Ifyou are asked to solve a system ofequations in which there is no linear equation to start with, you can sometimes begin by isolating and substituting a variable that is squared in both equations.

Answer:

16 units

Step-by-step explanation:

The area of a rhombus is given by the formula A = bh.  The base would be CB and the height would be DP.  We will use the distance formula to find the length of each:

[tex]d=\sqrt{y_2-y_1)^2+(x_2-x_1)^2}[/tex]

For CB, we have

[tex]d=\sqrt{(2-0)^2+(3--1)^2}=\sqrt{2^2+4^2}=\sqrt{4+16}=\sqrt{20}[/tex]

For DP we have

[tex]d=\sqrt{(2--1.2)^2+(-5--3.4)^2}=\sqrt{3.2^2+1.6^2}=\sqrt{10.24+2.56}=\sqrt{12.8}[/tex]

This makes the area of the rhombus

[tex]A=bh=\sqrt{20}\times \sqrt{12.8}=\sqrt{20\times 12.8}=\sqrt{256}=16[/tex]

The area of a rhombus can be found using the formula (diagonal1 * diagonal2) / 2. In this case, the area is 24 cm^2.

The area of a rhombus can be found using the formula:

Area = (diagonal1 * diagonal2) / 2

where diagonal1 and diagonal2 are the lengths of the two diagonals of the rhombus.

For example, if diagonal1 = 6 cm and diagonal2 = 8 cm, the area of the rhombus is:

Area = (6 * 8) / 2 = 24 cm2

Therefore, the area of rhombus ABCD is 24 cm2.

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angle a = arctan(5/7) = 35.5

angle b = arctan(7/5) = 54.5

Answer is C

Answer:

(C)35.5° and 54.5°

Step-by-step explanation:

It is given that ABC is a right angled triangle which is right angled at C and AC=7 inches and CB=5 inches.

Now, using the trigonometry, we have

From ΔABC, we have

[tex]\frac{BC}{AC}=tanA[/tex]

[tex]\frac{5}{7}=tanA[/tex]

[tex]0.714=tanA[/tex]

[tex]A=tan^{-1}(0.714)[/tex]

[tex]A=35.5^{\circ}[/tex]

Again, from ΔABC, we have

[tex]\frac{AC}{BC}=tanB[/tex]

[tex]\frac{7}{5}=tanB[/tex]

[tex]1.4=tanB[/tex]

[tex]B=tan^{-1}(1.4)[/tex]

[tex]B=54.5^{\circ}[/tex]

Therefore, the measure of missing angles in triangle ABC are 35.5° and 54.5°respectively.

Thus, option C is correct.

Answer:

first one

Step-by-step explanation:

The number line represents the graph of x ≤ 0 is number line (b)

The inequality expression is given as:

x ≤ 0

The inequality symbol ≤ means that:

Hence, the number line represents the graph of x ≤ 0 is number line (b)

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The value of m from the given expression would be; -10.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We have been given the expression as

0.61m - 1.51m = 9

Combine Like Terms;

-0.9m = 9

Divide -0.9 To Both Sides;

-0.9m/-0.9 = 9/-0.9

Simplify;

m = -10

Hence, m equals to -10.

The value of m from the given expression would be; -10.

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The eccentricity of a completely flat ellipse ranges from one (1) to zero (0).

Eccentricity of an ellipse is the measure of how 'out of round' an ellipse is.  

The eccentricity of an ellipse ranges from 0 to 1.

If the eccentricity is 0, it is not squashed at all and it will remain a circle.

However, if the eccentricity is 1, it is completely squashed and looks like a straight line.

Thus, the eccentricity of a completely flat ellipse ranges from one (1) to zero (0).

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Hey there!

         [tex]\bold{A.\downarrow}[/tex]

      [tex]\bold{B.\downarrow}[/tex]

         [tex]\bold{C.\downarrow}[/tex]

          [tex]\bold{D\downarrow}[/tex]

[tex]\boxed{\boxed{\bold{Answer:D.2^4\times6^4}\checkmark}}[/tex]

Good luck on your assignment and enjoy your day!

~[tex]\bold{LoveYourselfFirst:)}[/tex]

300t = 350(t-1)

300t = 350t-350

-50t=-350

t = -350 /-50

t = 7 hours

Natural numbers are closed under multiplication but not under subtraction and division: subtracting or dividing two natural numbers can lead to results that aren't natural numbers (negative numbers or fractions, respectively).

The student's question pertains to the closure of natural numbers under the operations of subtraction, multiplication, and division. Natural numbers are numbers used for counting and ordering that include all positive integers from 1 onwards. Let's evaluate each of these operations with respect to closure:

Subtraction: Natural numbers are not closed under subtraction because subtracting a larger number from a smaller one results in negative numbers, which are not part of the natural numbers. For example, 3 - 5 = -2 is not a natural number.

