The sum of two numbers is 10 the larger number is four times the smaller number this is the system of equations used to represent the scenario is Y equals negative X +10 and Y equals 4X what is the larger number

Answer:

[tex]y=7x+49[/tex]

Step-by-step explanation:

To find the slope of a line which is perpendicular to another line, you need to find the opposite reciprocal of the first line's slope.

To find the opposite, flip the slope's sign. Your original slope is [tex]-\frac{1}{7}[/tex], so your opposite slope is positive [tex]\frac{1}{7}[/tex].

To find the reciprocal, flip the fraction. This changes your slope from [tex]\frac{1}{7}[/tex] to [tex]\frac{7}{1}[/tex], which may be written as just 7.

Therefore, your slope is 7.

To find your b term (your y-intercept) given that your x-intercept is -7, you can make use of point-slope form.

[tex]y-y1=m(x-x1)[/tex]

(m=slope)

If your x-intercept is -7, then the point at which your line intersects the x-axis is (-7, 0).

[tex]y-0=7(x-(-7))\\y=7(x+7)\\y=7x+49[/tex]

Answer:

13 times 2

52 divided by 2

20 plus 6

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

its all of them except for A cuz i got it wrong with the other answer.

Step-by-step explanation:

A regular pentagon is a polygon that has 5 equal sides as well as 5 lines of symmetry.

A pentagon is a polygon that has five sides and five angles. A regular pentagon is a pentagon in which all the sides are equal. A line of symmetry is a line that cuts a shape exactly in half.

A regular pentagon is a polygon that has 5 equal sides as well as 5 lines of symmetry.

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Answer:

C

Step-by-step explanation:

Note that C is exactly -1/4(4x-8) = -1/4*4x -1/4*(-8) = -x+2, so the system with C is the same equation twice, and obviously has an infinite number of solutions.

Answer:

(6-[tex]\sqrt{21}[/tex])  (6+[tex]\sqrt{21}[/tex])

Step-by-step explanation:

The solution set of the equation  x2 = 12x – 15 is O (6 - 121,6 + V21).

The answer is option D.

What is a quadratic equation?

                                 ax²+bx²+c=0

Calculation

equation x2 = 12x - 15

can be written as

    x² - 12x = -15

On square by adding (-b/2)2 on both sides of the equation

     x²- 12x + (-12/2)² = -15 + (-12/2)²

We get

 ⇒ x² - 12x + (-6)² = -15 + (-6)²

  ⇒  x²- 12x + 36 = -15 + 36

    ⇒  (x - 6)2 = 21

    Taking square root on both sides

⇒x - 6 = ± √21

⇒x - 6 = √21 and x - 6 = - √21

⇒x = (6 + √21 ) and x = (6 - √21)

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Answer:

That would be C.

Step-by-step explanation:

Hope this helps!

The set of fractions {2/3, 5/12, 3/8} is ordered from greatest to least. which is the correct answer would be an option (C).

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

Descending order is defined as when numbers (or other items) are arranged from the largest numbers to the least numbers, it is said to be in descending order.

Ascending order is defined as when numbers (or other items) are arranged from the least numbers to the largest numbers, it is said to be in ascending order.

According to option (C),

two over three, five over twelve, three over eight

2/3, 5/12, 3/8

⇒ 2/3 < 5/12 <3/8

Therefore, the set of fractions is ordered from greatest to least.

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Answer:

A. 36

Step-by-step explanation:

By using hypotenuse theorem we can find the height of the support.

In hypotenuse we square both the given measures, then subtract them. if slant measure is given we subtract the square of the other side from the square of the slant and find the square root of the result. if we have to find the slope, then we add the squares of the 2 given sides and find the square root of the result.

so, in this case:

(39×39) - (15×15)

=1521 - 225

=1296

= square root of 1296

= 36

Hope it helps u ....

