Let first consider the equations one by one and will be solving one by one ;
[tex]{:\implies \quad \sf x+\dfrac{1}{y}=4}[/tex]
Multiplying both sides by y will lead ;
[tex]{:\implies \quad \sf xy+1=4y}[/tex]
[tex]{:\implies \quad \boxed{\sf xy=4y-1\quad \cdots \cdots(i)}}[/tex]
Now, consider the second equation which is ;
[tex]{:\implies \quad \sf y+\dfrac{1}{x}=\dfrac14}[/tex]
Multiplying both sides by x will yield
[tex]{:\implies \quad \sf xy+1=\dfrac{x}{4}}[/tex]
[tex]{:\implies \quad \sf xy=\dfrac{x}{4}-1}[/tex]
[tex]{:\implies \quad \boxed{\sf xy=\dfrac{x-4}{4}\quad \cdots \cdots(ii)}}[/tex]
As LHS of both equations (i) and (ii) are same, so equating both will yield;
[tex]{:\implies \quad \sf 4y-1=\dfrac{x-4}{4}}[/tex]
Multiplying both sides by 4 will yield
[tex]{:\implies \quad \sf 16y-4=x-4}[/tex]
[tex]{:\implies \quad \sf 16y=x}[/tex]
Dividing both sides by y will yield :
[tex]{:\implies \quad \boxed{\bf{\dfrac{x}{y}=16}}}[/tex]
Hence, the required answer is 16
A shipping box has to have specific dimensions to hold an item. The volume must be 7500 cubic inches. The length must be 5 times the width and the height must be 5 inches more than the width. Give the dimensions of the box below. Give your answers as whole numbers or decimals rounded to 1 decimal place.
The dimension of the box is 50in by 10in by 15in
How to calculate the volume of a figureThe volume of an object is the quantity of substance it contains.
The formula for calculating the volume of the box is expressed as:
V = lwh
where:
l is the lengthw is the widthh is the heightGiven the following parameters
length = 5w
height = w + 5
Substiute
7500 = 5w(w)(w+5)
7500 = 5w²(w+5)
1500 = w³+5w²
w³+5w² - 1500 = 0
Factorize to determine the width
On factorizing, the width of the box is 10 inches
Recall that:
l = 5w
l = 5(10)
l = 50inches
Get the height
h = w + 5
h = 10 + 5
h = 15inches
Hence the dimension of the box is 50in by 10in by 15in
Learn more on volume of box here: https://brainly.com/question/14957364
Find the measure ments of angels 2, 3, and 4
Answer:
3-is 85
2- is 95
4-95
Step-by-step explanation:
for 1 is 85
85-180=95
Help me please so i can get points real quick!!
please find the area of the shaded region. EFGH is a square
Please help will mark the brainliest
Answer: 1 1/2 cup of water
Step-by-step explanation: 3 3/4 - 2 1/4 = 1/2 | 3 - 2 = 1 | 3/4 - 1/4 = 2/4 = 1/2
[tex]a^{2} +1=6a[/tex] then what is [tex]7 [a^{2}+\frac{1}{a^{2} }[/tex]
will mark brainliest
Answer:
238
Step-by-step explanation:
Given equation: [tex]a^2+1=6a[/tex]
Rearrange so that it is equal to zero:
[tex]\implies a^2-6a+1=0[/tex]
Quadratic formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
Using the quadratic formula to solve the given equation:
[tex]\implies a=\dfrac{-(-6) \pm \sqrt{(-6)^2-4(1)(1)} }{2(1)}[/tex]
[tex]\implies a=\dfrac{6 \pm \sqrt{32}}{2}[/tex]
[tex]\implies a=3 \pm 2\sqrt{2}[/tex]
[tex]\implies a^2=17 \pm 12\sqrt{2}[/tex]
Substituting this into [tex]7\left(a^2+\dfrac{1}{a^2}\right)[/tex]
[tex]\implies 7\left(17 \pm 12\sqrt{2}+\dfrac{1}{17 \pm 12\sqrt{2}}\right)[/tex]
For [tex]17+12\sqrt{2}[/tex]:
[tex]\implies 7\left(17+12\sqrt{2}+\dfrac{1}{17+12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{(17+12\sqrt{2})^2}{17+12\sqrt{2}}+\dfrac{1}{17+12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{(17+12\sqrt{2})^2+1}{17+12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{289+408\sqrt{2}+288+1}{17+12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{578+408\sqrt{2}}{17+12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{34(17+12\sqrt{2})}{17+12\sqrt{2}}\right)[/tex]
[tex]\implies 7(34)[/tex]
[tex]\implies 238[/tex]
For [tex]17-12\sqrt{2}[/tex]:
[tex]\implies 7\left(17-12\sqrt{2}+\dfrac{1}{17-12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{(17-12\sqrt{2})^2}{17-12\sqrt{2}}+\dfrac{1}{17-12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{(17-12\sqrt{2})^2+1}{17-12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{289-408\sqrt{2}+288+1}{17-12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{578-408\sqrt{2}}{17-12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{34(17-12\sqrt{2})}{17-12\sqrt{2}}\right)[/tex]
[tex]\implies 7(34)[/tex]
[tex]\implies 238[/tex]
Calculate the perimeter of the shape below. Show your work,
Answer:
68 is the perimeter.
Step-by-step explanation:
You can find the perimeter by adding up all of the sides. 13 + 11 + 3 + 7 = 34. To find the other sides of the shape you do 11 + 7 and 13 + 3. 11 + 7 = 18. 13 + 3 = 16. 18 + 16 = 34. 34 + 34 = 68.
Find the measure of each missing side length. Round to the nearest tenth.
Answer:
x = 24.0
Step-by-step explanation:
We will need to use one of the trigonometric ratios to find x.
If we use 58 as the reference angle, we can use tan to find x, as [tex]tan=\frac{opposite}{adjacent}[/tex]
[tex]tan (58)=\frac{x}{15}\\ 15*tan(58)=x\\x=24.005\\x=24.0[/tex]
A tool set is on sale for $180 after a markdown of 40% off the regular price. Find the regular
price.
Answer:
$180 + $72 = $252
Step-by-step explanation:
$180 * 40%
$180 * 0.40 = $72
$180 + $72 = $252
mrs.eng brought 4 packs of glue sticks. Each packs has 5 glue sticks. Her class uses 2 of the glue sticks for a project.
Answer:
same as other answer
Step-by-step explanation:
Find the volume of a prism with base area 32 cm2 and height 1.5 cm.
Answer: 48
Step-by-step explanation:
Fill in the table using this function rule
y=28-3x
Answer:
2 = 22
3 = 19
5 = 13
6 = 10
Step-by-step explanation:
To help with future questions, take whatever is for the x and plug it into the equation
Answer:
22,19,13,10
Step-by-step explanation:
First, Replace the x in the equation with parenthesis (), then inside of the () put the x value in the table so it would look like: y=28-3(2). Then solve by multiplying 2 by 3 so you have y=28-6. Then just subtract 6 from 28 to get 22. Rinse and repeat for the rest of the values. Your first value will be 22, second 19, third 13, and lastly 10. Hope this helps!
A parallelogram has an area of 28 square inches. If the parallelogram is 4 inches long, what is its
width?
Answer:
7 inches
Step-by-step explanation:
The area of a parallelogram is Base x Height.
Area = 28 in^2 = (4 in)*(Height)
Height = 7 inches
brainliest and 50 points
find the area of the polygon
A) 76.16m
B) 37.08m
C) 30.58
D) 19m
Answer:
38.08 m²
Step-by-step explanation:
Given:
Height = 5.6 mParallel side (1): 10.8 metersParallel side (2): 2.8 metersFormula:
[tex]\text{Area of trapezium} = \dfrac{\text{Sum of parallel sides}}{2} \times \text{Height}[/tex]
Substitute the measures in the formula:[tex]\implies \text{Area of trapezium} = \dfrac{\text{Sum of parallel sides}}{2} \times \text{Height} \\\\\\ \implies \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \dfrac{\text{10.8 + 2.8}}{2} \times 5.6[/tex]
Simplify the equation as needed:[tex]\\\\\\\implies \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \dfrac{\text{13.6}}{2} \times 5.6 \\\\\\ \implies \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = {\text{13.6}} \times 2.8 \\\\\\ \implies \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \boxed{38.08 \ \text{m}^{2}}[/tex]
Mark spent $35.50 at the mall. He bought one sweater and some socks. The sweater
cost $20.50 and each pair of socks cost $2.50 each. How many pairs of socks (s) did
Mark buy?
The pressure on a scuba diver at sea level is 14.7 pounds per square inch (psi). The pressure increases 0.445 psi for each foot of depth. Suppose the pressure on a diver is 41.4 psi. How deep is she?
Answer:
14.7÷41.4=0.355
the answer is 0.355
Find the side length of the regular octagon whose perimeter is 674 centimeters??
Quick Answer
Smarties
Answer:
a=84.25cm
Step-by-step explanation:
John wants to purchase a new freezer chest to store food. The amount of space in the freezer chest is known as A. Volume B. Area C. Perimeter
Answer:
A. Volume
Step-by-step explanation:
Volume is how much space is in a substance so that means it is A
Answer:
Volume
Step-by-step explanation:
The amount of space that a substance or object occupies is called Volume.
An archer shoots an arrow up towards a target located on a hill, which is shown by the graph.
A graph of a line and a parabola intersecting at (46.5, 9.3).
Which set of equations best models the point of intersection of the arrow and the target?
y = 0.006x2 + 0.35x + 6 and y = x
y = –0.006x2 + 0.35x + 6 and y = –x
y = 0.006x2 + 0.35x + 6 and y = 0.2x
y = –0.006x2 + 0.35x + 6 and y = 0.2x
As no graph is shown some basic information of parabola can be helpful
As it's. a hill hence the parabola facing downwardsa is negativeAnd a coordinate is given check it whether it is equal to second part of options
(46.5,9.3)We get
y≠xy≠-xy=0.2xLast two are radar now
As a must be negative option D has such similarities.
Option D is correct (Assumption)Answer:
[tex]\sf y = -0.006x^2 + 0.35x + 6\quad and\quad y = 0.2x[/tex]
Step-by-step explanation:
As the archer shoots the arrow up, the trajectory of the arrow can be modeled as a parabola that opens downwards. Therefore, this is a quadratic equation with a negative leading coefficient.
From inspection of the answer options, the path of the arrow is :
[tex]y=-0.006x^2+0.35x+6[/tex]
This means the options for the line equation are [tex]y=-x[/tex] and [tex]y=0.2x[/tex]
We are told that the point of intersection of the line and the parabola is at (46.5, 9.3). As both the x-value and y-value are positive, the equation of the line must be [tex]y=0.2x[/tex]
To confirm, substitute [tex]x=46.5[/tex] into the equation:
[tex]\implies y=0.2(46.5)=9.3[/tex]
The hypotenuse of a right triangle ensures 17cm and one of its legs measures 13cm
Answer:
sqrt (120)
Step-by-step explanation:
Use pythag theorem
Leg1 ^2 + Leg2^2 = Hypot ^2
13^2 + Leg2^2 = 17^2
Leg2^2 = 17^2 - 13^2
Leg2 = sqrt (120)
Boyce invested an average of $450 per month since age 34 in various securities for his retirement savings. His investments averaged a 4% annual rate of return until he retired at age 63. Given the same monthly investment and rate of return, how much more would Boyce have in his retirement savings had he started investing at age 20? Assume monthly compounding.
a $113,320. 00
b $321,946. 93
c $78,624. 00
d $224,749. 27
If Boyce had started investing when he was 20 the amount he would have more than he does in his retirement savings would be b. $321,946.93.
How much more would Boyce have?First convert the interest to a monthly rate:
= 4% / 12 months
= 1 / 3 %
Period:
= (63 - 34) x 12 months a year
= 348 months
Amount saved:
= Amount x ( (1 + rate) ^ number of periods - 1) / rate
= 450 x ( (1 + 1/3%)³⁴⁸ - 1 ) / 1/3%
= $294,811.07
If he started saving at 20, the number of periods would be:
= (63 - 20) x 12
= 516 months
Amount saved:
= 450 x ( (1 + 1/3%)⁵¹⁶ - 1 ) / 1/3%
= $616,758
The difference is:
= 616,758 - 294,811.07
= $321,946.93
Find out more on future value savings at https://brainly.com/question/26662056.
PLS HELP WILL GIVE BRAINLIEST NO DAM SCAMS
Answer:
From what I can actually read:
Step-by-step explanation:
289 x 76= 21946
25 x 68= 1700
36 x 75= 2700
200 x 60= 12000
200 x 70= 14000
683 x 18= 12294
548 x 63= 34524
629 x 8= 5032
529 x 37= 19537
548 x 63= 34524
100 x 10= 1000
551 x 64= 35264
456 x 12= 5472
42 x 8= 336
68 x 14= 952
And it dosen't matter if you have a multi- numberd equation, because either way you can use a calculator to do the math. and a trick for multiplying by 10 or 100 or 1000: is lets say you have 5 x 1000, instead of doing any math just multiply 1 x 5= 5 then add 3 zero's because 1000 has 3 zeros. You can do this with any number like 10,100,1000,10000 ; you could go on forever.
HEL;P PEWLASE PEALSE
[tex]\sin \angle F~~= \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\~~~~~~~~~~~~=\dfrac{GE}{EF}\\\\~~~~~~~~~~~~=\dfrac 2 3\\\\\implies \angle F=\sin^{-1} \left(\dfrac 23} \right)=41.8^{\circ}\\\\\text{Hence the measure of angle F is}~ 41.8^{\circ}[/tex]
A normal distribution has a mean of 97 in the standard deviation of 12 find the probability that a value selected at random is in the following interval: at least 85
Answer:
the answer is not you or anything is not
another question plssss
Answer:
(a) ∠1 and ∠5
Step-by-step explanation:
Complementary angles are angles whose measures total 90°. The angles do not have to be adjacent.
__
In this geometry, we can see that angles 1 and 2 are complementary, as are angles 4 and 5, since their respective sums are right angles. Angles 2 and 5 are vertical angles, so have the same measure.
∠1 + ∠2 = 90° . . . . . . adjacent angles that total a right angle
∠1 +∠5 = 90° . . . . . substitute ∠5 for ∠2, since measures are equal
This means angles 1 and 5 are complementary.
What is the sum? 2x/x2 + x-4/9x
Answer:
(x² + 14x)/(9x²)
Step-by-step explanation:
To do this calculation process:
The first term: 2x/x² = 2/x.
Then: (2/x) + (x - 4)/(9x).
We should common the denominator by multiplying the denominators of the two terms (9x)(x) = 9x² and dividing each denominator by the common denominator.
So, it will be equal:
[(2)(9x) + (x - 4)(x)]/9x² = (18x + x² - 4x)/9x² = (x² + 14 x)/9x².
How do you use exponents in a test
Answer:
An exponent is a number that is to a certain value, like 5^2.
The ^2 means multiply by itself by itself ONCE,
so it would be 5x5.
5^3 means multiply it by itself TWO TIMES,
and going on and on.
Let's say you have a test and the question it's asking is to simplify 5^4.
It's 5x5x5x5, multiplying it by itself FIVE TIMES.
Hope this helped!
On the number line below, the numbers a and b are the same distance from 0. What is a + b? Explain how you know.
If we start at zero and move a units to the right, and then move the same number of units to the left, we will be back at 0. We can also represent this symbolically. Since a and b are the same distance from zero but are on opposite sides of zero, we know that they are opposites, so b = -a
Answer:
If we start at zero and move a units to the right, and then move the same number of units to the left, we will be back at 0. We can also represent this symbolically. Since a and b are the same distance from zero but are on opposite sides of zero, we know that they are opposites, so b = -a.
1 A 600g packet of chocolate coffee beans cost $ l2 much is this per 100g?
Answer:
$ 2 per 100g,
Step-by-step explanation:
100g = 1/6 of 600g so:
Cost per 100g = 12 * 1/6
= $ 2.
Answer:
$2
Step-by-step explanation:
12 divided by 6
qyestion/ graph above
Answer:
2010
Step-by-step explanation:
I do not think so
