The solutions to each equality are given as follows:
D) s = -1.
E) n = 10/7.
F) k = 3.
How to solve the equalities?The expressions are solved applying the distributive property when needed, then combining the like terms, and finally isolating the variable.
The solution for item d is given as follows:
3 - 2s + 2 = 13 + 6s -> Distributive property.
8s = 5 - 13 -> Combine the like terms.
8s = -8
s = -8/8
s = -1.
The solution for item e is given as follows:
2(n + 9) = -6(2n - 5) + 8
2n + 18 = -12n + 30 + 8 -> Distributive property.
14n = 20 -> Combine the like terms.
n = 20/14
n = 10/7.
The solution for item f is given as follows:
5(4k - 3) - 5k = 10 + 2(3k + 1)
20k - 15 - 5k = 10 + 6k + 2
15k - 15 = 12 + 6k
9k = 27
k = 27/9
k = 3.
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evaluate the function at 0, -3, and 2. f (x )equals 5 to the power of x if the answer is a fraction such as 1 third please type 1/3. or you may write it as a decimal. f (0 )equals f (negative 3 )equals f (2 )equals
the evaluation of the function at 0, -3, and 2 is 1, 1/125, and 25, respectively.
f(0) = 1, f(−3) = 1/125, f(2) = 25
f(0) = 5^0 = 1
f(−3) = 5^−3 = 1/5^3 = 1/125
f(2) = 5^2 = 25
f(0) = 5^0 = 1
f(−3) = 5^−3 = 1/5^3 = 1/125
f(2) = 5^2 = 25
The function f(x) is equal to 5 to the power of x. This means that when evaluating the function at different points, we need to take the number 5, and raise it to a certain power depending on the value of x.
When evaluating the function at 0, the power is 0, so 5 to the power of 0 is equal to 1. When evaluating the function at -3, the power is -3, so 5 to the power of -3 is equal to 1/125. Finally, when evaluating the function at 2, the power is 2, so 5 to the power of 2 is equal to 25.
Therefore, the evaluation of the function at 0, -3, and 2 is 1, 1/125, and 25, respectively.
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2/3 p + 3 p = 3/5.
]
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Answer:
p = 9/55
Step-by-step explanation:
2/3p + 3p = 3/5.
2/3p + 9/3p = 3/5
11/3p = 3/5
Divided both sides by 11/3
p = 9/55
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Which line is secant?
A secant line is a line that intersects a curve at two points.
A secant line is typically used to approximate the slope of a curve at a particular point. For example, if you want to find the slope of the tangent line to a curve at a point x = a, you can draw a secant line through that point and another point nearby, and use the slope of the secant line to approximate the slope of the tangent line.
To find the slope of the tangent line using a secant line, you can use the following formula:
Slope of tangent line = (y2 - y1)/(x2 - x1)where (x1, y1) and (x2, y2) are points on the secant line.
By taking the limit of this formula as x2 approaches x1, we can find the slope of the tangent line at the point where x = x1. This is known as the limit definition of the derivative.
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What is the solution to this equation 3 x 2 − 12 d − 2?
The solution to the equation 3 x 2 − 12 d − 2 is 1/3.
Solving the equation for d because the value of d would be the required solution to this equation:
Now
3 x 2 − 12 d − 2 = 0
6 - 12 d - 2 = 0
Sitting the constant terms to the right side of the equation while keeping the term with d to the left-hand side of the equation:
Now
-12d = -6 + 2
-12d = -4
d = -4/-12
d= 1/3
After solving the given equation for d, the solution of the equation is determined to be 1/3.
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Drew is single and files using the head of household filing status. His agi is $95,000. He has two qualifying children: sage, age 5, and peppa, age 17. What is the amount of drew's 2022 child tax credit? $2,000 $3,600 $4,000 $6,600.
The amount of Drew's 2022 child tax credit is $2,000.
Gross income less adjustments to income is known as adjusted gross income (AGI). Your salary, dividends, capital gains, company revenue, retirement payouts, and other sources of income are all included in your gross income.
