The area of the square is (x²/2) square units.
We are given a square. The length of the diagonal of the square is x units. We have to find the area of the square in terms of "x".
Let the side of the square be denoted by the variable "s". We will use the Pythagorean theorem to find the length of the side of the square.
s² + s² = x²
2s² = x²
s² = x²/2
s = √(x²/2)
s = (x/√2)
The area of the square is given by the square of the side length. Let the area of the square be denoted by the variable "A".
A = s²
A = (x/√2)²
A = x²/2
Hence, the area of the square is (x²/2) square units.
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If you are tossing a six-sided die, what is the probability of getting either a 1 or a 2 on your first toss and a 1 or a 2 on your second toss?.
A six sided dice is tossed twice. The probability of getting either a 1 or a 2 on your first toss and a 1 or a 2 on your second toss is 1/9 .
A dice has six faces or sides and it is throws twice . When a dice is toss first time,
Total possible outcomes on toss = 6 ={ 1,2,3,4,5,6}
In our first toss we want to get 1 or 2
So, favourable outcomes of getting 1 or 2 = 2
Probability of getting 1 or 2 on first toss= favourable cases /total outcomes = 2/6 = 1/3
For second toss, we want to get a1 or a2 again.
Total possible outcomes = 6
Probability of getting a1 or a2 on second toss= 2/6= 1/3
Now, Multiply these probsbilites togethers and chance of getting 1 or 2 on first and second which is 1/3× 1/3 = 1/9
Hence , probability of getting either a 1 or a 2 on your first toss and a 1 or a 2 on your second toss is 1/9.
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Solve the equation.
x-2/5=2/3-3x-2/6
Answer:
11/48
Step-by-step explanation:
x-2/5=2/3-3x-2/6
collect like terms
x-2/5 + 3x = 2/3 - 2/6
taking LCM on both sides
[(x-2) + 5(3x)]/5 = [2(2) -2]/6
(16x - 2)/5 = 2/6
cross multiply
6(16x - 2) = 5(2)
96x - 12 = 10
96x = 22
therefore; X = 22/96
= 11/48
CHECK:
(11/48 - 2)/5 = 2/3 - 3(11/48) - 2/6
(-85/48)/5 = 2/3 - 11/16 - 2/6
-85/48 × ⅕ = -17/48
-17/48 = -17/48
Answer:
[tex]x=\frac{11}{60}[/tex]
Step-by-step explanation:
Given the equation
[tex]x-\frac{2}{5}=\frac{2}{3}-3x-\frac{2}{6}[/tex]
Lets solve for x.
Simplify the right side of the equation.
Cancel the common factor of 2 and 6 .
Factor 2 out of 2 .
[tex]x-\frac{2}{5}=\frac{2}{3}-3x-\frac{2(1)}{2(3)}[/tex]
[tex]x-\frac{2}{5}=\frac{2}{3}-3x-\frac{1}{3}[/tex]
Combine the numerators over the common denominator.
[tex]x-\frac{2}{5}=-3x-\frac{2-1}{3}[/tex]
[tex]x-\frac{2}{5}=-3x-\frac{1}{3}[/tex]
Move all terms containing x to the left side of the equation.
Add [tex]3x[/tex] to both sides of the equation.
[tex]x-\frac{2}{5}+3x=\frac{1}{3}[/tex]
Add [tex]x[/tex] and [tex]3x[/tex].
[tex]4x-\frac{2}{5}=\frac{1}{3}[/tex]
Move all terms not containing x to the right side of the equation.
Add [tex]\frac{2}{5}[/tex] to both sides of the equation.
[tex]4x=\frac{1}{3}+\frac{2}{5}[/tex]
To write [tex]\frac{1}{3}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{5}{5}[/tex] .
[tex]4x=\frac{1}{3}*\frac{5}{5} +\frac{2}{5}[/tex]
To write [tex]\frac{2}{5}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{3}{3}[/tex]
[tex]4x=\frac{1}{3}*\frac{5}{5} +\frac{2}{5}*\frac{3}{3}[/tex]
Simplify.
Write each expression with a common denominator of 15 , by multiplying each by an appropriate factor of 1 .
[tex]4x=\frac{11}{15}[/tex]
Divide each term in [tex]4x=\frac{11}{15}[/tex] by 4 and simplify.
[tex]x=\frac{11}{60}[/tex]
Kareem correctly answered 85% of the questions on his last math test. If he missed 6 problems, how many questions were on the test
Answer:
40 questions
Step-by-step explanation:
100-85=15
15/100=6/x
cross multiply
15x=100(6)
15x=600
x=40
there were 40 questions on the test
hopes this helps please mark brainliest
growth or decay, and determine the percentage rate of increase or decrease.
y
=
660
(
0.902
)
x
The expression y = 660(0.902)ˣ represents a decay , the rate of decrease is 9.8% .
In the question ,
it is given that ,
the the exponential function is y = 660(0.902)ˣ
we need to determine that , the equation represents a growth or decay .
0.902 is the variable that will determine a growth or decay .
Since, 0.902 is less than 1 , so it represents a decay function .
To find the rate we subtract 0.902 from 1
= 1 - 0.902
= 0.098
= 9.8% decrease rate
Therefore , The expression y = 660(0.902)ˣ represents a decay , the rate of decrease is 9.8% .
The given question is incomplete , the complete question is
Identify if it's Growth or Decay , and determine the percentage rate of increase or decrease , the function is y = 660(0.902)ˣ ?
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Graph the line with the given point and slope. the line through (0,0) with slope 6/5
Check the picture below.
6. Erin leaves home at 11am. She cycles at a speed of 16 miles per hour for 90 minutes. She
stops for half an hour. Erin then cycles home and arrives at 3pm.
(a) Draw a distance-time graph to show Erin's journey.
(b) What is Erin's average speed on the return part of her cycle?
The average speed of Erin on the return part is 12 miles/hour
Given, Erin leaves home at 11am. She cycles at a speed of 16 miles per hour for 90 minutes. She stops for half an hour. Erin then cycles home and arrives at 3pm.
We have to find the average speed on the return part of her cycle.
Now, using distance formula, we get
Distance = Speed × Time
Distance = 16 miles per hour × 90 × 1/60 hours
Distance = 24 miles
As, average speed = Total distance/Total time
Average speed = 24 miles / 2 hours
Average speed = 12 miles per hour
Hence, the average speed of Erin on the return part is 12 miles/hour
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find the value of x that makes 22=x/(-13)
Answer:
x=−286
Step-by-step explanation:
22=(x)/(-13) just follow the order
Math trigonometry non right angle help please
guys please
Answer:
about 21.3 cm²
Step-by-step explanation:
Given a triangle with three sides 6 cm, 8 cm, and 12 cm, and smallest angle 26.4°, you want the area.
Area using sine formulaA = 1/2ab·sin(C)
A = 1/2(12 cm)(8 cm)·sin(26.4°) ≈ 21.34 . . . . square units
Area using Heron's formulaThe semiperimeter is ...
s = (6 +8 +12)/2 = 13
The area is ...
A = √(s(s -a)(s -b)(s -c))
A = √(13·(13 -12)(13 -8)(13 -6)) = √(13·1·5·7) = √455
A ≈ 21.33 . . . . square centimeters
The area of the triangle is about 21.3 cm².
__
Additional comment
The problem with over specifying the dimensions of a geometry problem is that it is often difficult to make them consistent. Here, the area values agree to three significant figures. That is about all we can expect, given the angle precision is 3 significant figures.
Your answer depends on the set of dimensions you choose to use. It will be different yet if you use the Law of Sines to find angle A or B for the Sine Formula, especially if you round the angle value to tenths.
The attachment shows the solution using side lengths only.
it takes an airplane 1 hour 30 minutes to fly 600 km against the wind. the return trip with the wind takes only 1 hour. find the total flying time for the round trip if there was no wind.
The total flying time for the round trip if there was no wind would be 2 hours 24 minutes. The result is obtained by using the elimination method.
What is elimination method?The elimination method is a method for solving system of linear equations where we eliminate one variable so that we can get an equation in one variable. In doing that, we can either add or subtract the equations.
Given the case that an airplane takes 1 hour 30 minutes to fly 600 km against the wind. It takes only 1 hour in the return trip.
What would be the total flying time for the round trip if there was no wind?
Let's say:
v = the speed of the airplanew = the speed of the windWhen the airplane leaves,
v - w = 600 km / 1.5 hour
v - w = 400 kph ... (equation 1)
When the airplane returns,
v + w = 600 km / 1 hour
v + w = 600 kph ... (equation 2)
We eliminate the equation 2 and 1 to get the speed of the airplane.
v - w = 400 kph
v + w = 600 kph +
2v = 1000 kph
v = 1000 ÷ 2
v = 500 kph
For the round trip, the airplane would fly 600 × 2 = 1200 km.
The total flying time if there was no wind would be
t = s/v
t = 1200/500
t = 2.4 hour
t = 2 hours 24 minutes
Hence, the total flying time for the round trip if there was no wind is 2 hours 24 minutes.
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In one day, the bakery made 719 bagels. The bagels were divided into 9 equal shipments. A few bagels
were left over and given to the baker. How many bagels did the baker get?
Answer:
8 bagels
Step-by-step explanation:
This is a remainder division problem. We need to divide 719 by 9 and find the remainder.
First off, 9 is bigger than 7, so we need to move to the next digit. How many times does 9 go into 71? 9 times 7 is 63! That's the closest smaller number we can get, so I will write a 7 in the long division problem above the 1. I will subtract 63 from 71 to get 8.
7
9 | 719
-63
8
Now, the 9 can be brought down, making our 8 into an 89. How many times does 9 go into 89? 9 times 9 is 81! That's the closest we can get! I will write a 9 by the 7 above the 9 in 719, and write 81 below the 89. Subtracting these leaves us with a remainder of 8.
79
9 | 719
-63 ↓
89
-81
8
This means that the bagels were sent in 9 equal shipments of 79 bagels each, and the baker was left with 8 bagels!
A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 5 grams and the amount of gold in each necklace is 24 grams. The jeweler made a total of 12 bracelets and necklaces using 155 grams of gold. Determine the number of bracelets made and the number of necklaces made.
Uplift occurs at a rate of 0. 1 m per 1,000 years. How much will the uplift change over 1,000,000 years? responses 0. 1 m 0. 1 m 100 m 100 m 1,000 m 1,000 m 1,000,000 m.
As per given information about change in uplift it occurs at the rate of 0.1 m per 1,000 years then change in uplift over 1,000,000 years is equal to 100m.
As given in the question,
Rate of occurring of uplift is equal to 0.1m per 1000 years
Represent the given relation in equality form we get,
Change of uplift in 1000 years = 0.1 m
⇒ 1 year = 0.1 m / 1000
⇒ 1,000, 000 years = ( 0.1 m / 1,000 ) × 1,000, 000
⇒ 1,000, 000 years = ( 1 m / 10,000 ) × 1,000, 000
⇒ 1,000, 000 years = 100 m
Therefore, for given information about change in uplift it occurs at the rate of 0.1 m per 1,000 years then change in uplift over 1,000,000 years is equal to 100m.
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I need help for #4 You have to find the slope and I missed a day at school and I am confused on what to do
A student used the equation below to create a table.
y = 2.50x
The student used 15 as one of the values for the x. Which ordered pair could be taken from the table?
O a 17.50, 15)
Ob (15, 17.50)
Oc 37.50, 15)
Od (15,37.50)
The resulting ordered pair is (15, 37.50) when the value of x as 15.
Ordered pair
Ordered pair refers a set of numbers that tells us where to find a point on a coordinate grid. In the grid, the first number represents the value on the x-axis and the second number represents the value on the y-axis.
Given,
A student used the equation below to create a table.
y = 2.50x
The student used 15 as one of the values for the x.
Here we need to find the resulting ordered pair.
Through the given question we have identified that the given function is,
y = 2.50x.
Here x represents the number of students.
Now, we have to calculate the y value for 15 number of students,
So, here we have to apply the value x as 15, then we get,
y = 2.50 (15)
Now, we have to perform the multiplication on it,
y = 37.50
Therefore, the resulting ordered pair is (15, 37.50)
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The scale of a map is 1:20 000. What area does 8 cm² represent?
The 8 cm² area on a map represent the actual area = 3200000000 cm² .
Scale factor of a map
S = 1/20000
The scale factor for area is found by squaring the scale factor for length. Thus the scale factor for area is S^2
When applied to the area we consider S^2 as a scale factor.
The area on the map = 8 cm²
So The actual area = 8 × (20000)^2 = 8× 20000×20000
=3200000000 cm² = 320000 m² =32 hectare.
So the 8 cm² area on a map represent the actual area = 3200000000 cm² .
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Determine which statements are the converse, inverse, and contrapositive of the following statement.
If it is after midnight, Anissa is sleeping.
All rights reser
If Anissa is sleeping, it is not after midnight.
If Anissa is sleeping, it is after midnight.
If it is not after midnight, Anissa is sleeping.
If it is not after midnight, Anissa is not sleeping.
If Anissa is not sleeping, it is not after midnight.
Converse
Contrapositive
Inverca
The statements are characterized as converse, inverse, and contrapositive statements as follows:
A) If it is after midnight, Anissa is sleeping: Converse statements(B) If Anissa is sleeping, it is not after midnight: Inverse statements(C) If Anissa is sleeping, it is after midnight: Converse statements(D) If it is not after midnight, Anissa is sleeping: Inverse statements(E) If it is not after midnight, Anissa is not sleeping: Contrapositive statements(F) If Anissa is not sleeping, it is not after midnight: Contrapositive statementsConverse statements:
If anything, we would say the opposite: "If the grass is wet, it's pouring." "If it is NOT raining, then the grass is NOT wet," would be our inverse claim. If the grass is not wet, it is not raining, according to our contrapositive.Inverse statements:
Each of the original statements is presupposed to be false in an inverted statement. "If it is not snowing" would be the polar opposite of "If it is snowing." "Then it is not chilly" would be the polar opposite of "then it is cold."Contrapositive statements:
When you reverse the hypothesis and the conclusion in a statement and reject both of them, you have a contrapositive statement. When the hypothesis and the conclusion are switched in this example and both are negated, the outcome is: If it is not a triangle, then it is not a polygon.So, the given sentences are:
(A) If it is after midnight, Anissa is sleeping: Converse statements(B) If Anissa is sleeping, it is not after midnight: Inverse statements(C) If Anissa is sleeping, it is after midnight: Converse statements(D) If it is not after midnight, Anissa is sleeping: Inverse statements(E) If it is not after midnight, Anissa is not sleeping: Contrapositive statements(F) If Anissa is not sleeping, it is not after midnight: Contrapositive statementsTherefore, the statements are characterized as converse, inverse, and contrapositive statements as follows:
A) If it is after midnight, Anissa is sleeping: Converse statements(B) If Anissa is sleeping, it is not after midnight: Inverse statements(C) If Anissa is sleeping, it is after midnight: Converse statements(D) If it is not after midnight, Anissa is sleeping: Inverse statements(E) If it is not after midnight, Anissa is not sleeping: Contrapositive statements(F) If Anissa is not sleeping, it is not after midnight: Contrapositive statementsKnow more about converse statements here
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Answer:
1,2,4
Step-by-step explanation:
edem
Challenge and each go to a hardware tore to buy wire. The table how the cot y in dollar for of the wire they need. Need of the wire. Need of the wire. How much will each of them pend for wire?
This is the required final answer Emily spends $300y/x and Andy spends $432y/x for wire.
The answer provided below has been developed in a clear step-by-step manner.
1 foot =12 inches
1 yard=36 inches
Emily needs (25×12)=300 inches wire
and Andy needs (12×36)=432inches wire
As the cost for x inches wire is $y
cost for a 1-inch wire is $x/y
So, the cost for 300 inches of wire is $300y/x
cost for 432 inches of wire is $432y/x
so, Emily spends $300y/x
and Andy spends $432y/x for wire.
More than 20 different currencies go by the name dollar. The Australian dollar, Brunei dollar, Canadian dollar, Hong Kong dollar, Hogan dollar, Jamaican dollar, Liberian dollar, Namibian dollar, New Taiwan dollar, New Zealand dollar, Singapore dollar, United States dollar, Trinidad and Tobago dollar, and a number of others are among them. Like many nations that use the peso as their currency, the majority of those currencies are denoted by the dollar sign $.
The word "dollar" is a translation of the German word "thaler," which means "person or thing from the valley" in English. America's monetary unit is called after the "thaler," the name given to the first silver mine-produced coins, which were initially coined in Joachimsthal, Bohemia, in 1519.
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i have ordered beads to make jewelry i received 45 beads and 45% of them are yellow how many yellow beads have i received
The person has about 20 yellow beads.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, the person received 45 beads out of which 45% are yellow.
Therefore, the number of yellow beads is,
45% of 45
= (45×45)/100
= 2025/100
= 20.25
≈ 20
Hence, the person has about 20 yellow beads.
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f(x)=x² + 6x + 2; Find f(-6)
Answer: 2
Step-by-step explanation:
if you plug in -6 into x, we get
36 - 36 + 2
the 36s will cancel each other out, leaving us with only 2 as our final answer.
Answer: -70
Step-by-step explanation:
-[tex]6^{2}[/tex] + 6(-6)+2
= -36 - 36 + 2
= - 70
Jessie uses 20 liters of gasoline to travel 200 kilometers, how many liters of gasoline will he use on a trip of 700 kilometers?.
Trip of 700 km required 70 liter gasoline
For go 200 km Distance total gasoline required = 20 liter
For go 1 km Distance total gasoline required = 20÷200
= 0.1 liter
Total trip distance =700 km
Total gasoline required for going 700 km = Total distance×Gasoline required for 1 km
Total gasoline required for going 700 km = 700×0.01
= 70 liters
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70 liters of gasoline will be used on a trip of 700 kilometers.
Given that,
200 kilometer is covered by 20 liters of gasoline.
For go 1 km Distance total gasoline required = 20÷200
= 0.1 liter
Now,
Let x be the liters of gasoline required for a 700-km trip.
⇒ 20/200 = x/700
⇒ (200) (x) = (20) (700)
⇒ 200x = 14,000
⇒ 200x/200 = 14,000/200
or, x = 70
Therefore, the answer is :
70 liters of gasoline will be needed for a 700 kilometer of trip.
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-6.6 < 1.7 + u Solve the inequality for u.
Simplify your answer as much as possible.
Solving the inequality -6.6 < 1.7 + u for u, the solution is simplified as: u > -8.3 or -8.3 < u.
What is an Inequality?In maths, an inequality is defined as a statement that is used to compare two quantities that are unequal. For example, we can state that 5 is greater than 3 + 1, or 5x is less than 4x + 3x. We can equally state that a given value of a variable can be equal to or greater than a number, and so on.
Basically, we are comparing two unequal quantities when we state inequalities.
Given the inequality, -6.6 < 1.7 + u, we are asked to solve the inequality for u. That is, we need to find the possible value that u represents in the inequality or that would make the inequality true.
Therefore:
-6.6 < 1.7 + u
Subtract 1.7 from both sides
-6.6 - 1.7 < 1.7 + u - 1.7 [subtraction property of equality]
-8.3 < u
It can be rewritten as:
u > -8.3
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A telecommunications company will be laying new fiber optic cables underground. One cable will be perpendicular to the road shown, passing through the point ( 7, 2 . At what point will the cable pass through the road?
The point at which this cable would pass through the road shown is at the y-intercept of (0, -17/2).
How to determine an equation and the point on this perpendicular line?Mathematically, the slope of a straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
By critically observing the road shown in the graph above, the points on the line include the following:
Points (x, y) = (0, -2)
Points (x, y) = (-3, 0)
Substituting the given points into the formula, we have;
Slope, m = (0 + 2)/(-3 - 0)
Slope, m = 2/-3
Slope, m = -2/3.
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
-2/3 × m₂ = -1
-2m₂ = -3
m₂ = 3/2
At point (7, 2), a linear equation for the line can be calculated by using the point-slope form:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represent the points.c represents the y-intercept.Substituting the given points into the formula, we have;
y - 2 = 3/2(x - 7)
y - 2 = 3x/2 - 21/2
y = 3x/2 - 21/2 + 2
y = 3x/2 - 17/2
At the y-intercept of (0, -17/2), the cable pass through the road.
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f(x) = 2x; translate up 5 units, reflect in x-axis.
After f(x) = 2x translated up 5 units, then it reflect in x-axis is g(x) = f(2x)+5.
What does a graphing translation mean?
A graph can be vertically translated by moving the base graph up or down in the y-axis direction. Each point on a graph is moved k units vertically to translate the graph by that many units.The rules for transforming a function f(x) into g(x):
g(x) = a·f(b(x-c)) + d
a = vertical dilation (stretch); reflects across x-axis if negativeb = horizontal dilation (stretch); reflects across y-axis if negativec = horizontal translation (shift); shift right if c is positive, left if c is negatived = vertical translation; up if d is positive, down if d is negativeHence, After f(x) = 2x translated up 5 units, then it reflect in x-axis is g(x) = f(2x) + 5.
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Rewrite the following equation in slope-intercept form.
8x + 19y = 3
Answer:y=8x-5
Step-by-step explanation:
you put the problem into slope intercept form y minus y one equals the slope the parentheses x minus x one then use the distributor property so then it’s y=
ASAP! exponent rules
Answer:
C: 9
Step-by-step explanation:
3^4/3^2
3*3*3*3/3*3 cancel out 2 threes from the bottom and top.
3*3=9
Please help pleaseee
Measure of angle M is 76°, angle N is 76° and side LN is 18 in.
According to figure,
LM = 18 in
∠NLM = 28°
In triangle LMN
LN = LM
= 18 in
Therefore, ∠LMN = ∠LNM = x (LN = LM)
∠LMN + ∠NLM + ∠LNM = 180°
x + 28 + x = 180
2x + 28 = 180
2x = 180 - 28
2x = 152
x = 152/2
x = 76
Hence, ∠M = ∠N = 76°.
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HELP PLEASEEE!!!!! i dont know what to do
Answer:
1. 51°
2. 55°
3. 5x + 10
Step-by-step explanation:
1. We know ∠B + 39° = 90°, so ∠B = 90 - 39 = 51
2. We can use an algebraic equation to solve this problem.
2x + 70 = 180
2x + 70 (-70) = 180 (-70)
2x (/2) = 110 (/2)
x = 55
3. ∠ABD = (3x + 10) + (2x) = 5x + 10
The histogram below shows information about the honey produced by some beehives in one year. 400 beehives each produced between 16 kg and 18 kg of honey. Use this information to work out the value of x on the frequency density axis. If your answer is a decimal, give it to 1 d.p.
The value of x on the frequency density axis is 200.
What is frequency?
The frequency of a repeated event is its number of instances per unit of time. In some cases, it is also referred to as temporal frequency or ordinary frequency to underline differences with spatial and angular frequencies, respectively.
What is density?
The mass of a substance per unit of volume is its density. Density is most frequently represented by the symbol, however, the Latin letter D may also be used.
Here, we have
x is about half of the number of beehives producing 16 to 18 kg of honey, for the middle blue bar.
x = half of 400
x = 200
Hence, The value of x on the frequency density axis is 200.
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What is the sum of the x-values that represent the solution for this system of equations?
1+2x=y
y=4x^2+6x−2
The graph of the function, f(x) = x2 - 5x - 7 opens
and has a
value.
The parabola has a positive leading coefficient, which means that it opens upwards.
The graph opens up or down?We want to find the leading coefficient and see how the parabola opens.
A general quadratic equation is written as:
y = A*X^2 +b*X+ c
Where a is the leading coefficient.
If a is positive, then the parabola opens upwards, and if a is negative, the parabola opens downwards.
In this case, the equation is:
y = x^2 - 5x - 7
The leading coefficient is a = 1, it is positive, so the parabola opens upwards.
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