Given: g(z)=5z+2.1
1. What is the value of g(z) if z= -4?
2. What is the value of g(z) if z= -7?
3. What is g(-8)?
Answer/Step-by-step explanation:
Given the function, [tex] g(z) = 5z + 2.1 [/tex], the table can be completed by substituting the given value of z as follows:
Question 2: z = -7
[tex] g(-7) = 5(-7) + 2.1 [/tex]
[tex] g(-7) = -35 + 2.1 [/tex]
[tex] g(-7) = 32.9 [/tex]
Question 3: z = -8
[tex] g(-7) = 5(-8) + 2.1 [/tex]
[tex] g(-7) = -40 + 2.1 [/tex]
[tex] g(-7) = 37.9 [/tex]
Write 5.48 repeating as a mixed number in simplest form
Answer:5 12/25
Step-by-step explanation:
48-24-12
over
100-50-25
The perimeter of a rectangle is 16cm. If the length is doubled, the perimeter is 26. What are the length and width of the rectangle? Please explain all steps required, thanks ahead of time!
Answer:
Length is 5, width is 3.
Step-by-step explanation:
The formula for the perimeter of a rectangle is:
[tex]P=2l+2w[/tex]
Where P is the perimeter, l is the length, and w is the width.
With the original length and width, the perimeter is 16, thus:
[tex]16=2l+2w[/tex]
Now, if we double the length, the 2l will become 4l. Also, the perimeter will change to 26. Thus:
[tex]26=4l+2w[/tex]
Now, we have a system of equations. We can solve it using elimination. Multiply everything by -1 in the first equation:
[tex]16=2l+2w\\-16=-2l-2w[/tex]
Now, add the equations:
[tex]-16=-2l-2w\\26=4l+2w[/tex]
-16 plus 26 is 10. -2l plus 4l is 2l. The 2w cancel. Thus:
[tex]10=2l[/tex]
Divide both sides by 2:
[tex]l=5[/tex]
So, the original length was 5.
To find the original width, substitute 5 back into the first equation:
[tex]16=2(5)+2w[/tex]
Multiply:
[tex]16=10+2w[/tex]
Subtract 10 from both sides:
[tex]2w=6[/tex]
Divide both sides by 2:
[tex]w=3[/tex]
So, the original width was 3.
And we're done!
Checking:
Originally, our length was 5 and 3. This means that the perimeter is 2(5+3)=2(8)=16 which is correct.
After we double our length, our length will be 10. This means that the new perimeter is 2(10+3)=2(13)=26. So, our answers are correct!
Let's assume that length be L and width be B.
Perimeter of rectangle is given by,
Perimeter = 2( L + B)
So,
⇒ 16 cm = 2 ( L + B )
⇒ 8cm = L + B _______( Say equation 1)
Now, we are given that when length is doubled perimeter is 26.
So,
⇒ 26 cm = 2 ( 2 L + B )
⇒ 13 cm = 2 L + B
⇒ 13 cm = L + L + B
Now use equation-1
⇒13 cm = L + 8cm
⇒13 cm - 8 cm = L
⇒5 cm = L
Therefore length is 5cm.
Now substitute this value in equation 1
⇒L + B = 8 cm
⇒5cm + B = 8 cm
⇒B = 8 cm - 5 cm
⇒B = 3 cm
Therefore breadth is 3 cm.
PLEASE HELP ME WITH ALL THE QUESTION BE HONEST PLEASE URGENT!
Answer:
59
Step-by-step explanation:
1. -35
2. +9
3. -23
4. +3
5. +5
6. -7
7. +125
8. -18
Add them all up in a calculator and you get 59
PLEASE BELP ASAP
Find the area of the shape
below.
9 cm
11 cm
6 cm
15 cm
Answer:
105 cm squared
Step-by-step explanation:
15×6 to get the rectangle =90
then we have a triangle left so you do 15- 9 for the base =6 and multiply that by hight (6×5=30) and since it's a triangle and not a square we have to divide that answer by 2 and we get 15. Add those together, we get 105. Hope that helped!
The area of the shape below is 105 cm².
What is the area of a Rectangle?The area of a rectangle is calculated by multiplying the length and width of the rectangle.
What is the area of a Triangle?
The area of a triangle is equal to half of the product of the triangle's base and height.
How to solve the problem?Cut the shape given into a triangle and a rectangle as given in the following figure. Then the area of the shape is the sum of the area of the triangle and the area of the rectangle. In the shape, we can clearly specify that the base of the triangle is (15-9) cm=6cm and the height is
(11-6)cm=5cm.
Thus,
The area of the rectangle in the figure is (6×15) cm²=90 cm², and
the area of the triangle in the figure is (1/2)(6×5) cm²=15 cm².
Hence, the area of the shape is 90+15 cm² = 105 cm².
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dilations help me please
Answer:
D'(1, - 1 )
Step-by-step explanation:
Assuming the dilatation is centred at the origin, then multiply the coordinates of D by [tex]\frac{1}{2}[/tex] , that is
D(2, - 2 ) → D'([tex]\frac{1}{2}[/tex] (2) , [tex]\frac{1}{2}[/tex] (- 2) ) → D'(1, - 1 )
Which expression is equal to 3/4? 3 - 4, 4 - 3, 3 divided by 4 or.. 4 divided by 3 ?
Answer:
3 divided by 4
Step-by-step explanation:
the slash mark means divided.
What is the distance between the building B (4, 6) and the station K (–6, –2)? Use a calculator to round to the nearest tenth.
Answer:
The answer is
12.8 unitsStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
B (4, 6) and K (–6, –2)
The distance is
[tex] |BK| = \sqrt{ ({4 + 6})^{2} + ({6 + 2})^{2} } \\ = \sqrt{ {10}^{2} + {8}^{2} } \: \: \: \: \: \: \: \: \: \\ = \sqrt{100 + 64} \: \: \: \: \: \: \: \: \: \\ = \sqrt{164} \\ = 2 \sqrt{41} \\ = 12.80[/tex]
We have the final answer as
12.8 to the nearest tenthHope this helps you
Tavon has a gift card for $130 that loses $3 for each 30-day period it is not used. He has another gift card for $110 that loses $2.50 for each 30-day period it is not used. a. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal. b. What will the value of each card be when they have equal value? a. If x is the number of 30-day periods, then the equation can be used to find the number of 30-day periods until the values of the gift cards will be equal.
(Type an equation. Use integers or decimals for any numbers in the equation.)
Answer:
55
Step-by-step explanation:
The required solution is 40 and after 40days $10 left for each of the gift card.
It is required to find the solution.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
The first equation is 130 - 3x because you start with $130 and subtract 3 for each 30 day period.
The second equation is 110-2.50x
Set them equal to each other: 130 - 3x = 110 - 2.50x
Solve for x:
130 - 3x = 110 - 2.50x
130-110=3x-2.50x
20=0.50x
40 = x
After 30-40 day periods (1200 days), both cards should have equal value.
Card 1 after 40 periods,
=130 - 3(40) = $10 left
Card 2 after 40 periods
=110 - 2.5(40) = $10 left
Therefore, the required solution is 40 and after 40days $10 left for each of the gift card.
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Evaluate the following: 6+ (5 + 1).
Answer:12
Step-by-step explanation:6+(5+1)
5+1=6
6+(6)=12
Name the intersection of plane R and line JL
Answer:
K
Step-by-step explanation:
As per diagram, the intersection of the line JL and plane R is the point K
Correct option is the last one
if anyone could help i would appreciate it.
Answer:
i think underroot 29 is a midpoint of this two unit
Answer:
B(-6,7)
mid point (1,5)
Step-by-step explanation:
A=-2,-3 M (-4,2) is the midpoint between A and B
x of M=(xA+xB)/2
-4=-2+xB/2
-4(2)=-2+xB
xB=-6yM=(yA+yB)/2
2=(-3+yB)/2
2(2)=-3+yB
yB=4+3
yB=7Find mid point of AB A(-1,4), B(3,6)midpoint (xa+xb/2 , ya+yb/2)
(-1+3/2 ,4+6/2)
(1,5)
if f(x) = 6x - 4, which is f(x) when x=8 ?
GEOMETRY HELP PLEASE, ITS URGENT
A line that is perpendicular to 3y=11-8x has slope m=
Step-by-step explanation:
for a perpendicular,
make x the subject.
8x=11-3y
x=11/8 +3/8
for a perpendicular, the gradient
x= -1/m
x= (-1/11/8) - (-1/3y/8)
x= 8/3y -8/11.
therefore the gradient (m) = 8/3y -8/11.
How do I simplify -2i squared?
Answer:
-2x^2
Explanation:
=-2*x^2
=-2*(x*x)
=-2x^2
hii anyone mind helping me with this question :D
Answer:
0.0045
Step-by-step explanation:
:)
Helo please I need help
Answer:
9:16
Step-by-step explanation:
In a similar rectangle , the ratio of lengths should be equal to ratio of widths.
Ratio of lengths =
[tex] \frac{length \: of \: rectangle \: 1}{length \: of \: rectangle \: 2} = \frac{3}{4} [/tex]
Hence , Ratio of widths =
[tex] \frac{width \: of \: rectangle \: 1}{width \: of \: rectangle \: 2} = \frac{3}{4} [/tex]
Area of rectangle 1 = Length 1 × Width 1 = 3×3 = 9
Area of rectangle 2= Length 2 × Width 2= 4×4= 16
Ratio of areas of both rectangles =
[tex] \frac{area \: of \: rectangle \: 1}{area \: of \: rectangle \: 2 \: } = \: \frac{9}{16} [/tex]
SOMEBODY HELP ASAP!! 33 POINTS!
What is the surface area, in square inches, of a prism with a length of 12 inches, a width of 9 inches, and a height of 2 inches?
Answer:
Surface Area would be 200² inches.
Step-by-step explanation:
SA=2(12*9)+2(9*2)+2(12*2)
SA=2(108)+2(18)+2(24)
SA=216+36+48
SA=200² in.
5 (t+3)=-3.5 solve for t
Answer:
t=-3.7
Step-by-step explanation:
5 (t+3)=-3.5
solving the bracket we have;
5t+15=-3.5
collect like terms
5t=-3.5-15
5t=-18.5
divide both sides by 5;
t=-3.7
The value of t in the given algebraic expression is; t = -2.3
We are given the equation;
5(t + 3) = 3.5
Using distributive property on the left hand side, we have;
5t + (5 × 3) = 3.5
5t + 15 = 3.5
Using subtractive property of equality, subtract 15 from both sides to get;
5t + 15 - 15 = 3.5 - 15
5t = -11.5
Divide both sides by 5 to get;
5t/5 = -11.5/5
t = -2.3
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Noah borrowed $17 from his mother. He then paid back $8 of the amount he owed.
Complete the statements to represent the change in the amount of money that
Noah's mother has.
Click the arrows to choose an answer from each menu.
The change in the amount of money that Noah's mother
has can be represented by the
expression Choose... The expression can be simplified to Choose... which
shows that Noah still owes Choose... to his mother.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Amount Noah borrowed from his mother = $17
Amount paid = $8
Change in the amount of money Noah's mother has :
Let initial amount her mother has = x
Hence, the amount she has after Noah paid $8 to her will be :
Initial amount - amount borrowed + amount paid
= x - $17 + $8.
The simplified amount = x - $9
The amount Noah still owes :
Total amount owed - amount paid
$17 - $8 = $9
The change in the amount of money that Noah's mother will be $ 9.
What is Algebra?Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.
Noah borrowed $17 from his mother. He then paid back $8 of the amount he owed.
Then the amount owed will be given as the difference between the initial amount and paid amount.
→ $ 17 - $ 8
→ $ 9
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-a + 4a - 9 = 8a + 6
Answer:
-3=a
Step-by-step explanation:
-a+4a-9=8a+6
3a-9=8a+6
3a-9-6=8a+6-6
3a-15=8a
3a-3a-15=8a-3a
-15=5a
-15/5=5a/5
-3=a
What is the sum of a number, x, and it’s opposite?
Answer:
The opposite of a number is its additive inverse. The sum of a number and its opposite is zero
Step-by-step explanation:
Answer:
- x, 0
Step-by-step explanation:
The opposite of x is - x because they cancel each other out. It doesn't matter what x is because - x and x are the same amount of distance from each other.
The sume of x and its opposite is 0.
Hope This Helps :)
What is the measurement of this angle
Answer:
15
Step-by-step explanation:
Stickers come in packs of 5. Max buys 12 packs. He gave his three friends some stickers. They each receive the same number. He has 27 stickers left. How many stickers did max give each of his friends?
Answer: 11 stickers each
Step-by-step explanation:
given data:
packs of stickers bought by mark = 12 ( 5 ) = 60 stickers
no of stickers left with mark = 27
= Total no of stickers – stickers remaining with mark
= 60 – 27
= 33 stickers
he gave his 3 friends equal number of stickers.
3x = 33
x = 11
number of stickers received by each friend is 11
Nolan is driving to a concert and needs to pay for parking. There is an automatic fee of $8 just to enter the parking lot and when he leaves the lot he will have to pay an additional $3 for every hour he had his car in the lot. How much total money would Nolan have to pay for parking if he left his car in the lot for 6 hours? How much would Nolan have to pay if he left his car in the lot for t hours?
Answer:
i. $26
ii. $(8 + 3t)
Step-by-step explanation:
Given that: automatic fee is $8, and fee per hour is $3. Then;
i. If he left his car in the lot for 6 hours, amount to be paid can be calculated as thus;
since fee per hour is $3, then for 6 hours; the fee = 6 x $3
= $18
Total amount to be paid after 6 hours = automatic fee + $18
= $8 + $18
= $26
For parking his car for 6 hours, he would pay $26
ii. Amount paid for t hours = automatic fee + $ 3 x t
= $(8 + 3t)
[tex]\sqrt[3]{-8/27} = -2/3[/tex]
Two fifths of d is subtracted from 7
Answer:
See Below
Step-by-step explanation:
[tex]\frac{2}{5} -7[/tex]
First, let's make 7 into an improper fraction
7x5 =35
2/5 - 35/5 = -33/5
Find the GCF of 38, 76, and 114.
GCF = 38
Step-by-step explanation:38 = 2×19
76 = 4×19 = 2²×19
114 = 2×3×19
GCF = 2×19 = 38