On the other hand, one may receive money from the Child Tax Credit (CTC) during tax time to assist with such expenses. On their tax return, eligible parents and caretakers can claim a credit of up to $2,000 for each kid under the age of 17 (i.e., 16 years old or younger) at the end of the tax year for which you claim the credit.
Since Peppa is already 17 and that leaves Sage as the only child for him to qualify, he amount of Drew's 2022 child tax credit is $2,000.
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Please draw and explain in easier terms. I have an disorder. The Valley High Marching Band is selling candy bars for a fundraiser. Sierra sold some candy bars. Breanna sold twice as many candy bars as Sierra. Together Sierra and Breanna sold no less than 45 candy bars. Write an inequality to represent this situation. Give three possible solutions for how many candy bars Sierra sold.
The system of inequality of the situation is y = 2x and x + y ≥ 45 and the possible number of candy bars Sierra sold are 15, 16 and 17
How to write an inequality to represent this situation.From the question, we have the following parameters that can be used in our computation:
Sierra sold some candy bars. Breanna sold twice as many candy bars as Sierra. Together Sierra and Breanna sold no less than 45 candy bars.Represent Sierra with x and Breanna with x
Based on the readings from the question, we have the following inequalities
y = 2x
x + y ≥ 45
Three possible solutions for how many candy bars Sierra sold.Substitute y = 2x in x + y ≥ 45
So, we have
x + 2x ≥ 45
Evaluate
3x ≥ 45
Divide by 3
x ≥ 15
This means that the number of candy bars Sierra sold are at least 15
The possible numbers are 15, 16 and 17
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Solve please please please
Answer:
ML = 10
Step-by-step explanation:
Given:
LN = ML + 2
JL = 15
LK = 18
We use AAA Similarity Criterion: If two triangles are equiangular, then they are similar. By equiangular, it means that the measurements of the corresponding angles of the two triangles are equal. It is also called the Angle Angle Similarity Theorem.
If lines MN and JK are parallel, then ∠LMN=∠LJK and ∠LNM=∠LKJ and hence ΔMLN∼ΔJLK. Based on the proportionality of the sides, we compose an equation and solve it:
LK/JL = LN/ML
18/15 = LN/ML
6/5 = LN/ML
Since LN = ML + 2, the equation can be written:
6/5 = (ML + 2)/ML
6/5 = 1 + 2/ML
1/5 = 2/ML
ML/5=2
ML=10
For which problem situation could the equation 45x + 55x = 350 be used?
Two vehicles start from the same point traveling in the same direction. One vehicle travels 55 miles per hour (mph) and the other 45 mph. When will the two vehicles be 350 miles apart?
A car, traveling 45 mph, leaves Dallas heading for Odessa 350 miles away. At the same time, a truck leaves Odessa for Dallas traveling 55 mph on the same road. When will the two vehicles meet?
A 350 mile telephone cable is cut so the shorter piece 45/55 is of the whole cable. How long is each piece?
A 350 mile telephone cable costs $55 per mile for one section and $45 per mile for a different section. What is the total cost of the cable?
Answer:
Step-by-step explanation:
The equation 45x + 55x = 350 could be used to solve the following problem:
Two vehicles start from the same point traveling in the same direction. One vehicle travels 55 miles per hour (mph) and the other 45 mph. When will the two vehicles be 350 miles apart?
Step by step You and a friend are hiking and find yourselves near the top of a waterfall. There is a path to hike down that takes 1.5 miles to reach the bottom safely and go swimming. There is also a path that is 1.2 miles down to a great place to eat lunch. Your friend wants to stay at the top of the waterfall and fly his drone overhead to take pictures from the sky. A drone is a flying robot that can be remotely controlled with computer software or technology. Draw a vertical number line to help you answer the questions.
Part A: How far would the drone need to fly up in the air to be the opposite distance from you when you are eating lunch? (3 points)
Part B: How far would the drone need to fly up in the air to be the opposite distance from you when you are swimming? (3 points)
Part C: What does the value of zero represent in this problem? (3 points)
Part D: Use absolute value to show that if you hike down to go swimming and then hike back to the top to meet your friend that you hiked the same distance in both directions. (3 points)
The values for the questions are given below.
What is Distance between Two Points?Distance between two points is the magnitude of the distance you travelled without regarding to the direction.
Let the point at the top of the waterfall is origin, where the value is 0.
Distance from the top of the waterfall to the point where they can swim = 1.5 miles or -1.5 miles since it is down the origin
Distance from the top of the waterfall to the point where they can eat lunch = 1.2 miles or -1.2 miles since it is down the origin
Part A :
When the drone needs to be in opposite distance from you when you are eating lunch, the distance of drone from the top of the waterfall must be 1.2 miles.
Total distance from the place where you eat lunch to the drone = 1.2 + 1.2 = 2.4 miles
Part B :
When the drone needs to be in opposite distance from you when you are swimming, the distance of drone from the top of the waterfall must be 1.5 miles.
Total distance from swimming to the drone = 1.5 + 1.5 = 3
Part C :
The value of 0 represent the top of the waterfall.
Part D :
If you hike down to go swimming, distance travelled = |-1.5| = 1.5 miles
If you hike up from the swimming point to the top of the waterfall, distance travelled = +1.5 miles
Both the distance are same.
Hence all the parts are answered.
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2x – 3 = 3 solve by graphing
x=3 is the solution of equation 2x-3=3 which represent the line parallel to y axis such that x coordinate is always 3
What is axis?In mathematics, an axis is a line that is used to take or indicate measurements. The coordinate plane's x and y axes are two of its most important axes. The x-axis is represented by a horizontal number line, and the y-axis by a vertical number line. The perpendicular intersection of these two axes yields the coordinate plane. The x-axis and y-axis are also known as the ordinate and abscissa, respectively.
in the question we have:
⇒ 2x - 3 = 3
⇒ 2x = 6
⇒ x = 3
which represent a line parallel to y axis where x is always equal to 3 .To plot graph take any y such that point is (3, y) .
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can someone help me really quick
The expression 2.4x−3.9y−1.2x+ay is equivalent to 1.2x+1.2y.
What is the value of a?
Enter your answer as a decimal, like this: 42.5
Answer:
[tex]a=5.1[/tex]
Step-by-step explanation:
[tex]2.4x-1.2x-3.9y+ay=1.2x+y(a-3.9) \\ \\ \implies 1.2=a-3.9 \implies a=5.1[/tex]
What is -10x+18y=4 ?
-10x+18y=4 is an equation in the slope-intercept form, where y is the dependent variable, x is the independent variable, -10 is the coefficient of x, 18 is the coefficient of y and 4 is the constant.
This is a Linear equation and it represent a straight line in a two-dimensional coordinate system. The slope of the line is -10/18 or -5/9 and the y-intercept is 4/18 or 2/9.
It is important to note that the equation represents all the points that are on that line, where x and y are coordinates of those points, and for each value of x, there is a corresponding value of y that makes the equation true.
prove the diagonals of a square bisect the vertical angles
The diagonals of a square bisect the vertical angles
(i) In an ABCD diagram,
AB=AB ( common line)
BC=AD ( opposite sides of a square)
ABC=BAD (90 degrees)
ΔABC≅ΔBAD( By SAS property)
AC=BD ( by CPCT)
In an OAD and an OCB,
AD=CB ( opposing sides of a square)
∠OAD=∠OCB ( transversal AC )
∠ODA=∠OBC ( transversal BD )
ΔOAD≅ΔOCB (ASA property)
OA=OC ----(i)
Furthermore, OB=OD ----(ii)
AC and BD divide each other at I and (ii).
Currently in an OBA and ODA,
(From (ii)) OB=OD
BA=DA
OA=OA ( common line )
(by CPCT) AOB=AOD---(iii)
∠AOB+∠AOD=180° (linear pair)
2∠AOB=180°
∠AOB=∠AOD=90°
∴ AC and BD bisect each other at vertical angles.
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n is a whole number. 2n is greater than 36, 5n is less than 100. what is the value of n?
Answer:
3567
Step-by-step explanation:
Answer:
19
Step-by-step explanation:
19x2=38
38 is bigger than 36
19x5=95
95 is less than 100
19 is a whole number
so the answer is 19You deposit $200 in an account. The account earns $15 simple interest in 3 years. What is the annual interest rate?
When Elizabeth began college, the price of her school books were $345. One year later, the cost for her books increased by 7%. If the price for books continued to increase by 7% each year, what is the price of books after 5 years? Round your answer to the nearest dollar.
need this asap
Answer:
The initial cost of Elizabeth's books is $345. After one year, the cost of her books increased by 7%, which is an increase of $345 x 7/100 = $24.15
So, the cost of her books after one year is $345 + $24.15 = $369.15
To find the price of her books after five years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where A is the final amount, P is the initial principal (or starting amount), r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, P = $345, r = 7/100, n = 1, and t = 5
So, A = $345 (1 + 7/100)^5 = $345 * 1.07^5 = $475.14
Rounding this to the nearest dollar, we get $475.
Therefore, the price of Elizabeth's books after five years is $475.
art 1 of 2
Suppose the function f(x)=9.09x represents the number of Chinese yuan equivalent to x British pounds and the function gly)=0.17y represents the
number of U.S. dollars equivalent to y Chinese yuan.
a. Write a composite function that represents the number of U.S. dollars equivalent to x British pounds.
b. Find the value in U.S. dollars of an item that costs 15 British pounds.
A: The composite function that represents the number of U.S. dollars equivalent to x British pounds is 1.54x
B: An item that costs 15 British pounds is equivalent to 23.10 U.S. dollars.
What is the composite function?
A composite function is a function that is formed by the composition of two or more functions. It is a new function that is made by plugging the output of one function into another function. The notation for a composite function is f(g(x)) or f(g), where f and g are the two functions being composed.
a. To write a composite function that represents the number of U.S. dollars equivalent to x British pounds, we want to substitute the output of f(x) into g(y). So, we want to find g(f(x))
g(f(x)) = g(9.09x) = 0.17(9.09x) = 1.54x
So, the composite function that represents the number of U.S. dollars equivalent to x British pounds is 1.54x
b. To find the value in U.S. dollars of an item that costs 15 British pounds, we substitute x = 15 into the composite function:
1.54(15) = 23.10
So, an item that costs 15 British pounds is equivalent to 23.10 U.S. dollars.
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2. Pick two different values of t so that the function has a negative average
rate of change between the two values. Determine the average rate of
change.
1. The average rate of change for P between 1992 and 2000 is -1.025.
2. For values of t = 1996 and t = 1992, the function has a negative average rate of change, and value of rate of change will be -2.4.
3. For values of t = 2000 and t = 1996, the function has a positive average rate of change, and value of rate of change will be 0.35.
What is Rate?Rate is a mathematical term which we use, When two quantities are compared and expressed as a ratio and both have different units.
1. we need to calculate the average rate of change in 1992 & 2000
percentage of voters in 2000 = 34.5
percentage of voters in 1996 = 33.1
percentage of voters in 1992 = 42.7
it is known that,
Rate of change = change in percentage/change in years
Rate of change in between 1992 &1996 is,
R₁= (33.1 - 42.7)/(1996-1992)
R₁= -2.4
Rate of change in between 1996 & 2000 is,
R₂= (34.5-33.1)/(2000-1996)
R₂= 0.35
Average rate of change = (R₁ + R₂)/2
Average rate of change = (-2.4 + 0.35)/2
Average rate of change = -1.025
2. One of the pair of values of t for which rate of change will be negative are 1996 & 1992,
R= (33.1 - 42.7)/(1996-1992)
R= -2.4
3. One of the pair of values of t for which rate of change will be positive are 1996 & 2000,
R= (34.5-33.1)/(2000-1996)
R= 0.35
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Please help me I suck at mathhh
Answer:
firstly this is a right angle, so we will use Pythagoras' theorem.C² = A² + B²X² = 10² + 12²X² = 244X = √244X = 15.62X ~ 15.6draw the structure of 12-crown-4, a compound that is commonly used to bind certain metal ions.
The structure of 12-crown-4 is shown below.
12-Crown-4, also known as lithium ionophore V and 1,4,7,10-tetraoxacyclododecane, is a crown ether with the chemical formula C8H16O4. It is a lithium cation-specific cyclic tetramer of the chemical compound ethylene oxide.
12-crown-4 combines with alkali metal cations, similar to other crown ethers. It has a strong selectivity for the lithium cation due to the cavity diameter of 1.2–1.5.
LiClO4 can be used as a template cation in a modified Williamson ether synthesis to create 12-Crown-4:
(CH2CH2O)4 + 2 NaCl + 2 H2O = (CH2OCH2CH2Cl)2 + (CH2OH)2 + 2 NaOH
In the presence of gaseous boron trifluoride, it can also result from the cyclic oligomerization of ethylene oxide.
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Help me pleaseeee I suck at mathhh
Answer:
x = 2
Step-by-step explanation:
16 + b^2 = 20
b^2 = 4
b = 2
Danielle won 55 pieces of gum playing
horseshoes at the county fair. At school
she gave one to every student in her math
class. She only has 30 remaining. How
many did she give away?
Answer:
25
Step-by-step explanation:
25
The perimeter of a square is 12 feet less than five times its side length. Find the perimeter of the square.
The square's perimeter is its four sides because all of its sides are equal. The square's 12 cm perimeter is what we are given, hence the measurement is perimeter.
How do you calculate a square's side length using the perimeter?Pictures for 12 feet less than five times the length of the sides make up a square's perimeter. Recognize the square's perimeter.
P = 4 side is a formula for calculating a square's perimeter. The side length of the square is determined by rearranging the previous formula to side = P/4 when the perimeter is known. So, by multiplying the perimeter by 4, it is possible to determine the length of a square's sides.
The square's perimeter is its four sides because all of its sides are equal. The square's 12 cm perimeter is what we are given, hence the measurement is perimeter.
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the critical value of t for a two-tailed test with 6 degrees of freedom using α = .05 is
The critical value of t for a two-tailed test with 6 degrees of freedom and a significance level of 0.05 is 2.45. This means that any value of t greater than or less than 2.45 is statistically significant.
The critical value of t can be calculated using a t-test table with the corresponding degrees of freedom and significance level. The critical value of t for a two-tailed test is an important statistic used to determine the statistical significance of a result. It is calculated using a t-test table with the corresponding degrees of freedom and significance level (α). The critical value of t for a two-tailed test with 6 degrees of freedom and a significance level of 0.05 is 2.45. This means that any value of t greater than or less than 2.45 is statistically significant. This value can be used to compare the difference between two sample means, where a larger value will indicate a greater difference between the two means. The critical value of t is used to determine the probability that the difference between two sample means is due to random chance and not a real effect.
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by making x =1/3, y= -2/5 and x=1/4 find (x *y) + z
Answer:
7/60
Step-by-step explanation:
solution
(x*y) + z
(1/3*-2/5) + 1/4
-2/15 + 1/4
LCM 60
-8 + 15/60
7/60
Answer:
7/60
Step-by-step explanation:
Looking at the numbers:
x = 1/3
y = -2/5
z = 1/4
We can simply add them into the equation:
(x × y) + z
(1/3 × -2/5) + 1/4 =?
1/3 × -2/5 ≅ -0.1333333 or [tex]\frac{-1333333}{10000000}[/tex]
-0.1333333 + 1/4 = 0.1166667 or [tex]\frac{7}{60}[/tex]
If the middle term of a quadratic trinomial is positive, then the sum of the factors for the middle term must be ___.
The middle term of a quadratic trinomial is positive, then the sum of the factors for the middle term must be negative.
In a quadratic trinomial in the form [tex]ax^2 + bx + c[/tex], the middle term is represented by bx. When the middle term is positive, it means that b (the coefficient of x) is positive. To factor the quadratic trinomial, to find two numbers that multiply to b and add up to the coefficient of the middle term.
Since b is positive, the two factors must have the same sign (both positive or both negative) to add up to a positive value. However, the middle term itself is positive, indicating that the two factors add up to a positive value.
Hence, both factors must be negative so that their sum is positive.
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This graph shows how the distance Daniel runs depends on the number of track practices he attends.
The rate of change that Daniel runs depends on number of tracks, so the rate of change is 8/5 = 1.6 miles per practice.
What is rate of change?You should be aware that rate of change is the same thing as slope. In slope as y increases, x also increases. vice versa.
Daniel runs depends on the number of track practices he attends.
The rate of change (ROC) is the speed at which a variable changes over a specific period of time. ROC is often used when speaking about momentum, and it can generally be expressed as a ratio between a change in one variable relative to a corresponding change in another; graphically, the rate of change is represented by the slope of a line. The ROC is often illustrated by the Greek letter delta (Δ).Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable.
The formula for rate of change is:
R = (D2 - D1)/T
Rate of change = change in y/ change in x
= 10-2/5-0
=8/5
=1.6
In conclusion the ratio of Daniels run is 1.6
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A panel of 3 women and 4 men is to be set up from 8 women and 7 men. Find the number of ways in which the panel can be (a)Formed (b)Formed if it must have at least 2 women (c)Formed if Miss A refuses to serve on the panel if Mr. B is a member.
The number of ways in which a panel of 3 women and 4 men can be formed is 1960 ways.
What are combinations?Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant.
a. The number of ways In which a panel of 3 women and 4 men can be formed Is:
[tex]$$\begin{aligned}& 8 C_3 * 7 C_4 \\& \frac{8 !}{(8-3) ! 3 !} * \frac{7 !}{(7-4) ! 4 !} \\& 56 * 35 \\& 1960\end{aligned}$$[/tex]
The number of ways In which a panel of 3 women and 4 men can be formed Is 1960 ways.
b. The number of ways In which a panel with at least 2 women can be formed Is:
[tex]$$\begin{aligned}& 8 C_2 * 7 C_5+8 C_3 * 7 C_4+8 C_4 * 7 C_3+8 C_5 * 7 C_2+8 C_6 * 7 C_1+8 C_7 * 7 C_0 \\& 28 * 21+56 * 35+70 * 35+56 * 21+28 * 7+8 * 1 \\& 588+1960+2450+1176+196+8 \\& 6378 \text { ways }\end{aligned}$$[/tex]
The number of ways In which a panel with at least 2 women can be formed is 6378 ways.
c. The ways in which Miss A refuses If Mr. B is a member can be calculated by reducing one woman and one man from the Inltal members:
[tex]$$7 C_3 * 6 C_4$$[/tex]
420
The panel formed when Miss A refuses can be calculated as:
1960 - 420
1540 ways.
Hence the panel if Miss A refuses on the panel if Mr. B is a member can be formed in 1540 ways.
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Enter any three different expressions that are equal to 1/4 + 5/4
Answer:
6/4, 1 1/2, 1.5
Step-by-step explanation:
Three different expressions that are equal to 1/4 + 5/4 are (1/4) + (5/4), (2/4) + (4/4), and (2/8) + (10/8).
Explanation:Three different expressions that are equal to 1/4 + 5/4 are:
(1/4) + (5/4)(2/4) + (4/4)(2/8) + (10/8)Explanation:
When we add 1/4 and 5/4, we get (1+5)/4 = 6/4 = 3/2Alternatively, we can simplify the fractions first: 1/4 + 5/4 = (1+5)/(4+4) = 6/8 = 3/4. Then, we can express 3/4 as a sum of unit fractions: 3/4 = 2/4 + 1/4 = 1/2 + 1/4.We can also express 3/4 using different denominators. 1/4 + 5/4 = (1/4)*(2/2) + (5/4)*(2/2) = 2/8 + 10/8 = 12/8 = 3/2.Learn more about expressions that are equal to 1/4 + 5/4 here:https://brainly.com/question/33187767
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Gabriella swims downward 5 meters per second for 3 seconds. She then swims up 5 meters toward the surface of the water
a: write an expression to represent the total distance Gabriella travels
b:what is the total distance Gabriella travels?
a. The expression to represent the total distance is 5 × 3 + 3.
b. The total distance Gabriella travelled is 18 metres.
How to represent a situation with an expression?Gabriella swims downward 5 meters per second for 3 seconds. She then swims up 5 meters toward the surface of the water.
Therefore, the expression that represent the distance Gabriella travels can be represented as follows:
distance = speed × time
distance = 5 × 3
Therefore,
total distance = 5 × 3 + 3
Therefore, the total distance of Gabriela is 5(3) + 3 = 15 + 3 = 18 metres.
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