The value of x that is a counterexample to the student's conjecture is (a) x = -1/4
How to determine the value of x?From the question, we have the following statement that can be used in our computation:
x = Non-negative number
Student's conjecture:
x + 4 < x²
Using the options, we have:
(a) x = -1/4
x + 4 < x²
-1/4 + 4 < (-1/4)²
3.75 < 1/16 -- false
(b) x = -4
x + 4 < x²
-4 + 4 < (-4)²
0 < 16 -- true
(c) x = 1
x + 4 < x²
1 + 4 < (1)²
5 < 1 -- false
This cannot be used because x is non-negative
(c) x = 4
x + 4 < x²
4 + 4 < (4)²
8 < 16 -- true
The false statements are the counterexamples
Hence, the value of x is (a) x = -1/4
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Complete question
Given that x is a nonnegative number, a student conjectured that x + 4 < x². Which value of x is a counterexample to the student's conjecture?
Responses
A. x=−1/4
B. x=−4
C. x = 1
D. x = 4
How do I solve these?
Applying the knowledge of congruent triangles, the measures are solved as:
6. X = 14; AC = 11; T = 14; WZ = 16; WY = 60; AB = 60; m∠A = 64°; m∠Y = 64°; m∠W = 50°
7. X = 7; YZ = 28; T = 9; WZ = 10; WY = 11; AB = 28; m∠A = 31°; m∠C = m∠W = 99°
How to Solve for the Measures of Congruent Triangles?To solve for the missing measures of triangles that are congruent to each other, recall that triangles that are congruent will have corresponding sides that are equal and also corresponding angles that are equal.
6. Triangles ABC and YWZ are congruent, therefore:
m∠A = m∠Y; m∠B = m∠W; m∠C = m∠Z
AB = WY; AC = YZ; BC = WZ
Therefore:
5X - 4 = 66
Solve for X
5X = 66 + 4
5X = 70
X = 14
AC = YZ = 11
AB = WY
5T - 10 = 4T + 4
5T - 4T = 10 + 4
T = 14
BC = WZ = 16
WZ = 16
WY = 4T + 4 = 4(14) + 4
WY = 60
AB = WY = 60
AB = 60
m∠A = m∠Y
m∠A = 180 - 50 - 66
m∠A = 64°
m∠Y = 64°
m∠B = m∠W = 50°
m∠W = 50°
7. Triangles ABC and ZYW are congruent, therefore:
m∠A = m∠Z; m∠B = m∠Y; m∠C = m∠W
AB = YZ; AC = WZ; BC = WY
Therefore:
5X - 4 = 3X + 10
Solve for x
5X - 3X = 4 + 10
2X = 14
X = 7
AB = YZ
2T + 10 = 4T - 8
2T - 4T = -10 - 8
-2T = -18
T = 9
YZ = 4T - 8 = 4(9) - 8
YZ = 28
AC = WZ = 10
WZ = 10
WY = 11
AB = YZ = 28
AB = 28
m∠A = m∠Z = 3X + 10 = 3(7) + 10
m∠A = 31°
m∠C = m∠W = 180 - 31 - 50 = 99°
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can somone please help meeeeeeee
Answer:
121.5
Step-by-step explanation:
1.5 x 9 x 9 (the equation for volume (minus the 1/2 inch that Isaac's grandmother said to leave out) = 121.5
The map above is being reduced by a scale factor of 1/9 and printed for the subway
station. How many square inches will the new map take up?
O 315 square inches
O 72 square inches
24 square inches
O 35 square inches
Answer:
35 square inches
Step-by-step explanation:
21x15=315
315/9=35
Therefore, the answer is 35 square inches
Evaluate the expression below without using a calculator
With the help of trignometric identities we can say that the answer is = 0.672355, nearly.
What is trignometric equation?A trigonometric equation is any equation that contains a trigonometric function. Up until now we have introduced trigonometric functions, but not fully explore them. In the lessons within this SparkNote on trigonometric equations, we'll learn exactly how to solve trigonometric equations.As mentioned in Trigonometric Identities, a trigonometric equation that holds true for any angle is called a trigonometric identity. There are other equations, though, that only are true for certain angles.They are generally known as conditional equations, but in this text we'll just call them equations. We'll learn some techniques for solving general equations, as well as how to derive an infinite number of solutions to an equation based on a single solution to that equation.acc to our question-
cos(75)= 2-√3tan(22/7)= 1+√2.sin 3π/6= √2-√√2/2Learn more about trignometric equation:
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How can 33 over 9 be expressed as a decimal?
