Step-by-step explanation:
First, convert the mixed fraction into an improper fraction:
\(1\dfrac{2}{5} = \dfrac{7}{5}\)
Rewrite 2 as 2/1 and then cross-multiply to combine:
\(\dfrac{2}{1} - \dfrac{7}{5} = \dfrac{(2)(5) - (7)(1)}{(1)(5)} = \dfrac{10 - 7}{5} = \dfrac{3}{5}\)
Rubin grew 9 tomatoes with 6 seed packets. How many seed packets does Rubin need to have 21 tomatoes in his garden
Answer:
3 because 9x3 is 24 and that’s the closest u can get unless u turn into fraction
Step-by-step explanation:
The 14 seed packet needed to grow 21 tomatoes.
How many seed packets?
What is arithmetic?The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.
Given that:
It is given that rubin grew 9 tomatoes with 6 seed packets.
The 9 tomatoes by the 6 seed packs that were necessary to grow them, resulting in 1.5 tomatoes per seed pack.
Divide 21 by this 1.5 to find the number of seed packs needed to grow 21 tomatoes, result would be 14.
So, the 14 seed packet needed to grow 21 tomatoes.
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What is the surface area of a cylinder with a radius of 10 cm and a height of 30 cm
Help me I’ll mark you brainly!
Answer:
- 6x² -x⁴/6 -1 because 6x² is co effectient
How many solutions does this system have? no solutions one unique solution O O two solutions O or an infinite number of solutions
Answer:
no solutions
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
equation of blue line is y = x + 2 , in slope- intercept form
with slope m = 1
equation of red line is y = x - 3 , in slope- intercept form
with slope m = 1
• Parallel lines have equal slopes
then the blue and red lines are parallel.
the solution to the system is at the point of intersection of the 2 lines
since the lines are parallel then they do not intersect each other.
thus the system shown has no solution.
86% percent of senators support a bill.
. (a) What is demographics?
Demographics are data that describe populations and their characteristics. Demographic analysis is the study of a population's characteristics such as age, race, and gender.
What is demography?Demography is the statistical study of populations, particularly human populations. Demographic analysis investigates and quantifies population dimensions and dynamics; it can apply to entire societies or groups defined by criteria such as education, nationality, religion, and ethnicity.
Age, gender, occupation, cultural background, and family status are the five major demographic segments. Demographic analysis is the study of a population's characteristics such as age, race, and gender. Demographic data is a statistical representation of socioeconomic information such as employment, education, income, marriage rates, birth and death rates, and so on.
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Help!!!! Please
Asap
Answer:
events at A and B are independent because P(A)(B)≠P(A)
Y=2x+2 graph the equation using the slope and y-intercept
Answer:
See graph attached
Step-by-step explanation:
Our life is simple because the equation \(y=2x+2\) is already put in slope-intercept form.
This form is called slope-intercept because it states exactly what it's called: The number multiplied by \(x\) (the constant of proportionality, in this case, 2) is the slope - and the y-intercept is what is being added to the equation (in this case, also 2, since there is a +2 at the end.)
With this info, we can start graphing.
We know that the y-intercept is 2, meaning one point will be (0,2).
We also know that the slope is 2, meaning every time x increases by 1, y will increase by 2. So the next point is (1, 4), the next is (2, 6), and so on.
Hope this helped!
The graph of the function y = 2x + 2 is added as an attachment
Sketching the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
y = 2x + 2
The above function is a linear function that has been transformed as follows
Slope = 2y-intercept = 2Next, we plot the graph using a graphing tool by taking not of the above transformations rules
The graph of the function is added as an attachment
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What is the degree of the polynomial, y^2+7x^14-10x^2?
The degree of the polynomial is 14
How to determine the degree of the polynomial?The polynomial is given as:
y^2+7x^14-10x^2
Here, we assume that the variable of the polynomial is x
The highest power of x in the polynomial y^2+7x^14-10x^2 is 14
Hence, the degree of the polynomial is 14
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find the measure of an angle image attached please help
Answer: 147.2° ≈ 148°
Step-by-step explanation: {n-2}×180°/n
Please help me out I am really struggling
The linear function for the temperature is given as follows:
T(x) = 25 - 3x.
