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Explanation:
In math, the term "substitution" basically means "replace". Keep in mind that x is a placeholder for a number. Think of it as a box we place a number inside.
We have the items {6, 16, 24} to use as replacements for x. We only do one number at a time
Let's try x = 6
4 + x < 20
4 + 6 < 20 ... replace x with 6
10 < 20 ... this is a true statement as 10 is less than 20
So x = 6 is a solution
Let's try x = 16
4+x < 20
4+16 < 20
20 < 20 ... this is false because we can't have a number smaller than itself
Lastly, let's try x = 24
4+x < 20
4+24 < 20
28 < 20 ... also false; 28 is not smaller than 20
We've shown that x = 16 and x = 24 are not solutions. Only x = 6 is a solution from the set {6,16,24}. This is why the answer is choice B.
-----------------
Alternative method:
4+x is the same as x+4. We can add two numbers in any order we want.
x+4 < 20 solves to x < 16 after subtracting 4 from both sides. So the set of solutions is anything smaller than 16. Looking at {6,16,24} we see that the only allowed answer is x = 6.
x = 16 is not a solution because x < 16 would turn into 16 < 16, but again we can't have a number smaller than itself.
kindly help me with this
evaluate the integral
[tex] \gamma \binom{2}{1} \frac{2x}{{x}^{2} + 1} dx[/tex]
Answer: ln5 - ln2 ≈ 0.919
Step-by-step explanation:
[tex]\int\limits^2_1 {\dfrac{2x}{x^2+1}} \, dx\qquad \qquad =\int\limits^2_1 {(x^2+1)^{-1}} \, 2xdx[/tex]
Let u = x² + 1 → du = 2x
[tex]\text{Then we have:}\quad \int\limits^2_1 {u^{-1}} \, du \qquad =ln|u|\bigg|^2_1[/tex]
Substitute u = x² + 1
[tex]ln|x^2+1|\bigg|^2_1\quad =ln|2^2+1|-ln|1^2+1|\quad = ln|5|-ln|2|[/tex]
Find the critical numbers for f(x)=cos(x)+sin^2(x) on the interval [0,2pi]
Answer:
Step-by-step explanation:
Rad [0,2[tex]\pi[/tex]]
f(x)=cos(x)+sin²(x)=cos(x)+1-cos²(x)
--[cos(x)-1/2]²+5/4=f(x)
when cos(x)=1/2,the f(x) has Max=5/4
cos(x)=1/2,x=[tex]\pi[/tex]/3(Rad) or 60°(Deg)
Simplify
(5/7)a²+13-(5/7)a-3
Answer:
c
Step-by-step explanation:
combine like terms:
5/7a^2+-5/7a+10
HOPE THIS HELPS!!!!!!:)
The slope is the rate of change for temperature. If the temperature increases (gets hotter) as the distance from the surface increases, then the slope is positive. If the temperature decreases (gets colder) as the distance from the surface increases, then the slope is negative. What is the slope of your equation?
Answer:
add pic
Step-by-step explanation:
Answer:
m=6.5
Step-by-step explanation:
thats what you type in
what is the slope line through (0, 5) and (-2, -1)
Answer:
3 or 3/1
Step-by-step explanation:
Slope is also known as rise/run.
The formula used to find slope is y^2-y^1/x^2-x^1.
The work is below:
-1-5/0-2
-6/-2
3/1
m=3
When we calculate the slope using the formula, we find that the slope(m) equals to 3/1 or 3 which means that you rise up by 3 and run to the right 1.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
The slope of the line through (0, 5) and (-2, -1) will be 3 or 3/1.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same). A measure of steepness is a slope. When building roads, one must determine how steep the road will be. These are some examples of slopes in real life.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given the line is passed through the following points,
(x₁,y₁)=(0, 5)
(x₂,y₂)=(-2, -1)
The slope of the line is found as,
m=(y₂-y₁) / (x₂-x₁)
Substitute the given values,
m=-(1-5)/(0-2)
m=(-6)/(-2)
m=3/1
The slope(m) equals 3/1, or 3 when we compute the slope using the formula, meaning that you rise up by 3 and move to the right by 1.
Thus, the slope of the line through (0, 5) and (-2, -1) will be 3 or 3/1.
Learn more about the slope here:
brainly.com/question/3605446
#SPJ2
Tim wants to build a rectangular fence around his yard. He has feet of fencing. If he wants the length to be twice the width, what is the largest possible length? Write an equation and solve.
Answer:
how many feet of fencing does he have?
\
Step-by-step explanation:
please help me immediately
Step-by-step explanation:
[tex]diameter \: = \sqrt{ { 24}^{2} + {7}^{2} } = 25 [/tex]
[tex]shaded \: area \: = circle - tringle[/tex]
[tex]shaded \: area = ( \frac{\pi}{4} \times {25}^{2} ) - ( \frac{1}{2} \times 7 \times 24)[/tex]
[tex]shaded \: area \: = (490.6) - (84) = 406.6 \: = 407 \: {cm}^{2} [/tex]
Suppose that 24 inches of wire costs 72 cents. At the same rate, how much (in cents) will 38 inches of wire cost?
Answer:
114
Step-by-step explanation:
if,
24inches=72cents
38inches=?
we cross multiplication,
38times72=2736 divide with 24=114
The answer is114
Answer:
114............
Step-by-step explanation:
(will give brainliest) Find the area of the shaded regions.
Answer:
84.78cm^2
Step-by-step explanation:
first we do pi*r^2.
3.14*6^2=113.04
Then, because we know that 1/4 of the circle is missing, just multiply 113.04 by .75.
113.04*.75=84.78cm^2
Answer:
84.78cm^2
Step-by-step explanation:
What is the length of the short leg in the 30-60-90 triangle shown below?
Answer:
it is D. 5
Step-by-step explanation:
The long side (B) will always be (A root 3) meaning, if you just take away the square root of 3, then you get the short side A
Answer:
[tex]\boxed{Shortest\ Leg = 5}[/tex]
Step-by-step explanation:
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Where θ = 60 , opposite = [tex]5\sqrt{3}[/tex] and adjacent = shortest leg
=> Tan 60 = [tex]5\sqrt{3}[/tex] / shortest leg (Tan 60 = √3)
=> Shortest Leg = [tex]\frac{5\sqrt{3} }{\sqrt{3} }[/tex]
=> Shortest Leg = 5
Point Q is located at (-4, 6). Point R is located at (8, 6) What is the distance from point Q to point R?
Answer:
12 units
Step-by-step explanation:
Notice that as we go from Q to R, x (the horizontal distance) increases by 12 and y (the vertical distance) does not change. Thus, the distance between the two points is merely the horizontal distance, 12 units.
find the length of the missing sides
Answer:
x = 4√3
y = 8√3
Step-by-step explanation:
This is a special 30° 60° 90° right triangle
In this special triangle if the side length that sees 30° is represented by x and the side length that sees 90° is represented by 2x and the side length that sees 60° x√3
Here, the side length that sees 60° is given as 12
12 = x√3 and x = 4√3 therefore y is 8√3
The hypotenuse of an isosceles right triangle is 4sqrt(2) units. How many square units are in the area of the triangle?
Answer:
8sqrt(2)
Step-by-step explanation:
An isosceles is a triangle with 2 45 degree angles and one 90 degree angle.
if the hypotenuse side=4sqrt(2) than that means the other 2 sides have to be just 4 units.
the formula for a triangle is than (base×height)÷2
4×4sqrt(2)=16sqrt(2)
(16sqrt(2))/2=8sqrt(2)
Answer:
19.595 units²
Step-by-step explanation:
Find length of other sides:
An isosceles triangle has 2 sides equal. It has two 45 degrees angles and one 90 degrees angle. We can use Pythagorean theorem.
[tex](4\sqrt{2} )^2 =a^2 +a^2[/tex]
[tex]32 =2a^2[/tex]
[tex]16=a^2[/tex]
[tex]4=a[/tex]
The 2 equal sides measure 4 units.
Find area:
base × height × 1/2
The height can be found by Pythagorean theorem.
height² = 4² + 4sqrt(2)²
height² = 16 + 32
height² = 48
height = 6.928
base is given
4sqrt(2) × 6.928 × 1/2
= 19.595343
bob has to pack 192 boxes. this morning, he packed 84 boxes in 3 1/2 hours. if bob continues at the same rate, how long will it take him to pack the remaining boxes?
Answer:
4.5 hours
Step-by-step explanation:
Total number of boxes = 192
84 boxes = 3.5 hours
Remaining boxes = (192 - 84) = 108 boxes
84 boxes = 3.5 hours
1 box = (3.5 ÷ 8) hours
108 boxes = 3.5 × 108/84
108 boxes = 4.5 hours (Answer)
Answer:
4.5 hours! The person above me is is correct.
Step-by-step explanation:
Which statement is true of triangles P and Q? Triangle P has side lengths of 6, 8, 10 and angle measures of 53.1 degrees, 90 degrees, 36.9 degrees. Triangle Q has side lengths of 18, 24, 30 and angle measures of 53.1 degrees, 90 degrees, 36.9 degrees.
Answer:
Triangle P and Triangle Q are mathematically similar shapes (?).
Step-by-step explanation:
Hi, so the question asks which statement is true, given the following information, but you haven't written what statements we can choose from.
After reading the information, we can see that Triangle Q is the same shape as Triangle P but just larger.
I'm assuming that one of the statements given is about Triangle P and Triangle Q being mathematically similar shapes?
If you need to show your working out, here it is:
18 ÷ 6 = 3
24 ÷ 8 = 3
30 ÷ 10 = 3
All the angles are the same.
This means that the length scale factor is +3 from Triangle P to Triangle Q, the area scale factor is +9 (because 3 x 3 = 9) from Triangle P to Triangle Q, and that the two shapes are mathematically similar.
*DISCLAIMER* The majority of question askers on Brainly seem to be from the US, and I'm not, so the way I work things out / the mathematical terms I use might be different. Sorry!
Hope this helped anyway!
Bluey :)
Answer:
It's c
Step-by-step explanation:
already did this
What is the slope of the line shown on the graph? A)3 B)1/3 C)−3 D)−1/3
Answer:
1/3
Step-by-step explanation:
The slope of the line is found by
m = (y2-y1)/(x2-x1)
we have two point ( 0,0) and ( 3,1)
= ( 1-0)/( 3-0)
= 1/3
Suppose Tom has 18 coins totaling $3.00. If he has only dimes and quarters how many of each type does he have
Answer:
8 dimes and 10 quarters
Step-by-step explanation:
Answer:
8 quarters and 10 dimes
Step-by-step explanation:
8 quarters = $2 + 10 dimes = $1 = 18 coins and $3
What happens when the multiplicity of a real root is odd?
Answer:
A: the graph will cross the x-axis
Answer:
A: the graph will cross the x-axis
Step-by-step explanation:
Here are the shopping times in minutes) of a sample of 19 shoppers at a local grocery store.
45, 22, 34, 30, 28, 27, 33, 35, 40, 26, 41, 29, 42, 44, 25, 46, 32, 38, 36
Draw the histogram for these data.
Frequency
Х
6
?
6-
5-
4
3
0
0
0
0
0
0-
22-26
37-41
42-46
27-31 32-36
Times (in minutes)
Answer:
22-26: frequency = 3
27-31: frequency = 4
32-36: frequency = 5
37-41: frequency = 3
42-46: frequency = 4
Please help and explain!! I really don't get this
Translate the following into an algebraic expression: A number is 30% of 20% of the number x.
Answer:
.06x
Step-by-step explanation:
So 20 percent of x has to first be represented. So would do .2x. So then we have to find 30% of that number. So we multiply .2x*.3 and we get 0.06x.
I believe this is correct but tell me if I'm wrong
Answer:
0.06x
Step-by-step explanation:
.2x*.3=0.06x
help me plzzzz i need help i need help right now right now
Answer:
the third one is correct
A lion can eat a sheep in 2 hours, a wolf can eat a sheep in 3 hours, and a dog can eat the sheep in 6 hours. How long would it take a lion, a wolf, and a dog all together to eat the poor sheep?
Answer:
1 hour
Step-by-step explanation:
The lion's speed is 1 sheep / 2 hours = ½ sheep/hour.
The wolf's speed is 1 sheep / 3 hours = ⅓ sheep/hour.
The dog's speed is 1 sheep / 6 hours = ⅙ sheep/hour.
Their combined speed is ½ + ⅓ + ⅙ = 1 sheep/hour.
So working together, it will take them 1 hour to eat 1 sheep.
Answer:
1 hour
Step-by-step explanation:
1/2 + 1/3 + 1/6 = 1
Which is the factored form of 64p3 + 125?
Select one:
O a. (4p + 5)2
O b. (4p + 5)(16p? + 20p + 25)
O c. (4p - 5)(16p² – 20p + 25)
O d. (4p + 5)(16p– 20p + 25)
Answer:
q .no d
Step-by-step explanation:
64p^3+125
4p^3+ 5^3
(4p+ 5 ) ( 4p^2- 4p *5 + 5^2)
(4p+5) (16p- 20p+ 25)
Answer:
The answer is
(4p + 5)( 16p² - 20p + 25)Step-by-step explanation:
64p³ + 125
Write the number in exponential form of 3
That's
4³p³ + 5³
Multiply the terms
That's
(4p)³ + 5³
Using the formula
a³ + b³ = ( a + b)(a² - ab + b²)Factor the expression
That's
( 4p + 5 )[ (4p)² - 4p(5) + 5²) ]
Solve the terms in the bracket
We have the final answer as
(4p + 5)( 16p² - 20p + 25)Hope this helps you
What is the solution to the equation 32x − 1 = 243? Question 18 options: A) x = 2 B) x = 3 C) x = 4 D) x = −2
Answer:
x = 4
Step-by-step explanation:
To solve this equation, first you want to write the whole thing out.
32x - 1 = 243
Next you want to get the variable by itself, so you are going to use inverse operations. in the equation, it is 32x - 1, so you are going to add one to both sides, getting you this:
32x = 244
Now for the final step you are going to get x alone, so you are going to use inverse operations once more and divide 32 on both sides getting you your answer.
x = 4
Now if you want to check your work simply plug in x, and if it is equal, you got the correct answer!
I hope this helped and good luck with your math!
I'm really sorry if I'm wrong though, even though I already finished this unit a while ago I struggled on this one even though it is so easy compared to the equations I have now.
Answer:
x=3
Step-by-step explanation:
Find the exact value of the following. The distance traveled by a car going 65 miles per hour for 3.5 hours is ____ miles.
Answer:
227.5
Step-by-step explanation:
D=ST so X= 65 x 3.5 = 227.5 miles
D=Distance = x
S=Speed = 65
T=Time = 3.5
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!
Answer:
2. x = -16 y = -10.5
3. x = 4
4. x = 3 y = 2/9 or 0.2222222222222...
Step-by-step explanation:
2.
in my stategy, you plus -5x + 8y = -4 with 6x - 8y = -12
+8y and -8y could delete each other, then y will be gone.
-5x + 6y = 1x = x because -5 + 6 = 1
so then you could got x = (-4) + (-12) which means x = -16
if x = -16 that will then means
(-5) x (-16) + 8y = -4
80 + 8y = -4
8y = -4 - 80
8y = -84
y = -10.5
3.
This question has already given you that y = -5
that means, 3x + 6 × (-5) = -18
3x + -30 = -18
3x = -18 - (-30)
3x = 12
x = 4
4.
Like the 2. qestion, you first plus the 2 equation together,
+9y + -9y = 0
-7x + 4x = -3x
-19 + 10 = -9
than means
-3x = -9
x = 3
then put the x = 3 in one of the equation.
4 x 3 - 9y = 10
12 - 9y = 10
-9y = 10 - 12
-9y = -2
-7 x 3 + 9y = -19
-21 + 9y = -19
9y = -19 + 21
9y = 2
y = 2/9 or 0.2222222222...
Wish this could help you!
Answer:
Step-by-step explanation:
FIRST ,
ADD BOTH EQUATIONS
THEREFORE X=-16 , Y =-21/2
SECOND,
SUBSTITUTE Y=-5 IN EQN.1
THEREFORE X= 4 , Y=-5
THIRD ,
ADD BOTH EQUATIONS
THEREFORE X= 3 , Y= 2/9
MARK ME AS BRAINLIEST PLS...........................................
If you're good at trigonometry please help me with 10 a and b and show full working out ty ;)
Answer:gjcnlfjdk
Step-by-step explanation:
Please Help the question is below!!!
Answer:
A is right its acute angle
Step-by-step explanation:
because supplementary is 180
therefore A +B = 180
since we know A
B = 180- A
B = 73
which is an acute angle as its less than 90
pls mark me brainliest pls
Answer:
Step-by-step explanation:
(a) Acute
A=107 deg
B=?
given A+B=180
=> B=180-A
= 180-107
= 73
SO, B is an acute angle.
(SAT Prep) Find the value of x.
Answer: 40 degrees
Step-by-step explanation:
Since the rectangle is 90 degrees and we know that the line is 180 degrees if u add 90 and 50 it becomes 140. Now u subtract from 180 to get 40 hope that helps and is a correct answer :)