Answer:
x = -3 , y = 2
Step-by-step explanation:
Solve the following system:
{y - 2 x = 8 | (equation 1)
{-3 x - y = 7 | (equation 2)
Swap equation 1 with equation 2:
{-(3 x) - y = 7 | (equation 1)
{-(2 x) + y = 8 | (equation 2)
Subtract 2/3 × (equation 1) from equation 2:
{-(3 x) - y = 7 | (equation 1)
{0 x+(5 y)/3 = 10/3 | (equation 2)
Multiply equation 2 by 3/5:
{-(3 x) - y = 7 | (equation 1)
{0 x+y = 2 | (equation 2)
Add equation 2 to equation 1:
{-(3 x)+0 y = 9 | (equation 1)
{0 x+y = 2 | (equation 2)
Divide equation 1 by -3:
{x+0 y = -3 | (equation 1)
{0 x+y = 2 | (equation 2)
Collect results:
Answer: {x = -3 , y = 2
The solution to the system of equations -2x + y = 8 and -3x - y = 7 is (x, y) = (-3, 2). The correct answer is option A.
Let's use the elimination method:
-2x + y = 8
-3x - y = 7
By adding the two equations together, we can eliminate the y variable:
(-2x + y) + (-3x - y) = 8 + 7
-2x - 3x + y - y = 15
-5x = 15
Dividing both sides by -5, we get:
x = -3
Now, substitute this value of x back into one of the original equations. Let's use -2x + y = 8:
-2(-3) + y = 8
6 + y = 8
y = 8 - 6
y = 2
Therefore, the solution to the system of equations -2x + y = 8 and -3x - y = 7 is (x, y) = (-3, 2).
Therefore, the correct answer is option A.
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The complete question is as follows:
The system of linear equations -2x+y=8 and -3x-y=7 is graphed below. What is the solution to the system of equations?
A. (–3, 2)
B. (–2, 3)
C. (2, –3)
D. (3, 2)
How many students tired out for the volleyball team is this a statistical or no
That question is not a statistical question since there will be only one answer. If it were to be statistical it would have multiple answers an example of that type of question would be, Why did you decide to try out for the volleyball team? This is statistical because some could say they joined for fun, credits, to do something active, etc.. there would be multiple answers. Your question, How many students tried out for the volleyball team isn't statistical since it will have one answer such as, 26 students, 15 student, 2 students, etc...
Hope this helped!
The question about how many students tried out for a volleyball team relates to statistics. It involves collecting, analyzing, and interpreting numerical data. For example, the number of students trying out for the team can be used as statistical data.
Explanation:The question 'How many students tried out for the volleyball team?' is one that relates to statistics. This is because it seeks to gather numerical data (in this case, the number of students) related to a specific event (trying out for the volleyball team). Therefore, the process of answering this question would involve collecting, analyzing, interpreting, presenting, or organizing this data.
For instance, let's say that 30 students tried out for the volleyball team. This count is a piece of statistical data which may be further used to compare with previous years, calculate percentages, or make projections for following years.
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The scores on a test are normally distributed with a mean of 110 and a standard deviation of 22. What is the score that is 3 standard deviations below the mean?
Answer:
Step-by-step explanation:
If the mean is 110, and the standard devaition is 22,
1 standard dev. below the mean is 110-22
2 standard dev below the mean is 110-22-22
3 standard dev below the mean is 110-22-22-22
Hope that helps!
The score that is 3 standard deviations below the mean will be 44.
What is the z-score?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The scores on a test are normally distributed with a mean of 110 and a standard deviation of 22.
Then the score that is 3 standard deviations below the mean will be
The first standard deviation below the mean will be
⇒ 110 - 22
⇒ 88
The second standard deviation below the mean will be
⇒ 110 - 22 - 22
⇒ 66
The third standard deviation below the mean will be
⇒ 110 - 22 - 22 - 22
⇒ 44
More about the z-score link is given below.
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how do you solve 5x³ divided by (5x) ³?
Answer:
[tex]\frac{1}{25}[/tex]
Step-by-step explanation:
note that (5x)³ = 5³x³ = 125x³
Hence
[tex]\frac{5x^3}{125x^3}[/tex]
Cancel the x³ on numerator/denominator and divide the 5 and 125 by 5
= [tex]\frac{1}{25}[/tex] ← in simplified form
ILL GIVE BRAINLIEST PLS HELP ME
When a system of equations appears on a graph, what are the characteristics of a system with one solution? No solution? Infinite solutions?
