Answer:
log[3(x+4)] is equal to log(3) + log(x + 4), which corresponds to choice number three.
Step-by-step explanation:
By the logarithm product rule, for two nonzero numbers [tex]a[/tex] and [tex]b[/tex],
[tex]\log{(a \cdot b)} = \log{(a)} + \log{(b)}[/tex].
Keep in mind that a logarithm can be split into two only if the logarithm contains the product or quotient of two numbers.
For example, [tex]3(x + 4)[/tex] is the number in the logarithm [tex]\log{[3(x + 4)]}[/tex]. Since [tex]3(x + 4)[/tex] is a product of the two numbers [tex]3[/tex] and [tex](x + 4)[/tex], the logarithm [tex]\log{[3(x + 4)]}[/tex] can be split into two. By the logarithm product rule,
[tex]\log{[3(x + 4)]} = \log{(3)} + \log{(x + 4)}[/tex].
However, [tex]\log{(x + 4)}[/tex] cannot be split into two since the number inside of it is a sum rather than a product. Hence choice number three is the answer to this question.
Answer:
c
Step-by-step explanation:
Which set of numbers is included in the solution set of the compound inequality?
{-7,5, 18, 24, 32}
{-9, 7, 15, 22, 26}
{16, 17, 22, 23, 24}
{18, 19, 20, 21, 22}
Answer:
It's the first set.
Step-by-step explanation:
X ≤ 18 or x > 22.
The first set is included in the solution.
Its not the second because 22 is not included.
Nor the third also because of the 22.
Nor the third because of the 19, 20, 21 and the 22.
A set is a mathematical model for a collection of items; it contains elements or members, which can be any mathematical object.
What is Compound inequality ?A compound inequality is created when two simple inequalities are combined. This article explains how to graph and solve compound equations.
How to solve?Compound inequality includes number not included in selected region given in graph hence including numbers 18,19,20,21,22
Which is option D
Hence correct option is {18,19,20,21,22}
Learn more about compound inequality
https://brainly.com/question/234674
#SPJ2
I'm not exactly a geek at math and measurements is one of the things I have always messed up at.
Anyone mind helping me?
Check the picture below.
well, √180 is about 13.4, and √72 is about 8.5, clearly 2*8.5 ≠ 13.4.
which graph shows a negative rate of change for the interval 0 to 2 on the axis?
Answer:
the answer to your question is the fourth one listed on your multiple choice, where it shows it curving at the lowest point out of all the others , in the 4th quadrant
A line passes through (2,8) and (4,12). Which equation Best represents the line
Answer:
y = 2x + 4
Step-by-step explanation:
First, find the rate of change [slope], m = -y₁ + y₂\-x₁ + x₂. Next, you do either\or:
12 = 2(4) + b; 4 = b
8 = 2(2) + b; 4 = b
No matter which ordered pair you use, you will ALWAYS get the same answer, IF you put them in their correct places.
I am joyous to assist you anytime.
solve 4 by 216 raise to minus 2 by 3 + 1 by 256 raise to 3 by 4 + 2 by 243 raise to 1 by 5
Answer:
214....
Step-by-step explanation:
If the question is : solve 4 by 216 raise to minus 2 by 3 + 1 by 256 raise to minus 3 by 4 + 2 by 243 raise to minus 1 by 5
The given expression can be written as:
4/(216)-2/3+1/(256)-3/4+2/(243)-1/5
This expression has three terms.
Notice that the exponents are negative:
We will change the division into multiplication so that the exponents will become positive;
4*(216)^2/3+ 1*(256)^3/4+ 2*(243)^1/5
If we multiply 6 three times it will give us 6^3=6*6*6=216
If we multiply 4 four times it will give us 4^4=4*4*4*4=256
If we multiply 3 five times it will give us 3^5=3*3*3*3*3=243
So we will write it as:
=4*(6^3)^2/3+ 1(4^4)3/4 +2(3^5)^1/5
=4(6)^2+(4)^3+2(3)
=4*36+64+6
=144+64+6
=214
The answer is 214....
assume this graph is a transformation from f(t)=-6t^2 what does the term -3.7 do to the rocket’s graph? what does the value t=3.7 represent and what happens to the rocket
@jdoe0001
Answer:
Eq.
y = -6(x-3.7)^2 + 82.14
the value t = 3.7 represents the maximum amplitude of the rocket in-flight.
