Answer:
{ - 2, 10 }
Step-by-step explanation:
Given
x² - 8x = 20
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 4)x + 16 = 20 + 16, that is
(x - 4)² = 36 ( take the square root of both sides )
x - 4 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 4 to both sides )
x = 4 ± 6
Thus
x = 4 - 6 = - 2
x = 4 + 6 = 10
Answer:
d is it
Step-by-step explanation:
Which of the following is an example of the law of syllogism? A. If an animal is a penguin, then it can’t fly. If an animal can’t fly, then it still may have wings. An animal may have wings. Therefore, the animal is a penguin. B. If an animal is a penguin, then it can’t fly. An animal is a penguin. Therefore, the animal can’t fly. C. If an animal is a penguin, then it can’t fly. An animal can’t fly. Therefore, the animal is a penguin. D. If an animal is a penguin, then it can’t fly. If an animal can’t fly, then it still may have wings. An animal is a penguin. Therefore, the animal may have wings. Please select the best answer from the choices provided
I believe the answer would be A.
is (0,0) a solution to this system? y ≥ x^2-4 y<2x-1
Answer:
No.
Step-by-step explanation:
To determine if the ordered pair is a solution, simply plug it into the equation and check. In other words:
[tex]y\geq x^2-4[/tex]
[tex]0\geq (0)^2-4[/tex]
[tex]0\geq -4[/tex]
This is true. 0 is greater than -4.
[tex]y<2x-1[/tex]
[tex]0<2(0)-1[/tex]
[tex]0<-1[/tex]
This is not true. 0 is greater than -1.
Thus, (0,0) is not a solution.
Answer:
(0,0) is not a solution of the given system.
Step-by-step explanation:
0≥-4 true
0>1 false
(0,0) is not a solution of the system.
Is 540171 divisible by 9?
Image is attached below.
If the sum of the digits its divisible by 9,
then the original number is divisible by 9.
Since 18 (the sum of the digits) is divisible by 9,
the number 540,171 is also divisible by 9.
Answer:
Yes, The number is divisible by 9
Step-by-step explanation:
If you divide the number by 9 you will get 60019. Also if we add the numbers we will get 18 which is also divisible by 9.
Hope this helps.
The prime factorization of K is: K = 3·5·7. List all the composite factors of K.
Answer: 105, 15, 35, 21
Step-by-step explanation:
3 x 5 x 7 = 105
3 x 5 = 15
5 x 7 = 35
3 x 7 = 21
The list of all composite factors of K are 15, 21, 35, 105.
What is Prime Number?A number which can be divisible by only 1 and the number itself, that number is said to be a Prime Number.
What is Composite Number?A number which can be divisible by factors other than 1 and itself are called Composite Numbers.
What is Prime Factorization?The process to write a number by the product of its prime numbers is called Prime Factorization.
Here given that the prime factorization of K is given by,
[tex]K=3\times5\times7[/tex]
Hence the number is [tex]K=105[/tex].
Composite factors of a number are given by the product of prime factors of that number in different combinations.
Here prime factors are 3,5,7
The composite factors are given by,
[tex]3\times5=15\\5\times7=35\\3\times7=21\\3\times5\times7=105[/tex]
Thus the composite factors of K are given by 15,21,35,105.
Learn more about Prime Factorization here -
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Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Answer:
Step-by-step explanation:
(0,5), (1,0)
(0-5)/(1-0)= -5/1= -5
y - 0 = -5(x - 1)
y = -5x + 5
Which choice is the most efficient first step to solve this set of equations?
Answer:
x + 2x = 30 is the correct answer.
Instructions: Find the following information using the given image.
Here we are trying to find the altitude
Hypotenuse: 100
Segment Adjacent to the Leg: 36
X=
Answer:
Hypotenuse: 100
Segment Adjacent to the leg: 36
x=60
Step-by-step explanation:
I submitted and it was correct
The altitude of the triangle is approximately 76.81 units.
To find the altitude of the triangle, we can use the given information:
Hypotenuse: 100
Segment adjacent to the leg: 36
Let's denote the altitude as 'h' and the other leg of the right triangle as 'x'.
Using the Pythagorean theorem, we can relate the three sides of the triangle:
[tex]h^2 + x^2 = 100^2[/tex]
We also know that the adjacent segment (36) plus the other leg (x) equals the hypotenuse (100):
36 + x = 100
From the second equation, we can solve for x:
x = 100 - 36
x = 64
Now, substitute the value of x into the Pythagorean theorem equation to solve for h:
[tex]h^2 + 64^2 = 100^2\\\\h^2 + 4096 = 10000\\\\h^2 = 10000 - 4096\\\\h^2 = 5904[/tex]
Taking the square root of both sides to solve for h:
h = √5904
h ≈ 76.81
Therefore, the altitude of the triangle is approximately 76.81.