Multiplication: Natural numbers are closed under multiplication because the product of any two natural numbers is always a natural number. For example, 2 x 3 = 6, and both the numbers and result are natural numbers.

Division: Natural numbers are not closed under division because the division of two natural numbers can result in a fraction or a decimal that is not a natural number. For example, 1 / 2 = 0.5, which is not a natural number.

When a natural number is subtracted or divided by another, the result might not always be a natural number, indicating that natural numbers are not closed under these operations.

The closure property holds for addition and multiplication of natural numbers, but not for subtraction and division.

The closure property states that when you add two natural numbers, the result is always a natural number. For example, 2 + 3 = 5.

Subtraction is not closed under natural numbers. For example, if you subtract 3 from 2, you get -1, which is not a natural number.

The closure property holds for multiplication as well. When you multiply two natural numbers, the result is always a natural number. For example, 2 x 3 = 6.

Division is not closed under natural numbers. For example, 2 ÷ 3 = 0.67, which is not a natural number.

Answer:

The length of A'B' is 4 unit.

Step-by-step explanation:

Translation is a rigid transformation in which a figure or a line segment is shifted or moved without changing its shape and size,

That is, if the measurement of segment AB is 4 unit then after translation by any factor its measurement will not change,

So, the measurement of segment A'B' would be 4 unit.

Verification :

Let the coordinates of A and B are [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] respectively,

Also, the rule of translation 1 unit right is,

[tex](x,y)\rightarrow (x+1, y)[/tex]

By the distance formula,

The measure of segment AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Thus, if A'B' is the transformed segment of segment AB,

Then, coordinates of A' and B' are [tex](x_1+1, y_1)[/tex] and [tex](x_2+1, y_2)[/tex]

So, the measure of segment A'B' = [tex]\sqrt{(x_2+1-x_1-1)^2+(y_2-y_1)^2}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Hence, the measure of AB = measure of A'B'

Answer: Yes ΔRWS≈ΔQWT.

Step-by-step explanation:

We know that when two chords intersect each other inside a circle, the products of their segments are equal.

Therefore, [tex]QW\times WS=TW\times RW\\\Rightarrow\frac{QW}{RW}=\frac{TW}{WS}[/tex]

Now in triangle QWT and triangle RWS

∠QWT=∠RWS     [Vertically opposite angles]

[tex]\frac{QW}{RW}=\frac{TW}{WS}[/tex]

Therefore, By SAS similarity rule

ΔRWS≈ΔQWT

Therefore, yes ΔRWS≈ΔQWT.

Final answer:

It will take 4 years for the balance of an account to grow from $5000 to $6500 at a 7.5% simple interest rate. The formula for simple interest I = P × r × t is used, and after rearranging to solve for t, we find t = 4 years.

Explanation:

To calculate how long it will take for the balance of an account to reach a certain amount with simple interest, we can use the formula for simple interest: I = P × r × t, where I is the interest earned, P is the principal amount (initial deposit), r is the annual interest rate, and t is the time in years. In this case, we want to find out when the account balance will be $6500 after depositing $5000. The total interest earned to reach $6500 will be $6500 - $5000 = $1500.

The given annual interest rate is 7.5% (or 0.075 when converted to decimal form). We will rearrange the simple interest formula to solve for t:

t = I / (P × r)

Now, substituting the given values:

t = $1500 / ($5000 × 0.075)
t = $1500 / $375
t = 4 years

Therefore, it will take 4 years for the balance of the account to be $6500 at a 7.5% simple interest rate.

The number of ways the golfer can make his choices is 4 hats times 3 gloves times 2 shoes, resulting in 24 different combinations.

The student is asking about the number of different ways a golfer can choose from 4 hats, 3 gloves, and 2 pairs of shoes. To find the total number of combinations, we multiply the number of choices for each category. Thus, the number of ways the golfer can make his choices is:

4 (hats) × 3 (gloves) × 2 (shoes) = 24 combinations.

This is not an instance where factorial calculation (4!) is necessary, since the golfer does not need to select one of each item in a specific order but simply needs to choose one from each category.

To calculate the number of ways the golfer can make his choices, we can use the concept of permutations.

For the hats, there are 4 choices. For the gloves, there are 3 choices. And for the shoes, there are 2 choices.

To find the total number of combinations, we multiply the number of choices for each category together: 4 hats * 3 gloves * 2 pairs of shoes = 24 different ways the golfer can make his choices.

Final answer:

The golfer can choose his accessories in 24 different ways by selecting 1 out of 4 hats, 1 out of 3 gloves, and 1 out of 2 pairs of shoes, and multiplying the choices together (4 × 3 × 2).

