Answers
Answer: 14 m
Step-by-step explanation:
8 m + 6 m = 14 m
Answer:
10 cm.
Step-by-step explanation:
We have been given a cuboid. We are asked to find the shortest distance from A to B is the given diagram.
We know that shortest distance from A to B will be equal to hypotenuse of right triangle with two legs 8 meters and 6 meters.
[tex]AB^2=8^2+6^2[/tex]
[tex]AB^2=64+36[/tex]
[tex]AB^2=100[/tex]
Now, we will take square root of both sides of our given equation as:
[tex]AB=\sqrt{100}[/tex]
[tex]AB=10[/tex]
Therefore, the shortest distance from A to B is 10 cm.
Related Questions
It takes 36 minutes for 7 people to paint 4 walls.
How many minutes does it take 9 people to paint 7 walls?
Answers
Answer:
49 minutes
Step-by-step explanation:
It would take 49 minutes for 9 people to paint 7 walls.
4 walls need 262 people/minutes (7)(36)
9 people could do that in 49 minutes (441/9)
Answer:
49 minutes
Step-by-step explanation:
first we need to find the rate at which a person paints the walls :
it takes 36 minutes to paint 4 walls by 7 people :
so for 7 people the rate at which they paint the walls is : [tex]\frac{4}{36}[/tex] walls/minute
if we simplify we get [tex]\frac{1}{9}[/tex]
now that was for 7 people , for 1 person the rate is : [tex]\frac{1}{9} \frac{1}{7}[/tex] which is [tex]\frac{1}{63} walls / minute[/tex]
now we have the rate for one person
so for 9 people they will paint [tex]\frac{9}{63} =\frac{1}{7}[/tex] walls/minute
so it takes them 7 minute to paint 1 wall
which means it takes them 7 x7 = 49 minutes to paint 7 walls
which is the rationalized form of the expression the square root of x divided by the square root of x +the square root of 7
Answers
Answer:
I assume your goal is to rationalize the denominator -
So you need to multiply the denominator by its conjugate.
So we have:
[tex]\frac{\sqrt{x} }{\sqrt{x}-\sqrt{7} } *\frac{\sqrt{x} +\sqrt{7} }{\sqrt{x} +\sqrt{7}}[/tex]
->
[tex]\frac{x-\sqrt{7}\sqrt{x} }{x-7}[/tex]
gg
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!
Harry and Larry are having a barbecue dinner. The probability of Harry staining his shirt during the dinner is 1/5. The probability of Larry staining his shirt during the dinner is 15%.
Which of these events is more likely?
Choose 1 answer:
(Choice A)
Harry stains his shirt during the dinner.
(Choice B)
Larry stains his shirt during the dinner.
(Choice C)
Neither. Both events are equally likely.
Answers
Answer:
(Choice A)
Harry stains his shirt during the dinner.
Step-by-step explanation:
If Harry and Larry are having a barbecue dinner and the probability of Harry staining his shirt during the dinner is 1/5 and the probability of Larry staining his shirt during the dinner is 15%, Harry stains his shirt during the dinner is more likely.
Harry - 1/5 as a percent: 20%
Larry - 15% as a decimal: 0.15
Therefore 20% is more than 15 percent.
This makes the answer, Harry stains his shirt during the dinner.
Answer:
(Choice A)
Harry stains his shirt during the dinner.
Step-by-step explanation:
If Harry and Larry are having a barbecue dinner and the probability of Harry staining his shirt during the dinner is 1/5 and the probability of Larry staining his shirt during the dinner is 15%, Harry stains his shirt during the dinner is more likely.
Harry - 1/5 as a percent: 20%
Larry - 15% as a decimal: 0.15
Therefore 20% is more than 15 percent.
This makes the answer, Harry stains his shirt during the dinner.
I will add brainlist from the last question its just that I have to wait till it appears!
THIS IS IXL QUESTION
Answers
Least to greatest:
-1 < -0.2 < 0.3When ordering decimals from least to greatest, it's crucial to understand place value. When ordering, I usually like to start with whole numbers and put them first and then I think about the numbers after the decimal.
The length of an edge of a cube is 4 ft.
What is the volume of the cube?
Enter the answer.
[1] ft3
Answers
Answer:
V = 64 ft^3
Step-by-step explanation:
The volume of a cube is given by
V = s^3 where s is the side length of the cube
V = (4)^3
V = 64 ft^3
Answer:
64 ft
Step-by-step explanation:
Volume=Height*Length*Base
=4*4*4
=16*4
=64 ft
Let f(x) = 9x3+ 21x2^ - 14 and g(x) = 3x + 1. Find "
f (x) over g (x)
Answers
Answer:
[tex]\frac{f(x)}{g(x)}=3x^2+6x-2-\frac{12}{3x+1}[/tex]
Step-by-step explanation:
The first function is [tex]f(x)=9x^3+21x^2-14[/tex]
The second function is [tex]g(x)=3x+1[/tex].
[tex]\frac{f(x)}{g(x)}=\frac{9x^3+21x^2-14}{3x+1}[/tex]
We perform the long division as shown in the attachment to obtain the quotient as: [tex]Q(x)=3x^2+6x-2[/tex] and remainder [tex]R=-12[/tex].
Therefore:
[tex]\frac{f(x)}{g(x)}=3x^2+6x-2-\frac{12}{3x+1}[/tex]
where [tex]x\ne -\frac{1}{3}[/tex]
Answer:
on the flvs test it is option A
Step-by-step explanation:
Which is the correct calculation for the volume of the pyramid?
Answers
Answer:
h×a²×1/3
Step-by-step explanation:
where h is the vertical height of pyramid a is the length of base ..this formula is applicable for square based pyramid only.
Answer:
1/3 A h.
Step-by-step explanation:
The volume of a pyramid is 1/3 * area of the base * height = 1/3 A h.
So for example the area of a square-based pyramid = 1/3 s^2 h where s is the length of a side of the square.
A group of 8 friends (5 girls and 3 boys) plans to watch a movie, but they have only 5 tickets. How many different combinations of 5 friends could
possibly receive the tickets?
A. 13
B. 40
C. 56
b. 64
Answers
[tex]_8C_5=\dfrac{8!}{5!3!}=\dfrac{6\cdot7\cdot8}{2\cdot 3}=56[/tex]
What type of triangle can an isosceles triangle be? Secalene acute obtuse isosceles
Answers
An isosceles triangle is the following options, acute and isosceles, which is B and D. Remember that an isosceles triangle has 2 sides that are the same, so its D and every isosceles triangles are acute, not obtuse, so its B.
Hope this helped!
Nate
Answer:
Acute triangle
Step-by-step explanation:
A isosceles triangle is a triangle that has two equal sides.
It would not be a scalene triangle because in scalene triangles all the sides have different lengths.
It might be an acute triangles because all the angles in an acute triangle would be acute angles.
it wouldn't be an obtuse triangle because in an obtuse triangle there is at least one obtuse angle and the other 2 angles would be either acute, right, or obtuse.
It could be an isosceles triangle but that wouldn't make sense since its already an isosceles triangle.
Hope This Helps!!!
For each geometric sequence, write a recusive rule by finding the commom ratio by calculating the ration of consecutive terms. Write an exlicit rule for the sequence by writing each term as the product of the first tern and a power of the common ratio.
n- 1, 2, 3, 4, 5
An- 2, 6, 18, 54, 162
Answers
Answer:
[tex]a_n=2.(3)^{n-1}[/tex]
Step-by-step explanation:
Given sequence is:
2,6,18,54,162
So the common ratio can be found by dividing the second term by first term:
r = 6/2 = 3
The standard formula for geometric sequence is:
[tex]a_n=a_1r^{n-1}[/tex]
Putting the value of r
[tex]a_n=2.(3)^{n-1}[/tex]
So,
[tex]a_1=2.(3)^{1-1} => 2.3^0 = 2*1 = 2\\a_2=2.(3)^{2-1} => 2.3^1 = 2*3 = 6\\a_3=2.(3)^{3-1} => 2.3^2 = 2*9 = 18\\a_4=2.(3)^{4-1} => 2.3^3 = 2*27 = 54\\a_5=2.(3)^{5-1} => 2.3^4 = 2*81 = 162[/tex]
Matrices X and Y both measure 2x2 and are inverses of each other. Which matrix represents their product?
