Write this equation in slope-intercept form.
5x + 5y = 15

A set of simultaneous equations is often known as a system of equations or an equation system. The solution of the system of equations is (1.894,2.791).

A set of simultaneous equations, often known as a system of equations or an equation system, is a finite collection of equations for which common solutions are sought.

Inconsistent System

For a system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

The solution of the two of the given function will be when the graph of the two the function will intersect with each other.

Using the graph the solutions are (1.894,2.791).

Hence, the solution of the system of equations is (1.894,2.791).

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Answer:

\(-16\)

Step-by-step explanation:

\(f(5)=4(5)-1=19 \\ \\ g(5)=2^5+3=35 \\ \\ (f-g)(5)=f(5)-g(5)=19-35=-16\)

You can use tangent trigonometric ratio since that deals with perpendicular and base and since the case is related physically to the right triangle, thus it would be useful here.

The height of the roof is \(5\sqrt{2}\\\\\) , the correct option is B.

Given

A right triangle is shown.

An altitude is drawn from the right angle to the opposite side to form another right angle.

The length of the altitude is h.

The length of one of the sides is 10.

Since the triangle is isosceles, hence the base angles will be 45 degrees.

Therefore,

The height of the roof is;

\(\rm Cos 45=\dfrac{Base}{Hypotenuse}\\\\Cos45=\dfrac{h}{10}\\\\h = 10 \times cos45'\\\\h=10\times \dfrac{1}{\sqrt{2} }\\\\h = 5 \times \sqrt{2} \times \sqrt{2} \times \dfrac{1}{\sqrt{2}}\\\\h=5 \times \sqrt{2} \\\\h=5 \sqrt{2}\)

Hence, the height of the roof is \(5\sqrt{2}\\\\\) .

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Answer:

b

Step-by-step explabnation:

Answer:

1/2

Step-by-step explanation:

we know that 1/4 of them failed, meaning that 3/4 of them passed.

1/3 of 3/4 is 1/4, meaning that 1/4 of the class got an A.

If 1/4 failed, and 1/4 passed with an A, that leaves 2/4 of the class that passed but didnt get an A, which simplifies to 1/2.

Hope this helps, and don't forget to mark brainliest <3

Answer:

x = 23

Step-by-step explanation:

if line j is parallel to line k then

5x + 9 + 33 + x = 180 add like terms

6x + 42 = 180 subtract 42 from both sides

6x = 138 divide both sides by 6

x = 23

Assuming an annual appreciation rate of 5.4 percent, collection of 47 1952 silver dollars, purchased at face value, will be worth approximately $148.51 when you retire in 2057.

To calculate the future value of your collection, we can use the formula for compound interest: FV = PV * (1 + r)ⁿ, where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years. In this case, the present value is the face value of the silver dollars, which is equal to 47 * $1 = $47.

To find the future value in 2057, we need to calculate the number of years from the present to 2057, which is 2057 - current year. Assuming the current year is 2023, the number of years is 2057 - 2023 = 34.

Plugging in the values, we have

FV = $\(47 * (1 + 0.054)^{34\) = $\(47 * (1.054)^{34\) ≈ $148.51.

Therefore, your collection of 47 1952 silver dollars will be worth approximately $148.51 when you retire in 2057, assuming they appreciate at an annual rate of 5.4 percent.

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For the given sequences, we can find reasonable formulas to represent the terms as follows:

1. {an} = {-8, -16, -24, -32, ...} can be represented by an = -8n.

2. {an} = {-3, 2, -3, 9, 27, ...} can be represented by an = (-1)^(n+1) * 3^n.

3. {an} = {1, 0, -1, 0, 1, 0, -1, 0, ...} can be represented by an = sin(nπ/2).

1. For the sequence {an} = {-8, -16, -24, -32, ...}, we observe that each term is obtained by multiplying the index n by -8. Hence, a reasonable formula for this sequence is an = -8n.

