Answer:
Domain is [-5, 5]
Range is [-3, 17]
Step-by-step explanation:
R1 = {(x, y)| y = 2x + 7, where x∈ R and -5 ≤ x ≤ 5}
The domain is given by the all possible input values of x . Here the function is defined for -5 ≤ x ≤ 5, so the domain is [ - 5, 5].
The range is given by the output values of he function.
When x = - 5
f (- 5) = 2 (-5 ) + 7 = - 3
When x = 5
f (5) = 2 (5) + 7 = 17
So, the range is [ -3 , 17].
ax + by = c and mx + ny = d and an # bm then these simultaneous equations have a) Only one common solution. b) No solution. c) Infinite number of solutions. d) Only two solutions.
Answer:
a) Only one common solutionStep-by-step explanation:
The first line has slope of a/b and the second one has slope of m/n.
As an ≠ bm ⇒ a.b ≠ m/n, the slopes are different.
Since the slopes are different the lines are not parallel, hence they intersect at one point.
This means there is one solution only.
ax + by = c and mx + ny = d and an # bm then these simultaneous equations have Only one common solution.
[tex]\sf{ }[/tex] [tex]\sf{ }[/tex]
Find the height h of the triangle.
Answer:
A, 12 times the square root of 3
Step-by-step explanation:
24 sqaured plus 12 squared=432
square root of 432=20.9
12 times the sqaure root of 3=20.9
Plot point C in GeoGebra to verify that it indeed lies on AB. You can enter the coordinates in the Input window to plot the point . Also , verify the distances you calculated in question 3 using GeoGebra . Take a screenshot showing the distances displayed by GeoGebra , and paste it below .
Answer:
The picture of file
Step-by-step explanation:
Your'e welcome
Given a line segment that contains the points A,B, & C in order, if AB = x, BC = x, and AC is equal to 36, then x = _____.
Select one:
a. 18
b. 6
c. 36
d. 12
Answer:
a. 18
Step-by-step explanation:
AB+BC = AC
x + x = 36
2x = 36
x = 36/2
x = 18
the area of a circle is 616 m square find the radius 5 equals to 22/7
Step-by-step explanation:
[tex]here \: is \: your \: solution : - \\ \\ GIVEN \: \: -:- \\ \\ = > \: area \: of \: circle \: = 616 \: m {}^{2} \\ \\ \ = > pi = 22 \div 7 \\ \\ = > we \: need \: to \: find \: radius \: \\ \\ = > area \: of \: circle \: = \pi \: r {}^{2} \\ \\ = > \: \pi \: r {}^{2} = 616 \: m {}^{2} \\ \\ = > \: r {}^{2} \times (22 \div 7) = 616 \\ \\ = > \: r {}^{2} =( 616 \times 7) \div 22 \\ \\ = > \: r { }^{2} = 4312 \div 22 \\ \\ = > r {}^{2} = 196 \\ \\ = > \: r = \sqrt{196} \\ \\ = > \: r = 14 \: \: \: (ANSWER✓✓✓) \\ \\ HOPE \: IT \: HELPS \: YOU \: (◕ᴗ◕✿)[/tex]
5) On each birthday Rosa gets as many roses as she is old in years. She still has all the dried flowers and there are now 120 of them. How old is she? A) 10 B) 12 C) 14 D) 15 E) 20
Answer:
D) 15
Step-by-step explanation:
This is an arithmatic progression.
The formula for the sum of arithmatic progression is
[tex]s = \frac{n}{2} (2a + (n - 1)d)[/tex]
where d is the common difference between successive terms and a is the first term. By applying this formula,
[tex]120 = \frac{n}{2} (2(1) + (n - 1)(1)) \\ 120 = \frac{n}{2} (1 + n) \\ n(1 + n) = 240 \\ n {}^{2} + n - 240 = 0 \\ (n - 15)(n + 16) = 0 \\ n = 15 \: or \: n = - 16(reject)[/tex]
You have a large container of castor oil. You have used 34 quarts of oil.
Fifteen percent of the castor oil remains. How many quarts of castor oil
remain?
co
=====================================================
Explanation:
x = original amount of caster oil (in quarts)
Since 15% remains, this means you used 85% of the original amount x.
