[tex]~~~(2x-6)(2x+6)\\\\=(2x)^2 -6^2~~~~~~~~~~~~~~~~~~~~~;[a^2 -b^2 = (a+b)(a-b)]\\\\=4x^2 -36[/tex]
Bella can rake the leaves in 3 hours and Jordan can complete the same task in 4 hours. If they work together, how long will it take Bella and Jordan to rake the leaves? Round your answer to the nearest hundredth of an hour.
Using the together rate, it is found that it will take 1.71 hours for Bella and Jordan to rake the leaves.
What is the together rate?It is the sum of each separate rate.
In this problem, the rates are given as follows:
Together: 1/x.Bella's: 1/3.Jordan's: 1/4.Hence:
[tex]\frac{1}{x} = \frac{1}{3} + \frac{1}{4}[/tex]
[tex]\frac{1}{x} = \frac{4 + 3}{12}[/tex]
[tex]x = \frac{12}{7}[/tex]
x = 1.71.
It will take 1.71 hours for Bella and Jordan to rake the leaves.
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Plsss help I’m so confused
Answer:
The answer is 1001101
Step-by-step explanation:
77 base 10 to base 2 is 1001101
Work out the area of a circle with diameter 1.8cm.
Take pi to be 3.142 and give your answer to 1 decimal place
Step-by-step Explaination:
Diameter = 1.8 cm
Radius (r) = 1.8/2 = 0.9
According to formula...
Area of circle = π(r)^2
= 3.142 * 0.9 * 0.9
= 2.54502 cm
Answer to 1 decimal place :-2.5 cm...ans Hope it helps you!!Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
Using translation concepts, it is found that the correct statements are given as follows:
g(x) > h(x) for x = -1.For positive values of x, g(x) > h(x).For negative values of x, g(x) > h(x).What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the functions are:
g(x) = x².h(x) = -x².h(x) = -x² = -g(x), which means that h(x) is a reflection of g(x) over the x-axis. Since [tex]g(x) \geq 0[/tex] for all values of x, [tex]h(x) \leq 0[/tex] for all values of x, which means that they are equal at the origin and g is greater for other values of x, hence the correct statements are:
g(x) > h(x) for x = -1.For positive values of x, g(x) > h(x).For negative values of x, g(x) > h(x).More can be learned about translation concepts at https://brainly.com/question/4521517
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erved.
6
What is the reason for step 3 of this proof?
OA
Alternate Interior Angles Theorem
OB.
Corresponding angles in congruent triangles are congruent.
OC. For parallel lines cut by a transversal, corresponding angles are congruent.
OD.
Vertical Angles Theorem
OE.
SAS criterion for congruence
Vertical Angles Theorem is the reason for step 3 of this proof. Hence, option D is correct.
What is Vertical Angles Theorem?Theorem of vertical angles or angles that are vertically opposing According to the theorem, two opposing vertical angles that are created when two lines cross one other are always equal to one another.
As AE = EC and BE = ED (by the definition of bisection) suggest that triangles AEB and CED are congruent (by the SAS criterion for congruence),
It is claimed in step 3 of the provided proof that mAEB = mCED. The corresponding angles of two triangles are equal when they are congruent. Since mAEB = mCED, it follows that the measure of angle AEB must be equal to the measure of angle CED.
This step is crucial because it proves the equality of the respective angles in the congruent triangles AEB and CED. This equality is then utilized in step 4 to prove that the two triangles satisfy the SAS criterion, which is a congruence criterion.
Steps 5 through 11 then employ the congruence of triangles AEB and CED to demonstrate that the quadrilateral ABCD is a parallelogram.
Thus, option D is correct.
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The complete question is given below-
What is the reason for step 3 of this proof?Given: and bisect each other.
Prove: Quadrilateral ABCD is a parallelogram.
Proof:
Statement Reason
1. and bisect each other. given
2. AE = EC
BE = ED definition of bisection
3. mAEB = mCED
4. ABE CDE SAS criterion
5. ACD CAB Corresponding angles of congruent triangles are congruent.
6. converse of Alternate Interior Angles Theorem
7. mBEC = mAED Vertical Angles Theorem
8. BEC DEA SAS criterion for congruence
9. DBC BDA Corresponding angles of congruent triangles are congruent.
10. converse of Alternate Interior Angles Theorem
11. Quadrilateral ABCD is a parallelogram. definition of a parallelogram
a Alternate Interior Angles Theorem
B. Corresponding angles in congruent triangles are congruent.
C. For parallel lines cut by a transversal, corresponding angles are congruent.
D. Vertical Angles Theorem
E. SAS criterion for congruence
A restaurant's seating is completely full. There
are some four-person tables and 8 tables withcouples. If there are 56 people here, how many
four-person tables are there?
4951 to the nearest 1000
Answer:
5000
makes the best sense
A water tank that initially contained 200 gallons of water is leaking water at a constant rate of 4 gallons per minute. For the amount of time the tank has water, which of the following function models gives the number of gallons, G. in the tank t minutes after the leak started?
a. g(t) = 196 - t
b. g(t) = 200 - 4t
c. g(t) = 200t - 4
d. g(t) = 200t - 4r^2
e. g(t) = 200(3/4)^t
Answer:
b. g(t) = 200 - 4t
Step-by-step explanation:
I don't know how to explain this, but here is the answer.
f(x) = 3 and g(x) = x – 2
3 = x – 2
5 = x
Answer:
3=1×5-2
Step-by-step explanation:
you minus 5-2 is 3 and one threes three
For ten school days, the numbers of bikes parked at a school bike rack are 10, 12, 8, 11, 13, 9, 2, 1, 9, and 12.
a. What is the mean number of bikes per day? [already answered]
b. Identify two outliers for the data. Describe how the outliers affect the mean.
"the numbers, Mason, what do they mean??"
The mean number is 8.7 and the outliers 1 and 2 reduce the mean value
How to determine the mean number?The dataset is given as:
10, 12, 8, 11, 13, 9, 2, 1, 9, and 12.
The mean number is calculated using:
Mean = Sum/Count
So, we have:
Mean = (10+ 12+ 8+ 11+ 13+ 9+ 2+ 1+ 9+12)/10
Evaluate
Mean = 8.7
Hence, the mean number is 8.7
The outlier and how it affects the meanOutliers are relatively far from other data elements of the dataset
In the given dataset, 1 and 2 are far from other data element.
So, the outliers are 1 and 2
Because 1 and 2 smaller than other data elements, they affect the mean by reducing the mean value
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Answer:87/10 is the answer because there are no tens
Step-by-step explanation:
Which function is positive for the entire interval [–3, –2]? On a coordinate plane, a curved line with a minimum value of (0, negative 3) crosses the x-axis at (negative 3, 0) and (3, 0), and crosses the y-axis at (0, negative 3). On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5). On a coordinate plane, a curved line with a minimum value of (2, 4) and a maximum value of (0.5, 6), crosses the x-axis at (negative 1.5, 0) and crosses the y-axis at (0, 5). On a coordinate plane, a curved line with a minimum value of (negative 1.75, negative 3.9) and a maximum value of (0, 2), crosses the x-axis at (negative 2.2, 0), (negative 0.75, 0), and (0.75, 0), and crosses the y-axis at (0, 2).
The function that is positive for the entire interval [–3, –2] is the graph of the function (b)
How to determine the function?See attachment for the proper representation of the available options
For a function to be positive on the interval [-3,-2];
It means that the y values must be in the positive quadrant from x = -3 to x =-2
From the list of options, we have:
The y values from x = -3 to x =-2 is at the positive quadrant for the second graph i.e. option B
Hence, the function that is positive for the entire interval [–3, –2] is the graph of the function (b)
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tìm số hữu tỉ
(x-5/6)^2=1/36
Answer:
x = [tex]\frac{2}{3}[/tex] , x = 1
Step-by-step explanation:
(x - [tex]\frac{5}{6}[/tex] )² = [tex]\frac{1}{36}[/tex] ( take square root of both sides )
x - [tex]\frac{5}{6}[/tex] = ± [tex]\sqrt{\frac{1}{36} }[/tex] = ± [tex]\frac{1}{6}[/tex] ( add [tex]\frac{5}{6}[/tex] to both sides )
x = [tex]\frac{5}{6}[/tex] ± [tex]\frac{1}{6}[/tex] , then
x = [tex]\frac{5}{6}[/tex] - [tex]\frac{1}{6}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
x = [tex]\frac{5}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{6}{6}[/tex] = 1
Find the area of the polygon.
2 cm
3 cm
1 cm
3 cm
4 cm
Answer:
the area of the problem is 20
The chart below shows conversion between yards and inches.
Conversion Chart
Yards
Inches
3
108
6
?
8
288
11
396
What is the missing value in the table?
144
180
198
216
step by step explanation :
to converting yard to inches you have to multiply whatever number u are given in yard by 36 to get your figure in inches
o multiply whatever number u are given in yard by 36 to get your figure in inches so we multiply 6 *36 to give us 216
o multiply whatever number u are given in yard by 36 to get your figure in inches so we multiply 6 *36 to give us 216answer:
216
i need help. due today
Answer:
19
Step-by-step explanation:
7x +2 = 135. Vertically opposite angles
7x=133
x=19
Find the value of x.
how do you do .22 x .4
Answer: 0.088
Step-by-step explanation:
There are two ways. My way is complicated, but never wrong!
0.22 converted to a fraction is 22/100,
explanation: you know this because the denominator must be 10, 100, 1000, 10000 etc... and must be one more digit than the numerator.
and 0.4 into a fraction is 4/10. but we have to have same denominators so we multiply 4/10 by 2 4 x 10 = 40; 10 x 10 = 100.
now multiply...
40 x 22 = 880
100 100 100
and turn it into a decimal, by reversing how we turned it into a decimal.
so it's 0.088!
How many combinations exist of the letters W, X, Y, Z, taking two at a time?
04
06
012
Step-by-step explanation:
C(4,2)
Use combinations formula,
c(n,r)=n!/r!(n-r)!
c(n,r)=4!/2!(2!)
[tex]c = \frac{4 \times 3 \times 2 \times 1 }{2 \times 1 \times 2 \times 1} [/tex]
[tex]c = 3 \times 2 \times 1[/tex]
[tex]c = 6[/tex]
Type the correct answer in each box. Round the vector's magnitude to the nearest tenth.
Vector u has its initial point at (14,-6) and its terminal point at (-4, 7). Write the component form of u and find its magnitude.
Component form of u is (-18,13) and The magnitude of u is 22.2
What is a vector?A vector is a two-dimensional entity with both magnitude and direction. A vector can be visualized geometrically as a directed line segment.
The component form of a vector is an ordered pair that describes the change in x and y values
This is mathematically expressed as (Δx, Δy) where Δx=x₂-x₁ and Δy=y₂-y₁
Given ;
Initial points of the vector as (14,-6)
The terminal point of the vector is (-4,7)
Here x₁=14,x₂=-4, y₁=-6,y₂=7
The component form of the vector u is (-4-14,7--6) =(-18,13)
Finding the Magnitude of the vector
u=√(x₂-x₁)²+(y₂-y₁)²
u=√-18²+13²
u=√324+169
u=√493
u=22.2
Therefore the Component form of u is (-18,13) and The magnitude of u is 22.2
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help pls i need it really fast
Answer:19 for first answer. Second answer is subtract 16 from both sides
Step-by-step explanation:76/4 first answer
grades are do today please help
Answer:
length of PR is [tex]4\sqrt{5}[/tex]
Is an isosceles triangle
because PQ is congruent to QR
Step-by-step explanation:
Calculate length of P(-6,0) R(2,4)
=> apply distance formula
[tex]\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]\sqrt{\left(2-\left(-6\right)\right)^2+\left(4-0\right)^2}[/tex]
[tex]4\sqrt{5}[/tex]
Calculate length of P(-6,0) Q(-3,4)
[tex]\sqrt{\left(-3-\left(-6\right)\right)^2+\left(4-0\right)^2}[/tex]
= 5
5(PQ) = 5(QR)
5/8 multiplied by 4/10 (pls answer asap)
Answer:Flying potatox x plus y yes
Step-by-step explanation:
Answer:
the answer is 1/4 if the question is a fraction
4.3 Mr Mokwebo 's two sons, Refentse and Tokelo have just passed grade 7 and grade 9 respectively. He will give them some money to buy chocolates at Jubilee Mall as a reward for their hardwork. Refentse will receive R21 less than Tokelo. Altogether they will need R253 to buy the chocolates. Set up an equation and calculate how much each will get. Let Tokelo 's money be x 4.3.1 Write down Refentse 's money in terms of x. (1) 4.3.2 Set up an equation and calculate how much each will get. (4) [22] Total: 60
The amount of money each of Mr Mokwebo 's two sons; Tokelo and Refentse will get is R116 and R95 respectively.
How to write and solve equation:Amount needed to buy chocolate = R253Tokelo's money = xRefentse's money = x - 21Total amount needed = Tokelo's money + Refentse's money
253 = x + (x - 21)
253 = x + x - 21
253 = 2x - 21
253 - 21 = 2x
232 = 2x
divide both sides by 2
x = 232/2
x = 116
Therefore,
Tokelo's money = x = R116
Refentse's money = x - 21
= 116 - 21
= R95
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Drag each tile to the correct box.
Match each equation with its solution.
Equation
Solution
arrowRight
arrowRight
arrowRight
arrowRight
The correct match of each tile of the equation with its solution is:
n - 13 = - 12 →→→ 1n/5 = -1/5 →→→ -1n + 15 = - 10 →→→ -25How do we match each tile to the correct box?To match each tile to the correct box, we have to solve the arithmetic operations in the box, then drag the correct tile that matches our answer into the box.
From the image attached below;
1.
n - 13 = - 12
Let us add (+13) to both sides to eliminate (-13), i.e.
n - 13 + 13 = - 12 + 13
n = 1
2.
n/5 = -1/5
multiply both side by 5
n/5 × (5) = -1/5 × (5)
n = -1
3.
n + 15 = - 10
n +15 - 15 = - 10 - 15
n = -25
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Abc car share inc. offers car sharing for a $199 yearly fee plus $14/hr for the
use of its car share. what is the total cost for a person who purchases a car
share and uses it for 72 hours total time?
The total cost for a person who purchases a car share and uses it for 72 hours is $1207.
What is the total cost?The total cost is a function of the yearly fee and the cost per hour.
Total cost = yearly fee + (total hours the car was used for x cost per hour)
$199 + (72 x $14)
$199 + $1008 = $1207
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Solve for x. Round to the nearest tenth of a degree, if necessary.
[tex]~~~~~\sin \theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\ \implies \sin x = \dfrac{HI}{GI}\\\\\\\implies \sin x = \dfrac{39}{62}\\\\\\\implies x= \sin^{-1} \left( \dfrac{39}{62} \right)\\\\\\\implies x =38.9^{\circ}[/tex]
Select the correct answer from each drop-down menu.
This graph shows the relationship between demand and price for goods sold at a shop. Anna plots the data on a scatter plot and draws a line of best fit to represent the relationship as shown.
This is not the line of best fit because the line . Anna could get a better fit by the y-intercept and the slope.
This is not the line of best fit because the line is not through the middle of the data points.
What is line of best fit?
The line of best fit is a line through a scatter plot of data points that best expresses the relationship between those points.
In this case, this is not the line of best fit because the line is not through the middle of the data points.
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A. Z
B. <
C. S
D. >
E. =
F. 2
55? 35
Answer:
ABCD=EF
Step-by-step explanation:
A. Z
B. <
C. S
D. >
E. =
F. 2
55? 35
please help me with this if you can? thanks alot :)))
The probabilities are:
P(red) = 5/24P(orange) = 0 P(blue) = 1/3P(not green)= 17/24P(green or black) = 11/24P(not yellow) = 1.How to find the probabilities?
The probability of getting a particular color of marble, is given by the quotient between the number of marbles of that color and the total number of marbles.
Here we have:
5 red marbles.7 green marbles.4 black marbles.8 blue marbles.So the total number is 5 + 7 + 4 + 8 = 24.
Then:
P(red) = 5/24P(orange) = 0/24 = 0 (because there are 0 orange marbles).P(blue) = 8/24 = 1/3P(not green) = (24 - 7)/24 = 17/24P(green or black) = (4 + 7)/24 = 11/24P(not yellow) = 24/24 = 1 (because there aren't yellow marbles).If you want to learn more about probability, you can read:
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Evaluate
11
% of
953.23
m
Give your answer rounded to 2 DP.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{11\% of 953.23}}{\left( \cfrac{11}{100} \right)953.23}\implies 104.86[/tex]