Answer:
w = 4
w = -1/2
Step-by-step explanation:
so first of all this looks like a quadratic equation . I say this because you can subtract 4 to get 0 on one side . so you will have 2w²-2w-4=0.
to solve quadratic equations you need to use the quadratic formula . keep in mind you can only use the quadratic formula when your own quadratic equation is set set equal to 0. quadratic formula is equal to:
x= (-b±sqrt(b²-4ac))÷2a
now because this is a quadratic you can identify the values x, b, a, and c. we know that if it is a quadratic equation then the equation will be ax²+ BX + C. this is the basic formula for a quadratic equation so your values will be a equals 2 and B = -7 and C equals -4 and W equals X .
now because we know these values we can substitute it into the quadratic formula that i mentioned earlier .
x=(-(-7) ± sqrt( (-7)²-(4×2×(-4)) ) ) ÷ (2×2)
when you're simplify this you get
x= (7±sqrt(49+32))÷4
x= 7±sqrt(81) ÷ 4
x= (7±9)÷4
for quadratics it's normal that the x value is going to be two different values so don't panic at that !
the first x value
x= (7+9)÷4
= 16÷4
=4
the second x value
x= (7-9)÷4
=(-2)÷4
=-1/2
now remember that we said W equals X so the value of w will be 4 or -1/2 .
The slopes are different, and the y-intercepts are different. The slopes are different, and the y-intercepts are the same. The slopes are the same, and the y-intercepts are different. The slopes are the same, and the y-intercepts are the same.
Answer:
The slopes are the same and the y-intercepts are different.
Explanation:
Given:
[tex]\begin{gathered} x+2y=8 \\ 2x+4y=12 \end{gathered}[/tex]Recall that the slope-intercept equation of a line is generally given as;
[tex]y=mx+b[/tex]where;
m = slope of the line
b = y-intercept of the line
Let's go ahead and rewrite the first equation in slope-intercept form as seen below;
[tex]\begin{gathered} x+2y=8 \\ 2y=-x+8 \\ y=-\frac{1}{2}x+\frac{8}{2} \\ y=-\frac{1}{2}x+4 \end{gathered}[/tex]We can see from the above that the slope(m) of the first equation is -1/2 and the y-intercept(b) is 4.
Let's go ahead and rewrite the second equation in slope-intercept form as seen below;
[tex]\begin{gathered} 2x+4y=12 \\ 4y=-2x+12 \\ y=-\frac{2}{4}x+\frac{12}{4} \\ y=-\frac{1}{2}x+3 \end{gathered}[/tex]We can see from the above that the slope(m) of the second equation is -1/2 and the y-intercept(b) is 3.
We can see from the above that, for the two equations, the slopes are the same, and the y-intercepts are different.
Are 1 to 0.4 and 9 3.6 proportional?
The ratios 1 to 0.4 and 9 to 3.6 are proportional.
A ratio is a relationship between two objects that is expressed using numbers or amounts.
If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
Consider the ratio 1 to 0.4 and 9 to 3.6,
Let,
x = 1 to 0.4 = 1 : 0.4
= 1/0.4
= 10/4
= 5/2
Let, y = 9 to 3.6
y = 9 : 3.6
y = 9/3.6
y = ( 9 × 10 ) / 36
y = 10/4
y = 5/2
Therefore,
x = y
1 : 0.4 = 9 : 36
Hence, the ratios 1 to 0.4 and 9 : 3.6 are proportional.
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19. Write ten-million (10,000,000) in scientific notation.
5
0105
01 x 106
01 x 107
01 × 108
Answer:
1 × 10⁷
Step-by-step explanation:
the correct answer is 1 × 10⁷
Singer A and Singer B had the two top-grossing concert tours for a certain year, together generating $438 million in ticket sales. If Singer B took in $22 million less than Singer A, how much did each tour generate?
To answer this question, we have that both singers generated $438 million in tickets sales.
