The side length of the square is a = 9.75 units
What is the area of a square?A square is a four sided quadrilateral with all of the side having equal lengths. The total internal angle of a square is 360° with each side perpendicular to each other.
A square is a 4 sided polygon where all the sides are of equal length.
The area of the square is the square of any one of its side
Let a be the side of the square
Area of the square = a²
Given data ,
Let the area of the square be represented as A
Now , the value of A is
Area of the square = a²
The exact value of the side length of a square with an area of 95 square units can be found by taking the square root of 95.
√95 ≈ 9.74679434481 (approximate value)
Hence , the exact value of the side length of the square is approximately 9.74679434481 units
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What are the factors of x ^ 2 - 9
The factors of x² - 9 is +3 , -3.
What is factors ?
A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them. Factors can be found using either division or multiplication.
A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics.
The numbers that can divide a number exactly are called factors. There is therefore no residual after division. The numbers you multiply together to obtain another number are called factors. A factor is therefore another number's divisor.
x² - 9 = 0
x² = 9
x = √9
x = ± 3
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Rewrite the following equation is standard form. y = 9x - 1 Hint: The standard form of a linear equation is Ax + By = C where A and B are not both zero and A, B and C are integers whose GCF is 1. thats this problem
The standard form of a linear equation is Ax + By = C where A and B are not both zero and A, B and C are integers whose GCF is 1.
To convert the equation y = 9x - 1 to standard form, we need to rearrange it as:
9x - y = 1
We can divide both sides by -1 to get
-9x + y = -1
Which is the standard form of the equation.
So the standard form of the equation is:
-9x + y = -1
i don’t get this :(
Answer: x = 10
Step-by-step explanation:
triangle shows angles are 38°, (7x+1)°, (10x+9)°(outside of the triangle)
total angle of the triangle is 180°
then
38°+ (7x+1)°+ [180-(10x+9)°] = 180°
Simplifying
38 + (7x + 1) + [180 + -1(10x + 9)] = 180
Reorder the terms:
38 + (1 + 7x) + [180 + -1(10x + 9)] = 180
Remove parenthesis around (1 + 7x)
38 + 1 + 7x + [180 + -1(10x + 9)] = 180
Reorder the terms:
38 + 1 + 7x + [180 + -1(9 + 10x)] = 180
38 + 1 + 7x + [180 + (9 * -1 + 10x * -1)] = 180
38 + 1 + 7x + [180 + (-9 + -10x)] = 180
Combine like terms: 180 + -9 = 171
38 + 1 + 7x + [171 + -10x] = 180
Remove brackets around [171 + -10x]
38 + 1 + 7x + 171 + -10x = 180
Reorder the terms:
38 + 1 + 171 + 7x + -10x = 180
Combine like terms: 38 + 1 = 39
39 + 171 + 7x + -10x = 180
Combine like terms: 39 + 171 = 210
210 + 7x + -10x = 180
Combine like terms: 7x + -10x = -3x
210 + -3x = 180
Solving
210 + -3x = 180
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-210' to each side of the equation.
210 + -210 + -3x = 180 + -210
Combine like terms: 210 + -210 = 0
0 + -3x = 180 + -210
-3x = 180 + -210
Combine like terms: 180 + -210 = -30
-3x = -30
Divide each side by '-3'.
x = 10
Simplifying
x = 10
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what is the answer to this
Given polynomials p(x), q(x), and r(x), p(x) + ( q(x) + r(x) ) = ( p(x) + q(x) ) + r(x)
To verify the associative property of addition, begin by finding the sum of the polynomials:
(3x + 4) + ((5x2 - 1) + (2x + 6))
The sum of the Polynomial as required to be used to verify the additive property is; 5x² + 5x +9.
What is the sum of the polynomials?Given polynomials p(x), q(x), and r(x), p(x) + ( q(x) + r(x) ) = ( p(x) + q(x) ) + r(x).
Hence, to justify the associative property; we must sum up the polynomials given in two ways as follows;
Method 1;
(3x + 4) + ( (5x² - 1) + (2x + 6) )
3x + 4 + ( 5x² + 2x + 5 )
3x + 4 + 5x² + 2x + 5.
Therefore, the sum is; 5x² + 5x + 9
Method 2;
(3x + 4) + ( (5x² - 1) + (2x + 6) )
= ( 3x + 4 + 5x² - 1 ) + ( ( 2x + 6 ) )
= 5x² + 3x + 3 + ( (2x + 6) )
5x² + 3x + 2x + 3 + 6
5x² + 5x +9
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During a series of plays in a football game, a running back carried the ball for the yardages given by 6, -3, 2, -1, 7,
-4, and -2. Find his total yards and his average yards per carry.
The total yards for the running back was
The area issue with the suggested remedy is that the playing field is 118 feet by 56 yards in size.
Define the area.To determine area, multiply length by width. L times B is the formula for calculating area. Area or Radius = r2(=3.14) These methods can also be used to calculate the areas of different quadrilaterals, which are polygonal shapes with four sides and an aspect lower than 90 degrees. Application. Since its inception, area has been the foundation of geometry.
Here,
Our calculation of w = 56 reveals that the parallelogram is 56 yards long.
We can simplify the calculation by altering w to 56 in order to obtain the length of the rectangle but since width is the same as 2w + 6 already.
The rectangle is depicted as having a length of 118 yards.
Accordingly, the playing field measures 118 yards by 56 yards.
Therefore, the size of the game field—118 yards x 56 yards—is the solution to the current problem.
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. Donna could buy a half-gallon tub of ice
cream for $4.99 or a small tub for $2.39.
What else does Donna need to know in
order to decide which size is the better
buy?
Answer: D the size of small tub
Step-by-step explanation: he needs to more if he is going to get his moneys worth
Donna need to know the size of small tub in order to decide which size is the better buy. the correct option is D.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given that Donna could buy a half-gallon tub of ice cream for $4.99 or a small tub for $2.39.
We can see that he needs to more if he is going to get his moneys worth.
ice cream = $4.99
small tub = $2.39.
He need to know the size of small tub
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Find the measure of the missing angles.
Answer:
c is 80 and b is 100
Answer: C would be 80 degrees, and B would be 100 degrees
Hope this helps! :D
The temperature in two different ovens increased at a steady rate. The temperature in oven A is represented by the equation y=25x+72 , where x represents the number of minutes and y represents the temperature in degrees Fahrenheit. The temperature of oven B is shown in the graph.
From the equation y = 25x + 72, the initial temperature is 72°F, the rate of change in the oven temperature is 25 degrees Fahrenheit per minute
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
The standard form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
Let y represent the temperature of the oven in degrees Fahrenheit after x minutes.
Given the equation:
y = 25x + 72
This means that the rate of change is 25 degrees Fahrenheit per minute.
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NO LINKS!!
1. Is it possible for the sequence t(n) = 5·2ⁿ to have a term with the value of 200? If so, which term is it? If not, justify why not.
2. Is it possible for the function f(x) = 5·2ˣ to have an output of 200? If so, what input gives this output? If not, justify why not.
Answer:
1) No,2) Yes, x ≈ 5.32-----------------------------
Part 1Given sequence:
t(n) = 5 · 2ⁿIf t(n) = 200, we can try to find the value of n:
5 · 2ⁿ = 2002ⁿ = 40There is no integer solution, since 32 < 40 < 64 or 2⁵ < 40 < 2⁶, the value of n should be between 5 and 6.
The sequence should include integer numbers, so there is no solution.
Part 2Given function:
f(x) = 5 · 2ˣSolve for x if f(x) is 200:
5 · 2ˣ = 2002ˣ = 40log 2ˣ = log 40x log 2 = log 40x = log 40 / log 2x = 5.32 (rounded)Answer:
1. No
[tex]\textsf{2.} \quad x=\dfrac{\ln 40}{\ln 2} \approx5.32\;(\sf 2\;d.p.)[/tex]
Step-by-step explanation:
Question 1Given sequence:
[tex]t(n)=5 \cdot 2^n[/tex]
To determine if the sequence has a term with a value of 200, substitute t(n)=200 into the equation and solve for n:
[tex]\implies 5 \cdot 2^n=200[/tex]
[tex]\implies 2^n=40[/tex]
[tex]\implies \ln 2^n=\ln 40[/tex]
[tex]\implies n\ln 2=\ln 40[/tex]
[tex]\implies n=\dfrac{\ln 40}{\ln 2}[/tex]
[tex]\implies n=5.3219280...[/tex]
In a sequence, n is a positive integer. Therefore, it is not possible for the sequence to have a term with the value of 200, as when t(n)=200, n is not a positive integer.
Question 2Given function:
[tex]f(x)=5 \cdot 2^x[/tex]
To determine if the function has an output of 200, substitute f(x)=200 into the function and solve for x:
[tex]\implies 5 \cdot 2^x=200[/tex]
[tex]\implies 2^x=40[/tex]
[tex]\implies \ln 2^x=\ln 40[/tex]
[tex]\implies x=\dfrac{\ln 40}{\ln 2}[/tex]
[tex]\implies x=5.3219280...[/tex]
Therefore, it is possible for the function to have an output of 200 when:
[tex]x=\dfrac{\ln 40}{\ln 2}[/tex]
Select the correct answer.
In the given diagram, line segment BD bisects angle ABC. Segment BD is extended to E, where line segment EC is parallel to
line segment AB. Write a two-column proof to show that AB = BC
Due to the fact that parallel lines produce congruent alternate interior angles, ADB = CBD by ASA.
what is angle ?A pair of angles is considered to be complementary if their sum equals 90 degrees. Two angles are referred to as submissive if their sums total 180 degrees. Follow-up pains involve using freshly baked sorrowful bread. Prior to, before, ahead of The angles of 30 and 60 degrees, for example, are supplementary. In contrast to a supplemental angle, which is two angles joined to create a 90 degree angle, a supplementary angle is two angles combined to create a 180 degree angle. If the sum of two angles is 90 degrees, they are said to be complementary.
given
∠CDB = ∠ABD
and
∠ADB = ∠CBD
∠RQP = ∠SQP
since perpendicular lines form congruent right angles. PQ || PQ by reflexive so ∠PQR = ∠PQS by AAS.
Due to the fact that parallel lines produce congruent alternate interior angles, ADB = CBD by ASA.
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Answer: EC=BC; property of isosceles triangle
Step-by-step explanation: Got it right on Edmentum/Plato
The debate club needs $240.00 to attend a debate tournament. The
club decides to sell cups of iced tea and lemonade at baseball games.
Iced tea will be sold for $.50 per cup and lemonade will be sold for
$.80 per cup.
How much is needed of each to raise $240?
Answer: 480 and 300
Step-by-step explanation:
240 divided by 0.50 = 480
240 divided by 0.80 = 300
What fraction is less than 7/8?
the radius of a circle is 5in. Find its area in terms of pie
Answer:
78.54in2
Step-by-step explanation:
which key is longer: 5 cm or 2 in.?
and how do you convert it?
Answer:
2 inches is longer than 5 cm.
Step-by-step explanation:
1 inch is exactly 2.54 cm. In this case, we should convert the inches to centimeters to have a better view of the problem. 2 inches times 2.54 equals 5.08 cm. 5.08 cm is longer than 5 cm. Therefore, the answer is 2 inches.
the answer is
2 in
2x2.54=5.08
5.08>5
Find the number n of hours you need to study on Saturday so that the mean number of hours you study per day is 2.25.
