5. Solve for x.
10x + 44
8x - 23
what’s the equation to solve this?

Step-by-step explanation:

step 1. 4x + 27 + 3x = 90 (definition of a rectangle)

step 2. 7x = 63 (collect like terms. subtract 27 from both sides)

step 3. x = 9 (divide both sides by 7)

Answer:

Step-by-step explanation:

Let the price for children and adults package be represented with x and y respectively.

For the first week the sum of the package will be as follows:

3x+8y = 126

For the two weeks after:

6x+4y= 108

So, we will be having two equations

3x+8y = 126..... (1)

6x+4y= 108.......(2)

These are simultaneous equations

From equation 1

3x+8y = 126

3x = 126-8y

X = 126-8y/3 ............. (3)

Put equation 3 into 2

6 ( 126-8y)/3 +4y = 108

756-48y/3 +4y = 108

756-48y+12y/3 = 108

Cross multiplying

756-48y+12y= 108×3

756-48y+ 12y = 324

Collecting like terms

756-324 = 48y-12y

432= 36y

Divide both sides by 36

432/36 = 36y/36

y= 12

Substituting y into equation 1

3x+8= 126

3x+96=126

3x= 126-96

3x= 30

Divide both sides by 3

3x/3 = 30/3

x = 10

Hence for each of the packages for children and adults. It will be 10 and 12 respectively.

Answer:

Δ ABC and Δ DEF are similar because their corresponding sides are proportional

Step-by-step explanation:

Two triangles are similar if their corresponding sides are proportional which means the corresponding sides have equal ratios

In the two triangles ABC and DEF

∵ AB = 4 units

∵ DE = 2 units

∴ \(\frac{AB}{DE}=\frac{4}{2}=2\)

∵ BC = 6 units

∵ EF = 3 units

∴ \(\frac{BC}{EF}=\frac{6}{3}=2\)

∵ CA = 2 units

∵ FD = 1 units

∴ \(\frac{CA}{FD}=\frac{2}{1}=2\)

∴ \(\frac{AB}{DE}=\frac{BC}{EF}=\frac{CA}{FD}=2\)

∵ All the ratios of the corresponding sides are equal

∴ The corresponding sides of the two triangles are proportional

∴ Δ ABC is similar to Δ DEF

Answer:

12 free throws

10 2-pointers

4 3-pointers

Step-by-step explanation:

Let x = 1 point

y = 2 point

z = 3 point

x + y + z = 26

x = y + 2

x = 3z

Let's make it to where the last two equations are in terms of x

Subtract 2 from both sides of the middle equation

x = y + 2

- 2 - 2

y = x - 2

Divide both sides by 3 in the bottom equation

x/3 = 3z/3

z = x/3

Now plug in the new y and z

x + x - 2 + x/3 = 26

2x + x/3 - 2 = 26

Add 2 to both sides

2x + x/3 - 2 = 26

+ 2 + 2

2x + x/3 = 28

Add up the x terms and don't forget about common denominators

6x/3 + x/3 = 28

7/3x = 28

Multiply both sides by 3/7 to isolate the x variable

(7/3x = 28)3/7

x = 12

Now plug the new x into the original equations to find the remaining variables.

12 = y + 2

- 2 - 2

y = 10

12 = 3z

12/3 = 3z/3

z = 4

12 free throws

10 2-pointers

4 3-pointersAnswer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

If it has really helped u plz don't forget to thank me plz...

The coordinates of point T exists (0,5) and the midpoint of ST is (5,-2) then the coordinates of point T is S(10, -9).

Use midpoint formula and assume S(x, y):

(0 + x)/2 = 5

⇒ x / 2 = 5

⇒ x = 10

(5 + y)/2 = -2

⇒ 5 + y = -4

⇒ y = -4 - 5

⇒ y = -9

The complete question is:

The coordinates of point T are (0,5). The midpoint of ST is (5,-2). Find the coordinates of point S.​

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Answer:

B=28

Step-by-step explanation:

Hi there!

\(\large\boxed{x \leq -9}\)

3x - 7 ≥ 4x + 2

Subtract 3x from both sides:

3x - 3x - 7 ≥ 4x - 3x + 2

-7 ≥ x + 2

Subtract 2 from both sides:

-7 - 2 ≥ x + 2 - 2

-9 ≥ x

x ≤ -9

Answer:

q=y + K/n

Step-by-step explanation:

Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

Answer:???

