Answers
[tex]\bf \cfrac{10x-2}{7x}=\cfrac{8x}{5x+3}\implies (10x-2)(5x+3)=(7x)(8x) \\\\\\ 50x^2-10x+30x-6=56x^2\implies 0=6x^2-20x+6 \\\\\\ 0=3x^2-10x+3\implies 0=(3x-1)(x-3)\implies x= \begin{cases} \frac{1}{3}\\\\ 3 \end{cases}[/tex]
Related Questions
the graph that represents 4 ≤ x
Answers
Answer:
Refer attachment.
Step-by-step explanation:
Given: Equation as 4 ≤ x
We have to plot the graph for that represents the given equation 4 ≤ x.
Consider the given equation 4 ≤ x.
It can be read as x takes values which is greater than and equal to 4.
So, the graph of this equation 4 ≤ x is given as shown below.
What pair of numbers has the geometric mean of 44
Answers
so 16×121 = 1936
so the pair is 16 and 121
The possible pair of numbers that has the geometric mean of 44 is 16 and 121 and this can be determined by using the concept of geometric progression.
Given :
The geometric mean of 44.
The following steps can be used in order to determine the pair of numbers that has the geometric mean of 44:
Step 1 - The concept of geometric progression can be used in order to determine the pair of numbers that has the geometric mean of 44.
Step 2 - Let the two numbers be 'a' and 'b'.
Step 3 - According to the given data, the geometric mean of 44, that is:
[tex]\rm \sqrt{ab} = 44[/tex]
Step 4 - Simplify the above expression.
ab = 1936
Step 5 - So, the possible pair of numbers that has the geometric mean of 44 is 16 and 121.
For more information, refer to the link given below:
https://brainly.com/question/4853032
A number divided by three less two is at most two
Answers
3-2 = 1
x/1 ≤ 2
X ≤ 2
The required number would be x ≤ 2 which represents the number divided by three less two is at most two.
What is inequality?Inequality is defined as mathematical statements with at least two terms including non-equal variables or integers.
What is algebra?
Algebra is the study of mathematical symbols, whereas logic is the manipulation of those symbols.
The number divided by three less two equals the number specified in the question.
Let the required number would be x
As per the given condition, translate the phrase into an algebraic inequality as:
⇒ x/(3 - 2) ≤ 2
Apply the subtraction operation, and we get
⇒ x/1 ≤ 2
⇒ x ≤ 2
Therefore, the required number would be x ≤ 2.
To learn more about the inequalities click here:
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A shop sells three types of boots (football, rugby and hiking). Sales are usually in the ratio 6 : 2 : 3 last month, 24 pairs of football boots were sold. How many boots altogether were sold last month?
Answers
Answer:
Total number of boots sold = 44
Step-by-step explanation:
Ratio of football, rugby and hiking boots sold = 6 : 2 : 3
24 pairs of football boots were sold.
That is
6 n = 24
n = 4.
Number of rugby boots sold = 2 n = 2 x 4 = 8
Number of hiking boots sold = 3 n = 3 x 4 = 12
Total number of boots sold = 6n + 2n + 3n = 11n = 11 x 4 = 44
Total number of boots sold = 44
Add. (−x^3 + 26x^2 − 7x−13) + (6x^4 − x^3 + 8x+27) Express the answer in standard form. Enter your answer in the box.
Answers
hope this helps
Letter grades earned by a particular student in history class.
a. qualitative/nominal
b. qualitative/ordinal
c.quantitative/continuous
d.quantitative/ discrete
i think the answer is d
Answers
The enrollment at a high school for the year 2007 is approximately 1500. The growth of the school population can be represented by the equation P = 1500(1.04)x where x represents the years after 2007. After how many years will the population of the school be approximately 1900?
Answers
P=1500 (1.04)^x
When have to find x, when population, p=1900
Put value of P=1900 in above equation.
