The answer is (-1,1) and (1,5)
What is the value of x in the equation 1/5 x-2/3y = 30, when y = 15?
Answer:
The value of x is 200 in the equation 1/5x - 2/3y = 30, when y = 15
Step-by-step explanation:
Given
equation: x - 2/3y = 30
when y = 15
Plug in y:
1/5x - 2/3(15) = 30
1/5x - 10 = 30
add 10 to both sides,
1/5x - 10 + 10 = 30 + 10
1/5x = 40
multiply both sides by 5
1/5x * 5= 40 * 5
x = 200
Answer:
x = 200
Step-by-step explanation:
[tex]\frac{1x}{5} -\frac{2y}{3} =30[/tex]
Given that, y = 15.
So, to find the value of x you have to replace y with 15 and make the x the subject.
Let us do that now.
[tex]\frac{1x}{5} -\frac{2*15}{3} =30\\[/tex]
[tex]\frac{1x}{5} -\frac{30}{3} =30\\[/tex]
[tex]\frac{1x}{5} =30+ \frac{30}{3}\\[/tex]
[tex]\frac{1x}{5} =\frac{30}{1} + \frac{30}{3}\\[/tex]
[tex]\frac{1x}{5} =\frac{30*3}{1*3} + \frac{30}{3}\\[/tex]
[tex]\frac{1x}{5} =\frac{90}{3} + \frac{30}{3}\\[/tex]
[tex]\frac{1x}{5} =\frac{120}{3}[/tex]
Use cross multiplication.
[tex]1x*3=120*5\\3x=600[/tex]
Divide both sides by 3.
x = 200
Find the midpoint between the given points: (2,-1), (10,-9)
Answer: (6, -5)
Step-by-step explanation: I used the midpoint formula and this is what I got. I hope this helps!
The formula:
(xm, xy) = (x1 + x2/2, y1 + y2/2)
Which number is irrational?
C
-4
C
2
g
O 11
O 8.26
The irrational number in the given options is √11
What is an irrational number?Irrational numbers are set of all real numbers in mathematics that are not rational numbers in nature. By the word rational, we mean that they cannot be expressed or represented in a fraction of a/b.
where;
a = numeratorb = denominatorIn other words, it is impossible to describe an irrational number as the ratio of two integers.
From the given options, the square root of 11 is the only number that cannot be expressed as a fraction, therefore, we can conclude that it is considered the only irrational number in the given options.
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if the figure forms the base of a right solid 110 centimeters high, find the surphase area.
the answer should be 5 inches I guess
Please help it is 10th grade Equations of lines and circles 7. Michael is hanging out in the park and needs to keep his so
a. If Michael is standing at the coordinate (5, 2), and each unit represents a foot, what
equation could be used to show the proper social distance needed?
-6-5 -3-2
12 3456
b. If Jake is standing on the coordinate (1, 1), are the two friends properly distanced?
2
45
Step-by-step explanation:
1) the required equation in common form is:
(x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - coordinates, where Michael is standing; r - the social distance;
According to the common form and given coordinates (x₀=-5; y₀=2; r=6) it is possible to make up the required equation:
(x+5)²+(y-2)²=6².
2) if the distance between two friends is:
[tex]d=\sqrt{(-5-1)^2+(2-1)^2}=\sqrt{37}, \ then[/tex]
this distance is longer than social (6 ft). For more info see the attachment.
Students were asked to prove the identity (sec x)(csc x) = cot x + tan x.
Let's prove that (sec x)(csc x) is equal to cot x + tan x
[tex]\Longrightarrow \sf (sec(x) )(csc(x))[/tex]
[tex]\Longrightarrow \sf \dfrac{1}{\cos \left(x\right)\sin \left(x\right)}[/tex]
[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)+\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]
[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)} + \dfrac{\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]
[tex]\Longrightarrow \sf \dfrac{\cos\left(x\right)}{\sin \left(x\right)} + \dfrac{\sin \left(x\right)}{\cos \left(x\right)}[/tex]
[tex]\Longrightarrow \sf cot(x) + tan(x)[/tex]
Hence student A did correctly prove the identity properly.
Also Looking at student B's work, he verified the identity properly.
So, Both are correct in their own way.
Part BIdentities used:
[tex]\rightarrow \sf sin^2 (x) + cos^2 (x) = 1[/tex] (appeared in step 3)
[tex]\sf \rightarrow \dfrac{cos(x) }{sin(x) } = cot(x)[/tex] (appeared in step 6)
[tex]\rightarrow \sf \dfrac{sin(x )}{cos(x) } = tan(x)[/tex] (appeared in step 6)
find the value of x? thanks
Answer:
x=1
Step-by-step explanation:
20(3x-3/5) = 20(2x-2/4)
12x-12= 10x-10
12x-10x =12-10
x= 1
Answer:
Step-by-step explanation:
Solution
3x - 3 2x - 2
===== = ====== Cross Multiply
5 4
4(3x - 3) = 5(2x - 2) Remove the brackets. Distributive Property
12x - 12 = 10x - 10 Subtract 10 x from both sides
12x-10x - 12 = 10x-10x - 10 Combine
2x - 12 = - 10 Add 12 to both sides
2x-12+12 = -10 + 12 Combine
2x = 2 Divide by 2
2x/2 = 2/2
Answer
x = 1
If x=0,what is the value of (8x)^0
[tex] {8x}^{0} \\( {8 \times 0})^{0} \\ {0}^{0} \\ it \: is \: undefined[/tex]
PLEASE GIVE BRAINLIEST
Given sinθ=1/2 determine the value of sec θ. 0°<θ<90°
Given Choices
2/√3
√3/2
2
1
Answer:
[tex]sec(\theta)=\frac{2}{\sqrt3}[/tex]
Step-by-step explanation:
Given [tex]sin(\theta)=\frac{1}{2}[/tex] , to find [tex]sec(\theta)[/tex], it will be helpful to visualize a right triangle (triangle with a 90 degree angle) associated with that particular θ. There are a few ways to go about this:
A general solution methodAll of the basic trigonometric functions, applied to an angle) are a ratio of two specific sides of any right triangle that holds that angle.
Remember that the Sine of an angle is defined specifically, the ratio of the opposite side (the side across from the angle in the Sine function), and the hypotenuse (the side across from the right angle). You might remember this through SohCahToa
[tex]sin(\theta)=\frac{opp}{hyp}[/tex]
In our case, since [tex]sin(\theta)=\frac{1}{2}[/tex] , so [tex]\frac{opp}{hyp}=\frac{1}{2}[/tex] . While there are an infinite number of triangles that have that ratio of those sides, they are all "similar" triangles (corresponding angles congruent, and corresponding sides are proportional, yielding common ratios of sides), and for ease, we can consider simply the triangle where the value of the numerator is the length of the opposite side, and the value of the denominator is equal to the hypotenuse. So, [tex]opp=1[/tex], and [tex]hyp=2[/tex].
While we haven't actually talked about θ yet, we can still set up the triangle that has these sides so that we can visualize what the triangle looks like. (see image)
This triangle represents the triangle for the unknown θ in the original sine function. We're tasked with finding the secant of that particular unknown θ.
Working toward Secant
Here, it will be helpful to remember either the reciprocal identities for[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex], or the definition of the secant function [tex]sec(\theta)=\frac{hyp}{adj}[/tex].
I find that most people remember the reciprocal identities more easily than keeping track of the definitions, so, since secant is related to cosine, it will be important to remember that [tex]cos(\theta)=\frac{adj}{hyp}[/tex]. From there, take the reciprocal of the cosine-value to get the secant-value (which matches the definition of the secant function).
Either way, it comes down to knowing the lengths of the side adjacent to theta, and the hypotenuse. We already know the length of the hypotenuse, so we just need the length of the adjacent side.
Applying the Pythagorean Theorem
Fortunately, because it is a right triangle, the Pythagorean Theorem applies: [tex]a^{2} +b^{2} =c^{2}[/tex] (where c is the length of the hypotenuse, and a & b are the lengths of the legs)
Substituting the known values for the sides we do know...[tex](adj)^{2} +(1)^{2} =(2)^{2}\\(adj)^{2} +1 =4[/tex]
...isolating "adj" by subtraction...
[tex](adj)^2=4-1\\(adj)^2=3[/tex]
...applying the square root property...
[tex]adj=\sqrt{3}[/tex] or [tex]adj=-\sqrt{3}[/tex]
Identifying which Quadrant the triangle is in
Since we were given that [tex]0^o < \theta < 90^o[/tex], our triangle is an acute triangle (as drawn in the diagram), and is in quadrant I (indicating that both legs will be measured with a positive value.
Thus, we discard the negative solution and conclude that [tex]adj=\sqrt{3}[/tex].
Finding the final solution
From there, [tex]cos(\theta)=\frac{adj}{hyp}[/tex] implies [tex]cos(\theta)=\frac{\sqrt3}{2}[/tex], and through the reciprocal relationship (or simply the definition of secant, whichever is easier for you to remember), [tex]sec(\theta)=\frac{2}{\sqrt3}[/tex]
Note: This method did not require knowing what the angle θ was.
Alternative method using the Unit CircleIf you know well the values of special triangles in the unit circle, you may have identified that [tex]sin(\theta)=\frac{1}{2}[/tex] is associated with [tex]\theta=30^o[/tex]. If so, if you also recall that the ordered pair associated with that point on the unit circle is [tex](\frac{\sqrt3}{2} ,\frac{1}{2} )[/tex], and that the [tex]cos(\theta)=x\text{-coordinate on the unit circle}[/tex], then you can quickly identify that [tex]cos(\theta)=\frac{\sqrt3}{2}[/tex].
This method still ends the same: recalling the reciprocal relationship between cosine and secant, giving [tex]sec(\theta)=\frac{2}{\sqrt3}[/tex].
The table displays the scores of students on a recent exam. Find the mean of the
scores to the nearest 10th.
Score Number of Students
70
7
75
5
80
4
85
1
90
6
Answer:
78.7
Step-by-step explanation:
To find the mean, we can do the sum of all scores divided by the total amount of scores.
We see that there are 7 scores of 70, and 70*7=490.
We see that there are 5 scores of 75, and 75*5=375.
We see that there are 4 scores of 80, and 80*4=320.
We see that there is 1 score of 85, and 85*1=85.
We see that there are 6 scores of 90, and 90*6=540.
Now we can do [tex]\frac{490+375+320+85+540}{7+5+4+1+6} =\frac{1810}{23} =78.7[/tex]
Given f ( x ) = 1 x + 10 , find the average rate of change of f ( x ) on the interval [ 8 , 8 + h ] . Your answer will be an expression involving h .
Answer: 1
Step-by-step explanation:
[tex]f(8+h)=8+h+10=18+h\\\\f(8)=8+10=18[/tex]
So, the average rate of change is:
[tex]\frac{(18+h)-18}{(8+h)-8}=\frac{h}{h}=\boxed{1}[/tex]
The question is wrong, the expression will not be in terms of h since it is a linear function.
Hi people! Can you help me figure this out? I'll mark brainliest!
D. 12.5
The equation to find the average rate of change is
[tex] \frac{y2 - y1 }{x2 - x1} [/tex]
To find the average rate of change between points (0,20) and (8,120) you need to plug it into the equation so it'll be
[tex] \frac{120 - 20}{8 - 0} [/tex]
this simplifies to
[tex] \frac{100}{8} [/tex]
which is 12.5
Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a 13%, percent monster truck tax. Which of the following expressions could represent how much Camacho pays in total for the truck?
The total price of the truck =$x + $ 0.13x
We have given that,
Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a 13%, percent monster truck tax.
We have to determine the expressions that could represent how much Camacho pays in total for the truck.
We will consider the price of the truck to be $x
What is the tax?And the amount of tax in the percentage would be 13%
13/100 = $ 0.13x (this is the actual amount of the tax)
Now we will calculate the total price of the truck =$x + $ 0.13x
= $ x(1 + 0.13)
If there is any confusion please leave a comment below.
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Suppose we want to choose 7 colors, without replacement, from 9 distinct colors
If the order of the choices does not matter, how many ways can this be done?
The number of ways to choose the colors is 36
How to determine the number of ways?The given parameters are:
Colors = 9
Colors to choose = 7
Since order does not matter, then it is combination
This is calculated using:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
This gives
[tex]^nC_r = \frac{9!}{7!2!}[/tex]
Evaluate
[tex]^nC_r = 36[/tex]
Hence, the number of ways is 36
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Please help! thank youuuu
Use polynomial long division to divide. Determine whether the divisor evenly divides into the dividend.
(8x-5)/(2x+1)
Answer:
The solution is 4 - 9/(2x + 1)
No, the divisor does not evenly divide into the dividend
Step-by-step explanation:
Please see the attached image
Solve the following multiplication problem.
9 cu yd 17cu in
× 135
−−−−−−−−−−−−−−−−−−−
The multiplication of the expression will be 1215 cubic yd 2295 cubic inches.
What is multiplication?It is also known as the product. If the object n is given to m times, then we just simply multiply them.
The expression is given below.
(9 cubic yd and 17 cubic in) × 135
On multiplication, we have
135 × 9 cubic yd and 135 × 17 cubic in
1215 cubic yd and 2295 cubic inches
1215 cubic yd 2295 cubic inches
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The multiplication is 56,689,335 cu in
What is Number system?A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.
9 cu yd 17cu in
1 cu yard = 46656 cu inches
9 cu yard = 9*46656 = 419904 cu inches
Now, total inches
= 419904 cu inches + 17 cu in
= 419,921 cu inches.
and, the multiplication is
=56689335
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Calculate the length of the diagonal of the state of Wyoming.
The length of the diagonal of the state of Wyoming is 457 miles.
What is the length of the diagonal?The length of the diagonal of the diagonal can be determined using Pythagoras theorem.
The Pythagoras theorem: a² + b² = c²
where:
a = lengthb = basec = hypotenuse√365² + 275² = 457 miles
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A patient takes 75mg of a medication every 12 hours; 60% of the medication in the blood is eliminated every 12 hours. (a) Let dn equal the amount of medication (in mg) in the bloodstream after n doses, where d1 = 75. Find a recurrence relation for dn.
The recurrence relation is dn = 0.4d(n-1) where d1 = 75
How to determine the recurrence relation?The given parameters are:
Initial, d1 = 75Rate of elimination, r = 60%Since, the medication is eliminated from the blood; then it means that the function is an exponential decay function.
This is represented as:
d(n) = d(n - 1) * (1 - r)
Substitute r = 60%
d(n) = d(n - 1) * (1 - 60%)
Evaluate the difference
d(n) = d(n - 1) * 0.4
Evaluate the product
dn = 0.4d(n-1)
Hence, the recurrence relation is dn = 0.4d(n-1) where d1 = 75
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Alex's recipe calls for 1/3 cup of chocolate chips for every 2 cups of flour. If he increases the
amount of flour to 3 cups, how many cups of chocolate chips will he need?
Answer:
1 cup
Step-by-step explanation:
1/3 cup of chocolate chips : 2 cup of flours
So 1/3:2 = x:3
Because we want to find x, the number of how many cups of chocolate chips he needs.
you can cross multiply where you get 1/3·3=2x
which is 1=2x and x=1
From this diagram, select the
pair of lines that must be
parallel if angle 2 is congruent to angle 6. If there is no pair of lines, select none
Answer:
A). O is parallel to qif angle 2 is congruent to 6 them the slope of line o and q is equal
that is line o is parallel to q
How do I find dy/dx of the following?
Answer:
[tex]\displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2\sqrt{x^{3}}} \ - \ \displaystyle\frac{12}{x^{5}}[/tex]
Step-by-step explanation:
[tex]y \ = \ x^{3} \ - \ \displaystyle\frac{1}{\sqrt{x}} \ + \ \displaystyle\frac{3}{x^{4}} \\ \\ y \ = \ x^{3} \ - \ x^{-\frac{1}{2}} \ + \ 3x^{-4} \\ \\ \displaystyle\frac{dy}{dx} \ = \ 3x^{3 \ - \ 1} \ - \ \left(-\displaystyle\frac{1}{2}\right)x^{-\frac{1}{2} \ - \ 1} \ + \ \left(-4 \ \times \ 3\right)x^{-4-1}[/tex]
[tex]\displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2}x^{-\frac{3}{2}} \ - \ 12x^{-5} \\ \\ \displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2\sqrt{x^{3}}} \ - \ \displaystyle\frac{12}{x^{5}}[/tex]
Section B 13. Amanda produces the newsletter for an editorial club. Each newsletter contains pages printed on both sides in colour and in black. The graphic designer informs Amanda that the upcoming issue of the newsletter will have 4 pages printed in colour and 20 pages printed in black. Every 4 pages printed in colour will cost x cents. Every 4 pages printed in black will cost y cents. (i) Find an expression for the cost of printing one copy of the newsletter. (1 (ii) Each newsletter costs 14 cents to print. Give an example of the cost of printing 4 pages in colour and the cost of printing 4 pages in black. [ An educational institution in Shanghai wants to subscribe to this newsletter. In Singapore, each newsletter costs S$2.20. The conversion rate is ¥1 = S$0.198 45. (iii) Without using a calculator, estimate the price of one newsletter in Y. Each sheet of paper has a mass of 4.5 g. (iv) How heavy is one copy of the newsletter?
Answer:
The answer is 3.2
Multiply (Make sure to show work on a separate sheet of paper)
Please use the equation writer that is on top. Look for this sign √ and click on it. That will allow you to write an exponent.
(2x−4)(x−6)
Answer:
[tex]2x^{2}[/tex] - 16x + 14
Step-by-step explanation:
(2x - 4)(x - 6)
= (2x + −4)(x + −6)
= (2x)(x) + (2x)(−6) + (−4)(x) + (−4)(−6)
= [tex]2x^{2}[/tex] − 12x − 4x + 24
= [tex]2x^{2}[/tex] - 16x + 14
About 5% of hourly paid workers in a region earn the prevailing minimum wage or less. A grocery chain offers discount rates to companies that have at least employees who earn the prevailing minimum wage or less. Complete parts (a) through (c) below. Company B has 540 employees. What is the probability that Company B will get the discount?
The probabilities for various binomial distribution have been determined.
The complete question is
About 5% of hourly paid workers in a region earn the prevailing minimum wage or less. A grocery chain offers discount rates to companies that have at least 30 employees who earn the prevailing minimum wage or less. Complete parts (a) through (c) below.
(a) Company A has 285 employees. What is the probability that Company A will get the discount? (Round to four decimal places as needed.)
(b) Company B has 502 employees. What is the probability that Company B will get the discount? (Round to four decimal places as needed.)
(c) Company C has 1033 employees. What is the probability that Company C will get the discount? (Round to four decimal places as needed.)
What is Probability ?Probability is a stream in mathematics that study the likeliness of an event to happen .
On the basis of the given data
(a) Let X is a random variable that denotes the number of employees that earn less than prevailing average.
Here X has binomial distribution with
n=285 and p=0.05.
As np and n(1-p) are greater than 5 so using normal approximation X has normal distribution with parameters
μ= np-285 * 0.05
= 14.25
standard deviation is given by
[tex]\sigma=\sqrt{np(1-p)}=\sqrt{285* 0.05* 0.95}\\\\=3.6793[/tex]
Applying continuity correction.
The z-score for X = 30-0.5 = 29.5 is
[tex]z=\dfrac{29.5-14.25}{3.6793}\\\\=4.14[/tex]
The probability that Company A will get the discount is given by
[tex]P(X\geq 30)=P(z > 4.14)=0.0000[/tex]
(b) Let X is a random variable that denotes the number of employees that earn less than prevailing average.Here X has binomial distribution with
n=502 and p=0.05.
[tex]\rm \mu=np=502* 0.05=25.1[/tex]
standard deviation
[tex]\rm \sigma=\sqrt{np(1-p)}=\sqrt{502\cdot 0.05\cdot 0.95}=4.8831[/tex]
Applying continuity correction.
The z-score for X = 30-0.5 = 29.5 is
[tex]\rm z=\dfrac{29.5-25.1}{4.8831}=0.90[/tex]
The probability that Company B will get the discount is
[tex]P(X\geq 30)=P(z > 0.90)=0.1841[/tex]
(c)Let X is a random variable that denotes the number of employees that earn less than prevailing average.Here X has binomial distribution with
n=1033 and p=0.05.
[tex]\mu=np=1033\cdot 0.05=51.65[/tex]
standard deviation
[tex]\rm \sigma=\sqrt{np(1-p)}=\sqrt{1033*0.05* 0.95}=7.0048[/tex]
Applying continuity correction.
The z-score for X = 30-0.5 = 29.5 is
[tex]\rm z=\dfrac{29.5-51.65}{7.0048}=-3.16[/tex]
The probability that Company C will get the discount is
[tex]\rm P(X\geq 30)=P(z > -3.16)=0.9992[/tex]
Therefore the probabilities for various binomial distribution have been determined.
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Write the equation in standard form. Then factor the left side of the equation
3x2 + 19x = 14 .
A. (3x – 2)(x + 7) = 0
B. (3x + 2)(x – 7) = 0
C. (2x – 3)(x + 7) = 0
D. (2x + 3)(x + 7) = 0
the value of a savings account can be found using the equation 300(1.03)^24. the interest is compounded monthly.
the interest rate is _____ per year
a. 12%
b. 0.25%
c. 36%
d. 1.5%
The interest rate is 36% per year if the value of a savings account can be found using the equation 300(1.03)²⁴ option (c) is correct.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
We have:
The value of a savings account can be found using the equation =
= 300(1.03)²⁴
From the function:
F(x) = a(1+r)ˣ
On compare:
1 + r = 1.03
r = 0.03
or
r = 3% monthly
r = 3×12 = 36% yearly
Thus, the interest rate is 36% per year if the value of a savings account can be found using the equation 300(1.03)²⁴ option (c) is correct.
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If the formula for an arithmetic sequence is a subscript n equals 11 plus 6 left parenthesis n minus 1 right parenthesis, then what term in the sequence is the value 107?
An arithmetic sequence is a sequence in which the difference between any two consecutive terms of the sequence is equal. The number of term 107 is 17th.
What is Arithmetic Sequence?
An arithmetic sequence is a sequence in which the difference between any two consecutive terms of the sequence is equal.
a_n = a₁ + (n-1)r
where,
a_n is the nth term of the sequence,
a₁ is the first term of the sequence,
r is a common difference between every two terms.
Given the formula for the nth term of the arithmetic sequence is,
[tex]a_n = 11+6(n-1)[/tex]
Now, the number of term that 107 will be,
107 = 11 + 6(n-1)
96 = 6(n-1)
16 = n- 1
n =17
Hence, the number of term that 107 is 17.
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Math: Surface Area word problem..10 pts for your help!
The formula for the surface area N(t) of the balloon after t seconds is [tex]N(t) = \frac {64}9\pi t^2[/tex]
How to determine the surface area?We have:
[tex]S(r) = 4\pi r^2[/tex]
Also, we have:
[tex]P(t) = \frac 43t[/tex]
The above can be rewritten as:
[tex]r = \frac 43t[/tex]
Substitute [tex]r = \frac 43t[/tex] in S(r) to determine the function N(t)
[tex]S(r) = 4\pi (\frac 43t)^2[/tex]
Express as N(t)
[tex]N(t) = 4\pi (\frac 43t)^2[/tex]
Expand the exponent
[tex]N(t) = 4\pi *\frac {16}9t^2[/tex]
Evaluate the product
[tex]N(t) = \frac {64}9\pi t^2[/tex]
Hence, the formula for the surface area N(t) of the balloon after t seconds is [tex]N(t) = \frac {64}9\pi t^2[/tex]
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A 4. Which of the following statements is false?
All squares are rectangles.
All rectangles are parallelograms.
• All parallelograms are quadrilaterals.
All rhombuses are squares
Answer: Choice D) All rhombuses are squares
=============================================================
Explanation:
Let's go through the answer choices to see which are true and which are false.
A) This is a true statement since all squares have all four angles of 90 degrees each. Any square is a rectangle, but not the other way around. We can cross choice A off the list.B) This is also a true statement. The opposite sides of a rectangle are parallel, which by definition makes it a parallelogram. Any rectangle is a parallelogram, but not the other way around. Cross choice B off the list.C) Yet another true statement. Parallelograms have four sides, which means they are quadrilaterals. Cross choice C off the list.D) This is false. Yes some rhombuses are squares, but others are not. A rhombus has all four sides the same length. If all four angles were 90 degrees each, then we'd have a square. But if the rhombus has its angles that aren't 90 degrees, then we have a non-square rhombus. Any square is a rhombus, but not the other way around.Check out the venn diagram below showing the connection between the geometric shapes mentioned. The large outer rectangle represents the set of all quadrilaterals. Inside this is the oval representing all parallelograms. Then inside the oval is the set of rectangles and the set of rhombuses. The overlapping region of the rectangles and rhombuses is the set of squares, marked in blue.
As you can see, picking any square will get us a rhombus and a rectangle automatically. However, picking any rhombus will not guarantee it's a square.
Find the x-intercept of the line whose equation is 8x + 2y = 4.
Answer: (I am copying and pasting my answer from the same question you did before in case you are waiting for an answer on this instead.)
1/2
Step-by-step explanation:
To find the x-int of any equation, you will need to replace the y with a 0 since when the x-int is when y is 0.
8x+2y = 4 ➨ 8x+2*0 = 4
Now I will do 2*0 which anything times 0 is equal to 0. And we are left with the equation of:
8x = 4
Now I will divide both sides by 8, which isolates our x.
x = 1/2
The x-int is 1/2.
Answer:
(0.5 , 0) or (1/2 , 0)
Step-by-step explanation:
Any x-intercept must be at (x,0), so we substitute y=0 into the equation.
8x + 2(0) = 4
8x = 4
x = 1/2 = 0.5
Therefore, the x-intercept is at (0.5 , 0) or (1/2 , 0)
