Answer:
[tex]F(x)=3x^2-1[/tex]
Step-by-step explanation:
We have been given the function [tex]G(x)=3x^2[/tex], it is shifted down 1 unit. Now, whenever a function is shifted up or down we just the idea of vertical shift which says:
To shift a function up by 'k' units we use:
[tex]g(x)+k[/tex]
To shift a function down by 'k' units we use:
[tex]g(x)-k[/tex]
Here, in our case we have to shift the function down by 1 unit, so we will subtract 1 from the function:
[tex]F(x)=G(x)-1=3x^2-1[/tex]
So the required function is [tex]3x^2-1[/tex].
Which inequality is equivalent to -m ≥ 15?
A. m ≥ 15
B. m ≥ -15
C. m ≤ -15
D. m ≤ 15
Answer:
c
Step-by-step explanation:
The inequality equivalent to -m ≥ 15 is m ≤ -15, achieved by multiplying both sides of the inequality by -1, which reverses the inequality symbol. So the correct answer is C. m ≤ -15.
The question asks which inequality is equivalent to the inequality -m ">≥ 15. To find the equivalent inequality where m is positive, we need to multiply or divide both sides of the inequality by -1, remembering that doing so reverses the inequality symbol. Therefore, multiplying both sides by -1 gives m ≤ -15, which means that the inequality that is equivalent to -m ≥ 15 is m ≤ -15.
So the correct answer is C. m ≤ -15.
Subtract the following polynomials
subtracting term by term
(3.1x - 4.3x ) + (2.8z - (- 1.2z ) )
= - 1.2x + (2.8z + 1.2z ) = - 1.2x + 5z
What is the value of –2x2 + 4y if x = –2 and y = 3?
You would first substitute x and y into the equation so: -2(-2)^2+4(3)
Then you solve:
-2(-2)^2+4(3)
8+12
so your answer will be 20
I WILL GIVE BRAINLYYYY PLS HELPPPPPPPPPPPPPPPPPP
Two planes left the same airport traveling in opposite directions. The first plane left at 9:00 a.m. and 2.25 hours later, the two planes were 1825 miles apart. The second plane left at 10:00 a.m. and its average rate was 108 miles per hour slower than the first plane's average rate. Let x represent the first plane's average rate. What was the first plane's average rate? Enter an equation that can be used to solve this problem in the first box. Solve for x and enter the first plane's average rate in the second box.
WHAT IS THE EQUATION AND WHAT IS THE ANSWERRR???
Answer:
The Average rate of the first plane is 560 mph
Step-by-step explanation:
x = first plane's average rate (in mph)
x−108 = second plane's average rate (in mph)
First planes total distance = 2.25x
Second planes total distance = 1.25(x−108)
2.25x + 1.25(x−108) = 1825
x = 560
Help please 7 an 8...........
Answer:
Question 7
Total area of the quadrilateral [tex]27[/tex].
Question 8
Angles on the side of a straight line adds up to 180°
Therefore we can write the sum of all the angles as;
[tex]x+4x+20=180[/tex]
Then you can solve the equation to find the [tex]x[/tex].
Step-by-step explanation:
(7)
First Plot the coordinates in the Cartesian plane. Then join all the points. Now you should get a graph as the graph shown in "red lines" in the attachment.
To make it easier we add another point in the graph as "E(2,3)". Now we have two shapes, one is a rectangle ABED and the other is a triangle BEC. Addition of these to makes the ABCD quadrilateral.
Before finding the areas we need to find the lengths of each side.
AB=3-(-1)=4
AD=BE=2-(-4)=6
EC=4-3=1
Area of ABED rectangle = AB*AD
=[tex]4*6[/tex]
=[tex]24[/tex]
Area of the BEC triangle= [tex]\frac{1}{2}[/tex]*BE*EC
=[tex]\frac{1}{2} *6*1[/tex]
=[tex]3[/tex]
Therefore, total area of the quadrilateral = [tex]24+3[/tex]
=[tex]27[/tex]
(8)
Angles on the side of a straight line adds up to 180°
Therefore we can write the sum of all the angles as;
[tex]x+4x+20=180[/tex]
Then you can solve the equation to find the [tex]x[/tex] as follows.
[tex]5x+20=180[/tex]
[tex]5x=160[/tex]
[tex]x=32[/tex]
Then you can find 4x° also by multiplying x by 4.
rearrange 2y=x into y=mx+b
You want to get y by itself
y=1/2 x
y=mx+b
m=1/2 b=0
y = [tex]\frac{1}{2}[/tex] x + 0
given 2y = x ( divide both sides by 2 )
y = [tex]\frac{1}{2}[/tex] x + 0
A book store has twice as many history books as science books. The store has 81 history and science books altogether how many of wach kind does the bookstore have? Write equation too....
let h= history books
science books = s
h=2s there are 2 times as many history as science so to get them equal we double the science
h+s=81 there are 81 total history and science books
2s+s=81 substitute 2s for h in the above equation
3s = 81 combine like terms
s = 27
There are 27 science books
h=2s
h=2(27)
h=54
there are 54 history books
Use order of operation to solve 4[2.5+3(20+7)]
Using order of operations , the expression ⇒4[2.5+3(20+7)] = 334
What is order of mathematical operations?Order of mathematical operations are done in order with respect to PEDMAS rule.
PEDMAS: Parenthesis → Exponents→ Division→ Multiplication→ Addition→ Subtraction.
it states that we will start will solving brackets or Parenthesis then will solve powers or exponents , then division and so on in the same order as given in PEDMAS rule
For given expression 4[2.5+3(20+7)]
First solve brackets (20+7)
⇒4[2.5+3(20+7)] = 4[ 2.5 + 3(27)]
Then solve bracket 2(27) = 81
⇒4[2.5+3(20+7)] = 4[ 2.5 + 3(27)] = 4[ 2.5 + 81]
Solve the bracket [ 2.5 +81]
⇒4[2.5+3(20+7)] = 4[ 2.5 + 81] = 4[83.5] = 334
Also, Learn more about order of operation from the link below:
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SHOW WORK
1) copper has density of 8.92 g/cm^3. How many milliliters of water would be displaced if 46kg of copper granules were poured into a barrel filled with water?
2) If the density of water is 1.00 g/mL, will the substances above float or sink in the water??
Answer:
1) Volume of water displaced = 5.16 L
2) Copper sinks in water.
Explanation:
1) Density of copper = 8.92[tex]g/cm^3[/tex]
Mass of copper = 46 kg = 46000 g
We know that, Density = Mass / volume
So, Volume = Mass/ density
Volume of copper = 46000/8.92 = 5156.95 [tex]cm^3[/tex]
Since the density of copper 8.92[tex]g/cm^3[/tex] is greater than density of water 1[tex]g/cm^3[/tex], the copper immerses in water. Since it immerses it will displace a volume of water which is equal to the volume of copper.
So volume of water displaced = volume of copper = 5156.95 [tex]cm^3[/tex] =5.16 L of water
2) Since the density of copper 8.92[tex]g/cm^3[/tex] is greater than density of water 1[tex]g/cm^3[/tex], the copper immerses in water. So copper sink in water.
Which statement about the graph of f(x)=e^x is true?Please Help
O It crosses the x-axis at e.
O It crosses the y-axis at e.
O It passes through the point (1,e).
O It passes through the point (e,1).
The function f(x) = e^x never crosses the x-axis and crosses the y-axis at point (0,1). It does not pass through the point (e,1), but it does pass through the point (1,e). Hence, the correct statement is 'It passes through the point (1,e)'.
Explanation:The function f(x) = e^x is an exponential function where 'e' is Euler's number, approximately equal to 2.71828. Its graph has distinctive traits which are related to the options provided.
The statements 'It crosses the x-axis at e' and 'It crosses the y-axis at e' are incorrect because the graph of f(x) = e^x never crosses the x-axis, and it crosses the y-axis at the point (0,1), not e.
The statement 'It passes through the point (e,1)' is also incorrect. This function, f(x) = e^x, will pass through the point (1,e), not (e,1). Hence, the option 'It passes through the point (1,e)' is the true statement about the graph of the function.
Learn more about exponential function here:https://brainly.com/question/15352175
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. The dimensions of a large broken window are 122⁄3 feet wide and 81⁄3 feet tall. How many square feet of glass are required to replace the window?
Answer:
[tex]1098[/tex] square feet of glass is needed to replace the window.
Step-by-step explanation:
Square feet is the unit of measure of Area. How many square feet of glass are required to replace the window can be found by calculating the area of the window.
Area of the window = Width * Length
=[tex]\frac{122}{3}*\frac{81}{3}[/tex]
=[tex]\frac{122*81}{3*3}[/tex]
=[tex]\frac{9882}{9}[/tex]
=[tex]1098[/tex] square feet.
∴ we need [tex]1098[/tex] square feet of glass.
1098 ft²
Area = width × height
= [tex]\frac{122}{3}[/tex] × [tex]\frac{81}{3}[/tex]
= [tex]\frac{122(81)}{3(3)}[/tex] = [tex]\frac{9882}{9}[/tex]= 1098 ft²
The temperature outside is 12 Celsius, overnight the temperature drops 15 degrees. What is the temperature now?
A bag contains 5 blue marbles, 3 red marbles and 4 yellow marbles.
What is the probability of choosing one yellow marble and then a red marble with replacement?
[tex]|\Omega|=12^2=144\\|A|=4\cdot3=12\\\\P(A)=\dfrac{12}{144}=\dfrac{1}{12}[/tex]
Answer:
Step-by-step explanation:
The longest side of an acute triangle measures 30inches. The two remaining sides are congruent, but their length is unknown. What is the smallest possible perimeter of the triangle, rounded out the nearest hundredth
The two short sides must be longer than those required in an isosceles right triangle. The ratio of side length to hypotenuse length in a 45°-45°-90° triangle is 1 : √2. So, such a triangle requires side lengths of 30/√2 ≈ 21.213 inches. Its perimeter will be about
... (30 +21.213 +21.213) in = 72.426 in
Since the perimeter needs to be slightly longer than that for the triangle to be acute, the smallest possible perimeter is ...
... 72.43 in
Find the quotient 4/15÷1/6
Answer:
1 3/5
Step-by-step explanation:
4/15÷1/6
Copy dot flip
4/15 * 6/1
24/15
Divide the top and bottom by 3
8/5
Change the improper fraction to a mixed number
5 goes into 8 1 time with 3 left over
1 3/5
1. Evaluate a/b + c^2d for a = 6,b=3,c=4,and d=5
A. 42
B. 18
C. 82
D. 360
2.What is the product? 6(-3)
A. -18
B. -3
C. 18
D. 9
3. Simplify the expression (4/7)^3
A. 343/64
B. 12/21
C. 12/49
D. 64/343
Will mark brainliest for correct answers :D
Answer:
1) C
2) A
3) D
Step-by-step explanation:
A) We substitute the values for a ,b , c and d in the given equation.[tex]\frac{6}{3} +4^2 (5) \\= 2+80\\=82[/tex]
Hence option c. 82 is the answer.
2) The product 6(-3)
Since positive x negative gives negative
we get -(6x3) = -18
Option A is the answer.
3) For this we have to find cube of a fraction with numerator 4 and denominator 7
We find cube of numerator first = 4x4x4 =64
Cube of denominator = 7x7x7 = 343
Hence cube of fraction = 64/343
Option D
72 is equal to 80% of a number n
Write and solve an equation to find n
Write the percent as a decimal.
Please Help
According to question
[tex] 80\% of n = 72[/tex]
Change percentage to decimal by dividing it by 100
[tex] (80\div100)\mul n=72[/tex]
[tex]0.80\times n =72[/tex]
Now, crossmultiply we get,
[tex] n = \frac{72}{0.80}[/tex]
Now sloving we get
[tex] n = 90[/tex]
Q#16 I need help please
For this case we have the following expressions:
[tex]x = -4y + 4\\\\2x + 8y = 8\\[/tex]
Rewriting the second equation we have:
[tex]2x = -8y + 8\\[/tex]
It is observed that by multiplying the first equation by 2, the second equation is obtained.
Thus, the equations are linearly dependent and since the lines are equal then they are intercepted in infinite points. Therefore, the system has endless solutions.
Answer:
Option D
Find the value of {2/3}^3 Explain or show how you got your answer.
[tex]\frac{8}{27}[/tex]
(2/3)^3 = [tex]\frac{2^{3} }{3^{3} }[/tex] = (2 × 2 × 2 )/(3 × 3 × 3 ) = [tex]\frac{8}{27}[/tex]
Answer:
Step-by-step explanation:
A company produces metal slabs for industrial use. the slabs come in 3 thicknesses: 5in, 10in, and 15in. the weights of each thickness for each metal are given below. metal 1: 150lbs, 300lbs, 600lbs metal 2: 130lbs, 260lbs, 390lbs metal 3: 310lbs, 620lbs, 930lbs metal 4: 140lbs, 280lbs, 420lbs for which of the metals is weight not proportional to thickness
Given slabs thicknesses 5in, 10in, and 15in.
Therefore, ratio of thicknesses in simplest form would be 1:2:3.
Metal 1 thicknesses = 150lbs, 300lbs, 600lbs
Dividing by 150, we get ratio of Metal 1 thicknesses = 1:2:4.
Metal 2 thicknesses = 130lbs, 260lbs, 390lbs.
Dividing by 130, we get ratio of Metal 2 thicknesses = 1:2:3.
Metal 3 thicknesses = 310lbs, 620lbs, 930lbs.
Dividing by 310, we get ratio of Metal 3 thicknesses = 1:2:3.
Metal 4 thicknesses = 140lbs, 280lbs, 420lbs.
Dividing by 140, we get ratio of Metal 4 thicknesses = 1:2:3.
We can see the ratios of thicknesses of Metal 1 are 1:2:4 but it should be 1:2:3.
Therefore, Metal 1 weight is not proportional to thickness.
Answer:
Weights of metal 1 is not proportional to thickness.
Step-by-step explanation:
We have been given 3 thicknesses of metal slabs and the weights of each thickness for each metal. We are asked to find out which of the metals weight is not proportional to thickness.
We can see that the thicknesses of slabs are first three multiples of 5 that is 5 inches, 10 inches and 15 inches.
Now let us see which of the metals have not their weights proportional to their thicknesses.
In our first option we can see that 300 is 2 times 150 and 600 is 4 times 150 which is not proportional to thickness. In order to metal 1's weight to be proportional with it's thickness it should be 450 lbs instead of 600.
Our second metal's weight is proportional to it's thickness as 130, 260 and 390 are 3 first consecutive multiples of 130.
Our third and fourth metal's weights are also proportional to their thicknesses.
Therefore, metal 1's weight is not proportional to thickness.
Rameen’s heating bill is $5.42 per month plus $1.08 per therm. How many therms can Rameen use if he wants his heating bill to be a maximum of $87.50? Write the solution in interval notation.
Write and solve an inequality:
Total(t) = $5.42 + ($1.08/therm)(t) ≤ $87.50.
First, subtract $5.42 from $87.50: then ($1.08/therm)(t) ≤ $82.08
Next, divide both sides by $1.08 per therm:
t ≤ ($82.08) / ($1.08/therm) = 76 therms (maximum). Thus, Rameen's usage could be [0,76] (therms).
Answer:
[0,76]
Step-by-step explanation:
Step 1. Read the problem.
Step 2. Identify what you are looking for.
the number of therms Rameen can buy
Step 3. Name what you are looking for. Choose a variable to represent that quantity.
Let t= the number of therms.
Step 4. Translate. Write a sentence that gives the information to find it. Translate into an inequality.
$5.42 plus $1.08 times the number of therms is less than or equal to $87.50.
5.42+1.08t≤87.50
Step 5. Solve the inequality.
1.08tt≤82.08≤76
Step 6. Check the answer in the problem and make sure it makes sense.
Yes, 5.42+1.08(76)=87.50.
Step 7. Answer the question with a complete sentence.
Rameen can buy no more than 76 therms if he wants his heating bill to be a maximum of $87.50.
Since it is not possible to buy a negative number of therms, the lest number of therms Rameen can buy is 0.
In interval notation, the amount of therms Rameen can buy is [0,76].
Use the identity a^3+b^3=(a+b)^3−3ab(a+b) to determine the sum of the cubes of two numbers if the sum of the two numbers is 4 and the product of the two numbers is 1.
Your identity says ...
... sum of cubes = (sum)³ -3(product)(sum)
... = 4³ -3·1·4
... = 64 -12 = 52
_____
The two numbers are 2±√3, and the sum of their cubes is indeed 52.
Simplify. 8√-76 Enter your answer, in simplest radical form, in the box.
Answer:
6i\sqrt{19}
Step-by-step explanation:
Divide. (5 1/4)÷(−2 1/2) Enter your answer as a mixed number, in simplified form, in the box.
Answer:
2 1/10
Step-by-step explanation:
(5 1/4)/(2 1/2)
Change mixed fraction to improper fractions
(21/4)/(2 1/2)
(21/4)/(5/2) =21/10
=2 1/10
Answer:
2 1/10
Step-by-step explanation:
What is the slope of a line that is perpendicular to line m
the slope of a perpendicular line = - [tex]\frac{3}{5}[/tex]
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange 5x - 3y = 2 into this form
subtract 5x from both sides
- 3y = - 5x + 2 ( divide all terms by - 3 )
y = [tex]\frac{5}{3}[/tex] x - [tex]\frac{2}{3}[/tex]
with slope m = [tex]\frac{5}{3}[/tex]
the slope of a line perpendicular = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{3}{5}[/tex]
Q # 4 if anybody can help me
Solution:
Given equation of line [tex]-4x+2y=24[/tex]
To find the x-intercept of the equation, substitute [tex]y=0[/tex] in the equation,
[tex]\Rightarrow -4x+2(0)=24\\\Rightarrow -4x=24\\\Rightarrow x=-\frac{24}{4} =-6[/tex]
Hence, x-intercept of the equation is [tex](-6,0)[/tex].
To find the y-intercept of the equation, substitute [tex]x=0[/tex] in the equation,
[tex]\Rightarrow -4(0)+2y=24\\\Rightarrow 2y=24\\\Rightarrow y=\frac{24}{2} =12[/tex]
Hence, y-intercept of the equation is [tex](0,12)[/tex].
I just posted three questions that are the same thing if you can give me the answer to it you'll have 3 of the same answers plus all the points a total of 25 points and I will Mark brainiest if you can answer the past three questions I posted they're all the same question can somebody please help I've been up all day and night I just want to go to bed can somebody please help
3.8 miles per week
the miles ran last month is 2.8
let 2.8 be original , that is 100%
an increase of 36.2% is then
100 + 36.2 = 136.2% = [tex]\frac{136.2}{100}[/tex] = 1.362
multiply 2.8 by this quantity
= 2.8 × 1.362 = 3.8 miles per week ( to nearest tenth )
Given: C∉ BD ,△ABC D∈ ray BC ,AB=AC=BC Prove: BD>DA>AB
Triangle ABC is equilateral, because AB=BC=AC=a. Then
m∠A=m∠B=m∠C=60°.
Let point D lie on the ray BC to the right from points B and C and let CD=x. Then BD=a+x, AB=a.
Consider triangle ACD. In this triangle, m∠ACD=180°-m∠ACB=180°-60°=120°.
By the cosine theorem,
[tex]AD^2=AC^2+CD^2-2\cdot AC\cdot CD\cdot \cos \angle ACD,\\\\AD^2=a^2+x^2-2\cdot a\cdot x\cdot \cos 120^{\circ},\\\\AD^2=a^2+x^2+ax,\\\\AD=\sqrt{a^2+x^2+ax}.[/tex]
Since [tex]a^2+x^2+ax=a^2+x^2+ax+ax-ax=(a+x)^2-ax,[/tex] then
[tex]AD^2=(a+x)^2-ax<(a+x)^2=BD^2\Rightarrow AD<BD[/tex]
and
[tex]AD^2=a^2+x^2+ax>a^2=AB^2\Rightarrow AD>AB.[/tex]
Therefore, you get double inequality
[tex]AB<AD<BD[/tex] or [tex]BD>AD>AB.[/tex]
Answer:
The proof is below
Step-by-step explanation:
Please look at the attachment below
Please let me know if this is wrong
Let me know if you have any questions
If right please give me brainiest
Thanks
What is 24 divided by 5/6?
28.8
hope this helps :)
28 4/5 That is the answer for the question
How can you write 0.326 in two other forms