Answer:
2×10¹⁰ m²Step-by-step explanation:
Dimensions of rectangle:
5×10⁵ m and 4×10⁴ mThe area is the product of the two dimensions:
5×10⁵ m × 4×10⁴ m =20×10₉ m² =2×10¹⁰ m²Tomika heard that the diagonals of a rhombus are perpendicular to each other. Help her test her conjecture. Graph quadrilateral ABCD on a coordinate grid with A(1, 4), B(6, 6), C(4, 1), and D(–1, –1).
a. A rhombus has 4 sides that are equal length. Is ABCD a rhombus? Show how you know.
b. Write the equations of the lines on which the diagonals lie. That is, write the equations of lines AC and BD.
c. Compare the slopes of lines AC and BD. What do you notice?
Answer:
a. The four sides of the quadrilateral ABCD are equal, therefore, ABCD is a rhombus
b. The equation of the diagonal line AC is y = 5 - x
The equation of the diagonal line BD is y = 5 - x
c. The diagonal lines AC and BD of the quadrilateral ABCD are perpendicular to each other
Step-by-step explanation:
The vertices of the given quadrilateral are;
A(1, 4), B(6, 6), C(4, 1) and D(-1, -1)
a. The length, l, of the sides of the given quadrilateral are given as follows;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
The length of side AB, with A = (1, 4) and B = (6, 6) gives;
[tex]l_{AB} = \sqrt{\left (6-4 \right )^{2}+\left (6-1 \right )^{2}} = \sqrt{29}[/tex]
The length of side BC, with B = (6, 6) and C = (4, 1) gives;
[tex]l_{BC} = \sqrt{\left (1-6 \right )^{2}+\left (4-6 \right )^{2}} = \sqrt{29}[/tex]
The length of side CD, with C = (4, 1) and D = (-1, -1) gives;
[tex]l_{CD} = \sqrt{\left (-1-1 \right )^{2}+\left (-1-4 \right )^{2}} = \sqrt{29}[/tex]
The length of side DA, with D = (-1, -1) and A = (1,4) gives;
[tex]l_{DA} = \sqrt{\left (4-(-1) \right )^{2}+\left (1-(-1) \right )^{2}} = \sqrt{29}[/tex]
Therefore, each of the lengths of the sides of the quadrilateral ABCD are equal to √(29), and the quadrilateral ABCD is a rhombus
b. The diagonals are AC and BD
The slope, m, of AC is given by the formula for the slope of a straight line as follows;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Therefore;
[tex]Slope, \, m_{AC} =\dfrac{1-4}{4-1} = -1[/tex]
The equation of the diagonal AC in point and slope form is given as follows;
y - 4 = -1×(x - 1)
y = -x + 1 + 4
The equation of the diagonal AC is y = 5 - x
[tex]Slope, \, m_{BD} =\dfrac{-1-6}{-1-6} = 1[/tex]
The equation of the diagonal BD in point and slope form is given as follows;
y - 6 = 1×(x - 6)
y = x - 6 + 6 = x
The equation of the diagonal BD is y = x
c. Comparing the lines AC and BD with equations, y = 5 - x and y = x, which are straight line equations of the form y = m·x + c, where m = the slope and c = the x intercept, we have;
The slope m for the diagonal AC = -1 and the slope m for the diagonal BD = 1, therefore, the slopes are opposite signs
The point of intersection of the two diagonals is given as follows;
5 - x = x
∴ x = 5/2 = 2.5
y = x = 2.5
The lines intersect at (2.5, 2.5), given that the slopes, m₁ = -1 and m₂ = 1 of the diagonals lines satisfy the condition for perpendicular lines m₁ = -1/m₂, therefore, the diagonals are perpendicular.
Which of the following is a solution of the function graphed below?
Answer:
Option A
Step-by-step explanation:
It's a point on the function's graph
Help me with this please
Answer:
15 cans or D
Step-by-step explanation:
so it’s a pattern every 5 days add 3 cans
so Now do a table
5 = 3
10 = 6
15 = 9
20 = 12
25 = 15
Answer:
15 cans
D
Step-by-step explanation:
Set up a proportion.
3 cans / 5 days = x cans / 25 days
Note: both sides contain the same units on top and the same units on the bottom of each fraction.
3/5 = x / 25 Cross multiply
5x = 3*25
5x = 75
x = 75 / 5
x = 15
A model house has a scale of 3 cm : 6 m.
If the model house is 9 cm wide, then how
wide is the real house?
Chef Rita is cooking for a Sunday brunch. She knows that 22 pancakes can feed 8 people. She is wondering how many people (p)(p)left parenthesis, p, right parenthesis she can feed with 55 pancakes. She assumes each person eats the same quantity of pancakes.
How many people can Rita feed with 55 pancakes?
Answer:we can solve the problem by setting a simple proportion.
We know that 22 pancakes can feed 8 people, so we have to find the number x which corresponds to the number of people that can be feeded with 55 pancakes:
Solving the proportion, we find
So, 55 pancakes can feed 20 people.
Step-by-step explanation:
Find the median of the
data. 7,5, 12, 8, 2,9,4
Answer:
7
Step-by-step explanation:
First, put them in numerical order: 2, 4, 5, 7, 8, 9, 12
Then cross out one from each side until you get to the middle
The median of the given data set 7,5, 12, 8, 2,9,4 is 7.
What are the mode and median?Mode is the highest frequency number while the median is the middle value of a data set after writing either increasing or decreasing manner.
For example;
Set { 1,2,2,3,4,5,6} here mode is 2 and median is 3.
Given the data set,
7,5, 12, 8, 2,9,4
If we write it in increasing order then,
2, 4, 5, 7, 8, 9, 12
Now median is middle value so here 7 is in between 3 - 3 from left and right.
Hence "The median of the given data set 7,5, 12, 8, 2,9,4 is 7".
To learn more about mode and median,
https://brainly.com/question/300591
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Erica sells magazine subscriptions and makes a flat rate of $5.35 for each subscription she sells. If Erica made $42.80 on Monday, $64.20 on Tuesday and $74.90 on Wednesday, how many subscriptions did she sell in the three days
to find the number of subscribtion sold we divide the money she made by the price of subscription
monday:
42.80/5.35=8 subscriptions sold
tuesday:
64.20/5.35=12 subscriptions sold
wednesday:
74.90/5.35=14 subscriptions sold
8+12+14=34 subscriptions sold in 3 days
Answer:
34 subscriptions she sold
A store sells a 1/1/4 pound package of turkey for $9 whats the unit price of the turkey in the package
Answer:
$7.20
Step-by-step explanation:
The first step is to convert 1 1/4 to decimal form. 1/4=0.25, which when added to the 1 gives a total weight of 1.25 pounds. Dividing this by the price to find the unit price, you get 9/1.25=$7.20 per pound of turkey. Hope this helps!
A shirt originally cost $46.25, but it is on sale for $37.00. What is the percentage decrease of the price of the shirt? If necessary, round to the nearest percent.
Answer:
20%
Step-by-step explanation:
Original cost = $46.25
Decreased cost = $37.00
Decrease in cost = 46.25 - 37.00 = $9.25
Percentage decrease
[tex] = \frac{9.25}{46.25} \times 100 \\ \\ = \frac{92500}{4625} \\ \\ = 20\% [/tex]
help solve for x please!
x to the third power= -8
Answer:
X = 2
Step-by-step explanation:
2 x 2 x 2 = 8
Hope this helps. Pls give brainliest.
Answer:
2 :)
Step-by-step explanation:
here are two receipts from a meal in a restaurant one persons subtotal is $24.95 if the tax rate at the restaurant is 9.5% how much will their sale tax be?
Answer:
$24.95X.095=$2.37
Answer:
Step-by-step explanation: 3.27
The original price of an iPad is $429. The sale price is 30% off the original price. What is the sale price of the iPad? Show your work.
Answer:
297.3
Step-by-step explanation:
30% of 429 is 128.7
429 which is the original price - 128.7 which is the price off = 297.3
Answer:
$300.30
Step-by-step explanation:
100% - 30% = 70%
429 * 0.70 = 300.30
Therefore the sale price of the ipad is $300.30!
Please mark brainliest and have a nice day!
A 64-ounce bottle of apple juice costs $1.35. What is the approximate unit price for this bottle of apple juice?
The approximate unit price for the juice is about $0.50
Step-by-step explanation:
To find the unit price of an item, you must divide the price ($1.35) by how many units the item has (64 ounces). So 64 divided by 1.35 would be 47, or 50 since it's asking for the approximate unit price. Convert it and you have your answer. $0.50. Hope this helps :) I apologize if it's not completely correct
Help me please I'm so stuck lol 15 pts.!!
Answer:
r = 0.1
Step-by-step explanation:
Constant proportionality or slope(rate of change) is found by Y divided by X.
1.4(y) ÷ 14(x) = 0.1(slope)
1.6(y) ÷ 16(x) = 0.1(slope)
2.1(y) ÷ 21(x) = 0.1(slope)
Check Work:
14 x 0.1 = 1.4
16 x 0.1 = 1.6
21 x 0.1 = 2.1
Answer:
1/10.
Step-by-step explanation:
The proportionality equation is given to you: [tex]y = rx[/tex]
Next, plug in the given [tex]x[/tex] and [tex]y[/tex] variables into the equation:
When: [tex]x = 14[/tex] & [tex]y = 1.4[/tex]
[tex]1.4 = r(14)\\1.4 = 14r\\(1.4)/14 = (14r)/14\\1.4/14 = r\\r = 0.1[/tex]
When: [tex]x = 16[/tex] & [tex]y = 1.6[/tex]
[tex]1.6 = r(16)\\1.6 = 16r\\(1.6)/16 = (16r)/16\\r = 1.6/16\\r = 0.1[/tex]
When: [tex]x = 21[/tex] & [tex]y = 2.1[/tex]
[tex]2.1 = r(21)\\[/tex]
[tex]21r = 2.1\\(21r)/21 = (2.1)/21\\r = 2.1/21\\r = 0.1[/tex]
r = 0.1 in all of the given, ∴ 0.1 is your answer. Change the decimal into a fraction:
0.1 = 1/10
1/10 is your answer.
~
find the selling price: original price of a radio: 53.50 discount: 30
Answer:
48.69
Step-by-step explanation:
Step-by-step explanation:
30% off $53.50
= 70% of $53.50
= $53.50 * (70/100) = $37.45.
hi guys can you help me with this maths calculation
$36 - $17.85 =
Answer and Step-by-step explanation:
36 dollars minus 17.85 dollars equals $18.15, or 18 dollars and 15 cents.
All you have to do is subtract 36 by 17.85
36 - 17 = 19
100 - 85 = 15
1 is subtracted from 19 because of the decimal.
18.15
#teamtrees #WAP (Water And Plant)
Justin and Elena each launched a toy rocket into the air. The height of Justin's rocket is modeled by the equation h = –16t2 + 60t + 2. Elena launched his rocket from the same position, but with an initial velocity double that of Justin's. Which equation best models the height of Elena's rocket? h(t) = at2 + vt + h0
Answer:
b
Step-by-step explanation:
A drama club made $3,200 from a school play. Seventy-five percent of that amount came from ticket sales. Identify the values of the variables in the model. Then use the model to find the amount of ticket sales.
a =
b =
The amount of ticket sales is $
.
Answer: $2400
Step-by-step explanation:
Based on the question above, a will be the percentage of tickets that were sold while b will be tickwt sales. Therefore,
a = 75%
b = 75% × $3,200
= 0.75 × $3200.
= $2400
Based on the information above, the amount of tickets sales is $2400
(-2/10)^4 power
HELP MEE PLS
Answer:
1/625
Step-by-step explanation:
simply
(-1/5)^4
1/625
Answer:
The answer is 1/625
Step-by-step explanation:
hope this helps
Ricardo bought a bicycle that was discounted 20% off the original price. If the original price was $110.00, what was the price of the bicycle after the discount was applied?
Answer:
88$
Step-by-step explanation:
if two lines are perpendicular , what do we know about their slopes ?
Answer:
If two lines are perpendicular and neither one is vertical, then one of the lines has a positive slope, and the other has a negative slope. Hope this helps.
Step-by-step explanation:
5) The sides of a quadrilateral are in the ratio 1:2:3:6. The perimeter is 138 cm.
Answer:
The first side is 11.5cm, the second is 11.5cm×2 = 23cm, the third is 11.5cm × 3 = 34.5cm,
and the fourth side is 11.5cm × 6 = 69cm.
Step-by-step explanation:
A quadrilateral is a 4 sided shape, while perimeter is the addition of all the sides of the quadrilateral. Since the sides of the quadrilateral is not stade, assume the sides of the quadrilateral is x, therefore 1:2:3:6 = x:2x:3x:6x. The total ratio is x+2x+3x+6x=12x, therefore 12x= 138 , x = 11.5cm, Therefore the first side is 11.5cm, the second is 11.5cm×2 = 23cm, the third is 11.5cm × 3 = 34.5cm, and the fourth is 11.5cm × 6 = 69cm.
(x+2)² (x-100)²
Do it
Answer:
x⁴-196x³+9204x²+32200x+40000
Step-by-step explanation:
(x+2)(x+2)×(x-100)(x-100)=
(x²+4x+4)×(x²-200x+10000)=
(x⁴-200x³+10000x²+4x³-800x²+40000x+4x²-800x+40000)
=x⁴-196x³+9204x²+32200x+40000
x⁴-196x³+9204x²+32200x+40000
Convert 0.008 to a percentage???
working out pleaseeee brainlest
Answer:
0.8%
Step-by-step explanation:
8/1000 x 100%
8/10 = 0.8% or 4/5%
Answer:
0.8%
Step-by-step explanation:
it is the answer answer
Evaluate the expression yz when x= 3, y=6 and z=12.
Answer: 72
Step-by-step explanation:
y=6, z=12
yz=6 x 12=72
Please help me.
The coordinates for the vertices of quadrilateral ABCD are A(-3,2) B(-2,6) C(2,7) and D(1,3). Use this information to answer the questions below.
Slope of side AB:
A. 1/4
B. 4/1
C. -1/4
D. -4/1
Slope of side CD
A. 1/4
B. 4/1
C. -1/4
D. -4/1
Slope of side DA
A. 1/4
B. 4/1
C. -1/4
D. -4/1
Classify the quadrilateral
A. Square
B. Rectangule
C. Rhombus
D. Parallelogram
E. Trapezoid
What is the cube root of 864
Answer:
Cube root of 864 can be represented as 3√864.
Answer:
9.52441
Step-by-step explanation:
[tex] \sqrt[3]{864} [/tex]
[tex] = \sqrt[3]{(9.524 \times 9.524 \times 9.524)} [/tex]
[tex] = 9.52441[/tex]
*BRAINIEST & 25 POINTS*
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
*irrelevant answers will be reported*
Answer:
63 degrees
Step-by-step explanation:
All angles add up to 180
(5x+6) + (4x-6) + (5x-2) = 180
put like terms together
5x+4x+5x + 6-6-2 = 180
14x -2 = 180
add 2 to both sides
14x = 182
divide both sides by 14
x=13
angle G is 5x-2, so if x=13, angle G is 5(13) -2
= 65 -2 = 63 degrees
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and crown if right
Please help me ASAP!
Answer:
A and B are parallel to D and C
or
A and D to B and C
basically do a line and expand them if they touch they are not parralelogram but if they don't they are
Prove that: (Sec A- cosec A)(1+ tan A+cot A) = tan A× sec A - cot A × cosec A
Answer:
Step-by-step explanation:
[tex](sec A-cosecA)(1+tanA+cotA)=tanAsecA-cotAcosecA[/tex]
we take the LHS so here goes,
[tex](sec A-cosecA)(1+tanA+cotA)=tanAsecA-cotAcosecA\\(\frac{1}{cosA} -\frac{1}{sinA})(1+\frac{sinA}{cosA}+\frac{cosA}{sinA})\\\\(\frac{sinA-cosA}{sinAcosA})(\frac{sinAcosA+sin^2A+cos^2A}{sinAcosA})\\[/tex]
since , [tex]sin^2A+cos^2A=1[/tex]
the identity becomes,
[tex](\frac{sinA-cosA}{sinAcosA})(\frac{1+sinAcosA}{sinAcosA})\\\\(\frac{sinA+sin^2AcosA-cosA-cos^2AsinA}{sin^2Acos^2A})\\\\[/tex]
now, we know,
[tex]sin^2A=1-cos^2A[/tex] and [tex]cos^2A=1-sin^2A[/tex]
the identity becomes,
[tex](\frac{sinA+(1-cos^2A)cosA-cosA-(1-sin^2A)sinA}{sin^2Acos^2A} )\\\\[/tex]
[tex](\frac{sinA+cosA-cos^3A-cosA-sinA+sin^3A}{sin^2Acos^2A})[/tex]
sin A and cos A cancel out it becomes zero
[tex]\frac{sin^3A-cos^3A}{sin^2Acos^2A} \\\\[/tex]
Splitting the denominator the identity becomes
[tex]\frac{sin^3A}{sin^2Acos^2A}-\frac{cos^3A}{sin^2Acos^2A} \\\\\frac{sinA}{cos^2A} - \frac{cosA}{sin^2A} \\\\\frac{sinA}{cosA}(\frac{1}{cosA})-\frac{cosA}{sinA}(\frac{1}{sinA})\\\\[/tex]
Hence,
[tex]tanAsecA-cotAcosecA[/tex]