Note how 15% + 85% = 100%
So,
85% of x = 34 quarts
0.85x = 34
x = 34/0.85
x = 40
You started with 40 quarts of oil.
15% of that remains, meaning 0.15*40 = 6 quarts of oil are left over.
-----------
We could also solve like this
(amount used)/(amount total) = (percent)/(100)
34/x = 85/100
34*100 = x*85
3400 = 85x
85x = 3400
x = 3400/85
x = 40
So we end up with the same x value as before, and we follow the same set of steps at the end of the first section to end up with the answer of 6 quarts.
What are the solutions to the quadratic equation 3(x – 42 = 752
Nathan is 1.55 meters tall. At 1 p.m., he measures the length of a tree's shadow to be 38.15 meters. He stands 32.9 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter .
Answer:
11.26 m
Step-by-step explanation:
The height of the tree is about 11.25 meters.
What are similar triangles?When the respective sides are proportional and the corresponding angles are congruent, two triangles are said to be similar.
Given that, the height of the person is 1.55 meters, the length of the tree's shadow is 38.15 meters, and the distance between the person and the tree is 32.9 meters.
Let the height of the tree be x.
Note that the scenario makes two similar triangles.
Since the ratio of the side lengths of similar triangles is proportional, it follows:
(38.15 - 32.9)/1.55 = 38.15/x
5.25/1.55 = 38.15/x
3.39 = 38.15/x
x = 38.15/3.39
x = 11.25
Hence, the height of the tree is about 11.25 meters.
Learn more about similar triangles: https://brainly.com/question/25882965
#SPJ2
which describes the graph of y=-(x+5)^2+3
Answer:
Maximum at (-5, 3)
Step-by-step explanation:
The quadratic equation is in vertex form, which specifically shows the vertex.
Since the a is negative, you get a maximum y value of 3.
Vertex form: y=a(x-h)^2+k
If each of the n production workers in a factory assembles one instrument every t minutes, how many instruments does the factory assemble in 7.5 hours of production
Answer:
The number of instruments assembled in 7.5 hours are 450 n/t.
Step-by-step explanation:
The number of instruments assembled in t minutes = n
the number of instruments assembled in 1 minute = n / t
Total time = 7.5 hours = 7.5 x 60 = 450 minutes
So, the number of instruments assembled in 450 minutes are
[tex]\frac{n}{t}\times 450\\\\\frac{450 n}{t}[/tex]
At a certain store, a CD costs $12. If the cost of CDs were graphed as the output, compared to the number of
CDs purchased as input, which of the following would not be true of the graph?
A. The set of points would all lie on the same line.
B. The set of points would include the origin.
C. The set of points would rise from left to right.
D. The set of points would not graph a function.
Please select the best answer from the choices provided
A
B
C
D
How do u solve this ?
Find the first five terms of the sequence described.
Answer:
I dont think i dont know this but its 10?
If α and β are the zeroes of the polynomial 6y 2 − 7y + 2, find a quadratic polynomial whose zeroes are 1 α and 1 β .
Answer:
[tex]2y^2-7y+6=0[/tex]
Step-by-step explanation:
We are given that [tex]\alpha[/tex] and [tex]\beta[/tex] are the zeroes of the polynomial [tex]6y^2-7y+2[/tex]
[tex]y^2-\frac{7}{6}y+\frac{1}{3}[/tex]
We have to find a quadratic polynomial whose zeroes are [tex]1/\alpha[/tex] and [tex]1/\beta[/tex].
General quadratic equation
[tex]x^2-(sum\;of\;zeroes)x+ product\;of\;zeroes[/tex]
We get
[tex]\alpha+\beta=\frac{7}{6}[/tex]
[tex]\alpha \beta=\frac{1}{3}[/tex]
[tex]\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha \beta}[/tex]
[tex]\frac{1}{\alpha}+\frac{1}{\beta}=\frac{7/6}{1/3}[/tex]
[tex]\frac{1}{\alpha}+\frac{1}{\beta}=\frac{7}{6}\times 3=7/2[/tex]
[tex]\frac{1}{\alpha}\times \frac{1}{\beta}=\frac{1}{\alpha \beta}[/tex]
[tex]\frac{1}{\alpha}\times \frac{1}{\beta}=\frac{1}{1/3}=3[/tex]
Substitute the values
[tex]y^2-(7/2)y+3=0[/tex]
[tex]2y^2-7y+6=0[/tex]
Hence, the quadratic polynomial whose zeroes are [tex]1/\alpha[/tex] and [tex]1/\beta[/tex] is given by
[tex]2y^2-7y+6=0[/tex]
Urgenteeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
help and explain//////////////////////////////////////////////
Answer:
(f + g)(x) = 5x - 3
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= 2x + 4 + 3x - 7 ← collect like terms
= 5x - 3
Answer:
5x - 3
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
= 2x + 4 + ( 3x - 7 )
= 5x - 3
Heya Kitties!
What is the value of x?
18x−16=−12x−4
x =
Answer:
2/5
Step-by-step explanation:
18x+12x=-4+16
30x=12
x=2/5
Answer:
18x-16=-12x-4
18x+12x=-4+16
30x=12
x=12/30
x=2/5
Which expressions are equivalent to 6 - 4.5+ (-8) ?
A 6 + 4.5 + 8
B 6 + 4.5 - 8
C 6 – 4.5'+8
D 6 - 4.5 - 8
E 6+(-4.5) - 8
F 6+(-4.5) + (-8).
G 6+ (-4.5) - (-8)
Answer:
I'm pretty sure the answers are options D , E and F .
Step-by-step explanation:
So here's how I did it , I got the original expression , solved it and the answer I found is -6.5. So then I solved all the others and D , E and F gave me -6.5.
Hope this helps lol
(x+4y)^(6)
Can Someone please me how to do this PLEASE!
What is the value of x?
Answer:
D. 30°
Step-by-step explanation:
By exterior angle theorem:
x° + 70° = 100°
x° = 100° - 70°
x° = 30°
x = 30
How is mathematical thinking established? How can we have mathematical thinking?
修改翻译结果
Translate How is mathematical thinking established? How can we have mathematical thinking? in to Chinese.
数学思维是如何建立的？ 怎样才能有数学思维？
Question
The quotient of a number and 5 has a result of 2. What is the number?
Answer:
10.
Step-by-step explanation:
Answer:
The number is 10.
Step-by-step explanation:
x/5 = 2
Multiply both sides by 5.
5 * x/5 = 5 * 2
x = 10
Answer: The number is 10.
Decrease £19064.67 by 9.5%
Give your answer rounded to 2 DP. (decimal place)
Please Help !!!
Answer:
17253.52
Step-by-step explanation:
100-9.5=90.5
19064.67*0.905=17253.52
Helppp and explain pls and thankyou
Answer:
None of both
Step-by-step explanation:
It say y = lxl
so it mean if y = 3 so x = 3 or -3
What is the total value of digit 7 in the number 32.8794
Answer:
hundredth
Step-by-step explanation:
numbers after the decimal point start counting from
tenth
hundredth
Answer:
0.07 or 7 hundredths
Step-by-step explanation:
(12.3456)- I'll use this as my example
1-tens place
2-ones place
3- tenths place
4= hundredths place
5-thousandths place
6- im pretty sure its the 10 thousandths place
This year, Carlos planted 6 more than one-third of the cucumber plants he planted last year. How many cucumber
plants did he plant this year if last year he planted 12 plants?
6
9
10
12? PLEASE HELP SMB
Answer:
10 plants
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
He planted 10 this year because last year he planted 12, and 1/3 of that is 4. He planted 6 more than that this year, so 4+6=10.
find f(-2)for f(x)=5*3^x
f ( - 2 ) = 5 × 3^( - 2 )
f ( - 2 ) = 5 × 1/9
f ( - 2 ) = 5/9
2m^2-5m-3=0 by factorization
Answer:
M= 6, -1
Step-by-step explanation:
Factoring these numbers, it will result in (m-6)(m+1). So, m= 6,-1
What is the value of k?
Answer:
Step-by-step explanation:
recall that the inside angles of a triangle add up to 180°
and also that the angle 115° is the other part of a 180° total
180=115+y
180-115 =65
then the inside angle at Y is 65°
add the three inside (interior of the triangle) angles up
180= 65 + (4k+5) + (6k+10)
180 = 65 + 10k + 15
180 = 80 + 10k
100 = 10k
10 = k
see how I did that?
