[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{|48 - 6| + |- 35 + 7|}[/tex]
[tex]\mathsf{|48 - 6| = \boxed{\bf 42}}[/tex]
[tex]\mathsf{= 42 +| -35 + 7|}[/tex]
[tex]\mathsf{|-35 + 7| = \boxed{\bf -28}}[/tex]
[tex]\mathsf{= 42 + |- 28|}[/tex]
[tex]\mathsf{= 42 + 28}[/tex]
[tex]\boxed{\mathsf{= \bf 70}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf 70}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
3. A drinking straw of length 21 cm is cut into 3 pieces. The length of the first piece is x cm.
The second piece is 3 cm shorter than the first piece. The third piece is twice as long as the
first piece
State, in terms of x, the length of EACH of the pieces.
(2 marks)
(ii)
Write a simplified expression, in terms of x, to represent the sum of the lengths of
the three pieces of drinking straw.
(2 marks)
(iii)
Hence, calculate the lengths for the 3 pieces of straw
(4marks)
Answer:
I'll setup the problem and you can do the calculations
Step-by-step explanation:
Total length of straw - L
Length of piece 1 - x
Length of piece 2 - y
Length of piece 3 - z
What's given and the answer to (i)
y = x - 3
z = 2x
(ii) L = x + y + z = x + x - 3 + 2x
L = 4x-3
(iii) x = (21+3)/4 = 24/4
leaving you to calculate x
then substitute x into expressions for y & z above and you will have the answer
comment if you have questions
Angel went to the store to buy some chicken. The price per pound of the chicken is $4 per pound and he has a coupon for $2.75 off the final amount. With the coupon, how much would Angel have to pay to buy 2 pounds of chicken? Also, write an expression for the cost to buy p pounds of chicken, assuming at least one pound is purchased.
Answer:
$5.25 for 2lbs
Step-by-step explanation:
C=total cost
C=4p-2.75
---
C=4(2)-2.75
C=$5.25
Answer:
$5.25 the expression is $4p-2.75
which best describes the transformation that occurs from the graph of f(x)=x^2 to g(x)=(x-2)^2+3??
answer right 2, up 3
any function with the following form is a transformation from f(x) = x²
g(x) = (x – a)² + b
were a moves the function to the right when a is a positive number and to the left when its a negative number, and b moves the function up when b is positive and down when its negative.
then for a=2 positive and b=3 positive, we have
right 2, up 3
Answer:
answer right 2, up 3
Step-by-step explanation:
2x²+5x-3=0
using completing the square method
Answer:
[tex]2 {x}^{2} + 5x - 3 = 0 \\ 2( {x}^{2} + \frac{5}{2} x - \frac{3}{2} ) = 0 \\ 2( {x}^{2} + \frac{5}{2} x + {( \frac{5}{4} )}^{2} ) - \frac{3}{2} - {( \frac{5}{4} )}^{2} ) = 0 \\ ( {(x + \frac{5}{4} )}^{2} = \frac{49}{16} \\ x + \frac{5}{4} = ± \frac{7}{4} \\ x = 0.5 \: \: and \: \: 3[/tex]
Answer:
x= [tex]\frac{1}{2}[/tex] or x= -3
Step-by-step explanation:
[tex]\boxed{x^{2} +kx=(x+\frac{k}{2})^{2} -(\frac{k}{2})^{2} }[/tex]
First ensure that the coefficient of x² is 1.
x² +[tex]\frac{5}{2}[/tex]x -[tex]\frac{3}{2}[/tex]= 0
[x +([tex]\frac{5}{2}[/tex] ÷2)]² -([tex]\frac{5}{2}[/tex] ÷2)² -[tex]\frac{3}{2}[/tex]= 0
(x +[tex]\frac{5}{4}[/tex])² -([tex]\frac{5}{4}[/tex])² -[tex]\frac{3}{2}[/tex]= 0
(x +[tex]\frac{5}{4}[/tex])²- [tex]\frac{25}{16}[/tex] -[tex]\frac{3}{2}[/tex]= 0
(x +[tex]\frac{5}{4}[/tex])² -[tex]\frac{49}{16}[/tex]= 0
(x +[tex]\frac{5}{4}[/tex])²= [tex]\frac{49}{16}[/tex]
x +[tex]\frac{5}{4}[/tex]= [tex]\sqrt{\frac{49}{16} }[/tex] (square root both sides)
x +[tex]\frac{5}{4}[/tex]= ±[tex]\frac{7}{4}[/tex]
x= -[tex]\frac{5}{4}[/tex] +[tex]\frac{7}{4}[/tex] or x= -[tex]\frac{5}{4}[/tex] -[tex]\frac{7}{4}[/tex]
x= [tex]\frac{1}{2}[/tex] or x= -3
If an angle does not have a measure of 88°, then the angle is not an acute angle.
In a flight of 600km,an aircraft was alowed down due to bad weather. Its average speed for the trip reduced to 200km/hr and the time increased by 30 minutes. Find the duration of the flight.
Answer:
The duration of the flight is 1 hour
Step-by-step explanation:
Since average speed = distance traveled / time
Let the duration of the flight be in z hours
So, (600km/z hours) - (600km/ z hours + (1/2)) = 200km/hr
Note: 1/2 is used as a result of 30 minutes increased in time which is half an hour.
200 = (600/z ) - (600/z + (1/2))
Multiply 2 through on (600/z + (1/2))
200 = (600/z ) - (1200 / (2z + 1))
Divide through by 200
= z(2z + 1) = 3
convert to quadratic equation
2z² + z = 3
2z² + z - 3 = 0
(2z + 3) ( z-1) = 0
z-1 = 0
z = 1 hour
Find the missing side of the triangle. Round your answers to the nearest tenth if necessary.
15.3 m
10 m
24.6 m
22.4 m
Answer:
Solution given:
perpendicular[p]=x
base[b]=11.6m
hypotenuse[h]=19.2m
by using Pythagoras law
h²=p²+b²
19.2²-11.6²=x²
x=[tex]\sqrt{234.08}[/tex]
x=15.3m
option
a.
15.3 m
Answer:
15.3 m
Step-by-step explanation:
c refers to the longest side (hypotenuse) whereas a and b referes to the two other smaller sides of atriangle.
pythagoras theorem
a^2 + b^2 = c^2
11.6^2 + x^2 = 19.2^2
134.56 + x^2 = 368.64
x^2 = 368.64 - 134.56
x^2 = 234.08
x=[tex]\sqrt{234.08[/tex]
x=15.29
x=15.3 m
Select the number line model that matches the expression
|8 - 1|
Answer:
B
Step-by-step explanation:
Trust
What is the vertex of y=-X2+2x?
Answer:
(1,1)
Step-by-step explanation:
Graph: y = -x^2 + 2x
Please answer and explain
Answer: It is a 3% chance
The solutions of x² = 16x - 28 are
1) -2 and -14
2) 2 and 14
3) -4 and -7
4) 4 and 7
When adding two
rational numbers what
will the sign be if both
numbers are positive?
Answer:
Step-by-step explanation:
Adding two rational numbers results in a positive sum.
David is six times older than Janet. If David is 48 years old, how old is Janet?
Answer:
David is six times older than Janet. If David is 48 years old, how old is Janet? Janet is 8 years old.
Step-by-step explanation:
48÷6=8
Write as a single fraction in its simplest form.
how do you do this?
Answer:
(-12x - 25) / (x + 3) (x - 5)
Step-by-step explanation:
1 - 2x/(x+3) + (x+3)/(x - 5)
= {(x + 3)(x - 5) - 2x(x - 5) + (x + 3)(x - 3)} / (x + 3) (x - 5)
= {(x² -5x + 3x - 16) - (2x² + 10x) + (x² - 3x + 3x - 9)} / (x + 3) (x - 5)
= x² - 2x - 16 - 2x² - 10x + x² - 9 / (x + 3) (x - 5)
= x² - 2x² + x² - 2x - 10x - 16 - 9 / (x + 3) (x - 5)
= (-12x - 25) / (x + 3) (x - 5)
What is the. Length of a
Answer:
One of the altitude formed from the vertex to the base and its magnitude given as 12cm
There is also a hypotenuse whose length is 15cm
By pythagorean theorem b^2 +a^2= c^2
so 12^2+a^2 = 15^2
=> 144+a^2 = 225
=> a^2 = 225-144
=> a^2 = 81
so the length of a = √81 = 9 cm (ans)
Hope it helps
Answer:
c
Step-by-step explanation:
The diagram shows equilateral triangle RST with altitude SV
It is given that RV = 6 meters. What is the length of ST?
Answer:
ST is 12 meters
Step-by-step explanation:
The given triangle ΔRST = An equilateral triangle
The altitude of ΔRST = SV
The length of segment RV = 6 meters
Given that ΔRST is an equilateral triangle, the base angles of the triangles = 60°, therefore, in the formed triangles, ΔRSV, and ΔTSV, ∠RSV = ∠TSV = 90° - 60° = 30°
∴ ΔRSV, and ΔTSV are congruent, based on ASA rule of congruency
∴ Side VT in ΔTSV is congruent to side RV in triangle ΔRSV
The midpoint of side ST
VT ≅ RV
Therefore, VT = RV = 6 meters
RT = RV + VT = 6 + 6 = 12 By segment addition property
In equilateral triangle, ΔRST, all the sides are equal, therefore;
RT = RS = ST = 12 m
ST = 12 meters.
please help me rules of differantion
Answer:
Step-by-step explanation:
Do this by making this 2-part function into one all-in. Do this by finding a common denominator and then writing the function as one, over the common denominator, x. When we do this we get the function:
[tex]y=\frac{3x^3-2}{x}[/tex] and we will use the rule for quotients, which is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all over the denominator squared. For us, that is, in steps:
[tex]y'=\frac{x(9x^2)-(3x^3-2)(1)}{x^2}[/tex] which simplifies to
[tex]y'=\frac{9x^3-3x^3+2}{x^2}[/tex] which simplifies finally to
[tex]y'=\frac{6x^3+2}{x^2}[/tex]. Nothing else you do can make this any more simplified.
Solve for x: 3 over 4 x + 5 over 8 = 4x x = Write your answer as a fraction in simplest form. Use the "/" symbol for the fraction bar. (2 poin
Answer:
x = 5/26
Hope this helps! GL!
What is the value of h(2)?
Step-by-step explanation:
answer is 0
because x= 2 and y =3 make a circle
Whats the answer to this ??
answer is 4
it is the cube root of 4
4×4×4 = 64
The answer of value is 4.
A ball is thrown into the air from the top of a building. The height, h(1), of the ball above ground, t seconds after it is
thrown, can be madeled by the function h(t) = -16t2 + 64t + 80. Based on the function, the "80"
represents what?
a. The time when the ball hits the ground
b. The distance the ball travels.
C. The speed of the ball
d. The initial height of the ball
Answer:
d
Step-by-step explanation:
dddddddddddddddddddd
LAWD please help. I have summer school
Me too. It's the third option. :)
Answer:
I think its the third bubble. Hopefullly this helps. im pretty sure its correct.
Step-by-step explanation:
1st. add rt to both sides so that it cancels out. That should give you xy= s+rt.
2nd. Then divide x from both sides to single out the y. since x is multiplying with y you must use the inverse operation and divide by X. This should leave you with y= (s+rt)÷x
solve for x round to the nearest tenth if necessary
Answer:
x ≈ 7.7
Step-by-step explanation:
Using the sine ratio in the right triangle
sin69° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{HI}{GI}[/tex] = [tex]\frac{7.2}{x}[/tex] ( multiply both sides by x )
x × sin69° = 7.2 ( divide both sides by sin69° )
x = [tex]\frac{7.2}{sin69}[/tex] ≈ 7.7 ( to the nearest tenth )
factoring polynominaly
Answer:
Most of the question is missing. If you could type out the rest, we might be able to help you.
You begin solving the equation 4−5=59 4 - 5 x = 59 by subtracting 4 4 from both sides. Which is the best choice for Step 2 2 ?
Answer:
4 – 5x = 59, x = -11
Step-by-step explanation:
The given equations is :
4 – 5x = 59
Subtracting 4 both sides,
4 – 5x -4 = 59-4
-5x = 55
Dividing both sides by -5.
x = -11
So, the answer of the given equation is -11.
PLEASE PLEASE PLEASE HELP ME WITH THIS QUESTION I KEEP GETTING SPAM ANSWERS, THANK YOU!
EXPLAINING YOUR ANSWER = BRAINLIEST
The area is 96 square units.
The length, x, of the base is ___ units.
Given :
Δ Area of the Triangle is 96 square units
Δ Height of the Triangle is 9.6 units
We know that:
[tex]\bigstar \ \ \boxed{\sf{\textsf{Area of a Triangle is given by} : \dfrac{1}{2} \times Base \times Height}}[/tex]
[tex]\implies \sf{\dfrac{1}{2} \times Base \times 9.6 = 96}[/tex]
[tex]\implies \sf{\dfrac{1}{2} \times Base = \dfrac{96}{9.6}}[/tex]
[tex]\implies \sf{\dfrac{1}{2} \times Base = \dfrac{960}{96}}[/tex]
[tex]\implies \sf{\dfrac{1}{2} \times Base = 10}[/tex]
[tex]\implies \sf{Base = 20 \ units}[/tex]
the sum of the squares of two consecutive integers is 481. Find the integers
Answer:
{15, 16} or {-15, -16}
Step-by-step explanation:
Quick solution:
take half of the sum (approx. 240), sqrt(240)=15.5
So the numbers are 15 and 16. and also the negative equivalents since squares are always positive.
Exact method:
Let
x=smaller integer,
x+1 = next integer.
sum:
x²⁺(x+1)^2 = 481
2x^2 + 2x + 1 = 481
2x^2 + 2x - 480 = 0
x^2 + x -240 = 0
x = 15 or x = -16
so the integers are
either
{15, 16} or {-15, -16}
The sum of the squares of two consecutive integers is 481 will be -15 & -16 and 15 and 16.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Successive numbers are those that follow one another continually, from lowest to biggest. For instance, the numbers 1, 2, 3, 4, 5, and so on are all consecutive.
Assume 'x' is the number and the successive number is (x + 1).
The sum of the square of the consecutive number is 481. Then the equation of the number is given as,
x² + (x + 1)² = 481
Simplify the equation, then we have
x² + (x + 1)² = 481
x² + x² + 2x + 1 = 481
2x² + 2x - 480 = 0
x² + x - 240 = 0
x² + 16x - 15x - 240 = 0
x(x + 16) - 15(x + 16) = 0
(x + 16)(x - 15) = 0
x = 15, -16
Then the successive numbers are given as,
x + 1 = 15 + 1
x + 1 = 16
x + 1 = - 16 + 1
x + 1 = - 15
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
A truck is carrying pineapple juice, tomato juice, and cherryjuice bottles in a ratio of 3:5:4. If there are 80 tomato juice bottles, then how many juice bottles in total?
PLEASE HELP!!
Answer:
192
Step-by-step explanation:
The ratio of pineapple to tomato to cherry is 3 to 5 to 4.
That means for some number x,
we have 3x pineapple, 5x tomato, and 4x cherry.
We are asked to find the total number which is 3x+5x+4x which is equal to 12x.
We are given that there are 80 tomato and we also have 5x tomato. These two expressions are therefore equal and we need to solve 80=5x which leads to x=80/5=16.
So the total amount is 12x=12(16)=192.
write an equivalent logarithmic equation for e^x=24
Answer:
x=ln 24
Step-by-step explanation:
e^x=24
If we take the ln of both sides
ln e ^x= ln 24
x=ln 24
Please give real answers with an explaination. 30 points + I will give brainliest. No Docs/No Files/No Links only answer with explaination.
Answer:
I'm not the best at explaining but I'll try my best. The x value to the bottom right is 61 degrees because the two sides are equal. Knowing that, there are 180 degrees in a triangle and 61 degrees plus 61 degrees adds up to 122. So, the value for x at the top is 58 degrees.