The graph is given by the image presented at the end of the answer.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation shown as follows:
y = mx + b
The coefficients m and b have the meaning presented as follows:
m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.The slope and the intercept for the function in this problem are given as follows:
m = -3, as for each km, the temperature decays by 3ºC.b = 25, as at sea level, the temperature is of 25ºC.Hence the function is given as follows:
T(x) = 25 - 3x.
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A rectangular room is 1.3 times as long as it is wide, and its perimeter is 27 meters. Find the dimension of the room.
The dimensions of the room are approximately 5.87 meters by 7.63 meters.
Let's assume the width of the room is "x" meters.
According to the problem, the length of the room is 1.3 times the width, so the length would be 1.3x meters.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 27 meters.
Perimeter = 2(length + width)
Substituting the values we know:
27 = 2(1.3x + x)
Simplifying:
27 = 2(2.3x)
27 = 4.6x
Dividing both sides by 4.6:
x = 27 / 4.6
x ≈ 5.87
The width of the room is approximately 5.87 meters.
To find the length, we can multiply the width by 1.3:
Length = 1.3 * 5.87 ≈ 7.63
The length of the room is approximately 7.63 meters.
Therefore, the dimensions of the room are approximately 5.87 meters by 7.63 meters.
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solve if a chocolate cake is divided into six equal slices and each slice has 280 calories, how many calories are in the whole cake?
Answer:
1680
Step-by-step explanation:
280 times 6 gives you total calories
In this problem, p is in dollars and x is the number of units.
Find the producer's surplus at market equilibrium for a product if its demand function is p = 121 − \(x^{2}\) and its supply function is p = \(x^{2}\) + 6x + 65. (Round your answer to the nearest cent.)
The market equilibrium is the point where the demand and supply functions are equal
The producer's surplus at market equilibrium for a product is #105
How to determine the producer's surplusThe functions are given as:
\(p = 121 - x^2\)
\(p = x^2 + 6x + 65\)
Equate both functions
\(x^2 + 6x + 65 = 121 - x^2\)
Collect like terms
\(x^2 + x^2 + 6x + 65 - 121 = 0\)
Evaluate the like terms
\(2x^2 + 6x -56 = 0\)
Divide through by 2
\(x^2 + 3x -28 = 0\)
Expand
\(x^2 + 7x - 4x - 28 = 0\)
Factorize
\(x(x + 7) - 4(x +7)= 0\)
Factor out x + 7
\((x - 4)(x +7)= 0\)
Solve for x
x = 4 or x = -7
The number of units cannot be negative,
So, we have:
x = 4
Substitute 4 for x in \(p = 121 - x^2\)
\(p = 121 - 4^2\)
p = 105
Hence, the producer's surplus at market equilibrium for a product is #105
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What is the constant up a proportionally in a equation y=x/g
Answer:
Step-by-step explanation:
\(y=(\frac{1}{g} )x\)
Constant up a proportionally is \(\frac{1}{g}\).
Triangle ABC was dilated using the rule DO,4. Triangle A'B'C' is the result of the dilation.
Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O B is three-fourths.
What is OB'?
1.5 units
3 units
4.5 units
6 units
Mark this and return
Answer:
(b) 3 units
Step-by-step explanation:
You want to know the length of OB' when OB = 3/4 and ∆ABC is dilated about point O by a factor of 4.
DilationThe dilation factor multiplies every length.
If OB is 3/4, then OB' is 4(3/4) = 3.
The length of OB' is 3 units.
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The diameter of the circle above is 12 cm. What is the circumference of the circle? (Use = 3.14.)
Answer:
37.68
Step-by-step explanation:
i had this one
you roll two 6-sided number cubes
where is the question I dont see it
show full solutions.15. Name the indicated parts of this diagram.
Given:
A circle with a center at C.
Required:
We need to find the names of the given parts.
Explanation:
Recall that radius is a line segment extending from the center of a circle to the circumference.
Line segment AC extends from the center C of a circle to the circumference.
\(AC=Radius\)Recall that the arc of a circle is defined as the part of the circumference of a circle.
AE is the part of the circumference of a circle.
\(AE=Arc\)Recall that a straight line segment joins and is included between two points on a circle.
D and E are two points on a circle.
A straight line DE line segment joins and is included between two points D and E on a circle.
\(DE=Chord\)Recall that meeting a curve or surface in a single point if a sufficiently small interval is considered a straight line tangent to a curve.
AB is tangent.
\(AB=Tangent\)Recall that an inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords.
\(\measuredangle ADE=\text{ Inscribed angle.}\)Recall that a central angle is an angle formed by two radii with the vertex at the center of the circle.
\(\measuredangle ACE=\text{ Central angle}\)Recall that an angle formed by an intersecting tangent and chord has its vertex "on" the circle.
\(\measuredangle\measuredangle CAB=\text{ Tangent Chord Angle}\)Final answer:
\(AC=Radius\)\(AE=Arc\)\(DE=Chord\)\(AB=Tangent\)\(\measuredangle ADE=\text{ Inscribed angle.}\)\(\measuredangle ACE=\text{ Central angle}\)\(\measuredangle\measuredangle CAB=\text{ Tangent Chord Angle}\)HELP PLSSSS I will GIVE BRAINLYEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
NO LINKS!!! URGENT HELP PLEASE!!!
Please help with the Special triangles #19, 21, and 23
\(\begin{array}{llll} 19. & \text{x}= \frac{9\sqrt{6}}{2}, & \text{y}= \frac{9\sqrt{6}}{2}, & \text{z}= 18\\\\21. & \text{x}= 6, & \text{y}= 6\sqrt{3}, & \text{z}= 6\sqrt{6}\\\\23. & \text{x}= 10\sqrt{3}, & \text{y}= 5\sqrt{3}, & \text{z}= 15\\\\\end{array}\)
===========================================================
Work Shown:
Problem 19
The triangle up top is a 30-60-90 triangle. The short leg is opposite the smallest angle 30 degrees. Double the short leg to get the hypotenuse.
z = 2*9 = 18.
The long leg is found like so
\(\text{long leg} = (\text{short leg})*\sqrt{3}\\\\\text{long leg} = 9\sqrt{3}\\\\\)
These two formulas apply to 30-60-90 triangles only.
The long leg of the 30-60-90 triangle up top is the hypotenuse of the 45-45-90 triangle at the bottom.
For 45-45-90 triangles, we can say:
\(\text{hypotenuse} = (\text{leg})*\sqrt{2}\\\\\text{leg} = \frac{\text{hypotenuse}}{\sqrt{2}}\\\\\text{leg} = \frac{\text{hypotenuse}*\sqrt{2}}{2}\\\\\text{leg} = \frac{9\sqrt{3}*\sqrt{2}}{2}\\\\\text{leg} = \frac{9\sqrt{3*2}}{2}\\\\\text{leg} = \frac{9\sqrt{6}}{2}\\\\\)
This represents the lengths of x and y. For any 45-45-90 triangle, the two legs are the same length (the right triangle is isosceles).
--------------------------------
Problem 21
Focus on the 30-60-90 triangle up top.
The hypotenuse of 12 divides in half to get x = 12/2 = 6 as the short leg.
The long leg is \(6\sqrt{3}\)
This is also the leg of the 45-45-90 triangle down below. Therefore, we have \(y = 6\sqrt{3}\)
Multiply the leg by sqrt(2) to find the hypotenuse.
\(\text{hypotenuse} = \text{leg}*\sqrt{2}\\\\\text{z} = 6\sqrt{3}*\sqrt{2}\\\\\text{z} = 6\sqrt{3*2}\\\\\text{z} = 6\sqrt{6}\\\\\)
--------------------------------
Problem 23
Focus on the triangle on the right. This is a 45-45-90 triangle.
The hypotenuse is 15sqrt(2), which must mean each leg is 15 units long. Therefore, z = 15. The unmarked vertical leg is also 15 units long.
This vertical side is the leg of the 30-60-90 triangle on the left. It's the long leg.
\(\text{long leg} = (\text{short leg})*\sqrt{3}\\\\\text{short leg} = \frac{\text{long leg}}{\sqrt{3}}\\\\\text{short leg} = \frac{(\text{long leg})*\sqrt{3}}{3}\\\\\text{y} = \frac{15\sqrt{3}}{3}\\\\\text{y} = 5\sqrt{3}\\\\\)
Double this short leg to get the hypotenuse of the 30-60-90 triangle.
\(x = 2y\\\\x = 2*5\sqrt{3}\\\\x = 10\sqrt{3}\\\\\)
Answer:
Question 19:
x = (9√6)/2 unitsy = (9√6)/2 unitsz = 18 unitsQuestion 21:
x = 6 unitsy = 6√3 unitsz = 6√6 unitsQuestion 23:
x = 10√3 unitsy = 5√3 unitsz = 15 unitsStep-by-step explanation:
45-45-90 triangleA 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : 1 : √2. Therefore, the formula for the ratio of the sides is b : b : b√2 where:
b is each side opposite the 45 degree angles (legs).b√2 is the side opposite the right angle (hypotenuse).30-60-90 triangleA 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : √3 : 2. Therefore, the formula for the ratio of the sides is c: c√3 : 2c where:
c is the shortest side opposite the 30° angle.c√3 is the side opposite the 60° angle.2c is the longest side (hypotenuse) opposite the right angle.Question 19Side z is the hypotenuse of a 30-60-90 triangle where the leg opposite the 30° angle measures 9 units. Therefore, c = 9.
\(\implies z=2c =2 \cdot 9=18\; \sf units\)
Therefore, the other leg of the same triangle (opposite the 60° angle) measures c√3 = 9√3 units.
Sides x and y are the congruent legs of a 45-45-90 triangle with hypotenuse measuring 9√3 units. Therefore b√2 = 9√3, so b = (9√6)/2.
\(\implies x=\dfrac{9 \sqrt{6}}{2}\; \sf units\)
\(\implies y=\dfrac{9 \sqrt{6}}{2}\; \sf units\)
Question 21Side x is the side opposite the 30° angle in a 30-60-90 triangle with a hypotenuse of 12 units. Therefore, 2c = 12 so c = 6.
\(\implies x=6\; \sf units\)
Therefore, the other leg of the same triangle (opposite the 60° angle) measures c√3 = 6√3 units.
Side y is one of the congruent legs of a 45-45-90 triangle where the other congruent leg measures 6√3 units.
\(\implies y=6\sqrt{3}\; \sf units\)
Side z is the hypotenuse of a 45-45-90 triangle where the congruent legs measure 6√3 units. Therefore b = 6√3.
\(\implies z=b\sqrt{2} = 6 \sqrt{3} \sqrt{2}=6\sqrt{6}\; \sf units\)
Question 23Side z is one of the congruent legs of a 45-45-90 triangle where the hypotenuse measures 15√2 units. Therefore, b√2 = 15√2, so b = 15.
\(\implies z=b=15\; \sf units\)
Side x is the hypotenuse of a 30-60-90 triangle where the leg opposite the 60° measures 15 units. Therefore, c√3 = 15, so c = 5√3.
\(\implies x=2c=2 \cdot 5\sqrt{3}=10\sqrt{3}\; \sf units\)
Side y is the side opposite the 30° angle in a 30-60-90 triangle where the hypotenuse measures 10√3 units. Therefore, 2c = 10√3, so c = 5√3.
\(\implies y=c=5\sqrt{3}\; \sf units\)
3x^3-2x^2+7x+9 divided by x^2-3x
The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).
What is Division?A division is a process of splitting a specific amount into equal parts.
We have to find 3x³-2x²+7x+9 divided by x²-3x
3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.
The steps to solve this are given below.
Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.
Step 2: Then divide it by the divisor and write the answer on top as the quotient.
Step 3: Subtract the result from the digit and write the difference below.
Step 4: Bring down the next digit of the dividend (if present).
Step 5: Repeat the same process.
Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).
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Bill wants to drive to Atlanta, Georgia. Atlanta is 1,450 miles from Bill's home. If Bill has 3 days available that he can drive to Atlanta, what is the minimum number of miles that he can drive each day?
482
483
484
485
Step-by-step explanation:
we need to divide 1450 by 3 to see how many miles should be driven each day to reach to goal in 3 days.
the wording seems to tell us we cannot use fractions of miles. we only can use whole miles.
1450 / 3 = 483.333333...
to be sure to reach Atlanta in 3 days when driving the same amount of miles every day, the minimum per day is then 484 miles per day (no fractions).
because 483 miles per day would give us only 1,449 miles in total and leave us 1 mile short of the target.
Please me get the correct answer
Answer:
i think 56
Step-by-step explanation:
it looks like 7 and 8 so that = 56
complete-the-sequence-1/1-1/2-1/9-1/64,..
i am trying to figure its formula to find its 10th term .
The 10the term of the sequence -1/1, -1/2, -1/9, -1/64....is -1/1,000,000,000
Sequence-1/1, -1/2, -1/9, -1/64
This can be written as;
-1/1° , -1/2¹, -1/3², -1/4³, -1/5⁴, -1/6^5, -1/7^6, - 1/8^7, -1/9^8, -1/10^9
So,
First term = -1/1,
Second term = -1/2,
Third term = -1/9,
Fourth term = -1/64,
Fifth term = -1/625,
Sixth term = -1/7,776,
Seventh term = -1/117,649,
Eighth term = -1/2,097,152,
Ninth term = -1 / 43,046,721,
Tenth term = -1/1,000,000,000
Therefore, the 10th term is -1/1,000,000,000
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if f(5x)=f(5)+f(x) then prove f(1)=0
Answer:
2&4+44-24÷333×6385
Step-by-step explanation:
so it can be a cardinal product
If functions f(5x)=f(5)+f(x) then f(1)=0.
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that f(5x)=f(5)+f(x)
f of five times of x equal to f of five plus f of x.
We need to prove f(1) is equal to zero.
f(5x)=f(5)+f(x)
Let plug in x value as one
f(5×1)=f(5)+f(1)
f(5)=f(5)+f(1)
Subtract f(5) from both sides
f(1)=0
Hence, if functions f(5x)=f(5)+f(x) then f(1)=0.
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During bowling practice, Marley rolled 14 strikes out of 70 attempts. What percent of Marley's attempts were
Answer:
1/5
Step-by-step explanation:
If you divide 70/14 you will get 5.
Knowing this i can determining that every 5 attempts will get a strike.
This means 1/5 attempts will land with a strike.
Evaluate −x^2−5 y^3 when x = 4 and y = 1
Answer:
Simplify:
\(-4^2-5(1^3)\)
So you get:
\(-21\\\)
Answer:
\(\huge\boxed{-21}\)
Step-by-step explanation:
-x²-5y³
Given that x = 4, y = 1
\(-(4)^2-5(1)^3\)
\(-16-5(1)\\-16-5\\-21\)
At age 20, someone sets up an IRA (individual retirement account) with an APR of 5%. At the end of each month he deposits $65 in the account. How much will the IRA contain when
←he
retires at age 65? Compare that amount to the total deposits made over the time period.
After retirement the IRA will contain $ 131,718.42
(Do not round until the final answer. Then round to the nearest cent as needed.)
The total deposits made over the time period is $
(Type a whole number)
CETT
Answer:
total deposits: $35,100
Step-by-step explanation:
You have the value of an annuity earning 5% with payments of $65 a month for 45 years as $131,718.42. You want to know the total value of payments.
Payments12 payments per year of $65 for 45 years will have a total value of ...
12·65·45 = 35100
Total deposits will be $35,100.
can someone help me out-? thanks hopefully the picture is there- :,D
Answer:
2a-12-16b
Step-by-step explanation:
\(4((\frac{a}{2} -3)-4b)=\)\(4((\frac{a-3(2)}{2} )-4b)\)\(=2(a-3(2))-4(4B)=2a-12-16b\)