Step-by-step explanation:
Given system of equations :
x+5y=10 and 3x+y=1.
Let us solve the system of equation by substitution.
Solving second equation 3x+y=1 for y first.
3x+y=1.
Subtracting 3x from both sides, we get
3x-3x+y=1-3x
y = 1-3x.
Substituting y=1-3x in first equation x+5y=10, we get
x+ 5(1-3x) = 10.
x + 5 -15x =10
-14x +5 = 10.
Subtracting 5 from both sides, we get
-14x +5-5 = 10-5
-14x =5
Dividing by -14 on both sides, we get
-14x/-14=5/-14
x= -0.36.
Plugging x=-0.36 in second equation y=1-3x, we get
y = 1-3(-0.36) = 1+1.08 = 2.08.
Therefore, approximate solution is (-0.36, 2.08).Answer:
A (–0.3, 2.1)
Step-by-step explanation:
I is the origin and P is the (4,3). Rx and Ray are reflections around the x- and y- axes
(4,-8)
(-4,8)
(-4,-8)
Answer:
The correct option is 1. The image of (2,4) is (4,-8).
Step-by-step explanation:
The given rule is
[tex]R_x{\circ}D_{o,2}:(2,4)[/tex]
The transformations perform from right to left. [tex]D_{o,2}[/tex] means dilation with scale factor 2 and center of dilation is origin.
The given rule defines the dilation with scale factor 2 and center of dilation is origin followed by reflection across x-axis.
If a figure dilated by scale factor k and the center of dilation is origin, then
[tex](x,y)\rightarrow (kx,ky)[/tex]
The scale factor is 2,
[tex](x,y)\rightarrow (2x,2y)[/tex]
[tex](2,4)\rightarrow (4,8)[/tex]
If a figure reflected across x-axis, then x-coordinate remains the same but the sign of y-coordinate is changed.
[tex](x,y)\rightarrow (x,-y)[/tex]
[tex](4,8)\rightarrow (4,-8)[/tex]
Therefore image of (2,4) is (4,-8) and option 1 is correct.
In a geometric sequence {an}, if a1 = 4 and r = 0.2, the first 4 terms in the sequence are A) {4, .8, .16, .032,...}. Eliminate B) {4, 20, 100, 500,...}. C) {4, 4.2, 4.4, 4.6,...}. D) {4, 3.8, 3.6, 3.4,...}.
Hey man, your answer is (A) I took the test!!!
The first 4 terms in the sequence are :
A) { 4 , 0.8 , 0.16 , 0.032 , . . . }Further explanationFirstly , let us learn about types of sequence in mathematics.
Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.
[tex]\boxed{T_n = a + (n-1)d}[/tex]
[tex]\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}[/tex]
Tn = n-th term of the sequence
Sn = sum of the first n numbers of the sequence
a = the initial term of the sequence
d = common difference between adjacent numbers
Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.
[tex]\boxed{T_n = a ~ r^{n-1}}[/tex]
[tex]\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}[/tex]
Tn = n-th term of the sequence
Sn = sum of the first n numbers of the sequence
a = the initial term of the sequence
r = common ratio between adjacent numbers
Let us now tackle the problem!
Given:
a = 4
r = 0.2
Solution:
[tex]T_n = a ~ r^{n-1}[/tex]
[tex]T_1 = 4 \times 0.2^{1-1} = 4 \times 1 = 4[/tex]
[tex]T_2 = 4 \times 0.2^{2-1} = 4 \times 0.2 = 0.8[/tex]
[tex]T_3 = 4 \times 0.2^{3-1} = 4 \times 0.04 = 0.16[/tex]
[tex]T_4 = 4 \times 0.2^{4-1} = 4 \times 0.008 = 0.032[/tex]
Therefore , the first 4 terms in the sequence are :
A) { 4 , 0.8 , 0.16 , 0.032 , . . . }Learn moreGeometric Series : https://brainly.com/question/4520950Arithmetic Progression : https://brainly.com/question/2966265Geometric Sequence : https://brainly.com/question/2166405Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Arithmetic and Geometric Series
Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term
A lot is in the shape of a trapezoid. The sum of the bases is 280 feet. If the area of the lot is 8,400 square feet, what is the distance across the lot, i.e., the altitude of the figure? The altitude of the trapezoid is feet.
Answer:
The altitude of the trapezoid is 60 feet.
Step-by-step explanation:
Trapezoid
Sum of the bases: B+b=280 feet
Area of the trapezoid: A=8,400 feet^2
Altitude of the trapezoid: h=?
The formula to calculate the area of a Trapezoid is:
A = (1/2) (B+b) h
Replacing the given values:
8,400 feet^2 = (1/2) (280 feet) h
(1/2) (280 feet) = (140 feet)
8,400 feet^2 = (140 feet) h
Solving for h: Dividing both sides of the equation by 140 feet:
8,400 feet^2 / (140 feet) = (140 feet) h / (140 feet)
60 feet = h
h = 60 feet
Answer: The altitude of the trapezoid is 60 feet.
Answer:
60
Step-by-step explanation:
which expression is equivalent to 4 times the sum of 3 and x
Answer:
4(3+x)
Step-by-step explanation:
If any thing is in the brackets you need to do it first
so if you do 3 + x × 4 it will give yo 4x + 3 or 3 +4x
The given expression 4 (x + 3) is equivalent to the expression 4x + 12.
What is an equivalent function?The equivalent operations are those that have various forms but have the same outcome.
The expression is given below.
→ 4 (x + 3)
The expression can be written as
→ 4x + 12
The given expression 4 (x + 3) is equivalent to the expression 4x + 12.
More about the equivalent link is given below.
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Logarithms- How to answer these questions?
Answer:
2. m = b³ (= 216)
3. logp(x) = -4
Step-by-step explanation:
2. The given equation can be written using the change of base formula as ...
... log(m)/log(b) + 9·log(b)/log(m) = 6
If we define x = log(m)/log(b), then this becomes ...
... x + 9/x = 6
Subtracting 6 and multiplying by x gives ...
... x² -6x +9 = 0
... (x -3)² = 0 . . . . . factored
... x = 3 . . . . . . . . . value of x that makes it true
Remembering that x = log(m)/log(b), this means
... 3 = log(m)/log(b)
... 3·log(b) = log(m) . . . . . multiply by the denominator; next, take the antilog
... m = b³ . . . . . . the expression you're looking for
___
3. Substituting the given expression for y, the equation becomes ...
... logp(x^2·(p^5)^3) = 7
... logp(x^2) + logp(p^15) = 7 . . . . . use the rule for log of a product
... 2logp(x) + 15 = 7 . . . . . . . . . . . . . use the definition of a logarithm
... 2logp(x) = -8 . . . . . . . . . . . . . . . . subtract 15
... logp(x) = -4 . . . . . . divide by 2
Answer:
For #3: [tex]\log_px=-4[/tex]
Step-by-step explanation:
I'm a little rusty on my logarithm rules for #2, but here's an explanation of #3.
Logarithms: the Inverse of ExponentsIn a sense, we can think of operations like subtraction and division as different ways of representing addition and multiplication. For instance, the same relationship described by the equation 2 + 3 = 5 is captured in the equation 5 - 3 = 2, and 5 × 2 = 10 can be restated as 10 ÷ 2 = 5 without any loss of meaning.
Logarithms do the same thing for exponents: the expression [tex]2^3=8[/tex] can be expressed in logarithms as [tex]\log_28=3[/tex]. Put another way, logarithms are a sort of way of pulling an exponent out onto its own side of the equals sign.
The ProblemOur problem gives us two facts to start: that [tex]log_p(x^2y^3)=7[/tex] and [tex]p^5=y[/tex]. With that, we're expected to find the value of [tex]\log_px[/tex]. [tex]p^5=y[/tex] stands out as the odd-equation-out here; it's the only one not in terms of logarithms. We can fix that by rewriting it as the equivalent statement [tex]log_py=5[/tex]. Now, let's unpack that first logarithm.
Justifying Some Logarithm RulesFor a refresher, let's talk about some of the rules logarithms follow and why they follow them:
Product Rule: [tex]\log_b(MN)=\log_bM+\log_bN[/tex]
The product rule turns multiplication in the argument (parentheses) of a logarithm into addition. For a proof of this, consider two numbers [tex]M=b^x[/tex] and [tex]N=b^y[/tex]. We could rewrite these two equations with logarithms as [tex]\log_bM=x[/tex] and [tex]\log_bN=y[/tex]. With those in mind, we could say the following:
[tex]\log_b(MN)=\log_b(b^xb^y)[/tex] (Substitution)[tex]\log_b(b^xb^y)=log_b(b^{x+y})[/tex] (Laws of exponents)[tex]\log_b(b^{x+y})=x+y[/tex] ([tex]\log_b(b^n)=n[/tex])[tex]x+y=\log_bM+\log_bN[/tex] (Substitution)And we have our proof.
Exponent Rule: [tex]\log_b(M^n)=n\log_bM[/tex]
Since exponents can be thought of as abbreviations for repeated multiplication, we can rewrite [tex]\log_b(M^n)[/tex] as [tex]\log_b(M\times M\cdots \times M)[/tex], where M is being multiplied by itself n times. From there, we can use the product rule to rewrite our logarithm as the sum [tex]\log_bM+\log_bM+\cdots+\log_bM[/tex], and since we have the term [tex]\log_bM[/tex] added n times, we can rewrite is as [tex]n\log_bM[/tex], proving the rule.
Solving the ProblemWith those rules in hand, we're ready to solve the problem. Looking at the equation [tex]\log_p(x^2y^3)=7[/tex], we can use the product rule to split the logarithm into the sum [tex]\log_p(x^2)+\log_p(y^3)=7[/tex], and then use the product rule to turn the exponents in each logarithm's argument into coefficients, giving the equation [tex]2\log_px+3\log_py=7[/tex].
Remember how earlier we rewrote [tex]p^5=y[/tex] as [tex]log_py=5[/tex]? We can now use that fact to substitute 5 in for [tex]log_py[/tex], giving us
[tex]2\log_px+3(5)=7[/tex]
From here, we can simply solve the equation for [tex]\log_px[/tex]:
[tex]2\log_px+15=7\\2\log_px=-8\\\\\log_px=-4[/tex]
Which of the function below is that inverse of f(x)=x^-25
Answer:
g⁻¹(x) = ±√(x + 25)
Step-by-step explanation:
g(x) = x² - 25 Rename g(x) as y
y = x² - 25
=====
Solve for x
y = x² - 25 Add 25 to each side
y + 25 = x² Take the square root of each side
x = ±√(y + 25) Switch x and y
y = ±√(x + 25) Rename y as g inverse
g⁻¹(x) = ±√(x + 25)
=====
See the graphs of g(x) and g⁻¹(x) below.
g(x) is the red line. g⁻¹(x) is the purple line.
Each graph reflects the other about the dashed line representing the function y = x.
in the figure above CD is the perpendicular bisector of AB. three students explained how they proved ADC is congruent to BDC
who's explanation is incorrect??
Answer:
All explanations are correct
Step-by-step explanation:
In triangle ABC, CD is the perpendicular bisector of AB, thus using ΔADC and ΔBDC,
AC=BC ( Since CD is perpendicular to AB, therefore C is equidistant from both A and B)
∠ADC=∠BDC=90°(CD perpendicular AB)
CD=CD( Reflexive property)
therefore, by SAS rule of congruency,
ΔADC≅ ΔBDC,
Also, In the same triangles, AC=BC ( Since CD is perpendicular to AB, therefore C is equidistant from both A and B)
CD=CD( Reflexive property)
AD=BD (D is the midpoint and divides AB into two equal halves)
Thus, by SSS rule of congruency,
ΔADC≅ ΔBDC,
Thus, all the three explanations are correct.
In the given case, we can conclude that All explanations are correct
In triangle ABC, let CD be the perpendicular bisector of AB. We can use the properties of triangles to demonstrate that ΔADC is congruent to ΔBDC.
AC=BC: This holds true because CD is perpendicular to AB, making point C equidistant from both A and B.
∠ADC=∠BDC=90°: Since CD is perpendicular to AB, both angles ADC and BDC are right angles.
CD=CD: This is a reflexive property, stating that any line segment is equal to itself.
By applying the SAS (Side-Angle-Side) rule of congruency using the above properties, we can conclude that ΔADC is congruent to ΔBDC.
Furthermore, we can establish that in these congruent triangles:
AC=BC (since C is equidistant from A and B due to CD being perpendicular to AB).
CD=CD (reflexive property).
AD=BD (as D is the midpoint of AB).
Hence, using the SSS (Side-Side-Side) rule of congruency, we can also conclude that ΔADC is congruent to ΔBDC.
Therefore, all three explanations correctly demonstrate the congruence of these triangles.
Learn more about Perpendicular Bisector Theorem here:
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Which number sentence is true
Answer:
B is the right one i bet u 100 point s
Answer:
B is the correct answer.
The brackets ║ represent absolute value. Absolute value is ALWAYS positive. I hope this helps you!
-Mikayla
45 POINTS!
PLEASE HELPPPPPPPPPPPPPP!
Answer:
This is a direct variation where the constant of variation is 5/9
Step-by-step explanation:
The equation for direct variation is y = kx
5x-9y =0
Lets try to get this equation in the above form
Add 9y to each side
5x-9y +9y = 9y
5x = 9y
Divide each side by 9
5/9 x = 9y/9
5/9x = y
This is in the form y = k x where k =5/9
7 1/3 ∙ x = 1.6 ÷ 6/11
x = __
Please Help!
Answer:
x= 0.4
Step-by-step explanation:
We need to solve and find the value of x
7 1/3x = 1.6 ÷ 6/11
Converting mixed fraction into improper fraction
22/3 x = 1.6 ÷ 6/11
Converting ÷ sign by X and reciprocating the term
22/3 x = 1.6 * 11/6
Now divide both sides by 3/22
x = 1.6 * 11/6 * 3/22
x = 1.6 * 1/2 * 1/2
x = 1.6/4
x = 0.4
S0, x= 0.4
convert angle 180° to radians
Answer:
180 degrees in radians is π
Step-by-step explanation:
0° = 0 radians
90°= π/2
180 °= π
270°= 3π/2
360° = 2π
and so on
Leonard paid $35 registration fee to join the gym. He pays $10 each month.
How much will he pay to use the gym for 6 months?
i’m in algebra 2 and it’s long division please help
[tex]\dfrac{5x^4+10x^3-7x+1}{x+2}=(5x^4+10x^3-7x+1):(x+2)[/tex]
[tex]_+\begin{matrix}(5x^4&+&10x^3&-&7x&+&1)&:&(x+2)&=5x^3-7\\-5x^4&-&10x^3\end{matrix}\\\overline{_+\begin{matrix}\ \ =&&&&=&\ \ \ -&7x&+&1\\&&&&&&7x&+&14\end{matrix}}\\\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\ 15}[/tex]
[tex]\dfrac{5x^4+10x^3-7x+1}{x+2}=(5x^4+10x^3-7x+1):(x+2)=5x^3-7+R(15)\\\\5x^4+10x^3-7x+1=(x+2)(5x^3-7)+15[/tex]
Final answer:
Long division is a method used to divide two polynomials in algebra. It involves arranging the dividend and divisor, determining the term of the quotient, subtracting and repeating until there are no more terms left to bring down.
Explanation:
In algebra, long division is a method used to divide two polynomials. It is especially useful when the dividend (the polynomial being divided) has a higher degree than the divisor (the polynomial dividing the dividend).
Here's a step-by-step explanation:
Arrange the dividend and divisor in descending order.Determine the term of the quotient by dividing the leading terms of the dividend and divisor.Multiply the entire divisor by the term of the quotient and subtract it from the dividend.Repeat steps 2 and 3 until there are no more terms left to bring down.The result is the quotient and any leftover terms are the remainder.Let me know if you need further assistance or if there's anything else I can help you with!
A customers photo cell phone bill this month is $50 and 50 Cent the company charges a monthly fee of $18 +5 cents for each car used in to represent the number of calls
can someone help me and explain how you did it?
Answer:
Step-by-step explanation: To find a y intercept you must find what y is when x is 0 so because it already tells you on the table the y intercept is 4. To find slope take 2 x intercepts and 2 y intercepts. For this well take the 0,4 and 5,1. The take the y from both pairs and minus them so it will look like 4 minus 1. Then draw a line under the equation under this line do the same thing but with the x's from both pairs so 0-5 then you will get as a result of both -3/5 as your slope.
Answer:
slope: -3/5
y-intercept: (0, 4)
slope-intercept form: y = -3/5x + 4
Step-by-step explanation:
Finding the slopeTo find the slope of this line, you would take two points from the table and substitute their coordinates into the slope formula.
Slope formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
I'm going to use the points (0, 4) and (5, 1). You can really use any point from the table. Substitute these points into the formula to find the slope.
(0, 4), (5, 1) → [tex]\frac{1-4}{5-0} \rightarrow \frac{-3}{5}[/tex]
This means the slope of the line is -3/5.
Finding the y-interceptThe y-intercept will always have the value of x be 0 (so the point is solely on the y-axis), so by looking at the table we can see that the y-intercept is at (0, 4).
Finding the slope-intercept formSince we have the slope and a point of the line, we must use point-slope form to find the equation of the line in slope-intercept form. Substitute in the point (0, 4) --you could use any point from the table-- and the slope -3/5 into the point-slope form equation.
point-slope form: y - y1 = m(x - x1) --you'll be substituting the point coordinates and slope into y1, x1, and m.
y - (4) = -3/5(x - (0))
Simplify.
y - 4 = -3/5x
Add 4 to both sides.
y = -3/5x + 4 is the equation of the line in slope-intercept form (you have both the slope and the y-intercept in this form).
the area of kens rectangular yard is 480 square feet. the yard is 24feet wide. in order to fence in the garden completely on all four sides,how many feet of fencing would ken need to buy.
Answer:
88 ft
Step-by-step explanation: Start with the formula for the area of a rectangle:
A = L*W, where L is the length and W is the width.
Here, the width is W = 24 ft, and the area i s 480 ft^2. Thus,
A = 480 ft^2 = L (24ft), which yields L = (480/24) ft = 20 ft.
The length of the fencing required is actually the perimeter of the yard, which is P = 2L + 2W.
Substituting 20 ft for L and 24 ft for W, we get:
P = perimeter of yard = amount of fending needed:
P = 2(20 ft) + 2(24 ft) = 88 ft
Ken would need 88 ft of fencing to enclose his entire yard.
Ken needs to buy 88 feet of fencing to enclose his rectangular yard, which has an area of 480 square feet and is 24 feet wide.
To find out how much fencing Ken would need to buy to enclose his rectangular yard, we first need to calculate the dimensions of the yard. We know the area of the yard is 480 square feet and the width is 24 feet.
To find the length, we use the following equation for the area of a rectangle (Area = length imes width):
480 square feet = length x 24 feet
By dividing both sides by 24 feet, we obtain:
length = 480 / 24
length = 20 feet
Now, to calculate the total amount of fencing needed, we add together the lengths of all four sides:
Total fencing = 2 imes (length + width)
Total fencing = 2 imes (20 feet + 24 feet)
Total fencing = 2 imes 44 feet
Total fencing = 88 feet
Therefore, Ken needs to buy 88 feet of fencing to enclose his yard completely on all four sides.
Park Crest Middle School has a population of about 400 8th graders. Parkcrest is one of several middle schools in the state which has a total of 806, 240 8th graders. Use powers of 10 to estimate about how many times greater the States population of eighth-graders is compared to the number of 8th graders at Park Crest Middle School.
Answer:
[tex]8.05 * 10^{5}[/tex]
Step-by-step explanation:
Thinking process:
the population of Park Crest Middle School = 400 children
The population in the state = 806, 240 children
The difference:
[tex]806240 - 400\\= 805840[/tex]
Expressing the difference in standard form gives:
8.05 × 10⁵
what is 3/20 as a percentage
Answer:
15%
Step-by-step explanation:
Percent means out of 100. Lets get the denominator out of 100
3/20 * 5/5 = 15/100
This is 15%
Final answer:
To convert the fraction 3/20 to a percentage, first convert it to a decimal by dividing 3 by 20. Then, multiply the decimal by 100 to get the percentage.
Explanation:
To express 3/20 as a percentage, you can multiply the fraction by 100. The calculation is (3/20) * 100 = 15%. Therefore, 3/20 as a percentage is 15%. This means that 3 out of every 20 parts represent 15% of the whole. In percentage terms, it provides a convenient way to compare the fraction to 100, making it easier to understand its relative size or portion in relation to the total. In this case, 15% indicates the proportion of the whole that is represented by the fraction 3/20.
What is the equation of the graph below?
Answer:
[tex]y=cos(x+\pi )[/tex]
Step-by-step explanation:
From the graph, we can see that y = -1 when x = 0.
So to check whether which of the given options is the equation of the given graph, we will set our calculator to the radian mode and then plug the value of x as 0.
1. y = cos(x + pi/2) = cos(0 + pi/2) = 0
2. y = cos(x+2pi) = cos(0+2pi) = 1
3. y = cos(x+pi/3) = cos(0+pi/3) = 1/2 = 0.5
4. y = cos(x+pi) = cos(0+pi) = -1
Therefore, the equation of this graph is y = cos(x+pi) = cos(0+pi) = -1.
What is the 41st term in sequence 8,10,12,14,.....?
Drag each tile to the correct box.
A scientist is studying the growth rates of three samples of bacteria in different conditions. The following three functions represent the number of bacteria in the three samples after x hours.
Order the samples by their average growth rate over the interval [1, 3], from least to greatest.
Answer: C < B < A
Step-by-step explanation:
First, let's evaluate the growth rate of A from [1, 3]
[tex]f(x) = 200\bigg(\dfrac{3}{2}\bigg)^1[/tex]
= 300
coordinate is (1, 300)
[tex]f(x) = 200\bigg(\dfrac{3}{2}\bigg)^3[/tex]
= 675
coordinate is (3, 675)
Average growth rate (AGR) is: [tex]\dfrac{675-300}{3-1} = \dfrac{375}{2} = 187.5[/tex]
AGR (A) = 187.5
*************************************************************************************
Next, let's evaluate the growth rate of B from [1, 3]
The coordinates are already provided as (1, 120) and (3, 480)
Average growth rate (AGR) is: [tex]\dfrac{480-120}{3-1} = \dfrac{360}{2} = 180[/tex]
AGR (B) = 180
*************************************************************************************
Lastly, let's evaluate the growth rate of C from [1, 3]
f(x) = 600(1.2)ˣ
f(x) = 600(1.2)¹
= 720
coordinate is (1, 720)
f(x) = 600(1.2)³
= 1036.8
coordinate is (3, 1036.8)
Average growth rate (AGR) is: [tex]\dfrac{1036.8-720}{3-1} = \dfrac{316.8}{2} = 158.4[/tex]
AGR (C) = 158.4
The letters in the word Mississippi are put into a bag. What’s the probability of randomly selecting a vowel from the bag ?
- 3/11
- 2/11
- 1/11
- 4/11
share $500.00 between four children in the ratio 2:3:5:10.
the cheap answer is, we divide 500 by (2+3+5+10) and then distribute accordingly.
[tex]\bf \cfrac{500}{2+3+5+10}\implies \cfrac{500}{20}\implies \cfrac{25}{1}\implies 25 \\\\\\ \stackrel{2\cdot 25}{2}~~:~~\stackrel{3\cdot 25}{3}~~:~~\stackrel{5\cdot 25}{5}~~:~~\stackrel{10\cdot 25}{10}\qquad \implies \qquad 50~~:~~75~~:~~125~~:~~250[/tex]
use the law of cosines to find each missing side
Answer:
29.03 units
Step-by-step explanation:
x^2 = 10^2 + 19^2 - 2*19*20 cos 122
= 100 + 361 - 720 * -0.52992
= 842.54
x = 29.03
Morita works in a florist shop and makes flower arrangements. She outs 10 flowers in each case, and 2/10 of the flowers are daisies. If Morita makes 4 arrangements, how many daisies does she need. Show how you can check your answer. Last weekend, Morita used 10 daisies to make flower arrangements. How many flowers other than daisies did she use to make the arrangements? Explain your reasoning.
Answer:
8 daisies
Step-by-step explanation:
You have to multiply the amount of vases by daisies.
Answer:
Givens
Morita outs 10 flowers in each case.2/10 of the flowers are daisies.Morita makes 4 arrangements.We know that Morita arranges 4 cases, each of them has 10 flowers.
So, if there are 2/10 daisies per case, that means each can contains 2 daisies.
But, she did 4 arrangements. There are 2x4 = 8 daisies in total.
Now, last weekend, Morita used 10 daisies to make flower arrangements, and we know she tend to use 2/10 of the flowers as daisies, that means this fraction represents daisies,
[tex]\frac{2}{10}x=10\\ x=\frac{100}{2}\\ x=50[/tex]
Therefore, there are 50 flowers in total.
Mrs Wong is going on a trip. She has 14 books that she hasn’t read yet but she wants to bring only 2 on the trip. In how many ways can she choose 2 books to bring on the trip
In combinatorics, we use the combination formula to calculate the number of ways Mrs. Wong can choose 2 books out of 14. The result is 91 ways.
Explanation:The subject of this question is combinatorics, a topic in mathematics dealing with combinations of objects belonging to a finite set in accordance with certain constraints, such as those specified in this question. In this case, Mrs. Wong has 14 special objects (books) and wants to choose 2 out of them.
We use the combination formula in this scenario. The combination formula is given by C(n, r) = n! / [(n-r)!*r!], where n represents the total number of objects, r is the number of objects to choose, and '!' denotes factorial.
Substituting n as 14 and r as 2 into the formula, we get: C(14,2) = 14! / [(14-2)!*2!] = 91.
Therefore, Mrs. Wong can choose 2 books out of 14 in 91 different ways.
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The question is about combinations in mathematics. Using the formula for combinations, we find that Mrs. Wong can choose 2 books out of 14 in 91 different ways.
Explanation:This is a problem of combinations in mathematics. Mrs. Wong can choose two out of 14 unread books in a certain number of ways, and we're tasked to find that number.
Considering that order of selection does not matter, we can use the formula for combination: nCr = n! / r!(n-r)!. Here, 'n' is the total number of items, 'r' is the items to be chosen.
So the combinations she can make, denoted as 14C2, can be calculated like this:
14C2 = 14! / 2!(14-2)! = (14*13) / (2*1) = 91 ways
Therefore, Mrs Wong can choose 2 books out of 14 in 91 ways.
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what is the
the sum of the multiples of 35 rom 36 to 153
Answer:
70, 105, 140
Step-by-step explanation:
Lucy cuts 4 squares with side length x in. from the corners of a 12 in. by 18 in. cardboard rectangle. She folds the remaining cardboard to make a tray that is x in. high. Write and simplify a polynomial function for the volume V of the tray in terms of x.
please help, i am loosing a braincell each day
Answer:
Volume of tray =[tex]4x^{3} -60x^{2} +216x[/tex]
Step-by-step explanation:
The Dimensions of rectangular cardboard is given by 12 inches by 18 inches
Length of the rectangular cardboard = 18 inches
Width of the rectangular cardboard = 12 inches
if the square of sides x inches is cut from each corner of the rectangular cardboard and folded to make a tray, then we have
Length of the tray = length of cardboard - 2 (side of the square )
= [tex]18-2x[/tex]
Width of the tray = width of cardboard - 2( side of square)
= [tex]12-2x[/tex]
height of tray = sides of square
= x
volume of tray = Length × width × height
Volume of tray = [tex]x(18-2x)(12-2x)[/tex]
first we multiply (12-2x) and (18-2x)
Volume of tray =[tex]x(18(12-2x)-2x(12-2x))\\[/tex]
=[tex]x(216-36x-24x+4x^{2})[/tex]
=[tex]x(4x^{2}-60x+ 216)[/tex]
=[tex]4x^{3} -60x^{2} +216x[/tex]
Hence the volume of tray =[tex]4x^{3} -60x^{2} +216x[/tex]
The volume of the Tray is given by the equation [tex]4x^3-60x^2+216x[/tex] and this can be determined by using the given data.
Given :
Lucy cuts 4 squares with side length x in. from the corners of a 12 in. by 18 in. cardboard rectangle. She folds the remaining cardboard to make a tray that is x in.If the square is cut from each corner of the cardboard and folded to make a tray, then according to the given data:
Tray length = 18 - 2x
Tray width = 12 - 2x
Tray height = x
Now, the volume of the tray is given by the expression:
The volume of Tray = [tex]x(12-2x)(18-2x)[/tex]
Simplify, the above expression.
[tex]\rm Volume = (12x - 2x^2)(18-2x)[/tex]
[tex]\rm Volume = 216x -24x^2-36x^2+4x^3[/tex]
[tex]\rm Volume = 4x^3-60x^2+216x[/tex]
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What is 2pi/ 5radians in degrees
Answer:
2/5 * pi radians = 72 degrees
Step-by-step explanation:
To convert radians to degrees, we multiply by 180/pi
2 * pi/5 * 180/pi =
The pi/pi cancels leaving
2/5 * 180
360/5
72
2/5 * pi radians = 72 degrees
what three things must a ordered pair have?
Answer: An x and y value, parenthesis around the values, and a comma in between them.
Examples of ordered pairs: (2, 5), (1872, 1683), (-3, 7), (7/8, -10/2)