Answer:
Step-by-step explanation:
The vertices (-2, -3) and (-2, 4) are on the same vertical line and are separated by 4 - (-3), or 7, units. The vertices (-2, 4) and (5, 4) are on the same horizontal line (y = 4) and separated horizontally by 5 - (-2), or 7, units. If you can picture this in your mind, you'll see a 45-45-90 isosceles triangle with leg lengths 7 (there are two such legs).
The next thing to do is to calculate the length of the hypotenuse of this triangle. Using the Pythagorean Theorem, we get:
d = √(7² + 7²) = 7√2 ft.
The perimeter of this triangle is thus 7 ft by 7 ft by 7√2 ft, or approximately 23.9 feet, or 7.97 yd
and ...
The area of the triangular shape is A = (1/2)(base)(height), which here is
A = (1/2)(7)(7) = 49/2 ft^2, or 16.4 yd^2
Are AB→ and Ray −BA→ the same ray? Explain. both have an arrow pointing right over them}
Answer:
No
Step-by-step explanation:
No, they are not because ray AB starts at point A and continues forever while ray BA does the opposite, it starts at point B and continues forever.
AEFG is located at E (0,0), F (-7, 4), and G (0,8). Which statement correctly classifies AEFG?
AEFG is a scalene triangle.
AEFG is an isosceles triangle.
AEFG is an equilateral triangle.
AEFG is a right triangle.
Answer:
ΔEFG is an isosceles triangle
Step-by-step explanation:
x^2+4x+y^2-10y+20=30 find the center of the circle by completing the square
Answer:
a). Center of the circle = (-2, 5)
b). Equation of the line ⇒ y = [tex]-\frac{4}{5}x+\frac{58}{5}[/tex]
Step-by-step explanation:
Equation of the circle is,
x² + 4x + y²- 10y + 20 = 30
a). [x² + 2(2)x + 4 - 4] + [y²- 2(5)y + 25] - 25 + 20 = 30
[x² + 2(2)x + 4] - 4 + [y² - 2(5)y + 25] - 25 + 20 = 30
(x + 2)² + (y - 5)²- 29 + 20 = 30
(x + 2)² + (y - 5)²- 9 = 30
(x + 2)² + (y - 5)² = 39
By comparing this equation with the standard equation of a circle,
Center of the circle is (-2, 5).
b). A point (2, 10) lies on this circle.
Slope of the line joining this point to the center (-2, 5),
[tex]m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
= [tex]\frac{10-5}{2+2}[/tex]
= [tex]\frac{5}{4}[/tex]
Let the slope of the tangent which is perpendicular to this line is '[tex]m_{2}[/tex]'
Then by the property of perpendicular lines,
[tex]m_{1}\times m_{2}=-1[/tex]
[tex]\frac{5}{4}\times m_{2}=-1[/tex]
[tex]m_{2}=-\frac{4}{5}[/tex]
Now the equation of the line passing though (2, 10) having slope [tex]m_{2}=-\frac{4}{5}[/tex]
y - y' = [tex]m_{2}(x-x')[/tex]
y - 10 = [tex]-\frac{4}{5}(x-2)[/tex]
y - 10 = [tex]-\frac{4}{5}x+\frac{8}{5}[/tex]
y = [tex]-\frac{4}{5}x+\frac{8}{5}+10[/tex]
y = [tex]-\frac{4}{5}x+\frac{58}{5}[/tex]
Therefore, equation of the line will be, y = [tex]-\frac{4}{5}x+\frac{58}{5}[/tex]
Please answer correctly !!!!!! Will mark brainliest answer !!!!!!!!
Answer:
-6 =x
Step-by-step explanation:
g(x) = -3x -8
g(x) = 10
10 = -3x-8
Add 8 to each side
10+8 = -3x-8+8
18 = -3x
Divide by -3
18/-3 = -3x/-3
-6 =x
which expression is equivalent to 4(5x+3y)?
Just number 4
Answer:
Answer choice 4
Step-by-step explanation:
4(5x+3y)
By distributive property, this can be rewritten as:
4(5x)+4(3y)=
20x+12y
or answer choice 4. Hope this helps!
Answer:
4) 20x+12y
Step-by-step explanation:
You have to use distivtive property
I hope this helps
Alberto sanded a wooden floor with his electric sander at a constant rate. Suppose
1
3
he sanded 40 square feet of floor in hours. How large an area would he have
5
sanded in 1 hour?
The list shows numbers in order from least to greatest. Negative 34, negative 2 and three-fourths, blank, negative 1.5, 0, 2.3, 10, 25 and one-fifth Which is an integer that can be inserted on the blank line in the list?
Options
-2.5-2[tex]-1\dfrac{9}{10}[/tex]-1Answer:
(B) -2
Step-by-step explanation:
Given the list
[tex]-34.-2\dfrac{3}{4} ,x, -1.5,0,2.3,10,25\dfrac15[/tex]
This list has been arranged in order from the least to the greatest.
We are required to find an Integer that can be inserted on the blank line (I have used x) in the list.
An integer is defined as a positive or negative whole number.
Out of the given options, only -1 and -2 are integers. However:
-1 is greater than -1.5Therefore, it cannot be our result.
The correct answer is -2.
Answer:
-2 i did i what he said then revewied my quiz and it was right
Step-by-step explanation:
Solve 3 (3 - 3x) +4= -5.
Answer:
x=2
Step-by-step explanation:
3 (3 - 3x) +4= -5
Subtract 4 from each side
3 (3 - 3x) +4-4= -5-4
3 (3 - 3x)= -9
Divide by 3
3/3 (3 - 3x) = -9/3
3-3x = -3
Subtract 3 from each side
3-3x-3 = -3-3
-3x = -6
Divide by -3
-3x/-3 = -6/-3
x = 2
What is the equivalent trig ratio to sin 25?
Answer:
The answer is "[tex]\bold{\cos 65}[/tex]"
Step-by-step explanation:
Given:
[tex]\Rightarrow \bold{\sin 25}\\[/tex]
[tex]\Rightarrow \sin 25[/tex] can be written as [tex]\frac{\sin 25}{1}[/tex]
[tex]\therefore \tan \theta = \frac{\sin \theta }{cos \theta}[/tex]
[tex]\Rightarrow \sin 25[/tex] can be written as [tex]\cos (90-65)[/tex]
The answer is "[tex]\bold{\cos 65}[/tex]".
This is the formula for the
area of a triangle. Solve the
equation for height, A
Answer: 2A/base = Height
Step-by-step explanation:
[tex]A=\frac{base*height}{2} \\2A=base*height\\\frac{2A}{base} =height[/tex]
Mr. Malone is contemplating which chauffeured car service to take to the airport. The first costs $28 upfront and $2 per mile. The second costs $13 plus $5 per mile. For a certain driving distance, the two companies charge the same total fare. What is the distance?
Answer:
The distance is 8 miles.
Step-by-step explanation:
First, we need to write an equation for each of chauffeured car services.
The first one = 28 + 2x = ?
The second one = 13 + 5x = ?
Next, we need to figure out what x is. Usually I just plug in random numbers, but I'm sure there's a better way to do it.
I first plugged in 2 as x.
28 + 4 = 32
13 + 10 = 23
That didn't work, so I then plugged in 5.
28 + 10 = 38
13 + 25 = 38
So 5 would be the correct answer for what is the distance.
A man drove 14 mi directly east from his home, made a left turn at an intersection, and then traveled 3 mi north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?
This would make a right triangle. Use the Pythagorean theorem to solve.
X = sqrt(14^2+ 3^2)
X = sqrt( 196 + 9)
X = sqrt(205)
X = 14.3178
Rounded = 14.3 miles
A brick weighs w kg. Write an expression for the weight of 12 bricks.
What are the sums? Complete the equations.
