in the alphabet chart.

(9 P 4) × (26 P 3) = 9!/(9-4)! x 26!/(26-3)! = 47,174,400

The length of u, to the nearest inch, is 1818 inches.

To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.

In this case, we'll use the following formula:

a/sin(A) = b/sin(B) = c/sin(C)

Let's label the sides and angles of the triangle:

Side a = u (length of u)

Side b = t (820 inches)

Side c = v (length of v)

Angle A = m/U (132°)

Angle B = m2V (25°)

Angle C = 180° - A - B (as the sum of angles in a triangle is 180°)

Now, we can use the Law of Sines to set up the equation:

u/sin(A) = t/sin(B)

Plugging in the given values:

u/sin(132°) = 820/sin(25°)

To find the length of u, we'll solve this equation for u.

u = (820 \(\times\) sin(132°)) / sin(25°)

Using a calculator, we can evaluate the right side of the equation to get the approximate value of u:

u ≈ (820 \(\times\) 0.9397) / 0.4226

u ≈ 1817.54 inches

Rounding to the nearest inch, we have:

u ≈ 1818 inches

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Answer:

x0 is the answer I just did that question and got it right

Answer:  Answer is in the steps

Step-by-step explanation:

If we given the angle measure in variables then we will sum them up equal 180 and solve for x to determine the angle measure.

9x + x  +x+4 = 180  

   11x + 4 =  180

            -4   -4

11x = 176

x=16  

In this  case we can find the angle measures by using the expressions.

x = 16  degrees

x+4 =  20 degrees

9x =  144 degrees  

well, to get the equation of a line all we need is two points, so let's simply pick two points off the table, hmmmm say (1 , -3) and hmmm (11 , -43)

\((\stackrel{x_1}{1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{11}~,~\stackrel{y_2}{-43}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-43}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{11}-\underset{x_1}{1}}}\implies \cfrac{-43+3}{10}\implies \cfrac{-40}{10}\implies -4\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{-4}(x-\stackrel{x_1}{1}) \\\\\\ y+3=-4x+4\implies y=-4x+1\)

A digit to make the number divisible by 3 is by adding the digit 2 to the number 1234.

To make the number 1234 divisible by 3, we can find the sum of its digits and determine if it is divisible by 3. If the sum of the digits is divisible by 3, then the original number is also divisible by 3.

Let's calculate the sum of the digits in 1234:

1 + 2 + 3 + 4 = 10

The sum of the digits is 10. Since 10 is not divisible by 3, we need to add or subtract a digit to make the sum divisible by 3.

To find the digit we need to add or subtract, we can use the fact that the difference between the original sum and the next multiple of 3 is the required digit.

The next multiple of 3 greater than 10 is 12 (12 - 10 = 2). Therefore, we need to add 2 to the number 1234 to make it divisible by 3.

1234 + 2 = 1236

we obtain the number 1236, which is divisible by 3.

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Answer:

$3040 profit made

Step-by-step explanation:

$13×95=$1235 cost to make all the shoes they sold

$45×95=$4275 money she made

$4275-$1235=$3040 profit

Answer: 66%

Step-by-step explanation: To convert a fraction to a percentage, divide the top number by the bottom number. For example, \(\frac{1}{4}\) is 25% because if divide them, (1÷4=0.25) then we get 25%. So, for this problem, we solve 2÷3, which equals 0.66, or 66%.

hope this helps!

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