After rotating a point C 90° counterclockwise about the origin the coordinates of C' would be (-2, 1)
In this question, we have been given a triangle ABC.
A point C is at (1, 2)
The triangle is rotated counter clockwise 90° about the origin.
We need to find the coordinates of C' which is image of vertex C after rotation.
We know that, if we rotate a point 90° counterclockwise about the origin a point (x, y) becomes (-y, x).
Here C(1, 2) is rotated 90 degrees counterclockwise about the origin.
So, the coordinates of C' would be,
C' = (-2, 1)
Therefore, after rotating a point C 90° counterclockwise about the origin the coordinates of C' are (-2, 1)
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Subtract. 15/57−6/45
please help me if u can i need this really fast <33
The resulting value after the subtraction of 15/57 - 6/45 is 37/285
Subtraction:
Subtraction is an arithmetic operation that represents the operation of removing the particular objects from a collection.
It is signified by the minus sign, −.
Given,
Here we need to find the value of the subtraction of 15/57 - 6/45.
The fractions have unlike denominators.
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(57, 45) = 855
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD.
This is basically multiplying each fraction by 1.
[tex]\frac{15}{57}\times\frac{15}{15}-\frac{6}{45}\times\frac{19}{19}[/tex]
Complete the multiplication and the equation becomes
=> 225/855 - 114/855
Complete the multiplication and the equation becomes
=> 111/855
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 111 and 855 using
GCF(111,855) = 3
[tex]= > \frac{111 \div 3}{855 \div 3} = \frac{37}{285}[/tex]
Therefore, resulting value is 37/285.
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AX + 6939 + x4(G.CO.C.10)Solve for xFind the measure of angle A:
The sum of the angles of a triangle always equals 180°, then we can formulate the following expression:
(x + 69)° + (39 + x)° + 90° = 180°
By combining like terms in the above equation, we get:
x + x + 69 + 39 + 90 = 180
2x + 198° = 180°
We can solve for x to get:
2x + 198 - 198 = 180 - 198
2x = 180 - 198
2x = -18
x = -18/2
x = -9
Then, x equals -9.
In order to calculate the measure of angle A, we just have to replace the value of x into the equation 39 + x, then we get:
mmm
Then, the measure of angle A equals 30°.
what is the equation of the line that passes through the point (6,1) and hs the slope of -1/2?
The equation of the line: y=-1/2x+4
Describe slope.A line's slope is the ratio of how much y increases as x increases by a specific amount. How steep a line is, or how much y climbs as x rises, is determined by its slope. The slope is constant anywhere along the line (the same).
The slope of the line and its passing point are given to us.
Using this information, we can write the equation in point-slope form as follows:
y-y1 = m(x-x1)
y-1 = -1/2(x-6)
y-1 = -1/2x+3
Move -1 to the right now by performing the reverse operation:
y = -1/2x+3+1
y = -1/2x+4
Hence, The equation of line is y = -1/2x+4
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What is the solution set of the following equation?
-8x + x + 15 = -7x + 12
Ø
{all reals}
{1/7}
The solution set of the equation is Ø.
Which expressions are equivalent to the one below? Check all that apply.
log(105)
A. 5
B. 5.log 10
C. 1
D. 5.10
The given expression is equivalent to option (A)
What is an expression?
An expression, often referred as a mathematical expression, is a continuous collection of signs that are well-formed in accordance with context-dependent principles. Numbers (predictor variables), parameters, processes, functions, brackets, capitalization, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's sequence of operations and other features. In algebra, a value may be designated by an expression; this value may rely on the values given to the variables that the expression contains. The semantics associated with the symbols in the expression determine this value. The expression's context determines which semantics to use. It is unclear if two lambda expressions are equivalent. The phrases used to represent real numbers are the same way.
The given expression is equivalent to option (A)
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A bus arrives at the bus depot every half hour from 6:00am until 7:00pm every day. How many times in a week does a bus arrive at the depot?
Answer:
175
Step-by-step explanation:
0 = 6:00 am
1 = 6:30 am
2 = 7:00 am
3 = 7:30 am
4 = 8:00 am
5 = 8:30 am
6 = 9:00 am
7 = 9:30 am
8 = 10:00 am
9 = 10:30 am
10 = 11:00 am
11 = 11:30 am
12 = 12:00 pm
13 = 12:30 pm
14 = 1:30 pm
15 = 2:00 pm
16 = 2:30 pm
17 = 3:00 pm
18 = 3:30 pm
19 = 4:00 pm
20 = 4:30 pm
21 = 5:00 pm
22 = 5:30 pm
23 = 6:00 pm
24 = 6:30 pm
25 = 7:00pm
25 * 7(days a week) = 175
____ + _____= 16 + +____ - ______=12 = = 26 16
In the first line, we are going to have that if you put 7 then to have the sum rigth the next space have to be 9, following that idea the space down of the 9 have to be also 7 and the first space on the second line have to be 19. So we are going to have 7 + 9 = 16 in the first line and in the second line 19 - 7 = 12, and the other two operations are going to be solve also 7 + 19 = 26 and 9 + 7 = 16.
Then the answer is 7 + 9 = 16 in the first line and in the second line 19 - 7 = 12.
8. Gerald's account balance is -$45.72. He writes a check for $32.80 and then deposits a $420.99 paycheck. What is his balance now?
Answer:
$342.47
Step-by-step explanation:
Gerald currently has -45.72 dollars.
If he gives writes a check to someone else, you lose money. Since he wrote a check for $32.80, subtract 32.8 from -45.72.
After writing the check, Gerald has -78.52 dollars. If you receive a paycheck and deposit it into your bank account, you add money. Add 420.99 to -78.52.
$342.47
Find the rule for the line that passes through each of these pairs of points. Use : y - y1 = m(x - x1).
(4, -8) and (0,4)
(3,1) and (-3, -1)
The rule for the line that passes through the points (4, -8) and (0, 4) is 3x + y = 4
The rule for the line that passes through the points (3, 1) and (-3, -1) is x - 3y = 0
Equation of a line and rule for a lineFrom the question, we are to determine the rule for the line that passes through each of the given pairs of points
For (4, -8) and (0, 4)
First, we will determine the slope, m, of the line
Using the formula,
m = (y₂ - y₁)/(x₂ - x₁)
m = (4 - (-8))/(0 - 4)
m = (4 + 8)/-4
m = 12/-4
m = -3
Now, for the rule
Using the formula,
y - y₁ = m(x - x₁)
Then,
y - (-8) = -3(x - 4)
y + 8 = -3x + 12
3x + y = 12 - 8
3x + y = 4
The rule is 3x + y = 4
For (3, 1) and (-3, -1)
The slope, m is
m = (-1 - 1)/(-3 - 3)
m = -2/-6
m = 1/3
Now, for the rule
Using the formula, y - y₁ = m(x - x₁)
y - 1 = 1/3(x - 3)
3(y - 1) = x - 3
3y - 3 = x - 3
-3 + 3 = x - 3y
0 = x - 3y
x - 3y = 0
Hence, the rule is x - 3y = 0
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What value of m makes this equation true? m/4−3=9
Answer:
m = 48
Step-by-step explanation:
m/4-3 = 9
lets add 3 on both side
m/4 = 12
now lets multiply both sides by 4
m = 48
Answer: m=48
Step-by-step explanation:
48/4=12
12-3=9
9=9
Therefore m=48 as it makes the equation true.
Solve the quadratic equation by completing the square. x^2+8x+9=0First choose the appropriate form and fill in the blanks with correct numbers. Then solve the equation. If there is more than one solution, separate with commas.
The quadratic equation given in the question is
[tex]x^2+8x+9=0[/tex]Step 1: Keep x terms on the left and move the constant to the right side by subtracting 9 on both sides
[tex]\begin{gathered} x^2+8x+9=0 \\ x^2+8x+9-9=0-9 \\ x^2+8x=-9 \end{gathered}[/tex]Step 2: Take half of the coefficient of the x term and square it
The coefficient of the x term is 8
[tex]\begin{gathered} (8\times\frac{1}{2})^2 \\ =(\frac{8}{2})^2 \\ =4^2 \\ =16 \end{gathered}[/tex]Step 3: Add 16 to both sides in the equation in step 1
[tex]\begin{gathered} x^2+8x=-9 \\ x^2+8x+16=-9+16 \\ x^2+8x+16=7 \\ \end{gathered}[/tex]Step 4: Re-write the perfect squares on the left
[tex]\begin{gathered} x^2+8x+16=7 \\ (x+4)^2=7 \\ \text{Which will give us } \\ (x+4)^2-7=0 \\ (x+4)^2=7 \end{gathered}[/tex]Hence,
We will have (x+4)²=7
To solve for the value of x, we will equate to zeros and make x the subject of the formula
[tex](x+4)^2=7[/tex]Step 5: Add 7 to both sides
[tex]\begin{gathered} (x+4)^2-7+=0+7 \\ (x+4)^2=7 \end{gathered}[/tex]Step 6: Square root both sides
[tex]\begin{gathered} (x+4)^2=7 \\ \sqrt[]{(x+4)}^2=\sqrt[]{7} \\ (x+4)=\pm\sqrt[]{7} \\ \end{gathered}[/tex]Step 7: Isolate the x on the left side and solve for x by subtracting 4 from both sides
[tex]\begin{gathered} (x+4)=\pm\sqrt[]{7} \\ x+4-4=\pm\sqrt[]{7}-4 \\ x=\pm\sqrt[]{7}-4 \\ \text{therefore,} \\ x=-4+\sqrt[]{7} \\ x=-4-\sqrt[]{7} \end{gathered}[/tex]Therefore,
The value of x is
x = -4+√7 , -4-√7
What is the remainder when P (x) is divided by (x + 1)?
Answer:
4
Explanation:
From the graph, the roots of the polynomial are -2, 1, and 1.
Therefore, the polynomial P(x) is defined below:
[tex]P(x)=(x+2)(x-1)(x-1)[/tex]When P(x) is divided by x+1, the remainder will be the value of x when x+1=0
When x+1=0
[tex]x=-1[/tex]Therefore:
[tex]\begin{gathered} P(-1)=(-1+2)(-1-1)(-1-1) \\ =1\times-2\times-2 \\ =4 \end{gathered}[/tex]The remainder when P (x) is divided by (x + 1) is 4.
0Is (2, 9) a solution to these simultaneous equations?
y = 3x + 3
y = x + 7
==============================================
Explanation:
The given solution is (2,9) which means x = 2 and y = 9 pair up together.
Replace x with 2 and replace y with 9.
Let's do so for the first equation
y = 3x+3
9 = 3*2+3
9 = 6+3
9 = 9
We get the same thing on both sides, which confirms the first equation.
Now let's check the second equation.
y = x+7
9 = 2+7
9 = 9
This equation is confirmed as well.
Both equations are true when (x,y) = (2,9) which confirms it is indeed the solution to the system.
----------------------------
If you are a visual learner, then I recommend graphing out the equations using a tool like GeoGebra or Desmos.
The two lines intersect at (2,9) which visually confirms it is the solution.
Probability trees
.. inhale attached
The probability of the team winning exactly one of their first two games is 0.1382.
What is a probability tree diagram?Without utilizing sophisticated calculations, a probability tree diagram is used to show the probability that an event will occur. It shows each potential result of an action. A probability tree serves as a visual representation of all the outcomes of an event while also calculating the probability of each occurrence.Given is a probability tree diagram with the respective probabilities of winning and losing a game by the teams.
To find the probability of the team winning exactly one of their two games multiply their probabilities of winning in the first game and losing in the second game and vice versa and find the sum of the two cases.
From the probability tree diagram,
P = (0.83 × 0.06) + (0.17 × 0.52)
P = 0.0498 + 0.0884
P = 0.1382
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5(3x – 2) + 11 = 106
please show work on computer
solve for x
Answer: 7
Step-by-step explanation:
5(3x – 2)= 15x-10
15x-10+11 = 15x+1
15x + 1 = 106 -1
15x = 105 /15
x = 7
The current I in an electrical conducter varies inversely as the resistance R of the conducter. The current is 1/6 ampere when the resistance is 36288 ohms. What is the current when the resistance is 49392 ohms?
The current when the resistance is 49392 ohms is 0.122 amperes.
If a current passes through two points is directly proportional to voltage and inversely proportional to the resistance.
The ohm's law is V=IR
Here V is the voltage, I is the current and R is the resistance.
Here we need to find the current flow through the conductor. The unit of current in amperes.
The current is I = 1/6 amperes when resistance is R = 36288 ohms.
To find voltage :
I = V/R
1/6 = V/36288
6V = 36288
V = 36288/6
V = 6048
Therefore, the voltage is 6048 volts.
Now, the current when the resistance is R = 49392 ohms:
I = V/R
I = 6048/49392
= 0.122 amperes.
Hence the current is 0/122 amperes.
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question: 1/3x+4=x-2
please help
Answer: x=9
Step-by-step explanation:
During christmas abok store sold 32 books. If the ratio of books to bookmarks sold was 4:1 how many bookmarks did the store sell?
Answer:
8 bookmarks were sold
Step-by-step explanation:
Answer: The answer is 8 not sure how to explain it. Can I get a brainliest plsssssssssssss
word problems QKB
Mr. Olsen's class went to the science museum to see dinosaur fossils. They saw a young
brontosaurus that was 5 feet tall. They also saw an adult brontosaurus that was 15 feet tall.
How many times as tall as the young brontosaurus was the adult brontosaurus?
f(x) =x^2-3x-18 vertex?
Answer:
(3/2, -81/4)Step-by-step explanation:
Rewrite in vertex form and use this form to find the vertex (h, k).
Answer:
[tex]\sf Vertex \left(\dfrac{3}{2}, \dfrac{-81}{4}\right)[/tex]
Step-by-step explanation:
Vertex of quadratic function: Write the equation in vertex form by using the method completing the square.y = x² - 3x - 18
Add 18 to both sides.
y + 18 = x² - 3x
Divide the co-efficient of x by 2 and square the result and then add it to both sides.
Co-efficient of x = 3. Divide 3 by 2and add (3/2)² to both sides
[tex]\sf y + 18 + \left(\dfrac{3}{2}\right)^2= x^2 - 3x + \left(\dfrac{3}{2}\right)^2\\\\\\y + 18+\dfrac{9}{4}=x^2 - 3x + \dfrac{9}{4}\\\\\\[/tex]
[tex]\sf y + \dfrac{18*4}{1*4}+\dfrac{9}{4}=\left(x - \dfrac{3}{2}\right)^2\\\\\\y + \dfrac{72}{4}+\dfrac{9}{4}=\left(x - \dfrac{3}{2}\right)^2\\\\\\y + \dfrac{81}{4}=\left(x-\dfrac{3}{2}\right)^2\\\\ y = \left(x-\dfrac{3}{2}\right)^2 -\dfrac{81}{4}\\\\[/tex]
Vertex form: f(x) = (x - h)² + k
where h and k are the vertex co-ordinates.
[tex]\sf \boxed{\bf Vertex \left(\dfrac{3}{2}, \dfrac{-81}{4}\right)}[/tex]
lütfen acil yapabilir misiniz
Answer:
te mando un feo vida okay
The equation y=0.29x+209 gives the cost y of renting a car if the care is driven x miles. Based on this equation, for every mile the car is driven the cost of increases by how much?
The car-driven cost increases with an increase in miles. After substituting x = 1,2,3,4.... you will find that it is increasing by 0.29 every time.
What is an equation?Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right is shown to be equal in reference to one another.
According to the question,
y = 0.29 x + 209
Where x is the number of miles and y is representing the driving cost of the car.
Substitute x = 1,2,3,4...... in the above equation.
y₁ = 0.29 (1) + 209 = 209.29
y₂ = 0.29 (2) + 209 = 209.58
y₃ = 0.29 (3) + 209 = 209.87
y₄ = 0.29 (4) + 209 = 210.16 and so on.
Now, take the difference,
y₂ - y₁ = 0.29
y₃ - y₂ = 0.29
y₄ - y₃ = 0.29
Hence, it is clear that with an increase in each mile the cost is increasing by 0.29.
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In 8x - 5 what are the monomials?
8x - 5 are the monomials
How Do You Identify Monomials ?A monomial in algebra is an expression with just one term. In other words, a polynomial with a single term is a monomial. Monomials typically consist of numbers, variables, multiplied numbers and variables, or multiplied numbers and multiple variables. A monomial, often known as a power product, is a product of variables, sometimes with repetitions, and powers of variables with nonnegative integer exponents. Monomials are negative numbers. A monomial is a product of any combination of real numbers, variables, and/or positive integer powers of those variables, according to the definition of a monomial.
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If the standard deviation of the data values in a sample is 19, what is the variance of the data values?
When the standard deviation of a data set is 19 then the datasets variance will be :
361
What is the relation between standard deviation and variance? This same standard deviation of a set of numbers is the distance between them and the mean. The variance is a measure of how far each point deviates from the mean on average. Variance is the average of all data points within a group, whereas standard deviation is the square root of the variance.variance formula :
variance = σ2
We are given a data set with a standard deviation of 19 and are asked to calculate the variance of the data values.
standard deviation = 19
We know that the variance of a data set is equal to the square of the standard deviation of the data values, so if the standard deviation is 19, the variance will be 19².
variance = standard deviation²
variance = 19²
= 361
As a result, the variance of the data values is 361.
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Your car has 10 gallons of gas. You use 1 gallon for every 20 miles you travel.
Answer:
You would travel 200 miles before running out of gas.
Step-by-step explanation:
1:20 so 10:200 each time you multiple by 10
the cube root of 64 is 4. how much larger is the cube root of 65.1? estimate using the linear approximation.
The exact difference is 0.022916
Given that the cube root of 64 is 4
We need to find how much larger is the cube root of 65.1 using the linear approximation.
Linear approximations:
They are ways to define a line tangent to a curve. At a particular range near the tangent point, the line can serve as an approximation for the function. However, linear approximations are determined through a combination of differentiation.
Here, when the tangent point is defined at x=a
then the linear approximation of a function is defined as f(x) ≈ f(a)+f′(a)(x−a)
Consider a = 64 f(x) = x^(1/3)
f'(x) = 1/3 x ^(-2/3)
So linear approximation is f(x) = 4 + 1/3 (64)^(-2/3) * (x-64)
x = 65.1
f(65.1) = 4 + 1/3 (64)^(-2/3) * (65.1 - 64)
f(65.1) - 4 = 1/3 1.1 (64)^(-2/3) = 1/3 * 1.1 * 1/16 = 1.1 / 48 = 0.0229
The exact difference is 0.022916
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Which of the following criteria always proves triangles congruent? Select all that apply.
Responses
Corresponding congruent Angle-Side-Angle
Corresponding congruent Angle-Side-Angle
Corresponding congruent Side-Angle-Side
Corresponding congruent Side-Angle-Side
Corresponding congruent Side-Side-Angle
Corresponding congruent Side-Side-Angle
3 congruent sides
2 congruent sides
3 congruent angles
The criteria that always proves triangles are congruent are;
Option A; Corresponding congruent Angle-Side-Angle
Option B; Corresponding congruent Side-Angle-SideOption
D: 3 congruent sides
How to illustrate the information?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.
According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.
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Whatttttttttttttt is x+2y+3z
all of those numbers are unlike terms, you can’t combine them, so there is no answer! :)
I need help with this question
10x i think is the correct answer
Ryan has a bank account balance of -$19.43. As soon as he realizes this, he deposits $36.40 in the account. What is Ryan's bank account balance after the deposit is made? $16.97 $ 55.83 - $16.97 - $55.83
The Answer is $16.97
explanation:
At first Ryan have balance of -$19.43 that is negative balance.
And after that he deposited $36.40.
so now we need to find how much money has he have in account :
For that add -$19.43 + $36.40 = $16.97 .
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