Answers
3z - 4 ≤ 17
add 4 to both sides:
3z-4 + 4 ≤ 17 + 4
simplify:
3z ≤ 21
divide both sides by 3 :
3z / 3 ≤ 21 / 3
z ≤ 21 / 3
z ≤ 7
hope this helps!
Related Questions
please help!!!
Write an expression for the volume of a cylinder with a height 7in. greater than the radius.
Answers
Explanation:
1) The general formula for the volumen, V, of a cylinder with radius r and height h is:
V = π r² h
2) Now you have the condition that the height is 7 inches greater than the radius, that is:
h = 7 + r
3) Replace h with its expression
V = π r² (7 + r)
4) Expand the product (use distributive property):
V = π (7r²) + π r³ = 7 π r² + π r³
Answer: 7 π r² + π r³
find the volume of the specificed cone. Use 3.14 for pie, and round your answer to the nearest whole number.
Radius=9 in., Height=8 in.
a. 1017 cu. in.
b. 151 cu. in.
c. 678 cu. in.
d. 1356 cu. in.
Answers
Which equation represents a parabola with a focus at (0,-2) and a directrix of y=6?
Answers
Hey there!!
First, let's learn the parabola formula when the focus and the directrix is given.
Formula :
[tex]y = \frac{( x - a ) ^{2} }{ 2 ( b - k ) } + \frac{( b + k ) }{2}[/tex]
We have ,
Focus : ( 0 , -2 )
Hence, a = 0 and b = -2
And k = 6
Now, we will just have to plug in the values and find out the equation.
[tex]y = \frac{( x - 0 )^{2} }{2 ( - 2 - 6 )} + \frac{( - 2 + 6 ) }{2}[/tex]
[tex]y = \frac{x^{2} }{-16}+ 2[/tex]
The final equation would be :
[tex]y = \frac{-x^{2} }{16} + 2[/tex]
Hope my answer helps!!
I am posting my work for an application of integrals problem. I would love to know if anyone else agrees with my work!
Answers
The results from a graphing calculator are in agreement.
I don't understand this question. Could anyone excplain to me what it wants me to do and what the answer is?
What is the diameter of a sphere that has a surface area of 1041 square inches?
A) 9.1
B) 22.5
C) 40.3
D) 18.2
Answers
I got the answer by solving it
A=4*π*r^2
Where r=radius
r = diameter/2 or d/2
So
area of a sphere = 4*π*(d/2)^2
Plug in the area given
1041 = 4*π*(d/2)^2
Solve for d
1041/(4* π)=82.84
82.84 = (d/2)^2
Sqrt(82.84)=d/2
9.10=d/2
9.10*2= d
18.2=d
So the answer is 18.2 in
The average of paula's two test scores must be 80 or more for her to get at least a b in the class. she got a 72 on here first test. what grades can she get on the second test to make at least a b in the class
Answers
brianna deposit $680.00 into savings account that pays a simple interest rate of 1.29% how much will she earn after 3 years
Answers
0.0129(680) + 680
But because it is 3 years:
3(0.0129(680)) + 680
0.0387(680) + 680
We can make it simpler:
1.0387(680)
Multiply:
706.316
We can round up:
She will have $706.32, and earn $26.32
Roger goose had a 500-yard head start on willa. if willa's speed was 40 yards per second and roger's speed was only 20 yards per second, how long did it take willa to catch up
Answers
We have then:
For Roger:
r = 20 * t + 500
For Willa:
r = 40 * t
Equating the equations:
20 * t + 500 = 40 * t
We cleared t:
40 * t - 20 * t = 500
20 * t = 500
t = 500/20
t = 25 s
Answer:
it did take willa 25 s to catch up Roger.
(08.05 HC) The work of a student to solve a set of equations is shown: Equation A: y = 15 − 2z Equation B: 3y = 3 − 4z Step 1: −3(y) = −3(15 − 2z) [Equation A is multiplied by −3.] 3y = 3 − 4z [Equation B] Step 2: −3y = 15 − 2z [Equation A in Step 1 is simplified.] 3y = 3 − 4z [Equation B] Step 3: 0 = 18 − 6z [Equations in Step 2 are added.] Step 4: 6z = 18 Step 5: z = 3 In which step did the student first make an error?
Answers
Simplifying
-3(y) = -3(15 -2z)
should yield
-3y = -45 +6z
not
-3y = 15 -2z
Answer:
STEP 2
Step-by-step explanation:Simplifying
-3(y) = -3(15 -2z)
should yield
-3y = -45 +6z
Find the derivative of f(x) = negative 10 divided by x at x = -12.
Answers
What is the domain of the function
Answers
Answer:
The domain of the function is x>=-7
Step-by-step explanation:
The domain is all the values that x can take so the function is defined, that means we can find a value of y
The sqrt is defined only for positive values and zero. So the expression in the sqrt must satisfy that
6x + 42 >=0
We only have to find x
6x >=-42
x>=-42/6
x>=-7
So the answer is D x>=-7
Solve a(x - b) - 2k = l for k
Answers
ax - ab - 2k = l
Subtract ax, add ab to both sides
- 2k = l - ax + ab
Divide by - 2 to isolate variable K
k = (l - ax + ab) / - 2 or [tex]k = \frac{l - ax + ab}{-2} [/tex]
The length of a rectangle is 4 inches less than twice its width. If the area of the rectangle is 70 square inches, what are its demensions
Answers
A = w * l
Where,
w: width
l: long
Substituting values we have:
70 = w * (2w-4)
Rewriting we have:
70 = 2w ^ 2-4w
2w ^ 2 - 4w - 70 = 0
Solving the polynomial we have:
w1 = -5
w2 = 7
We take the positive root because it is a dimension.
w = 7 inches
Then, the length will be:
l = 2w-4
l = 2 (7) -4
l = 14-4
l = 10 inches
Answer:
its demensions are:
w = 7 inches
l = 10 inches
x-----------> the length side of rectangle
y----------> the width side of rectangle
we know that
70=x*y--------> x=70/y-----------> equation 1
x-4=2y--------> equation 2
substitute equation 1 in equation 2
[70/y]-4=2y--------> multiply by y------> 70-4y=2y²----> 2y²+4y-70=0
using a graph tool ----> to resolve the second order equation
see the attached figure
the solution is
y=5
x=70/y--------> x=70/5=14
the answer is
the dimensions are
length=14 in
width=5 in
A box is 10 cm long, 5 cm wide, and 2 cm high. What is the surface area of the box? (S.A. = 2lw + 2lh + 2wh)
Answers
Answer:
your answer is 160 cm2
Step-by-step explanation:
ez
The equation of a parabola is given. y=−16x2+7x−80 What is the equation of the directrix of the parabola?
Answers
y=−16x²+7x−80
see the answer in the attached figure
the answer is y=-5
Which of the following best describes the following set of numbers? 6 + 8 + 10 + 12 + ... + (4 + 2n) + ...
answers:
Arithmetic SequenceGeometric SeriesGeometric SequenceArithmetic Series
Answers
6+8+10+12+.....+(4+2n)+
the common difference is:
8-6=10-8=12-10=2
since the series has a common difference then it is known as:
Arithmetic series.
Answer:
The term that best describes the given set of numbers is:
Arithmetic Series.
Step-by-step explanation:
We are given a series of numbers as:
6 + 8 + 10 + 12 + ... + (4 + 2n) + ...
Clearly as wee could see that each term in the given expression is separated by a plus sign, Hence, the given expression is a series and not a sequence.
Also as we could see that each in the series is more than the preceding term by 2 i.e. the common difference of the term is 2.
( Since, the set of numbers is given as:
[tex]a_0+a_1+a_2+a_3+....[/tex]
where,
[tex]a_n=2n+4[/tex]
[tex]when,n=0\\\\a_1=4\\\\when,n=1\\\\a_1=6\\\\and\ so\ on[/tex]
Also,
[tex]a_0-a_1=2\\\\Simialrly\\a_2-a_1=2\\\\and\ so\ on[/tex]
Hence, the common difference is 2. )
Hence, the given series is an Arithmetic series.
What is the surface area of a sphere with the given dimension? Express your answer to nearest hundredth. Use 3.14 for pi. Radius = 5cm.
Answers
[tex]4 \pi (5^2) = 4(3.14)*25 = 100 * 3.14 = 314[/tex]
I got 314 cm^2 is the surface area, but it always helps to double check work! Hope this helps!
Surface Area = 4πr²
r = 5cm
π = 3.14
Using the values we get:
Surface Area = 4(3.14)(5²) = 314 cm²
Thus, the surface area of the sphere is 314 cm²
ANSWER TRUTHFULLY WILL NAME YOU BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!
The ordered pairs (1,5) (2,25) (3,125) (4,625) and (5,3125) represent the function y=5^x. How does this rule represent the function?
A) y=x5
B) y=5x
C) y=5^5=x
D) y=x+5
Answers
A) is technically the same as B), but B) expresses correct function notation.
B) 5 = 5(1) ⇒ 5 = 5
25 = 5(2) ⇒ 25 ≠ 10
B) is incorrect.
C) I'm not sure what you mean y=5^5=x, but I'm going to use [tex]y=5^{x} [/tex] because it's close to what you wrote:
[tex]5=5^{1} =\ \textgreater \ 5=5 \\ 25=5^{2} =\ \textgreater \ 25=25 \\ 125=5^{3} =\ \textgreater \ 125 = 125 \\ 625=5^{4}=\ \textgreater \ 625=625 \\ 3125=5^{5}=\ \textgreater \ 3125=3125[/tex]
The function [tex]y=5^{x} [/tex] works for the points given.
D) 5 = 1 + 5 ⇒ 5 ≠ 6
D) is not correct.
Please check your functions; I'm not sure that C) is a function. In any case, the answer is C) because all the other answers are wrong.
Melissa pulls the pep club to see which sport they like. She finds that 45 students like soccer only, 35 students like football only, and 15 students like soccer and football. There is no one who doesn't like at least one of the two sports mentioned. Which venn diagram would be an appropriate model for the data melissa collected
Answers
please help asap 50 pts
Answers
I tried plugging in all the answers, and found that C works the best. Hope that helps.
Good luck!
-RxL
for the function f(x)= -(x + 1)^2 + 4 identify the vertex, domain, and range
Answers
Domain = All real numbers
Range = All y values such that y ≤ 4
Answer:
Vertex = (-1, 4)
Domain = All real numbers i.e. R
Range = (-∞, 4)
Step-by-step explanation:
The vertex of the quadratic equation:
f(x) = a(x - h)² + k
Here, Vertex = (h,k)
Thus, Vertex = (-1, 4)
Domain = All real numbers i.e. R
Range = All real numbers less than or equal to 4 i.e. (-∞, 4) or f = ≤ 4.
Further, the possible values of x are called Domain.
And, the possible output we get as y is called Range.
Give an exact answer in simplified form. 5y+3 > -7y + 13 5y+3>−7y+13 (see pic
Answers
5y+3>-7y+3
putting like terms together we obtain:
5y+7y>3-3
2y>0
dividing both sides by 2 we get:
(2y)/2>0/2
thus
y>0
Answer: y>0
Th answer to the inequality will be evaluated as follows:
5y+3>-7y+3
putting like terms together we obtain:
5y+7y>3-3
2y>0
dividing both sides by 2 we get:
(2y)/2>0/2
thus
y>0
Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x.
m<O = 135
(See picture down below)
a) 45
b) 315
c) 270
d) 67.5
Answers
This divides the 4-sided polygon into two right triangles. For example, the upper right triangle has an acute angle whose measure is 135 degrees / 2, or 67.5 degrees, and the another acute angle whose measure is x/2.
x/2 and 67.5 degrees are complementary angles, so x/2 + 67.5 deg = 90 deg. Thus, x/2 = 22.5 deg, and so x = 45 deg. (answer)
The length of a rectangle is 7 cm less than twice its width. if the area of the rectangle is 39 cm2, find the dimensions of the rectangle.
Answers
Greg wants to move out of his dormitory and into an apartment near his college. His parents agreed, on the condition that the rent is no more than 25% of the cost of dorm living. To get an idea of rent amounts for one-bedroom apartments, Greg looks at listings in a local newspaper and on an Internet site.
Which answer best describes the sample and population?
A. Sample: listings in a local newspaper and on an Internet site
Population: all available apartments near the college
B. Sample: all available apartments near the college
Population: all available dormitories near the college
C. Sample: all available dormitories near the college
Population: all available apartments near the college
D. Sample: all available apartments near the college
Population: listings in a local newspaper and on an Internet site
Answers
the population would be all available apartments
the answer would be
A. Sample: listings in a local newspaper and on an Internet site
Population: all available apartments near the college
What is the length of the unknown side of the right triangle? (1 point) A right triangle with hypotenuse x and legs 5 and 12 13 17 25 60
Answers
5,12 --> 13
Why? Pythagorean theorem.
5 squared plus 12 squared equals 169. The square root of that is 13.
[tex] \sqrt{{(12)}^{2} + {(5)}^{2}} = 13[/tex]
Someone please help
Answers
What is the focus of the parabola? y=−1/4x^2−x+3
Enter your answer in the boxes.
(__ ,__ )
Answers
the equation of the parabola is of the form
y=ax²+bx+c
in this problem
y=−1/4x²−x+3
where
a=-1/4
b=-1
c=3
the coordinates of the focus are
(-b/2a,(1-D)/4a)
where
D is the discriminant b²-4ac
D=(-1)²-4*(-1/4)*3-----> D=1+3---> D=4
therefore
x coordinate of the focus
-b/2a----> 1/[2*(-1/4)]----> -2
y coordinate of the focus
(1-D)/4a------> (1-4)/(-4/4)---> 3
the coordinates of the focus are
(-2,3)
Claudia is on a motorcycle trip. She checked the odometer at the beginning of the trip, and it showed 16,789 miles. After 15 days it showed 22,189 miles. If Claudia rode the same number of miles each day how many miles did she ride in a day?
A.360 miles
B 540 miles.
C.771 miles
D.1,479 miles
please help me
Answers
Total miles = 5,400
Days = 15
Divide total by how many days:
5,400 ÷ 15 = 360
Answer = A.360
Hope this helped :)
22,189 - 16,789 = 5,400
5,400 / 15 = 360
360 miles a day
Mrs. Cantonwine teaches 2 math classes. There are 28 students in 6A and 21 students in 6B. She divided both classes into groups of equal size. How many students are in a group?
Answers
In order to figure out how many students are in each group, we'll need to find the greatest common factor of the two class sizes. The greatest common factor is 7. This means that 7 students are in each group.
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!