√4x²-20x+25=5-2x
HELP PLEASE!!! P.S the entire equation 4x²-20x+25 is under the square root
Answer:
The equal is valid for x≤ 5/2
Step-by-step explanation:
sqrt(4x²-20x+25)=5-2x
Square both sides
(sqrt(4x²-20x+25))^2=(5-2x)^2
Foil the term on the right (5-2x)(5-2x) = 25 -10x-10x+4x^2 = 25 -20x+4x^2
(4x²-20x+25)=25-20x+4x^2
The left side is equal to the right side
We need to check for extraneous solutions
The break point is 5-2x =0
5 =2x
x =5/2
Check x < 5/2
Let x=0
sqrt(4x²-20x+25)=5-2x
sqrt(25)=5
True
Check x=5/2
sqrt(4x²-20x+25)=5-2x
sqrt(4(25/4)-20*5/2+25)=5-2(5/2)
sqrt(25-50+25)=5-5
0=0
True
Check x>5/2
Let x=10
sqrt(4x²-20x+25)=5-2x
sqrt(4*100-20*10+25)=5-2*10
sqrt(400-200+25)=5-20
sqrt(225) = -15
15 does not equal -15
False
The equal is valid for x≤ 5/2
How to get the area of the trapezoid
Answer:
50
Step-by-step explanation:
The formula for the area of a trapezoid is a+b/2h. a is the top of the trapezoid (5). b is the bottom of the trapezoid(15). h is the height of the trapezoid(5). First you add 5 and 15 together to get 20. Then you divide by 2 to get 10. Now you do 10 x 5 to get 50 as your answer. 5+15/2 = 10(5) = 50
There are 6 shipping boxes that each contain 36 kg of merchandise from a toy store. Before the boxes are loaded onto a delivery truck, the same amount of additional merchandise is added to each box. The total weight of all of the boxes is 258 kg. How much additional weight was added to each box?
Answer: 7 kg
Step-by-step explanation:
The accompanying table shows the value of a car over time that was purchased for 14100 dollars, where x is years and y is the value of the car in dollars. Write an exponential regression equation for this set of data, rounding all coefficients to the nearest thousandth. Using this equation, determine the value of the car, to the nearest cent, after 15 years.
Answer:
equation: 14506.226(0.870)^x
answer: 1796.15
Step-by-step explanation:
Plugging in the tables into your calcuator
a= 14506.226
b= .870
y=ab^x
y= 14506.226(0.870)^x
= 1796.15
The equation of the exponential regression is [tex]\rm y = 14100 \ e^{-0.087x}[/tex]. And the value of a car after 15 years is $ 3,823.53.
What is an exponent?Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.
The accompanying table shows the value of a car over time that was purchased for 14100 dollars, where x is years and y is the value of the car in dollars.
The exponential regression equation will be given as
[tex]\rm y = A_o e^{kx}[/tex]
Where A₀ is the coefficient of exponential regression and k is the constant.
For x = 0, the value of y will be $ 14100. Then we have
[tex]\rm 14100= A_o e^{k*0}\\\\ A_o \ \ \ \ = 14100[/tex]
Then the equation will be
[tex]\rm y = 14100 \ e^{kx}[/tex]
For x = 1, the value of y will be $12,929. Then we have
[tex]\rm 12929= 14100 e^{k*1}\\\\ e^k \ \ \ \ = 0.91695[/tex]
Taking ln both sides, then we have
[tex]\begin{aligned} \rm ln\ e^k &= ln \ 0.91695\\\\\rm k*ln \ e &= -0.087\\\\\rm k &= -0.087 \end{aligned}[/tex]
Then the equation will be
[tex]\rm y = 14100 \ e^{-0.087x}[/tex]
Then after 15, the value of a car will be
[tex]\rm y = 14100 \ e^{-0.087*15}\\\\\rm y = 14100 * 0.2712\\\\\rm y = 3823.53[/tex]
More about the exponent link is given below.
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How far will a skier travel in 2 1/2 minutes? Explain how you figured it out
1 minute= 60 seconds
3600 meters 60 seconds would be 1440 traveled
and 1440 + 1440 + 720= 3600
Hope this helps :)
10 points
Which equation should you solve to find x?
Answer:
B.
Step-by-step explanation:
Using SOHCAHTOA,
sin 24 = 4/10
cos 24 = x/10
tan 24 = 4/x
Answer: B.
Option B. is correct. Using cosine formula the equation cos 24° = [tex]\frac{x}{10}[/tex] is used to find value of 'x'.
What is cosine?The ratio of the "adjacent side of a right angle triangle to the hypotenuse" is called cosine and given by the symbol 'cos'.
According to the question,
Angle of Right angle triangle is 24°
Adjacent = x
Opposite = 4
Hypotenuse = 10
In order to value of 'x' only if using cosine formula.
Formula for cosine = [tex]\frac{adjacent}{hypotenuse}[/tex]
= [tex]\frac{x}{10}[/tex]
Hence, the equation cos 24° = [tex]\frac{x}{10}[/tex] is used to find value of 'x'.
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Which expression represents the following calculation?
Add 3 to the quotient of 8 divided by 6.
(8 + 6) + 3
(8 + 6) = 3
(8 + 3) = 6
6+ (3 * 8)
Answer:
[tex](8 \div 6) + 3[/tex]
Step-by-step explanation:
Required
The equivalent expression
To do this, we take it one step at a time.
First, the quotient of 8 divided by 6;
This means 8 divided by 6: [tex](8 \div 6)[/tex]
3 added to it;
The expression becomes: [tex](8 \div 6) + 3[/tex]
I need help with all of these ASAP thank you so much
Answer:
C
Step-by-step explanation:
Functions meet the vertical line test:
a vertical line will intersect the graph at most at one point
C doesn't pass the vertical line test and is therefor not a function
A phone company offers two monthly plans. Plan A costs $10 plus an additional $0.15 for each minute of calls. Plan B costs $19 plus and additional $0.10 for each minute of calls.
For what amount of calling do the two plants cost the same?
What is the cost when the tow plans cost the same?
Answer:
Step-by-step explanation:
A phone company offers two monthly plans. Plan A costs $10 plus an additional $0.15 for each minute of calls. Plan B costs $19 plus and additional $0.10 for each minute of calls.
For what amount of calling do the two plants cost the same?
Where would (2,-4) go on the coordinate plane?
Answer:
in the 4th quadrant
WRITE THE SOLUTION TO THE FOLLOWING SYSTEMS
HURRY ILL GIVE BRAINLIEST!!!!!!!
Answer:
1) (2,4)
2) (5,-2)
Step-by-step explanation:
those are the points at which the lines cross making them the solutions to the equations
Three (3) people share a car for a period of one year and the mean number of kilometres
traveled by each person is 152 per month
How many kilometres will be travelled in a year?
Answer:
456
Step-by-step explanation:
It is shared by 3 people so it will be multiplied by 3.
Answer:
5472
Step-by-step explanation:
If the mean between three people is 152 kilometers per month, the distance travelled in a month is 152 * 3 = 456.
Then we multiply 456 by 12 to get the number of km travelled in a year.
456 * 12 = 5472
The dot plot shows the number of goals Erin's soccer team scored this season Goals Scored Per Game 2 Which is a true statement about the dot plot? The team never scored exactly 2 goals in a single game. OThe team scored exactly 1 goal in 3 games this season. OThe most goals the team scored in a single game were 8. O The team scored exactly 3 goalsin 4 games this season. thank you so much
Answer:
The answer is A. The team never scored exactly 2 goals in a single game.
Step-by-step explanation:
Edg 2021
The correct answer is Option A , The team never scored exactly 2 goals in a single game.
What is a dot plot ?A dot plot, also known as a strip plot or dot chart, is a simple form of data visualization that consists of data points plotted as dots on a graph with an x- and y-axis.
These types of charts are used to graphically depict certain data trends or groupings.
The team never scored exactly 2 goals in a single game.
It is Option A , because it says the team never scored exactly 2 goals in a single game
and the dot plot shows 0 dots in number 2 which means A. is the correct answer.
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# form the greatest and smallest 4 digit number repetition of digits is allowed
1) the number is an even number and 2)the number is an odd number
Answer:
1) The smallest is 1000, and the greatest is 9998.
2) The smallest is 1001 and the greatest is 9999.
Step-by-step explanation:
Four digit numbers:
The set of four digit numbers is: {1000, 1001, ...., 9998, 9999}
Even numbers:
End in 0, 2, 4, 6, 8
Odd numbers:
End in 1, 3, 5, 7, 9
1) the number is an even number
The smallest is 1000, and the greatest is 9998.
2)the number is an odd number
The smallest is 1001 and the greatest is 9999.
Determine if the following statements are true or false, and explain your reasoning. If false, state how it could be corrected. (a) If a given value (for example, the null hypothesized value of a parameter) is within a 95% confidence interval, it will also be within a 99% confidence interval. true false
Answer:
True
Step-by-step explanation:
Margin of error of a confidence interval:
The margin of error of a confidence interval has the following format:
[tex]M = z\frac{s}{\sqrt{n}}[/tex]
In which z is related to the confidence level(the higher the confidence level the higher z is), s is related to the standard deviation and n is the size of the sample.
A higher confidence level leads to a larger margin of error, that is, a wider interval. The interval expands around it's lower and upper bounds, which means that if a value is part of a lower confidence interval(such as 95%), it will be part of the higher(such as 99%), and the answer to this question is true.
Which statement is false?
A. Negative numbers are always less than positive numbers.
B. The sum of two negative numbers is always negative.
O C. The difference between two negative numbers is sometimes positive.
D. The product of two negative numbers is always negative.
E. The quotient of two negative numbers is always positive.
Answer:
So, the option (D) is the answer.
Step-by-step explanation:
A. The negative numbers are always less than positive numbers.
It is true.
For example, - 2 < + 2
B. The sum of two negative numbers is always negative.
It is true.
For example, - 3 + (- 3) = - 6
C. The difference between two negative numbers is sometimes positive.
It is true.
For example, (- 3) - (-4) = 1
D. The product of two negative numbers is always negative.
It is false.
For example, (-3)(-3) = 9
E. The quotient of two negative numbers is always positive.
It is true.
For example, (-3)/(-1) = 3
What does growth mean in math
please help, thanks!
Answer:
[tex]x=99^{\circ},\\y=81^{\circ}[/tex]
Step-by-step explanation:
The sum of the interior angles of a polygon with [tex]n[/tex] sides is [tex]180(n-2)[/tex]. Since the shape in the figure has 5 sides, the sum of its interior angles is [tex]180(5-2)=180\cdot 2=540^{\circ}[/tex].
Therefore, we can set up the following equation:
[tex]95+125+105+116+x=540,\\441+x=540,\\x=\boxed{99^{\circ}}[/tex]
Since [tex]\angle x[/tex] and [tex]\angle y[/tex] make up one side of a line, they are supplementary, as each side of a line is [tex]180^{\circ}[/tex].
Thus, we have:
[tex]x+y=180,\\99+y=180,\\y=\boxed{81^{\circ}}[/tex]
Find the exact value
Sin(300-45)
Answer:
sin ( 300 - 45 )
Step-by-step explanation:
sin (300 - 45 )
= - 0. 965
= - 0. 97
In parallelogram ABCD shown, point E and F are located on diagonal BD and point G is located on side AB such that GE and CF are perpendicular to BD. Prove: trainge BEG is similar to traingle DFC
Answer:
Match the Statement number with the Reason number.
Step-by-step explanation:
Statements:
1.GE is perpendicular to BD
CF is perpendicular to BD
2. Angle GED equal 90
Angle DFC equal 90
3. Angle GED is congruent to Angle DFC
4. Angle GBE is congruent to Angle FDC
5. Triangle BEG is similar to DFC
Reasons:
1.Given
2. Definition of perpendicular lines
3. Transitive property
4. Alternate Interior Angles
5. AA Similarity
By satisfying essential conditions for two triangles to be similar, we can say that triangle BEG is similar to triangle DFC.
What is a parallelogram?A quadrilateral in which opposites sides are equal and parallel. Also, opposite angles are equal to each other.
As we know that AB║ DC
so,∠GBE = ∠CDF (alternate angles)
∠GEB= ∠DFC = 90°
so triangle BEG≈DFC
Therefore, we can say that triangle BEG is similar to triangle DFC
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Answer this please Help
Answer:
x=10.75 in
Step-by-step explanation:
A = 390 = x(3x+4)
3x²+4x-390 =0
ax²+bx+c=0
x= (-b±√b²-4ac)/2a
x= (-4±√(16+4680))/6 = (-4±2√1174)/6 = (-2±√1174)/3
We will consider only the x that gives us a positive answer because the dimensions cannot be negative.
x= (-2+√1174)/3 = 10.75456113≈ 10.75
What does 7 x 1/3 equal to
[tex]7 \times \frac{1}{3} \\ \\ = \frac{7 }{3} [/tex]
PLEASE ANSWER THIS
PLEASE URGENT WORK
I M CRYING
Answer:
b=69(alternate angle)
b=37(alternate angle)
50 PTS AND BRAINLIEST FOR CORRECT ANSWER
Answer: I asked my teacher, she said it is c
Step-by-step explanation:
Answer:
yes it's c
have a great day
If the equation y = |x| is graphed and then
moved up 3 units on the y-axis, what will be
the equation of the new graph?
Answer:
Step-by-step explanation:
The new equation will be
y = abs(x) + 3
I have made a graph to show you this.
The red graph is y = abs(x)
The blue graph is y = abs(x) + 3
You need only look at the point 0,0 to see what happened. On the red graph (0,0) is the lowest point. When you add 3 to get the lowest point, you should notice that the lowest point is now (0,3)
Last week, Becky went to dance class 4 times. Each class was 3/2 hours. This week, Becky went to dance class 5 times. Each class was 1 hour which week did Becky spend more total time in dance class
Answer:
Last week
Step-by-step explanation:
last week because, the class that week was only 1 hour and last weeks was 3/2 an hour
What is the value of X equal?
Answer:
113º
Step-by-step explanation:
(x + 14) + (180 - 83) + x + 90 + x = 540
3x + 201 = 540
3x = 339
x = 113
cotx= is also equal to
[tex] \huge\frak{Answer:-}[/tex]
[tex] \rm{cot \: x = cos \: x \: sin \: x}[/tex]
_____________[tex]\huge \mathtt \purple{Answer:-}[/tex]
[tex] \sf \red{cot \: x \: = \: cos \: x \: sin \: x}[/tex]
____________Professor Stats has 40 students in her statistics class. 24 of the students are male. If she randomly selects 6 of her students at random, without replacement, the probability of selecting 4 men in the sample is
Answer:
the answer is 332
Step-by-step explanation:
quizlet
The area of a parallelogram is 120 cm ^ 2 and the height is 30 cm . Find the corresponding base
Answer:
4 cm
Step-by-step explanation:
The Area of a parallelogram is given by :
Area = base * height
Area = 120 cm² ; height = 30
Area = base * height
120 = base * 30
Base = 120 / 30
Base of parallelogram = 4 cm