First, we need to find the slope of the line:
Let:
(5, -4) = (x1,y1)
(-9, -8) = (x2,y2)
m = (y2-y1)/(x2-x1) = (-8-(-4))/(-9-5) = -4/-14 = 2/7
Also, we need to find the midpoint:
let:
MP = (xp,yp)
xp= (x1+x2)/2 = (5-9)/2 = -2
yp = (y1+y2)/2 = (-4-8)/2 = -6
MP = (-2, -6)
Now, the slope for the perpendicular bisector is -m = -7/2
y = -mx + b
Using the midpoint
-6 = -7/2(-2) + b
-6 = 7 + b
Solving for b:
b = -13
Therefore, the equation for the perpendicular bisector is:
y = -7x/2 - 13
The highest recorded temperature in Massachusetts was one hundred seven degrees Fahrenheit on August 27, 1975. The average monthly high temperature is 81.7 degrees Fahrenheit. How many degrees hotter than average was the temperature on August 27, 1975?
Answer:
25.3°F
Explanation:
We need to find the difference between the temperature on August 27, 1975, and the average temperature. So, the difference is equal to:
107 °F - 81.7°F = 25.3°F
It means that on August 27, 1975, the temperature was 25.3°F hotter than average.
At the grocery store, halibut costs $20 per pound and salmon costs $17 per pound. Which of the following situations can be modeled by the equation below? 20(x-5) = 17xA) The cost of x pounds of salmon is $5 less than the cost of x pounds of halibutt B) The cost of x pounds of halibut is $5 less than the cost of x pounds of salmon C) The cost of pounds of salmon is the same as the cost of x-5 pounds of halibutD) The cost of x pounds of halibut is the same as the cost of x-5 pounds of salmon.
Answer: C.
The cost of x pounds of salmon is the same as the cost of x-5 pounds of halibut
[tex]\begin{gathered} \text{halibut }\rightarrow\text{ \$20 and (x-5) pounds} \\ \text{salmon }\rightarrow\text{ \$17 and x pounds} \end{gathered}[/tex]Explanation:
Given the model;
[tex]20(x-5)=17x[/tex]where x is the number of pounds.
The cost per pound of Halibut is;
[tex]\text{ \$20}[/tex]So, the corresponding number of pounds of Halibut on the model is;
[tex]x-5[/tex]Also, the cost per pound of Salman is;
[tex]\text{ \$17}[/tex]the corresponding number of pounds of Salmon on the model is;
[tex]x[/tex]Since they are equal to each other, then the cost of x pounds of salmon is the same as the cost of x-5 pounds of halibut
[tex]\begin{gathered} \text{hailbut }\rightarrow\text{ \$20 and (x-5) pounds} \\ \text{salmon }\rightarrow\text{ \$17 and x pounds} \end{gathered}[/tex]What number makes the equation true? Enter the answer in the box.+5= 9
The complete information for the question was not provided by the student, however we can assume that the box is either to the left or to the right of the equal sign:
If it's to the left, we have:
Box + 5 = 9
Box = 9 - 5
Box = 4
If it's to the right, we have:
5 = 9 - Box
5 - 9 = - Box
-4 = - Box
4 = Box
Answer: No matter if the box is to the left or to the right of the equal sign, the number in the box that makes the equation true is 4
find the correct area
The figure consist of trapezium and rectangle.
Determine the area of figure.
[tex]\begin{gathered} A=\frac{13+24}{2}\cdot4+24\cdot7 \\ =37\cdot2+168 \\ =74+168 \\ =242 \end{gathered}[/tex]Thus area of the figure is 242 inch square.
Find the inverse function of f.f(x) = 7 - 9x3f^-1(x) =
ANSWER
[tex]f^{-1}(x)=\sqrt[3]{\frac{7-x}{9}}[/tex]EXPLANATION
We want to find the inverse function of the given function:
[tex]f(x)=7-9x^3[/tex]To do this, we have to make x the subject of the formula.
Let f(x) be y:
[tex]\begin{gathered} y=7-9x^3 \\ 9x^3=7-y \\ x^3=\frac{7-y}{9} \\ \Rightarrow x=\sqrt[3]{\frac{7-y}{9}} \end{gathered}[/tex]Now, replace x with f^(-1)(x) and y with x:
[tex]f^{-1}(x)=\sqrt[3]{\frac{7-x}{9}}[/tex]That is the inverse function of f.
Is 8.012 greater or less than 8.03
In order to compare the numbers, we need to check each pair of digits that are in the same position before and after the decimal point.
We start from the left to the right. If the result of one number is greater, than this number is greater than the other number. If the digits of both numbers are the same, we move to the next digit and compare them.
So we have:
Unit position: 8 and 8
Equal results, so let's check the next digit.
Tenth position: 0 and 0.
Equal results, so let's check the next digit.
Hundredth position: 1 and 3.
3 is greater than 1, so the second number is greater than the first one.
Therefore 8.012 is less than 8.03.
add and subtract scientific notation 1) 5.1 x 106 + 2.3 x 106 =
Solucionamos de la siguiente manera:
[tex]5.1\cdot10^3+2.3\cdot10^6=(5100)+(2300000)=2305100[/tex]Como ya se sabe, la notación 10^3 representa miles y la notación 10^6 representa millones, por lo que al sumarles obtendremos notación de 10^6 (generalmente); aunque en nuestro caso al llevarle nuevamente a notación científica obtendremos lo siguiente:
[tex]2.3051\cdot10^2[/tex][Otra parte de la notación científica es que esta indica cuantos valores a derecha o izquierda se "mueve" el punto.]
7 - 6u = 5u + 29 solve for u
Answer:
u = -2
Explanation:
Given the expression;
7 - 6u = 5u + 29
We are to find the value of u;
Collect like terms;
-6u - 5u = 29 - 7
-11u = 22
Divide both sides by -11;
-11u/-11 = 22/-11
u = -2
Hence the value of u is -2
The solution of u in the equation is,
⇒ u = -2
Given that;
the expression is,
⇒ 7 - 6u = 5u + 29
Now, We have to find the value of u;
⇒ 7 - 6u = 5u + 29
Combine like terms;
⇒ -6u - 5u = 29 - 7
⇒ -11u = 22
Divide both sides by -11;
⇒ -11u/-11 = 22/-11
⇒ u = -2
Therefore, the value of u is -2.
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someone help me please this is the last question and can't get it wrong
We can use the fact that the sum of angles in a triangle is 180degrees and the sine rule to find the missing angle and sides. This will give us a single unique triangle.
So the right answer is 1 triangle
erica has 32 pairs of shoes. 5/8 of erica's shoes are high heels how many of her shoes are high heels?
Given Data:
Total number of shoes Erica has is: t=32
The portion of high heel shoes is: r=5/8
The expression to calculate the total number of high heel shoes is,
[tex]\begin{gathered} \text{Total Number of high h}eel\text{ shoes=r}\times t \\ =\frac{5}{8}\times32 \\ =5\times4 \\ =20 \end{gathered}[/tex]Thus, Erica has 20 high heel shoes.
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
The population of a city was 136 thousand in 1992. The exponential growth rate was 1.7% per year.a) Find the exponential growth function in terms of t, where t is the number of years since 1992.P(t) = 136,000 e 0.0177
We will have that the expression will be:
[tex]p(t)=136000(1+0.017)^t[/tex]Grayson needs to order some new supplies for the restaurant where he works. The restaurant needs at least 261 forks. There are currently 205 forks. If each set on sale contains 10 forks, which inequality can be used to determine the minimum number of sets of forks Grayson should buy?
ANSWER
[tex]10x\ge56[/tex]EXPLANATION
We have that the restaurant needs at least 261 forks.
