| 7 3 2|
8 2 7
6 8 5
7(10 - 56) - 3(40 - 42) + 2(64 - 12)
7(-46) - 3(-2) + 2( 52)
-322 + 6 + 104
= -212
Simplify the expression 3^2/ 3^1/4 to demonstrate the quotient of powers property. Show any intermittent stepsthat demonstrate how you arrived at the simplified answer.
We are given a quotinet of two power expressions to be used to demonstrate the quotient property of powers:
[tex]\frac{3^2}{3^{\frac{1}{4}}}=3^2\cdot3^{-\frac{1}{4}}=3^{(\frac{8}{4}-\frac{1}{4})}=3^{\frac{7}{4}}[/tex]ANother way of doing it is to represent 3^2 as 3 to the power 8/4 so as to have the same radical expression.
Recall that fractional exponents are associated with radicals, and in this case the power "1/4" represents the fourth root of the base "3". That is:
[tex]3^{\frac{1}{4}}=\sqrt[4]{3}[/tex]So we also write 3^2 with fourth root when we express that power "2 = 8/4":
[tex]3^2=3^{\frac{8}{4}}=\sqrt[4]{3^8}[/tex]So now, putting that quotient together we have:
[tex]\frac{\sqrt[4]{3^8}}{\sqrt[4]{3}}=\sqrt[4]{\frac{3^8}{3}}=\sqrt[4]{3^7}=3^{\frac{7}{4}}[/tex]So we see that we arrived at the same expression "3 to the power 7/4"
in both cases. One was using the subtraction of the powers as the new power for the base 3, and the other one was using the radical form of fractional powers.
Find the equation of a line in the form y=Mx+b MATH HW
Using y=mx+b form first we calculate the slope.
We'll use points (0,-8) and (-8,0).
[tex]\begin{gathered} m=(-8-0)\div(0--8) \\ m=-\frac{8}{8} \\ m=-1 \end{gathered}[/tex]Next we calculate our b intercept
[tex]\begin{gathered} 0=-1(-8)+b \\ b=-8 \end{gathered}[/tex]So the equation is y=-x-8
What is the value of x?12 units15 units20 units25 units
Explanation
Step 1
set the equations:
we have three rectangles triangles,so
Let
triangle STR and triangle RTQ
so,
a) for triangle STR
let
[tex]\begin{gathered} \text{ hypotenuse: RS} \\ \text{adjacent side;RT}=x \\ \text{opposite side:ST=9} \\ \text{angle:m}\angle R \end{gathered}[/tex]so, we can use the Pythagorean theorem,it states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)
so
[tex]\begin{gathered} (RS)^2=(ST)^2+(RT)^2 \\ (RS)^2=(9)^2+(x)^2\rightarrow equation(1) \end{gathered}[/tex]b) for triangle RTQ
[tex]\begin{gathered} \text{ hypotenuse: RQ} \\ \text{adjacent side;TQ}=16 \\ \text{opposite side:RT=x} \\ \text{angle:m}\angle Q \end{gathered}[/tex]again, let's use the P.T.
[tex]\begin{gathered} (RQ)^2=(RT)^2+(TQ)^2 \\ (RQ)^2=(x)^2+(16)^2\Rightarrow\text{equation}(2) \end{gathered}[/tex]c)
we know the triangles STR and SQR are similar, so
[tex]m\angle R=m\angle Q[/tex]also,
[tex]\begin{gathered} \tan m\angle R=\tan m\angle Q \\ \frac{oppositeside_R}{\text{adjacent sideR}}=\frac{oppositeside_Q}{\text{adjacent sideQ}} \\ \frac{9}{x}=\frac{SR}{RQ}\rightarrow equation\text{ (3)} \end{gathered}[/tex]finally, we can set a new equation with triangle SQR
d)again, let's use the P.T.
[tex]\begin{gathered} (SQ)^2=(SR)^2+(RQ)^2 \\ \text{replace} \\ (9+16)^2=(SR)^2+(RQ)^2 \\ (25)^2=(SR)^2+(RQ)^2\rightarrow equation(4) \end{gathered}[/tex]Step 2
solve the equations
[tex]\begin{gathered} (RS)^2=(9)^2+(x)^2\rightarrow equation(1) \\ (RQ)^2=(x)^2+(16)^2\Rightarrow\text{equation}(2) \\ \frac{9}{x}=\frac{SR}{RQ}\rightarrow equation\text{ (3)} \\ (25)^2=(SR)^2+(RQ)^2\rightarrow equation(4) \end{gathered}[/tex]solution:
a)
[tex]\begin{gathered} \text{isolate (x) in equation(1) and (2) and set equal } \\ (RS)^2=(9)^2+(x)^2\rightarrow equation(1) \\ (RS)^2-(9)^2=(x)^2 \\ \text{and} \\ (RQ)^2=(x)^2+(16)^2\Rightarrow\text{equation}(2) \\ (RQ)^2-\mleft(16\mright)^2=(x)^2 \\ (RQ)^2-(16)^2=(x)^2 \\ \text{hence} \\ (RS)^2-(9)^2=(RQ)^2-(16)^2 \\ \text{isolate (RS)}^2 \\ (RS)^2=(RQ)^2-(16)^2+(9^2) \\ (RS)^2=(RQ)^2-175\rightarrow equation(5) \end{gathered}[/tex]b) now using equation (4) and equation(5) we can set system of 2 equations and 2 unknown values, so
[tex]\begin{gathered} (25)^2=(RS)^2+(RQ)^2\rightarrow equation(4) \\ (RS)^2=(RQ)^2-175\rightarrow equation(5) \\ replce\text{ eq(5) into equation (4)} \\ (25)^2=(RS)^2+(RQ)^2\rightarrow equation(4) \\ so \\ (25)^2=(RQ)^2-175+(RQ)^2 \\ 625+175=(RQ)^2+(RQ)^2 \\ 800=2(RQ)^2 \\ \mleft(RQ\mright)^2=\frac{800}{2} \\ (RQ)^2=400 \\ RQ=20 \end{gathered}[/tex]so
RQ=20
now, replace in equation (5) to find RS
[tex]\begin{gathered} (RS)^2=(RQ)^2-175\rightarrow equation(5) \\ (RS)^2=(20)^2-175 \\ (RS)^2=225 \\ RS=\sqrt[]{225} \\ RS=15 \end{gathered}[/tex]RS=15
finally, replace RS in equation (1) to find x
[tex]\begin{gathered} (RS)^2=(9)^2+(x)^2\rightarrow equation(1) \\ (15)^2=(9)^2+(x)^2 \\ 225-81=x^2 \\ 144=x^2 \\ \sqrt[]{144}=\sqrt[]{x^2} \\ 12=x \end{gathered}[/tex]therefore, the answer is
12 unitsI hope this helps yuo
An item has a listed price form 45. If the sale tax rate is 9?% how much is the sales tax.
In order to calculate the sales tax to 45, calculate the 9% of 45, just as follow:
(9/100)(45) = 4.05
Hence, the sales tax is $4.05
Solve the Exponential Function: [tex]x^2 * 2 - 2^x = 0[/tex]
Given the equation of the exponential function:
[tex]x^2\cdot2-2^x=0[/tex]We will solve the equation using the graph
the graph of the function is as shown in the following picture:
The solution to the equation will be the values of (x) at the point of intersection with the x-axis
As shown, there are 3 points of x-intercepts
So, the solution to the equation will be:
[tex]x=\mleft\lbrace-0.58,1,6.32\mright\rbrace[/tex]
how do I solve x without measuring it, i need help with the third question please
Answer:
Explanation:
Based on the given figure, the two angles ( 54° and x) are supplementary.
So, they add up to 180°.
54 + x =180
We subtract 54 from 180 to get the value of x:
x=180-54
Calculate
x= 126°
Therefore, the value of x is 126°.
what is the volume of the sphere with a radius of 2 inches ?
The volume of a sphere is
[tex]\text{volume}=\frac{4}{3}\pi^{}^{}r^3[/tex]Therefore,
[tex]\begin{gathered} \text{volume}=\frac{4}{3}\times3.14\times2^3 \\ \text{volume}=33.4933333333=33.49\text{ cubic inches} \end{gathered}[/tex]For each line the SLOPE between the 2 points given - simplify each fraction to prove that the lines have a CONSTANT rate of change : 1) Point T : 2) Point R : 3) Point S : 4) Slope of TR : 5) Slope of RS : 6) Slope of TS : 7) Describe the SLOPE of the line : 8) Therefore the CONSTANT RATE OF CHANGE IS ...?
the point T on the line is T(-7,6)
point R = R(-3,0)
point S = S(1,-6)
the slope of TR is
[tex]\begin{gathered} m=\frac{6-0}{-7-(-3)} \\ m=-\frac{6}{4} \\ m=-\frac{3}{2} \end{gathered}[/tex]slope of RS,
m = (0 - (-6))/(-3-1)
= - 6/4
= -3/2
slope of TS
m = (-6-6)/ 1-(-7)
= -12/ 8
= -3/2
the slope of the line or the constant rate of change is m = -3/2
These three pizzas are all the same size. Which one has the greatest number of equal pieces?
Given the following question:
It tells us that these pizzas are the same size
We are trying to find out which one of these pizza's have the greatest number of equal pieces.
For first pizza
It's cut up in four different pieces and these four pieces are equal
For the second pizza it is cut up in three different pieces and these three pieces are equal.
For the third pizza it is cut up in two pieces, these pieces are indeed equal.
Again the question is asking us which one has the GREATEST NUMBER of equal pieces
4, 3, 2
4 > 3
4 > 2
= 4
Your answer is the first pizza.
Use the graph to answer the question about discontinuity refer to image
Given the graph of the function
We will check the discontinuity of the function at x = -3
So, as shown in the graph :
as the function reach to x = -3 from the right and the left , the value of the function = -1
But at x = -3 , the function does not have a value
So, there is a discontinuity at x = -3, but can be removed if f(-3) = -1
So, the answer is : option A
There is a discontinuity that can be removed by defining f(-3) = -1
How would I solve 11 I’m confused on it I’m sorry I’m a bit slow
In order to better understand the question, let's draw an image representing the situation:
We want to find the distance x of this triangle. To do so, we can use the Pythagorean theorem, which states that the length of the hypotenuse squared is equal to the sum of each leg squared.
So we have:
[tex]\begin{gathered} 110^2=55^2+x^2 \\ 12100=3025+x^2 \\ x^2=12100-3025 \\ x^2=9075^{} \\ x=95.26\text{ ft} \end{gathered}[/tex]Rounding to the nearest tenth, we have a distance of 95.3 ft.
For #'s 12 - 13, find the area of each figure.
Using the distance(d) formula to obtain the length AB,BC,CA.
The distance formula is,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Given
[tex]\begin{gathered} A\rightarrow(5,-6) \\ B\rightarrow(-5,-3) \\ C\rightarrow(5,6) \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} AB=\sqrt{(-5-5)^2+(-3--6)^2}=\sqrt{(-10)^2+(-3+6)^2}=\sqrt{100+3^2}=\sqrt{109} \\ BC=\sqrt{(5--5)^2+(6--3)^2}=\sqrt{10^2+9^2}=\sqrt{100+81}=\sqrt{181} \\ CA=\sqrt{(5-5)^2+(6--6)^2}=\sqrt{0^2+12^2}=\sqrt{144}=12 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} AB=\sqrt{109}=10.44030\approx10.4 \\ BC=\sqrt{181}=13.45362\approx13.5 \\ CA=12 \end{gathered}[/tex]Using Heron's formula to solve for the area
[tex]\begin{gathered} Area=\sqrt{s(s-a)(s-b)(s-c)} \\ s=\frac{a+b+c}{2} \end{gathered}[/tex]where,
[tex]\begin{gathered} a=10.4 \\ b=13.5 \\ c=12 \\ \\ s=\frac{10.4+13.5+12}{2}=17.95 \end{gathered}[/tex]Therefore, the area is
[tex]undefined[/tex]Using the digits 1 to 9 at most one time each, fill in the boxes to make the equality true:
___ / ___ = ____ / ____ = ____
The complete equality will be;
⇒ 1 / 2 = 3 / 6 = 4 / 8
What is Proportional?
Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
By using the digits 1 to 9 at most one time each, fill in the boxes to make the equality true.
Now,
All the numbers from 1 to 9 are;
= 1, 2 ,3 , 4, 5, 6, 7, 8, 9
Let a proportion = 1 / 2
Hence, The equivalent ratio of 1/2 are;
= 3 / 6 and 4 / 8
Thus, The complete equality will be;
⇒ 1 / 2 = 3 / 6 = 4 / 8
Learn more about the proportion visit:
https://brainly.com/question/870035
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What is mZADB in Circle D? 57° 85.5° 28.5° 114°
We want to know the measure of the angle ADB on the circle D.
For doing so, we remember that:
• The measure of an inscribed angle is ,half ,of the measure of the arcs it intercepts.
,• The measure of an arc is ,equal ,to the measure of the central angle it generates (whose vertex is the center of the circle).
In the graph, we see that the angle ACB is inscribed, and thus, the measure of the arc AB is given by:
[tex]\hat{AB}=2m\angle ACB=2\cdot(57^{\circ})=114^{\circ}[/tex]But, the arc AB is equal to the central angle it generates, this is:
[tex]\hat{AB}=m\angle ADB=114^{\circ}[/tex]This means that the measure of ∠ADB is 114°.
A rectangular certificate has an area of 35 square inches. Its perimeter is 24 inches. What arethe dimensions of the certificate?
Explanation
Given that the area of the rectangular certificate is 35 inches and its perimeter is 24 inches. Therefore, if L represents the length of the certificate and w represents its width, therefore;
[tex]\begin{gathered} lw=35---1 \\ 2(l+w)=24---2 \end{gathered}[/tex]Therefore, we can say
[tex]l=\frac{35}{w}[/tex]We will substitute the above in equation 2
[tex]\begin{gathered} 2(\frac{35}{w}+w)=24 \\ \frac{70}{w}+2w=24 \\ multiply\text{ though by w} \\ 70+2w^2=24w \\ 2w^2-24w+70=0 \\ 2(w^2-12w+35)=0 \\ w^2-7w-5w+35=0 \\ (w-7)-5(w-7)=0 \\ (w-7)(w-5)=0 \\ w=7\text{ or w=5} \end{gathered}[/tex]Since the width must be shorter than the length therefore the width will be 5 inches.
Hence;
[tex]l=\frac{35}{5}=7[/tex]Answers:
The dimensions are:
Length = 7 inches
Width = 5 inches
Find the probability to generate a 4 digit even number from 1, 2, 3, 5.A.1/4B.1/2C.1D.0
give the following numbers
1, 2, 3, 5
we were asked to find the probability of generating a 4 digit even number from the numbers give above
recall,
Probabily = Number of possible outcome/Total number of outcomes
Number of possible outcome is = 1
Total number of outcomes is = 4
therefore,
Probability = 1/4
so the probability of generating a 4 digit even number from 1, 2, 3, 5 is 1/4
so the correct option is A which is 1/4
-4(e+6)(b+3) (-7)-8(v-7)(2n+3)65(c+d)27(3x-1)(e-f)32(-3m+1)(2b-3) (-9)5(s+7)(t+7)36(-2v+4)(m-n) (-3)4e+7e+55-4x-8-3h-2h+6h+97-5y+2+14z+3-2z-z
By using the distribution property in the following algebraic expressions, you obtain:
6) -4(e + 6) = (-4)(e) + (-4)(6) = -4e - 24
7) (b + 3)(-7) = (b)(-7) + (3)(-7) = -7b - 21
8) (2n + 3)6 = (2n)(6) + (3)(6) = 12n + 18
9) 5(c + d) = (5)(c) + (5)(d) = 5c + 5d
10) 27(3x - 1) = (27)(3x) + (27)(-1) = 81x - 27
11) (e - f)(3) = (e)(3) + (-f)(3) = 3e - 3f
where you have taken into account, that each term inside a parenthesis must be multiplied by all terms of the other facto. Furthermore, you took into account the signs multiplcation rule (+ x + = +, - x - = +, - x + = -, + x - = -), and also you mulitiplied coefficients by coefficients for cases in which you have numbers and variables.
find the missing length, assume that segments that appear to be tangent are tangent.
Since the side that measures 16 is tangent to the circle, it is perpendicular to the side that measures 12.
IT makes a right triangle.
Since it is a right triangle we can apply the Pythagorean theorem:
c^2 = a^2 + b^2
Where:
c= hypotenuse (longest side )= ?
a & b =the other 2 legs of the triangle.
Replacing:
?^2 = 12 ^2 + 16^ 2
Solve for the missing side:
?^2 = 144+256
?^2 = 400
?=√400
? = 20
The location of a point moved from (1, - 3) to (-2, -1) by translation. Find the translation rule
moved from (1, - 3) to (-2, -1)
x'= x -3
y=
2 The ratio of males to females in the class is 5 to 9. If the lunchroom has the same ratio but 45 females, how many males are in the lunchroom?
Answer:
Explanation:
From the question, we are given the ratio of males to females in the class as 5 to 9.
Total ratio = 5+9 = 14
Let the total number of student in the class be x. If there are 45 females then;
9/14 * x = 45
9x/14 = 45
Cross multiply;
9x = 14 * 45
x = 14 * 5
x = 70
Hence the total number of student in the class is 70
Get the number of male students;
Total students = Male + Female
70 = Male + 45
Male = 70-45
Male = 25
Answer:
Step-by-step explanation:
To get 45 females, you have to multiply 9 by a number. That number is 5 because 5 times 9 is 45. So what you do here is what you do with the other number, (5), so 5 times 5 is 25. That means there were 25 males in the lunchroom.
Launch Problem The barista at Kellie's Coffee needs to make 10 12-ounce iced coffees. Each iced coffee is made with 2 ounces of oat milk, 8.2 ounces of cold brew coffee and 1.8 ounces of hazelnut flavoring. How much of each ingredient will be necessary to make the order of iced coffees? 2. How many ounces of cold brew coffee will be needed to make the order of iced coffee?
we have,
for 1 iced coffee:
2 ounces of oat milk
8.2 ounces of cold brew coffee
1.8 ounces of hazelnut.
then
answer 1:
for 10 iced coffee, we will need
2 x 10 = 20 ounces of oat milk
8.2 x 10 = 82 ounces of cold brew coffee
1.8 x 10 = 18 ounces of hazelnut flavoring
answer 2:
82 ounces of cold brew coffee are needed
3/5 of a number is 18. What is the number
Let
x -----> the number
we have that
(3/5)x=18
solve for x
x=18*5/3
x=30
the number is 30Question attached!!Answer choices 1. The graph has a relative minimum 2. The graph of the quadratic function has a vertex at (0,5)3. The graph opens up 4. The graph has one x- intercept 5. The graph has a y-intercept at (5,0)6. The axis of symmetry is x=0
Consider the following table:
this table represents the following graph:
According to this graph (parabola), and remembering that an absolute minimum is also a relative minimum:
we can conclude that the correct answer is:
Answer:1. The graph has a relative minimum 2. The graph of the quadratic function has a vertex at (0,5)3. The graph opens up 6. The axis of symmetry is x=0Graph the following Y=x-4
Ok, so
We want to find the line:
[tex]y=x-4[/tex]First, remember that a line can be described with the following formula:
[tex]y=mx+b[/tex]Where "m" is its slope and b is its y-intercept.
Based in our equation, we got that m = 1 and b = - 4. So, we have a line with slope = 1, and y-intercept = -4.
To graph it, we have to take two points that lie on the line, and join them. We already know that the line has y-intercept at ( 0 , -4 ), so that's one point.
To find the other point, we could make y = 0 to find the x-intercept as follows:
[tex]\begin{gathered} y=x-4 \\ x-4=0 \\ x=4 \end{gathered}[/tex]Now, we have the x-intercept at (4 , 0) so that's other point.
We join both points:
So that's the graph for y = x-4.
Answer:
Step-by-step explanation:
1. When x is 0, y=-4, so plot the point (0,4) on the graph.
2. When y is 0, x=4, so plot the point (4,0) on the graph.
3. Draw a line between them and you're done.
Are the angles congruent If yes, how do you know?
From the given diagram, notice that DE is congruent to AB, EC is congruent to BC and the angles ABC and DEC are congruent.
Since two sides of the triangles and the included angle are congruent, we know from the SAS congruence theorem that ABC and DEC are congruent.
Therefore, the answer is: yes, the triangles ABC and DEF are congruent due to the SAS theorem.
7. Write an equation and solve. Round to the nearest hundredth where necessary.
19 is what percent of 40?
Answer:
47.5%
Step-by-step explanation:
Find the inverse of the function below and sketch by hand a graph of both the function and is inverse on the same coordinate plane. Share all steps as described in the lesson to earn full credit. Images of your hand written work can be uploaded. f(x)=(x+3)^2 with the domain x \geq-3
In order to find the inverse of f(x), let's switch x by f^-1(x) and f(x) by x in the function, then we solve the resulting equation for f^-1(x).
So we have:
[tex]\begin{gathered} f(x)=(x+3)^2 \\ x=(f^{-1}(x)+3)^2 \\ \sqrt[]{x}=f^{-1}(x)+3 \\ f^{-1}(x)=-3+\sqrt[]{x} \end{gathered}[/tex](The domain of f(x) will be the range of f^-1(x), so the range of f^-1(x) is y >= -3)
In order to graph the function and its inverse, we can use some points that are solutions to each one.
For f(x), let's use (-3, 0), (-2, 1) and (-1, 4).
For f^-1(x), let's use (0, -3), (1, -2) and (4, -1).
Graphing f(x) in red and f^-1(x) in blue, we have:
Graphing it manually, we have:
Wallpaper was applied to one rectangular wall of a large room. The dimensions of the wall are shown below. I will send the graph.
Given:
Wallpaper was applied to one rectangular wall of a large room. The dimensions of the wall is 42 feet and 25.5 feet.
Total cost of wallpaper was $771.12
Required:
What was the cost, in dollars, of the wallpaper per square feet.
Explanation:
We know the area of rectangle is length multiplied by breadth.
Here, we have
[tex]\begin{gathered} A\text{rea of wall =}42\times25.5 \\ =1071 \end{gathered}[/tex]Now,
The cost of wallpaper per square feet is
[tex]\begin{gathered} =\frac{771.12}{1071} \\ =0.72 \end{gathered}[/tex]Answer:
Hence, $0.72 is the answer.
match the blanks to their missing phrases to complete the proof
blank A: a^2 + b^2 = c^2
blank B: Definition of unit circle
blank C: sin θ = y/1 = y
Explanation:
In order to prove the identity given, we first start with Pythagoras's theorem
[tex]a^2+b^2=c^2[/tex]which is blank a.
Next, we apply the theorem to the circle to get
[tex]x^2+y^2=r^2[/tex]then we make the substitutions.
Since it is a unit circle r = 1 (blank B) and using trigonometry gives
[tex]\cos \theta=\frac{x}{r}=\frac{x}{1}=x[/tex][tex]\boxed{x=\cos \theta}[/tex]and
[tex]\sin \theta=\frac{y}{r}=\frac{y}{1}=y[/tex][tex]\boxed{y=\sin \theta}[/tex]which is blank C.
With the value of x, y and r in hand, we now have
[tex]x^2+y^2=1[/tex][tex]\rightarrow\sin ^2\theta+\cos ^2\theta=1[/tex]Hence, the identity is proved.
-2x - 14 =-2(Solve for x)
Explanation
[tex]-2x-14=-2[/tex]Step 1
add 14 in both sides,
[tex]\begin{gathered} -2x-14=-2 \\ -2x-14+14=-2+14 \\ -2x=12 \end{gathered}[/tex]Step 2
divide both sides by -2
[tex]\begin{gathered} -2x=12 \\ \frac{-2x}{-2}=\frac{12}{-2} \\ x=-6 \end{gathered}[/tex]I Hope this helps you