Answers
4x² - 4x - 5x + 5 = 0
4x(x - 1) - 5(x - 1) = 0
(4x - 5)(x - 1) = 0
Set each binomial equal to zero.
4x - 5 = 0
4x = 0 + 5
4x = 5
x = 5/4
x - 1 = 0
x = 0 + 1
x = 1
Your solutions are x = 1, 5/4
Related Questions
What is the answer for 6
Answers
Formula for SA of a pyramid is: lw+l(√w/2)^2+h^2+w√l/2^2+h^2
We're given all pieces of information, b(l)=9 w=9 h=16
You should be able to plug those values into the equation yourself.
What’s the correct answer?
Answers
Answer: 6 m
This statement:
"Jared has run two-thirds of an 18-kilometer race" can be written as an equation:
[tex]18km.\frac{2}{3}=12km[/tex]
This means two-thirds of 18 km is equivalent to 12 km
If we substract this value to the total, we have the values of the kilometers left to run:
[tex]18km-12km=6km[/tex]
Therefore the correct option is D
im not sure how to do this please help
Answers
the answer is 1.292
An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 220 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden.
Answers
2L + 2w = 220
w = 2/3 L
We can input the w:
2(2/3 L) + 2w = 220
10/3L = 220
10L = 660
L = 66
The width is 44
The length is 66
Stan borrows $5,500 at a rate of 12% interest per year. What is the amount due at the end of 5 years if the interest is compounded continuously? In your final answer, include your calculations. PLEASE EXPLAIN.
Answers
Final answer:
To calculate the amount due at the end of 5 years with continuous compound interest, use the formula A = P*e^(rt), where A is the amount due, P is the principal, e is Euler's number, r is the interest rate, and t is the time. In this case, the amount due is approximately $10,021.66.
Explanation:
To calculate the amount due at the end of 5 years with continuous compound interest, we can use the formula A = P*e^(rt), where A is the amount due, P is the principal (initial amount borrowed), e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years.
In this case, the principal is $5,500, the interest rate is 12% or 0.12, and the time is 5 years.
So, A = $5,500 * e^(0.12 * 5) = $5,500 * e^0.6 ≈ $5,500 * 1.82212 ≈ $10,021.66.
Therefore, the amount due at the end of 5 years with continuous compound interest is approximately $10,021.66.
How many sucrose molecules are in 3.0 moles of sucrose
Answers
Write 806000000 in scientific notation
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Then when you move the decimal left it means it’s positive so you moved it over 8 times
Answer: 8.06 x 10^8
if you have the equation (x+3) squared = 43 when taking the square root of both sides how many solutions will you have
Answers
Answer
21.3 i think hope this can help
the slope of line one is negative 1/2 and line one is parallel to line two. what is the slope of line two?
Answers
please help i will be the happiest person alive
100 points and branliest
Answers
Answer:
Q1: The correct option is: 16
Q2: The correct options are: [tex]\frac{AB}{DE}=\frac{AC}{DF}[/tex] and [tex]\frac{AC}{DF}=\frac{BC}{EF}[/tex]
Q3: The correct option is: [tex]\overline{BC}=12; \overline{EF}=16[/tex]
Step-by-step explanation:
Question 1:
As here [tex]\triangle RST\sim \triangle MNO[/tex], so the ratio of the corresponding sides will be equal. That means.....
[tex]\frac{RS}{MN}=\frac{RT}{MO}\\ \\ \frac{8}{x}=\frac{6.5}{13}\\ \\ 6.5x=8*13\\ \\ x=\frac{8*13}{6.5}=16[/tex]
So, the length of the side [tex]x[/tex] will be 16.
Question 2:
If two triangles are similar, then the ratio of their corresponding sides should be equal. So, here the ratios of the corresponding sides are............
[tex]\frac{AB}{DE}=\frac{1}{3} \\ \\ \frac{BC}{EF}=\frac{2}{6}=\frac{1}{3}\\ \\ \frac{AC}{DF}=\frac{2}{7}[/tex]
So we can see that the ratio of side [tex]AC[/tex] and side [tex]DF[/tex] is not equal with the other ratios.
Thus, the proportions that show the triangles are not similar: [tex]\frac{AB}{DE}=\frac{AC}{DF}[/tex] and [tex]\frac{AC}{DF}=\frac{BC}{EF}[/tex]
Question 3:
Given that, [tex]\frac{AB}{DE}=\frac{BC}{EF}[/tex]
The ratio of [tex]AB[/tex] and [tex]DE[/tex] is given as [tex]\frac{3}{4}[/tex]
So, the ratio of [tex]BC[/tex] and [tex]EF[/tex] will be also [tex]\frac{3}{4}[/tex]
Among the four options, if [tex]BC=12[/tex] and [tex]EF=16[/tex], only then the ratio will be [tex]\frac{3}{4}[/tex]
[tex]\frac{BC}{EF} =\frac{12}{16}= \frac{3}{4}[/tex]
So, the lengths of [tex]BC[/tex] and [tex]EF[/tex] could be 12 and 16 respectively.
Answer:
the correct answer is c
Step-by-stepth explanation:
20/36= x/1200
in this situation, what does x equal?
Answers
Cross multiply.
36 × x and 20 × 1,200
36x = 24,000
x = 666.67
x equals 667, or 666.67.
Briana wants to go to the movies. The price for a student ticket is 2.75 less than the price for the adult’s ticket. If you represent the price of the student ticket using the variable “x”, how would you write the algebraic expression for the adult’s ticket price?
Answers
Adult ticket= x+2.75
Below are the data collected from two random samples of 100 members of a large travel club regarding the type of vacation they prefer:
Sample Adventure Beach Cruise Ski
A 74 5 2 19
B 71 6 2 21
Which of the following inferences can be made based on the data?
A. More members prefer a cruise vacation and a ski vacation than an adventure
vacation.
B. More members prefer a beach vacation and a ski vacation than a cruise vacation.
C. Most members prefer a beach vacation.
D. Most members prefer a cruise vacation.
Answers
There are a total of 5+19+6+21 = 51 people that prefer either a beach or a ski vacation, while only 2+2=4 people prefer a cruise vacation.
Answer:
B. More members prefer a beach vacation and a ski vacation than a cruise vacation.
What is the value of a in the question a/35 +20= 18
Answers
Steps:
1)35( a/35+20)= 18*35
2)35(a/35)+35(20)=18*35
3)35/35a+ 35(20)=18*35
4)35a/35+35(20)=18*35
5)35a/35*700=18*35
6)a+700=18*35
7)a+700=630
8)Subtract 70 both sides
9)Which gives you -70
Hope it helps :))
Javier’s fuel tank holds 12 3⁄4 gallons of gasoline when completely full. He had some gas in the tank and added 10.3 gallons of gasoline to fill it completely.
How many gallons of gasoline were in the tank before Javier added some?
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The number of gallons of gasoline in the tank before Javier added some is 2 3/4 gallons.
1. Subtract 10.3 gallons (the amount he added) from 12 3/4 gallons (the total capacity of the tank).
2. Calculate 12 3/4 - 10.3 to find the remaining amount of gasoline in the tank.
To subtract mixed numbers, we first convert them into improper fractions:
[tex]\[ 12 \frac{3}{4} - 10 \frac{3}{10} \][/tex]
[tex]\[ = \frac{(12 \times 4) + 3}{4} - \frac{(10 \times 10) + 3}{10} \][/tex]
[tex]\[ = \frac{48 + 3}{4} - \frac{100 + 3}{10} \][/tex]
[tex]\[ = \frac{51}{4} - \frac{103}{10} \][/tex]
To subtract fractions, we need a common denominator. Here, the least common denominator (LCD) is 20.
[tex]\[ = \frac{51 \times 5}{4 \times 5} - \frac{103 \times 2}{10 \times 2} \][/tex]
[tex]\[ = \frac{255}{20} - \frac{206}{20} \][/tex]
[tex]\[ = \frac{255 - 206}{20} \][/tex]
[tex]\[ = \frac{49}{20} \][/tex]
Now, we convert the improper fraction back to a mixed number:
[tex]\[ = 2 \frac{9}{20} \][/tex]
Therefore, Javier had 2 9/20 gallons of gasoline in the tank before adding more.
Javier had 2.45 gallons of gasoline in his tank before he added 10.3 gallons to fill it to its full capacity of 12.75 gallons.
To find how many gallons of gasoline were in Javier's tank before he added some, we need to subtract the amount he added from the total capacity of the tank. Javier's fuel tank can hold 12 3/4 gallons when full, which is equal to 12.75 gallons. He added 10.3 gallons to fill it up. Therefore, the amount of gas in the tank before he added more can be calculated as follows:
Amount of gasoline initially in the tank = Total capacity - Amount added
Amount of gasoline initially in the tank = 12.75 gallons - 10.3 gallons
Amount of gasoline initially in the tank = 2.45 gallons
Thus, Javier had 2.45 gallons of gasoline in the tank before he added the 10.3 gallons.
The Grand Canyon is approximately 29 kilometers long. Mariner Valley is a canyon on Mars that is approximately 212 kilometers long. About how many times longer is Mariner Valley than the Grand Canyon?
Answers
Mariner Valley = 212 km
Number of times longer = 212 ÷ 29 = 7.31 times (Nearest hundredth)
Answer: 7.31 times
Answer:
7.31 times.
Step-by-step explanation:
We have been given that Grand Canyon is approximately 29 kilometers long. Mariner Valley is a canyon on Mars that is approximately 212 kilometers long.
To find the number of times Mariner Valley is longer than the Grand Canyon, we will divide 212 by 29.
[tex]\frac{212}{29}=7.3103448\approx 7.31[/tex]
Therefore, the Mariner Valley is 7.31 times longer than the Grand Canyon.
[30 Points] Can you guys help me with this, please? Thank you in advance.
Answers
Part (a):
We are given that:
Total number of files = 250 files
% of photos = 12%
This means that:
number of photos = percentage of photos * total number of files
number of photos = 12% * 250
number of photos = 0.12 * 250
Part (b):
We need to get the number of photos. This means that we will simply compute the result of the equation we obtained from part (a) as follows:
number of photos = 0.12 * 250
number of photos = 30 photos
Question (2):
Part (a):
We know that:
Total amount spent should be less than $80
Amount spent on food = $68.25
Price per each carton of juice = $3
Assuming that number of juice cartons is x, therefore:
amount spent on juice = $3x
Putting the above into inequality, we can find that:
total amount spent > amount spent on food + amount spent on juice
80 > 68.25 + 3x
80 - 68.25 > 68.25 + 3x - 68.25
11.75 > 3x
Part (b):
Now, we want to get the number of cartons, this means that we will solve the inequality in part (a) for x as follows:
11.75 > 3x
11.75 / 3 > 3x / 3
3.9 > x
Now, we can not buy 0.9 carton of juice. This means that we need to approximate the result.
We have:
x < 3.9
The nearest whole number that satisfies this inequality is 3.
This means that Quan can buy a maximum of 3 cartons of juice to satisfy his budget inequality
Question (3):
Part (a):
We can represent the hexagonal using trapeziums and rectngles which are considered simpler polygons.
The division as well as the dimensions are shown in the attached image.
Part (b):
To get the area of the hexagonal, we will get the area of the overall rectangle and remove from it the area of the two dotted triangles.
This can be done as follows:
area of rectangle = length * width = 11 * 24 = 264 in²
area of top right triangle = 0.5 * base * height = 0.5 * 4 * 5 = 10 in²
area of bottom left triangle = 0.5 * base * height = 0.5 * 10 * 4 = 20 in²
Now, we have:
area of hexagonal = 264 - 10 - 20
area of hexagonal = 234 in²
Another solution to get the area:
We can get the area by getting the area of each of the simpler polygons and add them.
This can be done as follows:
area of left trapezium = [tex] \frac{7+11}{2} * 10 = 90 [/tex] in²
area of middle rectangle = 10 * 11 = 110 in²
area of right trapezium = [tex] \frac{6+11}{2} * 4 = 34[/tex] in²
Therefore:
area of hexagonal = 90 + 110 + 34 = 234 in²
Hope this helps :)
Two cylinders, A and B, are created.
Cylinder A has volume V
Cylinder B has the same height as Cylinder A
Cylinder B has half the diameter of Cylinder A
Create and expression the represents the volume of Cylinder B in terms of V
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The length of the minute hand is 150% of the length of the hour hand.
In one hour, how much farther does the tip of the minute hand move than the tip of the hour hand? Round your answer to the nearest tenth.
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[tex]s=r\cdot\theta[/tex]
where [tex]\theta[/tex] is the central angle in radians
In one hour, the hour hand makes 1/12 of a revolution (2π radians), so travels ...
[tex]s_{h}=(30\,mm) \times \frac{1}{12}\cdot 2\pi=5\pi\,mm[/tex]
In one hour, the minute hand makes 1 full revolution, so travels
[tex]s_{m}=(1.5 \cdot 30\,mm) \times 2\pi = 90\pi\,mm[/tex]
The difference in distance traveled is ...
[tex]s_{m}-s_{h}=(90\pi-5\pi)\,mm=85\pi\,mm \approx 267.0\,mm[/tex]
In an hour, the minute hand, which is 1.5 units long, travels a full revolution or approximately 9.4 units, while the hour hand, 1 unit long, covers one-twelfth, or about 0.5 units. Therefore, the minute hand travels approximately 7.9 units more than the hour hand.
Explanation:This question can be solved by first examining the distance each hand travels. In an hour, the minute hand completes a full revolution around the clock face, moving a distance equal to the clock's circumference. If we call the length of the minute hand 1.5 units, then its distance traveled is 2π(1.5).
In contrast, the hour hand moves onto the next hour, covering on-twelfth of the clock's face, or 2π(1/12) using a length of 1 unit for the hour hand. Substract the second measure from the first to find the difference. Thus, the minute hand travels about 7.9 units farther than the hour hand.
Learn more about Circumference here:https://brainly.com/question/37011717
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What is an rational number between 9.5 and 9.7 and include decimal approximation to the nearest hundredth
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Choose the equivalent percent for 4/5
40%,64%,80%,20 or none of these
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Answer:
80%
Step-by-step explanation:
To convert a fraction to percent, we need to multiply the fraction with 100.
Multiply 100 and [tex]\frac{4}{5}[/tex], we get,
[tex]\frac{4}{5} (100)[/tex] = 4 × 20
= 80%
Hence, the correct option is (C) 80%.
How many cubic feet of water can a 18 inch by 19 inch by 36 inch aquarium hold?
Answers
Volume = 18 x 19 x 36 = 12312 in³
Answer: 12312 in³
What is the decimal equivalent of the fraction?
5/33
A) 0.15⎯⎯⎯⎯
B) 0.15
C) 0.1⎯⎯5
D) 0.15⎯⎯
Answers
The decimal equivalent of the fraction 5/33 is option A. o.15....
What are Fractions?Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.
Here p, called the numerator and q, called the denominator, are real numbers.
The given fraction is 5/33.
We have to find the decimal corresponding to the given fraction.
For that divide 5 by 33.
5 is not divisible by 33.
So add 0 and it become 50.
50 = (33 × 1) + 17
And the quotient is 0.1 with remainder 17.
Now 17 is not divisible by 33.
Add 0 and it becomes 170.
170 = (33 × 5) + 5
Quotient becomes 0.15 with remainder 5.
Again the remainder is 5 and add 0 and becomes 50.
It continues.
So the quotient is 0.1515....
Hence the decimal form is 0.(15) repeating.
Learn more about Fractions here :
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PLEASE HELP ASAPPPPP
A piece of cardboard has two circles punched out of it.
What is the approximate area of the remaining cardboard? Use 3.14 for pi and round to the nearest whole number.
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(area of rectangle) - 2(area of circle)
There is a 2 in front of the area of the circle, since there are two identical circles punched out of the rectangle.
First, find the area of the rectangle. The area of the rectangle is given by the following formula:
length * width
You already have your two values for length and width. Plug those values into the formula:
[tex]14 * 18 = 236[/tex]
236 is the area of the rectangle.
Now we'll find the area of the circle.
The diameter of the circle is 2. The radius is one half of the diameter, so the radius is 1.
The area of a circle is found with the following formula:
[tex]A = \pi r^{2}[/tex]
pi is equal to 3.14, so replace the pi symbol with the 3.14. Then, plug your radius into the equation.
[tex](3.14) * 1^{2} = 3.14[/tex]
The area of the circles is 3.14.
Plug your areas into the first equation above.
[tex]236 - 2(3.14) = 236 - 6.28 = 229.72[/tex]
The approximate area of the cardboard is 229.72.
How long is each side of a square that has an area of 25 meters?
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[tex]25 = x \times x \\ 25 = {x}^{2} \\ \sqrt{25} = \sqrt{ {x}^{2} } \\ 5 = x[/tex]
Each side is 5m
triangle shown to the right is 120 sq units. find the base and height
Answers
120 = 1/2 * base * height
Multiply by 2 on both sides. This will cancel out the 1/2 on the right side of the equation and isolate our variables, the base and height. You get:
240 = base * height
There wasn't enough information given on the triangle (at least in your description) for the most accurate answer so your answer just becomes any pair of factors at equal to 240.
1, 240
2, 120,
3, 60
4, 80
6, 40
8, 30
10, 24
12, 20
16, 15
Those are all the possibilities not including fractional factors (ex: 1/4 and 960).
Raul walks 3/8 of a mile to school Laurie walks two thirds of a mile to school how much longer is Lori's walk then Raul's walk
Answers
First you have to make the denominators the same
2/3 = 16/24
3/8 = 9/24
Now you subtract them
16/24 - 9/24 = 7/24
The answer is 7/24
Hope this helps!
Suppose and exponential function is to fit to a set of data. Which of the following residual plots indicates that this function was an appropriate fit for the data?
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The appropriate fit for an exponential data is given by D.
This is because it shows the perfect exponential fit for the residuals.
if a triangular prism has dimensions of 11,14 and 8 what is the volume
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Roger pushes a box on a 30° incline. If he applies a force of 60 newtons parallel to the incline and displaces the box 10 meters along the incline, how much work will he do on the box?
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Force = m * a
m = 60 newtons
a = cos30 (since Roger applies force parallel to the incline, we will use cosine)
F = 60 * cos30
F = 51.9615... N
Work done = F * d
F = 51.9615... N
d = 10 meters
W = 51.9615... N * 10 meters
W = 519.6152... Joules or 520 J
Roger does 600 joules of work on the box when he applies a force of 60 newtons and displaces the box 10 meters along a 30° incline.
When Roger pushes a box on a 30° incline with a force of 60 newtons and displaces the box 10 meters along the incline, the work done on the box can be calculated.
Work is given by the equation W = F imes d imes cos(heta), where W is the work, F is the force applied, d is the displacement, and heta is the angle between the force and the direction of displacement. In this case, because the force is applied parallel to the incline and displacement is along the incline, the angle heta is 0°, making cos( heta) equal to 1.
To find the work done by Roger, we calculate it as:
W = 60 N imes 10 m imes cos(0°)
W = 60 N imes 10 m imes 1
W = 600 joules.
Hence, Roger will do 600 joules of work on the box.