Answer:
[tex] \rm Numbers = 4 \ and \ -3.[/tex]
Step-by-step explanation:
Given :-
The sum of two numbers is 1 .
The product of the nos . is 12 .
And we need to find out the numbers. So let us take ,
First number be x
Second number be 1-x .
According to first condition :-
[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]
Hence the numbers are 4 and -3
Answer:
Step-by-step explanation:
If the product of 2 integers is -12, then that equation looks like this:
xy = -12
If the sum of those same 2 integers in 1, then that equation looks like this:
x + y = 1
Let's solve the second equation for x and plug it into the first equation. Solving the second equation for x gives us
x = 1 - y and plug that into the first equation in place of x to get:
(1 - y)y = -12 and
[tex]y-y^2=-12[/tex] Now move everything over to one side and factor to find y:
[tex]-y^2+y+12=0[/tex] and the 2 values for y are
y = -3 and y = 4. Let's see what happens when we solve for x.
If xy = -12 and y is -3:
x(-3) = -12 so
x = 4
If xy = -12 and y is4:
x(4) = -12 so
x = -3
So it looks like the 2 integers are -3 and 4
Helppppp pls and thankyouuu
Answer:
20 minutes on the stationary bike
10 minutes on the treadmill
Step-by-step explanation:
x = minutes on bike
y = minutes on treadmill
x + y = 30
12x + 15y = 390
x = 30-y
12(30-y) + 15y = 390
360 - 12y + 15y = 390
3y = 30
y = 10
x + 10 = 30
x = 20
Type the correct answer in the box.
The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below.
V = 3721
Write the formula to calculate the height, h.
Answer:
V=1/3(pi)*r^2*h
Step-by-step explanation:
Think about a cylinder. If you combine 3 cones, you get a cylinder. Find the volume of a cylinder
Answer:
Step-by-step explanation:
V = 1/3 r^2 * π * h
3V = r^2 *π * h
3V/π = r^2 * h
h = 3V/(r^2 * π)
Find the measure of the indicated angle
Answer:
x=44°..
Step-by-step explanation:
base angle of isosceles triangle are equal68+68+x=180°{sum of angle of triangle}136°+x=180°x=180-136°x=44°hope it helpsstay safe healthy and happy. ..Answer:
the value of x is 44 i hope it will help you
HELP PLEASE I NEED COOR!!!!!
y−5=43(x−5)
Answer:
y=43x-210
Step-by-step explanation:
Distribute 43
then add five on each side
you get y=43x-210, 43 and 210 cannot be sipilified so that is the answer.
Answer:
y=43x-210
Step-by-step explanation:
Distribute 43 through the parenthesis.
y-5=43x-215
Move the constant to the right and change its sign.
y=43x-215+5
Calculate sum.
y=43x-210
Hope i helped :)
what is the length of segment DC? no links.
Answer:
33 units
Step-by-step explanation:
AB = BC
2x + 7 = 23
2x = 16
x = 8
DC = DA
DC = 4x + 1
DC = 4(8) + 1
DC = 33
try it, let's see can u do or not
Answer:
Step-by-step explanation:
From the given trapezium, the following can be observed:
i. trapezium ABCD
ii. AB || DC
iii. EF || AB
iv. EF || DC
Let AD ≅ BC, then:
AD = AE + ED
BC = BF + FC
So that with the condition that;
AE ≅ BF
and
ED ≅ CF
So then;
AE:ED ≅ BF:FC
Which implies that;
[tex]\frac{AE}{ED}[/tex] = [tex]\frac{BF}{FC}[/tex]
Which expressions are equivalent to 6 - 4.5+ (-8) ?
A 6 + 4.5 + 8
B 6 + 4.5 - 8
C 6 – 4.5'+8
D 6 - 4.5 - 8
E 6+(-4.5) - 8
F 6+(-4.5) + (-8).
G 6+ (-4.5) - (-8)
Answer:
I'm pretty sure the answers are options D , E and F .
Step-by-step explanation:
So here's how I did it , I got the original expression , solved it and the answer I found is -6.5. So then I solved all the others and D , E and F gave me -6.5.
Hope this helps lol
Can someone help me with this math homework please!
Answer:
the first row in the table has x = -2 and f(x) = 1
therefore,
f(-2) = 1
f(x) = -2
when x = 4 as in 3rd row.
Please help me I need this doing for my maths hwk and I really don’t know
Complete the transformations below. Then enter the final coordinates of the figure.
A" (,)
B" (,)
C" (,)
HELP! PLZ.
Answer:
Step-by-step explanation:
If a point (x, y) is translated by 4 units horizontally right and 1 unit upwards, coordinates of the image point will be,
(x, y) → (x + 4. y + 1)
Therefore, vertices of the image triangle ABC will be,
A(2, 2) → A'(2+4, 2+1)
→ A'(6, 3)
B(5, -1) → B'(5+4, -1+1)
→ B'(9, 0)
C(1, -2) → C'(1+4, -2+1)
→ C'(5, -1)
Then reflected across y-axis.
Rule for the reflection across y-axis will be,
(x, y) → (-x, y)
A'(6, 3) → A"(-6, 3)
B'(9, 0) → B"(-9, 0)
C'(5, -1) → C"(-5, -1)
Answer:
A"(-6, 3)
B"(-9, 0)
C"(-5, -1)
Step-by-step explanation:
Graph the image of T(
–
10,
–
7) after a rotation 270° counterclockwise around the origin.
Answer:
[tex]T' = (-7,10)[/tex]
Step-by-step explanation:
Given
[tex]T = (10,7)[/tex]
[tex]r = 270^o[/tex] counterclockwise
Required
Graph of T'
The rule to this is:
[tex](x,y) \to (-y,x)[/tex]
So, we have:
[tex]T(10,7) \to T' (-7,10)[/tex]
Hence:
[tex]T' = (-7,10)[/tex]
See attachment for graph
Describe the graph of the line y = 15
A) line with slope of 15
B) crosses the x-axis
C) vertical line
D) horizontal line
A rectangular living room has a perimeter of 30 meters. Its area is 50 square meters. What are the dimensions of the living room?
Answer:
The one of (L,b)= (5m, 10m) is the only correct answer.
Step-by-step explanation:
P= 2(L+b)
A= L×b
make b subject of formula in area we have;
b= A/L
in perimeter; p= 2(L +(A/L))
p= (L²+A)/L
pL= L²+A
L²-pL+A= 0
L²-30L+50=0
L²-25L-5L+50=0
L(L-25)-5(L-25)=0
(L-5)(L-25)= 0
L= 5 or 25m
substitute in A
50= 5b or 50= 25b
b= 10 or 2m
Helppppppp and explain pls and thankyouuu
Answer:
so the correct asnwer is c
Answer:
Step-by-step explanation:
y4+5y2+9 factorise please help me
[tex]\displaystyle\ y^4 +5y^2+9=(y^2+3)^2-y^2=(y^2-y+3)(y^2+y+3)[/tex]
Answer:
Solution given;
[tex] y^{4}+5y²+9[/tex]
keeping [tex]y^{4} and 9 together [/tex]
[tex]y^{4}+9+5y²[/tex]
[tex](y²)²+3²+5y²[/tex].....[I]
we have
a²+b²=(a+b)²-2ab
or
a²+b²=(a-b)²+2ab
same like that
[tex](y²)²+3²=(y²+3)²-6y² or (y²-3)²+6y²[/tex]
remember that while adding or subtracting the left term 5y² either adding 6y²or subtracting 6y²
should make the term perfect square
while subtracting it makes perfect square
so
we take
(y²)²+3²=(y²+3)²-6y²
again
substituting value of
(y²)²+3² in equation 1 and it becomes
(y²+3)²-6y²+5y²
solve like terms
(y²+3)²-y²
again
we have
a²-b²=(a+b)(a-b)
by using this.
(y²+3+y)(y²+3-y)
rearrange it
(y²+y+3)(y²-y+3) is a required factorisation form.
Help me with the diagram please!!!
Answer:
(B) 30
Step-by-step explanation:
Imagine you drew a line from Point T until it touched Line PR. Let's call that point where it touched Line PR "Point Z".
That line (called Line TZ) would be perpendicular to PR, forming a 90 degree angle.
Now, TZW is a triangle.
To find x, we need to find the angle measurment of Angle ZTW.
This is where we use the hexagon.
A hexagon's interior angle sum is 720, meaning each interior angle is equal to 120 degrees. So Angle UTS would equal 120 degrees.
However, Line TZ bisects that 120 degree angle, so Angle ZTW would equal 60 degrees (because 120/2 = 60).
Now we have two angles of the triangle: 90 & 60.
A triangle's interior angle sum is 180.
Add 90 & 60, which is 150, and subtract 150 from 180.
The result is 30, which is the angle measurement of x.
Hope it helps (●'◡'●)
(08.07A LC)
The two-way table below shows the number of students in a school who like mathematics and/or physics:
Do Not Like Mathematics
Total
Like Mathematics
Like Physics
15
20
35
Do Not Like
Physics
30
Total
20
45
65
How many more students like physics than mathematics?
O 10
PES
O 15
an
HEHEHE
O 20
REBBBBBBBBBBBBBBB
O 25
Answer:
25
Step-by-step explanation:
you would do the total which is 45-20
Help me solve this please
Answer:
a
Step-by-step explanation:
thats not how u find the lengths
Solve the inequality. w/-2<8
Answer:
w > -16
Step-by-step explanation:
I NEED HELP SOMEONE PLEASE HELP MEEEE!!!
9.75 ft is the answer
[tex]By \: Pythagoras \: Theorem, \\ \boxed{ {hyotenuse}^{2} = {base}^{2} + {height}^{2} } \\ \\ here \\ hypotenuse = 12ft \\ base = 7 ft\\ height = x\ \\ \\ \ {12}^{2} = {7}^{2} + {x}^{2} \\ \implies144 = 49 + {x}^{2} \\ \implies {x}^{2} = 144 - 49 \\ =95 \\ x = \sqrt{95 } \\ = 9.75 ft\\ \\ \\ [/tex]
23 x 32 is the prime factorization for which one of these choices?
⟶ 2³ × 3² is the prime factorization for which one of these choices?
Let's check,
1) 6 = 3 × 2 [So, obviously not this choice]
2) 25 = 5 × 5 = 5² [Not this either]
3) 36 = 3 × 2 × 2 × 3 = 3² × 2² [Doesn't match with 2³ × 3²]
4) 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3² [Matches]
⟶ The answer is, choice 72.
[tex]\underbrace{ \overbrace{ \mathfrak{Carry \: On \: Learning}}}[/tex]
please help i have class soon :(
John used digits from 0 to 6 only to create a three-digit PIN code. He forgot his PIN code. He remembers that his code contains different ascending digits. What is the maximum number of combinations John has to check to find his PIN code?
this was incorrect.
im sorry :(
Answer:
35
Step-by-step explanation:
We know that the numbers have to be in ascending order. If, for example, the first digit is 0, and second digit is 1, then we would have 5 other numbers in the ones place that would be larger. If the second digit is 2, then would would have 4 other numbers that would be larger, and so on. So if 0 is the first digit, then we would have 5+4+3+2+1=15 combinations. If 1 is the first digit, then we would have 4+3+2+1 combinations. Eventually, we would get 35.
Find the Value of x a.86 b.79 c.65 .72
Answer: D
Step-by-step explanation:
360° - 90° - 90° - 108° = 72°
(Sum of angles in a quadrilateral = 360°)
A carpet manufacturer is inspecting for flaws in the finished product. If there are too many blemishes, the carpet will have to be destroyed. He finds the number of flaws in each square yard and is interested in the average number of flaws per 10 square yards of material. If we assume the standard deviation of the number of flaws per square yard is 0.6, the sample mean, , for the 10 square yards will a standard deviation of
Answer:
10 square meters will have a standard deviation of 1.897.
Step-by-step explanation:
Standard deviation for n instances of a variable:
If the standard deviation for one instance of a variable is [tex]\sigma[/tex], for n instances of the variable, the standard deviation will be of [tex]s = \sigma\sqrt{n}[/tex]
The standard deviation of the number of flaws per square yard is 0.6
This means that [tex]\sigma = 0.6[/tex]
For the 10 square yards will a standard deviation of
[tex]n = 10[/tex], so:
[tex]s = \sigma\sqrt{n} = 0.6\sqrt{10} = 1.897[/tex]
10 square meters will have a standard deviation of 1.897.
Find the x of a triangle.
This triangle is an isosceles triangle because it has two congruent sides. Therefore, the two bottom angles are also congruent. And, the sum of the interior angles of a triangle is 180 degrees.
180 = 104 + (9x - 25) + (9x - 25)
180 = 104 + 18x - 50
180 = 54 + 18x
126 = 18x
x = 7
Hope this helps!
A trader bought some oranges at 5c each She finds that 6 of them are rotten. She sells the rest at 8c each and makes a profit of $4,50. How many oranges did she buy? (Hint: let the number of oranges be x. Work in cents.)
can someone please help me
Express the form 3:15 as n:1 make n a decimal
Answer:
0.2 = n
Step-by-step explanation:
Since we want to express 3:15 as n:1, we can say that they are equal ratios, so
3:15 = n:1. Next, ratios can be written as fractions, so 3/15 = n/1 .
3/15 = n/1
Since anything divided by 1 equals itself, we can write this as
3/15 = n
0.2 = n
Printed Pages in Color Time (min), x 2 6 8 18 Number of pages, y 3 9 12 27 What is the constant of variation?
Answer:
3/2
Step-by-step explanation:
formula k = y/x
comes from
y = kx
k = constant of variation
when y = 3 , x = 2
k = 3/2
Express the trigonometric ratios sinA in term of cosA
Answer:
sinA = ± [tex]\sqrt{1-cos^2A}[/tex]
Step-by-step explanation:
Using the Pythagorean identity
sin²A + cos²A = 1 ( subtract cos²A from both sides )
sin²A = 1 - cos²A ( take the square root of both sides )
sinA = ± [tex]\sqrt{1-cos^2A}[/tex]
m.c.m (35;50)
m.c.d (35;50)
m.c.m (116;92)
m.c.d (116;92)
Ayudaaa
9514 1404 393
Answer:
350, 5, 2668, 4
Step-by-step explanation:
a) mcm(35, 50) = 35·50/mcd(35, 50) = 35·50/5 = 350
__
b) mcd(35, 50) = 5
35 = 5·7; 50 = 5·10
__
c) mcm(116, 92) = 116·92/mcd(116, 92) = 116·92/4 = 2668
__
d) mcd(116, 92) = 4
116 = 4·29, 92 = 4·23