Explanation:

The question asks us to calculate the total number of ways the golfer can choose his outfit accessories assuming he chooses one of each type. To do this, we need to consider each type of accessory independently and multiply the number of choices for each type.

The golfer has 4 different hats, 3 pairs of gloves, and 2 pairs of shoes to choose from. Since these choices are independent of each other, we simply multiply the number of options for each type of accessory:

Thus, the total number of combinations is 4 hats × 3 gloves × 2 shoes = 24 different ways the golfer can choose his accessories for the round of golf.

This is an example of a fundamental counting principle problem, where we multiply the number of choices in each step to get the total number of combinations.

Final answer:

By adding the fractions of votes for the museum (5/12) and zoo (5/24), converting them to a common denominator, and subtracting from the whole, we find that 3/8 of the class voted for the nature park.

Explanation:

To determine what fraction of the class voted for the nature park, we first need to add up the fractions of the class that voted for the museum and the zoo, and then subtract that sum from the whole class, which is represented as 1 (or 12/12). Since 5/12 of the class voted for the museum and 5/24 of the class voted for the zoo, we need to find a common denominator to add these fractions together. The lowest common denominator for 12 and 24 is 24.

First, we convert 5/12 to a fraction with a denominator of 24, which would be 10/24 (since 5 × 2 = 10 and 12 × 2 = 24). Now we can add the two fractions:

10/24 (votes for the museum)

5/24 (votes for the zoo)

Therefore, 10/24 + 5/24 = 15/24. After that, we subtract the sum from the whole to find out what fraction voted for the nature park:

12/12 - 15/24 = 24/24 - 15/24 = 9/24.

Hence, 9/24 of the class voted for the nature park. However, we can simplify 9/24 by dividing the numerator and the denominator by their greatest common divisor, which is 3, giving us 3/8.

Therefore, 3/8 of the class voted for the nature park.

We are asked about the fraction of pizza each student gets, so the relevant numbers here is only 14 students and 7 pizzas. SO the fraction of pizza each student get is the ratio of the two:

fraction = 7 pizzas / 14 students

fraction = 1 / 2

So each student gets 1/2

Each student receives 4 slices out of 8, or half a pizza, which is represented by the fraction 1/2. There are 56 slices available in total (7 pizzas times 8 slices each), and when that is divided by 14 students, it equals 4 slices per student.

The question asks for the fraction of one pizza that each student receives at a pizza party. Given that there are 14 students and 7 pizzas, each pizza is cut into 8 slices. This information can be used to calculate the total number of slices available and then divide that by the number of students to determine the fraction of a pizza each student gets.

First, we find the total number of slices by multiplying the number of pizzas by the number of slices per pizza:

7 pizzas x 8 slices per pizza = 56 slices

Next, we divide the total number of slices by the number of students to find how many slices each student will receive:

56 slices ÷ 14 students = 4 slices per student

Since each pizza has 8 slices, 4 slices represent half a pizza. Therefore, the fraction of one pizza that each student receives is 1/2.

Answer:

Factor: [tex](x-3)(x-3)[/tex]

Step-by-step explanation:

Given: [tex]x^2-6x+9[/tex]

Factor the given polynomial. It is quadratic equation.

[tex]\Rightarrow x^2-6x+9[/tex]

Using formula: [tex]a^2-2ab+b^2=(a-b)^2[/tex]

So, first we make given polynomial to perfect square.

[tex]\Rightarrow x^2-2\cdot x\cdot 3+3^2[/tex]

[tex]a\rightarrow x[/tex]

[tex]b\rightarrow 3[/tex]

[tex]\Rightarrow (x-3)^2[/tex]

[tex]\Rightarrow (x-3)(x-3)[/tex]

Hence, The factor of given polynomial is [tex]\Rightarrow (x-3)(x-3)[/tex]

Factorizing the polynomial expression x² - 6x + 9 = (x - 3)²

Factorization is the simplification of an expression into a smaller expression using its factors.

To factor the polynomial expression. x² - 6x + 9, we proceed as follows

Since we have the polynomial expression x² - 6x + 9, we multiply x² by 9 to get x² × 9 = 9x².

Now, we desire to find the factors of 9x² so that the sum of those factors equal - 6x

Thus, we have 9x² = -3x × (-3x)

So, -6x = -3x - 3x

Thus, we replace this with -6x, so

x² - 6x + 9 = x² - 3x - 3x + 9

So, factorizing, we have that

x² - 3x - 3x + 9 =  x(x - 3) - 3(x - 3)

= (x - 3)(x - 3)

= (x - 3)²

So, factorizing x² - 18x + 81 = (x - 9)²

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