One solution
The two (or more) equations would only intersect once
No solution
Lines never intersect
The lines are parallel
Infinite solutions
The lines are the exact same
That’s all the characteristics I know
Does anyone know ? Reply
Answer: When I converted it on a calculator it gave me 3/125 hope that is what you were looking for.
Step-by-step explanation:
Answer:3 over 125
plzz give brainliest i am 100% sure
Step-by-step explanation:
Steps to convert decimal into fraction
Write 0.024 as
0.024
1
Multiply both numerator and denominator by 10 for every number after the decimal point
0.024 × 1000
1 × 1000
=
24
1000
Reducing the fraction gives
3
125
The type of transformation PQRS undergoes is a . If vertex Q is at (-4, -5), then vertex Q′ is at ?
Answer:
(-4, -5) it gives the answer in the question
Step-by-step explanation:
A quadratic equation of the form 0=ax^2+bx+c has a discriminate value of -16. How many real number solutions does this equation have?
Answer:
0
Step-by-step explanation:
The disciminant [tex]\Delta[/tex] tells you how many real solutions a quadratic equation has, depending on its sign:
[tex]\Delta>0\implies\text{2 solutions}\\\Delta=0\implies\text{1 solution}\\\Delta<0\implies\text{no solutions}[/tex]
ANSWER
0
EXPLANATION
The discriminant of a quadratic equation in the form
[tex]a {x}^{2} + bx + c = 0[/tex]
is given by
[tex]D = {b}^{2} - 4ac[/tex]
The discriminant of a quadratic equation tells us the nature of the roots of that quadratic equation.
If the discriminant is negative, the equation has no real roots.
If the discriminant us positive, the equation has two real roots.
If the discriminant is zero, the equation has a repeated root.
Since the discriminant is -6, the equation has no real roots.
In other words, the number of real roots is 0.
A normal distribution has mean = 56.3 cm, and
84% of the data fall above 50.2 cm. Find the standard
deviation.
Answer:99.7 percent
Step-by-step explanation:
For a data set with a symmetric distribution , approximately 68.3 percent of the values will fall within one standard deviation from the mean, approximately 95.4 percent will fall within 2 standard deviations from the mean, and approximately 99.7 percent will fall within 3 standard deviations from the mean.
Please simplify this expression thanks
Answer:
Step-by-step explanation:
Factor numerator: x^2 + x - 12 = (x + 4)(x - 3)
Factor denominator: x^2 + 7x + 12 = (x + 3)(x + 4)
Notice that the numerator and denominator have a common factor (x + 4).
They can cancel.
What is left is (x - 3)/(x + 3)
Triangle XYZ is translated 4 units up and 3 units left to yield ΔX'Y'Z'. What is the distance between any two corresponding points on ΔXYZ and ΔX'Y'Z′
Answer:
The distance between any two corresponding points on ΔXYZ and ΔX'Y'Z′ is equal to [tex]5\ units[/tex]
Step-by-step explanation:
we know that
To find the distance, apply the Pythagoras Theorem
Let
x ----> the distance between any two corresponding points on ΔXYZ and ΔX'Y'Z′
[tex]x=\sqrt{4^{2}+3^{2}} \\ \\x=\sqrt{25}\ units\\ \\x=5\ units[/tex]
If you subtract 12 from my number and multiply the difference by-3 the result is -54 what is my number
first, make an equation:
[tex] - 54 = - 3x - 12[/tex]
then, add twelve to both sides to remove it from the right:
[tex] - 42 = - 3x[/tex]
then just divide by (-3) to get the value of x:
[tex]x = 14[/tex]
The student's question involves setting up and solving a simple algebraic equation. By following the order of operations and isolating the variable, we find that the unknown number is 30.
To solve the problem stated, 'If you subtract 12 from my number and multiply the difference by -3 the result is -54', let's establish a variable to represent the unknown number. Let's call this number 'x'. According to the problem, we need to perform two operations on this number:
1. Subtract 12 from the number x. 2. Multiply the result by -3, which should result in -54.
This establishes the equation:
(x - 12) × -3 = -54
To find x, we'll follow these steps:
Divide both sides of the equation by -3 to isolate the term (x - 12): (x - 12) = -54 / -3 (x - 12) = 18
Add 12 to both sides of the equation to solve for x: x - 12 + 12 = 18 + 12 x = 30
Therefore, the number we're looking for is 30.
The triangles in the image are similar.
Solve for x.
A) 7
B) 6
C) 10
D) 5
ANSWER
A) 7
EXPLANATION
The given triangles are similar
Hence the corresponding sides are in the same proportion.
[tex] \frac{3x + 4}{30} = \frac{30}{36} [/tex]
Simplify the right hand side:
[tex]\frac{3x + 4}{30} = \frac{5}{6}[/tex]
Cross multiply;
6(3x+4)=5×30
Expand
18x+24=180
18x=150-24
18x=126
[tex]x = \frac{126}{18} = 7[/tex]
Which of the following statements are true?
Answer:
option A and B are correct.
Step-by-step explanation:
Given: [tex]p(t) = \frac{64}{1 + 11e^{-.08t} }[/tex]
Option A: [tex]\lim_{t \to \infty} \frac{64}{1 + 11e^{-.08(\infty)} } = \frac{64}{1 + 0} = 64[/tex]
Option A is true,
Option B: [tex]P(0) = \frac{64}{1 + 11} = 5.33[/tex]
Option B is also true.
Option C:
[tex]P(t + 1) = \frac{64}{1 + 11e^{-.08(t + 1)} } = \frac{64}{1 + 10.15e^{-.08t} } \\1.08 · P(t) = \frac{64 · 1.08 }{1 + 11e^{-.08t} } = \frac{69.12}{1 + 11e^{-.08t} }[/tex]
P(t + 1) ≠ 1.08 · P(t)
Option C is incorrect.
Option D: It is also incorrect, because according to option 2 earth's population will not grow exponentially without Bound.
The probability it will snow in the next two weeks is 1/12 for this week and 1/4 for next week.
What is P(snow this week, then snow next week)?
Answer:
1/48
Step-by-step explanation:
The probability of both happening is equal to the product of each probability.
P(A and B) = P(A) × P(B)
P = 1/12 × 1/4
P = 1/48
Answer:
i agree that the answer is 1/48
Step-by-step explanation:
which of the following is a zero from the function f(x)=(x+3)(x-7)(x+5)? X=-7, X=-3, X=3, X=5
Answer:
x = - 3
Step-by-step explanation:
To find the zeros set f(x) = 0, that is
(x + 3)(x - 7)(x + 5) = 0
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 7 = 0 ⇒ x = 7
x + 5 = 0 ⇒ x = - 5
How many possible 7 digit phone numbers can be created from the digits 0 through 9 if numbers cannot be repeated and the first number cannot equal 0?
A.181,440
B.544,320
C.604,800
D.10,000,000
Please select the best answer from the choices provided
A
B
C
D
The correct answer is C. 604,800.
To calculate this, we can use the formula for permutations:
P(n, k) = n! / (n-k)!
In this case, we have 9 digits (0-9), and we want to create a 7-digit phone number. Since the first digit cannot be 0, we have 9 choices for the first digit, and 9 remaining choices for each subsequent digit (since numbers cannot be repeated).
So, the total number of possible phone numbers is:
P(9, 7) = 9! / (9-7)! = 9 × 8 × 7 × 6 × 5 × 4 × 3 = 604,800
Therefore, the correct answer is C. 604,800.
Use a half-angled identity to find the exact value of sin 75 degrees
Answer:
[tex]\sin 75\degree=\frac{\sqrt{2+\sqrt{3}}}{2}[/tex]
Step-by-step explanation:
The haf-angle formula is given by:
[tex]\sin \frac{1}{2}\theta =\sqrt{\frac{1-\cos \theta}{2} }[/tex]
[tex]\sin 75\degree=\sin \frac{1}{2}(150\degree)[/tex].
This implies that:
[tex]\sin \frac{1}{2}(150\degree) =\sqrt{\frac{1-\cos 150\degree}{2} }[/tex]
[tex]\sin \frac{1}{2}(150\degree) =\sqrt{\frac{1--\frac{\sqrt{3}}{2}}{2}}[/tex]
[tex]\sin \frac{1}{2}(150\degree) =\sqrt{\frac{2+\sqrt{3}}{4}}[/tex]
We simplify the square root to obtain:
[tex]\sin \frac{1}{2}(150\degree)=\frac{\sqrt{2+\sqrt{3}}}{2}[/tex]
Answer:
[A] [tex]\frac{\sqrt{2 + \sqrt{3} } }{2}[/tex]
Just need question # 12. Thanks
There are two lines from the center of the circle labeled 5.
The lines at 90 degrees from the 5 are chords. Because both lines are the same distance from the center they are the same length.
The one on the top is labeled as 9, so the line on the bottom is also 9 units long.
X is half the length, so would b 9 /2 = 4.5 units long.
Which of the binomials below is a factor of this trinomial?
4x2 + 21x + 5
Answer:
B. 4x + 1
Step-by-step explanation:
4x^2 + 21x + 5
= (4x + 1)(x + 5)
Factors of this trinomial are (4x + 1) and (x + 5)
Answer
(4x + 1)
Answer:
4x+1
Step-by-step explanation:
just toook the test
Please help! The figure is a rhombus, and I am trying to find the measure of angle ADB
Answer:
86 - 9x
Step-by-step explanation:
In a rhombus, adjacent angles are supplementary. So:
∠ADE + ∠EDC + ∠DCE + ∠ECB = 180
Also, the diagonals of a rhombus are perpendicular. Since the sum of a triangle's angles add up to 180:
∠EDC + 90 + ∠DCE = 180
∠EDC + ∠DCE = 90
Substituting:
∠ADE + 90 + ∠ECB = 180
∠ADE + ∠ECB = 90
∠ADE + 9x + 4 = 90
∠ADE = 86 - 9x
∠ADB is the same as ∠ADE, so the answer is 86 - 9x.
Angle ∠ADB is 41°.
RhombusIt is a polygon that has four sides and four corners. The sum of the internal angle is 360 degrees. In Rhombus opposite sides are parallel and all sides are equal. And its diagonals intersect at the right-angle.
Given
A rhombus ABCD,
∠DCA = 13x - 16
∠ACB = 9x + 4
To findThe measure of ∠ADB.
How to get the measure of ∠ADB?We know that the angle ∠DCA and ∠ACB are equal.
13x - 16 = 9x + 4
13x - 9x = 4 + 16
4x = 20
x = 5
So the angle ∠DCA and ∠ACB will be
∠DCA = 13x - 16 = 64 - 16 = 49
∠ACB = 9x + 4 = 45 + 4 = 49
The sum of the internal angle is 360 degrees
∠ABC + ∠BCD + ∠CDA + ∠DAB = 360
∠CDA + ∠BCD + ∠CDA + ∠BCD = 360
∠ABC + ∠BCD = 180
∠CDA + 98 = 180
∠CDA = 82
So we know
2 x ∠ADB = ∠CDA
2 x ∠ADB = 82
∠ADB = 41
Thus, Angle ∠ADB is 41°.
More about the rhombus link is given below.
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Find the area of the rhombus.
Please need help
Answer:
96cm2
Step-by-step explanation:
Area of rhombus=1÷2×d1×d2
=1÷2×12×16
=96
96cm². The are of the rhombus of the image is 96cm².
The key to solve this exercise is breaking down the rhombus in four equals right triangles, each triangle has the sides 10cm, 8cm and 6cm. We can calculate the area of one right triangle and multiply by 4 in order to get the total area of the rhombus.
The area of a triangle is [tex]A_{t}=\frac{bxh}{2}[/tex] where b is the base and h is the height.
The base of the one right triangle is 8cm and the height is the leg adyacent to the right angle that is 6cm. Calculating the area of the right triangle:
[tex]A_{t}=\frac{8cmx6cm}{2}=\frac{48cm^{2} }{2} =24cm^{2}[/tex]
The total area of the rhombus is [tex]A = 4A_{t}[/tex]
[tex]A = 4x24cm^{2}=96cm^{2}[/tex]
a.
8 + 12 + 16 + 20; 56
c.
8 + 12 + 16 + 20; 120
b.
8 + 16 + 32 + 64; 56
d.
8 + 16 + 32 + 64; 120
Answer:
a. 8 + 12 + 16 + 20; 56Step-by-step explanation:
[tex]\sum\limits_{k=2}^54k\\\\\text{Make a sum with components equal to 4k,}\\\text{ where k = 2, k = 3, k = 4 and k = 5}:\\\\4(2)=8\\4(3)=12\\4(4)=16\\4(5)=20\\\\8+12+16+20=56[/tex]
Can someone plz help me.