Step-by-step explanation:

Answer:

74.85 (Plato/Edmentum)

Step-by-step explanation:

#1: 28.97 + 45.876

#2: 74.846

#3: 74.85

The limit of the sequence \({ln(155n + e^{-24n})/(184n + tan(162n))^{1/n}}\) as n approaches infinity is ln(155/184).

We are given that;

Sequence= \({ln(155n + e^{-24n})/(184n + tan(162n))^{1/n}}\)

Now,

To find the limit of a sequence, we need to determine whether the sequence approaches a fixed value as its index approaches infinity1.

One way to do this is to use the definition of limit2, which says that lim n→∞ {an} = L if given ǫ > 0, an≈ ǫ L for n ≫ 1.

Another way is to use a limit calculator 3, which can compute both one-dimensional and multivariate limits with ease.

Therefore, by geometric sequence the answer will be ln(155/184).

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The distribution of the given function is a uniform distribution.

A strictly increasing function is the one which increases continuously in a given interval. If f-1(u) is a strictly increasing function of u, then the distribution of f-1(u) is the same as that of u. This is because a strictly increasing function preserves the rank ordering of its input, so if u-1 and u-2 are two random variables with a uniform distribution on the interval (0,1), then the rank order of f-1(u-1) and f-1(u-2) will be the same as the rank order of u-1 and u-2. Since the uniform distribution is defined by the rank order of its values, this means that the distribution of f-1(u) is also uniform on the interval (0,1).

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The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles is 244 minutes.

When the distribution is normal, we use the z-score formula.

In a set with mean µ and standard deviation σ , the z-score of a measure X is given by:

Z = (X – µ) / σ

The Z-score shows how many standard deviations the measure is from the mean. After finding the Z-score, need to look at the z-score table and discover the p-value associated with the z-score. This p-value is the probability that the value of the measure is smaller than X, means, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

So, in this case, given that:

µ = 249, σ = 20

The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles:

100 – 80 = 20th percentile, which is X when Z has a p-value of 0.2. So, X when Z = –0.253.

Now, put all the values into the formula:

Z = (X – µ) / σ

–0.253 = (X – 249) / 20

X – 249 = –0.253 * 20

X = 244

Hence, the candle burns for 244 minutes.

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Answer:

507x223 is greater than 530 x 200

914x385 is less than 900 x 400

Answer:

Absolute value means taking the positive value, ie drop the negative sign.

Absolute value brackets are: | value |

|(4,-4)| = (4,4)

|(-3,-4)| = (3,4)

Hope that helps

Slope of the line passing through (-5,-4)  and (-1,3)is 1.75

The slope formula

slope = (y₂ - y₁) / (x₂ - x₁)

Notice that the slope of a line is easily calculated by hand using small, whole number coordinates. The formula becomes increasingly useful as the coordinates take on larger values or decimal values.

The  points belong to an increasing, linear function.

Equation: y = 1.75x + 4.75.

m=7/4=1.75.

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The length of the segment joining the points (1, -8) and (5, 0) is approximately 8.94 units.

find the length of the segment joining the points (1, -8) and (5, 0), we can use the distance formula. The distance formula is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, (x1, y1) = (1, -8) and (x2, y2) = (5, 0).

Substituting the values into the distance formula, we have:

d = √((5 - 1)^2 + (0 - (-8))^2)

= √(4^2 + 8^2)

= √(16 + 64)

= √80

≈ 8.94

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The risk of explosion in the process industry is 6.6594e-06 per year.

To calculate the risk of explosion, we need to consider the probability of a gas release, the probability of ignition, and the probability of fatal injury.

Step 1: Calculate the probability of an explosion.

The probability of a gas release per year is given as\(1.23 * 10^-^5\).

The probability of ignition is 0.54.

The probability of fatal injury is 0.32.

To calculate the risk of explosion, we multiply these probabilities:

Risk of explosion = Probability of gas release * Probability of ignition * Probability of fatal injury

Risk of explosion = 1.23 * \(10^-^5\) * 0.54 * 0.32

Risk of explosion = 6.6594 *\(10^-^6\) per year

Therefore, the risk of explosion in the process industry is approximately 6.6594 * 10^-6 per year.

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3. 2 is the mean of the sampling distribution of the sample mean for samples of size 16.

Hence,

3. 2 is the mean of the sampling distribution of the sample mean for samples of size 16.

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The probability of a student running the mile in less than 332 seconds is 0.0003.

We can use the z-score to solve this problem.

First, we need to calculate the z-score for the given time of 332 seconds:

z = (332 - 470) / 60

z = -7.8

Next, we need to use the z-score to calculate the probability of a student running the mile in less than 332 seconds. To do this, we can use the z-score table, which gives the probability of a value being less than a certain z-score.

Using the table, the probability of a student running the mile in less than 332 seconds is 0.0003.

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Answer:

b = 12.6

Step-by-step explanation:

a*2 + b*2 = c*2

6*2 + b*2 = 14*2

36 + b*2 = 196

Subtract 36 from both sides

36 + b*2 = 196

-36             -36

b*2 = 160

Find the square root of both

b = 12.64911064  or 12.6

The equation in states that the total fee for a family of 5 entering the park is $45.

Fee is a payment made to an individual or organization in exchange for a service or product. Fees can also be charged for use of a facility, such as a gym or park.

This can be calculated using the following equation:

Total Fee = 3 (car fee) + 5 (person fee)

       = 3 x $3 + 5 x $3

      = $45

This equation illustrates that the family of five will pay a total fee of $45. The car fee is $3 and the fee for each person is also $3. Therefore, the total fee for the family of five is $45.

The total fee for a family of five entering the park is $45.

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Complete question -

A national park charges 3$ for each car that enters and also a fee for each person that enters. A family of 5 enters the park in 1 car and pays a total of 45$. What equation represents this scenario

Answer:

40

Step-by-step explanation:

To evaluate the given integral by reversing the order of integration, we first need to write it in terms of the new order. This can be done by considering the limits of integration for each variable. The original integral is:∫[0 to 3]∫[0 to 9] 5e^(2x) dx dyTo reverse the order of integration, we need to first consider the limits of integration for y. The limits for y are from 0 to 3, which means that the integral with respect to y will have these limits.

To evaluate the integral by reversing the order of integration. The given integral is:

∫(from 0 to 3) ∫(from 5 to 9) 5e^(x^2) dx dy.

To reverse the order of integration, we first need to find the new limits of integration. Currently, the region is defined by:

0 ≤ y ≤ 3
5 ≤ x ≤ 9

We will switch the order of integration to dy dx. To do this, we express y in terms of x:

x = 5
x = 9

So the new region is defined by:

5 ≤ x ≤ 9
0 ≤ y ≤ 3

Now, we rewrite the integral with the new order of integration:

∫(from 5 to 9) ∫(from 0 to 3) 5e^(x^2) dy dx.

Now, let's evaluate the integral step by step:

Step 1: Evaluate the inner integral with respect to y.

∫(0 to 3) 5e^(x^2) dy = 5e^(x^2) * y | evaluated from y=0 to y=3
= 15e^(x^2)

Step 2: Evaluate the outer integral with respect to x.

∫(5 to 9) 15e^(x^2) dx

Unfortunately, this integral does not have a closed-form . To obtain a numerical result, you would need to use numerical integration methods, such as Simpson's rule or the trapezoidal rule.

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The simplification form of the provided expression is g . 6² . p⁴ option (B) g . 6² . p⁴ is correct.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

The expression:

\(= \rm \dfrac{(g^3)(6^3)(p^7)}{(6)(g^2)(p^2)(p)}\)

After using the properties of integer exponent:

\(\rm =\dfrac{g^3\cdot \:6^2p^7}{g^2p^2p}\)

\(\rm =\dfrac{g\cdot \:6^2p^5}{p}\)

= g . 6² . p⁴

Thus, the simplification form of the provided expression is g . 6² . p⁴ option (B) g . 6² . p⁴ is correct.

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When b is 3, the value of the expression \(2b^3 + 5\) is 59.

To evaluate the expression\(2b^3 + 5\) when b is 3, we substitute the value of b into the expression and perform the necessary calculations.

Given that b = 3, we substitute this value into the expression:

\(2(3)^3 + 5\)

First, we evaluate the exponent, which is 3 raised to the power of 3:

2(27) + 5

Next, we perform the multiplication:

54 + 5

Finally, we add the two terms:

59

Therefore, when b is 3, the value of the expression \(2b^3 + 5\) is 59.

In summary, by substituting b = 3 into the expression \(2b^3 + 5\), we find that the value of the expression is 59.

It's important to note that the provided equation has multiple possible solutions for x, but when b is specifically given as 3, the value of x is approximately 3.78.

It's important to note that in this equation, we substituted the value of b and solved for x, resulting in a specific value for x. However, if we wanted to solve for b given a specific value of x, we would follow the same steps but rearrange the equation accordingly.

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