Answer:
C; A singleton set
Step-by-step explanation:
Mathematically, when a number is non-negative; it is either positive or zero
Now, this is because 0 identifies as neither a positive or a negative number
hence, when we find the difference between the two sets, the only number that stands out unmatched is the value 0
What this mean is that we are having a set with a single number result
So we have our answer as {0}
Which is a singleton set
The expression 13.25×5+6.5 gives the total cost in dollars of renting a bicycle and helmet for 5 days. The fee for the helmet does not depend upon the number of days.
Answer:
13.25×5+13, cost per day with a helmet.
Step-by-step explanation:
Numerical Expressions • Practice
Answer:
13.25×5+13, Per day without a helmet
Step-by-step explanation:
Triangle Q R S is shown. Line R Q extends through point P. Angle Q S R is 35 degrees. Angle S R Q is 58 degrees. Exterior angle S Q P is x degrees. What is the value of x?
The triangle is missing and so i have attached it.
Answer:
x = 93°
Step-by-step explanation:
From the triangle attached, we can say that;
<SQP + <SQR = 180°
This is because sum of angles on a straight line equals 180°.
Secondly, we know that sum of angles in a triangle also equals 180°.
Thus;
<SQR + <QSR + <SRQ = 180
From the attached triangle, we see that;
<QSR = 35°
<SRQ = 58°
Thus;
<SQR + 35° + 58° = 180°
<SQR + 93° = 180°
<SQR = 180° - 93°
<SQR = 87°
From earlier on, we saw that;
<SQP + <SQR = 180°
Plugging in <SQR = 87°, we have;
<SQP + 87° = 180°
<SQP = 180° - 87°
<SQP = 93°
We are told in the question that <SQP is denoted by x.
Thus;
x = 93°
Answer:
The value of x is answer D: 93
The polygons in each pair are similar. Find the missing side length.
Answer:
12
Step-by-step explanation:
We can say that two polygons are similar to each other if both of the polygons have the same shape and their corresponding sides are in the same proportion, hence the ratio of their corresponding sides are equal to each other.
As we can see from the problem since both of the polygons are similar, hence the ratio of their corresponding sides are in the same proportion, therefore let x represent the missing length, hence:
[tex]\frac{x}{15} =\frac{32}{40} =\frac{32}{40} \\\\\frac{x}{15} =\frac{32}{40} \\\\x=\frac{32*15}{40} \\\\x=12[/tex]
Helpo pleasssse
On my hw I have a parabola that opens down with its vertex at (-3,-6)......
For the range would I say that {yER | y > -6} OR {yER | y < -6} ????
I'm just confused from the negative numbers
Answer: The range is [tex]\{y \in \mathbb{R}\ | \ y \le -6\}[/tex]
Explanation:
The parabola opens down, forming a "frowny face" in a way (just without the eyes). Or you can think of it as a hill or mountain. This means that the vertex (-3,-6) is at the top of that mountain. It's the highest point of that parabola.
The range is the set of all possible y values. We see that y = -6 is the largest it can get. So y = -6 or y is smaller than this. We would then write [tex]y \le -6[/tex] to describe all the possible y values.
Therefore, the range is [tex]\{y \in \mathbb{R}\ | \ y \le -6\}[/tex]
This translates to "y is a real number such that y is -6 or smaller".
So the second answer you wrote is close, but you forgot the "or equal to" portion of the inequality sign.
See below for a visual example of what's going on.
What is the axis of symmetry for y = 3x^2 + x - 2
which inequality is represented on the number line shown?
Answer: A x> -2
Step-by-step explanation:
After 10 years, Hamid's account earned $900 in interest. If the interest rate (in decimal form) is 0.08, how much did Hamid initially invest? Without substitution, solve the formula chosen in the previous step for the unknown variable in terms of the known variable(s).
Answer:
Hamid initially invested $1,125.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After 10 years, Hamid's account earned $900 in interest.
This means that [tex]t = 10, E = 900[/tex]
Interest rate of 0.08:
This means that [tex]I = 0.08[/tex]
How much did Hamid initially invest?
We have to find P. So
[tex]E = P*I*t[/tex]
[tex]900 = P*0.08*10[/tex]
[tex]P = \frac{900}{0.8}[/tex]
[tex]P = 1125[/tex]
Hamid initially invested $1,125.
y=8200(0.96)^x growth or decay find
Answer:
This would be a .04 or 4% decay.....
for every "time unit" (x in this case) you will be multiplying
the amount by .96 ... in other words if you started with one dollar
the results would be 96 cents... after two "time" steps you would have
only 92 cents (.96 *.96)
Step-by-step explanation:
It took francisco 60 minutes to walk from his house to his grandmother’s house. what is 60 written as a product of factors greater than 1? each factor can have only 1 and itself as factors.
Answer:
2 × 2 × 3 × 5
Step-by-step explanation:
Given that,
The number = 60
To find,
Factors of 60 greater than 1 = ?
Procedure:
As we know,
Any of various numbers multiplied together to form a whole.
To find the factors of a number, we will have to do its prime factorization.
So,
The prime factorization of 60:
1 * 2 * 2 * 3 * 5 = 60
Since the factors greater than 1 are asked, the factors would be;
2 * 2 * 3 * 5
Thus, 2 * 2 * 3 * 5 is the correct answer.
Emily puts away basketballs after the gym class. there are 15 basketballs, and each rack holds 4 basketballs. how many racks does Emily completely fill? How many basketballs are left?
Answer:
emily fills 3 racks
3 basketballs are Left!
Step-by-step explanation:
15/4 = 3.3
can someone help me out
b) 2x (x - y) + 3y (x - y)
Use distributive law
[tex]\boxed{\sf a(b+c)=ab+ac}[/tex]
Now
[tex]\\ \sf\longmapsto 2x(x-y)+3y(x-y)[/tex]
[tex]\\ \sf\longmapsto 2x^2-2xy+3xy-3y^2[/tex]
[tex]\\ \sf\longmapsto 2x^2-3y^2-2xy+3x^2[/tex]
[tex]\\ \sf\longmapsto 2x^2-3y^2+xy[/tex]
Taking common
Answer: 2x (x-y) + 3y (x-y)
= ( x-y ) ( 2x-3y )
Can someone help me on this please
A person walks on average 4000 steps per day. If one step is about 2 feet long, how much would the average person walk per week? HELP
Answer:
56000 ft
Step-by-step explanation:
4000 steps a day.
7 days in a week.
2 ft per step
so, we calculate how many steps in a week
4000 × 7 = 28000
and then we calculate the distance by saying each of these steps is 2 ft
so,
28000 × 2 = 56000 ft
as a little extra thought :
there are 5280 ft in a mile.
so, the person walks
56000 / 5280 miles = 10.61 miles
in a week.
32
Two forces one is 10N and other is 6N act on a body The directions are unknown the resultant force on the body is
a. between 4 and 16N
b. more than 6N I
c. more than 1ON
d between 6 and 16N
If Forces are acting on opposite direction
[tex]\\ \rm\hookrightarrow F_{net}=F_2-F_1[/tex]
[tex]\\ \rm\hookrightarrow F_{net}=10-6[/tex]
[tex]\\ \rm\hookrightarrow F_{net}=4N[/tex]
If both acting on same direction
[tex]\\ \rm\hookrightarrow F_{net}=F_1+F_2[/tex]
[tex]\\ \rm\hookrightarrow F_{net}=10+6[/tex]
[tex]\\ \rm\hookrightarrow F_{net}=16N[/tex]
Hence
[tex]\boxed{\sf 4N\leqslant F_{net}\leqslant 16N}[/tex]
Suppose that d varies jointly with r and t, and d = 110 when r = 55 and t = 2. Find r when d = 40 and t = 3.
Answer:
r = 13.33
Step-by-step explanation:
d = k*r*t
Where,
k = constant of proportionality
d = 110 when r = 55 and t = 2
d = k*r*t
110 = k * 55 * 2
110 = 110k
k = 110/110
k = 1
Find r when d = 40 and t = 3
d = k*r*t
40 = 1 * r * 3
40 = 3r
r = 40/3
= 13.333333333333
Approximately,
r = 13.33
A. -5x+4y=-20
B. -5x-4y=-20
C. -5x+4y=0
D. 5x+4y=-20
Find the values of x and y.
Answer:
I think it's 43 and 43 degrees. I just subtracted 180-94, got 86, and divided it so yea.
Given an arithmetic progression 17,13,9,..... find the number of terms required so that its sum is - 33 .
Answer:
11 terms.
Step-by-step explanation:
We are given the arithmetic sequence:
17, 13, 9, ...
And we want to find the number of terms required such that the sum is -33.
Recall that the sum of an arithmetic series is given by:
[tex]\displaystyle S = \frac{k}{2}\left( a + x_k\right)[/tex]
Where k is the number of terms, a is the first term, and x_k is the last term.
The desired sum is -33. The first term is 17 as well. Thus:
[tex]\displaystyle (-33) = \frac{k}{2} \left( (17) +x_k\right)[/tex]
Simplify:
[tex]-66 = k(17 + x_k)[/tex]
We can write a direct formula to find the last term x_k. The direct formula of an arithmetic sequence has the form:
[tex]x_ n = a + d(n-1)[/tex]
Where a is the initial term and d is the common difference.
The initial term is 17 and the common difference is -4. Hence:
[tex]\displaystyle x_n = 17 - 4(n-1)[/tex]
Then the last term is given by:
[tex]x_k = 17 - 4(k-1)[/tex]
Substitute:
[tex]\displaystyle -66 = k\left( 17 + \left( 17 - 4(k-1)\right)\right)[/tex]
Solve for k:
[tex]\displaystyle \begin{aligned} -66 &= k(17 + (17 - 4k + 4)) \\ -66 &= k(38 -4k) \\ -66 &= -4k^2 + 38k \\ 4k^2 -38k -66 &= 0 \\ 2k^2 - 19k -33 &= 0 \\ (k-11)(2k+3) &= 0 \\ k-11&= 0 \text{ or } 2k+3 = 0 \\ \\ k &= 11 \text{ or } k = -\frac{3}{2}\end{aligned}[/tex]
Since we cannot have a negative amount of terms, we can ignore the second solution.
Therefore, the given sequence must have 11 terms such that it sums to -33.
Answer:
Here is 2 methods
Step-by-step explanation:
1) we use excel to find n=11 for lasy students
2) mathematical method
[tex]u_1=17\\u_2=13=17+(2-1)*(-4)\\u_3=9=17+(3-1)*(-4)\\\\\\\boxed{u_n=17+(n-1)*(-4)}\\\\\\\displaystyle s_n=\sum_{i=1}^nu_i\\=\sum_{i=1}^n(17+(i-1)*(-4))\\\\\\=(\sum_{i=1}^n 17) + (-4)*\sum_{i=1}^n (i) +4*\sum_{i=1}^n (1)\\\\\\=17*n+4*n-4*\frac{n*(n+1)}{2} \\\\\\=21n-2n^2-2n\\\\\\=-2n^2+19n\\\\=-33\\\\\\\Longrightarrow\ 2n^2-19n-33=0[/tex]
[tex]\Delta=19^2+4*2*33=625=25^2\\\\n=\dfrac{19-25}{4} =-1.5\ (excluded)\ or\ n=\dfrac{19+25}{4}=11\\\\[/tex]
A giant pie is created in an attempt to break a world record for baking. The pie is shown below:
What is the area of the slice of pie that was cut, rounded to the nearest hundredth?
Answer:
Area of the slice of pie = 22.09 ft²
Step-by-step explanation:
Area of the slice of pie = Area of the sector of the circle with the central angle 45°
Area of the sector = [tex]\frac{\theta}{360^{\circ}}(\pi r^{2} )[/tex] [Here, r = radius of the circle]
= [tex]\frac{45^{\circ}}{360^{\circ}}(\pi )(\frac{15}{2})^2[/tex]
= 22.09 ft²
Area of the slice of pie = 22.09 ft²
Answer:
22.08ft^2
Step-by-step explanation:
A = πr^2(x/360) d = 15
Since r is half of diameter this means that r = 15/2 =7.5
so Lets use the Area of Sector formua
A =3.14(7.5)^2 (45/360)
A =3.14(56.25) (45/360)
A = 176.625 (45/360)
A = 176.625 (0.125)
A = 22.078125
rounded to the nearest 10th would make it 22.08
I really need this answered!
Answer:
Its AA similaroty theorem
A walker has travelled 9 km along a trail. If he has completed 80% of the trail, how much further does he still have to go?
Answer:
2.25 km to go
Step-by-step explanation:
In order to get this answer, you have to figure out how many km 10% is, 0.1125. Then multiply that by the remaining 20% because he already finished 80% of the trail. So, 0.1125 x 20 = 2.25.
Hope this helps! :)
Product of the zeroes of polynomial 3x²-2x-4 is ? No spam ❌ Want accurate answers ✔ No spa.
full explain
9514 1404 393
Answer:
-4/3
Step-by-step explanation:
Quadratic ax² +bx +c can be written in factored form as ...
a(x -p)(x -q)
for zeros p and q. The expanded form of this is ...
ax² -a(p+q)x +apq
Then the ratio of the constant term to the leading coefficient is ...
c/a = (apq)/a = pq . . . . the product of the zeros
For your quadratic, the ratio c/a is -4/3, the product of the zeros.
_____
Additional comment
You will notice that the sum of zeros is ...
-b/a = -(-a(p+q))/a = p+q
Answer:
[tex] \green{ \boxed{ \bf \: product \: of \: the \: zeros \: = - \frac{4}{3} }}[/tex]
Step-by-step explanation:
We know that,
[tex] \sf \: if \: \alpha \: and \: \beta \: \: are \: the \: zeroes \: of \: the \: \\ \sf \: polynomial \: \: \: \pink{a {x}^{2} + bx + c }\: \: \: \: then \\ \\ \small{ \sf \: product \: of \: zeroes \: \: \: \alpha \beta = \frac{constant \: term}{coefficient \: of \: {x}^{2} } } \\ \\ \sf \implies \: \pink{ \boxed{\alpha \beta = \frac{c}{a} }}[/tex]
Given that, the polynomial is :
[tex] \bf \: 3 {x}^{2} - 2x - 4[/tex]
so,
constant term c = - 4coefficient of x^2 = 3[tex] \sf \: so \: product \: of \: zeroes \: \: = \frac{ - 4}{3} = - \frac{4}{3} [/tex]
pls pls pls pls help
Step-by-step explanation:
[tex]s = \pi \times {r}^{2} = \pi \times {6}^{2} = 36\pi[/tex]
[tex]h = 18 \times \sin(60) = 9 \sqrt{3} [/tex]
[tex]v = s \times h = 36\pi \times 9 \sqrt{3} = 324 \sqrt{3} \pi[/tex]
Given: The equation of a parabola is x2 = 8y.
Step 3: Where does the directrix for the given parabola lie? Enter the equation for the directrix line. Use your keyboard and the keypad to enter your answer. Then click Done.
Answer:
x=-2
Step-by-step explanation:
Answer:
Since a = 2, the equation for the directrix line will be y = −2.
Step-by-step explanation:
sin x = 4/5, cos x = 2/5 find the value of tan x
Answer:
2 is the answer . the explanation is in the attachment .
help please tries 2 times
Answer:
(2,1)
Step-by-step explanation:
2x - 2y = 2
5x + 2y = 12
again just add them in this case
7x = 14
x = 2
4 - 2y = 2
-2y = -2
y = 1
can i get some help solving this
Answer:
A =147 cm^2
Step-by-step explanation:
A = pi r^2
The radius is 7 and let pi = 3
A = 3*7^2
A = 3*49
A =147
how many degrees does a unit angle measure a 10° B 90° c 180 degrees d 100 degrees
please ans this question pleaseee
Answer:
[tex]{ \tt{ \tan {}^{4} \theta + { \sec }^{2} \theta }} \\ { \tt{ = ({ \tan }^{2} \theta ){}^{2} + { \sec }^{2} \theta }} \\ = { \tt{ {-(1 - { \sec }^{2} \theta) }^{2} + { \sec }^{2} \theta }} \\ { \tt{ = -(1 - 2 { \sec }^{2} \theta + { \sec }^{4} \theta) + { \sec}^{2} \theta}} \\ { \tt{ = -(1 - { \sec }^{2} \theta) + { \sec }^{4} \theta}} \\ { \tt{ = -{ \tan}^{2} \theta + { \sec }^{4} \theta }} \\ = { \tt{ { \sec}^{4} \theta - { \tan }^{2} \theta}} \\ { \bf{hence \: proved}}[/tex]
