Final answer:
A system of equations will have the solution (2,0) if, when substituting x=2 and y=0, both equations are satisfied. This can be a linear equation where the y-intercept is set to be the negative double of the slope, or a conic section represented by a quadratic equation that intersects the x-axis at x=2.
Explanation:
Systems of equations that will have a solution of (2,0) must satisfy the condition that when x=2 and y=0, both equations are true. Considering the information provided about quadratic and differential equations, to find a system with the solution (2,0), one can set up a system of any two equations and test if the point (2,0) satisfies them. For instance, any linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept, will have a solution of (2,0) if b is set to -2m. Similarly, a second-order differential equation can be constructed with known solutions, including the point (2,0).
A system with a linear equation y = mx - 2m, where m can be any value.
A homogeneous linear differential equation with boundary conditions that result in the point (2,0) being a solution.
A conic section represented by a quadratic equation that intersects the x-axis at x=2.
For example, the quadratic equation ax² +2hxy+by² = 0, can be factored into two linear factors with no constant term, which means it represents two lines intersecting at the origin. If one of these lines passes through the point (2,0), it would confirm that our solution fits this system as well.
“the sum of -52 and 18 times a number is 2.” The number is
Answer:
50 is the answer
Step-by-step explanation:
Paula’s paycheck varies directly with the number of hours she works. If she earns $52.50 for 6h of work, how much will she earn for 11 h of work? Round your answer to the nearest cent
Answer:
$96.25
Step-by-step explanation:
Find the unit rate of pay:
$52.50
------------- = $8.75/hr
6 hours
Now multiply this rate by 11 hours:
($8.75/hr)(11 hrs) = $96.25
Answer: $ 96. 25
Step-by-step explanation:
It is said that two variables x and z vary directly if they meet the following relationship:
[tex]z = kx[/tex]
Where k is the constant of variation.
In this case z represents the gains and x represents the hours of work.
Now we must find the value of the constant k.
We know that for 6 hours of work the earnings are $ 52.50
So
[tex]x = 6[/tex]
[tex]z = \$\ 52.50[/tex]
[tex]52.50 = 6k[/tex]
[tex]k= \frac{52.50}{6}[/tex]
[tex]k= 8.75[/tex]
Then the equation is:
[tex]z = 8.75x[/tex]
Finally when x = 11, then:
[tex]z = 8.75*11\\\\z =\$\ 96.25[/tex]
ASAP GUYS!!!! (I NEED TO FINISH THIS QUICK) Graph Complete the sequence of transformations that produces △X'Y'Z' from △XYZ. A clockwise rotation °______ about the origin followed by a translation ______ units to the right and 6 units down produces ΔX'Y'Z' from ΔXYZ.
Answer:
A clockwise rotation 90° about the origin followed by a translation
2 units to the right and 6 units down produces Δ X'Y'Z' from Δ XYZ
Step-by-step explanation:
* Lets revise the rotation and translation
- If point (x , y) rotated about the origin by angle 90° anti-clock wise
∴ Its image is (-y , x)
- If point (x , y) rotated about the origin by angle 180° anti-clock wise
∴ Its image is (-x , -y)
- If point (x , y) rotated about the origin by angle 270° anti-clock wise
∴ Its image is (y , -x)
- If point (x , y) rotated about the origin by angle 90° clock wise
∴ Its image is (y , -x)
- If point (x , y) rotated about the origin by angle 180° clock wise
∴ Its image is (-x , -y)
- If point (x , y) rotated about the origin by angle 270° clock wise
∴ Its image is (-y , x)
- If the point (x , y) translated horizontally to the right by h units
∴ Its image is (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
∴ Its image is (x - h , y)
- If the point (x , y) translated vertically up by k units
∴ Its image is (x , y + k)
- If the point (x , y) translated vertically down by k units
∴ Its image is = (x , y - k)
* Now lets solve the problem
- Δ XYZ has vertices X = (-5 , 3) , Y = (-2 , 3) , Z = (-2 , 1)
∵ Δ XYZ rotate 90° clockwise about the origin the image will be (y , -x)
∴ The image of X is (3 , 5)
∴ The image of Y is (3 , 2)
∴ The image of Z is (1 , 2)
- From the graph
∵ X' = (5 , -1)
∵ Y' = (5 , -4)
∵ Z' = (3 , -4)
- Every x-coordinate add by 2
∴ There is a translation 2 units to the right
- Every y-coordinate subtracted by 6
∴ There is a translation 6 units down
- From all above
* A clockwise rotation 90° about the origin followed by a translation
2 units to the right and 6 units down produces ΔX'Y'Z' from ΔXYZ
Answer:
A clockwise rotation 90° about the origin followed by a translation
2 units to the right and 6 units down produces Δ X'Y'Z' from Δ XYZ
Step-by-step explanation:
from the top of a tower that is 300 ft high, a person observes the base of a tree at an angle of depression of 45. identify the horizontal distance from the tower to the tree rounded to the nearest foot?
answers:
A: 300ft
B: 245 ft
C: 212ft
D: 162 ft
i will give brainliest !! help ASAP
Answer:
A
Step-by-step explanation:
Connect the top of the tower (assuming the person's height can be ignored), the bottom of the tower, and the tree to form a right triangle.
Since the person is looking down at a 45 degree, it means the triangle is a equilateral triangle, so the length from the base of the tower to the base of the tree is also 300ft.
What is the slope of the line illustrated in the picture below?
Note: One scale is equivalent to 1
Answer:
-2
Step-by-step explanation:
y = -2x + 2; your y-intercept is [0, 2] and your x-intercept is [1, 0] (not all the time your x-intercept will be an endpoint). Simply do rise\run until you hit another endpoint, starting from your y-intercept. As you can see, you go two blocks south, then one block over east. Do you understand?
Answer:
The slope is -2
Step-by-step explanation:
Slope = Rise/Run = -2/1 = -2
Determine the value of cot 36º.
a. 1.85964798
b. 3.85369695
c. 3.45827451
d 1.37638192
Please select the best answer from the choices provided
A b c d
Answer:
d 1.37638192Step-by-step explanation:
Use a table with trigonometric functions (look at the photo) or use the calculator knowing that:
[tex]\cot\theta=\dfrac{1}{\tan\theta}=\left(\tan\theta\right)^{-1}[/tex]
Identify the polynomial a^2-b+c-d3
Answer:
This is four term polynomial.
Step-by-step explanation:
Polynomial comes from poly(meaning “many”) and nomial (in this case meaning “term”). So it says “many terms” A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
In this expression, we are to determine the polynomials depending on the number of terms present in the expression. The prefixes of the classification suggest the number of terms present.
a^2 - b + c - d^3
This is an example of a four-term polynomial. The first term is a^2, second one is -b, the third one is c, and the fourth one is -d^3.
Solve the equation.
—10x + 1 + 7х = 37
Answer:
X=- 12
Step-by-step explanation:
Answer:
x = -12
Step-by-step explanation:
—10x + 1 + 7х = 37
Combine like terms
-3x +1 = 37
Subtract 1 from each side
-3x+1-1 = 37-1
-3x = 36
Divide each side by -3
-3x/-3 = 36/-3
x = -12
Can someone help me out please ?
Answer:
2 + r = 7
Step-by-step explanation:
To write an equation for the image, simply look on both sides and add everything together. On the left side we have seven 1's, which adds up to 7. On the right side, we have 2 1's, which add up to 2, and a variable r. Now, we do not know the value of the variable r, so we simply leave it be. Therefore, the right side is equal to 2 + r. Since the image represents a balanced equation, the left side must equal the right side.
Left side = 7
Right side = 2 + r
Left side = Right side
7 = 2 + r
2 + r = 7
Shayla is tracking the weight of the smallest dog in a litter. use the table to write a linear function that models the puppy growth
week 0 weight in ounces 3
week 1 weight in ounces 6
week 2 weight in ounces 9
week 3 weight in ounces 12
A. y= 3x+3
B.y = 1/3x+3
C. y= 3x+12
D. y=1/3x+12
The linear function that models the puppy's growth is A. y = 3x+3.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given Shayla is tracking the weight of the smallest dog in a litter.
Week 0 weight in ounces 3, week 1 weight in ounces 6, week 2 weight in ounces 9, and, week 3 weight in ounces 12.
From this, we can conclude that every week weight of the dog is increasing by 3 ounces.
This can be numerically expressed as y = 3x+3.
Where y is the total weight and x represents the no. of weeks.
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Please help right now
Solve log x = 5.
Answer:
100000
Step-by-step explanation:
Since we have the natural base of the log, the base is 10.
Now think of it this way, since we are solving for the value that is being "logged" we can say 10 to the power of 5 equals what?
And since 10^5 is 100000, x is 100000.
The value of x is 100000.
A logarithm helps us know by what power a number must be raised to get the desired number.
A natural log is a log with base 10.
For example,
We want to know by what power must 10 be raised so we get 1000 as an output,
therefore, we can write it as,
[tex]\bold{log_{10} 1000 = 3}[/tex]
[tex]\bold{10^3 = 1000}[/tex]
where, 10 is the base meaning number to which power is to be raised,
1000 is the desired number,
And 3 is the answer.
Now, looking at our question,
[tex]\bold{log\ x= 5}[/tex]
can be written as
[tex]\bold{log_{10} x= 5}[/tex]
[tex]\bold{10^5 = x}[/tex]
[tex]\bold{10^5 = 100000}[/tex]
Therefore, 10 is been raised to the power of 5 giving the desired result which is 100,000.
Hence, the value of x is 100000.
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{(–8, –6), (–5, 2), (–8,1), (7, 3)} fuction?
Answer:
No
Step-by-step explanation:
A function has only one y value for each x value. Here, we have two points that have the same x value but different y values: (-8, -6) and (-8, 1). So this is not a function.
find the derivative in the form dy/dx
ANSWER
[tex]\frac{dy}{dx} = x{(3x)}^{ {x}^{2} } (ln(9 {x}^{2} ) + 1)[/tex]
EXPLANATION
The given equation is;
[tex]y = {(3x)}^{ {x}^{2} } [/tex]
Take natural log of both sides:
[tex] ln(y) = ln({(3x)}^{ {x}^{2} } )[/tex]
This implies that,
[tex]ln(y) = {x}^{2} ln({(3x)})[/tex]
We differentiate to get,
[tex] \frac{1}{y} \frac{dy}{dx} = ln(3x) (2x) + {x}^{2} ( \frac{1}{x} )[/tex]
This simplifies to
[tex] \frac{dy}{dx} =y (2x ln(3x) + x)[/tex]We substitute for y to get:
[tex]\frac{dy}{dx} = {(3x)}^{ {x}^{2} } (2x ln(3x) + x)[/tex]
Or
[tex]\frac{dy}{dx} = x{(3x)}^{ {x}^{2} } (2ln(3x) + 1)[/tex]
[tex]\frac{dy}{dx} = x{(3x)}^{ {x}^{2} } (ln(9 {x}^{2} ) + 1)[/tex]
The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the come to the volume of the prism?
base area=B
base area =B
volume of cone
volume of prism
1
2
volume of cone
volume of prism
1
3
volume of cone
volume of prism
2
3
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Answer:
[tex]\large\boxed{\dfrac{V_{cone}}{V_{prism}}=\dfrac{1}{3}}[/tex]
Step-by-step explanation:
[tex]\text{The formula of a volume of a cone:}\ V_{cone}=\dfrac{1}{3}B_cH_c\\\\B_c-base\ area\ of\ a\ cone\\H_c-height\ of\ a\ cone\\\\\text{The formula of a volume of a prism:}\ V_{prism}=B_pH_p\\\\B_p-base\ area\ of\ a\ prism\\H_p-height\ of\ a\ prism\\\\\text{The cone and the prism have the same base area and height.}\\\text{Therefore}\\\\V_{cone}=\dfrac{1}{3}BH\ \text{and}\ V_{prism}=BH\\\\\text{The ratio of the volume of the cone to the volume of the prism:}[/tex]
[tex]\dfrac{V_{cone}}{V_{prism}}=\dfrac{\frac{1}{3}BH}{BH}=\dfrac{1}{3}[/tex]
The solution is, 1:3 the ratio of the volume of the come to the volume of the prism.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
The cone in the diagram has the same height and base area as the prism.
now, we know that,
The formula of volume of a cone:
if 'B' is the base of the cone,
and 'h' is the height of the cone,
its volume is V = (1/3) (Bh) cubic units.
The formula of volume of a prism:
if 'B' is the base of the prism,
and 'h' is the height of the prism,
its volume is V = (Bh) cubic units.
The cone in the diagram has the same height and base area as the prism.
so, the ratio of the volume of the come to the volume of the prism:
The formula of volume of a cone: The formula of volume of a prism
= 1/3 *BH : BH
=1/3
=1:3
Hence, The solution is, 1:3 the ratio of the volume of the come to the volume of the prism.
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4+m/8=3/4 can anybody help?
Answer:
C. -26
Step-by-step explanation:
First, subtract by 4 both sides of equation.
4+m/8-4=3/4-4
Then, simplify.
4+m/8-4=m/8
3/4-4=-13/4
m/8=-13/4
Multiply by 8 both sides of equation.
8m/8=8(-13/4)
Simplify to find the answer.
8(-13/4)
-8*13/4
13*8/4=-104/4
104/4=-26
X=-26 is the correct answer.
C. -26 is the correct answer.
For this case we must solve the following equation:
[tex]4+ \frac {m} {8} = \frac {3} {4}[/tex]
We subtract 4 on both sides of the equation:
[tex]\frac {m} {8} = \frac {3} {4} -4\\\frac {m} {8} = \frac {3-16} {4}\\\frac {m} {8} = \frac {-13} {4}[/tex]
We multiply by 8 on both sides of the equation:
[tex]m = \frac {-13 * 8} {4}[/tex]
[tex]m = -26[/tex]
Answer:
Option C
The table shows the height in feet of several students in Miss Patel’s class
Answer:
a. 21/4, 11/2, 49/10, 5/1
b. James 5.5, Olivia 5 1/4, Feng 5, Carmela 4.9
Step-by-step explanation:
Answer with Step-by-step explanation:
Olivia: [tex]5\dfrac{1}{4}[/tex]
= [tex]\frac{21}{4}[/tex] (21/4=5.25)
James: 5.5
= [tex]\dfrac{55}{10}[/tex]
= [tex]\dfrac{11}{2}[/tex]
Carmela: 4.9
= [tex]\dfrac{49}{10}[/tex]
Feng: 5
= [tex]\dfrac{5}{1}[/tex]
b. Heights from greatest to least is:
James 5.5
Olivia 5.25
Feng 5
Carmela 4.9
Point M lies between points L and N on .
If LN = 12x + 16, what is the length of in units?
16 units
40 units
48 units
64 units
Answer:
LN=64 units
Step-by-step explanation:
step 1
Find the value of x
we know that
LN=LM+MN -----> equation A
see the attached figure to better understand the problem
we have
LN=12x+16
LM=10x+8
MN=5x-4
substitute the values in the equation A
12x+16=(10x+8)+(5x-4)
Solve for x
12x+16=15x+4
15x-12x=16-4
3x=12
x=4
step 2
Find the value of LN
LN=12x+16
LN=12(4)+16=64 units
f y is 6 when x is 3 and y varies directly with x, find y when x is 8.
Answer:Y = 16
Step-by-step explanation:
Y=6 and x = 3
If Y varies directly as x, then
Y = kx
Substitute the value of Y and x
6 = k * 3
Make k the subject of the formula
K = 6/3
k = 2
:. The equation connecting Y and x is
Y=2x
When x = 8
Y = 2*8
Y= 16
Yes, that is correct.
I even searched it, and saw that the answer was 16.
Nice Job!! :)
Given f(x) = 10x + 4 and g(x) = 3x - 8, what is f(x) + g(x) ?
- 7x - 4
- 13x + 4
- 7x + 4
- 13x - 4
Answer:
13x - 4
Step-by-step explanation:
f(x) + g(x) = 10x + 4 + 3x - 8.
First, we must rearrange it so we can add like terms.
10x + 3x + 4 - 8.
Add together 10x and 3x.
13x + 4 - 8.
Subtract 4 - 8.
13x - 4.
Therefore, the answer is 13x - 4.
Answer:
The answer has to be 13x-4
Step-by-step explanation:
10x+4 + 3x-8
13x+4-8 (Combine like terms)
13x-4
Dylan and Dusty plan to take weekly surfing lessons together. If the 2-hour lessons are $20 per person and they plan to spend $100 each on new surfboards, what is the maximum number of lessons the two can take if the total amount spent for lessons and surfboards is at most $480?
Answer:
they can both take 7 lessons each
Answer:
Each one can take 7 lessons.
Step-by-step explanation:
Dylan and Dusty plan to take weekly surfing lessons together.
They want to spend $100 each on new surfboards = $100 × 2
= $200
They want to spent total amount for lessons and surfboards is at most $480.
After spending on two new surfboards the money left with
= 480 - 200
= $280
The charges for 2-hours classes for surfing lessons = $20 per person
The charges for 1 hour classes for them = $20.00
With $280 they will be able to take maximum number of lessons
= [tex]\frac{280}{20}[/tex]
= 14 lessons
Each one can take 14/2 = 7 lessons.
the PE clasd has 12 boys and 8 girls what is the maximum number of teams that the teacher can divide the class into so that each team has an equal number of boys and girls the greatest common factor of the numbers of girls and boys
Answer:
4
Step-by-step explanation:
We are given that a PE class has 12 boys and 8 girls. The teacher needs to divide in maximum number of teams so that each team has an equal number of boys and girls.
For this, we will factors of 12 and 8 and their greatest common factor.
12 = 4 × 3 = 2 × 2 × 3
8 = 4 × 2 = 2 × 2 × 2
The greatest common factor is 4, therefore the maximum number of teams with equal number of boys and girls is 4.
Help me please I just don’t get it ♀️
Answer:
[tex]\large\boxed{1.\ the\ slope\ is\ \dfrac{1}{4}}\\\boxed{2.\ y=3x-5}\\\boxed{3.\ (3, 6)}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_2}\\\\l\ \parallel\ k\iff m_1=m_2\\\\m-slope\\b-y-intercept\to(0,\ b)\\\\1.\\\\y=-4x+1\to m_1=-4\\\\m_2=-\dfrac{1}{-4}=\dfrac{1}{4}[/tex]
[tex]2.\\y=3x+2\to m_1=3\\\\m_2=3,\ b=-5\\\\y=3x-5[/tex]
[tex]\text{Calculate}\ a\ \text{and}\ b:\\\\a=\dfrac{6-(-9)}{5}=\dfrac{15}{5}=3\\\\b=\dfrac{8-(-2)}{5}=\dfrac{10}{5}=2\\\\\text{Calculate the coordinates of a point:}\\\\x=-9+4a\to x=-9+4(3)=-9+12=3\\\\y=-2+4b\to y=-2+4(2)=-2+8=6[/tex]
Is this question a statistical question Which student spends the most time playing musical instruments? explain why or why not
i will mark brainliest, please help if you can
Statistical questions are questions that are answered by collecting variable data, which can be given as an average/range/percentage. This question has a single answer, and therefore it is not a statistical question. A statistical question would be, for example, What is the average amount of time students in this class spend playing musical instruments?
What are the solutions to x^2 + 4x - 12 = 0?
Answer:
That can be factored:
(x +6) * (x -2)
Therefore, x = -6 and x =2
Step-by-step explanation:
For this case we have the following quadratic equation:
[tex]x ^ 2 + 4x-12 = 0[/tex]
We can factor the equation, for it, we must find two numbers that when multiplied give as result -12 and when summed give as result +4. These numbers are: +6 and -2.
Then, the factorization is given by:
[tex](x + 6) (x-2) = 0[/tex]
Thus, the solutions are:
[tex]x_ {1} = - 6\\x_ {2} = 2[/tex]
Answer:
[tex]x_ {1} = - 6\\x_ {2} = 2[/tex]
What is the volume of this solid?
Joshua sells a pack of pens for $3.15, which is 5 percent more than he pays for them. Which equation will help find x, the amount he pays for a pack of pens? How many solutions will this equation have?
A.
x + 0.05x = 3.15, which has infinitely many solutions
B.
x + 0.5x = 3.15, which has one solution
C.
x + 0.05x = 3.15, which has one solution
D.
0.05x = 3.15, which has no solution
Answer:
C.
x + 0.05x = 3.15, which has one solution
Step-by-step explanation:
Let x = the price Joshua pays for the pack of pens
He add 5% (=.05 in decimal form)
That is x* .05
The new cost is 3.15
x+.05x = 3.15
This will have one solution
Answer:
The correct option is C.
Step-by-step explanation:
It is given that Joshua sells a pack of pens for $3.15, which is 5 percent more than he pays for them.
Selling price of a pack of pens = $3.15
Let x be the amount he pays for a pack of pens.
x + 5% of x = 3.15
It can be written as
[tex]x+\frac{5}{100}x=3.15[/tex]
[tex]x+0.05x=3.15[/tex]
[tex]1.05x=3.15[/tex]
Divide both sides by 1.05.
[tex]x=\frac{3.15}{1.05}[/tex]
[tex]x=3[/tex]
The required equation is x+0.05x=3.15 and this equation has one solution.
Therefore, the correct option is C.
Which inequality represents all values of x for which the product below is defined?
√5x * √x+3
A. x>0
B. x≤-3
C. x≥-3
D. x≥0
Answer:
D
Step-by-step explanation:
you cannot take the root of a negative number so that eliminates B and C. you can take the root of 0 to be 0 so D is valid.
The correct inequality will be x≥0
What are inequalities?Inequality a statement of an order relationship which are greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
How to know which inequality represents all values of x ?We know that a negative value under square root is not defined.So, here the values of x will be all the numbers greater or equal to 0
So the correct inequality will be x≥0
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..(07.01 LC)
Look at the triangle:
What is the value of cos xº? (1 point)
Answer:
[tex]\cos x=15\div 17[/tex]
Step-by-step explanation:
Recall the mnemonics SOH-CAH-TOA.
The CAH means the cosine ratio is the ratio of the adjacent side to the hypotenuse.
From the given triangle;
[tex]\cos x=\frac{Adjacent}{Hypotenuse}[/tex]
The side adjacent to the [tex]x\degree[/tex] is 15cm and the hypotenuse is 17cm.
We substitute the values to get;
[tex]\cos x=\frac{15}{17}[/tex] or [tex]\cos x=15\div 17[/tex].
Tom saves $750 a year. Bill saves $60 a month. How much more does Tom save a year than Bill?
Make a Selection:
A. $690
B. $30
C. $360
D. $60
NEXT >>
Answer:
B) 30
Step-by-step explanation:
Bill saves 60 dollars a month so first you have to find out how much he saves in a year
To find that you multiply 60 by 12 since there are 12 months in a year
60*12 = 720
Tom saves 750 in a year so you have to subtract 750 by 720 to know how much more tom saves
750 - 720 = 30
Tom saves Option(B) $30 more than Bill in a year.
What is the method to calculate the money saved by tom which is more than Bill ?It is given that Tom saves $750 a year where as Bill saves $60 a month.
Thus savings for Bill in a month is $60 .
For 1 year, Bill saves -
(12 * $60) = $720 .
Now definitely Tom saves more than Bill,
Savings made by Tom more than Bill is -
= ($750 - $720) = $30 .
Therefore, Tom saves Option(B) $30 more than Bill in a year.
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Evaluate this exponential expression.
3.(5+4)2 - 42=
what’s the answer
Answer:
[tex]12[/tex]
Step-by-step explanation:
[tex]3 \times (5 + 4) \times 2 - 42 \\ \\ 1. \: 3 \times 9 \times 2 - 42 \\ 2. \: 54 - 42 \\ 12[/tex]