Answers
We are given the following statement.
If a number is an integer, then it is either positve or negative.
In the above statement, the 1st part is the condition and the 2nd part is conclusion.
Condition = a number is an integer
Conclusion = it is either positve or negative
Therefore, the conclusion of the conditional is option B.
A number is either positive or negative.
Related Questions
I’m having trouble with this calculus practice problem Below are the answer options A. -2B. 1C. 3D. The limit does NOT exist
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Given
[tex]\lim _{x\to-3^+}h(x)[/tex]Solution
The limit is tending to -3 from the right, that is why it is written as
[tex]-3^+[/tex]From the graph, we will trace the graph from the right to -3
The final answer is -2
For what values of k will the sum of the solutions of x^2 - (k^2 - 3k)x + 24=0 be 10?
Answers
The Solution:
Given the equation below:
[tex]x^2-(k^2-3k)x+24=0[/tex]We are required to find the value of k that will make the sum of the solutions to be 10.
Step 1:
Let:
[tex]\begin{gathered} k^2-3k\text{ be represented with b} \\ \text{ So that we have} \\ k^2-3k=b\ldots eqn(1) \end{gathered}[/tex]So, the given equation becomes:
[tex]x^2-bx+24=0[/tex]We shall the Quadratic Formula Method to solve for x in terms of b.
In this case,
[tex]\begin{gathered} a=1 \\ b=-b \\ c=24 \end{gathered}[/tex]Substituting, we get
[tex]x=\frac{-b\pm\text{ }\sqrt[]{(-b)^2-(4\times1\times24)}}{2(1)}[/tex][tex]x=\frac{-b\pm\text{ }\sqrt[]{b^2-96}}{2}[/tex]So, the solutions to the given equation are:
[tex]\begin{gathered} x=\frac{-b+\text{ }\sqrt[]{b^2-96}}{2} \\ \text{ or} \\ x=\frac{-b-\text{ }\sqrt[]{b^2-96}}{2} \end{gathered}[/tex]Equating their sum to 10.
[tex]\begin{gathered} \frac{-b+\text{ }\sqrt[]{b^2-96}}{2}+\frac{-b-\text{ }\sqrt[]{b^2-96}}{2}=10 \\ \\ \\ \frac{-b+\text{ }\sqrt[]{b^2-96}+-b-\text{ }\sqrt[]{b^2-96}}{2}=10 \end{gathered}[/tex]Simplifying, we get
[tex]\begin{gathered} \frac{-2b}{2}=10 \\ \\ -b=10 \end{gathered}[/tex]Substituting for b, we get
[tex]\begin{gathered} -(k^2-3k)=10 \\ k^2-3k=-10 \\ k^2-3k+10=0 \end{gathered}[/tex]Solving for k by the Quadratic Formula method of solving quadratic equation, we get
[tex]k=\frac{-b\pm\text{ }\sqrt[]{b^2-4ac}}{2a}[/tex]Where
[tex]a=1,b=-3\text{ and c=10}[/tex]Substituting, we get
[tex]k=\frac{-(-3)\pm\text{ }\sqrt[]{(-3)^2-(4\times1\times10)}}{2(1)}[/tex][tex]k=\frac{3\pm\text{ }\sqrt[]{9^{}-40}}{2}=\frac{3\pm\text{ }\sqrt[]{-31}}{2}[/tex][tex]\begin{gathered} k=\frac{3+\text{ }\sqrt[]{-31}}{2}\text{ or }k=\frac{3-\text{ }\sqrt[]{-31}}{2} \\ \end{gathered}[/tex]Therefore, the correct answer is
[tex]k=\frac{3+\text{ }\sqrt[]{-31}}{2}\text{ or }k=\frac{3-\text{ }\sqrt[]{-31}}{2}[/tex]Alternatively,
We can use the sum of roots formula below:
[tex]\begin{gathered} \text{ Sum of roots = }\frac{-b}{a} \\ \text{if given a quadratic equation of the form ax}^2+bx+c=0 \end{gathered}[/tex]So, we get
[tex]\begin{gathered} a=1 \\ b=-(k^2-3k) \\ c=24 \end{gathered}[/tex]So,
[tex]\begin{gathered} \text{ Sum=}\frac{--(k^2-3k)}{1}=10 \\ \\ k^2-3k=10 \\ \\ k^2-3k-10=0 \end{gathered}[/tex]Then you can now solve from here as have done in the previous method.
Solve the quadratic equation above for k.
I need help with this 6-9 should be matched with either A-H
Answers
Explanation
To answer the question, we will make use of some of the properties of a parallelogram
These are
The opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary.
Each diagonal of a parallelogram separates it into two congruent triangles.
The diagonals of a parallelogram bisect each other.
Therefore
For question 6
[tex]\begin{gathered} mTherefore, the answer to question 6 is AQuestion 7
[tex]mThe answer to question 7 is EQuestion 8
[tex]\begin{gathered} DF=FB \\ Diagonals\text{ bisect each other} \\ DF=17 \end{gathered}[/tex]The answer to question 8 is C
Question 9
[tex]\begin{gathered} mThe answer to question 9 is F[tex] \sqrt{16} [/tex]can you do a step by step explanation to find the square root.
Answers
Explanation
Step 1
a square root is given by:
[tex]\begin{gathered} \sqrt[]{a}=b \\ \text{where} \\ b^2=a \end{gathered}[/tex]look for values for b
[tex]undefined[/tex]El producto de 2 por la diferencia de x y y
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La diferencia de 'x' y 'y' se puede escribir asi:
[tex]undefined[/tex]Mike needs to calculate the angle a rafter makes a with a ceiling joist of a house. The roof has a rise of 5.5 for a run of 12’. What is the angle of the rafter ?
Answers
Let's illustrate the given information.
To determine the angle of this rafter, we can use the tangent function. The formula is:
[tex]\tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}}[/tex]Our angle in the illustration is the one colored in red. The opposite side of the angle measures 5.5 inches while the adjacent side measures 12 inches. Let's plug in this data to the formula above.
[tex]\tan \theta=\frac{5.5}{12}[/tex]To be able to get the measure of angle, let's get the arc tan of the angle.
[tex]\theta=\tan ^{-1}\frac{5.5}{12}\approx24.62[/tex]Hence, the rafter must be angled 24.62 degrees away from the ceiling joist of the house.
An 8-pack of batteries cost $9.44.what is the price, in dollars , of one battery?A)- $0.85B)- $1.18C)- 1.44D)- 2.36
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In order to determine the cost of only one battery, calculate the quotient in between the cost of 8 batteries over 8:
$9.44/8 = $1.18
Hence, one battery costs $1.18
PLEASE HELP!! ALGEBRA 1 HW I WILL GIVE BRAINLYEST
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Answer:
answer Is -5/2 becouse if the line Is horizontal his equation Is y=k and in this case k= -5/2
2/9 + 4/9 ..........
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We will do the operation:
[tex]\frac{2}{9}+\frac{4}{9}[/tex]As both fractions have the same denominator, we add the numerators, and we obtain:
[tex]\frac{2}{9}+\frac{4}{9}=\frac{6}{9}=\frac{2}{3}[/tex]Where we simplified 6/9 to 2/3 by dividing by 2.
This means that 2/9+4/9 is 2/3.
use the order of operations to find the value of the following expression
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Average movie prices in the unites States are, in general, lower than in other countries. it would cost $77.94 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $73.86. How much does an average movie ticket cost in each countires?Japan average:Switzerland average:
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If "J" is the average price in Japan and "S" is the average price is "S", then since we are told that three tickets in Japan plus two tickets in Switzerland cost $77.94 we have the following relationship:
[tex]3J+2S=77.94,\text{ (1)}[/tex]We are also told that three tickets in Switzerland plus two tickets in Japan would cost $73.86. This gives us the following equation:
[tex]2J+3S=73.86,(2)[/tex]We get two equations with two variables. To solve this system we will multiply equation (1) by -2:
[tex]-6J-4S=-155.88,(3)[/tex]Now we multiply equation (2) by 3:
[tex]6J+9S=221.58,(4)[/tex]Now we will add equation (3) and equation (4):
[tex]-6J-4S+6J+9S=-155.88+221.58[/tex]Now we add like terms;
[tex]5S=65.7[/tex]Dividing both sides by 5:
[tex]S=\frac{65.7}{5}=13.14[/tex]Now we replace the value of S in equation (1):
[tex]3J+2(13.14)=77.94[/tex]Solving the operation:
[tex]3J+26.28=77.94[/tex]Subtracting 26.28 to both sides:
[tex]\begin{gathered} 3J=77.94-26.28 \\ 3J=51.66 \end{gathered}[/tex]Dividing both sides by 3:
[tex]J=\frac{51.66}{3}=17.22[/tex]Therefore, the average in Japan is $17.22 and the average in Switzerland is $13.14.
please help me ASAP!!!
Answers
1)
The expression :
[tex]\begin{gathered} 2^3\cdot2^5=2^8 \\ \text{Tha base are same so, the exponents are add up} \end{gathered}[/tex]1-same Base Product
2)
The expression:
[tex]\begin{gathered} \frac{5^5}{5^2}=5^3 \\ \text{The base are same and they are divison from so the exponents will subtract} \\ \end{gathered}[/tex]2- Same base Quotient
3)
The expression:
[tex]\begin{gathered} (3^2)^3=3^6 \\ \text{The }power\text{ to pwer will multiply sor 2}\times3=6 \end{gathered}[/tex]3-Power to power
4)
The expression:
[tex]\begin{gathered} 8^0=1 \\ The\text{ zero power is always equal to 1} \end{gathered}[/tex]4- Zero power
Answer:
1) same Base Product
2) Same base Quotient
3) Power to power
4) Zero Power
Drag each label to the correct location. Not all labels will be used.The dimensions of a rectangular section of forest land are 5.5 x 105 meters and 4.2 x 104 meters. Complete the following sentences.2.31 x 1032.31 x 1042.31 x 10523.1 x 102.31 < 101023.1 x 1010square meterssquare kilometersThe area of the land issquare meters in scientific notation.We can represent this area assquare kilometers in scientific notation.Hint: 1 square kilometer is equal to 1 x 106 square meters.The unitis more appropriate to represent the area of the forest land in scientific notation.
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The area of the land would be (4.2x10^4)(5.5x10^5)=23.1x10^9
and we can represent this area in scientific notation like: 2.31x10^10
the unit more appropriated for the area is: square kilometers
Help please look at the image and also use these terms recursive: f(1) = 2, f(n) = 2*f(n-1). explicit: we need to take 1st term/pattern.
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The explicit formula for a geometric sequence is given by:
[tex]f(n)=f(1)r^{n-1}[/tex]where r is the common ratio of the sequence.
For this sequence the common ratio is 2 and the first term is 2, therefore its explicit formula is:
[tex]f(n)=2(2)^{n-1}[/tex]The recursive formula for a geometric sequence is given by:
[tex]\begin{gathered} f(1) \\ f(n)=rf(n-1) \end{gathered}[/tex]Therefore in this case we have:
[tex]\begin{gathered} f(1)=2 \\ f(n)=2f(n-1) \end{gathered}[/tex]a line that passes through points (2, 40) and (20, 4)
Answers
Answer
y - 40 = -2 (x - 2)
We can simplify this
y - 40 = -2x + 4
y = -2x + 4 + 40
y = -2x + 44
Explanation
The general form of the equation in point-slope form is
y - y₁ = m (x - x₁)
where
y = y-coordinate of a point on the line.
y₁ = This refers to the y-coordinate of a given point on the line
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
x₁ = x-coordinate of the given point on the line
We need to calculate the slope and to use one of the points given as (x₁, y₁)
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex](x₁, y₁) and (x₂, y₂) are (2, 40) and (20, 4)
[tex]\text{Slope = }\frac{4-40}{20-2}=\frac{-36}{18}=-2[/tex]Slope = m = -2
(x₁, y₁) = (2, 40)
x₁ = 2, y₁ = 40
y - y₁ = m (x - x₁)
y - 40 = -2 (x - 2)
We can simplify this
y - 40 = -2x + 4
y = -2x + 4 + 40
y = -2x + 44
Hope this Helps!!!
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.0.50 : 0.25
Answers
Answer:
2/1
Explanation:
Given the ratio:
[tex]0.50\colon0.25[/tex]Divide both sides by 0.25
[tex]\begin{gathered} \frac{0.50}{0.25}\colon\frac{0.25}{0.25} \\ =2\colon1 \\ =\frac{2}{1} \end{gathered}[/tex]Thus, the ratio as a fraction in simplest form is 2/1.
nes ing Online book David's dad drove at a constant rate for 25 miles. It took him 20 minutes. At what rate was David's dad driving (in miles per hour)? 55 miles per hour 65 miles per hour 75 miles per hour ps 85 miles per hour #
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In order to calculate the rate (that is, the speed) David's dad was driving in miles per hour, first let's convert the time from minutes to hours using a rule of three:
[tex]\begin{gathered} 1\text{ hour}\to60\text{ minutes} \\ x\text{ hours}\to20\text{ minutes} \\ \\ 60x=20\cdot1 \\ x=\frac{20}{60}=\frac{1}{3} \end{gathered}[/tex]Now, to find the speed, we just need to divide the distance by the time:
[tex]\text{speed}=\frac{25}{\frac{1}{3}}=25\cdot3=75\text{ mph}[/tex]So the speed is 75 mph, therefore the answer is the third option.
Determine the equation of the line that passes through the point (1/9,−3) and is parallel to the line −8y+4x=4.
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Given:
The point lies on the line is (1/9, -3).
The parallel line is -8y+4x=4.
Required:
We need to find the equation of the line.
Explanation:
Consider the parallel line.
[tex]-8y+4x=4[/tex]Subtract 4x from both sides.
[tex]-8y+4x-4x=4-4x[/tex][tex]-8y=4-4x[/tex]Divide both sides by (-8).
[tex]-\frac{8y}{-8}=\frac{4}{-8}-\frac{4x}{-8}[/tex][tex]y=-\frac{1}{2}+\frac{1}{2}x[/tex][tex]y=\frac{1}{2}x-\frac{1}{2}[/tex]Which is of the form
[tex]y=mx+b[/tex]where slope,m=1/2.
We know that the slope of the parallel lines is the same.
The slope of the required line is m =1/2.
Consider the line equation.
[tex]y=mx+b[/tex]Substitute x =1/9, y=-3, and m=1/2 in the equation to find the value of b.
[tex]-3=\frac{1}{9}(\frac{1}{2})+b[/tex][tex]-3=\frac{1}{18}+b[/tex]Subtract 1/18 from both sides.
[tex]-3-\frac{1}{18}=\frac{1}{18}+b-\frac{1}{18}[/tex][tex]-3\times\frac{18}{18}-\frac{1}{18}=b[/tex][tex]\frac{-54-1}{18}=b[/tex][tex]b=-\frac{55}{18}[/tex]Substitute m=1/2 and b =-55/18 in the line equation.
[tex]y=\frac{1}{2}x-\frac{55}{18}[/tex]Multiply both sides by 18.
[tex]18y=18\times\frac{1}{2}x-18\times\frac{55}{18}[/tex][tex]18y=19x-55[/tex]Final answer:
[tex]18y=19x-55[/tex]question number 1 and 2 and find measure of. angle 1
Answers
Explanation
Step 1
vertical angles:
Vertical angles are pair angles formed when two lines intersect
[tex]m\measuredangle x=m\measuredangle y[/tex]so, we need to find a vertical angle in
a)
Figure 1:
blue angles are vertical, so
[tex]m\measuredangle HML\text{ and m}\measuredangle JMK[/tex]Figure 2:
hence, a pair of vertical angle is
[tex]\begin{gathered} \\ m\measuredangle LQM\text{ and m}\measuredangle\text{PQN} \end{gathered}[/tex]Step 2
pair of adjacent angles:
Adjacent angles are two angles that have a common vertex and a common side but do not overlap
[tex]m\measuredangle x\text{ is adjacent to m}\measuredangle y[/tex]then
a)
for Figure 1
pair of adjacent angles
[tex]m\measuredangle HMJ\text{ and m}\measuredangle JMK[/tex]b) for Figure 2
pair of adjacent angles
[tex]m\measuredangle LQM\text{ and m}\measuredangle LQR[/tex]I hope this helps you
What is the length of the side opposite the 30° angle? Explain your reasoning.
Answers
Given the triangle ABC as shown below:
The length of the side opposite the 30° angle is evaluated as follows:
Step 1:
Given that the 30° angle is the focus angle, label the sides of the triangle.
Thus,
[tex]\begin{gathered} \text{where }\theta=30^{\circ} \\ AC\Rightarrow hypotenuse\text{ (the longest side of the triangle)} \\ AB\Rightarrow opposite\text{ (the side opposite the focus angle)} \\ BC\Rightarrow adjacent \\ \text{thus, } \\ AC\text{ = 44} \\ AB\text{ = x (unknown length)} \end{gathered}[/tex]Step 2:
Evaluate the unknown side using trignometric ratios.
By trigonometric ratios,
[tex]\begin{gathered} \sin \theta\text{ = }\frac{opposite}{hypotenuse}=\frac{AB}{AC} \\ \cos \text{ }\theta\text{ = }\frac{adjacent}{hyptenuse}=\frac{BC}{AC} \\ \tan \text{ }\theta\text{ = }\frac{opposite}{adjacent}=\frac{AB}{BC} \end{gathered}[/tex]From the above trigonometric ratios, sine θ is used to evaluate the value of the unknown side.
This because the sine θ gives the ralationship between the hypotenuse and the unknown side of the triangle.
Thus,
[tex]\begin{gathered} \sin \theta\text{ = }\frac{opposite}{hypotenuse}=\frac{AB}{AC} \\ AB\text{ = x} \\ AC\text{ = 44} \\ \theta\text{ = 30} \\ \Rightarrow\Rightarrow\sin 30\text{ = }\frac{x}{44} \\ 0.5\text{ = }\frac{x}{44} \\ \Rightarrow x\text{ = 0.5}\times44 \\ x\text{ = 22} \end{gathered}[/tex]Hence, the value of the unknown side is 22.
Please help me if you could if you can't I understand. what fractions are equivalent to 2/3 and 7/12 using the least common denominator?
Answers
2/3 ---->8/12
7/12 ----> 7/12
1) Equivalent fractions have the same value proportionally, so let's find out equivalent fractions:
[tex]\frac{2}{3}+\frac{7}{12}[/tex]2) To find equivalent fractions and sum those fractions, let's factorize 3 and 12 dividing them only by Prime Numbers, when one of those numbers can't be divided then we repeat it below:
As we can see on the first line, 12 can be divided by 2 and 3 cannot.
So we repeat 3 on the line below.
We then picked 6 and divided by 2, and then repeated below 3.
Then divided3 by 3
3) Now we can rewrite 2/3 + 7/12 as:
So using the Least Common Denominator we have 2/3 (8/12) and 7/12 (7/12) as their equivalent fractions. Note that 7/12 in this case is equivalent to itself.
Hello. I think that I'm overthinking this. I'm pretty sure it's a monomial?
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The expression 5x⁶ - x⁴ is a binomial because we have two terms.
Even if they have the same variable x, their exponents are not the same.
If y varies inversely as x and y = 41 when x = 28, find y if x = 27. (Round off your answer to the nearest hundredth.)Answer How to enter your answer (Opens in new window) 6 Pointsy = 0y
Answers
When y varies inversely as x:
[tex]y=\frac{k}{x}[/tex]y= 41 when x=28; uses the given data to find k:
[tex]\begin{gathered} 41=\frac{k}{28} \\ \\ k=41*28 \\ \\ k=1148 \end{gathered}[/tex]Use the next formula to the given variation:
[tex]y=\frac{1148}{x}[/tex]Find y if x=27:
[tex]\begin{gathered} y=\frac{1148}{27} \\ \\ y=42.52 \end{gathered}[/tex]Answer: y=42.52Can you help me with this and break it down if you can ?
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Given:
[tex]\begin{gathered} y=3x^2\text{ + 13x -50} \\ y\text{ = 13x }-\text{ 2} \end{gathered}[/tex]Subtracting equation 2 from 1:
[tex]\begin{gathered} y-y\text{ = }3x^2\text{ + 13x - 50 -(13x - 2)} \\ 0=3x^2\text{ + 13x - 50 - 13x + 2} \\ 3x^2\text{ -48 = 0} \end{gathered}[/tex]Solving for x:
[tex]\begin{gathered} 3x^2\text{ - 48 = 0} \\ 3x^2\text{ = 48} \\ \text{Divide both sides by 3} \\ x^2\text{ = }\frac{48}{3} \\ x^2\text{ = 16} \\ \text{Square root both sides} \\ x\text{ = }\sqrt[]{16} \\ x\text{ = }\pm\text{ 4} \end{gathered}[/tex]Substituting the value of x into equation 2:
[tex]\begin{gathered} y\text{ = 13x - 2} \\ y\text{ = 13(}\pm4)\text{ - 2} \\ y\text{ = 52 - 2 } \\ =\text{ 50} \\ or\text{ } \\ y\text{ = -52 - 2} \\ =\text{ -54} \end{gathered}[/tex]Hence, the solution to the system of equations is:
(4, 50) and (-4 , -54)
This statement is false or true?Expression that contain one variable can be proven true or false by replacing the variable with a number.
Answers
The statement is false.
An expression has no value of true since it is not an equation.
Given the dot product w•w = 29, find the magnitude of w.
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Given the dot product expression as shown:
[tex]w\cdot w=29[/tex]Determine the value of 'w"
[tex]w^2=29[/tex]Take the square root of both sides to have:
[tex]\begin{gathered} \sqrt{w^2}=\pm\sqrt{29} \\ w=\pm\sqrt{29} \end{gathered}[/tex]Since we only need the magnitude of "w" and the magnitude is the positive value of the variable, hence;
[tex]|w|=\sqrt{29}[/tex]This gives the modulus of "w"
donuts at Krispy Kreme are always perfectly round. The diameter of the circular donut is 6 inches. Which of the following is closest to the circumference of the donut?
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The circumference of a donut is computed as follows:
[tex]C=\pi\cdot D[/tex]where D is the diameter of the donut. Substituting with D = 6,
[tex]\begin{gathered} C=\pi\cdot6 \\ C=18.85\text{ in} \end{gathered}[/tex]In the diagram below, AB is a diameter of the circle. If arc CB measures 98 °, find the measure of < ABC.
Answers
In this problem
arc ACB=180 degrees -----> because AB is a diameter
arc ACB=arc AC+ arc CB ----> by addition angles postulate
substitute given values
180=arc AC+98
arc AC=82 degrees
Find out the measure of angle mm by inscribed angle
mm
The answer is option APLEASE just give me the answers and not a whole defintion of every single word. I just want quick answers so I can check my work. *don't worry, this is just a math practice
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7. m and n are parallel because both alternate interior angles are equal.
8.m and n are parallel because Alternate exterior angles are equal.
9.m and n are parallel Because corresponding angles are equal.
10. m and n are parallel because corresponding and consecutive angles are equal.
11. m and n are parallel because alternate exterior angles are equal.
12.m and n are parallel because vertical (opposite) angles are equal.
Write the nth rule for each geometric sequence.5) 7, 14, 28, 56...
Answers
We have the next numbers
[tex]7,14,28,56[/tex]as we can see we have double of the previous number, so the rule is
[tex]a_n=a_{n-1}\cdot2[/tex]we need to prove the rule
[tex]a1=7[/tex][tex]a2=7\cdot2=14[/tex][tex]a3=14\cdot2=28[/tex][tex]a4=28\cdot2=56[/tex]as we can see the rule is appropriate for the geometric sequence