Day Hours
Sunday 2
Monday 1.75
Tuesday 2.5
Wednesday 2.75
Thursday 3
Friday 0
Saturday n
The value of n of hours you need to study on Saturday is,
⇒ n = 3.75
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
The mean number of hours you study per day is 2.25.
Now, By definition of mean we get;
⇒ Mean = (2 + 1.75 + 2.5 + 2.75 + 3 + 0 + n) / 7
⇒ 2.25 = (12 + n) / 7
⇒ 2.25 × 7 = 12 + n
⇒ 15.75 = 12 + n
⇒ n = 15.75 - 12
⇒ n = 3.75
Thus, The value of n = 3.75
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Find the solution set for the inequality. 8a < -56
a<-7 is the solution of the inequality. 8a < -56
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is 8a < -56
Eight times of a less than minus fifty six
8a < -56
Divide both sides by a
a<-56/8
a less than minus fifty six divided by eight
a<-7
Hence, a<-7 is the solution of the inequality. 8a < -56
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Answer:
[tex] \sf \: a < - 7[/tex]
Step-by-step explanation:
Now we have to,
→ find the required value of a.
The inequation is,
→ 8a < -56
Then the value of a will be,
[tex] \sf \rightarrow \: 8a < - 56[/tex]
[tex] \sf \rightarrow \: a < \frac{ - 56 \: }{ \: 8} [/tex]
[tex] \sf \rightarrow \boxed{ \sf a < - 7}[/tex]
Hence, the value of a is -7.
HELPPP I NEED TO FIND THE VALUE FOR K AND J PLEASE!!
if you could explain that would be amazing!! :))
On solving the provided question, we can say that we know that all angles of a parallelograms are 360 => x = 23
What is parallelograms?A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two sets of parallel sides. In a particular kind of quadrilateral known as a parallelogram, both sets of opposite sides are parallel and equal. There are four different kinds of parallelograms, including three unique kinds. Parallelograms, squares, rectangles, and rhombuses are the four different shapes. Having two sets of parallel sides makes a quadrilateral a parallelogram. In a parallelogram, the opposing sides and angles are both the same length. On the same side of the horizontal line, the interior angles are additional angles as well. 360 degrees is the total number of interior angles.
as we know that all angles of a parallelograms are 360
then, 3j +6k +(k+10) + (5j-9) = 360
3x + 6x + x +10 + 5x -9 = 360
15x = 349
x = 349/15
x = 23.2666666667 = 23
x = 23
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Morgan cycled from Town A to Town B at an average speed of 15 km/h. She reached Town B at 6 P.M. If she increased her average speed to 20 km/h, she would arrive at 5 P.M. At what time would she arrive at Town B if she cycled at an average speed of 25 km/h?
Answer: Morgan will arrive at Town B at 5pm - 36 minutes = 4:24pm if she cycled at an average speed of 25km/h.
Step-by-step explanation: To solve this problem, we can use the formula: distance = speed x time.
We know that at 15km/h, Morgan reaches Town B at 6pm, and at 20km/h, she reaches Town B at 5pm.
We can use this information to find the distance between Town A and Town B and the time it takes to travel this distance at 25 km/h.
First, let's find the distance between Town A and Town B:
distance = speed x time
distance = 15 km/h x time
time = distance / 15 km/h
time = (distance / 15) hours
Since we know that when Morgan travel at 15km/h to reach town B at 6pm, we can use the time to calculate the distance:
time = 6pm - 5pm = 1hour
distance = 15 km/h x 1 hour = 15 km
Next, we can use this distance and the new speed 25km/h to calculate the arrival time:
time = distance / speed
time = 15 km / 25 km/h = 0.6 hours = 36 minutes
So, she will arrive at Town B at 5pm - 36 minutes = 4:24pm if she cycled at an average speed of 25km/h.
Please note that this calculation is assuming that the distance between Town A and Town B is a constant, and assuming that the time of arrival at 15km/h and 20km/h are accurate.
Sophia is buying a car and needs to take out a loan for $21, 000. The bank is offering
a monthly interest rate of 0.4%, for a 4 year loan. Using the formula below, determine
her monthly payment, to the nearest dollar.
On solving the provided question, we can say that Principal = 21,000, interest = 0.4% and time = 4 yrs => SI = $336
what is interest ?Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it. The majority of the time, interest is calculated as an annual percentage of the loan balance. This proportion is referred to as the loan's interest rate.
here,
Principal = 21,000
interest = 0.4%
time = 4 yrs
SI = Principal X Interest X time / 100
SI = 21000*0.4*4/100 = $336
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An equation for a tangent to the graph of y = arcsin y/2 at the origin is
A. x-2y = 0 B. x-y = 0 C. x=0 D. y=0
Option A is the correct answer. An equation for a tangent to the graph of y=arcsiny/2 at the origin is x-2y = 0
The given equation is:
y=arcsiny/2---(1)
So to find the equation of the tangent line we required Fielding's first slope and we can find the slope by differentiating the equation of graft with respect to X.
The second thing we require is the point, also we have to find the slope accessible to zero
dy/dx=1/2/√1-x^/4
Also given that points meet at the origin means (0,0) the values of x, and y is 0 and substituted in the derivative equation, we get
y'(0)=1/2
y-0=1/2(x-0)
2y-0=x
x-2y=0
Therefore, An equation for a tangent to the graph of y = arcsin y/2 at the origin is x-2y=0
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Which of the following decribes the domain and range of the function?
The domain is x < 2 or x ≥ 3 and the range y > - 3
What is the domain of a function?The domain of a function is the interval of valid inputs to the function.
What is the range of a function?The range of a function is the interval of valid outputs to the function.
How to find the domain and range for the function?Since we have the function
f(x) = -x/2 - 2 if x < 2 and f(x) = 2x - 4 if x ≥ 3.To find the domain of the function, we see that the values of x are between x < 2 or x ≥ 3.
So, the domain is x < 2 or x ≥ 3.
To find the range of the function, since
f(x) = -x/2 - 2 if x < 2 and f(x) = 2x - 4 if x ≥ 3.
Using the first function f(x) = -x/2 - 2 if x < 2 and substituing x = 2, we have that
f(2) = -2/2 - 2 = - 1 - 2 = -3
Since f(x) cannot be less than f(2), then
f(x) > - 3
So, y > - 3
Also, using the second function f(x) = 2x - 4 if x ≥ 3. and substituting x = 3 into the equation since this is the minimum value of x, then
f(3) = 2(3) - 4
= 6 - 4
= 2
Since this is the minimum value of f(3) = 2
So, y > 2
Since y > -3 and y > 2, combining both expressions, we have that
y > - 3
So, the range is y < -3
So, the domain is x < 2 or x ≥ 3 and the range y > - 3
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is your image exactly the same in size as you are where it is apparently to be found by using plane mirror
When you are using the plane mirror, the image is going to have to be the same in size as you are.
How is an image reflected in the plane mirror?When using the plane mirror and trying to get a reflection from the plane mirror, it would be found that the image that we are looking at in the mirror would turn out to be the same as the object that is being reflected. That is, your image is going to be exactly the same way.
The reason for this is because, the plane mirror is known to reflect light at the same angle that it received the light. This would cause the distance and the size of the object to be replicated in that image that has been reflected.
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THE ANSWER, IS IT;
x= 0.5,1
x= 0.5,2
x= 1,4
x= 2,4
The solutions to this system are (x, y) = (1, 4), (x, y) = (0.5, 2), respectively.
How to find the solution of a nonlinear equation by graphic approach
Herein we find the case of a nonlinear system of the form f(x) = 0, which cannot be solved analytically. This solutions to this system by graphic approach, by means of algebra properties:
f(x) = 0
g(x) - h(x) = 0
g(x) = h(x)
By transitive property:
y = g(x)
y = h(x)
The solution to this system of the point of intersection of g(x) and h(x). The procedure is summarized below:
Graph g(x) on Cartesian plane.Graph h(x) on Cartesian plane.Mark the points of intersection.If we know that g(x) = 4 · x and h(x) = 4ˣ, then the solution to the nonlinear equations:
Points of intersection: (x, y) = (1, 4), (x, y) = (0.5, 2).
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Devyn wants to buy her favorite treats from the candy shop in the mall. she grabs a scoop full and brings it to the front to be weighed. the treats cost 2.45 per pound, and she has 3.7 pounds. how much will the treats cost?
Answer: To calculate how much the treats will cost, you need to multiply the cost per pound of the treats by the number of pounds Devyn wants to buy.
Cost = Price per pound x Number of pounds
Cost = 2.45 x 3.7
By performing this calculation we can get that the treats will cost : 2.45 x 3.7 = 9.095
So the treats will cost $9.095.
Step-by-step explanation:
Answer:
9.07 units of money------------------------------------------------
Multiply the cost per pound by the amount of pounds:
2.45*3.7 = 9.065 ≈ 9.07 unitsA local animal shelter has 2 types of animals - dogs amd cats. The animals in the shelter can be classified into 2 age groups - babies (puppies and kittens) or adults. The fur of the animals varies between 5 different colors - black, brown, tan, grey, or mixed. What is the total number of possible outcomes?
Question number 2: What is the probability someone will adopt an adult cat has grey fur? Simplify the fraction.
1) The total number of possible outcomes is; 20 outcomes
2) The probability that someone will adopt an adult cat that has grey fur is; 5%
How to solve Conditional Probability?In probability theory, conditional probability is defined as a measure of the probability of an event occurring, given the fact that another event has already occurred.
From the question;
Types of animals = 2 types
1) Dogs
2) Cats
Classification of Animals into age groups;
1) Babies
2) Adults
Colors of the fur of the animals;
1) Black
2) Brown
3) Tan
4) Grey
5) Mixed
1) The total number of possible outcomes = 2 * 2 * 5 = 20 outcomes
2) The probability that someone will adopt an adult cat that has grey fur is; P(Adult cat and grey fur) = 0.5 * 0.5 * (1/5) = 0.05 = 5%
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Use the figure to find the Slant Height. 4 5 √(11)
The length of the slant height will be 4 units. Then the correct option is A.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
Let 's' be the slant height. Then the length of the slant height will be given as,
5² = s² + (6/2)²
25 = s² + 9
s² = 25 - 9
s² = 16
s = 4 units
The length of the slant height will be 4 units. Then the correct option is A.
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The missing diagram is given below.
5t-26=18t I need help with this!!
Answer:
t=-2
Step-by-step explanation:
5t-26=18t
5t-26+26=18t+26
simplify and subtract 18t from both sides
please help beg please RADIUS EASY PLEAASEEE
Answer:
Below
Step-by-step explanation:
Circumference of circle = pi * d = pi * 2r
so: circ / 2pi = r 56.52/(2 * 3.14) = r = 9 inches
AREA of a circle = pi * r^2
= 3.14 * 9^2 = 254.34 in^2
The sum of two numbers is less than 2 if we sub the second number from the first the difference in s greater than 1
Therefore , the solution of the given problem of system of inequalities comes out to be option a.
What is the system of inequalities?This system of inequalities defines a region in the x-y plane. The first inequality represents all the points below a line with the equation y = 2 - x, and the second inequality represents all the points above a line with the equation y = x - 1. The solution to the system is the set of points that lie in the intersection of these two regions, which is a certain area of the x-y plane.
Here,
Given : This riddle can be represented by the following system of inequalities:
x + y < 2 (the sum of two numbers is less than 2)
x - y > 1 (if we subtract the second number from the first, the difference is greater than 1)
Where x and y are the two numbers.
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