Answer:
The side length of the square will be 11 cm.
Step-by-step explanation:
Tessa wants to make a bandana for her dog by folding a square cloth into a 45-45-90 triangle.
Her dog's neck has a circumference of about 32 cm. the folded bandana needs to be an extra 16 cm long so Tessa can tie it around her dog's neck.
So, the hypotenuse of the 45-45-90 triangle has a length of (32 - 16) = 16 cm.
As a 45-45-90 triangle is an isosceles right triangle with side length a cm (say), then
[tex]\sqrt{a^{2} + a^{2}} = 16[/tex]
⇒ 2a² = 16² = 256
⇒ a² = 128
⇒ a = 8√2 cm.
Therefore, the side length of the square will be 8√2 cm ≈ 11 cm. (Answer)
The side length of the square should be [tex]34cm[/tex] (to the nearest cm)
After folding the square cloth into a bandana, the diagonal has to be [tex]32cm+16cm=48cm[/tex] so that it can tie around the dog's neck.
Using Pythagoras' theorem, the relationship between the sides of the square cloth and the diagonal will be
[tex]diagonal=\sqrt{side^2+side^2}\\diagonal=side\sqrt{2}[/tex]
substituting and solving for the required side length, we get
[tex]48=side\sqrt{2}\\side=24\sqrt{2}\approx 34cm[/tex]
So, the required side length of the square is [tex]34cm[/tex] (to the nearest cm)
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X+2y=4 convert equation from standard form to slope intercept form
Answer:
y = -(1/2)x + 2
Step-by-step explanation:
2y = -x + 4
y = (-x + 4)/2
y = -(1/2)x + 2
PLEASE HELP
What is the twenty-first term of the sequence given by
xn = 4n − 3 ?
87
72
81
6
Answer:
81
Step-by-step explanation:
To find the 21 st term substitute n = 21 into the formula
[tex]x_{21}[/tex] = 4(21) - 3 = 84 - 3 = 81
A rectangle has a width of 8 and a perimeter of 40 what is the length of the rectangle?
8/x=14/7 what does x equal
Answer:
when you have two fractions that equal each other you want to solve by using cross multiply
What cross multiply is, is when you multiply diagonally so:
8/x=14/7
you would take 14*x and 8*7
14x=56 (you would then divide each side by 14)
x=4 (14/14=1, 56/14=4)
8/4=14/7
To check your work you could simplify
8/4=2
14/7=2
2=2, which is true
x=4
Hope this helps ;)
The ratio of boys to girls is 10:7. If there is 84 girls, how many boys are there?
Answer:1
Step-by-step explanation:
HELP!! which is the measure of wx shown in the diagram below
Answer:
A. 25°
Step-by-step explanation:
We are given a circle and two intersecting lines of circle meets at s and form an angle 34° at S.
Also, we have W and X points on circle that form a minor arc and T and R makes a major arc of angle 93°.
In order to find the value of minor arc WX, we need to apply following formula:
Subtends angle on intersection of lines = [tex]\frac{Major Arc- Major Arc} {2}[/tex]
Plugging values in above formula, we get
34= [tex]\frac{93 - x }{2}[/tex]
On cross multiplication, we get
34 × 2 = 93-x
68 = 93 -x
x = 93-68
x= 25.
Therefore, measure of arc WX = 25°.Hope this helps and you understand !!!!!!
How many 60-degree angles does it take to make a full turn?
Answer:
6
Step-by-step explanation:
360 is a full turn so, 360 divided by 60 is 6
vanssea earns base salary of $400.00 every week with an additional 5% commission on everything she sells. Vanessa sold $1650.00 worth of items last week. What was Vanessa's total pay last week?
Answer: She earns 482.50
Step-by-step explanation:
1. If two nonvertical lines are parallel, what do we know about their slopes? If two lines are perpendicular and neither is parallel to an axis, what do we know about their slopes? Why must the lines be nonvertical?
Non-vertical parallel lines have equal slopes, while slopes of non-vertical, non-horizontal perpendicular lines are negative reciprocals of each other. Vertical lines are defined as having an infinite slope, thus they must be non-vertical to consider their slopes.
Explanation:When considering the slopes of lines on a graph with perpendicular axes, like the x-axis and the y-axis, we can draw several conclusions about parallel and perpendicular lines. If two non-vertical lines are parallel, their slopes are equal, because the tilt of the lines with respect to the horizontal axis is the same. For example, if we have two equations of lines in the form y = mx + b, where m represents the slope and b represents the y-intercept, parallel lines would have the same value of m.
If two lines are perpendicular and neither line is parallel to an axis, then their slopes are negative reciprocals of one another. This holds true because the product of the slopes of two perpendicular lines is -1. For example, if the slope of one line is a, the slope of the line perpendicular to it will be -1/a.
It is necessary for the lines to be non-vertical because a vertical line does not have a well-defined slope; its slope is considered infinite. Therefore, the definition of perpendicular lines in terms of slope only applies to non-vertical lines.
How do I solve systems of equations algebraically
Answer:
You solve equations algebraically by using equations to answer and having variables rather than the arithmetic way (doing the work).
Ex: instead of 20÷5=4 (arithmetic), you do
20=5x
A company makes a profit of $50 per software program and $35 per video game. The company can produce at most 200 software programs and at most 300 video games per week. Total production cannot exceed 425 items per week. How many items of each kind should be produced per week in order to maximize the profit?
IDENTIFY VARIABLES, STATE OBJECTIVE FUNCTION, AND STATE THE CONSTRAINTS.
Answer:
200- software (x) 225- video game (y) = 425 items
Step-by-step explanation:
software- 200 = $10,000 video-225 = $7,875
total= $17,875
200x + 225y = $17,875
7. You go out to dinner and the bill is $40 and you want to leave the server a 15% tip. How much of a tip are you going leave?
The tip i will leave is of 6 dollars.
What is percentage ?Percentage is the value per hundredth. Suppose we have 500 dollars and we need find 50% of it.We know 50% of 500 dollars is half of it which is 250 dollars.
To find 50% of 500 dollars we put the the given percentage on numerator and divide by hundred and multiply it by the given amount.
∴ (50/100)×500
= 250 dollars.
According to the given question
You go out to dinner and the bill is $40 and you want to leave the server a 15% tip.
We have to find what is 15% of 40 dollars which is
= (15/100)×40 dollars.
= 6 dollars.
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Explain how you know that 7/12 is greater than 1/3 but less than 2/3
Answer:
Step-by-step explanation:
7/12 is greater than 1/3 because it has a greater numerator and denominator it is less than 2/3 because the numerator is smaller
solve the following formula c=1/2f(q+b) for q
Answer:q= (2C - fb)/f
Step-by-step explanation:
multiplying both sides by 2 we have,
2C = fb + fq,
subtract both sides by fb
fq = 2C - fb,
dividing both sides by f
q= (2C - fb)/f
In the figure, angle D measures 31⁰ and angle A measures 27⁰
1.The measurement of angle B is
A.59⁰
B.63⁰
C.90⁰
2. The measurement of angle F is
A.59⁰
B.63⁰
C.90⁰
Answer:
1)B:63°
2)A:59°
Step-by-step explanation:
1.ABC is a right triangle at C then angle ACB=90°(right angle)
Angle CAB=27°(see the given)
measure of the angles in any triangle is 180°
then angle CBA=
measure of all the angles - (measure ACB+measure CAB)
=180°-(90°+27°)
=63°
2. Same explanation of angle B:
in the right triangle DEF: angle DEF=90°
angle D=31°(given)
Then measure of angle A=180°-(angle E + angle D)
=180-(90+31)=59°
What is equivalent to 8 1/4
Answer:
33/4
Step-by-step explanation:
8x4 +1 = 33
Answer:
33/4
Step-by-step explanation:
work out 35% out of £120
Answer:
42
Step-by-step explanation:
120*35=4200
4200/100=42
PLZ HURRY! Which mapping diagram represents a function from x → y?
A function from x to y represents a situation where each x value is linked to a unique y value. This can be represented in a mapping diagram, such as with the points (1,5), (2,10), (3,7), and (4,14). Such a diagram showcases the fact that different x values trigger different y values, demonstrating the dependence of y on x.
Explanation:A function from x to y implies that when the value of x changes, it directly influences the value of y. One way to represent this is through a mapping diagram.
A mapping diagram that represents a function can be visualised as each value of x corresponding to a unique value of y. For example, refer to the following points: (1,5), (2,10), (3,7), and (4,14). Here, every x value is paired with a unique y value. When these points are plotted, there's no x value that corresponds to more than one y value, demonstrating the dependence of y on x.
Therefore, a function from x to y is represented by a mapping diagram where different x values are linked to unique y values, showing the dependency of y values on the x values.
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What is the slope of the line below? Give an exact number
Answer:
The slope of straight line in the graph is
m = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Slope of a given line is [tex]m = \frac{y_{2}-y_{1} }{x_{2} - x_{1} }[/tex]........(1)
The point (-2,0) lie on x-axis in the graph and another point ( 0, 1) lie on y- axis.
so [tex](x_{1} , y_{1}) = (-2,0) and (x_{2} , y_{2}) = (0,1)[/tex]
substitute these values in equation (1)
[tex]m = \frac{1-0}{0-(-2)}[/tex]
[tex]m = \frac{1}{2}[/tex]
slope of given line is [tex]m = \frac{1}{2}[/tex]
Which operations are commutative and
associative?
addition
O subtraction
multiplication
division
Answer:
additionmultiplicationStep-by-step explanation:
When learning about commutative and associative properties, we learn that ...
a + b = b + a . . . . . addition is commutative
ab = ba . . . . . . . . . multiplication is commutative
But we also know that ...
a - b ≠ b - a . . . . . . subtraction is not commutative
a/b ≠ b/a . . . . . . . . division is not commutative
__
We also learn that ...
a + (b+c) = (a+b) +c . . . . addition is associative
a(bc) = (ab)c . . . . . multiplication is associative
And of course, ...
a - (b -c) ≠ (a -b) -c . . . . subtraction is not associative
a/(b/c) ≠ (a/b)/c . . . . . . . division is not associative
_____
However, you can use associative and commutative properties in problems involving subtraction and division if you write the expression properly:
a - (b - c) = a +(-(b -c)) = a +((-b) +c) = (a +(-b)) +c . . . . keeping the sign with the value makes it an addition problem, so the associative property can apply
(a/b)/c = (a(1/b))(1/c) = a(1/b·1/c) = writing the division as multiplication by a reciprocal makes it so the associative property can apply
Answer:
addition
multiplication
What is the volume of a shipping cube with dimensions of 2 1/2 feet? 6 3/4 cubic feet 15 5/8 cubic feet 8 1/8 cubic feet
Answer:
The volume of shipping cube is [tex]15\frac{5}{8}\ cubic\ feet.[/tex]
Step-by-step explanation:
Given:
The dimensions of a shipping cube of 2 1/2 feet.
Now, to find the volume of shipping cube.
Side of cube = [tex]2\frac{1}{2}\ feet.[/tex]
Side = [tex]\frac{5}{2}\ feet[/tex]
So, to get the volume of cube we put formula:
[tex]Volume=(side)^3[/tex]
[tex]Volume=(\frac{5}{2})^3[/tex]
[tex]Volume=\frac{125}{8}[/tex]
[tex]Volume=15\frac{5}{8} \ cubic\ feet.[/tex]
Therefore, the volume of shipping cube is [tex]15\frac{5}{8}\ cubic\ feet.[/tex]
Answer:
b
Step-by-step explanation:
9y-4-11y+7
Terms:
Like terms:
Coefficient:
Constants:
9y - 4 - 11y + 7
Terms: 9y, -4, -11y, 7
Like terms: 9y and -11y
Coefficient : 9, -11
Constants: 7, -4
Solution:
Given expression is:
9y - 4 - 11y + 7
We have to find the terms, like terms, coefficient and constants
Terms:Each term in the expression is called terms
It includes, numbers, variables also
Terms : 9y and -4 and -11y and 7
Coefficients:A coefficient is a number used to multiply a variable
Here the terms with variables are 9y and -11y
Coefficient : 9, -11
Like terms:"Like terms" are terms whose variables are the same and thier powers is also same
Like terms : 9y and -11y
Constants:The constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number
Constants: 7 and -4
(889 x 27) + 50 is
than 889 x 27
Final answer:
The expression (889 x 27) + 50 is greater than 889 x 27, because adding 50 to any product will always result in a larger number.
Explanation:
The student's question is asking to compare the result of the expression (889 x 27) + 50 with 889 x 27, without actually calculating the precise values.
First, let's evaluate the structure of the expressions. When we have an expression of the form (a x b) + c, adding any number c to the original product of a and b will always result in a value greater than the original product. This is a basic property of arithmetic progression.
Based on this property, we know that (889 x 27) + 50 is definitely greater than 889 x 27 because we are adding a positive number (50) to the original product, hence the sum must be larger.
Find the Quotient.
5,483 ÷ 4
Answer:
1370.75
Step-by-step explanation:
Teri bought 360 rubber band 2 make a bracelet
15% of the bands were white and the rest were red. After using 140 bands to make her 1st bracelet , 20% of the remaining bands were white
How many red bands did teri use on the bracelet
Answer:
Step-by-step explanation:
No. of white bands = 15% of 360 = (15/100)*360= 54
No.of red bands = 360 - 54 = 306
No. bands remaining = 360 - 140 = 220
No. of remaining white bands = 20% of 220= (20/100)*220 = 44
No. of remaining red bands = 220 - 44 = 176
No. of red band used = No.of red bands - No of remaining bands
= 306 - 176 = 130
A box of markers weighed 4 2/5 ounces. If a teacher took out 5/8 of the markers, what is the weight of the markers she took out? *
Multiply the weight by the amount they took out:
4 2/5 x 5/8
Rewrite as 22/5 x 5/8
(22 x 5) / (5 x 8)
Simplify:
110/40
Rewrite as a proper fraction:
2 3/4 ounces.
x+5÷9=3
What is the number where when you add 5 then divide it by 9 it is 3?
Answer:
22 + 5 ÷ 9 = 3
Proof:
27/9
= 3
the number is 22
A car is purchased with a loan of $8.000 for two years with simple interest. The amount that is paid back is $8,160
Which function represents the interest on this loan after years!
The function that represents the interest on this loan after years is Interest = Principal × Rate × Time.
Explanation:The function that represents the interest on this loan after years can be calculated using the formula for simple interest:
Interest = Principal × Rate × Time
In this case, the principal is $8,000, the rate is unknown, and the time is 2 years. The interest paid back is $8,160, so we can rewrite the formula as:
$8,160 = $8,000 × Rate × 2
Dividing both sides of the equation by $8,000 × 2 gives:
Rate = $8,160 / ($8,000 × 2)
Solving this equation gives a rate of 0.51, or 51%.
5x/3 + 1/3 =12 find x
Answer:
x = 7.002 or 7
Step-by-step explanation:
5x/3 + 1/3 = 12
- 1/3 - 1/3
5x/3 = 11 2/3
3(5x/3) = 3(11 2/3)
5x = 35.01
x = 7.002 or 7
A. Does the table represent a proportional relationship?
B. If the relationship is proportional, what is the constant of proportionality?
Total wight in pounds. 12 18 30 60
Number of books. 10 15 25 50
A. Yes the table represents a proportional relationship
B. The constant of proportionality is 1.2
Step-by-step explanation:
Two quantities are proportional if:
One of them is equal to the constant times the other oneIf x and y are proportion, then y = k x, where k is constant∵ Total wight in pounds ⇒ 12 , 18 , 30 , 60
∵ Number of books ⇒ 10 , 15 , 25 , 50
- Divide each two corresponding data to check if all they give
the same constant or not
∵ 12 ÷ 10 = 1.2
∵ 18 ÷ 15 = 1.2
∵ 30 ÷ 25 = 1.2
∵ 60 ÷ 50 = 1.2
- That means the total wight is equal to constant times the
number of books
∴ Total wight = 1.2 Number of books
∴ The total wight and the number of books are in a proportional
relationship
A. Yes the table represents a proportional relationship
∵ Total wight = 1.2 Number of books
∴ The constant of proportionality = 1.2
B. The constant of proportionality is 1.2
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