Answer:
[tex]=\frac{4y^2}{x^2}[/tex]
Step-by-step explanation:
[tex]\frac{(8x^2y^3)}{(2x^4y)}[/tex]
[tex]=\frac{(8x^2y^3)}{(2x^4y)}\\[/tex]
[tex]=\frac{8y^2}{2x^2}[/tex]
[tex]=\frac{4y^2}{x^2}[/tex]
I Hope This helps :)
Reuben rented a truck for one day. There was a base fee of $14.95, and there was an additional charge of 80 cents for each mile driven. Reuben had to pay
$135.75 when he returned the truck. For how many miles did he drive the truck?
Answer:
hczgdjatulsfulsitsfisfula7tl7roa7pts
find the area dimensions are in centimeters.
Answer:
[tex]9600cm^{2}[/tex]
Step-by-step explanation:
Get the area of the triangle and the rectangle, then subtract the triangle's area for the rectangle's
A tower on a college campus was built with a faulty foundation and is starting to lean. A student climbs to the tilted top and drops a rope down to the ground. The
end of the rope lands 3 feet from the base of the tower and measures 57 feet from
the top of the building to the ground. What is the angle that the tower is leaning?
Round your answer to the nearest degree, and enter the number only
Answer:
leaning at 3 degrees off of normal (to the nearest whole degree)
Step-by-step explanation:
To visualize, let's assume the tower is leaning to the right, (as viewed by us).
If the rope is dropped from the top to the ground, the tower, the rope and the ground (between the rope and the tower) form a right triangle.
The height and base of the triangle are given
Often we're looking for the angle near the ground, but here, we're looking for the angle between the rope and the tower because the angle is congruent to the angle that the tower forms with it's original vertical position (alternate interior angles). If the tower was standing straight up and hadn't been leaning at all, we wouldn't say that the tower was leaning 90°... we would say it was leaning 0°. Whereas if the tower fell over and was laying flat on the ground, we would say it was leaning at 90°. So, we're not measuring the angle between the tower and the ground, but rather the angle between the tower where it should be, and where it is... which is the same angle as the rope forms with the tower.
Recall that [tex]tan(\theta)=\dfrac {opp}{hyp}[/tex]
Since we know the two legs of the right triangle, one can setup a tangent relationship with the two legs, but remember that the "opposite" side is going to be the ground, and the "adjacent side" will be the rope.
[tex]tan(\theta)=\dfrac {ground}{rope}\\tan(\theta)=\dfrac {3ft}{57ft}\\tan(\theta)=\frac {3}{57}\\\theta=tan^{-1}(\frac {3}{57})\\\theta=3.012787504^o\\\theta \approx 3^o\\[/tex]
Instructions: Write the equation of the line in Point-Slope Form
given the information below. Use Point One.
Point One (-3, 3)
=
Point Two (-2,-1)
Point-Slope
=
Point-Slope Form:
Answer: [tex]y-3=-4(x+3)[/tex]
Step-by-step explanation:
The slope is
[tex]\frac{-1-3}{-2-(-3)}=\frac{-4}{1}=-4[/tex]
So, using the point (-3, 3) to substitute into point-slope form, the equation is [tex]\boxed{y-3=-4(x+3)}[/tex]
if the third place value of a number is 64 , What base is the number in ?
A) 2
B) 4
C) 8
D) 16
Answer:
B
Step-by-step explanation:
4, 16, 64 should be the correct order
Problem
Suppose that J is between H and K. If HJ=2x+4, JK=3x+3, and KH=22, find the lengths of HJ and JK. Remember to always draw an image first and to pay attention to what the question is asking for!
Solution
Find the Segment Addition Postulate
Use the Segment Addition Postulate and then substitute what we know. Do not use any spaces in your answers.
HJ+JK= Answer
( Answer
)+( Answer
)= Answer
Find x
Once we combine our like terms we get:
Answer
x+ Answer
= Answer
x= Answer
Find HJ and JK
Our questions asked us for the lengths of HJ and JK so we must plug in the value of x to solve for those values. We were given HJ=2x+4 and JK=3x+3.
HJ=2x+4
HJ=2( Answer
)+4
HJ= Answer
And
JK=3x+3
JK=3( Answer
)+3
JK= Answer
3x-4
Check Work
View checked work
Answer:
The lengths of HJ and JK are 50 and 72 respectively.
Given:
J is between H and K.
