Five less than 3 times a number b is greater than the opposite of 8.


Answer:

12

Step-by-step explanation:

The figure is a right triangle with hypotenuse = QS

The  base from the graph = 4 units
(or you can just subtract the x-coordinates 2 - (-2) = 4)

The height from the graph is 3 units
(Or you can subtract the y-coordinates: 1 - (-2) = 3)

Since this is a right triangle the square of the hypotenuse = sum of squares of the other two sides

QS² = 3² + 4² = 9 + 16 = 25

QS, the hypotenuse = √25 = 5

The perimeter = sum of the sides = 3 + 4 + 5 = 12 units

there are four lateral faces

Answer:

1

2

4

Step-by-step explanation:

a. The center of the circle is (-2, -1).

b. The radius of the circle is √136.

c. The equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.

a. To find the center of the circle, we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

In this case, the endpoints of the diameter are P(-7, -4) and Q(3, 2).Applying the midpoint formula:

Midpoint = ((-7 + 3)/2, (-4 + 2)/2)

= (-4/2, -2/2)

= (-2, -1)

Therefore, the center of the circle is at the coordinates (-2, -1).

b. To find the radius of the circle, we can use the distance formula, which calculates the distance between two points (x1, y1) and (x2, y2). The radius of the circle is half the length of the diameter, which is the distance between points P and Q.

Distance = √\([(x2 - x1)^2 + (y2 - y1)^2]\)

Using the distance formula:

Distance = √[(3 - (-7))^2 + (2 - (-4))^2]

= √\([(3 + 7)^2 + (2 + 4)^2]\)

= √\([10^2 + 6^2\)]

= √[100 + 36]

= √136

Therefore, the radius of the circle is √136.

c. The equation for a circle with center (h, k) and radius r is given by:

\((x - h)^2 + (y - k)^2 = r^2\)

In this case, the center of the circle is (-2, -1), and the radius is √136. Substituting these values into the equation:

\((x - (-2))^2 + (y - (-1))^2\) = (√\(136)^2\)

\((x + 2)^2 + (y + 1)^2 = 136\)

Therefore, the equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.

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The requried, probability that both the first digit in the last digit of the three-digit number is even numbers is 20%.

To count the number of three-digit numbers with distinct digits that can be formed using the digits 1, 2, 3, 5, 8, and 9, we can use the permutation formula:

P(n, r) = n! / (n-r)!

In this case, we have n = 6 (since we have 6 digits to choose from) and r = 3 (since we want to form three-digit numbers). Using the formula, we get:

P(6, 3) = 120

We can choose the first digit in two ways (2 or 8), and we can choose the last digit in three ways (2, 8, or 6). For the middle digit, we have four digits left to choose from (1, 3, 5, or 9), since we cannot repeat digits. Therefore, the number of three-digit numbers with distinct digits that have an even first and last digit is:

2 x 4 x 3 = 24

The total number of three-digit numbers with distinct digits is 120, so the probability that a randomly chosen three-digit number with distinct digits has an even first and last digit is:

24/120 = 0.2 or 20%

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Answer:

The answer is 5q + 9.

Step-by-step explanation:

1) Collect like terms.

\(5q + (22 - 13)\)

2) Simplify.

\(5q + 9\)

hence, the answer is 5q + 9.

The common ratio of the resulting sequence is 1.4.

Given that, the three terms are 60, 100 and 180.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

Let the same constant is added to the given number is x.

60+x, 100+x and 180+x

Now, the common ratio is

(100+x)/(60+x) = (180+x)/(100+x)

⇒ (100+x)(100+x)=(180+x)(60+x)

⇒ (100+x)²=10800+180x+60x+x²

⇒ 10000+200x+x²=10800+180x+60x+x²

⇒ 10000+200x=10800+180x

⇒ 20x=800

⇒ x=40

The three number are 100, 140 and 220

The common ratio is 140/100 =1.4

Therefore, the common ratio of the resulting sequence is 1.4.

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The approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Total of 22 is more than 4500 is equivalent to average of 22 is more than \($\frac{4500}{22}\)=204.545

\($$\begin{aligned}P(\bar{x} > 204.545) & =1-P(\bar{x} < 204.545) \\& =1-P\left(\frac{\bar{x}-\mu}{\sigma / \sqrt{u}} < \frac{204.545-195}{35 / \sqrt{22}}\right) \\& =1-P(z < 1.2792) \\\end{aligned}$$\)

                        = 1 - 0.8997

                        = 0.1003

                        = 10.03%

Therefore, the approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

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The prime factorization of 45 written as exponents from least to greatest is 45 = 3² × 5¹

Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, which includes 1 and the number.

Using prime factorisation, we shall consider the first five prime numbers which are; 2, 3, 5, 7, and 11.

45 cannot be divided by 2 without a remainder so we use 3;

45/3 = 15

15 can also be divided by 3 so;

15/3 = 5

3 cannot divide 5 without a remainder so we use 5;

5/5 = 1

hence;

45 = 3 × 3 × 5

45 = 3² × 5¹

Therefore, the prime factorization of 45 written as exponents from least to greatest is 45 = 3² × 5¹

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Answer:

A. V + 18 < 30

Step-by-step explanation:

First of all, less than is the sign that points to the left,

Secondly, I'm guessing that y is actually V,

Before Ray gave Jan cards, she had 18,

so it is 18 plus V (the number of cards Ray gave her),

SO,

V + 18 < 30

The solutions to the vectors a, b, and c are infinite. Given that there is just one equation and two variables

A quantity or phenomenon with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation.

Given, three vectors a, b, and c that make 0◦, 90◦, and 180◦ angles with w.

w is a vector: w = <1, 2>

Since magnitude is not given we will form the equation in the terms of x and y for all three vectors

a makes a 0-degree angle with w

So, the multiple of a and w will be 1

x + 2y = -1

b makes a 90-degree angle with w

So, the multiple of a and w will be 0

x + 2y = 0

c makes a 180-degree angle with w

So, the multiple of a and w will be -1

x + 2y = 1

Therefore, Vector a, b, and c will have infinite solutions Since there are two variables and one equation only

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Answer:

I think 1.75

Step-by-step explanation:

the long side is two times the amount of the tall side so take the smaller long side and divide by two.

Answer:

Step-by-step explanation:

Substitution method can be applied in four steps. Step 1: Solve one of the equations for either x = or y = . Step 2: Substitute the solution from step 1 into the other equation. Step 3: Solve this new equation Happy too help!

It took Ringani 2.8 years  to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.

To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the time in years

In this case, we have:

P = R8,500.00

A = R30,000.00

r = 7.04% = 0.0704 (in decimal form)

n = 1 (compounded annually)

We want to find the value of t.

Using the formula, we can rearrange it to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the given values, we have:

t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))

Calculating this using a calculator, we find that t is approximately 2.8 years.

Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.

The correct answer choice is C. 2.8 years.

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Answer:

Step-by-step explanation:

The adjacent angle to the missing angle must sum to 180 degrees. So a=180-74=106 degrees. The sum of the three angles of the triangle must also sum to 180.

x+49+106=180

x+155=180

x=25

Answer:

106

Step-by-step explanation:

x+49=74

x=74-49=25

y=74=180

y=180-74=106

im sorry im late if u see this yw!

Option (c) 3.

Step-by-step explanation:

The given expression is, \({ \pink{ \sf{(x - 5) - 1}}} \: { \to} \: { \red{ \tt{ {eq}^{n} (1)}}}\)

x = 9 (given).

Substitute the value of x in Eqⁿ (1)

\({ \pink{ \sf{(9 - 5) - 1}}}\)

\({ \pink{ \sf{4 - 1}}}\)

\({ = { \boxed{ \blue{ \sf{3}}}}}\)

Answer:

x=0.4

Step-by-step explanation:

isolate the variable by dividing each side by factors that don't contain the variable

The slope intercept form of the given equation is,

y = 5x - 1/4

Given an equation of a line as,

5x - y = 1/4

We have to write the equation of the line in slope intercept form.

