Answer:
Step-by-step explanation:
Set h=0 for ground height, then solve for t
-16t^2 -20t +240 = 0
divide by -4
4t^2 +5t - 60 = 0
use the quadratic formula
t= -5/8 + or - (1/8)square root of (25 +4(4)(60)). Ignore the negative square root
=-5/8 + (1/8)sqr(960+25)
= -5/8 + (1/8)sqr(985)
=-5/8 + (1/8)sqr(5(197))= slightly less than -5/8 +(10/8)(sqr10) = about -5/8 +32/8 = 27/8 = 3.3 seconds
the ball's initial velocity is negative, meaning the ball was thrown downward. Then add the effect of gravity, and it should hit the ground in a short time, even when thrown from an initial height of 240 feet.
plug t=2 into the original equation for height. You should get slightly above ground, near zero
-16(2)^2 -20(2) +240 = -64 -40+240 = 136
try t=3
-16(9) -20(3) +240 = -144 -60 +240 = 36
try t=4
-16(16) -20(4) +240 =-256 -80 +240 =-96
the time to hit ground should be between t=3 and 4, but closer to t=3, maybe about 3 1/3 seconds
You apply for a debt consolidation loan for $43,000 for 4 years. If your credit score is 760 or greater, then the annual percentage rate is 6%. If your score is less than 760, then the rate is 7%. How much, in dollars, can you save per month by having a credit score of 760 or greater? Round your answer to the nearest cent
Please help asap !!! I will give points !!!
The value of p when q is 2 is 1
What is inverse variation?Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.
This means that has x increases y will decrease and vice versa.
If p is inversely proportional to q , then p = kq
when p = 2, q = 4
2 = k4
k = 2/4
k = 1/2
When q = 2
p = 1/2 × 2
p = 1
Therefore the value of p is 1
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-4 is less than w, and 0 is greater than w
Answer:
-3,-2,-1 is less than -4 and not greater than
Step-by-step explanation:
Enter your answer in the box.
Answer:
I think it may be 160?
Step-by-step explanation:
400/5 is 80 there's 2 yellow so 2x80= 160 times
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed
The answer is C. Mean, because Desert Landing is symmetric.
What is distributions?A distribution refers to the pattern of how data is spread out or distributed across different values or intervals. It is a way to describe and analyze the shape, center, and spread of a set of data.
According to question:To determine the location with the most consistent temperature, we need to measure the variability of the temperature data in both locations. The measure of variability that is appropriate for this purpose is the Mean, which measures the spread of the middle of the data.
The answer is C. Mean, because Desert Landing is symmetric. depending on the shape of the distributions. If the temperature data in Desert Landing is symmetric, then the Mean would be appropriate to measure the spread of the data. If the temperature data in Sunny Town is skewed, then the Mean would also be appropriate to measure the spread of the data. However, if the temperature data in either location is not skewed, then the range would not be an appropriate measure of variability.
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Age of first heart attack - The horizontal axis is age. The vertical axis is frequency (number of people who had their first heart attack at that age). The population is people in the US who have had at least one heart attack. What is the shape of distribution:
A.skewed right
B. skewed left
C. uniform
D. symmetric
what value of x is in the solution set of the inequality 2(3x-1)>4x-6
Answer: the solution set of the inequality 2(3x-1)>4x-6 is all values of x greater than -2.
Step-by-step explanation: To solve the inequality 2(3x-1)>4x-6, we first simplify the left side by distributing the 2, which gives us 6x-2. Substituting this back into the original inequality, we get:
6x-2 > 4x-6
Next, we isolate the variable term (6x) by subtracting 4x from both sides:
2x-2 > -6
Then, we add 2 to both sides to isolate the variable term completely:
2x > -4
Finally, we divide both sides by 2 to solve for x:
x > -2
Therefore, the solution set of the inequality 2(3x-1)>4x-6 is all values of x greater than -2.
Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
The equivalent value of the equation is 18x-9=72 and x=4.5
Given data ,
Let the equation be represented as A
Now , the value of A is
(3/5)(30x-15)=72
On simplifying the equation , we get
3(6x-3)=72
On further simplification , we get
18x-9=72
x=81/18
x=4.5
Hence , the equation is 18x-9=72
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Sam invest $6500 into account earning 5% interest compounded quarterly how long will it take to double his money?
Answer:
20 quartesrs
Step-by-step explanation:
20 quarters
What is the mean of the distribution below?
CODE: Enter the mean as your code. Do NOT round your answer. Enter all
decimal places. Put the decimal in the correct spot as well
,10
X
X
X
X
X
Movie Theme
Weights of Dogs
X
X X X X
15
X
X
X
25
Weight in pounds
X
X
30
The mean of the distribution in this problem is given as follows:
19.5625 pounds.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the cardinality of the data-set, which represents the number of observations in the data-set.
The dot plot shows the absolute frequency of each observation in the context of the problem.
Considering the dot plot, the sum of the observations in this problem is given as follows:
2 x 12 + 4 x 15 + 1 x 16 + 1 x 18 + 2 x 20 + 1 x 22 + 3 x 25 + 2 x 29 = 313.
The number of observations is given as follows:
2 + 4 + 1 + 1 + 2 + 1 + 3 + 2 = 16.
Hence the mean is given as follows:
313/16 = 19.5625 pounds.
Missing InformationThe problem is given by the image presented at the end of the answer.
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A submarine is 42 feet belpw rhe surface of water .a shark directly above the submarine is 19 feet below the surface of the water.how many feer above the submarine is to the shark
The number of feet above the submarine is the shark is 23 feet.
Given that, a submarine is 42 feet below the surface of the water and shark is 19 feet below the surface of the water.
Here, location of shark = 42-19
= 23 feet
Therefore, the number of feet above the submarine is the shark is 23 feet.
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"Your question is incomplete, probably the complete question/missing part is:"
A submarine is 42 feet below the surface of the water a shark directly above the submarine is 19 feet below the surface of the water how many feet above the submarine is the shark.
Drag each inequality to the column which is labeled with its solution.
( look at photo for reference )
Drag the solution of each inequality as shown below:
3(x - 5) + x < 13 : x<7
2(x + 8) > 4x + 2 : x<7
3x + 2(x - 8) > x : x > 4
2(x + 6) < 3x + 8 : x > 4
How to solve the inequalities?An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4
3(x - 5) + x < 13
3x -15 + x < 13
4x -15 < 13
4x < 13 + 15
4x < 28
x < 28/4
x < 7
2(x + 8) > 4x + 2
2x + 16 > 4x + 2
2x - 4x > 2 - 16
-2x > -14
x < -14/(-2) (Note: Sign will change if you divide with negative numbers)
x < 7
3x + 2(x - 8) > x
3x + 2x -16 > x
5x - 16 > x
5x - x > 16
4x > 16
x > 16/4
x > 4
2(x + 6) < 3x + 8
2x + 12 < 3x + 8
2x - 3x < 8 - 12
-1x < -4
x > -4/(-1)
x > 4
Therefore, drag the solution of each inequality accordingly.
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Find the area of the regular polygon below and round your answer to the nearest tenth.
Explain your reasoning. Show all your work.
1) What is the perimeter of the regular polygon?
2) What is the apothem length? Show all your work and explain how you found the apothem.
3) What is the area of the regular polygon? Show your work.
7 sides each side is 10 in long
The area of the regular polygon is 311.5 in2.
We are given that;
A polygon
Now,
To find the perimeter of the regular polygon, we need to multiply the number of sides by the length of each side. The polygon has 7 sides and each side is 10 in long, so the perimeter is 7 * 10 = 70 in.
To find the apothem length, we need to use some trigonometry.
The central angle is 360/7 degrees, since there are 7 equal angles in a regular polygon. Half of the side length is 5 in, since each side is 10 in long. The apothem is the adjacent side of the right triangle. We can use the tangent function to find the apothem: tan(360/14) = 5/a, where a is the apothem. Solving for a, we get a = 5/tan(360/14) ≈ 8.9 in.
To find the area of the regular polygon, we need to plug in the values of P and a into the formula A = (1/2)P*a.
A = (1/2)708.9 ≈ 311.5 in2.
Therefore, by the area the answer will be 311.5 in2.
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Sean says the value of a to the -3rd power is always less than 1 if a is positive.
Christine says the value of a to the -3rd power is always less than 1 when a is negative
Which one is correct, and for the one that is incorrect enter the number that proves in to be incorrect (if none say none).
Sean's statement is correct. Christine's statement is incorrect when a is negative.
The value of a to the -3rd power is always less than 1 if a is positive.
For example, if a = 2, then a to the -3rd power is 1/8, which is less than 1. Therefore, Sean's statement is correct.
The value of a to the -3rd power is always less than 1 if a is positive, but it is always greater than 1 if a is negative.
For example, if a = 2, then a to the -3rd power is 1/8, which is less than 1. But if a = -2, then a to the -3rd power is -1/8, which is greater than 1.
Therefore, Christine's statement is incorrect when a is negative.
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Identify the center, radius, domain and range of the circle eith equation. Make sure to scroll down through all thr answer choices
(x+2)^2+(y-5)^2 = 9
Answer: Centre: (-2,5)
Radius = 3
so
Diameter = 6
Domain: (-5,1)
Range: (2,8)
Answer:
center (-2,5)
radius =3
domain = -5< x <1
range 2 <y<8
Step-by-step explanation:
siiuu
Timothy and Sean are masseur. Timothy charges $45 for each massage and Sean charges $55 for each massage. This week
Timothy made $102 in tips and Sean made $96 in tips. Given that T and S represent the number of massages given by Timothy
(T) and Sean (S), which expression can be used to represent their combined earnings for the week?
Answer: 45T + 55S +102 + 96= Combined income
Step-by-step explanation:
what are the coefficients in the polynomial
Answer: 7 and -4
Step-by-step explanation:
Coefficients are numbers in front of variables
6 doesn't have a variable so it's a constant
7 and -4 are the coefficients
2079 [Optional] Set A Q.No. 20a] In how many different ways can the letters of the word "DETERRANT" be arranged so that the repeated letters do not come together?
There are 70,560 different ways to arrange the letters of the word "DETERRANT" so that the repeated letters do not come together.
How many ways the word "DETERRANT" be arranged so that the repeated letters do not come togetherThe word "DETERRANT" has 9 letters, out of which there are 2 E's, 2 R's, and 1 T.
To determine the total number of possible arrangements, we begin with 9! (9 factorial), which counts all possible arrangements if all letters are distinct.
We must, however, account for the repeated letters. For the two E's, we divide by 2, which is the number of different ways they can be arranged without changing the overall arrangement. Likewise, we divide by 2! for the two R's.
As a result, the total number of arrangements with repeated letters that do not come together is:
9! / (2! x 2!) - 8! / (2! x 2!) = 90720 - 20160 = 70560
Therefore, there are 70,560 different ways to arrange the letters of the word "DETERRANT" so that the repeated letters do not come together.
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in how many ways can first , second , and third prizes be awarded in a cont with 925 contestants? assume there is no ties
Answer:
Step-by-step explanation:
[tex]\frac{925!}{(925-3)!}= 923*924*925=788,888,100[/tex]
To determine the number of ways the first, second, and third prizes can be awarded in a contest with 925 contestants, we can use the concept of permutations.
For the first prize, there are 925 contestants eligible to win. After the first prize is awarded, there are 924 remaining contestants for the second prize. Finally, for the third prize, there are 923 remaining contestants.
The number of ways to award the prizes can be calculated as the product of the number of choices for each prize:
Number of ways = 925 * 924 * 923
Calculating this expression, we find:
Number of ways = 779,449,100
Therefore, there are 779,449,100 ways to award the first, second, and third prizes in the contest with 925 contestants.
The distance between Marisa's house and the post office is 720 m. If she walks from her house to the post office at an average speed of 80 m/min, how long will she take?
Okay, let's break this down step-by-step:
* The distance between Marisa's house and the post office is 720 m
* Marisa walks at an average speed of 80 m/min
* To calculate the time:
** Distance / Speed = Time
** 720 m / 80 m/min = 9 minutes
Therefore, if the distance is 720 m and Marisa's average walking speed is 80 m/min, it will take her 9 minutes to walk from her house to the post office.
How to get the square root of a number?
Answer:
Step-by-step explanation:
What is the Formula for Calculating the Square Root of a Number? The square root of any number can be expressed using the formula: √y = y½. In other words, if a number has 1/2 as its exponent, it means we need to find the square root of the number.
In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number.
The square root of a number "a" is denoted by the symbol "√a" or "a^(1/2)." For example, the square root of 9 is 3 because 3 * 3 = 9.
Use the internet to identify a major league ballpark in which the distance from home plate to the center field fence and the height of the center field fence require that a ball hit 2 feet above the ground will necessitate an angle of elevation less than .86 degrees to just clear the center field fence. what is the name and location of the major league ballpark that you identified? what is the distance from home plate to the center field fence and what is the height of the center field fence in the ballpark? What is the angle of elevation that is required for a hit ball to just clear the center field fence when it is hit 2 ft above the ground? Round to the nearest hundredth of a degree.
We can actually deduce here that the major league ballpark that I identified is T-Mobile Park in Seattle, Washington.
How to find the angle of elevation?The distance from home plate to the center field fence is 409 feet and the height of the center field fence is 8 feet.
Thus, to solve for the angle of elevation, we can use the following equation:
tan θ = (y - h) / d
Where:
θ is the angle of elevation
y is the height of the fence
h is the height of the ball
d is the distance to the fence.
tan θ = (8 - 2) / 409
tan θ = 0.602
θ = [tex]tan^{-1}[/tex] (0.602)
θ = 0.85°
The angle of elevation that is required for a hit ball to just clear the center field fence when it is hit 2 ft above the ground is 0.85°.
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Here are two triangles show that the triangles are similar what is the scale factor from triangle abc to abc
The two triangles are similar because angle C = C' and angle A = A'. The scale factor is 4/3
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. The corresponding angles of similar triangles are congruent.
Also, the ratio of corresponding sides of similar triangles are equal.
Therefore to show that that the two triangles are equal;
Tan A = 4/3
Tan A = 1.333
A = 53.1°
Tan A' = 5.3/4
Tan A' = 1.33
A' = 53.1°
Therefore the two triangles are similar.
The scale factor = 4/3
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The world famous gambler from Philadelphia, Señor Rick, proposes the following game of chance. You roll a fair die. If you roll a 1, then Señor Rick pays you $55. If you roll a 2, Señor Rick pays you $10. If you roll a 3, you win nothing. If you roll a 4 or a 5, you must pay Señor Rick $35, and if you roll a 6, you must pay Señor Rick $25. What is the expected value for this game if you pay $1 to play?
The expected value for this game, when you pay $1 to play, is -$4.00. This means that, on average, you can expect to lose $4.00 per game in the long run.
To calculate the expected value for the game, we need to multiply each outcome by its respective probability and then sum them up.
Let's calculate the expected value for each outcome:
Outcome 1: Roll a 1 and receive $55.
The probability of rolling a 1 on a fair die is 1/6.
Expected value = (1/6) × $55 = $9.17
Outcome 2: Roll a 2 and receive $10.
The probability of rolling a 2 on a fair die is 1/6.
Expected value = (1/6) × $10 = $1.67
Outcome 3: Roll a 3 and win nothing.
The probability of rolling a 3 on a fair die is 1/6.
Expected value = (1/6) × $0 = $0
Outcome 4: Roll a 4 or 5 and pay Señor Rick $35.
The probability of rolling a 4 or 5 on a fair die is 2/6 or 1/3.
Expected value = (1/3) × (-$35) = -$11.67 (negative because you have to pay)
Outcome 5: Roll a 6 and pay Señor Rick $25.
The probability of rolling a 6 on a fair die is 1/6.
Expected value = (1/6) × (-$25) = -$4.17 (negative because you have to pay)
Now, let's sum up the expected values:
Expected value = $9.17 + $1.67 + $0 - $11.67 - $4.17
= -$4.00
The expected value for this game, when you pay $1 to play, is -$4.00. This means that, on average, you can expect to lose $4.00 per game in the long run.
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rewrite the mixed numbers as the sum of whole number and a fraction rewrite the whole number as a sum of fraction each equal to 1
The mixed fraction expression 2³/₄ can be rewritten as: ⁴/₄ + ⁴/₄ + ³/₄
How to write mixed fractions?There are different fractions such as mixed fraction, improper fraction, proper fraction e.t.c.
Now, we are given the fraction as an improper fraction in the form of 2³₄.
Rewriting as a whole number and a fraction gives:
2 + ³/₄
Breaking down the whole number into a fraction is done as:
1 + 1 + ³/₄
= ⁴/₄ + ⁴/₄ + ³/₄
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100 Points! Algebra question. Photo attached. Find the exact value of the expression. Please show as much work as possible. Thank you!
Answer:
[tex]2-\sqrt{3}[/tex]
Step-by-step explanation:
Find the exact value of the expression, tan(15°).
The method I am about to show you will allow you to solve this problem without any tables or calculators. Although, memorizing the unit circle and trigonometric identities is required.
[tex]\tan(15 \textdegree)\\\\\Longrightarrow \tan(\frac{30 \textdegree}{2} )\\\\\text{Use the half-angle identity:} \ \tan(\frac{A}{2})=\pm \sqrt{\frac{1-\cos(A)}{1+\cos(A)} }=\frac{\sin(A)}{1+\cos(A)} =\frac{1-\cos(A)}{\sin(A)} \\\\\Longrightarrow\frac{1-\cos(30 \textdegree)}{\sin(30 \textdegree)} \\\\\text{From the unit circle:} \ \cos(30 \textdegree)=\frac{\sqrt{3} }{2} \ \text{and} \ \sin(30 \textdegree)=\frac{1}{2}\\[/tex]
[tex]\Longrightarrow \frac{1-\frac{\sqrt{3} }{2}}{\frac{1}{2}}\\\\\Longrightarrow 2(1-\frac{\sqrt{3} }{2})\\\\\therefore \boxed{\boxed{\tan(15 \textdegree)=2-\sqrt{3} }}[/tex]
Thus, the problem is solved.
Answer:
[tex]\tan 15^{\circ} = 2 - \sqrt{3}[/tex]
Step-by-step explanation:
To find the exact value of tan 15°, we can use trigonometric identities and the unit circle.
We know that tan(x) can be expressed as the ratio of sin(x) and cos(x). We can also write 15° as (60° - 45°).
Therefore, tan 15° can be expressed as:
[tex]\tan15^{\circ}=\tan(60^{\circ}-45^{\circ})=\dfrac{\sin(60^{\circ}-45^{\circ})}{\cos(60^{\circ}-45^{\circ})}[/tex]
Now use the trigonometric angle identities to rewrite the ratio in terms of sin 60°, cos 60°, sin 45° and cos 45°.
[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Trigonometric Angle Identities}\\\\$\sin (A - B)=\sin A \cos B - \cos A \sin B$\\\\$\cos (A - B)=\cos A \cos B + \sin A \sin B$\\\end{minipage}}[/tex]
Therefore:
[tex]\begin{aligned}\tan15^{\circ}&=\dfrac{\sin(60^{\circ}-45^{\circ})}{\cos(60^{\circ}-45^{\circ})}\\\\&=\dfrac{\sin60^{\circ}\cos45^{\circ}-\cos60^{\circ}\sin45^{\circ}}{\cos 60^{\circ} \cos 45^{\circ}+ \sin 60^{\circ}\sin 45^{\circ}}\end{aligned}[/tex]
In the unit circle, the cosine of an angle is represented by the x-coordinate of a point on the circle, and the sine of an angle is represented by the y-coordinate of that same point → (x, y) = (cos θ, sin θ). Therefore, we can use the unit circle to identity the values of sin 60°, cos 60°, sin 45° and cos 45°:
[tex]\sin 60^{\circ}=\dfrac{\sqrt{3}}{2}[/tex]
[tex]\cos 60^{\circ}=\dfrac{1}{2}[/tex]
[tex]\sin 45^{\circ}=\dfrac{\sqrt{2}}{2}[/tex]
[tex]\cos 45^{\circ}=\dfrac{\sqrt{2}}{2}[/tex]
Substitute these into the equation and simplify:
[tex]\begin{aligned}\tan15^{\circ}&=\dfrac{\sin(60^{\circ}-45^{\circ})}{\cos(60^{\circ}-45^{\circ})}\\\\&=\dfrac{\sin60^{\circ}\cos45^{\circ}-\cos60^{\circ}\sin45^{\circ}}{\cos 60^{\circ} \cos 45^{\circ}+ \sin 60^{\circ}\sin 45^{\circ}}\\\\&=\dfrac{\dfrac{\sqrt{3}}{2}\cdot \dfrac{\sqrt{2}}{2}-\dfrac{1}{2}\cdot \dfrac{\sqrt{2}}{2}}{\dfrac{1}{2}\cdot \dfrac{\sqrt{2}}{2}+ \dfrac{\sqrt{3}}{2}\cdot \dfrac{\sqrt{2}}{2}}\\\\\end{aligned}[/tex]
[tex]\begin{aligned}&=\dfrac{\dfrac{\sqrt{2}}{2} \left(\dfrac{\sqrt{3}}{2}-\dfrac{1}{2}\right)}{\dfrac{\sqrt{2}}{2} \left(\dfrac{1}{2}+ \dfrac{\sqrt{3}}{2}\right)}\\\\&=\dfrac{\dfrac{\sqrt{3}}{2}-\dfrac{1}{2}}{ \dfrac{1}{2}+ \dfrac{\sqrt{3}}{2}}\\\\&=\dfrac{\dfrac{\sqrt{3}-1}{2}}{\dfrac{1+\sqrt{3}}{2}}\\\\&=\dfrac{\sqrt{3}-1}{1+\sqrt{3}}\end{aligned}[/tex]
Simplify further by multiplying the numerator and denominator by the conjugate of the denominator:
[tex]\begin{aligned}&=\dfrac{\sqrt{3}-1}{1+\sqrt{3}}\cdot \dfrac{1-\sqrt{3}}{1-\sqrt{3}}\\\\&=\dfrac{(\sqrt{3}-1)(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\&=\dfrac{\sqrt{3}-3-1+\sqrt{3}}{1-\sqrt{3}+\sqrt{3}-3}\\\\&=\dfrac{2\sqrt{3}-4}{-2}\\\\&=-\sqrt{3}+2\\\\&=2-\sqrt{3}\end{aligned}[/tex]
Therefore, the exact value of tan 15° is (2 - √3).
Find the missing side length.
a
26
24
Answer:
a = 10
Step-by-step explanation:
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
a² + 24² = 26²
a² + 576 = 676 ( subtract 576 from both sides )
a² = 100 ( take square root of both sides )
a = [tex]\sqrt{100}[/tex] = 10
I’m struggling please help thank you always
Answer:
- 3 , 7 , - 13 , 5x + 2
Step-by-step explanation:
A
to evaluate f(0) substitute x = 0 into f(x)
f(0) = 5(0) - 3 = 0 - 3 = - 3
B
substitute x = 2 into f(x)
f(2) = 5(2) - 3 = 10 - 3 = 7
C
substitute x = - 2 into f(x)
f(- 2) = 5(- 2) - 3 = - 10 - 3 = - 13
D
substitute x = x + 1 into f(x)
f(x + 1)
= 5(x + 1) - 3 ← distribute each term in the parenthesis by 5
= 5x + 5 - 3 ← collect like terms
= 5x + 2
Answer:
A) -3
B) 7
C) -13
D) 5x+2
Step-by-step explanation:
For A, B, and C substitute the value stated in the parenthesis.
A) f(0) means to find the value when x=0, so we substitute 0 where x is in the function.
[tex]5(0)-3[/tex]
Then use PEMDAS and multiply first and then subtract 3 from the product.
[tex]5(0)=0\\0-3=-3[/tex]
B) Take the same steps as before with a different value. Substitute 2 for x.
[tex]5(2)-3\\5(2)=10\\10-3=7[/tex]
C) Also the same thing as the previous problems. Substitute -2 for the value of x.
[tex]5(-2)-3\\5(-2)=-10\\-10-3=-3[/tex]
D) Similar to above substitute x+1 where x is.
[tex]5(x+1)-3\\[/tex]
Then distribute 5(x+1) to get
[tex]5x+1(5)\\5x+5[/tex]
Then simplify the equation
[tex]5x+5-3=5x+2[/tex]
A wall 24 inches is conrete, 5 inches is brick, and 9 inches is limestone. What fracrion of the wall is concrete?
The fraction of the wall that is concrete is 12/19
What is a fraction?A fraction is a mathematical representation of a part of a whole or a division of one quantity by another. It consists of two parts: a numerator and a denominator, separated by a horizontal line called a fraction bar or a division slash.
The numerator represents the number of parts or the quantity being considered, while the denominator represents the total number of equal parts or the divisor. The numerator and denominator are both whole numbers or integers.
In this problem, to determine the fraction that is concrete, we have to know the total length of the wall.
length of wall = 24 + 5 + 9 = 38 inches
The fraction of the wall that is concrete = 24 / 38 = 12/19
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Solve the following equation. 25 + 2 � = 3 ( 4 � + 3 ) 25+2x=3(4x+3)
The solution to the equation is x = 1.6.
Let's start by distributing the 3 on the right side of the equation:
25 + 2x = 12x + 9
Next, we can simplify the equation by moving all the x terms to one side and all the constant terms to the other side. To do this, we'll subtract 2x from both sides:
25 = 10x + 9
Then, we'll subtract 9 from both sides:
16 = 10x
Finally, we'll divide both sides by 10:
x = 1.6
So the solution to the equation is x = 1.6.
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