Answer:
1) (-2)+3
-2+3
=1
2) (-14)+(-7)
-14-7
=-21
3) 3-(-8)
3+8
=11
4) (-9)+14
-9+14
=5
5) (-8)-(-2)
-8+2
=-6
6) 5+(-8)
5-8
=-3
7) (-27)-24
-27-24
=-51
8) (-41)+(-40)
-41-40
=-81
9) 38-(-17)
38+17
=55
10) (-44)+(-9)
-44-9
=-53
11) (-16)-(-36)
-16+36
=20
12) (-6)-24
-6-24
=-30
hope this helps :)
Evaluate 3x3y?, if x=-2 and y=-1
Answer:
18
Step-by-step explanation:
(3x)(3y)
= (3)(-2)(3)(-1)
= 18
Can someone help me with this. Ill post a picture of everything.
Answer:
DCD, CDCStep-by-step explanation:
DDD
DDC
DCDCDD
CCC
CCD
CDCDCC
What is the solution to 3/(2x+1) = 9/3x?
Answer:
Solution x = - 1
Step-by-step explanation:
3 / (2x+1) = 9 / 3x
Cross multiply
3(3x) = 9(2x + 1)
Distributive property
9x = 18x + 9
Subtract 18x from both sides
-9x = 9
Divide both sides by -9
x = -1
HEEEELLLLLPPPPPP PPPPPLLLLLLZZZZZZ
Answer:
(6,4)
Step-by-step explanation:
y = x-2
y =4
Set the two equations equal
x-2 =4
Add 2 to each side
x-2+2 = 4+2
x =6
Now we need to find y
y =4
(6,4)
Answer:
Step-by-step explanation:
For question 4, the top equation has an x and a y value in it. The second equation is just a y value. So put the 4 into the top equation.
4 = x - 2 Add 2 to both sides
4 + 2 = x -2 + 2
6 = x
You can actually graph this to show that the solution set is (6,4) The solution set is marked (6,4).
The read line is y = x - 2
The blue line is y = 4
A pet store sells puppies and kittens in the ratio 5 : 4.
If their sales of puppies and kittens combined came to 36, how many puppies did they sell?
I found it by random. You times the ratio by 4 to get 36 puppies and kittens combined.
If the puppies was 5 then 5 x 4 = 20 puppies in their sales.
If the puppies was 4 then 4 x 4 = 16 puppies in their sales.
I couldn't tell if the ratio was in the according order of puppies and then kittens or if that was just saying what the ratio was about.
Let us consider the ratio to be x
So, as per the question's statement, we can write it as;
[tex]5x+4x=36[/tex]
⇒[tex]9x=36[/tex]
We will divide 9 on both the sides, we get;
⇒[tex]x=\frac{36}{9}=4[/tex]
So, for getting the number of puppy sold we have to multiply it with 5, we get;
[tex]5x=5*4=20[/tex]
They have sold 20 puppies.
Hence, the answer is [tex]20[/tex] puppies.
How do you calculate a ratio?
Divide data A by data B to find your ratio. In the example above, 5/10 = 0.5. Multiply by 100 if you want a percentage. If you want your ratio as a percentage, multiply the answer by 100
How to simplify a ratio?Ratios can be fully simplified just like fractions. To simplify a ratio, divide all of the numbers in the ratio by the same number until they cannot be divided any more
.Learn more about ratios, refer to:
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Find the solution set of the inequality 14- 3x < -1.14
Final answer:
To solve the inequality 14 - 3x < -1.14, subtract 14 from both sides, then divide by -3 and remember to reverse the inequality, resulting in the solution set x > -5.05.
Explanation:
To find the solution set of the inequality 14 - 3x < -1.14, follow these steps:
Subtract 14 from both sides of the inequality: -3x < -1.14 - 14.Now, the inequality looks like -3x < -15.14.Divide both sides of the inequality by -3, remembering that dividing by a negative number reverses the inequality: x > 15.14 / -3.The solution is x > -5.05.Therefore, the solution set for the inequality is all real numbers greater than -5.05.
Which graph represents the function f(x) 2x-1/x-1 f(x) 2x-1/x-1
Answer:
See attached file
Step-by-step explanation: