Answer:
x = -4.5
Step-by-step explanation:
Given:
0.1x + 0.008 = 0.06x − 0.172
Collect like terms
0.1x - 0.06x = -0.172 - 0.008
0.04x = - 0.18
x = -0.18/0.04
x = -4.5
Check:
0.1x + 0.008 = 0.06x − 0.172
0.1(-4.5) + 0.008 = 0.06(-4.5) - 0.172
- 0.45 + 0.008 = -0.27 - 0.172
-0.442 = -0.442
The graph of y = x4 – 2x2 + 1 is shown.
On a coordinate plane, a curved line has two minimum values at (negative 1, 0) and (1, 0) and one maximum value. Point A is at (negative 0.5, 0.5), point B is at (0, 1), point C is at (1, 0), and point D is at (1.6, 3).
Which point is a relative maximum?
A
B
C
D
Answer:
B
Step-by-step explanation:
relative maximum
is
the highest point after it comes from infinity
and
the highest point before it goes back to infinity
Find all solutions to the equation
in the interval [0, 21). Enter the
solutions in increasing order.
sin 2x = 2 sin x
x = [?],[1]
TT
Remember: sin 20 = 2 sin 0 cos 0
Answer:
[tex]x=0, \\x=\pi[/tex]
Step-by-step explanation:
Recall the trigonometric identity [tex]\sin 2x=2\sin x\cos x[/tex].
Therefore, given [tex]\sin 2x=2\sin x[/tex], rewrite the left side of the equation:
[tex]2\sin x\cos x=2\sin x[/tex]
Subtract [tex]\sin x[/tex] from both sides:
[tex]2\sin x\cos x-2\sin x=0[/tex]
Factor out [tex]2\sin x[/tex] from both terms on the left:
[tex]2\sin x(\cos x-1)=0[/tex]
We now have two cases:
[tex]\begin{cases}2\sin x=0, x=k\pi\text{ for }k\in \mathbb{Z}\\\cos x-1=0,x=k2\pi\text{ for }k\in \mathbb{Z}\end{cases}[/tex]
Since the problem stipulates that [tex]x[/tex] is in the interval [tex][0, 2\pi)[/tex], we have:
[tex]\text{For }x\in [0, 2\pi):\\\sin x=0\rightarrow \boxed{x=0, x=\pi}\\\cos x-1=0\rightarrow \boxed{x=0}[/tex]
Recall that square brackets mean inclusive and parentheses mean exclusive. Therefore, [tex]2\pi \notin [0, 2\pi)[/tex].
determine if 5yx - 17xy are like terms
Step-by-step explanation:
yes they are because they have the same variables which are X& Y
Answer:
5yx-7xy
they are like terms, it's all multiplication just a different arrangement
5xy-7xy=-2xy
Step-by-step explanation:
hope this is helpful
On the unit circle, which of the following angles has the terminal point
coordinates.
A. 45
B. 135
C. 225
D. 315
Answer: C. 225
Step-by-step explanation:
A bakery offers 4 different flavors of cake, 3 types of icing, 6 toppings, and 3 different sizes. If one option is chosen from each list, how many different cakes are possible? *
Answer:
216 different cakes are possible.
Step-by-step explanation:
Given that a bakery offers 4 different flavors of cake, 3 types of icing, 6 toppings, and 3 different sizes, if one option is chosen from each list, to determine how many different cakes are possible the following calculation must be performed:
4 x 3 x 6 x 3 = X
12 x 18 = X
216 = X
Therefore, 216 different cakes are possible.
Factor 60 − 36w, to identify the equivalent expressions.
Step-by-step explanation:
60-36w6(10-6w)hope it helps
stay safe healthy and happy..Answer:
all of the answers are correct
Step-by-step explanation:
For the function G defined by G(x)=5x+3, find G(r+5)
Given function:
g(x) = 5x + 3Find
g(r+5)Substitute x with r = 5:
g(r + 5) = 5(r + 5) + 3 = 5r + 25 + 3 = 5r + 28
Answer:
G ( r + 5 ) = 5r + 28
Step-by-step explanation:
Given ;
G ( x ) = 5x + 3
To Find :-
G ( r + 5 )
Solution :-
plug r + 5 as x in the function.
G ( r + 5 ) = 5 ( r + 5 ) + 3distribute 5
G ( r + 5 ) = 5r + 25 + 3combine like terms
G ( r + 5 ) = 5r + 28HELPP!
The functions f(x) and g(x) are described using the following equation and table:
f(x)=-4(1.09)x
Answer:
A: The y-intercept of f(x) is equal to the x-intercept of g(x)
Step-by-step explanation:
From the equation of f(x) given, we have;
f(x) = -4(1.09)^(x)
Now,the y-Intercept will be the point where x = 0.
Thus;
f(0) = -4(1.09)^(0)
f(0) = -4
Now,from the table given for g(x), we can see that at x = 0,g(x) = -4.
Thus,it means that the y-intercept of f(x) is equal to the x-intercept of g(x)
If f(x) = k where k is a constant, and the points (6,1) and (8,1) lie on the graph of y = f(x), what is the value of f(0)?
I think the answer is 1 but not 100% sure.
Answer:
The value of f(0)=1
Step-by-step explanation:
We are given that
[tex]f(x)=k[/tex]
[tex]y=f(x)[/tex]
(6,1) and (8,1) lies on the graph of y=f(x)
We have to find the value of f(0).
[tex]f(6)=1[/tex]
[tex]f(8)=1[/tex]
[tex]f(x)=k[/tex]
By comparing ,we get
k=1
Therefore, [tex]y=f(x)=1[/tex]
Now, substitute x=0
[tex]f(0)=1[/tex]
Hence, the value of f(0)=1
Priya has planted a garden shaped like a right triangle. She knows that one leg of the triangle is 11 meters long and that the angle formed by that leg and the hypotenuse is 50 degrees . If Priya wants to build a fence around her garden. How many meters will she need? Round to the nearest hundredth and you must submit work to receive credit.
Answer:
She will need 41.22 meters.
Step-by-step explanation:
She knows that one leg of the triangle is 11 meters long and that the angle formed by that leg and the hypotenuse is 50 degrees .
The leg is adjacent to the hypothenuse. We know that the cosine of an angle [tex]\theta[/tex] is given by:
[tex]\cos{\theta} = \frac{l}{h}[/tex]
In which l is the length of the adjacent side and h is the hypothenuse.
Considering that we have [tex]\theta = 50, l = 11[/tex], we can find the hypothenuse.
Looking at a calculator, the cosine of 50 degrees is 0.6428.
So
[tex]0.6428 = \frac{11}{h}[/tex]
[tex]0.6428h = 11[/tex]
[tex]h = \frac{11}{0.6428}[/tex]
[tex]h = 17.11[/tex]
The other leg:
In a right triangle, with legs [tex]l_1[/tex] and [tex]l_2[/tex], and hypothenuse h, the pythagorean theorem states that:
[tex]l_1^2 + l_2^2 = h^2[/tex]
We already have one of the legs and the hypothenuse, so:
[tex]11^2 + l^2 = 17.11^2[/tex]
[tex]l^2 = 17.11^2 - 11^2[/tex]
[tex]l = \sqrt{17.11^2 - 11^2}[/tex]
[tex]l = 13.11[/tex]
How many meters will she need?
This is the perimeter of the garden, which is the sum of its dimensions, of 11 meters, 13.11 meters and 17.11 meters. So
[tex]P = 11 + 13.11 + 17.11 = 41.22[/tex]
She will need 41.22 meters.
Casey wants to buy a gym membership. One gym has a $150 joining fee and costs $35 per month. Another gym has no joining fee and costs $60 per month. When would Casey pay the same amount to be a member of either gym? How much would he pay?
Answer:
x=6
Step-by-step explanation:
150+35x=60x
-35x -35x
150= 25x
Please help me!
The Farmer's Ranch House
9. The farmer's house is shown in the diagram below. He wants to build a screened-in patio on the back of his house.
Use the figure to answer the questions. (6 points)
a The area of the patio is planned to be (x + 10x - 200) square feet. What will the length be?
Patio
Patio
**10) - 0-10)
Original
House
b.
What is the area of the original house in simplest form?
Terigth
c
The farmer decides to extend the width of the patio. The area of the patio with the extension is now (x2 + 12x-160) square feet. By how
many feet will the patio be extended from what you found in part a?
Answer:
The answer is below
Step-by-step explanation:
a) The patio is in the form of a rectangle. The patio has a width of (x - 10) ft. Therefore given that the area of the patio is x² + 10x - 200, hence:
[tex]Area=length*breadth\\\\x^2+10x-200=length*(x -10)\\\\x^2+20x-10x-200=length*(x -10)\\\\x(x+20)-10(x+20)=length*(x -10)\\\\(x-10)(x+20)=length*(x -10)\\\\length=x +20[/tex]
b) Area of original house = length of house * breadth of house
The length of house = length of patio = x + 20; breadth of house = x + 10; therefore:
Area of original house = (x + 20)(x + 10) = x² + 10x + 20x + 200
Area of original house = x² + 30x + 200
c) If the width is extended, hence:
[tex]Area=length*breadth\\\\x^2+12x-160=(x+20)*width\\\\x^2+20x-8x-160=(x+20)*width\\\\x(x+20)-8(x+20)=(x+20)*width\\\\(x-8)(x+20)=(x+20)*width\\\\width=x-8\\\\Extended \ width=(x-8)-(x-10)\\\\Extended \ width=2\ feet[/tex]
2.4x-15=1
3. 2y+3= -11
4.2y+7= -7
5. 3w+3=3
Answer:
2. x=4
3. y= -7
4. y = -7
5. w = 0
Step-by-step explanation:
2.
4x-15=1
4x=16
x=4
3.
2y+3= -11
2y=-14
y= -7
4.
2y+7= -7
2y = -14
y = -7
5.
3w+3=3
3w = 0
w = 0
If g(x) = 2 |x| − 1, what is g(−2.3)?
Answer:
g(-2.3) = 3.6
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
g(x) = 2|x| - 1
Step 2: Evaluate
Substitute in x [Function g(x)]: g(-2.3) = 2|-2.3| - 1Absolute values: g(-2.3) = 2(2.3) - 1Multiply: g(-2.3) = 4.6 - 1Subtract: g(-2.3) = 3.6Solve the equation. Where necessary, indicate when the equation has no solution or is an identity.
5(2X + 8) - 5x = 5(5x + 6)
Answer:
x=0.5
Step-by-step explanation:
10x-40-5x=2x+30
5x+10=25x
10=20x
x=0.5
80 divided by 1.94 ≈
Answer:
41.34
Step-by-step explanation:
80/1.94
= 41.34
Given triangles MNP and QRP are similar triangles, and side MN equals 16 in and QR equals 48 in, what is the scale factor of the dilation from triangle MNP to QRP? "
Answer:
Scale Factor 3
Step-by-step explanation:
According to the Question,
Given That, triangles MNP and QRP are similar triangles, and side MN equals 16 in and QR equals 48 .Therefore, the scale factor of the dilation from triangle MNP to QRP is
Scale Factor = QR/MN ⇒ 48/16 ⇒ Scale Factor 3a man buys a car for rs 80000 and spends rs 20000 more for repairing He sells it for rs 125000.find his gain percent
Step-by-step explanation:
rs 80000+rs 20000=100000
rs 125000-rs 100000=25000
rs 25000÷rs 125000=0.2
0.2 × 100= 20%
Answer: 20%
Answer:
20%
Step-by-step explanation:
Use arthmetic, comes out as 0.2 = 20%
the amount of snowfall in jan was 2 3/4 feet. the amount of snowfall in february was 1 2/3 feet. how much snow fall was there in january? (write answer in the simplest form)
Answer this is an example 4 you
To do this problem, you need to change the way the fractions are displayed so that you can simplify them.
The first step is to change them to improper fractions: fractions like 4/3 that represent more than 100% (parts adding to more than one whole).
For example, to change the first fraction in this way, multiply the number in front (2) by the bottom number:
2 * 3 = 6
This means the 2 can also represent 6 / 3. Remember that 1 equals 3/3 so 2 equals 6/3. Now add this to the 1/3 you started with, and you end up with 7/3.
Do the same for the other fraction.
Now that you have both fractions written in this way, you can multiply each by the other's denominator to arrive at their LCD (least common denominator). It won't always be least, but you can always simplify further. In this case, the numbers are small enough that it likely won't matter.
You will end up with a fraction of halves: some number x, over 2, meaning x number of halves.
Your other fraction is 7/3. So the common denominator is the bottom numbers multiplied together: 2 * 3 = 6.
To change 7/3 to a fraction of sixths, you multiply the whole thing by two. This gets the bottom number to be six.
7 * 2 = 14
3 * 2 = 6
So this fraction can also be written as 14/6. Once again, do the same to the other fraction (but multiply by 3, to get the other fraction into sixths also, since it is currently halves).
Now you have two fractions that are both in parts of six. A ratio (x:y) is nothing more than a fraction itself. So if you had for example the ratio
2/5 : 10/5
This ratio could also be written as 1/5 : 5/5, or 1/5 to 1. Both numerators (the top number) are divisible by 2, so you can divide them both by 2 and end up with a simplified version of the same ratio.
Whatever ratio you end up with (14/6 : some other fraction), do the same thing to it. See if any of the numbers share a common factor, and simplify where possible. If it's not possible to simplify further, you're done.
A certain area can support 124 deer. Initially, there were 2 deer in the area, and the number has been growing at an average rate of 10% per month. Approximately how long will it take for the deer to have a population of 76, assuming logistic growth
Answer:
≈ 38.16 monthsStep-by-step explanation:
Initial number of deer = 2Growth rate is 1.1 times as 100% + 10% = 110% = 1.1Target number is 76.The equation of the growth is:
d(n) = 2*1.1^nSince the target number is 76 we get:
2*1.1^n = 761.1^n = 38log 1.1^n = log 38n = log 38/log 1.1n ≈ 38.16Answer: 46 months
Step-by-step explanation:
A circle has a central angle of 6 rad that intersects an arc of length 14 inches. Which equation find the length of the radius, R, of the circle?
Answer:
Step-by-step explanation:
θ=l/r
where θ is central angle in degrees.
l=length of arc.
r=radius of circle.
6=14/r
6r=14
r=14/6=7/3 =2 1/3 inches.
modrater give answer
if 107x = 22224446668880
Thane value of 1x
22224446668880÷107=207705109054.19
Answer:
[tex]107x = 22224446668880 \\ x = \frac{22224446668880}{107} \\ x = 0.0207705109[/tex]
PLEASE HELP ASAP
In the diagram below, ΔABC ≅ ΔSTR. Complete the statement BC ≅
A. AC
B. TR
C. ST
D. SR
Answer:
a
Step-by-step explanation:
The complete statement is BC ≅ TR.
What is triangle theorem?In mathematics, the Pythagorean theorem, or Pythagoras' theorem, exists a fundamental relation in Euclidean geometry among the three sides of a right triangle. It expresses that the area of the square whose side exists the hypotenuse stands equivalent to the sum of the areas of the squares on the other two sides.
Using the similarity of triangle theorem BC ≅ TR
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What is the y-intercept of the line 10x - 5y = 40
10x - 5y = 40
-5y = -10x + 40 || : (-5)
y = 2x - 8
Among 1,200 Chinese tourists who are visiting Nepal,45 of them already visited India,40 have visited Pakistan and 15 have visited both the countries. Illustrate this information in a venn_diagram and How many tourists have not visited any of these two countries.
30 visited nepal only 25 visited Pakistan only. 15 tourists at the intersection of the two circles and 1130 have not visited either
Answer:
We're provided - Total number of Chinese tourist = 1200 i.e n ( U ) = 1200 , number of Chinese who visited India = 45 i.e n ( I ) = 45 , number of Chinese tourists who visited Pakistan = 40 i.e n ( P ) = 40 & number of tourist who have visited both Pakistan and India = 15 i.e n ( I ⋂ F ) = 15. We're asked to find out the number of tourist who have not visited any of these two counties i.e [tex] \tt{n( \overline{i \:⋃ \: f}) = 15}[/tex].[tex] \large{ \tt{✽ \: SOLUTION}} : [/tex]
[tex] \large{ ✺ \: \tt{n(U) = n(I) + n(P) - n(I ⋂\: P) + n \: ( \overline{I \:⋃ P }\: )}}[/tex]
[tex] \large{ \tt{⟹ \: 1200 = 45 + 40 - 15 + n \: ( \overline{ I \: ⋃ P})}}[/tex]
[tex] \large{ \tt{⟹1200 = 70 + n \: ( \overline{ I \:⋃ P)}}}[/tex]
[tex] \large{ \tt{⟹ \: 1200 - 70 = n \: ( \overline{I\: ⋃ \: P})}}[/tex]
[tex] \large{ \tt{⟹1130 = n \: ( \overline{I \: ⋃ \: P})}}[/tex]
Hence , 1130 Chinese tourists have not visited any of these two countries. [ See the attached picture for Venn diagram ]- Hope I helped! Let me know if you have any questions regarding my answer and also notify me , if you need any other help! :)
Two triangles are similar. A side of one is 2 units long. The corresponding side of the other is 5 units long. What is the ratio of:
A) their perimeters?
B) their areas?
Answer:
b
Step-by-step explanation:
what is the correct length and width for the rectangle?
Answer:
Length = 14
Width = 7
Step-by-step explanation:
Length of a rectangle is twice its width.
let, the width be x, so the length becomes 2x
now the perimeter is 42, and we know the formula to find the perimeter is 2(length+width)
so, 2(2x+x)=42
or, 2×3x=42
or, 6x=42
or, x=7
so the width is 7 and the length is, 2×7 = 14
Answered by GAUTHMATH
A certain forest covers an area of 3600km^2. Suppose that each year this area decreases by 6%. What will the area be after 8 years?
Answer:
= 1728km2
Step-by-step explanation:
From the formula A = PRT/100%
Where; A is final
P is initial
T is time taken
R is the rate
Therefore A = 3600 × (6/100) × 8
= 1728km2
Express 200 g as a percentage of 4 kg
Answer:
5%
Step-by-step explanation:
Both should be in same measurement. so convert 4 kg to gram
1 Kg = 1000 g
4 kg = 4 * 1000 = 4000 g
[tex]\frac{200}{4000}*100=\frac{2}{40}*100\\\\=\frac{1}{20}*100 = 1 * 5\\[/tex]
= 5%
the school is located 0.8 miles west of willows house the park is 1.5 miles north what is the distance between willows house and the park
Answer:
0.7
Step-by-step explanation:
1.5 - 0.8 = 0.7 :)) hope u get it right!!!
The distance between the school and the park will be 0.7 miles.
What is the distance?Distance is defined as the length between the two points just like in the question it is the length between the school and the park.
Given that:-
The school is located 0.8 miles west of willows house The park is 1.5 miles northThe distance will be calculated as:-
Distance = 1.5 - 0.8 = 0.7 miles
Therefore the distance between the school and the park will be 0.7 miles
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