Under a dilation centered at the origin, the point (-4 , 3) has image at (8 , -6) The dilation is
Answer:
Balanced chemical equations only show formulae, not names. A balancing number, written in normal script, multiplies all the atoms in the substance next to it.
evaluate the variable expression when a=-4, b=2, c=-3, and d =4. b-3a/bc^2-d
Answer:
Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is
[tex]\dfrac{b-3a}{bc^{2}-d}=1[/tex]
Step-by-step explanation:
Evaluate:
[tex]\dfrac{b-3a}{bc^{2}-d}[/tex]
When a=-4, b=2, c=-3, and d =4
Solution:
Substitute, a=-4, b=2, c=-3, and d =4 in above expression we get
[tex]\dfrac{b-3a}{bc^{2}-d}=\dfrac{2-3(-4)}{2(-3)^{2}-4}\\\\=\dfrac{2+12}{18-4}\\\\[/tex]
[tex]\dfrac{b-3a}{bc^{2}-d}=\dfrac{14}{14}=1[/tex]
Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is
[tex]\dfrac{b-3a}{bc^{2}-d}=1[/tex]
Your neighbor has decided to enlarge his garden. The garden is rectangular with width 6 feet and length 15 feet. The new garden will be similar to the original one, but will have a length of 35 feet. Find the perimeter of the original garden and the enlarged garden.
Answer:
Original garden: 42 feet
Enlarged garden: 98 feet
Step-by-step explanation:
Perimeter = length (2) + width (2)
Original perimeter:
P = 15(2) + 6(2)
P = 30 + 12
P = 42 feet
In this problem, similar is proportional, so the new garden will be proportional to the old one.
If the original length was 15 and the new length is 35, then 15 would have had to have been multiplied by 2 1/3. That means you need to multiply 6 by 2 1/3, which is 14. That means the dimensions of the enlarged yard is 14 (width) × 35 (length).
Enlarged perimeter
P = 35(2) + 14(2)
P = 70 + 28
P = 98 feet
Final answer:
The perimeter of the original rectangular garden is 42 feet, and the perimeter of the enlarged garden, which is similar in proportion to the original, is 98 feet.
Explanation:
The original garden has a width of 6 feet and a length of 15 feet. The perimeter of a rectangle is calculated by adding the lengths of all its sides. In this case, the perimeter of the original garden is 2(6 feet + 15 feet) = 2(21 feet) = 42 feet.
Since the new garden is similar to the original one, and its length is 35 feet, it means that the width will also increase in the same proportion. The original length to width ratio is 15:6 which simplifies to 5:2. Applying this ratio to the new length of 35 feet will give us the new width:
35 feet / 5 = 7 feet (per unit of the ratio)
7 feet * 2 = 14 feet (new width)
The perimeter of the enlarged garden is then 2(14 feet + 35 feet) = 2(49 feet) = 98 feet. So, the perimeter of the original garden is 42 feet and the perimeter of the enlarged garden is 98 feet.
Tabitha earns $8.50 per hour at her summer job. She wants to save money to buy a tablet that costs $289 plus 6% sales tax. Tabitha has already saved $75. write and solve an inequality that shows how many hours Tabitha will need to work to have enough money to buy the tablet.
Answer:
The Inequality that shows number of hours Tabitha will need to work to have enough money to buy the tablet is [tex]75+8.5x\geq 306.34[/tex].
Tabitha needs to work at least 28 hours to buy the tablet.
Step-by-step explanation:
Amount earn per hour = $8.50
Amount already saved = $75
Cost of tablet = $289
Sales tax = 6%
We to write and solve the inequality number of hours Tabitha will need to work to have enough money to buy the tablet.
Solution:
Let the number of hours she need to work be 'x'.
First we will find the total amount required to buy tablet.
Amount of sales tax = [tex]\frac{6}{100}\times289 = \$17.34[/tex]
Now Total cost to buy tablet will be equal to sum of Cost of tablet and Amount of sales tax.
framing in equation form we get;
Total cost to buy tablet = [tex]289+17.34 = \$306.34[/tex]
Now we can say that;
Amount already saved plus Amount earn per hour multiplied by Amount earn per hour should be greater than or equal to Total cost to buy tablet.
framing in equation form we get;
[tex]75+8.5x\geq 306.34[/tex]
hence The Inequality that shows number of hours Tabitha will need to work to have enough money to buy the tablet is [tex]75+8.5x\geq 306.34[/tex].
On solving the above Inequality we get;
First we will subtract both side by 75 we get;
[tex]75+8.5x-75\geq 306.34-75\\\\8.5x\geq 231.34[/tex]
Dividing both side by 8.5 we get;
[tex]\frac{8.5x}{8.5}\geq \frac{231.34}{8.5}\\\\x\geq 27.21[/tex]
Hence Tabitha needs to work at least 28 hours to buy the tablet.
When one end of a seesaw is 9 inches above the ground and the other one is 21 inches above the ground how far are the ends above the ground when the seesaw is level
Answer:
15
Count down from 21 and count up from 9 till you have the same number.
21 9
20 10
19 11
18 12
17 13
16 14
15 15
Now they are the same height.
Step-by-step explanation:
When a seesaw is level, the height of both ends above the ground is the average of the heights when one end is lifted. In this case, both ends are 15 inches above the ground when the seesaw is level.
Explanation:The question is asking for the height of the ends of a seesaw when it is in a level or balanced position. A seesaw balances when it is level, and both ends are at the same height. Considering the given details, one end is 9 inches and the other is 21 inches above ground, when they switch positions due to the seesaw's pendulum-like movement. But when the seesaw is level, both ends are at the same height. Therefore, the height of both ends of the seesaw when it is level is the average of 9 inches and 21 inches. You calculate this average by adding the two given distances and dividing by 2. So:
((9 inches + 21 inches) / 2) = 15 inches
So, when the seesaw is level, both ends are 15 inches above the ground.
Learn more about seesaw here:https://brainly.com/question/21623981
#SPJ2
The test scores for a math test are displayed in the following box plot. What percent of the students scored at least 75 on the test?
Please show the picture of the box plot otherwise your question is unanswerabe.
(-8,-4)&(2,-9) fint the distance between each pair of points
Answer:
[tex]5 \sqrt{5} [/tex]
Step-by-step explanation:
We want to find the distance between (-8,-4) and (2,-9).
We use the distance formula:
[tex]d = \sqrt{ {(x_2-x_1)^2} +(y_2-y_1)^2 } [/tex]
We substitute the coordinates to get:
[tex]d = \sqrt{ {(2- - 8)^2} +( - 9 - - 4)^2 } [/tex]
We simplify to obtain:
[tex]d = \sqrt{ {(2 + 8)^2}+( - 9 + 4)^2 } [/tex]
Add the numbers within the parenthesis to get:
[tex]d = \sqrt{ {(10)^2}+( -5)^2 } [/tex]
Find the squares of the numbers under the radical
[tex]d = \sqrt{ {100}+25} [/tex]
[tex]d = \sqrt{125} = 5 \sqrt{5} [/tex]
Find the value of the polynomial 3xy+7x^2−3x^2y+3y^2x−2x^2−2xy+4x^2y−2y^2x, when x=1 and y=−2
Answer:
[tex]5[/tex]
First Method:
Substitute the given values in for [tex]x[/tex] and [tex]y[/tex].Solve.This isn't the only method, but it seems the least likely to result in an incorrect answer.
If [tex]x=1[/tex] and [tex]y=-2[/tex], find the solution to:
[tex]3xy+7x^2-3x^2y+3y^2x-2x^2-2xy+4x^2y-2y^2x[/tex]
Substitute [tex]1[/tex] for [tex]x[/tex] and [tex]-2[/tex] for [tex]y[/tex].[tex]3xy+7x^2-3x^2y+3y^2x-2x^2-2xy+4x^2y-2y^2x\\3(1)(-2)+7(1)^2-3(1)^2(-2)+3(-2)^2(1)-2(1)^2-2(1)(-2)+4(1)^2(-2)-2(-2)^2(1)[/tex]
Wow. That's a lot. Let's try simplifying things. I'd start by multiplying all our [tex]1[/tex]'s because any number multiplied by [tex]1[/tex] is that very same number, so we can easily reduce the length of our equation without much worry for messing up our math in the process.[tex]3(-2)+7-3(-2)+3(-2)^2-2-2(-2)+4(-2)-2(-2)^2[/tex]
It still looks like torture trying to figure out this equation, but let's take it in chunks instead of all at once.[tex]3(-2)+7-3(-2)+3(-2)^2-2-2(-2)+4(-2)-2(-2)^2[/tex]
First, I'm going to deal with all the exponents, and turn them into integers.[tex]3(-2)+7-3(-2)+3(4)-2-2(-2)+4(-2)-2(4)[/tex]
Notice that things are starting to look less complicated. We are taking our math in chunks. This will make it less likely for us to mess up, although it is more time consuming.Now, let's do multiplication. Any number within a parentheses is going to be multiplied by the number next to it. Remember that this only applies when there is no sign between them. I'm going to go one at a time.[tex]3(-2)+7-3(-2)+3(4)-2-2(-2)+4(-2)-2(4)\\-6+7-3(-2)+3(4)-2-2(-2)+4(-2)-2(4)\\-6+7+6+3(4)-2-2(-2)+4(-2)-2(4)\\-6+7+6+12-2-2(-2)+4(-2)-2(4)\\-6+7+6+12-2+4+4(-2)-2(4)\\-6+7+6+12-2+4-8-2(4)\\-6+7+6+12-2+4-8-8\\[/tex]
This is a lot of steps, but hopefully it doesn't looks as bad after seeing that I just did multiplication over and over. I'll go over another method after this that may make things less complicated.Now, we add these together. It doesn't matter what order you do this in.[tex]-6+7+6+12-2+4-8-8\\7+4+6+12-6-2-8-8\\11+18-8-16\\29-24\\5[/tex]
Our final answer is [tex]5[/tex].
Here's another method:
If [tex]x=1[/tex] and [tex]y=-2[/tex], find the solution to:
[tex]3xy+7x^2-3x^2y+3y^2x-2x^2-2xy+4x^2y-2y^2x[/tex]
Because we know that any number multiplied by [tex]1[/tex] will be that same number, let's just substitute in [tex]x[/tex] for now.[tex]3xy+7x^2-3x^2y+3y^2x-2x^2-2xy+4x^2y-2y^2x\\3(1)y+7(1)^2-3(1)^2y+3y^2(1)-2(1)^2-2(1)y+4(1)^2y-2y^2(1)\\[/tex]
Now, just like before, we can multiply [tex]1[/tex] without doing complicated math. Just basically get rid of it even when it's squared because [tex]1^2=1*1=1[/tex].[tex]3(1)y+7(1)^2-3(1)^2y+3y^2(1)-2(1)^2-2(1)y+4(1)^2y-2y^2(1)\\3y+7-3y+3y^2-2-2y+4y-2y^2\\3y^2-2y^2+3y-3y-2y+4y+5\\y^2+2y+5[/tex]
Looks a LOT less complicated. Substitute [tex]-2[/tex] in for [tex]y[/tex] and get your final answer.[tex]y^2+2y+5\\(-2)^2+2(-2)+5\\4-4+5\\5[/tex]
how many solutions does the system of inequalities graphed below have?
A. 0
B. 1
C. 2
D. infinitely many
Answer:
A 0
Step-by-step explanation:
because the lines are a paraell and they don't touch
A solution is a point that is in both shaded regions at the same time. This is impossible due to the fact the regions do not overlap. This is like saying there is a number larger than 1 and this same number is less than -1 at the same time. This is why there are no solutions to this system of inequalities.
A school charges $4.99 per child, $6.00 per adult, and $2.50 per baby, to go see the school play. How much money would they collect if 12 kids, 25 adults, and 6 babies came to see the play?
Answer:
$224.88
Step-by-step explanation:
4.99×12= 59.88 for kids
6×25=150 for adults
2.50×6=15 for babies
59.88+150+15= $224.88 collected in total
The coordinates of the midpoints of GH are M (4,3) and the coordinates of one endpoints are G (5,-6) the coordinates of the other endpoints are
Answer:
The co - ordinates of another end point is
(x,y) = (3, 12)
Step-by-step explanation:
step :-
mid point formula:-
Let [tex](x_{1} ,y_{1} ) and (x_{2} ,y_{2} )[/tex] be any two end points
Mid point of two given points are
[tex](\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} )[/tex]
let (x,y ) be the another end point
given one end point is (5,-6)
now by using mid-point formula , we get
[tex](\frac{x+5}{2} , \frac{y-6}{2} )[/tex] this is equating to given mid-point is M(4,3)
now [tex](\frac{x+5}{2} , \frac{y-6}{2} )=(4,3)[/tex]
simplify , we get
[tex]\frac{x+5}{2} =4 and \frac{y-6}{2} =3[/tex]
cross multiplication and simplify
[tex]x+5 = 8 and y-6=6[/tex]
x = 3 and y = 12
The another point is (x,y) = (3,12)
hemraj made $135 for 9 hours of work. at the same rate, how many hours would he have to work to make $165?
Answer:
11 hrs
Step-by-step explanation:
so he made 135 for 9 hrs.....thats (135/9) = $ 15 an hr
so if he made 165, he would have to work (165/15) = 11 hrs <==
The sum of three consecutive even numbers is 84. What is the smallest of the three numbers?
Answer: 26
Step-by-step explanation: In this problem we have 3 consecutive even numbers whose sum is 84 and it asks us to find the smallest number.
Consecutive even numbers can be represented as x, x + 2, and x + 4.
Since the sum of these is 84, our equation reads
x + (x + 2) + (x + 4) = 84.
Simplifying on the left we get 3x + 6 = 84.
Subtract 6 from both sides and we have 3x = 78.
Divide both sides by 3 and x = 26.
So our smallest number is 26.
To find the smallest of three consecutive even numbers that sum up to 84, we set up an equation and solve for 'x', where 'x', 'x+2', and 'x+4' represent the numbers. Solving this gives us the smallest number, which is 26.
Explanation:Finding the Smallest of Three Consecutive Even NumbersIf the sum of three consecutive even numbers is 84, we can find the smallest number by setting up an equation. Let's denote the smallest even number as 'x'. The next consecutive even number would be 'x + 2', and the one after that would be 'x + 4'. The sum of these three numbers should equal 84:
x + (x + 2) + (x + 4) = 84
Simplifying this equation, we get:
3x + 6 = 84
Subtracting 6 from both sides, we have:
3x = 78
Now, dividing both sides by 3 gives us:
x = 26
Therefore, the smallest of the three consecutive even numbers is 26.
Will mark brainliest and 15 points
Answer: its going in straight lines
Step-by-step explanation:
An 8-oz tub of yogurt causes two dollars and a 32 ounce tube cost is six dollars what fraction of the cost of the large tube is the small tub?
The required fraction is [tex]\bold{\frac{1}{3}}[/tex]
Solution:
Given:
Cost of 32 ounces tub = $6
Cost of 8 ounces tub = $2
To find:
what fraction of the cost of the large tube is the small tub.
From the given, here we can understand that the large tub is the 32 ounces tub and the smaller one is the 8 ounces tub.
Let k be the required fraction.
Therefore, [tex]\bold{k\times6=2}[/tex]
On solving we get,
[tex]\bold{\Rightarrow k=\frac{2}{6}\rightarrow k=\frac{1}{3}}[/tex]
What is the measure of angle x, in degrees, in the figure shown? A triangle with angle measure 60 degrees and 53 degrees. The third angle has an unknown measure, x degrees.
Answer: x = 67
Step-by-step explanation:
60+53+x = 180
The degrees of a triangle always equal 180
113+x = 180
Subtract the 113 from the 180
x= 67
Answer:113
explanation: hope it helps☺
sum of (-3y-5)+(5m+7y)+(6+9m)
Answer:
4y+14m+1
Step-by-step explanation:
Remove the brackets
-3y-5+5m+7y+6+9m
Rearrange the terms
7y-3y+5m+9m+6-5
Adding like terms
4y+14m+1
Simplify the expression 2j+4j+j+7
Answer:
7j+7
Step-by-step explanation:
2j+4j+j+7
combine like terms
7j+7
Sorry I don't really know how to explain it, but you just have to combine terms with the same unit
95-a (b+c) when a=9, b= 3, and c = 7.4
Answer:
95-9 (3+7)
95-9 (10)
86 (10)
= 8600
Step-by-step explanation:
32 loaves of bread total, wheat loaves has 8 more then the rye loaves. How many wheat loaves are there?
Answer:
Step-by-step explanation:
Let the no. Of rye bread = x
Wheat bread = x + 8
The total bread is 32
: x + x + 8 = 32
2x = 32 - 8
2x = 24
x = 24/2
x = 12
No. Of wheat bread = x + 8 = 12+8
No. Of wheat bread = 20
Answer:
Wheat loaves is 20
Step-by-step explanation:
Let wheat loaves be A
And rye loaves be B
A + B = 32
Hence A = B + 8
So, B + B + 8 = 32
2B = 24
B = 12
A = 20
What is the remainder when 16,055 is divided by 16? Please i need help
Answer:
16,055/16 = 1003
The remainder would be 7
Step-by-step explanation:
Word Problem: You are traveling to your aunt's house that is 239 miles away. If you are currently twice as far from home as you are from your aunt's, how far have you traveled?
Answer:
119.5
Step-by-step explanation:
What is the complete factorization of 64x2 - 48x + 9?
O A. (8x - 3)(8x+3)
B. (8x - 3)2
OC. 4(4x - 3)2
D. 4(4x - 3)(4x+3)
Please helppp
Answer:
B) (8x-3)²
Step-by-step explanation:
64x2 - 48x + 9= (8x)² - 2*8x*3 + 3²
Compare with a² - 2ab +b² = (a-b)²; a = 8x and b =3
=(8x-3)²
What is the solution to the system of equations?
(3x+2y = 39
(5x-y=13
O (4,7)
O (7,4)
O (12,5)
(5, 12)
Answer:
X = 5
Y= 12
Step-by-step explanation:
3x + 2y = 39 —> (1)
5x - y = 13 —> (2)
Multiply (2) with 2
10x - 2y = 26 —> (b)
(1) + (b)
This will eliminate the y factor, leaving:
13x = 65
Therefore, x = 65/14
X= 5. Put this value of 5 in equation 1, which gives;
15 + 2y = 39
2y = 39-25
2y = 24
Y = 12
Answer:
x=5
y = 12
Step-by-step explanation:
3x + 2y = 39
2y = 39 - 3x
y = (39 - 3x) / 2
5x - y = 13
5x - ((39 - 3x) / 2) = 13
5x - 39/2 + 3/2x = 13
5x + 3/2x = 13 + 39/2
13/2x = 65/2
x = 65/2 * 2/13
x = 65/13
x = 5
y = (39 - 3x) / 2
y = (39 - 3*5) / 2
y = (39 - 15) / 2
y = 24/2
y = 12
I’m so cunfused! Help please?
Answer:
36
Step-by-step explanation:
To obtain the required number, multiply 27 by the inverse of [tex]\frac{3}{4}[/tex]
The inverse of [tex]\frac{3}{4}[/tex] is [tex]\frac{4}{3}[/tex] ( fraction turned upside down ), thus
[tex]\frac{4}{3}[/tex] × 27 ← divide 3 and 27 by 3
= 4 × 9 = 36
4 2/5 divided by 1 1/5
20 POINTS FOR REAL please answer
The data on the graph show the foot lengths and forearm lengths for a group of people. The line of best fit for the data is shown. Use the equation of the line of best fit to predict the length of a person’s forearm if the length of their foot is 8 inches.
A graph is labeled as Foot Length versus Forearm Length. The horizontal axis is labeled as Length of Foot left parenthesis inches right parenthesis and the vertical axis is labeled as Length of Forearm left parenthesis inches right parenthesis. The values on the horizontal axis range from 0 to 15 in increments of 1 and the values on the vertical axis range from 0 to 15 in increments of 1. Several points are scattered throughout the graph and a line is shown which passes between these points and the equation of the line is labeled as y equals 1 decimal point 1 1 x minus 0 decimal point 8 3.
A.
8.88 inches
B.
6.94 inches
C.
9.16 inches
D.
8.05 inches
Answer:
Option D.
8.05 inches
Step-by-step explanation:
Let
x ----> Length of Foot in inches
y ----> Length of Forearm in inches
we have
[tex]y=1.11x-0.83[/tex]
For x=8 in
substitute the value of x in the linear equation and solve for y
[tex]y=1.11(8)-0.83=8.05\ in[/tex]
find the discriminant 7x^2-5x+1=0
Answer:
Therefore,
[tex]Discriminant=-3[/tex]
Step-by-step explanation:
Given:
[tex]7x^{2}-5x+1=0[/tex]
To Find:
Discriminant = ?
Solution:
For a Quadratic Equation ax²+bx+c=0
The Discriminant is given as
[tex]Discriminant=b^{2}-4ac[/tex]
On comparing we get
[tex]a=7\\b=-5\\c=1[/tex]
Substituting the values we get
[tex]Discriminant=(-5)^{2}-4\times 7\times 1\\Discriminant=25-28\\Discriminant=-3[/tex]
Therefore,
[tex]Discriminant=-3[/tex]
How dose 4x+7=19. Work
Answer:
3
Step-by-step explanation:
4x+7=19
4x=19-7
4x=12
x=12/4
x=3
Help please, giving brainliest.
Answer:
3
Step-by-step explanation:
30 x 3