-10 + 50
Answer:
40
Step-by-step explanation:
-10+50
40
Jade buys a blouse and a skirt for 3/4 of their original price. Jade pays a total of $31.50 for the two items. If the original price of the blouse is $18, what is the original price of the skirt?
Answer:
The skirt was originally 24 dollars
Step-by-step explanation:
3/4 ( b+s) = 31.50
where b is the original price of the blouse and s is the original price of the skirt
b = 18
3/4 ( 18+s) = 31.50
Multiply each side by 4/3
4/3 * 3/4 ( 18+s) = 31.50 *4/3
18+s =42
Subtract 18 from each side
18+s-18 = 42-18
s =24
The skirt was originally 24 dollars
a = 6 and b = 24 work out the values a) a+b b) ab c) b/a d) d) (a+b)^2
Answer:
a) 30
b) 144
c) 4
d) 900
Step-by-step explanation:
a) 6 + 24 = 30
b) 6 * 24 = 144
c) 24 ÷ 6 = 4
d) [tex]30^2=900[/tex]
Answer:
a) 30
b) 144
c) 4
d) 900
Step-by-step explanation:
a) 24+6
b) 6(24)
c) 24/6
d) (24+6)^2
Hosiste product of 2 and 5 shown on anumber ine?
[tex]the \: right \: answer \: is \: of \: option \: d \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
A rectangle has an area of 590.4m2
One of the sides is 8.2m in length.
Work out the perimeter of the rectangle.
Answer:
hope this helps you
Simplify: x(x-2)-3x(2x-1)
Answer:
-5x^2 +x
Step-by-step explanation:
x(x-2)-3x(2x-1)
Distribute
x^2 -2x -6x^2 +3x
Combine like terms
-5x^2 +x
Answer:
x^2-2x-6x^2+3x
x^2+x-6x^2
-5x^2+x
A trail mix contains peanuts raisins and m&ms in the mix the amount of peanuts is three times the amount of m&ms;and the amount of raisins is two times the amount of m&ms.let m represent the amount of m&ms.write and simplify an expression for the total number of pieces of food in the trail mix
Answer:
6m
Step-by-step explanation:
m =number of M&M's
3m=number of peanuts
2m=number of raisins
m+3m+2m=total number of pieces of food=6m
3/16 Write as a decimal and as a percent
Answer:
0.1875 as a decimal and 18.75% as a percent
Step-by-step explanation:
0.1875 is the decimal. Move point over 2 spots right to get percent.
O is the centre of the circle and ABC and EDC are tangents to the circle. Find the size of angle BCD. You must give reasons in your answers.
Answer:
mBCD = 28°
Step-by-step explanation:
The angle mBFD inscribes the arc mBD, so we have that:
mBFD = mBD/2
76 = mBD/2
mBD = 152°
The angle mBOD is a central angle related to the arc mBD, so we have that:
mBOD = mBD = 152°
In the quadrilateral BODC, the sum of internal angles needs to be equal to 360° (property of all convex quadrilaterals). The angles mCBO and mCDO are right angles, because EDC and ABC are tangents to the circle.
So, we have that:
mBOD + mCDO + mBCD + mCBO = 360
152 + 90 + mBCD + 90 = 360
mBCD = 360 - 90 - 90 - 152
mBCD = 28°
What is the quotient when (x + 2) is divided into the polynomial 2x2 - 2x - 12?
Answer:
2(x-3)
Step-by-step explanation:
2x² - 2x - 12= 2(x²-x+6)= 2(x²+2x- 3x+6)= 2(x-3)(x+2)
(2x² - 2x - 12)/(x+2)= 2(x-3)(x+2)/(x+2)= 2(x-3)Factorize the following expression ab-a-b+1
Group 'em together
a b − a + 1 − b
a b − a = a ( b − 1 )
Notice that there will be a 1 as without it it'll simply be ab
1 − b = 1 ( 1 − b )
Notice that it doesn't match with the upper one... so we'll change the signs
1 ( 1 − b ) = − 1 ( b− 1 )
(try to multiply them now!!
Jot them down in one expression
a ( b − 1 ) − 1 ( b − 1 )
You get!!!!!!
( a − 1 ) ( b − 1 )
Toilet rolls come in packs of 4 and 9
The 4 pack is priced at £2.04
The 9 pack is priced at £4.68
By calculating the price per toilet roll, determine which pack is better value . Show your working
Answer:
4 pack priced at £2.04 is better value deal.
Step-by-step explanation:
The 4 pack is priced at £2.04
cost of one pack will be equal total price divided by no. of roll in one pack
cost of one pack will be £2.04 /4 = £0.51
The 9 pack is priced at £4.68
cost of one pack will be £4.68 /9 = £0.52
As price per toilet roll for 4 pack is £0.51 which is less than
price per toilet roll for 9 pack which is £0.52
4 pack priced at £2.04 is better value deal.
Answer:
4 pack priced at £2.04 is better value deal.
Step-by-step explanation:
Divide 8848 by 16(Show working)
Answer:
553
Step-by-step explanation:
5 5 3
---------------------
16 / 8 8 4 8
8 0
---------------
8 4
8 0
----------------
4 8
4 8
-----------
0
The quotient is 553.
4 8
----------
0
the nth term of a sequence is 3n2/2
Question:
The nth term of a sequence is [tex]\frac{3n^2}{2}[/tex] . Find the fifth term of the sequence
Answer:
The 5th term of the sequence is 37.5
Step-by-step explanation:
Given
[tex]nth\ term = \frac{3n^2}{2}[/tex]
Required
Find the 5th term
To find the 5th term, we simply substitute 5 for n in the above expression.
This gives
[tex]5th\ term = \frac{3 * 5^2}{2}[/tex]
[tex]5th\ term = \frac{3 * 5 * 5}{2}[/tex]
[tex]5th\ term = \frac{75}{2}[/tex]
[tex]5th\ term = 37.5[/tex]
Hence, the 5th term of the sequence is 37.5
solve v=1/3 bh for b
Answer:
3v/h = b
Step-by-step explanation:
1/3 is a given fraction and to get rid of it you must multiply by it's reciprocal of 3/1 or 3. You will also multiply the other side by 3
3 * v = (1/3 bh) * 3 --> 3v = bh
divde both sides by h and you get 3v over h = b
3v/h = b
Hope this helps!
Answer:
3v/h = b
Step-by-step explanation:
v = 1/3bh
3v = bh
3v/h = b
Charlie invests £1200 at 3.5% per annum compound interest.
Work out the value of Charlie's investment after 3 years.
Answer:
£1,330.46Step-by-step explanation:
Using the compound interest formula [tex]A = P(1+\frac{r}{n} )^{nt}[/tex]
A = amount compounded after n years
P = principal (amount invested)
r = rate (in %)
t = time (in years)
n = time used to compound the money
Given P = £1200., r = 3.5%, t = 3years, n = 1 year(compounded annually)
[tex]A = 1200(1+0.035)^{3}\\ A = 1200(1.035)^{3}\\ A = 1200* 1.108717875\\A = 1,330.46[/tex]
Value of Charlie's investment after 3 years is £1,330.46
The perimeter of a room is 43 ft. The width is 9 1 2ft. What is the length?
Answer: The length is 12 ft.
Step-by-step explanation:
So a room is likely to be in a shape of a rectangle. And to to find the perimeter of a rectangle will use the formula P = 2w + 2l so in this case we know the perimeter and and the width but we need to find the length.
so using the formula we could do this
43 = 2(9.5) + 2l
43 = 19 + 2l subtract 19 from both sides
-19 -19
24 = 2l Divide both sides by 2
l = 12
The length is 12.
Check: 43 = 2(9.5) + 2(12)
43 = 19 + 24
43 = 43 correct so the length is 12.
