Answer:
The possible dimensions are;
If Rectangle B has a dimension of 1 unit x 2 units, then Rectangle A has a dimension of 0.315 units x 12.685 units
Step-by-step explanation:
Let;
Length of Rectangle A be a
Width of Rectangle A be b
Length of Rectangle B be c
Width of Rectangle B be d
Thus;
Area of Rectangle A = a × b
Area of Rectangle B = c × d
We are told that the area of Rectangle A is twice the area of Rectangle B:
Thus;
2cd = ab - - - - - eq. 1
perimeter of Rectangle A = 2a + 2b
perimeter of Rectangle B = 2c + 2d
We are told that the perimeter of Rectangle A is 20 units greater than the perimeter of Rectangle B. Thus, we now have;
20 + 2c + 2d = 2a + 2b - - - - eq. 2
We have 4 unknowns which are (a, b, c and d) but only 2 equations, so we need to reduce to 2 unknown variables and calculate the other ones. In this way, one of the infinite solutions is obtained.
Let's assume that c = 1 and d = 2, we obtain:
From eq 1, we have;
2 * 1 * 2 = a*b
ab = 4 or a = 4/b
From eq 2, we have;
20 + 2(1) + 2(2) = 2a + 2b
26 = 2a + 2b
Putting a = 4/b into this, we have;
26 = 2(4/b) + 2b
Multiply through by b to get;
26b = 8 + 2b²
So,we have;
2b² -26b + 8 = 0
Using quadratic formula for this,
b = 0.315 or 12.685
When, b = 12.685, a = 4/12.685 = 0.315
When, b = 0.315, a = 4/0.315 = 12.685
So, the possible dimensions are;
If Rectangle B has a dimension of 1 unit x 2 units, then Rectangle A has a dimension of 0.315 units x 12.685 units
The equation of the graphed line in slope-point form using (2,-1) is ___, and it’s equation in slope-intercept form is ___.
Answer:
[see below]
For "slope-point" form:Slope point (also called "Point-slope") form is: [tex]y-y_1=m(x-x_1)[/tex]
[tex](x_1,y_1)\text{ -Coordinate} \\m\text{ -Slope}[/tex]
Finding the Slope:We need to find the slope of the line given.
Slope is: [tex]m=\frac{y2_-y1}{x_2-x_1}[/tex]
We are given the points (2,-1) and (-2,-2).
[tex]m=\frac{-2-(-1)}{-2-2}=\frac{-1}{-4}=\boxed{\frac{1}{4}}[/tex]
The slope of the line is 1/4.
Creating the Point-Slope Equation:Replace 'm' with 1/4 and '(x1, y1)' with (2, -1).
[tex]y-y_1=m(x-x_1)\rightarrow\boxed{y+1=\frac{1}{4}(x-2)}[/tex]
[tex]\text{The equation of the graphed line in slope-point form using (2,-1) is:}\\y+1=\frac{1}{4}(x-2)[/tex]
Creating the Slope Intercept Form Equation:Slope intercept form is: [tex]y=mx+b[/tex]
We can convert our point slope equation into slope intercept form.
[tex]y+1=1/4(x-2)\\\\y+1=1/4x-0.5 \leftarrow \text{Distribute}\\y+1-1=1/4x-0.5-1 \leftarrow \text{Subtraction Property of Equality}\\\boxed{y=\frac{1}{4}x-1.5}[/tex]
The equation of the line in slope intercept form is: [tex]y=\frac{1}{4}x-1.5[/tex] OR [tex]y=\frac{1}{4}x-\frac{3}{2}[/tex].
Which of the following values are in the range of function graph below? check all that apply
Answer:
B: -2
C: 0
D: -1
Step-by-step explanation:
We are looking at only the range in this problem. That means we are looking for y-values that are associated with this graph. Since the graph only includes negative values, you can rule out A, E, and F because they are positive. The answer choices you have left are the correct choices.
Answer:
-1
-2
-5
0
Step-by-step explanation:
1) Evaluate [(1/3)-3 X (1/2)-3 ] ÷ ( ¼)-3
2) If (7-3)2 x 7x+4 = 77, find the value of x.