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

y < -3x-2 -----> inequality A

The solution of the inequality A is the shaded area below the dashed line y=-3x-2

The slope of the dashed line is negative m=-3

The-y-intercept of the dashed line is (0,-2)

The x-intercept of the dashed line is (-0.67,0)

y > -3x+8 -----> inequality B

The solution of the inequality B is the shaded area above the dashed line y=-3x+8

The slope of the dashed line is negative m=-3

The-y-intercept of the dashed line is (0,8)

The x-intercept of the dashed line is (2.67,0)

using a graphing tool

The system of inequalities y < -3x-2 and y > -3x+8 has no solution (parallel lines)

see the attached figure

Answer:

0

Step-by-step explanation:

Quadratic equation

[tex]x=\frac{-b+-\sqrt{b^{2}-4*a*c} }{2*a}[/tex]

The discriminant is the part of the quadratic formula within the square root symbol: [tex]{b^{2}-4*a*c}[/tex].  The discriminant indicates if there are two solutions, one solution, or none.

The discriminant can be positive, zero or negative which determines how roots exist for the given quadratic equation.

So, a positive discriminant tell us that the quadratic has two different real solutions.

A discriminant of zero tell us that the quadratic has two real and equal solutions.

And a negative discriminant tell us that none of the solutions are real numbers.

In this case: 25x^2-10x+1=0

We can see that

a= 25    b=-10   c=1

Using:  [tex]{b^{2}-4*a*c}[/tex]

We have  [tex]-10^{2}-4* 25*1 =100-100=0[/tex]

the answer is zero, so the quadratic has two real and equal solutions

Answer:

What is the value of the discriminant of f?

0

How many x-intercepts does the graph of f?

1

Step-by-step explanation:

I promise you i just got this question and this is the answer

Answer:

x=200 Minutes

Step-by-step explanation:

Using the given information, we can set up slope equations for each set of numbers. Plan A has an equation of y=.05x+30. Plan B has an equation of y=.1x+20. These plans both equal y, so they can be made equal to each other. This looks like .05x+30=.1x+20. Subtract 20 from each side to aid in getting x by itself. This will look like .05x+10=.1x. Subtract .05x from each side to get all the x's to one side. This looks like .05x=10. Divide by .05 to get x. 10/.05=200. This shows how many minutes it takes for the plans to cost the same.

Answer:

David might be 40

Step-by-step explanation:

Brianna = 20 + 20 = 40 = David

James = 10 x 2 = Brianna

David = 40 - 20 = Brianna

To find David's age, we can use the given information and algebraic equations. We can determine James' age, which is x, and use it to calculate David's age as 4x. Thus, David is 40 years old.

To find the age of David, we need to first determine the age of James. Let's assume James is x years old.

According to the given information, Brianna is twice as old as James, so Brianna's age would be 2x years.

Similarly, David is four times as old as James, so David's age would be 4x years.

Finally, we're told that Brianna is 20 years younger than David. So, the equation would be: 2x = 4x - 20.

To solve this equation, we can subtract 2x from both sides, which gives us: -2x = -20. Then, dividing both sides by -2, we get x = 10. Therefore, James is 10 years old and David is 4x = 4 * 10 = 40 years old.

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The value of the expression (5^1/2)^2 is 5.

The value of the expression (51/2)2 can be found by simplifying the expression inside the parentheses first.

When you raise a number to a fractional power, you are taking the square root of that number.

So, 51/2 is equal to the square root of 5.

Applying this to the given expression, (51/2)2 is equal to (√5)2.

When you square a square root, the result is the number inside the square root.

Therefore, the value of the expression is 5.

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This is a relation but not a function.

Functions must have that there is a unique y for a given x, which clearly doesn't work here because all lines of a given x have 2 y-values. However, it is a relation because there is a given set of points which are defined to be within the set of the ellipse (if it's defined which members of two sets, the range and domain, go together, then you have a relation)

iam thinking its D but iam not 100% sure.

Answer:

Option D (r(t) = 3.50t +25 ; r(8) = 53)

Step-by-step explanation:

The fixed cost to rent the kayak $25. This is the cost which remains fixed irrespective of the usage of the kayak. The variable cost of using the kayak is the cost which depends on the usage of the kayak. It is mentioned that the kayak is used for 4 hours and the company charges $3.5 for every half hour. The cost function is given by:

r(t) = 25 + 3.5t ; there r is the total cost of using the kayak and t is the number of half-hours the kayak is used.

4 hours means that there are 8 half-hours. Therefore, t=8. Put t=8 in r(t).

r(8) = 25 + 3.5*(8) = 25 + 28 = 53.

Therefore, Option D is the correct answer!!!

Answer:

The Answer would be D.

r(t) = 3.50t +25

r(8) = 53

Step-by-step explanation:

The Rental Company charges a fixed price of $25 to rent the kayak, as well as an additional $3.50 for each half hour. So the only variable we are looking at would be the amount of time the kayak was rented. We can model this question with the following equation.

[tex]f(x) = 25 + 3.50x[/tex]

with x being the time the kayak was rented in 30 min intervals. Since the kayak was rented for 4 hours we can multiply this by 2 to get 8 (30 min intervals). Now we can plug this into the formula and solve it.

[tex]f(8) = 25 + 3.50(8)[/tex]

[tex]f(8) = 25+  28[/tex]

[tex]f(8) = 53[/tex]

So to rent the kayak for 4 hours it would cost $53

Answer:

m∠P = 70°, m∠T = 20°, m∠SKP = 40° , and m∠MKT = 70°

Step-by-step explanation:

* Lets explain how to solve the problem

- In Δ PST

∵ m∠S = 90°

∴ m∠T + m∠P = 90° ⇒ interior angles of a triangle

∵ m∠SPK/m∠KPT = 5/2

- The ratio between the two angles are 5 : 2 , multiply the parts of the

  ratio by x, where x is a real number

∴ m∠SPK = 5x

∴ m∠KPT = 2x

∵ m∠SPK + m∠KPT = m∠P

∴ m∠P = 5x + 2x = 7x

- In ΔPKT

∵ KM ⊥ PT

∵ MP = Mt

∴ KM is perpendicular bisector of PT

∴ ΔPKT is an isosceles triangle with KP = KT

∵ KP = KT

∴ m∠KPT = m∠T

∵ m∠KPT = 2x

∴ m∠T = 2x

∵ m∠T + m∠P = 90°

∵ m∠P = 7x

∵ m∠T = 2x

∴ 2x + 7x = 90 ⇒ solve for x

∴ 9x = 90 ⇒ divide both sides by 9

∴ x = 10

∵ m∠P = 7x

∴ m∠P = 7(10) = 70°

∴ m∠P = 70°

∵ m∠T = 2x

∴ m∠T = 2(10) = 20°

∴ m∠T = 20°

- In ΔSKP

∵ m∠S = 90°

∵ m∠SPK = 5x = 5(10) = 50°

∴ m∠SKP = 180° - (90° + 50°) = 180° - 140° = 40° ⇒ interior angles of a Δ

∴ m∠SKP = 40°

- In Δ KMT

∵ m∠KMT = 90°

∵ m∠T = 20°

∴ m∠MKT = 180° - (90° + 20°) = 180° - 110° = 70° ⇒ interior angles of a Δ

∴ m∠MKT = 70°

Answer:

28

Step-by-step explanation:

opposite of the opposite of 28

- (-28)

A negative of a negative is a positive

+28

Answer:

28 is the answer from the 3 choices

Answer:

x=1

Step-by-step explanation:

Since you know two sides and are trying to find the missing side, you can use the Pythagorean Theorem. So fashion the equation like this:

x^2 + 3^2 = sqrt10^2. After simplify, which leads to x^2 + 9 =10. Then have the variable to one side by subtracting 9 on both sides. This leads to x^2=1. Finally, square root both sides which leads to 1. Note that any root of 1 is 1. So your answer becomes x=1.

Hope this helps!

Thus, based on the observed pattern and the linear model, we can expect the Photography Club to have 13 members in the sixth month.

Based on the updated coordinate points provided for the graph, which are (1,4), (2,5), (3,7), (4,9), and (5,11), we can describe the data and predict the number of members for the sixth month as follows:

1. Describe the Data:

  - At month 1, there are 4 members.

  - At month 2, there is an increase to 5 members.

  - At month 3, there are 7 members.

  - At month 4, there are 9 members.

  - At month 5, there are 11 members.

2. Identify the Pattern:

  - From month 1 to 2, the increase is 1 member.

  - From month 2 to 3, the increase is 2 members.

  - From month 3 to 4, the increase is 2 members.

  - From month 4 to 5, the increase is 2 members.

3. Predict the Number of Members for the Sixth Month:

  - We observe that after the first month, the number of members increases by 2 each month.

  - Assuming the pattern continues, we can predict that in the sixth month, the number of members will increase by 2 from the fifth month.

Therefore, the predicted number of members for the sixth month would be:

[tex]\[ 11 \text{ members at month 5} + 2 \text{ increase} = 13 \text{ members at month 6} \][/tex]

We can plot the provided data points and extend the line to the sixth month to visually confirm our prediction. Let's do that.

The linear model fitted to the given data points predicts approximately 12.6 members for the sixth month. Since the number of members must be a whole number, we can round this to 13 members.

Answer:

[tex]\large\boxed{y=-\dfrac{1}{3}x+\dfrac{1}{3}}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

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

We have the points (-5, 2) and (4, -1). Substitute:

[tex]m=\dfrac{-1-2}{4-(-5)}=\dfrac{-3}{9}=-\dfrac{1}{3}[/tex]

Put the value of the slope and the coordinates of the point (-5, 2) to the equation of a line:

[tex]2=-\dfrac{1}{3}(-5)+b[/tex]

[tex]2=\dfrac{5}{3}+b[/tex]          subtract 5/3 from both sides

[tex]\dfrac{1}{3}=b\to b=\dfrac{1}{3}[/tex]

Finally:

[tex]y=-\dfrac{1}{3}x+\dfrac{1}{3}[/tex]

The surface area of a sphere that is 8 inches is 201.06in²

Answer:

64 π inches^2  or 201.06 inches^2  to the nearest hundredth.

Step-by-step explanation:

The radius = 1/2 * the diameter

= 1/2 * 8

= 4 inches.

The surface area = 4 π r^2

4 π 4^2

= 64 π inches^2

or  201.06 inches^2  to the nearest hundredth.

Answer:

(3x-2) (9x^2 + 6x +4)

Step-by-step explanation:

27x^3−8

This is the difference of cubes

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

a^3 =27x^3  so a = 3x

b^3 =8  so b=2

a^2 = (3x)^2 = 9x^2   ab = (3x)*2 = 6x   b^2 = 2^2 =4

27x^3 -8 = (3x-2) (9x^2 + 6x +4)

Answer: b. The slope is -0.5. Starting at 4.0, the GPA will decrease by 0.5 for every text sent in class.

Step-by-step explanation:

We know that the equation of a line in intercept form is given by :-

[tex]y=mx+c[/tex], where m is the slope and c is the y-intercept.           (i)

Given : Sloane believes there is a correlation between the number of texts sent in class and GPA. She collected data and found that the line of best fit for the data can be modeled by the equation :-

[tex]y = 4.0-0.5x[/tex]

When we compare it to (i), we get

m=-0.5 and c=4.0

It means the slope is -0.5 and the function is starting at 4.0 and the GPA will decrease by 0.5 for every text sent in class (since its negative).

The correct option is B which is ''The slope is −0.5. Starting at 4.0, the GPA will decrease by 0.5 for every text sent in class''.

Given

The data can be modeled by the equation;

[tex]\rm y = 4.0 - 0.5x[/tex]

The standard form of the linear equation is;

[tex]\rm y = mx+c[/tex]

Where m is the slope of the equation and c is the intercept.

On comparing the given equation with the standard equation;

[tex]\rm y = 4.0 - 0.5x\\\\y = -0.5x+4.0[/tex]

The slope of the line m is -0.5 and intercept c is 4.0.

Hence, the slope is −0.5. Starting at 4.0, the GPA will decrease by 0.5 for every text sent in class.

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Answer:

The value of x is 7 ⇒ 1st answer

Step-by-step explanation:

* Lets revise a fact in the circle

- The two tangents drawn from a point out side the circle are equal

∵ RSTUV is circumscribed about a circle

∴ Each side of the pentagon is a tangent to the circle

- Look to the attached figure to know how we will solve the problem

- Each tangent divided into two parts

# RS = x + y

∵ RS = 8

∴ x + y = 8 ⇒ (1)

# RV = x + n

∵ RV = 12

∴ x + n = 12 ⇒ (2)

- Subtract (2) from (1)

∴ y - n = -4 ⇒ (3)

# ST = y + z

∵ ST = 12

∴ y + z = 12 ⇒ (4)

# TU = z + m

∵ TU = 15

∴ z + m = 15 ⇒ (5)

- Subtract (5) from (4)

∴ y - m = -3 ⇒ (6)

# UV = m + n

∵ UV = 9

∴ m + n = 9 ⇒ (7)

- Add (6) and (7)

∴ y + n = 6 ⇒ (8)

- Lets solve equation (3) and equation (8) to find y

∵ y - n = -4 ⇒ (3)

∵ y + n = 6 ⇒ (8)

- Add (3) and (8)

∴ 2y = 2 ⇒ divide two sises by 2

∴ y = 1

- Lets substitute the value of y in equation (1)

∵ x + y = 8 ⇒ (1)

∵ y = 1

∴ x + 1 = 8 ⇒ subtract (1) from both sides

∴ x = 7

* The value of x is 7

Answer:

120

Step-by-step explanation:

<2 = 120 degrees

<3 = <2  vertical angles

Assuming b is parallel to c

<3 = <6  alternate interior angles

<6 = <7 vertical angles

<2 = <7 =120

Answer:

They are adding 16 to the number each time. So the next number in the sequence would be 78.

Step-by-step explanation:

d(1) = 14

d(n) = d (n-1) + 16

14 + 16 = 30

30 + 16 = 46

46 + 16 = 62

62 + 16 = 78 and so on...

The recursive formula of the arithmetic sequence is [tex]d_{n}=d_{n-1} +16[/tex].

A recursive formula is a formula that defines any term of a sequence in terms of its preceding term(s).

The recursive formula of an arithmetic sequence is, [tex]a_{n}=a_{n-1} +d[/tex]

From the question

14, 30, 46, 62, .......

d = [tex]62-46 =46-30=30-14=16[/tex]

d = 16

As per sequence

d(1) = 14

[tex]d_{n}-d_{n-1} =d=16[/tex]

[tex]d_{n}=d_{n-1} +16[/tex]

The recursive formula of the arithmetic sequence is [tex]d_{n}=d_{n-1} +16[/tex].

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Answer:

2x^2 -8x

Step-by-step explanation:

2x(x-4)

Distribute the 2x

2x*x -2x*4

2x^2 -8x

Answer:

x=2

Step-by-step explanation:

Quotient means division

20/(x+3) =4

Multiply each side by (x+3)

(x+3)*20/(x+3) =4(x+3)

20 = 4(x+3)

Divide each side by 4

20/4 = 4(x+3)/4

5 = x+3

Subtract 3 from each side

5-3 = x+3-3

2 =x

Answer:

A: Step 1: 6x − 10 = 1; Step 2: 6x = 11

Step-by-step explanation:

First: remove parentheses by multiplying factors.

6x - 10 = 1

Second: Move the constants to the right side of the equation

6x = 1 + 10

6x = 11

Answer: The correct answer is "Step 1: 6x − 10 = 1; Step 2: 6x = 11"

Step-by-step explanation:

Answer:

The average weight of African elephant is about 2 .5 to 7 tons or we can say that 1800 kg to 6300 kg.

Weight of females are about 3 to 4 tons .On the other hand weight of males are about 2.5 to 7 tons.

African element can live up to 70 years but on the other hand the life of Asian

elephants up to 60 years.

The appropriate measurement for the weight of an African elephant is between 2,268 to 6,350 kg. Male elephants can grow significantly larger than the female elephants.

African elephants are the largest land animals in the world. They are larger than the Asian elephant. The average weight of the African elephants is between 2,268 to 6,350 kg, the trunk alone can weigh as much as 140 kg and they can grow between 2.5 to 4 m in height.

On the other hand, the Asian elephant's weight is between 2000 to 5000 kg. African elephants are famous for their large ears, that help them to stay cool in hot African weather. Both male and female African elephant has ivory tusks, but the male's tusk is longer and heavier than the female's.  

Elephants are herbivores. It means they only eat grasses, herbs, fruits, plants, and trees. African elephants can eat 150 kg of food a day. An elephant’s brain can weigh as much as 4-6 kg, they are famous as intelligent creatures. There are two kinds of African elephants which are the Savanna elephant and the Forest elephant. Savanna elephants are larger than forest elephants.

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Keywords: African elephant, Asian elephant, the average weight of an elephant