HJ=2x+4
JK=3x+3
HK=22
Step-by-step explanation:
The total length is given as:
HJ+JK=HK
⇒ (2x+4)+(3x+3)=22
⇒ 5x+7=22
⇒ 5x=22-7
⇒ 5x=15
⇒ x=3
Thus, the length of HJ is (2x+4)=(2*3+4)=10
And the length of JK is (3x+3)=(3*3+3)=12
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The lengths of HJ and JK are 50 and 72 respectively.
Given: J is between H and K. the length of HJ=2x+4, JK=3x+3, and HK=22.
The line HJ and JK are collinear then the total length is given as: HJ+JK=HK
substitute values
⇒ (2x+4)+(3x+3)=22
⇒ 5x+7=22
⇒ 5x=22-7
⇒ 5x=15
⇒ x=3
Thus, the length of HJ is (2x+4)=(2*3+4)=10
And the length of JK is (3x+3)=(3*3+3)=12
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Lashawn makes scrambled eggs with 3 spoonfuls of salsa for every 2 eggs. Gilberta adds 7 spoonfuls of salsa for every 5 eggs.
Whose scrambled eggs have a stronger salsa taste?
A. Lashawn's eggs
B. Gilberta's eggs
C. The dishes of scrambled eggs have equal salsa tastes
Lashawn's scrambled eggs have a stronger salsa taste than Gilberta's scrambled eggs. Then the correct option is A.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Lashawn makes scrambled eggs with 3 spoonfuls of salsa for every 2 eggs.
Gilberta adds 7 spoonfuls of salsa for every 5 eggs.
Then the scrambled eggs have a stronger salsa taste will be
Lashawn's eggs = 3/2 = 1.5
Gilberta's eggs = 7/5 = 1.4
Lashawn's scrambled eggs have a stronger salsa taste than Gilberta's scrambled eggs.
Then the correct option is A.
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If each pound of beef costs $3.69, how much does 2 pounds cost? Round to the nearest cent.
Answer: Two pounds of beef costs $7.38.
Step-by-step explanation:
Multiply the cost for one pound by the amount of pounds you need.
$3.69×2=$7.38
I hope this helps!!
The cost of renting a car is $47 /week plus $0.25 /mile traveled during that week. An equation to represent the cost would be y=47+0.25x , where x is the number of miles traveled.
Answer:
a. 61.25
b. 70
c. 212
Step-by-step explanation:
a. What is your cost if you travel 57 miles?
The cost is $ .
y=47+0.25x
y=47+0.25(57)
y=47+14.25
answer: 61.25
b. If your cost was $64.50, how many miles were you charged for traveling?
You were charged for traveling miles.
64.50-47=0.25x
17.50=1/4x
17.50*4
answer 70=x
c. Suppose you have a maximum of $100 to spend for the car rental. What would be the maximum number of miles you could travel?
The maximum number of miles you could travel is miles.
100-47
53=1/4x
answer : x= 212
Need help with algebra homework
Answer:
the answer for this problem is A, big
what is 2 plus two.
please answer quickly
Answer:
2 + 2: 4
or 2 + 2: 5 from the dystopian novel 1984.
PLEASE HELP ME WITH MY MATH
The definition for the graphed function is the one shown in option d:
y = -x + 2 if x < 1
y = -2x + 1 if x ≥ 1.
Which piecewise function coincides with the graph?Here we have a piecewise function, where for the first part we have a linear equation with a negative slope (for x < 1, we know that the symbol "<" must be used because of the open dot at the end of the line).
Then, we have another linear equation with a negative (and steeper) slope. This time there is a closed dot, so the domain for this second part is x ≥ 1.
With that we can conclude that the correct option is:
d:
y = -x + 2 if x < 1
y = -2x + 1 if x ≥ 1.
Where you can see that the second part has a larger (in module) slope, and the domains are defined as we saw above.
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Find the equation of the line that
is perpendicular to y = -8x + 2
and contains the point (-4,1).
Answer:
Step-by-step explanation:
slope of line ⊥ to y=-8x+2
is -1/-8=1/8
eq. of line with slope 1/8 thro' (-4,1) is
y-1=1/8 (x+4)
8y-8=x+4
8y=x+4+8
8y=x+12
y=1/8 x+12/8
or
y=1/8 x+3/2
Find the area.
help pls
Answer:
30 square feet
Step-by-step explanation:
The area of a trapezoid is equal to (a+b)/2 * h
In this case, the value of a is 5, b is 10, and h is 4. You can substitute those numbers into the formula and get the answer of 30.
The sum of a number and 3 is less than 10 if x denotes the number what would be the possible values of x
x>13
x<13
x>7
x<7
Answer:
x<7
Step-by-step explanation:
Consider the number x (as mentioned in the question). Now carefully pay attention to the given condition
⇒"The sum of a number and 3 is less than 10"
Remember the notation of the term "less than" in mathematical context is indicated by "<" sign. Hence our inequality is
⇒ x+3<10
adding or subtracting any number from the both sides of an inequality DOESN'T change its direction. Thus, if we cancel out 3 from both sides it won't swap the inequality. Therefore
⇒ x+3-3<10-3
⇒ [tex]x<7[/tex]
In terms of interval notation
[tex]\implies x\in( -\infty,7)[/tex]
In conclusion
The answer is D) [tex]x < 7[/tex]
Let the number be x
The sum of number and 3
x+3Is less than 10
x+3<10Lets solve it
x<10-3x<7Hence
Option D is correct
George buys a computer. He pays a deposit of £200 and six monthly instalments of £55_
How much does George pay for his computer in total?
The set of all numbers greater than or equal to −5 and less than 5.
Answer:
No. greater than of equal to (-5) = -4,-3,-2,-1,0,1,2,3,4,5,6...........
No. less than 5 = 4,3,2,1 ,0,-1......
{ -4,-3,-2,-1,0,1,2,3,4}
Calculate the length of the diagonal of the state of Wyoming.
The length of the diagonal of the state of Wyoming is 457 miles.
What is the length of the diagonal?The length of the diagonal of the diagonal can be determined using Pythagoras theorem.
The Pythagoras theorem: a² + b² = c²
where:
a = lengthb = basec = hypotenuse√365² + 275² = 457 miles
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Find the ratio of 18 inches to 2 yards B
A. 3/4 B. 1/4
C. 1/5 D. 2/5
Answer:
B. 1 / 4
Step-by-step explanation:
Step 1: We can turn 2 yards into 6 feet.
Step 2: Then we can turn 6 feet into 72 inches.
Step 3: We plug it into the ratio, getting 18 / 72.
Step 4: Simplify. We get 1 / 4 as the answer. Therefore, we choose B.
Given positive integers $x$ and $y$ such that $2x^2y^3 + 4y^3 = 149 + 3x^2$, what is the value of $x + y$?
Answer:
5
Step-by-step explanation:
2x²y³ + 4y³ = 149 + 3x²
[tex] 2x^2y^3 - 3x^2 = 149 - 4y^3 [/tex]
[tex] x^2(2y^3 - 3) = 149 - 4y^3 [/tex]
[tex] x^2 = \dfrac{149 - 4y^3}{2y^3 - 3} [/tex]
[tex] x = \pm \sqrt{\dfrac{149 - 4y^3}{2y^3 - 3}} [/tex]
Try y = 1
[tex]x = \pm \sqrt{\dfrac{149 - 4(1)}{2(1)^3 - 3}} = \pm \sqrt{-145} = i\sqrt{145}[/tex]
For y = 1, x is imaginary.
Try y = 2
[tex] x = \pm \sqrt{\dfrac{149 - 4(2)^3}{2(2)^3 - 3}} = \pm \sqrt{9} = \pm 3[/tex]
Since x and y are positive integers, ignore x = -3.
When x = 3, y = 2.
x + y = 3 + 2 = 5
The value of x + y is 5.
What is Polynomial?Polynomials are expressions which consist of variables, constants, coefficients and exponents.
We have the equation,
2x²y³ + 4y³ = 149 + 3x²
2x²y³ - 3x² = 149 - 4y³
x² (2y³ - 3) = 149 - 4y³
x² = (149 - 4y³) / (2y³ - 3)
x = √[(149 - 4y³) / (2y³ - 3)]
Now, we have to find two positive integers.
We can use trial and error method here.
Trial putting y = 1.
x = √[(149 - 4 × 1³) / (2 × 1³ - 3)]
= √[145 / (-1)]
= √(-145)
There is no real root for √(-145). So y = 1 is not applicable.
Trial putting y = 2.
x = √[(149 - 4 × 2³) / (2 × 2³ - 3)]
= √[117 / 13]
= √(9)
= ± 3
But we need positive integers. So we ignore -3.
So x = 3 and y = 2 ⇒ x + y = 5
Hence x + y = 5.
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also can someone check this too? just want to make sure i got the the first part right before proceed further
Answer:
the answers are all right
find the slope of the line that passes through (3,10) and (1,17)
Answer:
[tex]m=- \frac{7}{2}[/tex]
Step-by-step explanation:
The slope of a line passing through the two points [tex]\displaystyle{\large{{P}={\left({x}_{{1}},{y}_{{1}}\right)}}}[/tex] and[tex]\displaystyle{\large{{Q}={\left({x}_{{2}},{y}_{{2}}\right)}}}[/tex] is given by [tex]\displaystyle{\large{{m}=\frac{{{y}_{{2}}-{y}_{{1}}}}{{{x}_{{2}}-{x}_{{1}}}}}}[/tex].
We have that [tex]x_1=3[/tex], [tex]y_1=10[/tex], [tex]x_2=1[/tex], [tex]y_2=17[/tex].
Plug the given values into the formula for slope: [tex]m=\frac{\left(17\right)-\left(10\right)}{\left(1\right)-\left(3\right)}=\frac{7}{-2}=- \frac{7}{2}[/tex]
Answer: the slope of the line is [tex]m=- \frac{7}{2}[/tex].
Answer:
slope = - [tex]\frac{7}{2}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{x_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 10 ) and (x₂, y₂ ) = (1, 17 )
m = [tex]\frac{17-10}{1-3}[/tex] = [tex]\frac{7}{-2}[/tex] = - [tex]\frac{7}{2}[/tex]
You invest $1600 in an account paying 5.4% interest compounded daily. What is the account's effective annual yield? Write as a decimal.
Answer:
For a principle amount of $1600 and rate 5.4%, the effective annual yield is 5.55% if interest is compounded annually.
Step-by-step explanation:
Concept: The annual percentage yield (APY) or the effective annual yield is the real rate of return earned on an investment, taking into account the effect of compounding interest.
The principle amount is $1600, rate is 5.4% and period is 365 days. The formula to find yield is [tex]Y = (1+\frac{r}{n} )^{n} -1[/tex]. All the values are to be inserted in the formula. Here n = 365 and r = 5.4%.
[tex]Y=(1+\frac{0.054}{365} )^{365} -1\\Y=(1.000148)^{365} -1\\Y=5.55%[/tex]
The annual yield is 5.55%.
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You are given that cos(A)=−5/13, with A in Quadrant II, and sin(B)=7/25, with B in Quadrant II. Find cos(A+B). Give your answer as a fraction.
The value of cos(A+B) is 36/325.
What is Trigonometry?The branch of mathematics concerned with specific functions of angles and their application to calculations.
Given:
cos(A)=−5/13
sin(B)=7/25
Now Using identity,
sin²A + cos² A= 1
sin A= √1 - cos² A
sin A = √1- 25/169
sin A= √144/169
sin A= 12/13
Again,
sin²B + cos² B= 1
cos B= √1 - sin² B
cos B = √1- 49/625
cos B= √576/625
cos B= -24/25
Now,
cos (A +B) = cos A cos B - sin A sin B.
= -5/13* (-24/25) - 12/13* 7/25
= 120/325 - 84/325
= 36/325
Hence, the value of cos (A + B) is 36/325.
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how many ways are there to make $3 with pennies, nickels, and dimes
Answer:
10
Step-by-step explanation:
Challenge time! Isn't time to give your brains a break? Its a fun challenge! EARN 20 POINTS NOW
Answer:
The answer is 64
Step-by-step explanation:
If you find this answer helpful pls mark it the brainliest answer
it's easy 64 the key is in the pic.
Suppose we have already saved $55 towards the cost of a new television set.
We plan to save $6 more each week for the next several weeks.
i) Write an equation for the total amount T we will have after w weeks from now.
ii) Find the total amount that would be saved after 8 weeks.
Step-by-step explanation:
T = 55 + 6w
after 8 week $103
Simplify this problem!!!
Answer:
C
Step-by-step explanation:
HOPE THAT HELPSBDNQBDB
What is x, the distance between points A and A'? D.15
The value of x that fills the coordinate are 7 or -5
Distance between two pointsThe formula for calculating the distance between two points is expressed as:
D = √(x2-x1)² +(y2-y1)²
Substitute the given coordinates
10 = √(15-7)² +(1-x)²
100 = 8² +(1-x)²
(1-x)² = 100 - 64
(1-x)² = 36
1- x = -6
x = 7 or -5
Hence the value of x that fills the coordinate are 7 or -5
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Complete question
If the distance between two points (x, 7) and (1, 15) is 10, find the value of x.
Is 3.5 greater than 3.39
Answer:
yes
Step-by-step explanation:
