Tom Harris is twenty-four years old. He wishes to purchase $7,000 of a ten-year term insurance. What will be his annual premium?

Answer:

Center: (0,0)

Vertices: (0,-5), (0,5)

Foci: (0,-3) (0,3)

Step-by-step explanation:

The value of the expression √75 + √125 is 5 (√3 + √5 ).

A number is a fundamental mathematical unit. For counting, measuring, and comparing quantities, we utilize numbers. A set of symbols, or numerals, used to represent numbers is known as a number system.

A square root is a factor of a number that yields the original number when multiplied by itself.

Consider the expression √75 + √125,

Let's assume x = √75 + √125

Now,

75 = 5 × 15 = 5 × 3 × 5

125 = 5 × 25 = 5 × 5 × 5

Therefore,

x = √75 + √125

x = √ [ 5 × 3 × 5] + √ [ 5 × 5 × 5 ]

x = 5√3 + 5√5

x = 5 × [ √3 + √5 ]

x = 5 × [ 1.73 + 2.24 ]

x = 5 × 3.97

x = 19.85

√75 + √125 = 19.85

Hence, the value of √75 + √125 is equal to 19.85.

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If the expression is log₃ 7(2 x-3)², then the expansion of the expression is [[tex]log_{3}[/tex] 7+ [tex]log_{3}[/tex] [tex](2x-3)^{2}[/tex]]

Given that the expression is log₃ 7(2 x-3)².

We are told to find the expansion of the expression.

Logarithmic function is basically the opposite of the exponential function and is denoted by log or ln.

It says that [tex]log_{a} b[/tex]= [tex]log_{x}b /log_{x}a[/tex].

The expression is log₃ 7(2 x-3)².

We know that log mn=log m +log n.

log₃ 7(2 x-3)²=[[tex]log_{3}[/tex] 7+ [tex]log_{3}[/tex] [tex](2x-3)^{2}[/tex]]

We know that log [tex]a^{b}[/tex]=log b/log a but we are not changing here,So,

log₃ 7(2 x-3)²=[[tex]log_{3}[/tex] 7+ [tex]log_{3}[/tex] [tex](2x-3)^{2}[/tex]]

Hence if the expression is log₃ 7(2 x-3)², then the expansion of the expression is [[tex]log_{3}[/tex] 7+ [tex]log_{3}[/tex] [tex](2x-3)^{2}[/tex]]

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Answer:

(a+b) (a+2ab+b2−3a2b)

Step-by-step explanation:

2.

x^2-4y

/2

4^2- (4*-3)

/2

16+12

/2

28/2

14

The inverse of the expression y = 5 · (x - 6)² - 5 is x = √[(y + 5) / 5] + 6. (Correct choice: D)

According to the statement we have a function of the form y = f(x) and we need to find its inverse, that is, finding the equation of x in terms of y. This can be done by using algebra properties:

y = 5 · (x - 6)² - 5                          Given

y = 5 · [(x - 6)² - 1]                         Distributive property

y / 5 + 1 = (x - 6)²                          Compatibilities with multiplication and addition / Existence of additive and multiplicative inverses / Associative and modulative properties

x - 6 = √(y / 5 + 1)                         Definition of square root / Symmetric property

x = √(y / 5 + 1) + 6                         Compatibility with addition / Existence of additive inverse / Associative, commutative and modulative properties

x = √[(y + 5) / 5] + 6                      Addition of fractions with different denominators / Result

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The surface area is the sum of the area of the surfaces. The surface area of the box is 360x^2 - 216x

The formula for calculating the surface area of a box is expressed according to the equation:

Surface area = 2(lw + wh +lh)

Given the following parameters

length = 6x

width = 12x - 9

height = 6x

Substitute

Surface area = 2(6x(12x-9) + (12x-9)(6x) +(6x)(6x))

Expand

Surface area = 2(72x^2-54x) + (72x^2-54x) + 36x^2)

Surface area = 2(180x^2-108x)

Surface area = 360x^2 - 216x

Hence the surface area of the box is 360x^2 - 216x

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Answer:

4x - 5 = 131 where x is the first number.

Step-by-step explanation:

Let the first number be x.

Seconder number = 2x + 7.

Third number = x - 12.

So, the equation is :-

x + 2x + 7 + x - 12 = 131

4x - 5 = 131

4x = 136

x = 34

First number = 34, second = 2(34) + 7 = 75 and third number = 34-12 = 22.

Answer: 8,938 [tex]\frac{8}{9}[/tex] or 8,938.8889 meters per second

Step-by-step explanation:

     To solve this problem, we will use a process called dimensional analysis (that you have probably done many times without realizing it).

     What is dimensional analysis? Let's say you know there are 12 inches in a foot, and you want to know how many inches are in 2 feet. 12 * 2 = 24 inches in a foot, that's dimensional analysis!

     Here is the process you would take to solve your problem:

➜ If we have the units [tex]\frac{hour}{hour}[/tex], they "cancel" out to become one. This way, we make sure we end up with the correct units, [tex]\frac{meters}{second}[/tex].

➜ We take units we know, such as 3,600 seconds in an hour, and multiply them by the original value until we end up with the measurement we want.

[tex]\displaystyle 20,000\; \frac{miles}{hour}*\frac{1 \;hour}{3,600\; seconds} *\frac{1,609\;meters}{1\;mile}=\frac{20,000*1*1,609\;meters}{3,600\;seconds} =\frac{32,180,000\;meters}{3,600\;seconds} = 8,938.89\; \frac{meters}{second}[/tex]

     In other words;

           8,938.89 meters per second

The given expression , the value of x is 2.

given,

equivalent expression = -3(2x - 4)

                                    = -6x + 12

                                  x  = 2

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

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Answer:

624

Step-by-step explanation:

650 * .80 = 520520 * 1.20 = 624

the answer for your question is true. I believe.

Answer:

y = -2

Step-by-step explanation:

Given equation:

[tex]3(-4y-5)=8y+25[/tex]

Distribute:

[tex]\implies 3 \cdot -4y - 3 \cdot 5=8y+25[/tex]

[tex]\implies -12y - 15=8y+25[/tex]

Add 15 to both sides:

[tex]\implies -12y - 15+15=8y+25+15[/tex]

[tex]\implies -12y =8y+40[/tex]

Subtract 8y from both sides:

[tex]\implies -12y-8y =8y+40-8y[/tex]

[tex]\implies -20y =40[/tex]

Divide both sides by -20:

[tex]\implies \dfrac{-20y}{-20} =\dfrac{40}{-20}[/tex]

[tex]\implies y =-2[/tex]

Now we have to,

→ solve for the required value of y.

Let's solve the problem,

→ 3(-4y - 5) = 8y + 25

→ -12y - 15 = 8y + 25

→ -12y - 8y = 25 + 15

→ -20y = 40

→ y = -40/20

→ [ y = -2 ]

Hence, the value of y is -2.

Answer:

I deleted my answer bc i accidentally answered the wrong question

We get the value of h(1) × g(1) as - 14 for the functions g (x) = x - 3 and h (x) = x² + 6.

We are given the two functions as:

g (x) = x - 3 and h (x) = x² + 6

Now, we will first find h (1)

h (1) = (1)² + 6

h(1) = 1 + 6

Add them, we get:

h (1) = 7

Now, we will find g (1):

g (1) = 1 - 3

g (1) = - 2

Now we will find the expression  h(1) × g(1):

h(1) × g(1) = 7 × ( - 2 )

h(1) × g(1) = - 14

Therefore, we get the value of h(1) × g(1) as - 14 for the functions g (x) = x - 3 and h (x) = x² + 6.

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Answer:

Option 2

Step-by-step explanation:

The distances will be the same because the bisector will create congruent triangles, and the desired equalities follow from CPCTC and the definition of congruency.

An expression that can be used to determine the total amount of credit cards opened at the two locations is: (a + b) (t) = 45 + 3t.

Given,

Number of credit cards opened at location a = a (t) = 20 + 4t

Number of credit cards opened at location b = b (t) = 25 - t

Hence,

Total amount of credit card:

(a + b) (t) = (20 + 4t) + (25 - t)

(a + b) (t) = 20 + 4t + 25 - t

(a + b) (t) = 45 + 3t

Therefore an expression that can be used to determine the total amount of credit cards opened at the two locations is: (a + b) (t) = 45 + 3t.

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I think this is one of those trick questions!

I'm going to say the answer is... 90°

because it states within the question that ∠A and ∠B are vertical angles

That is my educated guess. I hope it's helpful!

Pls let me know if my answer is incorrect.

Answer:

first one = -50

second one = 0.2

Step-by-step explanation:

Answer: bro if your on a computer or phone just use a calculator lol but ill put the answer below

Step-by-step explanation:

-15 divided by 0.3= -50

-4 divided by -20 = -24

Answer:

f(- 1) = - 5

Step-by-step explanation:

substitute x = - 1 into f(x)

f(x) = x² + 2x - 4 , then

f(- 1) = (- 1)² + 2(- 1) - 4 = 1 - 2 - 4 = - 5

Answer:

(0, - 9 )

Step-by-step explanation:

x = 2y + 18 → (1)

5x = - 3y - 27 → (2)

substitute x = 2y + 18 into (2)

5(2y + 18) = - 3y - 27

10y + 90 = - 3y - 27 ( add 3y to both sides )

13y + 90 = - 27 ( subtract 90 from both sides )

13y = - 117 ( divide both sides by 13 )

y = - 9

substitute y = - 9 into (1)

x = 2(- 9) + 18 = - 18 + 18 = 0

solution is (0, - 9 )

Answer:

The square of -3 is 9

Step-by-step explanation:

(-3)^2=9

Answer:

It is: 8^4 times 3^2 = 36,864

Answer:

8^4 x 3^2

Step-by-step explanation:

There's 4 8's and 2 3's so that's the number the exponents will be

Applying the negative exponent rule, the value of 9^-1/2 is calculated as: 1/3.

