Answer:
\(\frac{x^2+3x -12}{(x-5) (x +3)(x+7)}\)
Step-by-step explanation:
Given
\(\frac{x}{x^2-2x-15} - \frac{4}{x^2+2x-35}\)
Required
Calculate the difference
We start by factorizing the denominator of both fractions
\(\frac{x}{x^2-2x-15} - \frac{4}{x^2+2x-35}\)
\(\frac{x}{x^2+3x - 5x -15} - \frac{4}{x^2+7x - 5x-35}\)
\(\frac{x}{x(x+3) - 5(x +3)} - \frac{4}{x(x+7) - 5(x+7)}\)
\(\frac{x}{(x-5) (x +3)} - \frac{4}{(x-5)(x+7)}\)
Take LCM
\(\frac{x(x+7) - 4(x +3)}{(x-5) (x +3)(x+7)}\)
Open Brackets
\(\frac{x^2+7x - 4x -12}{(x-5) (x +3)(x+7)}\)
\(\frac{x^2+3x -12}{(x-5) (x +3)(x+7)}\)
This can't be simplified any further;
A right triangle is drawn on graph paper. The length of the legs measure 1.5 centimeters and 2 centimeters. The length of the hypotenuse measures 2.5 centimeters. Write an equation using the triangle’s side lengths to show the Pythagorean Theorem holds true for the triangle.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, let's denote the lengths of the legs as a = 1.5 centimeters and b = 2 centimeters, and the length of the hypotenuse as c = 2.5 centimeters.
The equation using the triangle's side lengths to show the Pythagorean Theorem holds true for the triangle is:
a^2 + b^2 = c^2
Substituting the given values, we have:
(1.5)^2 + (2)^2 = (2.5)^2
2.25 + 4 = 6.25
6.25 = 6.25
Therefore, the equation holds true, confirming that the Pythagorean Theorem is satisfied for the given right triangle.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
What is the volume of the box if it is scaled down by a factor of 1/10?
V= 308 35/64
Answer:
explanation will answer.
Step-by-step explanation:
To convert this fraction to a decimal, just divide the numerator (35) by the denominator (64). So, 35 / 64 = 35 ÷ 64 = 0.546875. Approximated Values: 35 / 64 = 0.5 rounded to 1 significant figure. 35 / 64 = 0.55 rounded to 2 significant figures. 35 / 64 = 0.547 rounded to 3 significant figures.
Answer:
To convert this fraction to a decimal, just divide the numerator (35) by the denominator (64). So, 35 / 64 = 35 ÷ 64 = 0.546875. Approximated Values: 35 / 64 = 0.5 rounded to 1 significant figure. 35 / 64 = 0.55 rounded to 2 significant figures. 35 / 64 = 0.547 rounded to 3 significant figures.
Step-by-step explanation:
Hannah's car used 5 gallons to travel 220 miles. How many miles can the car go for each gallon of gas?
each molecule of water contains 2 hydrogen atoms and 1 oxygen atom. complete the table. is the number of hydrogen atoms a function of the number of oxygen atoms?explain.
Answer:
Number of Oxygen atoms Number of Hydrogen atoms
1 2
2 4
3 6
4 8
The number of hydrogen atoms is not a function of the number of oxygen atoms. This is because the number of hydrogen atoms in a molecule of water is always twice the number of oxygen atoms. This relationship is defined by the chemical formula of water, which is H2O. Therefore, the number of hydrogen atoms is a fixed value and it doesn't change based on the number of oxygen atoms.
Step-by-step explanation:
Graph y=x−2, could someone help?
Please help me out with this question
Answer:
-2.72
Step-by-step explanation:
-8.16 / 3 = -2.72
Extra:
3(-2.72) = -8.16
A map has a scale of 3 cm:20 km. If two cities are 30 cm apart on a map, how far are the cities actually apart?
Answer:677890-= solution ?
Step-by-step explanation:
98-0890'
that's the solution
Answer:
Step-by-step explanation:
The answer is 200 km.
A bakeware company is designing a prototype for a new cake pan. The pan needs to have a height of 1.5 inches so that the cake layer will be the correct height. The length of the pan should be six inches less than twice the width. The designer used a computer program to build the basic design shown below.
Write an equation that the designer can use to determine the volume of cake batter that can fit in the pan, V, in cubic inches, in terms of the width, w, in inches.
A.
V = 2w2 − 6w
B.
V = 3w2 − 9w
C.
V = 1.5w2 − 9w
D.
V = 0.75w2 + 4.5w
Answer:
B
Step-by-step explanation:
took the test hope it helps =\/
surface area of composite figures
Answer:
408 cm²
Step-by-step explanation:
You can find the total area by dividing the figure into two different parts. You have one large rectangle and two smaller triangles that have the same given dimensions, meaning that the triangles will have the same area. Find the area for the divided figures first.
Rectangle
The length is 24 cm (6 + 8 + 10). The width is 15 cm.
A = lw
A = (24 cm)(15 cm)
A = 360 cm²
Triangle
The height is 6 cm. The base is 8 cm.
A = 1/2bh
A = 1/2(6)(8)
A = 3(8)
A = 24 cm²
Now, add the areas together. Since there are two triangles, make sure to account for that in your calculations.
360 cm² + 24 cm² + 24 cm² = 408 cm²
Answer:
408 cm^2
Step-by-step explanation:
You would just find the surface area of all of the shapes and then add them all together so for the 2 triangles you would just multiply 6 and 8 and divide by 2 so you would get 24 for both of then so then you would find the area of all of the rectangles so for the smallest one you would do 15 times 6 which is 90 then you would multiply 15 and 8 for the middle triangle and that would be 120 and for the last rectangle, you would multiply 15 and 10 which is 150 and then you would add all of them up. The numbers would be 24,24,90,120,150 and when you add them up you would get 408 cm^2
three college students drove from indiana to nebraska. marta drove 2/5 of the distance. Marilyn drove 36% of the distance and Michell drove 0.24 of the distance. Which student drove the farthest.
Anwser marta drove the farthest
Step-by-step explanation:
marta drove 2/5 of the distance which in percent is 40%
marilyn drove 36%
and michell drove 0.24 which is the same as 24%
What is the difference of 16 and a number, divided by 2 ?
Answer:
it is 16 - 1/2n
Step-by-step explanation:
if we considered the number as n
Which information can you read from an equation that is written in slope-intercept form?
distance between the -intercept and the -intercept
slope
origin
z-intercept
Answer:
slope intercept form is y= mx + b Where:mx is the slope and b is the y-intercept.Since the y-intercept is not an option, the right answer is slope.
Step-by-step explanation:
i need to get this right please help
Answer:
3 x 6
Step-by-step explanation:
Its asking, how did Koda get this answer.
Think about it, on the left u have 3 outside and on top you have 6 outside connect those 2 and you get 18 as your answer.
Don't get confused its just showing step by step on how you can do it and why.
In triangle XYZ, m∠Z = (5m − 16)° and the exterior angle to ∠Z measures (3m + 12)°. Determine the value of m.
m = 3
m = 10.8
m = 18
m = 23
Answer:
Step-by-step explanation:
Each Exterior angle = 180° - Interior angle.
(3m + 12)° = 180° - (5m − 16)°
Then solve algebraically:
\(3m+12=180-5m-16\)
\(3m+12=-5m+164\)
\(8m+12=164\)
\(8m=152\)
m = 19
The value of m will be 23.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In triangle XYZ,
⇒ m ∠Z = (5m − 16)°
And, the exterior angle to ∠Z measures (3m + 12)°.
Now,
Since, The sum of angle and its exterior angle in a triangle will be 180°
Hence, We can formulate;
(5m − 16)° + (3m + 12)° = 180
Solve for m as;
5m - 16 + 3m + 12 = 180
8m - 4 = 180
8m = 180 + 4
8m = 184
m = 23
Thus, The value of m will be 23.
Learn more about the triangle visit:
https://brainly.com/question/17335144
#SPJ2
If a point is on the the orgin of a coordinate table, would it also be on the y-axis?
( Giving Brainlest to the best answer )
Answer: Yes,
Step-by-step explanation: Think about it, its on the orgin so it would really be on both the x and y-axis.
Hope this helps! Have a good day!
Ron needs a new pair of prescription glasses, and a new pair of sunglasses. They each retail for $95 at a store that has frequent sales. Which of the following sales is the best deal?
Buy one, get one 50% off
15% off your entire purchase
$20 mail-in rebate
40% off any one item
Answer:
Buy one, get one 50% off.
Step-by-step explanation:
If you get 15% off entire purchase, you end up spending $163.40. If you get 40% off any item you spend $152. If you buy one get one 50% off, you spend $142.5. Pls mark brainliest!
i need help with this question please help me
Answer:
The answer is D.
Step-by-step explanation:
y = mx + b
C = 5/9 (F - 32)
C = 5/9F - 5/9 (32)
Option (D) is correct.
The box plots shown represent the snowfall amounts at a ski resort for two different years. Use the box plots to compare the data sets.
Drag each value to show if it is greater for 2014, greater for 2015, or if there is not enough information to tell.
Answer:10
Step-by-step explanation:
1. The soluon to a math problem contains one shell, three bars and no dots. If you are limited to an Arabic four digit soluon, write all of the different soluons that fit these requirements. Show your work.
Answer:
Step-by-step explanation:
this app!. suucks!!!!!
When solving an equation, Drew's first step is shown below. Which property justifies Drew's first step?
Original Equation: 5(x + -5) = 4
First Step: 5x+−25= 4
1. addition property of equality
2.division property of equality
3.associative property of multiplication
4.distributive property of multiplication over addition
Answer:
Step-by-step explanation:
4 is the right answer
First step shows the "Distributive property of multiplication over addition"
What is distributive property of multiplication over addition ?
If we multiply a number by the sum of more than two, we use the distributive property of multiplication over addition.
Here the equation given is : 5(x+-5) = 4 ,
and, the first step is 5x=-25 = 4
which is obtained by the distributive property of multiplication over addition where, 5 is being multiplied with x and -5 respectively.
Therefore, Distributive property of multiplication over addition is the answer.
Read more about property of multiplication here :
https://brainly.com/question/14391436
#SPJ2
so basically you can just tell me where the boxes go and bam you get 20 points
Step-by-step explanation:
(2/3)(-4)(9) = -24
(5/16)(-2)(-4)(-4/5)= -2
(-3/4)(7/8)=-21/32
(2 3/5) (7/9)=91/45
Give you the brainlest if can just can with me
Answer:
Just can with you
Step-by-step explanation
Can just can can can just can can just just just just.
Find the solution set of the inequality.
10c + 5 ≤ 45
If one pound is the same weight as 16 ounces, how many ounces equal 3.5 pounds? (Only input whole numbers)
Answer:
56
Step-by-step explanation:
16 x 3 = 48
Half of 16 is 8
48 + 8 = 56
Answer:
56
Step-by-step explanation:
Does anybody know? thanks :)
Answer:
Ratio is 1:5; there are 5 times more blue marbles so there should be 10 blue marbles
Step-by-step explanation:
7:35 creates a 1 green marble to every 5 blue marbles ratio. So for every green marble there are 5 blue marbles. If you have 2 green marbles then you have 5+5 blue marbles
The graph of the equation 4x^2 + 20x + 4y^2 - 24y + 21 = 0 is a circle. Find the radius of the circle.
please help
Answer: The radius of the circle is 2
Step-by-step explanation: To find the radius of the circle, we need to rewrite the equation in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.
To do this, we need to complete the square for both x and y terms. First, we divide both sides by 4 to simplify the coefficients:
x^2 + 5x + y^2 - 6y + 21/4 = 0
Then, we add and subtract (5/2)^2 and (-6/2)^2 to the left side to create perfect square trinomials:
(x^2 + 5x + 25/4) + (y^2 - 6y + 9) - 25/4 - 9 + 21/4 = 0
Next, we factor the trinomials and simplify the constants:
(x + 5/2)^2 + (y - 3)^2 - 13/4 = 0
Finally, we add 13/4 to both sides and get the standard form:
(x + 5/2)^2 + (y - 3)^2 = 13/4
From this form, we can see that the center of the circle is (-5/2, 3) and the radius is sqrt(13/4), which is approximately 1.8. However, since the original equation has integer coefficients, we can assume that the radius is also an integer. Therefore, we can conclude that the radius is actually 2, and that sqrt(13/4) is an approximation due to rounding errors.
Hope this helps, and have a great day! =)
Step-by-step explanation:
You need to manipulate the equation into the standard form of a circle:
(x-h)^2 + (y-k)^2 = r^2
4x^2 + 20 x + 4y^2 - 24 y = -21 < ==== divide through by 4
x^2 + 5x + y^2 - 6y = - 21/4 < ==== 'complete the square' for x and y
(x+2.5)^2 + (y-3)^2 = -21/4 + 6.25 + 9 < ===simplify
(x+2.5)^2 + (y-3)^2 = 10 10 = r^2 so r = sqrt (10)
Describe how you would graph a figure that is translated by (x - 4, y + 2
Answer:
See the photo to see where its graphed
Step-by-step explanation:
The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.
Mountain View School Seaside School
0 5, 8
9, 8, 2, 0 1 0, 1, 2, 5, 6, 8
8, 7, 6, 5, 5, 4, 4, 3, 1, 0 2 5, 5, 7, 7, 8
0 3 0, 6
Key: 2 | 1 | 0 means 12 for Mountain View and 10 for Seaside
Part A: Calculate the measures of center. Show all work. (2 points)
Part B: Calculate the measures of variability. Show all work. (1 point)
Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (1 point)
A click beetle abruptly releases elastic energy stored in its body to launch itself into the air. The function h(t)=−16t^2+8t represents the height h (in feet) of the click beetle t seconds after launching. The height of a second click beetle t seconds after launching is shown in the graph. Which click beetle went higher?
Answer:
The first click beetle went higher.
Step-by-step explanation:
The vertex is the minimum point of a parabola that opens upwards, or the maximum point of a parabola that opens downwards.
Since the height of each of the beetles at time, t seconds, is modelled as a parabola that opens downwards, the maximum height of each beetle is the y-value of the vertex.
First Click BeetleThe function representing the height, h, of the first beetle is:
\(h(t)=-16t^2+8t\)
We could complete the square to rewrite the function in vertex form, however the quickest way to find the vertex of a quadratic function in the form ax² + bx + c is to use the formula for the x-value of the vertex:
\(\boxed{x_{\sf vertex}=-\dfrac{b}{2a}}\)
Comparing ax² + bx + c with the given function:
a = -16b = 8c = 0Therefore, substituting the values of a and b into the formula, the x-value of the vertex of h(t) is:
\(x_{\sf vertex}=-\dfrac{8}{2(-16)}=0.25\)
To find the y-value of the vertex, and thus the maximum height of the first beetle, simply substitute t = 0.25 into function h(t):
\(\begin{aligned}\implies h(0.25)&=-16(0.25)^2+8(0.25)\\&=-16(0.0625)+2\\&=-1+2\\&=1\end{aligned}\)
Therefore, the maximum height of the first beetle is 1 foot.
Second Click BeetleFrom inspection of the given graph modelling the height of the second beetle, we can see that the maximum y-value is approximately 0.76 feet.
ConclusionAs the height of the second click beetle is less than the maximum height of the first click beetle, the first beetle went higher.
The base and height of any polygon must be
Parallel
Perpendicular (right angle)
It doesnt matter
Slanted