There are currently 205 forks.
First, we have to find the number of forks that the restaurant currently needs.
We do that by finding the difference between the number of forks they have from the number of forks they need:
261 - 205 = 56 forks
They need at least 56 forks.
We have that each set of forks on sale has 10 forks each.
Let the number of sets they need be x.
This means that the amount of forks they should buy must be greater than or equal to 56. That is:
[tex]\begin{gathered} x\cdot10\ge56 \\ \Rightarrow10x\ge56 \end{gathered}[/tex]That is the inequality that can be used to determine the minimum number of sets of forks Grayson should buy.
The ratio of 8th graders in a chess club to the total number of members is 0.45.What is the decimal in fraction form?Enter the correct answers in the boxes.
The ratio of 8th graders in a chess club to the total number of members is 0.454545...
This is called a repeating decimal.
Let us convert this decimal into a fraction.
[tex]x=0.4545\ldots[/tex]Step 1:
Multiply by 100
[tex]\begin{gathered} 100\times x=100\times0.4545\ldots \\ 100x=45.45\ldots \end{gathered}[/tex]Step 2:
Subtract x
[tex]\begin{gathered} 100x-x=45.45\ldots-0.4545 \\ 99x=45 \end{gathered}[/tex]Step 3:
Finally, divide by 99
[tex]\begin{gathered} \frac{99x}{99}=\frac{45}{99} \\ x=\frac{45}{99} \end{gathered}[/tex]Therefore, the fraction form is
[tex]x=\frac{45}{99}[/tex]I need to know the answer and how to solve
We have by theorem that supplementary angles add up to 180° [The sum of both angles gives as result a straight line; then, the following is true:
[tex]151+x=180\Rightarrow x=29[/tex]So, the value of x is 29°.
Someone please help me with this problem in the most simple easy way possible no long explanation needed.
ANSWER:
2797.74 cubic inches
EXPLANATION:
Given:
Height of the cylinder(h) = 11 inches
Radius of the cylinder(r) = 9 inches
Pi = 3.14
To find:
The volume(V) of the cylinder
We'll go ahead and determine the volume(V) of the cylinder using the below formula;
[tex]\begin{gathered} V=\pi r^2h \\ =3.14*9^2*11 \\ =31.4*81*11 \\ =2797.74\text{ cubic inches} \end{gathered}[/tex]So the volume of the cylinder is 2797.74 cubic inches
The circle has center O. Its radius is 3 m, and the central angle a measures 60°. What is the area of the shaded region?Give the exact answer in terms of pi, and be sure to include the correct unit in your answer
Explanation
The area of a portion of a circle with radius 'r' and angle 'a' (in radians) is:
[tex]A_{\text{portion}}=\frac{1}{2}\cdot r^2\cdot a[/tex]In this problem r = 3m, a = 60º.
First we have to express the angle in radians:
[tex]a=60º\cdot\frac{\pi}{180º}=\frac{1}{3}\pi[/tex]The area of the shaded region is:
[tex]\begin{gathered} A=\frac{1}{2}\cdot(3m)^2\cdot\frac{1}{3}\pi \\ A=\frac{1}{2}\cdot9m^2\cdot\frac{1}{3}\pi=\frac{3}{2}\pi \end{gathered}[/tex]Answer
The area is:
[tex]A=\frac{3}{2}\pi[/tex]16. The area of the rectangle is x^2+14x+24.Find the length and width (the factors),then determine the perimeter of the rectangle.Length:Width:Perimeter:
Given a rectangle of width W and length L, the area is calculated by:
A = W.L
The perimeter of the rectangle is:
P = 2(W + L)
We are given the area of a rectangle with the equation:
[tex]A=x^2+14x+24[/tex]To find the dimensions of the rectangle, we must factor the polynomial.
It's easily done by inspection: find two numbers that added result in 14 and multiplied result in 24. Those numbers are 12 and 2, thus:
[tex]x^2+14x+24=(x+2)(x+12)[/tex]The factors are the width and the length of the rectangle (the width smaller than the length), thus:
Width = x+2
Length = x + 12
Now calculate the perimeter:
P = 2( x + 2 + x + 12)
P = 2( 2x + 14)
Perimeter = 4x + 28
A recipe calls for 1/2 cup sugar, a cup of flour and 1/3 cup of milk. I need to make 3 batches. How much of each ingredient will I need?
The recipe calls for
1/2 cup of sugar : 1 cup of flour : 1/3 cup of milk for 1 batche
We need to make 3 batches, so
Multiply each ingredient bu 3
Sugar = 1/2 * 3 = 3/2 cups
Flour = 1 * 3 = 3 cups
Milk = 1/3 * 3 = 1 cup
3/2 cups of sugar : 3 cups of flour : 1 cup of milk
I need help with this please and thank you im just really confused
To find the values of x and z, apply the opposite angles theorem.
Opposite angles are angles that can be said to be non-adjacent angles formed by two intersecting lines.
Opposite angles are congruent.
• Measure of angle Z:
∠z and 110 are opposite angles.
Thus, we have:
m∠z = 110°
• Value of x:
Given that total measure of angles = 360
We have:
[tex](5x-20)=\frac{360-110-110}{2}[/tex]Let's solve for x:
[tex]\begin{gathered} 5x-20=\frac{140}{2} \\ \\ 5x-20=70 \\ \\ \text{Add 20 to both sides:} \\ 5x-20+20=70+20 \\ \\ 5x=90 \end{gathered}[/tex]Divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{90}{5} \\ \\ x=18 \end{gathered}[/tex]ANSWER:
x = 18
z = 110°
2x - 1 if x < 0Evaluate g (4) for g(x)for g(x) = x²W√xif 0 ≤ x ≤ 5.if x > 5
Solution
Question A:
[tex]\begin{gathered} \text{ To find the rate we compare with the equation below:} \\ A=P(1+r)^t \\ \\ \text{ Thus, } \\ 1+r=0.9 \\ \text{ Subtract 1 from both sides} \\ r=0.9-1 \\ r=-0.1 \end{gathered}[/tex]- Rate of depreciation is 10%
Question B:
[tex]\begin{gathered} v=34000(0.9)^t \\ \text{ when } \\ v=\frac{34000}{2}=17000 \\ \\ 17000=34000(0.9)^t \\ \text{ Divide both sides by 34000} \\ 0.5=(0.9)^t \\ \text{ Take the natural log of both sides} \\ \ln0.5=t\ln0.9 \\ \\ \therefore t=\frac{\ln0.5}{\ln0.9} \\ \\ t=6.578813...\approx6.58years \end{gathered}[/tex]- The number of years is 6.58years
Your lacrosse team wins 4 of the games that it plays. Describe huikelihood of winning.
the statement say us the rate of winning is 3/4 then the probability is the same
but performance it on decimals
[tex]\frac{3}{4}=0.75[/tex]probability is 0.75
The plastic lid of a cylindrical container is a circle. The lid has a radius of 9centimeters. What is the circumference of the lid?
We are asked to determine the circumference of a 9 cm radius circle. To do that we will use the following formula:
[tex]S=2\pi r[/tex]Where:
[tex]\begin{gathered} S=\text{ circumference} \\ r=\text{ radius} \end{gathered}[/tex]Now, we substitute the value of the radius:
[tex]S=2\pi(9cm)[/tex]Solving the operations:
[tex]S=18\pi=56.55cm[/tex]Therefore, the circumference is 56.55 cm.
is( 1,9)a solution to the equation y=x
is( 1,9) a solution to the equation y=x
answer is
is not a solutionbecause y=x means
the value of x is equal to the value of y
and 1 is not equal to 9
Distance travelled = rate (or speed) * time.If Alan drives 44 miles at a constant speed of 44 mph. How long will it take? (Be sure to includeunits.)
We are given that Alan at a constant speed of 44 miles per hour. We are asked to determine the time to travel a distance of 44 miles. To do that we will use the following formula:
[tex]d=vt[/tex]Where:
[tex]\begin{gathered} d=\text{ distance} \\ v=\text{ velocity} \\ t=\text{ time} \end{gathered}[/tex]Now, since we are asked to determine the time we will divide both sides by the velocity:
[tex]\frac{d}{v}=t[/tex]Now we substitute the values:
[tex]\frac{44miles}{44\frac{miles}{hour}}=t[/tex]Now we solve the operations:
[tex]1\text{hour}=t[/tex]Therefore, the time to travel 44 miles is 1 hour.
What numeric value of b would make the following two expressions equivalent? bx +2.4 and 6(2x+0.4) + 3x
For the two expressions to be equivalent, then we would have;
[tex]bx+2.4=6(2x+0.4)+3x[/tex]We solve the right hand side and we'll now have;
[tex]\begin{gathered} bx+2.4=12x+2.4+3x \\ bx+2.4=15x+2.4 \\ \text{Collect all like terms and you'll have} \\ 2.4-2.4=15x-bx \\ 0=15x-bx \\ Add\text{ bx to both sides of the equation} \\ 0+bx=15x-bx+bx \\ bx=15x \\ \text{Divide both sides by x} \\ \frac{bx}{x}=\frac{15x}{x} \\ b=15 \end{gathered}[/tex]The first option is the correct one.
b = 15
After a 30% discount, the price of a t-shirt was $14. What was the price BEFORE the discount?
Price after discount = $14
discount = 30%
x (1-30/100) = 14
x (1-0.3) = 14
x 0.7 = 14
Solve for x (original price )
x = 14/0.7
x = 20
22% 38% 1/4 21/10 three 5/10 and 3/8 from least to greatest value
The ascending order for the given values will be 22%<1/4<3/8<38%<21/10<3 5/10 as the definition of ascending order will be "When numbers are arranged in ascending order, they are done so from smallest to largest."
What is ascending order?When numbers are arranged in ascending order, they are done so from smallest to largest. Ascending order, also known as increasing order of importance, is the exact opposite of descending order. The order of the items is lowest to highest value. The smallest value is placed first in the order, and the biggest value is placed last. As a result, if you were to put the numbers from the previous section in ascending order, they would be as follows: 11, 20, 49, 80, 56, and so on. The first number is always the smallest, in this case 11. The last number is always the largest, in this case 80.
Here,
22%=0.22
38%=0.38
1/4=0.25
21/10=2.1
3 5/10=3.5
3/8=0.375
22%<1/4<3/8<38%<21/10<3 5/10
According to the definition of ascending order, the given values will be in ascending order as follows: 22%<1/4<3/8<38%<21/10<3 5/10 "Numbers are arranged from smallest to largest when they are arranged in ascending order."
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Which of the following completes the statement below?MZBAC = {(MBC + mED00חוBERXRmZEADA0DBDC
Answer:
m(arc)ED
Explanation:
In the diagram:
[tex]m\angle\text{BAC}=\frac{1}{2}(m\widehat{BC}+m\widehat{ED})[/tex]The first option is correct.
Name:Date:6. The table shows the postage charges for sending letters to Country A.How much does it cost to send a letter weighing 80 ounces to Country A?First 30 Ounces60For Every Additional 10 Ounces35
The first 30 ounces costs 60¢.
For every additional 10 ounces the cost increases in 35¢.
From the given 80 ounces, the first 30 costs 60¢ and the other 50 ounces, by considering it is 5 times 10 ounces, cost 5*(35¢) = 175¢.
Then, the total cost is:
total = 60¢ + 175¢ = 235¢