Answer:
112
Step-by-step explanation:
It appears that the relation is f(a, b) = a(a+b).
f(3, 4) = 3(3+4) = 21
f(2, 5) = 2(2+5) = 14
f(7, 7) = 7(7+7) = 98
f(8, 6) = 8(8+6) = 112
__
The symbol "+" has apparently been repurposed from its usual meaning in math. It is being used as an infix operator with two arguments. We have shown the relation above as a function f with two arguments (a, b). In our definition ...
f(a, b) = a(a+b)
the symbol "+" has its usual meaning.
_____
Additional comment
This sort of question requires a little bit of "out of the box" thinking. It helps immensely if you're familiar with your addition and multiplication facts. Then you are in a position to recognize how the outputs may be related to the inputs.
How could Brent use a rectangle to model the factors of \large x^2-7x+6?
He could draw a diagram of a rectangle with dimensions x – 4 and x + 3 and then show the area is equivalent to the sum of x2, –4x, 3x, and half of –12.
He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.
He could draw a diagram of a rectangle with dimensions x + 7 and x – 1 and then show the area is equivalent to the sum of x2, 7x, –x, and 6.
He could draw a diagram of a rectangle with dimensions x – 3 and x – 4 and then show the area is equivalent to the sum of x2, –3x, –4x, and half of 12.
Answer:He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.
Step-by-step explanation:
He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.
He could draw a diagram of a rectangle with dimensions x + 7 and x – 1 and then show the area is equivalent to the sum of x2, 7x, –x, and 6.
He could draw a diagram of a rectangle with dimensions x – 3 and x – 4 and then show the area is equivalent to the sum of x2, –3x, –4x, and half of 12.
PLEASE HELP !!
Given that p II q, fill in the reasons why each statement is true.
Answer:
1. Given
2. Def of Vertical Angles
3. Alternate Interior Angles
4. Def of Vertical angles
5. Opposite exterior angles
Step-by-step explanation:
I need help
solve for x
log16x=1/4
Answer:
[tex]log16x = \frac{1}{4} \\ x = \frac{ {10}^{ \frac{1}{4} } }{16} \\ x = 0.111[/tex]
A
D
С
B
If mZABD = 60°, then mZDBC = [?]°
Answer:
60
Step-by-step explanation:
Since the angles are shown equal in the diagram, ABD=DBC=60
A boat covers a certain distance downstream in 3 hrs and the same distance upstream in 5 hrs. If the speed of the boat in still water is 8km/hour, find the speed of the stream.
help me please I am struggling to solve this question
Answer:
The stream's speed is 2 km/hr. We don't need to know the distance.
Step-by-step explanation:
Let the stream's speed = x
rate * time = d
The distance is the same going upstream as it is coming back down stream.
d_upstream = d_downsteam
(8 + stream)*3 = (8 - stream)*5
(8 + x)*3 = (8 - x)*5 Remove the brackets
24 + 3x = 40 - 5x Subtract 24 from both sides.
3x = 40 - 24 - 5x
3x = 16 - 5x Add 5x to both sides
3x + 5x = 16
8x = 16 Divide by 8
x = 16/8
x = 2
Select the correct answer from each drop-down menu.
A student begins a proof of the law of cosines. His work is shown.
(png/image displayed in download)
The next step in the proof is to write an expression for the length of side AZ in terms of ____
Then the student should write an expression for the length of side AY in terms of____
Next he can use the ____
to relate x, y, z, and ____
(____) = blank, not known
1. blank choices
y,z and x
y,z and y
x,z and z
2. blank choices
z and Y
x and Z
z and X
3. blank choices
Pythagorean Theorem
Law of sines
tangent function
4. blank choices
X
Z
Y
Thanks for your time, have a nice day!
Answer:
1. y, z, and X
2. x and Z
3. Pythagorean theorem
4. X
Step-by-step explanation:
hope this helps
Please help quickly Its due in 5 minutes !!
Can u help solve this
Answer:
- 5/3
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -1 -9)/(4 - -2)
= (-1-9)/(4+2)
= -10/6
- 5/3
Answer:
[tex]slope = \frac{y2 - y1}{x2 - x1} \\ = \frac{ - 1 - 9}{4 - - 2} \\ \frac{ - 10}{6} \\ = - \frac{5}{3} \\ thank \: you[/tex]
Which point represents the center of the circle shown below?
X
T
Given the preimage and image, find the dilation scale factor
Answer:
it should be 2 as your answer
a can of soft drink weighs 340g when rounded off to the nearest whole number, what is the lowest possible weight of the can of soft drink
======================================================
Explanation:
When we round that value mentioned above to the nearest whole number, we end up with 340 grams. So we have to think in reverse of the rounding process to try to see which values round to 340, and go for the lowest one.
Something like 339.49 will round to 339 grams. The same applies to 339.499 and so on. This means the lowest we can go is 339.5
Going the opposite direction, there technically is no largest possible value. We could have 340.49 or 340.499 or 340.4999 and so on. These values are all approaching 340.5 but never actually get there.
In short, the possible weights x are [tex]339.5 \le x < 340.5[/tex] where rounding any of those x values to the nearest whole number will get you 340 grams. We see that 339.5 grams is the smallest possible x value.
The shaded area in the distribution below represents approximately 95% of the data. Use the diagram to find the mean and the standard deviation.
Answer:
85 i guess
Step-by-step explanation:
The mean of the distribution is 70 and the standard deviation of the distribution is 4.
The shaded area in the distribution below represents approximately 95% of the data. This means that the shaded area is equal to 1.96 standard deviations from the mean.
The 68-95-99.7 rule states that 95% of the data in a normal distribution falls within 2 standard deviations of the mean. So, the shaded area in the distribution below represents the area between 1.96 standard deviations below the mean and 1.96 standard deviations above the mean.
The mean of the distribution is the center of the shaded area. The standard deviation of the distribution is the distance from the mean to the edge of the shaded area.
In this case, the mean of the distribution is approximately 70. The standard deviation of the distribution is approximately 4.
Here is a step-by-step explanation of how to find the mean and the standard deviation:
Identify the shaded area in the distribution.
Remember that the shaded area represents 95% of the data.
Use the 68-95-99.7 rule to determine that the shaded area is between 1.96 standard deviations below the mean and 1.96 standard deviations above the mean.
Find the mean by averaging the two points on the distribution that are 1.96 standard deviations from the mean.
Find the standard deviation by subtracting the mean from one of the points on the distribution that is 1.96 standard deviations from the mean.
Therefore, the mean of the distribution is approximately 70 and the standard deviation of the distribution is approximately 4.
To learn more about standard deviation here:
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plss i reallly need help
Answer:
7x^2 +7x
------------------
x^2 -9
Step-by-step explanation:
7x (x+1)
------- * ----------
(x+3) (x-3)
Multiply
7x^2 +7x
------------------
x^2 +3x-3x-9
7x^2 +7x
------------------
x^2 -9
Answer:
7x^2 +7x / x^2 -9
Step-by-step explanation:
Given that
∠4
∠
4
has a measurement of 103°, what is the measurement of
∠2
Answer:
103 = <2
Step-by-step explanation:
Angle 4 and angle 2 are vertical angles and vertical angles are equal
<4 = <2
103 = <2
Answer:
103
Step-by-step explanation:
Angle 4 and Angle 2 are congruent so they have the same value.
Find the input (x) of the function y=5x-3 if the output (y) is 32
Answer:
x = 7
Step-by-step explanation:
Given
y = 5x - 3 ← equate 5x - 3 to 32
5x - 3 = 32 ( add 3 to both sides )
5x = 35 ( divide both sides by 5 )
x = 7 ← input
Answer:
x=7
Step-by-step explanation:
y=5x-3
y = 32
32 = 5x- 3
Add 3 to each side
32+3 = 5x-3+3
35 = 5x
Divide by 5
35/5 = 5x/5
7 =x
What is the volume of the regular pyramid?
576m
96 m
480 m
240 m
Answer:
volume is 576
Step-by-step explanation:
all you do to find volume is multiply LxWxH which will give you volume so just take 18m x 4m x 8m = 576m hopefully its a simply and direct explanation make me brainlist please !!!
The volume of a pyramid is 720 m³.
What is a pyramid?A pyramid is a structure where outer surfaces are triangular and converge to a point at the top.
The volume of a pyramid with a square base is given as:
Volume = 1/3 x base area x height
We have,
Base area:
A = (1/2) x apothem x perimeter
where the perimeter is the total length of all five sides of the pentagon.
So,
= 1/2 x 4 x (5 x 8)
= 2 x 40
= 80 m²
Height.
= 18 m
Now,
The volume of a pyramid.
= 1/2 x 80 x 18
= 80 x 9
= 720 m³
Thus,
The volume of a pyramid is 720 m³.
Learn more about pyramid here:
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What is the volume, in terms of cubic inches, of a cone with a diameter of 8 inches and a height of 6 inches?
Answer: [tex]100.544\ in.^3[/tex]
Step-by-step explanation:
Given
Diameter of the cone [tex]d=8\ in.[/tex]
Height of the cone [tex]h=6\ in.[/tex]
Volume of the Cone is given by
[tex]\Rightarrow V=\dfrac{1}{12}\pi d^2h[/tex]
[tex]\Rightarrow V=\dfrac{1}{12}\times \pi\times 8^2\times 6\\\\\Rightarrow V=16\pi \\\Rightarrow V=100.544\ in.^3[/tex]
The volume of the cone is [tex]100.544\ in.^3[/tex]
√25x+75 +3√x-2 =2+4√x-3 +√9x-18
Answer:
Step-by-step explanation:
[tex]\large \boldsymbol{ \boxed{\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b} }} \\\\\\ \sqrt{25x+75} +3\sqrt{x-2} =2+4\sqrt{x-3} +\sqrt{9x-18} \\\\ \sqrt{25} \cdot \sqrt{x+3}+3\sqrt{x-2} =2+4\sqrt{x-3} +\sqrt{9}\cdot \sqrt{x-2} \\\\5\sqrt{x+3} +3\sqrt{x-2} \!\!\!\!\!\!\!\!\!\!\bigg{/} \ \ =2 +4\sqrt{x-3} +3\sqrt{x-2} \!\!\!\!\!\!\!\!\!\!\bigg{/} \\\\(5\sqrt{x+3})^2 =(2+4\sqrt{x-3} )^2 \\\\ \ \ \ let \ \ t=x+3 \ \ ; \ \ \ t-6=x-3 \\\\ \big(5\sqrt{t} \ \big)^2=(2+\sqrt{t-6} )^2 \\\\[/tex] [tex]\large \boldsymbol{} 25t=4+16\sqrt{t-6} +16(t-6) \\\\(9t+92)^2=(16\sqrt{t-6} )^2 \\\\81t^2+1656t+8464=256(t-6)\\\\81t^2+1400t+10000=0 \\\\ D=1400^2-324000=-128000=> \\\\D<0 \ \ no \ \ solutions[/tex]
If (x/3)-1 is twice as large as (x/4)-3, what is the value of x?
Answer:
30
Step-by-step explanation:
Answer:
x = 30
Step-by-step explanation:
The equation modelling the statement is
[tex]\frac{x}{3}[/tex] - 1 = 2 ( [tex]\frac{x}{4}[/tex] - 3 ) ← distribute parenthesis by 2
[tex]\frac{x}{3}[/tex] - 1 = [tex]\frac{x}{2}[/tex] - 6 ( multiply through by 6 to clear the fractions )
2x - 6 = 3x - 36 ( subtract 2x from both sides )
- 6 = x - 36 ( add 36 to both sides )
30 = x
Rewrite the following expression using the properties of rational exponents. Be sure your answer is in simplest form
(2 • 6) 3/2
Answer:
24√3
Step-by-step explanation:
(2 • 6)^(3/2) =
= 12^(3/2)
= √(12³)
= √1728
= √(2^6 • 3² • 3)
= 2³ • 3 • √3
= 24√3
The midpoint of AB is M(-6,1). If the coordinates of A are (-7, -3), what are
the coordinates of B?
Answer:
B = (1, -4)
Step-by-step explanation:
the midpoint formula is ((x1 + x2) / 2 , ( y1 + y2) / 2)
M = (-6,1) and A = (-7,-3)
if we make A (x1, y1), we can plug in and solve for B (x2, y2)
-7 + x2 = -6
x2 = 1
1 + y2 = -3
y2 = -4
B = (1, -4)
PLEASE HELP. In the triangles below, DF MN, DG MP, D P. Can you prove that DFG MNP? Explain your answer. (15 points)
Complete question is;
In the triangles attached , DF is congruent to MN,DG is congruent to MP, angle D is congruent to angle P. Can you prove that triangle DFG is congruent to MNP.
Answer:
Proved below
Step-by-step explanation:
From the attached triangles, we can see that;
∠D corresponds to ∠M
∠F corresponds to ∠N
∠G corresponds to ∠P
But we are told that ∠D is congruent to ∠P. Thus, since we have 2 other congruent sides in the triangles, we can conclude that Side-Angle-Side Postulate (SAS) congruency theorem that triangle DFG is congruent to MNP.
What is the radius and diameter of the following circle? 5.1 cm
Answer:
A circle of radius = 0.8117 or diameter = 1.623 or circumference = 5.1 cm has an area of: 2.07 × 10 -10 square kilometers (km²) 0.000207 square meters (m²) 2.07 square centimeters (cm²)Step-by-step explanation:
Find the surface area of the composite solid.
A.
502 m2
B.
574 m2
C.
646 m2
D.
720 m2
Answer:
A is the answer I pretty sure
Answer:
i think the answer is 502 m2
Could someone please help me out?
Answer:
4.5
Step-by-step explanation:
let,
k×9²=300
k = 300/81
or, k = 100/27
as two triangles are similar,
if smaller triangle's corresponding side is x (let), then,
kx²=75
100x²/27=75
x²=75×27/100
x=√81/4
x=9/2
x=4.5
simple geometry problem i cant understand
Answer:
23.5
Step-by-step explanation:
m∠Y = (m∠RTS - m∠VTX)/2
m∠Y = ((180 - m∠RTV) - (180 - m∠VTX))/2
m∠Y = ((180 - 95) - (180 - 142))/2
m∠Y = (85 - 38)/2
m∠Y = 47/2
m∠Y = 23.5
6. Sarah shops for DVDs with a $30.00 gift certificate. She finds a DVD that has an original price of $34.50
and is on sale for 25% off. Determine if Sarah has enough money to buy the DVD including 13% sales tax.
9514 1404 393
Answer:
yes, Sarah has enough to buy the DVD
Step-by-step explanation:
The discount causes the price to be multiplied by 1 -25% = 0.75. The tax causes the price to be multiplied by 1 +13% = 1.13. After these multipliers are applied, the final price is ...
$34.50(0.75)(1.13) = $29.24
Sarah's $30 gift certificate will cover the entire amount due.
Answer:
The answer is 5.5 because it tell you what it is
Step-by-step explanation:
What is the greatest common factor of 24s3, 12s4, and 18s?
Answer:
24s3
Step-by-step explanation:
24s3 is the greatest common factor of 24 S3 12 s4 and 18s.
What’s 304.9% as a decimal
Answer:
3.049
Step-by-step explanation:
A boat travels 84 miles in 4 hours. How should you calculate the unit rate of miles to hours
Answer:
The boat is going 21 MPH
Step-by-step explanation:
If the boat is going 84 miles in 4 hours, and you want to find the unit rate, divide 84 by 4.
84/4 = 21
Hope this helps!