Answer:
3.6
................................
There are 11 counters in a bag.
8 of the counters are green.
3 of the counters are blue.
Sid takes at random two counters from the bag.
Work out the probability that Sid takes one counter of each colour
(Hint: Fractions can be written in the form a/b. eg [tex]\frac{5}{28}[/tex] would be written as 5/28)
The probability of Sid takes at random counters from the bag is 24/55
The total number of counters = 11
Total number of green counters = 8
Total number of blue counters = 3
Probability = Number of favorable outcomes / Total number of outcomes
Total number of outcome = 55
Number of outcome that Sid will get both green = 28
Number of outcome that Sid will get both blue = 3
Number of favorable outcome = 55 - 28 - 3
= 24
Probability = Number of favorable outcomes / Total number of outcomes
= 24/55
Hence, the probability of Sid takes at random counters from the bag is 24/55
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N is an integer. Work out:
a. the smallest possible value of N if N >= 6.5
b. the largest possible of N if N < -3
c. the possible values of N if N >= -2 and N <2.
According to the integer N,
a) The smallest possible value of N is 6.5 if N >= 6.5
b) The largest possible value of N is -2 if N < - 3
c) The possible value of N is {-2, -1, 0, 1} if N >= -2 and N < 2.
Integer
Integer refers a collection of whole numbers and negative numbers.
Given,
Here we have the integer N.
And we need to find the following:
a. the smallest possible value of N if N >= 6.5
b. the largest possible of N if N < -3
c. the possible values of N if N >= -2 and N <2.
Part a). smallest possible value of N if N >= 6.5
Here the smallest number is 6.5 because other value are greater than this one.
Part b). the largest possible of N if N < -3
The largest possible number is -2, because the other values on N are less than -2.
Part c). the possible values of N if N >= -2 and N <2.
Here the possible values between these are {-2, -1, 0, 1}.
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a professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. the professor has informed us that 8.75 percent of her students received grades of a. what is the minimum score needed to receive a grade of a?
The minimum score needed to receive a grade of 'a' is 87.92
Given that,
At a nearby university, a professor noticed that her students' exam results were regularly distributed, with a mean of 73 and a standard deviation of 11. 8.75 percent of the professor's students achieved grades of A, she told us.
Mean = μ = 73
Standard deviation = σ = 11
Using the standard normal table,
⇒ P(Z > z) = 8.75%
⇒ 1 - P(Z < z) = 8.75%
= 1 - P(Z < z) = 0.0875
= P(Z < -1.36) =1- 0.0875
= P(Z < 1.3563) =0.9125
∴ Z = 1.3563 ( Using standard normal z-table )
Using z-score formula ;
x= z * σ + μ
x=1.3563 * 11 + 73
x=87.92
So, the minimum score needed to receive a grade of 'a' is 87.92
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Two cities are 45 miles apart train one is 70 mph train 2 is 60 mph
Answer:
Hi! I'm pretty sure the question is: Two cities are 45 miles apart. Two trains, with speeds of 70 mph and 60 mph, leave the two towns at the same time so that one is catching up to the other. How long after the trains leave will they be 10 miles apart for the first time? How long after the trains leave will they be 10 miles apart for the second time?
I have had a similar question before, and I will answer yours. :)
Step-by-step explanation:
T1 - the time the trains are moving to each other.
For time T1, the first train will go the distance of 70*t.
The second train, for time t, will go the distance 60*t.
Both for time t1 - 70t+60(t1) = (70+60)*(t1).
45 - (70+60)*t is the distance between trains that left after t hours.
For the first time, they will be 10 miles apart when they are moving into each other
45 - (70+60)*t = 10
45-10 = (70+60)*t
35 = 130*t
t=35/130 h =7/26 h = 0.27 h
The train meets when distance = 0
45 - (70+60)*t = 0
45 = 130t
t =45/130 h = 9/26 h = 0.35 h when trains met.
