Answers
Answer:
-3, 1, 4 are the x-intercepts
Step-by-step explanation:
The remainder theorem tells you that dividing a polynomial f(x) by (x-a) will result in a remainder that is the value of f(a). That remainder will be zero when (x-a) is a factor of f(x).
In terms of finding x-intercepts, this means we can reduce the degree of the polynomial by factoring out the factor (x-a) we found when we find a value of "a" that makes f(a) = 0.
__
For the given polynomial, we notice that the sum of the coefficients is zero:
1 -2 -11 +12 = 0
This means that x=1 is a zero of the polynomial, and we have found the first x-intercept point we can plot on the given number line.
Using synthetic division to find the quotient (and remainder) from division by (x-1), we see that ...
f(x) = (x -1)(x² -x -12)
We know a couple of factors of 12 that differ by 1 are 3 and 4, so we suspect the quadratic factor above can be factored to give ...
f(x) = (x -1)(x -4)(x +3)
Synthetic division confirms that the remainder from division by (x -4) is zero, so x=4 is another x-intercept. The result of the synthetic division confirms that x=-3 is the remaining x-intercept.
The x-intercepts of f(x) are -3, 1, 4. These are the points you want to plot on your number line.
Related Questions
The probability that an event will occur is 7/8 which of these best describes the likehood of the even occurring
Answers
Very Likely
think of it this way
you have a 7/8 chance of getting electrocuted by sticking your hand in the toaster
you have a 1/8 chance of this event not occurring when you stick said hand in the toaster
so its VERY LIKELY that you will be electrocuted if you stick your hand in a toaster
hope that helps!
An aeroplane at an altitude of 200m observes the angle of depression of opposite points on the two banks of a river to be 45 and 60 find the widht of river
Answers
Answer:
84.5 m
Step-by-step explanation:
It is often helpful to draw a diagram for word problems involving geometric relationships. One for this problem is shown below.
The mnemonic SOH CAH TOA reminds you of the relationship between sides of a right triangle:
Tan = Opposite/Adjacent
Here we're given angles of depression measured from the horizontal (as shown in the diagram), but it is more convenient to use angles measured from the vertical. In particular, ∠BAO is the complement of 60°, and its tangent is the ratio OB/OA:
tan(30°) = OB/OA
OB = (200 m)·tan(30°) ≈ 115.47 m . . . . . . multiply by OA, use OA=200 m
Likewise, we have ...
OC = (200 m)·tan(45°) = 200 m
Then the width of the river is the difference between these values:
BC = OC -OB = 200 m - 115.47 m = 84.53 m
Why does the PCI require banks to protect customers’ card data?
A.
to protect banks from hackers and malware
B.
to help improve the cyber community
C.
to establish good practices in the banking community
D.
to protect consumers from online fraud and theft
Answers
Answer:
D. to protect consumers from online fraud and theft
Step-by-step explanation:
The point of protection of personal identifying and financial data is to prevent fraud and theft.
___
The reason why hackers and malware attack banks is to get to data that would enable fraud and theft. "Good practices" prevent such data compromise, so protecting customers from fraud and theft.
Answer:
Why does the PCI require banks to protect customers’ card data?
A.
to protect banks from hackers and malware
B.
to help improve the cyber community
C.
to establish good practices in the banking community
D.
to protect consumers from online fraud and theft
Step-by-step explanation:
#platofam
PLEASE HELP! I'm on a time limit!! Identify the translation of the figure with the vertices L(1,−1), M(4,−3), and N(3,−5), along the vector ⟨2,5⟩.
L ′(3, 4), M ′(2, 6), N ′(5, 0)
L ′(3, 4), M ′(6, 2), N ′(5, 0)
L ′(1, 3), M ′(6, 2), N ′(0, 5)
N ′(3, 4), M ′(6, 2), N ′(5, −1)
Answers
Answer:
It's the second option.
Step-by-step explanation:
You add 2 to the x coordinate and 5 to the y coordinate.
So L' = (1 + 2, -1+5)
= (3, 4).
Answer:
L ′(3, 4), M ′(6, 2), N ′(5, 0)
Without using technology, describe the end behavior of f(x) = −3x4 + 7x2 − 12x + 13.
Answers
Following are the description on the function behavior:
Given:
[tex]\bold{f(x) = -3x^4 + 7x^2 - 12x + 13}[/tex]
To find:
Function behavior=?
Solution:
We use Power and Polynomial Functions features in the absence of technology. As the function [tex]\bold{f(x) = -3x^4 + 7x^2 -12x + 13}[/tex]
For final behaviour of power functions of such form[tex]\bold{f(x)=ax^n}[/tex] wherein n is a non-negative integer depends on the power and the constant.
So, the leading term, [tex]\bold{f(x)=-3x^4}[/tex]
When the negative constant and even power are:
[tex]\to x \to \infty\\\\\to f(x) \to -\infty[/tex]
At
[tex]x \to -\infty\\\\f(x) \to -\infty[/tex]
Therefore, the final answer is "Down on the left down on the right "
Learn more:
brainly.com/question/13821048
The end behavior of [tex]\( f(x) = -3x^4 + 7x^2 - 12x + 13 \)[/tex] is described as "Down on the left, down on the right," The correct answer is option a) Down on the left, down on the right.
To determine the end behavior of the polynomial [tex]\( f(x) = -3x^4 + 7x^2 - 12x + 13 \)[/tex] without using technology, we analyze the leading term, which dominates the behavior of the function as x approaches positive or negative infinity.
1. Identify the leading term: The leading term of [tex]\( f(x) \) is \( -3x^4 \)[/tex].
2. Consider the degree and leading coefficient:
- The degree of the polynomial is 4.
- The leading coefficient (coefficient of the term with the highest power of [tex]\( x \)) is \( -3 \)[/tex].
3. Determine the end behavior:
- As [tex]\( x \to +\infty \), \( -3x^4 \)[/tex] approaches [tex]\( -\infty \)[/tex] because [tex]\( x^4 \)[/tex] grows much faster than the negative coefficient affects it. Therefore, [tex]\( f(x) \to -\infty \)[/tex].
- As [tex]\( x \to -\infty \)[/tex], [tex]\( -3x^4 \)[/tex] also approaches [tex]\( -\infty \)[/tex] for the same reason. Hence, [tex]\( f(x) \to -\infty \)[/tex].
4. Conclusion: Based on the analysis:
- The polynomial [tex]\( f(x) = -3x^4 + 7x^2 - 12x + 13 \)[/tex] decreases to [tex]\( -\infty \)[/tex] as x goes to both positive and negative infinity.
Therefore, the end behavior of [tex]\( f(x) \)[/tex] is described as "Down on the left, down on the right", which corresponds to option a). This indicates that the graph of [tex]\( f(x) \)[/tex] starts high on the left and continues downward indefinitely in both directions.
Complete question : Without using technology, describe the end behavior of f(x) = −3x4 + 7x2 − 12x + 13.
a Down on the left, down on the right
b Down on the left, up on the right
c Up on the left, down on the right
d Up on the left, up on the right
The product is k2 – k + .
Answers
Come on, now. Incomplete question.
Answer:
is it late now
Step-by-step explanation:
The value of a collector’s item is expected to increase exponentially each year. the item is purchased for $500. after 2 years, the item is worth $551.25. which equation represents y, the value of the item after x years? y = 500(0.05)x y = 500(1.05)x y = 500(0.1025)x y = 500(1.1025)x
Answers
Answer:
[tex]y=500(1.05)^x[/tex]
Step-by-step explanation:
The standard form for an exponential equation is
[tex]y=a(b)^x[/tex]
We have 2 unknowns, a and b, but that's all good because we have 2 (x, y) coordinates we can utilize in order to find a and b. In our coordinate pair, x is the number of years gone by and y is the value after that number of years. The problem tells us that an item was purchased for $500. That translates to "before any time has gone by, the initial value of the item is $500". In other words, with x being time, no time has gone by, so x = 0. When x = 0, y = 500. (0, 500). Do the same for the next set of numbers. When x = 2 years gone by, the value is $551.25, so the coordinate is (2, 551.25). Now we use them to find a. Use the first coordinate:
[tex]500=a(b)^0[/tex]
Anything raised to the 0 power = 1, therefore:
[tex]500 = a(1)[/tex] and a = 500.
Now onto the next coordinate point using the a value we just found:
[tex]551.25 = 500(b)^2[/tex]
Divide both sides by 500 to get
[tex]1.1025=b^2[/tex]
so b = 1.05.
Now we have the values for a and b, so we fill in:
[tex]y = 500(1.05)^x[/tex]
Is the histogram symmetric, skewed right, or skewed left? Explain your answer .
Answers
Answer:
It’s skewed left
Step-by-step explanation:
The main mass of the graph is on the left. Follow the shape of the graph to find this
To determine if a histogram is symmetric or skewed, we assess the relative positions of the mean, median, and mode. A symmetric distribution has these three values approximately equal and the histogram's halves mirror each other. A right-skewed histogram has a tail extending right, whereas a left-skewed histogram's tail extends left.
Explanation:When analyzing whether a histogram is symmetric, skewed right, or skewed left, certain aspects of the distribution of data are considered. Symmetry in a histogram indicates that if a vertical line were drawn at some midpoint, the left and right sides would be mirror images. In a symmetric distribution, the mean, median, and mode are usually equivalent or very close to each other. To determine skewness, we look at the arrangement of these three measures: for a skew to the right, the mode is often less than the median, which is less than the mean. Conversely, a distribution skewed to the left typically has the mean less than the median, which is less than the mode.
A histogram for a right-skewed distribution will often show a tail extending to the right, indicating that larger numbers in the dataset are more spread out. On the other hand, a histogram with a left-skewed distribution will show a tail that extends to the left, which implies that the lower numbers are more spread out.
PLEASE HELP ME WITH THIS MATH QUESTION
Answers
Answer:
Permutations and combinations
Step-by-step explanation:
For any three songs chosen of the 8 options would use the formula of combinations of 8 taken by 3, to find which of the 3 to play first, permutation formula
There is a flu outbreak at your school that starts with 10 people. The number of ill students increases by 20% each hour. Write an exponential function to represent the total number of ill students, f(x), where x is the number of hours after the outbreak. How long does it take for at least 100 people to be ill with the flu?
a. About 10 hours
b. About 13 hours
c. About 20 hours
d. Not enough information
Answers
Answer:
d
Step-by-step explanation:
what does ' f ' represent?
The exponential function for the total number of ill students is [tex]f(x) = 10 * (1.20)^x,[/tex] where x is the number of hours after the outbreak. To reach at least 100 ill students, it takes about 13 hours. So correct answer is option B.
To represent the total number of ill students f(x) as an exponential function where x is the number of hours after the outbreak, we use the initial value of 10 people sick and an hourly increase rate of 20%. The function is: [tex]f(x) = 10 * (1 + 0.20)^x[/tex].
To find how long it takes for at least 100 people to be ill, we set f(x) \\>= 100 and solve for x:
[tex]10 * (1.20)^x \ > = 100\\(1.20)^x \ > = 10x\\\\log(1.20) \ > = \log(10)\\x > = \log(10) \\ \\log(1.20)\\x = 12.2[/tex]
Therefore, it takes about 13 hours for at least 100 people to be ill. So the answer is b. About 13 hours.
If the volume of the rectangular prism is represented by 6x2 – 2x + 8 and the base area is 2x – 4, which expression represents the height?
Answers
The expression that represents the height of the rectangular prism is 3x + (10 / (2x - 4)) found by dividing the given volume expression by the base area expression.
To find the expression that represents the height of the rectangular prism, we need to rearrange the formula for the volume of a prism, which is Volume = Base Area x Height. Given the volume of the rectangular prism as 6x^2
- 2x + 8 and the base area as 2x - 4, we divide the volume by the base area to find the height:
Height = Volume / Base Area
Height = (6x^2 - 2x + 8) / (2x - 4)
This simplifies to:
Height = 3x + (10 / (2x - 4))
Therefore, the expression that represents the height is 3x + (10 / (2x - 4)).
Which graph correctly solves the system of equations below? y = − x2 + 1 y = x2 − 4
A) quadratic graph opening up and quadratic graph opening down. They do not intersect.
B) quadratic graph opening up and quadratic graph facing down. They intersect at negative 2, negative 3 and 2, negative 3.
C) Two intercepting parabolas are shown, one facing downward and one facing upward. The downward facing parabola has a maximum at (0,1) and intercepts the x axis at 1 and negative 1. The upward facing parabola has a minimum at (0,-4) and intercepts the x axis at 2 and negative 2
D) two quadratic graphs opening up. They intersect at 0, negative 4.
Answers
Answer:
C) Two intercepting parabolas are shown, one facing downward and one facing upward. The downward facing parabola has a maximum at (0,1) and intercepts the x axis at 1 and negative 1. The upward facing parabola has a minimum at (0,-4) and intercepts the x axis at 2 and negative 2
Step-by-step explanation:
As shown in the attached, the graph of y = -x² +1 has its vertex at (0, 1) and opens downward. It crosses the x-axis at ±1. The graph of y = x² -4 has its vertex at (0, -4), opens upward, and crosses the x-axis at ±2. The description of this graph matches choice C.
if WXYZ is a square, which statements must be true? plz help <3
Answers
Answer with step-by-step explanation:
A. WX is perpendicular to XY - TRUE:
(since X is adjacent to X and Y and all angles are 90 degrees in a square, therefore WX is perpendicular to XY)
B. ∠W is congruent to ∠X - TRUE:
(all angles in a square are equal to each other)
C. ∠W is supplementary to ∠X - TRUE:
(∠W and ∠X both are right angles which add up to 180 degrees so they are supplementary angles)
D. WXYZ is a rhombus - TRUE:
(a rhombus has all sides equal in length and so has a square so it is a rhombus)
E. WXYZ is a trapezoid - FALSE:
(a trapezoid has only one pair of parallel sides while a square has two pairs of parallel sides)
F. WX is parallel to YZ - TRUE:
(WX and YZ are parallel to each other)
Use long division or synthetic division to find the quotient of
Answers
Answer:
2x^2-x+1
Step-by-step explanation:
Answer:
2x² - x + 1
Step-by-step explanation:
[tex]\frac{(2x^{2}-x+1)(x+1)}{(x+1)} = 2x^{2}-x+1[/tex]
Graph the following system of linear inequalities. Identify at least two points in the solution: y < 5 - 2x | x + 5y > -7
Answers
Answer:
(1,2) and (2,-1)
Step-by-step explanation:
we have
[tex]y< 5-2x[/tex] ----> inequality A
The solution of the inequality A is the shaded area below the dashed line [tex]y=5-2x[/tex]
[tex]x+5y>-7[/tex] ---->inequality B
The solution of the inequality B is the shaded area above the dashed line [tex]x+5y=-7[/tex]
The solution of the system of inequalities is the triangular shaded area between the two dashed lines
If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area
Two points in the solution are(1,2) and (2,-1)see the attached figure
Find the average value of y equals the square root of the quantity 64 minus x squared, on its domain.
Answers
Answer:
2π ≈ 6.283
Step-by-step explanation:
The average value of the function is the area under it, divided by the base. This function describes a semicircle of radius 8, so its area is ...
A = 1/2πr² = 1/2π·8² = 32π
The width of the base is the diameter of the semicircle, so is 16. Then the average value is ...
32π/16 = 2π . . . . . average value of y
The graph of F(X), shown below, has the same shape as the graph of
G(x) = x2, but it is shifted up 1 unit. What is its equation?
Answers
Answer:
Option B. [tex]F(x)=x^{2}+1[/tex]
Step-by-step explanation:
we know that
[tex]G(x)=x^{2}[/tex]
This is the equation of a vertical parabola open upward wit vertex at (0,0)
The rule of the translation of G(x) to F(x) is equal to
(x,y) ----> (x,y+1)
therefore
The vertex of the function f(x) is the point (0,1) and the equation is equal to
[tex]F(x)=x^{2}+1[/tex]
Find the area of the trapezoid.
Answers
For this case we have that by definition, the area of the trapezoid is given by:
[tex]A = \frac {1} {2} (B + b) * h[/tex]
Where:
B: It is the major base
b: It is the minor base
h: It's the height
Substituting the values according to the data of the figure:
[tex]A = \frac {1} {2} (2.1 + 0.9) * 1.3\\A = \frac {1} {2} (3) * 1.3\\A = \frac {1} {2} * 3.9\\A = 1.95[/tex]
Thus, the area of the trapezoid is[tex]1.95 m ^ 2[/tex]
ANswer:
Option B
PLEASE HELP ME WITH THIS MATH QUESTION
Answers
Answer:
r=4ft
h=8ft
Area of cyclender=?
by using formula,
A=πr²h
=22/7×4²×8
=402.28ft²Ans.
ANSWER
301.6 ft²
EXPLANATION
The surface area of a cylinder is calculated using the formula;
[tex]S.A = 2\pi \: r(r + h)[/tex]
From the diagram the height of the cylinder is 8 feet and the radius is 4 feet.
We substitute the values into the formula to obtain,
[tex]S.A = 2\pi \: 4(4+ 8)[/tex]
This simplifies to:
[tex]S.A = 8\pi \: (12)[/tex]
[tex]S.A = 96\pi[/tex]
Or
[tex]S.A = 301.6 {ft}^{2} [/tex]
to the nearest tenth.
PLZ HELP MARKIN BRAINIEST!!!
Answers
Answer:
d. (x - 5)(x - 5)
Step-by-step explanation:
x² - 10x + 25
we look for a two number when added gives you the sum -10 and when multiplied gives you the product 25
sum = - 10
product = 25
the two numbers are
-5,-5
x² - 5x - 5x + 25
(x² - 5x) (- 5x + 25)
x(x-5)-5(x-5)
(x-5)(x-5)
Hope this helps and if it does mark as brainliest.thx
Answer:
[tex]\large\boxed{x^2-10x+25=(x-5)(x-5)}[/tex]
Step-by-step explanation:
[tex]x^2-10x+25=x^2-2(x)(5)+5^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=(x-5)^2=(x-5)(x-5)[/tex]
A hotel manager found that his gross recipients for the day, including a 7% sales tax, totaled to $3479.64. Find the amount of sales tax collected.
(I ask for someone to please, quickly, help me answer he question, I can't seem to properly do it myself.)
Answers
Answer:
$227.64
Step-by-step explanation:
The relevant relations are ...
sales + tax = total
tax = 7% × sales
Using the second equation, we can write sales in terms of the tax as ...
sales = tax/0.07
Substituting this into the first equation gives ...
tax/.07 + tax = total . . . . . substitute for sales
tax(1/0.07 + 1) = total . . . . factor out tax
tax ((1 +.07)/.07) = total . . . simplify to a single fraction
Multiply by the inverse of this fraction:
tax = .07/1.07 × total = (7/107)($3479.64)
tax = $227.64
mary is solving the equation 5^x + 4 =11. her first steps are shown.
step 1. 5^x + 4 =11
step 2. 5^x =7
step3. In5^x=In7
which shows step 4?
A. In 5 = x In 7
B. x In 5 = In 7
C. ^-In 5 = In 7 * x
D. x = In 7 - In 5
Answers
Answer:
Option B. x In 5 = In 7
Step-by-step explanation:
we have
[tex]5^{x}+4=11[/tex]
step 1
[tex]5^{x}+4=11[/tex]
step 2
Subtract 4 both sides
[tex]5^{x}+4-4=11-4[/tex]
[tex]5^{x}=7[/tex]
step 3
Apply ln both sides
[tex]ln(5^{x})=ln(7)[/tex]
step 4
[tex]xln(5)=ln(7)[/tex]
step 5
Divide by ln(5) both sides
[tex]x=ln(7)/ln(5)[/tex]
Solve for the following system of equations.
-7x+6y=9
-2x-5y+16
x=?
y=?
Answers
Answer:
x = -3 and y = -2
Step-by-step explanation:
It is given that,
-7x + 6y = 9 ----(1)
-2x - 5y = 16 -------(2)
To find the solution of given equations
eq(1) * 2 ⇒
-14x + 12y = 18 ------(3)
eq(2) * 7 ⇒
-14x - 35y = 112 ---(4)
eq (3) - eq(4) ⇒
-14x + 12y = 18 ------(3)
-14x - 35y = 112 ---(4)
0 4y = -94
y = 94/(-47) = -2
Substitute the value of y in eq (2)
-2x - 5y = 16 -------(2)
-2x - 5*-2 = 16
-2x +10 = 16
-2x = 6
x = 6/-2 = -3
Therefore x = -3 and y = -2
Answer:
[tex]x=-3\\\\y=-2[/tex]
Step-by-step explanation:
Given the system of equations [tex]\left \{ {{-7x+6y=9} \atop {-2x-5y=16}} \right.[/tex], you can use the Elimination Method to solve it.
You can multiply the first equation by -2 and the second equation by 7, then add both equations and solve for the variable "y":
[tex]\left \{ {{14x-12y=-18} \atop {-14x-35y=112}} \right.\\...........................\\-47y=94\\\\y=\frac{94}{-47}\\\\y=-2[/tex]
Substitute the value of "y" into any original equations and solve for the variable "x". Then:
[tex]-7x+6y=9\\\\-7x+6(-2)=9\\\\-7x-12=9\\\\-7x=9+12\\\\x=\frac{21}{-7}\\\\x=-3[/tex]
An action movie production team needs glass spheres to hold a green liquid that looks like an explosive. If all of the available 3,392.92 cubic inches of the liquid is to be poured into 30 glass spheres, what should the diameter of each sphere be? Assume that each sphere is filled to the top.3 inches4 inches6 inches8 inches9 inches
Answers
Answer:
6 inches
Step-by-step explanation:
3392.92 cubic inches of liquid distributed in 30 spheres would give each sphere's volume to be:
[tex]\frac{3392.92}{30}=113.1[/tex]
Now we equate 113.1 to the formula for volume of a sphere and solve for r:
[tex]\frac{4}{3}\pi r^3=113.1\\r^3=\frac{113.1}{\frac{4\pi}{3}}\\r^3=27\\r=\sqrt[3]{27} =3[/tex]
The radius of each of those spheres is 3
We know diameter is twice the radius , so diameter would be 3 * 2 = 6 inches
Answer:
6 inches
Step-by-step explanation:
I just took a test on Plato/Edmentum with this question and this was the right answer
~Please mark me as brainliest :)
What is true of the function g(x) = –2x2 + 5? G(x) is the multiplication of g and x. –2x2 +5 is the input of the function. The variable x represents the independent variable. The variable g represents the input of the function
Answers
Answer:
See below.
Step-by-step explanation:
The variable x represents the independent variable. The dependent variable is the function g(x) . The value of g(x) depends on the value of x.
Answer:
The variable x represents the independent variable ( C )
Step-by-step explanation
What is the measure of RCD in the figure below?
Answers
Answer:
35 degrees.
Step-by-step explanation:
Triangles PDC and RDC are congruent ( By HL - The hypotenuse and one leg are equal).
Therefore m < RCD = 35 degrees.
The measure of of RCD in the figure is 35 degrees.
What is congruence?
Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
In PDC and RDC,
angle DPC= angle DRC
CD=CD
PD=DR
By SAS congruence criteria,
ΔPDC ≈ ΔRDC
PCD= RCR= 35. (CPCT)
Learn more about congruence here:
https://brainly.com/question/7888063
#SPJ2
Parametric Equations? How do you do them? I don't even know how to graph them and its so confusing because all the equations I put in say they're not written correctly???
Answers
Answer:
A rectangular equation, or an equation in rectangular form is an equation composed of variables like x and y which can be graphed on a regular Cartesian plane.
Parametric equations are a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as "parameters." For example, while the equation of a circle in Cartesian coordinates can be given by r^2=x^2+y^2, one set of parametric equations for the circle are given by
x=r cost
y=r sin
Note that parametric representations are generally nonunique, so the same quantities may be expressed by a number of different parameterizations. A single parameter is usually represented with the parameter t, while the symbols u and v are commonly used for parametric equations in two parameters.Parametric equations provide a convenient way to represent curves and surfaces, as implemented, for example, in the Wolfram Language commands ParametricPlot[{x, y}, {t, t1, t2}] and ParametricPlot3D[{x, y, z}, {u, u1, u2}, {v, v1, v2}]. Unsurprisingly, curves and surfaces obtained by way of parametric equation representations are known as parametric curves and parametric surfaces, respectively.
Also if you dont know how to graph them you can Use DESMOS graphing calculator
two tables, congruent trapezoids, are placed together to make a corner desk, as shown
A. 8 square ft
B. 10 square ft
C. 16 square ft
D. 20 square ft
Answers
Answer:
D
Step-by-step explanation:
3 and 7 are the main factors so you add them and get 10 but since it’s two equilateral trapezoids then you get another 10 being 20 square feet.
Answer:
D) 20 square feet
Step-by-step explanation:
We are given two congruent isosceles trapezoids and placed together formed to make a corner of the desk.
We need to find the area.
We know that the area of a trapezoid = [tex]\frac{h}{2} [base 1+ base 2][/tex]
Where "h" is the height of the trapezoid.
Given: h = 2 ft, base 1 = 7ft and base 2 = 3ft
Now plug in these values in the above formula, we get
Area of a 1 trapezoid = [tex]\frac{2}{2} [7 + 3][/tex]
= 10 square feet
The two trapezoids are congruent.
So the area of the given figure = 2(10) = 20 square feet.
How long will it take to earn $1800 in interest if $6000 is invested at a 6% annual interest rate? how many years
Answers
Answer:
Total interest will $1800 after 5 years.
Step-by-step explanation:
It is given that the principle amount is $6000.
Rate of interest rate is 6% per annum.
Total interest is $1800.
Formula for simple interest is
[tex]I=\frac{P\times r\times t}{100}[/tex]
Where, P is principle, r is rate of interest in percent and t is time in years.
Substitute P=6000, r=6 and I=1800 in the above formula.
[tex]1800=\frac{6000\times 6\times t}{100}[/tex]
[tex]1800=\frac{36000t}{100}[/tex]
[tex]1800=360t[/tex]
Divide both sides by 360.
[tex]\frac{1800}{360}=t[/tex]
[tex]5=t[/tex]
Therefore the total interest will $1800 after 5 years.
Answer:
b. 5 years
Step-by-step explanation:
Find the distance between these points. R(-1, 0), S(8, 6) √(26) √(85) 3√(13)
Answers
Answer:
[tex]|RS|=3\sqrt{13}[/tex] units.
Step-by-step explanation:
The distance between the two given points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by:
[tex]d=\sqrt{(x_2-x-1)^2+(y_2-y_1)^2}[/tex]
We want to find the distance between R(-1, 0) and S(8, 6).
We plug in these points into the distance formula to get:
[tex]|RS|=\sqrt{(8--1)^2+(6-0)^2}[/tex]
[tex]|RS|=\sqrt{(9)^2+(6)^2}[/tex]
[tex]|RS|=\sqrt{81+36}[/tex]
[tex]|RS|=\sqrt{117}[/tex]
[tex]|RS|=3\sqrt{13}[/tex] units.