Answers
The Pythagorean theorem is [tex]a^2+b^2=c^2[/tex], where a and b are two legs of a right triangle and c is the hypotenuse (the longest side).
Solving the QuestionWe're given a triangle with the following:
One of the legs measure 2 unitsThe other leg measures b unitsThe hypotenuse is 6 units longWe can plug these values into the Pythagorean theorem as a, b and c:
[tex]a^2+b^2=c^2\\2^2+b^2=6^2[/tex]
Now, isolate b:
[tex]b^2=6^2-2^2\\b=\sqrt{6^2-2^2}\\b=\sqrt{36-4}\\b=\sqrt{32}[/tex]
Answer[tex]b=\sqrt{32}[/tex]
Related Questions
At a Phil's Cafe, a dinner meal is made up of an appetizer, a main course, a dessert and a drink. The choices for the appetizer are soup or salad; for the main course are chicken, fish, steak or lobster; for the dessert are ice cream, pie, sorbet, or a pastry; the drinks are coffee, tea or milk. How many different dinner meals are possible
Answers
The number of different meals possible is 96, computed using combinations.
The combination is a method of choosing a number of articles from a larger set of articles in no particular order.
In the question, we are asked about the different dinner meals possible when a dinner meal is made up of an appetizer, a main course, a dessert, and a drink.
The choices for the appetizer are soup or salad, so the number of ways of choosing an appetizer = 2C1 = 2.
The choices for the main course are chicken, fish, steak, or lobster, so the number of ways of choosing a main course = 4C1 = 4.
The choices for the dessert are ice cream, pie, sorbet, or pastry, so the number of ways of choosing a dessert = 4C1 = 4.
The choices for the drink are coffee, tea, or milk, so the number of ways of choosing a drink = 3C1 = 3.
The total number of ways is the product of all of them.
Therefore, the total number of ways = 2*4*4*3 = 96.
The number of different meals possible is 96, computed using combinations.
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Two circles, each of radius 5 units, are drawn in the coordinate plane with their
centers (0, 0) and (8, 0) respectively. How many points where both coordinates are
integers lie within the intersection of these circles, including its boundary?
Answers
The points where both coordinates are integers lie within the intersection of these circles, including its boundary are 8 points.
To answer the question, we need to find the equation of the circles.
What is the equation of a circle?The equation of a circle with center (h, k) and radius r is
(x - h)² + (y - k)² = r²
Equation of first circle
Given that the first circle has
center (0, 0) and radius, r = 5,Its equation is
(x - 0)² + (y - 0)² = 5²
x² + y² = 25 (1)
Equation of second circle
Given that the second circle has
center (8, 0) and radius, r = 5,Its equation is
(x - 8)² + (y - 0)² = 5²
x² - 16x + 64 + y² = 25 (2)
Point of intersection o the circlesTo find the point of intersection of both circles, subtracting (1) from (2), we have
x² - 16x + 64 + y² = 25 (2)
-
x² + y² = 25 (1)
-16x + 64 = 0
-16x = -64
x = -64/-16
x = 4
Substituting x = 4 into (1), we have
x² + y² = 25
4² + y² = 25
16 + y² = 25
y² = 25 - 16
y² = 9
y = ±√9
y = ±3
So, the circles intersect at (4,-3) and (4, 3).
So, all the points that lie within their points of intersection where both coordinates are integers including their points of intersection are
(4, -3), (3, -2), (2, -1), (1, 0), (0, 1), (1, 2), (2, 3) and (3, 4).So, there are 8 points.
So, all the points where both coordinates are integers lie within the intersection of these circles, including its boundary are 8 points.
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can you pls helpppp lol there’s the picture igs
Answers
Using the bisection concept, it is found that the measure of angle PQR is of 130º.
What is a bisection?A bisection divides an angle into two equal angles. In this problem, the angles are given as follows:
(3x + 5)º.(2x + 25)º.Hence the value of x is given as follows:
3x + 5 = 2x + 25
x = 20º.
Hence the measure of angle PQR is given as follows:
m<PQR = 3x + 5 + 2x + 25 = 5x + 30 = 5 x 20º + 30º = 130º.
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Which triangle is a 30°-60°-90° triangle?
Answers
Answer:
Option A
Step-by-step explanation:
30° - 60° - 90° triangle:The ratio of the side of 30-60-90 triangle is x : x√3 : 2x
The angle opposite to 90° = 2x
2x = 10
x = 10÷2
x = 5
The side opposite to 30° is x which is 5.
The side opposite to 60° is x√3 = 5√3
The ratio of sides of 30-60-90 triangle:
5 : 5√3 : 10
Answer:
The first one is correct
Step-by-step explanation:
I got a 100 on the test, hope this helps
Simplify. Rewrite the expression in the form 3^n3 n 3, start superscript, n, end superscript. 3^4\cdot 3^2=3 4 ⋅3 2 =3, start superscript, 4, end superscript, dot, 3, squared, equals
Answers
The expression 3⁴ × 3² when rewritten in the form 3ⁿ is; (3²)³
How to use law of exponents?
We want to find the expression;
3⁴ × 3²
Now, according to law of exponents, we know that;
y² × y³ = y⁽² ⁺ ³⁾
Thus, applying that exponent form to our question gives us;
3⁴ × 3² = 3⁽⁴ ⁺ ²⁾ = 3⁶
Now, we want to find the answer in the form 3ⁿ. Thus;
3⁶ = (3²)³
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Answer: 3^6 on khan academy
Step-by-step explanation: add the exponents 4 and 2 and you get the exponent 6
The amount of soda in a half-liter bottle follows a normal distribution. Assume μ = 500 ml and σ = 10 ml. A government auditor will fine the company if a random sample of 5 bottles has a sample mean under 490 ml. Find the probability the company will be fined.
Answers
The probability that the company will be fined is 0.1587.
How to illustrate the probability?From the information given, it was assumed that μ = 500 ml and σ = 10 ml.
Also, the random sample of 5 bottles has a sample mean under 490 ml.
Here, the probability will be:
= P(x < 490)
= P[(z < (490 - 500)/10]
= P (z < -10/10)
= P(z < -1)
Looking at this under the z table, the probability will be 0.1587
The probability is 0.1587.
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A spinner is spun that has 15 equal-sized sections numbered 1 to 15. What is the probability the spinner lands on a multiple of five?
Answers
Answer:
1/5
Step-by-step explanation:
P(event) = # of favorable outcomes / # of total outcomes. Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40 ... and there are 3 multiples of 5 within 1 to 15. So the # of favorable outcomes is 3. # of total outcomes is 15 because there are 15 equal-sized sections.
P = 3/15 = 1/5
ken needs to order 8 new uniform for the soccer team. Each uniform cost $14 and a pair of shorts. The cost of the shorts, c is unknown. 2 equivalent expressions for the cost of 8 uniforms
Answers
The equivalent expressions for the costs are 8 * (14 + c) and 112 + 8c
How to determine the total cost?The given parameters are:
Number of uniform = 8
Cost of each = $14
The cost of the uniforms and the shorts is then calculated as:
Cost = Number of uniforms * (Cost of uniform + Cost of short)
This gives
Cost= 8 * (14 + c)
Expand
Cost = 112 + 8c
Hence, the equivalent expressions for the costs are 8 * (14 + c) and 112 + 8c
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Determine the vertex of the quadratic relation y=2(x+2)(x-6)
Answers
Answer:
(2, -32)
Step-by-step explanation:
1) Expand them.
y = 2(x² - 6x + 2x - 12)
y = 2(x² - 4x - 12)
y = 2x² - 8x - 24.
2) Complete the square to find the vertex.
y = 2([x² - 4x)] - 24
y = 2[(x - 2)² - 4] - 24
y = 2(x - 2)² - 8 - 24
y = 2(x - 2)² - 32
The vertex: (2, -32)
or you can use this: x = -b/2a
x = -(-8)/2(2)
x = 8/4
x = 2
Substitute the value into the original equation for y.
y = 2(2)² - 8(2) - 24
y = 2(4) - 16 - 24
y = 8 - 16 - 24
y = -32
Vertex: (2, -32)
Answer:
(2, -32)
Step-by-step explanation:
The vertex of the graph of a quadratic equation is on the line of symmetry, halfway between the x-intercepts. It can be found by evaluating the equation at that point.
Line of symmetryThe given function is written in factored form, so the x-intercepts are easy to find. They are the values of x that make the factors zero:
(x +2) = 0 ⇒ x = -2
(x -6) = 0 ⇒ x = 6
The midpoint between these values of x is their average:
x = (-2 +6)/2 = 4/2
Then the x-coordinate of the vertex, and the equation of the line of symmetry is ...
x = 2
VertexUsing this value of x in the quadratic relation, we find the y-value at the vertex to be ...
y = 2(2 +2)(2 -6) = 2(4)(-4)
y = -32
The coordinates of the vertex are (x, y) = (2, -32).
Area=
I need some help solving this question I'm stuck. Thanks
Answers
Answer: 36 square units
Work Shown:
area = base*height/2
area = 12*6/2
area = 72/2
area = 36
The base and height are always perpendicular to each other. The triangle formula above applies to obtuse triangles, as well as any other type of triangle. It might help to rotate the triangle so that side IJ is at the bottom rather than the top.
A company has two large computers. The slower computer can send all the company's email in minutes. The faster computer can complete the same job in minutes. If both computers are working together, how long will it take them to do the job
Answers
Both the computers will take 18 minutes to do the job together.
The slower computer sends all the company's email in 45 minutes.
The faster computer completes the same job in 30 minutes.
Let's take minutes t to complete the task together.
As they complete one job, we get the following equation:
[tex]\frac{t}{45}[/tex]+[tex]\frac{t}{30}[/tex]=1
LCM of 45 and 30 is:
45 = 3 x 3 x 5
30 = 2 x 3 x 5
LCM = 2 x 3 x 3 x 5 = 90
Now, solving for t;
⇒[tex]\frac{2t+3t}{90} = 1\\\frac{5t}{90} =1\\5t=90\\[/tex]
Dividing both sides by 5;
[tex]\frac{5t}{5}=\frac{90}{5}[/tex]
We get t = 18
Hence, it will take both the computers 18 minutes to do the job together.
A company has two large computers. The slower computer can send all the company's emails in 45 minutes. The faster computer can complete the same job in 30 minutes. If both computers are working together, how long will it take them to do the job?
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A scuba diver is 30 ft below sea level. Which of the following best describes this situation?
1. |30|
2. |-30|
3. -30
4. ±30
Answers
Reason
1 and 2 are absolute values so they are 30, the 4th answer is plus or minus, the question says “below sea level” which is a negative number so it is -30.
y≥-x+4 linear inequality graph
Answers
The slope m = -1 and the y-intercept = ( 0, 4 ).
The graph is a solid line, shaded area above the boundary line since y is greater than -x + 4.
What is the graph of the inequality?Given that;
y ≥ -x + 4
First, we use the slope intercept form y = mx + b to determine the slope and y-intercept.
y ≥ -x + 4
y = mx + b
We can see that;
m = -1
b = 4
Hence, the slope m = -1 and the y-intercept = ( 0, 4 ).
The graph is a solid line, shaded area above the boundary line since y is greater than -x + 4.
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What term best describes 3x + 5?
Answers
Answer: Algebraic expression
Step-by-step explanation:
HURRY ANSWER NOW PLS
Which scenario is modeled by the equation (x) (0.6) = 86 dollars and 46 cents?
A. A picnic table is on sale for 60 percent off. The sale price of the picnic table is x, $144.10.
B. A picnic table is on sale for 40 percent off. The sale price of the picnic table is x, $144.10
C. A picnic table is on sale for 60 percent off. The original price of the picnic table is x, $144.10.
D. A picnic table is on sale for 40 percent off. The original price of the picnic table is x, $144.10
Answers
Using proportions, the scenario modeled by the equation 0.6x = 86.46 is:
D. A picnic table is on sale for 40 percent off. The original price of the picnic table is x, $144.10.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
When a product is 40% off, 100 - 40 = 60% of the original price x is paid, hence the expression for the price is:
0.6x.
In this problem, the expression is:
0.6x = 86.46
x = 86.46/0.6
x = 144.1.
Hence option D is correct.
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there is a mound of g pounds of gravel in a quarry. throughout the day, 300 pounds of gravel are added to the mound. two orders of 900 pounds are sold and the gravel is removed from the mound. at the end of the day, the mound has 1,300 pounds of gravel. write the equation that describes the situation. then solve for g.
Answers
The required equation is g+300-900-900=1300.
The value of g is 2800 pounds.
What is the solution to the equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Initially, there is a mound of g pounds of gravel, then 300 pounds are added, and then two orders of 900 pounds are sold. At the end of the day, the mound has 1,300 pounds of gravel.
The equation for the given information is formed as follows:
g+300-900-900=1300
Solve the equation to find the value of g,
g+300-1800=1300
g-1500=1300
g=1300+1500
g=2800
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For two functions, a(x) and b(x), a statement is made that a(x) = b(x) at x = 2. What is definitely true about x = 2? (2 points) Group of answer choices Both a(x) and b(x) have a maximum or minimum value at x = 2. Both a(x) and b(x) have the same output value at x = 2. Both a(x) and b(x) cross the x-axis at 2. Both a(x) and b(x) cross the y-axis at 2.
Answers
The statement that is definitely true about x = 2 is Both a(x) and b(x) have the same output value at x = 2.
How to find the statement that is true about the functions a(x) = b(x) at x = 2?If we have two functions a(x) and b(x), a statement is made that a(x) = b(x) at x = a, this implies that the values of the functions a(x) and b(x) are equal at x = a.
Given that the two functions a(x) and b(x), a statement is made that a(x) = b(x) at x = 2.Then the statement that is definitely true about x = 2 is Both a(x) and b(x) have the same output value at x = 2.
So, the statement that is definitely true about x = 2 is Both a(x) and b(x) have the same output value at x = 2.
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will give brainliest plus 10 points
Answers
Answer:
The distance is 7.3 units.
Step-by-step explanation:
Two given points: (-3, 1) and (4, -1)
[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Here given:
x₂ = 4x₁ = -3y₂ = -1y₁ = 1Applying the formula:
[tex]\sf d = \sqrt{(4 - (-3))^2 + (-1 - 1)^2}[/tex]
[tex]\sf d = \sqrt{(7)^2 + (-2)^2}[/tex]
[tex]\sf d = \sqrt{49 + 4}[/tex]
[tex]\sf d = \sqrt{53} \ \approx \ 7.28 \ \approx \ 7.3 \ (rounded)[/tex]
Answer:
7.3
Step-by-step explanation:
The distance of a line segment between two points (x1, y1) and (x2, y2) is given by the formula
[tex]d = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]
If we look at the graph,
the leftmost point of the line is at (-3, 1). Let's call this (x1, y1)
the rightmost point is at (4, -1). Let's call this (x2, y2)
Substituting these values into the distance formula gives us
[tex]d = \sqrt{(4-(-3)^2 + (1-(1)^2} \\ \\d = \sqrt{(7)^2 + (-2)^2} \\ \\d = \sqrt{49 + 4} \\\\d = \sqrt{(x2-x1)^2 + (y2-y1)^2}\\\\d = \sqrt{53} = 7.28[/tex]
Rounded to one decimal place, this is 7.3
MATH HELP!!! 100PTS!!!
Let p(x)=2x−4 and r(x)=6x−1/9x+1.
Solve p(x)=r(x) for x exactly. If there is more than one answer, enter your exact solution(s) in a comma separated list.
Answers
Answer:
[tex]x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}[/tex]
Step-by-step explanation:
Given functions:
[tex]p(x)=2x-4[/tex]
[tex]r(x)=\dfrac{6x-1}{9x+1}[/tex]
Solve for p(x) = r(x):
[tex]\begin{aligned}p(x) & = r(x)\\\implies 2x-4 & = \dfrac{6x-1}{9x+1}\\(2x-4)(9x+1)&=6x-1\\18x^2+2x-36x-4&=6x-1\\18x^2-40x-3&=0\end{aligned}[/tex]
As the found quadratic equation cannot be factored, use the Quadratic Formula to solve for x:
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]a=18, \quad b=-40, \quad c=-3[/tex]
Substitute the values of a, b and c into the quadratic formula and solve for x:
[tex]\begin{aligned}\implies x & =\dfrac{-(-40) \pm \sqrt{(-40)^2-4(18)(-3)} }{2(18)}\\\\& =\dfrac{40 \pm \sqrt{1816}}{36}\\\\& =\dfrac{40 \pm \sqrt{4 \cdot 454}}{36}\\\\& =\dfrac{40 \pm \sqrt{4}\sqrt{454}}{36}\\\\& =\dfrac{40 \pm2\sqrt{454}}{36}\\\\& =\dfrac{20 \pm\sqrt{454}}{18}\end{aligned}[/tex]
Therefore, the solutions are:
[tex]x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}[/tex]
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Write the equation of the line that passes through the point (-8,-3) with : slope of -1/4
Answers
Answer:
In slope-intercept form:
[tex]y = - \frac{1}{4} x - 5[/tex]
In standard form:
[tex]x + 4y = - 20[/tex]
Step-by-step explanation:
[tex] - 3 = - \frac{1}{4} ( - 8) + b[/tex]
[tex] - 3 = 2 + b[/tex]
[tex]b = - 5[/tex]
[tex]y = - \frac{1}{4} x - 5[/tex]
[tex] - 4y = x + 20[/tex]
[tex] - x - 4y = 20[/tex]
[tex]x + 4y = - 20[/tex]
A Ski resort tracks the proportion of seasonal employees who are rehired each season. Rehiring a seasonal employee is beneficial in many ways, including lowering the costs incurred during the hiring process such as training costs. A random sample of 833 full-time and 386 part-time seasonal employees from 2009 showed that 434 full-time employees were rehired compared with 189 part-time employees (a) Is there a significant difference in the proportion of rehires between the full-time and part-time seasonal employees? (Use α = 0.10) (a-1) Choose the appropriate hypotheses. Assume TTF is the proportion of full-time employees and πrho is the proportion of part-time employees (a-2) Specify the decision rule. (A negative value should be indicated by a minus sign. Round your answers to 3 decimal places.)
(a-3) Find the test statistic Zcalc (Do not round the intermediate calculations. Round your answer to 3 decimal places.)
Answers
The test statistic z will be equal to -0.946 and it shows that there is no significant difference in the proportion of rehires between full time and part time.
Given sample sizes of 833 and 386 and result of samples 434 and 189.
[tex]n_{1} =833, n_{2}=386[/tex]
Proportion of full time=434/833=0.52
Proportion of part time=189/386=0.49.
Difference in proportion =0.52-0.49
[tex]H_{0}:[/tex]TTF- i∈ rho=0
[tex]H_{1}:[/tex] TTF+i∈ rho≠0.
Mean of difference=0.03
Z=(X-μ)/σ
σ=[tex]\sqrt{0.4517/447}[/tex]
=0.0317
σ=0.0317
z=(0-0.03)/0.0317
=-0.03/0.0317
=-0.317
p value will be =0.1736.
Because p value is greater than 0.01 so we will accept the null hypothesis which shows that there is no significant difference in the proportions.
Hence there is no significant difference in the proportion of rehires between full time and part time.
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PLS HELP
13. A box contains about 250 marbles in 5 different colors. James selected a random sample of 30 marbles and counted 16 red, 5 blue, 5 green, 3 white, and 1 yellow.
Which statement is NOT a valid inference about all of the marbles in the box?
There is exactly 1 yellow marble in the box.
There are about 25 white marbles in the box.
There are about the same number of blue and green marbles.
There are more red marbles than any other color.
Answers
Answer:
Invalid statement: There is exactly 1 yellow marble in the box
Step-by-step explanation:
The probability of finding a yellow marble is Py = 1/30, according to the sample. Then, the number of yellow marbles expected to find in the box is:
N x Py > 1 ,
where N = 250 (number of marbles in the box).
Thus, we expect to find more than one yellow marble in the box and the Invalid statement is: "There is exactly 1 yellow marble in the box".
Volume=
Please help thankss
Answers
4^2=64
Answer:
Volume = 64
Step-by-step explanation:
To find the volume of the cube use the formula.
Formula: l×b×h
l=length
b=base
h=height
Use the information given to solve using the formula.
4×4×4=64
The volume of this cube is 64.
Hope this helps!
If not, I am sorry.
someone please help me with problem #7 !!!
Answers
Answer: b and d
Step-by-step explanation:
Since the roots are x=2 and x=6, we can write the equation as
[tex]f(x)=a(x-2)(x-6)[/tex]
Substituting in the coordinates of the vertex,
[tex]-4=a(4-2)(4-6)\\\\-4=-4a\\\\a=1[/tex]
So, the equation is [tex]f(x)=(x-2)(x-6)[/tex]
On expanding, we get [tex]f(x)=x^2 - 8x+12[/tex]
How many integers in the set of all integers from 1 to 200, inclusive, are not the cube of an integer
Answers
Cubing of integers from 1 to 5 will have their cubes in the interval 1 to 200. There are such 5 positive numbers (1,2,3,4,5).
To calculate the variety of integers, locate and subtract the integers of the hobby after which subtract 1. As evidence of the concept, calculate the wide variety of integers that fall between five and 10 on more than a few lines. We realize there are four (6, 7, 8, 9).
All entire numbers are integers (and all herbal numbers are integers), however now not all integers are whole numbers or natural numbers. as an example, -five is an integer but not an entire variety or a natural quantity. An integer is an entire variety (not a fractional number) that can be fine, bad, or 0. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.forty three, 1 3/four, three.14, . 09, and five,643.1.
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Consider the relation given by the graph below.
a) Is the relation a function? Why or why not?
b) Determine the domain and range of the graph.
Answers
The given relation is function, because the curve of y = p(x) has its exist for every x in its domain(-6, 3) and the range of the function is lies between (-1, 9).
What are functions?
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent while Y is dependent variable.
As Clearly the shows in the graph the structure is decreasing, increasing and then decreasing. And implies, curve is continuous in its limits and for every x (-6,3) there is exist in range of y(-1, 9).
Thus, The given relation is function, and domain is (-6, 3) and the range of the function is lies between (-1, 9).
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Find the GCF of the monomials: 32x^2 and 24x^2y
Answers
Answer:
8x^2
Explanation:
First, do prime factorization of each of the coefficients:
32 ⇒ 2^5
24 ⇒ 2^3, 3
The greatest common factor (GCF) of the coefficients is 2^3 = 8.
Next, find the GCF of the variables:
x^2
x^2, y
The GCF of the variables is x^2.
Finally, multiply the GCF of the coefficients by the GCF of the variables to get:
8x^2
Answer: 4x^2
Step-by-step explanation: I took the test and got this answer right
can you help me I am stuck
Answers
Answer:
False, False, True
Step-by-step explanation:
Matrix addition or subtraction can only be performed on two matrices if they are the same dimensions. The number of rows for both must match, and the number of columns for both must match. If either is different, they cannot be combined with addition or subtraction.
So, the first two questions are false because the first number from each pair doesn't match (and neither does the second number from each pair, but we just need one mismatch for it to fail).
The last question is true because both of the first numbers are a 3, and both of the second numbers are a 4.
Math is literally so hard
Answers
Answer:
C
Step-by-step explanation:
negative exponent flips the fraction
4^2=16
x^2 becomes x^4
y becomes y^2
Sorry I didn’t know how to crop the photo
(Please help, quickly if possible.)
Which types of dilation are the given scale factors?
Select Expansion or Contraction to correctly describe the type of dilation for each given scale factor.
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Answers
A scale factor is a contracting scale such that x < 1, where x is the scale factor.
For example, if the scale factor x is less than 1, then it must be decreasing in size, and thus be contracting in size.
But, if the scale factor is greater than 1, then it is expanding in size and increasing.
1) -5 is expanding. It is greater than one.
2) -1/4 is contracting. It is less than one.
3) 3.5 is expanding. It is greater than one.
4) 6/7 is contracting. It is less than one.