Then, we can rewrite it in algebraic expressions as follows:
[tex]A+B=438[/tex]However, we know that singer B took in $22 million less than singer A:
[tex]B=A-22[/tex]Now, we can substitute this expression in the original one as follows:
[tex]A+A-22=438[/tex]And to solve this equation, we can add the like terms, and then add 22 to both sides of the equation as follows:
[tex]2A-22+22=438+22\Rightarrow2A=460\Rightarrow\frac{2A}{2}=\frac{460}{2}[/tex][tex]A=230[/tex]Then, to find the earnings of singer B, we have:
[tex]A+B=438\Rightarrow B=438-A[/tex]Then, B is equal to:
[tex]B=438-230\Rightarrow B=208[/tex]Then, we can check that A + B is:
[tex]A+B=230+208=438[/tex]And we can see that singer B took in $22 million less than singer A:
[tex]B=230-22=208[/tex]In summary, therefore, we can say that each tour generated:
Singer A generated $230 million in ticket sales and Singer B generated $208 million.
P(-9,-4) Q(-7,-1) whats is PQ
Step-by-step explanation:
I assume the question is about the distance between both points.
2 points in the coordinate grid create a right-angled triangle :
their direct connection (distance) is the Hypotenuse (the baseline, it is the side opposite of the 90° angle), and the x and y coordinate differences are the legs.
so, we can use Pythagoras to get the distance.
c² = a² + b²
c being the Hypotenuse, a and b being the legs.
so,
distance² = (-9 - -7)² + (-4 - -1)² = (-9 + 7)² + (-4 + 1)² =
= (-2)² + (-3)² = 4 + 9 = 13
distance = sqrt(13) = 3.605551275...
just in case, if you needed the line equation connecting these 2 points, I would assume the slope-intersect form
y = ax + b
"a" being the slope, "b" being the y-intersect (the y-value when x = 0).
the slope is always the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.
using the 2 given points
x changes by +2 (from -9 to -7).
y charges by +3 (from -4 to -1).
the slope is
+3/+2 = 3/2
and our equation looks like
y = 3x/2 + b
now we use the coordinates of 1 point, e.g. (-7, -1), to get b
-1 = 3/2 × -7 + b = -21/2 + b
-1 + 21/2 = b
-2/2 + 21/2 = b
19/2 = b
our equation is then
y = 3x/2 + 19/2
or
y = (1/2)×(3x + 19)
9. Dice A has ten sides, what is the probability a five of NOT rolling a one, a three or a five?
Answer:
Step-by-step explanation: Take awa thoese and it would be 70%
The Nutty Professor sells cashews for $7.00 per pound and Brazil nuts for $4.00 per pound. How much of each type should be used to make a 33 pound mixture that sells for $5.64 per pound? pounds of cashews pounds of Brazil nuts
Let's call X the number of pounds of cashews and Y the number of pounds of Brazil nuts.
Now, we want to make 33 pounds of the mixture, so:
X + Y = 33
Adittionally, every pound mixture will be sell for $5.64 per pound. It means that:
7X + 4Y = 5.64*33
7X + 4Y = 186.12
Because every pound of cashews cost $7 and every pound of Brazil nuts cost $4
Then, we can solve for X on the first equation and replace it on the second as:
[tex]\begin{gathered} X+Y=33 \\ X=33-Y \end{gathered}[/tex][tex]\begin{gathered} 7X+4Y=186.12 \\ 7(33-Y)+4Y=186.12 \end{gathered}[/tex]So, we can solve for Y as:
[tex]\begin{gathered} 7\cdot33-7\cdot Y+4Y=186.12 \\ 231-7Y+4Y=186.12 \\ 231-3Y=186.12 \\ -3Y=186.12-231 \\ -3Y=-44.88 \\ Y=\frac{-44.88}{-3} \\ Y=14.96 \end{gathered}[/tex]Now, we can calculate X as:
[tex]\begin{gathered} X=33-Y \\ X=33-14.96 \\ X=18.04 \end{gathered}[/tex]Therefore, we need to use 18.04 pounds of cashews and 14.96 pounds of Brazil nuts to make a 33 pounds mixture that sells for $5.64 per pound
Answer 18.04 pounds of cashews and 14.96 pounds of Brazil nuts
Olivia picked 256 strawberries. She divided the strawberries evenly into 6
baskets. How many strawberries are in each basket? How many are left over
Answer:
42 strawberries in each backet with 4 left over
Step-by-step explanation:
256 divided by 6=42.6666667
42x6=252
256-252
Answer:
42 with 4 left over
Step-by-step explanation:
256/6
4 2
6. 256
4
24
16
12
4
solve the following equation for x4x-3=21
Solving for x :
[tex]\begin{gathered} 4x-3=21 \\ \rightarrow4x=21+3\rightarrow4x=24 \\ \rightarrow x=\frac{24}{4} \\ \\ \Rightarrow x=6 \end{gathered}[/tex]what is the y dash coordinate of the solution to the following system of equations
Solution
Step 1:
Write the systems of equations
[tex]\begin{gathered} 3x\text{ - 6y = 6 eq\lparen1\rparen} \\ -3x\text{ + 3y = 9 eq\lparen2\rparen} \end{gathered}[/tex]Step 2
To find the value of y, add both equations
[tex]\begin{gathered} -3x\text{ + 3y + 3x - 6y = 6 + 9} \\ -3y\text{ = 15} \\ y\text{ = }\frac{15}{-3} \\ y\text{ = -5} \end{gathered}[/tex]your checking account is overdrawn by $120.22. you write a check for $80.25. what is the balance in your account???
The amount or balance left in the bank account is $39.97.
The amount of money held in a financial institution, such as a savings or checking account, at any particular time is known as the account balance. The net amount, which includes all debits and credits, is always the account balance.
The current balance in the bank account is $120.22.
The check was issued for $80.25.
Let x be the balance left in the account.
Then,
The balance left = Initial balance in the account - The amount for which the check was issued
x = Initial balance in the account - The amount for which the check was issued
x = $120.22 - $80.25
x = $39.97
The balance left in the bank account is $39.97.
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Let sin 0= 4/9. Find the exact value of cos 0.
Statement Problem: Let;
[tex]\sin \theta=\frac{4}{9}[/tex]Find the exact value of;
[tex]\cos \theta[/tex]Solution:
In trigonometry, the ratio of the sine is defined as;
[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]Thus,
[tex]\text{opposite}=4,\text{ hypotenuse=9}[/tex]By Pythagoras theorem, the square of the longest side (hypotenuse) is the sum of squares of the opposite and the adjacent sides.
[tex]\begin{gathered} (\text{hypotenuse)}^2=(\text{opposite)}^2+(\text{adjacent)}^2 \\ (\text{adjacent)}^2=(\text{hypotenuse)}^2-(\text{opposite)}^2 \\ (\text{adjacent)}^2=9^2-4^2 \\ (\text{adjacent)}^2=81-16 \\ (\text{adjacent)}^2=65 \\ \text{adjacent}=\sqrt[]{65} \end{gathered}[/tex]The ratio of the cosine is defined as;
[tex]\begin{gathered} \cos \theta=\frac{adjacent}{hypotenuse} \\ \end{gathered}[/tex]Hence,
[tex]\cos \theta=\frac{\sqrt[]{65}}{9}[/tex]Jordan Will hike the trail shown at a rate of 5mi/h. write a linear equation to represent the distance Jordan still has to walk after X hours. what does the Y-intercept of the equation represent?
using linear equation
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} x=\text{time in hours} \\ y=dis\tan ce \\ m=5 \end{gathered}[/tex][tex]y=5x+31[/tex]The y - intercept which is equals to 31 represents the distance he still has to walk .
The picture I put in I understand girls more
Using long division:
Question 9
1 pts
The price of gasoline has risen from $3.52/gallon last week to $4.31/gallon this week.
What is the percent change? Round answer to the tenths place.
Question 10
1 pts
Answer: 122.4% increase
Divide the new cost from the old
4.31 / 3.52 = 1.22443181818
Multiply by 100 to get a percent.
= 122.443181818%
= 122.4
What is the % change from $250 to $303
Solution
- The question tells us to find the % change from $250 to $303.
- To calculate the percentage change, we use the formula given below:
[tex]\Delta\text{ \%}=\frac{\text{New}-\text{Old}}{\text{Old}}\times100\text{ \%}[/tex]- The New is $303 and the Old is $250. Thus, we can calculate the percentage change as follows:
[tex]\begin{gathered} \Delta\text{ \%}=\frac{\text{New}-\text{Old}}{\text{Old}}\times100\text{ \%} \\ \\ =\frac{303-250}{250}\times100\text{ \%} \\ \\ =0.212\times100\text{ \%} \\ \Delta\text{ \%}=21.2\text{ \%} \end{gathered}[/tex]Final Answer
The percentage change from $250 to $303 is 21.2%
What is 19.5 / 3 = decimal division
Answer:
6.5
Step-by-step explanation:
19.5 divided by 3 is 6.5
if you want to double check, you can multiply 3 by 6.5 and find it is 19.5
Pls help me, I’ll send you the pictures of the things you have to choose.
EXPLANATION
Since we have 3 1/2 slices of cake, and we need to distribute a half of slice by each friend, we need to divide 3 1/2 by 2, as follows:
[tex]\frac{(3\frac{1}{2})}{2}=\frac{7}{4}=1\frac{3}{4}[/tex]Therefore, since each friend gets a half slice of cake, we can affirm that each whole slice of cake can be divided into two halves.
Now, adding from half to half to obtain 3 1/2 slices of cake, give us:
1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 = 7 slices
So, 3 1/2 slices of cake is a total of 7 halves.
Because each friend gets half of a slice of cake, we can affirm there are 7 friends.
Answer:
See below
Step-by-step explanation:
3 + one half slices each whole (3 of them ) can be cut into two halves
6 halves + 1 half = 7 halfves
if everyone gets a a half, there are 7 people
Use exponential notation to simplify the given expressionsPresent your answer using only positive integer exponentsAswer the first one
We will use the next rule
[tex]\sqrt[n]{x^m}=x^{\frac{m}{n}}[/tex]Then
[tex]\sqrt[7]{x^6}\ast\sqrt[5]{x}=x^{\frac{6}{7}}\ast x^{\frac{1}{5}}=x^{\frac{6}{7}+\frac{1}{5}}[/tex][tex]x^{37/35}[/tex]Tyler wants to crate a scale drawing of his bedroom. His bedroom is a rectangle with length 5m and width 4m. He decides on a scale of 1 to 80.
The scale drawing with length 0.0625m and width 0.05m.
What is scale factor?To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilised. It is employed to change the size of an object.
When both the original dimensions and the new dimensions are known, the scale factor may be determined. When employing the scale factor, there are two terms that must be understood. When a figure's size is increased, we refer to this as scaling up, and when its size is decreased, we refer to this as scaling down.
Given:
length= 5m
width= 4m
and,
The scaled dimension = (Actual dimension) x (scale factor) ...(i)
scale factor =1/50
(1) The actual width = 4 m.
So, the width of the door on the scale drawing= 4x (1/80)= 0.05 m
(2)The actual length = 5 m.
So, the length of the door on the scale drawing= 5 x (1/80)= 0.0625 m
Hence, the scale drawing with length 0.0625m and width 0.05m.
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Simplify.10(15 + n)50 + n0 150 + nO 150 + 10 n150 n
ANSWER
150 + 10n
EXPLANATION
We want to simplify:
10(15 + n)
To do this, we have to use the distributive property:
a(b + c) = a*b + a*c
Therefore:
10(15 + n) = (10 * 15) + (10 * n)
= 150 + 10n
That is the answer
Triangle ABC with vertices A(-9,-7) B(-6,-2) C(-3,-6) is translated 5 units to the right and 3 units up then the image is reflected on the x-axis. What are the coordinates of the final image?
Triangle ABC with vertices A(-9,-7) B(-6,-2) C(-3,-6) is translated 5 units to the right.
A(-9 + 5 ,-7) B(-6 + 5,-2) C(-3 + 5 ,-6) = A ( -4, -7 ) , B ( -1 , -2 ) C ( 2 , -6 )
3 units up: A ( -4, -7 + 3 ) , B ( -1 , -2+ 3 ) C ( 2 , -6+ 3 )
The coordinates of the final image is = A( -4, -4 ) B ( -1 , 1 ) C ( 2 , -3)
Two trains leave the same station, each 40 minutes apart. Train X leaves first at 9:45 am and heads west at a speed of 144 km/h. Train Y leaves at noon and travels directly east at a speed of 165 km/h. How far apart are these trains at 1:30 pm? Show your work.
Using the relation between velocity, distance and time, it is found that these trains are 1049 km apart at 1:30 pm.
What is the relation between velocity, distance and time?Velocity is given by the distance divided by the time, hence the following equation is built to model the relationship between these variables:
v = d/t.
In which:
v is the velocity.d is the distance.t is the time.For Train X, the time and the velocity are given as follows:
Time of t = 3.75 hours, as 1:30 pm is 3 hours and 45 minutes after 9:45 am, and 45 minutes = 45/60 = 0.75 of an hour.Velocity of v = 144.Hence the distance of train X from the station is:
dX = 144 x 3.75 = 540 km.
For Train Y, the time and the velocity are given as follows:
Time of t = 3.0.833 hours, as 1:30 pm is 3 hours and 5 minutes after the train left the station (40 minutes less than train X).Velocity of v = 165.Hence the distance of train Y from the station is:
dY = 165 x 3.0833 = 509 km.
They travel in opposite directions, hence we add the distances of each from the station to find their distances as follows:
540 km + 509 km = 1049 km.
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Sketch the graph of y= (x - 3)2 - 25, then select the graph that correspondsto your sketch.10140-1010101010111010HO-101010-20C.D.A.B.A. Graph AB. Graph BC. Graph CD. Graph D
Therefore,
[tex]\begin{gathered} when\text{ x=0} \\ y=(0-3)^2-25=9-25=-16 \end{gathered}[/tex]when x = 0, y =-16 we can confirm the graph is C.
I need help on #5 Please help me on my hw
Given:
The given problem is:
[tex](x+3)^2\ne x^2+9[/tex]Using the identity:
[tex](a+b)^2=a^2+b^2+2ab[/tex]Now substitute a = x and b = 3 in this identity:
[tex]\begin{gathered} (x+3)^2=x^2+3^2+2\times x\times3 \\ =x^2+9+6x \end{gathered}[/tex]Hence , the correct solution to the problem is:
[tex](x+3)^2=x^2+6x+9[/tex]How much will a girl pay for a bag price at $15 if a discount of 10% is offered?
First, calculate how much is the discount equal to. Then, substract the discount from the original price to find the selling price.
Since the discount is 10%, find how much is 10% of $15 by multiplying 15 times 10/100:
[tex]15\times\frac{10}{100}=1.5[/tex]Then, 10% of 15 is equal to 1.5. Now, substract 1.5 from 15 to find the final price:
[tex]15-1.5=13.5[/tex]Therefore, the girl will pay $13.5. The answer is:
[tex]\text{ \$13.5}[/tex]
Mr. Bowen used 2 gallons of paint on 1/3 of his fence. How many more gallons of
paint does he need to finish paining the entire fence?
Answer:
4
Step-by-step explanation:
→ Work out how much he needs in total
2 × 3 = 6
→ Minus how much he has used
6 - 2 = 4
Solve using Gaussian eliminationX+2y=7. And. Y=3x+2
Let's rewrite the system as:
[tex]\begin{cases}x+2y=7_{\text{ }}{(1)} \\ 3x-y={-2_{\text{ }}}(2)\end{cases}[/tex]Using elimination:
[tex]\begin{gathered} (1)+2(2) \\ x+6x+2y-2y=7-4 \\ 7x=3 \\ x=\frac{3}{7} \end{gathered}[/tex]Replace x into (2):
[tex]\begin{gathered} y=3(\frac{3}{7})+2 \\ y=\frac{23}{7} \end{gathered}[/tex]Rajendra has 4 pounds of trail mix. He is putting them into bags that hold1 pounds each. Does he have enough trạil mix to completely fill 3 bags? Explain why orwhy not.
This question gettin me mad tight
The graph shows the value parent function
Which statement best describes the function?
A - the function is increasing when x > 0
B - the function is increasing when x< 0
C- the function is always increasing
D - the function is never increasing
