The two integers are equal to 1 and 7 respectively.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Let x represent the smaller number. Then the given relationships say ...
1/x + 2/(x+6) = 9/7
Multiplying by 7x(x+6), we have ...
7(x+6) +14x = 9x(x+6)
9x² +54x = 21x +42 . . . . .eliminate parentheses, swap sides
9x² +33x = 42 . . . . . . . . ...subtract 21x
3x² +11 -14 = 0 . . . . . . . . . .subtract 42 and divide by 3
(3x +14)(x -1) = 0 . . . . . . . . factor
Values of x that make this true are x = 1 and x = -14/3. Then for the positive integer x=1, the other integer is x+6=7.
Therefore, the two integers are equal to 1 and 7 respectively.
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Hayden has $35 to spend on school supplies. he wants to buy notebooks, pencils, scissors, and a binder. if the total cost of the pencils and notebooks is greater than $16, which inequality represents the dollar amount, d, that Hayden can spend on the binder?
(1) d < 19
(2) d > 19
(3) d < 51
(4) d > 51
Answer:
1 or 3
Step-by-step explanation:
Ava's pet pig is older than Izzy's pet pig, which is 2 years old. Ava adopted her pig when it was 1 year old, and she has had it for 2 years. Help plss
Directions: Write an equation of the line in slope intercept form from the given points (-2, 6) & (0, 4)
Answer:
y = -x + 4
Step-by-step explanation:
m = y2-y1 / x2-x1
m = 4-6/ 0-(-2)
m = -2/2
m = -1
y = -x + b
4 = -(0) + b
b = 4
y = -x + 4
Could you please give me brainliest for this? Thanks!
**WILL MARK BRAINLIEST**
Cell phone Plan A costs $80 per month and comes with a free $630 phone. Cell phone Plan B costs $45 per month but does not come with a phone. If you buy the $630 phone and choose Plan B, how many months is it until your cost is the same as Plan A's? Be sure to:
a) Write an equation to represent the situation where x represents the number of months.
b) Show your work to solve the equation from part a using inverse operations.
c) State the answer.
a) An equation representing the situation where x represents the number of months when Plan A and Plan B cost the same is 80x = 630 + 45x.
b) Using inverse operations, we can state that 80x - 45x = 630 or 35x = 630, and x = 18.
c) From this equation, we determine that x is 18 months.
What is an equation?An equation is a mathematical statement that shows that two or more mathematical expressions are equal or equivalent.
Equations use the equation symbol (=) to depict the equality of the expressions.
Plan A Plan B
Monthly charge $80 $45
Free phone $0 $630
Mathematical Expression:Let Plan A = 0 + 80x
Let Plan B = 630 + 45x
The month the two plans' costs are equal can be derived by equating the two expressions above:
80x = 630 + 45x
80x - 45x = 630
35x = 630
x = 18 months
Thus, solving the equation, we can conclude that choosing Plan B will take 18 months to equal the cost of Plan A and thereafter, be considered cheaper than Plan A.
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I need help with this
B(x) as a product of linear factors is B(x) = (x+2)(x+7)(x-1)
What is a linear factor?The linear factors of a polynomial are the first-degree equations that are the building blocks of more complex and higher-order polynomials. Linear factors appear in the form of ax + b and cannot be factored further.
if ( x+2) is a factor of the polynomial, then x+2 can divide the polynomial without remainder.
see attached document for detailed division of the polynomial [tex]x^{3}+8x^{2} +5x-14[/tex].
In conclusion B(x) as a product of linear factors is B(x) = (x+2)(x+7)(x-1)\
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Find the value of the expression
96 (32÷n÷ 2)-s-t^r
for n = 4, r = 3, s = 9, and t = 2.
Answer:
1,519
Step-by-step explanation:
96 ( 32 ÷ n ÷ 2 ) –s –t^r
since n = 4, r = 3, s = 9, and t = 2. we will just substitute for the values like this
96 ( 32 ÷ (4 ÷ 2) ) –9 ( –2³)
96 ( 32 ÷ 2 ) –9 –8
96 ( 16 ) –17
=1,536 –17
=1,519
i hope i helped
Amy, Brenda and Carleen own a cat, a dog and a fish, but not necessarily in that order. Amy hats cats, and Brenda cannot own a pet with hair because of her allergies. What does Carleen own?
