Answer:
Length of garden will be 30 metres.
Step-by-step explanation:
Let the Width of garden be x metres.
then,
Length of garden will be (x+6) metres.
Area = Length × Breadth
720 = x X (c+6)
720 = x²+6x
0 = x²+6x-720
As we can see above equation is a quadratic equation in the form of ax²+bx+C.
so,
[tex] = \frac{ - b ± \sqrt{{b}^{2} - 4ac} }{2a} \\ = \frac{ - 6 ± \sqrt{{6}^{2} - 4 \times 1 \times - 720} }{2} \\ = \frac{ - 6 ± \sqrt{36 + 2880} }{2} \\ = \frac{ - 6 ± \sqrt{2916} }{2} \\ = \frac{ - 6 ± 54}{2}\\= \frac{-6+54}{2} ... \frac{ - 6 - 54}{2} \\ = \frac{48}{2} ... \frac{ - 60}{2} \\ = 24... - 30[/tex]
One of the Roots of the Quadratic equation is 24 and other is -30.
And as we know width of any garden cannot be negative so the width of garden will be 24 metres.
As we got the width,
adding 6 to it will give us the Length,
So,
24 metres + 6 = 30 metres.
Length of the garden is 30 metres.
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what is the slope of a line parallel to the line whose equation is 4x - 2y = 7?
Answer:
Here the slope is 2.
Step-by-step explanation:
The first step here is to solve for y. This will lead us to the correct slope value. Subtracting 4x from both sides, we get -2y = 7 - 4x.
Dividing both sides by -2, we get y = -7/2 + 2x. The coefficient of x is the slope. Here the slope is 2.
The slope of a line parallel to the line 4x - 2y = 7 is 2. This is calculated by modifying the given equation into the form y = mx + b and determining the value of 'm', which represents the slope, and parallel lines share the same slope.
Explanation:To find the slope of a line parallel to the given line, 4x - 2y = 7, we first need to put the given equation in the standard form y = mx + b, where 'm' represents the slope of the line.
We can do this by isolating 'y' in the equation. So, 4x - 2y = 7 becomes 2y = 4x - 7. Then, we divide the entire equation by 2 to solve for 'y', which gives us y = 2x - 7/2. Thus, the slope 'm' of this line is 2.
Lines that are parallel to each other have the same slope, so the slope of the line parallel to the given line is also 2.
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match to the corresponding value
ANSWER
Midline y=-1
Period= 2π
Amplitude=3
Frequency=1
EXPLANATION
The given function completes one cycle on the interval 0 to 2π.
Therefore the period of the function is
[tex]2 \pi[/tex]
The midline divides the graph into two equal halves.
This line is y=-1
The cycle repeated once on the interval [0,2π] hence the frequency is 1.
The amplitude is the distance from the midline to the peak.
=2--1=3
How many different ways can you make change with a $3?
you can get 12 quarters
at noon it was -18 °F in Billings MT At the some time it was 32 °F in mesa AZ how much warmer was mesa than billings at noon
50 F
32 F - - 18 = 32 F + 18= 50 F
Which function is equivalent to f(x) = lnx?
f(x) = log3x
f(x) = log10x
f(x) = logbx
f(x) = logex
Answer:
[tex]f(x)=log_ex[/tex]
Step-by-step explanation:
By definition, we can write ln instead of log. WHEN??
Whenever the base of the logarithm is the number "e".
Hence, when we have:
[tex]Log_e[/tex]
We can write it in shortcut as:
[tex]Log_e=ln[/tex]
Hence, ln x can also be written as [tex]Log_ex[/tex]
Fourth answer choice is right.
Answer:
[tex]f(x) = log_e(x)[/tex]
Step-by-step explanation:
[tex]f(x) = ln x[/tex]
For logarithmic function ln(x) the base of ln is 'e'
[tex]f(x) = log_3(x)[/tex]
The base of log is 3 . so it is not equivalent to [tex]f(x) = lnx[/tex]
[tex]f(x) = log_{10}(x)[/tex]
The base of log is 10 . so it is not equivalent to [tex]f(x) = lnx[/tex]
[tex]f(x) = log_b(x)[/tex]
The base of log is b . so it is not equivalent to [tex]f(x) = lnx[/tex]
[tex]f(x) = log_e(x)[/tex]
The base of log is e . so it is equivalent to [tex]f(x) = lnx[/tex]
How many hours will it take the reptile food to reach 72.5
now divide 76.5 by 8.5
76.5/8.5 = 9 hours
Answer please the question thank you
Answers
Part a: Opposite
Part b: cos
Part c: Adjacent
Explanation
If you doing sine, cosine, and tangent, just remember SOHCAHTOA.
Examine the lines that are cut by transversals to determine the measure of angle 1.
What is the measure of angle 1?
m <1= ?
1) 48
2) 59
3) 73
4) 132
Why?
A) It is adjacent to the 48-degree angle
B) It is an alternate exterior angle to the 48-degree angle
C) It corresponds to the 48-degree angle
D) It is supplementary to the 48-degree angle
Answer:
1) 48
C) It corresponds to the 48-degree angle
Step-by-step explanation:
k║l
1) <1 = 48
because corresponding angles are equal
Why?
C) It corresponds to the 48-degree angle
Answer:
1) 48 and C) It corresponds to the 48-degree angle.
Step-by-step explanation:
Seeing the parallel lines k and l, and the transversal line m, we have that 48° and angle 1 are corresponding angles because k and l are parallel, then, the angle formed with the same transversal line will have the same measure.
So, the measure of angle 1 is 48 (option 1) and the reason is C) It corresponds to the 48-degree angle.
Identify the excluded values of the rational expression x^2+2x-3/x^2+5x+6
Answer:
x cannot equal -3, and x cannot equal -2
Step-by-step explanation:
Answer:
The excluded values of the rational expression are -3 and -2.
Step-by-step explanation:
If a ration function is defined as [tex]R(x)=\frac{p(x)}{q(x)}[/tex], then the excluded values of the rational function are those values for which q(x)=0.
The given rational expression is
[tex]\frac{x^2+2x-3}{x^2+5x+6}[/tex]
Factories the numerator and denominator.
[tex]\frac{x^2+3x-x-3}{x^2+3x+2x+6}[/tex]
[tex]\frac{x(x+3)-1(x+3)}{x(x+3)+2(x+3)}[/tex]
[tex]\frac{(x+3)(x-1)}{(x+3)(x+2)}[/tex] .... (1)
Equate the denominator equal to 0.
[tex](x+3)(x+2)=0[/tex]
Using zero product property,
[tex]x+3=0\Rightarrow x=-3[/tex]
[tex]x+2=0\Rightarrow x=-2[/tex]
Therefore the excluded values of the rational expression are -3 and -2.
Cancel out the common factors of equation (1)
[tex]\frac{x - 1}{x + 2}[/tex] for (x≠-3)
It means x=-2 is vertical asymptote and x=-3 is hole.
How does the variable of Data Set A compare to the variability of Data Set B? Data Set A: 18, 24, 29, 30, 39 Data Set B: 26, 29, 39, 40, 52
Answer:
Data set B has a higher range than data set A and thus B has a higher degree of variability than A.
Step-by-step explanation:
There are several measures of variability in Statistics among them being;
The range
The inter-quartile range
Variance and standard deviation
To compare the variability of two or more sets of data, we can compute any of the above measures of dispersion and compare them across the various data sets.
In this question we have been given two data sets;
Data Set A: 18, 24, 29, 30, 39
Data Set B: 26, 29, 39, 40, 52
The simplest measure of variability or dispersion is the range. The range is defined as the difference between the maximum and the minimum values in a data set.
The range of data set A is; 39 - 18 = 21
The range of data set B is; 52 - 26 = 26
Data set B has a higher range than data set A and thus B has a higher degree of variability than A.
Vivek has a maximum of 49 seconds to chop tomatoes and zucchinis. It takes him 6 seconds to chop each tomato, and 4 seconds to chop each zucchini.
Write an inequality that represents the number of tomatoes (T) and zucchinis (Z) Vivek can chop within this time limit.
Answer:
[tex]6T+4Z\leq 49[/tex]
Step-by-step explanation:
Let
T----> the number of tomatoes
Z---> the number of zucchinis
we know that
The inequality that represent this situation is
[tex]6T+4Z\leq 49[/tex]
using a graphing tool
The solution is the triangular shaded area
see the attached figure
Rewrite the repeated addition problem as a multipication problem and solve. 9/12+9/12=?
[tex]\bf \stackrel{\textit{let's recall that }}{a+a \implies a(1+1)\implies a(2)\implies 2a} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{a}{\cfrac{9}{12}}+\stackrel{a}{\cfrac{9}{12}}\implies \stackrel{a}{\cfrac{9}{12}}(1+1)\implies \cfrac{9}{12}(2)\implies 9\cdot \cfrac{2}{12}\implies 9\cdot \cfrac{1}{6}\implies \cfrac{9}{6}\implies \cfrac{3}{2}[/tex]
What is the area of the parallelogram?
A. 39.20 cm^2
B. 39.33 cm^2
C 56.58 cm^2
D. 78.66 cm^2
E. 93. 38 cm^2
The area is the length x the height.
Length = 11.40 cm
Height = 6.90 cm
Area = 11.40 * 6.90 = 78.66 cm^2
The answer is D.
write and solve an problem that illustrates the use of the find a pattern strategy.
Answer:
I don't know either
Step-by-step explanation:
A bag contains 4 red marbles, 16 yellow marbles, 5 purple marbles, 16 blue marbles, and 10 green marbles. What is the probability of pulling out a red or green marble? Enter your answer in decimal form, rounded to two decimal places.
Answer:
0.27
Step-by-step explanation:
Red marbles = 4
Yellow marbles = 16
Purple marbles = 5
Blue marbles = 16
Green marbles = 10
Total marbles
= 4 + 16 + 5 + 16 + 10
= 51
Red and Green marbles
= 4 + 10
= 14
P(Red or green marbles)
= 14/51
= 0.27
Answer:
0.27
Step-by-step explanation:
Red marbles = 4
Yellow marbles = 16
Purple marbles = 5
Blue marbles = 16
Green marbles = 10
Total marbles
4 + 16 + 5 + 16 + 10 = 51
Red and Green marbles
= 4 + 10
= 14
P(Red or green marbles)
= 14/51
= 0.27
hope this helps pls make my answer the brainliest
Which expression is equivalent to...? Screenshots attached, please help.
For this case we must simplify the following expression:
[tex]\sqrt [3] {64 * a ^ 6 * b ^ 7 * c ^ 9}[/tex]
We rewrite:
[tex]64 = 4 ^ 3\\a ^ 6 = (a ^ 2) ^ 3\\b ^ 6 * b = ((b ^ 2) ^ 3 * b)\\c ^ 9 = (c ^ 3) ^ 3[/tex]
So:
[tex]\sqrt [3] {4 ^ 3 * (a ^ 2) ^ 3 * (b ^ 2) ^ 3 * b * (c ^ 3) ^ 3} =\\\sqrt [3] {4 * a ^ 2 * b ^ 2 * c ^ 3) ^ 3 * b} =[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]4a ^ 2b ^ 2 c ^ 3 \sqrt [3] {b}[/tex]
Answer:
Option B
Ken will flip a Fair coin and then randomly choose one of the three colored cords the possible outcomes are shown below what is the probability that Tails will turn up and that he will choose a red card. head and tails has the possibke outcomes of red, blue, and green
50% is ur answer your welcome
The large rectangle was reduced to create the small rectangle.What is the missing measure on the small rectangle?
Answer:
x = 4 in
Step-by-step explanation:
scale factor of reduction is
[tex]\frac{6}{18}[/tex] = [tex]\frac{1}{3}[/tex], thus
x = [tex]\frac{1}{3}[/tex] × 12 = 4
Order the numbers from least to greatest 1, -3 and 2
the answer would be -3,1,2
Hello!
From Least To Greatest Your Numbers Would Be
-3 1 2
find a • b. u = <8,7>, v=<9,7>
Answer:
[tex]\large\boxed{\vec{u}\circ\vec{v}=121}[/tex]
Step-by-step explanation:
[tex]\vec{a}=<x_a,\ y_a>,\ \vec{b}=<x_b,\ y_b>\\\\\vec{a}\circ\vec{b}=x_ax_b+y_ay_b\\\\====================================\\\\\vec{u}=<8,\ 7>,\ \vec{v}=<9,\ 7>\\\\\vec{u}\circ\vec{v}=(8)(9)+(7)(7)=72+49=121[/tex]
What is the name of the polygon
Polygons are categorized according to their side count. The following are the designations for polygons depending on the number of sides they exhibit:
3 sides: Triangles
4 sides: Quadrilaterals
Special cases of quadrilaterals include rectangles, squares, parallelograms, rhombuses, and trapezoids.
5 sides: Pentagons
6 sides: Hexagons
7 sides: Heptagons or Septagons
8 sides: Octagons
9 sides: Nonagons
10 sides: Decagons
Polygons are classified based on the number of sides they possess. Here are the names for polygons with different numbers of sides:
Triangles: The simplest polygon with three sides, often classified based on angles as equilateral, isosceles, or scalene.
Quadrilaterals: Four-sided polygons, encompassing various shapes with specific characteristics. For example, squares have equal sides and right angles, while rectangles have opposite sides of equal length and right angles.
Pentagons: Five-sided polygons, commonly found in geometry and nature.
Hexagons: Six-sided polygons frequently seen in beehives and some crystal structures.
Heptagons or Septagons: Seven-sided polygons, less commonly encountered in everyday geometry.
Octagons: Eight-sided polygons, often used in architecture and design.
Nonagons: Nine-sided polygons, less commonly discussed but still defined geometrically.
Decagons: Ten-sided polygons, exhibiting symmetry and regularity in shape.
The question probable may be:
What is the name of the polygon
Which has :
3 sides - ?
4 sides - ?
5 sides - ?
6 sides - ?
7 sides - ?
8 sides - ?
9 sides - ?
10 sides - ?
A frequency polygon is a statistical tool used in mathematics to represent the distribution of data visually, much like a line graph, but specifically connected to a histogram. They are particularly helpful for interpreting continuous data and spotting trends within datasets.
Explanation:Although the question seems to be incomplete, it appears to ask about the terminology used in mathematics, particularly pertaining to polygons. However, if we connect the dots with the provided reference, it seems the actual topic is 'frequency polygons' in the context of statistics. A frequency polygon is a graphical representation of data in statistics, where it's used to illustrate the distribution of a dataset and is similar to a line graph. It is typically made by connecting the midpoints of the tops of bars of a histogram with straight lines, making the data visually easy to interpret. By doing so, it helps in understanding how values are distributed over an interval and is often used to compare different sets of data on the same graph.
Continuous data can sometimes be difficult to analyze, but frequency polygons simplify this by offering a clear, visual interpretation. They are helpful in identifying trends and patterns in data which are not immediately obvious when looking at a table of values or a histogram alone.
CAN SOMEONE PLES HELP ME OUT HERE!
Answer: 1/6
Step-by-step explanation:
1/6+1/6+16 hope this helps!
Choose the graph that represents the following set. The whole number greater than 3
Step-by-step explanation:
Whole numbers means 0,1,2,3,4,5 ........................................ up to infinity.
We need to find graph of whole number greater than 3
The numbers are 4, 5 , 6 , 7 , 8 , 9 ............................................... up to infinity.
The graph representing this is the second graph.
Second graph is the correct answer.
Answer: graph number 2 is correct
Step-by-step explanation:
i just wanted to verify for others
PLEASE HELLLLLLLPPPPPP!!!!!
Answer:
A.
Step-by-step explanation:
First, let's define the types of numbers.
Real numbers: a value that represents a quantity along a continuous line
ex: 1, 5, -6, 0.125, 45.5258,
Integer: Zero, any positive or negative number
ex: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5....
Whole numbers: a number without fractions [not negative]
ex: 0, 1, 2, 3, 4, 5.....
Rational numbers: any number that can be expressed as the quotient or fraction
ex: 1, 2, 3, 4, 5
Irrational numbers: any number that can't be expressed at the quotient or fraction
ex: pi, [3.14.... (never ending decimal)] square root of 2....
Based on this information, the false statment would be A. I believe, because
pi is a real number and it is an irrational number.
I hope this helps!!! :)
Find the distance between (3,4) and (4,7)
Answer:
is the last one if not the second option would be the 2 second
Step-by-step explanation:
A large basin has the shape of a hemisphere with a radius of 25 inches. Calculate the area of rhe circle of water if the basin is filled to a depth of 10 inches
Answer:
100pi in^2, or 314.16 in^2 to nearest hundredth.
Step-by-step explanation:
The areas of the surface of water for full basin and area for the surface when the depth is 10 inches are in the ratio 25^2 : 10^2 = 6.25 : 1. (because the depth of the water = radius of the water when the basin is full).
The area for a full basin = pi r^2 = 625pi in^2.
So the area when depth is 10 inches = 625pi / 6.25 = 100pi in^2.
At the beginning of the day, Meredith has 85.4 pounds of apple to sell at the farmers market. The table shows the change in the original amount that she has after the first several hours.
Hour | Change In Apples (lb)
--------------------------------------------
1 | -8.5
2 | -12 2/3
3 | -16 1/5
4 | -10.2
--------------------------------------------
After 4 hours, about how many pounds of apples does Meredith have left?
the answer is I think -10.2
To find out how many pounds of apples Meredith has left after 4 hours, we need to subtract the total change in apples from the original amount.
Explanation:To find out how many pounds of apples Meredith has left after 4 hours, we need to subtract the total change in apples from the original amount. Let's calculate step-by-step:
Hour 1: -8.5 poundsHour 2: -12 2/3 poundsHour 3: -16 1/5 poundsHour 4: -10.2 poundsTo find the total change, we need to add the individual changes:
Total Change = -8.5 + (-12 2/3) + (-16 1/5) + (-10.2) = -47 61/60 pounds
Now, we subtract the total change from the original amount:
Final Amount = 85.4 - 47 61/60 pounds
Calculate the final amount to find out how many pounds of apples Meredith has left.
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I need help with the math problem
Answer:
Part A) The perimeter of the court is [tex]P=139.25\ ft[/tex]
Part B) [tex]5\ cans[/tex]
Step-by-step explanation:
Part A) we know that
The perimeter of the court is equal to the perimeter of the square plus the perimeter of semicircle
[tex]P=4D+\frac{\pi D }{2}[/tex]
we have that
[tex]D=25\ ft[/tex]
substitute
[tex]P=4(25)+\frac{(3.14*25)}{2}[/tex]
[tex]P=139.25\ ft[/tex]
Part B)
Find the area above the foul line (labelled II)
The area of a semicircle is equal to
[tex]A=\frac{\pi r^{2}}{2}[/tex]
we have
[tex]r=25/2=12.5\ ft[/tex]
substitute
[tex]A=\frac{(3.14)(12.5)^{2}}{2}[/tex]
[tex]A=245.31\ ft^{2}[/tex]
Round to the nearest whole number
[tex]A=245\ ft^{2}[/tex]
One can of paint covers 50 square feet of floor
so
Calculate how many cans of blue paint does the school need to purchase
[tex]245/50=4.9\ cans[/tex]
Round up
[tex]5\ cans[/tex]
How many solutions does the equation -5x+10x+3=5x+6 have?
Answer:
No Solutions
Step-by-step explanation:
-5x+10x+3=5x+6
5x+3=5x+6
5x=5x+3, which isn't true
ANSWER
The equation has no solution.
EXPLANATION
The given equation is
-5x+10x+3=5x+6
Group similar terms
-5x-5x+10x=6-3
-10x+10x=6-3
0=3
This statement is not true.
Hence the equation has no solution.
which of the following represent the values of x, y, and z.
Answer:
Part 1) [tex]z=4\sqrt{3}\ units[/tex]
Part 2) [tex]y=4\sqrt{2}\ units[/tex]
Part 3) [tex]x=4\sqrt{6}\ units[/tex]
Step-by-step explanation:
see the attached figure with letters to better understand the problem
step 1
Find the value of z
In the right triangle DBC
[tex]cos(C)=\frac{4}{z}[/tex] ----> equation A
In the right triangle ABC
[tex]cos(C)=\frac{z}{12}[/tex] ----> equation B
equate equation A and equation B
[tex]\frac{4}{z}=\frac{z}{12}[/tex]
[tex]z^{2}=48[/tex]
[tex]z=4\sqrt{3}\ units[/tex]
step 2
In the right triangle DBC
Applying the Pythagoras Theorem
[tex]z^{2}=y^{2}+4^{2}[/tex]
we have
[tex]z=4\sqrt{3}\ units[/tex]
substitute
[tex](4\sqrt{3})^{2}=y^{2}+4^{2}[/tex]
[tex]48=y^{2}+16[/tex]
[tex]y^{2}=48-16[/tex]
[tex]y^{2}=32[/tex]
[tex]y=4\sqrt{2}\ units[/tex]
step 3
Find the value of x
In the right triangle ABC
Applying the Pythagoras Theorem
[tex]12^{2}=x^{2}+z^{2}[/tex]
we have
[tex]z=4\sqrt{3}\ units[/tex]
substitute
[tex]12^{2}=x^{2}+(4\sqrt{3})^{2}[/tex]
[tex]144=x^{2}+48[/tex]
[tex]x^{2}=144-48[/tex]
[tex]x^{2}=96[/tex]
[tex]x=4\sqrt{6}\ units[/tex]
Answer:
B
Step-by-step explanation:
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