Solve for u in (7 + u)^2 - (5 + u)^2 = 6v
u = 3(v - 4)/2
Substitute u = 3(v - 4)/2 into (2 - v)^2 - (6 - v)^2 = 4u
8v - 32 = 6(v - 4)
Solve for v in 8v - 32 = 6(v - 4)
v = 4
Substitute v = 4 into u = 3(v - 4)/2
u = 0
Therefore,
u = 0
v = 4
Consider triangle QRS. The legs each have a length of 10 units.
What is the length of the hypotenuse of the triangle?
5 units
units
10 units
units
Answer: [tex]10\sqrt{2}units[/tex]
Step-by-step explanation:
You must apply the Pytagorean theorem, which is shown below:
[tex]a^2=b^2+c^2[/tex]
Where:
a is the hypotenuse and b and c are the legs of the triangle.
Then, if you know the lenght of the legs of the triangle, you can solve for the hypotenuse.
Therefore, keeping the above on mind, you obtain the following result:
[tex]a=\sqrt{b^2+c^2}[/tex]
[tex]a=\sqrt{(10units)^2+(10units)^2}\\a=10\sqrt{2}units[/tex]
The length of the hypotenuse of the triangle is 10√2 units
The triangle is a right angle triangle.
Right angle triangleRight angle triangles are triangle that has one of its angles as 90 degrees.
Using Pythagoras theorem, we can find the length of the hypotenuse with the length of the two legs.
Therefore,
c² = a² + b²c² = 10² + 10²
c² = 100 + 100
c = √200
c = 10√2
learn more on right angle triangle here: https://brainly.com/question/2796771?referrer=searchResults
A baseball team won 20 games in the last 10 games what percent of the games did the team win
Answer:
I believe your problem is
"A baseball team won 10 games in the last 20 games, what percent of the games did the team win?"
In which case the answer is 50 % of the games
Step-by-step explanation:
The total amount of games played is equal to
20 games
If we apply a rule of three
20 games ------------------------100 %
10 games ------------------------- x
x = (10 games / 20 games) * 100%
x = 0.5*100% = 50%
find the length of the unknown side . round your answer to the nearest tenth
may somebody help me please
Answer:
20cm or A
Step-by-step explanation:
pythagorean theorem
25^2=15^2+b^2
625=225+b^2
b^2=400
b=20
A because it is the number in between 15 and 25 because the line is shorter
Triangle ABC is similar to triangle DEF. The length of
AC is 12 cm. The length of
BC is 18 cm. The length of
DF is 10 cm.
What is the length of
EF?
Answer: [tex]EF=15cm[/tex]
Step-by-step explanation:
You know that the triangle ABC and the triangle DEF are similar.
Therefore, if the lenght of AC is 12 centimeters and the lenght of DF is 10 centimeters, then you can find the ratio as following:
[tex]ratio=\frac{DF}{AC}\\\\ratio=\frac{10cm}{12cm}\\\\ratio=0.8333[/tex]
Then, the calculte the length of EF, you must multiply the lenght BC of the triangle ABC by the ratio obtained above.
Therefore, the lenght EF is the following:
[tex]EF=0.8333(18cm)\\EF=15cm[/tex]
Answer:
The length of EF = 15 cm.
Step-by-step explanation:
We are given that the two triangles, ABC and DEF, are similar to each other,
Given that the length of AC = 12 cm, BC = 18 cm and DF = 10 cm, we are to find the length of EF.
For this, we can simply use the ratio method.
[tex] \frac { EF } { BC } = \frac { DF } { AC } [/tex]
[tex] \frac { EF } { 18 } = \frac { 10 } { 12 } [/tex]
[tex] E F = \frac { 10 } { 12 } \times 18 [/tex]
EF = 15 cm
what is in (e^A)? A, A+1, ln A + ln e, 1 + ln A
Answer:
[tex]\large\boxed{\ln e^A=A}[/tex]
Step-by-step explanation:
[tex]Use\\\\\log_ab^n=n\log_ab\\\\\log_aa=1\\\\\ln a=\log_e a\to\ln e=1\\====================================\\\\\ln e^A=A\ln e=A(1)=A[/tex][/tex]
Zero property 2x^3+x^2-3x=0
Solve for x. Use the completing square method. x^2+8x=7
Answer:
√23 - 4 , -√23 - 4
Step-by-step explanation:
By completing the square
half of 8 is 4
7+4^2= 23
(x+4)^2=23
Answer:
√23 - 4 , -√23 - 4
Step-by-step explanation:
If sign Tera angle equal 2/3 and tangent test angle is less than zero what is the value of cosine teta angle
Answer:
The value of cosФ = -√5/3
Step-by-step explanation:
∵ sinФ = 2/3
∵ tanФ is less than 0
* Lets think about that:
the value of sin is positive and the value of tan is negative
according to ASTC rule:
- All are positive in the first quadrant
- sin only positive in the second quadrant
- tan only positive in the third quadrant
- cos only positive in the fourth quadrant
∴ Angle Ф lies on the second quadrant
∴ The value of cosФ is less than 0
∵ sin²Ф + cos²Ф = 1
∵ sinФ = 2/3
∴ (2/3)² + cos²Ф = 1
∴ cos²Ф = 1 - 4/9 = 5/9
∴ cosФ = ± √5/3
∵ Angle Ф lies on second quadrant
∴ cosФ = -√5/3
The cosine of the angle θ, given that sine θ is 2/3 and tangent θ is negative, is -√(5/9) since the angle is in the second quadrant.
Explanation:If the sine of an angle (θ) is 2/3 and the tangent of that angle is less than zero, this indicates that the angle is in the second or fourth quadrant, where tangent values are negative. However, since sine is positive, the angle θ must be in the second quadrant. To find the cosine of θ, we can use the Pythagorean identity: sin² θ + cos² θ = 1. Substituting the sine value, we get (2/3)² + cos² θ = 1, which simplifies to 4/9 + cos² θ = 1. Solving for cosine gives us cos² θ = 1 - 4/9 = 5/9. The cosine value itself will be negative because cosine is negative in the second quadrant, so cos θ = -√(5/9).
What is the polynomial 3y^2+(y+7)^2-15 after it has be simplified
Answer:
4y^(2)+14y+31
Step-by-step explanation:
First you need to do (y+7)(y+7)
y^2+7y+7y+49
y^2+14y+49
Add it all together
y^2+14y+49+3y^2-15
4y^(2)+14y+31
Which expression is equivalent to 9th to the 5th power?
Answer:
option C
9 x 9 x 9 x 9 x 9
Step-by-step explanation:
Given in the question the expression
[tex]9^{5}[/tex]
The exponent corresponds to the number of times the base is used as a factor.
in which base = 9
exponent = 5
a)9 x 5
45
b)[tex]5^{9}[/tex]
c)[tex]9^{5}[/tex]
d)[tex]9^{5} x 5^{9}[/tex]
Find two numbers if their sum is six and their difference is 36
Answer:
Step-by-step explanation:
Let the two numbers be x and y
x + y = 6
x - y = 36 Add the two equations.
2x = 42 Divide by 2
2x/2 = 42/2
x = 21
x + y = 6 Substitute for x
21 + y = 6 Subtract 21
21-21 + y = 6-21
y = - 15
Christina weighs 17 pounds more than twice her younger sister Sarah's weight when both girls stood on a frieght scale, the reading was 179 pounds how much does christina weigh
Answer: Christina weighs 98 pounds.
Step-by-step explanation: The formula to solve this problem is x + 17 + x = 179, where x equals Sarah’s weight.
X + 17 + x = 179
First you need to combine the x values:
2x + 17 = 179
Next, subtract 17 from both sides:
2x = 162
Finally, divide both sides by 2:
X = 81
Sarah’s weight is 81 pounds and Christina weighs 17 pounds more, which is 98 pounds. You can double check your work by adding both of their weights (98 + 81) to make sure that your answer is correct.
Final answer:
By setting up a system of equations with the given information, we can solve for Christina's weight. Christina weighs 125 pounds.
Explanation:
To determine how much Christina weighs, we can set up an equation based on the information given. Let's define Sarah's weight as 's' and Christina's weight as 'c'. According to the question, Christina weighs 17 pounds more than twice Sarah's weight. So we can write the equation as:
c = 2s + 17
The combined weight of Christina and Sarah on the freight scale is 179 pounds. We represent this with another equation:
c + s = 179
Now we have a system of two equations:
c = 2s + 17c + s = 179Substituting the expression for 'c' from the first equation into the second equation gives us:
(2s + 17) + s = 179
Combining like terms, we have:
3s + 17 = 179
Moving 17 to the other side by subtracting 17 from both sides:
3s = 179 - 17
3s = 162
Dividing both sides by 3 to find Sarah's weight:
s = 162 / 3
s = 54
Now that we know Sarah weighs 54 pounds, we can find Christina's weight using the first equation:
c = 2(54) + 17
c = 108 + 17
c = 125
So, Christina weighs 125 pounds.
solve the equation m + 45 = 32
Answer:
m=-13
Step-by-step explanation:
What you do is you minus 45 from each side to get.
m=-13 as your answer.
Answer: -13
Step-by-step explanation:
Subtract 45 from 32 u get -13 = m
In the poportion 1/z =4/5/8 which number is equal to z in the proportion
Answer:
case 1) [tex]z=10[/tex]
case 2) [tex]z=5/32[/tex]
Step-by-step explanation:
case 1) we know that
Using proportion
[tex]\frac{1}{z}=\frac{(4/5)}{8}[/tex]
solve for z
[tex]\frac{1}{z}=\frac{(4/5)}{8}\\ \\z(4/5)=8\\ \\z=8*5/4\\ \\z=10[/tex]
case 2) we know that
Using proportion
[tex]\frac{1}{z}=\frac{4}{5/8}[/tex]
solve for z
[tex]\frac{1}{z}=\frac{4}{5/8}\\ \\4z=5/8\\ \\z=5/32[/tex]
need geometry help ASAP please!
Answer:
1. 121 π unit²
2. 143°
3. 151 unit²
Step-by-step explanation:
1.
Area of a circle is given by the formula A = πr²
where
A is the area,
r is the radius of the circle
From the given diagram, we can see that the radius is 11, hence the area will be:
[tex]A=\pi r^2\\A=\pi (11)^2\\A=121\pi[/tex]
The answer is [tex]121\pi[/tex] units^2
2.
The unshaded secctor and the shaded sector equals the circle. We know that circle is 360°. The unshaded sector has an angle of 217°. So the shaded part will be 360 - 217 = 143°
The measure of the central angle of the shaded sector is 143°
3.
Area of a sector is given by the formula [tex]A=\frac{\theta}{360}*\pi r^2[/tex]
Where
[tex]\theta[/tex] is the central angle of the sector (in our case it is 143°)
r is the radius (which is 11)
Plugging in all the info into the formula we have:
[tex]A=\frac{\theta}{360}*\pi r^2\\A=\frac{143}{360}*\pi (11)^2\\A=150.99[/tex]
rounding to the nearest whole number, it is 151 units^2
Robert has 20 pieces of candy in a bag: 4 mint sticks, 6 jelly treats, and 10 fruit tart chews. If he eats one piece every 4 minutes, what is the probability his first two pieces will both be mint sticks?
A. 1/25
B. 9/380
C. 3/95
D. 2/5
Final answer:
The probability of Robert eating two mint sticks consecutively from a bag of candy is 3/95, which is found by multiplying the individual probabilities of selecting a mint stick on the first and second draw.
Explanation:
The question involves calculating the probability that the first two pieces of candy Robert eats are both mint sticks. To find this probability, follow a step-by-step process to consider all possible outcomes.
Step 1: Probability of first mint stick
Initially, Robert has 20 pieces of candy with 4 being mint sticks. So, the probability of picking a mint stick first is:
4 mint sticks / 20 total pieces = 1/5 or 0.20.
Step 2: Probability of second mint stick
After eating one mint stick, there remain 3 mint sticks out of 19 total pieces. Thus, the probability now becomes:
3 mint sticks / 19 total pieces = 3/19.
Step 3: Combined probability
To find the probability of both events happening consecutively, multiply the separate probabilities:
(1/5) * (3/19) = 3/95, which simplifies to 0.0316, or about 3.16% chance.
Therefore, the correct answer is C. 3/95.
Is 16 gallons equal, less, or more than 64 quarts?
Answer:
less 13 gallons equals 52 quarts
Step-by-step explanation:
Equal to. There are 4 quarts in 1 gallon. So 16x4=64
You work 35 hours/week for 52 weeks and are given the option to be paid hourly or to go on salary. In which situation will you earn the most?
$17.50/hour and a $1,500 bonus at the end of the year
$32,000/year
$18.50/hour
$30,000/year with a 5% bonus
I think $18.50 would earn you the most money.
The first choice would earn you $33,350
The second choice would earn you $32,000
The third choice would earn you $33,670
I think the last choice would earn you $31,500
Hope this helps.
Answer:
Third plan $18.50/hour.Step-by-step explanation:
Givens
Work 35 hours per week.Work for 52 weeks.First situation.$17.50 per hour and $1,500 bonus at the end of the year, that is, at the ends of the 52 weeks.
If you work 35 hours per week for 52 weeks, with this plan, you gain
[tex]17.50 \times 35 = \$ 612.50[/tex]
Then, after 52 weeks: [tex]\$612.50 \times 52=\$ 31,850[/tex]
So, with the first plan, you make $31,850 + $1,500 = $33,350.
Second plan.Just $32,000 per year. It's a little bit better than the first situation.
Third plan.$18.50 per hour.
So, per week would be: [tex]18.50 \times 35 = \$647.50[/tex]
After 52 weeks you make: [tex]\$647.50 \times 52=\$33,670[/tex]
So, with the third plan, you make $33,670.
Fourth plan.$30,000 per year with a 5% bonus, which mean
[tex]30,000 + 0.05(30,000)=30,000+1,500=31,500[/tex]
So, with this plane you make $31,500 a year.
Therefore, as you can deduct, the best option is the third plan, $33,670 per year.
can you please help me?
Answer:
C / (2 pi) = r
Step-by-step explanation:
C = 2 pi r
Divide each side by 2 pi
C / (2 pi) = 2 pi r/ (2 pi)
C / (2 pi) = r
Geoff purchased an annual golf pass for a municipal golf course in his town. He pays a flat fee for the annual golf pass and then each round he plays he must pay the additional cost for a golf cart.
A linear model of this situation contains the values (30, 1,181) and (44, 1,363), where x represents the number of times he plays each year, and y equals the total amount he spends on golf in one year.
What is the flat fee for the annual golf pass?
Answer:
$791
Step-by-step explanation:
Find the equation of the line passing thru (30, 1,181) and (44, 1,363), The y-intercept of this equation will answer this question: it represents the annual golf pass.
Moving from (30, 1,181) to (44, 1,363), we see x increasing by 14 from 30 to 44 and y increasing by 182 from 1181 to 1363.
Thus, the slope of this line is m = rise / run = 182 / 14 = 13.
Subst. the knowns (30, 1,181) and m = 13 into the standard equation for a straight line in slope-intercept form, y = mx + b, we get:
1181 = 13(30) + b. Then 1181 - 390 = 791.
The flat fee is $791, payable at the beginning of each year.
Answer:
The answer is $760
Step-by-step explanation:
First, find the rate of change, or slope, from the two given points.
Next, find the equation for the linear model using the slope and a point.
The initial value is the value of y when x equals 0.
In this case, the initial value is the flat fee for the annual golf pass.
Therefore, the flat fee for the annual golf pass is $760.
A standard television tube produces 525 scans of the television screen per 1/30 of a second. How many scans will a tube make during a 30-second commercial?
➷ First find the number of scans produced per second
To do this, multiply the number of scans by 30:
525 x 30 = 15750
So, there are 15750 scans produced per second
You need the value for 30 seconds, so multiply by 30 again
15750 x 30 = 472500
Your answer would be 472500
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
The perimeter of a rectangle is 88 m. If the width were doubled and the length were increased by 12 m, the perimeter would be 152 m. What is the length of the original rectangle?
Answer: 24 meters.
Step-by-step explanation:
The perimeter of a rectangle is given by the formula:
[tex]P=2l+2w[/tex]
Where l is the lenght and w is the width.
The perimeter of the original rectangle is 88 m, then:
[tex]88=2l+2w[/tex] [EQUATION 1]
Where l is the length of the original rectangle
You know that if the width were doubled and the length were increased by 12 m, the perimeter would be 152 m. Therefore the new length is:
[tex]l+12[/tex]
The new width is:
[tex]2w[/tex]
Susbtitute into the equation of the perimeter and solve for w:
[tex]152=2(l+12)+2(2w)\\4w=152-(2l+24)[/tex]
[tex]w=\frac{128-2l}{4}[/tex] [EQUATION 2]
Substitute the Equation 2 into Equation 1 and solve for the length, as you can see below:
[tex]88=2l+2(\frac{128-2l}{4})[/tex]
[tex]88=2l+2(\frac{128-2l}{4})\\88-2l=\frac{128-2l}{2}\\\\176-4l=128-2l\\176-128=4l-2l\\\frac{48}{2}=l\\\\24=l[/tex]
Therefore, the length of the original rectangle is 24 m.
Answer:
Length of original rectangle = 24 m
Step-by-step explanation:
Perimeter of rectangle
P = 2(l + b)
l - length and b - width
It is given that,the perimeter of a rectangle is 88 m. If the width were doubled and the length were increased by 12 m, the perimeter would be 152 m
Perimeter of original rectangle = 88 m
2(l + b) = 88
l + b = 44
b = 44 - l
To find length and width
length l = l + 12 and width = 2(44 - l) then,
Perimeter = 152 m
we can write,
2( l + 12 + 2(44 - l)) = 152
l + 12 + 88 - 2l = 152/2 = 76
100 - l = 76
l = 100 - 76 = 24
Therefore length = 24 m
width = 44 - l = 44 - 24 - 20 m
If the original price of a pair of shoes is $80 but a sign above the shoes reads “Sale - 20% discount”, then what price would a costumer pay for the shoes (excluding tax)?
A.) 64
B.) 6
C.) 16
D.) 80
E.) 60
Answer:
A.) 64
Step-by-step explanation:
The first step is identifiying the original price of the shoes and the discount
Next you will decide what type of equation you will need. For this situation, you would need a subraction equation.
80 - 20% = ?
If you choose to slove with a calculator, don't put 0.2 in the place of 20%. We dont do this because it will result in a different answer. 80 - 0.2 = 79.8.
Now we solve the problem
80 - 20% = 64
The number of fish in a lake decreased by 25% between last year and this year last year there were 60 fish in the lake what is the population this year? If you get stuck consider drawing a diagram
Answer:
45
Step-by-step explanation:
Decreasing by 25% means that there is 25% less of last years amount or 0.25x less. It also means that this year there is only 75% of what was last year actually in the lake or 0.75x. Since last year, there were 60 fish, this means this year there is 0.75(60) = 45. This year has 45 fish.
Answer:
45
Step-by-step explanation:
is √4 rational or irrational?
Rational number since a rational number is Any integer
On a map the scale is 1 inch :150 miles. If the map distance is 3 inches, find the actual distance
Answer: 450 miles
Step-by-step explanation:
3 inches / 1 inch = 3 times 150 miles = 450 miles
Given the triangle below, what is m triangleA, rounded to the nearest tenth?
Answer:
B because it is close to 30
Step-by-step explanation:
Answer:
The correct answer is option A 17.8°
Step-by-step explanation:
From the figure attached with this answer,
We can see a perpendicular from B to side AC
To find BD
In triangle BDC, its angles are 30°, 60° and 90°
Therefore the sides are in the ratio 1 :√3 : 2
Here BC = 11
BD : DC : BC = 1 :√3 : 2 = 11√3/2 : 11/2 : 11
Therefore BD = 11/2
To find the value of m<A
We have
Sin ∅ = Opposite side /Hypotenuse
AB = 18 and BD = 11/2
Sin A = BD/AB =(11/2)/18 = 11/36 = 0.3055
m<A = Sin⁻¹(0.3055) = 17.79 ≈ 17.8°
Therefore the correct answer is option A 17.8°
How far did Eddie travel after his break? (The break is the part with only the straight line!)
The break ended at 4pm when he was at 15 km.
The ride ended at 6pm when he was at 45 km.
From 4 to 6pm he rode 45 - 15 = 30 km.
Answer: it would be 30 kilometer
Step-by-step explanation:
45-15=30
Find the equation of the line with m = 2 and passes through the point ( 4 , − 5 ) . Write your answer in standard form A x + B y = C .
Answer:
2x - y = 13
Step-by-step explanation:
To write the equation of a line use the formula [tex]y - y_1 = m(x-x_1)[/tex].
Substitute m = 2 and (4,-5).
[tex]y --5 = 2(x-4)\\y + 5 = 2(x - 4)\\y + 5 = 2x - 8\\y = 2x -13\\-2x + y = -13\\2x - y = 13[/tex]
Plz someone help me
Describe the transformation of the graph of.....
Answer:
This graph is reflected over the x-axis
Step-by-step explanation:
This is because the negative is a coefficient in front. This causes the graph to flip, which is the same as a reflection over the x-axis
Answer:
A
Step-by-step explanation:
Since we're dealing with the b value here, we are talking about an x axis reflection.