1900=1500(1.04)^x
Divide both sides by 1500
19/15=(1.04)^x
1.27=(1.04)^x
Take natural log.
ln(1.27)= ln(1.04)^x
ln(1.27)=x ln (1.04)
Divide both sides by ln (1.04)
x=6 years
Answer: 6 years
Jason's insurance company pays for 80% of the cost of an ambulance ride, after he pays a $200 deductible. The ambulance ride costs $1200.
How much wold Jason pay for an ambulance ride?
A) 200
B) 240
C) 400
D) 440
Answers
fitness center currently has 320 members. Monthly membership fees are $45. The manager of the fitness center has determined that each time the membership fees increase by $5, approximately 10 members leave and go to a different gym.
Write an equation that can be used to find the revenue of the fitness center in dollars, y, after x price increases of $5.
y = -50x2 + 1,150x + 14,400
y = -50x2 + 3,425x + 14,400
y = -50x2 + 2,975x + 14,400
y = -50x2 + 2,050x + 14,400
Answers
y = -50x2 + 1,150x + 14,400 - This one seems to be the closest to the answer
Answer:
y= -50x^2+1,150x+14,400
Step-by-step explanation:
fitness center currently has 320 members. Monthly membership fees are $45. The manager of the fitness center has determined that each time the membership fees increase by $5, approximately 10 members leave and go to a different gym.
LEt x be the number of price increases of $5
y is the revenue
Revenue= membership fee * members
for x number of increase in fee by 5 then member ship fee becomes 45+5x
approximately 10 members leave, so members becomes (320-10x)
y = (45+5x) (320-10x)
Multiply it using FOIL method
y=45 * 320 +45*(-10x) + 5x * 320 + 5x * (-10x)
y=14400 - 450x + 1600x - 50x^2
Combine like terms
y= -50x^2+1150x+14400
You have two accounts with balances $450 and $35. you want to bring up the balance in the second account but do not want the balance of the first to drop below $215. how much can you transfer from the first to the second account?
a.$35
b.$215
c.$235
d.$450 submit
Answers
$450 - $215= $235
You can transfer $235.
The answer is C) $235.
Hope this helps! :)
What is the absolute value of -4-2i
Answers
All absolute value is asking is how far away it is from zero.
Please answer ASAP! :)
What is the slant height if the surface area is 243 square centimeters?
8 cm
10 cm
11 cm
9 cm
Answers
The answer is 9cm
SA = r + r 2
452.16 m 2 = (3.14)(6 m)(x) + (3.14)(6 m) 2
452.16 m 2 = (3.14)(6 m)(x) + (3.14)(36 m 2)
452.16 m 2 = (18.84 m)x + 113.04 m 2
339.12 m 2 = (18.84 m)x
18 m = x
Answer:
Option D. 9 cm
Step-by-step explanation:
Surface area of the given figure is S = 243 cm² and we have to find the slant height.
We can see this figure comprises of 1 square and 4 triangles.
Let the slant height of the given triangles is L.
So area of one triangle = [tex]\frac{1}{2}(Slant height).(Base)[/tex]
and the area of square = side² = 9² = 81 cm²
Now surface area of total figure = Area of square + 4×(area of a triangle)
[tex]243=9^{2}+\frac{4}{2}(9.L)[/tex]
243 = 81 + 2×9L
18L = 243 - 81 = 162
[tex]L=\frac{162}{18}[/tex]
L = 9 cm
Therefore Option D. 9 cm is the correct answer.
The pair of values below is from an inverse variation. Find the missing value.
(4,14), (10,y)
Answers
x1y1 = x2y2
Now you just have to plug in the information.
4 x 14 = 10 x y2
What do you do now? You isolate the variable, y2. You do this by dividing y2 by the number it is multiplied.
Like this: [tex] \frac{y2}{10} [/tex]
As we all know, what you do to one side you must do to the other. But before you do that, you need to multiply the 4 by the 14.
4 x 14 = 56
Now you can divide by 10.
[tex] \frac{56}{10} [/tex]
The answer should be 5.6. Hopefully this helped!
How many 2 digit numbers can you make using the digits 1,2,3,4 without repeating the digits
Answers
−12.7=y−3.4
Can you guys please help me solve this. Thanks!
Answers
[tex]-12.7 = y-3.4 [/tex]
From here, we must clear the value of y.
For this, we follow the following steps:
1) we add 3.4 on both sides of the equation:
[tex]-12.7 + 3.4 = y-3.4 + 3.4 [/tex]
2) We rewrite the right side of the equation:
[tex]-12.7 + 3.4 = y + 0 -12.7 + 3.4 = y[/tex]
3) We do the algebraic sum of the left side of the equation:
[tex]-12.7 + 3.4 = y -9.3 = y[/tex]
Therefore, the solution of the equation is:
[tex]y = -9.3 [/tex]
Answer:
y = -9.3
Stan guessed on all 10 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he got at least 2 questions correct? Round the answer to the nearest thousandth.
Answers
The probability that he got at least 2 questions correct is 0.756
Lets assume, the event of getting a question correct is P
As, each question has 4 answer choices and only one choice is correct,
So, P = [tex] \frac{1}{4} [/tex]
When
the probability of getting 1 success in 1 trial is p, then the probability of getting exactly x successes out of n trials is given by the
formula :
(ⁿCₓ )(P)ˣ (1-P)ⁿ⁻ˣ
Here the total number of questions is 10. So, n= 10
Stan needs to get at least 2 questions correct, that means he can get 2, 3, 4, 5, 6, 7, 8, 9 or 10 questions correct.
Now according to the formula,
P(x=2) = ¹⁰C₂ ([tex] \frac{1}{4} [/tex])² ([tex] 1- \frac{1}{4} [/tex])¹⁰⁻²
= ¹⁰C₂ [tex] (\frac{1}{16})(\frac{3}{4})^8 [/tex]
= 0.281567573
P(x=3) = ¹⁰C₃ ([tex] \frac{1}{4} [/tex])³ [tex] (\frac{3}{4})^7 [/tex]
= (120) ([tex] \frac{1}{4} [/tex])³ [tex] (\frac{3}{4})^7 [/tex]
= 0.250282287
P(x=4) = ¹⁰C₄ ([tex] \frac{1}{4} [/tex])⁴ [tex] (\frac{3}{4})^6 [/tex]
= (210)([tex] \frac{1}{4} [/tex])⁴ [tex] (\frac{3}{4})^6 [/tex]
= 0.145998001
P(x=5) = ¹⁰C₅ ([tex] \frac{1}{4} [/tex])⁵ [tex] (\frac{3}{4})^5 [/tex]
= (252) ([tex] \frac{1}{4} [/tex])⁵ [tex] (\frac{3}{4})^5 [/tex]
= 0.058399200
P(x=6) = ¹⁰C₆ ([tex] \frac{1}{4} [/tex])⁶ [tex] (\frac{3}{4})^4 [/tex]
= (210) ([tex] \frac{1}{4} [/tex])⁶ [tex] (\frac{3}{4})^4 [/tex]
= 0.016222000
P(x=7) = ¹⁰C₇ ([tex] \frac{1}{4} [/tex])⁷ [tex] (\frac{3}{4})^3 [/tex]
= (120) ([tex] \frac{1}{4} [/tex])⁷ [tex] (\frac{3}{4})^3 [/tex]
= 0.003089904
P(x=8) = ¹⁰C₈ ([tex] \frac{1}{4} [/tex])⁸ [tex] (\frac{3}{4})^2 [/tex]
= (45) ([tex] \frac{1}{4} [/tex])⁸ [tex] (\frac{3}{4})^2 [/tex]
= 0.000386238
P(x=9) = ¹⁰C₉ ([tex] \frac{1}{4} [/tex])⁹ [tex] (\frac{3}{4})^1 [/tex]
= (10) ([tex] \frac{1}{4} [/tex])⁹ [tex] (\frac{3}{4})^1 [/tex]
= 0.000028610
P(x=10) = ¹⁰C₁₀ ([tex] \frac{1}{4} [/tex])¹⁰
= 0.000000953
Now we will just add all the probabilities and get:
0.281567573 + 0.250282287+ 0.145998001+ 0.058399200+ 0.016222000+0.003089904+0.000386238+ 0.000028610 +0.000000953
= 0.755974766
= 0.756 (rounding to the nearest thousandth)
So, the probability that he got at least 2 questions correct is 0.756
Answer:
Step-by-step explanation:
C on edge Test
distance between 1,3 and -3, -1
Answers
Help please!!!!!!!!!
Answers
If the exponents on the highest variable are the same in the horizontal asymptote is the division of coefficient on the top with the bottom. In plain English what that means is that if you make m = 1 then the coefficients are 2 and 1 (2 in the numerator and 1 in the denominator). If m is any other value greater than 1 there is not a horizontal asymptote.
C <<<====answer.
Third one down.
Rewrite 20/6 as a mixed number.
Answers
20/6 = 3 R2 = 3
Thus, 3 is our whole number that resides next to the fraction.
Now take this number, multiply it by the denominator, and subtract this value from the numerator: 20 - 3(6) = 2. This is the numerator of the fraction in our mixed number.
Now simply add the denominator under this new numerator and place the three next to this fraction: 3 2/6.
The improper fraction number 20/6 is converted into a mixed fraction number as 3 ¹/₃.
What is the mixed fraction number?The mixed fraction number is the combination of the whole number and the proper fraction number. In a proper fraction number, the numerator is smaller than the denominator.
The improper fraction is 20/6.
Convert the improper fraction into a fraction number.
⇒ 20 / 6
⇒ 10 / 3
⇒ (9 + 1) / 1
⇒ 9/3 + 1/3
⇒ 3 ¹/₃
The improper fraction number 20/6 is converted into a mixed fraction number as 3 ¹/₃.
More about the mixed fraction number link is given below.
https://brainly.com/question/29019463
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Find the supplement of the complement of a 51 degree angle
Answers
Supplementary = 180 degrees
Compliment of 51:
90 - 51 = 39 degrees
Supplement of 39:
180 - 39 = 141 degrees
The supplement of the compliment of a 51 degree angle is 141 degrees.
If the endpoints of AB have the coordinates A(9, 8) and B(-1, -2), what is the midpoint of AB?
A. 5,3
B. 4,5
C. 5,5
D. 4,3
Answers
D. (4,3)
Explanation:
The endpoints of the line are given as (9,8) and (-1,-2)
1- Computing the x-coordinate of the midpoint:
Xmidpoint = (x1+x2) / 2 = (9+-1)/2 = 8/2 = 4
2- Computing the y-coordinate of the midpoint:
Ymidpoint = (y1+y2) / 2 = (8+-2) / 2 = 6/2 = 3
Based on the above, the midpoint is (4,3)
Hope this helps :)
A book is in the shape of a right rectangular prism. It measures 812 inches tall, 7 inches wide, and 212 inches thick.
What is the volume of the book?
a 4712 in³
b 8012 in³
c 14834 in³
d 17912 in³
Answers
the Volume of a prism=a*b*c
a----> tall--------> 8 1/2 in=8.5 in
b-----> wide-----> 7 in
c-----> thick-----> 2 1/2 in=2.5 in
therefore
V=8.5*7*2.5=148.75 in³------------equal a 148 3/4 in³
the answer is the option c 148 3/4 in³
Which of the binomials below is a factor of this trinomial?
3x2 + 18x + 24
A. x + 4
B. x - 4
C. x - 3
D. x + 3
Answers
Final answer:
The binomial factor of the trinomial 3x^2 + 18x + 24 is 'x + 4', which corresponds to Option A.