If a number has a negative exponent, i.e. a^-1/2, it can be rewritten and expressed as:

a^-1/2 = 1/a^½

1/a^½ can also be rewritten or expressed as:

1/a^½ = 1/√a

Thus, we would apply the negative exponent rule to find the value of the expression, 9^-1/2 as explained below:

9^-1/2 = 1/9^½

Rewrite 1/9^½ as 1/√a

1/9^½ = 1/√9

Take the square root of 9

1/√9 = 1/3

This implies that, the value of the expression, 9^-1/2 is 1/3.

In conclusion, applying the negative exponent rule, the value of 9^-1/2 is determined as: 1/3.

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Answer:

f(-8)= -7660

Step-by-step explanation:

f(-8)= 3(-8)^2·5(-8)+20

We will get  lne¹⁰ itself after simplifying the given expression lne¹⁰.

So,

Then,

Therefore, we will get  lne¹⁰ itself after simplifying the given expression lne¹⁰.

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The answer is 127.5146314631

What is 87.65 decimal in octal? 87.65 from decimal to octal is 127.5146314631. Here we show you how to write 87.6510 in octal and how to convert 87.65 from base-10 to base-8.

To convert decimal number 87.65, we convert its integer and fraction part individually and then add them to get the equivalent octal number, as below:

To convert integer 87 to octal, follow these steps:

Divide 87 by 8 keeping notice of the quotient and the remainder. Continue dividing the quotient by 2 until you get a quotient of zero.

Then just write out the remainders in the reverse order to get the equivalent octal number.

87 / 8 = 10 with remainder 7

10 / 8 = 1 with remainder 2

1 / 8 = 0 with remainder 1

Here is the answer to 87 decimal to octal number:

127

For converting decimal fraction 0.65 to octal number, follow these steps:

Multiply 0.65 by 8 keeping notice of the resulting integer and fractional part. Continue multiplying by 8 until you get a resulting fractional part equal to zero (we calcuclate upto ten digits).

Then just write out the integer parts from the results of each multiplication to get equivalent octal number.

0.65 × 8 = 5 + 0.2

0.2 × 8 = 1 + 0.6

0.6 × 8 = 4 + 0.80000000000001

0.80000000000001 × 8 = 6 + 0.40000000000009

0.40000000000009 × 8 = 3 + 0.20000000000073

0.20000000000073 × 8 = 1 + 0.60000000000582

0.60000000000582 × 8 = 4 + 0.80000000004657

0.80000000004657 × 8 = 6 + 0.40000000037253

0.40000000037253 × 8 = 3 + 0.20000000298023

0.20000000298023 × 8 = 1 + 0.60000002384186

Here is the answer to 0.65 decimal to octal number:

0.5146314631

Therefore, decimal number 87.65 converted to octal is equal:127.5146314631

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Answer:

j = 3

Step-by-step explanation:

Recall the slope formula:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Now, simply substitute the values from the question.

[tex]\frac{1}{3} =\frac{-4+3}{j-6}[/tex]

Now, use the cross-multiplication method. (remember, when subtracting negatives, the negative becomes a positive)

[tex]1(j-6)=3(-4+3)[/tex]             Cross Multiplication

[tex]1(j-6)=3(-1)[/tex]                   Simplify

[tex]j-6=-3[/tex]                            Distributive Property

[tex]j=3[/tex]                                     Addition Property

Therefore, j = 3.

The the distance between the school and Nokesville be on the map is 0.7 inches.

What is scaling ?

It is the technique to resize drawing with comparing to actual size of object which uses proportion or ratio. For example, Mapping of earth, drawing prototype of automobiles.

It is given that :

The distance between the school and Target is 4.2 miles and on a map the ratio is 0.5 inches is equal to 3 miles that is :

3 miles = 0.5 inches on map

Now to find the distance between the school and Nokesville be on the map we first find for 1 miles on the map and then multiply it by 4.2 miles :

3 miles = 0.5 inches on map

1  miles = 0.5/3 inches on map

4.2 miles = (0.5/3) x 4.2 inches on map

4.2 miles = 0.7 inches inches on map

Therefore, the the distance between the school and Nokesville be on the map is 0.7 inches.

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