The GCF of 10c and 12d using the distributive property is 2.
Greatest Common Factor:The largest of all the common factors between any two or more numbers is known as the GCF (Greatest Common Factor).
A single term can be multiplied by the sum or difference of two or more other words according to the distributive property.
According to Distributive property,
=> ab + ac = a(b + c)
Where 'a' will be the GCF of ab and ac.
Here we have
10c and 12d
By using the Distributive property,
=> 10c + 12d = 2 (5c + 6d)
Therefore,
The GCF of 10c and 12d using the distributive property is 2.
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Choose the correct classification of 2x4 − 8x5 − 2x2 5.
Answer: The correct classification of 2x4 - 8x5 - 2x2 + 5 is 5th-degree polynomial.
We know that the highest exponent of a polynomial is called the degree of the polynomial.
The highest degree of the given polynomial is 5. Hence, from the above-written concepts, we can say that the degree of the polynomial is 5.
Thus, the polynomial is a 5th-degree polynomial.
Step-by-step explanation:
Write and solve the inequality that represents -1/5 is greater than or equal to the product of -2/7 and a number
Answer:
(-1/5)>=(-2/7)×x
by dividing both sides by (-2/7)
(-1/5)÷(-2/7)<=x
Simplify the inequality
7/10<=x so x>=0.7 so x belongs to the interval [7,inf)
Jane is an 8-year-old girl who weighs 25.6 kg and enjoys lots of outdoor activities. She likes fruit but does not like vegetables or milk. How many grams of protein are recommended for Jane
As calculated from the given data Jane's calorie intake is 1200 per day.
From the details given in the question we can say that Jane doesn't likes milk. Hence, she lacks dairy fat in her food. As per the given case she likes vegetables and eats fruit a lot. Therefore, and the grams of total caloric intake for her should be 1200 calories per day.
She does, however, lack fats from dairy products like milk. A child of 8 years old is thought to need at least 2 cups of milk or its equivalent each day. Jane is getting enough carbohydrates because she consumes 225 gram per day as opposed to the recommended 130 gram.
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Subtract the linear expressions.
(3/4x−1)−(1/3x+4)
What is the difference?
Enter your answer in the box. Enter fractions as simplified fractions.
Answer:
5-60x
12x
Step-by-step explanation:
= 3/4x-1 - 1/3x-4
= 3/4x - 5 - 1/3x
= 9-60x-4
12x
= 5 - 60x
12x
The sides of a square all have a side length of y. Write a simplified area function in terms of y for a rectangle whose length is 8 times the side length of the square and whose width is 4 units longer than the side length of the square.
The simplified area function in terms of y for the rectangle is 8y² + 32.
How to calculate for the area of rectangleThe area of rectangle is derived by multiplying the length by the width.
The square have all side length to be y each, if the length of the rectangle is 8 times the side length of the square then;
Length of rectangle = 8y
if the width of the rectangle is 4 units longer than the side length of the square then;
Width of rectangle = y + 4
area of rectangle = 8y(y + 4)
by expansion;
area of rectangle = 8y² + 32
Therefore, 8y² + 32 is the simplified area function in terms of y for the rectangle.
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R is the midpoint of segment PS, Q is the midpoint of segment RS. P is located at (10,-2) and S is located at (5,4). What are the coordinates of Q?
Answer:
(6.25,2.5)
Step-by-step explanation:
what is the order of 3 over 4, -7 over 10, -3 over 4, 8 over 10 least to greatest
Please see the attachment below for the answer and work. Hope this helps and you can read my handwriting.
Question 3 of 23
Which graph below shows the solutions for the linear inequality y≤¹x-3?
OA. Graph D
B. Graph B
C. Graph C
D. Graph A
Graph D (A) is the correct graph that shows the solutions for the linear inequality y≤¹x-3.
What is linear inequality?A linear inequality is an equation that contains a variable, such as x, and is written in the form ax + b < c, where a, b, and c are constants. Linear inequalities are used to describe a range of values that satisfy a given condition. They are used in many areas of mathematics, including graphing, solving equations, and finding the maximum or minimum of a function. Linear inequalities are also used in economics, engineering, and other sciences.
This can be seen by the fact that the graph is a straight line going from the bottom left to the top right, and the line is below the x-axis at the point (3, 0). This means that all points on the line or below it are part of the solution set. The other graphs, B, C and D, are not accurate solutions for the linear inequality.
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Two pumps are filling a swimming pool. If one can fill it alone in 30 hours and together they fill it in 7 hours, how fast could the other pump fill it by itself (round your answer to the nearest tenth of an hour)?
The number of hours taken by the other pump to fill it by itself will be 9.13 hours.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The pool is being filled by two pumps. If one person can complete it in 30 hours by themselves, and two people can fill it in 7 hours.
Then the number of hours taken by the other pump to fill it by itself will be given as,
1 / x + 1 / 30 = 1 / 7
1 / x = 1 / 7 - 1 / 30
1 / x = 23/210
x = 9.13 hours
The number of hours taken by the other pump to fill it by itself will be 9.13 hours.
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A package of bandages contains small and large bandages in a 3 to 5 ratio. Which of the following is a possible number of total bandages in the package?
According to the information, it can be inferred that the total content of the box is 45 bandages in a ratio of 3:5.
How to identify the correct option?To identify the correct option we must take into account the proportion of bandages of each type that are in the box. Based on this information, we must identify a number in which the proportion of bandages is maintained. Based on the above, the correct answer would be 45, since this number can maintain the proportion of the bandages as shown below.
45 bandages = 15 small bandages and 25 large bandages.Additionally, the other answer options are not correct because the proportion of bandages of different types is not maintained.
Note: This question is incomplete because there is some information missing. Here is the complete information:
Options:
A.25
B.30
c.45
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It must be in a fraction and a equation to find the amount of time the dough rises in the bowl.
The amount of time spent in the bowl is 1 1/4 hours
How to determine the amount of time spent in the bowlFrom the question, we have the following parameters that can be used in our computation:
Total time = 1 1/2 hours
Time to rise = 1/4 hour
This means that
Time spent in the bowl = Total time - Time to rise
Substitute the known values in the above equation, so, we have the following representation
Time spent in the bowl = 1 1/2 - 1/4
Evaluate the like terms
Time spent in the bowl = 1 1/4
Hence, the time is 1 1/4 hours
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The prime factorizations of 16 and 24 are shown below.
Prime factorization of 16: 2, 2, 2, 2
Prime factorization of 24: 2, 2, 2,3
Using the prime factorizations, what is the greatest common factor of 16 and 24?
O 2
O 2'2
© 2'2'2
O 2 2 2 2'3
The greatest common factor of 16 and 24 is 2×2×2
What is the greatest common factor?The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.
Given that, The prime factorizations of 16 and 24 are shown below.
Prime factorization of 16: 2, 2, 2, 2
Prime factorization of 24: 2, 2, 2, 3
Now, choosing the common factors = 2, 2, 2
Therefore, the GCF = 2, 2, 2
Hence, The GCF of 16 and 24 is 2, 2, 2
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If ƒ(x ) = 3x + 1, then ƒ(a + h ) - ƒ(a ) = h 3 h 3 h + 2
h
3 h
3 h + 2
Answer:
3h
Step-by-step explanation:
Given function:
[tex]f(x) = 3x + 1[/tex]
To find f(a + h), substitute x = a + h into f(x).
Similarly, to find f(a), substitute x = a into f(x).
Therefore:
[tex]\begin{aligned}\implies f(a+h)-f(a)&=[3(a+h)+1]-[3(a)+1]\\&=[3a+3h+1]-[3a+1]\\&=3a+3h+1-3a-1\\&=3a-3a+3h+1-1\\&=3h\end{aligned}[/tex]
The scale on a map is 1.2 cm = 6.4 km. The actual distance from Point A to Point B is 20 km. How far is that on the map in cm?
Answer:
3.75 cm
Step-by-step explanation:
We know
1.2 cm = 6.4 km
Point A to Point B = 20 km
To find it, we take
20 divided by 6.4 then times 1.2 = 3.75 cm
So, 20 km is 3.75 cm far on the map.
isosceles triangle CAR is inscribed in Circle E. If m arc CR = 130 degrees, find : a) m
Measure of arc AC equals measure of arc CR = 130° when m arc CR = 130°. CAR = 1/2 CER = 1/2 *120° = 60°, ACR = 1/3 * 180° = 60°, ARC = 1/3* 180° = 60°.
What is angle ?Two straight lines or rays intersect at a same terminus to make an angle. The latter is known as the vertex of the angle, while the rays are known as its sides, occasionally as its legs, and occasionally as its arms. Two lines converge at a common point to form an angle. They are expressed by the sign ° and are measured in degrees. Acute, right, obtuse, and reflex angles are four crucial types.
given
CAR is isosceles . so the angle of CER is 120° . ∠ACR = 60° and the inscribed angle of an arc is equal to half of the central angle of the arc ( the circumference angle theorem )
a) ∠ CAR = 1/2 ∠CER = 1/2 *120° = 60°
B) ∠ACR = 1/3 * 180° = 60°
C) ∠ARC = 1/3* 180° = 60°
D) measure of arc AC = measure of arc CR = 130°
E) measure of arc AR = measure of arc CR = 130 °
Measure of arc AC equals measure of arc CR = 130° when m arc CR = 130°. CAR = 1/2 CER = 1/2 *120° = 60°, ACR = 1/3 * 180° = 60°, ARC = 1/3* 180° = 60°.
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2. A large rectangular swimming pool is 1,000 feet long, 100 feet wide, and 10 feet deep.
The pool is filled to the top with water.
a. What is the area of the surface of the water in the pool?
b. How much water does the pool hold?
c. Express your answers to the previous two questions as powers of 10.
Answer: it is 1,000,000
Choose the term that best matches the given definition. Numerical descriptor of a particular group of interest. Answer O Population Parameter O Population O Sample Statistic O Sample
Numerical descriptor of a particular group of interest is called population parameter.
A population parameter is a fixed quantity or statistical measure that is plugged into a generic distribution or frequency function to characterize a specific population. A population parameter is a constant but unknowable feature that characterizes the distribution of all values over an entire population.
Common population parameters include the mean, variance, shape and scale parameters for gamma and exponential distributions, the median, the mode, etc. Population parameters also aid in drawing conclusions regarding the shape of the curves, such as how distributed or peaked the data is or where the majority of the data is concentrated.
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Which of the following proves these triangles are congruent?
Answer:
ASA
Step-by-step explanation:
They are congruent by ASA because they share congruent sides indicated by the single dash marks, their angles correspond to each other, and their vertical angles would have to be congruent. Reading from left to right, the angle comes first, then the side, and then the angle again to make ASA.
Prove that d/dx (csc (x)) = -csc(x)*cot(x). Fill in the blanks
step 1: d/dx(csc(x))=(d/dx)(1/blank)
step 2: =(blank)(0)-1(blank)
step 3: (blank)/(sin^2x)
step 4: -(1/sin x)*(blank/sin x)
step 5: = -csc(x)*cot(x)
We will use the first principle of differentiation, to prove the function.
What is the first principle of differentiation?y = f(x) with respect to its variable x. If this limit exists and is finite, then we say that: Wherever the limit exists is defined to be the derivative of f at x.
Given function cosec x
d(cscx)dx = d(1/sinx)dx
= limh→0 1/sin(x+h)-1/sinx / (x+h)-x
= limh→0 sinx - sin(x + h)/sinxsin(x + h) /h
= limh→0 sinx - sin(x + h) / h sinx sin(x + h)
= limh→0 -(sin(x + h) - sinx)/h sinx sin(x + h)
= limh→0 - (sin(x + h) - sinx)h × 1/limh→0 sinx sin(x + h)
= -cosx × 1/sin2x
= -cosx/sinx × 1/sinx
= -cotx cscx
Therefore, proved the derivative of cosec x to be -cot x cosec x using the first principle of differentiation.
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GUYS, PLEASE HELP ASAP I BEG:
An aeroplane flies 22 miles due south followed by 34 miles due east. On what bearing is the aeroplane's starting position from its current position to the nearest degree?
Step-by-step explanation:
set x as right graph
tan x degree =22/34
x degree =arc tan 22/34
32.91 degree
√22^2+34^2
√1640
40.50miles
so it's current position is 32.91 degree north by west 40.50 miles
what is equivalent to -14 - 35d
Answer:
[tex] \sf \: -7(5d + 2) [/tex]
Step-by-step explanation:
Now we have to,
→ find the equivalent expression.
The expression is,
→ -14 - 35d
Let's solve the problem,
→ -14 - 35d
→ -7(2) - 7(5d)
→ -7(2 + 5d)
→ -7(5d + 2)
Hence, answer is -7(5d + 2).
What is fraction grade 4?
Fractions are a part of mathematics that involve comparing two or more values. In grade 4, students learn to identify, name, and write fractions, as well as compare, add, subtract, multiply, and divide fractions.
In grade 4, students learn more detailed concepts related to fractions. They will learn to identify, name, and write fractions, as well as compare, add, subtract, multiply, and divide fractions. They will also learn to convert fractions to decimals and percents, as well as solve real-world problems involving fractions. They will gain a better understanding of how fractions are used in everyday life and how to use them to solve problems. Through hands-on activities, students will gain a greater understanding of fractions, and how to use them to solve problems.
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Students learn more intricate fractional concepts in grade 4. They will gain knowledge of how to recognize, label, and write fractions as well as how to compare, combine, subtract, multiply, and divide them.
Comparing two or more numbers is a component of fractions in mathematics. In addition to learning how to compare, add, subtract, multiply, and divide fractions, fourth graders also learn how to name, recognize, and write fractions.
Additionally, they will learn how to solve fractional problems in the real world and convert fractions to decimals and percents. They will have a greater understanding of fraction usage in daily life and how to apply it to problem-solving. Students will learn more about fractions and how to apply them to solve issues through practical exercises.
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Choose ALL answers that describe the quadrilateral TUVW if TU || VW,
UV || WT, TV = UW, and diagonals are perpendicular: TV LUW.
Parallelogram
Rectangle
□ Rhombus
Square
Trapezoid
The given quadrilateral is found to be a square. The correct option is (D).
What is a parallelogram?A parallelogram is a type of quadrilateral of which the opposite sides are equal and parallel. A diagonal of a parallelogram divides it into two congruent triangles.
For the quadrilateral TUVW the data is given as,
TU || VW, UV || WT, TV = UW and TV ⊥ UW.
Here, TU and VW are pairs of opposite side.
And, TV and UW are diagonals.
Now, the pair of opposite sides are parallel.
Which implies it is a parallelogram.
Again, the equality of diagonals implies it is rectangle.
Then, the perpendicular nature of diagonals satisfy the condition for a square.
Hence, the given quadrilateral is a square.
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A study of 120{,}000120,000120, comma, 000 randomly selected photos posted to a social media site determined that 4\%4%4, percent were "selfies," photos of oneself. If the percent of selfies is consistent throughout the rest of the photos on the site, and there are 202020 billion photos, how many billions of photos on the site are selfies?.
0.8 billion of photos on the site are selfies. if 4%, percent were "selfies," photos of oneself
This problem can be solved by a simple rule of three.
A study of 120,000 randomly selected photos posted to a social media site determined that 4% were "selfies," photos of oneself. This means that for 1 photo, 0.04 are selfies.
There are 20 billion photos, how many billions of photos on the site are selfies?
1 - 0.04
20 - x
x= 20*0.04
x=0.8
0.8 billion of photos on the site are selfies. if 4%, percent were "selfies," photos of oneself
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if the scale factor of two similar polygons is 5:9, then find the ratio of the perimeters of the smaller polygon to the bigger polygon
The ratio of the perimeters of the two polygons is the same as the ratio of their scale factors. Since the scale factor of the smaller polygon to the bigger polygon is 5:9, the ratio of their perimeters is also 5:9.
Translate this sentence into an equation.
Six more than the quotient of a number and 7 is equal to 9.
Use the variable c for the unknown number.
Do not add spaces to your answer.
The equation is represented as 6 + c/7 = 9 where c is the unknown number and the value of c = 21
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 as A
Now , the value of A is
Let the number be represented as c
A = Six more than the quotient of a number and 7 is equal to 9
Substituting the values in the equation , we get
6 + ( c / 7 ) = 9 be equation (1)
On simplifying the equation , we get
6 + c/7 = 9
Subtracting 6 on both sides of the equation , we get
c/7 = 9 - 6
c/7 = 3
Multiply bu 7 on both sides of the equation , we get
c = 21
Therefore , the value of c is 21
Hence , the equation is 6 + c/7 = 9 and c = 21
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A street that is 234m long is covered in snow. City workers are using a snowplow to clear the street. A tire on the snowplow has to turn 39 times in traveling the length of the street. What is the diameter of the tire?
As the snowplow moves finishing all 234 m long road, it turns 39 times, using this information, the diameter of the tire of the snowplower is 1.9098m.
How do you calculate the circumference of a tire?Taking a tire in 2Dimensions for ease of calculations, the tire appears to be a circle, hence the circumference of the tire is given by the formula pi * d, where pi = 1.34 and d is the diameter of the circle or tire.
What is the relationship between the circumference and the area of a circle?The circumference of a circle and the area of a circle are related through the mathematical constant pi (π). The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle. The formula for the area of a circle is A = πr^2. As we can see, both formulas involve pi (π) and the radius of the circle. The relationship between the two is that the circumference of a circle is directly proportional to the radius and the area of a circle is directly proportional to the square of the radius.
As per the given condition in the question,
Length of the road = 234 m
number of turns taken by the snowplow(n) = 39
diameter(d) of the tire = ?
As the tire rolls through all the distance of 234 m, we can use the relation,
length of the road = n * circumference of the tire
or , 234 = 39 * pi * d
hence, d = 1.9098 m
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Let [tex]f(x)=9-2^x[/tex]
Graph y=f(x) for [tex]1\leq x\leq 3[/tex]
Come up with a method to approximate [tex]A(f,1\leq x\leq 3)[/tex]
Using this method, calculate the area that approximates [tex]A(f,1\leq x\leq 3)[/tex]
Note that this will be an approximate answer using the graph.
I NEEEEED HELPPP!!! PKEASE
Answer:
The Equation in Point-Slope Form of the Line Passing through (4, 0) and (2, 6) is 3x + y = 12.
Your family opens a small buffet restaurant. They spend $5000 to buy new dining tables and kitchen supplies. They spend $200 per day on food and utilities. They charge $15 per guest for an all you can eat dinner buffet. If they serve 12 guests a night, how long until they break even?
Answer:
They never break even.
Step-by-step explanation:
Number of days: x
Expenses for x days:
Fixed cost: $5000
Cost per day: $200
Cost for x days: 200x
Income for x days:
12 × $15 × x = 180x
Number of days: x
Total expenses = Total income
200x + 5000 = 180x
Just the daily expense of $200 on food and utilities is greater than the daily income of $180. Then there is the additional initial expense of $5,000, so they will never break even. They start by having an expense of $5,000, and each day they spend $20 more than they receive.