2. The sequence {an} = {-3, 2, -3, 9, 27, ...} appears to be alternating between positive and negative values. Moreover, each term is related to the exponentiation of 3, starting with 3^1, then 3^2, and so on.

To incorporate the alternation, we introduce (-1)^(n+1) to switch the sign. Therefore, a reasonable formula for this sequence is an = (-1)^(n+1) * 3^n.

3. The sequence {an} = {1, 0, -1, 0, 1, 0, -1, 0, ...} exhibits a repeating pattern where the terms alternate between 1, 0, and -1. This pattern can be represented using a trigonometric function.

We can use the sine function to achieve this periodic behavior, where the argument is (nπ/2). Hence, a reasonable formula for this sequence is an = sin(nπ/2).

By considering the patterns and characteristics of each sequence, we can establish reasonable formulas to represent the terms.

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Answer:

6√2=z

Step-by-step explanation:

As we are given a right angle we simply can apply the formula a²+b²=c².
A = 3
B = z

C =  8+1 which we add to get 9
Now, we plug this into the equation

9²=z²+3²

81=z²+9

72=z²

√72=z

√2x2x2x3x3 (expanding 72)

6√2=z

The surface area of the rectangular prism is 88 square inches.

Given that:

Length, L = 6 inches

Width, W = 2 inches

Height, H = 4 inches

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

SA = 2(6 x 2 + 2 x 4 + 4 x 6)

SA = 2 (12 + 8 + 24)

SA = 2 x 44

SA = 88 square inches

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Answer:

23.56 length units

Step-by-step explanation:

To calculate the perimeter of a triangle, we need to calculate the length of all the sides, then sum up the lengths.

To calculate each side, we take the differences of the coordinates of consecutive vertices, square, add, and take square-root (Pythagoras theorem).

Side 1: (3,-2), (5, -8)

difference in coordinates=(2,-6), length=sqrt(2^2+6^2) = sqrt(40)

Side 2: (5, -8), (-2,1)

difference in coordinates=(7,-9), length=sqrt(7^2+9^2) = sqrt(130)

Side 2: (-2,1), (3,-2)

difference in coordinates=(5,-3), length=sqrt(5^2+3^2) = sqrt(34)

Perimeter

= sum of sides

= sqrt(40)+sqrt(130)+sqrt(34)

= 6.32+11.40+5.83

= 23.56 approximately

The missing number of the algebraic expression is; x = 15

We are given the algebraic expression that we should find the number x, If 11/3 of x is 55.

This can be expressed as;

(11/3)x = 55

Multiply through by 3 to get;

(11/3)x * 3 = 55 * 3

11x = 165

Divide both sides by 11 to get;

11x/11 = 165/11

x = 15

Which we conclude that 15 is the missing number.

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Answer:

16

Step-by-step explanation:

The values of c for which the vectors v(-1, 2, c) and w(-7, 8, 9) are orthogonal are c = -1 and c = 17.

In order for two vectors to be orthogonal, their dot product must be zero. The dot product of two vectors v = (v1, v2, v3) and w = (w1, w2, w3) is given by v · w = v1w1 + v2w2 + v3w3.

Let's calculate the dot product of v(-1, 2, c) and w(-7, 8, 9):

v · w = (-1)(-7) + (2)(8) + (c)(9)

= 7 + 16 + 9c

= 23 + 9c

For the vectors to be orthogonal, the dot product must be zero, so we have:

23 + 9c = 0

Solving this equation for c, we get:

9c = -23

c = -23/9

Therefore, the vectors v(-1, 2, c) and w(-7, 8, 9) are orthogonal when c = -23/9.

However, we need to find all the values of c for which the vectors are orthogonal. Since the equation 9c = -23 only gives us one solution, we need to explore further. Let's substitute c = -23/9 back into the dot product equation:

v · w = 23 + 9(-23/9)

= 23 - 23

= 0

The dot product is zero, which means that the vectors v(-1, 2, c) and w(-7, 8, 9) are orthogonal when c = -23/9.

So, the only values of c for which the vectors v and w are orthogonal are c = -23/9 and c=17.

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Answer

The base of this triangle must be at least 9 feet.

Base ≥ 9 feet.

Explanation

We are given the required height of the the triangle and the minimum requirement for the area of the triangle. We are then asked to solve for the inequality that represents the possible lengths of the base of the triangle.

The area of a triangle is given as

Area = ½ × Height × Base

For this triangle,

Height = 8 feet

Area ≥ 36 square feet (At least 36 square feet).

Base = ?

½ × Height × Base ≥ 36

½ × 8 × Base ≥ 36

4 (Base) ≥ 36

Divide both sides by 4

Base ≥ 9 feet.

Hope this Helps!!!

Answer:

5 m

Step-by-step explanation:

V = l × w × h

480 = 12 × 8 × h

h = 480 ÷ 96 = 5 m

Answer:

5m

Step-by-step explanation:

Well volume is V=Bh. So you do 12 times 8= 96 thats your base. So you need to them do 480 divided by 96 which equals 5 so therefore 5 is your answer. Also just to make sure that's the right answer, do 12 times 8 times 5. That equals 480.

Answer:

3 miles

Step-by-step explanation:

1/8*24=3

Answer:

Step-by-step explanation:

He ran 24 times around the track1

Circumfrence of track=1/8 Mile

Total distance he covered=1/8*24

Distance = 3 miles

The coupon that gives the lower price, based on the percentage discounts is Coupon B.

To find the coupon that gives the lower price, apply the coupons to the price of the bicycle to see which value would be less after the coupon is applied.

Coupon A value after discount is:

= 81 x ( 1 - discount)

= 81 x ( 1 - 20%)

= $64.80

Coupon B value after discount is:

= 81 - 19

= $62

The coupon that gives the lower price is Coupon B.

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Answer:

it B

Step-by-step explanation:

i hope it help

The lengths of the diagonals are approximately 10.6 cm and 31.8 cm.

To solve this problem, we can use the formula for the area of a rhombus, which is A = (d₁ x d₂)/2, where A is the area, and d₁ and d₂ are the lengths of the diagonals.

We are given that the area of the rhombus is 168 square centimeters, so we can substitute this value into the formula:

=> 168 = (d₁ x d₂)/2.

We are also given that one diagonal is three times as long as the other, so we can express the length of one diagonal in terms of the other: d₁ = 3d₂.

Substituting this expression for d₁ into the formula for the area, we get:

168 = (3d₂xd₂)/2 336 = 3d₂²2 d₂² = 112 d₂ = √(112) = 10.6 (to the nearest tenth of a centimeter)

Using the expression for d₁ in terms of d₂, we can find the length of the other diagonal:

d₁ = 3d₂ = 3(10.6) = 31.8 (to the nearest tenth of a centimeter)

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The transformations to the graph of the quadratic function are given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

Additionally, when the function is multiplied by |a| > 1, it is said that the function is vertically stretched by a factor of a.

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Answer:

Ratio = Diameter of ball/Diameter of neuron

Ratio = 0.04 m/5×10⁻⁶ m

Ratio = 8,000

Therefore, the tennis ball is 8,000 times larger than the neuron,

Step-by-step explanation:

The value of m∠J in the triangle is 65°

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

We have triangle HIJ and m∠H = (4x + 1)°, m∠I = (2x-6)° and m∠J = (6x-7)°.

Since the sum of angle in a triangle is 180°. We can say:

m∠H +  m∠I +  m∠J = 180°

(4x + 1)° + (2x-6)° + (6x-7)° = 180°

4x + 1 + 2x-6 + 6x-7 = 180

12x - 12 = 180

12x = 180 + 12

12x = 192

x = 192/12

x = 16

To find m∠J = (6x-7)°, put x = 12 into  m∠J = (6x-7)°. That:

m∠J = 6(12) - 7

m∠J = 72 - 7

m∠J = 65°

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The equation of the parabola that models the shape of the arch is y = 0.03125x^2 - 1.25x, where y represents the height above the x-axis and x represents the horizontal distance from the vertex of the parabola.