Trains began to move apart from each other after 9/26 h moving,
After t2 time trains will be (70+60)*(t2) = 130*(t2) mi apart from each other.
130*(t2) = 10
t2 = 1/13h = 0.08h after they met, they are apart from each other 10 mi.
So after the beginning of the movement, it will be time when they met + time when they were moved 10 mi apart from each other
9/26 h+1/13h = 11/26 h = 0.42 h
please help asap will give brainliest
1. The angles measures are larger than the original angle measures is a false statement.
2. If two sides parallel in the original figure, then those sides are parallel in the final figure is true statement.
3. The final angle measure are the same as the original angle measure is false statement.
4. The original figure and the final figure may not be congruent is true statement.
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carter has 24 posters in his room. if he arranges them into 6 equal rows, how many posters will be in each row?
If he arranges them into 6 equal rows, 4 posters will be in each row.
Define division.One of the fundamental arithmetic operations in mathematics is the division, which is the process of dividing a group of items into equal pieces. Every day, we might employ the division approach in various situations. Fraction division differs significantly from natural number division. We must change the division operator into a multiplication operator when dividing fractions. Therefore, the dividend should be multiplied by the inverted divisor.
Given,
Total posters = 24
Arranging them into 6 equal rows,
Dividing:
24÷ 6
Reciprocating,
24 × 1/6
4
If he arranges them into 6 equal rows, 4 posters will be in each row.
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What is the solution to this inequality? x - 1 . 5 > 2 . 5 Question 1 options: x < 4 x < 1 x > 1 x > 4
The solution to the inequality is X > 4
InequalityInequality is a set of mathematical expression which the individual side is not equal to other side
To solve for x in the inequality x - 1 . 5 > 2, we followed the step;
Step 1: Add 1.5 to both sides
x - 1.5 + 1.5 > 2 . 5 + 1.5
X > 4
Therefore, the solution to the inequality is X > 4
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1/2x-7=1/3(x-12) Explain or show your reasoning.
Answer: x=18
Step-by-step explanation:
It just does ok
What is the image of the point (-7,9) after a rotation of 90 counterclockwise?
The point (9,7) is the image of the point after a rotation of 90° counterclockwise.
Given that,
The points (-7,9).
We have to find the image of the point after a rotation of 90° counterclockwise.
Because the hands of a clock move in a clockwise manner, we can rotate a point either in that direction or in the opposite direction when we rotate it. In mathematics, clockwise is defined as a negative rotation and counterclockwise as a positive rotation.
Consider the point on the coordinate plane (x,y). You may always swap the x- and y-coordinates and then multiply the new x-coordinate by -1 to rotate this point by 90 degrees around the origin in a clockwise orientation.
(x,y)→(y,-x)
(-7,9)→(9,7)
Therefore, The point (9,7) is the image of the point after a rotation of 90° counterclockwise.
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3. Is this graph a function?
This is a function.
This is not a function.
This cannot be determined from this graph.
Answer:
that is a quadratic function so yes it is a function
Step-by-step explanation:
it is a function becausr you can write an equation with it. Hope I could help!
I need help like asap !!!
only numbers and decimal points
Answer:
a = 4.52 km
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ (7.2)² = a² + (5.6)²
→ 51.84 = a² + 31.36
→ a² = 51.84 - 31.36
→ a = √20.48
→ [ a = 4.52 km ]
Hence, value of a is 4.52 km.
monique and tara each make an ice-cream sundae. monique gets 3 scoops of cherry ice-cream and 1 scoop of mint chocolate chunk ice-cream for a total of 84g of fat. tara has 1 scoop of cherry and 3 scoops of mint chocolate chunk for a total of 60g of fat. how many grams of fat does 1 scoop of each type of ice cream have?
The amount of fat in Cherry ice-cream is 24 grams.
The amount of fat in the Mint Chocolate Chunk ice-cream is 12 grams.
Writing data into equations using Algebra,3C + M = 84...(1)C + 3M = 60...(2)
Multiplying equation (2) by 3 and then subtracting equation (1) from
the result gives, 3 * (C +3M) = 3 × 603C + 9M = 180...(3)(3C + 9M = 180) - (3C + M = 84) = 8M =96M= 12
The amount of fat in the Mint Chocolate Chunk ice-cream, M = 12
grams C + 12*3 = 60C = 60-36 = 24
The amount of fat in Cherry ice-cream C = 24 grams As a result, Cherry ice cream contains 24 grams of fat and Mint Chocolate Chunk ice cream contains 12 grams of fat.
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Express 35cents to $2.25 as a ratio in its lowest terms
Answer:
7 cents:$0.45
Step-by-step explanation:
(whatever you do to one side you do the same to the other)
35 divided by 5= 7
2.25 divided by 5= 0.45
Four congruent parallelograms are joined to make the shape below.
24 cm
The total shaded area is 192 cm²
Work out the value of x.
x cm
5 cm
For the given four congruent parallelograms and the shaded area of 192cm² then value of x is equal to 8cm.
As given in the question,
Given four congruent parallelograms
Shaded area of the parallelogram is 192cm²
As four parallelograms are congruent
Let the area of each parallelogram is A
4A = 192
⇒A = 48cm²
For two parallelogram base length = 24cm
Base length of each parallelogram = 12cm
Area of parallelogram = base × height
48 = 12 × height
⇒ height = 4cm
Value of x = 2 times of height
= 2 (4)
= 8cm
Therefore, for the given four congruent parallelograms and the shaded area of 192cm² then value of x is equal to 8cm.
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Given l||m and m∠1 = 60°, select all angles that are also equal to 60°. 8 2 6 7 5 4 3
Answer:
2 , 3 , 4
Step-by-step explanation:
Corresponding angles: When two parallel lines are intersected by a transversal, the angles on the same side and same position of the transversal are same.
∠3 = ∠1
Vertically opposite angles: When two lines intersect, the opposite angles are congruent.
∠2 = ∠1
∠4 = ∠3
So, ∠1 = ∠2 = ∠3 = ∠4 = 60°
HELP ME PLEASE.
f(x) = √2x
g(x) = √50x
Find (f g)(x). Assume x ≥ 0.
A. (f.g)(x) = 10√
B. (f.g)(x) = √52x
C. (f.g)(x) = 10x
D. (f g)(x) = 50x
The representation of the composite function (fg)(x) is (fg)(x) = 10x
How to determine the possible value of the composite function?From the question, we have the following function definitions
f(x) = √2x
g(x) = √50x
The function to calculate is given as (fg)x
This can be calculated using
(fg)(x) = f(x) * g(x)
Substitute √2x for f(x) and √50x for g(x) in the above equation
So, we have
(fg)(x) = √2x * √50x
Evaluate the products
(fg)(x) = √100x²
Evaluate the exponents
(fg)(x) = 10x
Hence, the possible equation is (fg)(x) = 10x
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(30 x 5) + (9 x 5) =
150 + 45 = 195
Answer:
thats correct
Step-by-step explanation:
max and orlena bought 23 acres of land for $110,400. they bought some of the acres at $4000 per acre and some at $6300 per acre. how many acres did they buy at each price?
They bought 15 acres at $ 4000 per acre and 8 acres at $6300 per acre
Let,
They bought x acres at $ 4000
and ( 23-x ) acres at $ 6300
From information,
By using algebra,
4000x + 6300(23-x) = 110,400
4000x - 6300x+ 144900 = 110,400
-2300x = 110,400-144900
- 2300x = - 34500
x =34500 /2300
x = 15
x = 15
They bought 15 acres at $ 4000 per acre
(23 - 15 ) = 8 acres at $6300 per acre
Hence, they purchased 8 acres for $6300 per acre and 15 acres for $4,000 each.
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the nth term of a gp 145800. if the fist term is 2 and the common ratio is 3. find the sum of the gp
The sum of the geometric progression with the features stated in the text is given as follows:
S = 2.62 x 10^(43).
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The sum of a finite geometric sequence with n terms is given as follows:
[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]
In this problem, the first term and the common ratio are given as follows:
[tex]a_1 = 2, n = 3[/tex]
Hence the equation is:
[tex]a_n = 2(3)^{n - 1}[/tex]
The nth term is of 1458000, hence the number of terms of the sequence is obtained as follows:
[tex]a_n = 2(3)^{n - 1}[/tex]
[tex]1458000 = 2(3)^{n - 1}[/tex]
[tex]3^{n - 1} = 729000[/tex]
[tex]3^{n - 1} = 3^{90}[/tex]
Then:
n - 1 = 90
n = 91.
Thus the sum of the sequence is given as follows:
[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]
[tex]S_{91} = \frac{2(1 - 3^{91})}{1 - 3}[/tex]
S = 2.62 x 10^(43).
Typing mistakeThe problem is solvable with an nth term of 1,450,800, not 145,800, as 145,800/2 is not a root of 3.
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the initial number of views for a reader board was 25. the number of views is growing exponentially at a rate of 18% per week. what is the number of views expected to be four weeks from now? round to the nearest whole number.
The number of views in the four weeks round to the whole number is 48.
Here it is given that the initial number of views for a reader board was 25 and it gets increased at the rate of 18% per week.
We have to find the number of views in the fourth week.
On the first week the increase = 25 + 25× 18%
= 25 + 25 × 18/100
= 25 + 4.5
= 29.5
The second week increase = 29.5 + 29.5 × 18%
= 29.5 + 5.31
= 34.81
The third week increase = 34.81 + 34.81 × 18%
= 34.81 + 6.2658
= 41.0758
The fourth week increase = 41.0758 + 41.0758 × 18%
= 41.0758 + 7.393644
= 48.469444
Therefore the number of views in the four weeks is 48.
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It cost Hassan $5.31 to send 59 text messages. How much does each text cost to send?
Each text will cost Hassan $0.09
What is rate ?A rate is a special ratio in which the two terms are in different units. It can also be defined as the amount of money that is charged for goods or services. For example, if a 12 malt can of costs 69¢, the rate is 69¢ for 12 malt. Then 1 malt will cost ¢69/12.
Similarly $5.31 is the cost of 59 text messages
Therefore a text message will cost $5.31/12=$0.09
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the ratio of drummers to guitar players who tried out for a band is 10:45 .
How many times the number of drummers is the number of guitar players?
Answer:
4.5
Step-by-step explanation:
45/10=4.5
don't need explanation just the answer
The function, changes from f(x) = (3x)³ - 8 to g(x) = (9x)³ - 8 when it is dilated, the statementr which best describes the graph is, the graph is streched towards the x axis by a factor of 1/3
When an object is dilated the image formed is larger or smaller, but there is a difference in the size of the shape.
the rule of function change f(x) = (3x)³ - 8 to g(x) = (9x)³ - 8
3x = 9xk
k = 1/3
Therefore, the function, changes from f(x) = (3x)³ - 8 to g(x) = (9x)³ - 8 when it is dilated, the statement which best describes the graph is, the graph is streched towards the x axis by a factor of 1/3
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Indicate the distance of the segment using the given
information. Round to the nearest tenth.
5. Find AX. A(-4, 5), X (1, −2)
The distance of segment AX sis found to be 8.6 units using the distance formula.
What exactly is the distance formula?[tex]\sqrt{[x_{2}-x_{1}]^{2} + [y_{2}-y_{1}]^{2} }[/tex] is the distance formula. This works for any two points in two-dimensional space with coordinates (x₁, y₁) for the first and (x₂, y₂) for the second. You may easily remember it if you remember that it is Pythagoras' theorem, that the distance is the hypothenuse, and that the coordinate lengths are the difference between the x and y components of the points.Why do we employ the distance formula?In complex numbers, the distance formula is used to express the plane and its magnitude. Furthermore, distance formulae can be used to calculate the distance between two planes in three-dimensional or n-dimensional planes. It is also used to calculate the magnitude formula.Given: A(-4, 5), X (1, −2)
We need to find the distance of the segment AX.
Distance of AX is given as :
[tex]\sqrt{[1-(-4)]^{2} + [-2-5]^{2} } \\= \sqrt{25 + 49}\\ = \sqrt{74}\\ =8.6[/tex]
Therefore, the distance of segment AX sis found to be 8.6 units using the distance formula.
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what is the answer what is the answer what is the step by step answer to learn to do it
Answer: 1.01% sale tax.
Step-by-step explanation:
First you must take your tax price before and the tax price after and divide them. This gets you 1.01.
To be sure this is your answer you can multiply the 1.01% by 53 and it gives you 53.53$ (If you don't understand I suggest looking at a video from khan academy they explain things much better than I do.)
Hope that helped in some way :)
