Answer:
Transitive
If x = 2y and 2y = 8, then x = 4.
find the area of the shaded polygons
Answer:
4 square units
Step-by-step explanation:
The vertices of the figure are on grid points, so it is appropriate to use Pick's theorem to find the area.
__
formulaPick's theorem tells you the area is ...
A = i +b/2 -1
where i is the number of grid points interior to the figure (0), and b is the number of grid points on the boundary (10).
applicationUsing the counted values in the formula, we find the area to be ...
A = 0 +10/2 -1 = 4
The area of the polygon is 4 square units.
_____
Additional comment
There are several other ways to find the area. Here are a couple:
decompose the figure
A horizontal line 1 unit up from the bottom will divide the figure into a trapezoid and a triangle. The trapezoid has bases 4 and 1, and height 1, so its area is ...
A = 1/2(b1 +b2)h = 1/2(4 +1)(1) = 5/2
The triangle has base 1 and height 3, so its area is ...
A = 1/2bh = 1/2(1)(3) = 3/2
Then the total area is 5/2 +3/2 = 8/2 = 4 square units.
subtract empty space
The figure occupies a 4×4 square with triangles removed from the left side and the top. Each of those triangles has a base of 4 and a height of 3. The remaining (shaded) area is ...
A = s² -1/2bh -1/2bh
A = 4² -1/2(4)(3) -1/2(4)(3) = 16 -12 = 4 square units
Problem is in the picture
A box contains 7 plain pencils and 5 pens. A second box contains 4 color pencils and 4 crayons. One item from each box is chosen at random. What is the probability that a pen from the first box and a crayon from the second box are selected?
Write your answer as a fraction in simplest form
Answer:
5/24
Step-by-step explanation:
Probability of selecting a pen :
⇒ Number of pens / Total items in Box 1
⇒ 5 / 7 + 5
⇒ 5/12
=============================================================
Probability of selecting a crayon :
⇒ Number of crayons / Number of items in box 2
⇒ 4 / 4 + 4
⇒ 4/8
⇒ 1/2
===========================================================
Probability (of both events) :
⇒ 5/12 × 1/2
⇒ 5/24
Graph the function.
f(x)=3z-5
Use the Line tool and select two points to graph
The plot of the graph is attached and points have been determined
The two among them are (5,-2) ,(15,4).
What is a Line Function ?
A line function is what can be written in the form of
y =mx +c
where m is the slope and c is the intercept on y axis.
The equation given here is y = (3/5)x -5
m = 3/5
c = -5
The plot of the graph is attached and points have been determined
The two among them are (5,-2) ,(15,4)
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the area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and the breadth is increased by 3 units if we increase the length by 3 units and the breadth by 2 units then the area is increased by 67 square units find the dimensions of the rectangle.
length = 17 units, breadth = 9 units
Step-by-step explaination:-
Let the length and the breadth of the rectangle be x units and y units respectively.
Then the area of rectangle = xy square units
According to given conditions, we have
(x -5)(y + 3) = xy - 9 and (x + 3)(y + 2) = xy + 67
=> xy + 3x - 5y - 15 = xy - 9
and xy + 2x + 3x + 6 = xy + 67
=> 3x - 5y - 6 = 0......eqn(i)
and 2x + 3y - 61 = 0.....eqn(ii)
Multiplying equation (i) by 2 and equation (ii) by 3, we get...
6x - 10y - 12 = 0....eqn(iii) and,
6x + 9y - 183 = 0....eqn(iv)
Subtracting equation (iii) from equation (iv), we get...
19y - 171 = 0 => y = 9.
Substituting this value of y in equation (ii), we get
2x + 3 × 9 - 61. = 0 => 9x - 34 = 0 => x = 17.
Hence, the length of rectangle = 17 units and
breadth = 9 units.
Hope it helps you!!Which number line represents the solution set for the inequality -4(x + 3) ≤-2-2x?
++
-7 -6 -5 -4 -3 -2 -1 0 1 2 3
4
5 6 7
O
-7 -6 -5 -4 -3 -2 -1 0 1 2 3
4 5 6 7
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-7 -6 -5 -4 -3 -2 -1 0 1
2
3
4
6 7
ليا
نی
für
fe
LO
5
Answer:
x<_-5
Step-by-step explanation:
-4(x+3)<_-2-2x
-4x-12<_-2-2x
-4x+2x<_-2+12
-2x<_+10
divide both side by -2
-2x/2<_10/-2
x<_-5
it is D
if p(a)=a^3-6a^2+11a-9 and p(a)=-3,find the value of a?
Which of these show the correct shape after the translation?
I CAN’T SHOW ALL OF THE ANSWER CHOICES BUT CAN SOMEONE TELL ME IF I CHOSE THE RIGHT ANSWER?
The option that depicts a translation is option B. See the attached image and the explanation for this answer below.
What is Translation in Mathematics?Translation in Math refers to the movement of a shape vertically or horizontally along the x or y-axis without altering its original dimensions.
Going by the above definition, it is clear that Option B is the translated image (assuming that the original image is as given in the image attached.
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Using a table of values, determine the solution to the equation below to the nearest fourth of a unit.
2-5x=2x-3
The solution to the equation below to the nearest fourth of a unit is 0.7142
Equations and expressions
Given the equation as shown below;
2-5x=2x-3
Collect the like terms
-5x - 2x = -3 - 2
-7x = -5
Divide both sides by -7
x = -5/-7
x = 5/7
x= 0.7142
Hence the solution to the equation below to the nearest fourth of a unit is 0.7142
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I need help ASAP PLEASE > How does the graph of f(x) = (x + 7)3 − 8 compare to the parent function g(x) = x3? (Please explain with your on words)
Answer:
The graph has been moved 7 units to the left and 8 units down.
Step-by-step explanation:
When numbers are added directly to the "x" value, the graph shifts to the left. If negative numbers are added directly to the "x" value, the grap shifts to the right. Therefore, if there is a +7 directly altering the "x" value, the function shifts 7 units to the left.
When a number is added to the overall function, it shifts upwards. If this number is negative, the entire function shifts downwards. Therefore, if there is a -8 outside altering the function, then it has been shifted 8 units down.
Carol has some dimes and quarters. If she has 19 coins worth a total of $3.10, how many of each type of coin does she have?
Round 0.007492 to four decimal places.
The revenue from selling x necklaces is r(x) =10x. The cost of buying x necklaces is c(x)=4x+15. The profit from selling x necklaces is p(x)=r(x)-c(x).
Answer:
the revenue is 280 by 190
The parabola y=x^2y=x
2
y, equals, x, squared is shifted up by 777 units and to the left by 111 unit.
What is the equation of the new parabola?
y=y=y, equals
Answer:
Step-by-step explanation:
The parabola y=x^2 is shifted up by 7 units and to the left by 1 unit.
Answer:
y=(x+1)^2 +7
When the parabola y=x² is shifted up by 7 units and to the left by 1 unit then the equation of the new parabola is y = (x-1)² + 7.
When a parabola is shifted vertically or horizontally, its equation changes accordingly.
In this case, the parabola y = x² is shifted up by 7 units and to the left by 1 unit.
Adding a constant value to the function shifts the graph vertically.
In this case, adding 7 to the original function y = x² will shift it up by 7 units:
y = x² + 7
Subtracting a constant value from the input of the function shifts the graph horizontally.
In this case, subtracting 1 from the x-values of the function y = x² + 7 will shift it to the left by 1 unit:
y = (x-1)² + 7
Hence, the equation of the new parabola after both shifts is y = (x-1)² + 7.
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Above is a table that gives the interest per every $100 financed. Use the table to determine the annual percentage rate for a 35 month loan that charges $22.38 per every $100 financed.
a.
13%
c.
15%
b.
14%
d.
16%
The annual percentage rate for a 35 month loan that charges $22.38 per every $100 financed is seen from the table to be 14%.
How to determine Annual Percentage Rate?From the table, the APR for 35 months loan that charges $22.38 per every $100 financed is seen to be 14%.
Thus, we can conclude that the annual percentage rate for a 35 month loan that charges $22.38 per every $100 financed is seen from the table to be 14%.
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Answer:
a. 13%
Step-by-step explanation:
E2020!
Integration questions .
[tex]\\\\\ \textbf{a)}\\\\~~~\displaystyle \int (6x- \sin 3x) ~ dx\\\\=6\displaystyle \int x ~ dx - \displaystyle \int \sin 3x ~ dx\\\\=6 \cdot \dfrac{x^2}2 - \dfrac 13 (- \cos 3x) +C~~~~~~~~~~~;\left[\displaystyle \int x^n~ dx = \dfrac{x^{n+1}}{n+1}+C,~~~n \neq -1\right]\\\\ =3x^2 +\dfrac{\cos 3x}3 +C~~~~~~~~~~~~~~~~~~~~;\left[\displaystyle \int \sin (mx) ~dx = -\dfrac 1m ~ (\cos mx)+C \right]\\[/tex]
[tex]\textbf{b)}\\\\~~~~\displaystyle \int(3e^{-2x} +\cos (0.5 x)) dx\\\\=3\displaystyle \int e^{-2x} ~dx+ \displaystyle \int \cos(0.5 x) ~dx\\\\\\=-\dfrac 32 e^{-2x} + \dfrac 1{0.5} \sin (0.5 x) +C~~~~~~~~~~~~~~;\left[\displaystyle \int e^{mx}~dx = \dfrac 1m e^{mx} +C \right]\\\\\\=-\dfrac 32 e^{-2x} + 2 \sin(0.5 x) +C~~~~~~~~~~~~~~~~~;\left[\displaystyle \int \cos(mx)~ dx = \dfrac 1m \sin(mx) +C\right]\\\\\\=-1.5e^{-2x} +2\sin(0.5x) +C[/tex]
2)[tex]\textbf{a)}\\\\y = \displaystyle \int \cos(x+5) ~ dx\\\\\text{Let,}\\\\~~~~~~~u = x+5\\\\\implies \dfrac{du}{dx} = 1+0~~~~~~;[\text{Differentiate both sides.}]\\\\\implies \dfrac{du}{dx} = 1\\\\\implies du = dx\\\\\text{Now,}\\\\y= \displaystyle \int \cos u ~ du\\\\~~~= \sin u +C\\\\~~~=\sin(x+5) + C[/tex]
[tex]\textbf{b)}\\\\y = \displaystyle \int 2(5x-3)^4 dx\\\\\text{Let,}\\~~~~~~~~u = 5x-3\\\\\implies \dfrac{du}{dx} = 5~~~~~~~~~~;[\text{Differentiate both sides}]\\\\\implies dx = \dfrac{du}5\\\\\text{Now,}\\\\y = 2\cdot \dfrac 1 5 \displaystyle \int u^4 ~ du\\\\\\~~=\dfrac 25 \cdot \dfrac{u^{4+1}}{4+1} +C\\\\\\~~=\dfrac 25 \cdot \dfrac{u^5}5+C\\\\\\~~=\dfrac{2u^5}{25}+C\\\\\\~~=\dfrac{2(5x-3)^5}{25}+C[/tex]
3)[tex]\textbf{a)}\\\\y = \displaystyle \int xe^{3x} dx\\\\\text{We know that,}\\\\ \displaystyle \int (uv) ~dx = u \displaystyle \int v ~ dx - \displaystyle \int \left[ \dfrac{du}{dx} \displaystyle \int ~ v ~ dx \right]~ dx\\\\\text{Let}, u =x~ \text{and}~ v=e^{3x} .\\\\y= \displaystyle \int xe^{3x} ~dx\\\\\\~~= x\displaystyle \int e^{3x} ~ dx - \displaystyle \int \left[\dfrac{d}{dx}(x) \displaystyle \int e^{3x}~ dx \right]~ dx\\\\\\[/tex]
[tex]=x\displaystyle \int e^{3x}~ dx - \displaystyle \dfrac 13 \int \left(e^{3x} \right)~ dx\\\\\\=\dfrac{xe^{3x}}3 - \dfrac 13 \cdot \dfrac{ e^{3x}}3+C\\\\\\= \dfrac{xe^{3x}}{3}- \dfrac{e^{3x}}{9}+C\\\\\\=\dfrac{3xe^{3x}}{9}- \dfrac{e^{3x}}9 + C\\\\\\= \dfrac 19e^{3x}(3x-1)+C[/tex]
please help!!!! needs to be submitted
The coordinates of the image of triangle are transformation are X = (1,3), Y = (5,-3) and Z = (-1, -7)
How to determine the transformation?From the figure, the coordinates of the triangle are:
A = (-1, -1)
B = (1, 2)
C = (-2,4)
The transformation rule is given as:
[tex]\triangle XYZ = T_{ < 3,1 > }(R_{x-axis}(D_2(\triangle ABC)))[/tex]
This means that, we start by dilating the triangle by a scale factor of 2.
So, we have:
A' = (-2, -2)
B' = (2, 4)
C' = (-4,8)
Next, we rotate the triangle across the x-axis
So, we have:
A'' = (-2, 2)
B'' = (2, -4)
C'' = (-4,-8)
Lastly, we translate the triangle by (x + 3,y + 1) to get the triangle XYZ
So, we have:
X = (1,3)
Y = (5,-3)
Z = (-1, -7)
See attachment for the image of the transformation
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Joan has 7/8 of her book left to read. If she reads ¼ each day, how many days will it take her to finish?
Answer:
4 days
Step-by-step explanation:
first convert 1/4 to eighths
2/8=1/4
to make 2/8 equal 7/8
you have to multiply by 4 for it to be 8/8
it cant be 7/8 because that would be three and a half days and they only read 1/4 each day
so it would take 4 days to finish
calculate volume of a planet if radius is 6050 and answer in scientific notation
to the 2 significant number
Answer:
9.3*10^11
Step-by-step explanation:
4/3πr^3=9.3*10^11
Determine the angle of elevation if the slope is 0.3415
Using the slope concept, considering it's value of 0.3415, it is found that the angle of elevation is of 18.86º.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
Hence, we have that:
[tex]\tan{\alpha} = 0.3415[/tex]
[tex]\alpha = \arctan{0.3415} = 18.86^\circ[/tex]
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PLS help me with my math
i dont know either your on your own
Step-by-step explanation:
i just dont know
please answer this question
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :-• [tex]\sf{ Polynomial :- ax^{2} + bx + c }[/tex]
• The zeroes of the given polynomial are α and β .
Let's Begin :-Here, we have polynomial
[tex]\sf{ = ax^{2} + bx + c }[/tex]
We know that,
Sum of the zeroes of the quadratic polynomial
[tex]\sf{ {\alpha} + {\beta} = {\dfrac{-b}{a}}}[/tex]
And
Product of zeroes
[tex]\sf{ {\alpha}{\beta} = {\dfrac{c}{a}}}[/tex]
Now, we have to find the polynomials having zeroes :-
[tex]\sf{ {\dfrac{{\alpha} + 1 }{{\beta}}} ,{\dfrac{{\beta} + 1 }{{\alpha}}}}[/tex]
Therefore ,
Sum of the zeroes
[tex]\sf{ ( {\alpha} + {\dfrac{1 }{{\beta}}} )+( {\beta}+{\dfrac{1 }{{\alpha}}})}[/tex]
[tex]\sf{ ( {\alpha} + {\beta}) + ( {\dfrac{1}{{\beta}}} +{\dfrac{1 }{{\alpha}}})}[/tex]
[tex]\sf{( {\dfrac{ -b}{a}} ) + {\dfrac{{\alpha}+{\beta}}{{\alpha}{\beta}}}}[/tex]
[tex]\sf{( {\dfrac{ -b}{a}} ) + {\dfrac{-b/a}{c/a}}}[/tex]
[tex]\sf{ {\dfrac{ -b}{a}} + {\dfrac{-b}{c}}}[/tex]
[tex]\bold{{\dfrac{ -bc - ab}{ac}}}[/tex]
Thus, The sum of the zeroes of the quadratic polynomial are -bc - ab/ac
Now,Product of zeroes
[tex]\sf{ ( {\alpha} + {\dfrac{1 }{{\beta}}} ){\times}( {\beta}+{\dfrac{1 }{{\alpha}}})}[/tex]
[tex]\sf{ {\alpha}{\beta} + 1 + 1 + {\dfrac{1}{{\alpha}{\beta}}}}[/tex]
[tex]\sf{ {\alpha}{\beta} + 2 + {\dfrac{1}{{\alpha}{\beta}}}}[/tex]
[tex]\bold{ {\dfrac{c}{a}} + 2 + {\dfrac{ a}{c}}}[/tex]
Hence, The product of the zeroes are c/a + a/c + 2 .
We know that,
For any quadratic equation
[tex]\sf{ x^{2} + ( sum\: of \:zeroes )x + product\:of\: zeroes }[/tex]
[tex]\bold{ x^{2} + ( {\dfrac{ -bc - ab}{ac}} )x + {\dfrac{c}{a}} + 2 + {\dfrac{ a}{c}}}[/tex]
Hence, The polynomial is x² + (-bc-ab/c)x + c/a + a/c + 2 .
Some basic information :-• Polynomial is algebraic expression which contains coffiecients are variables.
• There are different types of polynomial like linear polynomial , quadratic polynomial , cubic polynomial etc.
• Quadratic polynomials are those polynomials which having highest power of degree as 2 .
• The general form of quadratic equation is ax² + bx + c.
• The quadratic equation can be solved by factorization method, quadratic formula or completing square method.
Emma makes 14 dozen cookies in one hour how many individual cookies can she make in 4.5 hours
A hockey season ticket holder pays $88.56 for her tickets plus $5.00 for a program each game. A second person pays $19.76 for a ticket to every game, but doesn't buy programs. In how many games will they have paid the same amount?
Answer: x = 6
Step-by-step explanation: If you take 88.56 + 5x = 19.76x, an equation, you should first rearrange the variables to the left side of the equation: 5x - 19.76x = -88.56.
Next, you should combine your like terms. So, -14.76 = -88.56.
Then, divide both sides of the equation by the coefficient of variable. So, x = -88.56 / -14.76./
Lastly, calculate. Determine the sign for multiplication or division, so x = 88.56 / 14.76. Multiply both the numerator and denominator with the same integer. So, x = 8856 / 1476. Cross out the common factor, then you get your answer of x = 6
The square below represents one whole.
Express the shaded area as a fraction, a decimal, and a percent of the whole.
The shaded area expressed as a fraction, a decimal, and a percent of the whole is 23/100, 0.23 and 23% respectively
Fractions, Decimals and PercentagesFrom the question, we are to express the shaded area as a fraction, a decimal, and a percent of the whole.
In the diagram, there are 100 total squares and 23 of them are shaded
Expressing the shaded area as a fraction, we get
[tex]\frac{23}{100}[/tex]
Expressing the shaded area as a decimal, we get
[tex]\frac{23}{100}[/tex] = 0.23
Expressing the shaded area as a percent , we get
[tex]\frac{23}{100}\times 100\%[/tex] = 23%
Hence, the shaded area as a fraction, a decimal, and a percent of the whole is 23/100, 0.23 and 23% respectively
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Triangle P Q R is shown. Angle Q P R is a right angle. The length of Q P is 8 StartRoot 3 EndRoot and the length of P R is 8.
Consider triangle PQR. What is the length of side QR?
Answer: Length of side QR is 16 units.
Step-by-step explanation: Given that dimensions of PQR
QPR= 90degrees
The surface area of a right cone which has a base diameter of 6 units and a height of 8 units is:
75 units squared.
108 units squared.
151 units squared.
188 units squared.
The area of a 2D form is the amount of space within its perimeter. The surface area of the cone is 108.79967 units².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Given the diameter of the cone is 6 units, therefore, the radius of the cone is 3 units, and the height of the cone is 8 units. Thus, the surface area of the right cone is,
A=πr [r+√(h²+r²)]
A = 108.79967 units²
Hence, the surface area of the cone is 108.79967 units².
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Which choice describes the value of m when –5(m + 1) ≤ 23?
A 28
5
m
B 28
5
m
C 18
5
m
D 18
5
The first step to solving almost any problem is to determine what the question is asking and what is given to us to help solve that problem. Looking at the problem statement, they are asking for us to determine which option best describes the value of m in the expression provided. The only thing that we are provided with is an expression which we need to solve for m.
Let's begin to solve the expression for m by first dividing both sides by -5. However, since we are dividing by a negative, that means that we must flip the sign.
Divide both sides by -5
[tex]-5(m + 1) \le 23[/tex][tex]\frac{-5(m + 1)}{-5} \le \frac{23}{-5}[/tex][tex]m + 1 \ge -\frac{23}{5}[/tex]The next step that we must take is to subtract 1 from both sides but before that let's convert it into an improper fraction with a denominator of 5 so we can easily deal with it with the other fraction.
Subtract both sides by 1
[tex]m + \frac{5}{5} - \frac{5}{5} \ge -\frac{23}{5} - \frac{5}{5}[/tex][tex]m \ge -\frac{23}{5} - \frac{5}{5}[/tex][tex]m \ge \frac{-23 - 5}{5}[/tex][tex]m \ge \frac{-28}{5}[/tex]We have finally came up to our final answer which would state that m is greater than or equal to negative 28 over 5. The options that you have provided seem like the formatting has messed up but I'm sure that on your side you can see the correct answer.
Use the spinner below to find the probability of getting the following number after 1 spin. P(multiple of 3) = (Round to 4 decimal places)
The value of the probability P(multiple of 3) is 0.3333
How to determine the probability?The spinner that completes the question is added as an attachment
From the attached spinner, we have:
Total section = 12Multiples of 3 = 4The probability is then calculated as:
P(multiple of 3) = Multiples of 3/Total
This gives
P(multiple of 3) = 4/12
Evaluate
P(multiple of 3) = 0.3333
Hence, the value of the probability is 0.3333
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The radius of Circle A is 3 ft. The radius of Circle B is 3 ft greater than the radius of
Circle A. The radius of Circle C is 3 ft greater than the radius of Circle B. The radius of Circle D is 2 ft
less than the radius of Circle C. What is the area of each circle? How many times greater than the
area of Circle A is the area of Circle D?
Answer:
Step-by-step explanation:
Ar of circle
A= 49π
B=100π
C=169π
D=121π
Ar of circle A is less than Ar of circle D