Answer:
a=3; (3,5) and (4,0) for the graph
Step-by-step explanation:
ax-y=4
x=3, y=5 so...
a(3)-5=4
3a-5=4
+5 +5
3a=9
/3 . /3
a=3
For the graph, use (3,5) and substitute x and y for anything:
ax-y=4
if x=0...
a(0)-y=4
-y=4
y=4
a=3; (3,5) and (4,0) for the graph!
help plz ill give extra points ?
Answer:
Step-by-step explanation:
Not sure
Answer:
45 degrees
Step-by-step explanation:
they are both the same half so 90 divided by 2 is 45
Ben starts walking along a path at 2 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 7 mi/h. How long (in hours) will it be before Amanda catches up to Ben?
Answer:
Amanda will catch up Ben after 0.6 hours.
Step-by-step explanation:
Amanda begins jogging along the same path at 7 mi/h.
This means that Amanda's position, after t hours, is given by:
[tex]A(t) = 7t[/tex]
Ben starts walking along a path at 2 mi/h.
Amanda leaves after one and a half hour, which means that Ben will be at position 2*1.5 = 3. So Ben's position after t hours is given by:
[tex]B(t) = 3 + 2t[/tex]
How long (in hours) will it be before Amanda catches up to Ben?
This will happen when:
[tex]A(t) = B(t)[/tex]
So
[tex]7t = 3 + 2t[/tex]
[tex]5t = 3[/tex]
[tex]t = \frac{3}{5}[/tex]
[tex]t = 0.6[/tex]
Amanda will catch up Ben after 0.6 hours.
It would take Amanda 0.6 hours or 6/10 hours to catch up with Ben.
This question comes from a topic in mathematics called rates and it's used to compare two values with each other and how one value affects the other value.
Let s represent the distance Amanda travels until she meet Ben.
We can set a timer on our phone when she leaves in order to track the time taken.
Let t represent the time taken.
Set of EquationWe can come up with two equations from these scenario
d - 3 = 2t------ equation (i)d = 7t ----- equation (ii)Substitute equation (ii) into equation (i)
[tex]7t -3 =2t[/tex]
collect like terms
[tex]7t-2t=3\\5t=3\\t=3/5\\t=0.6[/tex]
From the above, we can see it took her 0.6 hours to catch up with Ben.
Learn more about rates here;
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Find three positive numbers whose sum is 140 and whose product is a maximum. (Enter your answers as a comma-separated list.)
Answer:
[tex]\frac{140}{3}, \frac{140}{3}, \frac{140}{3}[/tex]
Step-by-step explanation:
Let the numbers be [tex]x, y\ and\ z.[/tex]
Such that:
[tex]x + y + z = 140[/tex]
Make z the subject
[tex]z = 140 -x - y[/tex]
For their product to be maximum, we have:
[tex]f(x,y,z) = xyz[/tex]
Substitute [tex]z = 140 -x - y[/tex] in [tex]f(x,y,z) = xyz[/tex]
[tex]f(x,y) = xy(140 - x - y)[/tex]
Open bracket
[tex]f(x,y) = 140xy - x^2y - xy^2[/tex]
Differentiate w.r.t x and y
[tex]f_x=140y - 2xy - y^2[/tex]
[tex]f_y=140x - x^2 - 2xy[/tex]
Since the products are maximum, then [tex]f_x = f_y = 0[/tex]
For [tex]f_x=140y - 2xy - y^2[/tex]
[tex]140y - 2xy - y^2 = 0[/tex]
Factorize:
[tex]y(140 - 2x - y) = 0[/tex]
Split
[tex]y = 0\ or\ 140 - 2x - y = 0[/tex]
Make y the subject
[tex]y = 0\ or\ y = 140 - 2x[/tex]
For [tex]f_y=140x - x^2 - 2xy[/tex]
[tex]140x - x^2 - 2xy = 0[/tex]
---------------------------------------------------
Substitute y = 0
[tex]140x - x^2 -2x*0 = 0[/tex]
[tex]140x - x^2 = 0[/tex]
Factorize
[tex]x(140 - x)= 0[/tex]
[tex]x = 0\ or\ 140-x = 0[/tex]
[tex]x = 0\ or\ x = 140[/tex]
---------------------------------------------------
Substitute [tex]y = 140 - 2x[/tex]
[tex]140x - x^2 - 2xy = 0[/tex]
[tex]140x - x^2 - 2x(140 - 2x) = 0[/tex]
[tex]140x - x^2 - 280x + 4x^2 = 0[/tex]
Re-arrange
[tex]4x^2 -x^2 +140x - 280x = 0[/tex]
[tex]3x^2 -140x = 0[/tex]
Factor x out
[tex]x(3x - 140) = 0[/tex]
Divide through by x
[tex]3x - 140 = 0[/tex]
[tex]3x = 140[/tex]
[tex]x = \frac{140}{3}[/tex]
Recall that: [tex]y = 140 - 2x[/tex]
[tex]y = 140 - 2 * \frac{140}{3}[/tex]
[tex]y = 140 - \frac{280}{3}[/tex]
Take LCM
[tex]y = \frac{140*3-280}{3}[/tex]
[tex]y = \frac{140}{3}[/tex]
Recall that:
[tex]z = 140 -x - y[/tex]
[tex]z = 140 - \frac{140}{3} - \frac{140}{3}[/tex]
Take LCM
[tex]z = \frac{3 * 140- 140 - 140}{3}[/tex]
[tex]z = \frac{140}{3}[/tex]
Hence, the numbers are:
[tex]\frac{140}{3}, \frac{140}{3}, \frac{140}{3}[/tex]
Answer please eeeeeeeee
9s is correct
hope this helps
PLZ HELP PLZZZZZZZZZZZZZZZZ
Answer:
d
Step-by-step explanation:
fill in the blank with the correct answer.
Answer:
I believe the correct answer is option B. 7 x 10
Step-by-step explanation:
Hope this helps if not I'm very sorry ^^"
Answer:
7*8
17*8=(10*8)+(7*8)
136=80+56
136=136
The term-to-term rule for a sequence is " Add 1 and then double"
The first two terms are 2 and 6
Find the next term
The next term of the sequence is 14.
What is Sequence?A sequence in mathematics is a ordered set of objects or numbers which are related with something.
For example, 1, 3, 5, ..... is a sequence of odd numbers.
Given that,
The term-to-term rule for a sequence is " Add 1 and then double"
First term = 2
Second term = 6
6 is got by adding 1 to 2 and then doubling it.
2 + 1 = 3
3 × 2 = 6
In the same way,
Third term = (6 + 1)2 = 7 × 2 = 14
Hence the next term of the sequence is 14.
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Information about three circles is listed below.
• Circle P has a diameter of 26 cm.
• Circle Q has a diameter of 52 cm.
• Circle R has a radius of 52 cm. Based on this information, which statement is true?
A.The diameter of circle P is the same length as the diameter of circle R.
B. The radius of circle P is the same length as the radius of circle Q.
C The diameter of circle P is the same length as the radius of circle Q.
D. The radius of circle P is the same length as the diameter of circle R.
Answer:
C The diameter of circle P is the same length as the radius of circle Q.
Step-by-step explanation:
Brainliest if correct Multiply 3/7 by 4/5
Answer:
Step-by-step explanation:
x1 / y1 times x2 / y2 where are two fractions
x1/y1 times x2/y2 = x1 times x2 / y1 times y2 = z1 / z2 z is a new fraction
fractions multiply like regular wholes number, which can also be represented in fractional form
Examples:
2/1 times 3/1 = 2x3 /1x1 6/1
10/2 x 18/3 = 180/6 now look at 10/2 = 5 18/3 = 6 5x6 = 30
5 x 6 = 30
Now apply to your fractions:
3/7 x 4/5 = 3x4 / 7x5
12/35
8th grade math, please help.
I’ll give you brainliest if you want.
-Find the volume-
Answer:
113.10
Step-by-step explanation:
Answer:
how to make sugar cookies :)
Step-by-step explanation:
2 ¾ cups all-purpose flour
1 teaspoon baking soda
½ teaspoon baking powder
1 cup butter, softened
1 ½ cups white sugar
1 egg
1 teaspoon vanilla extract
GggggghggggggggggggggggggggTry
Answer:
try this 20+10 = 20x10 = 20-10=
Step-by-step explanation:
add the first one, than times the other one, after subtract the last one.
What is the product of 3/7x2/5
Answer:
0.1714285714285714
Step-by-step explanation:
Which method is the best method for solving the equation?
[tex]8x^{2} - 13x + 3 = 0[/tex]
Answer:
Step-by-step explanation:
Which Method Should Be Used to Solve a Quadratic Equation? Quadratic equations are of the form ax2 + bx + c = 0 where a, b and c are real numbers, a ≠ 0. Quadratic equations have two solutions, but it is possible that one solution may repeat. happy to help
The graph represents a quadratic function. Write the function in vertex form.
Answer:
y=3(x+3)^2-8
Step-by-step explanation:
Vertex form:
y=a(x-h)^2+k
h=-3, k=-8
y=a(x+3)^2-8
sub (-4,-5)
-5=a(-4+3)^2-8
a=3
y=3(x+3)^2-8
PLS HELP MEEEEEEEEEEEEEEEEEE
Answer:
9.42477796 ≈ 9.4
Step-by-step explanation:
Ao= π*r
= π*(6/2)
=π*3= 9.42477796 ≈ 9.4
Fred bought 9 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 43 cards left. How many cards did Fred start with ?
Helpp I need this todayyyyyy
Answer:
86 - 9 = 77
Step-by-step explanation:
A farmer sells 8.5 kilograms of pears and apples at the farmer's market. 2 5 of this weight is pears, and the rest is apples. How many kilograms of apples did she sell at the farmer's market?
Answer:
6 kilograms of apples
Step-by-step explanation:
8.5-2.5=6
Hope I helped
What is 5/9 divided by 4/9 answer
Answer:
1.25
Step-by-step explanation:
5/9 divided by 4/9 is 1.25
A university researcher wants to estimate the mean number of novels that seniors read during their time in college. An exit survey was conducted with a random sample of 9 seniors. The sample mean was 7 novels with standard deviation 2.29 novels. Assuming that all conditions for conducting inference have been met, which of the following is a 94.645% confidence interval for the population mean number of novels read by all seniors?
A. 7 + or - 1.960 (2.29/underroot 8).
B. 7 + or - 1.960 (2.29/underroot 9).
C. 7 + or - 2.262 ((2.29/underroot 9).
D. 7 + or - 2.306 (2.29/underoot 8).
E. 7 + or - 2.306 (2.29/underoot 9).
Answer:
Population mean = 7 ± 2.306 × [tex]\frac{2.29}{\sqrt{9} }[/tex]
Step-by-step explanation:
Given - A university researcher wants to estimate the mean number
of novels that seniors read during their time in college. An exit
survey was conducted with a random sample of 9 seniors. The
sample mean was 7 novels with standard deviation 2.29 novels.
To find - Assuming that all conditions for conducting inference have
been met, which of the following is a 94.645% confidence
interval for the population mean number of novels read by
all seniors?
Proof -
Given that,
Mean ,x⁻ = 7
Standard deviation, s = 2.29
Size, n = 9
Now,
Degrees of freedom = df
= n - 1
= 9 - 1
= 8
⇒Degrees of freedom = 8
Now,
At 94.645% confidence level
α = 1 - 94.645%
=1 - 0.94645
=0.05355 ≈ 0.05
⇒α = 0.5
Now,
[tex]\frac{\alpha}{2} = \frac{0.05}{2}[/tex]
= 0.025
Then,
[tex]t_{\frac{\alpha}{2}, df }[/tex] = 2.306
∴ we get
Population mean = x⁻ ± [tex]t_{\frac{\alpha}{2}, df }[/tex] ×[tex]\frac{s}{\sqrt{n} }[/tex]
= 7 ± 2.306 × [tex]\frac{2.29}{\sqrt{9} }[/tex]
⇒Population mean = 7 ± 2.306 × [tex]\frac{2.29}{\sqrt{9} }[/tex]
Answer:
E
Step-by-step explanation:
on ap classroom
A drum used for percussion has sides modeled by a hyperbola. The total height of the drum is 35 inches. The diameter at the top of the drum is 16 inches, and the minimum diameter is 8 inches, occurring at a height of 22 inches. Determine the equation of a hyperbola that models the sides of the drum assuming that the center of the hyperbola occurs at the height where the diameter is the least.
look at the screen shot ya know
The equation of a hyperbola that models the sides of the drum assuming that the center of the hyperbola is (35 + a)²/a² - 8²/b² = 1 and (22+ a)²/a² - 4²/b² = 1
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that the total height of the drum is 35 inches.
The diameter at the top of the drum = is 16 inches, and
The minimum diameter is 8 inches, occurring at a height of 22 inches.
The equation of the hyperbola be denoted as;
x²/a² - y²/b² = 1
From the question, with x and y coordinates representing height and radius respectively,
Then,
When x = 35 + a, y is = 16/2 = 8 and
At x = 22+ a, y is = 8/2 = 4
Thus,
(35 + a)²/a² - 8²/b² = 1
(22+ a)²/a² - 4²/b² = 1
By solving, we have, a = 128.95 and b = 14.75
Therefore a= 128.95 and b = 14.75
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The solution to a system of equations is (6,3) choose 2 equations that might make up the system
The area of the base is given by The volume of a hexagonal prism is given by 35x ^ 5 + 20x ^ 4 - 57x ^ 3 + x ^ 2 + 18x - 30 5x ^ 2 - 6 Find an expression for the height of the hexagonal prism.
Answer:
Step-by-step explanation:
The height of given hexagonal prism is 7x³+4x²-3x+5.
Given that, the volume of a hexagonal prism is [tex]35x ^ 5 + 20x ^ 4 - 57x ^ 3 + x ^ 2 + 18x - 30[/tex] and the area of the base is 5x² - 6.
What is a hexagonal prism volume?A hexagonal prism is a three-dimensional solid shape with 8 faces that including hexagon bases.
Volume of a hexagonal prism = Area of a base × Height.
Here, [tex]35x ^ 5 + 20x ^ 4 - 57x ^ 3 + x ^ 2 + 18x - 30[/tex] = 5x² - 6 × Height
Height = [tex]35x ^ 5 + 20x ^ 4 - 57x ^ 3 + x ^ 2 + 18x - 30[/tex] ÷ 5x² - 6
5x² - 6| [tex]35x ^ 5 + 20x ^ 4 - 57x ^ 3 + x ^ 2 + 18x - 30[/tex] | 7x³+4x²-3x+5
[tex]35x^5[/tex] (+) 42x³
____________________
[tex]20x^4[/tex] - 15x³+x²+18x-30
(-)[tex]20x^4[/tex] (+)24x²
____________________
- 15x³+25x²+18x-30
(+)15x³ (-)18x
____________________
25x²-30
(-)25x²(+)30
___________________
0
So, height = 7x³+4x²-3x+5
Therefore, the height of given hexagonal prism is 7x³+4x²-3x+5.
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What is the slope of the line?
Answer: 2
Step-by-step explanation:
Plzzzzzzz help this is tonight plzzzzzzz
Answer:
Step-by-step explanation:
tto blurrry
factor the trinomial completely. 10x^2+7x-12
Answer: i think the answer is (5x - 4)(2x +3) if it id wrong i am sorry ok
don't forget to drop a heart
Answer:
the answer is (2x + 3)(5x - 4)
Step-by-step explanation:
Anyone know? Thanks
Answer:
the answer is the x-intercepts are about(0,-6) and (0,2) hope this helps
Step-by-step explanation:
Select the correct answer.What is 2/5 divided by 4/7 by equal to?A.7/5 B.7/10 C.10/7 D.7/5
Answer:
5/7
Step-by-step explanation:
5/7
It is always good to double-check your math to make sure you did it right. When I entered 4/7 for x in this equation x / (4/5) = (5/7), we get the following true equation which means the math is correct.
(4/7) / (4/5) = (5/7)
please help me please i really need help please
9514 1404 393
Answer:
62°
Step-by-step explanation:
Angles A and H are alternate exterior angles, so are congruent.
∠H = 62°
Which expression is equivalent to (-4+5y-2x) + (5x+7+10y)
Answer:
3 + 3x + 15y
Step-by-step explanation:
You may find it easier to write these two expressions into column form:
(-4+5y-2x)
+ (5x+7+10y)
Combine like terms (do this for constants, x and y terms):
(-4+5y-2x)
+ (5x+7+10y)
-------------------
3 + 3x + 15y
Find the area of the shape shown below.
Answer:
10 square units.
Step-by-step explanation:
Remark
No matter how weird it looks, the figure is a trapezoid. It has 2 parallel lines.
The height has 2 right angles, one at each end.
Givens
b1 = 2
b2 = 8
h = 2
Formula
Area = 1/2 * (b1 + b2 ) * h
Solution
Area = 1/2 * (2 + 4 + 2 + 2) * 2 Be sure you understand where all those 2s came from.
Area = 10 square units