Explanation:
The student is asking which binomial is a factor of the trinomial 3x2 + 18x + 24. To find a factor, you can either factor the trinomial directly or use the zero product property, which states that if a product equals zero, then at least one of the factors must be zero. Since we're looking for a binomial factor and not solving for x, we'll factor the trinomial.
Factors of 3x2 are 3x and x, and factors of 24 that add up to 18 (when multiplied by 3 or 1 from the 3x2 term) are 6 and 4. Thus, the trinomial can be factored as (3x + 4)(x + 6). So, the binomial that is a factor of the trinomial is x + 4, which is Option A.
Factor completely x^2 + 16.
(x + 4)(x + 4)
(x + 4)(x − 4)
Prime
(x − 4)(x − 4)
Answers
Look at some real estate want ads in your newspaper. Enter the price of a two-bedroom home and a three-bedroom home. If you find some abbreviations you do not understand, ask your teacher.
Answers
3 Bedroom house for $122,900, 1610 square feet
3 Bedroom house for $129,000, 1460 square feet
2 Bedroom house for $72,500, 1,230 square feet
2 Bedroom house for $89,700, 1,350 square feet
An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a cylinder, as shown below:
Hourglass with sand measuring 47 millimeters high
© 2011 Jupiterimages Corporation
Each cone of the hourglass has a height of 12 millimeters. The total height of the sand within the top portion of the hourglass is 47 millimeters. The radius of both the cylinder and cone is 4 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass?
A(6.4)
B(62.4)
C(8.5)
D(56.0)
Answers
V=π(4²)(35)=560π mm³.
The volume of a cone is given by the formula V=1/3πr²h². In this instance, r is 4 and the height is 12 mm.
V=1/3π(4²)(12)=π(1/3)(12)(4²)=π(4)(4²)=64π mm³.
This gives a total volume of 560π+64π=624π mm³ of sand.
Since the sand goes down to the bottom at a rate of 10π mm³/second, it will take 624π/10π=62.4 seconds for the sand to all drain out.
Answer:
62.4
Step-by-step explanation:
Paula ran 24 foot with the football and then passed it 15 feet to newt. Newt ran 70 yards for a touchdown. What was the total number of feet the ball traveled?
Answers
70 yards = 210 feet
210 + 39 = 249
The ball traveled a total of 249 feet.
what are the values of x and y?
Answers
we have that
cos(alfa) triangle ABD=12/y
and
cos(alfa) triangle ABC=y/28
then
12/y=y/28----------> y²=12*28=336----------> y=√336=4√21
y=4√21
applying the Pythagorean theorem triangle ABC
(16+12)²=x²+y²----------? x²=28²-(4√21)²--------> x²=784-336
x=√448=8√7
the answer is
x=8√7
y=4√21
The temperature on Saturday was 6 1/2 °C. On Sunday, it became 3 3/4 °C colder. What was the temperature on Sunday?
Answers
Answer:
The temperature on Sunday was 2.75 degrees Celsius.
Step-by-step explanation:
The temperature on Saturday was = [tex]6\frac{1}{2}[/tex] or 6.5 degree Celsius
The temperature on Sunday became [tex]3\frac{3}{4}[/tex] or 3.75 degrees colder.
When the temperature falls of it gets colder, this means the new temperature is less than the previous one. The lower the temperature, the more colder it is.
So, in the question, the temperature gets colder by 3.75 degrees, so the temperature must have been = 6.5-3.75 = 2.75 or [tex]2\frac{3}{4}[/tex] degrees Celsius.
Therefore, the temperature on Sunday was 2.75 degrees Celsius.
"if a six sided dice is rolled 2 times. what is the probability of obtaining a 2"
Answers
2/6 because there's less than half a chance to get 2 on a six-sided dice.
hope this helps