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Instructions: Find the following information using the given image.
X=
Answer:
I think x=46 but I'm not sure, hope this helps
Nicole is trying to determine an algebraic expression to represent the amount of dog biscuits she needs to purchase for a dog show. She does not know how many dogs will attend the event but wants to have 2 biscuits per dog plus an additional 35 dog biscuits. If d represents the number of dogs, which expression represents the number of dog biscuits Nicole will need for the event? d + 5 2 d + 35 2 d 2 d minus 35
Answer:
2d + 35
Step-by-step explanation:
2 per dog (d) plus an additional 35 treats = 2d + 35
Answer:
b
Step-by-step explanation:
Help, please. Ty if you do :D
Find the value. X3-4 when x=-3?? PLEASE HELP !!!! ASAP!!!!
Answer:
The other person is correct, my bad I got mixed up with the numbers
Answer:
-31
Step-by-step explanation:
Assuming that you mean
[tex]x^3-4\\(-3)^3-4\\-27-4\\-31[/tex]
Tom, Kristen, Kaley, and Bill bought 333 granola bars to share among themselves. They divided each granola bar into 444 equal portions. Kristen ate 111 portion from each granola bar.
Answer:
Kristen had (3/4) of a granola bar in total.
Then the three other people have 2.25 granola bars to share amongst themselves.
Step-by-step explanation:
Complete Question
Tom, Kristen, Kaley, and Bill bought 3 granola bars to share among themselves. They divided each granola bar into 4 equal portions. Kristen ate 1 portion from each granola bar.
How many granola bars did Kristen eat.
Solution
4 of them bought 3 granola bars.
Then they divide each granola bar into 4 equal portions.
Each of the 3 granola bars gets divided into 4 equal portions, where each granola bar now has (4 × 1/4) portions.
Each portion is (1/4) of a granola bar.
Kristen then takes 1 portion from the 3 granola bars.
This means she had 3 × (1/4) granola bars.
Kristen had (3/4) of a granola bar in total.
Then the other three people had [3 - (3/4)] of a granola bar to share amongst themselves. It means they had (9/4) or 2.25 granola bars to share amongst themselves.
Hope this Helps!!!
Natalie is shopping for new clothes and does not want to spend more than $65. She buys one dress for $26 and wants to buy a few shirts that cost $13 each. Which inequality represents the number of shirts she can buy? A. x≥7 B. x≤7 C. x≥3 D. x≤3
Answer:
D. x ≤ 3
Step-by-step explanation:
26 + 13x ≤ 65
13x ≤ 65-26
13x ≤ 39
13x ≤ 39 ÷13
x ≤ 3
Identify the vertex of the parabola. (1, −3) (−4, 0) (−1, −3) (−3, 1)
Answer:
Vertex(-3,1)
Step-by-step explanation:
We have a graphical representation of our parabola.
Showing both the x axis and the y axis and showing the values of each point of the parabola on it.
As we can see we have some major points like point p = (-4,0)
And point q = (-1,-3)
What I want to point out is that every unit represent a two then half of it represents a one.
So the position of our vertex which is the maximum point on the graph
X axis = -3
Y axis =1
So the point our vertex is located
Vertex(-3,1)
You’re rectangular 12 feet long and 8 feet wide. Your friend’s rectangular vegetable garden 50 feet long and 10 feet wide are the garden similar?
Answer:
No
Step-by-step explanation:
For shapes to be similar, their ratios of length-to-length and width-to-width must be the same. When you divide the larger length by the smaller length and the larger width by the smaller width, do you get the same number? No, so these rectangles are not similar.
Answer:
Not similar
Step-by-step explanation:
Well let’s find the areas first.
My garden)
12*8
=96
Freind’s garden)
50*10
=500
The two gardens are not similar whatsoever.
Thus,
the two gardens are not similar.
Hope this helps :)
300=x^2+15x what is x?
Answer:
x = -26.3746, 11.3746
Step-by-step explanation:
Easiest and fastest way to solve for x is to graph x² + 15x - 300 and analyze where the graph crosses the x-axis.
Alternatively, you can use the Quadratic Formula to help solve for x.
Consider U = {xlx is a real number}.
A = {xlx € U and x + 2 > 10}
B = {x\x € U and 2x > 10}
Which pair of statements is true?
5 & A; 5 € B
6 € A; 6 & B
8 € A; 8 € B
9 € A; 9&B
Due to weather, a barge captain decides to reach her destination in two legs: one due north and one due west. On a direct route, her destination is about 1{,}8301,8301, comma, 830 miles \text{(mi)}(mi)start text, left parenthesis, m, i, right parenthesis, end text away; see the figure above. If after traveling 605 \text{ mi}605 mi605, start text, space, m, i, end text due north the captain determines it is time to head due west, how many more miles are left in the trip? (Round the answer to the nearest mile.)
Answer:
There are about 568 miles left of the trip
Step-by-step explanation:
Notice that the 830 miles direct trip would be the hypotenuse of a right angle triangle. The captain goes due North for 605 mi, and then needs to turn west.
Please see the attache image to guide you.
So the question is what is the length of the third side (x) of that right angle triangle which accounts for the distance that has to be sailed due west. So we use the Pythagorean theorem:
[tex]hyp^2=leg_1^2+leg_2^2\\830^2=605^2+x^2\\x^2=830^2-605^2\\x=\sqrt{830^2-605^2} \\x=568.22\,\,mi[/tex]
Analyze the diagram below and complete the instructions that follow.
Find the value of x.
Answer:
x=30
Step-by-step explanation:
2x=y-x
3x=y
2y=180
y=90
x=30.
6th grade RATIOS
I don’t know how this is supposed to work do I start as
3:9 or 3:4 or 4:9 or 4:3 or 9:4? How do I start?
Answer:
i would say b
Step-by-step explanation: if they all slept 4 hours a night then all 9 would have a total of 36 and a night would be 1 so 36 to 1
maria claims that any fraction located between 1/5 and 1/7 on a number line must have a denominator of 6. Enter a fraction that shows marias claim is incorrect. Choose an answer: a: 6/35 b: 13/70 c: 9/35 d: 16/70
I want to make this clear, this is NOT MY ANSWER! Someone else has already answered this question on here I'm just pasting their answer here so you can get the full details on how it was solved.
We know that 1/5 > 1/6 > 1/7
If we change the numbers to decimals we can see what decimals we can use that are between the number 1/5 and 1/7 .
1/5=.20
1/7≈.14
We can use any number between these two decimals to create a fraction. Let us use .16
.20>.16>.14
Now we can change that number to a fraction.
.16=16/100 which reduced to 4/25
Let's verify:
1/5 > 4/25 > 1/7 find LCM
35/175 > 28/175 > 25/175
One fraction that is between 1/5 and 1/7 that does not have a denominator of 6 is 4/25.
A can in the shape of a cylinder has a diameter of 6 centimeters and a height of 10 centimeters. Which measurement is closest to the total surface area of the can in square centimeters? 245.04 cm2 203.19 cm2 376.99 cm2 188.50 cm2
Answer:
245.04 cm²
Step-by-step explanation:
Use the formula for the surface area of a cylinder: 2[tex]\pi[/tex]r² + 2[tex]\pi[/tex]rh
Now, we can plug in the values:
2[tex]\pi[/tex](3)² + 2[tex]\pi[/tex](3)(10)
18[tex]\pi[/tex] + 60[tex]\pi[/tex] = 245.04
The total surface area of the can is 244.92 square centimeters which is closest to 245.04 square centimeters.
We have a can in the shape of a cylinder has a diameter of 6 centimeters and a height of 10 centimeters.
We have to determine total surface area of the can in square centimeters.
What is the formula to calculate the total surface area of a cylinder with radius 'r' and height 'h'.The total surface area of a cylinder with radius 'r' and height 'h' is given by -
A = 2πr(h + r)
According to the question, we have -
diameter of can = 6 cm
Then, the radius will be (r) = 6/2 = 3 cm
Height of can (h) = 10 cm
Substituting the values, we get -
A = 2 x 3.14 x 3 (10 + 3)
A = 2 x 3.14 x 3 x 13
A = 6 x 13 x 3.14
A = 78 x 3.14
A = 244.92 square centimeters.
Hence, the total surface area of the can is 244.92 square centimeters which is closest to 245.04 square centimeters.
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Which is the graph of the sequence defined by the function f(x) = 100(0.5)x - 1?
Answer:
Step-by-step explanation:
The graph choices have not been posted.
There is also a doubt as to what is really wanted, is it
A. f(x) = 100(0.5)^x - 1
or
B. f(x) = 100(0.5)^(x - 1)
I have included a graph for each. Feel free to make a choice between the two, A is red, and B is blue.
Answer:
it's B
Step-by-step explanation:
i literally just did it on ed
∠ADB and ∠BDC represent a linear pair because points A, D, and C lie on a straight line. Calculate the sum of m∠ADB and m∠BDC. Then move point B around and see how the angles change. What happens to the sum of m∠ADB and m∠BDC as you move point B around?
Answer:
Hello There. ☆°~-----__▪●▪__-----~°☆
If points A, D and C lie on a straight line, then angles ∠ADB and ∠BDC are supplementary angles and
m\angle ADB+m\angle BDC=180^{\circ}.
1. If you move point B right from the initial position, then m∠ADB increases and m∠BDC decreases, but m\angle ADB+m\angle BDC=180^{\circ}.
2. If you move point B left from the initial position, then m∠ADB decreases and m∠BDC increases, but m\angle ADB+m\angle BDC=180^{\circ}.
3. When point B lie on the line ADC, then:
a. Point B lies on the right hand from point D: m\angle ADB=180^{\circ} \\m\angle BDC=0^{\circ} ;
b. Point B lies on the left hand from point D: m\angle ADB=0^{\circ} \\m\angle BDC=180^{\circ} .
4. When point B is reflected about the line ADC situation is the same as in parts 1 and 2.
Hope It Helps!~ ♡
ItsNobody~ ☆
Answer:
The sum of m∠ADB and m∠BDC remains the same: m∠ADB + m∠BDC = 180°.
Step-by-step explanation:
PLATO answer.
A regular four-sided die and a regular eight-sided die are rolled to form a sum. a) Determine the probability distribution for the sum of the two dice. Show Steps b) Create a frequency histogram for the probability distribution. c) Determine the expected sum of the two dice.
Answer:
4+8=12 so,if its 12 so
Step-by-step explanation:
the some will be 12
12-8=4
12-4=8
the population of a town increases by 4 % every year . In the last year the population of the town was 110000.
Find the present population of the town .
Find the population of the town in the next year
Answer:
114,400 and 118,976.
Step-by-step explanation:
Let's represent this using a function. Let's let:
[tex]P(y)[/tex] represent the total population, and [tex]y[/tex] represent the total number of years since last year.
We know that the population grows by 4% every year or 0.04 every year. This is exponential growth. We can write this as:
[tex]P(y)=110000(1.04)^y[/tex]
Note that the coefficient is 110000 because that is the year we are starting with. Also, note that it is 1.04 because we are essentially adding .04 to the original population.
Anyways, to find the present population, set y equal to 1 (because 1 year after last year is the present year)
[tex]P(1)=110000(1.04)^1=114400[/tex]
The present population is 114,400 people.
For next year, set y equal to 2 (2 years after last year is next year)>
[tex]P(2)=110000(1.04)^2=118976[/tex]
The population next year will be 118,976 people.
PLEASE ANSWER THIS FAST IM BEGGING YOU A student worked the following problem: Solve: 2(10x + 3) − x = 44 Their work is shown below: Step 1: 20x + 6 − x = 44 Step 2: 19x + 6 = 44 Step 3: 19x = 38 Step 4: x = 2 Which of the following statements is correct? There is an error in Step 1. There is an error in Step 2. There is an error in Step 3. No errors were made. The problem was worked correctly.
Answer:
3. No errors were made. The problem was worked correctly.
Step-by-step explanation:
2(10x + 3) − x = 44
Distribute
20x +6 -x =44
Combine like terms
19x +6 = 44
Subtract 6 from each side
19x =38
Divide by 19
19x/19 =38/19
x =2
how many solutions do y=3x-4 y=-2x+7
Answer:
One.
Step-by-step explanation:
It is a linear equation. This means that x is raised to the first power, which there can only be one solution.
Answer:
Hi, the correct answer to your question is Y,X would be (29,11)
ONE SOLUTION
Step-by-step explanation:
First you have to... solve for y
Y equals 2x+7
Next you have to use the variable y and put in into an equation.
2x+7 - 3x = -4 (Also) :) - x = -11
Now you have to solve the equation for the variable x
Which will be 11 (x will be 11)
Finally you have to use x to solve for y
2(11)+7 = 29
Now we have 11 and 29 so the answer to your question will be
= (29,11)
Also this means it has one solution
Btw this is a linear equation...
Hope this helps you! :)
help plz i will make a brainllest quick
plzzz
Answer:
a
Step-by-step explanation:
Answer:
the answer is a.
Step-by-step explanation:
I did this one.
In a causal-comparative study, what is the difference between independent variables and dependent variables? independent variables cause the effect measured in the dependent variables dependent variables cause the effect measured in the independent variables dependent variables are those that affect each other; independent variables do not independent variables exist before the study; dependent variables do not
Answer: independent variables cause the effect measured in the dependent variables
Step-by-step explanation: In a causal - comparative study, the dependent variables refers to the variable whose changes is being measured or observed. The changes or alteration of the dependent variable is induced by the different values of the independent variable. In causal - comparative study, the different independent variables is assumed to have a direct impact on the output or values of the dependent variable which is measured by the experimenter. Therefore, the independent variable does not change, but causes the observed changes noticed in the dependent variable.