Carleen owns a Dog as her pet.
What is logical thinking?The logical thinking definition is analysing a situation or problem using reason and coming up with potential solutions.
Given that, Amy, Brenda and Carleen own a cat, a dog and a fish, but not necessarily in that order.
It is saying that Amy hats a cat, which ca be meant she has a pet cat
Therefore, Amy owns a pet cat.
Now, Brenda can not have a hairy pet because she has allergic conditions, so the only pet in the given list with no hair is the fish
Therefore, Brenda owns a pet fish.
Now, only Carleen is left, and a pet dog is left.
Therefore, Carleen owns a pet dog.
Hence, Carleen owns a Dog as her pet.
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emma ray and norman shared 4/5 of a pizza. Do you think thet had 1/3 each? yes or no?
Answer: ya
Step-by-step explanation:bc
If you invest $5400 in a savings account at 5.8%,
how much interest will you earn is 6 years?
Answer:
116.64
Step-by-step explanatio hope this helps
If a person travels 440 meters in 11 seconds, what is the average speed of the person?
Step-by-step explanation:
speed=distance÷time
A.V.S=440÷11=40m/s
hope it helps.. Please mark brainliest.
Answer:
40 m/s
Step-by-step explanation:
Find:
We are asked to find the unit rate, How many meters per 1 second?
Know:
440 meters in 11 seconds
Solve:
440 meters in 11 seconds
? meters in 1 second
440/11 = 40 meters per second
Answer:
The average speed of the person is 40 m/s
Can you guys please help?
A science fair has 405 projects. The coordinator displays the projects in rows of 42. How many rows have exactly 42 projects?
I really do not understand this. It would really help me if after you have answered the question, you could explain how you got that answer. Thank you!
Total 9 rows will have exactly 42 projects.
What are the fundamental mathematical operations?The Fundamental mathematical operation are Addition,Subtraction
Multiplication and Division.
Given,
The total number projects in the science fair is 405.
The coordinator displays the projects in rows of 42.
To know the exact number of rows having 42 projects
we will divide total project by 42 i.e; 405/42.
The quotient will be the number of row exactly having 42 projects
and the last row will contain less than 42 projects which is remainder.
i.e; Dividing 405 by 42
quotient will be 9.
remainder will be 27.
So,Total 9 rows will have exactly 42 projects.
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find the differece of 7/10 and 4/40 select all that applly
A.32/40
b.24/40
c.3/5
d.1 3/5
e.24/10
Answer:
Both answers C & E are correct
Step-by-step explanation:
[tex]\sf\frac{7}{10}-\frac{4}{40}[/tex]
First, make the denominator the same to solve the fraction.
For that, multiply both the numerator and denominator by 4 in the fraction 7/10.
[tex]\sf\frac{7*4}{10*4}-\frac{4}{40}\\\\\sf\frac{28}{40}-\frac{4}{40}\\\\\sf\frac{28-4}{40}\\\\\sf\frac{24}{40}[/tex]
To write the answer in its simplest form divide both the numerator and denominator by 8.
[tex]\sf\frac{3}{5}[/tex]
Therefore, the answer is [tex]\sf\frac{24}{40}[/tex] = [tex]\sf\frac{3}{5}[/tex]
Rodrigo pays $165.40 per month on his car loan.
How much does he pay on his loan in 1 year?
Answer:
$1984.80
Step-by-step explanation:
165.40 times 12 equals 1984.80
Answer:
He pays $1984.80 on his loan in one year.
Step-by-step explanation:
If he pays 165.40 per month, and there are 12 months in one year, then we must multiply the values together.
165.4*12 = 1984.8
He pays $1984.80 on his loan in one year.
8 - 90 + 2x = 36
What will this. I need help
Answer: x = 59
Step-by-step explanation:
i dont know what you are trying to figure out but x = 59 im guessing u need
Answer:
Step-by-step explanation:
First, add
90
and subtract
2
x
from each side of the equation to isolate the
x
term while keeping the equation balanced:
8
x
−
90
+
90
−
2
x
=
2
x
−
36
+
90
−
2
x
8
x
−
2
x
−
90
+
90
=
2
x
−
2
x
−
36
+
90
(
8
−
2
)
x
−
0
=
0
+
54
6
x
=
54
Now, divide each side of the equation by
6
to solve for
x
while keeping the equation balanced:
6
x
6
=
54
6
6
x
6
=
9
x
=
9
Please help me as soon as possible.
