Given the following question:
[tex]\sqrt[3]{1000}[/tex][tex]\begin{gathered} \sqrt[3]{1000} \\ \sqrt[3]{1000}=\sqrt[3]{10^3} \\ 10^3=1000 \\ \sqrt[3]{10^3} \\ \sqrt[n]{a^n}=a \\ \sqrt[3]{10^3}=10 \\ =10 \end{gathered}[/tex]Your answer is 10.
Angles A and B are adjacent on a straight line. Angle A has a measure of (2r +20) and angle B has a measure of 130.. What is the measure of r?
When two angles are adjacent on a straight line, then the sum of the two angles equals 180 (that is sum of angles on a straight line). Therefore;
[tex]\begin{gathered} (2r+20)+130=180 \\ \text{Subtract 130 from both sides and you'll have} \\ 2r+20=50 \\ \text{Subtract 20 from both sides and you'll have} \\ 2r=30 \\ \text{Divide both sides by 2 and you'll have} \\ r=15 \end{gathered}[/tex]The measure of r is 15
Solve the inequality. Express your answer using set notation or interval notation. Graph the solution set.
Answer:
(D) {xIx ≥ 5} or [5, ∞)
Explanation:
Given inequality: 5x - 11 ≥ 9 + x
By collecting the like terms, we have
5x - x ≥ 9 + 11
4x ≥ 20
Divide bothsides by 4
4x/4 ≥ 20/4
x ≥ 5
In set notation, we have {5, ∞}
The graph of the solution set is
RATIONAL FUNCTIONSSynthetic divisiontable buand write your answer in the following form: Quotient *
The given polynomial is:
[tex]\frac{2x^4+4x^3-6x^2+3x+8}{x\text{ + 3}}[/tex]Using the long division method:
The equattion can be written in the form:
Quotient + Remainder / Divisor
[tex](2x^3-2x^2\text{ + 3) +}\frac{-1}{x+3}[/tex]Trini bought some jeans that she had been saving up for. She purchased them for $88 but has wornthem 4 times already. So far, what is the cost of wear for the jeans?
In order to find the cost of wear for the jeans, we just need to divide the cost of the jeans by the number of times Trini worn it.
So we have:
[tex]\frac{88}{4}=22[/tex]Therefore the cost of wear so far is $22.
Which fraction is less than 3/5 is it 5/7, 9/15, 4/6, 7/12
Answer: 7/12
Step-by-step explanation:
3/5=0.6
5/7=0.71428571428
9/15=0.6
4/6=0.66666
7/12=0.583333
Answer: 7/12
Step-by-step explanation:
I have attached my work.
27. If figure A and figure B are similar with a ratio of similarity of 2, and the perimeter of figure A is 28 units,what is the perimeter of figure B?
SOLUTION
Since the two shapes are similar, that is A and B similar with a ratio of 2, then we have that
[tex]\begin{gathered} \frac{length\text{ A}}{lemgth\text{ B}}=\frac{2}{1}=\frac{perimeter\text{ A}}{perimeter\text{ B}} \\ \frac{2}{1}=\frac{perimeter\text{ A}}{perimeter\text{ B}} \\ \frac{2}{1}=\frac{28}{perimeter\text{ B}} \end{gathered}[/tex]Cross multiplying we have
[tex]\begin{gathered} 2Perimeter\text{ B = 28} \\ Perimeter\text{ B = }\frac{28}{2} \\ =14\text{ units } \end{gathered}[/tex]hence the answer is 14 units
sketch the graph of and identify the axis of symmetry
Given the following equation:
[tex]y=(x-1)^2+2[/tex]We will sketch the graph and identify the axis of symmetry.
the given function is a quadratic function with a vertex at (1, 2)
the graph of the function will be as follows:
As shown, the graph of the function has an axis of symmetry at x = 1
So, the answer will be option 3) x = 1
Find the area and the perimeter of the following rhombus. round to the nearest whole number if needed.
ANSWER
[tex]\begin{gathered} A=572 \\ P=96 \end{gathered}[/tex]EXPLANATION
To find the area of the rhombus, we have to first find the length of the other diagonal.
We are given half one diagonal and the side length.
They form a right angle triangle with half the other diagonal. That is:
We can find x using Pythagoras theorem:
[tex]\begin{gathered} 24^2=x^2+16^2 \\ x^2=24^2-16^2=576-256 \\ x^2=320 \\ x=\sqrt[]{320} \\ x=17.89 \end{gathered}[/tex]This means that the length of the two diagonals is:
[tex]\begin{gathered} \Rightarrow2\cdot16=32 \\ \Rightarrow2\cdot17.89=35.78 \end{gathered}[/tex]The area of a rhombus is given as:
[tex]A=\frac{p\cdot q}{2}[/tex]where p and q are the lengths of the diagonal.
Therefore, the area of the rhombus is:
[tex]\begin{gathered} A=\frac{32\cdot35.78}{2} \\ A=572.48\approx572 \end{gathered}[/tex]The perimeter of a rhombus is given as:
[tex]P=4L[/tex]where L = length of side of the rhombus
Therefore, the perimeter of the rhombus is:
[tex]\begin{gathered} P=4\cdot24 \\ P=96 \end{gathered}[/tex]What is the value of x in the proportion2 1/4 = 1 1/2_________x = 3 3/5A. 2 2/5B. 5 2/5C. 8 1/10D. 12 3/20
First, we transform the mixed fractions
[tex]\begin{gathered} 2\frac{1}{4}=2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4} \\ 1\frac{1}{2}=1+\frac{1}{2}=\frac{2}{2}+\frac{1}{2}=\frac{3}{2} \\ 3\frac{3}{5}=3+\frac{3}{5}=\frac{15}{5}+\frac{3}{5}=\frac{18}{5} \end{gathered}[/tex]Then, we use cross multiplication
[tex]\begin{gathered} \frac{\frac{9}{4}}{x}=\frac{9}{4}\times\frac{1}{x}=\frac{9}{4x} \\ \frac{\frac{5}{2}}{\frac{18}{5}}=\frac{3}{2}\times\frac{5}{18}=\frac{15}{36} \end{gathered}[/tex]so, we have
[tex]\frac{9}{4x}=\frac{15}{36}[/tex]Finally, we solve for x, we multiply x on both sides
[tex]\begin{gathered} \frac{9}{4x}x=\frac{15}{36}x \\ \frac{15}{36}x=\frac{9}{4} \\ x=\frac{\frac{9}{4}}{\frac{15}{36}} \\ x=\frac{9}{4}\times\frac{36}{15} \\ x=\frac{9\times9\times4}{15\times4} \\ x=\frac{81}{15} \\ x=\frac{27}{5} \end{gathered}[/tex]Since 27/5 = 5+2/5.Then,
[tex]x=5\frac{2}{5}[/tex]Then the answer is the second one.
Margo borrows $1200, agreeing to pay it back with 4% annual interest after 17 months. How much interest will she pay?
Answer:
$68
Step-by-step explanation:
P = $1200
R = 4%
T = 17months (Convert to years; 17 months ÷ 12 months)
Formular for Interest; I = PRT
100
I = $1200 × 4 × 17
100 × 12
I = $68
Two segments of Parallelogram ABCD are shown below.  Which coordinate pair BEST represents the location of Point D, the fourth vertex of Parallelogram ABCD? A. (6, 1) B. (7, 0) C. (8,2) D. (7,1)
Given coordinates of A(2,-1), B(1,3), C(6,5)
Let the coordinates of D(x,y)
Let join AC and BD:
SO by mid point rule:
Coordinates of midpoint by AC are:
[tex](\frac{2+6}{2},\text{ }\frac{-1+5}{2})\rightarrow(4,2)[/tex]And the midpoint of BD are same as AC:
[tex]\begin{gathered} \frac{1+x}{2}=4 \\ 1+x=8 \\ x=7 \end{gathered}[/tex][tex]\begin{gathered} \frac{3+y}{2}=2 \\ 3+y=4 \\ y=4-3 \\ y=1 \end{gathered}[/tex]hence the coordinates of D are (7,1)
Option D is correct.
The rate of growth of a particular population is given by dP/dt=50t^2-100t^3/2, where P is population size and t is fine and years. Assume the initial population is 25,000. a) determine the population function, P(t)b) estimate to the nearest year how long it will take for the population to reach 50,000
SOLUTION
Step1: write out the giving equation
[tex]\frac{dp}{dt}=50t^2-100t^{\frac{3}{2}}[/tex]Step2: Integrate both sides of the equation above
[tex]\int \frac{dp}{dt}=\int 50t^2dt-\int 100t^{\frac{3}{2}}dt[/tex]Then simplify by integrating both sides
[tex]p(t)=\frac{50t^{2+1}}{2+1}-\frac{100t^{\frac{3}{2}+1}}{\frac{3}{2}+1}+c[/tex][tex]p(t)=\frac{50}{3}t^3-40t^{\frac{5}{2}}+c[/tex]since the initial value is 25,000, then
the Population function is
[tex]\begin{gathered} p(t)=\frac{50}{3}t^3-40t^{\frac{5}{2}}+25000\ldots\ldots..\ldots\text{.. is the population function} \\ \text{where t=time in years} \end{gathered}[/tex]b). For the population to reach 50,000 the time will be
[tex]\begin{gathered} 50000=\frac{50}{3}t^3-40t^{\frac{5}{2}}+2500 \\ 50000-25000=\frac{50}{3}t^3-40t^{\frac{5}{2}} \\ 25000=\frac{50}{3}t^3-40t^{\frac{5}{2}} \\ \text{Then} \\ \frac{50}{3}t^3-40t^{\frac{5}{2}}-25000=0 \\ \end{gathered}[/tex]Multiply the equation by 3, we have
[tex]\begin{gathered} 50t^3-120t^{\frac{5}{2}}-75000=0 \\ \end{gathered}[/tex]To solve this we rewrite the function as
[tex]14400t^5=\mleft(-50t^3+75000\mright)^2[/tex]The value of t becomes
[tex]\begin{gathered} t\approx\: 15.628,\: t\approx\: 9.443 \\ t=15.625\text{ satisfy the equation above } \end{gathered}[/tex]Then it will take approximately
[tex]16\text{years}[/tex]
In 2019, the USDA reported that acreage for wheat was approximately 45.6 million acres;this is down 5% from 2018. Which of the following can you conclude?a) The 2018 wheat acreage was 47.88 million acres.b) The 2018 wheat acreage was 48.0 million acres.c) The 2019 wheat acreage was 43.43 million acres.d) The 2019 wheat acreage was 43.32 million acres.
Given that the USDA reported the acreage for wheat in 2019 was approximately 45.6 million acres; and was down 5% from 2018. We were asked to pick an option that would represent the right conclusion to the given statement.
To do this, we would assume that the acreage for wheat in 20 18 is x. Since 2018 differs from 2019 by 5%
This implies that the representation of 2019 acreage would be;
[tex]100\text{\%-5\%=95\%}[/tex]Therefore, we can have
[tex]\begin{gathered} \frac{95}{100}\times x=45.6 \\ \text{Cross multiply} \\ 95x=45.6\times100 \\ \text{Divide both sides by 95} \\ \frac{95x}{95}=\frac{45.6\times100}{95} \\ x=48 \end{gathered}[/tex]Therefore the 2018 acreage was;
Answer: Option B
simplifying with like terms; 2(m+10)
In order to simplify the expression, we would multiply the terms inside the bracket by the term outside. It becomes
2 * m + 2 * 10
= 2m + 20
A cylinder whose height is 3 times its radius is inscribed in a cone whose height is 6 times its radius. What fraction of the cone's volume lies inside the cylinder? Express your answer as a common fraction.
The fraction of the cone's volume that lies inside the cylinder would be; V = 44/21 r^4
How to find the volume of a right circular cone?Suppose that the radius of the considered right circular cone is 'r' units.
And let its height be 'h' units. The right circular cone is the cone in which the line joining the peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.
Then, its volume is given :
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
Let the radius of the cylinder is r
The height of the cylinder is h = 3r
The height of the cone is h = 6r
The fraction of the cone's volume that lies inside the cylinder would be;
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
[tex]V = \dfrac{1}{3} \times 3.14 \times r^3 \times 6r \: \rm unit^3[/tex]
V = 44/21 [tex]r^{4}[/tex]
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Answer:
4/9
Step-by-step explanation:
is there one solution to the following system of equations by elimination 3x + 2y equals 3 3x + 2y equals 19
3x+2y= 3 (a)
3x+2y= 19 (b)
Subtract (b) to (a) ; elimination method.
3x+ 2y = 3
-
3x+2y= 19
_________
0 = 19
Since both variables were eliminated, the system has no solutions.
option c.
X-1 what is the answer
Answer:
x - 1 = x - 1
Step-by-step explanation:
If you were expecting a singular solution, you won’t get it. You’ll likely instead get a lot of smart alecks snidely answer your question. Looks like you already have actually.
But they speak true. x – 1 on its own like that wont really get you anything. Now if you asked something along the lines of “What is x – 1 equal to if x is equal to 5?” then you’d get one solid definitive solution: 4.
Answer:
YES!!!!!
Step-by-step explanation:
LOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLLOLOLOLOLOLOLOLOL
A tank in the shape of a hemisphere has a diameter of 10 feet. If the liquid that fills the tank has a density of 74.4 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Step 1
State the volume of a hemisphere.
[tex]v=\frac{2}{3}\pi r^3[/tex]Where;
[tex]\begin{gathered} r=\frac{diameter}{2}=\frac{10}{2}=5ft \\ \end{gathered}[/tex]Step 2
Find the volume of the hemisphere
[tex]v=\frac{2}{3}\times\pi\times5^3=\frac{250\pi}{3}ft^3[/tex]Step 3
Find the total weight of the liquid in the tank
[tex]\begin{gathered} \text{Density}=\frac{mass}{\text{volume}} \\ 74.4=\frac{mass}{\frac{250\pi}{3}} \\ \text{mass}=19477.87445lb \\ \text{mass}\approx19478lb \end{gathered}[/tex]Hence the total weight of the liquid in the tank to the nearest full pound = 19478lb
use the quadratic formula to find both solitions to the quadratic equation given below x^2+6×=16
Answer:
x1=4
x2=-8
Step-by-step explanation:
x^2+6x-16=0
a=1 b=6 c=-16
D=b^2 - 4ab= 36+64=100
D>0, 2 sqrt
x1= -b+sqrt{D} /2= -6+10/2= 4
x2= -b-sqrt{D} /2= -6-10/2= -8
(That's what we were taught!)
Dave and his brother. Theo, are selling cookies by the pound at the school bake sale Dave sold 14 84 pounds of cookies and Theo sold 21.45 pounds of cookies How many pounds did they sell altogether? A 35 29 OB 36 39 C36 25 0 D. 36 29
For tis problem we have that Dave sold 14.84 pounds of cookies and Theo sold 21.45 pounds of cookies.
If we want to find the total of pounds that they sold together we just need to add the two values and we have:
[tex]14.84+21.45=36.29\text{pounds}[/tex]The reason is because 0.84+0.45=1.29
14+21=35. And finally 35+1.29=36.29
And the best answer for this case would be D. 36.29
Suppose theta is an angle in the standard position whose terminal side is in quadrant 1 and sin theta = 84/85. find the exact values of the five remaining trigonometric functions of theta
we know that
The angle theta lies in the I quadrant
[tex]sin\theta=\frac{84}{85}[/tex]step 1
Find out the value of the cosine of angle theta
Remember that
[tex]sin^2\theta+cos^2\theta=1[/tex]substitute given value
[tex]\begin{gathered} (\frac{84}{85})^2+cos^2\theta=1 \\ \\ cos^2\theta=1-\frac{7,056}{7,225} \\ \\ cos^2\theta=\frac{169}{7,225} \\ \\ cos\theta=\frac{13}{85} \end{gathered}[/tex]step 2
Find out the value of the tangent of angle theta
[tex]tan\theta=\frac{sin\theta}{cos\theta}[/tex]substitute given values
[tex]\begin{gathered} tan\theta=\frac{\frac{13}{85}}{\frac{84}{85}}=\frac{13}{84} \\ therefore \\ tan\theta=\frac{13}{84} \end{gathered}[/tex]step 3
Find out the cotangent of angle theta
[tex]cot\theta=\frac{1}{tan\theta}[/tex]therefore
[tex]cot\theta=\frac{84}{13}[/tex]step 4
Find out the value of secant of angle theta
[tex]sec\theta=\frac{1}{cos\theta}[/tex]therefore
[tex]sec\theta=\frac{85}{13}[/tex]step 5
Find out the value of cosecant of angle theta
[tex]csc\theta=\frac{1}{sin\theta}[/tex]therefore
[tex]csc\theta=\frac{85}{84}[/tex]Witch phrase best describes the position of the opposite of +4
To find the position that is opposite to +4, we need to consider 0 as a "mirror point", then we check which point has the same distance to 0 as the distance from +4 to 0:
The position which is opposite to +4 is the position -4.
This position is 4 units to the left of 0 and 8 units to the left of +4.
Looking at the options, the correct option is the second one.
figure0123456vehicles4122028364452linear ?pattern ?constant?
Problem
Solution
For this case we need to verify if the pattern is linear so we cna check this doing the following operations:
(12-4)/(1-0) =8
(20-12)/(2-1) =8
(28-20)/(3-2) =8
(36-28)/(4-3) =8
(44-36)/(5-4) =8
(52-44)/(6-5) =8
And as we can see we have the same constant so we can conclude that we have a linear pattern with a constant value of k=8
That means for every increase in the figure the vehicles increase by 8
We can also find the formula for the linear pattern and we have:
4 =8 (0)+b
And solving for b we got
b= 4
And the equation y=mx+b is:
y= 8x +4
1.- (picture) 2.-Assuming that the global population is seven billion and that no person receives the letter more than once, the maximum number of mailings is fourteen. Suppose that you are one of the recipients of mailing number 8 and there are ten names on the list (so your five outgoing letters will be in mailing number 9 and there will be nine names above yours on the list). If everyone who receives the letter participates, how much money will you receive?$
Kindly check below
Question 1) We can see that in the column "number of recipients" there is a Geometric Sequence whose common ratio is 5.
2) Therefore, we can fill in those gaps with the following:
[tex]\begin{gathered} Number\:of\:mailings|\:Number\:of\:recipients \\ 1\:|\:5 \\ 2\:|\:25 \\ 3\:|\:125 \\ 4\:|\:625 \\ 5\:|\:3125 \\ 6\:|\:15625 \\ 7\:|\:78125 \\ 8\:|\:390625 \\ 9\:|\:1953125 \\ 10\:|\:9765625 \\ 11\:|\:48828125 \\ 12\:|\:244140625 \\ 13\:|\:1220703125 \\ 14\:|\:6103515625 \\ \\ % \end{gathered}[/tex]3) Thus is the table.
answer this question that stumbles tons of people around the world!!
The values of x and y in the angles formed by the straight lines are:
x = 18.5
y = 37
What are Angles on a Straight Line?If two or more angles lie on a straight line, they will have a sum of 180 degrees when added together. Therefore, all angles on a straight line have a sum of 180 degree.
Therefore:
16 + 90 + 2y = 180 [straight line angle]
Combine like terms
106 + 2y = 180
Subtract both sides by 106
106 - 106 + 2y = 180 - 106 [subtraction property of equality]
2y = 74
2y/2 = 74/2
y = 37
Also,
16 + 90 + 4x = 180
106 + 4x = 180
4x = 180 - 106 [subtraction property of equality]
4x = 74
4x/4 = 74/4
x = 18.5
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Transform y f(x) by translating it right 2 units. Label the new functiong(x). Compare the coordinates of the corresponding points that makeup the 2 functions. Which coordinate changes. x or y?
If we translate y = f(x) 2 units to the right, we would have to sum and get g(x) =f(x+2).
That means the x-coordinates of g(x) are going to have 2 extra units than f(x).
[tex](x,y)\rightarrow(x+2,y)[/tex]Therefore, with the given transformation (2 units rightwards) the function changes its x-coordinates.URGENT TWO WAY TABLES
Answer: A) 6 B) 19.5
Step-by-step explanation:
A) 2,4,6,8,10
B) 8+16+30+24=78
78/4=19.5
Let me known if question b was right
REDUCE 48/96 TO THE LOWEST TERMS
Christian buys a $3500 computer using an installment plan that requires 17% down and a 3.7% interest rate. How much is the down payment?
1) Gathering the data
$3500 computer
17% down
3.7% interest rate.
2) Since we want to know how much is that down payment, we must turn that 17% into decimal form, then multiply it by the computer value:
17%=0.17
3500 x 0.17 = $595
3) So Christian must pay $595 as the down payment
circumference of the back wheel=9 feet, front wheel=7 feet. On a certain distance the front wheel gets 10 revolutions more than the back wheel. What is the distance?
The distance would be 315 feet which is a certain distance the front wheel gets 10 revolutions more than the back wheel.
What is the Circumference of a circle?The Circumference of a circle is defined as the product of the diameter of the circle and pi.
C = πd
where 'd' is the diameter of the circle
Given that the circumference of the back wheel=9 feet, the front wheel=7 feet. At a certain distance, the front wheel gets 10 revolutions more than the back wheel.
Both wheels must move at the same distance. If the number of revolutions taken by the back wheel is x, then the number of revolutions taken by the front wheel is x+10.
Because the distance traveled is the same as:
⇒ 9x = 7(x+10)
⇒ 9x = 7x+70
⇒ 9x - 7x = 70
⇒ 2x = 70
⇒ x = 35
We obtain x = 35 revolutions.
So the total distance traveled is 35×9=315 feet or 45×7=315 feet.
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