Answer :
(1) [tex][(\frac{1}{3})^{-3}\times (\frac{1}{2})^{-3}]\div (\frac{1}{4})^{-3})=3.375[/tex]
(2) [tex]x=\frac{45}{56}[/tex]
Step-by-step explanation :
Part 1:
The given expression is:
[tex][(\frac{1}{3})^{-3}\times (\frac{1}{2})^{-3}]\div (\frac{1}{4})^{-3})[/tex]
[tex]=[(\frac{1}{(\frac{1}{3})^3})\times (\frac{1}{(\frac{1}{2})^3})]\div (\frac{1}{(\frac{1}{4})^3})[/tex]
[tex]=[27\times 8]\div (64)[/tex]
[tex]=[216]\div (64)[/tex]
[tex]=\frac{27}{8}[/tex]
[tex]=3.375[/tex]
Part 2:
The given expression is:
[tex](7-3)2\times (7x+4)=77[/tex]
[tex](4)2\times (7x+4)=77[/tex]
[tex]8\times (7x+4)=77[/tex]
[tex]56x+32=77[/tex]
[tex]56x=77-32[/tex]
[tex]56x=45[/tex]
[tex]x=\frac{45}{56}[/tex]
Thus, the value of x is [tex]\frac{45}{56}[/tex]
Work out (4×10to the power of6) ×(2×10to the power of7) Give your answer in standard form.
Answer:
80,000,000,000,000 or 80 billion
Step-by-step explanation:
10 to the power of 6 is 1000000
1000000x 4 is 4000000
4000000 X 2 x 10 to the power of 7
4000000x (2 x10000000)
4000000 x 20000000
Is 8e+13
the number is 80,000,000,000,000
An insurance company checks police records on 582 accidents selected at random and notes that teenagers were at the wheel 15.6% of the time. The standard deviation is 1.2%. Determine the confidence interval that is likely to contain the percent of all teenagers at the wheel when an accident occurred.
Answer:
At 95% confidence level, the confidence interval that is likely to contain the percent, [tex]\hat p[/tex], of all teenagers at the wheel when an accident occurred is given as follows;
12.7% < [tex]\hat p[/tex] < 18.6%
Step-by-step explanation:
The parameters given are as follows;
Sample size, n = 582
Proportion of accidents where teenagers are at the wheel, [tex]\hat p[/tex] = 15.6%
x = 0.156*582 ≈ 91
The formula for the confidence interval is as follows;
[tex]CI=\hat{p}\pm z\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
Where:
z = z value at the confidence level
We therefore have;
[tex]CI=0.156\pm z\times \sqrt{\dfrac{0.156(1-0.156)}{582}}[/tex]
[tex]CI=0.156\pm z\times 1.504 \times 10^{-2}[/tex]
At a confidence level of 95%, z = 1.96
The confidence interval at 95% confidence level is therefore;
12.7% < [tex]\hat p[/tex] < 18.6%.
Yesterday,your checking account statement showed a balance of $17.Your friend paid back $30 today.What is your balance now?
The $30 your friend paid back will go into the checking account, so the balance will increase by that amount. Therefore, your balance will be $17 + $30 = $47.
On a road trip you see a sign "350 km to Indianapolis". About how many hours will it take you to drive to Indianapolis if you are traveling at 72 mi/h (1 mile\approx≈1.61 km). Round your answer to the nearest hundredth.
Answer:
Time t = 3.02 hours
Step-by-step explanation:
Given;
Distance d = 350 km
Speed v = 72 mi/h
Since 1 mile ≈ 1.61 km
Converting the speed to km/h
Speed v = 72 mi/h × 1.61km /mi
Speed v = 115.92 km/h
Speed = distance/time
Time t = distance/speed = d/v
Substituting the values;
Time t = 350 km/115.92 km/h
Time t = 3.019 hours
Time t = 3.02 hours (to the nearest hundredth.)
Is it possible to ride a bike 200 miles in 13 hours
Answer:
no
Step-by-step explanation:
because even going back to back it would take you about one or two days
Multiply the polynomials
College students borrowed $6000 for 2 years at a simple interest of 12%. How much would they owe at the end of 2 years?
Answer:
Principal amount (P) = $6000
Rate (R) = 12%
Time = 2 years
Simple interest, I = P X R X T / 100
= 6000 X 12 X 2 / 100
= 144000 / 100
= 1440
=> Simple interest, I = $1440
Amount they would owe at the end of 2 years,
= P + I
= 6000 + 1440
= $7440
pls answer this thanks
Answer:
1) 1/10
2)2/10
3)8/10
Step-by-step explanation:
the numbers 1 and 10 both have 1 in them
Dexter read 11 science fiction books and 5 history books. Lena read 9 science fiction books and 4 history books. Compare the students’ ratios of science fiction books to history books.
1. Determine the ratios’ form:
science fiction books to history books
2. Write the ratios as fractions:
Dexter: 11
5
; Lena: 9
4
3. Rewrite with a common denominator.
4. Compare.
5. Answer the question.
Determine which shows the correct comparison of the ratios for this problem.
StartFraction 5 Over 20 EndFraction greater-than StartFraction 4 Over 20 EndFraction
StartFraction 26 Over 20 EndFraction greater-than StartFraction 25 Over 20 EndFraction
StartFraction 11 Over 20 EndFraction greater-than StartFraction 9 Over 20 EndFraction
StartFraction 44 Over 20 EndFraction less-than StartFraction 45 Over 20 EndFraction
Answer:
the answer is d 44/20 44/20
Integrate (x^2+1)/(x+1) dx
Answer:
me puedes explicar más
The base of a rectangular prism has an area of 121212 square centimeters. The height of the rectangular prism is 333 centimeters. What is the volume, in cubic centimeters, of this rectangular prism?
Answer:
36 cm³
Step-by-step explanation:
Volume of rectangular prism =( L * B * H) or (area * height)
= 12 cm² * 3 cm
= 36 cm³
Answer:
What is the area of the base of the rectangular prism?
18 square centimeters
What is the height of the rectangular prism?
6 centimeters
What is the volume of the rectangular prism?
108 cubic centimeters
Step-by-step explanation:
the sum of 3x^2 + x - 7 and x^2 + 10 can expressed as
Answer:
4x^2 + x + 3
Step-by-step explanation:
Here, we want to find the sum of the two polynomials
That would be ;
3x^2 + x-7 and x^2 + 10
Adding means we are taking like terms together
That would be
3x^2 + x ^2 + x -7 + 10
= 4x^2 + x + 3
Answer:
It's D
Step-by-step explanation:
2 people can plough through a field in 6 hours How long will it take for 1 person to plough through a field How long will it take for 3 people to plough through a field
Answer:
3 people 4 hours and and one person 12 hours
Step-by-step explanation:
your welcome
PLZ HLP MEEEEEEEEEEEEEEEEEEEEE A median of a triangle is a line or segment that passes through a vertex and bisects the _______ opposite that vertex.
Answer: Correct answer is Side
Step-by-step explanation:
Fine 3 consecutive numbers where the product of the similar two numbers is 28 less than the square of the largest number
Answer:
8, 9, and 10
Step-by-step explanation:
see attachment
Determine and state the coordinates of the center and the length of the radius of a circle whose equation is
x2 + 6x + y2 - 4y = 10
Answer: center = (-3, 2) radius = √23
Step-by-step explanation:
The equation of a circle is: (x - h)² + (y - k)² = r²
where center = (h, k) and radius = r
Complete the square for both x and y:
[tex]x^2+6x+\bigg(\dfrac{6}{2}\bigg)^2+y^2-4y+\bigg(\dfrac{-4}{2}\bigg)^2 = 10 +\bigg(\dfrac{6}{2}\bigg)^2+\bigg(\dfrac{-4}{2}\bigg)^2\\\\\\(x+3)^2+(y-2)^2=23\\\\\\\rightarrow (h,k)=(-3,2)\\\\\rightarrow r^2=23\quad \rightarrow r=\sqrt{23}[/tex]
Identify the terms and like terms in the expression. A3 + 4 + 2t – 9 + t Which statements are true? Check all that apply. The expression contains seven terms. The terms in the expression are a3, 4, 2t, 9, and t. The constants, 4 and 9, are like terms. Like terms have the same variables to the same powers. A3, 2t, and t are variables, so they are like terms. 2t and t are like terms.
Answer:
• The constants, 4 and 9, are like terms.
• 2t and t are like terms
• Like terms have the same variables to the same powers
Step-by-step explanation:
A3+4+2t-9+t
• The constants, 4 and 9, are like terms.
• 2t and t are like terms
• The terms in the expression are a3, 4, 2t, 9, and t. This could have been among if the a3 is written as A3
Answer:
options 2,3,4,6
if f(x)=4x-1 and g(x)=x^2+7 ,find G(f(x))
Answer:
16x² - 8x + 8
Step-by-step explanation:
f(x)=4x-1
g(x)=x²+7
g(f(x)) = g(4x-1) = (4x - 1)² + 7 = 16x² - 2*4x*1 +1² + 7= 16x² - 8x + 8
What is the slope of the line in the graph?
Step-by-step explanation:
slope = Change of y/ change of x
= 4/4
= 1
slope + or > 0 y increases when x increases
Caleb bought some snacks at the store that cost a total of $9.38. If Caleb paid with a $20 bill, how much change did he get back?
Answer:
10.62
Step-by-step explanation:
20- 9.38 = 10.62
Mark the statements that are true.
Answer:
Hi there!
The correct choices are: A, B, C
Step-by-step explanation:
π in radians equals to 180°
A is correct because 180/3 = 60
C is correct because 180/4 = 45
The measure angles π and π/4 is true
What is Radian and degree?Radian, When we rotate the radius completely around the circle, it completes one rotation. The angle subtended at the center of the circle by the radius after one complete rotation is 2π radians. The angle in radians subtended by the radius at the center of the circle is the ratio of the length of the arc to the length of the radius. When the length of the arc becomes equal to the length of the radius, the angle subtended at the center becomes 1 radian. We denote the unit radian as rad. Radians is the SI unit of measuring angles.
Degree Angles are measured in degrees. One revolution is divided into 360 equal parts and each part is called a degree. The angle subtended at the center of the circle after one complete rotation of the radius is 360°. The symbol for degrees is denoted by '°'. Degrees is not an SI unit to measure angles but it is an accepted unit to measure. Hence, while solving problems, it is preferred to convert the unit of angle from radians to degrees to understand it better. The instrument used to measure an angle in degrees is a protractor. Comparing the measures of the angle for a complete rotation, we observe,360 Degrees = 2π Radians180 Degrees = π Radians
According to the question
To convert radians to degrees, multiply by 180/p,
like this: degrees = radians x (180 / π )
To convert degrees to radians,
multiply by p/180, like this
radians = degrees x ( π/180)
(A)
This will use the formula for radians to degrees. π/3 x (180/π) The pi's cancel, leaving you with: 180/3 = 60 degrees False
(B)
An angle that measures π/6 radians also measures 30°π/6 x (180/π) = 30 degrees. True
(C)
An angle that measures π/3 radians also measures 60°π/3 x (180/π) = 60 degrees. True
(D) An angle that measures 180 degrees also measures π/2π/2 x (180/π) = 90 degrees. False
hence, measure angles π and π/4 is true, therefore option B and C are true
To learn more about radian and degree from here https://brainly.in/question/3390676
#SPJ2
Will crown the first answer the brainliest
No 1 = ⅓ No 2 = ½I hope it helps
plesase help me to solve full process . the marked price of a table fan is Rs 1400 and 10% discount is allowed on it. Find it C.P. with 15% VAT.
[tex]answer = Rs 1449\\ solution \\ marked \: price = rs \: 1400 \\ discount \: percent = 10 \: percent \\ discount \: amount = \: discount \: percent \: of \: mp \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 10 \: percent \: of \: 1400 \\ \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 140 \\ \\ sp = mp - \: discount \\ \: \: \: \: \: \: \: = 1400 - 140 \\ \: \: \: \: \: = 1260 \\ vat \: amount = \: vat \: percent \: of \: sp \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \: 15 \: percent \: of \: 1260 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 189 \\ sp \: with \: vat = \: sp + \: vat \: amount \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1260 + 189 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = Rs1449 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
I WILL GIVE BRANILEST! PLEASE HELPPPPPP a round flower garden with a radius of 23 metres is surrounded by a pathway of 2 metres wide. Calculate the circumference and area of the outer pathway.
Answer:
50pi circumference
96pi area
Step-by-step explanation:
The outer pathway is a circle of radius 25, so the circumference is
2*pi*25 or 50pi
The are is pi*r^2 or 625 pi - pi*23^2 = 96pi
Danielle works at a toy store that sells remote control cars. She wants to fit 60 car boxes into a large crate. The car boxes have dimensions of 50 cm × 30 cm × 20 cm. The crate has dimensions of 140 cm × 120 cm × 110 cm. Predict whether all 60 boxes fit in the crate. Show your calculations to support your answer. Explain your thinking.
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Work out m and c for the line
y= x + 3
m=
c=
Answer:
1
3
Step-by-step explanation:
The equation of a graph is normally written in form Mx+c.
So, here there is x+3.
Thus, m = 1
C = 3
Hope this helps
y+7=-2(x+3)
intercept form ):
Answer:
y = -2x - 13
Step-by-step explanation:
Answer:
y = - 2x - 13
Step-by-step explanation:
First, distribute out the two on the right side of the equation.
y + 7 = - 2x - 6
Next, subtract 7 from both sides to isolate the y variable on the left side.
y = - 2x - 13
That is your answer in slop-intercept form.