Answer:
y = x^2 +3x-10
Step-by-step explanation:
If we know the roots of a quadratic function, we know that
y = (x -a) (x-b) where a and b are the roots
y = (x-2 ) (x--5)
y = (x-2)(x+5)
We need to foil this out to get this in standard form of ax^2 + bx+c
FOIL (x-2) (x+5)
First x*x: x^2
outer : 5*x = 5x
inner: -2x = -2x
last : -2*5 = -10
Add them up
x^2 +5x-2x-10
x^2 +3x-10
Final answer:
A quadratic equation in standard form with roots 2 and -5 is obtained by multiplying (x - 2)(x + 5), which simplifies to x² + 3x - 10 = 0.
Explanation:
To write a quadratic equation in standard form with integer coefficients that has roots 2 and -5, we use the fact that if α and β are roots of a quadratic equation, the equation can be written as:
ax² + bx + c = 0
Where:
The quadratic equation in standard form using the roots 2 and -5 is given by:
(x - 2)(x + 5) = 0
Expanding this we get:
x² + 5x - 2x - 10
Which simplifies to:
x² + 3x - 10 = 0
Thus, the quadratic equation with integer coefficients and roots 2 and -5 is x² + 3x - 10 = 0.
a) Use synthetic division to show that 2 is a solution of 2h3 +14h2 − 72 = 0 .
b) Using part a, find the dimensions of a box that has a volume of 72 cubic
inches where the width is twice the height and the length is 7 inches more than the height.
4. Find k so that 4x-3 is a factor of 20x3+23x2-10x+k
Answer:
Length=9 inches,width=4 inches, height =2 inches.
k= [tex]-\frac{111}{8}[/tex]
Step-by-step explanation:
a) If by synethetic division method the remainder equals i.e in the last row and last column if figure yield is 0 then 2 is one of the factor i.e one of the solution of given equation.
Remainder is 0.
Hence 2 is the solution of given equation.
b) Given a box having volume 72 cubic inches
Let Height = x inches
∵ length is 7 inches more than the height
⇒ Length = x+7 inches
& also width is twice the height
⇒ Width = [tex]2\times x[/tex]
Given Volume = 72 cubic inches
[tex]length\times width\times height[/tex] = 72
[tex](x+7)\times (2x)\times x[/tex] - 72 = 0
From part a, 2 is the solution of above equation
⇒ Length = x+7 = 2+7 = 9 inches
Width = [tex]2\times2[/tex] = 4 inches
Height = x = 2 inches
Given [tex]4x-3[/tex] is a factor of [tex]20x^3+23x^{2} -10x+k[/tex]
Hence, [tex]20(\frac{3}{4})^3 +23(\frac{3}{4}) ^{2} -10(\frac{3}{4})+k=0[/tex]
[tex]\frac{135}{16}+\frac{207}{16}-\frac{120}{16} +k=0[/tex]
[tex]\frac{111}{8}+k=0[/tex]
k= [tex]-\frac{111}{8}[/tex]
Synthetic division confirmed that 2 is a solution to the equation 2h3 +14h2 - 72 = 0. Using this information, we found the dimensions of a box with given characteristics to be: height, 2 inches; width, 4 inches; length, 9 inches. Lastly, used synthetic division again to find k so that 4x-3 is a factor of 20x3+23x2-10x+k.
Explanation:To solve the first portion of the question, we will use synthetic division to prove that 2 is a solution of the given equation (2h3 +14h2 - 72 = 0). By placing the coefficients into a row (2, 14, 0, -72) and bringing down the first coefficient (2), we multiply by our solution (2), add down the column, and repeat until the end. If we reach 0 at the end, this shows that 2 is indeed a solution.
For the second part of the question, we are given the volume of the box as 72 cubic inches, and we already know from part a that the height, h, of the box is equal to our solution, 2. So, the width of the box would be twice the height, or 2*2 = 4 inches. The length of the box is 7 inches more than the height, or 2+7 = 9 inches.
Lastly, to find the value of k so that 4x-3 is a factor of 20x3+23x2-10x+k, one would set up synthetic division using the roots of 4x-3 and the coefficients of the polynomial, then solve for k when the remainder equals zero.
Learn more about Synthetic Division here:https://brainly.com/question/28824872
#SPJ3
10x^2 − 9y^2 is not the difference of two squares. Identify the correct explanation for this statement.
A Neither 9y^2 nor 10x^2 are perfect squares.
B 10x^2 is not a perfect square.
C 9y^2 is not a perfect square.
D Both 9y^2 and 10x^2 are perfect squares.
Answer:
B
Step-by-step explanation:
9y² is a perfect square since [tex]\sqrt{9y^2}[/tex] = 3y
10x² is not a perfect square since [tex]\sqrt{10x^2}[/tex] = [tex]\sqrt{10}[/tex] x
Answer:
B is the answer for this equation
What is the area of a rectangle with vertices at (1, 7) , (5, 3) , (3, 1) , and (−1, 5) ?
PLEASE HELPPPPPPP
and explain
Answer:
Given the vertices of the rectangle ABCD:
A = (1, 7) , B = (5, 3), C = (3,1) and D = (-1, 5)
Distance(D) formula for two points is given by;
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula:
[tex]AB = \sqrt{(5-1)^2+(3-7)^2}=\sqrt{(4)^2+(-4)^2} = \sqrt{16+16} = \sqrt{32} = 4\sqrt{2}[/tex] units
[tex]BC= \sqrt{(3-5)^2+(1-3)^2}=\sqrt{(-2)^2+(-2)^2} = \sqrt{4+4} = \sqrt{8} = 2\sqrt{2}[/tex] units.
[tex]CD = \sqrt{(-1-3)^2+(5-1)^2}=\sqrt{(-4)^2+(4)^2} = \sqrt{16+16} = \sqrt{32} = 4\sqrt{2}[/tex] units
[tex]DA= \sqrt{(-1-1)^2+(7-5)^2}=\sqrt{(-2)^2+(2)^2} = \sqrt{4+4} = \sqrt{8} = 2\sqrt{2}[/tex] units.
Since, the Opposite sides of a rectangle are the same length.
⇒AB = CD and BC =DA
Area of rectangle is equal to multiply its width by length.
Area of rectangle ABCD = [tex]CD \times BC[/tex]
= [tex]4\sqrt{2} \times 2\sqrt{2} = 8 \times 2 = 16[/tex] square units.
Therefore, the area of rectangle is, 16 square units.
Solve for the missing variables. (Geometry)
Answer:
92 degrees is x
88 degrees is y
Answer:
x=92. y= 88
Step-by-step explanation:
all three corners of a tri. equal 180
so 39+49=88
180-88=92 now y and x= 180 also so y
Which ordered pair is a solution to the inequality? 4x + y > - 6
A) (1, -12)
B) (0, -9)
C) (-1, -1)
D) (-3, 0)
The answer: C) (-1, -1)
The table below illustrates the decay of a sample of radioactive uranium. Time in Days, x 0 1 2 3 4 5 Sample Remaining (grams), U 500 255 130 66 34 17 Which equation best models this set of data where U represents the amount of sample remaining, in grams, at time x?
[tex]\underline{\ x|\ \ 0\ \ |\ \ 1\ \ |\ \ 2\ \ |\ \ 3\ \ |\ \ 4\ \ |\ \ 5\ \ |}\\U|500\ |\ 255|\ 130|\ 66\ \ |\ 34\ |\ \ 17\ |\\\\U=a(b)^x\\\\for\ x=0,\ U=500\\\\500=a(b)^0\\\\500=a(1)\to \boxed{a=500}\\\\for\ x=1,\ U=255\\\\255=500(b)^1\\\\255=500b\qquad\text{divide both sides by 500}\\\\b=\dfrac{255}{500}\\\\b=\dfrac{255:5}{500:5}\\\\b=\dfrac{51}{100}\to \boxed{b=0.51}\\\\\text{Therefore we have the equation of the function:}\\\\U=500(0.51)^x[/tex]
[tex]\text{Check for other values of x:}\\\\for\ x=2\\\\U=500(0.51)^2=130.05\approx130\qquad CORRECT\\\\for\ x=3\\\\U=500(0.51)^3=66.3255\approx66\qquad CORRECT\\\\for\ x=4\\\\U=500(0.51)^4=33.826\approx34\qquad CORRECT\\\\for\ x=5\\\\U=500(0.51)^5=17.25125\approx17\qquad CORRECT[/tex]
[tex]Answer:\ \boxed{U=500(0.51)^x}[/tex]
aiutami con la mia matematica
Una lampada è in vendita e il suo prezzo è ridotto da $ 80 a $ 50.
Qual è la percentuale di diminuzione?
0.3
0.375
0.625
30
37.5
62.5
Kevin compra 4 sedie pieghevoli. Ogni sedia costa $ 13,50. L'imposta sulle vendite è del 6,5%.
Qual è l'importo delle tasse di vendita per gli acquisti di Kevin?
Inserisci la tua risposta nella casella.
In my fish tank, the ratio of red fish to blue fish is 1:5. There are 15 blue fish. How many red fish are there?
To find the number of red fish in a tank where the ratio of red to blue fish is 1:5 and there are 15 blue fish, divide the number of blue fish by the blue part of the ratio (15 ÷ 5) and multiply by the red part (1), resulting in 3 red fish.
Explanation:The question asks how many red fish are there in a fish tank if the ratio of red fish to blue fish is 1:5 and there are 15 blue fish. To solve this, you can use the ratio provided. Since the ratio of red to blue fish is 1:5, for every 1 red fish, there are 5 blue fish.
Given there are 15 blue fish, you can divide the number of blue fish by the ratio part for blue fish to find out how many parts of red fish there are.
Step 1: Find the ratio part representing red fish. It is 1.
Step 2: Divide the number of blue fish by the blue ratio part (5) to find how many times the ratio fits into the blue fish population. 15 blue fish ÷ 5 = 3.
Step 3: Multiply the result by the red ratio part. 3 × 1 = 3 red fish.
What is the weight of a bowling ball with a 5 in. radius if we know that one cubic inch weighs 1/100th of a pound?
A. 6.54 lb.
B. 5.24 lb.
C. 9.86 lb.
D. 10.99 lb
Answer:
Option B is correct.
Weight of a bowling ball is 5.24 Ib
Step-by-step explanation:
Assume: The shape of the bowling ball is perfectly spherical.
Given:
Radius of a bowling ball= 5 inches (r) .
One cubic inch weighs [tex]\frac{1}{100}[/tex]th of a pound.
Density of a bowling ball = [tex]\frac{1}{100} Ibs/in^3[/tex]
Volume of sphere is given by:
[tex]V = \frac{4}{3} \pi r^3[/tex] where V is the volume and r is the radius of the sphere.
Substitute the value of r =5 and [tex]\pi = 3.14[/tex] in above we get;
[tex]V = \frac{4}{3} \cdot 3.14 \cdot 5^3 =\frac{4}{3} \cdot 3.14 \cdot 125[/tex]
Simplify:
[tex]V = 523.3333... in^3[/tex]
To find the weight of a bowling ball:
[tex]Weight = Volume \times Density[/tex]
Then;
[tex]Weight = 523.33333.. \times \frac{1}{100} =\frac{523.3333..}{100} = 5.2333...[/tex]
Therefore, the weight of a bowling ball ≈ 5.24 Ib
Answer:
The weight of a bowling ball is 5.24 pounds.
Option (B) is correct.
Step-by-step explanation:
Formula
[tex]Volume\ of\ a\ sphere = \frac{4}{3}\pi\ r^{3}[/tex]
Where r is the radius of a sphere.
As given
The radius of the ball is 5 in.
As the shape of the ball is spherical .
Thus
[tex]Volume\ of\ a\ ball = \frac{4}{3}\pi\ 5^{3}[/tex]
[tex]\pi = \frac{22}{7}[/tex]
Thus
[tex]Volume\ of\ a\ ball = \frac{4\times 22\times 5\times\ 5\times 5}{3\times 7}[/tex]
[tex]Volume\ of\ a\ ball = \frac{11000}{21}[/tex]
Volume of a ball = 523.8 in³ (Approx)
As
[tex]1\ in^{3} = \frac{1}{100}\ pound[/tex]
Thus
Convert 523.8 in³ into pounds.
[tex]523.8\ in^{3} = \frac{523.8}{100}\ pound[/tex]
[tex]523.8\ in^{3} = 5.24\ pound\ (Approx)[/tex]
Therefore the weight of a bowling ball is 5.24 pounds.
Therefore Option (B) is correct.
Tours of the art museum are offered every 1/3 hour starting at 10A.M. The museum closes at 4:00 P.M. How many tours are offered eavch day?
Answer:
Each day, [tex]18[/tex] tours are offered.
Step-by-step explanation:
We were given that, the museum starts at,
10:00 AM and closes at 4:00 PM.
The total duration is [tex]4:00PM-10:00AM=16:00GMT-10:00GMT=6hours[/tex]
Since the tour of the museum are offered every [tex]\frac{1}{3}[/tex] hour each day, we can calculate the number of tours that will be offered within the 6 hours as follows
[tex]Number\:of\:tours=\frac{6}{\frac{1}{3} }[/tex]
We rewrite to obtain,
[tex]Number\:of\:tours=6\div \frac{1}{3}[/tex]
We multiply by the reciprocal of the second fraction to get,
[tex]Number\:of\:tours=6\div \frac{3}{1}=18[/tex]
Therefore 18 tours will be offered each day in the art museum.
Answer: Therefore, the art museum offers 18 tours each day.
Step-by-step explanation: The art museum offers tours every 1/3 hour starting at 10 A.M. and closes at 4:00 P.M. To determine how many tours are offered each day, we need to find the total number of 1/3 hour intervals between 10 A.M. and 4:00 P.M.
First, we need to convert the closing time to the same format as the starting time. Since there are 60 minutes in an hour, we can write 4:00 P.M. as 16:00.
Next, we calculate the number of hours between the starting and closing times by subtracting 10 from 16, which gives us 6 hours.
Since there are 3 intervals in each hour, we multiply the number of hours by 3 to find the total number of 1/3-hour intervals. In this case, 6 hours multiplied by 3 equals 18 intervals.
Therefore, the art museum offers 18 tours each day.
A cruise ship can cover 17 nautical miles in 306 minutes. How many nautical miles will it travel in 162 minute
Set up a proportion:
17 miles in 306 minutes, write as 17/306
X miles in 162 minutes, write as X/162
Now set to equal and solve:
17/306 = x/162
Cross multiply:
17 * 162 = 306 *x
2754 = 306x
Divide both sides by 306:
x = 2754 / 306
x = 9
It will travel 9 nautical miles.
Write an equation of the line,in point slope form, that passes through the two given points. Points: (-13,9),(11,-3)
It’s for number 7. I know it shows me the right answer but I am doing corrections and I need some help in how to solve it. Please help!
The equation in point slope form is y-y1 = m(x-x1)
The first point given is (-13,9) so this is used for Y1 and X1.
m is the slope which is found by the change in Y over the change in x.
The slope is -3 - 9 / 11 - -13, which equals -1/2
So the equation becomes y-9 = -1/2(x+13)
Answer:
y-9=-1/2(x+13)
Step-by-step explanation:
To find the slope for the line, we use
m = (y2-y1)/(x2-x1)
since we know the points( -13,9) and (11,-3)
m= (-3-9)/(11--13)
=(-3-9)/(11+13)
=-12/24
= -1/2
We can use the point slope form to make the equation for the line
y-y1=m(x-x1)
y-9=-1/2(x--13)
y-9=-1/2(x+13)
Place the decimal point in the answer below to make it correct. Explain your reasoning
Answer:
AC is greater than BC because segment AC is the hypotenuse of right triangle ABC, and the hypotenuse is the longest side of a right triangle.
Will mark brainliest!! Help plzz
Answer:
-4 is the simplified form. of the given expression.
Step-by-step explanation:
We have been given an expression:
[tex]-64^\frac{1}{3}[/tex]
We can rewrite 64 as [tex]4^3[/tex]
the given expression will be rewritten as:
[tex](-(4)^3)^\frac{1}{3}[/tex]
powers will get cancel out we get:
[tex]-4[/tex] is the required simplified form.
Which of these sets of points lie within plane w?
Robert climbed 775775 steps in 12\dfrac1212 2 1 ? minutes. How many steps did he average per minute?
Answer:
62 steps per minute.
Step-by-step explanation:
We have been given that Robert climbed 775 steps in [tex]12\frac{1}{2}[/tex] minutes.
To find the the average steps per minute we will divide 775 by [tex]12\frac{1}{2}[/tex].
[tex]\text{The average steps per minute}=775\div 12\frac{1}{2}[/tex]
Let us convert our mixed fraction into improper fraction.
[tex]\text{The average steps per minute}=775\div \frac{25}{2}[/tex]
Dividing a number by a fraction is same as multiplying the number by the reciprocal of fraction.
[tex]\text{The average steps per minute}=775\times \frac{2}{25}[/tex]
[tex]\text{The average steps per minute}=31\times2[/tex]
[tex]\text{The average steps per minute}=62[/tex]
Therefore, Robert climbed 62 steps per minute.
Answer:
62 Steps per minute. <3
Step-by-step explanation:
Quinn has a large family. She has 4 cousins who live in Texas, 3 cousins who live in Nebraska, and 9 cousins who live in Michigan. What is the ratio of Quinn's cousins who live in Texas to her cousins who live in Michigan?
Answer:
the required ratio is: 4:9
Step-by-step explanation:
Quinn has 4 cousins who live in Texas, 3 cousins who live in Nebraska, and 9 cousins who live in Michigan.
We have to find the ratio of Quinn's cousins who live in Texas to her cousins who live in Michigan
The required ratio is:
[tex]Ratio=\frac{\text{Number of Quinn's cousins who live in Texas}}{\text{cousins who live in Michigan}}[/tex]
[tex]Ratio=\frac{4}{9}[/tex]
Hence, the required ratio is: 4:9
The ratio of Quinn's cousins who live in Texas to her cousins who live in Michigan is 4:9. This means for every 4 cousins in Texas, there are 9 cousins in Michigan.
Explanation:The subject of this question is Mathematics. Specifically, it involves calculating ratios. In this case, the student wants to know the ratio of Quinn's cousins who live in Texas to her cousins who live in Michigan.
The ratio of something is simply a way to compare quantities. Here, we have 4 cousins in Texas and 9 cousins in Michigan. So, to get the ratio from Texas to Michigan, we simply write it as '4:9' or we can say, 'for every 4 cousins in Texas, there are 9 cousins in Michigan'.
In summary, the ratio of Quinn's cousins who live in Texas to her cousins who live in Michigan is 4:9.
Learn more about Ratio here:https://brainly.com/question/32531170
#SPJ3
a storage container is a rectangular prism with a volume of 392 cubic inches. the height of the container is 3 inches less than its length and its width is twice the length. what are the dimensions of the container?
Answer:
Step-by-step explanation:
Let the length of the rectangular prism = x inches
Width of the rectangular prism = 2 x length = 2x inches
Height of the rectangular prism = 3 inches less than the length = (x -3) inches
Volume of the rectangular prism = length x width x height = 392 cubic inches
= (2x) inches x (x) inches x (x -3) inches = 392 cubic inches
= x2(x-3) = 196 cubic inch
X = 8.59 inch
Length of the rectangular prism = x inches = 7 inch
Width of the rectangular prism = 2 x length = 2 x 7 inch = 14 inch
Height of the rectangular prism = 3 inches less than the length = (x -3) inches = 7 – 3 = 4 inch
The dimensions of the storage container are 7 inches in length, 14 inches in width, and 4 inches in height. The volume equation is solved for length by substituting the relationships between height, width, and length into the formula for volume.
To find the dimensions of a rectangular prism storage container with a volume of 392 cubic inches, we need to set up equations based on the information given. The height (h) of the container is 3 inches less than its length (l), so h = l - 3. The width (w) of the container is twice the length of the container, so w = 2l. Knowing that volume = length * width * height (V = lwh), we can substitute the expressions for h and w into the volume equation to obtain an equation with one unknown:
V = l * (2l) * (l - 3)
Substituting the known volume into the equation, we get:
392 = l * (2l) * (l - 3)
This is a cubic equation that can be solved for l (the length of the container). Once l is found, we can also find h and w since they are defined in terms of l.
Let's solve the equation:
[tex]392 = 2l^2 * (l - 3)[/tex]
Divide both sides by 2 to simplify:
[tex]196 = l^2 * (l - 3)[/tex]
Now we expand and solve for l:
[tex]196 = l^3 - 3l^2[/tex]
Moving all terms to one side gives:
[tex]l^3 - 3l^2 - 196 = 0[/tex]
By trial and error or using a cubic equation solver, we find that l = 7 inches. Now we can find the height and width:
h = l - 3 = 7 - 3 = 4 inches
w = 2l = 2 x 7 = 14 inches
Therefore, the dimensions of the storage container are 7 inches in length, 14 inches in width, and 4 inches in height.
Write the equation of the conic section with the given properties:
An ellipse with vertices (-8, 0) and (8, 0) and a minor axis of length 10.
Answer:
[tex]\frac{x^2}{64} + \frac{y^2}{25} =1[/tex]
Step-by-step explanation:
An ellipse with vertices (-8, 0) and (8, 0)
Distance between two vertices = 2a
Distance between (-8,0) and (8,0) = 16
2a= 16
so a= 8
Vertex is (h+a,k)
we know a=8, so vertex is (h+8,k)
Now compare (h+8,k) with vertex (8,0) and find out h and k
h+8 =8, h=0
k =0
a minor axis of length 10.
Length of minor axis = 2b
2b = 10
so b = 5
General formula for the equation of horizontal ellipse is
[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b} =1[/tex]
a= 8 , b=5 , h=0,k=0. equation becomes
[tex]\frac{(x-0)^2}{8^2} + \frac{(y-0)^2}{5} =1[/tex]
[tex]\frac{x^2}{64} + \frac{y^2}{25} =1[/tex]
Lucy planted a lemon tree and a cherry tree. The lemon tree is 6 feet tall. The cherry tree is 3 7/10 times as tall as the lemon tree. How tall is Lucy's cherry tree?
To calculate the height of Lucy's cherry tree, we first convert 3 7/10 to an improper fraction, resulting in 37/10. Then we multiply the height of the lemon tree (6 feet) by 37/10 to get 22.2 feet. Thus, the cherry tree is 22.2 feet tall.
To find the height of Lucy's cherry tree, which is 3 7/10 times as tall as her lemon tree, we start with the known height of the lemon tree, which is 6 feet tall. We then multiply this height by the factor 3 7/10 to determine the height of the cherry tree.
First, let's convert the mixed number to an improper fraction to simplify the calculation:
Multiply the whole number part (3) by the denominator of the fraction part (10): 3 × 10 = 30.Add this to the numerator of the fraction part (7): 30 + 7 = 37.Now we have an improper fraction of 37/10.Next, we'll multiply the height of the lemon tree by this fraction:
6 feet × 37/10 = (6 × 37) / 10 = 222 / 10 = 22.2 feet.
So, the height of Lucy's cherry tree is 22.2 feet tall.
VAT is at 19%. Jeremy buys a calculator for ?58.31. What is the amount of VAT paid
Answer:
€9.31
Step-by-step explanation:
The relationship of tax to price is ...
... tax : price = 0.19 : 1
Then the relationship of tax to total cost is ...
... tax : (tax + price) = 0.19 : (0.19 +1) = 0.19 : 1.19 = 19 : 119
So, the tax is 19/119 times the total cost. In this problem, ...
... VAT = 19/119 × €58.31
... VAT = €9.31
Somebody please help with this problem
Step-by-step explanation:
We have been given that AE=BE and [tex]\angle1\cong \angle2[/tex].
We can see that angle CEA is vertical angle of angle DEB, therefore, [tex]m\angle CEA=m\angle DEB[/tex] as vertical angles are congruent.
We can see in triangles CEA and DEF that two angles and included sides are congruent.
[tex]\angle 1\cong \angle 2[/tex]
[tex]AE=BE[/tex]
[tex]\angle CEA\cong\angle DEB[/tex] or [tex]\angle 3\cong \angle 4[/tex]
Therefore, [tex]\Delta CEA\cong \Delta DEB[/tex] by ASA postulate.
Since corresponding parts of congruent triangles are congruent, therefore CE must be congruent to DE.
Sis buys 5 pieces of fabric each piece of fabric is 1 7/10 yards long what is the total length of the fabric she buys one yard of the fabric cost $5 how much does she pay for all five pieces of fabric
Fred is running on the school track. He can run 10 3 4 laps in 4 5 of an hour. How many laps can Fred run in one hour?
Answer:
[tex]13\frac{7}{16}[/tex] laps can Fred run in one hour.
Step-by-step explanation:
Given Statement: Fred is running on the school track. He can run [tex]10\frac{3}{4}[/tex] laps in [tex]\frac{4}{5}[/tex] of an hour.
Unit rate are expressed as a quantity of 1, such as 3 feet per second or 7 miles per hour, they are called unit rates
From the given condition we have;
In [tex]\frac{4}{5}[/tex] he can run [tex]\frac{43}{4}[/tex] laps
Unit rate per hour = [tex]\frac{\frac{43}{4} }{\frac{4}{5} }[/tex]
=[tex]\frac{43}{4} \times \frac{5}{4} = \frac{215}{16}[/tex] laps
Therefore, Fred can run in one hour is, [tex]13\frac{7}{16}[/tex] laps.
Final answer:
To determine how many laps Fred can run in one hour, we used a proportion equation, converting 10 3/4 laps to an improper fraction and then solving for x. Fred can run approximately 13.44 laps in one hour.
Explanation:
Calculating Laps per Hour
To find out how many laps Fred can run in one hour, we need to perform a simple proportion based on the information given. Fred can run 10 3/4 laps in 4/5 of an hour. To find out how many laps he can run in a full hour (1 hour), we set up the proportion equation:
\[\left(\frac{10 \frac{3}{4}}{\frac{4}{5}}\right) = \left(\frac{x}{1}\right)\]
First, we convert 10 3/4 to an improper fraction, which is \(\frac{43}{4}\). Then we solve for \(x\) by multiplying both sides by 1, which simplifies our proportion to:
\[x = \frac{43}{4} \times \frac{5}{4}\]
Next, we multiply the numerators and then the denominators:
\[x = \frac{43 \times 5}{4 \times 4}\]
\[x = \frac{215}{16}\]
Finally, we divide 215 by 16 to get \(x = 13.4375\), which means Fred can run approximately 13.44 laps in one hour.
An electrician sent Bonnie an invoice in the amount of 'a' dollars for 6 hours of work that was done on Saturday. The electrician charges a weekend fee 'f' in addition to an hourly rate 'r'. Bonnie knows what the weekend fee is. Write a formula Bonnie can use to find 'r', the rate the electrician charges per hour.
Answer:
(a-f)/6 = r
Step-by-step explanation:
The total Bonnie must pay is the weekend fee plus the hourly rate times the hours worked
Cost = weekend fee * hourly rate* hours
hours = 6
weekend fee =f
hourly rate = r
Cost = a dollars
Substituting in what we know
a = f+ 6r
We want to solve for r
Subtract f from each side
a-f =f-f +6r
a-f = 6r
Divide each side by 6
(a-f)/6 = 6r/6
(a-f)/6 = r
A jewelry store purchases a necklace for 150. They markup the necklace 75% how much will the jewelry store sell the necklace for ?
The selling price of the necklace is calculated by adding a 75% markup to the original purchase price of $150, which results in a selling price of $262.50.
To calculate the selling price of a necklace that a jewelry store purchased for $150 with a 75% markup, you first need to find out how much 75% of the purchase price is and then add that to the original purchase price. To do this, multiply the purchase price, $150, by 75% (or 0.75). This calculation gives you the markup amount:
Markup amount = $150 imes 0.75 = $112.50
After finding the markup amount, you add it to the original purchase price to find the selling price:
Selling price = Original purchase price + Markup amount
Selling price = $150 + $112.50 = $262.50
Therefore, the jewelry store will sell the necklace for $262.50.
Help me with this! Brainliest for the best answer.
Answer: -3/5
Step-by-step explanation:
All you have to do is use rise over run!
basically form a triangle and count how much up and how much over. :D
Identify the perimeter and area of an equilateral triangle with height 9 cm. Give your answer in simplest radical form. PLEASE HELP!!
The side length of the equilateral triangle would be 6√3. Therefore, the perimeter would be 18√3 and the area would be 27√3.
Area is derived from side length multiplied by height, which is 9, then dividing by 2.
MATH HELP PLEASE!!
find the area of the shaded region.
use the formula A= pi r^2 to find the area of the circle.
a. 8pi x + 24pi
b. 8pi x - 24pi
c. x^2 + 8pi x + 24pi
d. x^2 +8pi x - 24pi
Answer:
d
Step-by-step explanation:
A circle is divided into 8 sectors. Each sector has an area of approximately 5 square inches. What is the approximate area of the circle?
Question 5 options:
A. 25 square inches
B. 40 square inches
C. 15.7 square inches
D. 78.5 square inches