(-x^2+2x+3) + (-x^2-2x-1) = -2x^2 + 2
============================================
Explanation:
We have two large red tiles labeled with -x^2 on them. They add to -2x^2 which is found in every answer choice listed. This means that we must have a plus sign between the two parenthesis groups. If we had a subtraction sign, then -x^2 minus -x^2 would turn into 0x^2 or just 0, and the x^2 terms would go away entirely.
Because we must have a plus sign between the parenthesis, this means the answer is between C and D.
Now focus on the x terms. The slash marks mean that all of the x terms pair up and add to 0. They go away as there aren't any x terms that haven't been slashed. That explains why there are no x terms on the right hand side of any of the answer choices.
The question is: which of C or D has the x terms add to 0x? The answer would be choice D since 2x + (-2x) = 2x-2x = 0x. Choice C has 2x+2x = 4x which is what we don't want.
Lastly, choice D is further proven correct by noticing that the constants 3 and -1 add to 3+(-1) = 3-1 = 2. We have two small blue squares that add to 2 after the cancellations have happened.
Which is the best estimate for the percent equivalent of 7 Over 15
Approximate what the value of [tex]7/15[/tex] is by using calculator.
[tex]7/15\approx0.47[/tex].
And now just multiply by 100 to get percentage.
[tex]100\cdot0.47=\boxed{47\%}[/tex].
Hope this helps.
Answer:
24%
Step-by-step explanation:
7\15 x 100
simplify and get=140\3
dived140\3=48\2
simplify 48\2=24%
what are three different whole numbers whose sum and product are equal
Three different whole numbers whose sum and product are equal are 1, 2, and 3.
1 + 2 + 3 = 6
1 x 2 x 3 = 6
As demonstrated above, the sum and product of 1, 2, and 3 is the same.
Hope this helps!! :)
Answer:
1 2 and 3
Step-by-step explanation:
“a railroad bridge spans a gorge 40 feet wide and connects two cliffs at heights of 98 and 158 feet above the bottom of the gorge. a train is crossing this gorge from the higher cliff to the lower. when the front of the train has traveled three-fourths of the bridge's length, how many feet is it above the bottom of the bottom of the gorge?”
Answer:
Height above the bottom gorge is 113 feet
Step-by-step explanation:
The width of the gorge = 40 feet
The height of the higher cliff = 158 feet
The height of the lower cliff = 98 feet
The length of the bridge = √((158-98)² + 40²) = 72.11 feet
The slope of the bridge = (158-98)/40 = 1.5
The length of 1/4 of the bridge from the lower cliff =72.11 - 3/4×72.11 = 18.03 feet
The angle of inclination of the bridge = tan⁻¹(1.5) = 56.31°
The height above the bottom at 3/4 from the higher cliff = The height above the bottom at 1/4 from the lower cliff = 98+ 18.03×sin(56.31 ) = 113 feet
Which can also be found directly from the heights of the two cliffs knowing that 3/4 from the higher cliff = 1/4 from the lower cliff giving;
Height above the bottom gorge = 98 + 1/4×(158 - 98) = 113 feet.
What is the slope of (3,-2) (2,-4)
Answer:
2
Step-by-step explanation:
We can use the slope formula
m = (y2-y1)/(x2-x1)
= ( -4 - -2)/ ( 2-3)
= ( -4+2)/( 2-3)
= -2/ -1
= 2
40 = 90^2/16 sinx cosx find x
Answer:
x = 4.545Step-by-step explanation:
Given the expression
[tex]40=\frac{90^2}{16} sinxcosx\\\\Cross\ multiplying;\\\\16*40 = 90^2 sinxcosx\\\\640 = 90^2 sinxcosx\\\\\frac{640}{8100} = sinxcosx\\ from\ trig\ identity, sin2x = 2sinxcosx\\sinxcosx = sin2x/2\\[/tex]
[tex]Hence, \ \frac{640}{8100} = \frac{sin2x}{2} \\\\\frac{2*640}{8100} = sin2x\\ \\\frac{1280}{8100}=sin2x\\ \\0.158 = sin2x\\\\2x = sin^{-1} 0.158\\\\2x = 9.09\\x = 9.09/2\\x =4.545[/tex]
Help ASAP! Will award brianliest!
Answer:
1: yes AB2×4
2:not possible
3:(11,2)
(20,12)
Step-by-step explanation:
1:compare the orders given which is 2×3 and 3×4 so to get if it's possible to multiply you just cancel out the same numbers if present i.e 3
2:so I took the first column of m multiply the first row of n (add values you get i.e -2×1+1×-4+0×2=-6) but on the second value of the first row I got 8 not 3 so I said not possible
3 you multiply row by column
(1×1+0×7+2×5=11. 1×4+0×2+-2×1=2)
(3×1+1×7+2×5=20. 3×4+1×2+2×-1=12)
therefore
(11,2)
(20,12)
at the rate of 15 per 6 oz. bar of chocolate, how much would a pound
Answer:
40
Step-by-step explanation:
We know there are 16 oz in a pound
We can use ratios
15 x
----- = ----------
6 oz 16 oz
Using cross products
15 * 16 = 6x
240 = 6x
divide by 6
240/6 = 6x/6
40 =x
You have already run 4 miles. If you run at a speed of 8 miles per hour, how many total miles will you run in 2 more hours? Choose the correct equation and solution to this problem.
Answer:
20 miles
Step-by-step explanation:
I'm not sure if that is exactly how you solve it but
If its
8x+4 as the equation and x is the number of hours run
the total number of miles run should be 20 miles
8(2)+4=20
Answer:
20 miles
Step-by-step explanation:
miles already covered = 4
rate of speed = 8miles / hour
miles to be covered = 8 miles/hr× 2 hr= 16 miles ( because distance is velocity × time)
total miles covered = 16 + 4 = 20 miles.
HELLLLLLPPPPPP MEEEE PLEASEEEEE!!!!!! Find the times (to the nearest hundredth of a second) that the weight is halfway to its maximum negative position over the interval . Solve algebraically, and show your work and final answer in the response box. Hint: Use the amplitude to determine what y(t) must be when the weight is halfway to its maximum negative position. Graph the equation and explain how it confirms your solution(s).
Answer:
0.20, 0.36 seconds
Step-by-step explanation:
We have already seen that the equation for y(t) can be written as ...
y(t) = √29·sin(4πt +arctan(5/2))
The sine function will have a value of -1/2 for the angles 7π/6 and 11π/6. Then the weight will be halfway from its equilibrium position to the maximum negative position when ...
4πt +arctan(5/2) = 7π/6 or 11π/6
t = (7π/6 -arctan(5/2))/(4π) ≈ 0.196946 . . . seconds
and
t = (11π/6 -arctan(5/2))/(4π) ≈ 0.363613 . . . seconds
The weight will be halfway from equilibrium to the maximum negative position at approximately 0.20 seconds and 0.36 seconds and every half-second thereafter.
△ABC and △JKL are two triangles such that ∠A≅∠J and ∠B≅∠K. Which of the following would be sufficient to prove that the triangles are congruent? A ACJL=BCKL B ∠C≅∠L C AB≅JK D BC≅Jk
We need to know the rules of congruence of triangles to solve the given problem. The required condition that is sufficient to prove that the triangles are congruent is option (C) AB≅JK.
There are three rules of congruence of triangles, if two triangles satisfy any one of these rules then we can say that the triangles are congruent. The three rules are, SSS which means three sides are equal, ASA which means two angles and their corresponding sides are equal and SAS which means that two sides and the angle between them is equal. When two angles are said to be congruent it means they have the same measure that is they are equal. In this question we know that ∠A≅∠J and ∠B≅∠K , we can see that two angles are equal, if we can have the corresponding side of these two angles to be equal then we can say that the two triangles are congruent. The corresponding side of these angles are AB and JK.
Therefore we can see that the required condition to prove that the triangles are congruent is option (C) AB≅JK.
Learn more about congruency of triangles here:
https://brainly.com/question/2736828
#SPJ1
3. Consider the sequence,-8, -5, -2, 1, ...
a) Determine the explicit formula for the general term, 1,, of this sequence in simplified
form. (2 marks)
b) Use this formula to determine the value of t20. (1 mark)
c) Algebraically determine which term has a value of 40. (1 mark)
Answer:
a) [tex]a_n=3\,n-11[/tex]
b) [tex]a_{20}=49[/tex]
c) term number 17 is the one that gives a value of 40
Step-by-step explanation:
a)
The sequence seems to be arithmetic, and with common difference d = 3.
Notice that when you add 3 units to the first term (-80, you get :
-8 + 3 = -5
and then -5 + 3 = -2 which is the third term.
Then, we can use the general form for the nth term of an arithmetic sequence to find its simplified form:
[tex]a_n=a_1+(n-1)\,d[/tex]
That in our case would give:
[tex]a_n=-8+(n-1)\,(3)\\a_n=-8+3\,n-3\\a_n=3n-11[/tex]
b)
Therefore, the term number 20 can be calculated from it:
[tex]a_{20}=3\,(20)-11=60-11=49[/tex]
c) in order to find which term renders 20, we use the general form we found in step a):
[tex]a_n=3\,n-11\\40=3\,n-11\\40+11=3\,n\\51=3\,n\\n=\frac{51}{3} =17[/tex]
so term number 17 is the one that renders a value of 40
Which glide reflection describes the mapping ABC DEF. This is practice for me plz, give answer with explanation. Non-sense answer will get reported
Answer:
c. translation (x,y) -> (x-4, y-1) followed by reflection about y=0
Step-by-step explanation:
The strategy is to translate B to E then reflect about the x-axis (y=0)
From B to E, the process is
(x,y) -> (x-4, y-1)
Therefore it is a translation (x,y) -> (x-4, y-1) followed by reflection about y=0
Please can someone help
Answer:
a) 0
b) 1
c) 0
Step-by-step explanation:
These are common values from the unit circle but you could also just check with your calculator. Just be sure to set it to degree mode and not radian mode.
a fish tank is : 16 in
Height : 10 in
Width : 8 in how many gallons is it ? NEED HELP ASAP
Answer:
5.541 gallons
Step-by-step explanation:
The fish tank is 1280 cubic inches, which equates to 5.541 US liquid gallons.
Answer:
5.54 gallons (aprox.)
Step-by-step explanation:
volume = 16in * 10in * 8in
volume = 1280in³
Convert cubic inch to gallons is:
1 inch³ = 0.004329 gallon
then:
1280in³ = 1280*0.004329 = 5.54 gallons (aprox.)
Find m∠ABC__________
Answer:
ill help!
Step-by-step explanation:
find angle CBD
once you find that angle subtract it from 90 because that is the measure of ABC which is a right angle. Because all right angles are 90 degrees you can prove that it is the difference from angle CBD and 90.
hope it helped have good one!
ASAP!!! PLEASE help me solve this question! No nonsense answers, and attach solutions please.
Answer:
2<F(x)<5
Step-by-step explanation:
We can guess that it come between 2 and 5 given the pattern that we see in the table, but there’s no reason we can’t solve it to be sure.
F(x)=3 (Times the square root of 1.5-1)+2
3(square root of .5)+2
3(0.7)+2
2.12+2
4.12
So, yes, it is between 2 and 5
2<F(x)<5
Divide 3x^4 - 4x^3 -3x -1 by x-1 Verify using division algorithm Steps please thanks
Answer:
3x³ − x² − x − 4 + (-5/(x−1))
Step-by-step explanation:
Use long division (see attached picture).
Which is the correct algebraic expression after combining like terms? 6 + 8 x minus 7 minus x 7 x minus 1 7 x + 13 9 x minus 1 9 x + 13
Answer:
7x-1
Step-by-step explanation:
i did the test
Answer:
7x-1
Step-by-step explanation:
correct answer on edge
A medical researcher tested a new treatment for poison ivy against the traditional ointment. He concluded that the new treatment is more effective. Explain what P-Value of 0.047 means in this context.
Answer:
A p-value if 0.047(same as 4.7%) means there is a 4.7% chance that there is no difference in how effective the new treatment is.
Step-by-step explanation:
When we talk of a p-value, we are referring to a conditional probability. What it tells us is the probability of getting results which are at least as unusual as the observed statistics in a case where we are given that the null hypothesis is not false.
A p-value if 0.047(same as 4.7%) means there is a 4.7% chance that there is no difference in how effective the new treatment is.
So what this means is that, in this case it is better that more data is collected to enable us know how effective the new treatment is
27 - (2 + 3) - 10 ÷ 2
Answer:
27_5_10/2
27_5_5
22_5
17
label missing angles 1, 2, 3, 4, and 5 if lines ‘m’ and ‘n’ are parallel
Answer:
see attached diagram
Step-by-step explanation:
1. 1 and 70 are angles on a line (supplementary)
2. vertical angles with 70
3. angles on a line are supplementary
4. 2 and 4 are supplementary interior angles between parallel lines m & n
5. corresponding angle with 70
What is the slope of the graph shown below?
A. -2
B. 1
C. 2
D. 1/2
Answer:
i think its the answe d but not sure
5x+4y=25 - (5x+2y=3)
Answer:
T1he values for x and y of the equations is y = 11, and x = -19/5.
Step-by-step explanation:
To solve this question, we need to rearrange the expression:
5x+4y=25 - (5x+2y=3)
Look, if we subtract one equation to the other, then:
5x+4y=25 [1]
-(5x+2y=3) [2]
Which is the same as:
5x+4y=25
-5x-2y=-3
Subtract them:
5x+4y=25
-5x-2y=-3
---------------
2y =22
y = 22/2 = 11
Then, y = 11.
To find x, we can substitute y in either equation [1] or [2].
Let us use [1]
5x+4y=25
5x+4(11)=25
5x+44=25
5x=25-44
5x=-19
x = -19/5
Then, the values for x and y of the equations is y = 11, and x = -19/5.
A point H is 20m away from the foot of a tower on the same horizontal ground. From the point H, the angle of elevation of the point (P) on the tower and the top(T) of the tower are 30° and 50° respectively.
( a) draw a diagram to illustrate the information above.
(b) calculate correct to 3 s.f,
( I) /PT/
(ii) the distance between H and the too of the tower.
(III) the position of H if the angle of depression of H from the too of the tower is to be 40°
Answer:
a. See Attachment 1
b. [tex]PT = 12.3\ m[/tex]
c. [tex]HT = 31.1\ m[/tex]
d. [tex]OH = 28.4\ m[/tex]
Step-by-step explanation:
Calculating PT
To calculate PT, we need to get distance OT and OP
Calculating OT;
We have to consider angle 50, distance OH and distance OT
The relationship between these parameters is;
[tex]tan50 = \frac{OT}{20}[/tex]
Multiply both sides by 20
[tex]20 * tan50 = \frac{OT}{20} * 20[/tex]
[tex]20 * tan50 = OT[/tex]
[tex]20 * 1.1918 = OT[/tex]
[tex]23.836 = OT[/tex]
[tex]OT = 23.836[/tex]
Calculating OP;
We have to consider angle 30, distance OH and distance OP
The relationship between these parameters is;
[tex]tan30 = \frac{OP}{20}[/tex]
Multiply both sides by 20
[tex]20 * tan30 = \frac{OP}{20} * 20[/tex]
[tex]20 * tan30 = OP[/tex]
[tex]20 * 0.5774= OP[/tex]
[tex]11.548 = OP[/tex]
[tex]OP = 11.548[/tex]
[tex]PT = OT - OP[/tex]
[tex]PT = 23.836 - 11.548[/tex]
[tex]PT = 12.288[/tex]
[tex]PT = 12.3\ m[/tex] (Approximated)
--------------------------------------------------------
Calculating the distance between H and the top of the tower
This is represented by HT
HT can be calculated using Pythagoras theorem
[tex]HT^2 = OT^2 + OH^2[/tex]
Substitute 20 for OH and [tex]OT = 23.836[/tex]
[tex]HT^2 = 20^2 + 23.836^2[/tex]
[tex]HT^2 = 400 + 568.154896[/tex]
[tex]HT^2 = 968.154896[/tex]
Take Square Root of both sides
[tex]HT = \sqrt{968.154896}[/tex]
[tex]HT = 31.1\ m[/tex] (Approximated)
--------------------------------------------------------
Calculating the position of H
This is represented by OH
See Attachment 2
We have to consider angle 50, distance OH and distance OT
The relationship between these parameters is;
[tex]tan50 = \frac{OH}{OT}[/tex]
Multiply both sides by OT
[tex]OT * tan50 = \frac{OH}{OT} * OT[/tex]
[tex]OT * tan50 = {OH[/tex]
[tex]OT * 1.1918 = OH[/tex]
Substitute [tex]OT = 23.836[/tex]
[tex]23.836 * 1.1918 = OH[/tex]
[tex]28.4= OH[/tex]
[tex]OH = 28.4\ m[/tex] (Approximated)
Help Please!! I can't seem to get the answer no matter how hard I try.... But it seems so easy.. Wjhsjwskwnw
Answer:
109 cm³
Step-by-step explanation:
Let the radius of semi-circle be r, then side of the cube is 2r and the height of the solid is also 2r
The circumference of the semi-circle can be calculated as:
2r + 1/2 × (2πr) = 11Then we can find the value of r:
r(2+π)=11r= 11/(2+π)r= 11/5.14r= 2.14 cmThe volume of the combined solid is the sum of volumes of the cube and the semi-cylinder:
V= (2r)³ + 1/2×πr²×2r= 8r³ + πr³= (8+π)×r³V= (8+3.14)×2.14³ = 109.1758 cm³The volume is approx. 109 cm³Please answer this question now
Answer:
[tex] Area = 400.4 m^2 [/tex]
Step-by-step Explanation:
Given:
∆UVW,
m < U = 33°
m < V = 113°
VW = u = 29 m
Required:
Area of ∆UVW
Solution:
Find side length UV using Law of Sines
[tex] \frac{u}{sin(U)} = \frac{w}{sin(W)} [/tex]
U = 33°
u = VW = 29 m
W = 180 - (33+113) = 34°
w = UV = ?
[tex] \frac{29}{sin(33)} = \frac{w}{sin(34)} [/tex]
Cross multiply
[tex] 29*sin(34) = w*sin(33) [/tex]
Divide both sides by sin(33) to make w the subject of formula
[tex] \frac{29*sin(34)}{sin(33)} = \frac{w*sin(33)}{sin(33)} [/tex]
[tex] \frac{29*sin(34)}{sin(33)} = w [/tex]
[tex] 29.77 = w [/tex]
[tex] UV = w = 30 m [/tex] (rounded to nearest whole number)
Find the area of ∆UVW using the formula,
[tex] area = \frac{1}{2}*u*w*sin(V) [/tex]
[tex] = \frac{1}{2}*29*30*sin(113) [/tex]
[tex] = \frac{29*30*sin(113)}{2} [/tex]
[tex] Area = 400.4 m^2 [/tex] (to nearest tenth).
2) The senior classes at High School A and High School B planned separate trips to the local
amusement park. The senior class at High School A rented and filled 2 vans and 14 buses with
294 students. High School B rented and filled 3 vans and 7 buses with 161 students. Each van
and each bus carried the same number of students. Find the number of students in each van and
in each bus.
A) Van: 9, Bus: 28 B) Van: 11, Bus: 27
C) Van: 20, Bus: 7 D) Van: 7, Bus: 20
Answer:
D) Van: 7, Bus: 20
Step-by-step explanation:
Add the amount of students together (455 students in total)
Then I added the amount of buses and vans together (5 Vans and 21 Buses)
Then I plugged in each answer
5 x 7 = 35
455 - 35 = 420
420 / 21 = 20
10500 people visited an art gallery in 2002.This was an increase of 25% on 2001.How many visitors were there in 2001?
Answer:
The amount in 2001 is 8400
Step-by-step explanation:
Let x be the amount in 2001
There is an increase of 25% to get to the amount in 2002
x+ .25x = 1.25 x
1.25x = 10500
Divide each side by 1.25
1.25x / 1.25 = 10500/1.25
x =8400
The amount in 2001 is 8400
Raul bought 6 tangerines and ate 2/3 of them. Omar bought 8 tangerines and ate 1/4 of them. Who ate more tangerines?
Rahul ate more tangerines...
which of the graphs best represents f(x)= -2 cos 4x-1?
Answer:
see file attached
Step-by-step explanation: