A number that is divisible by 2 is also divisible by 4. The counterexample of this conjecture should be a number that is divisible by 2 but not divisible by 4 .
What is Conjecture ?
A conjecture is a statement that is guessed by someone and it may or may not be true.
What is counterexample ?
A counterexample is an example that proves the conjecture to be false.
Let's go through the list of values and test the claim
Is 32 divisible by 2? Yes because 16*2 = 32. Is it also divisible by 4? Yes because 8*4 = 32. So we can cross choice A off the list
Is 12 divisible by 2? Yes because 6*2 = 12. Is it also divisible by 4? Yes because 3*4 = 12. So we can cross choice B off the list.
Is 40 divisible by 2? Yes because 2*20 = 40. Is it also divisible by 4? Yes because 4*10 = 40. Choice C is also crossed off the list.
Is 18 divisible by 2? Yes because 2*9 = 18. Is it also divisible by 4? No. We can see that by dividing 18/4 = 4.5 which is not a whole number result. Or you can list out the multiples of 4 which are 4, 8, 12, 16, 20 and we see that 18 is not on the list. This is a counter example to show that the claim "if number is divisible by 2, then it is also divisible by 4" is a false statement.
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Do males or females like basketball more? Show both raw numbers and percentages.
We can infer from the data set provided that more women than men are interested in basketball.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
From table given in question
Number of males that like basketball = 21
Number of females that like basketball = 29
Percentage of males that like basketball = (21/50)*100 = 42%
Percentage of females that like basketball = (29/50)*100 = 58%
So, from above data we can conclude that females like basketball more than that of males.
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The line passes through
(14,-6) and has a slope = -2/7
The equation of the line passing through the given points and having slope -2/7 is obtained as y = -2/7m - 2.
How to write the equation of a straight line in slope-intercept form?A straight line can be written in the slope-intercept form as, y = mx + c.
In order to obtain the slope, the ratio of the difference of the coordinates are taken and c is the y-intercept which can be found by substituting x = 0 in the equation.
The given point and the slope for line are as (14,-6) and -2/7 respectively.
The general form of slope-intercept equation is as below,
y = mx + c
Substitute the value of x = 14, y = -6 and m = -2/7 to get,
-6 = -2/7 × 14 + c
⇒ c = -6 + 4 = -2
Thus, the equation can be written as follows,
y = mx + c
Substitute m = -2/7 and c = -2 to obtain,
y = -2/7x + (-2)
⇒ y = -2/7m - 2
Hence, the equation of the line is given as y = -2/7m - 2.
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FORMATIVE AND SUMMAT assessment unit 4 Draw the figure's reflection in the y-axis.
The reflection of the quadrilateral across the y-axis is shown in the graph below.
What is a transformation of a shape?A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.
The reflection does not change the shape and size of the geometry. But flipped the image.
The quadrilateral has four sides and four angles. And the sum of the internal angles of the quadrilateral is 360 degrees.
The quadrilateral is given in the figure.
The reflection of the quadrilateral across the y-axis is shown in the graph below.
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Contruct a polynomial function with the tated propertie. Reduce all fraction to lowet term. Third-degree, with zero of −3, −1, and 2, and pae through the point (0,-14)
On solving the provided the question, we got that - f(x) = 7/3[x - (2)] [x - (-1)] (x +3) is the equation which is formed.
What is equation?An equation can be defined in a variety of ways. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions.
Gives zeroes are -
-3, -1 and 2
and it passes through (0, -14)
Constructing a function from a product of factors containing the zeros, with an unknown coefficient
f(x) = a [x - (2)] [x - (-1)] (x +3)
with a ≠ 0.
f(x) = a(x -2)(x + 1)((x +3)
Use f(0) = -14 to find a.
-14 = a(-2)(1)(3) = -6a
a = 7/3
Now,
f(x) = 7/3[x - (2)] [x - (-1)] (x +3)
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Determine which set of side measurements could be used to form a right triangle.
A. 3, 11, 20
B. 5, 9, 17
C. 6, 7, 8
D. 6, 8, 10
Answer:
D. 6, 8, 10
Step-by-step explanation:
Apply the Pythagorean theorem equation to all set of number, and see which one works.
A.
3² + 11² ≠ 20²
9 + 121 ≠ 400
131 ≠ 400
B.
5² + 9² ≠ 17²
25 + 81 ≠ 289
106 ≠ 289
C.
6² + 7² ≠ 8²
36 + 49 ≠ 64
85 ≠ 64
D.
6² + 8² = 10²
36 + 64 = 100
100 = 100
HELP ASAP ITS URGENT!!!!!!!
ILL GIVE 50 POINTS
Answer: It's in the picture
Step-by-step explanation:
PLEASE HELP ASAP!!! THIS IS DO TN HELP WOULD BE VERY APPRECIATED<3
Answer:
1
Step-by-step explanation:
3(-0.5)+2(7+0.8)
13+1.1
-1.5+2(7+0.8)
13+1.1
-1.5+15.6
14.1
14.1
14.1
divide
1
hope that helps :)
Given the area of a rectangle is A = x^(2) - 3x - 18, answer the following questions: What is the length of each side? What is the perimeter of the rectangle? Please answer I'm giving 30 points.
The dimensions of the rectangle in terms of x are (x-6) and (x+3).
What in mathematics is a quadratic equation?
x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given that:
A = x^(2) - 3x - 18
By solving this equation we can get the values of length and breath of rectangle
A = x^(2) - 6x + 3x - 18
A = x(x-6)+3(x-6)
A = (x-6)(x+3)
Hence the area of rectangle is equal to L * W
Hence, the dimensions of the rectangle are (x-6) and (x+3).
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In the function g(x)=9-5x what is the value of g(3)
Answer:
g(3) = - 6
Step-by-step explanation:
g(3) = 9 - 5(3)
g(3) = 9 - 15
g(3) = - 6
what is the answer to this question?
Answer:
47.21
Step-by-step explanation:
a=47.4
b=0.19
a – b
47.4 – 0.19
=47.21
Select all of the following that represent direct variation.
1. y = 5x
2. y = 2x + 1
3. 3 = xy
4. b = 1/2a
5. y= 2/x
6. m = 5n
The equations, y=5x, b = 1/2 a, m=5n are direct variations.
What is direct variation?A sort of proportionality known as "direct variation" occurs when one quantity directly changes in response to a change in another quantity. This suggests that if one quantity increases, the other quantity will also increase proportionately. Similar to the last example, if one quantity declines, the other amount also declines. The link between direct variation and the graph will be linear, resulting in a straight line.
We know that any equation, which can be expressed in the form of y=kx, can be called a direct variation.
y = 5x is in the form of y = kx, where k =5, hence this is a direct variation
y = 2x + 1 is not in the form of y = kx, hence this is not a direct variation
xy = 3 is not in the form of y = kx, hence this is not a direct variation
b = 1/2 a is in the form of y = kx, where k =1/2, hence this is a direct variation
y = 2/x is not in the form of y = kx, hence this is not a direct variation
m = 5n is in the form of y = kx, where k =5, hence this is a direct variation
Thus, y=5x, b = 1/2 a, m=5n are direct variation
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If the area of square 3 is 80 cm2 and the area of square 2 is 100 cm2, what is the area of square 1?
Answer: 180cm^2
Step-by-step explanation:
The equation is a^2 + b^2 = c^2
a^2 = area of square 3 = 80cm^2
b^2 = area of square 2 = 100cm^2
c^2 = a^2 + b^2 = 80 + 100 = 180cm^2
So answer is 180cm^2
Please help
What inequality does the number line show?
Write your answer starting with
x (example: x < 3)
Answer:
x < 5
Step-by-step explanation:
the dot is empty so we don’t consider 5
The coloured arrow continues to the left so we use this symbol : < (minor)
x<5
The inequality for the number line show is x<5.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
We can see that the inequality starts from 5 moves towards 2.
As, the starting of number line have open dot which shows we cannot include 5.
So, the inequality will have sign '<'.
Now, the inequality of the number line is
x < 5.
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(LOTS OF POINTS) The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $5500 to rent trucks plus an additional fee of $175.50 for each ton of sugar. The second company charges $4995 to rent trucks plus an additional fee of $200.75 for each ton of sugar.
a) For what amount of sugar do the two companies charge the same?
b) What is the cost when the two companies charge the same?
The amount of sugar that both companies would charge the same is 20 tons.
The cost when the two companies would charge the same is $9010.
What is the amount of sugar that both companies would charge the same?The linear equation that represents the total charge of the companies : cost to rent truck + (ton of sugar x cost per ton)
The linear equation that represents the total charge of the first company : $5500 + ($175 x s)
$5500 + $175s
The linear equation that represents the total charge of the second company : $4995 + ($200.75 x s)
$4995 + $200.75s
When the two companies charge the same, the two linear functions above would be equal.
$4995 + $200.75s = $5500 + $175s
In order to determine the value of s, take the following steps:
200.75s - 175.50s = $5500 - $4995
25.25s = 505
s = 505 / 27.25
s = 20
In order to determine when the cost of the two companies would be the same, substitute for s in either of the above linear functions.
$5500 + $175.50(20)
$5,500 + 3510 = $9010
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$25 jeans; 16% markup
29$ 16% of 25 is 4, so add it, and theres the answer
Step-by-step explanation:
What i the lope of the line that pae through the point (-7, -8)(−7,−8) and (-5, -6)(−5,−6)? Write your anwer in implet form
For the provided points (-7,-8) and (-5,-6) on the line, the slope is 1.
What is slope?The slope of a line is a measure of its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
Here,
Slope=(y2-y1)/(x2-x1)
=(-6-(-8))/(-5-(-7))
=2/2
=1
The slope of the line for given point (-7,-8) and (-5,-6) will be 1.
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pirya has picked 1 1/2 cups of raspberries, which is enough for 3/4 of a cake how many cups does she need for the whole cae
Pirya needs 1 1/2 cups of raspberries for 3/4 of a cake, so she needs 1 1/2 * (4/3) = 2 cups of raspberries for the whole cake.
What is fraction?A fraction is a numerical representation of a portion of a total. It consists of two integers, a numerator and a denominator, separated by a line or slash. The numerator reflects the number of equal portions of the whole that are being considered, while the denominator represents the total number of equal parts in the whole. For instance, the fraction "1/2" denotes one of two identical pieces, or half, of the whole. Mathematicians frequently utilize fractions to represent quantities, ratios, and proportions. They are also used in everyday life to signify amounts, such as one-half of a pizza or one-third of a cups of sugar.
How to solve?
she needs 1 1/2 * (4/3) = 2 cups of raspberries for the whole cake.
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they are 40 people in 15 teenagers what percentage of the people on your guestlist are teenagers
Answer: 6
Step-by-step explanation:
40x0.15
6 are teens
Which of the following equations represent linear functions?
a.) y=x2
b.) y=3x+2
c.) y=6
d.)y=x−−√
Answer:
b.) y=3x+2
Step-by-step explanation: The linear equation is y= mx + b
m is the slope and b is the y-intercept
Answer b is the linear equation!
please help me with this
Measure of angle I greater than angle K and J. Therefore, option D is the correct answer.
Given that, in triangle IJK, JK=18, KI=11, and IJ=14.
What is the triangle inequality theorem?If one side of a triangle is longer than another side, then the angle opposite the longer side will be larger than the angle opposite the shorter side.
Here, JK is the longest side and KI is the shortest side
So, opposite to side JK, angle I is the biggest and opposite to the side KI angle J is the smallest
Here, the measure of IJ is greater than the side KI, then the angle K opposite to side IJ is greater than the angle J
Thus, m∠I>m∠K>m∠J
Measure of angle I greater than angle K and J. Therefore, option D is the correct answer.
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Solve for x.
-12< -3x - 15 < 36
Enter your answer, as one inequality, in the box.
Step-by-step explanation:
-12 < -3x - 15 <= 36 | add 15 everywhere
3 < -3x <= 51 | divide by 3 everywhere
1 < -x <= 17 | multiply by -1 everywhere
-1 > x >= -17
or
-17 <= x < -1
remember that with every multiplication or division of a negative number the orientation of the inequality signs flip.
the same happens, of course, when we exchange the upper and lower limits from left to right and right to left, so that the smaller number is on the left, and the larger number on the right (yes, -1 is larger than -17).
PLEASE HELP!! WILL GIVE BRAINLIEST AND 25 POINTS!!
Find the value of x. Round your answer to the nearest degree.
A. 18°
B. 21°
C. 22°
Answer:
Sin(angle) = Opposite / hypotenuse
Sin(x) = 5/14
X = arcsin(5/14)
x = 20.9
X = 21 degrees.
the answer is da da b!
Step-by-step explanation:
Use f(x) = -4x+1, g(x) = x2 - 8x + 21, and h(x) = 19-3x|
Find h(8)-f(-7)
The function operation h(8) - f(-7) of the functions f(x) = -4x+1, and h(x) = 19-3x is -34.
What is the function operation h(8) - f(-7) in the given functions?A function is simply a relationship that maps one input to one output.
Given the data in the question;
f(x) = -4x + 1g(x) = x² - 8x + 21h(x) = 19 - 3xh(8) - f(-7) = ?First, solve for the output value of h(8) by replacing x with 8 and simplify.
h(x) = 19 - 3x
h(8) = 19 - 3(8)
h(8) = 19 - 24
h(8) = -5
Next, solve for the output value of f(-7) by replacing x with -7 and simplify.
f(x) = -4x + 1
f( -7 ) = -4( -7 ) + 1
f( -7 ) = 28 + 1
f( -7 ) = 29
Now, replace the function designators with the actual output values.
h(8) - f(-7) = -5 - ( 29 )
h(8) - f(-7) = -5 - 29
h(8) - f(-7) = -34
Therefore, the output of the function operation h(8) - f(-7) is -34.
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Use the following function rule to find f(–4).
f(x) =
–4 +
4
|x|
f(–4) =
By evaluating the function in x = -4, we will get:
f(-4) = 12
How to evaluate the function f(x)?Here we have the following function:
f(x) = -4 + 4*|x|
So we have an absolute value function.
We want to find f(-4), so we want to evaluate the function in x = -4, to do that, just replace the variable by that number.
We will get:
f(-4) = -4 + 4*|-4|
Remember that the absolute value of a negative number gives the opposite:
|-4| = 4
Then:
f(-4) = -4 + 4*|-4|
f(-4) = -4 + 4*4
f(-4) = -4 + 16 = 12
f(-4) = 12
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Which product is represented by the model?
A. 0.05×0.04=0.002
B. 5×0.4=2
C. 0.5×0.4=0.2
D. 0.5×0.04=0.02
0.05×0.04=0.002 is the product represented by the model
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given:
5 column (hundred grid) = 5/100 = 0.05
4 row (hundred grid) = 4/100 = 0.04
We need to find Area equation
Computation:
Area equation = 0.05 x 0.04
0.05 x 0.04 = 0.002
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Slope of (-8,-3) and (-8, -19)
Answer:
Undefined
Step-by-step explanation:
Knowledge Needed
Slope if is the constant change of the y-value when the x-value increases by 1 on a line.
Slope Formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Question
Plug in your points.
[tex]\frac{-19--3}{-8--8}[/tex]
[tex]\frac{-16}{0}[/tex]
Any number divided by 0 is undefined.
The slope is undefined. This means the line is completely vertical.
Last year, students planted 8 tomato plants and 16
garden. This year, the students planted
pepper plants in a school
15 tomato plants. They want to have the
same ratio of tomato plants to pepper plants as last year. Pepper plants cost
$4.33 each. What is the cost, in dollars, of the pepper plants for this year's garden?
Answer:
Step-by-step explanation:
From the ratio gotten, the total cost of the pepper will be $129.90.
How to solve a ratio
Since the students planted 8 tomato plants and 16 pepper plants in a school garden. The ratio will be:
= 8/16 = 1:2
This year, the students planted 15 tomato plants, the number of pepper will be:
= 15 × 2 = 30
Since pepper plants cost $4.33 each, the total cost will be:
= 30 × $4.33
= $129.90
Please help, need a diagram and correct calculations!!!
Buy the land !all angles will be greater than 30 °
How many piece of land he buy ?Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circular functions) that make up trigonometry.
A branch of mathematics called trigonometry examines connections between triangles' sides and angles. Due to the fact that every straight-sided shape can be decomposed into a group of triangles, trigonometry can be found throughout all of geometry.
cos x = 500²+800²-900²/-2(800)(900)
x = [tex]cos^{-1}[/tex](+1200000/+1440000)
=336°
Buy the land !all angles will be greater than 30 °
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A while ago, Kinsley bought shares of stock in a high-tech firm. At that time, the selling price was $18 per share. According to today's newspaper, a share is currently worth 50% more. What is the current value of one share?
Answer:
$27
Step-by-step explanation:
We find 50% of $18 and add it to $18.
50% of $18 = 5/100 × $18 = 0.5 × $18 = $9
Today, it is worth $9 more.
$18 + $9 = $27
How many solutions does the following equation have?
-14(z-5) = -14z +70
Choose 1 answer:
A. No solutions
B. Exactly one solution
C. Infinitely many solutions
Answer: C. Infinitely many solutions
Step-by-step explanation: If the answer is <0, then there is no solution; if it is >1, then there is more than one solution; if = 0, then there are Infinitely many solutions
-14(z-5) = -14z +70 can be write as
-14z + 70 = -14z + 70
-14z = -14z
z= 0
Because the answer is 0 so there Infinitely many solutions
If you can, please give me a Brainliest; thank you!
Answer:
C. Infinite many solutions.
Step-by-step explanation:
Simplify the left side of the equation. Note the parenthesis. Distribute -14 to all terms within the parenthesis:
-14(z - 5) = -14z + 70
-14z + 70 = -14z + 70
C. Infinitely many solutions is your answer, as no matter what number you plug in for the variable z, the equation would still be true.
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