The point has A has coordinates (-4, 6) and point B has coordinates (7, -2)
Calculate the length of the line AB (pls show working)

Answer:

1

Step-by-step explanation:

sec(x)*cos(x) + cos(x)-1/(sec(x))

We know that sex(x) = 1/(cos(x))

substitute it in our expression.

1/(cos(x)) * cos(x) + cos(x) - 1/(1/cos(x)) = 1+cos(x) - cos (x)= 1

ANSWER

A. 1

EXPLANATION

The given trigonometric expression is

[tex] \sec(x) \cos(x) + \cos(x) - \frac{1}{ \sec(x) } [/tex]

Recall and use the following reciprocal identities.

[tex] \frac{1}{ \sec(x) } = \cos(x) [/tex]

and

[tex] \sec(x) = \frac{1}{ \cos(x) } [/tex]

When we apply these identities, we get

[tex] \frac{1}{ \cos(x) } \times \cos(x) + \cos(x) - \cos(x) [/tex]

This simplifies to:

[tex]1 + 0 = 1[/tex]

The correct choice is A

Answer:x2_>16 B.

Step-by-step explanation:

For this case we will show that the correct option is option C.

[tex]x ^ 2 \leq16[/tex]

We find the value of the variable "x":

We apply root to both sides of the equation to eliminate the exponent:

[tex]x \leq \pm \sqrt {16}\\x \leq \pm4[/tex]

We found the first solution with the positive value:

[tex]x \leq4[/tex]

We use the negative value to find the other solution. Since it is an inequality, the sign of the inequality changes in the negative portion of the solution.

[tex]x \geq-4[/tex]

So, the roots are:

[tex]x_ {1} \geq-4\\x_ {2} \leq + 4[/tex]

The solution is given by the values of "x" greater than or equal to -4 and less than or equal to 4

Answer:

Option C

Answer:

y > –5x + 3

Step-by-step explanation:

we know that

1) The solution of the inequality is the shaded area above the dashed line

so

The linear inequality could be

y > –5x – 3

y > –5x + 3

y > –3x + 5

2) The slope of the dashed line is negative ----> the three options have slope negative

3) The y-intercept of the dashed line is (0,3)

therefore

The linear inequality is

y > –5x + 3

Answer:

[tex]y>-5x+3[/tex]

Step-by-step explanation:

To find the linear inequality , Let pick two points from the graph

Lets pick (0,3) and (1,-2)

Lets find out slope using the points

[tex]slope =\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]slope =\frac{-2-3}{1-0}=-5[/tex]

Slope m= -5

y intercept b= 3

Equation of the line is y=mx+b

[tex]y=-5x+3[/tex]

Now we look at the shaded part. we use test point (0,0)

(0,0) is not in the shaded region

[tex]y=-5x+3[/tex]

[tex]0=-5(0)+3[/tex]

0 >3 is false

[tex]y>-5x+3[/tex]

Replace x with 3 and solve for Y.

If y equals 8 in both equations, then it is a solution.

y = -5(3) +1 = -15+1 = -14

-14 does not equal 8 , so it is not a solution.

No because -5• 3 +1 does not equal 8 makings it impossible for it to work for that equation. Then 3•3-2 doesn’t equal 8 either so (3,8) is not a solution for these equations

Answer:

b.the graph of g(x) is the graph of f(x) compressed vertically

Step-by-step explanation:

The given functions are

[tex]f(x)=x^2[/tex]

and

[tex]g(x)=\frac{2}{5}x^2[/tex]

This is a transformation in the form

[tex]y=a*f(x)[/tex] where [tex]a=\frac{2}{5}[/tex]

Since 0<a<1, the graph of f(x) is compressed vertically by a factor of

[tex]\frac{2}{5}[/tex]

A function assigns the value of each element of one set to the other specific element of another set. The correct option is B.

A function assigns the value of each element of one set to the other specific element of another set.

When the graph of the two function f(x) and g(x) is plotted, then it can be observed that the graph of g(x) is the graph of f(x) compressed vertically.

Hence, the correct option is B.

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Answer:

900 feet / 5,280 = 0.1704545... miles

8 seconds / 3,600 = 0.0022222222 hours

0.1704545 miles / 0.0022222222 hours = 76.704525767 miles per hour

The car is well over the speed limit

Step-by-step explanation:

[tex] \frac{27}{30} \times 100\% \\ = 90\%[/tex]

Approximately 90 percent voted for her

Answer:

11877

Step-by-step explanation:

11100 * 7% = 777

11100 + 777 = 11877

When you multiply by 7%, you get the amount of additional tax. You add this to the original amount to get the answer.

Answer:

option D

8√2

Step-by-step explanation:

Given in the question a right angle triangle,

hypotenuse = x

height = 8

We can use trigonometry identity to solve x

we know that,

sinФ = opposite / hypotenuse

sin(45) = 8 / x

x = 8 / sin(45)

x = 8√2

Answer:

$100

Step-by-step explanation:

To find out how much money Gayle initially had, we solved the two equations provided by the problem: G + 20 = 2(J + 20) and J + 20 = G + 20 - 50. Solving these equations, it was found that Gayle initially had $90.

The question is asking us to figure out how much money Gayle had before their mother gave them each $20. Let's denote the amount of money Jerry initially had as J and the amount of money Gayle initially had as G. According to the problem, after the mother gave them $20 each, Gayle had twice the amount of Jerry's, which mathematically translates to G + 20 = 2(J + 20). Likewise, Jerry had $50 less than Gayle, which can be written as J + 20 = G + 20 - 50. Thus we are given a system of two equations that we can solve simultaneously.

Both equations can be simplified to G = 2J + 20 and J = G - 50. By substituting J = G - 50 in the first equation, we can solve for G to get G = 2(G - 50) + 20 which further simplifies to G = $90. Thus, Gayle initially had $90.

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Answer:

D

Step-by-step explanation:

The tenth column value is the first after the decimal point, that is 3

To round the required value of 3

• If the value following 3  ≥ 5, round 3 up to 4

• If the value following 3 < 5 , then leave as 3

Here the value following 3 is 5 so round 3 up to 4

All other digits remain unchanged.

Thus

3, 295.351 ≈ 3, 295.4 → D

Answer:

47 is greater than or equal to 5x+10y

Step-by-step explanation:

you can't spend more than $47 but you can spend less than or equal to that amount.

Answer:5x+10y=47

Step-by-step explanation:

 Given

$47 money needed to spend

Each cassette tape cost $5

and each CD cost $10

Given no of cassette be x and no of CD be y

Thus cost of x cassette is 5x

cost of Y CD's 10y

Total cost=5x+10y

5x+10y=47

Answer: The length and width are 20 square centimeters and 8 square centimeters

Explain: 20:8 can be reduced to 5:2 as a ratio. 20 times 8 equals 160.

Answer:

Step-by-step explanation:

l - length

w - width

length and width are in a ratio of 5:2

[tex]\dfrac{l}{w}=\dfrac{5}{2}[/tex]           cross multiply

[tex]2l=5w[/tex]          divide both sides by 2

[tex]l=\dfrac{5w}{2}[/tex]

the area is 160cm²

[tex]lw=160[/tex]

We have the system of equations:

[tex]\left\{\begin{array}{ccc}l=\dfrac{5w}{2}&(1)\\lw=160&(2)\end{array}\right[/tex]

Substitute (1) to (2):

[tex]\left(\dfrac{5w}{2}\right)(w)=160\\\\\dfrac{5w^2}{2}=160\qquad\text{multiply both sides by 2}\\\\5w^2=320\qquad\text{divide both sides by 5}\\\\w^2=64\to w=\sqrt{64}\\\\w=8[/tex]

Put the value of w to (1):

[tex]l=\dfrac{(5)(8)}{2}=\dfrac{40}{2}=20[/tex]

Answer:

Step-by-step explanation:

abs(x)>0

This statement is false because what happens when x = 0? For all other instances, the statement is true, but not for 0.

Zero is not greater than itself.

The required weight of Carmen's rabbit is given as 5 pounds and the equation is given as 9 = 2x -1.

As mentioned in the question,
Angelos's pet rabbit weighs 1 pound less than twice the weight of Carmen’s pet rabbit. Angelos rabbit weighs 9 pounds.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let the weight of the Carmen's be x,
According to the question,
Angelos pet rabbit weighs,
9 = 2x -1
x = 5

Thus, the required weight of Carmen's rabbit is given as 5 pounds.

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To find the weight of Carmen's pet rabbit, an equation is set up: 2w - 1 = 9, where w represents the unknown weight of Carmen's rabbit. Solving the equation, we find that Carmen's rabbit weighs 5 pounds.

To find the weight of Carmen's pet rabbit, we first need to translate the given information into a mathematical equation. The problem states that Angelo's pet rabbit weighs 1 pound less than twice the weight of Carmen's pet rabbit and Angelo's rabbit weighs 9 pounds. Let's denote the weight of Carmen's rabbit as w. The relationship can be written as:

2w - 1 = 9

To solve for w, we add 1 to both sides of the equation:

2w - 1 + 1 = 9 + 1

2w = 10

Now, we divide both sides by 2 to get the weight of Carmen's rabbit:

2w / 2 = 10 / 2

w = 5

Therefore, Carmen's pet rabbit weighs 5 pounds.