Equation of the line in slope intercept form is,

y = mx + c

Here m is the slope and c is the y intercept.

Rearranging the given equation,

5x = y + 1/4

5x - 1/4 = y

or,

y = 5x - 1/4

Hence the slope intercept form is y = 5x - 1/4.

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Answer:

First 5= vertically and 5=7 straight angle

So the different number has a 4 with a value of 40.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To solve this problem, we need to first identify the place value of the digit 4 in the given number.

The digit 4 is in the hundreds place in the number 431.67, so its value is 4 x 100 = 400.

According to the problem statement, the 4 in the different number represents a value which is one-tenth of the value of the 4 in 431.67. Therefore, the value of the 4 in the different number is:

400/10 = 40

To determine the value of the different number, we need to look at the other digits in the number. Since we don't have any information about the other digits, we cannot determine the value of the different number. The answer is that the value of the different number cannot be determined with the information given.

Therefore, So the different number has a 4 with a value of 40.

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Don't we need the full question?

The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

A division is a process of splitting a specific amount into equal parts.

We have to find 3x³-2x²+7x+9 divided by x²-3x

3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.

The steps to solve this are given below.

Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next digit of the dividend (if present).

Step 5: Repeat the same process.

Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

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Answer:

The equation of the line that passes  through the point (2, -1) and has a slope of -3 will be:

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

Given

substituting m = -3 and the point (2, -1) in the slope-intercept form of the line equation

y = mx+b

-1 = -3(2)+b

-1 = -6 + b

b = -1 + 6

b = 5

Thus, the y-intercept form of the line equation is b = 5

now substituting b = 5 and m = -3 in the slope-intercept form of the line equation

y = mx+b

y = -3x + 5

Thus, the equation of the line that passes  through the point (2, -1) and has a slope of -3 will be:

Answer:

The intensity of the 2011 earthquake was about 6 times the intensity of the 2003 earthquake.

Step-by-step explanation:

To compare the intensities, we first need to convert the magnitudes to intensities using the log formula. Then we will set up a ratio to compare the intensities.

Convert the magnitudes to intensities and write them in exponential form.

R=logI

2011 earthquake:

9.1I=logI=109.1

2003 earthquake:

8.3I=logI=108.3

Form a ratio of the intensities.

intensity for 2011intensity for 2003

Substitute in the values and divide by subtracting the exponents to find

109.1108.3100.8≈6.

The intensity of the 2011 earthquake was about 6 times the intensity of the 2003 earthquake.

Your answer:

The intensity of the 2011 earthquake was about 15 times the intensity of the 2003 earthquake.

The intensities of the two earthquakes will be 6.3095.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

In 2011, Japan encountered a serious quake with an extent of 9.1 on the Richter scale. In 2003, Japan encountered another extraordinary seismic tremor that deliberate 8.3 on the Richter scale.

The intensity of the earthquake is given as,

㏒ (I₁ / I₂) = M₁ - M₂

㏒ (I₁ / I₂) = 9.1 - 8.3

Simplify the equation, then we have

㏒ (I₁ / I₂) = 9.1 - 8.3

㏒ (I₁ / I₂) = 0.8

Take anti log, then we have

(I₁ / I₂) = 6.3095

The intensities of the two earthquakes will be 6.3095.

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(10+77-12)+(-672-18+51)

(87-12)+(-690+51)

75+(51-690)

75-639

-564

---

hope it helps

Answer:

\(y(x)=c_1cos(5x)+c_2sin(5x)+0.1xsin(5x)-0.1xcos(5x)\)

Step-by-step explanation:

The general solution will be the sum of the complementary solution and the particular solution:

\(y(x)=y_c(x)+y_p(x)\)

In order to find the complementary solution you need to solve:

\(y''+25y=0\)

Using the characteristic equation, we may have three cases:

Real roots:

\(y(x)=c_1e^{r_1x} +c_2e^{r_2x}\)

Repeated roots:

\(y(x)=c_1e^{rx} +c_2xe^{rx}\)

Complex roots:

\(y(x)=c_1e^{\lambda x}cos(\mu x) +c_2e^{\lambda x}sin(\mu x)\\\\Where:\\\\r_1_,_2=\lambda \pm \mu i\)

Hence:

\(r^{2} +25=0\)

Solving for \(r\) :

\(r=\pm5i\)

Since we got complex roots, the complementary solution will be given by:

\(y_c(x)=c_1cos(5x)+c_2sin(5x)\)

Now using undetermined coefficients, the particular solution is of the form:

\(y_p=x(a_1cos(5x)+a_2sin(5x) )\)

Note: \(y_p\) was multiplied by x to account for \(cos(5x)\) and \(sin(5x)\) in the complementary solution.

Find the second derivative of \(y_p\) in order to find the constants \(a_1\) and \(a_2\) :  

\(y_p''(x)=10a_2cos(5x)-25a_1xcos(5x)-10a_1sin(5x)-25a_2xsin(5x)\)

Substitute the particular solution into the differential equation:

\(10a_2cos(5x)-25a_1xcos(5x)-10a_1sin(5x)-25a_2xsin(5x)+25(a_1xcos(5x)+a_2xsin(5x))=cos(5x)+sin(5x)\)

Simplifying:

\(10a_2cos(5x)-10a_1sin(5x)=cos(5x)+sin(5x)\)

Equate the coefficients of \(cos(5x)\) and \(sin(5x)\) on both sides of the equation:

\(10a_2=1\\\\-10a_1=1\)

So:

\(a_2=\frac{1}{10} =0.1\\\\a_1=-\frac{1}{10} =-0.1\)

Substitute the value of the constants into the particular equation:

\(y_p(x)=-0.1xa_1cos(5x)+0.1xsin(5x)\)

Therefore, the general solution is:

\(y(x)=y_c(x)+y_p(x)\)

\(y(x)=c_1cos(5x)+c_2sin(5x)+0.1xsin(5x)-0.1xcos(5x)\)

The absolute value equation  that have the give solution set is

|x  - 1/12|  =  5/12

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

x−b=c

1/2 - b =  c

-1/3 - b = c

only possible

if | 1/2 - b|  = | -1/3 - b|

1/2 - b = b + 1/3

=> 2b = 1/6

=> b = 1/12

We have

|x  - 1/12|  =  5/12

The absolute value equation  that have the give solution set is

|x  - 1/12|  =  5/12

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In the given graph, the x-intercepts are (2,0) and (6,0).

The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.

The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).

The sign of the leading coefficient is positive, since it is 1/2.

To find the equation of the quadratic function, we start by using the vertex form:

\(y = a(x - h)^2 + k\)

where (h, k) is the vertex. Plugging in the given vertex (4,-2), we get:

\(y = a(x - 4)^2 - 2\)

Next, we use the other two points to find two additional equations:

\(6 = a(8 - 4)^2 - 2 (plugging in (8,6))\\0 = a(2 - 4)^2 - 2 (plugging in (2,0))\)

Simplifying these equations, we get:

\(6 = 16a - 2\\8a = 4 -- > a = 1/2 \\0 = 4a - 2 \\4a = 2 -- > a = 1/2 \\\)

So the equation of the quadratic function is:

\(y = (1/2)(x - 4)^2 - 2\)

Now, we can answer the questions:

The y-intercept is the point where the graph intersects the y-axis. To find it, we set x = 0 in the equation:

\(y = (1/2)(0 - 4)^2 - 2 = 6\)

So the y-intercept is (0,6).

To find the x-intercepts, we set y = 0 in the equation:

\(0 = (1/2)(x - 4)^2 - 2\)

Simplifying, we get:

\((x - 4)^2 = 4\\ - 4 = \pm 2 \\= 2, 6\)

So the x-intercepts are (2,0) and (6,0).

The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.

The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).

The sign of the leading coefficient is positive, since it is 1/2.

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