The length of the side is 10 units.
Solving Word Problems:To solve word problems, we try to assign variables to the quantities involved and use the given information to interpret the situation as a mathematical equation. Mathematical equations can then be solved using various techniques, so we get a solution which is then reinterpreted into the situation.
Now, According to the question:
Let the length of the side is 'L'
The area of a square is numerically 60 more than the perimeter.
Then, P = perimeter = 4L
A = area = [tex]L^2[/tex]
A = P + 60 ⇒
[tex]L^2[/tex] = 4L + 60
[tex]L^2[/tex] - 4L - 60 = 0
(L - 10)(L + 6) = 0
L = 10 or -6
L must be positive,
Since s can't be negative, L = 10 units.
Hence, The length of the side is 10 units.
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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
The image of a trapezoid is shown. An isosceles trapezoid with a short base of 3 meters and a height of 5 meters. The portion of the large base from the left vertex to the perpendicular is 4 meters. The portion of the large base from the right vertex to the perpendicular is 7 meters. What is the area of the trapezoid? 70 m2 38 m2 35 m2 19 m2
The area of the trapezoid is approximately 42.5 square meters. So, the answer closest to this value is 38 m^2.
What is trapezoid ?
A trapezoid is a quadrilateral with at least one pair of parallel sides. In a trapezoid, the parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. The height of a trapezoid is the perpendicular distance between the bases.
There are several types of trapezoids, including isosceles trapezoids, where the legs are of equal length, and right trapezoids, where one leg is perpendicular to both bases. Trapezoids are commonly used in geometry and can be used to find the area of various shapes, such as triangles and rectangles.
To find the area of the trapezoid, we can use the formula:
Area = (1/2) x (sum of bases) x height
Since the trapezoid is isosceles, the length of the two parallel sides are the same. Let's call that length "x". We can use this information to set up an equation:
3 + 4 + 7 + x = 2x
Simplifying, we get:
14 + x = 2x
x = 14
So the length of both parallel sides is 14 meters.
Now we can plug in the values into the area formula:
Area = (1/2) x (3 + 14) x 5
Area = 8.5 x 5
Area = 42.5
Therefore, the area of the trapezoid is approximately 42.5 square meters. So, the answer closest to this value is 38 m^2.
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Answer: B 38m squared.
Step-by-step explanation:
I took the test and got this question correct.
Evaluate: -2[-4+3(2-32+4⋅2-3)-3]
Answer:
68
Step-by-step explanation:
-2[-4+ 3(2 - 32 + 4 · 2 -3) - 3] Start in the center and work your way out.
-2[-4 + 3(2 - 32 + 8 -3) - 3]
-2[-4 + 3(-30 + 8 - 3) -3]
-2[-4 + 3(-22 -3) -3]
-2[-4 + 3(-25)-3]
-2[-4 -27 -3}
-2[-31 - 3]
-2(-34)
68
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.
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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What is the kinetic energy of a 3 kg ball that is rolling at 2 m/s
The kinetic energy of the 3 kg ball rolling at 2 m/s is 6 joules. The kinetic energy of an object is the energy it possesses due to its motion.
The kinetic energy of an object is the energy it possesses due to its motion. The formula for kinetic energy is given by:
Kinetic Energy = (1/2) * mass * velocity^2
In this case, the mass of the ball is 3 kg and its velocity is 2 m/s, so we can plug these values into the formula:
Kinetic Energy = [tex](1/2) * 3 kg * (2 m/s)^2[/tex]
Kinetic Energy = [tex](1/2) * 3 kg * 4 m^2/s^2[/tex]
Kinetic Energy = 6 J
So the kinetic energy of the 3 kg ball rolling at 2 m/s is 6 joules.
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1. A number is divided in the ratio 5:9. If the 1st is 35, find the other.
Step-by-step explanation:
solution
let first part be 5x and second part be 9x
so ,
5x = 35
x = 35\5
x = 7
Now 9x = 9*7 = 63
this might help you thank you
Find the missing value in the proportion 3/7 = 15/p.
A.21
B.35
C.45
D.75
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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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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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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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:
10. The temperature underwent a change of -18 degrees Fahrenheit between noon and midnight. It changed by the same amount each hour. Write and solve an equation to find h, the hourly change in temperature.
The hourly change in temperature is -1.5
What do you understand by Fahrenheit?Fahreheit temperature scale based on 32° for the freezing point of water and 212° for the boiling point of water, the interval between the two being divided into 180 equal parts.
The 18th- cenetury German physicist Daniel Gabreil Fahrenheit originally took as the zero of his scale the temperature of an equal ice-salt mixture and selected the values of 30° and 90° for the freezing point of water and normal body temperature, respectively, these later were revised to 32° and 96°, but the final scale required an adjustment to 98.6° for the latter value.
Given:
The temperature underwent a change of -18°F between noon and midnight.
To find:
The hourly change (h) in temperature
There are 12 hours between noon and midnight
So,
According to Question
Equation:
12h = -18
h = -18/12
h =-3/2
h = -1.5
The hourly change in temperature is -1.5
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The temperature underwent a change of -18 degrees Fahrenheit between noon and midnight, then the hourly change in temperature is -1.5.
What is Fahrenheit?
Fahrenheit temperature scale based on 32° for the freezing point of water and 212° for the boiling point of water, the interval between the two being divided into 180 equal parts.
The 18th-century German physicist Daniel Gabriel Fahrenheit originally took as the zero of his scale the temperature of an equal ice-salt mixture and selected the values of 30° and 90° for the freezing point of water and normal body temperature, respectively, these later were revised to 32° and 96°, but the final scale required an adjustment to 98.6° for the latter value.
Given:
The temperature underwent a change of -18°F between noon and midnight.
To find:
The hourly change (h) in temperature
There are 12 hours between noon and midnight
So,
According to Question
Equation:
12h = -18
h = -18/12
h =-3/2
h = -1.5
Therefore, The hourly change in temperature is -1.5
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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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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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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$
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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What is the area of this compound figure?
The area of this compound figure is 85 cm².
What is the area of the compound figure?
The area of the compound figure given is calculated by subtracting the small area of the figure from the big figure.
A (total) = 9 cm x 15 cm
A (total) = 135 cm²
The area of the small figure is calculated as follows;
A (small) = ( 9 cm - 4 cm ) x ( 15 cm - 5 cm )
A (small) = ( 5 cm ) x ( 10 cm )
A (small) = 50 cm²
The area of this compound figure = ( 135 cm² - 50 cm² ) = 85 cm²
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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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Jemma filled one-fourth of a barrel with compost on Saturday. Then she filled the remaining space with 4,200 g4,200 g4, comma, 200, start text, space, g, end text of compost on Sunday.
How many kilograms of compost are in the barrel?
.....kilograms?
The kilograms of compost in the barrel is 5.6 kg
How to determine the kilograms of compost in the barrel?From the question, we have the following parameters that can be used in our computation:
Amount filled on day 1 = 1/4
Remaining space = 4200 grams
The number of kilograms in the barrel is calculated as
Remaining space = (1 - 1/4) * Original space
Substitute the known values in the above equation, so, we have the following representation
(1 - 1/4) * Original space = 4200 grams
Convert to kg
(1 - 1/4) * Original space = 4.2 kg
So, we have
Original space = 4.2 kg/(1 - 1/4)
Evaluate
Original space = 5.6 kg
Hence, the original space is 5.6 kg
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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
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.
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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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.
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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Please help! 15 Points!
Answer:
Option C
Step-by-step explanation:
2*-1 = -2
2*0 = 0
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
a square with side length x is inscribed in a right triangle with sides of length 3, 4, and 5 so that one vertex of the square coincides with the right-angle vertex of the triangle. a square with side length y is inscribed in another right triangle with sides of length 3, 4, and 5 so that one side of the square lies on the hypotenuse of the triangle. what is x y ?
The value of x/y is 37/35, if a square with side length x is inscribed in a right triangle and a square with side length y is inscribed in another right triangle.
Note that triangle ABC and triangle FBE are similar,(by AAA)
As [tex]\angle B[/tex] is common in both, and [tex]\angle F= \angle A[/tex] as they both are 90°
so, the [tex]\angle C[/tex] will also be equal to [tex]\angle E[/tex]
so [tex]\frac{BF}{FR} = \frac{AB}{AC}[/tex]
This can be written as [tex]\frac{4-x}{x} = \frac{4}{3}[/tex]
solving: 12 - 3x = 4x
7x = 12 or x = 12/7
Similarly, triangle A'B'C' and triangle RB'Q are similar,
so RB' = [tex]\frac{4}{3}y[/tex] and C'S= [tex]\frac{3}{4}y[/tex]
Thus, C'B' = C'S+ SR+ RB'
or [tex]\frac{4}{3}y + y + \frac{3}{4} = 5[/tex]
solving y = 60/37
Now, x/y = [tex]\frac{12}{7} \times \frac{37}{60}[/tex] = 37/35
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En una empresa líder en investigación se quiere estimar la proporción de personas a favor de una nueva reforma política en el distrito A. ¿A cuántas personas se necesitará para la estimación, si de una muestra piloto se obtuvo que el 64. 1% de las personas están a favor de la reforma política, se desea estar seguro con un 97% de confianza y tener a lo más 4. 7% de error de estimación?
A sample of at least 870 people is needed to estimate the proportion of people in favor of the political reform in District A with a 97% confidence level and a maximum estimation error of 4.7%
To estimate the sample size, we can use the following formula:
n = (Z^2 * p * (1-p)) / E^2
where:
n = sample size
Z = the Z-score for a given confidence level (for 97% confidence, Z = 2.33)
p = the proportion in the pilot sample (0.641)
E = the maximum allowed error of estimation (0.047)
Plugging in the values, we get:
n = (2.33^2 * 0.641 * (1 - 0.641)) / 0.047^2
n = (5.3929 * 0.359) / 0.00222009
n = 1.928 / 0.00222009
n = 869.75
Since the sample size must be a whole number, we round up to the nearest whole number.
n = 870
Therefore, a sample of at least 870 people is needed to estimate the proportion of people in favor of the political reform in District A with a 97% confidence level and a maximum estimation error of 4.7%
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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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