Step-by-step explanation:
The standard equation of the parabola is written as
ax^2 +bx +c = 0
But we can rewrite it in vertex form. (See attached picture.)
y = a(x-h)^2 + k
If we look at the question, we can see that the vertex is
(h,k) = (3.7 , 82.14)
y = -6(x-3.7)^2 + 82.14
the value t = 3.7 represents the maximum amplitude of the rocket in-flight.
Answer:
t = 3.7 represents the time at which the rocket will reach at the maximum height.
Step-by-step explanation:
In the diagram,
We have a downward parabola having vertex (3.7, 82.14),
Since, a downward parabola is maximum at its vertex,
That is, the maximum value of the graph is 82.14 at 3.7,
Here, the graph shows the path of a rocket,
That is, it shows the distance covered by the rocket in different time,
Hence, the maximum distance covered is 82.14 unit at 3.7 time.
find the coordinates of P so that P partitions the segment AB in the ratio 1:1 is A(-4,15) and B(10,11)
Answer:
The coordinates of point P are (3 , 13)
Step-by-step explanation:
* Lets explain how to solve the problem
- Point P divides the segment AB in the ratio 1 : 1
- The ratio 1 : 1 means divide the segment into two equal parts
- Then P is the mid-point of segment AB
- If (x , y) are the coordinates of the mid-point of a segments whose
endpoints are (x1 , y1) and (x2 , y2) then;
[tex]x=\frac{x_{1}+x_{2}}{2},y=\frac{y_{1}+y_{2}}{2}[/tex]
∵ The coordinates of point A is (-4 , 15)
∵ The coordinates of point B is 10 , 11)
- Let point A is (x1 , y1) , point B is (x2 , y2) and point P is (x , y)
∵ x1 = -4 , x2 = 10 and y1 = 15 , y2 = 11
∴ [tex]x=\frac{-4+10}{2}=\frac{6}{2}=3[/tex]
∴ [tex]y=\frac{15+11}{2}=\frac{26}{2}=13[/tex]
∴ The coordinates of point P are (3 , 13)
Answer:
(3,13)
Step-by-step explanation:
I got it correct on founders edtell
if the cost of 15 bananas is rs 84 how many bananas can be bought for rs 140?
Answer:
25 bananas.
Step-by-step explanation:
The cost of one banana = 84/15 = rs 28/5 = rs 5.60.
So the number of bananas costing rs 140
= 140 / 5.60
= 25 bananas.
Multiply or divide as indicated.10x^5/2x^2
Answer:
5x³
Step-by-step explanation:
As discussed in one of my videos, whenever you divide, you subtract the exponents.
If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.
Find the value of the expression.
h(h + k)
for h = 4 and k = 6
Answer:
40
Step-by-step explanation:
In this question, substitute the values of h and k in the expression
Given h=4 and k=6
The expression will be;
h(h+k)
4(4+6)
solve the brackets first
4+6=10
rewrite the expression as
4(10)
open the brackets by multiplication
4×10=40
Answer:
40
Step-by-step explanation:
We must substitute the values provided to us:
[tex]h=4[/tex] and [tex]k=6[/tex]
in the expression:
[tex]h(h+k)[/tex]
we get the following:
[tex]4(4+6)[/tex]
solving the sum inside the parentheses:
[tex]4(10)[/tex]
and finally solving the multiplication
[tex]4(10)=40[/tex]
the value of the expression is 40.
PLEEEEEEASE HELP ME:D
Answer:
{ (1,1),(2,9),(4,8) } is the right answer. Mentioned relation has all the ordered pairs of x and y in the form of set, shown in the table.
Step-by-step explanation:
Tables can be used to describe functions. i.e. in given table two coordinates x,y used as ordered pairs and their values mentioned, the value x-coordinate comes first and than value of its corresponding y-coordinate .According to the table, if we take value of x=1 than we need to take corresponding value of y=1 written as ( 1,1 ), Similarly for if x=2, its corresponding value of 'y' will be y=3 written as ( 2,3 ) and so onThe entire table expressed in ordered pair gives set { (1,1),(2,9),(4,8) }.Answer details
Grade: Middle
Subject: Mathematics
Chapter: Representing Functions and relations
Keywords: relations, ordered pairs, tables and functions, set etc
Find the measure of angle x in the figure below
Answer:
[tex]\large\boxed{x=35^o}[/tex]
Step-by-step explanation:
We have the equation:
[tex]56^o+y+51^o=180^o\\\\(56^o+51^o)+y=180^o\\\\107^o+y=180^o\qquad\text{subtract}\ 107^o\ \text{from both sides}\\\\y=73^o\\\\\text{We know: the sum of the measures of the angles of the triangle}\\\text{is equal to}\ 180^o.\\\\\text{Therefore we have the equation:}\\\\x+y+72^o=180^o\qquad\text{put the value of}\ y\\\\x+73^o+72^o=180^o\\\\x+145^o=180^o\qquad\text{subtract}\ 145^o\ \text{from both sides}\\\\x=35^o[/tex]
PLEASE HELP!!!!!!!!!!!!!!!!!!
Give the dimensions of the rectangle with an area of 100 square units and whole
number
side lengths that has:
a. the largest perimeter
b. the smallest perimeter
Answer:
a. 2 and 50
b. 10 and 10
Step-by-step explanation:
Let's denote the side lengths by x and y.
The area is 100 which means that x*y=100.
The only whole numbers which satisfy this are the following:
2,50
4,25
5,20
10,10
Just go through them one by one and find your answer.
The rectangle with an area of 100 square units and whole number side lengths with the largest perimeter is 50 by 2 with a perimeter of 104 units. The smallest perimeter rectangle possible for the same area is a square measuring 10 by 10, which has a perimeter of 40 units.
Explanation:We are tasked with finding the dimensions of a rectangle with an area of 100 square units and whole number side lengths that will result in either the largest perimeter or the smallest perimeter.
Largest Perimeter Rectangle
To find the rectangle with the largest perimeter, we should aim for the rectangle to have the longest possible length and the shortest possible width while still maintaining an area of 100 square units. In the extreme case, this could be a rectangle with a length that approaches infinity and a width that is infinitely small, but we are limited to whole numbers. Therefore, the rectangle with the largest perimeter in this scenario would be 50 by 2, resulting in a perimeter of (50+2)*2 = 104 units.
Smallest Perimeter Rectangle
To find the rectangle with the smallest perimeter, we need to look for the most square-like dimensions, as a square has the smallest possible perimeter for a given area. For an area of 100 square units, the side lengths would be 10 by 10, so the perimeter would be 10*4 = 40 units.
2 Points
If y = 12x - 7 were changed to y = 12x + 1, how would the graph of the new
function compare with the original?
O
A. It would be steeper.
O
B. It would be shifted down.
O
c. It would be shifted up.
O
D. It would be less steep.
The graph's y intercept would be shifted up.
Intercept of the graphThe intercept of the original point is determined as follows;
y = 12x - 7, when compared to , y = mx + c
where;
c is the intercept = -7
The intercept of the second graph is determined as follows;
y = 12x + 1
New intercept = 1
The graph's y intercept will move from -7 to +1, thus, It would be shifted up.
Learn more about intercept here: https://brainly.com/question/1884491
Final answer:
The graph of the new function y = 12x + 1 would not be steeper or less steep than the original but would be shifted up compared to the graph of y = 12x - 7.(Option C)
Explanation:
Changing the equation from y = 12x - 7 to y = 12x + 1 does not alter the slope of the line, which remains 12 in both cases. The slope of a line represents the steepness and direction of the line, and since the slope (the coefficient of x) has not changed, the steepness and direction of the line will remain the same.
The change that does occur involves the y-intercept. The original line has a y-intercept at -7, while the new equation has a y-intercept at +1. This means the entire line is shifted vertically upwards by 8 units (from -7 to +1). Therefore, the correct answer to how the graph of the new function would compare with the original is that it would be shifted up.
What is the location of the point on the number line that is 3/5 of the way from a=2 to b=17
Answer:
11
Step-by-step explanation:
The distance that a is to b is b-a=17-2=15.
The line segment from a=2 to b=17 has length 15.
We need to know what is 3/5 of 15.
3/5 of 15 means what is 3/5 times 15?
(3/5)(15)=3(3)=9
So this means we are looking to make a line segment that is 9 units from 2 which is 2 to 11.
So 11 is 3/5 the way from a=2 to b=17.
Let's check from 2 to 11 that is a length of 9 and from 2 to 17 that is a length of 15.
Is 9/15 equal to 3/5?
Yes, 9/15 can be reduced to 3/5.
Which is an exponential growth function f(x)=6(0.25)x
f(x)=0.25(5.25)x
Answer: Second Option
[tex]f(x)=0.25(5.25)^x[/tex]
Step-by-step explanation:
The exponential growth functions have the following form:
[tex]f(x) = a(b)^x[/tex]
Where a is the main coefficient, b is the base and x is the exponent.
For this type of functions the base b must always be greater than 1. Otherwise it would be an exponential decay function
Among the options given, the only function whose base is greater than 1 is the second option:
[tex]f(x)=0.25(5.25)^x[/tex]
Answer:
The correct answer option is B. [tex] f ( x ) = 0 . 2 5 ( 5 . 2 5 ) ^ x [/tex].
Step-by-step explanation:
If the numbers are positive along with the base of the exponent which must be greater than 1, then it an exponential growth function.
1. [tex]f(x)=6(0.25)^x[/tex]:
Here the numbers are positive but the base of the exponent is 0.25 which is less than 1 so it is not an exponential growth function.
2. [tex] f ( x ) = 0 . 2 5 ( 5 . 2 5 ) ^ x [/tex]:
Positive numbers with base of the exponent greater than 1, therefore it is an exponential growth function.
At Sara's new job she spent $11.52, $6.48, $5.99, $14.00, and $9.50 on lunch the first week.
In the second week, she spent $4 more in total for the 5 lunches than the first week.
second
What is the increase in the mean for the second week compared to the first? Round the
answer to the nearest penny.
Answer:
A. 0.80
Step-by-step explanation:
First, you need to find the mean of the cost of Sara's lunches the first week. The mean is the 'average,' and to find the average, add all of your terms and divide by the amount of terms.
[tex]11.52+6.48+5.99+14+9.5\\18+5.99+14+9.5\\23.99+14+9.5\\37.99+9.5\\47.49[/tex]
Sarah's total cost for the first week was $47.49. Divide by your number of terms (5) for your average daily cost.
[tex]\frac{47.49}{5} =9.498[/tex]
This can be rounded to $9.50.
For the next week, Sara spent $4 more in total than the first week. So, add $4 to your total.
[tex]47.49+4=51.49[/tex]
Now, divide $51.49 by your number of terms (5) again to find your average for the second week.
[tex]\frac{51.49}{5} =10.298[/tex]
This can be rounded to $10.30.
Find the difference.
[tex]10.30-9.50=0.80[/tex]
Sara spent $0.80 more on average.
Elisondra is eating at a restraurant with three friends. They want to choose at random who will order first. If you model the situation with the spinner, how many equal-sized sections should the spinner have?
1/4
1
3
4
ANSWER ASAP PLEASE THANK YIOU
~~ Love joshthafish
Answer:
Elisondra and her three friends add up to four people, so the spinner should have 4 equal sized sections.
Answer:
D
Step-by-step explanation:
If the total area of a dartboard is 30,000 mm2 and the area of the second ring
is 15,000 mm2, what is the probability of landing in that second ring?
A. 30%
B. 15%
C. 20%
D. 50%
Answer:
probability is 50 percent
Step-by-step explanation:
total area= 30000
area of secknd ring=15000
therefore 15000/30000 times 100
equals 50 percent
Answer:
Option D.
Step-by-step explanation:
From he given information, we get
Total area of a dartboard = 30,000 mm²
The area of the second ring = 15,000 mm²
We need to find the probability of landing in that second ring.
[tex]Probability=\dfrac{\text{The area of the second ring }}{\text{Total area of a dartboard}}[/tex]
[tex]Probability=\dfrac{15000}{30000}[/tex]
[tex]Probability=0.5[/tex]
Multiply the probability by 100 to find the percentage.
[tex]Probability=0.5\times 100[/tex]
[tex]Probability=50[/tex]
Hence the correct option is D.
13. MONEY During the school week, Joshua spent $3 each
day on lunch. On Tuesday, he bought a $5 ticket to the school
play and on Friday he loaned $2 to his friend. When he
checked his wallet at the end of the day Friday, he had $3
left. How much money did he start the week with?
Answer:
Joshua had $25 on Monday.
Step-by-step explanation:
We are given the following information:
Money spend on each day for lunch = $3
Number of days he attend school in a week = 5
Total money spent on lunch = [tex]3\times 5 = \$15[/tex]
Money spent on Tuesday for ticket = $5
Money spent on Friday = $2
Money left on Friday = $3
Total money in the start of week =
[tex]15 + 5 + 2 + 3 = 25[/tex]
Thus, Joshua had $25 on Monday.
The Discriminant of a quadratic equationis is -6 .What types of solutions does the equation have ?
a.2 irrational solutions
b.1 real solution
c.2 complex conjugate solutions
d.2 rational solutions
Answer:
C
Step-by-step explanation:
The nature of the solutions are determined by the value of the discriminant.
Given a quadratic equation in standard form ax² + bx + c = 0 : a ≠ 0
Then the discriminant is Δ = b² - 4ac
• If b² - 4ac > 0 then 2 real and distinct solutions
• If b² - 4ac = 0 then solutions are real and equal
• If b² - 4ac < 0 then solutions are not real, 2 complex conjugate solutions
Here b² - 4ac = - 6 , hence 2 complex conjugate solutions → C
Use synthetic substitution to find g(3) and g(-6) for the function g(x)=x^5-5x^3-10x+4
Answer:
g(3)=82
g(-6)=-6632
Step-by-step explanation:
To find g(3) we are going to use synthetic division for dividing the polynomial x^5-5x^3-10x+4 by x-3.
So this means 3 goes on the outside.
Also since we are missing x^4 and x^2 term, we will need to put a 0 placeholders there.
3 | 1 0 -5 0 -10 4
| 3 9 12 36 78
|_____________________
1 3 4 12 26 82
So g(3)=82
To find g(-6) we will put -6 on the outside:
-6 | 1 0 -5 0 -10 4
| -6 36 -186 1116 -6636
--------------------------------------
1 -6 31 -186 1106 -6632
So g(-6)=-6632
Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 4.4% compounded daily. The annual percentage yield is (blank) %
Step-by-step answer:
APY (annual percentage yield) is the amount of interest in percent one would actually earn by investing a sum of money in a year.
It takes into account the interest rate expressed in any particular form, and the compounding period.
In the current market, most interest rates (for example, credit cards) are expressed in APR (Annual percentage rate) which is an underestimate of the actual amount to be paid, by NOT taking into account the compounding period, monthly (instead of annually) most of the time. The shorter compounding period increases the APY.
Here the APR is 4.4%. to take into account the compounding period, we divide the interest rate by 12 to give the monthly rate, 4.4%/12=0.044/12.
This rate will then be compounded 12 times to give the APY, or the future value after 12 months.
Future value = (1+0.044/12)^12 = 1.044898
Therefore the APY is 1.044898 less initial deposit, or
1.044898-1 = 0.044898, or 4.4898%, or 4.49% (rounded to 2 decimal places)
Describe how to transform the graph of g(x)= ln x into the graph of f(x)= ln (3-x) -2.
Answer:
The graph of g(x) = ㏑x translated 3 units to the right and then reflected
about the y-axis and then translated 2 units down to form the graph of
f(x) = ㏑(3 - x) - 2
Step-by-step explanation:
* Lets talk about the transformation
- If the function f(x) reflected across the x-axis, then the new
function g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then the new
function g(x) = f(-x)
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
* lets solve the problem
∵ Graph of g(x) = ㏑x is transformed into graph of f(x) = ㏑(3 - x) - 2
- ㏑x becomes ㏑(3 - x)
∵ ㏑(3 - x) = ㏑(-x + 3)
- Take (-) as a common factor
∴ ㏑(-x + 3) = ㏑[-(x - 3)]
∵ x changed to x - 3
∴ The function g(x) translated 3 units to the right
∵ There is (-) out the bracket (x - 3) that means we change the sign
of x then we will reflect the function about the y-axis
∴ g(x) translated 3 units to the right and then reflected about the
y-axis
∵ g(x) changed to f(x) = ㏑(3 - x) - 2
∵ We subtract 2 from g(x) after horizontal translation and reflection
about y-axis
∴ We translate g(x) 2 units down
∴ g(x) translated 3 units to the right and then reflected about the
y-axis and then translated 2 units down
* The graph of g(x) = ㏑x translated 3 units to the right and then
reflected about the y-axis and then translated 2 units down to
form the graph of f(x) = ㏑(3 - x) - 2
Answer:
c edge
Step-by-step explanation:
What is the domain and range of h(x)=(x+1)/(x^2+4x)
Answer:
h=x+1/x^3+4x^2
Step-by-step explanation:
hx^3+4hx^2=x+1
h^3+4x^2)=x+1
h(x^3+4x^2)/x^3+4x^2=x+1/x^3+4^2
h=x+1/x^3+4x^2
Answer:
hambger
Step-by-step explanation:ham de be gerf hamburger
Evaluate 9 ÷ 3[(18 − 6) − 22].
The expression 9 / 3[(18 - 6) - 22] evaluates to -0.3, following the order of operations: first compute the parentheses, then multiply, and finally divide.
To evaluate the expression 9 / 3[(18 - 6) - 22], we need to follow the correct order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Let's solve it step-by-step:
Next, multiply by 3. Since there are no explicit parentheses around the 3 and the expression, we interpret it as 3 times the result from step 1, 3 * (-10), which equals -30.
Finally, divide 9 by the result from step 2, 9 / -30. That gives us -0.3.
The final answer, after doing the calculations in the correct order, is -0.3.
Which information would best fill the blanks in row 3?
1.metallic bond and low melting point
2.metallic bond and high melting point
3. covalent bond and low melting point
4.covalent bond and high melting point
Answer:
covalent bond and low melting point- 3.
Answer:
C)
Step-by-step explanation:
egdenuity 2020
geometry-
true or false: we can use existing theorems to prove new theorems
Answer:
we can use existing theorems to prove new theorems - true
It is true that we can use existing theorems to prove new theorems.
In geometry, new theorems are sometimes dependent on existing theorems.
This means that some new theorems would not exist, if not for the support and the existence of related existing theorems.
Hence, the statement is true
Read more about geometry at:
https://brainly.com/question/25306774
Mrs. Gomez is a mother to 2 boys. The number of children she has is three times the number of boys she has. Her children are planning to buy her a bouquet of flowers. What is the biggest bouquet they can buy in which the ratio of pink flowers to blue flowers matches the ratio of girls to boys if the florist has 9 blue carnations and 12 pink carnations left?
a bouquet of 12 flowers, 4 pink and 8 blue
a bouquet of 14 flowers, 8 pink and 6 blue
a bouquet of 15 flowers, 6 pink and 9 blue
a bouquet of 18 flowers, 12 pink and 6 blue
Answer:
a bouquet of 18 flowers, 12 pink and 6 blue is correct.
Step-by-step explanation:
Step 1: Find the total number of children.
Number of boys = 2
Total number of children = 3 x number of boys
Total number of children = 3 x 2 = 6
Step 2: Find the ratio of girls to boys
Number of girls = total number of children - total number of boys
Number of girls = 6 - 2 = 4
Girls : Boys
4 : 2
2 : 1
Step 3: Find the ratio of pink and blue flowers
Pink : Blue = Girls : Boys = 2 : 1
Step 4: Check the statements. The ratio of Pink : Blue should be 2 : 1.
1) a bouquet of 12 flowers, 4 pink and 8 blue. Incorrect because in this statement the ratio of pink : blue is 4 : 8 = 1 : 2 instead of 2 : 1.
2) a bouquet of 14 flowers, 8 pink and 6 blue. Incorrect because in this statement the ratio of Pink : Blue 8 : 6 = 4 : 3.
3) a bouquet of 15 flowers, 6 pink and 9 blue Incorrect because in this statement the ratio of pink : blue is 6 : 9 = 2 : 3.
4) a bouquet of 18 flowers, 12 pink and 6 blue. This is correct because the ratio of pink : blue is 12 : 6 = 2 : 1.
!!
Answer:
A bouquet of 12 flowers, 4 pink and 8 blue
Step-by-step explanation:
Let
x----> the number of boys
y ---> the number of girls
z ---> the number of children
we know that
x=2 boys----> equation A
z=3x-----> z=3(2)=6 children ----> equation B
z=x+y ----> equation C
substitute the value of x and the value of z in the equation C and solve for y
6=2+y
y=6-2=4 girls
so
The ratio of girls to boys is equal to
2/4=1/2
therefore
The ratio of pink flowers to blue flowers is equal to 1/2
Let
a -----> the number of pink flowers
b -----> the number of blue flowers
so
For b=9 blue carnations -----> Find the value of a
1/2=a/b
1/2=a/9
a=4.5 pink carnations ----> It doesn't make sense (must be a integer)
For b=8 blue carnations -----> Find the value of a
1/2=a/b
1/2=a/8
a=4 pink carnations ----> It makes sense
therefore
A bouquet of 12 flowers, 4 pink and 8 blue
Solve for y
y-1= 5(x + 2)
[tex]\huge{\boxed{y=\bf{5x+11}}}[/tex]
Distribute the 5. [tex]y-1=5x+10[/tex]
Add 1 on each side. [tex]y=5x+11[/tex]
y−1=5(x+2)
Step 1: Add 1 to both sides.
y−1+1=5x+10+1
y=5x+11
Answer:
y=5x+11