The coordinates of Q(6, -4) under a reflection in the x-axis is Q'(6,4)
The coordinates of x will remain the same for reflection in the X axis, while y will change with the opposite sign.
From the question, we have
The coordinates of Q(6, -4) under a reflection in the x-axis is Q'(6,4).
Reflection:
A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and shape as the original, but it faces the opposite way. Changes in position during contemplation may also result in translation. Pre-image and image are terms used to refer to the same thing in this context. ABC and A'B'C are used to represent the pre-image and image, respectively. The coordinate system may be referred to by the reflection transformation (X and Y-axis).
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an airplane travels 600 miles against the wind in 5 hours, and makes the return trip with the same wind in 2 hours. find the rate of the wind.
Answer:
The speed of wind is 75 miles / hour
Step-by-step explanation:
Let's assume
speed of airplane is x miles /hour
speed of wind is y miles /hour
An airplane travels 600 miles against the wind in 4 hours
against wind means resultant speed will be less
so, speed =x-y
total distance traveled in 4 hour is
and this has to be equal to 600
Divide both sides by 4
makes the return trip with then same wind in 2 hours
with wind means resultant speed will be more
so, speed =x+y
total distance traveled in 2 hour is
and this has to be equal to 600
Divide both sides by 2
So, we get system of equations
now, we can solve it by adding both equations
now, we can solve for x
now, we can find y by plugging x into any one equation
Triangle UVW, with vertices U(-6,2), V(-4,6), and W(-8,5), is drawn inside arectangle, as shown below.What is the area, in square units, of triangle UVW?
Okay, here we have this:
Considering the provided vertices, we are going to calculate the requested area, so we obtain the following:
Then we will first calculate the measure of each side and later with Heron's formula we will find the area, then we have:
[tex]\begin{gathered} u=\sqrt{((-4-(-8))^2+(6-5)^2)} \\ u=\sqrt{4^2+1^2} \\ u=\sqrt{17} \end{gathered}[/tex][tex]\begin{gathered} w=\sqrt{(-6-(-4))^2+(2-6)^2} \\ w=\sqrt{2^2+(-4)^2} \\ w=\sqrt{20} \end{gathered}[/tex][tex]\begin{gathered} v=\sqrt{(-6-(-8))^2+(2-5)^2} \\ v=\sqrt{2^2+(-3)^2} \\ v=\sqrt{13} \end{gathered}[/tex]Then, the area is:
[tex]\begin{gathered} A=\sqrt{\frac{(\sqrt{13}+\sqrt{17}+\sqrt{20})}{2}(\frac{\sqrt{13}+\sqrt{17}+\sqrt{20}}{2}\sqrt{13})(\frac{\sqrt{13}+\sqrt{17}+\sqrt{20}}{2}\sqrt{17})(\frac{\sqrt{13}+\sqrt{17}+\sqrt{20}}{2}\sqrt{20})} \\ =\sqrt{49} \\ =7 \end{gathered}[/tex]Finally we obtain that the triangle's area is equal to 7 square units.
A report card shows that a student earns 21 points on a test with a total of 25 points. What percentage of the total points has the
student earned on the test?
Answer: The student got an 84%
Step-by-step explanation:
This one is comparatively simple because 25 is a factor of 100,
we just have to multiply each side by 4 so we get 81 out of 100
Cheers!
Rsmbro
A. Put the following values in order from least to greatest:
4²,-√4, √4²,-2√4, 6-47, √
The order of values in ascending order will be -4<-2<2<2.64<4<16 as the definition of ascending order says, "When numbers are arranged in ascending order, they are done so from smallest to largest".
What is ascending order?When numbers are arranged in ascending order, they are done so from smallest to largest. Climbing down the stairs of numbers starting with their highest value is another way to think of descending. The slide is descended while moving down it. Ascending order, in which the numbers are arranged from lower value to higher value, is the opposite of descending order. A number can be arranged in ascending order by going from smallest to largest from left to right.
Here,
4²=16
-√4=-2
√4²=4
-2√4=-4
6-4=2
√7=2.64
-4<-2<2<2.64<4<16
According to the definition of ascending order, "When numbers are arranged in ascending order, they are done so from smallest to largest," the order of values in ascending order will be -4<-2<2<2.64<4<16.
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When solving the following system of equations, which variable would be the easiest to solve for? {x+6y=25{2x+2y=9 A) the x in the first equationB)the y in the second equationC) the y in the first equationD) the x in the second equation
SOLUTION
From the first equation, we have
[tex]\begin{gathered} x+6y=25 \\ we\text{ can easily solve for x by subtracting 6y from both sides, we have } \\ x+6y-6y=25-6y \\ x=25-6y \end{gathered}[/tex]So we can easily solve for x in the first equation.
Hence the answer is option A
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
A state offers specialty license plates that contain 5 numbers followed by 2 letters. License plates are assigned randomly. All license plates are equally likely. Findthe number of possible license plates that can be issued using this system.O1.188,137,600 possible license platesO 12,500 possible license platesO 67,600,000 possible license plates039,917,124 possible license plates
Given:
There are 5 numbers followed by 2 letters.
Solution:
To find the answer, we will have a plate number that consists of 5 numbers followed by 2 letters. In that 5 numbers, each place has 10 choices-from 0 to 9. It will be: 10 * 10 * 10 * 10 * 10 = 100,000 .
Now, for the letters, there are 26 letters in the alphabet. We have two places for the letters and each place have 26 choices-from A to Z that will give us: 26 * 26 = 676
We will now multiply the acquired data for both the numbers and letters to arrive at the correct answer.
100,000 * 676 = 67,600,000
ANSWER: 67,600,000 possible license plates
a lion sprints after a giraffe. the lions speed is 22.4 meters per second (50 mph). how far will the lion get in fifteen seconds
Answer:
1100 feet, or 335.28 meters
If 9% of a number equals 3, find 36% of that number.
Theequation ^4 +^3 −−1=0a. Has four unequal complex rootsb. Has two equal real roots and two equal complex rootsc. Has two unequal real roots and two unequal complex rootsd. Has one real root of multiplicity 2 and a second real root of multiplicity 2e. Is not solvable
Answer:
Alternative C - Has two unequal real roots and two unequal complex roots
Step-by-step explanation:
The roots of this equation are:
(solved using the computer):
[tex]1,\text{ -1, }\frac{1-i\sqrt[]{3}}{2},\text{ }\frac{1+i\sqrt[]{3}}{2}[/tex]As we can see, we have two unequal real roots and two unequal complex roots.
Alternative C.
suppose that g(x) = f(x) -7 which statement best compares the graph of g(x) with the graph of f(x)
It implies that when F(x) shifts 7 units to the left, we get the value equal to G. (x). As a result, the graph of G(x) is the graph of F(x) with 7 units added to the left.
How is the graph of G related to the graph of f?The graph of g is the reflection of the graph of f. If g(x) = f(-x), then the graph of g is obtained from the graph of f by reflecting about the y-axis.
For instance, the result of multiplying f(x) and g(x) is h(x) = fg (x), or h(x)=f(x)g (x). if f is the function denoted by f(x) = x2 and g is the function denoted by g(x) = x + 3.
Therefore,
The Correct answer is : The two functions G(x) and F are provided to us (x).
We must determine which assertion most accurately contrasts the graphs of G(x) and F(x).
Suppose
F(x) = x [/ tex]
G(x) = x-7
When x = 1 is substituted
So, F(x) = 1
G(x) = 1-7 = -6
It implies that we obtain the value equal to the value of G when F(x) shifts 7 units to the left (x).
The graph of G(x) is therefore the graph of F(x) with 7 units added to the left.
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Kareem wants to give $11 to help kids who need school supplies. he also wants to buy a pair of shoes for $39. at least, how much money does he need to earn? brainly
Trevor asked his mother how old a tree is in my yard his mother says the sum of 10 and 2/3 of the trees age is in years is equal to (10+2/3)a =50, where A is the tree age in years. his equation is not correct. what error did he makea.the variable a should be mulitplied by 10 only and then added to 2/3b.the variable A should be multiplied by 2/3 only and then added to 10c.The variable A should be multiplied by 50, not by sum of 10 and 2/3d.c.The variable A should be multiplied by 2/3 and 50 and set equal to 10
Dhamby, this is the solution:
Betsie is going to buy 250 envelopes.
Here is some information about the cost of envelopes in two shops.
Value World
Pack of 10 envelopes for £1.99
Buy 2 packs get 1 pack free
Letters2go
Pack of 25 envelopes for £3.19
Betsie wants to buy the envelopes for the best possible price.
Which shop should Betsie buy the 250 envelopes from?
You must show how you get your answer.
The shop for which Betsie should buy the 250 envelopes from, using proportions, is Value World.
What is a proportion?A proportion is a fraction of a total amount, and this fraction is used to build relations, using basic arithmetic operations such as multiplication or division, to obtain the desired measures.
In this problem, the final price is obtained as follows:
Divide the price by the number of packs to find the unit rate.Multiply the unit rate by 250.Hence the final price at Value World is given as follows:
1.99/10 = 0.119.
She will pay for 2/3 of the 250 packs, as she buys 2 and gets one free, hence:
2/3 x 250 x 0.119 = £19.83.
At Letters2go, the final price is obtained as follows:
3.19/25 x 250 = £31.90.
Due to the lower price, she should purchase her envelopes at Value World.
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4. Find the value of x.*60°,150°3x°Ox= 20O х = 30Ox= 60
The sum of the angles of a quadilateral is 360 degree. So the equation for the sum of angles is,
[tex]\begin{gathered} 90^{\circ}+60^{\circ}+150^{\circ}+3x=360^{\circ} \\ 300^{\circ}+3x=360^{\circ} \\ 3x=360^{\circ}-300^{\circ} \\ x=\frac{60^{\circ}}{3} \\ =20^{\circ} \end{gathered}[/tex]So the value of x is 20.
A yearly coffee club subscription costs $65. Avery received an offer for 30 % off the subscription cost. What is the sale price of the subscription?
Answer:
$45.50
Step-by-step explanation:
We want to find 70% of the original cost.
[tex].70 \times 65 = 45.50[/tex]
1
Which graph represents the linear function below?
The graph that represents the given linear function is attached below.
We are given a function. A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input. The equation is linear in nature. It represents a straight line. The equation is given below.
(y - 4) = (4/3)(x - 2)
A line's general equation in slope-intercept form is y = mx + c. We will convert the given equation into this form.
y - 4 = (4/3)x - 8/3
y = (4/3)x - 8/3 + 4
y = (4/3)x + 4/3
The slope of the given equation is 4/3. The y-intercept for the given equation is 4/3.
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Work out the area and the perimeter of each semicircle. Give your answer correct to two decimal places (2 d.p.).
diameter = 24mm
The area of this semi-circle is 38.28 cm² and this can be determined by using the formula of area of the semi-circle.
Given :
The diameter of the semi-circle is 10 cm.
The area of the circle is given by the formula:
A=[tex]\pi[/tex]r²
where r is the radius of the circle.
So, the area of the circle whose radius is 5cm is given by:
A=[tex]\pi[/tex]×(5)²
A=25[tex]\pi[/tex]
The area of the circle is 25[tex]\pi[/tex] then the area of the semicircle whose radius is 5cm is given by:
A[tex]s[/tex]= 25/2([tex]\pi[/tex])
A[tex]s[/tex]=12.5[tex]\pi[/tex]
Now, substitute the value of [tex]\pi[/tex] in the above equation.
A[tex]s[/tex]=12.5×3.142
A[tex]s[/tex]=39.28cm²
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( 1 - v ) (5v +9 ) = 0Find v
We know that if XY = 0 then there are two options: X = 0 or Y = 0
Then, in this case:
If ( 1 - v ) (5v +9 ) = 0 then
( 1 - v ) = 0 or (5v +9) = 0
We find v for both cases:
1 - v₁ = 0
1 = v₁
5v₂ + 9 = 0
5v₂ = -9
v₂ = -9/5
Answer: v₁ = 1, v₂ = -9/5In a right triangle one of the acute angles is 1/4 the size of the other acute angle find the measure of the larger angle
In a right triangle, there are 2 acute angles and 1 right angle.
Let x be the measure of the larger acute angle, using the triangle sum theorem (that states that the sum of the interior angles of a triangle is 180) we have that:
[tex]\begin{gathered} x+\frac{1}{4}x+90=180 \\ \frac{5}{4}x=180-90 \\ \frac{5}{4}x=90 \\ 5x=360 \\ x=\frac{360}{5} \\ x=72 \end{gathered}[/tex]The larger acute angle measures 72°.
y varies directly with x. if y =75 when x =25, find x when y=25
Answer:
x = 8.33
Explanation:
y varies directly with x if y can be calculated as a constant k times x. So:
y = k*x
If y is equal to 75 and x is equal to 25, we can calculate the value of k as:
[tex]\begin{gathered} 75=k\cdot25 \\ \frac{75}{25}=\frac{k\cdot25}{25} \\ 3=k \end{gathered}[/tex]Therefore, y = 3*x
So, to find x when y = 25, we need to replace y by 25 and solve for x as follows:
[tex]\begin{gathered} 25=3\cdot x \\ \frac{25}{3}=\frac{3\cdot x}{3} \\ 8.33=x \end{gathered}[/tex]Therefore, x is equal to 8.33
The price of a necklace was increased by 10% to £121.
What was the price before the increase?
Answer:
the anwser is 110
Step-by-step explanation:
The price before was £108.9 because 10% of £121 is £12.1 so if you subtract that you would get £108.9
What is 66253/19
please help this must be turned in by tonight
Answer:
3487
Step-by-step explanation:
Use the drop-down menus to complete each statement to show why 65–√ is between 12 and 18.
it is proven that 6√5 between 12 and 18, Irrational numbers
What are Irrational numbers?
The group of real numbers known as irrational numbers are those that cannot be written as a fraction of the form p/q, where p and q are integers. Additionally, the decimal expansion of an irrational integer is neither terminating nor recurring.
Irrational numbers are real numbers that cannot be expressed as a straightforward fraction. These cannot be stated as ratios, such as p/q, where p and q are integers, q0. It is a contradiction of rational numbers.
It has been given in question 4 < 5 < 9 and we have to show 6√5 is between 12 and 18.
For box number 1.
4 < 5 < 9 ⇒ √4 < √5 < √9
For the box number 2.
√4 < √5 < √9 ⇒ 2 < √5 < 3
For the box number 3.
we multiply the inequality by 6.
6×(2 < √5 < 3)
⇒ 6×2 < 6×√5 < 6×3
So the 6×2 < 6×√5 < 6×3
⇒ 12 < 6√5 < 18
Hence it is proven that 6√5 between 12 and 18.
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The sum of three numbers is 11. Two times the smallest is 1 less than the largest, while the sum of the largest and smallest is 7.Use a linear system in three variables to find the three numbers.
ANSWER:
The numbers are 2, 4 and 5
STEP-BY-STEP EXPLANATION:
let x be the smallest, y the one that follows and z the largest
we have the following equations
[tex]\begin{gathered} x+y+z=11 \\ z-1=2x \\ x+z=7 \end{gathered}[/tex]We solve the system of equations as follows
[tex]\begin{gathered} z-1=2x\rightarrow z=2x+1 \\ x+z=7\rightarrow z=7-x \\ \text{ we equate noth equations} \\ 2x+1=7-x \\ 2x+x=7-1 \\ 3x=6 \\ x=\frac{6}{3}=2 \end{gathered}[/tex]now, for z:
[tex]\begin{gathered} z=7-2 \\ z=5 \end{gathered}[/tex]for y:
[tex]\begin{gathered} 2+y+5=11 \\ y=11-5-2 \\ y=4 \end{gathered}[/tex]Solve |x+ 4| = -6 im struggling with this problem
Recall that:
[tex]\begin{gathered} |a|\ge0 \\ \text{for all a}\in\R. \end{gathered}[/tex]Therefore the given equation has no solutions.
Answer: Option B.
What is the percent change from 112 to 96
well, the change is just 112 - 96 = 16.
now if we take 112 as the 100%, what's 16 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 112 & 100\\ 16& x \end{array} \implies \cfrac{112}{16}~~=~~\cfrac{100}{x} \\\\\\ 7=\cfrac{100}{x}\implies 7x=100\implies x=\cfrac{100}{7}\implies x\approx 14.29[/tex]
Solve the following exponential 4e^3x-1 = 5
Given
[tex]4e^{3x}-1=5[/tex]
Solving, step-by-step
[tex]\begin{gathered} 4e^{3x}-1=5 \\ e^{3x}=6/3 \\ 3x=\ln 1.5 \\ x=\frac{\ln 1.5}{3} \\ \end{gathered}[/tex]Customer account "numbers" for a certain company consist of 4 letters followed by 4 numbers. How many different account numbers are possible if repetitions of letters and digits are allowed?
45697600 different account numbers are possible if repetitions of letters and digits are allowed.
Calculation:-
The 4 letters can be chosen in 26 ways each and the two numbers in 10 ways each
Number of account numbers possible = 26^4 * 10^2 = 45697600
What is problem-solving?
Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
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If AC=13x-17, find x. Round your answer to the nearest tenth if necessary AB= 2x+4 BC= 19
x=3.7
1) Given that AC is the line segment made up by AB + BC We can set this equation:
AC=AB+BC
13x-17=2x+4+19 Combining like terms
13x-2x -17=2x-2x+23
11x -17=23
11x -17+17 = 23 +17
11x = 40 Dividing both sides by 11
x=3.63 Round to the nearest tenth
x=3.7