A parabola can be represented by the equation y = ax^2 + bx + c, where a, b, and c are constants. In this case, we know the height (y-coordinate) of the arch is 50 feet when the width (x-coordinate) of the base is 80 feet. This gives us one point on the parabola: (80, 50).

To find the equation of the parabola, we need to determine the values of a, b, and c. We can do this by plugging in the coordinates of the known point into the equation.

Using the coordinates (80, 50), we have:

50 = a(80)^2 + b(80) + c

Since we only have one point, we can't directly solve for a, b, and c. However, we can use another piece of information about the shape of the arch. The vertex of a parabola lies at the point (-b/2a, c - b^2/4a). In this case, the vertex of the parabola is at the midpoint of the base width, which is (40, 0).

Substituting the coordinates of the vertex into the equation, we get:

0 = a(40)^2 + b(40) + c

Now we have a system of two equations with three unknowns:

50 = a(80)^2 + b(80) + c

0 = a(40)^2 + b(40) + c

To solve this system, we can subtract the second equation from the first equation to eliminate the c term:

50 = a(80)^2 + b(80) - (a(40)^2 + b(40))

Simplifying further:

50 = 3200a + 40b - 1600a - 40b

50 = 1600a

Solving for a:

a = 50/1600

a = 0.03125

Substituting this value of a back into one of the original equations, we can solve for b:

0 = (0.03125)(40)^2 + b(40) + c

0 = 50 + 40b + c

Since we don't have the value of c, we can choose an arbitrary value, let's say c = 0. This simplifies the equation to:

0 = 50 + 40b

Solving for b:

b = -50/40

b = -1.25

So, the equation of the parabola is y = 0.03125x^2 - 1.25x.

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Answer:

36 degrees

Step-by-step explanation:

The total of the angles is only 90, so to get the answer all you would have to do is 90 - 54 to get 36

Answer:

d =3√5

Step-by-step explanation:

\((2,0) =(x_1,y_1)\\ (8, -3) =(x_2,y_2)\\\\d =\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\\\d=\sqrt{\left(8-2\right)^2+\left(-3-0\right)^2}\\\\d = \sqrt{(6)^2+(-3)^2}\\ \\d = \sqrt{36+9}\\ \\d = \sqrt{45} \\\\d = 3\sqrt{5}\)

Answer:

x = 70

y = 110

u = 110

v = 70

z = 110

w = 110

Step-by-step explanation:

u = 110

v = 70

vertical angles are congruent

z = 110

alternate angles or Z angles. They are equal.

y = 110

vertical angles are congruent

x + z = 180

x + 110 = 180

  - 110    -110

x = 70

w = 180 - 70

w = 110

Answer:

hope this help you .look it once

Answer:

*

*

*

*       *

*  *   *

*  *   *

*  *   *   *

*  *   *   *   *

______________

0  1  2    3   4   5

Step-by-step explanation:

Answer:

false. example: 6 x 10. 6 is an integer, but 6 x 10 = 60, not 0. hope this helps

Step-by-step explanation:

- Zombie

Answer:

C

Step-by-step explanation:

Hello There!

so

y = -5x^2 + 8x +4

where y = height of ball and x = seconds after ball was thrown

The plus 4 is the y intercept and because y equals height of ball the 4 would represent the height that the ball was thrown at

~TheMathWiz

Answer:

It is C

Step-by-step explanation:

Answer:

Te answer is (b)

Step-by-step explanation:

When you subtract negative numbers, the operation automatically becomes addition.

According to the rule negative plus negative equals positive.

(-1)-(-5)= 6

(-)+(-)=+

(-1)+(-5)= 6