Answer:
According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0. ... Also, we can say, if (x-a) is a factor of polynomial f(x), then f(a) = 0. This proves the converse of the theorem.
Write -93.74 as a mixed number.
A man is37years old and his child is eight.how many years ago was the product of their ages 96 as in quadratic equation step by step
Answer:
5 years
Step-by-step explanation:
Let x be the unknown numer of years ago when the product of the man and his child's age was 96.
》 x years ago, the man's age = 37 - x
the child's age = 8 - x
(37 - x)(8 - x) = 96
296 - 37x - 8x + x² = 96
x² - 45x - 296 - 96 = 0
x² - 45x - 200 = 0
x² - 5x - 40x - 200 = 0
x(x - 5) -40(x - 5) = 0
(x - 5)(x - 40) = 0
x = 5 years ago or x = 40 years ago
but x = 40 > son's present age.
Thus, x = 5.
Therefore, 5 years ago the product of the ages of the man and his child was 96.
please help me please.
Step-by-step explanation:
For every clockwise 90-degree rotation on a point (x, y), the resulted transformation will be (y, -x).
Now, counterclockwise 270 degree rotation is equivalent to clockwise 90 degree rotation. Then, for instance, point H=(2 ,-1) will be transformed into the image H'=( -1,2)
2(k + 1) = -4(k - 2)
Answer:
1
Step-by-step explanation:
2(k + 1) = -4(k - 2)
2k + 2 = --4k+8
2k+4k=8-2
6k=6
k=6/6
k=1
Write the equation of the line that passes through the points
(3,-2) and (6, 1).
y=x-5
y = 5x + 1
y = -x + 5
Answer:
It is y = x - 5
Step-by-step explanation:
General equation of a line:
[tex]{ \bf{y = mx + c}}[/tex]
m is the gradient, and c is y-intercept.
For gradient:
[tex]slope = \frac{y_{2} - y_{1} }{x _{2} - x_{1}} [/tex]
substitute:
[tex]slope = \frac{1 - ( - 2)}{6 - 3} \\ \\ = \frac{3}{3} \\ slope \: = 1[/tex]
m = 1
for y-intercept:
consider point (6, 1):
[tex]y = mx + c \\ 1 = (6 \times 1) + c \\ 1 = 6 + c \\ c = 1 - 6 = - 5[/tex]
therefore:
[tex]{ \sf{equation \: is \: \{y = x - 5 \}}}[/tex]
Find a16 of the sequence 1, 6, 11, 16, ....
A. 81
B. 66
C. 76
D. 71
Answer:
C. 76
Step-by-step explanation:
Since the numbers add up by 5, you can use this equation. 5x-4. Plug in 16 for x to get the answer which is 76.
X
6.
The table shows all the possible sums when rolling two number cubes numbered 1
What is the probability that rolling two cubes results in a sum of 8P
6
1
2
3
4
5
6
7
1
2
3
4
5
6
2 3 4 5
3 4 5 6
4 5 6 7
5 6 7 8
6 7 8 9
7 8 9 10
8 9. 10 11
7
8
9
10
11
12
Done
Answer:
Step-by-step explanation:
You can roll an 8 in the following ways
3 - 5
5 - 3
4 - 4
6 - 2
2 - 6
That's 5 ways that it can be done. There are a total of 36 ways to throw 2 dice.
The probability of getting an 8 is 5/36
Alicia has 8 more dollars than Fred. Altogether, Alicia and Fred have 26. dollars. Let "f" represent the amount of money, in dollars, that Fred has. Use "f" to write an expression that represents the amount of money that Fred has.
Use “f” to write an expression that represents the amount of money that Alicia has.
Write de equation to represent the problem situation
Solve your equitation showing each step of the solution
Based on your solution to your equation, state how much money Fred has
Based on your solution to your equation, state how much money Alicia has
Answer:
Fred has = 9 $
Alicia has = 9 + 8 =17 $
Step-by-step explanation:
Let, Fred has = f $
Then, Alicia has = f + 8 $ ;[as Alicia has 8 more dollars than fred]
Now, the required expression is
∴[tex]f+(f+8)=26\\=>2f+8=26\\=>2f=18\\f=9[/tex]
So, Fred has = 9 $
Alicia has = 9 + 8 =17 $
Hope you have understood this.....
ask me if you have any confusion.....
if you liked it pls mark it as the brainliest
if m<8= 23° find each measure.
straight angles ( 1 , 2 , 3 , 4 ) parallel to straight angles Angles ( 5 , 6 , 7 , 8 )
m<8 = m< 6 = 23° [ Opposite angles]
m< 4 = m< 2 = 23°
m<8 + m< 5 = 180°
23° + m< 5 = 180°
m<5 = 180 - 23 = 157
m< 5 = m< 7 = 157° [ Opposite angles]
m< 1 = m< 3 = 157° [ Opposite angles]
straight angles ( 1 , 2 , 3 , 4 ) parallel to straight angles Angles ( 5 , 6 , 7 , 8 )
So;m< 1 = 157m< 2 = 23m< 3 = 157m<4 = 23m< 5 = 157m< 6 = 23m< 7 = 157m< 8 = 23I hope I helped you^_^
Which multiple of 10 is closest to 18?
Answer:
I think it is 20
step by step explanation
Multiples of 10:-
10×1=1010×2=2010×3=3010×4=4018 is closest to 20
Hence our answer is 20
need help please cant understand this probplem
Answer:
No solution
Step-by-step explanation:
Distribute the right side of the equation.
This will make it 3/8f+1/2=3/8f - 18
And, since 3/8f plus 1/2 will never equal the same thing as 3/8f minus 18, there are no solutions
Answer and Step-by-step explanation:
First, distribute the 6 to the [tex]\frac{1}{16} f[/tex] and -3.
[tex]\frac{3}{8} f + \frac{1}{2} = \frac{6}{16} f - 18\\\\\frac{3}{8} f + \frac{1}{2} = \frac{3}{8} f - 18[/tex]
If you were to subtract [tex]\frac{3}{8} f[/tex] from both sides of the equation, you would be left with [tex]\frac{1}{2} = -18[/tex], which isn't correct.
This means that there are NO solutions to this equation, or no value of f that will make both sides of the equation equal to each other.
#teamtrees #PAW (Plant And Water)
I hope this helps!
5 +4.2 + 5 – 2. 2 - 1
Answer:
11
Step-by-step explanation:
You would add 5 + 4.2 + 5 - 2.2 - 1 in a calculator and it would come out to be 11.
Help me bro like this is difficult
what is the opposite of 7 plus the opposite of 9
Answer:
-7.11111111111
Step-by-step explanation:
1. Write each of these products as a quadratic
expression of the form x2+bx+c. That is, write
each product in standard form.
a. (x+3)(x + 5)
b. (x – 4)(x + 7)
C. (x-6)(x - 2)
Step-by-step explanation:
maybe I am wrong sorry for that but try to understand it
have a great day
María va de compras a una tienda departamental y adquiere los siguientes productos: 2 pantalones, 4 blusas, 3 pares de calcetas y 2 pares de tenis. El precio de los artículos por unidad es: pantalones $ 600.00, blusas: $350.00, calcetas: $120.00 y tenis: $ 950.00. Si María contaba con $5000.00, calcula cuánto dinero le sobró después de las compras realizadas.
Answer:
Pantalones = $600.00 × 2
$ 1,200.00
Blusas = $350.00 × 4
$ 1,400.00
Calcetas = $120.00 × 3
$ 360.00
Par de tenis = $950.00 × 2
$ 1,900.00
Total a pagar = $4,850.00
$5,000.00
- $4,860.00
Sobrante = $140.00
Which of the following is a point of tangency on the circle below?
Answer:
Answer D but read below.
Step-by-step explanation:
The point of tangency is the endpoint of either a radius or a diameter such that only one point of the circumference of the circle is concurrent with the endpoint of the diameter or radius of the circle.
Technically, it is none of them. E should be 180 degrees. That is really a sloppy question.
However I think you are expected to answer F which is answer D.
Answer:
The answer is D.
Step-by-step explanation:
I learned it in school.
BRAINIEST AWNSER 100 points PLEASE HELP
The number 1 is the identity for multiplication. Do you think
that division has an identity? Explain your reasoning.
Answer:
Yes, because if the multiplication identity is 1, the division identity may be -1 because it is the opposite.
Step-by-step explanation:
PLS HELP THIS IS WITH THE HELP OF SQAURES
Step-by-step explanation:
you heard of the Pythagoras formula for rectangular triangles ?
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90 degree angle), a and b are the other 2 sides touching the 90 degree angle.
so, in your case here we have therefore
x² = 8² + 6² = 64 + 36 = 100
x = sqrt(100) = 10
you know "sqrt" is an international abbreviation for square root : the opposite of squaring a number.
Which numbers in set A = ( -7,-4, 2, 14, 21,34, 42) are elements of b and c, shown below? Set b= ( even numbers) set c: ( multiples of 7) enter answers from largest to smallest.
Answer:
(14, 42)
Step-by-step explanation:
(-4, 2, 14, 34, 42) are all elements of b, and (-7. 14, 21, 42) are all elements of c. (14, 42) are the only elements that are in both sets
please help easy maths gradient thanks so much
Answer:
Y-2x=8
Y-x=8/2
Yx=4
Maths gradients
Answer:
b
Step-by-step explanation:
Can someone please solve this?
Answer: x = 3
Step-by-step explanation:
[tex]2x-7=\frac{1}{3}x-2\\\\6x-21=x-6\\\\5x-21=-6\\\\5x=15\\\\x=3[/tex]
A Cheetah running at 61 miles per hour is chasing an American Antelope that is running
at a rate of 1583 meters per minute.
Which animal is running at a faster rate?
Answer:
Cheetah
Step-by-step explanation:
American Antelope's speed = 94980 meters per hour
= 59 miles per hour
The Cheetah is faster than the American Antelope
HELPPP!!!!!!
How far is weather station A from the storm?
44.6 miles
19.7 miles
42.2 miles
31.2 miles
This value is approximate.
============================================================
Explanation:
Let's focus on the 48 degree angle. This angle combines with angle ABC to form a 90 degree angle. This means angle ABC is 90-48 = 42 degrees. Or in short we can say angle B = 42 when focusing on triangle ABC.
Now let's move to the 17 degree angle. Add on the 90 degree angle and we can see that angle CAB, aka angle A, is 17+90 = 107 degrees.
Based on those two interior angles, angle C must be...
A+B+C = 180
107+42+C = 180
149+C = 180
C = 180-149
C = 31
----------------
To sum things up so far, we have these known properties of triangle ABC
angle A = 107 degreesside c = side AB = 24 milesangle B = 42 degreesangle C = 31 degreesLet's use the law of sines to find side b, which is opposite angle B. This will find the length of side AC (which is the distance from the storm to station A).
b/sin(B) = c/sin(C)
b/sin(42) = 24/sin(31)
b = sin(42)*24/sin(31)
b = 31.1804803080182 which is approximate
b = 31.2 miles is the distance from the storm to station A
Make sure your calculator is in degree mode.
The weather station A is 31.2 miles from the storm
From the triangle shown:
m<B = 90° - 48°
m<B = 42°
m<A = 17° + 90°
m<A = 107°
m<A + m<B + m<C = 180° (Sum of angles in a triangle)
107° + 42° + m<C = 180°
m<C = 180° - 149°
m<C = 31°
The distance between the weather stations A and B = 24 miles
That is, AB = 24 miles
The storm is at point C
The length AC is found by using the rule of sines:
[tex]\frac{sinC}{AB}=\frac{sinB}{AC} \\\\\frac{sin31}{24}=\frac{sin42}{AC} \\\\\frac{0.515}{24} = \frac{0.669}{AC} \\\\0.02146=\frac{0.669}{AC}\\\\AC=\frac{0.669}{0.02146} \\\\AC=31.2 miles[/tex]
The weather station A is 31.2 miles from the storm
Learn more on sine rule here: https://brainly.com/question/4372174
Can someone pls help me with problems 4 and 5 pls this is due in a bit and I’m in a rush I’ll give 100 points it’s all I have
Answer:
Step-by-step explanation:
Answer:
#4Let M is the midpoint of DE.
Since D is at 8 and DE = 5.
DM = ME = 5/2 = 2.5
Point M is at:
8 + 2.5 = 10.5 if E is to the right of D8 - 2.5 = 5.5 if E is to the left of D#5Given
XY = 7, YZ = 2x - 1, XZ = 30Since XZ = XY + YZ, set up an equation and solve for x:
7 + (2x - 1) = 302x + 6 = 302x = 24x = 12#6The distance from your house to friend's is LN.
We have:
M is midpoint of LN, so LM = MNLM = 3xMN = 2x + 2Set up an equation, solve for x:
3x = 2x + 23x - 2x = 2x = 2Find the distance LM:
LM = 3*2 = 6Find the distance LN:
LN = 2*LM = 2*6 = 12What is the equation of the line graphed below?
5
(2, 1)
O A. y=-2x
B. y -
C. y = 2x
o D. y = 1/2 x
Answer:
C. Y=2x
Step-by-step explanation:
I hope this help you
How would I prove the congruency of these triangles?
Step-by-step explanation:
the radius cuts the segment into two equal parts because it is perpendicular to the chord
Answer:
Step-by-step explanation:
As O is the mid point of the circle
Similarly, B also becomes the mid point of the line AC.
So, line OB divides AB and BC equally.
Hence, lines AB = AC, but they are asking to prove congruency of triangles.
So, u have to join OA and OC.
Same way, line OB divides ∠OBA and ∠OBC.
So it is proved that AB = AC
What is the reference angle for 283°?
7. Is 5.787787778... a rational or irrational number?
Explain.
Answer:
Irrational
Step-by-step explanation:
Its irrational as it has no pattern of numbers after decimal point and the number are infinite
Answer:
irrational because it has a coma after one number
Two rectangles are similar. The smaller has a length of 8 cm and an area of 40 cm.
If the width of the larger rectangle is 10 cm, find its area.
Answer:
160 cm²
Step-by-step explanation:
If the two rectangles are similar, that means they have equal scale factors. The smaller rectangle has length of 8 cm and area of 40 cm, which means the width is 5 cm.
The width of the larger rectangle is 10 cm, which is double the width of the smaller, similar rectangle. So, to find the length of the larger rectangle, multiply 8 x 2, which gives you 16 cm for the length, since the scale factor is 2.
Now, just find the area of the larger rectangle by doing length x width. 16cm x 10 cm = 160 cm²
Answer:
160 cm^2
Step-by-step explanation:
Our strategy is to find the length of the larger rectangle so we can find the area. To find the length, we will rely on the fact the two rectangles are "similar": their sides are in equal proportions, or have the same "ratio."
We know that the smaller rectangle has a width of 5 cm because, when we substitute area and length into
A = lw
we get
40 = 8w
w = 5
when we divide both sides by 8.
Because of equal proportions:
Width : length of the smaller rectangle = Width : length of the larger rectangle
We can write an equation
5 / 8 = 10 / x
Cross multiply
5x = 80
x = 16
So the larger rectangle has a length of 16 cm and a width of 10 cm (given)
meaning the area is
16 * 10 = 160 cm^2
