Answer:
length- 10cm, width- 5cm
Step-by-step explanation:
You want to convert this into an algebraic equation.
Since a=lw, in this case, 50=lw. Subbing (x+3) for l and (x-2) for w, we get the equation (x+3)(x-2)=50.
Using FOIL, we can expand the brackets to make x²-2x+3x-6=50 and collect like terms to x²+x-6=50.
We want all the numbers on one side (to use the null factor law), so we subtract 50 from both sides. This gives x²+x-56=0.
From there, we factorise it, which becomes (x-7)(x+8)=0. (I used the cross method for this)
With the null factor law, one of the brackets must be equal to 0, meaning x-7=0 or x+8=0. This gives x as either 7 or -8.
With measurement, units must be positive, meaning it has to be 7. We can sub this for x in the 2 equations (length and width) to get the answers.
Length=x+3 becomes 7+3, which is 10cm.
Width=x-2 becomes 7-2, which is 5cm.
**This content involves writing, expanding, and factorising quadratic equations, and the null factor law which you may wish to revise. I'm always happy to help!
A line has a slope of -8 and includes the points (-10, 0) and (-9, z). What is the value of Z?
Answer:
Step-by-step explanation:
Let L be the given line, then, with a slope of -8
L : y = -8x + b
where b is to be determined from the included point A(-10,0).
Substitute point A in L to get
0 = -8 (-10) + b
solve to get
b = -80
therefore
L : y = -8x -80
Now substitute B(-9,z) in L
z = -8(-9) - 80 = -8
Please help find the diagonal distance thank you
Answer:
[tex]\huge\boxed{c=17\ ft}[/tex]
Step-by-step explanation:
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have:
[tex]leg=15ft\\leg=8ft\\hypotenuse=c[/tex]
Substitute:
[tex]c^2=15^2+8^2\\\\c^2=225+64\\\\c^2=289\to c=\sqrt{289}\to c=17(ft)[/tex]
Using the box method solve (x-4)(5x+3
Answer:
= X(5x+3)-4(5x+3)
= 5x²+ 3x- 20x-12
= 5x²-17x-12
Answer:
5x(squared)-17x-20
Step-by-step explanation:
What is the square unit of this figure?
Answer:
58
Step-by-step explanation:
Area = Area of entire recangle - area of cut out
a = (10 * 7) - (6 * 2)
a = 70 - 12
a = 58
ANSWER PLZ WILL MARK BRAINLIEST!!!!!!
Answer:
3x^2
Step-by-step explanation:
two thirds take away one half
Answer:
0.16666666666 is the answer of two thirds take away one half.
Mario can eat 21 hot dogs in 6 minutes. At the same place, how many minutes would it take him to eat 35 hot dogs?
Answer:
10 minutes
Step-by-step explanation:
Mario can eat e21 hot dog in 6 minutes
Let 35 hot dog eats in x minutes :
[tex]\frac{35}{x} =\frac{21}{6} \\x=\frac{35(6)}{21} \\x=10 min[/tex]
Therefore, mario would eat 35 dogs in 10 min.
7X^2+20x=24
X=?
Please answer to 2 d.p
Answer:
0.76
or
-0.76
hope this helps
what percentage of this 100 square grid is shaded. PLease i will mark your brainlist
Informal settlers who live nearby coastal areas and river side throw away about 4 million disposable diapers per year. how many diapers are thrown away each month??.
need help ༼ つ ◕_◕ ༽つ
Answer:
333,333 Three hundred and thirty-three thousand , three hundred and thirty-three
Step-by-step explanation:
4000000/12
help me to do this please
Answer:
a) (10×13) + 55 b) 185 Nu c)-75 or -205 (unsure of instruction)
Step-by-step explanation:
a) He spends 10 Nu a day for 13 days, meaning he has spent 10×13 Nu. He originally had this amount, plus the 55 he ends up with. This means he began with (10×13) + 55.
b) This can then be solved using BODMAS (or PEMDAS, whatever you call the order of operations).
We begin with the multiplication, which turns the expression to 130+55. We then move to addition, giving a final result of 185.
c) For this one, I'm not sure if it is if he did that from the beginning or from now, so I've done both.
If it's from the beginning, you would use 185-(20×13) to solve this. This gives 185-260, which solves to -75.
If it's from the point of 55 Nu, you would use 55-(20×13), which gives 55-260. This solves to -205.
**You may wish to revise writing integer expressions. I'm always happy to help!
Hey, could you help me? Thank you
Answer:
Step-by-step explanation:
you see 12=12 (side)
6=6 (side)
116°=116°(angle between sides)
now what can be the answer?
two sides and one angle equal
so SAS
On George's block, the ratio of cars to houses is 8 to 5. There are 32 cars, how many houses are there?
Answer:
Step-by-step explanation:
20 houses
Answer:
20
Step-by-step explanation:
You would set it up as 8:5=32:x. Since you are multiplying the number of cars by 4, you should do the same with houses. This gives 32:20, meaning there are 20 houses on the block.
**You may want to revise multiplying and dividing with ratios. I'm always happy to help!
Which set of numbers is included as part of the solution set of the compound inequality
x < 6 orx > 10?
Complete question is;
Which set of numbers is included as part of the solution set of the compound inequality
x < 6 or x > 10?
A) {–7, –1.7, 6.1, 10}
B) {–3, 4.5, 13.6, 19}
C) {0, 6, 9.8, 14}
D) {8.5, 9.1}
Answer:
B) {–3, 4.5, 13.6, 19}
Step-by-step explanation:
The given compound inequality x < 6 or x > 10 means that x must be less than 6 and greater than 10. And also that x cannot fall between 6 and 10.
Looking at the given options, the only set of values that fall into this compound inequality range is option B.
Given tan t = 2/3 and that pi <= t <= 3pi/2. Find exact value for each of the following:
a) sec t
b) cos t
c) sin t
d) csc t
e) cot t
well, first off let's notice something about angle "t", is between π and 3π/2, or namely the III Quadrant, where both "x" or adjacent side as well as "y" or opposite side are negative.
something else noteworthy is that, the hypotenuse is just a radius length and thus is never negative.
[tex]tan(t)=\cfrac{2}{3}\implies tan(t)=\cfrac{\stackrel{opposite}{-2}}{\underset{adjacent}{-3}}\qquad \textit{let's find the hypotenuse} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c =\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{(-3)^2+(-2)^2}\implies c = \sqrt{9+4}\implies c = \sqrt{13}[/tex]
[tex]\rule{34em}{0.25pt}\\\\ sec(t)=\cfrac{\stackrel{hypotenuse}{\sqrt{13}}}{\underset{adjacent}{-3}}~\hfill cos(t)=\cfrac{\stackrel{adjacent}{-3}}{\underset{hypotenuse}{\sqrt{13}}}\implies \cfrac{-3\cdot \sqrt{13}}{\sqrt{13}\cdot \sqrt{13}}\implies \cfrac{-3\sqrt{3}}{13}[/tex]
[tex]sin(t)=\cfrac{\stackrel{opposite}{-2}}{\underset{hypotenuse}{\sqrt{13}}}\implies \cfrac{-2\cdot \sqrt{13}}{\sqrt{13}\cdot \sqrt{13}}\implies \cfrac{-2\sqrt{13}}{13} \\\\\\ csc(t)=\cfrac{\stackrel{hypotenuse}{\sqrt{13}}}{\underset{opposite}{-2}}~\hfill cot=\cfrac{\stackrel{adjacent}{-3}}{\underset{opposite}{-2}}\implies \cfrac{3}{2}[/tex]
Write an algebraic inequality. A number increased by three is less than twice that number.
If f(x) = x2 – 1, and
g(x) = x + 2, then
f(g(x)) = [ ? ]x2+[ ]x+]
Answer:
f(g(x)) = x^2+4x+3
Step-by-step explanation:
f(x) = x^2 – 1
g(x) = x + 2
f(g(x))=g(x)^2-1=(x+2)^2-1=x^2+4x+4-1=x^2+4x+3
What are the factors of x^2 + 8x + 12?
Answer:
(x+2)(x+6)
Step-by-step explanation:
that is the answer because math
=>x^2+8x+12
=>x^2+6x+2x+12
=>x(x+6)+2(x+6)
=>(x+6)(x+2)
Hope it helps you
Tina has a greenhouse in which she grows strawberries. The sprinkler system in the greenhouse sprays a fine mist to ensure the strawberries get enough water. The strawberries are watered for a total of 2 hours and 45 minutes every day and the temperature in the greenhouse is kept constant at 25 °C. The clock below shows the time each morning when the sprinkler system is switched off
Answer:
a) 9:11 am
b) 77°F
Step-by-step explanation:
a) From the clock shown in the image attached, we can see that the time that the sprinkler system is switched off is at 11:56 am. Since the strawberries are watered for a total of 2 hours and 45 minutes every day, the time that the sprinkler is switched on can be gotten by subtracting 2 hours 45 minutes from 11:56 am. Hence:
Time sprinkler system is switched on = 11:56 am - 2 hours 45 minutes = 9:11 am
b) Temperature in °Farenheit = (1.8 * temperature in degree Celsius) + 32°
Temperature in °Farenheit = (1.8 * 25°) + 32° = 45° + 32°
Temperature in °Farenheit = 77°F
Which square—large, medium, or small—covers more of the plane? In 2-3 sentences, explain your reasoning for choosing the large, medium or small square.
Answer:
The large square covers more
Step-by-step explanation:
Given
See attachment for squares
Required
Which covers more plane
The large square has the highest dimension and by extension, it has the highest area.
This means that, less large squares will be needed to cover more areas compared to other sizes of the squares.
Take for instance, the following analysis;
Large square
Dimension: 3 by 3;
[tex]Area=3*3 = 9[/tex]
Medium Square
Dimension: 2 by 2
[tex]Area = 2 * 2 = 4[/tex]
Small square
Dimension: 1 by 1
[tex]Area = 1 * 1 = 1[/tex]
The square with the largest area covers more of the plane.
Hence, the large square covers more of the plane
ILL GIVE YOU BRAINLIEST IF ANSWERED RIGHT!!!! If the quadratic equation has the form y = ax ^2and y = ax ^2+ c, then their axis of symmetry must always be?
Answer:
x = 0
Step-by-step explanation:
The axis of the symmetry has the same x coordinate of the vertex
V (x) = -b/2a
in both equations b is equal to 0 and a 0/a number different from 0 gives always 0 as a result
Find the surface area of a cylinder that has the following information:
Height = 30 cm
Diameter = 10 cm
Answer:
[tex]A=1099.56cm^{2}[/tex]
Step-by-step explanation:
Formula to ind surface area of cylinder:
[tex]A=2\pi \frac{d}{2} h+2\pi (\frac{d}{2} )^{2}[/tex]
[tex]A=2\pi \frac{10}{2} (30)+2\pi (\frac{10}{2} )^{2}[/tex]
[tex]A=1099.557443cm^{2}[/tex]
Therefore, area will be:
[tex]A=1099.56cm^{2}[/tex]
hope this helps :)
Imperial measurements help please
Answer:
1. a. miles or feet
b. inches
c. ounces
d. gallons
2. a. 1:36
b. 1/1
c. 63,360
Step-by-step explanation:
how to get the interval?
Step-by-step explanation:
Decide on the number of classes.
Determine the range, i.e., the difference between the highest and lowest observations in the data.
Divide range by the number of classes to estimate approximate size of the interval
hope it helps.
stay safe healthy and happy...A rectangular football field is 64 meters wide and 100 maters long. A player runs from one corner of the field in a diagonal line to the opposite corner. How far did the player run?
Answer:
119 or 118.726577
Step-by-step explanation:
We should use the Pythagorean Theorem to solve this problem.
a^2+ b^2=c^2
64^2+100^2=c^2
4096+10000=14096
c^2=14096
c=\sqrt{14096}14096
And the root of 14096 is 118.726577.
So the Answer is About 119 meters, or 118.726577
hope this helps!
2 x10^14/8x10^9
How do you solve
Answer:
Step-by-step explanation:
[tex]\frac{2*10^{14}}{8*10^{9}}=\frac{1}{4}*10^{14-9}=\frac{1}{4}*10^{5}\\\\\\\frac{a^{m}}{a^{n}}=a^{m-n}\\\\[/tex]
In exponent division , if bases are same, then find the difference of the exponents
please may I get help please
whish way should I use
Answer: B.
Step-by-step explanation:
Data: Estimate of 7.21x3.86/10.09=x
Only step, Find the estimate for each number(7.21=7, 3.86=4, 10.09=10)
Explanation: How estimation work is that it numbers below 5 stays the same and numbers 5 and above round up so a number like 7.21 which has 2 and 1 as it's rounding numbers will stay the same however a number like 3.86 which has 8 and 6 as it's rounding numbers will round up
That's how we arrive at the answer of B.
I hope this helps(Mark brainliest if you'd like)
which ratio is equivalent to the ratio 2:52
Answer:
1:26
Step-by-step explanation:
You can divide both sides by 2.
I really really need help on this, please help me
What is the radius of a sphere with a volume of 28526 in 3 , 28526 in 3 , to the nearest tenth of an inch?
Answer:
19.0 in
Step-by-step explanation:
From the question given above, the following data were:
Volume (V) of sphere = 28526 in³
Pi (π) = 3.14
Radius (r) =?
The radius of the sphere can be obtained as follow:
V = 4/3 πr³
28526 = 4/3 × 3.14 r³
28526 = 12.56r³ / 3
Cross multiply
12.56r³ = 28526 × 3
12.56r³ = 85578
Divide both side by 12.56
r³ = 85578 / 12.56
Take the cube root of both side
r = ³√(85578 / 12.56)
r = 19.0 in
Thus, the radius of the sphere is 19.0 in
