The circumference of a donut is computed as follows:
[tex]C=\pi\cdot D[/tex]where D is the diameter of the donut. Substituting with D = 6,
[tex]\begin{gathered} C=\pi\cdot6 \\ C=18.85\text{ in} \end{gathered}[/tex]I need help answering the “explain how you found the slope and y intercept question. I did not know how to do this and mainly guessed and got the right answer so I need help explaining please
When we are given a straight line drawn on the cartesian graph, i.e, having x and y coordinates, the gradient/slope is the change on the y-axis relative to change on the x-axis.
The x-axis is the horizontal axis and the y-axis is the vertical axis.
To get the gradient, we simply pick two points on the line and name them points 1 and 2. Thus, they will have the following attributes:
[tex]\begin{gathered} Point1=(x_1,y_1) \\ Point2=(x_2,y_2) \end{gathered}[/tex]The gradient of a straight line is:
[tex]s=\frac{y_2-y_1}{x_2-x_1}[/tex]So, in our question, we can pick our points 1 and 2 at
Point 1 = (-2, 6), (1,-3),
Point 2 = (0, 0), (2,-6)
Applying our formulae, we get:
[tex]\begin{gathered} s=\frac{0-6}{0-(-2)_{}}=-\frac{6}{2}=-3 \\ s=\frac{-6-(-3)}{2-1}=-\frac{3}{1}=-3 \\ \text{Any two points will give us a gradient of -3} \end{gathered}[/tex]The gradient is -3.
As for the intercept on the y-axis, this is the point on the vertical axis where the graph cuts the graph. It can be visibly seen from our graph as occurring at y = 0.
However, it can be calculated via a formula to give us the form: y = mx + c.
where: m is the gradient/slope and c is the intercept on the y axis.
Formulae for getting conventional line equation is:
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \frac{y-6}{x-(-2)}=-3 \\ -3x-6=y-6 \\ \text{Adding 6 to both sides gives:} \\ -3x=y \end{gathered}[/tex]The line equation is therefore: y = -3x + 0
Slope = -3 AND
y-intercept = 0
in a stable there are H horses 6 of them are taken into the the yard to exercise ⁰how many are left in the stable
Explanation:
If there are H horses and 6 are taken into the yard, then we have 6 horses less in the stable.
Answer:
There are (H - 6) horses left in the stable
Find S3 of the sum of the geometric series. az = 4, a3 = 1, r= 1
Given:
a1 = 4
a3 = 1
r = ½
Let's find the S3 of the sum of the geometric series.
Apply the sum of geometric series formula below:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]Let's solve for S3.
Substitute the values into the equation.
Where: n = 3
Thus, we have:
[tex]S_3=\frac{4(1-(\frac{1}{2})^3)^{}^{}}{1-\frac{1}{2}}[/tex]Solving further:
[tex]\begin{gathered} S_3=\frac{4(1-(\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}))}{\frac{1}{2}} \\ \\ S_3=\frac{4(1-\frac{1}{8})}{\frac{1}{2}} \\ \\ S_3=\frac{4(\frac{7}{8})}{\frac{1}{2}} \\ \\ S_3=\frac{4\ast\frac{7}{8}}{\frac{1}{2}} \\ \\ S_3=\frac{\frac{7}{2}}{\frac{1}{2}} \\ \\ S_3=\frac{7}{2}\ast\frac{2}{1} \\ \\ S_3=7 \end{gathered}[/tex]Therefore, the S3 of the sum of the given geometric series is 7
ANSWER:
7
1 and ∠2 are complementary angles. The measure of ∠1 is 14°. The measure of ∠2 is 4x°. Find the value of x. The figure is not drawn to scale
1 and ∠2 are complementary angles. The measure of ∠1 is 14°. The measure of ∠2 is 4x°. Find the value of x.
Remember that
the sum of complementary angles is 90 degrees
so
<1+<2=90
substitute given values
14+4x=90
solve for x
4x=90-14
4x=76
x=1915) A = 3x - 5 B = -4x + 2 What's A-B? What's B-A?
A = 3x - 5 B = -4x + 2 What's A-B? What's B-A?
Part 1
A-B
substitute
(3x-5)-(-4x+2)
remove the parenthesis
3x-5+4x-2
combine like terms
7x-7Part 2
B-A
(-4x+2)-(3x-5)
remove parenthesis
-4x+2-3x+5
combine like terms
-7x+7Given a∥b , and c is not parallel to a or b, which statements must be true? Select each correct answer. m∠4=m∠8 the measure of angle 4 equals the measure of angle 8 m∠7=m∠10 the measure of angle 7 equals the measure of angle 10 m∠8=m∠9 the measure of angle 8 equals the measure of angle 9 m∠2=m∠7 the measure of angle 2 equals the measure of angle 7
The true statements from the given options about the congruent angles are; m∠4 = m∠8 and m∠2 = m∠7
How to identify congruent angles?From the image, the figure consists of three horizontally oriented lines, with two of them parallel and having a common transversal.
Option A; m∠4 and m∠8 are corresponding angles formed between line a and line b.
Given the line a is parallel to line b, we have; m∠4 ≅ m∠8 by corresponding angles theorem
m∠4 = m∠8 is true by definition of congruency
Option B; m∠7 and m∠10 are alternate interior angles
Given the line c is not parallel to line b, we have; b ∦ c
Therefore; m∠7 ≠ m∠10 by the inverse of the alternate interior angles theorem
Thus; m∠7 = m∠10 is False
Option C; m∠8 and m∠9 are alternate interior angles formed between non parallel lines.
Thus; m∠8 ≠ m∠9
m∠8 = m∠9 is false
Option D; m∠2 and m∠7 are alternate exterior angles, Thus;
m∠2 ≅ m∠7 by alternate exterior angles theorem
m∠2 = m∠7 is true, by definition of congruency
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Question 5 of 9Translate the phrase into a variable expression. Use the letter m to name thevariable. If necessary, use the asterisk (*) for multiplication and the slash(/) for division.... the total number of minutes billed on the phone bill split between 3phones...Answer here
SOLUTION
From the question, let the total number of minutes billed on the phone bill be m
Splitting this into 3 phones, we have
[tex]\frac{m}{3}[/tex]Hence the answer is m/3
2) Hazel McCurry offered $419,400 for a home that had been priced at $439,500. The seller agreed to the offer. If she made a $44,000 down payment, what is the mortgage loan amount?
ANSWER
$375,400
EXPLANATION
The price of the home was $439,500, but Hazel offered $419,400 so that was the selling price. The down payment was $44,000. Hence, the mortgage loan amount is,
[tex]\text{Mortgage Loan Amount}=419,400-44,000=375,400[/tex]PROBLEM:how many cubic meters of gas will a cubical tank that has an edge of 4 m long? Need solutionQUESTION:What is the topic all about
Given:
edge of a cube - 4 meters
Find: volume of the cube
Solution:
The formula for getting the volume of the cube is:
[tex]V=s^3[/tex]where s = the length of one side of a cube
Let's plug into the formula above the length of the side of the cube or the edge length.
[tex]V=(4m)^3[/tex]Then, solve for the volume.
[tex]V=4m\times4m\times4m[/tex][tex]V=64m^3[/tex]Therefore, the cubical tank that has an edge of 4 m long can hold 64 cubic meters of gas.
The question is all about the volume of a cube.
Bianca bought a baseplate of 12inches length and 10inches width. find the area of the baseplate
Solution.
Length of the Baseplate = 12inches
Width of the Baseplate = 10inches
[tex]\begin{gathered} \text{Area = Length }\times\text{ Breadth(Width)} \\ \text{ = 12 }\times10 \\ \text{ = 120 in}^2 \\ \end{gathered}[/tex]Final Answer = 120
Cassius is purchasing flower baskets to be placed on each table at a volunteer appreciation lunch. Store Acharges $19.25 per flower basket plus a $15.00 delivery fee. Store B charges $17.50 per flower basket plusa $30.00 delivery fee. Which inequality can determine x, the maximum number of flower baskets that canbe ordered for the total cost at Store A to be cheaper the total cost from Store B?O 19.25 + 15x > 17.5 + 30xO 19.25 + 15x < 17.5 + 30x19.25x + 15 < 17.5x + 30O 19.25x + 15 > 17.5x + 30
We will have the following expressions for store A and B respectively:
[tex]19.25x+15[/tex][tex]17.50x+30[/tex]From this, we can see that after certain ammount of flowers the price will be better if we arrage it as follows:
[tex]19.25x+15>17.50x+30[/tex]Calculate the area of the square JKLM if KM = 42 mm.
Calculate the area of the square JKLM if KM = 42 mm.
given that KM=42 mm
KM is also the diagonal of the square.
Also, the diagonal KM is the hypotenuse of a right triangle with sides JK and JM the Pythagoras theorem.
Now , let's remember that the angle formed by two sides of a square is equal to 90 degrees, this means, that the angle formed by the diagonal and any side must be the half, it is 45 degrees
so, if we solve the right triangle MLK we will find the length of the s
[tex]\begin{gathered} \text{cos}\emptyset=\frac{x}{\text{Hypotenuse}} \\ x=\text{Hypotenuse }\cdot\text{ cos}\emptyset \\ x=42\cdot\cos 45 \\ x=29.69 \end{gathered}[/tex]Now, is it a square, so the sides are equal, and the area is given by
[tex]\begin{gathered} \text{Area}=x^2 \\ A\text{rea}=(29.698)^2 \\ \text{Area}=882\text{ square milimeteres} \end{gathered}[/tex]so, the answer is 882 square millimeters
Write a translation rule that maps Point D(7,-3) onto point (2,5w
The given point is D(7,-3).
To map point D onto the point (2,5), we have to subtract 5 units to x-coordinate, and we have to sum 8 to y-coordinate.
Therefore, the translation rule is[tex](x,y)\rightarrow(x-5,y+8)[/tex]Let's prove it
[tex](7,-3)\rightarrow(7-5,-3+8)\rightarrow(2,5)[/tex]As you can see, the rule is correct.
A package for perfumed soap beads is in the shape of a triangular prism with equilateral triangle as it's bases. What is the total surface area of the soap beads package
Answer
Total Surface Area of the prism = 240 cm²
Explanation
The total surface area is the sum of all the area of the faces of this prism.
The prism has two triangular faces and three rectangular faces.
Area of one triangle = ½bh
b = base of the triangle = 8 cm
h = perpendicular height of the triangle = 3 cm
Area of one triangle = ½bh
Area of one triangle = ½ (8) (3) = 12 cm²
Area of two triangles = 2 (12) = 24 cm²
Area of rectangle at the base = LW
L = length of the triangle = 12 cm
W = width of the triangle = 8 cm
Area of rectangle at the base = LW
Area of rectangle at the base = (12) (8) = 96 cm²
For the two triangles at the side of the prism, we need to find the width using pythagoras theorem
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For the triangles,
a = Half of 8 = 4 cm
b = 3
hyp = W = ?
a² + b² = (hyp)²
4² + 3² = W²
16 + 9 = W²
W² = 25
Take the square root of both sides
W = 5
Area of rectangle at the side = LW
L = length of the triangle = 12 cm
W = width of the triangle = 5 cm
Area of rectangle at the side = LW
Area of rectangle at the side = (12) (5) = 60 cm²
Area of two rectangles at the side = 2 (60) = 120 cm²
Total Surface Area of the prism = (Area of the two triangles) + (Area of the two rectangles on the side) + (Area of the rectangle at the bottom)
Area of the two triangles = 24 cm²
Area of the two rectangles on the side = 120 cm²
Area of the rectangle at the bottom = 96 cm²
Total Surface Area of the prism = (Area of the two triangles) + (Area of the two rectangles on the side) + (Area of the rectangle at the bottom)
Total Surface Area of the prism = 24 + 120 + 96 = 240 cm²
Hope this Helps!!!
Eight times the result of subtracting 3 from a number is equal to the number increased by 25. What is the number? Write an equation that you could use to solve this problem. engagemy
Answer:
The number is 7.
[tex]x=7[/tex]Explanation:
Let us convert the sentences to a maths equation;
Let x represent the number.
"Eight times the result of subtracting 3 from a number"
[tex]8(x-3)[/tex]"the number increased by 25"
[tex]x+25[/tex]Since they are equal to each other, we have;
[tex]8(x-3)=x+25[/tex]Let's now solve the resulting equation;
[tex]\begin{gathered} 8(x-3)=x+25 \\ 8(x)+8(-3)=x+25 \\ 8x-24=x+25 \\ \text{add 24 to both sides} \\ 8x-24+24=x+25+24 \\ 8x=x+49 \\ \text{subtract x from both sides;} \\ 8x-x=x-x+49 \\ 7x=49 \\ \text{divide both sides by 7} \\ \frac{7x}{7}=\frac{49}{7} \\ x=7 \end{gathered}[/tex]Therefore, the number is 7.
[tex]x=7[/tex]
50 POINTS!!!!!!
1. Angles A and B are supplementary. Determine the measure of angle A if the measure of angle B is 109.6°.
A) 250.4°
B) 63.2°
C) 70.4°
D) 19.6°
Answer:
C) 70.4°Step-by-step explanation:
We know supplementary angles add up to 180°:
A + B = 180°Find the missing one:
A + 109.6° = 180°A = 180° - 109.6°A = 70.4°Correct choice is C.
f(x) is a linear function. f(0) = 7 and f(3) = 5. Find the equation for f(x).
Let us calculate the slope of the line. We get two points (0,7) and (3,5)
[tex]m=\frac{7-5}{0-3}=-\frac{2}{3}[/tex]given the slope we have that
[tex]f(x)=-\frac{2}{3}x+7[/tex]so the function is:
[tex]f(x)=-\frac{2}{3}x+7[/tex]what is the slope for a line that is perpindicular to the line y=4x+8
The slope for a line that is perpendicular to the line y=4x+8 is m = [tex]-\frac{1}{4}[/tex]
The given equation is y=4x+8
this equation is of the form y = mx + c
where on comparing we get the values as :
m or the value of the slope =4
and the constant is 8
Thus to find the perpendicular to the given slope
we simply have to find the negative reciprocal of the given slope
the given slope as mentioned above = 4
thus slope of perpendicular = [tex]-\frac{1}{4}[/tex]
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two scouts are camping at a national park. They were hiking when one of them sprains his ankle. They mark off their locations on the map below. How far will they have to travel to reach the medical center?
The distance the scouts have to travel to the clinic, found using Pythagorean Theorem is about 7.07 unit distance
What does the Pythagorean Theorem states?Pythagorean Theorem indicates that in a right triangle, the square of the hypotenuse side is the sum of the square of the other two sides.
The points on the graph are;
Campsite (8, 7)
Sprained ankle (3, 7)
Medical center (8, 2)
The distance between the point where the scout sprained his ankle and the Medical center is from (3, 7) to (8, 2)
The vertical distance the scouts have to travel = 2 - 7 = -5
The horizontal distance the scouts have to travel = 8 - 3 = 5
With the above vertical and horizontal distance, the scouts have to travel to reach the medical center, the direct distance can be calculated using Pythagorean theorem as follows;
Direct distance = √((-5)² + 5²) = 5·√2 ≈ 7.07
The distance the scouts have to travel is about 7.07 unit distance
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The length of a rectangular fish pond is 5 feet more than its width. The area of the fish pond is 143 squarefeet. Find the dimensions of the fish pond and its perimeter.What is the length of the fish pond? (Select]What is the width of the fish pond? Select]What is the perimeter of the fish pond? (Select]
We know that the length of the rectangle is 5 feet more than the width. Let x be the width of the rectangle, then its length is x+5. This can be see in the next picture
We also know that the area of the fish pond is 143 and that the area is given by
[tex]A=wl[/tex]Plugging the values we have that
[tex]143=x(x+5)[/tex]writting the equation in standard form we have that
[tex]\begin{gathered} 143=x(x+5) \\ 143=x^2+5x \\ x^2+5x-143=0 \end{gathered}[/tex]We know that any quadratic equation can be solve by
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]using it for our equation we have
[tex]\begin{gathered} x=\frac{-5\pm\sqrt[]{(5)^2-4(1)(-143)}}{2(1)} \\ =\frac{-5\pm\sqrt[]{25+572}}{2} \\ =\frac{-5\pm\sqrt[]{597}}{2} \\ \text{then} \\ x_1=\frac{-5+\sqrt[]{597}}{2}=9.72 \\ \text{and} \\ x_2=\frac{-5-\sqrt[]{597}}{2}=-14.72 \end{gathered}[/tex]As we know the quadratic equation leads to two solutions. Nevertheless the negative solution is not right in this case, since the distances have to be positive. Then x=9.72.
Once we have the value of x we can know the width a lenght
[tex]\begin{gathered} l=9.72 \\ w=14.72 \end{gathered}[/tex]And the perimeter is
[tex]\begin{gathered} P=2w+2l \\ =2(14.72)+2(9.72) \\ =48.88 \end{gathered}[/tex]The perimeter is 48.88 ft.
3/4 is 70% of what number
3/4 is 70% of what number, Let the number is x:
So, the expression will be :
70% of x = 3/4
[tex]\begin{gathered} \text{ 70\% of x = }\frac{3}{4} \\ \frac{70\times x}{100}=\frac{3}{4} \\ 70x=\frac{3}{4}\times100 \\ x=\frac{3\times100}{4\times70} \\ x=\frac{300}{280} \\ x=\frac{30}{28} \\ x=\frac{15}{14} \\ x=1.07142 \end{gathered}[/tex]x = 1.07142
The number is 1.07142
AХХ14DС1016BABBCCDAD0-14=1016 Х10x= 224x= 22.4
we get that
[tex]\frac{10}{16}=\frac{x}{14}\rightarrow x=14\cdot\frac{10}{16}=\frac{35}{4}=8.75[/tex]A boutique sells t-shirts for $30. They pay $12.50 for each shirt and spend $740 for the right to sell the brand in their store. How many t-shirts do they have to sell to break even?
First let's find the profit for each t-shirt, by subtracting the selling price and the buying price:
[tex]30-12.5=17.5[/tex]So they have a profit of $17.5 per t-shirt sold.
Now, to find the number of t-shirts they have to sell to break even, we just need to divide the right cost of $740 by the profit value of one t-shirt:
[tex]\frac{740}{17.5}=42.29[/tex]So they need to sell approximately 43 t-shirts to break even.
What is the place value of the 5 in 20.52?
In 20.52 you can see that number 5 is placed in the tenths, because it's the first number after the decimal point.
An expression is given.
2 x² + zx - 10
The expression can be written as (x+q) (q + r), where q, r, and z are integers.
What are possible integer values of q, r, and z?
In the text box, type your answer in this format:
q =
r =
z =
Expressions are mathematical statements without the equation sign
The possible integer values of q, r, and z are 1, -5 and 8
The expressions are given as:
[tex]2x^{2} + zx - 10[/tex] (say eq. 1)
(x + q)(x + r)
Both expressions are equal.
So, we have:
[tex]2x^{2} + z x - 10 = (x+q)(x+r)[/tex]
we know that , roots of a quadratic equation ([tex]ax^{2} + bx + c = 0[/tex]) are ,
[tex]m = \frac{-b + \sqrt{b^{2} - 4ac } }{2a} , n = \frac{-b - \sqrt{b^{2} - 4ac } }{2a}[/tex]
on comparing [tex]ax^{2} + bx + c = 0[/tex] with eq . 1 , we get
a = 2 , b = z , c = -10
Therefore , [tex]m = \frac{(-z) + \sqrt{}(z^{2} - 4.2.(-10) ) }{2.2} = \frac{-z + \sqrt{}z^{2} + 80 }{4}[/tex],
[tex]n = \frac{(-z) - \sqrt{}(z^{2} - 4.2.(-10) ) }{2.2} = \frac{-z - \sqrt{}z^{2} + 80 }{4}[/tex]
Now , we can express eq. 1 as ,
(x-m)(x-n)
By comparison, we have:
q = -m
r = -n
or
[tex]q = \frac{-z + \sqrt{}z^{2} + 80 }{4}\\r = \frac{-z - \sqrt{}z^{2} + 80 }{4}[/tex]
Assume that q = 1.
So, we have:
[tex]1 = \frac{-z + \sqrt{}z^{2} + 80 }{4}\\or\\4 = -z + \sqrt{z^{2} + 80 } \\[/tex]
Rearranging and Squaring both sides ,
[tex](z+4)^{2} = (\sqrt{z^{2} + 80 }) ^{2} \\z^{2} + 16 + 8z = z^{2} + 80\\8z = 64[/tex]
This gives , z = 8
Substitute , z= 8 in r
So, we have:
[tex]r = \frac{-8 - \sqrt{8^{2} + 80 } }{4} = \frac{-8 - \sqrt{144} }{4} = \frac{-8 - 12}{4} = -5[/tex]
Hence, the possible integer values of q, r, and z are 1, -5 and 8.
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Pete Smith found in his attic a woody woodpecker watch in its original box. It had a price tag on it for $4.80. The watch was made in 1947. Pete brought the watch to an antiques dealer and sold it for $37. What was the percent of increase in price?
We know that
• The watch value was $4.80 in 1947.
,• The watch value is $37 now.
To know the percentage of increase, we just have to divide
[tex]\frac{37}{4.80}\approx7.71[/tex]Then, we multiply by 100
[tex]7.71\cdot100=771[/tex]This means the new price represents 771% of the old price, that it's an increase of 671%.6 doctors is what percent of 75 doctors ?
Let:
N = Total number of doctors = 75
x = Fraction of the doctors = 6
y = Unknown percent
So:
[tex]\begin{gathered} N\cdot y=x \\ 75y=6 \\ solve_{\text{ }}for_{\text{ }}y\colon \\ y=\frac{6}{75} \\ y=0.08 \end{gathered}[/tex]Answer:
8%
the figures in each pair are similar. Find the unknown measures.
Hello, I have a question with my algebra homework. we started learning about finding slope on a graph. last year I did this but they gave 2 points to find it from. how do you find slope on a line when there is no labled points. I will attach the assignment so you can better understand what I need help with.Thanks,Hunter
Verify Claire says
The line 3 is not visible in the figure
Y S 18. Graph triangle DEF with vertices D(-5,2), E(1.3), and F(-4,-3). Then graph the image of the triangle after it is translated 4 units right and 3 units down. What are the vertices of triangle D'E'F? 4 3 2 1 o 1 2 J 4 SX YTY
Graphing the triangle DEF, we have:
Now, translating the triangle 4 units right and 3 units down, we have the new vertices:
[tex]\begin{gathered} D(-5,2)\to D^{\prime}(-5+4,2-3)=D^{\prime}(-1,-1) \\ E(1,3)\to E^{\prime}(1+4,3-3)=E^{\prime}(5,0) \\ F(-4,-3)\to F^{\prime}(-4+4,-3-3)=F^{\prime}(0,-6) \end{gathered}[/tex]Graphing the triangle D'E'F', we have: