In the expression 3/3=_/21, it can be observed that 7 is multipled by denominator 3 in order to obtain 21 in in denominator. So same number, 7 is also multiplied with the numerator also.
[tex]\frac{3}{3}\times\frac{7}{7}=\frac{21}{21}[/tex]So, 21 is to be filled at blank space.
What is the value of f(-5) in the piecewise function -3x + 1 when x > 1 f(x) = -2x when x = 1 2x - 1 when x < 1
Answer:
f(-5)=-11
Explanation:
Given the piecewise function:
[tex]f(x)=\begin{cases}{-3x+1,\text{ when }x>1} \\ {-2x,\text{ when }x=1} \\ {2x-1,\text{ when }x<1}\end{cases}[/tex]We want to find the value of f(-5).
When x=-5:
[tex]\begin{gathered} -5<1\implies f(x)=2x-1 \\ \text{ Therefore:} \\ f(-5)=2(-5)-1 \\ =-10-1 \\ =-11 \end{gathered}[/tex]The value of f(-5) is -11.
How many triangles can be formed by joining the vertices of a 10-sided polygon?
The total number of triangles formed by joining vertices of 10-sided polygon is given by the combination of 10 sides taken at 3, i.e. selection of 3 points from 10 points ( because a triangle has 3 vertices). This gives
[tex]10C3=\frac{10!}{3!(10-3)!}=\frac{10!}{3!\cdot7!}=\frac{10\cdot9\cdot8}{6}=\frac{720}{6}=120[/tex]Then, the answer is the last option: 120
Show that (3 * 8 * x)⁷ = 6⁷ * 4⁷ * x⁷
Answer:
Q.E.D.
Explanation:
Given the expression
[tex](3\times8\times x)^7[/tex]We want to show that it is equal to the right-hand side.
Now, we note that: 8 = 2 x 4
Substituting 8 = 2 x 4, we have:
[tex]=(3\times2\times4\times x)^7[/tex]We then go further to get:
[tex]=(6\times4\times x)^7[/tex]Distributing the exponent, we have:
[tex]=6^7\times4^7\times x^7[/tex]This is the given right-hand side of the equation as required.
Consider the following relation: (1,12) ,(3, 8) , (3, 11) , (6, 9) , (7, 11) . Whichordered pair could be removed so thatthe relation is a function?Group of answer choices
Answer: Rajesh Kumar
Step-by-step explanation I took the wok to poland
A couple of friends decide to race each other. Emmet can run 6 yards per second, whereas Ayana can run 9 yards per second. Because he is slower, Emmet also gets a head start of 30 yards. Shortly after they start running, Ayana will catch up to Emmet. How far will Ayana have to run?Write a system of equations, graph them, and type the solution.
We know the formula d=rt where d is distance, r is rate and t is time
Emmet:
d = 6 yd/s * t
Ayana:
d = 9 yd/s * t
We give Emmet 30 less yards to run
Emmet:
d - 30 = 6 yd/s * t
d = 6t + 30
Setting the equations equal to each other
9 * t = 6t + 30
Subtract 6t from each side
9t-6t = 30
3t = 30
Divide by 3
3t/3 = 30/3
t = 10 seconds
It will take 10 seconds for Ayana to catch up
Ayana:
d = 9 yd/s * t
d = 8 * 10 = 90 yds
Jason provided the following work when asked to convert 0.105 to its
simplest fraction form.
1. Why did Jason get the problem wrong?
2. Provide the work for properly writing the decimal in its simplest fraction
form.
Jason's Work:
0.105=
105/1000
21/200
Jason provided the work when asked to convert 0.105 to its simplest fraction form which is; 21/200
How to convert from decimal to fraction?For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. To get the decimal of the form a.bcd, we will count the digits that are there after the decimal point; then we write 10 raised to that many power as the denominator and the considered number without any decimal point as the numerator.
Given that Jason's Work:
0.105
Jason provided the work when asked to convert 0.105 to its simplest fraction form which could be;
0.105 = 105/1000
= 21/200
Hence, Jason provided the work when asked to convert 0.105 to its simplest fraction form which is; 21/200
Learn more about fractions;
https://brainly.com/question/729654
#SPJ1
8+7t=22 in verbal sentence
Eight plus Seven times t equals twenty-two
Explanation
Step 1
Let
a number= t
seven times a number= 7t
the sum of eigth and seven times a number=8+7t
the sum of eigth and seven times a number equals twenty-two=8+7t=22
or,in other words
Eight plus Seven times t equals twenty-two
I hope this helps you
Just give me the answer please, my device is at 10%
Solve for x
We can use sine
[tex]\begin{gathered} \sin 48^0=\frac{x}{17} \\ \text{Cross multiply} \\ x=17\times\sin 48^0 \\ x\text{ =17}\times0.7431448 \\ x=12.6\text{ } \end{gathered}[/tex]What is the gcf of 16 and 28
Answer:
4
Step-by-step explanation:
why is 10'15 equal to 10'11? explain ur thinking. ___ 10'4
Exponent rule is the following:
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex][tex]\text{Therefore, if for }\frac{10^{15}}{10^4}\text{ a is 15 and b is 4, therefore:}[/tex][tex]\frac{10^{15}}{10^4}=10^{15-4}[/tex][tex]So,\text{ }10^{\mleft\{15-4\mright\}}=10^{11}[/tex]Quadratic Factoring: Demonstrate solving some quadraticequations using the following methods: factoring, taking theroot, and completing the square.
The Solution:
Let's solve with the Factoring Method:
[tex]x^2-x-6=0[/tex][tex]\begin{gathered} x^2-3x+2x-6=0 \\ x(x-3)+2(x-3)=0 \\ (x+2)(x-3)=0 \end{gathered}[/tex][tex]\begin{gathered} x+2=0\text{ or }x-3=0 \\ x=-2\text{ or }x=3 \end{gathered}[/tex]Solving by the Completing the Square:
[tex]\begin{gathered} x^2-x=6 \\ x^2-x+(\frac{1}{2})^2=6+\frac{1}{4} \\ \\ (x-\frac{1}{2})^2=\frac{25}{4} \end{gathered}[/tex]Take the square root of both sides.
[tex]\begin{gathered} x-\frac{1}{2}=\sqrt{(\frac{25}{4})} \\ \\ x=\frac{1}{2}\pm\frac{5}{2}=\frac{1\pm5}{2} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{1+5}{2}=\frac{6}{2}=3 \\ \\ \\ x=\frac{1-5}{2}=\frac{-4}{2}=-2 \end{gathered}[/tex]Therefore, the answers is:
[tex]x=-2\text{ or }x=3[/tex]Angel Corporation produces calculators selling for $25.99. Its unit cost is $18.95. Assuming a fixed cost of $80,960, what is the breakeven point in units?
The breakeven point of Angel Corporation equals to 11,500 units.
How do we get the breakeven point?Given that the unit price is $25.99, so if they sell a x units, then, the revenue is: R(x) = $25.99*x
Given that the cost per unit is $18.95, plus a fixed cost of $80,960, then, the cost of x units is: C(x) = $80,960 + $18.95*x
Now, the breakeven point is a value of x such that the cost is equal to the revenue, so we need to solve:
$25.99*x = $80,960 + $18.95*x
$25.99*x - $18.95*x = $80,960
$7.04*x = $80,960
x = $80,960/$7.04
x = 11,500 units
Read more about breakeven point
brainly.com/question/9212451
#SPJ1
for each of the following polynomial functions, write the equation of a different polynomial function that has the same key characteristic. explain your thinking.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Draw the given graph.
STEP 2: Get the function plotted on the graph.
[tex]undefined[/tex]use the half angle identity to find the exact value of the trigonomic expression. given 0
Given a right angle triangle:
we need to find the measure of the angle θ
As shown:
The opposite side to the angle θ = 24
The adjacent side to the angle θ = 45
So,
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent}=\frac{24}{45} \\ \\ \theta=\tan ^{-1}\frac{24}{45}=28.0725 \\ \\ \sin \frac{\theta}{2}=\sin \frac{28.0725}{2}=\sin 14.036=0.2425 \end{gathered}[/tex]so, the answer will be sin θ/2 = 0.2425
Solve for x. Write the reasons next to each step.Submit723x+10
x = 26/3
Explanation:We would apply the mid-segment theorem:
The base of the smaller triangle = 1/2 (the base of the bigger triangle)
The base of the smaller triangle = 3x + 10
the base of the bigger triangle = 72
3x + 10 = 1/2(72)
Reason: Mid segment is parallel to the base of the large triangle. And it is equal to half the length of the base of the large triangle
simplifying:
3x + 10 = 72/2
3x + 10= 36
subtract 10 from both sides:
3x + 10 - 10 = 36 - 10
3x = 26
DIvide both sides by 3:
3x/3 = 26/3
x = 26/3
or x = 8 2/3
In the accompanying diagram of circle O, COA is adiameter, O is the origin, OA = 1, and mLBOA = 30. Whatare the coordinates of B?
Given:
COA is a diameter
O is the origin
OA = 1
m< BOA = 30
Re-drawing the diagram to show the coordinates of the B:
Let the coordinates of B be (x,y)
Using trigonometric ratio, we can find the length of side AB
From trigonometric ratio, we have:
[tex]tan\text{ }\theta\text{ = }\frac{opposite}{adjacent}[/tex]Substituting we have:
[tex]\begin{gathered} tan\text{ 30 = }\frac{y}{1} \\ Cross-Multiply \\ y\text{ = tan30 }\times\text{ 1} \\ y\text{ = 0.577} \\ y\text{ }\approx\text{ 0.58} \end{gathered}[/tex]Hence, the coordinates of B is (1, 0.58)
(−1/2x+7/10)−(−3/4x−1/5)
The expression (−1/2x + 7/10) − (−3/4x − 1/5) has a value of 1/4x + 9/10 when simplified
How to evaluate the expression?From the question, the expression is given as
(−1/2x+7/10)−(−3/4x−1/5)
Rewrite the expression properly to make it legible
So, we have
(−1/2x + 7/10) − (−3/4x − 1/5)
Expression the above parameter as an equation
This is represented as
(−1/2x + 7/10) − (−3/4x − 1/5) = (−1/2x + 7/10) − (−3/4x − 1/5)
Open the brackets
So, we have the following equation
(−1/2x + 7/10) − (−3/4x − 1/5) = −1/2x + 7/10 + 3/4x + 1/5
Collect the like terms in the equation
(−1/2x + 7/10) − (−3/4x − 1/5) = 3/4x − 1/2x + 7/10 + 1/5
Evaluate
(−1/2x + 7/10) − (−3/4x − 1/5) = 1/4x + 9/10
The expression cannot be further simplified
Hence, the solution to the expression (−1/2x + 7/10) − (−3/4x − 1/5) is 1/4x + 9/10
Read more about expression at
https://brainly.com/question/723406
#SPJ1
I really need help solving thisIt’s from my trig prep bookIt asks to answer (a) and (b)
The sum in summation notation is:
[tex]\sum ^4_{r\mathop{=}0}(-1)^r(4Crx^{4-r}y^r)[/tex]The expansion is:
[tex]81x^{20}-12x^{15}y^3+\frac{2}{3}x^{10}y^6-\frac{4}{243}x^5y^9+\frac{1}{6561}y^{12}[/tex]Explanation:Given the expression:
[tex](3x^5-\frac{1}{9}x^3)^4[/tex]In summation notation, this can be written as:
[tex]\sum ^4_{r\mathop=0}(-1)^r(4Crx^{4-r}y^r)[/tex]The simplified terms of the expression is:
[tex]\begin{gathered} 4C0(3x^5)^{\mleft\{4-0\mright\}}(\frac{1}{9}y^3)^0-4C1(3x^5)^{\mleft\{4-1\mright\}}(\frac{1}{9}y^3)^1+4C2(3x^5)^{\mleft\{4-2\mright\}}(\frac{1}{9}y^3)^2-4C3(3x^5)^{\mleft\{4-3\mright\}}(\frac{1}{9}y^3)^3+4C4(3x^5)^{\mleft\{4-4\mright\}}(\frac{1}{9}y^3)^4 \\ \\ =(3x^5)^4-4(3x^5)^3(\frac{1}{9}y^3)+6(3x^5)^2(\frac{1}{9}y^3)^2-4(3x^5)^{}(\frac{1}{9}y^3)^3+(\frac{1}{9}y^3)^4 \\ \\ =81x^{20}-12x^{15}y^3+\frac{2}{3}x^{10}y^6-\frac{4}{243}x^5y^9+\frac{1}{6561}y^{12} \end{gathered}[/tex]Based on the two data sets represented below, complete the following sentences.Options: "greater" or "less"
We can check that the median of the dataset T is 14, and its mean is also close to 14, while the median of the dataset U is 17 and its mean is close also close to 17. We can also check that the range of the dataset T is 14 and the data is more concentrated at its center, while the range of the dataset U is 20 and the data is more dispersed.
Therefore, we can state that The center of Data Set T is less than the center of Data Set U, and the spread of Data Set T is less than the spread of Data Set U.
how do we do this one there two parts to i t
Given:
[tex]8\sqrt{y}=x-5y[/tex]Find: differentiation
Explanation: on differentitaion with respect to x
[tex]\begin{gathered} 8\sqrt{y}=x-5y \\ \frac{8}{2}y^{\frac{-1}{2}}\frac{dy}{dx}=1-5\frac{dy}{dx} \\ 4y^{\frac{-1}{2}}\frac{dy}{dx}+5\frac{dy}{dx}=1 \\ (4y^{\frac{-1}{2}}+5)\frac{dy}{dx}=1 \\ \frac{dy}{dx}=\frac{1}{4y^{\frac{-1}{2}}+5} \end{gathered}[/tex][tex]\begin{gathered} \frac{-4}{2}y^{\frac{-3}{2}}\frac{dy}{dx}\frac{d^2y}{dx^2}+5\frac{d^2y}{dx^2} \\ 0=(-2y^{\frac{-3}{2}}\frac{dy}{dx}+5)\frac{d^2y}{dx^2} \\ \frac{d^2y}{dx^2}=0 \end{gathered}[/tex]put the value of
[tex]\frac{dy}{dx}[/tex]we get,
[tex]\begin{gathered} (-2\frac{y^{\frac{-3}{2}}}{4y^{\frac{-1}{2}}+5}+5)\frac{d^2y}{dx^2}=0 \\ \frac{d^2y}{dx^2}=0 \end{gathered}[/tex]Quantum Logic recently expanded its operations at a cost of $450,000. Management expects that the value of the investment will grow at a rate of 8% per year compounded quarterly for the next 5 years. Find the future value of the investment
Given:
Quantum Logic recently expanded its operations at a cost of $450,000.
So, P = 450,000
The rate of growth = r = 8% = 0.08
compounded quarterly, n = 4
We will find the future value of the investment (A) after t = 5 years
We will use the following formula:
[tex]A=P\cdot(1+\frac{r}{n})^{nt}[/tex]Substitute with the given values:
[tex]\begin{gathered} A=450,000\cdot(1+\frac{0.08}{4})^{4\cdot5} \\ \\ A=450,000\cdot1.02^{20}\approx668,676.33 \end{gathered}[/tex]So, the answer will be:
The future investment = $668,676.33
Order the following from least to greatest: 0.232, 1.2, 1.09, 0, 3, 0.9
Answer:
0, 0.232 , 0.9 , 1.09, 1.2 , 3
the length of a rectangle is 13 centimeters less then four times it’s width it’s area is 35 centimeters find the dimensions of the rectangle
Solution:
The area of a recatngle is expressed as
[tex]\begin{gathered} \text{Area of rectangle = L}\times W \\ \text{where} \\ L\Rightarrow\text{length of the rectangle} \\ W\Rightarrow\text{ width of the rectangle } \end{gathered}[/tex]Given that the length of the rectangle is 13 centimeters less than four times its width, this implies that
[tex]L=4W-13\text{ ---- equation 1}[/tex]Tha area of the rectangle is 35 square centimeters. This implies that
[tex]36=L\times W\text{ --- equation 2}[/tex]Substitute equation 1 into equation 2. Thus,
[tex]\begin{gathered} 36=L\times W \\ \text{where} \\ L=4W-13 \\ \text{thus,} \\ 36=W(4W-13) \\ open\text{ parentheses} \\ 36=4W^2-13W \\ \Rightarrow4W^2-13W-36=0\text{ ---- equation 3} \\ \end{gathered}[/tex]Solve equation 3 by using the quadratic formula expressed as
[tex]\begin{gathered} W=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}_{} \\ \text{where} \\ a=4 \\ b=-13 \\ c=-36 \end{gathered}[/tex]thus, we have
[tex]\begin{gathered} W=\frac{-(-13)\pm\sqrt[]{(-13)^2-(4\times4\times-36)}}{2\times4}_{} \\ =\frac{13\pm\sqrt[]{169+576}}{8} \\ =\frac{13\pm\sqrt[]{745}}{8} \\ =\frac{13}{8}\pm\frac{\sqrt[]{745}}{8} \\ =1.625\pm3.411836016 \\ \text{thus,} \\ W=5.036836016\text{ or W=}-1.786836016 \end{gathered}[/tex]but the width cannot be negative. thus, the width of the recangle is
[tex]W=5.036836016[/tex]From equation 1,
[tex]\begin{gathered} L=4W-13 \\ \end{gathered}[/tex]substitute the obtained value of W into equation 1.
Thus, we have
[tex]\begin{gathered} L=4W-13 \\ =4(5.036836016)-13 \\ =20.14734-13 \\ \Rightarrow L=7.14734 \end{gathered}[/tex]Hence:
The width is
[tex]5.036836016cm[/tex]The length is
[tex]7.14734cm[/tex]which of the following describes the two spheres A congruentB similarC both congruent and similarD neither congruent nor similar
The two spheres are similar since they have a proportion of their radius. This proportion is 9/6 (3/2) or 6/9 (2/3).
They are not congruent. They do not have the same radius.
Therefore, the spheres are similar.
Y=1/3x+2 standard form
3y - x = 6 is standard form for the given equation
What is standard form of linear equation ?The typical form for linear equations with two variables is Ax+By=C.For instance, the linear equation 2x+3y=5 is in standard form. Finding both intercepts of an equation in this style is quite easy (x and y).This form is also very useful when trying to solve systems of two linear equations.Calculationy = 1/3x + 2
3y = x + 6
3y - x = 6 is standard form
learn more about standard form of linear equation here :
brainly.com/question/17264364
#SPJ4
Mike made $120 last week working d days. Express the amount he made each day in terms of d.
Since he made $120 in d days
To find his earn in eac
Hello, may I please have some help with this question. Thank you.
The total distance that Kim walked in 3 days is 6 2/3 miles. We would convert this distance to mixed numbers. To do this, we would multiply 6 by 3 and add 2. The denominator would still be 3. It becomes
20/3 miles
If she walked 20/3 miles in 3 days, the number of miles that she walked per day would be
total distance/number of days
It becomes
(20/3) / 3
If we change the division sign to multiplication, it means that we would flip 3 such that it becomes 1/3. Thus, we have
20/3 * 1/3 = 20/9
= By converting to mixed numbers, we would find how many 9's are in 20. It is 2. The remainder is 20 - 18 = 2
Thus, the answer is
2 2/9 miles per day
16 1 point
Triangle congruence SSS is being shown?
True
False
|||
+||
Answer:
True
Step-by-step explanation:
SSS is being shown because the two sides are known by congruence marks, and the third side is known because it is equal--the two triangles are sharing it.
Use the graphs below to help you answer the question.
Which of the following is the best approximation to a solution of the equation e* = 4x+1?
A. 10
B. 2
C. 3
D. 1
Answer:
I would say the answer is D.
Step-by-step explanation:
If you solve for x you get 1/4.
In decimal form that is 0.4
write a linear equation to: slope=2 and goes through point (4, 11)
When you have to write a linear equation and you have the slope (m) and a point (4, 11) you:
1. Use the standard form of a linear equation:
[tex]y=mx+b[/tex]You know the value of:
m= 2
y= 11
x= 4
You make a substitution:
[tex]11=(2)(4)+b[/tex]You can find then the value of b:
[tex]11=8+b[/tex][tex]b=11-8=3[/tex]Then you have now the data to form the final linear equation:
[tex]y=2x+3[/tex]