Answer: (p+q)(p+3r)
Step-by-step explanation:
p²+pq+3qr+3pr
Do the grouping p²+pq+3qr+3pr=(p²+pq)+(3qr+3pr), and factor out p in the first and 3r in the second group.
p(p+q)+3r(p+q)
Factor out common term p+q by using distributive property.
(p+q)(p+3r)
Factorise 3(3x-y)-(y-3x)
Answer:
4(3x-y)
Step-by-step explanation:
Given:
[tex]\displaystyle \large{3(3x-y)-(y-3x)}[/tex]
To factor this kind of expression, first, find the common factor.
[tex]\displaystyle \large{3(3x-y)-(-3x+y)}\\\displaystyle \large{3(3x-y)+(3x-y)}[/tex]
Notice that in the expression, we have both same (3x-y). Therefore, (3x-y) is our factor.
Let u = 3x-y
[tex]\displaystyle \large{3u+u}\\\displaystyle \large{4u}[/tex]
Change u back to 3x-y:
[tex]\displaystyle \large{4(3x-y)}[/tex]
Therefore, the factored expression is 4(3x-y).
if x = 1/4 and Y = 3/7 evaluate the following expression 7x-4y
If x = 1/4 and Y = 3/7
Evaluate the following expression: 7x - 4y
[tex] \\ [/tex]
[tex] \rm{7 ( \frac{1}{4}) - 4( \frac{3}{7} ) } \\ [/tex]
Substitute the given value of x and y[tex] \rm { \orange{7 \times \frac{1}{4} }} - 4 \times \frac{3}{7} \\ [/tex]
Calculate the product of the rational numbers[tex] \rm{ \frac{7}{4} - \orange{ 4 \times \frac{3}{7 }} } \\ [/tex]
Calculate the product of the rational numbers[tex] \rm \orange{ \frac{7}{4} - \frac{12}{7} } \\ [/tex]
Find the difference between the two fractions[tex] = \small{\boxed{{\sf{ \frac{1}{28} }}}}[/tex]
Therefore, the answer is 1/28.
Answer:
Step-by-step explanation:
[tex]\text{Substitute the values of x and y in the expression}[/tex]
[tex]7x - 4y = 7*\dfrac{1}{4}-4*\dfrac{3}{7}[/tex]
[tex]\sf =\dfrac{7}{4}-\dfrac{12}{7}\\\\ [LCM \ of 4 \ and \ 7 = 28]\\\\ =\dfrac{7*7}{4*7}-\dfrac{12*4}{7*4}\\\\=\dfrac{49}{28}-\dfrac{48}{28}\\\\=\dfrac{1}{28}[/tex]
What is the distance from Point A to point D on the number line? Please help!
Answer:
5
Step-by-step explanation:
Hope this helps! Have a great day!
How many inches of snow fell each hour? (8th Math)
Answer:
2 inches
Step-by-step explanation:
If 10 inches of snow fell each hour, then you divide that by five hours to get your average, which then equals 2. So your answer is 2 inches per hour.
I hope this answered your question and helped you :)
Answer:
Looking at the graph it looks like 5 inches in 2 1/2 hours
Hope this helps :)
help me please need help missing lengths
Step-by-step explanation:
please mark me brilliant
Step-by-step explanation:
5. θ = 60°
→ To find the value of y ,
Cos θ = b/h
putting the values in terms of cos
Cos 60° = y/16
1/2 = y/16
16/2 = y
y = 8 unit
→ To find the value of x ,
Sinθ = P/h
putting the values in terms of sin
Sin60° = x/16
√3/2 = x/16
16×√3/2 = x
16×1.73/2 13.84 unit
6. θ = 30°
→ To find the value of y
tanθ = p/b
putting the values in terms of tan
tan 30° = 2/y
1/√3 = 2/y
2×√3 = y
3.46 unit = y
→ To find the value of x
Sin θ = p/h
putting the values in terms of sin
Sin 30° = 2/x
1/2 = 2/x
4 unit = x
Last year at a certain high school, there were 84 boys on the honor roll and 50 girls
on the honor roll. This year, the number of boys on the honor roll decreased by 25%
and the number of girls on the honor roll decreased by 16%. By what percentage did
the total number of students on the honor roll decrease? Round your answer to the
nearest tenth (if necessary).
Answer:
Step-by-step explanation:
Boys Girls
84 50
%decrease %decrease
-25% -16%
84=100% 50=100%
75% 84%
75/100×84 84/100×50
=63 =42
84+50=134
63+42=105
134-105=29
134=100%
29
29/134×100
21.6%
The area of a rectangle is 56 cm, Tho longth is 2 cm more than x and the width is 5 cm less than
twico x. Solve for x. Round to the nearest whole number,
Answer:
9
Step-by-step explanation:
Since Area = L × W
Thus,
Area = (x + 2)(2x - 5) = 56
x^2 +4x - 5x - 10 = 56
x^2 - x - 10 = 56
x^2 - x - 66
Using the quadratic formula:
a = 1
b = - 1
c = - 66
Solving:
[tex]\frac{x = (-b) +/- sqrt(b^2 - 4ac)}{2a}[/tex]
[tex]\frac{x = 1 + /- sqrt(1^2 - 4(1)(-66)}{2(1)}[/tex]
[tex]\frac{1 +/- sqrt (265)}{2}[/tex]
17.279/2
8.639
Round = 9
~Lenvy~
solve for y 3x+6y=30
Answer:
the answer= y=5−x/2
Answer: [tex]y=-\frac{1}{2} x+5[/tex]
Step-by-step explanation:
We need to isolate y by itself
Step 1) Subtract 3x from both sides
[tex]3x+6y=30\\3x-3x+6y=30-3x\\6y=30-3x[/tex]
Step 2) Divide both sides by 6 to isolate y
[tex]6y=30-3x\\\frac{6y}{6} =\frac{30}{6}-\frac{3x}{6} \\y=5-\frac{1}{2}x[/tex]
romina has a maximum of 90 minutes to make traditional mexican paper flowers she spends 15 minutes watching videos on how to make flowers then it takes her 3 minutes to do each flower romina writes the inequality 15 + 3f <90 to repesent the number of flowers F she has to make
Answer:
f<25, she can make less than 25 flowers to have enough time, (I think the inequalitie sign should have a line underneath it tho meaning, less than or equal to 25 flowers, which would only make sense)
Step-by-step explanation:
First you need I subtracted 15 from 90 which got me 75.
15 + 3f<90
-15 -15
_________
0 75
3f<75
__
3f
75 divided by 3f= 25
HELP PLEASE WORTH A LOT OF POINTSSSSSSSSS!! SHOW YOUR WORK PLEASEEEEE!!!!!!!!!!
Answer:
Step-by-step explanation:
Tan 70 = 16/x
x = 16/tan70
x = 5.824 to the nearest thousandth
tan 41 = 16 / (x + y)
tan 41 = 16 /(5.8235 + y)
tan41(5.8235 + y) = 16
5.8235 + y = 16/ tan41
y = (16/ tan41) - 5.8235
y = 12.582 to the nearest thousandth
Solve the system of equations y = 2x^2 + x – 6 and y = 4
Step-by-step explanation:
Substitute y = 4 into the first equation:
[tex]4=2x^2+x-6[/tex]
Subtract 4 from both sides:
[tex]2x^2+x-10=0[/tex]
We can factor in order to find values of x.
Factor the equation:
[tex]2x^2+x-10=0[/tex]
Factors of 10 we'll use:
5 and 2.
[tex](2x+5)(x-2)=0[/tex]
Set the parentheses equal to 0 then find the values of x:
[tex](2x+5)=0[/tex]
[tex]x=-2\frac{1}{2}[/tex]
[tex](x-2)=0[/tex]
[tex]x=2[/tex]
[tex]x=2, \: or \: -2\frac{1}{2} .[/tex]
Check:
[tex]4=2(2)^2+2-6[/tex]
[tex]4=2(4)+2-6[/tex]
[tex]4=4 \: \checkmark[/tex]
[tex]4=2(-2\frac{1}{2} )^2-2\frac{1}{2} -6[/tex]
[tex]4=2(6\frac{1}{4})-2\frac{1}{2} -6[/tex]
[tex]4=12\frac{1}{2} -2\frac{1}{2} -6[/tex]
[tex]4=10-6[/tex]
[tex]4=4 \: \checkmark[/tex]
f I read 245 pages of The Lightning Thief, what percent of the book have I read? (There are 377 pages total, Round to the nearest percent
Answer:
65%
Step-by-step explanation:
set a porportion
245 =x
377 100
245x100= 24500/377 = 64.9 rounded = 65%
A grocery store sells long grain rice for 2.49 per pound. Write an expression for the cost of y pounds of long grain rice.
I dont want to waste time thinking about it
Answer:
Step-by-step explanation:
Cost = 2.49 * y
You really should spend the time. Math is used everywhere.
In which quadrant does θ lie given that sinθ < 0 and cosθ < 0? Thank You!
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
Answer:
Quadrant III
Step-by-step explanation:
sin and cos are both less than zero thus negative
the x and y axis are both negative in QIII
sorry if the explaination is wrong but I know the answer is right bc I took the test
Hello! Mikosan here to help doll!
The Answer is: Quadrant 3
I hope this helps doll!
Have a great day love~
if your catering people and its $80 for 6-8 people how much would it be to cater 128 people
Answer:
Your answer(s) is $1,706.67, $1,462.86, or $1,280
Step-by-step explanation:
This really varies based on whether you take $80 as equal to 6 people, 7 people, or 8 people.
I'll list all three explanations and you can choose one.
6 people: 1,706.67 (rounded to nearest cent)
128 ÷ 6 = 21.33333333
21.33333333 × 80 = 1,706.67
7 people: 1,462.86 (rounded to nearest cent)
128 ÷ 7 = 18.28571428571429
18.28571428571429 × 80 = 1,462.86
8 people:
128 ÷ 8 = 16
16 × 80 = 1,280
In a 30 - 60 - 90° triangle x= 7.5 feet
What is the length of the hypotenuse?
Answer: 15ft or 7(2)
Step-by-step explanation:
The opposite side or the side standing up is the "x" side the hypotenuse is double the size of the opposite in a 30-60-90.
please help ! ASAP step by step explanation please
Answer:
0
Step-by-step explanation:
→ First find inverse cosine 1/2
60°
→ Now multiply this answer by 3 because then if you substitute it in you get 0.5
∝ = 180°
→ Now find sine of 180°
0
Instructions: Find the measure of the indicated angle.
Answer:
42 degrees
Step-by-step explanation:
The measure of the indicated angle is 42 degree.
What is Isosceles Triangle ?An isosceles triangle has two equal sides regardless of the direction the apex (or peak) of the triangle points. Some useful information regarding isosceles triangles is as follows:
It has two parallel sides.It has two equal angles, which are known as the basis angles.A right isosceles triangle is one in which the third angle is 90 degrees.We have a Triangle.
Then, using Isosceles Triangle Theorem
Angles opposite an isosceles triangle's equal sides are also equal.
According to the isosceles triangle theorem, if two sides of a triangle are congruent, then the angles opposite the congruent sides are likewise congruent.
So, x= 42 degree.
Learn more about Isosceles Triangle Theorem here:
https://brainly.com/question/30066983
#SPJ7
please help me with this
Answer:
94 Wins
Step-by-step explanation:
Here we need to find the mean, to do this we add up all the values then divide the sum by how many values we started out with.
97 + 103 + 92 + 95 + 84 = 471
471 / 5 = 94.2
since we got a decimal we can round to find an exact number; since the decimal is under .5 we will round down, 94
So 94 wins would be the correct answer. Hope this helped!
Write an equation for a line that passes through (1,-4) and (3,-5)
Answer:
y = -3/4x - 1/2
Step-by-step explanation:
Given:
Point 1: (1, -4)
Point 2: (3, -5)
Find:
The equation for the line that passes through Point 1 & Point 2
Solution:
y = mx + b
Will be the equation to arrive to at the very end, but we need m & b, the slope and the y-intercept
m = ( y2 - y1 ) / ( x2 - x1 ) = ( -5 - (-4) ) / ( 3 - 1 ) = -1 / 2
∴ m = - 1/2
Using either P1 or P2, plug in one of their respective x- and y-values into:
y = -1/2 x + b
I'll do (3, -5):
-5 = -1/2 ( 3 ) + b
-2 = -3/2 + b
-4 = -3 + 2b
-1 = 2b
∴ b = -1/2
∴ y = -3/4x - 1/2 is the equation of the line that passes thru both points (-5, 4) and (3, -2)
9n^2-10=890 solve by taking square roots
Answer:
n=3.3
Step-by-step explanation:
9n²-10=890 1. + 10 on both sides
9n² = 900
[tex]9n²[/tex]= 9n
[tex]900[/tex] = 30
9n=30 2. /9 on both sides
n=3.33
the 3's repeat
The probability of getting a soda at the movie theater is 70%. What is the probability that the next three guests in the movie theater will get a soda
The probability that the next three guests in the movie theater will get a soda, when the probability of getting a soda at the movie theater is 70% is 0.343 or 34.3%.
What is probability?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
The probability of getting a soda at the movie theater is 70%.
[tex]P=70\%\\P=\dfrac{70}{100}\\P=0.7[/tex]
By the chain rule, the probability of getting the soda to the next 3 guest is equal to the cube of the probability of getting a soda at the movie theater.
Thus, the probability that the next three guests in the movie theater will get a soda is,
[tex]P^3=0.7^3\\P^3=0.343[/tex]
Thus,the probability that the next three guests in the movie theater will get a soda, when the probability of getting a soda at the movie theater is 70% is 0.343 or 34.3%.
Learn more about the probability here;
https://brainly.com/question/24756209
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Giving brainliest to best answer! I need both of these done by 10:50! Pls help!
Hope it helps.
Do comment if you have any query.
hey, can you answer this for me?
9-3x=54?
[tex] \Large{\boxed{\sf x = -15}} [/tex]
[tex] \\ [/tex]
Explanation:Given equation:
[tex] \sf 9 - 3x = 54 [/tex]
[tex] \\ [/tex]
Subtract 9 from both sides:
[tex] \sf 9 - 3x - 9 = 54 - 9 \\ \\ \sf -3x = 45 [/tex]
[tex] \\ [/tex]
Divide each side by -3 :
[tex] \sf \dfrac{-3x}{-3} = \dfrac{45}{-3} \\ \\ \\ \boxed{\boxed{\sf x = -15}} [/tex]
[tex] \\ \\ [/tex]
▪️Learn more about equations here:
↣https://brainly.com/question/19225782
IMAGE BELOW I WILL GIVE BRAINLIEST
Answer: C: -4, -6 B:-14, -6 A:-14, -18
Step-by-step explanation: Multiply all of your points by 2
I need help with my math.
Ashton was born on the second Saturday in August many years ago. In that August, there were five Mondays and four Tuesdays. On what date was Ashton born?
Considering the situation described, it is found that Ashton was born on August 8.
What does the fact that there were five Mondays and four Tuesdays mean?It means that August 31 was on Monday, hence the same is valid for August 24, August 17, August 10 and August 3.
Hence, the first Saturday was August 1, and the second August 8.
A similar problem, involving the interpretation of a situation, is given at https://brainly.com/question/25537936
1 . what’s -3 p + 6 p = ?
Hurry please!!!
Answer: 3p
Step-by-step explanation: The reason is because -3 + 6 = 3, therefore -3p + 6p = 3p. I hope this helped! If I did anything wrong then please let me know! :)
[tex] - 3p + 6p[/tex]
solution:first you'll have to combine light terms, both are light terms so,
[tex] - 3p + 6p[/tex]
[tex] =3p[/tex]
A can of diced tomatoes has a height of 11.5 cm and a diameter of 10 cm.
What is the volume of the can? Use 3.14 for i.
DO NOT round your answer.
A cubic cm
Answer:
10 cm
Step-by-step explanation:
the can is shaped like a cylinder
first step is to find the radius and then multiply the figure by 2
volume of a cylinder = nr^2h
n = 22/7
r = radius
903 = 11.5 x r^2 x 3.14
r^2 = 903 / (3.14 x 11.5)
r = 5 cm
diameter = 10cm
What is the area of this composite figure?
I WILL GIVE BRAINLIEST
A figure is comprised of 2 rectangles. The first rectangle has a length of 10.5 centimeters and width of 15.5 centimeters. The second rectangle has a length of 18 centimeters and width of 11.5 centimeters.
135 centimeters squared
207 centimeters squared
249 centimeters squared
279 centimeters squared
Answer:
249 centimeters squared
Step-by-step Explanation:
The area of the rectangle: l x w, where l is the length and w is the width.
= 15.5 x 18
= 279
Area of the smaller rectangle: l x w, where l is the length and w is the width.
= 4 x 7.5
= 30
We do not need this 30.
Area of the shaded region:
= 279 - 30
= 249 cm²