Answer:
Step-by-step explanation:
(x-4) (x+10) ⇒ (x+a)(x+b)=x²+(a+b)x+ab
a=-4 , b=10
x²+(-4+10)x+-4(10)
x²+6x-40
(3x+4) (3x +5)
3(x+4/3) *3(x+5/3) ⇒ identity : (x+a)(x+b)=x²+(a+b)x+ab
a=4/3 b=5/3
3*3=9
9[x²+(4/3 +5/3)x+4/3(5/3)]
9[x²+9/3 x+20/9]
9x²+27x+20
(-3a +5b +4c)^2 ⇒
suitable identity is (a+b+c)²= a² + b² + c² + 2ab + 2bc + 2ca
a=-3a , b=5b , c=4c
9a²+25b²+16c²- 30ab +40bc - 24ca
If 3sinA+4cosA=5 then find the value of cosA
Answer:
cos(A) = 4/5
Step-by-step explanation:
3sinA+4cosA=5
Divide by 5 on both sides
(3/5)sinA+(4/5)cosA = 1 .................(1)
from which sin(A) = 3/5, cos(A) = 4/5 by inspection, since
(3/5)^2+(4/5)^2 = 1
For more details,
Let
cos(B) = (3/5), then
sin(B) = (4/5)
Substitute in (1)
cos(B)sin(A) + sin(B)cos(A) = 1 substitute trigonometric sum
sin(A+B) = 1 => A & B are complementary
cos(A) = sin(B) = 4/5
find the exterior angle of a triangle whose interior opposite angles are 43 degree and 27 degree
Answer:
[tex]\huge\boxed{Exterior\ angle = 70\°}[/tex]
Step-by-step explanation:
The measure of exterior angle is equal to the sum of opposite interior angles.
So,
Exterior angle = 43+27
Exterior angle = 70°
Given: Quadrilateral DEFG is inscribed in circle P. Prove: m∠G+m∠E=180∘
Answer:
The answer is below
Step-by-step explanation:
Let lines be drawn from D to F (line DF) and from F to G (line FG) as shown in the diagram attached.
∠FDE = ∠FGE (angles in the same segment).
Also, ∠EFD = ∠EGD (angles in the same segment)
∠FDE + ∠EFD = ∠FGE + ∠EGD = ∠FGD
Adding ∠FED on both sides gives:
∠FDE + ∠EFD + ∠FED = ∠FGD + ∠FED
But ∠FDE + ∠EFD + ∠FED = 180° (sum of angles in a triangle)
Therefore ∠FGD + ∠FED = 180°
m∠G + m∠E = 180° (sum of opposite angles in a cyclic quadrilateral is 180°)
If the geometric mean of a and 120 is 60, find the value of a.
Answer:
The answer is option 4.
Step-by-step explanation:
Given that the mean formula is total score/number of score. So we can assume that total score is (a+120), number of score is 2 and the mean value is 60. Then you have to find the value of a :
[tex] \frac{a + 120}{2} = 60[/tex]
[tex]a + 120 = 60 \times 2[/tex]
[tex]a + 120 = 120[/tex]
[tex]a = 120 - 120[/tex]
[tex]a = 0[/tex]
[tex] \text{ Geometric mean of two numbers } a \text{ and } b , \text{ where } a,b>0 \text{ is given by } G= \sqrt{ab}[/tex]
[tex] \sqrt{a\cdot120}=60 [/tex]
[tex] \implies 60 \cdot 2 \cdot a=60\cdot 60 \qquad \text{Squaring both sides} [/tex]
[tex] \implies a =30 [/tex]
) Martha went to the store with $75.00. She bought 3 pairs of socks for $4.00 each, she bought 2 shirts for $20.00 each, and she bought a skirt for $21.00. How much money did she have left?
Answer:
She had $2.00 left.
Step-by-step explanation:
PEMDAS
$75 - [(3 x $4) + (2 x $20) + $21 ]
$75 - [ $12 + $40 + $21]
$75 - [ $52 + $21]
$75 - $73
$2
A line passes through the point (-3, -3) and has a slope of 1/2. What is the equation of the line? A y= 1/2x + 3/2 B y= 1/2x -3/2 C y= 1/2x -1/2 D y= -1/2x -3/2
Answer:
[tex](B.) y= 1/2x -3/2[/tex]
Step-by-step explanation:
[tex](-3, -3) = (x_1,y_1)\\m = 1/2\\\\y-y_1=m(x-x_1)\\\\y -(-3)=\frac{1}{2} (x -(-3)\\\\y+3 = \frac{1}{2}(x+3)\\\\ y+3 = \frac{1}{2} x+\frac{3}{2}\\\\ y = \frac{1}{2} x +\frac{3}{2} -3\\\\y = \frac{1}{2} x - \frac{3}{2}[/tex]
Answer:
[tex]\Large \boxed{\mathrm{Option \ B}}[/tex]
Step-by-step explanation:
y = mx + b
(slope intercept form of a line)
m = slope
b = y-intercept
y = 1/2x + b
Only three options have a slope of 1/2.
y= 1/2x + 3/2
y= 1/2x - 3/2
y= 1/2x - 1/2
The line crosses the point (-3, -3), x = -3 and y = -3.
-3= 1/2(-3) + 3/2
-3= -3/2 + 3/2
-3 = 0
This is false.
-3= 1/2(-3) - 3/2
-3 = -3/2 - 3/2
-3 = -6/2
-3 = -3
This is true.
-3= 1/2(-3) - 1/2
-3 = -3/2 - 1/2
-3 = -2
This is false.
6 to the third power divided by 4+2 x 9(32x8-17x4)
Answer:
3438.
Step-by-step explanation:
6³ ÷ 4 + 2 × 9 (32 × 8 - 17 × 4)
= 6³ ÷ 4 + 2 × 9 (256 - 68)
= 6³ ÷ 4 + 2 × 9 × 188
= 216 ÷ 4 + 2 × 9 × 188
= 54 + 2 × 9 × 188
= 54 + 3384
= 3438
3438 is the answer.
The circle shown below is a unit circle, where ∠a=π/3 and the radius of the circle is 1.
Answer:
Step-by-step explanation:
20 POINTS! ***CORRECT*** ANSWER GETS BRAINLIEST!!!!
The fraction model below shows the steps that a student performed to find a quotient.
Which statement best interprets the quotient?
A. There are 5 1/6 three-fourths in 4 1/8
B. There are 5 1/6 three and one-eights in 3/4
C. There are 5 1/2 three and one-eights in 3/4
D. There are 5 1/2 three-fourths in 4 1/8
Answer:
(D) There are [tex]5 \frac{1}{2}[/tex] three-fourths in [tex]4 \frac{1}{8}[/tex]
Step-by-step explanation:
We can see that in this model, the student tried to put [tex]\frac{3}{4}[/tex] into [tex]4 \frac{1}{8}[/tex]. We know this because the top of Step 2 is [tex]4 \frac{1}{8}[/tex] and he is counting how many fourths in the bottom.
So this becomes the division statement:
[tex]4 \frac{1}{8} \div \frac{3}{4}[/tex].
We can convert [tex]4 \frac{1}{8}[/tex] into a mixed number by multiplying 8 and 4, then adding 1.
[tex]\frac{33}{8} \div \frac{3}{4}[/tex].
Multiply by the reciprocal:
[tex]\frac{33}{8} \cdot \frac{4}{3} = \frac{132}{24}[/tex]
Which simplifies down to
[tex]\frac{11}{2}[/tex], which is just [tex]5 \frac{1}{2}[/tex] in improper form.
Hope this helped!
Answer:
D
Step-by-step explanation:
HE SODA MACHINE
The soda machine at your school offers several types of soda. There are two buttons for your favorite drink, Blast,
while the other drinks (Slurp, Lemon Twister, and Diet Slurp) each have one button.
Describe the input and output of this soda machine.
While buying a soda, Ms. Whitney pushed the button for Lemon Twister and got a can of Lemon Twister.
Later she went back to the same machine, again pushing the Lemon Twister button, but this time she got a can
of Blast. Is the machine functioning consistently? Why or why not?
BLAST
BLAST
BLUSO
ooo
Students, write your resnonsel
Answer:
yes and no
Step-by-step explanation:
if a machine is work a lot lot LOT, then it might be jamed
or the teacher might have accidentally pressed blast and you might have not seen the buttons correctly
( also i am not a student of yours )
What is the y-intercept of the line passing through the point (9,-7) with a slope of -1/8 ?
Answer:
-47/8.
Step-by-step explanation:
If the line has a slope of -1/8, that means the equation y = mx + b will be y = -1/8x + b.
In this case, we are given a point: (9, -7). That means that x = 9 and y = -7.
-7 = (-1/8)(9) + b
b - 9/8 = -7
b = -56/8 + 9/8
b = -47/8 = -5.875 = -5 and 7/8, which is your y-intercept!
Hope this helps!
MATT plans to put concrete on a regular portion of his driveway. The portion is 8 feet long and 4 inches high. The price of concrete is $98 per cubic yard. The total cost of the concrete that needs is $58.07.
THIS IS THE COMPLETE QUESTION BELOW;
Matt plans to put concrete on a rectangular portion of his driveway. The portion is 8 feet long and 4 inches high. The price of concrete is $98 per cubic yard. The total cost of the concrete Matt needs is $58.07. Which of the following is closest to the width of the portion of the driveway on which Matt plans to put concrete?. . [1 foot = 12 inches; 1 yard = 3 feet]. a. 0.5 feet. b. 1.5 feet. c. 3 feet. d. 6 feet
Answer:
OPTION D is correct
d)6feet
Step by step Explanation:
We were given The price of concrete as $98 per cubic yard
Price= $98 /yrd³
But 1 foot = 12 inches
1 yard = 3 feet
Square both side we have,
Then 1yrd³ = 27 ft³.
So we can use this conversion factor to convert $98 /yrd³ to per ft³ as follows
$98 /yd³) ×(1 yrd³ / 27 ft³) = $ 98/27/ft³
If we denote the width of the portion as "y"
then the volume of the rectangular portion of the driveway =
= (8 ft) (1/3 ft) x = 8y/3 ft³
But we're given The total cost of the concrete Matt needs as $58.07,
Total cost = $58.07 = (8y/3)(98/27)
y= 5.99957 ft= 6feet
Therefore, the width of the portion of the driveway is 6feet
Can somebody please help me on tjis
Answer:
Segment addition postulate
Step-by-step explanation:
It’s the Segment addition postulate.
ab+bc=ac
Please solve (will make brainiest)
Answer:
1a) 1/64
1b) 1/169
1c) 1/9
Step-by-step explanation:
You have to apply Indices Law :
[tex] {a}^{ - n} = \frac{1}{ {a}^{n} } [/tex]
Question A,
[tex] {4}^{ - 3} = \frac{1}{ {4}^{3} } = \frac{1}{64} [/tex]
Question B,
[tex] {13}^{ - 2} = \frac{1}{ {13}^{2} } = \frac{1}{169} [/tex]
Question C,
[tex] {( - 3)}^{ - 2} = {( - \frac{1}{3}) }^{2} = \frac{1}{9} [/tex]
9e - 7 = 7e – 11
Please help!?,!;):)
Answer:
e=-2
Step-by-step explanation:
9e-7e=-11+7
2e=-4
e=-2
A square has a perimeter of 32 and one vertex at (6,8). what could be the location of another vertex of this shape?
PLEASE HELP I AM IN A RUSH!!!
Answer:
6,5
Step-by-step explanation:
Answer:
(6,0),(-2,8),(-2,0)
Please answer this question now
Answer:
98.1km²
Step-by-step explanation:
The name of the Triangle in this question is: WXV
In the question, we have:
Angle W = ? Unknown
Angle X = 119°
Angle V = 34°
Side w =?
Side x = 26km
Side v = ?
Step 1
We have to find the missing third angle = Angle W
Sum of angles in a triangle = 180°
= Angle W = 180° - (119 + 34)°
= 180° - 153°
Angle W = 27°
Step 2
Find the sides w and v using the sine rule
Sine rule =
a/ sin A = b/ Sin B
Hence for triangle WXV
w/ sin W = x/ sin X = v/ sin V
We have the following values
Angle W = 27°
Angle X = 119°
Angle V = 34°
We are given side x = 26km
a) Finding side w
w/ sin W= x/ sin X
w/sin 27 = 26/sin 119
Cross Multiply
sin 27 × 26 = w × sin 119
w = sin 27 × 26/sin 119
w = 13.49587km
w = 13.5km
b) Finding side v
x / sin X= v/ sin V
26/ sin 119 = v/sin 34
Cross Multiply
sin 119 × v = 26 × sin 34
v = sin 34 × 26/sin 119
v = 16.62324km
v = 16.62km
Step 3
Detemine the area of triangle WXV
We make use heron formula
= √s(s - w) (s - x) (s - v)
Where s = w + x + v/ 2
s = (13.5 + 26 + 16.62)/2
s = 56.12/2
s = 28.06
Area of the triangle = √28.06× (28.06 - 13.5) × (28.06 - 26 ) × (28.06 - 16.62)
Area of the triangle = √9628.137559
Area of the triangle = 98.123073530337km²
Approximately to the nearest tenth =98.1km²
What is the solution to the equation? Show your work and explain your answer. 4(x+2)−1=4x+7
Answer:
infinitely many solutions / all real numbers
Step-by-step explanation:
distribute the 4 on the left side of the equation
4 • x = 4x
4 • 2 = 8
4x + 8 - 1 = 4x + 7
combine like terms
4x + 7 = 4x + 7
0 = 0
since this expression is true, there are infinitely many solutions
in a polynomial function of degree 5, what is the maximum number of extreme that could be possible? (please explain with the answer if possible!)
Answer:
4 maximum extrema
Step-by-step explanation:
5th degree means that it can change direction 5 times, therefore creating a maximum of 4 extrema
Jorge’s monthly bill from his Internet service provider was $25. The service provider charges a base rate of $15 per month plus $1 for each hour that the service is used. Find the number of hours that Jorge was charged for that month.
Answer:
10 hours for the month
Step-by-step explanation:
What you know: The total amount Jorge was charged for the month was $25
The base rate is $15
He gets charged $1 per each hour
Setting it up:
15+1h=25
(the 15 is the base rate, plus the 1 dollar per hour (h) which both add to the total of 25 dollars for the month)
Subtract 15 from both sides of the equation to get your variable by itself
1h=10
then divide the 1 on both sides to get h (hours) by itself
h=10
And there's your answer, 10 is the number of hours that Jorge was charged for the month
Hopefully this helped :))
Answer:
10
Step-by-step explanation:
$25 - $15 = $10
and its $1 per hour so the answer is 10hrs
The data give the average number of days in May that are clear
I really need help
Answer:
C. 0.10, because 6 of the 60 days were clear
Step-by-step explanation:
As per the question, you're in San Antonio which indicates 1st look in San Antonio's row.
Then we want the chance or probability it's clear, so look in clear column. We will find the value that is "6"
So 6 on a total of 60 which is the huge total. Accordingly, Probability it is right, since that you are into the San Antonio. Then it becomes
[tex]= \frac{6}{60}[/tex]
= 0.1
Therefore the right answer is C.
Divisibility by 10 of number 7236
7236 is NOT divisible by 10
Step-by-step explanation:
any number that ends with zero is divisible by 10 but 7236 dosent end with zero so 7236 isnt divisible by 10
please simplify this question
Answer:
8 107/120 (Decimal: 8.891667)
Step-by-step explanation:
12 1 /2 −5 13 /72 +1 3 /5 − 1 /36
= 25 /2 −5 13 /72 +1 3 /5 − 1 /36
= 25 /2 − 373 /72 +1 3 /5 − 1 /36
= 527 /72 +1 3 /5 − 1 /36
= 527 /72 + 8/ 5 − 1 /36
= 3211 /360 − 1 /36
= 1067 /120
=8 107 /120
HOPE THIS HELPS!!!!!! :)
<3333333333
PLS HELP I WILL GIVE YOU A BRAINLIST AND A THANK YOU!!!!
Answer:
75
Step-by-step explanation:
We have a 90 degree angle and a 15 degree angle that add up to 105. The angle that is missing can be found by doing 180 - 105 = 75 (since it's a straight line). X is vertical from the 75 degree angle, so 75 is your answer.
Answer:
x= 75°
Step-by-step explanation:
i have added a sketch of it
Move ABC so it lies on top of , DEF, GHI and JKL. How many units do you have to move ABC from its original location to coincide with each of the other triangles? Specify how ABC moves up, down, left, or right.
Answer: triangleDEF - 3 units down
triangleGHI - 5 units left
triangleJKL - 4 units left and 5 units down
Step-by-step explanation:
how many are 5 raised to 4 ???
Answer:
625
Step-by-step explanation:
5⁴ = 5x5x5x5 = 625
PLS HELP I WILL GIVE BRAINLIST AND A THANK YOU!!!!! :)
Answer:
A
Step-by-step explanation:
Both angles together are supplementary, or they add up to 180 degrees.
(3x+12)+x=180 degrees
Answer:A. (3x+12)+x=180
Step-by-step explanation:
ANSWER QUICKLY PLZZZZZZ
Answer:
A= 17 B= 19
Step-by-step explanation:
Answer:
a) 17 cups water
b) 19 cups rice
Step-by-step explanation:
w = 1.5r + 0.5
For 11 cups of rice, r = 11.
w = 1.5(11) + 0.5
w = 16.5 + 0.5
w = 17
For 11 cups of rice, 17 cups of water are needed.
With 29 cups of water, w = 29.
29 = 1.5r + 0.5
28.5 = 1.5r
r = 19
With 29 cups of water, 19 cups of rice can be cooked.
Please help for 14 point 5 stars and 1 thanks! :]
Answer:
x=22000 ( bonds)
Step-by-step explanation:
total money invested=26000 , x for bonds and y stocks
x+y=26000 ⇒ x=26000-y
0.05 x + 0.08 y=1420 solve by substitute : x=26000-y
0.05(26000-y)+0.08 y =1420
1300-0.05y+0.08y=1420
0.03y=1420-1300
y=120/0.03
y= 4000 ( the amount invested in stocks)
the amount invested in bonds x= 26000-4000
x=22000 ( bonds)
check :
0.05(22000)+0.08(4000)= 1420 correct
Let P be a non zero polynomial such that P(1+x)=P(1−x) for all real x, and P(1)=0. Let m be the largest integer such that (x−1) m divides P(x) for all such P(x). Then m equals
Answer:
m = 0, P(3)/2, P(4)/6, P(5)/12 ..........
Step-by-step explanation:
For non zero polynomial, that is all real x as follows:
x = 1, 2, 3, 4 ............
Using, P(1 + x) = P(1 - x)
For x = 1: P(2) = P(0) = 1
For x = 2: P(3) = P(-1) = 2
Hence, P(x)/m(x - 1) can be solved as follows:
When = 1
P(2)/0 = 1
∴ m = 0
When x = 2
P(3)/m = 2
∴ m = P(3)/2
When x = 3
P(4)/2m = 3
∴ m = P(4)/6
When x = 4
P(5)/3m = 4
∴ m = P(5)/12
Hence, m = 0, P(3)/2, P(4)/6, P(5)/12......