Answer:

997

From right to left, the place values are, ones, tens, hundreds, thousands, etc.

The number with '7 ones', '9 tens', and '9 hundreds' is written as 997 in numeral form, by combining the values of each digit based on their place value.

When writing the number that consists of '7 ones', '9 tens', and '9 hundreds', we are dealing with a three-digit number where each place value represents a power of 10. To construct the number, we consider the value each digit represents:

The '9 hundreds' means 9 × 100 (which is 900).

The '9 tens' means 9 × 10 (which is 90).

The '7 ones' means 7 × 1 (which is 7).

Adding these values together, we have 900 (hundreds) + 90 (tens) + 7 (ones), which equals 997. This is the decimal representation of the number expressed by the student.

Therefore, the number 7 ones 9 tens 9 hundreds written in numeral form is 997.

Answer:

2(x-8)=8

x=12

Step-by-step explanation:

The equation for the given statement is 2(x-8)=2.

The given statement "Twice the difference of a number and 8 is equal to 2 ​

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, the difference between a number and 8 can then be written as 'x-8'. Twice that amount would be 2(x-8). If it's equal to 2, you can say 2(x-8)=2.

Therefore, the equation for the statement is 2(x-8)=2.

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Answer:

[tex]4\pi[/tex]

or

12.57

Step-by-step explanation:

I have a circular piece of fabric I am going to make a tablecloth. The radius of the fabric is 2 meters. What is the area of the tablecloth I can make

Essentially, you are attempting to find the area of a circle with a radius of 2 meters.

The formula for an area of a circle is [tex]\pi r^2[/tex], or pi times radius squared.

Plugging in 2 meters as your radius, that gets your answer to be [tex]4\pi[/tex], or 12.57 in decimal.

Answer:

a. 17 x 10 = 170

b. 24 x 100 = 2,400

c. 6 x 1000 = 6000

Step-by-step explanation:

Answer:

a. 170

b. 2,400

c. 6,000

Step-by-step explanation:

You need to make the multiplications that are indicated in each option:

Option a: you only need to multiply the first factor (17) by the digit that is not zero (1) of the second factor (10), and then write all the zeros that has the second factor:

 [tex]17*10=170[/tex]

Option b: you need to multiply the first factor (24) by the digit that is not zero (1) of the second factor (100), and then write all the zeros that has the second factor:

 [tex]24*100=2,400[/tex]

Option c: you have to multiply the the first factor (6) by digit that is not zero (1) of the second factor (1000), and then write all the zeros that has the second factor:

 [tex]6*1,000=6,000[/tex]

Answer:

y = 2x

Step-by-step explanation:

Given that y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 12 when x = 6

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{12}{6}[/tex] = 2, hence

y = 2x ← equation of variation

Answer:

180i^2 - 20j^2

Step-by-step explanation:

u.v

(12i+4j) . (15i-5j)

12i(15i-5j) + 4j(15i-5j)

180i square -60ij + 60ij-20j square

180i^2 - 20j^2

The value of the dot product of the two vectors is u · v = -160.

The product of vectors can refer to several different operations, including the dot product, cross product, and scalar multiplication.

Dot Product:

The dot product of two vectors u and v is a scalar given by the formula:

u · v = ||u|| ||v|| cos θ

We have,

To find the dot product of two vectors, we need to multiply their corresponding components and add up the results:

u · v

= (12i + 4j) · (15i - 5j)

= 12i · 15i + 12i · (-5j) + 4j · 15i + 4j · (-5j)

= 180i^2 - 60ij + 60ij - 20j² [since i² = j² = -1]

= 180(-1) - 20(-1) [since ij = ji = 0]

= -160

Therefore,

The value of the dot product of the two vectors is u · v = -160.

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Answer:

IT would be 6 because 10 X 6 = 60 just take away the 0

Step-by-step explanation:

Answer:

4200 divided by 10

Step-by-step explanation:

To make 4200 a multiple of ten after dividing it by a multiple of ten, we first find the number of 5's in 4200 to see how many 10's go into 4200. Since 4200 = 6*7*2*2*5*5, we see that there are 2 fives. This means that there are two tens too. Since we have to keep 4200 a multiple of ten after dividing it by another 10. So the only possible way to do that is dividing 4200 by 10.

Dividing 4200 by the power of 10, 100, results in the quotient 42, which is also a multiple of 10. This is achieved by moving the decimal point two places to the left in the number 4200 due to the two zeros in the power of 10.

In this mathematics problem, you are asked to divide 4200 by a multiple of 10 such that the result, or quotient, is also a multiple of 10. The key to this problem lies in understanding the concept of dividing by powers of 10.

When you divide a number by a power of 10, you move the decimal point to the left by as many places as there are zeros in the power of 10. So if you wanted to divide 4200 by a multiple of 10 so that the result is also a multiple of 10, you might choose 100 (10^2) as your divisor. Why? Because there are two zeros in the power of 10, which means you move the decimal point two places to the left in the number 4200.

So when you divide 4200 by 100, you get 42 which is a multiple of 10. Therefore, 4200 divided by a multiple of 10 (100 in this case) gives a quotient (42) that is also a multiple of 10.

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Answer:

Plain rolls: $16

Shinny rolls: $20

Step-by-step explanation:

So, we have 2 equations to start with, let p = plain rolls and s = shinny rolls:

1)  8p + 10s = 328

2) 9p + 2s = 184

We need to isolate one variable, usually I go for the one with the lowest multiplicative... so let's go for the '2s' and isolate the s from equation 2.

2s = 184 - 9p

3) s = (184 - 9p) / 2

And let's place that s equivalent into the first equation:

8p + 10 (184 - 9p)/2 = 328

8p + 5(184 - 9p) = 328

8p - 45p + 920 = 328

-37p = -592

p = 16

Then we go into any of the 3 equations to get the value of s.  Let's take the 3rd equation, it will be simpler:

s = (184 - 9p) / 2 = (184 - 9*16) / 2

s = (184 - 144)/2 = 40/2 = 20

Then last step, we enter the values for s and p in one of the first equations to validate it.  We haven't worked with first equation, so let's use that one:

8p + 10s = 328

8 (16) + 10 (20) = 328

128 + 200 = 328

328 = 328

Confirmed!

the answer is 10 units

[tex]distance = \sqrt{(9 - 1) ^{2} + (9 - 3) {}^{2} } \\ = \sqrt{ {8}^{2} + {6}^{2} } \\ = 10[/tex]

The distance between points (1, 3) and (9, 9) will be 10 units so option (b) will be correct.

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).

For instance, in this case (5,3), 5 will represent the x and 3 the y.

(9,0) is another illustration, where 9 stands for x and 0 for y.

Coordinates are always written in the form of small brackets the first term will be x and the second term will be y.

The distance between two points (x₁,y₁) and (x₂,y₂) is given by

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

So,

Distance between (1, 3) and (9, 9)

[tex]d = \sqrt {\left( {1- 9 } \right)^2 + \left( {3 -9 } \right)^2 }[/tex]

d = √(64 + 36) = 10 units.

Hence, The distance between points (1, 3) and (9, 9) will be 10 units

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The z-score for 2,500 g is –2.According to the empirical rule, 95% of babies have a birth weight of between 2,500 g and 4,500 g.5% of babies have a birth weight of less than 2,500 g or greater than 4,500 g.Normal distributions are symmetric, so 2.5% of babies weigh less than 2,500g.

2.5% of babies weigh less than 2,500g.

Empirical rule states that for a normal distribution, 68% of the values are within 1 standard deviation from the mean, 95% of the values are within 2 standard deviation from the mean and 99.7% are within 3 standard deviation from the mean.

Given that mean (μ) = 3,500 g and a standard deviation of σ = 500 g.

Hence 2.5% of babies weigh less than 2,500g.

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Answer:

[tex]\frac{1}{ab^{2} }[/tex] (a³ - 6b)

Step-by-step explanation:

[tex]\frac{-6}{ab} + \frac{a^{2} }{b^{2} }[/tex]

= [tex]\frac{-6b + a^{3} }{ab^{2} }[/tex]

= [tex]\frac{1}{ab^{2} }[/tex] (a³ - 6b)

Answer:

5-4(x+2)=3

1(x+2)=3

1x+2=3

3-2=1

Step-by-step explanation:

x=1

Answer:

the answer is B: 3

Step-by-step explanation:

you look at the verticle line on the left side of the box which represents the lower quartile then to the right of the verticle line represents the upper quartile

To find the interquartile range, subtract the lower quartile, 9.5, from the upper quartile, 12.5

12.5 - 9.5 = 3

Answer:

Every 20 days.

Step-by-step explanation:

I just did 5 times 4 to get the answer

In 20 days there will be both lessons on the same day again.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given:

Violin class= 4th day

singing lesson= 5th day

So, the possible number of days on which we have both violin and singing class

=4 x 5

=20 days

Hence,  20 days there will be both lessons on the same day again.

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