Answer:
Any ratio where the original sides are both multiplied by the same number.
For example,
4 : 5 (your ratio)
4 x 2 : 5 x 2 (multiply both sides by a number)
8 : 10 (equivalent ration)
Solve by completing the square
[tex]4x^2+12x=32\\\\\implies x^2+3x=8\\\\\implies x^2 +2 \cdot \dfrac 32 \cdot x+\left(\dfrac 32 \right)^2 - \left(\dfrac 32\right)^2 =8\\ \\\implies \left(x+\dfrac 32 \right)^2 = 8 + \dfrac 94 = \dfrac{41}4\\\\\implies x+\dfrac 32 = \pm\dfrac{\sqrt{41}}2\\\\\implies x = \pm \dfrac{\sqrt {41}}2 - \dfrac 32\\\\\text{The roots are}~ x = -\dfrac 32-\dfrac{\sqrt{41}}2~ \text{and}~~ x = -\dfrac 32+\dfrac{\sqrt{41}}2[/tex]
Shania is making eight gift bags to give out to her friends coming over to her house for a movie night. Each gilt bag will con
polishes and a manicure kit. Including tax, each nail polish costs $2.50 and each manicure kit costs $4.00.
The following expression shows the amount of money Shania will spend on gift bags.
8(2.5x + 4)
Answer: 20x + 32 or $20 spent on the nail polish & $32 spent on the kits
Formula:
bags($polishx + $kit)
Work:
8(2.5x + 4)
8 x 2.5x = 20x
8 x 4 = 32
A rectangle has a length of √ 72 meters and a width of √ 18 meters. Find its perimeter in exact and approximate forms, and then find its area.
The exact perimeter is _________ meters.
This is approximately ___________ meters. (Round your answer to the nearest tenth)
The area of the rectangle is ____________ square meters.
Answer:
The exact perimeter is [tex]18\sqrt{2}[/tex] meters.
This is approximately 25.5 meters (nearest tenth).
The area of the rectangle is 36 square meters.
Step-by-step explanation:
Area of a rectangle = width × length
Perimeter of a rectangle = (2 × width) + (2 × length)
Given:
length = [tex]\sqrt{72}[/tex] mwidth = [tex]\sqrt{18}[/tex] mPerimeter
[tex]\textsf{Perimeter}=2 \sqrt{18} +2\sqrt{72}[/tex]
[tex]=2 \sqrt{9 \cdot 2} +2\sqrt{36 \cdot 2}[/tex]
[tex]=2 \sqrt{9} \sqrt{2}+2\sqrt{36}\sqrt{2}[/tex]
[tex]=2 \cdot 3 \sqrt{2}+2\cdot 6\sqrt{2}[/tex]
[tex]=6 \sqrt{2}+12\sqrt{2}[/tex]
[tex]=18\sqrt{2} \textsf{ m}[/tex]
The exact perimeter is [tex]18\sqrt{2}[/tex] meters.
This is approximately 25.5 meters (nearest tenth).
Area
[tex]\textsf{Area}=\sqrt{18} \times \sqrt{72}[/tex]
[tex]=\sqrt{9 \cdot 2} \times \sqrt{36 \cdot 2}[/tex]
[tex]=3\sqrt{2} \times 6\sqrt{ 2}[/tex]
[tex]=18\sqrt{2}\sqrt{ 2}[/tex]
[tex]=18 \cdot 2[/tex]
[tex]=36 \textsf{ m}^2[/tex]
The area of the rectangle is 36 square meters.
18. Find the present value of a deferred annuity of ₱ 30,000.00 at the end of every year for 10 years. The first payment of a mother will be done at the end of the second year, and the money is compounded at 3% annually. a. ₱ 244,354.12 b. ₱ 248,452.51 c. ₱ 278,520.14 d. ₱ 291,245.18
Answer:
₱ 248,452.51
Step-by-step explanation:
₱ 248,452.51
The number 2 in the expression 5 + 2x is called the
coefficient of x. How does changing the coefficient to
6 change the meaning of the expression?
Changing the coefficient of x to 6 changes the meaning of the expression as 5 is added to 6 times x
Solution:
Given that number 2 in the expression 5 + 2x is called the coefficient of x
We are asked to find what happens when changing the coefficient to 6 changes the meaning of the expression
In the expression,
5 + 2x
This means 5 is added to 2 times x or 5 is added to twice of x
Number 2 is called the coefficient of x
When we change this coefficient to 6, the expression becomes,
5 + 6x
So now the meaning of expression becomes,
5 is added to 6 times x
So changing the coefficient of x changes the meaning of the expression
What is the area of the parallelogram QRST?
[tex]\text{Area of parallelogram QRST} = QR \times TU = 20 ~in \times 18~in =360 in^2[/tex]
A sample of radium has a weight of 1.5 mg and a half-life of approximately 6 years.
a. How much of the sample will remain after 6 years?
Answer:
0.75mg
Step-by-step explanation:
6 years is its half life, meaning that half of it will have iradiated by that point. 1.5 / 2 = 0.75
Stuart and Francisco designed a black rocket and a white rocket during an aerospace class. Both rockets were launched after class. During the launch, Stuart and Francisco recorded data of their rockets trajectories. Stuart modeled the black rockets distance from the ground, in feet, x seconds after it was launched with the graph. Francisco modeled the white rockets distance from the ground, in feet, x seconds after it was launched with the function g(x)= -16x^2 + 50x +7 . Both wanted to know what the greatest distance was from the ground for each rocket. Stuart obtained that his rockets greatest distance from the ground was [Drop down 1] while Francisco obtained a greatest distance of [Drop down 2].
We will see that for Stuart the maximum height is 30ft, and for Francisco it is 46.0625 ft
How to get the greatest distance from the ground?In the case of Stuart it is simple, as we have a graph, we just need to see the largest y-value on the graph. We can see that it is y = 30, then for Stuart, the largest distance from the ground is 30ft.
In the case of Francisco, we need to find the maximum of:
g(x)= -16x^2 + 50x +7
Notice that this is a quadratic of negative leading coefficient, so the maximum is at the vertex.
x = -50/(2*-16) = 25/16
Evaluating the function in 25/16 we get:
g(25/16) = -16*(25/16)^2 + 50*(25/16) +7 = 46.0625 ft
If you want to learn more about quadratic functions, you can read:
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A bead is formed by drilling a cylindrical hole of 2mm diameter through a sphere with an 8mm diameter. Estimate the volume of the bead to the nearest whole?
Volume of the bead = Volume of the sphere - volume of the cylindrical hole = 242.95 mm³.
What is the Volume of a Sphere and a Cylinder?Volume of a sphere = 4/3πr³Volume of a cylinder = πr²hVolume of the bead = Volume of the sphere - volume of the cylindrical hole
= 4/3π(4³) - π(1²)(8)
= 268.08 - 25.13
Volume of the bead = 242.95 mm³
Learn more about volume of sphere on:
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What is the mean of the data set?
21.2, 15.3, 20.5, 16.8, 30.2
Question 1 options:
19.2
20.8
21.5
Answer:
B. 20.8 (second option)Step-by-step explanation:
The mean is calculated by adding up their values, and then dividing them into elements of a set.
All of them should first be added together.
21.2+15.3+20.5+16.8+30.2
Solve.
[tex]\sf{21.2+15.3+20.5+16.8+30.2=104}[/tex]
The sum of the data set is 104.
The number of terms in the data set is n=5.
Therefore, the mean of the data set is 20.8, which is our answer.
I hope this helps you! Let me know if my answer is wrong or not.
the question is below please help by monday
Jodi has a collection of 153 shells. She gives 39 shells to her sister Sherri. Then their mother gives each sister 28 shells.
Part A
How many shells does Sherri have now?
A.
28
B.
67
C.
142
D.
181
Part B
How many shells does Jodi have now?
A.
28
B.
67
C.
142
D.
181
Answer:
Part-A= C
Part-B= B
Step-by-step explanation:
153-39=114
114+28=142
39+28=67
Answer:
Part A is b and Part B is c good luck
Rocio drops a ball from a height of 4 meters. Rocio observes that each time the ball bounces, it reaches a peak height which is 79% of the previous peak height, as shown at left. Which of the following equations correctly models the ball's peak height, h, in meters, after b bounces?
The exponential equation that correctly models the ball's peak height, h, in meters, after b bounces is given by:
[tex]H(b) = 4(0.79)^b[/tex]
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem:
Rocio drops a ball from a height of 4 meters, hence A(0) = 4.Each time the ball bounces, it reaches a peak height which is 79% of the previous peak height, hence 1 - r = 0.79.Thus, the equation is given by:
[tex]H(b) = 4(0.79)^b[/tex]
More can be learned about exponential equations at https://brainly.com/question/25537936
The diagram shown is two intersecting lines. The measure of 5 is 47°.
Answer:
a) 37º
b) 143º
c) 2x - 5 = 143
Step-by-step explanation:
a) Angles 5 and 7 are vertical angles and therefore have the same measurements.
b) Angles 5 and 6 form a straight line and are therefore supplementary (add up to 180º). 180 - 37 = 143.
c) We found the measure of angle 6 is 143º in part b. We can set that equal to 2x - 5. Therefore the equation is 2x - 5 = 143.
please someone help me! I’m not accepting any links or files.
:)
Answer:
400
Step-by-step explanation:
48 is 12% of x
12/100 = 48/x
3/25 = 48/x
1/25 = 16/x
x = 25 × 16
x = 400
Answer: 400
Answer:
400
Step-by-step explanation:
(48 x 100) / 12 = 400
I NEEDDD HELPPPP 50PTS !!!!!!!!!!!!!!
Answer:
$1225
$33,775
Step-by-step explanation:
Given:
price of current model = $35,000next model = 3.5% LESS than price of current modelTo find a percentage of an amount, convert the percentage into a decimal and multiply it by the amount:
3.5% = 3.5/100 = 0.035
⇒ Decrease in price = 0.035 × 35000 = $1225
Price of next model = price of current model - decrease in price
= 35000 - 1225
= $33,775
Decrease amount:-
3.5% of 350000.035(35000)$1225So
New price:-
35000-1225$33775100 divided by 35,513.22
Answer:
0.002816 or 0.003
Step-by-step explanation:
Be sure to use a calculator to double check the answer
Hope this helps!
A manager drew this box-and-whisker plot to represent the number of minutes each of his 27 employees took on their break. Each employee took a different amount of time.
How many employees took a break longer than 49 minutes?
Enter your answer in the box.
Answer:
6
Step-by-step explanation:
Longer than 49 is only 25% percentile.
27 X .25 = 6.75
Employees are whole numbers, therefore the answer is 6.
Answer:
6
Step-by-step explanation:
After a 25% reduction, a sweater is on sale for $41.25.
What was the original price?
Let the original price be x.
x * (1 - 0.25) = $41.25
0.75x = $41.25
x = $41.25 / 0.75 = $55
Answer:
$55
Step-by-step explanation:
____ decrease by 25%= $41.25, which the unknown number is $55.
You spent $24 more than Pam. If you spent $82, how much money did Pam spend?Write and solve an equation.
Answer:
58
Step-by-step explanation:
its basically saying that pam spent 24 dollars less than you. soo 82 - 24 = 58
Which statement about these triangles is true.
Picture Below
Answer:
For me I think it is a number 3
Step-by-step explanation:
The statement about these triangles which is true there are exactly three isosceles triangles, the correct option is B.
What is the right triangle?A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.
We are given that;
4 triangle figure
we can answer the question by counting how many triangles belong to each category. We have:
Three acute triangles: B, D, and E.
Three isosceles triangles: A, D, and E.
Two right triangles: A and C.
Two scalene triangles: B and C.
Therefore, the statement that is true about these triangles is:
Therefore, by the given triangle answer will be There are exactly three isosceles triangles.
Learn more about a right angle triangle;
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#SPJ2
Complete the table below with the amounts of raspberry juice, apple
juice and soda needed to make the different quantities of Fruit Fizz.
mixture must taste exactly the same each time.
geometry. find RN. pls help!!
Apply Thales theorem
[tex]\\ \rm\rightarrowtail \dfrac{MR}{RN}=\dfrac{MQ}{QP}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{10}{RN}=\dfrac{8}{5}[/tex]
[tex]\\ \rm\rightarrowtail 8RN=50[/tex]
[tex]\\ \rm\rightarrowtail RN=50/8[/tex]
[tex]\\ \rm\rightarrowtail RN=6.25[/tex]
Answer:
RN = 6.25
Step-by-step explanation:
Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
Therefore,
MQ : MP = MR : MN
⇒ 8 : (8 + 5) = 10 : (10 + RN)
⇒ 8 : 13 = 10 : (10 + RN)
⇒ [tex]\sf\dfrac{8}{13}=\dfrac{10}{10+RN}[/tex]
Cross multiply and solve:
⇒ 8(10 + RN) = 10 × 13
⇒ 80 + 8RN = 130
⇒ 8RN = 130 - 80
⇒ 8RN = 50
⇒ RN = 50 ÷ 8
⇒ RN = 6.25
d If the width of a rectangle with perimeter P is 6 units, what is its length?
Step-by-step explanation:
width is 6 units
P=2(l+w)
p=2(l+6)
l+6=p/2
l= (p/2)-6
The length of the reactangle with a width of 6 units and perimeter p units is (P/2)-6 units.
What is the perimeter of a rectangle?A perimeter is a closed route that surrounds, outlines, or embraces a rectangle. The perimeter of a rectangle is given by the formula,
[tex]\rm Perimeter= 2(Length +width)[/tex]
As it is given that the width of the rectangle is 6 units, while the perimeter of the rectangle is P. Now if we write about the perimeter of the rectangle, it can be written as,
[tex]\rm Perimeter= 2(Length +width)[/tex]
[tex]P = 2(l+6)\\\\\dfrac{P}{2} = (l+6)\\\\l = \dfrac{P}{2}-6[/tex]
Hence, the length of the reactangle with a width of 6 units and perimeter p units is (P/2)-6 units.
Learn more about Perimeter:
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Help help help help help
[tex]\mathbf{m}=-\frac{1}{2}[/tex]
Step-by-step explanation:⇒ Find the slope of the line that is perpendicular to y = 2x + 7 :
↓
[tex]\mathbf{m}=-\frac{1}{2}[/tex]
I hope this helps you
:)
What is the value of e?
1190
c
a
O A. 22°
OB. 48°
0 C. 61°
O D. 180°
Answer:
C. 61 degrees
Step-by-step explanation:
a line is 180 degrees
so e and 119 degrees makes a line
so you subtract 180-119= 61 degrees
*Pls help me*
No links
Answer:
See below ↓
Step-by-step explanation:
a. 4 ÷ (2/3) = 12/3 ÷ 2/3 = 12 ÷ 2 = 6
b. 4 ÷ 1 = 4
Attachment below.
Answer:
1: 6
2:4
Step-by-step explanation:
1. Find the area of the polygon
2. Find the area of the polygon
A=__ sq. un
3. In the figure, each of the small squares has an area of 1. What is the area of the shaded region?
(A) 50
(B) 45
(C) 100
(D) 55
Answer:
1. A = 40 units²
2. A = 72 units²
3. B) 45
Step-by-step explanation:
1. This shape comprises 4 congruent triangles with base of 5 units and height of 5 units.
Area of a triangle = 1/2 x base x height
Therefore, area of polygon = 4(1/2 x 5 x 4)
= 40 units²
2. This shape comprises two pairs of congruent triangles.
Area of a triangle = 1/2 x base x height
Therefore, area of polygon = 2(1/2 x 2 x 6) + 2(1/2 x 10 x 6)
= 72 units²
3. Count the number of shaded squares:
9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45 units²
Stacy performed an experiment in which she rolled a six-sided die multiple times. The results are shown below
Based on the results above, predict the number of times a 3 would be rolled if Stacy performs the experiment a total of 480 times
Answer:
5/9
Step-by-step explanation:
Let the probability of getting a multiple of 3 is "A"
Let the probability of getting an even number is "B"
Total number of outcomes=36
Total number of favourable outcomes of either a multiple of 3 or an even number are
(1,1) ,(1,2) ,(2,1) ,(1,3) ,(3,1) ,(2,2) ,(1,5) (5,1) ,(3,3) ,(2,4) ,(4,2) ,(2,6) ,(6,2) ,(3,5) ,(5,3) ,(4,4) ,(6,4) ,(4,6) ,(5,5) ,(6,6)
That is we have 20 favourable outcomes
Hence, Probability=\frac{\text{favourable outcomes}}{\text{total number of outcomes}}Probability=
total number of outcomes
favourable outcomes
Therefore, after substituting the values we get
probability=\frac{20}{36}probability=
36
20
After simplification we will get
probability=\frac{5}{9}probability=
9
5
sophia has 8 spend on lunch .Does she have enough money for a sandwich a drink and a bag of chips
Answer:
depends on how much each thing costs
Step-by-step explanation: