g(6) must be greater than 21 which is 22 only.
What is function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable.
Since g'(x) > 0 for all x and we know that g(x) is an increasing function.
Additionally, since g"(x) > 0 for all x, we know that g(x) is a concave-up function.
Since g(x) is increasing, we know that g(6) > g(5) = 18.
Now, we can use the fact that g(x) is concave-up to find a lower bound on g(6).
By the definition of concave-up, we know that the slope of the tangent line to g(x) is increasing.
This means that the slope of the line connecting (3,g(3)) to (5,g(5)) is less than the slope of the line connecting (5,g(5)) to (6,g(6)).
Using this information, we can find a lower bound on g(6):
g(5)- g(3) / (5-3) < g(6)- g(5)/ (6-5)
18- 12/2 < g(6)- 18
3 < g(6) - 18
g(6) > 21
Therefore, g(6) must be greater than 21.
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A straw is placed inside a rectangular box that is 2 inches by 1 inches by 3 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in the simplest radical form.
The length of the straw is 3.74 inches.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
In rectangular box,
Length (l) = 2 inches
Width (w) = 1 inches
Height (h) = 3 inches
Here, The straw is said to fit into the box diagonally from the bottom.
So, the length (s) of the straw is calculated as:
⇒ s = √ l² + w² + h²
⇒ s = √ 2² + 1² + 3²
⇒ s = √ 4 + 1 + 9
⇒ s = √ 14
⇒ s = 3.74 inches
Thus, The length of straw = 3.74 inches
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The length of the straw will be 3.7416 inches long in radical form.
What is Length of diagonal in cuboid?If a cuboid has length = l units, breadth = b units, and height = h units, then we can evaluate the length of the diagonal of a cuboid using the formula : X²=l²+b²+h²
Here,
As per the question the length of the straw is equal to length of the diagonal of Rectangular box.
l= 3 inch , b= 2 inch , h= 1 inch
Let us consider the length of the straw be 'x'.
As, Diagonal of Cuboid is,
X²=14
X=√14
i.e. X=3.7416
We get, X= 3.7416 (in radical form)
Hence, the length of the straw will be 5.91607 inches.
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Find values of a and b that make the following equality into identity:
(2x+5)/(x-8)(2x+1)=a/(x-8) + b/(2x+1)
Giving 30+ points!
The values of a and b in the fraction are 21/17 and -8/17
How to determine the values of a and bFrom the question, we have the following parameters that can be used in our computation:
(2x+5)/(x-8)(2x+1)=a/(x-8) + b/(2x+1)
Take the LCM
So, the expression can be expressed as
(2x+5)/(x-8)(2x+1)=a(2x+1) + b(x-8)/(x-8)(2x+1)
Multiply both sides by (x-8)(2x+1)
(2x+5) = a(2x+1) + b(x-8)
Open the brackets
2x + 5 = 2ax + a + bx - 8b
By comparison, we have
2a + b = 2
a - 8b = 5
Make a, the subject in a - 8b = 5
a = 5 + 8b
Substitute a = 5 + 8b in 2a + b = 2
10 + 16b + b = 2
Evaluate the like terms
17b = -8
Divide by 17
b = -8/17
Substitute b = -8/17 in a = 5 + 8b
a = 5 + 8 * -8/17
Evaluate
a = 5 - 64/17
So, we have
a = 21/17
Hence, the values are 21/17 and -8/17
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2. 15 - |-4a|
It says evaluate the expression.
If a = 2
Answer:
7
Step-by-step explanation:
So first you substitute A in
15-|-4(2)|
Then you multiply first because of GEMDAS or PEMDAS
15-|-8|
And because absolute value means how far away it is from 0, -8 is 8 away from 0 , thus |-8| is 8. So we simplify the equation
15-8
=7
I do not understand this problem pls help thank you
The value of x in the triangle LMO is 38°
What is an equation?An equation shows how two or more numbers and variables are related to each other.
∠KLO + ∠OLM = 180° (sum of angle in straight line)
134 + ∠OLM = 180°
∠OLM = 46°
∠OML + ∠OMN = 180° (sum of angle in straight line)
∠OML + 84 = 180°
∠OML = 96°
∠OLM + ∠OML + ∠LOM = 180° (angle in a triangle)
46 + 96 + x = 180
x = 38°
The value of x is 38°
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A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limits, until it reaches its destination 200 miles away. Letting x represent the amount of time in hours that the car is going 55 miles per hour, and y being the time in hours that the car is going 35 miles per hour, an equation describing the relationship is: 55x+35y=200
A: If the car spends 2.5 hours going 35 miles per hour on the trip, how long does it spend going 55 miles per hour?
B: If the car spends 3 hours going 55 miles per hour on the trip, how long does it spend going 35 miles per hour?
C: If the car spends no time going 35 miles per hour, how long would the trip take? Explain your reasoning.
Answer:
A. The car spends 2.05 hours going 55 miles per hour
B. The car spends 1 hour going 35 miles per hour
C. The trip takes 3.6 hour
Step-by-step explanation:
The equation is
55x+35y=200
Let's solve A
We know the car spends 2.5 hours going 35 miles per hour on the trip, so we put 2.5 in for y and solve for x
55x+35(2.5) = 200
55x + 87.5 = 200
55x = 112.8
x = 2.05 hours going 55 miles per hour
So, the car spends 2.05 hours going 55 miles per hour
Let's solve B
55(3)+35y=200
165 + 35y = 200
35y = 35
y = 1 hour
So, the car spends 1 hour going 35 miles per hour
Let's solve C
We know the car spends no time going 35 miles per hour, so we put 0 in for y and solve for x
55x+35(0)=200
55x = 200
x = 3.6 hours
So, the trip takes 3.6 hour
What is the first step for solving 2x 3 7?
the question is of set of equations and the solution is as follows,
the equation is 2x -3 = 7,
First, add 3 to each side to get
2x - 3 + 3 = 7 +3
2x = 10
x = 10/2
x =5.
equations
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For Example, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
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Is this a perfect square trinomial X² 14x 49?
x² + 14x + 49, this is a perfect square trinomial, which is expressed as
(x + 7)².
What is trinomial?Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."
An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.
A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.
Given that,
x² + 14x + 49
(x)² + 2(7x) + 49
= (x)² + 2(x)(7) + 7²
This is similar to a² + 2ab + b² = (a + b)²
so, we can write:
= (x + 7)²
= (x +7) (x + 7)
so, this is a perfect square trinomial.
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what is the answer to 415÷23
Answer: 18
Step-by-step explanation:
Answer: 18.04347826086957
Step-by-step explanation: you could use a calculator too-
Find the volume of the pyramid.
7 m
12 m
The volume is
16 m
cubic meters.
The value of volume of pyramids is 448 cubic meter.
How to calculate volume of pyramid?A triangular pyramid's volume can be calculated using the formula Volume= 1/3 Base area Height. The side, height, and slant height of a triangular pyramid are the three parameters needed to calculate its surface area.
The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape. The calculation is unaffected by how you refer to the various dimensions; for instance, you can use "depth" instead of "height."
Given,
Length=12m
Width=7m
height=16m
volume =l * w * h / 3
= 12*7*16/3
= 448 cubic meter
Therefore volume of pyramid is 448 cubic meter .
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The function f open argument x close argument varies inversely with x and f open argument x close argument equals 0.5 when x
The value of function f(x), when x=2.4 is f(x)=0.00625.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
If the function f(x) varies inversely with x, then this function is of the form -
f(x)=a/x
where a is unknown number.
Since f(x)=0.5 when x =0.3, then -
0.5 = a/0.3
a = 0.5 × 0.3
a = 0.15
So, the function now becomes -
f(x) = 0.15/x
Substituting for x = 2.4 -
f(2.4) = 0.15 / 2.4
= 15/240
= 1/16
= 0.00625
Therefore, f(x) value is obtained as 0.00625.
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The function f(x) varies inversely with x and f(x)=0.5 when x =0.3. what is f(x) when x=2.4?
How do you know if a triangle is a 45 45 90 triangle?
The two side lengths are congruent, and their opposite angles are congruent, and the hypotenuse is the length of either leg times the square root of two, √2.
A 45° 45° 90° triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.
A 45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2.
properties of 45°-45°-90°:
It's the only possible right triangle that is also an isosceles triangle, and it has the smallest ratio of the hypotenuse to the sum of the legs.It has the greatest ratio of the altitude from the hypotenuse to the sum of the legs.To know more about 45° 45° 90° triangle:
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A company wanted to determine the health care costs of its employees. A sample of 25 employees were interviewed and their medical expenses for the previous year were determined. Later the company discovered that the highest medical expense in the sample was mistakenly recorded as 10 times the actual amount. However, after correcting the error, the corrected amount was still greater than or equal to any other medical expense in the sample. Which of the following sample statistics must have remained the same after the correction was made
After the modification, the maximum amount of medical costs in the sample must have stayed the same.
After the wrongly recorded medical expense was repaired, the adjusted amount remained more than or equal to every other medical expense in the sample. This suggests that the sample statistic linked to the highest value must have remained unchanged after the modification.
The highest value, also known as the maximum or largest value, of the medical expenses in the sample, had to have remained constant. Even though the real quantity was mistakenly recorded as being 10 times its value, the rectified amount still had the highest value in the sample.
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An anchor cable supports a vertical utility pole forming a 51 degree angle with the ground. The cable is attached to the top of the pole. If the distance from the base of the
pole to the base of the cable is 5 meters, how tall is the pole? (Round to the nearest hundredth.) PLS HELP
The height of the pole anchored to a cable is 6.17 meters.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
Given, The anchor cable is forming an angle of 51° angle with the ground attached to a pole and the distance between them is 5 meters.
So, We need height or the opposite side length with an adjacent length of 5 meters.
We know, tan = opposite/adjacent.
tan51° = opposite/5.
opposite = tan51°×5.
opposite = 1.235×5.
opposite = 6.17 meters.
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d. -(y² - 2) = y²-5-2y², solve for y
Answer:
No solution
Step-by-step explanation:
-(y² - 2) = y²-5-2y²
= y^2 - 5 - 2y^2 = - (y^2 - 2)
= -y^2 - 5 = - (y^2 - 2)
= −(y^2 − 2)
= -y^2 - 5 = -y^2 + 2
-5 = 2
We know that -5 is not equal to 2
So, there is no solution
Answer:
2
Step-by-step explanation:
In triangle abc, i the circumcenter bc i equal to 72cm d i equal to 15cm find the radiu of the circumcircle
In triangle abc, i the circumcenter bc i equal to 72cm d i equal to 15cm then the radiu of the circumcircle is 39
A chord is the line segment joining two points of the circumference of a circle as shown in the image attached.
If the chord is passing through the center of the circle then it will become diameter which means the diameter is the longest possible chord inside a circle.
A chord is always within the circumference because it is inside the circle.
Whats the definition of a circumference?
a line that goes around or encloses a circle. : the outer boundary of a figure or area. 3. : the distance around something. the circumference of the earth at the equator.
since ABC is an equilateral triangle
therefore SD bisects BC
BD= BC/2
BD= 36
IN Triangle ABC
since angle BDS = 90 degree
Therefore
BS = 39
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Please help- thank you!!
Answer: u = -3
Step-by-step explanation:
To solve the equation, we will isolate the u variable by simplifying and using inverse operations.
Given:
4(3u + 5) = 2(2u - 2)
Distribute the 4 and the 2:
12y + 20 = 4u - 4
Subtract 20 from both sides of the equation:
12y = 4u - 24
Subtract 4u from both sides of the equation:
8u = -24
Divide both sides of the equation by 8:
u = -3
Solve the system by graphing
2x-3y=-6
7x-3y=9
Following is the graph of two given equations.
The mapping of functions of two variables onto a Cartesian coordinate system, which is made up of a horizontal x-axis, or abscissa, and a vertical y-axis, or ordinate, is done analytically through the use of graphs. The intersection of each axis, which is a real number line, at its zero point is known as the origin.
On solving the two equations,
2x-3y=-6 ....(1)
7x-3y=9 .....(2)
Firstly we will find common points by elimination -
The common points are - (3,4)
Then We can find all the values of equation (1)
2x-3y=-6
x 0 3 -3
y 2 4 0
7x-3y=9
x 0 3 10
y -3 4 20.33
The respective graph is attached below
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which answer is this
A.43
B.38
C.61
D.81
The sides of a triangle are 68, 61, and 46. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.
Answer: Acute
Step-by-step explanation:
The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex]. A and b are legs while c is hypotenuse. Hypotenuse is also the longest side. Let's plug them in and see if they are equal to each other.
[tex]46^2+61^2=68^2[/tex] [exponent]
[tex]2116+3721=4624[/tex] [add]
[tex]5837\neq4624[/tex]
Since they are not equal, then it is not a right triangle.
To tell is a triangle is acute, if the sum of the two shorter sides squared is greater than the longest side squared, then the triangle is acute.
At the end of the Pythagorean Theorem, we got 5837≠4624. 5837>4624, so that tells us that the triangle is acute.
What is the slope of a line that pass through the points (3,-2) and (5,-2)?
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{3}}} \implies \cfrac{-2 +2}{2} \implies \cfrac{ 0 }{ 2 } \implies \text{\LARGE 0}[/tex]
Answer:
slope = 0
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, - 2 ) and (x₂, y₂ ) = (5, - 2 )
m = [tex]\frac{-2-(-2)}{5-3}[/tex] = [tex]\frac{-2+2}{2}[/tex] = [tex]\frac{0}{2}[/tex] = 0
James made 7 identical bags using 5 yards of fabric. How much fabric did James use for each bag?
Answer:
James used 5 yards of fabric to make 7 identical bags, so he used 5/7 yards of fabric per bag.
Step-by-step explanation:
What is the value of 2 by 7 and 3 by 7?
the value of 2 by 7 and 3 by 7 is: 5/7. This can be solved using the concept of fraction of addition.
What is the fraction?A fraction is a piece of the entire. The number is stated in arithmetic as a quotient, which signifies the numerator divided by the denominator. Both are integers in a straightforward fraction. The numerator or denominator of a complex fraction is a fraction. A suitable fraction has a numerator that is smaller than its denominator.
Three main fractional kinds exist. They come in three varieties: appropriate fractions, incorrect fractions, and mixed fractions. The numerator and denominator words are known as fractions. We define its kinds in light of these two words.
the value of 2 by 7 and 3 by 7 is:
= (2/7) + (3/7)
= 5/7
When adding the fractions 2/7 and 3/7 we get 5/7, as the denominator is same.
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What are the solutions of the equation 9x4 minus 2x2 7 0?
The solution of the equations are x = √1 = ± 1
Now, According to the question:
The given equation is [tex]9x^4 - 2x^2 - 7 = 0[/tex]
Using the substitution rule we put [tex]x^{2}[/tex] = u .
The given equation now changes to
[tex]9u^2 - 2u - 7 = 0[/tex]--- (1)
Equation(1) is a simple quadratic equation which can be solved by factorization as follows:
[tex]9u^2 - 2u - 7 = 0[/tex]
(9u + 7)(u - 1) = 0
Therefore
9u + 7 = 0 → u = -7/9
u -1 = 0→ u = 1
Since u = [tex]x^{2}[/tex] implies
x = √-7/9 = ± i√7/9
x = √1 = ± 1
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The complete question is this:
What are the solutions of the equation [tex]9x^4 - 2x^2 - 7 = 0[/tex]? use u-substitution to solve.
You have a circle-shaped mirror in your bedroom. To figure out where to hang it, you must find the diameter of the circle. You know the radius is 34 centimeters. How long is the diameter in inches? (Diameter = 2xradius) ( 1in = 2.54cm)
A. 26.8 inches
B. 86.4 inches
C. 172.7 inches
D. 13.4 inches
The diameter of a given circle, measured in inches, is 26.8 inches, according to the solution.
The correct option is A.
What makes it called a circle?A circle is a circular shape that can be created by tracing a moving point in a plane so that its distance from thea specified point remains constant. From the Greek word kirks, which means hoop or ring, comes the term circle.
How can a circle be so strong?Circular shapes give us a feeling of completion, assurance, and harmony from a psychological perspective. They stand for the concepts of oneness, integration, and wholeness. In addition to lacking angles, they also lack a beginning and an end. Because of this, a circle is a strong, yet secure, kind, and benign element.
According to the given information:Given,
Radius of circle= 34cm=13.36 inches
Diameter= 2x radius
Diameter = 26.8 inches
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How do you calculate seed number?
To calculate seed number, divide the total number of inches available for crop by the in-row crop spacing. For example, 120 inches divided by one inch per pea seed equals 120 pea seeds.
What is seed?In botany, a seed is an undeveloped plant embryo and food reserve encased in a protective outer covering. In a broader sense, "seed" refers to anything that can be sown, such as seed and husk or tuber.
Seeds are formed when a ripened ovule is fertilised by pollen-derived sperm, resulting in a zygote. The embryo develops from the zygote within a seed, forming a seed coat around the ovule and growing to a certain size within the mother plant before growth stops.
The formation of seeds is a stage in the reproduction of seed plants (spermatophytes). Other plants, such as ferns, mosses, and liverworts, lack seeds and must reproduce exclusively through water.
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What do () mean in math?
Parentheses are employed to indicate changes to the usual order of operations.
Define round brackets.The well-known () symbols, often known as "round brackets," are used in pairs to group things together or designate the order of operations in an equation. You will frequently need to employ brackets in math when forming or resolving equations. They support number grouping and operation definition.
Mention other brackets as well.{}, [] are other type of brackets.
In mathematical expressions, parentheses are employed to indicate changes to the usual order of operations (precedence rules). In an expression like, the portion of the expression enclosed in parentheses,, is first assessed, and the outcome is then incorporated into the remaining portions of the expression.
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Han earns 33.00 for babysitting 4 hours at this rate how much will he earn if the babysitter for 7 hours explain your reasoning
Han will make $57.75 for 7 hours of babysitting.
What are equations?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".
Given is that Han earns $33 for babysitting 4 hours.
Han made $33 for 4 hours of work.
Then, he will make $(33/4) in 1 hour of work.
Then, he will make $(33/4 x 7) in 7 hours of work.
$(33/4 x 7)
$(33/4 x 7)
$(231/4)
$57.75
Therefore, Han will make $57.75 for 7 hours of babysitting.
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PLEASE I NEED THIS NOW
Rewrite this polynomial in terms of its simplest factors using the appropriate method: x2 − 3x − 18.
Use your keyboard and the keypad to enter your answer. Then click Done.
The polynomial in terms of its simplest factors is (x + 3)(x − 6)
How to rewrite the polynomial in terms of its simplest factorsFrom the question, we have the following parameters that can be used in our computation:
x2 − 3x − 18.
Rewrite as
x² − 3x − 18
Expand
x² − 3x − 18 = x² − 6x + 3x − 18
Factorize the expression
This gives
x² − 3x − 18 = x(x − 6) + 3(x − 6)
Factor out x - 6
x² − 3x − 18 = (x + 3)(x − 6)
Hence, the expression is (x + 3)(x − 6)
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How do you find out if a triangle is acute obtuse or right?
YG and h are parallel. what is the value of n
Answer:
139⁰
Step-by-step explanation:
since g and h are parallel
then n= 139⁰ (corresponding angles)