Answers
Answer:
When a matrix is multiplied by its inverse the result will be the identity matrix. If we multiply two matrix with the same size, the resulting matrix will have the same dimension.
Therefore, if we multiply the matrices X and Y we will get a 2x2 identity matrix, as follows:
[tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]
Answer:
[tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
Step-by-step explanation:
We are asked find the matrix that represent the product of matrices X and Y both measures [tex]2\times 2[/tex] and inverse of each other.
For a matrix multiplication to be defined, the number of columns in the first matrix must be equal to number of rows in the second matrix.
Since the both matrices are [tex]2\times 2[/tex] (same number of column and row), then the product of both matrices would result in [tex]2\times 2[/tex] matrices.
We also know that the multiplication of a matrix with its inverse results in identity matrix.
Therefore, our matrix would be a [tex]2\times 2[/tex] identity matrix as:
[tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex].
The function f(x) = -(x - 20)(x - 100) represents a company's monthly profit as a function of x, the number of purchase
orders received. Which number of purchase orders will generate the greatest profit?
20
O 60
O 80
O 100
Answers
Answer:
The correct option is B
Step-by-step explanation:
Lets put the values in the given function one by one: You will get the answer
f(x)=-(x - 20)(x - 100)
The first option is 20. Substitute the value in the function:
f(x)=-(20-20)(20-100)
f(x)=(- 0)(-80)
f(x)= 0
Second option is 60.
Substitute the value in the function
f(x)=-(x - 20)(x - 100)
f(x)=-(60 - 20)(60 - 100)
f(x)=(-40)(-40)
f(x)=160
Third option is 80:
Substitute the value in the function
f(x)=-(x - 20)(x - 100)
f(x)=-(80 - 20)(80 - 100)
f(x)=(-60)(-20)
f(x)=120
Fourth option is 100:
Substitute the value in the function
f(x)=-(x - 20)(x - 100)
f(x)=-(100 - 20)(100 - 100)
f(x)=(-80)(0)
f(x)= 0
Therefore the values we got are 0, 160, 120, 0
The greatest value is 160.
Thus the correct option is B....
Answer:
B.) 60
Step-by-step explanation:
To bill customers for water usage, one city converts the number of gallons used into units. This relationship is represented by the equation g = 748u, where g is the total number of gallons of water used and u is the number of units.
Determine which statements about the relationship are true. Choose two options.
Answers
Answer:
g is a dependent variable
u is an independent variable
Step-by-step explanation:
Given relationship is:
g=748u
Here two terms need to be defined
Independent Variable : The variable which can take any value. The independent variable is used to calculate the value of dependent variable
Dependent Variable: The dependent variable is determined by the independent variable.
Therefore,
The correct answer is:
g is a dependent variable
u is an independent variable ..
If sin0=-1/2 and 0 is in quadrant III then tan0=
Answers
Answer:
tan O = √3/ 3.
Step-by-step explanation:
The tangent is positive in quadrant 3.
The adjacent side has length √((2^2 - (-1)^2)
= -√3.
So tan O = -1 / -√3
= 1 / √3
= √3/ 3.
To determine tan(θ) for an angle θ where sin(θ) = -1/2 and θ is in quadrant III, we perform the following steps:
1. **Understand the given information:** When sin(θ) = -1/2, it means the opposite side to angle θ in a right triangle is -1 and the hypotenuse is 2. Since θ lies in the third quadrant, both sine and cosine values are negative, implying that the adjacent side length must also be negative.
2. **Use the Pythagorean theorem:** For a right triangle:
\[ \text{hypotenuse}^2 = \text{opposite}^2 + \text{adjacent}^2 \]
Substituting hypotenuse and opposite side values:
\[ 2^2 = (-1)^2 + \text{adjacent}^2 \]
Simplify and solve for the adjacent side:
\[ 4 = 1 + \text{adjacent}^2 \]
\[ 3 = \text{adjacent}^2 \]
\[ \text{adjacent} = \sqrt{3} \] or \[ \text{adjacent} = -\sqrt{3} \]
Since the angle is in the third quadrant where cosine is also negative, we must take the negative square root:
\[ \text{adjacent} = -\sqrt{3} \]
3. **Calculate tan(θ):** By definition,
\[ \tan(θ) = \frac{\text{opposite}}{\text{adjacent}} \]
Substitute the known side lengths:
\[ \tan(θ) = \frac{-1}{-\sqrt{3}} \]
4. **Simplify the expression:**
\[ \tan(θ) = \frac{1}{\sqrt{3}} \]
To rationalize the denominator:
\[ \tan(θ) = \frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} \]
\[ \tan(θ) = \frac{\sqrt{3}}{3} \]
Thus, if sin(θ) = -1/2 and θ is in quadrant III, then tan(θ) = √3/3. Note that in the context of trigonometry, it is often assumed that the angle and the ratios are dimensionless, so a negative 'opposite' simply reflects the direction along the coordinate axis rather than a literal negative length.
The equation y=mx+b is the slope-intercept form of a linear equation.
Solve y=mx+b for m
Answers
Answer: [tex]m=\frac{y-b}{x}[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
To solve for the slope "m", you can follow these steps:
- Subtract "b" from both sides of the equation:
[tex]y-b=mx+b-b\\\\y-b=mx[/tex]
- Divide both sides of the equation by "x". Then:
[tex]\frac{y-b}{x}=\frac{mx}{x}\\\\m=\frac{y-b}{x}[/tex]
13. For what value of b would the following system of equations have an infinite number of solutions? 9x + 12y = 21
6x + 8y = 7b Please explain and show steps :)
Answers
Answer:
b=2
Step-by-step explanation:
9x + 12y = 21
6x + 8y = 7b
To have an infinite number of solutions, the two equations must be equal
Take the first equation and divide by 3, since it is a factor of all the terms
9x/3 + 12y/3 = 21/3
3x+4y = 7
Then multiply by 2 to get the x term equal
2*3x + 2*4y = 2*7
6x +8y = 7*2
Comparing this to the second equation
6x + 8y = 7b
b must equal 2
Factor completely.
6x4 – 9x3 – 36x2 + 54x
3x(x2 + 6)(2x + 3)
6x(x2 – 6)(2x – 3)
3x(x2 – 6)(2x – 3)
6x(x2 + 6)(2x + 3)
Answers
Answer:
3x[x² - 6][2x - 3]
Step-by-step explanation:
Group each term carefully [two-by-two], and you will arrive at your answer.
60 POINTSZZZ HELLPP!!
Question 1(Multiple Choice Worth 5 points)
(06.07A MC)
What is the length of the third side of the window frame below?
(Figure is not drawn to scale.)
15 inches
27 inches
25 inches
32 inches
Question 2(Multiple Choice Worth 5 points)
(06.07A LC)
Ross calculated the missing side length of one of these triangles using the Pythagorean Theorem. Which triangle was it?
E
F
G
H
Question 3(Multiple Choice Worth 5 points)
(06.07A MC)
The figure shows the location of 3 points around a lake. The length of the lake, BC, is also shown.
(Figure is not drawn to scale.)
Which of the following options is closest to the distance (in miles) between points A and B?
3.46 miles
4.24 miles
4.90 miles
5.92 miles
Question 4(Multiple Choice Worth 5 points)
(06.07A LC)
The legs of a right triangle are 3 units and 8 units. What is the length of the hypotenuse? Round your answer to the nearest hundredth.
8.54 units
9.54 units
11.00 units
24.00 units
1st picture is for question 1 2nd picture 2nd question n 3ed for the 3ed question
Answers
A system of linear inequalities is shown below: y − x > 0 x + 1 < 0 Which of the following graphs best represents the solution set to this system of linear inequalities? The first line is a dashed line which joins ordered pairs negative 1, 5 and negative 1, negative 4. The second line is a dashed line and joins ordered pairs negative 2, negative 2 and 4, 4. The portion common to the right of the first line and above the second line is shaded The first line is a dashed line which joins ordered pairs negative 1, 5 and negative 1, negative 4. The second line is a dashed line and joins ordered pairs negative 2, negative 2 and 2, 2. The portion common to the left of the first line and above the second line is shaded The first line is a dashed line which joins ordered pairs negative 1, 5 and negative 1, negative 4. The second line is a dashed line and joins ordered pairs negative 2, negative 2 and 2, 2. The portion common to the left of the first line, above the second line and below the x axis is shaded The first line is a dashed line which joins ordered pairs negative 1, 5 and negative 1, negative 4. The second line is a dashed line and joins ordered pairs negative 2, negative 2 and 3, 3. The portion common to the left of the first line and above the x axis is shaded
Answers
Answer:
The first line is a dashed line which joins ordered pairs negative 1, 5 and negative 1, negative 4. The second line is a dashed line and joins ordered pairs negative 2, negative 2 and 4, 4. The portion common to the right of the first line and above the second line is shaded
Step-by-step explanation:
we have
First inequality
x+1 > 0
x > -1
The solution of the first inequality is the shaded area at right of the dashed line x=-1 (vertical line)
Second inequality
y-x > 0
y> x
The solution of the second inequality is the shaded area above the dashed line y=x
therefore
The first line is a dashed line which joins ordered pairs negative 1, 5 and negative 1, negative 4. The second line is a dashed line and joins ordered pairs negative 2, negative 2 and 4, 4. The portion common to the right of the first line and above the second line is shaded
see the attached figure to better understand tye problem
Find the value of x using the laws of sine.
Answers
Answer:
Rounded to nearest hundredths is 8.75.
Rounded to nearest tenths is 8.7.
Step-by-step explanation:
Law of sines:
[tex]\frac{\sin(A)}{\text{ side opposite to }A}=\frac{\sin(B)}{ \text{ side opposite to }B}[/tex]
Measure of angle [tex]A[/tex] is 28 and the side opposite to it is [tex]x[/tex].
Measure of angle [tex]B[/tex] is 105 and the side opposite to it is 18.
Plug in to the formula giving:
[tex]\frac{\sin(28)}{x}=\frac{\sin(105)}{18}[/tex]
Cross multiply:
[tex]18 \sin(28)=x \sin(105)[/tex]
Divide both sides by sin(105):
[tex]\frac{18 \sin(28)}{\sin(105)}=x[/tex] is the exact answer.
I'm going to type it in my calculator now:
18*sin(28) / sin(105) is what is going in there.
The output is 8.748589074.
Rounded to nearest hundredths is 8.75.
Rounded to nearest tenths is 8.7.
2y3 - 27 + 5y2 + (25 / 5)
What is the value of the expression when y = 2?
a)14
B)0
c)7
d)68
Answers
Answer:
The correct option is A
Step-by-step explanation:
The expression is
2y3 - 27 + 5y2 + (25 / 5)
Substitute the value of y=2 in the expression:
=2(2)³-27+5(2)²+(25/5)
We know that 2³ means multiply 2 three times
2³= 2*2*2=8
Likewise 2²=2*2=4
=2(8)-27+5(4)+(25/5)
=16-27+20+25/5
Now take the L.C.M which is 5
=80-135+100+25/5
Solve the values in the numerator:
=70/5
=14
Thus the correct option is A....
Carmen y Carlos hacen pizzas para vender. La materia prima necesaria para hacer una pizza grande les cuesta $5.00 y para una pizza pequeña $3.00. Si disponen de $570.00 y quieren hacer 150 pizzas, ¿cuántas pizzas de cada tamaño podrán hacer?
Answers
Answer:
A large pizza costs $5 and a small pizza costs $3.
Let 'x' be the number of large pizzas and 'y' the number of small pizzas. We have that:
x + y = 150
5x + 3y = 570
Solving the system of equations:
x + y = 150 → 3x + 3y = 450 → 3y = 450 - 3x
5x + 3y = 570 → 5x + 450 - 3x = 570
2x = 120
x = 60
y = 150 - 60 = 90
Therefore. Carmen y Carlos will make 60 large pizzas and 90 small pizzas.
identify an equation in point-slope form for the line perpendicular to y=-1/2x+11 that passes through (4,-8).
A. y+8=2(x-4)
B. y+8+1/2(x-4)
C.y-8=1/2(x+4)
D.y-4=2(x+8)
Answers
Answer:
A. y+8=2(x-4)
Step-by-step explanation:
A line perpendicular to y=-1/2x+11 would have slope +2, which is the negative reciprocal of -1/2.
Starting with the slope-intercept form of the equation of a straight line, find the y-intercept based upon this new line's passing through (4, -8):
y = mx + b becomes -8 = 2(4) + b. Then b = -16, and the desired new line is
y = 2x - 16.
Eliminate answer choices B and C, because 1/2 is not the correct slope.
Choice A is correct. Note that the result of subbing 4 for x and -8 for y into A: y + 8 = 2(x - 4) is a true equation: -8 + 8 = 2(4 - 4)
Also note that y + 8 = 2(x - 4) can be written in slope-intercept form:
y = -8 + 2x - 8, or y = 2x - 16 (same as obtained earlier)
Answer:Y+8=2(x-4)
Step-by-step explanation:
it’s correct I promise
Veronica works each day and earns more money per hour the longer she works. Write a function to represent a starting pay of $20 with an increase each hour by 5%. Determine the range of the amount Veronica makes each hour if she can only work a total of 8 hours.
Answers
Answer:
20 ≤ f(x) ≤ 28.14
Step-by-step explanation:
PLEASE ANSWER QUICK!!! Identify the equation of the circle that has its center at (-8, 15) and passes through the origin.
Answers
Equation of a circle
Midpoint at (a,b)
(x - a)^2 + (y - b)^2 = r^2
You know what the circle’s center is so you can substitute those values in
(x + 8)^2 + (y - 15)^2 = r^2
But you don’t know what the radius is. To find the radius, we know that the circle passes through the origin (0,0) so you just use the distance formula to figure out the radius length.
Distance formula:
Square root of (x1 - x2)^2 + (y1 - y2)^2
So...
Square root of (-8 - 0)^2 + (15 - 0)^2
Square root of 64 + 225
Square root of 289
r=17
So you substitute 17 into the equation of a circle formula and the result is:
(x + 8)^2 + (y - 15)^2 = 17^2
~~hope this helps~~
The equation of the circle is [tex](x+8)^{2} +(y -15)^{2} = 289[/tex].
What is the general equation for the circle?The general equation of the circle is [tex](x-h)^{2} +(y-k)^{2} = r^{2}[/tex].
Where, (h, k) is the center and r is the radius of the circle.
Let the equation of the circle be
[tex](x-h)^{2} +(y-k)^{2} =r^{2}..(i)[/tex]
According to the given question.
The center of the circle is (-8, 15).
⇒ (h, k) = (-8, 15)
And, the circle is passing through origin i.e. (0, 0).
Since, the center of the circle is (-8, 15).
So, the equation (i) can be written as
[tex](x-(-8))^{2} +(y - 15)^{2} = r^{2}[/tex]
Also, the circle is passing through (0, 0).
Therefore,
[tex](0+8)^{2} +(0-15)^{2} = r^{2}[/tex]
[tex]\implies 64+ 225 = r^{2} \\\implies 289 = r^{2} \\\implies r=\sqrt{289} \\\implies r = 17[/tex]
So, the radius of the circle is 17 unit and its center is (-8, 15).
Therefore, the equation of the circle is
[tex](x+8)^{2} +(y-15)^{2} = 289[/tex]
Hence, the equation of the circle is [tex](x+8)^{2} +(y -15)^{2} = 289[/tex].
Find out more information about equation of circle here:
https://brainly.com/question/10618691
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there are 63 students marching in a band, and they'are marching in 7 rows. how many students are in each row?
Answers
To find the number or rows, divide the total number of students by the number in each row.
63 / 7 = 9 rows.
Hello There!
If there are 63 students marching in the band and there is 7 rows, we can find out how many students are in each row by dividing 63 "number of students" by 7 "number of rows" and we will get an answer of 9.
Madeline is standing 2x- 4 feet from the base of a tree. The height of the tree is 5x + 6 feet. Find the equation that shows
the straight-line distance from Madeline's feet to the top of the tree in terms of x.
Provide your answer below:
Answers
Answer:
c = sqrt( 29x^2 + 44x + 52)
Step-by-step explanation:
This is an application of the Pythagorean theorem
c = sqrt(a^2 + b^2)
a = 2x - 4
b = 5x + 6
c = sqrt( (2x - 4)^2 + (5x + 6)^2 ) Substitute and expand
c = sqrt( 4x^2 - 16x + 16 + 25x^2 + 60x + 36) Collect like terms
c = sqrt( 4x^2 + 25x^2 - 16x + 60x + 16+36) Combine the like term pairs.
c = sqrt( 29x^2 + 44x + 52)
This does not factor into anything very nice.
Answer:
Madeline is standing 2x - 4 feet from the base of a tree, and the height of the tree is 5x + 6
Now we want to know the distance from Madeline's feet to the top of the tree.
You could picture it as a triangle rectangle, where the cathetus is the distance between Madeline and the tree and the distance between the floor and the top of the tree, in this case the distance between Madeline's feet and the top of the tree is the hypotenuse of such triangle rectangle, and can be obtained using the Pythagorean theorem: "the square of the hypotenuse is equal to the sum of the square cathetus"
then:
[tex]H^2 = (2x - 4)^2 + (5x + 6)^2[/tex]
[tex]H^2 = (4x^2 -16x + 16) + (25x^2 + 60x +36)[/tex]
[tex]H^2 = (29x^2 + 44x + 52)[/tex]
[tex]H = \sqrt{ (29x^2 + 44x + 52)}[/tex]
this is the distance from Madeline's feet to the top of the tree in terms of x.
The system of equations y=2x-1 and y=-1/4x+3 is shown on the graph below. What is a reasonable estimate for the solution?
Answers
Answer:
Something close to (1.8,2.6)
Step-by-step explanation:
y=2x-1
y=-1/4 x+3
Since y=2x-1 and y=-1/4 x +3 then 2x-1=-1/4 x +3.
I'm going to multiply both sides by 4 to get rid of the fraction:
8x-4=-x+12
Add x on both sides:
9x-4=12
Add 4 on both sides:
9x=16
Divide both sides by 9:
x=16/9 is approximately 1.8 when put into calculator.
Now if x=16/9 and y=2x-1, then y=2(16/9)-1=32/9-1=32/9-9/9=(32-9)/9=23/9.
y=23/9 is approximately 2.6 when put into calculator.
So we are looking for an ordered pair pretty close to (1.8,2.6).
The graph is shown to you so I will put one here as well:
Answer:
A. 1 3/4, 2 1/2
Step-by-step explanation:
Write an equation: After withdrawing $7 from a checking account, Carla’s balance was $89
Answers
The equation for the situation where Carla withdraws $7 and is left with an $89 balance is: B - $7 = $89. So Carla's initial balance was $96.
When writing an equation based on the statement that after withdrawing $7 from a checking account, Carla’s balance was $89, we are essentially working out what Carla's balance was before she made the withdrawal.
If we let the variable B represent Carla's initial balance, then after she withdraws $7, her new balance is B - $7.
Since it's given that her balance after the withdrawal is $89, we can write the following equation to represent the situation:
B - $7 = $89
To find the value of B, we would add $7 to both sides of the equation, which would give us:
B = $89 + $7
B = $96
So, Carla's initial balance before the withdrawal was $96.
What is the scale factor of LMN to OPQ?
Answers
Answer:
The scale factor is 1 because it has not increased or decreased and therefore are congruent