The graphs below have the same shape. What is the equation of the red graph?

Answer:

As baby porcupine is backed into cactus, so the spines of cactus will feel like spines of mother porcupine. So the baby porcupine will give  call to its mother.

Step-by-step explanation

He said hi Ma.

Answer: 7x + 1

Step-by-step explanation:

(6x-4)+(x+5)

Step 1: Remove Parentheses:

              6x-4+x+5

Step 2: Combine Like Terms:

             7x +1

Answer:

16 boxes

Step-by-step explanation:

16x5=80+150=230>15x16=240

Answer:

B ig

Step-by-step explanation:

A: 3(2x+7) = 6(X+4) - 3

<=> 6x+ 21 = 6x + 24 - 3 = 6x + 21

<=> 0 = 21 - 21 = 0

B: 3(6x-5)= 3(6x-5)+x

<=> 18x-15= 18x - 15 + x = 19x - 15

<=> 0 = x

C: 8(x-3) + 14= 2(4x+5)

<=> 8x - 24 + 14 = 8x - 10 = 8x + 10

<=> 0 = 0

D: 13x - 7 = 12( x - 1) +x + 5

<=> 13x - 7 = 12x -12 + x + 5 = 13x - 7

<=> 0 = 0

The missing part in the first triangle is 14

The missing part in the second triangle is 13.

The Pythagorean theorem is a fundamental theorem in geometry that applies specifically to right triangles.

According to Pythagorean theory, the square of the length of a right triangle's hypotenuse is equal to the sum of the squares of its legs.

For the first triangle as shown;

16^2 = 8^2 + t^2

t = √16^2 - 8^2

t = √192

t = 14

For the second triangle;

w= √8^2 + 10^2

w = 13

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Answer:

84%

Step-by-step explanation:

if 16% is lying the opposite of that is 84% which is not lying

this means that 84% of the male college students do not lie

Answer:

a=7b=9c=4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

each movie costs $2.75

there are 24 movies

24 x 2.75

=66

total cost=$66

Answer:

$66.

Step-by-step explanation:

All you need to do is $2.75 x 24 which equals to $66.00.

You can work this out by doing a long-multiplication method on paper or use a calculator.

Hope that helps. x

The other Washington DC landmark with coordinates (8,-10) is located in the fourth quadrant of the map.

To determine in which quadrant of the map a point with coordinates (8,-10) is located, we need to look at the signs of the x and y coordinates.

Since the x-coordinate (8) is positive and the y-coordinate (-10) is negative, this point is located in the fourth quadrant.

In general, the four quadrants of a Cartesian coordinate system are divided by the x and y-axes.

The first quadrant is located in the upper right-hand corner and contains points with positive x and y coordinates.

The second quadrant is located in the upper left-hand corner and contains points with negative x and positive y coordinates.

The third quadrant is located in the lower left-hand corner and contains points with negative x and y coordinates.

Finally, the fourth quadrant is located in the lower right-hand corner and contains points with positive x and negative y coordinates.

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Answer: $227,226.51

Step-by-step explanation:

First, we need to convert the period to weeks.

9 1/2 years = 9.5 years

1 year = 52 weeks

9.5 years = 494 weeks

Next, we can use the formula for the future value of an annuity:

FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)

where:

PMT = payment amount per period

r = annual interest rate

n = number of compounding periods per year

t = number of years

Plugging in the given values:

PMT = $300

r = 0.055 (5.5% expressed as a decimal)

n = 52 (compounded weekly)

t = 9.5 years = 494 weeks

FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)

FV = $227,226.51

Therefore, the future value of the annuity is approximately $227,226.51.

The expression represented by the model is 4. 6/13 - 2/7.

Expression in math is a combination of numbers, symbols, and operators, such as variables and constants, used to represent a mathematical relationship. It can be used to represent the solution of a problem or the evaluation of a function. Expressions are used in algebra, calculus, and other branches of mathematics to describe the relationships between different elements.

This expression can be seen by looking at the model; the shaded portion represents the fraction 6/13 and the portion that was subtracted from it is 2/7. Thus, the expression represented by the model is 6/13 - 2/7.

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The distance between points P and Q is √73

First, remember that the distance between two points whose coordinates are (a, b) and (c, d) is given by:

distance = √( (a - c)² + (b - d)²)

Here we can see that the coordinates of the two shown points are:

P = (-3, 2)

Q = (5, -1)

Replacing that in the distance formula we will get:

distance = √( (-3 - 5)² + (2 + 1)²)

distance = √( (-8)² + (3)²)

distance = √73

So the correct option is the third one.

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The Triangle Proportionality Theorem, also known as the Side Splitter Theorem, states that if a line is parallel to one side of a triangle, then it divides the other two sides proportionally.

Triangle Proportionality Theorem:

To prove this theorem, we begin by drawing a ΔABC with a line DE parallel to side AB. We then draw lines BD and CE, which intersect the parallel line DE at points F and G, respectively. By the properties of parallel lines, we know that ∠ADE and ∠ABD are congruent, and ∠AED and ∠ADB are congruent. Similarly, ∠CDE and ∠BDC are congruent, and ∠CED and ∠DCB are congruent.

We can then use the properties of similar triangles to show that ΔADE and ΔABC are similar, as are  ΔCDE and ΔACB. This means that the ratios of corresponding side lengths are equal:

BA/DE = CA/CE and CB/DE = AB/BD

We can then substitute CA - BA for CB in the first equation, and BD for AB in the second equation:

BA/DE = (CA - BA)/CE and CB/DE = BD/(CA - BA)

Cross-multiplying both equations, we obtain:

BA * CE = DE * (CA - BA) and CB * DE = BD * (CA - BA)

Adding the two equations, we get:

BA * CE + CB * DE = (DE + CE) * CA

Dividing both sides by CB * DE, we obtain:

BA/CB = (DE + CE)/CE * CA/DE = DE/CD

Thus, we have proven the Triangle Proportionality Theorem.

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Answer:

5≤x≤7

Step-by-step explanation:

For a given function f(x), the average rate of change in a given interval:

a ≤ x ≤ b

is given by:

\(r = \frac{f(b) - f(a)}{b - a}\)

Here we have:

f(x) = 4*log(x + 2)

And we want to see which interval has the smallest average rate of change, so we just need fo find the average rate of change for these 4 intervals.

1)  1≤x≤3

here we have:

\(r = \frac{f(3) - f(1)}{3 - 1} = \frac{4*log(3 + 2) - 4*log(1 + 2)}{2} = 0.44\)

2)  5≤x≤7

\(r = \frac{f(7) - f(5)}{7 - 5} = \frac{4*log(7 + 2) - 4*log(5 + 2)}{2} = 0.22\)

3) 3≤x≤5

\(r = \frac{f(5) - f(3)}{5 - 3} = \frac{4*log(5 + 2) - 4*log(3 + 2)}{2} = 0.29\)

4) −1≤x≤1

\(r = \frac{f(1) - f(-1)}{1 - (-1)} = \frac{4*log(1 + 2) - 4*log(-1 + 2)}{2} = 0.95\)

So we can see that the smalles average rate of change is in 5≤x≤7

3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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Answer:

6

Step-by-step explanation:

10-4 is 6 and they are on the same x axis

Answer:

15 girls

4x3=12 so u multiply 3 on both sides and 5 x 3=15

Answer: the ABC is up illogic of the Paul Graham that makes the box square root to DC=BA

Step-by-step explanation:

Statements                                                                 Reasons

1. AD ≅ BC; AD ∥ BC                                              1. given

2. ∠CAD and ∠ACB are alternate interior ∠s          2. definition of alternate                                                                                    interior angles

3. ∠CAD ≅ ∠ACB                                                    3. alternate interior                                                                                          angles are congruent

4. AC ≅ AC                                                              4. reflexive property

5. △CAD ≅ △ACB                                                  5. SAS congruency                                                                                                   theorem

6. AB ≅ CD                                                            6. Corresponding Parts                                                                                   of Congruent triangles are                                                                               Congruent (CPCTC)

7. ABCD is a parallelogram                                  7. parallelogram side                                                                                         theorem

Answer:

Option 2.

Step-by-step explanation:

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: \((- \infty} ,0)\) ∪ \((0, \infty} )\)

Range: \((- \infty} ,0)\)∪\((0, \infty} )\)

It can be seen that x = (3 ± √(9 + 32√3)) / 8, which can be expressed in surd form as (3 + √(9 + 32√3)) / 8 or (3 - √(9 + 32√3)) / 8.

To find x using the sine rule, we need to solve the equation:

sine(45) / x = sine(30) / (2x + 2√3)

Simplifying this equation, we have:

(2x - 1) / x = 1 / (2x + 2√3)

Cross-multiplying and simplifying further, we get:

(2x - 1)(2x + 2√3) = x

Expanding the brackets, we have:

\(4x^2 + 4\sqrt3x - 2x - 2\sqrt3 = x\)

Rearranging the terms and simplifying, we get:

\(4x^2 - 3x - 2\sqrt3 = 0\)

Using the quadratic formula, we can solve for x:

x = (-(-3) ± √((-3)^2 - 4(4)(-2√3))) / (2(4))

x = (3 ± √(9 + 32√3)) / 8

Therefore, x = (3 ± √(9 + 32√3)) / 8, which can be expressed in surd form as (3 + √(9 + 32√3)) / 8 or (3 - √(9 + 32√3)) / 8.

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Answer: The expression for the absolute value of x+2 when x is less than 2 is -(x+2).

Step-by-step explanation: When x is less than 2, x+2 is a negative number. The absolute value of a negative number is its opposite with the negative sign, so the absolute value of x+2 is -(x+2). Therefore, when x is less than 2, the expression for the absolute value of x+2 is -(x+2).

Joel be not able to make a right triangle with his fence because the given dimensions are not satisfying for Pythagoras theorem.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Dimensions of triangle he has to use for fencing are

15 feet, 8 feet, and 20 feet.

For making it a right triangle it must satisfy the "Pythagoras theorem" which states that

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

H²=B²+P²

20²=15²+18²

400=225+64

400≠289

No, it will not be able to make a right triangle.

Hence, Joel will be not able to make a right triangle with his fence because the given dimensions are not satisfying for pythagoras theorem.

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The complete question is given below:

Joel wants to fence off a triangular portion of his yard for his chickens. The three pieces of fencing he has to use are 15 feet, 8 feet, and 20 feet long.

1. Will he be able to make a right triangle out of his fence? Why or why not?

Using the method of undetermined coefficients, the particular solution is:

\(\mathrm{y_p(t) = 6e^{2t} \times cos(9t) + 3^{2t} \times sin(9t)}\)

To use the method of undetermined coefficients, we assume that the particular solution has the same form as the forcing term, but with undetermined coefficients.

Let's start by finding a particular solution for the equation:

y′′ − 4y′ + 81y = 48\(e^{2t}\)cos(9t) + 80\(e^{2t}\)sin(9t) + 3\(e^{(-t)\)

Since the forcing term contains both exponential and trigonometric functions, we'll assume that the particular solution is of the form:

\(y_p\)(t) = A*\(e^{2t}\)cos(9t) + B\(e^{2t}\)*sin(9t) + C\(e^{(-t)\)

where A, B, and C are undetermined coefficients that we need to determine.

Let's find the first and second derivatives of \(y_p\)(t):

\(y'_p\)(t) = (2A + 9B)*\(e^{2t}\)*sin(9t) + (2B - 9A)*\(e^{2t}\)*cos(9t) - C\(e^{(-t)\)

\(y''_p\)(t) = (4A - 81B)*\(e^{2t}\)*cos(9t) + (4B + 81A)*\(e^{2t}\)*sin(9t) + C\(e^{(-t)\))

Substituting these expressions into the differential equation, we get:

(4A - 81B)*\(e^{2t}\)*cos(9t) + (4B + 81A)*\(e^{2t}\)*sin(9t) + C\(e^{(-t)\)

4[(2A + 9B)*\(e^{2t}\)*sin(9t) + (2B - 9A)*\(e^{2t}\)*cos(9t) - C\(e^{(-t)\)

81[A*\(e^{2t}\)cos(9t) + B\(e^{2t}\)*sin(9t) + C\(e^{(-t)\)]

= 48\(e^{2t}\)cos(9t) + 80\(e^{2t}\)sin(9t) + 3\(e^{(-t)\)

Simplifying and grouping terms, we get:

[(4A + 18B)cos(9t) + (18A - 4B)sin(9t)]\(e^{2t}\)+ (81C + 3)\(e^{(-t)\) = 48\(e^{2t}\)cos(9t) + 80\(e^{2t}\)sin(9t) + 3\(e^{(-t)\)

Since the two sides of the equation must be equal for all values of t, we can equate the coefficients of the exponential and trigonometric functions on both sides:

4A + 18B = 48 => A = 6

18A - 4B = 80 => B = 3

81C + 3 = 3 => C = 0

Therefore, the particular solution is:

\(y_p\)(t) = 6\(e^{2t}\)*cos(9t) + 3\(e^{2t}\)*sin(9t)

Thus, the general solution of the differential equation is:

\(\mathrm{y(t) = y_h(t) + y_p(t)}\)

where \(y_h\)(t) is the complementary solution. Since the characteristic equation of the differential equation is r² - 4r + 81 = 0, it has two complex conjugate roots: r = 2 ± 9i. Therefore, the complementary solution is:

\(y_h\)(t) = \(c_1\)*\(e^{2t}\)cos(9t) + \(c_2\)\(e^{2t}\)*sin(9t).

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Answer:

four times "h" plus one-half is equal to two-thirds of "h".

\(h=-\frac{3}{20}\)

just in case u need it

a...cause she's having trouble concentrating,for her to work she needs to tell her realtor she can only receive text messages it enables her to know the process of the house hunt

The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

\($\frac{AB}{BC} = \frac{AD}{AB}$\)

Cross-multiplying, we get:

\($AB^2 = BC \cdot AD$\)

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

\($\frac{AC}{BC} = \frac{AD}{AC}$\)

Cross-multiplying, we have:

\($AC^2 = BC \cdot AD$\)

Now, we can substitute the derived expressions into the original equation:

\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)

It was made possible by cross-product property.

Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

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The length of the diameter of the sphere is 30 cm.

The surface area of a sphere is given by the formula:

\(A = 4\pi r^2\)

where A is the surface area and r is the radius of the sphere.

We are given that the surface area of the sphere is 900π cubic cm. Therefore:

\(A = 4\pi r^2 = 900\pi\)

Dividing both sides by 4π, we get:

\(r^2 = 225\)

Taking the square root of both sides, we get:

r = 15

The diameter of the sphere is twice the radius, so:

d = 2r = 30

Therefore, the length of the diameter of the sphere is 30 cm.

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Answer:

\(\frac{1}{50}\)

Step-by-step explanation:

2% = \(\frac{2}{100}\) = \(\frac{1}{50}\)

The slope of the road expressed as fraction is 2/100. When we simplify 2/100, the result obtained is 1/50

From the question given above, we were told that the grade of the road is 2% which is equal to the slope. Thus, we can express 2% as fraction as illustrated below:

2% = 2/100

2/100 can be simplified to it's lowest term as shown below:

2/100

Divide the numerator and denominator by 2

1/50

Thus,

2/100 = 1/50

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