Answer:
x=1
Step-by-step explanation:
8x+4y=12y
-4y -4y
8x=8y
x=1
A square and a rectangle have the same perimeter. The square has a side length of 8x units. The rectangle has a length of (5x+8) units and a width of 14 units. What will the perimeter of both the rectangle and the square
Answer:
The perimeter of both figures is equal to [tex]64\ units[/tex]
Step-by-step explanation:
step 1
we know that
The perimeter of a square is equal to
[tex]P=4b[/tex]
where
b is the side length of the square
we have
[tex]b=8x\ units[/tex]
substitute
[tex]P=4(8x)=32x\ units[/tex]
step 2
we know that
The perimeter of a rectangle is equal to
[tex]P=2(L+W)[/tex]
we have
[tex]L=(5x+8)\ units[/tex]
[tex]W=(14)\ units[/tex]
substitute
[tex]P=2(5x+8+14)=10x+44\ units[/tex]
step 3
Equate both perimeters and solve for x
[tex]10x+44=32x[/tex]
[tex]32x-10x=44[/tex]
[tex]22x=44[/tex]
[tex]x=2\ units[/tex]
step 4
Find the perimeter of both
square
[tex]P=32x=32(2)=64\ units[/tex]
rectangle
[tex]P=10x+44=10(2)+44=64\ units[/tex]
Translate "the product of z,x, and y"
into a mathematical expression
The mathematical expression for "the product of z, x, and y" can be represented as [tex]\( z \times x \times y \)[/tex].
The mathematical expression for "the product of z, x, and y" can be represented as [tex]\( z \times x \times y \)[/tex]. In this expression, the symbol [tex]\( \times \)[/tex] denotes multiplication, and the three variables [tex]\( z \), \( x \), and \( y \)[/tex] are multiplied together to obtain their product.
This expression succinctly captures the idea of multiplying these three variables. In mathematical terms, a product refers to the result of multiplying two or more numbers or variables.
Therefore, [tex]\( z \times x \times y \)[/tex] represents the outcome of multiplying the values represented by the variables [tex]\( z \), \( x \), and \( y \)[/tex].
This expression provides a clear and concise way to articulate the mathematical concept of the product of three variables.
The product of ( z ), ( x ), and ( y ) is: ( zxy ).
To translate the phrase "the product of ( z ), ( x ), and ( y )" into a mathematical expression, follow these steps:
1. Identify the Variables:
The variables involved in the expression are ( z ), ( x ), and ( y ).
2. Understand the Operation:
The term "product" indicates multiplication.
3. Write the Expression:
To express the product of ( z ), ( x ), and ( y ) mathematically, you simply multiply these variables together.
1. Start with the First Two Variables:
Multiply ( z ) and ( x ) together.
[tex]\[ z \times x \][/tex]
2.Include the Third Variable:
Now, multiply the result from the first step by ( y ).
[tex]\[ (z \times x) \times y \][/tex]
3. Simplify the Expression:
In multiplication, the order in which you multiply numbers does not matter due to the commutative property of multiplication. Therefore, we can drop the parentheses.
[tex]\[ z \times x \times y \][/tex]
Final ExpressionThe mathematical expression for "the product of ( z ), ( x ), and ( y )" is:
[tex]\[z \cdot x \cdot y\][/tex]
or simply:
[tex]\[zxy\][/tex]
This is the complete mathematical translation of the given phrase.
The diameter of your bicycle wheel is 34 inches. What is it’s radius
The diameter of a circle (or in this case a bicycle wheel) is how long it is from one side of the circle striaght across to the other side. The radius is half the diameter. So if the diameter is 34, then the radius would be 17.
17 inches
Diameter = 2 * radius
So you can rewrite that as
Radius = diameter / 2
34/2=17
Which shows how to find the value of this expression when x=-2 and y=5? (3x^3y^-2)^2
Answer:
Step-by-step explanation:
(3(-2)*3(5)*-2)^2
(-6*15*-2)^2
180^2
32,400
Answer:
[tex]\Rightarrow \dfrac{576}{625}[/tex]
Step-by-step explanation:
Given:
Expression, [tex](3x^3y^{-2})^2[/tex]
To find the value of expression at x=-3 and y=5
Put the values into expression
[tex]\Rightarrow (3(-2)^3(5)^{-2})^2[/tex]
[tex]\Rightarrow (3\cdot -8\cdot \dfrac{1}{25})^2[/tex] [tex]\because x^{-m}=\dfrac{1}{x^m}[/tex]
[tex]\Rightarrow (-\dfrac{24}{25})^2[/tex]
[tex]\Rightarrow \dfrac{576}{625}[/tex]
Hence, The value of expression would be [tex]\Rightarrow \dfrac{576}{625}[/tex]
Geometry! Please help!
Answer:
X=3
Y=9
Step-by-step explanation:
X is equal to the 3 and multipy 3 by its self to get Y=9
a right triangle has a leg of 11cm and a hypotenuse of 17cm what is the length of the other leg round to the nearest tenth
Answer: [tex]2\sqrt{42}cm[/tex] ≈12.96 cm
Step-by-step explanation:
To solve this exercise you must apply the Pythagorean Theorem, which is the shown below:
[tex]a^2=b^2+c^2[/tex]
Where a is the hypotenuse and b and c are the other legs.
You know that the triangle has a leg of 11 cm and the hypotenuse is 17 cm. Therefore, you can substitute values and solve for the other leg.
Then you obtain:
[tex](17cm)^2=b^2+(11cm)^2\\b=\sqrt{(17cm)^2-(11cm)^2}\\b=2\sqrt{42}cm[/tex]
b≈12.96 cm
PLEASE HELP ASAP!!!!!! WORTH 90 POINTS
Find each angle measure
Answer:
a) UXW = 78 b) UWY = 48 c) WZX = 48 d) XYZ = 42
Step-by-step explanation:
There are many ways you can do this, but I'll just describe one for each.
a) Angle YWV is vertical to XWZ, so they are congruent. Angle XWZ is an alternate interior angle with angle UXW, so UXW = 78.
b) All the angles that revolve around point W must add up to 360. We already know 4 angles due to vertical angles, so 78 + 78 + 54 + 54 = 264.
360 - 264 = 96. There are two angles left, and since they are vertical they must be congruent. 96/2 = 48, so angle UWY is 48 degrees.
c) We already know that the angle vertical to UWY is 48, so WZX is also 48 degrees because they are alternate interior angles.
d) Angle UWY is 48 degrees and angle WUY is 90 degrees because of the perpendicular line. Now we can find XYZ, the remaining angle.
90 + 48 = 138. 180 - 138 = 42. So XYZ = 42 degrees.
I hope this helped. I'm open to any questions you may have. :)
Answer:
a) UXW = 78 degrees
b) UWY = 48 degrees
c) WZX = 48 degrees
d) XYZ = 42 degrees
Step-by-step explanation:
Apply rules and theorems:
Angles in a triangle add up to 180 degrees.
Angles on a straight line add up to 180 degrees.
Right angles are 90 degrees.
Vertically opposite angles are equal.
With these we can solve for the angles.
2x + x = please help
Answer:
3x
Step-by-step explanation:
If you have 2x, that would mean there is 1x and 1x. T
he question asks what 2x+2x+1x is, and since all three have the same variable you can just add the coefficient.
The coefficients are 1, 1, and 1 since they are in front of the variable.
The variable is x.
Therefore, since 1+1+1=3, your answer is 3x.
What is the area of a right triangle with vertices of (-2,-4),(2,-4), and (2,5)?
Answer:
A = 18
Step-by-step explanation:
The formula for the area of a triangle is
A = ½bh
b = x₂ - x₁ = 2 - (-2) = 2 + 2 = 4
h = y₂ - y₁ = 5 - (-4) = 5 + 4 = 9
A = ½ × 4 × 9 = 18
The area of the triangle is 18.
This table shows the size in acres of four parks.
What is the median of the sizes of the four parks?
A. 27 acres
B. 30 acres
C. 34 acres
D. 49 acres
I think it would be B.30 here's why i think it would be 30 because it wants to know what the median. and i know that 49 and 27 is not it (i think) and 34 is not it so my answer is 30 PLEASE CORRECT ME IF I AM WRONG.
Answer: 30 acres
Step-by-step explanation: I got a 100% on my quiz!
a number is four times larger than the square of half the number
Answer:
Step-by-step explanation:
Let the number = x
Read carefully the sentence part beginning with 4 times larger
4* something
4 times larger than the square of 1/2 the number
4 * (x/2)^2
4*(x/2)^2 = x
4*x^2/4 = x
x^2 = x be very careful how you handle this. It looks like 0 might be an answer, but it isn't. If you divide x on both sides and you allow 0, you will get 0 / 0 and that is undefined. You must exclude that possibility with some sort of statement.
x cannot be 0.
x^2/x= x/x
x = 1
A yogurt company charges 72 cents for a 6 ounces container of yogurt. How much does it charge for an 8 ounce container?
Answer:
96¢
Step-by-step explanation:
We need to find out how much they charge per ounce so
0.72 divided by 6 = 0.12
so it's 12¢ They charge 12¢ an ounce
0.12 x 8 = 96
96¢ for 8 ounces
Hope this helps! Please mark as brainliest! Thanks!
find the size of angle acb
The answer is a 74 degree angle. This is a simple one to remember.
Use interger values of x from -3 to 3 to graph the equation y=-|-x|
Answer:
Step-by-step explanation:
The best way to do a question like this is to see what the answer is and then see if you can get it. The graph is labeled to show what the integer values for each integer point on the graph is.
I don't know what else to add, so if you have any additional problems, please list them under this question. I will see your comment.
A sample calculation would be
y = - abs(-x)
Let x = - 2
y = - abs(-2)
The absolute command changes - 2 to + 2
y = - abs(2)
y = - 2 because of the minus sign in front of the absolute value command.
So the point is (-2,-2)
What is the area of the circle if XY=10ft?
Answer options: 25pi ft2, 10pi ft2, 5pi ft2, 20pi ft2
Answer: [tex]25\pi\ ft^2[/tex] (First option)
Step-by-step explanation:
The formula for calculate the area of a circle is the one shown below:
[tex]A=r^2\pi[/tex]
Where r is the radius of the circle.
XY is the diameter. Then the radius is:
[tex]r=\frac{10ft}{2}\\r=5ft[/tex]
Substitute values into the formula shown above. Therefore, the area of the circle is:
[tex]A=(5ft)^2\pi \\A=25\pi\ ft^2[/tex]
Answer:
The correct answer is first option 25pi ft2
Step-by-step explanation:
Formula
Area of circle = πr²
r - Radius of circle
To find the area of given circle
Here XY = 10 ft
XY is the diameter of given circle
Radius r = Diameter/2 = 10/2 = 5 ft
Area = πr² = π5² = π x 5 x 5 = 25π ft²
Therefore area of given circle is 25π ft²
The correct answer is first option.
Write an equation of each line that passes through the following points in slope-intercept form:
A (8, –1) and B (–4, 17)
Answer:
[tex]\large\boxed{y=-\dfrac{3}{2}x+11}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the point A(8, -1) and B(-4, 17). Substitute:
[tex]m=\dfrac{17-(-1)}{-4-8}=\dfrac{18}{-12}=-\dfrac{3}{2}[/tex]
The equation of a line:
[tex]y=-\dfrac{3}{2}x+b[/tex]
Put the coordinates of the point A(8, -1) to the equation of a line:
[tex]-1=-\dfrac{3}{2}(8)+b[/tex]
[tex]-1=-3(4)+b[/tex]
[tex]-1=-12+b[/tex] add 12 to both sides
[tex]11=b\to b=11[/tex]
Finally we have the equation of a line in a slope-intercept form:
[tex]y=-\dfrac{3}{2}x+11[/tex]
A triangle has sides that are 2 inches, 2 inches, and 3 inches. Can you form more than one triangle with the given side lengths? Explain
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷ You cannot form more than one triangle with the sides, because any way you put it, it will always be the same.
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
TROLLER
Answer:
No
Step-by-step explanation:
No
SSS is a way of proving that two triangles are congruent. It also means that the shape and size of the triangle is fixed. There is only 1 way to draw it.
There is 1 other congruency that gives only 1 shape and size. It is SAS.
You have to reason out ASA. The way it is written (with the side between 2 angles, there is only 1 way possible to draw a triangle with shape and size consistent. The side must be between the 2 angles..
* A turtle and a snail start moving towards each other when they are 200 feet apart. The turtle is running at a speed of T feet per minute, and the snail is moving at a speed of S feet per minute. How soon will they meet?
Answer:
S+T
Step-by-step explanation:
round 4.2894 to two decimals
Answer:
4.29
Step-by-step explanation:
Answer:
Step-by-step explanation:
We want to round 4.732 to 2 decimal places, it will either round to 4.73 or 4.74. 4.732 rounded to 2 decimal places would be 4.73 (because it is the nearest number to 2 decimal places). 4.737 rounded to 2 decimal places would be 4.74
Find the surface area of a water tower
Answer:
SA = 3,140 ft³Step-by-step explanation:
We have:
h = 40 ft
2r = 20 ft → r = 10 ft
Substitute to the formula of a Surface Area of a cylinder:
[tex]SA=2\pi r^2+2\pi rh[/tex]
[tex]SA=2\pi(10^2)+2\pi(10)(40)=2\pi(100)+2\pi(400)\\\\=200\pi+800\pi=1,000\pi\ ft^3\\\\\pi\approx3.14\to SA\approx1,000(3.14)=3,140\ ft^3[/tex]
A fixed amount used as a standard of measurement is called a ___.
Answer:
The answer to the question is unit.
Step-by-step explanation:
A fixed amount used as a standard of measurement is called a Unit.
Standard units are the units we usually use to measure the weight, length or capacity of objects. The metric system is the main system of measurement units used in science.
Answer:
unit
Step-by-step explanation:
USA Testprep
Which net represents the figure?
Answer:
Last net.Step-by-step explanation:
All sides of the figure are triangles. Therefore, the last net represents this figure.
Answer:
It is the Last Net!
Step-by-step explanation:
I learned this in Class and on the lessons. Thankyou have a great day!
Which of the following describes the expression 4 divided by (5x1/2)?
Answer:
8/11
Step-by-step explanation:
drag each term to the correct location on the expression. each term can be used more than once, but not all terms will be used.
Consider the expression shown.
Factor the expression completely.
Answer:
Answer:
4(x-3)(x+6)
Step-by-step explanation:
We factor out the 4 first since all numbers are divisible by 4. That leaves us with x^2+3x-18.
Then we factor this to get (x-3)(x+6).
So the factored form of the equation is 4(x-3)(x+6)
Step-by-step explanation:
The factors of the equation 4x²+12x -72 will be 4(x-3)(x+6).
What is a quadratic equation?A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Factor out the 4 first since all numbers are divisible by 4. That leaves us with x² +3x -18.
4( x² +3x -18 ) = 4 ( x² + 6x - 3x -18 )
= 4 ( x(x+6) -3 (x + 6)
= 4 ( x + 6 ) ( x - 3 )
Hence, the factors are 4 ( x + 6 ) ( x - 3 ).
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What are two lines in the same plane that intersect at right angles?
Answer: perpendicular
Step-by-step explanation: perpendicular lines are lines that intersect at right angles.
Answer: Perpendicular lines intersect so much so that they create 4 90 degree angles around them.
Kermit's favorite iced tea is made with 15 tea bags in every 2 liters of water. Peggy made a 12 liter batch of iced tea with 90 tea bags.
What will Kermit think of Peggy's iced tea?
(Choice A)
A
It is too strong.
(Choice B)
B
It is too weak.
(Choice C)
C
It is just right.
Answer:
Choice C.
Step-by-step explanation:
Kermit likes :
15 tea bags
every 2 liters
Peggy:
90 tea bags
12 liters
You would simplify it by dividing 90 by 15, equaling 6. And 12 divided by 2, also equaling 6. Which would mean they are equal and Peggy's tea is exactly like Kermit's favorite iced tea.
Answer: The correct choice is
Choice (C) It is just right.
Step-by-step explanation: Given that Kermit's favorite iced tea is made with 15 tea bags in every 2 liters of water and Peggy made a 12 liter batch of iced tea with 90 tea bags.
We are to select the correct choice that describes the thinking of Kermit about Peggy's Iced tea.
The ratio of quantity of water and number of tea bags in Kermit's favorite iced tea is given by
[tex]R_k=2:15.[/tex]
And the ratio quantity of water and number of tea bags in Peggy's iced tea is given by
[tex]R_p=12:90=\dfrac{12}{90}=\dfrac{2}{15}=2:15.[/tex]
Since the ratio of water and number of tea bags in Peggy's iced tea is same as that in Kermit's favorite iced tea, so
Kermit will think that Peggy's iced tea is just right.
Choice (C) is CORRECT.
which algebraic expression is a polynomial?
it's the second one because the first has 2 over x which can't be a polynomial because it can't have a variable on the bottom same thing with the last one and the 3rd one it have a x in the square root sign
Answer:
B
Step-by-step explanation:
7 1/2 divided by 1 9/10 simplified
Answer:
[tex]\large\boxed{3\dfrac{18}{19}}[/tex]
Step-by-step explanation:
[tex]\text{First step:}\\\text{Convert the mixed number to the improper fractions:}\\\\7\dfrac{1}{2}=\dfrac{(7)(2)+1}{2}=\dfrac{15}{2}\\\\1\dfrac{9}{10}=\dfrac{(1)(10)+9}{10}=\dfrac{19}{10}\\\\7\dfrac{1}{2}:1\dfrac{9}{10}=\dfrac{15}{2}:\dfrac{19}{10}\\\\\text{Dividing by a fraction is the same as multiplying by the inverse of a fraction}\\\\=\dfrac{15}{2}\cdot\dfrac{10}{19}=\dfrac{15}{2\!\!\!\!\diagup_1}\cdot\dfrac{10\!\!\!\!\diagup^5}{19}=\dfrac{15}{1}\cdot\dfrac{5}{19}=\dfrac{75}{19}=3\dfrac{18}{19}[/tex]
First, convert the mixed fractions into improper fractions. Then, turn the division problem into a multiplication problem by utilizing the concept of reciprocal. This gives us 75/19, or about 3.95 in decimal.
We first need to convert the mixed fractions into improper fractions. To do this, we multiply the whole number by the denominator of the fractional part and then add the numerator, placing this sum over the original denominator. This makes 7 1/2 into 15/2 and 1 9/10 into 19/10. The division problem 7 1/2 divided by 1 9/10 simplifies to 15/2 divided by 19/10.
Next, we remember that dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is obtained by swapping the numerator and denominator. So, we change our division problem into a multiplication problem, transforming 15/2 divided by 19/10 into 15/2 * 10/19.
After multiplying these fractions, we get 150/38, which simplifies to 75/19, which is approximately 3.95 when converted to decimal.
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if ||M and M6 = 4X - 15 and m7 = x + 30 then m 6 =
Answer:
15Step-by-step explanation:
∠6 and ∠7 are Alternate Interior Angles.
The lines l and m are parallel, therefore ∠6 and ∠7 are congruent.
m∠6 = m∠7 → 4x - 15 = x + 30 add 15 to both sides
4x = x + 45 subract x from both sides
3x = 45 divide both sides by 3
x = 15
Answer:
[tex]\angle 6 =45^{\circ}[/tex]
Step-by-step explanation:
We are given that l || m
[tex]\angle 6 = 4x-15[/tex]
[tex]\angle 7 = x+30[/tex]
Since l || m
So, [tex]\angle 6 = \angle 7[/tex] (Alternate interior angles are equal )
So, [tex]4x-15 = x+30[/tex]
[tex]3x= 45[/tex]
[tex]x= 15[/tex]
[tex]\angle 6 = 4x-15=4(15)-15 = 45^{\circ}[/tex]
So, [tex]\angle 6 =45^{\circ}[/tex]
solve the following problems. remember, its easiest to solve the questions in the paranthesis first.
4 ÷ (5+12)
(3+6) + 17
(3+4) + (5÷6)
Problem 1:
Simplify 5+12+to 17.
4÷17
4 divided by 17 is 0.235294.
Problem 2.
Simplify 3+6+ to 9.
9 + 17 = 26.
Problem 3.
Change 3 + 4 to 7.
7+5÷6
Simplify 5 divided by 6 to 0.833333.
7 + 0.833333.
You simplify that to get 7.833333.
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