How many times as great is the value of 1.5 than the value of 0.15? Please Explain.
Answer:
Step-by-step explanation:
1.5/0.15=10
1.5 is 10 times greater than 0.15
The solution is 10
The number of times the number 1.5 is greater than the number 0.15 is 10
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented A
Now , the value of A is
Let the first number be P = 1.5
Let the second number be Q = 0.15
Now , the number of times the number P is greater than Q is given by the equation
A = P / Q
Substituting the values in the equation , we get
A = 1.5 / 0.15
On simplifying the equation , we get
A = 10
Therefore , the value of A is 10
Hence , the number of times 1.5 is greater than 0.15 is 10 times
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Select the conjecture with the rephrased statement of proof to show the diagonals of a parallelogram bisect each other.
D
A
E
C
B
In parallelogram ABCD, show triangle ADC is congruent to triangle CBA
O In parallelogram ABCD, show triangle DEA is congruent to triangle CEB
O In quadrilateral ABCD with AB congruent to CD and AD is congruent to BC, show ABCD is a parallelogram
O In parallelogram ABCD, show DE is congruent to BE and AE is congruent to CE
The conjecture and rephrased statement of proof to demonstrate that the diagonals of a parallelogram cross each other, taking into account the provided figure, is: DE and EB are congruent to one another in the parallelogram EFGH, while AE is congruent to EC.
Define Parallelogram.A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.
The parallelogram's diagonals are the lines connecting its two opposed ends. Sharing into two equal portions is known as bisecting. Congruent refers to a copy that has the same dimensions as the original and may therefore be used in place of it. When the diagonals of a parallelogram bisect one another, it signifies that they split into two equal pieces that are congruent with one another.
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The formula for the perimeter of a rectangle is P = 2l + 2w. Solve the
formula for w in terms of P and l.
Answer:
P-2l/2=w
Step-by-step explanation:
P = 21 + 2w
Solve for w
Subtract 21 from both sides.
P - 21 = 2w
Divide both sides by 2.
P-21/2 = w
A collector's model racecar is scaled so that 1 inch on the model equals 6 1/4 feet on the actual car. If the model is 2/3 inch high, how high is the actual car? explain
Answer:
50 inches, or 4 1/6 feet
Step-by-step explanation:
If one inch is equal to 6 1/4 feet, we can translate this number from feet to inches.
4 1/6 feet = 75 inches.
Now we can take 75 and find out 2/3 of it.
2/3 of 75 is 50.
The answer is 50 inches.
If you want to convert the answer from feet to inches, its simple.
12 × 4 = 48
50 - 48 = 2
2 inches is equal to 1/6 of a foot.
The answer in feet, is 4 1/6 foot.
Your body mass index (BMI) is your weight by kilograms divided by the square of your height in meters. Online BMI calculators allow you to enter weight in pounds and height in inches. High BMI is a common but controversial indicator of being overweight or obese. A study by the National Center for Health Statistics found that the BMI of American young women (ages 20-29) is approximately Normally distributed with mean 26.8 and standard deviation 7.4
Using z-score calculations, we can say that around 13.14%of the young women have a BMI (Body Mass Index) of less than 18.5 and are underweight.
How to find the probability from z-score?The formula for z-score is;
z = (x' - μ)/σ
We are given;
Population Mean; μ = 26.8
Population standard deviation; σ = 7.4
Average BMI; x' = 18.5
Thus;
z = (18.5 - 26.8)/7.4
z = -1.12
From online p-value from z-score calculator, we have;
p-value = 0.1314 = 13.14%
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Complete question is;
Your body mass index (BMI) is your weight by kilograms divided by the square of your height in meters. Online BMI calculators allow you to enter weight in pounds and height in inches. High BMI is a common but controversial indicator of being overweight or obese. A study by the National Center for Health Statistics found that the BMI of American young women (ages 20-29) is approximately Normally distributed with mean 26.8 and standard deviation 7.4
People with BMI less than 18.5 are often classed as “underweight.” What percent of young women are underweight by this criterion?
Two sisters are painting mugs. The younger sister can paint 2 mugs every half hour. The older sister can paint 6 mugs every hour. How long will it take the two sisters to paint 80 mugs?
The time it would take the two sisters to paint 80 mugs is 8 hours.
Calculating the time it would take to paint mugsFrom the question, we are to determine how long it would take the sisters to paint 80 mugs
From the given information,
"The younger sister can paint 2 mugs every half hour"
That is,
The younger sister can paint 4 mugs every hour
Also
"The older sister can paint 6 mugs every hour?"
Let x represent the number of hours it would take them to paint 80 mugs.
Then, we can write that
4x + 6x = 80
10x = 80
x = 80/10
x = 8
Hence, the time it would take is 8 hours
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5) a real estate agent bought two triangular 'kittitas' having a common side as shown in the figure from two people for rs 20,00,000 altogether. if he immediately sold the land in the shape of à quadrilateral at rs 15,00,000 per kattha, find his profit or loss.(1 kattha= 338.63 sq. m)
The information given regarding the computation of the profit or loss shows that there's a loss of RS 500,000.
How to calculate the profit?From the information given, it was stated that the real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 2000,000 altogether.
It was further depicted that he sold the land in the shape of a quadrilateral at Rs 1,500,000. In their case, the sale is less than the cost and therefore, there's a loss.
The loss will be:
= 2,000,000 - 1,500,000
= 500,000
Therefore, the information illustrated a loss of RS 500,000.
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Complete question
Mr. Gosain?(1 Aana = 31.8 m²) b) A real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 20,00,000 altogether. If he immediately sold the land in the shape of a quadrilateral at Rs 15,00,000 per Kattha, find his profit or loss.(1 Kattha= 338.63 sq. m) danta Excel in Mathematics - Book 9 86 36 m Approved by Curriculum Development Cen 20 m 29 m 25 m 21 m aktapur
Determine whether the point is on the graph of the equation 2x + 7y =13 (3,1) yes or no
Step-by-step explanation:
i think its no, but im not sure.
Isaac is going to a carnival that has games and rides. Each game costs $1.50 and each ride costs $5. Isaac spent $44.50 altogether at the carnival and the number of rides he went on is 5 more than the number of games he played. Determine the number of games Isaac played and the number of rides Isaac went on.
Answer:
g-games
r-rides
1.5 g + 2.5r= 16.5
g=2r
Step-by-step explanation:
g: # of games played
r: # of rides ridden
total amount spent: 1.50g + 2.50r = 16.50
relationship of games to rides: g = 2r
Hope this helped! :D
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The number of games is 3.
The number of rides is 8.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of rides = m + 5
Number of games = m
Now,
Each game costs $1.50 and each ride costs $5. Isaac spent $44.50 altogether at the carnival.
This means,
1.50m + 5(m + 5) = 44.50
1.50m + 5m + 25 = 44.50
6.50m = 44.50 - 25
m = 19.5/6.50
m = 3
Now,
The number of games = 3.
The number of rides.
= m + 5
= 3 + 5
= 8
Thus,
The number of games is 3.
The number of rides is 8.
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An initial sample of 171 g of a radioactive substance decays according to the function
A(t) = 171e ^ - 0.04(t) where t is given in years?
a) How many grams of the substance will remain after 59 years? Round your answer to the nearest decimal place.
b) What is the half-life of the substance? Round answer to the one decimal place.
There will be 0.48 grams will be left in the sample after 59 years.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
Since we have given that initial sample of 171 g of a radioactive substance decays according to the function
[tex]A(t) = 171e ^ {- 0.04(t) }[/tex]where t is given in years
Here, Initial amount of radioactive substance = 171 grams
We need to find the amount of substance that will be left in the sample after 59 years.
So, t = 59 years
So, it becomes,
[tex]A(t) = 171e ^ {- 0.04(59) }\\\\A(t) = 0.48[/tex]
Hence, there will be 0.48 grams will be left in the sample after 59 years.
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If log₂(4x + 6) = 4, then x = ____
You may enter the exact value or round to 4 decimal places.
Answer: -1/2
Step-by-step explanation: To solve this problem, we can use the properties of logarithms to isolate the variable x on one side of the equation. The properties of logarithms tell us that the logarithm of a product is the sum of the logarithms of the factors, and that the logarithm of a power is the exponent times the logarithm of the base.
If log₂(4x + 6) = 4, we can rewrite the left side of the equation as follows: log₂(4x + 6) = log₂(2^4 * (2x + 3))
Then, using the property of logarithms that the logarithm of a product is the sum of the logarithms of the factors, we can simplify the equation as follows: log₂(4x + 6) = 4 + log₂(2x + 3)
Now, we can use the property of logarithms that the logarithm of a power is the exponent times the logarithm of the base to simplify the equation even further: log₂(4x + 6) = 4 + 1 * log₂(2x + 3)
Since the logarithm of a power is the exponent times the logarithm of the base, this means that the logarithm of a number is the logarithm of that number divided by the logarithm of the base. Therefore, we can divide both sides of the equation by log₂ to isolate the variable x on one side of the equation:
log₂(4x + 6) / log₂ = 4 + 1 * log₂(2x + 3) / log₂
(4x + 6) / 1 = 4 + (2x + 3) / 1
4x + 6 = 4 + 2x + 3
4x + 6 = 2x + 7
2x = -1
x = -1/2
Therefore, if log₂(4x + 6) = 4, then x = -1/2.
According to Newton's Law of Cooling, if a body with temperature T₁ is placed in surroundings with temperature To, different
from that of T₁, the body will either cool or warm to temperature T(t) after t minutes, where T(t) = To + (T₁-To)ekt
A metal pan with temperature 120°F is placed in a freezer with temperature 0°F. After 5 minutes, the temperature of the pan
is 80°F. Use Newton's Law of Cooling to find the pan's temperature after 15 minutes.
After 15 minutes the pan will have a temperature of °F.
(Round to the nearest integer.)
After 15 minutes the pan will have a temperature of 36°F
How to determine the temperature of the pan after 15 minutes?
Newton's Law of Cooling, if a body with temperature T₁ is placed in surroundings with temperature To, different from that of T₁, the body will either cool or warm to temperature T(t) after t minutes, where T(t) = T₀ + (T₁-T₀)e^(kt)
Given: T₁ = 120°F, T₀ = 0°F. After 5 minutes, T(t) = 80°F
T(t) = T₀ + (T₁-T₀)e^(kt)
80 = 0 + (120-0)e^(5k)
80 = 120e^5k
e^5k = 80/120
e^5k = 2/3
5k = ln(2/3)
k = ln(2/3) / 5
k = -0.0811
The temperature of the pan after 15 minutes will be:
T(t) = T₀ + (T₁-T₀)e^(kt)
T(15) = 0 + (120-0)e^(-0.0811×15)
T(15) = 120e^(-0.0811×15)
T(15) = 36°F
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What is .65 as a fraction?
Simplified
Answer: 0.65=13/20
Step-by-step explanation: First, rewrite the decimal number as a fraction and put 1 in the denominator's place. 0.65/1
Then, multiply to get rid of 2 decimal places. Then, multiply top and bottom by 10^2 which equals 100
0.65/1 × 100/100= 65/100
Find the Greatest Common Factor or GCF of 65 and 100, and reduce the fraction by dividing both the numerator and denominator by GCF = 5,
[tex]\frac{65/5}{100/5}[/tex]=13/20
Hope this helps!
How can 1,000 as an exponential expression with 10 as the base
Answer:
10^3.
Step-by-step explanation:
How can you represent 1,000 as an exponential expression with 10 as the base?
You can represent 1,000 as 10^3. 10 x 10 x 10 = 1000. is read as “10 to the third power” or “10 cubed.”
all numbers are base 10 unless the teacher says to use another base so
there are 3 zeroes so
10^3 is the answer
Hannah is taking out a 8.1% loan to purchase an $15,000 car. The length of the loan is 8 years. How much will she pay in interest?
in January the depth of a lake was 943 feet in August the depth of the lake was 754.4 what is the percentage decrease of the depth of the lake from January to August
The percentage decrease of the depth of the lake from January to August is 20%.
What is percentage decrease?The difference between the initial and final numbers is shown as a percentage reduction. It displays a percentage loss of value compared to the original regardless of the units. The decrease is equal to the initial amount less the final amount.
Given,
The depth of lake in January = 943 feet
The depth of lake in August = 754.4 feet
The difference is = (943-754.4) feet
= 186.6 feet
So, the percentage decrease of the depth of the lake from January to August will be = (186.6 ÷ 943) × 100
= 20%
Therefore, the answer is 20%.
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