Answer:
-20+(-13)-7-(+11)+14= -37
Step-by-step explanation:
we make first : +(-13)= -13 then -(+11)=-11
then we calculate all the nb we have
-20-13-7-11+14= -37
For what values of $j$ does the equation $(2x+7)(x-5) = -43 + jx$ have exactly one real solution? express your answer as a list of numbers, separated by commas. thank you!
The values of 'j' are -11,5.
What is a Quadratic Equation?
Quadratic equations are the polynomial equations of degree 2 in one variable of the type [tex]f(x) = ax^{2} + bx + c = 0[/tex] where a, b, c, ∈ R and a ≠ 0.The standard form of a quadratic equation is [tex]ax^{2} + bx + c = 0[/tex] .Here, the given equation is (2x+7)(x-5) = - 43 + jx
On simplifying the equation we get,
[tex]2x^{2} -10x+7x-35=-43+jx\\2x^{2} -3x-35+43-jx=0\\2x^{2} -3x-jx+8=0\\2x^{2} -(3+j)x+8=0.....(1)\\[/tex]
By comparing the given equation with the standard form of the quadratic equation we get,
a = 2
b = - (3 + j)
c = 8
Therefore,
[tex](-(3+j))^{2} -4\times2\times8=0\\(3+j)^{2} -64=0\\(3+j)^{2} =64\\[/tex]
Take the square root of both sides,
[tex]\sqrt{(3+j)^{2} }=\sqrt{64} \\[/tex]
3 + j = ±8
Therefore,
3 + j = 8
j = 8 - 3
j = 5
or
3 + j = -8
j = -8 - 3
j = -11
Hence, the possible values of 'j' are -11,5.
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Find the area of a circle with radius, r =
7.4m.
Give your answer rounded to 2 DP.
r
C
The diagram is not drawn to scale.
Answer:
172.03 m²
Step-by-step explanation:
Hello!
Area of a circle: [tex]A = \pi r^2[/tex]
A = areaπ = pir = radiusPlug in the radius into the formula to find the area.
Find the Area[tex]A = \pi r^2[/tex][tex]A = \pi (7.4)^2[/tex][tex]A = 54.76\pi[/tex][tex]A = 172.0336137106 \approx 172.03[/tex]The area is approximately 172.03 m².
To calculate the radius of this circle, we must take into account that:
Data:
R = 7.4 π = 3.14To calculate the area of the circle, we apply the following formula:
A = π * r², wherea = area
π = pi
r = radius
Substituting the values of the equation:
[tex]\large\displaystyle\text{$\begin{gathered}\sf A=3.14*(7.4 \ m)^{2} \end{gathered}$}[/tex]Taking the square root
[tex]\large\displaystyle\text{$\begin{gathered}\sf A=3.14*54.76 \ m^{2} \end{gathered}$}[/tex]Multiplying
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf A=171.95 \ m^{2} \end{gathered}$}}[/tex]Answer: The approximate area of the circle is 171.95 m².
Lesson 13:Find a Sequence
Describe a sequence of reflections, rotations, and translations that takes ABCD onto
A'B'C'D'.
The sequence of transformation will be;
Rotate 120 degrees Counterclockwise around B, then Translate B to B' and reflect over segment BA.
How to Identify the Transformation?
We want to find the transformation that maps Quadrilateral ABCD onto Quadrilateral A'B'C'D'.
Looking at the given image, the sequence of transformation will be;
Rotate 120 degrees Counterclockwise around B, then Translate B to B' and reflect over segment BA.
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Please help me on this geometry question
Answer:
? = 3
Step-by-step explanation:
given a line parallel to a side of the triangle and intersecting the other 2 sides, then it divides those sides proportionally , that is
[tex]\frac{?}{6}[/tex] = [tex]\frac{2}{4}[/tex] ( cross- multiply )
4? = 12 ( divide both sides by 4 )
? = 3
Answer:
3
Step-by-step explanation:
Because the triangles are similar
6/4 = (?+6)/(2+4)
6/4 = (?+6)/6
Cross multiply
36 = 4?+24
4?=12
?=3
Given that f(x) = -6x and g(x) = x + 4, multiply the functions (f •g)(x).
Answer:
(f • g)(x) = -6x² - 24x
Step-by-step explanation:
The expression (f • g)(x) can be written in an expanded form, f(x) • g(x).
(f • g)(x) <----- Original expression
f(x) • g(x) <----- Rewritten expression
(- 6 x) • (x + 4) <----- Insert functions
-6x² - 24x <----- Multiply -6x and x, and multiply -6x and 4
telephone poll administered by a computer randomly generating numbers to call, found that 68% of Americans in the sample of 2000 were in favor of legalizing recreational marijuana use. Thus, almost 70% of Americans favor legalizing recreation marijuana use.
The method that was used to arrive at the approximate population probability is called; a reasonable statistical generalization
What is statistics generalization?Statistical generalization is a concept that involves inferring the results from a sample and applying it to a population. Carrying out this means that the sample must be selected randomly and be representative of the population.
Now, in this case, we see that the sample gave a probability of 68% to represent those were in favor of legalizing recreational marijuana use.
Now, since the conclusion was approximated to 70% to reflect the probability of the population then we can say that a reasonable statistical generalization was utilized.
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A line passes through points (2,5) and (6.-7) and has a y-intercept at (0,3). Write the linear equation of this line
Answer: -9/4.
The slope formula of the line passing through the points
slope and why intercept?
Answer:
Slope: -1/3
Y-intercept: 0
Step-by-step explanation:
The lines passes the y-axis at 0, and since the line is going downwards, the slope will be negative.
I hope it helps! Have a great day!
bren~
Air pressure may be represented as a function of height (in meters) above the surface of the Earth, as shown below. In this function, Po is the air pressure at the surface of the Earth, and h is the height above the surface of the Earth, measured in meters. Which expression best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth
The expression that best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth is 3,000ρg.
Air pressure at an altitude above the surface of the EarthThe air pressure at an altitude of 3,000 meters above the surface of the Earth is calculated as follows;
Po = ρgh
where;
ρ is density of airg is acceleration due to gravityh is the altitudeSubstitute the value of altitude into the equation;
Po = 3,000ρg
Thus, the expression that best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth is 3,000ρg.
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pls help math problem pls
Answer: The fourth choice
Step-by-step explanation:
(f - g)(x) = f(x) - g(x) = 4[tex]x^{2}[/tex] - 5x - (3[tex]x^{2}[/tex] + 6x - 4) = [tex]x^{2}[/tex] - 11x + 4
Δ
X
Y
Z
and
Δ
A
B
C
are similar triangles. Given the dimensions shown in the diagram, what is the area of
Δ
A
B
C
? Express the answer in square units.
Answer:
3.528
Step-by-step explanation:
the scale factor from the large triangle to the smaller triangle is 1/2. All of the side lengths of the small triangle is 1/2 the side lengths of the large triangle.
A = 1/2 (bh) The area of a triangle. I need to know the base and the height of the little triangle to figure out the area. If I use AC as the base, the length is given to me. It is 4.2. I do not have the height of the base, but I know that it is half of the height of the large triangle and that number is given to me. It is 3.36, if I divide that by 2, I get 1.68. Now I know all that I need to find the area.
A = 1/2(4.2)(1.68)
3.528Units^2
The function h(x) is given below.
h(x) = {(3,-5), (5, -7), (6, -9), (10, -12), (12,-16)}
Which of the following gives h¹(x)?
O ((3, 5), (5, 7), (6, 9), (10, 12), (12, 16)}
O ((-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)}
O ((3,-5), (5,-7), (6, -9), (10, -12), (12,-16)}
O ((5, 3), (7,5), (9, 6), (12, 10), (16, 12)}
Answer: Option (2)
Step-by-step explanation:
The inverse of a function swaps the domain and range.
The inverse of the function h(x) is
B. h'(x) = ((-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)}
Option B is the correct answer.
We have,
The function h(x) is given as:
h(x) = {(3, -5), (5, -7), (6, -9), (10, -12), (12, -16)}
To find h¹(x) (the inverse of h(x)), we need to swap the x and y values in each ordered pair.
The inverse function will have the y-values of h(x) as the x-values, and the x-values of h(x) as the y-values.
So,
h¹(x) would be:
h¹(x) = {(-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)}
Thus,
The inverse of the function h(x) is
B. h'(x) = ((-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)}
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use the graph to the right. Find the vertices of the image of QRTW for a dilation with center (0,0) and a scale factor of 10
The coordinates of QRTW after dilation by factor 10 are (-20,30),(-30,10),(20,-10),(-20,40).
Given that coordinates of QRTW before dilation are (-2,3),(-3,1),(2,-1),(-2,4) and figure QRTW is dilated by factor 10.
We know that if a figure is dilated its area, increases. The new coordinates can be calculated as x*factor from which it is dilated.
Coordinates are the points on the graph surface.
In our figure Q(-2,3), R(-3,1), S(2,-1), T (-2,4).
We have to just multiply each value with 10 to get the new coordinates of QRTW after dilation.
Q after dilation=(-2*10,3*10)=(-20,30)
R after dilation=(-3*10,1*10)=(-30,10)
S after dilation=(2*10,-1*10)=(20,-10)
T after dilation=(-2*10,4*10)=(-20,40)
Hence the vertices of the image QRTW after dilation are (-20,30),(-30,10),(20,-10),(-20,40).
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Round 5 358 708 to the nearest million
Answer:5 million
Step-by-step explanation: Because 300 thousand is below 500 thousand so if its below 500 thousand it cant round up it rounds down.
PLEASE HELP WILL GIVE YOU ALL MY POINTS In the picture, t || s, mz1 = 10x + 2, and mz2 = 12x - 22. Find the measure of angle 2.
Answer:
[tex]\huge\boxed{\sf < 2 = 122\°}[/tex]
Step-by-step explanation:
From the figure,
∠1 = ∠2 (Alternate angles are equal)We know that:
∠1 = 10x + 2∠2 = 12x - 22So,
10x + 2 = 12x - 22Add 22 to both sides
10x + 2 + 22 = 12x
10x + 24 = 12x
Subtract 10x to both sides
24 = 12x - 10x
24 = 2x
Divide 2 to both sides
12 = x
OR
x = 12Given that,
∠2 = 12x - 22
Put x = 12
∠2 = 12(12) - 22
∠2 = 144 - 22
∠2 = 122°[tex]\rule[225]{225}{2}[/tex]
Answer: 122°
Step-by-step explanation:
∠1 an ∠2 are alternate interior angles, which are angles that are inside both parentheses and are on alternate sides of the transversal. The Alternate Interior Angles Theorem states that if two lines are parallel and cut by a transversal, then the alternate interior angles formed are congruent.
Since the lines are parallel as given in the question, ∠1 and ∠2 are of equal measure. We can solve for ∠2 by first solving for x, then plugging it in ∠2's measure.
[tex]10x+2=12x-22[/tex]
[tex]-2x=-24[/tex]
[tex]x=12[/tex]
Putting x in the expression 12x-22, we get
[tex]12(12)-22\\144-22\\122[/tex]
Hence, the value of ∠2 is 122°.
The number of rows in an auditorium can be represented by the function f(x) = 80x. the number of seats in each row can be represented by the function g(x) = x 7. which function represents the total number of seats, h(x) = f(x)g(x)? h(x) = 136x h(x) = 80x2 560x h(x) = 80x 560 h(x) = 80x2 560
Applying multiplication of functions, the total number of seats in the auditorium is given by:
h(x) = 80x² + 560x.
How polynomial functions are multiplied?They are multiplied applying the distributive property, that is, all the terms are multiplied and then the common terms are added.
In this problem, the functions are given as follows:
f(x) = 80x.g(x) = x + 7.Then the multiplication is:
h(x) = f(x)g(x) = 80x(x + 7) = 80x² + 560x.
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Answer:
The answer is b
Step-by-step explanation:
:)
You measure 46 textbooks' weights, and find they have a mean weight of 77 ounces. Assume the population is normally distributed with a standard deviation of 12.2 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight. Give your answers correct to at least two decimal places. Lower Limit = Upper Limit =
Using the z-distribution, the 99% confidence interval for the true population mean textbook weight is (72.37, 81.63).
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The other parameters are given as follows:
[tex]\overline{x} = 77, \sigma = 12.2, n = 46[/tex]
Hence the lower and upper bound of the interval are given, respectively, by:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 77 - 2.575\frac{12.2}{\sqrt{46}} = 72.37[/tex][tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 77 + 2.575\frac{12.2}{\sqrt{46}} = 81.63[/tex]More can be learned about the z-distribution at https://brainly.com/question/25890103
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find the domain and range of f^-1 where f(x)=x+1/6x+7
Answer:
Step-by-step explanation:
hello here is an solution
The domain and range are (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6} and (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6} respectively.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is f(x)=(x+1)/6x+7
Let f(x)=y
(x+1)/6x+7=y
x+1=y(6x+7)
x+1=6xy+7y
6xy-x=7y-1
x(6y-1)=7y-1
Divide both sides by 6y-1
x=7y-1/6y-1
So f⁻¹(x)=1-7x/6x-1
The domain is (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6}
The range is (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6}
Hence, the domain and range are (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6} and (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6} respectively.
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Instructions: Given the coordinates, Complete the translation (x,y)→(x+2,y−2) C(−5,−1) D(−4,3) E(−3,2) F(−2,0)
the translations is,
C(-5,-1) → (-3,-3)
D(-4,3) → (-2,1)
E(-3,2) → (-1,0)
F(-2,0) → (0,-2)
What is Translation ?
The changes in the value of the x and y coordinates is known as translation.
Calculation:
The given points are C(-5,-1), E(-4,3), F(-3,2), F(-2,0).
according to the question (x,y)→(x+2,y-2)
this means x coordinate changes by addition of 2
And the y coordinate changes by subtraction of 2
Addition and Subtraction in the Coordinates,
C(-5,-1) → (-5+2,-1-2) → (-3,-3)
D(-4,3) → (-4+2,3-2) → (-2,1)
E(-3,2) → (-3+2,2-2) → (-1,0)
F(-2,0) → (-2+2,0-2) → (0,-2)
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Consider the volume of the region shown below, which shows a right circular cone with a top radius of 3 cm and height 9cm
Answer:
84.82 cm
Step-by-step explanation:
Volume of a cone: [tex]\frac{1}{3} \pi r^2h[/tex]
[tex]\frac{1}{3} \pi r^2h\\\\\\\\= \frac{1}{3}\pi (3)^2(9)\\\\= \frac{1}{3}\pi(9)(9)\\\\\\\= \frac{1}{3} \pi (81)\\\\= 27\pi \\[/tex]
≈ 84.82 cm
1. Chris takes 25 minutes to replace one car tyre.
Jim takes 5 minutes less to replace one car tyre.
At a car workshop, there are a total of x tyres to be replaced.
Jim replaces three more tyres than Chris, without exceeding the time Chris takes.
Form an inequality in x and solve it to find the minimum number of tyres to be replaced.
Chris and Jim must replace a total quantity of 17 tyres.
What is the minimum number of tyres to be replaced?
In this problem we must use an inequality of the form f(x) ≥ a, where f(x) is the difference between the number of tyres replaced by Jim and the number of tyres replaced by Chris:
(25/20) · x - x ≥ 3
(5/20) · x ≥ 3
x ≥ 12
Then, the minimum number of tyres to be replaced is n = 15 + 12 = 17 tyres.
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Mr. Krueger wanted a square platform built in the drama room at
school. He provided the carpenter with the desired area of the platform
to be built. Which function can he use to determine the side length of
the square platform?
F(x)=x²
F(x)=√x
F(x) = -=-=
F(x) = |x|
X + 2/3 = 8/9 x=? /////////////////////////////////////////
The value of x is 2/9
Given equation x +2/3 = 8/9
We need to find the value of x
Simplifying the equation is
x+2/3 = 8/9
x = 8/9 -2/3
Taking L.C.M of the denominators 3 and 9
The L.C.M is 9
So we will multiply the numerator and denominator with 1 in 8/9
And we will multiply the numerator and denominator with 3 in 2/3
Hence the new equation formed = 8/9-6/9
Solving this equation we get
8-6 / 9
= 2 / 9
Hence the value of x is 2/9
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The volume of a solid revolution generated by rotating the curve y = f(x) and x = f(y) between x = a and x = b , y = a and y = b through 360 degrees about the x-axis and y-axis is given
[tex]V_{x} =\int\limits^b_a {\pi y^{2} } \, dx[/tex] and [tex]V_{y} =\int\limits^b_a {\pi x^{2} } \, dy[/tex]
The diagram shows the line y = 1, the line y = 4 and part of the curve [tex]y=3x^2[/tex]. The shaded region is rotated through 360 degrees about the y-axis. Find the exact value of the volume of revolution obtained. Leave your answer in pi.
Answer:
[tex]\dfrac{5}{2}\pi[/tex]
Step-by-step explanation:
Rotation about the y-axis
[tex]\textsf{Volume}=\displaystyle \int^b_a \pi x^2\:\text{d}y[/tex]
where:
b = upper limita = lower limitx is a function of yGiven function of y: [tex]y = 3x^2[/tex]
Rewrite the given function as a function of y:
[tex]\implies x^2=\dfrac{1}{3}y[/tex]
Substitute the values into the formula:
[tex]\implies \displaystyle \int^4_1 \dfrac{1}{3}\pi y\:\:\text{d}y[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ay^n\:\text{d}y=a \int y^n \:\text{d}y$\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $y^n$}\\\\$\displaystyle \int y^n\:\text{d}y=\dfrac{y^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
Take out the constant and integrate:
[tex]\begin{aligned}\implies \dfrac{1}{3}\pi\displaystyle \int^4_1 y\:\:\text{d}y & = \dfrac{1}{3}\pi \left[\dfrac{1}{2}y^2\right]^4_1\\\\& =\dfrac{1}{3}\pi \left[\dfrac{1}{2}(4)^2-\dfrac{1}{2}(1)^2\right]\\\\&=\dfrac{1}{3}\pi\left[8-\dfrac{1}{2}\right]\\\\&=\dfrac{5}{2}\pi \end{aligned}[/tex]
Therefore, the exact value of the volume of revolution is:
[tex]\dfrac{5}{2}\pi[/tex]
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Andrei wants to fill a glass tank with marbles, and then fill the remaining space with water. www represents the volume of water andrei uses (in liters) if he uses nnn marbles. w=32-0.05nw=32−0.05nw, equals, 32, minus, 0, point, 05, n what is the volume of each marble?
Using linear function concepts, it is found that the volume of each marble is of 0.05 liters.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The linear function that gives the volume of water, when n marbles are inserted into the tank, is given by:
w = 32 - 0.05n
The slope of -0.05 means that for each marble inserted, there are 0.05 liters less for water, hence the volume of each marble is of 0.05 liters.
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Answer:
.05 liters
Step-by-step explanation:
Drag each tile to the correct box.
Each function is a transformation of the parent sine function. Based on the period, which graph represents each transformed function?
The first graph represents sin(2x), the second graph represents sin(-x) and the third graph represents sin(x/2) .
There are some rules for transformation of graph of various functions which are as follows :-
For F(x) →f(−x) = Reflection about the y-axisFor F(x) → f(ax) = It will depend upon value of a chosenIf |a|>1 then f(ax) is f(x) squashed horizontally by a factor of aIf 0<|a|<1 then f(ax) is f(x) is stretched horizontally by factor of aIf a<0 then is f(ax) is f(x) also reflected in the y-axisBy keeping in mind these rules it is easily observable that the first graph is sinx squashed horizontally by a factor of 2 while second graph is reflection of sinx about the y-axis and the third graph is sinx horizontally stretched by a factor of 2.
Thus the first graph represents sin(2x), the second graph represents
sin(-x) and the third graph represents sin(x/2)
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Which graph represents the solution to x<6?
. In your rectangular backyard, you know the width of the yard is three less than four times the length. If the perimeter of your yard is 24 yards, what is the width?
The width of the rectangular backyard is 9 yards.
How to find the width of the rectangle?The width of the yard is three less than four times the length.
Therefore,
w = 4l - 3
Perimeter of a rectangle = 2l + 2w
where
l = length
w = width
Hence,
24 = 2l + 2(4l - 3)
24 = 2l + 8l - 6
24 = 10l - 6
24 + 6 = 10l
30 = 10l
l = 30 / 10
l = 3 yards
Hence,
w = 4(3) - 3
w = 12 - 3
w = 9 yards
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Is x+2 a factor of the polynomial f(x)=2x^4-3x^2-4x+1?
a. f(2)=0, so (x+2) is a factor.
b. f(-2)=29, so (x+2) is not a factor.
c. f(-2)=0, so (x+2) is a factor.
d. f(2)=13, so (x+2) is not a factor.
Answer:
B
Step-by-step explanation:
the value of the x should be the same if we want to verify whether x+2 is a factor of f(x)
so if x=-2 ,f(-2) = 29
x+2=0 f(0) = 1
f(0) [tex]\neq[/tex] f(-2) ,so x+2 is not a factor
what it actually means it that if we move the graphic of f(x) to left along to x axis 2 units, the graphic of new one cannot coincide with the original one.
The figure shows an example of a multiplication problem where the numbers are coded by letters. Same letter represents same digits, and different letters represent different digits. Which digit does the letter x represent?
Based on the information provided, it can inferred that letter A is equivalent to 4.
What is the value of letter B?The image shows B + B+ A = A. This is only possible if letter adding 2 letters B is equal to 10. Now 10/2 = 5. This means B = 5.
What is the value of the letter A?It is known 5 + A + A = A. This is only possible is A is 4. 5 + 4+ 4 + 1 (from the previous addition) = 4 (+2 that is added in the next column).
Note: This question is incomplete below I add the missing image.
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