On solving the provided question we cans ay that The side of the square is w/2, then its area is: A = (w/2)² = w²/4
what is a square?A square is an equilateral quadrilateral with four equal sides and four equal angles according to Euclidean geometry. It is also known as a rectangle with two neighboring sides that have the same length. Having all four equal sides and all four equal angles, a square is an equilateral quadrilateral. 90 degree or straight angles are square angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. a neighboring rectangle with two equal sides. a quadrilateral with four right angles and four sides of equal length. a parallelogram having two adjacent, equal sides that form a right angle. straight-sided rhombus.
The side of the square is w/2, then its area is:
A = (w/2)² = w²/4
The darkened region represents the difference between the square's and rectangle's areas:
[tex]14w - w^2/4 = 84\\56w - w^2 = 336\\w^2 - 56w + 336 = 0[/tex]
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Help me with this math homework pls!
Rewrite every expression underneath, while replacing every sign "x" implied.
23 + 8b = .......
㎡ - 5g = .......
⅛ q + 7a/3 = .....
12k (g+h) =......
(2x + 3)(2 - 5x) = ......
The following expressions rewritten below;
23 + 8bm² - 5g(3q + 56a) / 2412kg + 12kh -10x² -11x + 6How to write algebraic expressions?23 + 8b
No common terms or factors
= 23 + 8b
㎡ - 5g
No common terms or factors
= m² - 5g
1/8 q + 7a/3
= (3q + 56a) / 24
12k (g+h)
= 12kg + 12kh
(2x + 3)(2 - 5x)
= 4x - 10x² + 6 - 15x
combine like terms
= -10x² -11x + 6
Therefore, algebraic expressions are solved by multiplying and combining like terms.
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NEED HELP
Solve for x.
X=
The measure of the angle x would be 25.2°.
What is a circle theorem?
The circle theorem is a set of mathematical rules and relationships that apply to circles and their components, such as chords, tangents, and angles. These theorems describe how the different parts of a circle relate to each other and are used to solve geometric problems involving circles. Some common circle theorems include the inscribed angle theorem, the chord-chord theorem, and the tangent-secant theorem.
By using the circle theorem, we can write
5x-7 = 119
5x = 119 + 7
5x = 126
x = 126/5
x = 25.2°
Hence, the measure of the angle x would be 25.2°.
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Which of the following sequences is an arithmetic sequence?
O {1, 2, 4, 7,...}
O {1, -2, 4, -8,...}
O {1, 4, 7, 10, ...}
O {1, 3, 9, 27,...}
Answer:
The third option
Step-by-step explanation:
The third option, {1, 4, 7, 10, ...} is an arithmetic sequence because you add 3 to get from 1 to 4, and then you add 3 to get to 7, and then you add another 3 to get to 10.
What is the answer to question 5
Anwer: EG=EF+EG => 6x+12+48=144
6x=144-12-48
6x=84
x=14
d)x=14
Solve the following system of inequalities graphically on set of axes below. State the coordinates of a point in the solution set.
Answer:
see below for a graph
(-8, 4) is in the solution set
Step-by-step explanation:
You want the graph and a solution point for the inequalities y ≤ -6/5x -4 and y ≥ 2/5x +4.
GraphThe solid boundary line of the first inequality will cross the y-axis at -4, and will have a "rise" of -6 units for each "run" of 5 units. Shading is below this boundary line.
The solid boundary line of the second inequality will cross the y-axis at +4 and will have a "rise" of 2 units for each "run" of 5 units. Shading is above this boundary line.
Solution setThe boundary lines make an X shape on the graph, crossing at the point (-5, 2). The solution set is in the left quadrant.
Point (-5, 2) is in the solution set, as are points in the doubly-shaded space to its left. (-8, 4) is one of those.
__
Additional comment
The boundary lines are solid because the "or equal to" case is included in each.
The ≤ symbol tells you y-values that satisfy the first inequality will be less than (or equal to) those on the boundary line.
The ≥ symbol tells you y-values that satisfy the second inequality will be greater than (or equal to) those on the boundary line.
Find the missing measurements of the triangle.
35
A
21
B
Round all answers to the nearest whole number.
Bc=?
The measure of BC from the triangle ABC is 40.82 units.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given that, in triangle ABC, AB=21 units and AC=35 units.
By using Pythagoras theorem,
BC²=AB²+AC²
BC²=21²+35²
BC²=441+1225
BC²=1666
BC=√1666
BC=40.82
Therefore, the measure of BC is 40.82 units.
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Ann spent 50% of her allowance on food 30 % of it on stationary and saved the remaining amount her allowance was $15 how much money did she save
At the end, Ann saves a total amount of 3 dollars according to the money she spent and on allowance according to the percentages.
