4- T = 3 (T-1)-5

A. 3
B. 6
C. No solution
D. Identity

If you can explain this to me I would really love that.

To find the length of the hypotenuse of a right triangle with legs measuring 3 cm and 4 cm, use the Pythagorean theorem formula c = √(a² + b²). Plugging in the values gives c = √(9 + 16), which results in a hypotenuse of 5 cm.

The student is asking how to find the length of the hypotenuse of a right triangle when the lengths of the other two sides are given. In this case, the legs of the triangle are 3 cm and 4 cm long. To find the hypotenuse, we use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This can be expressed as a formula: a² + b² = c². Solving for c, we can find the hypotenuse by taking the square root of the sum of the squares of the other two sides:

c = √(a² + b²)

Plugging in the values for a and b:

c = √(3 cm)² + (4 cm)²

c = √(9 cm² + 16 cm²)

c = √25 cm²

c = 5 cm

Therefore, the length of the hypotenuse is 5 cm.

a single linear equation: you sell a budweiser for $3 a bottle & make $42.

a device: you promote budweiser for $3 and heineken for $4.

the entire wide variety of beers you promote is 10 and you make total of $forty.

The slope-intercept form of a linear equation is y = mx + b. in the equation, x and y are the variables. The numbers m and b deliver the slope of the line (m) and the fee of y when x is zero (b). The value of y whilst x is zero is known as the y-ithat ntercept due to the fact (zero,y) is the factor at which the road crosses the y-axis.

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Given:

Amount of calories per 117.4 grams of Cereal X

 = 110 or 0.620068 per 1 gram of cereal X

Solution:

If there are  252.5 grams of cereal X then the amount of calories in it is computed as

0.620068 X 252.5

156.5671 or 157 (rounded off)

Answer:

The elevators descends at the rate of 25 feet per second or we can write the change in height of elevator is -25 feet per second, since the elevator is moving in opposite direction.  

Step-by-step explanation:

We are given the following information in the question:

The elevator descends 500 feet in 20 seconds.

Now, we know that at 0 second the lift was at 0 feet.

To calculate the change in the height of elevator per second, we use the following formula:

[tex]\text{Change in height per second} = \displaystyle\frac{y_2-y_1}{x_2-x_1}\\\\= \displaystyle\frac{500-0}{20-0} = \frac{500}{20} = 25\text{ feet per second}[/tex]

Hence, the elevators descends at the rate of 25 feet per second or we can write the change in height of elevator is -25 feet per second, since the elevator is moving in opposite direction.

The change in the elevator's height per second is -25 feet per second. This is calculated by dividing the total descent (500 ft) by the time taken (20 s). The negative value indicates a descent.

To determine the change in an object's height per second, we can use the formula for velocity, which is the displacement (change in position) divided by the time. In this case, the elevator descends 500 feet in 20 seconds. Therefore, the change in the elevator's height per second is 500 feet divided by 20 seconds.

The change in the elevator's height per second is -25 feet per second

The negative sign indicates that the elevator is descending, as opposed to ascending. It's important to note that this is an average rate of change because the question doesn't specify that the elevator's speed is constant.

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A function is defined as a relation between a set of inputs having one output each.

Input = 25 and output = $92.75

The cost of 25 pies is $92.75

A function is defined as a relation between a set of inputs having one output each.

The inputs are called the domain of the function.

The outputs are called the range of the function.

Example: f(x) = 2 + 3x

x = 1

f(1) = 2 + 3x1 = 2 + 3 = 5

1 = Domain

5 = Range

We have,

c(x) = 49 + 1.75x

x = number of pies

The cost of producing 25 pies:

c(25) = 49 + 1.75 x 25

        = 49 + 43.75    

        = $92.75

Thus the cost of 25 pies is $92.75

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Assuming that both tests measure the same thing, the equivalent sat score is 1994

The given parameters are:

ACT scores

Mean, μ = 21.5

Standard deviation, σ = 5.4

Score, x = 30

SAT scores

Mean, μ = 1498

Standard deviation, σ = 316

Start by calculating the z-score for the act score using:

[tex]z = \frac{x - \mu}{\sigma}[/tex]

This gives

[tex]z = \frac{30 - 21.5}{5.4}[/tex]

[tex]z = 1.57[/tex]

Next, calculate the z-score for the sat score using:

[tex]z = \frac{x - \mu}{\sigma}[/tex]

This gives

[tex]z = \frac{x - 1498}{316}[/tex]

Substitute 1.57 for z

[tex]1.57 =\frac{x - 1498}{316}[/tex]

Multiply both sides by 316

[tex]496.12 =x - 1498[/tex]

Solve for x

[tex]x = 496.12 + 1498[/tex]

[tex]x = 1994.12[/tex]

Approximate

[tex]x = 1994[/tex]

Hence, the equivalent sat score is 1994

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Final answer:

The equivalent SAT score to Alyssa's ACT score of 30 is calculated using Z-scores. The result is an SAT score of approximately 1996, rounded to the nearest whole number.

Explanation:

To determine what SAT score is equivalent to Alyssa's ACT score of 30, we use the concept of Z-scores. A Z-score represents the number of standard deviations an observation is from the mean of a distribution. The formula for calculating a Z-score is given by Z = (x - μ) / σ, where x is the score of interest, μ is the mean, and σ is the standard deviation.

First, we calculate the Z-score for Alyssa's ACT score:

ACT mean (μ) = 21.5

ACT standard deviation (σ) = 5.4

Alyssa's ACT score (x) = 30

Z-score for ACT = (30 - 21.5) / 5.4 ≈ 1.5741

Now we use Alyssa's ACT Z-score to find the equivalent SAT score by applying it to the SAT distribution. The SAT mean (μ) is 1498 and the SAT standard deviation (σ) is 316.Equivalent SAT score = SAT mean + (Z-score × SAT standard deviation)

Equivalent SAT score = 1498 + (1.5741 × 316) ≈ 1996

Therefore, rounding to the nearest whole number, the SAT score equivalent to Alyssa's ACT score of 30 is 1996.

The equation of the tangent line to the curve y = 6x/(2 + x²) at the point (2, 2) will be y-2=(1/3)x-2.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

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

It is given that,

f(x) = 6x/(2 + x²)

f'(x)=(6x)(2+x²)-6x(2+x²)/(2+x²)²

f'(2)=(6×2)(2+2²)-6x(2+2²)/(2+2²)²

f'(2)=1/3

The value of functions gives the slope of the equation passes through the point (2, 2).

y-y₀=m(x-x₀)

y-2=(1/3)x-2

Thus, the equation of the tangent line to the curve y = 6x/(2 + x²) at the point (2, 2) will be y-2=(1/3)x-2.

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Answer:

Zack can finish the 215 page book after 5 total hours of reading but Pam cannot.

Step-by-step explanation:

Pam read 126 pages of her summer reading book in 3 hours.

[tex]\texttt{Speed of Pam =}\frac{126}{3}=42page/hour[/tex]

Zack read 180 pages of his summer reading book in 4 hours. [tex]\texttt{Speed of Zack =}\frac{180}{4}=45page/hour[/tex]

Number of pages Pam read in 5 hours = 5 x 42 = 210 pages

Number of pages Zack read in 5 hours = 5 x 45 = 225 pages

We need to find will they both finish the 215 page book after 5 total hours of reading,

Here number of pages read by Zack is greater than 215 and number of pages read by Pam is less than 215.

So Zack can finish the 215 page book after 5 total hours of reading but Pam cannot.

Final answer:

The inequality representing "a cat weighs no more than 8 pounds" is expressed as w ≤ 8, where w symbolizes the cat's weight in pounds. This concept illustrates how inequality symbols are applied in algebra to represent the relationship between quantities, applicable in various real-world scenarios.

Explanation:

The question asks which inequality represents "a cat weighs no more than 8 pounds." In mathematical terms, this statement can be translated using an inequality symbol that indicates the cat's weight is either equal to or less than 8 pounds. The appropriate symbol for this is “≤”, which stands for “less than or equal to.” Therefore, the inequality that represents this statement is w ≤ 8, where w represents the weight of the cat in pounds.

Using inequality symbols to show how two metric measurements are related is a foundational concept in algebra, and it is crucial when working with real-world scenarios where quantities have upper or lower bounds. For instance, understanding this concept can apply to various situations such as determining the weight of a dog, or comparing soda in a can to ensure it does not exceed a certain weight limit. It's important to grasp how these symbols convey relationships between quantities.

Final answer:

To simplify the ratio 18 feet to 5 yards, convert yards to feet to get 15 feet, then divide both by the greatest common divisor, 3, ending up with a simplified ratio of 6:5.

Explanation:

To express the ratio 18 feet: 5 yards in simplest form, we first need to convert either yards to feet or feet to yards so that we are comparing the same units. Since we know that 1 yard is equal to 3 feet, we can multiply the number of yards by 3 to find out how many feet it equates to.

Now, let's calculate:

5 yards × 3 feet/yard = 15 feet

So the ratio 18 feet: 5 yards can be rewritten as 18 feet: 15 feet. To simplify this ratio, we divide both numbers by their greatest common divisor (GCD), which in this case is 3.

Here is the calculation:

18 feet ÷ 3 = 6

15 feet ÷ 3 = 5

Therefore, the ratio in simplest form is 6: 5.

Answer:

The temperature of Savannah's liquid to the nearest degree Fahrenheit is 93.1°.

Step-by-step explanation:

Given : In science class, Savannah measures the temperature of a liquid to be 34° Celsius. Her teacher wants her to convert the temperature to degrees Fahrenheit.

To find : What is the temperature of Savannah's liquid to the nearest degree Fahrenheit?

Solution :

The general formula to convert Celsius into Fahrenheit is

[tex]F = (C\times \frac{9}{5}) + 32[/tex]

Substitute C=34°,

[tex]F = (34\times \frac{9}{5}) + 32[/tex]

[tex]F = (34\times 1.8) + 32[/tex]

[tex]F = 61.2+ 32[/tex]

[tex]F =93.1[/tex]

Therefore, The temperature of Savannah's liquid to the nearest degree Fahrenheit is 93.1°.

The answer is [tex]\( 5^{0.75} = 5^{\frac{3}{4}} = \sqrt[4]{5^3} \)[/tex].

To solve[tex]\( 5^{0.75} \)[/tex], we first express 0.75 as a fraction in its simplest form. The number 0.75 is equivalent to [tex]\( \frac{3}{4} \)[/tex]. Therefore, [tex]\( 5^{0.75} \)[/tex] can be rewritten as [tex]\( 5^{\frac{3}{4}} \)[/tex].

Now, we can break down [tex]\( 5^{\frac{3}{4}} \)[/tex] using the properties of exponents. The exponent [tex]\( \frac{3}{4} \)[/tex] indicates that we are looking for the fourth root of 5 raised to the power of 3. Mathematically, this is expressed as [tex]\( \sqrt[4]{5^3} \)[/tex].

To find the value, we first calculate [tex]\( 5^3 \)[/tex], which is [tex]\( 5 \times 5 \times 5 = 125 \)[/tex]. Then we take the fourth root of 125. The fourth root of a number is the number that, when raised to the power of 4, gives the original number. In this case, we are looking for a number that, when raised to the power of 4, equals 125.

The fourth root of 125 is not an integer, but we can approximate it. We know that [tex]\( 2^4 = 16 \)[/tex]and [tex]\( 3^4 = 81 \)[/tex], so the fourth root of 125 must be between 2 and 3. Through calculation or using a calculator, we find that [tex]\( \sqrt[4]{125} \)[/tex] is approximately 3.3019.

Therefore, [tex]\( 5^{0.75} \)[/tex] is approximately 3.3019.

Answer:

[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{1}{2}(cos\frac{\pi}{12}-cos\frac{5\pi}{12})[/tex]

Step-by-step explanation:

We are given that

[tex] sin\frac{\pi}{4} sin\frac{\pi}{6}[/tex]

We have to correct value in blank space.

We know that identity

[tex] sin xsiny=\frac{cos(x-y)-cos(x+y)}{2}[/tex]

Using this identity

[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{cos(\frac{\pi}{4}-\frac{\pi}{6})-cos(\frac{\pi}{4}+\frac{\pi}{6})}{2}[/tex]

[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{cos(\frac{3\pi-2\pi}{12}-cos(\frac{3\pi+2\pi}{12})}{2}[/tex]

[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{1}{2}(cos\frac{\pi}{12}-cos\frac{5\pi}{12})[/tex]

Answer:[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{1}{2}(cos\frac{\pi}{12}-cos\frac{5\pi}{12})[/tex]

The shape of the cross-section for a square pyramid sliced perpendicular to its base but not through its vertex is a trapezoid.

A pyramid is a three dimensional shape (have length, width and height) with a polygon face and lateral faces which are triangular.

A square pyramid have a square base and triangular lateral faces.

The shape of the cross-section for a square pyramid sliced perpendicular to its base but not through its vertex is a trapezoid.

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Answer:

should be a trapezoid, in other words, its D

Step-by-step explanation: