Answer:
Given
The area of a rectangle is less than 81 square centimeters
length 9cm
width =x cm
Step-by-step explanation:
Area of rectangle=length ×width
= 9×X
Area of rectangle is less than 81 cm^2
So 9x-81=0
X=81/9
X=9
So the value of xis 9
What is the equation of the line represented by the table below?
x y
-3 1
6 4
12 6
30 12
Answer:
[tex]\displaystyle y-1=\frac{1}{3}(x+3)[/tex]
Step-by-step explanation:
Equation of a Line
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The table shows the relation between x and y. It contains the following points
(-3,1), (6,4), (12,6), (30,12).
Taking the two first points, we find the equation of the line:
[tex]\displaystyle y-1=\frac{4-1}{6+3}(x+3)[/tex]
[tex]\displaystyle y-1=\frac{3}{9}(x+3)[/tex]
Simplifying:
[tex]\displaystyle y-1=\frac{1}{3}(x+3)[/tex]
To ensure the rest of the points belong to the line, we test them:
For the point (12,6):
[tex]\displaystyle 6-1=\frac{1}{3}(12+3)[/tex]
[tex]\displaystyle 5=\frac{1}{3}(15)[/tex]
5=5
Since equality is true, the point belongs to the line.
For the point (30,12):
[tex]\displaystyle 12-1=\frac{1}{3}(30+3)[/tex]
[tex]\displaystyle 11=\frac{1}{3}(33)[/tex]
11=11
Since equality is true, the point belongs to the line.
Thus, the equation of the line is:
[tex]\mathbf{\displaystyle y-1=\frac{1}{3}(x+3)}[/tex]
Which ordered pair is a solution of the system of equations shown in the graph below?
Answer: A
Step-by-step explanation:
Answer:
(0,-1)
Step-by-step explanation:
because the line crosses through (0,-1) the vertex is (0,-4)
For any linear function f(x) = mx + b, when does 5f(x) = f(5x)?
a) always
b) when b = 0
c) when b = 5/4
d) when b = 5
Answer:
B
Step-by-step explanation:
Select the better deal in the pair. Then give the unit rate for the better deal.
$56/25 gal
or
$32.05/15 gal
Answer:
The better deal is $32.05/15 gal
Step-by-step explanation:
Divide:
56/25
=2.24
32.05/15
=2.13666667
=2.14
A microscope is set so it makes an object appear 6 × 10 2times larger than its actual size. A virus has a diameter of 2 × 10 -7meters. How large will the diameter of the virus appear when it's viewed under the microscope?
Answer:
The diameter of the virus will appear as 1.2 × 10⁻⁴ meters when viewed under the microscope
Step-by-step explanation:
From the question,
A microscope is set so it makes an object appear 6 × 10² times larger than its actual size. That is, when an object is viewed with the aid of the microscope, the object will be 6 × 10² times larger than its actual size.
Now, to determine how large the diameter of a virus that has a diameter of 2 × 10 ⁻⁷ meters will appear when viewed under the microscope, we will multiply the diameter of the virus by 6 × 10².
That is, 2 × 10 ⁻⁷meters × 6 × 10² = 1.2 × 10⁻⁴ meters
Hence, the diameter of the virus will appear as 1.2 × 10⁻⁴ meters when viewed under the microscope.
Find the interest on an investment of $45,000
compound annually at 5.25% for 6 years
A = P(1 + r)t
Answer:
The interest on the investment is $16,170.93811
Step-by-step explanation:
The rule of the compound interest is [tex]A=P(1+\frac{r}{n})^{nt}[/tex], where
A is the new valueP is the initial valuer is the rate in decimaln is the number of periods in timet is the time∵ The investment is $45,000
∴ P = 45,000
∵ The interest on the investment is compounded annually at 5.25%
∴ r = 5.25% = 5.25 ÷ 100
∴ r = 0.0525
∴ n = 1 ⇒ compound annually
∵ It is for 6 years
∴ t = 6
→ Substitute them in the rule above
∵ [tex]A=45,000(1+\frac{0.0525}{1})^{1(6)}[/tex]
∴ [tex]A=45,000(1.0525)^{6}[/tex]
∴ A = 61,170.93811
∵ I = A - P, where I is the interest
∴ I = 61,170.93811 - 45,000
∴ I = 16,170.93811
∴ The interest on the investment is $16,170.93811
Megan bought 2 1/4 pounds of bananas for $0.80 per pound and 1 1/2 pounds of strawberries for $1.10 per pound. How much more did Megan spend on bananas than on strawberries?
Answer:
$0.15
Step-by-step explanation:
Cost of each pounds of banana = $0.80
Number of pounds of banana = 2 1/4 pounds
Total cost of banana = $0.80 × 2 1/4 pounds
= 0.80 × 9/4
= 0.80 × 2.25
= 1.8
Total cost of banana = $1.8
Cost of each pounds of strawberry = $1.10
Number of pounds of strawberry = 1 1/2 pounds
Total cost of strawberry = $1.10 × 1 1/2 pounds
= 1.10 × 3/2
= 1.10 × 1.5
= 1.65
Total cost of strawberry = $1.65
How much more did Megan spend on bananas than on strawberries?
Total cost of banana - Total cost of strawberry
= $1.8 - $1.65
= $0.15
Answer:
$0.15
Step-by-step explanation:
Cost of each pounds of banana = $0.80
Number of pounds of banana = 2 1/4 pounds
Total cost of banana = $0.80 × 2 1/4 pounds
= 0.80 × 9/4
= 0.80 × 2.25
= 1.8
Total cost of banana = $1.8
Cost of each pounds of strawberry = $1.10
Number of pounds of strawberry = 1 1/2 pounds
Total cost of strawberry = $1.10 × 1 1/2 pounds
= 1.10 × 3/2
= 1.10 × 1.5
= 1.65
Total cost of strawberry = $1.65
How much more did Megan spend on bananas than on strawberries?
Total cost of banana - Total cost of strawberry
= $1.8 - $1.65
= $0.15
ASAP need answer I will give brainliest check out the picture
Answer:
Step-by-step explanation:
Bisect means in half so both angles equal each other, meaning the equations equal each other.
2x+7 = 4x-9
Subtract 4x from both sides
-2x+7 = -9
Subtract 7 from both sides
-2x = -16
x = 8, so the answer is the third choice
Bisect means in half so both angles equal each other, meaning the equations equal each other.
2x+7 = 4x-9
Subtract 4x from both sides
-2x+7 = -9
Subtract 7 from both sides
-2x = -16
x = 8, so the answer is the third choice
Two linear functions are shown below. Which function has the greater rate of change? Function A: 4 8 12. y 1 2 3 4 Function B: y= 0.75x - 2
Answer:
Function B
Step-by-step explanation:
✍️Rate of change for Function A:
Using any two pairs from the table of values given, say, (0, 1) and (4, 2):
Rate of change = [tex] \frac{y_2 - y_1}{x_2 -x_1} = \frac{2 - 1}{4 - 0} = \frac{1}{4} [/tex]
Rate of change for function A = ¼ = 0.25
✍️Rate of change for Function B:
Equation for Function B is given in the slope-intercept format, y = mx + b.
m = slope = rate of change.
Therefore, the function, y = 0.75x - 2 has a rate of change of 0.75.
Rate of change of Function B = 0.75.
✅0.75 if greater than 0.25, therefore, Function B has the greater rate of change.
The function which has a greater rate of change or slope is required.
Function B has a greater rate of change.
Rate of change is given by
[tex]m=\dfrac{\Delta y}{\Delta x}[/tex]
The ordered pairs for the first function are
[tex](0,1),(4,2),(8,3),(12,4)[/tex]
Slope
[tex]m=\dfrac{2-1}{4-0}=\dfrac{1}{4}=0.25[/tex]
Since, it is a linear equation the slope will be equal for all ordered pairs.
The point slope form of a line is
[tex]y=mx+c[/tex]
where
m = Slope or rate of change
c = y intercept
Here, the equation is
[tex]y=0.75x-2[/tex]
The slope is 0.75.
Function B has a greater rate of change.
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help me, please it would get 15 points
Answer:
Here are 5 (2,4), (3,6), (1,2), (4,8), (5,10)
Step-by-step explanation:
What is the slope intercept form for this ?
Answer:
150
Step-by-step explanation:
Answer:
y = 150x + 400
Explanation:
Slope intercept form is : y = mx + b
B is the y intercept, you can also think of it like a starting value, in this case Susan starts with $400 dollars
M is the slope, you can also think of it like a value that is consistently changing over time, in this case Susan saves(or earns) $150 each month.
If you want to figure how much money she will have in a certain number of months, plug the number of months (x), into the x in y = 150x + 400.
i need this asap, will give brainliest to fast answers!! :)
Answer: $22.50, but rounded to the nearest dollar its $23.00 Hope this helps :)
Step-by-step explanation: The unit rate it 1/0.75
The ratio of collectible cards Deshawn owns to cards that Stephanie owns is 5:2 Stephanie has 36 cards how will the ratio of Deshawn's cards to Stephanie's cards change if they both sell half there cards.
Given :
The ratio of collectable cards Deshawn owns to cards that Stephanie owns is 5:2.
Stephanie has 36 cards.
To Find :
How will the ratio of Deshawn's cards to Stephanie's cards change if they both sell half there cards.
Solution :
Number of card Deshawn had, n = 5/2 × 36
n = 90 .
Number of card after they sell half there cards :
[tex]n_D = \dfrac{90}{2}=45[/tex]
[tex]n_S=\dfrac{36}{2}=18[/tex]
Therefore, new ratio is [tex]\dfrac{45}{18}=5 : 2[/tex].
So, new ratio will be same.
Solve 2c − 8f = 24 for f. Show your work.
Answer:
f=2 c=4
Step-by-step explanation:
8 times 2 equals 16 plus 2 times 4 equals 24 in total.
n/56 divided by 3/24
Answer:
n/56 divided by 3/24 would be 1/7n
Step-by-step explanation:
What is 12.18 x 103 =
Answer:
1,254.54
Step-by-step explanation:
Answer:
1,254.54
Step-by-step explanation:
9) Brenn has $60 in his savings account. His brother Chris has $135 in his. Brenn decides to save $5 of his allowance each week, while Chris decides to spend his whole allowance along with $10 of his savings each week. After how many weeks will Brenn and Chris have the same amount of money in their savings accounts?
Answer:
9) 15
Step-by-step explanation:
x2 + 20x +__________
how solve these problem plssssss
Answer:
for the second question , all you have to do is substitute , the first point plotted is x and the second point is b , ploy those points in the equation and remember that to find x we make y= 0 and to find y we make x =0
A line intersects the points (3,-4) and (1,2).What is the slope intercept equation for this line
Answer:
y=-3x+5
Step-by-step explanation:
y=mx+b
m=(-4-2)/(3-1)=-3
b=y-mx
b =-4 - (3)(-3)
b=-4+9
b=5
A rubber tree is 95 inches tall and growing at a rate of 4 inches per year. A cactus is 40 inches tall and growing at arate of 5 inches per year. After how many years will the rubber tree be shorter than the cactus tree
22. Determine the value of c so that the line
segment with endpoints B(2, 2) and C(9,6)
BC
is parallel to the line segment with endpoints
D(c, -7) and E(5, -3).
help is appreciated !!!
Answer:
If the lines BC and DE are parallel, the value of c is c=-2
Step-by-step explanation:
We are given line segment BC with end points B(2, 2) and C(9,6) and line segment DE with endpoints D(c, -7) and E(5, -3).
Using slope formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex] we can find point c
When 2 lines are parallel there slope is same.
So, Slope of line BC =Slope of Line DE
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]
We have:
[tex]x_1=2, y_1=2, x_2=9, y_2=6 \ for \ line \ BC \ and \\\x_1=c, y_1=-7, x_2=5, y_2=-3 \ for \ line \ DE \[/tex]
Putting values and finding c
[tex]\frac{6-2}{9-2}=\frac{-3-(-7)}{5-c}\\ \frac{4}{7}=\frac{-3+7}{5-c} \\ \frac{4}{7}=\frac{4}{5-c} \\Cross \ multiply:\\4(5-c)=4*7\\20-4c=28\\-4c=28-20\\-4c=8\\c=\frac{8}{-4}\\c=-2[/tex]
So, If the lines BC and DE are parallel, the value of c is c=-2
The number of tons of wheat the government can afford to buy if it spends total of $100 million, wheat costs $300 per ton, and it must buy 5 fighter planes at $15 million each.
Total amount, T = $100 million.
Cost of wheat per ton, C = $300 .
Price per fighter plane, c = $15 million.
Now,
Price of 5 fighter planes, P = $( 15 × 5 ) = $75 million.
Amount left = $( 100 - 75 ) = $25 million.
So,
Number of tons of wheat government can buy is :
[tex]n=\dfrac{25\times 1000000}{300}\\\\n = 83333.33\ tons[/tex]
Therefore, number of tons of wheat the government can afford is 83333.33 tons.
Hence, this is the required solution.
Which of the following are solutions to the equation below?
Check all that apply.
x2 - 10x+ 25 = 17
I A. X = 17-5
B. x = --58-5
c. x= - - _17-5
D. x= 177 +5
E. x = 18 +5
F. x= -17 +5
Answer:
The answer is letter F po
Step-by-step explanation:
Use the formula
(b2)2 in order to create a new term. Solve for x
by using this term to complete the square.
Exact Form:x=±√17+5
HELP QUICKLY!!!
what is the y intercept of the line
Answer:
-23
Step-by-step explanation:
the equation of the line is y=-2/3x-23 so the b in the equation (y=mx+b) is the y int so that is -23
find the angle represented by x ( round the nearest tenth of a degree) A 16.2 B 16.4 c17.1 d17.4
Answer:
B. 16.4°
Step-by-step explanation:
reference angle = x = [tex] \theta [/tex]
Side length opposite to x = 20 ft = opp
Adjacent side length = 68 ft = adj
Apply the following trigonometric ratios formula:
[tex] tan(\theta) = \frac{opp}{adj} [/tex]
Plug in the values into the formula
[tex] tan(x) = \frac{20}{68} [/tex]
[tex] tan(x) = 0.2941 [/tex]
[tex] x = tan^{-1}(0.2941) [/tex]
[tex] x = 16.3886 [/tex]
x = 16.4° (nearest tenth)
Answer:
B. 16.4
Step-by-step explanation:
Help please uh thanks
Find the balance in the account.
$3,800 principal earning 2%, compounded annually, after 7 years
Answer:
A = $4360.515918 which rounded to the nearest penny is $4360.52
Step-by-step explanation:
The larger of two numbers is two more than five times the smaller number.if the sum of the two numbers is 80 find both number
Answer:
the smaller number is 13 and the larger number is 67
What is the measurement of each base angle?
Step-by-step explanation:
isosceles triangle6 X+8 = 9 X_25 9 X _6X =25 +83×= 33X=11base angle = 74