To solve this, you need to isolate/get the variable "x" by itself in the equation:
-3(x + 5) = -9 Distribute/multiply -3 into (x + 5)
(-3)x + (-3)5 = -9
-3x - 15 = -9 Add 15 on both sides
-3x - 15 + 15 = -9 + 15
-3x = 6 Divide -3 on both sides to get "x" by itself
[tex]\frac{-3x}{-3} =\frac{6}{-3}[/tex]
x = -2
I just realized I took unnecessary steps....you could've just divided -3 then subtracted 5
-3(x + 5) = -9 Divide -3 on both sides [two negative signs cancel each other out and become positive]
x + 5 = 3 Subtract 5
x = -2
12abx square - (9a square - 8b square)x - 6ab =0
The value of x is [tex]\frac{3a}{4b}[/tex] and [tex]-\frac{2b}{3a}[/tex]
Explanation:
The expression is [tex]12abx^{2} -(9a^{2} -8b^{2} )x-6ab=0[/tex]
Multiplying the term x withing the bracket, we get,
[tex]12abx^{2} -9a^{2} x+8b^{2} x-6ab=0[/tex]
Grouping the terms, we have,
[tex](12abx^{2} -9a^{2} x)+(8b^{2} x-6ab)=0[/tex]
Taking out the common terms in each bracket, we get,
[tex]3ax(4bx -3a)+2b(4bx-3a)=0[/tex]
Simplifying, we get,
[tex](3ax+2b)(4bx -3a)=0[/tex]
Equating each term to zero, we get,
[tex]\begin{aligned}3 a x+2 b &=0 \\3 a x &=-2 b \\x &=-\frac{2 b}{3 a}\end{aligned}[/tex] and [tex]\begin{aligned}4 b x-3 a &=0 \\4 b x &=3 a \\x &=\frac{3 a}{4 b}\end{aligned}[/tex]
Hence, the values of x is [tex]\frac{3a}{4b}[/tex] and [tex]-\frac{2b}{3a}[/tex]
Which number line represents the solutions to |x – 5| = 1?
Answer:
x = 4, 6
Step-by-step explanation:
The line would go from 4 to 6 with closed circles at each point
(Add images of the lines provided if you need clarification)
(12 r) (r 6) m=2
PLEASE HELP AND SHOW YOUR WORK!!!!
Answer:
seems like you need to learn how to do your own work.
Step-by-step explanation:
Ask instructor for help or go back to the book
Which number is a common factor of 32, 48. and 80?
12
10
8
9
Answer:
8 because 32÷8=4,48÷8=6,80÷8=10
The sum of two numbers is 14. Their difference is –146. Find the numbers.
Answer:
-66, 80
Step-by-step explanation:
Let x represent the first number. Then the second number is 14-x, and the difference is ...
x - (14-x) = -146
2x = -132 . . . . . . add 14, collect terms
x = -66 . . . . . . . . the first number
14-x = 14-(-66) = 80 . . . . . . the second number
Answer:
-66 & 80
Step-by-step explanation:
Let the two numbers be x and y
x + y = 14 (1)
x - y = -146 (2)
Adding (1) & (2),
2x = -132
x = -66
y = 14 - x = 14 - (-66) = 14 + 66
y = 80
What is the value of x in the equation 4 and StartFraction 3 Over 10 EndFraction minus (2 and two-fifths x + 5 and one-half) = one-half (negative 3 and three-fifths x + 1 and one-fifth)?
The value of x is –3.
Solution:
Given statement:
4 and Start Fraction 3 Over 10 End Fraction minus (2 and two-fifths x + 5 and one-half) = one-half (negative 3 and three-fifths x + 1 and one-fifth)
Let's convert this into algebraic expression.
[tex]$4\frac{3}{10} -\left(2\frac{2}{5}x+5\frac{1}{2}\right)=\frac{1}{2}\left(-3\frac{3}{5}x+1\frac{1}{5}\right)[/tex]
First convert mixed fraction into improper fraction.
[tex]$\frac{43}{10} -\left(\frac{12}{5}x+\frac{11}{2}\right)=\frac{1}{2}\left(-\frac{18}{5}x+\frac{6}{5}\right)[/tex]
[tex]$\frac{43}{10} -\frac{12}{5}x-\frac{11}{2}=-\frac{18}{10}x+\frac{6}{10}[/tex]
Now, take LCM and make the denominators same.
LCM of 2, 5, 10 = 10
[tex]$\frac{43}{10} -\frac{12\times2}{5\times2}x-\frac{11\times5}{2\times5}=-\frac{18}{10}x+\frac{6}{10}[/tex]
[tex]$\frac{43}{10} -\frac{24}{10}x-\frac{55}{10}=-\frac{18}{10}x+\frac{6}{10}[/tex]
Arrange like terms one side of the equation.
[tex]$\frac{18}{10}x -\frac{24}{10}x=\frac{6}{10}-\frac{43}{10}+\frac{55}{10}[/tex]
[tex]$\frac{18x-24x}{10} =\frac{6-43+55}{10}[/tex]
[tex]$\frac{-6x}{10} =\frac{18}{10}[/tex]
[tex]$-6x=\frac{18\times10}{10}[/tex]
[tex]$-6x=18[/tex]
Divide both sides of the expression by –6, we get
⇒ x = –3
Hence the value of x is –3.
Answer:
-3
Step-by-step explanation:
Give a real world example for a system of equations! Max points!!!
Answer:
likewise your friend is two times older than u and u r two times younger than him then assume the given sum as 120 so your friend"s age will be 2x and ur age will be y so the sum obtained Is 2x+y=120
Answer: Alex had 8 apples to share Amon him and three of his friends. What is 8 / 4 ? It is 2
Step-by-step explanation:
2 with an exponent of -2
Answer:
0.25
Step-by-step explanation:
2^-2=0.25
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-4, -2), B(-2, -2), C(-2, 7)C(−2,7)C, D(-4, 7
What is the area of rectangle ABCD?
Answer:
The area of rectangle ABCD is [tex]18\ units^2[/tex]
Step-by-step explanation:
Plot the figure to better understand the problem
we have the vertices
A(-4, -2), B(-2, -2), C(-2, 7), D(-4, 7)
see the attached figure
The area of the rectangle is equal to
[tex]A=LW[/tex]
where
L is the length
W is the width
In this problem we have
[tex]L=BC=7-(-2)=9\ units[/tex] ---> difference of the y-coordinates
[tex]W=AB=-2-(-4)=2\ units[/tex] ---> difference of the x-coordinates
substitute
[tex]A=(9)(2)=18\ units^2[/tex]
Final answer:
The area of rectangle ABCD is calculated as 18 square units by finding the product of its width (2 units) and height (9 units).
Explanation:
The area of rectangle ABCD with vertices A(-4, -2), B(-2, -2), C(-2, 7), and D(-4, 7) can be calculated by finding the lengths of the sides AB and BC. The length of AB (width) is the difference in the x-coordinates of A and B, which is |-2 - (-4)| = 2.
The length of BC (height) is the difference in the y-coordinates of B and C, which is |7 - (-2)| = 9. Therefore, the area of rectangle ABCD is the product of the width and height, which is 2 * 9 = 18 square units.
Water tank A has a capacity of 550 gallons and is 66% full. Water tank B is 53% full. The ratio of the capacity of Tank A to Tank B is 11:15.
How much water is in Tank A?
363 gallons of water is in Tank A
Solution:
Water tank A has a capacity of 550 gallons and is 66% full
Let, w = 550
p = 66 % = 0.66
The percent equation is: a = p . w
where,
"a" is the gallons of water in Tank A
p is the percent in fraction or decimal form
w is the capacity of tank A
Therefore,
[tex]a = 0.66 \times 550\\\\a = 363[/tex]
Thus 363 gallons of water is in Tank A
When Rosa tripped and fell into a muddy puddle at lunch (she was so embarrassed!), she knew
exactly what would happen: within ten minutes, the two girls who saw her fall would each tell
four people what they had seen. Within the next ten minutes, those eight students would each
tell four more people. Rosa knew this would continue until everyone in the entire school was
talking about her muddy experience. If there are 2016 students in the school, how many
"generations” of gossiping would it take before everyone in the school was talking about Rosa?
How many minutes would it take? Graph the situation.
Explanation of the number of generations and minutes it would take for gossip to reach everyone in a school.
Explanation:The total number of students in the school: 2016
Number of students each person tells: 4
Generations needed: Log base 4 of 2016 is approximately 4.033.
Number of minutes: Each generation is 10 minutes, so 4.033 generations would be approximately 40.33 minutes.
Graph: As the number of generations increases, the number of people reached grows exponentially.
Given the system
2X + 3Y = 18
-2X + 5Y = 14
Explain how you would solve this system using combination. Give the solution as a coordinate pair (X,Y)
2. Given the system
3x + 4y = 5
2x +7y = 12
Explain how you would solve this system using combination. Give the solution as a coordinate pair (X,Y)
Answer:
1.Therefore the solution of given system is (3,4)
2.Therefore the solution of given system is (-1,2)
Step-by-step explanation:
1.
Given the system
2x +3y =18...........(1)
-2x+5y =14...........(2)
Adding the equation (1) and (2)
2x+3y-2x+5y= 18+14
⇔8y = 32
⇔[tex]y = \frac{32}{8}[/tex]
⇔y = 4
Putting the value of y in equation (1)
2x + 3. 4=18
⇔2x+12 =18
⇔2x = 18-12
⇔2x = 6
⇔x =3
Therefore the solution of given system is (3,4)
2.
Given the system
3x +4y = 5..........(a)
2x +7y =12...........(b)
Equation (a) ×2 - equation (b)×3
2(3x+4y)- 3(2x+7y) = 2.5 -12.3
⇔6x + 8y -6x -21y = 10-36
⇔ -13y = -26
⇔[tex]y=\frac{-26}{-13}[/tex]
⇔y = 2
Putting the value of y in equation (a)
3x +4.2 =5
⇔3x = 5 -8
⇔3x = -3
⇔x = -1
Therefore the solution of given system is (-1,2)
In triangle VWX, VW = 4.5 inches, WX = 5.9 inches, Measure of angle W = 28 degrees, and Measure of angle X = 47 degrees. If Triangle P Q R is congruent to triangle W V X, which statement is true?
a.QR = 4.5 cm
b.QR = 5.9 cm
c.Measure of angle R = 28 degrees
d.Measure of angle R = 47 degrees
The true statement about triangle is: b. QR = 5.9 cm.
To understand what it means for two triangles to be congruent. When two triangles are congruent (△PQR ≌ △WVX), all corresponding sides and angles are equal.
Given:
VW = 4.5 inchesWX = 5.9 inches∠W = 28°∠X = 47°For the triangles to be congruent, the corresponding sides and angles must be equal. Let's match the corresponding parts:
QR corresponds to WXPQ corresponds to VWm∠R corresponds to m∠Wm∠Q corresponds to m∠XGiven this correspondence:
QR must be equal to WX, so QR = 5.9 inches (Option b).
m∠R must be equal to m∠W, so m∠R = 28° (Option c).
m∠Q must be equal to m∠X, so m∠Q = 47° (Option d).
However, m∠R and m∠Q cannot both be correct choices simultaneously; only one can be correct because they refer to the same angle in each corresponding pair QR = 5.9 inches is the correct choice considering the triangle sides.
Complete question
In triangle VWX, VW=4.5 inches, WX=5.9 incheß, m∠ W=28° , and m∠ X=47°. If △ PQR≌ △ WVX , which statement is true?
a. QR=4.5cm
b. QR=5.9cm
c. m∠ R=28°
d. m∠ R=47°
Use the linear combination method to solve this system of equations. What is the value of 3x+7y=3 X-7y=1
Answer:
look at the picture shown
Answer:
c
Step-by-step explanation:
A circuit board manufacturer can produce 2000 board per hour. How many days will it take to produce 16500 if the company has a 10 hour work shift
Answer:
B. Less than a day
Step-by-step explanation:
From the question, the circuit board manufacturer produces 2000 board per hour.
Let x be the number of hours it will take to produce 16500 boards .
That’s
2000 boards = 1 hour
16500 boards = x hour
Cross multiply
xhour x 2000 = 1 x 16500
x hour = 16500/2000
x hour = 8.25 hours
8.25 hours is less than a day
10.6666666667 as a fraction
The fraction form of the number 10.666666667 is,
⇒ 32/3
A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction.
Given that,
A number is,
⇒ 10.6666666667
For the fraction form,
Let us assume that,
⇒ x = 10.666666667 .. (i)
Multiply by 10 on both sides,
⇒ 10x = 106.666666667 .. (ii)
Subtract (ii) from (i);
⇒ 10x - x = 106.666666667 - 10.66666667
⇒ 9x = 96
Divide 9 on both sides,
⇒ x = 96/9
Or, it can be written as,
⇒ x = 32/3
So, the fraction form is, 32/3
To learn more about the fraction visit:
https://brainly.com/question/5454147
#SPJ6
Final answer:
To convert the decimal 10.6666666667 to a fraction, we write it as the sum of 10 and the repeating decimal 0.6666666667. The repeating decimal equates to 2/3 after simplification, leading to the mixed number 10 2/3 or the improper fraction 32/3.
Explanation:
To convert the decimal 10.6666666667 to a fraction, we need to express it as the sum of its whole number part and its fractional part. The whole number part is 10, and the fractional part is 0.6666666667.
First, let's focus only on the fractional part. To turn 0.6666666667 into a fraction, notice that it's a repeating decimal. If we denote the repeating part by 'x', the equation will be:
x = 0.6666666667
Multiplying by 10 gives:
10x = 6.6666666667
Subtracting the original equation from this new equation:
9x = 6
Now, we solve for 'x':
x = 6/9
However, this fraction can be simplified to:
x = 2/3
Therefore, the fraction form of 10.6666666667 is 10 2/3, which can also be written as an improper fraction:
(10 × 3/3) + 2/3=(30/3) + 2/3=32/3slope 3, y-intercept 6
Pirate Jack has an equal number of gold and silver coins. If Pirate Jack splits all of his coins into 7 equal piles for his parrots, he has 4 coins left. Or, if he splits all of his coins into 11 equal piles for his shipmates, he has 4 coins left. Assuming every pile has at least 1 coin, what is the least possible number of coins Pirate Jack has?
The least possible number of coins Pirate Jack has, is 81 coins.
Step-by-step explanation:
Given,
When the coins are divided into 7 equal piles, 4 coins are left.
When the coins are divided into 11 equal piles, 4 coins are left.
We will take LCM of both 7 and 11.
7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, ....
11 = 11, 22, 33, 44, 55, 66, 77, 88, ...
The least common multiple of 7 and 11 is 77.
As 4 coins are left, therefore, we will add those coins.
Total possible coins = 77+4 = 81
The least possible number of coins Pirate Jack has, is 81 coins.
Keywords: LCM, addition
Learn more about addition at:
brainly.com/question/11018983brainly.com/question/11145277#LearnwithBrainly
The population of deer in a given park is modeled by y = d(x) = A( 1 2 )x + B, where x is the elapsed time in years since 2019. According to the model, which is the best prediction of the number of deer in the park in 2099?
A) A
B) B
C) A + B
D) A − B
Answer:
Step-by-step explanation:
The answer is B) B :)
Answer:
The answer is B
Step-by-step explanation:
According to USA Test prep it says so, but i didn't quite get the explanation so bear with me. Thank you :)(:
Solve this system using any method (substition elimination) Thank you!!!
x - y = -3
-4x + y = -18
Answer:
look at the picture shown
The sum of two numbers is 18 the sum of greater numbers and twice the smaller numbers is 25 the numbers
Answer:
the numbers are 7 and 11
Step-by-step explanation:
If you add the smaller to the sum of numbers, you have the sum of the greater and twice the smaller. That is ...
18 + smaller = 25
smaller = 25 -18 = 7
larger = 18 -7 = 11
The two numbers are 7 and 11.
_____
If you like, you can write two equations. Let x and y represent the smaller and larger numbers, respectively.
x + y = 18
2x + y = 25
Subtract the first equation from the second:
(2x +y) -(x +y) = (25) -(18)
x = 7
y = 18-x = 18-7 = 11
The numbers are 7 and 11.
What is 1 2/4 x 3 5/6
Answer:
5.75
Step-by-step explanation:
We can first off make them improper fractions. They're easier to deal with.
1 2/4 = 6/4.
3 5/6 = 23/6
6/4 * 23/6.
Multiply numerators: 23 * 6 = 138.
Multiply denominators: 4 * 6 = 24.
138/24.
Simplify: 23/4
A family room has a circular rug with a radius of 7 m .
The rug's area is?
Answer:
The rug's area is equal to 49π m².
General Formulas and Concepts:
Geometry
Area of a Circle Formula: A = πr²
r is radiusStep-by-step explanation:
Step 1: Define
Identify given.
r = 7 m
Step 2: Find Area
[Area of a Circle Formula] Substitute in radius r:∴ the family room circular rug with a circle radius of 7 meters has an area of 49π m². And we have solved our problem!
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Topic: Geometry
An image point of a transformation has coordinates Y'(2, -4). If the pre-image point had coordinates Y(6, -12), what was the transformation and scale factor?
reflection with scale factor 3
reflection with scale factor 1/3
dilation with scale factor 3
dilation with scale factor 1/3
Answer:
Therefore the correct answer is the fourth one d.) dilation with scale factor 1/3
Step-by-step explanation:
i) the pre-image co-ordinates is Y(6, -12)
ii) the coordinates of the image is Y' (2, -4)
iii) therefore we can clearly see that if we divide the coordinates of the pre-image (6,-12) by 3 then we get the coordinates of the image(2,4).
Therefore this is a dilation with scale factor of 1/3.
Therefore the correct answer is the fourth one d.) dilation with scale factor 1/3
Final answer:
The transformation from the pre-image point Y(6, -12) to the image point Y'(2, -4) is a dilation with a scale factor of 1/3.
Explanation:
Given an image point Y'(2, -4) of a transformation and the pre-image point Y(6, -12), we can determine the type of transformation and the scale factor. The transformation is a type of change that affects the position, size, or shape of a figure. To find out the type of transformation and the scale factor, we compare coordinates.
Since the x-coordinate changed from 6 to 2, it has been reduced by a factor of 3 (6 divided by 3 equals 2). The y-coordinate changed from -12 to -4, which also has been reduced by a factor of 3 (-12 divided by 3 equals -4). This consistent reduction indicates that the transformation is a dilation. The objects are shrunk uniformly in both dimensions by the scale factor.
The correct answer is therefore dilation with scale factor 1/3.
1. Veronica cut a
triangular piece of
cookie cake with side
lengths that measure
3.6 cm, 6 cm and 4.8
cm.
The question is about calculating the center of mass for a triangular sandwich with a semicircular bite and determining the volume and uncertainty for a rectangular box.
Explanation:The question asked concerns finding the center of mass of a triangular sandwich after taking a semicircular bite out of it, which is a problem related to geometry and mass distribution. When solving such problems, one would typically have to calculate the area of the original triangle and the area of the semicircular bite, then find the centroid of both shapes.
For the rectangular box's volume and uncertainty, this is a measurement and uncertainty calculation question. Here, one must apply the formula for the volume of a rectangle (length imes width imes height) and use the rules of propagation of uncertainty to calculate the overall uncertainty of the volume measurement.
Please help!!!!
a + b = 10
a - b = 2
Solve the system of equations.
A) a = 5, b = 5
B) a = 2, b = 8
C) a = 6, b = 4
D) a = 3, b = 7
E) a = 12, b = -2
Answer:
C) a = 6, b = 4
Step-by-step explanation:
6 + 4 = 10
6 - 4 = 2
To solve the system, we first add both equations to find 'a = 6'. Then, substitute 'a' in one of the original equations to get 'b = 4'. The solution is 'a = 6' and 'b = 4', corresponding to answer choice C).
Explanation:To solve the system of equations:
a + b = 10a - b = 2We can add the two equations to eliminate the variable b. By adding them, we get:
2a = 12
Divide both sides of the equation by 2:
a = 6
With the value of a known, substitute a = 6 into either of the original equations. For example, substituting it into the first equation:
a + b = 10
6 + b = 10
b = 10 - 6
b = 4
Therefore, the solution to the system of equations is a = 6 and b = 4, which corresponds to answer choice C).
A dad has two daughters – Wendy and Julia. Wendy is twice as old as Julia. The man is now five times as old as Wendy, and in 4 years he will be six times as old as Julia. Find the present age of the father.
father is 50
Julia's age : a year-old
Wendy is twice the age of Julia
= > Wendy = 2a year-old
Dad's age : b year-old
" The man is now five times as old as Wendy " b / 2a = 5 <=> b = 10a
" In four years he will be six times as old as Julia " :
( B + 4 ) / (a + 4 ) = 6 + 4 = 6. <=> b (a + 4 )
<=> B = 6a +20
I have two equations :
6a + b = 20
b = 10a
= > 10a = 6a + 20 - > a = 5
- > B = 10a = 50
Answer:
50
Step-by-step explanation:
A person invests 7500 dollars in a bank. The bank pays 4% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 12800 dollars?
Answer:
13.6 years
Step-by-step explanation:
From the question;
Money invested (Principal) is 7500 dollars Rate of interest is 4% compounded annually Amount, (money accrued ) is 12800 dollarsWe are needed to determine the time it took for the money to reach the given amount;
To solve the question we need to know the compound interest formula, that is;[tex]A=P(1-\frac{r}{100})^n[/tex]
Where n is the interest periods;
Therefore, substituting the variables with the corresponding values, we can determine n.Therefore;
[tex]12800=7500(1-\frac{4}{100})^n[/tex]
Dividing both sides by 7500, we get;
[tex]1.7067=(1-\frac{4}{100})^n[/tex]
[tex]1.7067=(1.04)^n[/tex]
Introducing logarithms on both sides;
[tex]log1.7067=log(1.04)^n\\nlog1.04=log1.7067\\n=\frac{log1.7067}{log1.04} \\n=13.63[/tex]
Thus, n=13.6 years
Thus, it would take 13.6 years for the invested money to accumulate to 12800 dollars
!!! need help!! whats the answer?
NEED ANSWER ASAP!!!!!!!
in the system: {y=28+0.05x}
{y=25+0.07x}
what is the substitute for x where y is the same on both equations?
Hi there (◕‿-)
Since both equations are equal to y, they must equal each other. So set them to equal each other.
28 + 0.05x = 25 + 0.07x (✿ ♥‿♥)
Let's start by subtracting 25 from both sides!
3 + 0.05x = 0.07x (28-25=3, 25-25=0)
Now let's subtract 0.05 from both sides Ｏ(≧▽≦)Ｏ
3 = 0.02x
We need this x by itself, so let's get rid of it. Do this by divide both sides by 0.02 （ ´_⊃｀）
150 = x
So x = 150. Let's test this. Substitute 150 in for x in both equations! ＼（＾○＾）人（＾○＾）／
28+0.05(150) = 25+0.07(150)
28 + 7.5 = 25 + 10.5 (0.05*150=7.5, 0.07*150 = 10.5)
35.5 = 35.5
It works! (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧
So x = 150