Total Allowance of Ann = 15 dollars
Spent on food by Ann = [tex]\frac{15}{100}[/tex]*50
On food = 50 × [tex]\frac{15}{100}[/tex] = 7.5 dollars
Spent on stationary = 30% of Allowance
On stationary = 30 X[tex]\frac{15}{100}[/tex] = 4.5 dollars
Therefore, Money saved by Ann = Total Allowance - Money spent
Money saved = 15 dollars - 7.5 dollars - 4.5 dollars = 15-(7.5+4.5) dollars
Money saved = 3 dollars
Therefore, money saved by Ann is 3 dollars.
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a square $10$ cm on each side has four quarter circles drawn with centers at the four corners. how many square centimeters are in the area of the shaded region? express your answer in terms of $\pi$.
A square of 10 cm on each side has four quarter circles drawn with centers at the four corners, then the area of the shaded region is 21.46 centimeter square
The side of the square a = 10 cm
The area of the square = a^2
Substitute the values in the equation
The area of the square = 10^2
= 100 centimeter square
There are 4 quarter circle in the figure. We know 4 quarter circle is one circle
The area of the circle = πr^2
Where r is the radius of the circle
The radius of the circle = 5 cm
The area of the circle = π × 5^2
= 78.54 centimeter square
The area of the shaded region = The area of the square - The area of the circle
= 100 - 78.54
= 21.46 centimeter square
Therefore, the area of shaded region is 21.46 centimeter square
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Let U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {6, 8, 10}, B = {5, 6, 9, 12}, and C = {1, 3, 7}
A ∪ B?
The value for A∪B in probability form is 3/4. The value for A∪B in data set form is {5, 6, 8}.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
The event U has data - U = {1, 2, 3, 4, 5, 6, 7, 8}
The event A has data - A = {6, 8, 10}
The event B has data - B = {5, 6, 9, 12}
The event C has data - C = {1, 3, 7}
The probability formula is -
Probability = No. of outcomes that is favorable / Total number of outcomes
The value for A∪B is -
A∪B = 3/4
The value of A∪B in data set is the values that are present in U data set and in A and B data set.
So, the value is - {5, 6, 8}
Therefore, the value is 3/4 or {5, 6, 8}.
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write the equation for the given graph.
The absolute value function on the graph is:
f(x) = -|x + 4| - 5
What is the equation of the absolute value function?Remember that an absolute value function that has a vertex at (a, b) will be written as:
f(x) = |x - a| + b
Here the vertex is at (-4, -5), replacing that in the general formula we will get:
f(x) = |x + 4| - 5
And we also can see that the absolute value function opens downwards with slopes of 1, then there must be a leading coefficient of -1, the actual function is:
f(x) = -|x + 4| - 5
That is the graphed function.
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I get 64% off a table the sale price is $72, what is the original price?
The original price of the table was $200 before the 64% discount was applied.
What is the percentage?
Percentage is a way of expressing a fraction or proportion out of 100. It is commonly used to compare two quantities, indicate the change or growth of a quantity over time, or express the probability or chance of an event occurring.
If you received a 64% discount on the sale price of a table, and the sale price is $72, we can calculate the original price of the table as follows:
Determine the percentage of the original price that corresponds to the sale price after the discount:
If the sale price is 100% - 64% = 36% of the original price, after the 64% discount.
Use the percentage found in step 1 to calculate the original price:
Let x be the original price
x * 36% = $72
0.36x = $72
x = $72 / 0.36
x = $200
Therefore, the original price of the table was $200 before the 64% discount was applied.
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Solve 2 ―8―33 = 0 by factoring.
Answer:
the equation 2 - 8 + 33 = 0 can be factored as 27 = 0, which is a verified answer
Step-by-step explanation:
To factor the equation 2 - 8 + 33 = 0, we start by collecting all the terms on one side of the equation:
2 - 8 + 33 = 0
becomes
33 - 8 + 2 = 0
Next, we can rewrite this as:
33 - 6 = 0
Finally, we factor the left-hand side of the equation to get:
33 - 6 = (33 - 3) - 3 = 30 - 3 = 27 - 0
So the factored form of the equation 2 - 8 + 33 = 0 is 27 = 0.
Verification: We can verify that the factored form of the equation is correct by substituting 0 for 27 and checking that the equation holds. So, if we replace 0 for 27 in equation 27 = 0, we get:
27 = 0, which is true.
Therefore, the equation 2 - 8 + 33 = 0 can be factored as 27 = 0, which is a verified answer.
Deshaun rented a truck for one day. There was a base fee of $20.95, and there was an additional charge of 80 cents for each mile driven. Deshaun had to pay $250.55 when he returned the truck. For how many miles did he drive the truck?
Answer:
287 miles
Step-by-step explanation:
20.95+ .80x =250.55
250.55-20.95=229.6
.80x=229.6
229.6/.80=x
x=287 miles
For what values of x and y must ABCD be a parallelogram?
The correct answer is,
x = 39
y =21
What is Parallelogram ?A different type of quadrilateral known as parallelogram has both pairs of its opposite sides parallel and equal.
The figure shows a parallelogram ABCD with the parameters AB II CD and AD II BC. Furthermore, AB = CD and AD = BC.
In a parallelogram, the opponent angles are equal.. So it means that side /A is equal to side /C, let's equate the two angles and solve for x;
5y - 3 = x + 3y
2y - x = 3 ........(1)
Also, consecutive angles of a parallelogram are supplementary,
therefore,
/C + /D = 180
x + 3y + 2x = 180
3x + 3y = 180
x + y = 60 .......(2)
Now, add equations (1) and (2)
(2y-x) + (y+x) = 3 + 60
3y = 63
y = 21
now put this value of y in (2) we get,
x + y = 60
x + 21 = 60
x = 39
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you shuffle a standard deck of cards, then draw four cards.(a) what is the probability all four are the same suit? (b) what is the probability all four are red? (c) what is the probability each has a different suit?
a) Probability that all four are the same suit = 0.0106 b) Probability that all four are red =0.055 c) Probability each has a different suit = 0.105
Total number of cards =52
No. of cards for each suit =13
Total types of four suit =4 (heart, spades, diamonds, clubs)
Total numbers of ways = [tex]^{52}C_4[/tex] =270,725 ways
a) number of ways choosing four cards of the same suit
= [tex]^{13}C_4+^{13}C_4+^{13}C_4+^{13}C_4[/tex]
= [tex]4 \times ^{13}C_4\\[/tex]
= [tex]4 \times \frac{13!}{4!(13-4)!}[/tex]
=2860 ways
Probability that all four are the same suit is 2860/270,725 = 0.0106
b) Number of ways all four cards are red
=[tex]^{26}C_4[/tex]
= 4,950 ways
Probability that all four are red = 4950/270,725 =0.055
c) Number of ways each card has a different suit
=[tex]^{13}C_1\times^{13}C_1\times^{13}C_1\times^{13}C_1[/tex]
= 28,561 ways
Probability each has a different suit is 28561/270725 = 0.105
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Find the value of h such that the line 27hx -9y = -18 would be parallel to the line y = 1 - 6x
For given linear equations, 27hx -9y = -18 and y = 1 - 6x
h will be 2.
What is a linear equation, exactly?
When the greatest power of a variable is 1, the equation is said to be linear. Another term for it is a one-degree equation. The standard form of a linear equation with one variable is Ax + B = 0. There are three variables in this equation: x, A, and B. A denotes a coefficient. A linear equation with only two variables is commonly written as Ax + By = C. There are three more constants in addition to the constant C: the variables x and y, the coefficients A and B, and the variables.
Now,
As general equation of a line is y=mx + c where m=slope and c=constant
and here given lines are 27hx -9y = -18 and y = 1 - 6x
transforming these into general equations
y=-3hx+2 where m=-3h
and y=-6x+1 where m=-6
Now As slope of parallel lines is equal
therefore, -3h=-6
h=6/3
h=2
Hence,
h will be 2.
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a certain bacteria population obeys the population growth law. it is observed that the doubling time for the population is 4 hours. the length of time it will take for the population to increase to 3-times its original population is
According to the population growth law, the size of a population grows exponentially over time, with a growth rate proportional to population size. If the population doubling time is t, then the population size P can be written as:
[tex]P = P_0 * 2^{t/t_d)}[/tex]
where P_0 is the initial population size, t is the time elapsed, and t_d is the doubling time.
To find the time it will take for the population to increase to 3 times its original population size, we can set [tex]P = 3P_0[/tex] and solve for t:
[tex]3P_0 = P_0 * 2^{t/t_d}[/tex]
Dividing both sides by [tex]P_0[/tex] gives:
[tex]3 = 2^{t/t_d}[/tex]
Taking the logarithm of both sides (using any base) gives:
[tex]log(3) = log(2^{t/t_d} )[/tex]
Using the logarithmic identity
[tex]log(a^b) = b*log(a),[/tex]
we can rewrite this as:
[tex]log(3) = (t/t_d)*log(2)[/tex]
Solving for t, we get:
[tex]t = t_d * (log(3)/log(2))[/tex]
Substituting [tex]t_d[/tex] = 6 hours (given in the problem), we get:
[tex]t = 6 * (log(3)/log(2)) hours[/tex]
Simplifying using the change of base formula
[tex](log(a)/log(b) = log_b(a))[/tex], we get:
[tex]t = 6 * log_2(3)[/tex] hours
Therefore, the answer is (f) None of the above.
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Correct question should be
Click on image for question
thomas think that 3 7/8 +2 11/12 is pretty close to 56 but lorinda thinks it’s is closer to 6. Todd disagree with both of them , and thinks it is closer to 7! what do you think? be clear and complete in you’re response
Todd has done correct calculation its values is equal to 6.79, which is closer to 7.
What is a fraction?Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.
Numerator is a number on the top side, it indicates the number of equal parts taken or whole quantity and denominator is on the bottom side, it indicates the equal parts of the whole quantity.
Given that,
Two fraction numbers in the form of addition,
⇒ 3 7/8 + 2 11/12
It can be further solved as
⇒ (24 + 7)/8 + (24 +11)/12
⇒ 31/8 + 35/12
Now taking LCM of (8, 12)
LCM(8, 12) = 24
making denominator same in the both terms
⇒ 93/24 + 70/24
⇒ 163/24
⇒ 6.79
Thus, the values is closer to 7
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If it takes 2 cups of rice to make 5 servings, how many cups of rice are needed to make 12 servings?
12 servings of rice require six cups of rice. In order to make 12 servings, 6 cups of rice would be needed, or 2/5 of a cup.
1. It takes 2 cups of rice to make 5 servings.
2. Divide 12 by 5 to determine how many cups of rice are required to prepare 12 servings.
3. The final product is 2.4 cups.
4. Round up to the nearest whole number, which is 6 cups, to get 12 servings.
You will require 6 cups of rice to produce 12 servings of rice. The number of servings that can be made from 2 cups of rice can be used to determine this. 5 servings can be produced from 2 cups of rice. This indicates that 2/5 of a cup of rice is needed for each serving. Divide 12 by 5 to see how many cups of rice are required for 12 servings. This results in 2.4 cups of liquid. Round the amount up to the nearest whole number, which is 6 cups, to make 12 servings. 6 cups of rice are therefore required to make 12 servings.
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car rental company a charges an $80 service fee plus $22 per day. car rental company b does not have a service fee and charges $32 per day. which equation will help determine how many days it will take for the average charge per day for company a to be the same as the average charge per day for company b? responses 32d
Equation that will help determine how many days it will take for the average charge per day for company a to be the same as the average charge per day for company b is [tex]\frac{80+22d}{d} = 32d[/tex]
For finding the equation we will first form separate equations of both company a and company b and then we will equate the formed equation to find the number of days.
Let the number of days be d.
For company a, we will first add the service charges and per day charge multiplied with number of days, and then divide the sum with number of days.
= [tex]\frac{80+22d}{d}[/tex]
For company b, we will multiply the per day charges with the number of days.
= [tex]32d[/tex]
Now, we will equate both the formed equation
[tex]\frac{80+22d}{d} = 32d[/tex]
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HELP ASAP, GUITAR CLASS, WILL MARK FIRST ANSWER BRAINLIEST,
What is the name of the note shown above?
A
B
C
G
Answer:
C
Step-by-step explanation:
The spaces go F A C E. The note shown is C.
Find the missing value in the proportion 3/7 = 15/p.
A.21
B.35
C.45
D.75
i don’t understand what i’m supposed to do
The function with a greater stretch factor is the function graphed and the value is 3 times greater
How to find the function with the greater stretch factorThe function with a greater stretch factor is the function which has a greater number multiplying the function
The given equation is a(x) = 1/3 x³ while the function graphed is b(x) = x³+ 2
The stretch factor is determined by the coefficients which are
a(x): 1/3 and b(x): 1
comparing this numbers
= b(x) / a(x)
= 1 / 1/3
= 3
this shows that b(x) which is 1 is greater by 3 times.
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shaniece has a bag that contains strawberry chews, cherry chews, and lime chews. she performs an experiment. shaniece randomly removes a chew from the bag, records the result, and returns the chew to the bag. shaniece performs the experiment 57 times. the results are shown below: a strawberry chew was selected 31 times. a cherry chew was selected 2 times. a lime chew was selected 24 times. if the experiment is repeated 1200 more times, about how many times would you expect shaniece to remove a lime chew from the bag? round your answer to the nearest whole number.
Shaniece is expected to select a lime chew about 505 times in the next 1200 selections.
Based on the given results, Shaniece selected a lime chew 24 times out of 57 selections. To estimate the expected number of times she would select a lime chew in the next 1200 selections, we can use the proportion of lime chews selected in the first 57 selections:
The proportion of lime chews selected = 24/57
To estimate the expected number of lime chews in the next 1200 selections, we can multiply the proportion by the total number of selections:
expected number of lime chews in the next 1200 selections = (24/57) x 1200
The expected number of lime chews in the next 1200 selections = 505.263
Rounding to the nearest whole number, we would expect Shaniece to select a lime chew about 505 times in the next 1200 selections.
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Classify each pair of angles as Complementary, Supplementary, or Neither. Drag and drop the choices into the boxes to correctly complete the table. Each category may have any number of pair of angles. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response.
Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Complementary Supplementary Neither
Answer:
Complementary is 2 angles that add up to 90 degrees and supplementary is 2 angles that add up to 180 degrees
48+32=80 so that would be neither
101+77=178 so that would be neither
107+73=180 so that would be supplementary
Step-by-step explanation:
have a nice day.
Answer:
only here for points
Step-by-step explanation:
Show that x(x -3m) = 5m² is non-real
The equation x(x - 3m) = -5m² is non-real as the discriminant of the quadratic equation will be negative.
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by the rule presented as follows:
y = ax² + bx + c
The discriminant of the quadratic function is given as follows:
Δ = b² - 4ac.
The numeric value of the coefficient and the number of solutions of the quadratic equation is defined as follows:
Δ > 0: two real solutions.Δ = 0: one real solution.Δ < 0: two complex solutions = zero real solutions.The equation for this problem is defined as follows:
x(x - 3m) = -5m²
x² - 3mx + 5m² = 0.
The parameters are given as follows:
a = 1, b = -3m, c = 5m².
Hence the discriminant is given as follows:
Δ = (-3m)² - 4(1)(5m²)
Δ = 9m² - 20m²
Δ = -11m².
-11m² is always negative, hence the discriminant is negative and the equation is non-real.
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Jordan recorded the number of sit-ups he completed during the first 4 track practices. Which of Jordan's friends completed double the amount of sit-ups that Jordan completed during each practice?
The required proportionality relationship between Jordan and his friend for the sit-up is y = 2x.
What is proportionality?Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
Jordan recorded the number of sit-ups he completed during the first 4 track practices, we can establish the proportionality relationship between Jordan and his friend by comparing the number of sit-ups each completed during each practice.
Let's call the number of sit-ups that Jordan and his friend completed during each practice "x" and "y". Then, the number of sit-ups that his friend completed during each practice would be "2x".
The proportionality relationship between Jordan and his friend can be expressed as,
y = 2x
This means that for every 1 sit-up that Jordan completed, his friend completed 2 sit-ups, or that Jordan's friend completed twice the number of sit-ups that Jordan completed during each practice.
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The population of rabbits on an island is growing exponentially. In the year 2000, the population of rabbits was 950, and by 2003 the population had grown to 1000. Predict the population of rabbits in the year 2013, to the nearest whole number.
The population of rabbits in the year 2013 is 1186.
How to predict the population of rabbits in the year 2013?
To predict the population of rabbits in the year 2013, we can use exponential growth. The formula for exponential growth is:
P = P₀ * e^(rt)
where:
P = final population
P₀ = initial population (950)
r = the growth rate (we need to find this)
t = time elapsed (13 years)
We can use the data from 2003 to find the growth rate:
1000 = 950 * e^(r * 3)
1000 = 950 * e^(3r)
1000/950 = e^(3r)
ln (1000/950) = 3r
r = (ln(1000 / 950)) / 3
r = 0.0171
Now that we have the growth rate, we can use it to find the population in 2013:
P = 950 * e^(0.0171 * 13)
P = 1186
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Last week, Vanessa bought 14 shirts and 6 hats for a total of $198.
Today, Vanessa bought 10 shirts and 6 hats for a total of $150.
Assuming neither item has changed in price, what is the cost of a
shirt in dollars?
khora
Answer: Shirt-$12 Hat-$5
Step-by-step explanation:
14T + 6H = 198
10T + 6H = 150
4T=48
T=12$
10(12)+6H = 150
120 + 6H =150
H = 5$
I really need help! Can you help??
Answer:
To convert 6 feet into meters, first create a conversion factor to convert from feet to meters. Make sure the original unit is in the denominator, then cancel feet. Next, multiply the original measure by the conversion factor to get 1.8288 meters, or 1.83 meters if you simplified it.
Step-by-step explanation:
