The rate at which the base of the triangle is changing is equal to,
dB = -6.3 cm/minutes.
From the data given in the question.
The rate of increase in the area of the triangle, dA = 4.5 cm/minute
The rate of increase in the altitude of the triangle, dH = 3.5 cm/minute
The Area of the triangle, A = 87 square centimeters
The altitude of the triangle, H = 7.5 centimeters
The equation for the area of a triangle is equal to
A = 0.5×B×H
Plug in A and H to solve for B at that point:
87 = 0.5×B×7.5
B = 23.2
Differentiate the equation for the area of a triangle to find the rate of change of the area of a triangle (dA):
dA = 0.5× dB× H + 0.5×B × dH.
Plug in known variables to solve for the rate of change of the base dB
dA = 0.5 × dB × H + 0.5 × B × dH
4.5 = 0.5 × dB × 7.5 + 0.5 × 23.2 × 3.5
The rate at which the base of the triangle is changing is equal to,
dB = -6.3 cm/minutes.
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Sergio wants to hand a 40 1/2 inch by 28 2/3 inch canvas painting on a wall in his room. The width of the wall is 15 2/3 feet. The height of the wall is 3/4 the width of the wall. a. What is the area of the wall? b. How much of the wall will be uncovered after Sergio hangs the painting?
The most appropriate choice for area of rectangle will be given by-
a) Area of the wall = [tex]26508[/tex] [tex]in^2[/tex]
b) Area of wall left uncovered = [tex]25347[/tex] [tex]in^2[/tex]
What is area of rectangle?
Area of rectangle is the total space taken by the rectangle. If l is the length of the rectangle and b is the breadth of the rectangle, then area of the rectangle is given by
Area = [tex]l \times b[/tex]
Here,
Width of the wall = [tex]15\frac {2}{3}[/tex] feet = [tex]\frac{47}{3}[/tex] feet
Height of the wall = [tex]\frac{3}{4} \times \frac{47}{3}[/tex] feet
= [tex]\frac{47}{4}[/tex] feet
a) Area of the wall = [tex]\frac{47}{3} \times \frac{47}{4}[/tex] [tex]ft^2[/tex]
=[tex]\frac{2209}{12} \times 12 \times 12[/tex] [tex]in^2[/tex]
= [tex]26508[/tex] [tex]in^2[/tex]
b) Length of painting = [tex]40 \frac{1}{2}[/tex] in = [tex]\frac{81}{2}[/tex] in
Breadth of painting = [tex]28\frac{2}{3}[/tex] in = [tex]\frac{86}{3}[/tex] in
Area of painting = [tex]\frac{81}{2} \times \frac{86}{3}[/tex] [tex]in^2[/tex]
= [tex]1161[/tex] [tex]in^2[/tex]
Area of wall left uncovered = (26508 - 1161) [tex]in^2[/tex]
= 25347 [tex]in^2[/tex]
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How is adding positive and negative integers different from adding only positive integers on a number line?
1) To understand how that works, let me draw a number line:
If we only add positive numbers like 2 +3 = 5, 6+8 =14, etc. we'll only get a positive result (right to the zero) on the number line, we are moving to the right
2) If we add positive and negative numbers, for example:
2 +(-3) =2 -3=-1
0+(-1)= -1
6+(-2)= 4
On the number line, we are starting from one point and moving to the left.
SLook at point in the coordinate grid.If a line contains both points and the origin, which point would the line also contain? *(2 points)DS(12,8)(14,7)(15,9)(20, 12)5tvAle--AR
the point which will fall in the line is (14, 7)
Explanation:
The coordinates o f S = (2, 1)
When we draw a line from the origin (0, 0) touching the point S, we will see the next point will be (4, 2). Followed by (6, 3).
So when we look at the trend, we see that the x axis is the double of the y axis:
(2y, y) = (x, y)
(2,1 ) , (4, 2), (6, 3)
From the above, we can say the point which will fall in the line will follow that trend:
When we check the options, the only point with that trend is (14, 7).
This because (2(7), 7) = (2y, y)
Hence, the point which will fall in the line is (14, 7)
¡¡¡Help with this!!!
The value of sin 2x=0.8304 ,cos 2x=0.557,tan 2x=1.498 when the value of tan x is 8/15 and using the trigonometry identities as tan x as the formula in sin 2x, cos 2x, tan 2x.
What is trigonometry?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations (csc).
What is trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.
sin 2x=2 tan x/(1+(tan x)²)
cos 2x=(1-(tan x)²)/(1+(tan x)²)
tan 2x=sin 2x/cos 2x=2 tan x/(1-(tan x)²)
Here,
tan x=8/15
sin 2x=2 tan x/(1+(tan x)²)
= 2*8/15/(1+(8/15)²)
=(16/15)/(289/225)
=(16*15)/(289)
≈0.8304
cos 2x=(1-(tan x)²)/(1+(tan x)²)
=(1-(8/15)²)/(1+(8/15)²)
=(225-64)/(225+64)
≈0.557
tan 2x=sin 2x/cos 2x
tan 2x= 0.8304/0.557
=1.498
≈1.5
When the value of tan x is 8/15, the values of sin 2x=0.8304, cos 2x=0.557, and tan 2x=1.498 using the trigonometry identities as tan x as the formula in sin 2x, cos 2x, tan 2x.
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Lisa is putting money into a savings account, she starts with $350 in the savings account, and each week she adds $60
The total amount of money in the savings account after 11 weeks is $1010.
What is the total amount in the savings account?The from of the equation that can be used to determine the total amount of money in the savings account is a linear equation. A linear equation is an equation that has one variable that is raised to the power of one. When a linear equation is drawn on a coordinate graph, it is usually a straight line.
The form of the linear equation is:
Total amount = amount she starts with + (number of weeks x amount of money she adds each week)
S = $350 + ($60 x W)
S = $350 + $60W
Amount she would have in 11 weeks : $350 + ( 11 x $60)
$350 + 660 = $1010
Here is the complete question:
Lisa is putting money into a savings account. She starts with $350 in the savings account, and each week she adds $60. Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Jenny has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 11 weeks.
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please help with this geometry question i attempted it but dont understand it
You have the following vertices of a triangle:
A(1,1)
B(4,1)
C(4,5)
For the translation four untis to the right, consider this kind of translation means that it is necessary to sum 4 units to the x-coordinate:
A(1,1) => A'(1+4,1) = A'(5,1)
B(4,1) => B'(8,1)
C(4,5) => C'(8,5)
Next, a translation three units up is done by adding 3 units to the y-coordinate of points A', B' and C':
A'(5,1) => A''(5,1+3) = A''(5,4)
B'(8,1) => B''(8,4)
C'(8,5) => C''(8,8)
Next, a reflection around y=-1 consists in subtracting to the y-coordinate units equivalent to the vertical distance to the line y =-1, just as follow:
for the point A''(5,4) you can notice that the vertical distance of the y-coordinate, which is 4, to the line y=-1 is 5 units, then, it is necessary to subtract 5 units to such line:
A''(5,4) => A'''(5,-1-5)=A'''(5,-6)
for the point B''(8,4), the distance is again 5 units, then, you have:
B''(8,4) => B'''(8,-1-5) = B'''(8,-6)
for the point C''(8,8) the distance from y-coordinate y=8 to the line y=-1 is 9 units, then, yu subtract 9 units to -1:
C''(8,8) => C'''(8,-1-9) = C'''(8,-10)
Hence, the final points are:
A'''(5,6)
B'''(8,-6)
C'''(8,-10)
Suppose the function f and g are defined as follows.
In this session we will focus on calculating the composition of f and f.
given the function f, the composition f composition f is obtained by taking the definiton of f and replace the varaible x with the function f itself. So we are given that
[tex]f(x)=\frac{8}{5x}[/tex]So
[tex]f\circ f(x)=\frac{8}{5(\frac{8}{5x})}=\frac{8}{\frac{8}{x}}=\frac{8x}{8}=x[/tex]So we have that f composition f is the function x.
a company buys equal numbers of two different card forms. it utilizes 4/5 of one kind and 6/7 of the other. what fraction of the total number is unused?
12/35 fraction of the total number is unused from two different cards.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Assuming the total first kind of card form is 1 and the total second kind of card form is also one.
Given, a company buys equal numbers of two different card forms. it utilizes 4/5 of one kind and 6/7 of the other.
∴ The total unused card form is,
= (1 + 1) - (4/5 + 6/7).
= 2 - (28 + 30)/35.
= 2 - 58/35.
= (70 - 58)/35.
= 12/35.
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Identify a set of parallel and a set of perpendicular lines in this image.
m
B
LL
OBFCG, BF 1 CG
OBECG, AD 1 EH
O AD
EH, EHL BE
O AD EH, BF 1 CG
A set of parallel lines and a set of perpendicular lines are: BF║CG, AD⊥BF.
What are Parallel Lines?Parallel lines are straight lines that are of equal distance at every point away from each other, and therefore, do not intersect each other at any point. The sign "║" is used to indicate that two lines are parallel lines.
What are Perpendicular Lines?Lines that are said to be perpendicular lines are lines that intersect each other at right angle or 90 degrees. That is, at the point of their intersection, a right angle is formed which is 90 degrees. The sign "⊥" is used to indicate that two lines are perpendicular lines.
In the image given, lines BF and CG do not intersect at any point and they are of equal distance away from each other at every point, therefore, CG and BF are perpendicular lines.
Also, we can see that a right angle is formed at the point of intersection of lines AD and BF, therefore AD and BF are perpendicular lines.
Thus, we can state that: BF║CG, AD⊥BF.
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Graph the image of the figure on the right under the given translation.T(3, -1) (x,y)
Answer:
The only image with edges at the given coordinates is;
Given the figure in the attached image.
we want to identify the image after a translation;
[tex]T(3,-1)(x,y)[/tex]Using one of the edges of the figure;
[tex](x,y)=(-4,0)[/tex]Applying the above translation we have;
[tex](-4,0)\rightarrow(-4+3,0-1)=(-1,-1)[/tex]The edge of the image would be at;
[tex](-1,-1)[/tex]Therefore, the only image with edges at the given coordinates is;
Solve the following inequality.xe^x ≥7Choose one:1. x ≤ 1.522. no solution3. x ≤ 1.954. x ≥ 1.955. x ≥ 1.52
1) Considering e =2.72
Then let's plug it in the inequality, and calculate the natural logarithm.
[tex]\begin{gathered} xe^x\ge7 \\ x2.72^x\ge7 \\ 2.72^x\ge\frac{7}{x}^{} \\ \ln 2.72^x\ge\ln (\frac{7}{x}) \\ x\text{ }\ge1.52 \end{gathered}[/tex]2) Then option 5 is the answer
X≥ 1.52
Determine the point (x, y) on the unit circle associated with the following real numbers. Write the exact answer as an ordered pair. Do not round.S = 30
Remember that
In a unit circle, the radius of the circle is 1
see the figure below to better understand the problem
we have that
[tex]\sin (30^o)=\frac{y}{1}[/tex]and we know that
[tex]\sin (30^o)=\frac{1}{2}[/tex]so
[tex]\begin{gathered} \frac{y}{1}=\frac{1}{2} \\ y=\frac{1}{2} \end{gathered}[/tex][tex]\cos (30^o)=\frac{x}{1}[/tex]and we know that
[tex]\cos (30^o)=\frac{\sqrt[]{3}}{2}[/tex]so
[tex]x=\frac{\sqrt[]{3}}{2}[/tex]therefore
the coordinates (x,y) are
[tex](\frac{\sqrt[]{3}}{2},\frac{1}{2})[/tex]The number 24 is 4 times as many as 6.
Write this comparison as a multiplication equation.
+
Compare with multiplication
What is the solution of -8/2y-8 = 5/y+4 - 7y+8/y^2-16?
y = -4
y = -2
y = 4
y = 6
The correct option for the fraction with polynomials is y=6.
Fractions with polynomials.Expressions of more than two algebraic terms that contain different powers of the same variable is a polynomial.
The polynomial fraction is an expression of polynomial divided by another polynomial.
We can solve the fraction to get the value of y as follows;
[-8/(2y-8)]= [5/(y+4)]-[(7y+8)/(y²-16)]
[-8/(2y-8)]= [5/(y+4)]-[(7y+8)/(y+4)(y-4)]
[-8/(2y-8)]= [5(y+4)-(7y+8)]/(y+4)(y-4)] (L.C.M) of the fraction
[-8/(2y-8)]= (5y-20-7y-8)/(y+4)(y-4)
[-8/(2y-8)]= (-2y-28)/(y+4)(y-4)
[-8/2(y-4)]= (-2y-28)/(y+4)(y-4)
[-8/2(y-4)]= [-2(y-14)]/(y+4)(y-4)
[-4/(y-4)]= [-2(y-14)]/(y+4)(y-4)
Multiply both sides of the equation by -(y-4)
4= 2(y-14)/(y+4)
Cross multiply
4(y+4)=2(y+14)
Divide through by 2
2(y+4)=y+14
2y+8=y+14
collect like terms
2y-y=14-8
y=6.
Hence, we can state that the value of y for the polynomial with fraction is 6.
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Angle P in Triangle PQR has the same measure as Angle S in Triangle STU. Which other condition is necessary to prove that these triangles are similar?
△PQR is congruent to △STU (△PQR ≅ △STU) under ASA condition using options (B) and (D).
What is the congruency of triangles?Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, rotate, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. Therefore, if all three sides of two triangles are the same, then the triangles are said to be congruent. If we have a side, an angle between the sides, and then another side that is congruent, we know they are congruent. In other words, side, angle, side.So, to prove that △PQR ≅ △STU:
∠P = ∠S (Given)PQ = ST (Option B)∠Q = ∠T (Option D)So, with these three conditions, △PQR ≅ △STU is under ASA condition.
Therefore, △PQR is congruent to △STU (△PQR ≅ △STU) under ASA condition using options (B) and (D).
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x square root 7x + 10
factor the equation
algerbra 2
Answer:
Step-by-step explanation:
x
=
−
2
x
=
−
5
Explanation:
x
2
+
7
x
+
10
=
0
We could right the equation in another form using brackets.
(
x
+
2
)
(
x
+
5
)
=
0
In order to get two numbers to multiply and give 0, at least one number has to be 0.
a stands for the first bracket and b for the second.
a x b = 0
a=0 or b=0 to make this equation valid.
Therefore x= -2 or x= -5 because -2+2=0 and -5+5=0 according to both brackets.
whats the answer? one angle of a triangle mesuares 98°. the other two angles are congruent. enter and solve an equation to find the mesuare x of the congruent angles.
Congruent angles simply means angles that are equal. A triangle has three angles . Since one of the angle is given as 98 degree, the other 2 angles which are congruents are therefore equal. The total angle of a triangle is equals to 180 degree. Therefore,
[tex]\begin{gathered} x+x+98=180 \\ 2x+98=180 \\ 2x=180-98 \\ 2x=82 \\ x=\frac{82}{2} \\ x=41 \end{gathered}[/tex]x = 41 degree
4.(06.07 HC)A teacher is assessing the correlation between the number of hours spent studying and the average score on a science test. The table below shows the data:Number of hours spent studying 0 0.5 1(x)1.5 2 2.5 33.54Score on science test(y)57 62 67727782 879297Part A: Is there any correlation between the number of hours students spent studying and the score on the science test? Justify your answer. (4 points)Part B: Write a function which best fits the data. (3 points)Part C: What does the slope and y-intercept of the plot indicate? (3 points)(10 points)
For part A. One way to know if there is a correlation between the data is to graph the data set, like this
Then, as can you see the data presents a positive linear correlation.
For part B. You can take the coordinates of two points and find the slope of the line using the formula
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex]If you take
[tex]\begin{gathered} (x_1,y_1)=(1,67) \\ (x_2,y_2)=(3,87) \\ \text{ You have} \\ m=\frac{87-67}{3-1} \\ m=\frac{20}{2} \\ m=10 \end{gathered}[/tex]Now, using the slope formula, you can find the equation of the line in its slope-intercept form
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-67=10(x-1) \\ y-67=10x-10 \\ \text{ Add 67 on both sides of the equation} \\ y-67+67=10x-10+67 \\ y=10x+57 \end{gathered}[/tex]Therefore, the function that best fits the data is
[tex]y=10x+57[/tex]For part C. The slope of the plot is 10 and indicates that for every hour students spend time studying, they get 10 more points on the science test.
The y-intercept of the plot is 57 and indicates that if students study 0 hours for the science test, they will obtain 57 points as a grade.
separate 84 into two parts such that one part will be 12 less than twice the other
Answer:
32, 52
Step-by-step explanation:
84=x+y
x=2y-12
Solving the system of equations
Plug second equation into first
84=(2y-12)+y
84=3y-12
y=32
Plug y into first equation
84=x+32
x=52
3. Suppose that the scores on a statewide standardized test are normally distributed with a mean of 69 and a standard deviation of 6. Estimate the percentage of scores that were(a) between 57 and 81. %(b) above 81. %(c) below 63. %(d) between 51 and 81. %
Answer:
a) 95%
b) 2%
c) 16%
d) 98%
Explanation:
We have the following:
This is a normal distribution
Mean = 69
Standard Deviation = 6
a) Between 57 and 81%
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ x=57 \\ z=\frac{57-69}{6}=-\frac{12}{6} \\ z=-2 \\ \\ x=81 \\ z=\frac{81-69}{6}=\frac{12}{6} \\ z=2 \\ \end{gathered}[/tex]The probability that a score is between 57 & 81 is given by the Area between (z = -2) & (z = 2):
[tex]\begin{gathered} P=0.97725-0.02275 \\ P=0.9545 \\ P=95.45\approx95 \\ P=95\text{ \%} \\ \\ \therefore P=95\text{ \%} \end{gathered}[/tex]b) Above 81%
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ x>81 \\ z=\frac{81-69}{6} \\ z=\frac{12}{6}=2 \\ z=2 \end{gathered}[/tex]The probability that a score is above 81% is given by the area of the graph greater than (z = 2):
[tex]\begin{gathered} P=0.02275 \\ P=2.275\approx2.3 \\ P=2.3\approx2 \\ P=2\text{ \%} \\ \\ \therefore P=2\text{ \%} \end{gathered}[/tex]c) Below 63%
[tex]\begin{gathered} x<63 \\ z=\frac{63-69}{6} \\ z=-\frac{6}{6}=-1 \\ z=-1 \end{gathered}[/tex]The probability that a score is below 63% is given by the area of the graph lesser than (z = -1):
[tex]\begin{gathered} P=0.15866 \\ P=15.866\approx16 \\ P=16\text{ \%} \end{gathered}[/tex]d) Between 51 and 81
[tex]\begin{gathered} 51\le x\le81 \\ z=\frac{51-69}{6} \\ z=-\frac{18}{6}=-3 \\ z=-3 \\ \\ z=\frac{81-69}{6} \\ z=\frac{12}{6}=2 \\ z=2 \end{gathered}[/tex]The probability that a score is between 51 & 81 is given by the Area between (z = -3 & (z = 2):
[tex]\begin{gathered} P=0.97725-0.00135 \\ P=0.9759 \\ P=97.59\approx98 \\ P=98\text{ \%} \end{gathered}[/tex]Let x represent the unknown value, then write an algebraic expression for: double a quantity increased by nine
Answer:
2(x + 9)
Explanation:
Let x represent the unknown value.
Double a quantity increased 9 means;
*We'll multiply the quantity by 2
*Increased by signifies addition
*Quantity means we'll put the expression after it in brackets
Let's go ahead and write the required algebraic expression;
[tex]2(x+9)[/tex]Please help me with 24For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes.
Given the equation,
[tex]-9x^2+72x+16y^2+16y+4=0[/tex]Complete squares as shown below,
[tex]\begin{gathered} -9x^2+72x-a^2=-(9x^2-72x+a^2)=-9(x^2-8x+b^2) \\ \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \Rightarrow-9x^2+72x-a^2=-9(x^{}-4)^2 \\ \Rightarrow a^2=16\cdot9=144\Rightarrow a=12 \\ \Rightarrow-9x^2+72x-144=-9(x^{}-4)^2 \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} 16y^2+16y=16(y^2+y) \\ \Rightarrow16(y+\frac{1}{2})^2=16(y^2+y+\frac{1}{4}) \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} -9x^2+72x+16y^2+16y+4=0 \\ \Rightarrow-9(x-4)^2+16(y+\frac{1}{2})^2+4=-144+4 \\ \Rightarrow-9(x-4)^2+16(y+\frac{1}{2})^2=-144 \end{gathered}[/tex]Finally, the standard form is.
[tex]\begin{gathered} \Rightarrow-\frac{(x-4)^2}{16}+\frac{(y+\frac{1}{2})^2}{9}=-1 \\ \Rightarrow\frac{(x-4)^2}{16}-\frac{(y+\frac{1}{2})^2}{9}=1 \end{gathered}[/tex]As for the vertices, foci, and asymptotes,
[tex]\begin{gathered} c=\pm\sqrt[]{16+9}=\pm5 \\ \text{center:}(4,-\frac{1}{2}) \\ \Rightarrow\text{foci:}(4-5,-\frac{1}{2})_{},(4+5,-\frac{1}{2})_{} \\ \Rightarrow\text{foci:}(-1,-\frac{1}{2}),(9,-\frac{1}{2}) \end{gathered}[/tex]Foci: (-1,-1/2), (9,-1/2)
Vertices
[tex]\begin{gathered} \text{center:}(4,-\frac{1}{2}),\text{vertices:}(4\pm a,-\frac{1}{2}) \\ \text{vertices:}(4+4,-\frac{1}{2}),(4-4,-\frac{1}{2}) \\ \text{vertices:}(8,-\frac{1}{2}),(0,-\frac{1}{2}) \end{gathered}[/tex]Vertices: (8,-1/2), (0,-1/2)
Asymptotes:
[tex]\begin{gathered} y=\pm\frac{3}{4}(x-4)-\frac{1}{2} \\ \Rightarrow y=\frac{3}{4}x-\frac{7}{2} \\ \text{and} \\ y=-\frac{3}{4}x+\frac{5}{2} \end{gathered}[/tex]Asymptotes: y=3x/4-7/2 and y=-3x/4+5/2
Harley rides her bicycle the same distance every day for 4 days. The total distance she rides is 814 miles. How many miles does she ride each day?
Answer:
203.5
Step-by-step explanation:
just divide 814 by 4
Answer:
203.5 miles per day
Step-by-step explanation:
divide 814 by 4= 203.5
n a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer.
We can use the sine rule to find the hole angle, and then find the golfer angle:
[tex]\frac{200}{\sin(115)}=\frac{140}{\sin (Hole)}[/tex][tex]\text{Hole Angle = }\sin ^{-1}(\frac{140\times\sin (115)}{200})[/tex][tex]\text{Hole Angle = }39.37664303\text{ degre}es[/tex]Now we can find the golfer angle:
[tex]\text{Golfer = 180 - 115 - 39.38 }\cong25.6\text{ degre}es[/tex]Answer: 25.6 degrees.
Can someone please help answer this question on simultaneous equations?
Answer:
1 knife cost £6.6
Step-by-step explanation:
Simultaneous equation is;
4x = y ----------(equation 1)
12y + 16x = 105.64 ----------- (equation 2)
Rewrite equations:
4x=y;16x+12y=105.64
Step: Solve4x=yfor y:
4x=y
4x+−y=y+−y(Add -y to both sides)
4x−y=0
4x−y+−4x=0+−4x(Add -4x to both sides)
−y=−4x
−y/−1 = −4x/−1
(Divide both sides by -1)
y=4x
Step: Substitute 4x for y in 16x+12y=105.64:
16x+12y=105.64
16x+124x=105.64
64x=105.64(Simplify both sides of the equation)
64x/64 = 105.64/64
(Divide both sides by 64)
x=1.650625
Step: Substitute 1.650625 for x in y=4x:
y=4x
y=(4)(1.650625)
y=6.6025(Simplify both sides of the equation)
1 knife cost = 4x = 4(1.65) = 6.6
∴ 1 knife cost £6.6
a) Write 98 as the product of prime factors. Write the prime factors in ascending order.
Step-by-step explanation:
Write 98 as the product of prime factors. Write the prime factors in ascending order.
2 × 7 × 7
2 × 7 × 7 = 98
Answer: 2×7×7
Step-by-step explanation: 98= 2×7×7
Lets first know about what is prime factor :- A factor which is a Prime number and not a composite number.
prime factor in ascending order = 2,7
hence the required product of prime factor is 2×7×7 or 2×[tex]7^{2}[/tex]
Determine the midpoint of segment Ed coordinates e and d are 2 and -2
Answer: Midpoint = 0
Explanation:
The midpoint of segment ED can be calculated as:
[tex]\text{Midpoint}=\frac{E+D}{2}[/tex]Where E and D are the coordinates of E and D respectively.
So, replacing E by 2 and D by -2, we get:
[tex]\text{MIdpoint}=\frac{2+(-2)}{2}=\frac{2-2}{2}=\frac{0}{2}=0[/tex]Therefore the midpoint of segment ED is equal to 0.
If z = 1 istartroot 3 endroot, what is z5? 16 16istartroot 3 endroot â€"16 16istartroot 3 endroot 16 â€" 16istartroot 3 endroot â€"16 â€" 16istartroot 3 endroot
Complex number z has a power of 5 represented by (-16√3 + 16) + 4(-√3 + 3)i
Given that,
z = 1 + StartRoot 3 EndRooti, what is z5? 16 + 16StartRoot 3 EndRoot i –16 + 16StartRoot 3 EndRoot i –16 – 16StartRoot 3 EndRoot i 16 – 16StartRoot 3 EndRoot i
What is a complex number?
It is characterized as a number that can be expressed as x+iy, where x is a real number or the real portion of the complex number, y is the imaginary portion of the complex number, and I is the iota, which is just the square root of -1.
We have:
z = 1 + √3i
We have to find: z⁵
z⁵ = (1 + √3i)(1 + √3i)(1 + √3i)(1 + √3i)(1 + √3i)
z⁵ = (-2 + 2√3)(1 + √3i)(1 + √3i)(1 + √3i)
z⁵ = (-16√3 + 16) + 4(-√3 + 3)i
Therefore, the complex number z's power of 5 is -16√3 + 16) + 4(-√3 + 3)i
Learn more about the complex number here:
brainly.com/question/10251853
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Select all ratios equivalent to 13.14
52:56. 39:42. 3:4
if one shirt costs £13,how many can I buy with £419?
Answer:
32 shirts
Step-by-step explanation:
419÷13
=32.230
Answer:
32
Step-by-step explanation:
419 divided by 13
= 32.230