Translating the given word problem into a set of linear equations, Mariana's age is 15 years old.
Translate the given word problem into algebraic equations.
Let x be Mariana's age
Let y be Yaritza's age
Mariana is younger than Yaritza, their ages are consecutive odd integers.
Since the difference of consecutive odd integers is 2, then:
y = x + 2 ....... (1)
Sum of Mariana's age and 5 times Yaritza's age is 100.
x + 5y = 100 ..... (2)
Substitute equation (1) to equation (2)
x + 5y = 100
x + 5(x+2) = 100
6x + 10 = 100
6x = 90
x = 15
Thus, Mariana's age is 15 years old.
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Answer:
15
Step-by-step explanation:
i just got it right on delta
Write each statement as a conditional.
a. A triangle with all angles congruent is equilateral.
b. Alberto can go to the movies if he washes the car.
Answer:
Step-by-step explanation:
Write each statement as a conditional.
a. A triangle with all angles congruent is equilateral.
b. Alberto can go to the movies if he washes the car.
a. If all angles of a triangle are congruent then the triangle is an equilateral triangle
b. If Alberto washes the car he can go to the movies
shayna enlarged a square photo by adding 10 inches to each side so it could be seen on a large poster. the area of the enlarged photo is 256 square inches. in the equation (x 10)2
The dimensions of the original photo are 6 x 6.
What is an area?A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.
The formula for a square's area, A = s², is the side length raised to the power of two. The 256 in2 section of the larger image was made available to us. Additionally, it was mentioned that the length of the expanded image is equal to the original image's length plus ten inches.
We can therefore create an equation to solve for x, which stands for the length of the original snapshot, based on the aforementioned statements.
A = s²
where s = ( x + 10 )
A = ( x+10 )² = 256
Solving for x,
x = 6 in.
The dimensions of the original photo are 6 x 6.
The complete question is given below:-
Shayna enlarged a square photo by adding 10 inches to each side so it could be seen on a large poster. The area of the enlarged photo is 256 square inches. In the equation (x + 10)2 = 256, x represents the side measure of the original square photo. What were the dimensions of the original photo?
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What is the value of -7 + a, if the value of a is -3?
Answer:
[tex] \sf \large \: - 10[/tex]
Step-by-step explanation:
−7+a
Evaluate for a=−3
−7+−3
=−10
Answer:
-10 given a = -3
Step-by-step explanation:
-7 + -3 = -10
Hope this helps! :)
(x+5/2) + (x-3/3) = 3 1/6
Answer:
Step-by-step explanation:
x=2
ever since renata moved to her new home, she's been keeping track of the height of the tree outside her window. the variable hhh models the height of the tree (in centimeters), ttt years since renata moved in. h
The tree was 210 cm tall.
Let 'h(t) ' models the height of the tree in centimeters and 't' denotes the number of years since Renata moved in.
Given, h(t) = 210 + 33t
This is a linear function in 't'.
This function says that in each year the tree grows 33 cm tall.
We need to find the height of the tree when Renata moved in.
When Renata moved in, the number of years, t = 0
Applying this into h(t) , we get,
h(t) = 210 + 33 x 0 = 210 cm
Therefore the tree was 210 cm tall when Renata moved in.
The question was incomplete. Find the complete question here:
Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window. h(t) models the height of the tree (in centimeters), t years since Renata moved in. h(t)=210+33t
How tall was the tree when Renata moved in?
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can someone please help me? i’ve been struggling with factoring for a little bit now.
Factor.
81-22
Answer:59
Step-by-step explanation:
81-22=59
answer is 59 because 59 is a prime number
FIND THE LCM OF EACH SET OF NUMBERS USING THE PRIME FACTORIZATION METHOD.
(BEST ANSWER = BRAINLIEST)
1. {12,15}
2. {16,24}
3. {18,27}
4. {20,28}
5. {36,54}
6. {9,12,24}
7. {15, 20, 45}
8. {6,8,12}
9. {4,6,9}
10. {8,9,12}
The LCM of the set of numbers are:
1. {12,15} = 60
2. {16,24} = 48
3. {18,27} = 54
4. {20,28} = 140
5. {36,54} = 108
6. {9,12,24} = 72
7. {15, 20, 45} = 180
8. {6,8,12} = 24
9. {4,6,9} = 36
10. {8,9,12} = 72
What is the LCM?The least common multiple of two or more numbers is the least multiple that is common to two or more numbers. A multiple of a number is the product of an integer and that number. For example, the multiples of 6 are 12 and 18.
Prime factors of 12 = 2 x 2 x 3
Prime factors of 15 = 3 x 5
LCM = 2 x 2 x 3 x 5 = 60
Prime factors of 16 = 2 x 2 x 2 x 2
Prime factors of 24 = 2 x 2 x 2 x 3
LCM = 2 x 2 x 2 x 2 x 3 = 48
Prime factors of 18 = 2 x 3 x 3
Prime factors of 27 = 3 x 3 x 3
LCM = 2 x 3 x 3 x 3 = 54
Prime factors of 20 = 2 x 2 x 5
Prime factors of 28 = 2 x 2 x 7
LCM = 2 x 2 x 5 x 7 = 140
Prime factors of 36 =2 x 2 x 3 x 3
Prime factors of 54 = 2 x 3 x 3 x 3
LCM = 2 x 2 x3 x 3 x3 = 108
Prime factors of 9 = 3 x 3
Prime factors of 12 = 2 x 2 x 3
Prime factors of 24 = 2 x 2 x 2 x 3
LCM = 2 x 2 x 2 x 3 x 3 = 72
Prime factors of 15 = 3 x 5
Prime factors of 20 = 2 x 2 x 5
Prime factors of 45 = 3 x 3 x 5
LCM = 2 x 2 x 3 x 3 x 5 = 180
Prime factors of 6 = 2 x 3
Prime factors of 8= 2 x 2 x 2
Prime factors of 12= 2 x 2 x 3
LCM = 2 x 2 x 2 x 3 = 24
Prime factors of 4 = 2 x 2
Prime factors of 6= 2 x 3
Prime factors of 9= 3 x 3
LCM = 2 x 2 x 3 x 3 = 36
Prime factors of 8 = 2 x 2 x 2
Prime factors of 9= 3 x 3
Prime factors of 12 = 2 x 2 x 3
LCM = 2 x 2 x 2 x 3 x 3 = 72
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tracy bought a new flat-screen television. one side of the television screen is 49 inches and the other side is 27 inches..
The new flat screen television that Tracy bought has a diagonal length of 56 inch
With the information given we can calculate the diagonal length of the television using the Pythagorean theorem equation.
The formula and the procedure that we have to use is:
h2= a2 + b2
Where:
h= hypotenusea= minor sideb = major sideInformation about the problem:
h = ?b = 49 inchesa = 27 inchesApplying the Pythagorean theorem and finding the variable, we get:
h² = a² + b²
h² = (27 inch)² + (49 inch)²
h² = 729 inch² + 2401 inch²
h² = 3130 inch²
h = [tex]\sqrt{}[/tex]3130 inch²
h = 55.95 inch rounding up we get 56 inch
What is the Pythagorean theorem?It is a mathematical equation that relates the three sides of a right angled triangle (major side, minor side and hypotenuse) and states that the sum of the squared sides equals the squared hypotenuse. Its general equation is:
h² = a² + b²
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An electrically neutral atom of beryllium has four protons. Which statement is true? There are four protons in the nucleus. There is a charge of −4 on an atom of beryllium. There are four neutrons in the nucleus. There is a charge of +4 on an atom of beryllium.
The right answer is that there are four electrons.
What is an atomic number?The charge number of an atomic nucleus is the chemical element's atomic number, also known as the nuclear charge number.
For conventional nuclei, this is comparable to the proton number, or the number of protons found in the nucleus of each atom of that element.
Equal numbers of protons and electrons make up a neutral atom. This figure establishes the atom's atomic number.
The fourth element on the periodic table is beryllium.
Number of protons in Be-atom = 4
Number of electrons in Be-atom = 4
Therefore, it is true that there are four electrons.
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A. A person goes from a sauna at 1208F to an outside temperature of -208F. What is the change in temperature
The change in temperature should be 1208 - (-208).
What
is the slope of the line that passes through the points (-4, 6) and (-4, 18)?
Write your answer in simplest form.
Find the missing fraction.
5|2
13
Find the product of 18.6 and 3
Answer: 55.8 Hope this helps, please consider making me Brainliest.
Step-by-step explanation:
18.6 * 3 = (18 * 3) + (0.6 * 3) =
54 + 1.8 =
55.8
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Answer:55.6
Step-by-step explanation:
55.6
Michael makes a model to show the distances between the Sun and the planets.
Earth is 1.50 x 10¹¹ m from the Sun. The distance on the model is 30 cm. What is the ratio of the lengths of the model to the actual distance?
Step-by-step explanation:
do 1.50 times 10 and the multiple by 30 to get the answer
The ratio of the lengths of the model to the actual distance is approximately 2 x 10⁻¹³.
To find the ratio of the lengths of the model to the actual distance, we need to compare the lengths in the same unit. Let's convert the actual distance between the Sun and Earth from meters to centimeters, so both values are in centimeters.
1 meter = 100 centimeters
Actual distance from the Sun to Earth = 1.50 x 10¹¹ meters
Actual distance from the Sun to Earth in centimeters = 1.50 x 10¹¹ meters * 100 centimeters/meter
Actual distance from the Sun to Earth in centimeters = 1.50 x 10¹¹ meters * 100 centimeters/meter = 1.50 x 10¹³ centimeters
Now, we can compare the lengths:
Length on the model = 30 centimeters
Actual distance from the Sun to Earth = 1.50 x 10¹³ centimeters
The ratio of the lengths of the model to the actual distance is:
Ratio = Length on the model / Actual distance from the Sun to Earth
Ratio = 30 centimeters / (1.50 x 10¹³ centimeters)
To simplify this ratio, let's express the actual distance in scientific notation:
1.50 x 10¹³ = 15 x 10¹² = 1.5 x 10¹³
Now, the ratio becomes:
Ratio = 30 centimeters / (1.5 x 10¹³ centimeters)
Now, notice that both values are in the same unit (centimeters). We can proceed with the division:
Ratio ≈ 0.0000000000002
Therefore, the ratio of the lengths of the model to the actual distance is approximately 2 x 10⁻¹³. This means that every 1 centimeter on the model represents approximately 2 x 10⁻¹³ centimeters in actual distance between the Sun and Earth.
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find the error javier claimed that all cubic functions are odd. is he correct? if not, provide a counterexample.
Answer:
The cubic function f(x) = x3 is symmetric about the origin (it is an odd function). Here are some types of functions that are odd: Lines Through The Origin – any line with a zero y intercept (b = 0) and a nonzero slope (m not zero) will have equation f(x) = mx.
Step-by-step explanation:
Answer: No
f(x) = x³ + 2x − 5
Step-by-step explanation:
No
f(x) = x³ + 2x − 5
-8w > -6/5 What is the answer
Answer:
51
Step-by-step explanation:
Evaluate the expression for c =
10.
2c - 11 =
Alang has a points card for a movie theater.
He receives 55 rewards points just for signing up.
• He earns 3.5 points for each visit to the movie theater.
• He needs 83 points for a free movie ticket.
How many visits must Alang make to earn a free movie ticket?
The number of visits that Alang makes to earn a free movie ticket will be 8.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Alang has a rewards card at a cinema.
The mere act of joining up earns him 55 reward points.
Every time he enters a movie theater, he receives 3.5 points.
To receive a free movie ticket, he needs 83 points.
Let x be the number of visits. Then the equation is given as,
3.5x + 55 = 83
Simplify the equation, then the value of x will be
3.5x = 83 - 55
3.5x = 28
x = 28 / 3.5
x = 8
The number of visits that Alang makes to earn a free movie ticket will be 8.
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Answer:
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables are studied under the supposition or demand that they depend, by some law or rule, on the values of other variables.
Step-by-step explanation:
Use the function: f(x)=√√2x-5 to answer the following:
a) f(7)
b) f(x + 1)
c) f(-x)
d) the domain of f(x).
Answer:
the answer is a because if you calculate it correctly that the answer I got
Suppose A is (-2,4) and M is (3,1) and M is the Midpoint of AB, find the coordinates of AB
Can anyone find the value of x and y from the given figure?:
Answer:
little tricky question but i managed to do it..
adoncia makes a scale drawing of the front of the lincoln memorial she uses a scale of 15 ft in the monument to 1 in In the drawing the front of the monument is about 80ft high and 200ft long will adoncia drawing fit on an 8 1/2 in by 11 in sheet of paper
No, the Adoncia drawing will not fit on the drawing sheet.
Given adoncia is drawing to scale, she uses a 15-foot scale in the 1-inch monument. And in the drawing, the front of the monument is about 80 feet high and 200 feet long.
The given parameters are;
The scale of the drawing in the front of the monument is 15 ft = 1 in.
Actual size of the monument;
Height = 80 feet
Length = 200 feet.
So we have;
Required size of paper height = 80/15 = 16/3 = 5.33 in.
Required size of paper length = 200/15 = 40/3 = 13.33 in.
The size of the paper is 11 in. about the size of a standard 8.5-inch sheet of letterhead. equals 11 in.
Design length, 13.33" > Paper length > 11".
Therefore, when Adoncia draws a scale drawing of the front of the linco and she uses the 15ft scale in the 1in monument, the drawing does not fit on the paper.
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Allison is saving money to buy a video game system. in the first week her savings were $8 less than 2/5 the price of the system. in the second week, she saved 50 cents more than 1/2 the price of the system. she was still $37 short. find the price of the system.
Hence , the price of the system $295 .
The linear equations in one variable is associate degree equation that is expressed within the sort of ax+b = zero, wherever a and b square measure 2 integers, and x may be a variable and has just one resolution. as an example, 2x+3=8 may be a equation having one variable in it.Let the price of the system be "x" .
It is given that in the first week her savings were $8 less than 2/5 the price of the system which can be represented by equation
First week savings = (2/5)x -8
It is also given that in the second week, she saved 50 cents more than 1/2 the price of the system which can be represented by equation
Second week savings = (1/2)x +0.5
savings + short = price of system
(2/5)x -8 + (1/2)x +0.5 + 37 = x
(2/5)x + (1/2)x + 29.5 = x
4x + 5x/ 10 + 29.5 = x
9x/10+ 29.5 = x
0.9x + 29.5 = x
29.5 = x - 0.9x
29.5 = 0.1x
$ 295 = x
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The volleyball team had to play quite a bit last week. they practiced .5 hours on monday, 1.3 hours on tuesday, 2.2 hours on wednesday and .8 hour on thursday. if they wanted to practice a total of 6 hours last week, how many hours did they end up practicing on friday?
The volleyball team ended up practicing for 1.2 hours on Friday.
The total number of hours the volleyball team practiced on Monday, Tuesday, Wednesday, and Thursday can be determined by adding the values given in the statement.
Therefore,
the total number of hours the team practiced on Monday, Tuesday, Wednesday, and Thursday=0.5 hours+1.3hours+2.2hours+0.8hours= 4.8 hours
Total number of hours the team practiced last week = 6 hours
The number of hours they practiced on Friday can be calculated by subtraction of the total number of hours of the week from the total number of hours on Monday, Tuesday, Wednesday, and Thursday.
Hence, the number of hours the team practiced on Friday = 6 - 4.8= 1.2 hours.
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2 l2x+7l = 16
Please help me with this ASAP
Answer:
x = 1/2 and
x = -15/2
Step-by-step explanation:
First, get the absolute value alone on one side if the equation.
2 |2x + 7 | = 16
Divide both sides by 2.
| 2x + 7 | = 8
Once the absolute value sign is by itself, you will separate the equation into two separate equations.
2x+7=8 and 2x+7=-8
Solve these two equations separately and get two solutions.
2x + 7 = 8
Subtract 7.
2x = 1
Divide by 2.
x = 1/2 Here is one solution.
2x + 7 = -8
Subtract 7.
2x = -15
Divide by 2.
x = -15/2 Here is a second solution.
Answer:
x = - [tex]\frac{15}{2}[/tex] , x = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
2 | 2x + 7 | = 16 ( divide both sides by 2 )
| 2x + 7 | = 8
the absolute value function always gives a positive result, but the expression inside can be positive or negative , that is
2x + 7 = 8 ( subtract 7 from both sides )
2x = 1 ( divide both sides by 2 )
x = [tex]\frac{1}{2}[/tex]
or
- (2x + 7) = 8
- 2x - 7 = 8 ( add 7 to both sides )
- 2x = 15 ( divide both sides by - 2 )
x = - [tex]\frac{15}{2}[/tex]
As a check
substitute these values into the left side and if equal to the right side then they are a solution
x = [tex]\frac{1}{2}[/tex]
2 | 2([tex]\frac{1}{2}[/tex] ) + 7 | = 2 | 1 + 7 | = 2 | 8 | = 16 = right side
x = - [tex]\frac{15}{2}[/tex]
2 | 2(- [tex]\frac{15}{2}[/tex] ) + 7 | = 2 | - 15 + 7 | = 2 | - 8 | = 2 | 8 | = 16 = right side
then x = - [tex]\frac{15}{2}[/tex] and x = [tex]\frac{1}{2}[/tex] are the solutions
Rewrite x4y2 − 6x3y3 using a common factor.
1: x2y2(x2 − 6xy)
2: x2y(xy − 6xy2)
3: 6xy(x3y − x2y)
4: 6xy2(x2 − x2y)
The value of expression by using common factor is x³y² (x - 6y).
Here,
The expression is,
x⁴y² - 6x³y³
We have to solve by using common factor.
What is Mathematical expression?
The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.
Now,
The expression is,
x⁴y² - 6x³y³
By using common factor we solve as,
x⁴y² - 6x³y³ = x*x*x*x*y*y - 6*x*x*x*y*y*
= x³y² (x - 6y)
Hence, The value of expression by using common factor is x³y² (x - 6y).
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Maria wanted to bring back 5 million grains of sand from her trip to the beach. Each grain of sand weighs approximately 6.7 x 10^-7 kg. How heavy is the bag of sand that Maria brings home?
a
Multiply (5,000,000 x 6.7 x 10^-7) = (5 x 10^6) x (6.7 x 10^-7) = (5 x 6.7) x (10^(6 + - 7)) = 33.5 x 10^-1 = 3.35 kg
b
Multiply 5 x (6.7 x 10^-7) = 33.5 x 10^-7 = 3.35 x 10^-6 kg
c
Multiply (5,000,000 x 6.7 x 10^-7) = (5 x 10^6) x (6.7 x 10^-7) = (5 x 6.7) x (10^(6 + 7)) = 33.5 x 10^13 = 3.35 x 10^14 kg
d
Divide (5,000,000 / 6.7 x 10^-7) = (5 x 10^6) / (6.7 x 10^-7) = (5 / 6.7) x (10^(6 - 7)) = .74 x 10^-1 = 0.074 kg
PLEASE HELP
Answer:
3.35
Step-by-step explanation:
5,000,000*6.7 * 10^-7
= 5 * 10^6 * 6.7*10^-7
= 33.5 * 10^-1
= 3.35
The weight of 5 million grains of sand is 3.35 kg.
Option A is the correct answer.
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,
Weight of each grain of sand = 6.7 x [tex]10^{-7}[/tex] kg
Weight of 5 million grains of sand.
= 5,000,000 x 6.7 x [tex]10^{-7}[/tex] kg
= 5 x [tex]10^6[/tex] x 6.7 x [tex]10^{-7}[/tex]
= 33.5 x [tex]10^{-1}[/tex] kg
= = 3.35 kg
Thus,
The weight of the total grain of sand is 3.35 kg.
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Solve for a.
ab + c = d
Carol is baking cookies and needs 2/1/4 cups of flower 2/3 cups with sugar 1/4cups of brown sugar and 1/16 cups of baking soda use the information to answer the following question
Answers
3/8
2/3
2
2/2/3
The quotient when we divide the amount of white sugar by the brown sugar will be 2 2/3
How to calculate the value?From the information, it was stated that Carol is baking cookies and needs 2/1/4 cups of flower 2/3 cups with sugar 1/4cups of brown sugar and 1/16 cups of baking soda.
The quotient when we divide the amount of white sugar by the brown sugar will be:
= 2/3 ÷ 1/4
= 2/3 × 4/1
= 2 2/3
Therefore, the quotient is 2 2/3.
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Carol is baking cookies and needs 2 1/4 cups of flour 2/3 cup of white sugar 1/4 cup of brown sugar and 1/16 cup of baking soda use this information to answer the following questions
divide the amount of white sugar by the amount of brown sugar. what is the quotient? (must be a fraction)
80,000 as a scientific notation?