-15 + 18 is the same as 18 - 15, which is equal to 3.
Given the base band height of a triangle, calculate the area A using the formula for the area of a triangle: A ) bh
Solution
For this case the area is given by:
[tex]A=\frac{1}{2}bh[/tex]Then we can replace b = 5ft and h = 20 ft and we got:
[tex]A=\frac{1}{2}(5ft)(20ft)=50ft^2[/tex]I need help with his practice problems from my ACT prep guidePlease show your work in steps
Answer:
[tex]-\sqrt[]{6}+1[/tex]Explanation:
Given the below expression;
[tex]\frac{\tan(-\frac{2\pi}{3})}{\sin(\frac{7\pi}{4})}-\sec (-\pi)[/tex]Recall that;
[tex]\begin{gathered} \sec x=\frac{1}{\cos x} \\ \sin x=\cos (\frac{\pi}{2}-x) \end{gathered}[/tex]So we can rewrite the expression as;
[tex]\begin{gathered} \frac{\tan(-\frac{2\pi}{3})}{\cos(\pi-\frac{7\pi}{4})}-\frac{1}{\cos(-\pi)} \\ \frac{\tan(-\frac{2\pi}{3})}{\cos(-\frac{5\pi}{4})}-\frac{1}{\cos(-\pi)} \end{gathered}[/tex]Also, recall that;
[tex]\begin{gathered} \cos (-x)=\cos x \\ \tan (-x)=-\tan x \end{gathered}[/tex]So we'll have;
[tex]\frac{-\tan (\frac{2\pi}{3})}{\cos (\frac{5\pi}{4})}-\frac{1}{\cos (\pi)}[/tex]From the Unit circle, we have that;
[tex]\begin{gathered} \cos \pi=-1 \\ \cos (\frac{5\pi}{4})=\frac{-\sqrt[]{2}}{2} \\ \tan (\frac{2\pi}{3})=-\sqrt[]{3} \end{gathered}[/tex]Substituting the above values into the expression and simplifying, we'll have;
[tex]\begin{gathered} \frac{-(-\sqrt[]{3})}{\frac{-\sqrt[]{2}}{2}}-\frac{1}{-1}=\frac{\sqrt[]{3}}{\frac{-\sqrt[]{2}}{2}}+1=-\frac{2\sqrt[]{3}\sqrt[]{2}}{\sqrt[]{2}\cdot\sqrt[]{2}}+1 \\ =-\sqrt[]{6}+1 \end{gathered}[/tex]My name is nessalovetrillo i am prepping and studying to test out of my algebra class this is for a study guide Please see attached picture
Given:
S={(5,6),(-2,-9),(-9,6)}
To find the domain and range:
The domain is,
{-9, -2, 5}
The range is,
{-9, 6}
Which of the following sets of ordered pairs lies on the y-axis of a coordinate grid?
Solution
for this case the point that lies on the y axis need to satisfy that the x coordinate must be:
x= 0
then the best solution would be:
(0, -4)
Im in algebra 2 but we are also learning geometry the question asks to find the length of each arc
The length of the arc = 8π/3 mi
Explanation:The length of an arc is given by the fomula:
[tex]L=\frac{\theta}{360}\times2\pi r[/tex]The radius, r = 8 ml
[tex]\theta=60^0[/tex][tex]\begin{gathered} L=\frac{60}{360}\times2\pi\times8 \\ \\ L=\frac{16\pi}{6} \\ \\ L=\frac{8\pi}{3} \end{gathered}[/tex]The length of the arc = 8π/3 mi
Which of the following is a solution to the equation c + ( 4 -3c) - 2 = 0?A. -1B. 0C. 1D. 2
Given data:
The given equation is c+(4-3c)-2=0
The given equation can be written as,
c+4-3c-2=0
-2c+2=0
-2c=-2
c=1
Thus, the value of c is 1, so option C) is correct.
Find the radius of a circle in which a 24 cm chord is 4 cm closer to the center than a 16 cm chord. Round your answer to the nearest tenth.
The diagram representing the scenario is shown below
A represents the center of the circle. It divided each chord equally. Thus, we have CB = 16/2 = 8 for the shorter chord and DE = 24/2 = 12 for the longer chord
Assuming the distance between the
A
The answers available are SSS SAS CPCTC and definition of congruence
Solution
The diagram below will be of help
From the above, we have two sides to be equal and an angle to be equal
Therefore, the answer Side, Angle, Side (SAS)
Chloe's car used 15 gallons to travel 570 miles. How many gallons of gas would she need to travel 380 miles?
Answer:
10
Step-by-step explanation:
I divided 570 by 15 to see how many miles she can travel per gallon of gas which came out to be 38.
After that i divided the 380 by the 38. 380÷38 is 10.
Answer:
Need:
10 gallons
Step-by-step explanation:
Proportions:
15 gallons ⇒ 570 miles
A gallons ⇒ 380 miles
A = 15gallons * 380miles / 570miles
A = 10 gallons
please help 40 points!!
Answer:
The midpoint is (-1,1)
Equation: y = -x -2
Step-by-step explanation:
Midpoint:
([tex]\frac{-5+3}{2}[/tex], [tex]\frac{-5 + 3 }{2}[/tex]) You are taking the averages of the x values and the y values.
([tex]\frac{-2}{2}[/tex],[tex]\frac{-2}{2}[/tex])
(-1,-1)
Equation:
The slope of the 2 points given is
[tex]\frac{3 - -5}{3- - 5}[/tex] = [tex]\frac{8}{8}[/tex] = 1 The slope is the change of y over the change in x. Points are given in the form (x,y) So, I subtracted the y values on top and the x values on the bottom of the fraction.
The equation that is created is perpendicular to the original line, so it slope is the negative reciprocal.
1 as a fraction is [tex]\frac{1}{1}[/tex]. negative reciprocal means turn the fraction upside down and take the opposite value. If I flip [tex]\frac{1}{1}[/tex] upside down, I get the same fraction which is equal to 1. Now I will take the opposite sign. Since it is positive, the new slope will be negative
slope -1
x = -1
y = -1
I am using the point that will be on the new line. This is the midpoint that we just found (-1,-1) I am going to plug in the number that I know and solve for b or the y=intercept.
y = mx + b
- 1 = -1(-1) + b
-1 = 1 + b Subtract 1 from both sides of the equation
-2 = b
y = mx + b
y = -1x -2
or
y = -x -2
Why is it important to
line up the digits in each place-value position when subtracting?
Answer: it’s important because when you do that it makes it easier to remember what’s not a whole number and what is
Step-by-step explanation: the answer is basically the explanation
Patrick is buying a new car. He can choose the body style, color and engine type. If there are 54 ways he can select a car, with there body styles and two engine choices , his many colors are available
Given:
Total Number of ways = 54
Number of body styles = 3
Number of engine choices = 2
Let's find the number of colors available.
To find the number of colors available, we have:
Number of ways = Number of body styles x Number of engine choices x Number of colors
54 = 3 x 2 x c
Where c represent the available number of colors.
Let's find c.
54 = 3 x 2 x c
54 = 6c
Divide both sides by 6:
[tex]\begin{gathered} \frac{54}{6}=\frac{6c}{6} \\ \\ 9=c \\ \\ c=9 \end{gathered}[/tex]Therefore, there are 9 colors available to select from.
ANSWER:
9
A real estate agent has 18 properties that she shows. She feels that there is a 50% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling more than 4 properties in one week. Round your answer to four decimal places.
The probability of selling more than 4 properties in one week is 0.985.
What is probability?A probability formula can be used to calculate the likelihood of an occurrence by simply dividing the favorable number of possibilities by the entire number of possible outcomes.
The binomial distribution is a discrete probability distribution in probability theory and statistics that gives only two possible outcomes in an experiment: success or failure.
In this case, the real estate agent has 18 properties. Therefore, n = 18. p = 50% = 0.5.
The probability will be:
= P(X > 4)
= 1-0.0154 by using Excel command
= 0.985
The probability is 0.985.
Learn more about probability on:
https://brainly.com/question/24756209
#SPJ1
Use the tangent to find the length of side PR. Express your answer to the nearest tenth. P 559 The length of side PR is approximately units.
tan (Q) = opposite/ adjacent
tan (55º) = PR/ 4.9
________________________
1.43 = PR/ 4.9
PR= 1.4* 4.9 = 6.9
Answer
6.9
______________________________________
Can you see the updates?
Do you have any questions regarding the solution?
____________________
PR= tan (55)* 4.9 = 6.997925 ≅ 7
_________________________________
Find a.Round to the nearest tenth:a10 cm150°12°с=a = [ ? ]cmLaw of Sines: sin A=sin Bbasin cСEnter
Answer:
24.0 cm
Explanation:
To find the value of a, we will use the Law of sines, so
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}[/tex]So, replacing A = 150°, B = 12°, and b = 10 cm, we get:
[tex]\frac{\sin150}{a}=\frac{\sin 12}{10}[/tex]Now, we need to solve for a. First, cross multiply
[tex]10\cdot\sin 150=a\cdot\sin 12[/tex]Then, divide by sin12
[tex]\begin{gathered} \frac{10\cdot\sin150}{\sin12}=\frac{a\cdot\sin 12}{\sin 12} \\ \frac{10\cdot(0.5)}{0.208}=a \\ 24.0=a \end{gathered}[/tex]Therefore, a = 24.0 cm
The two-way table shows the number of students that do or do not do chores at home and whether they receive an allowance or not. I Allowance No Allowance 13 3 Do Chores Do Not Do Chores 5 a. How many total students do chores? b. What is the relative frequency of students that do chores and get an allowance to the number of students that do chores? Round to the nearest hundredth if necessary. chores nor get an allowance to the total number of What is the relative frequency of students that do not students? Round to the nearest hundredth if necessary, d. Of those that do not do chores what percentage still receive an allowance?
a) do chores 13 + 3 = 16
answer: 16 students
b) this is
[tex]\frac{chores\text{ and allowance}}{\text{chores}}=\frac{13}{16}=0.8125[/tex]answer: 0.81
c) this is
[tex]\frac{\text{no chores and no allowance}}{total}=\frac{4}{25}=0.16[/tex]answer: 0.16
d) this is
[tex]\frac{no\text{ chores and allowance}}{no\text{ chores}}\times100=\frac{5}{9}\times100=\frac{500}{9}=55.55[/tex]answer: 55.55%
The proof below may or may not be correct. If the proof is incorrect, determine the first step number that is not justified and the reason it is not justified.
The first step number that is not justified and the reason it is not justified:
From the attached image
[tex]<\text{ECF}\congStep 1: is said to be correct cause all the range are equivalent and parallel
Step 2: is said to be correct AECF is a parrelologram because it is a quadilateral with two opposite equal sides
Step 3: is correct
[tex]\begin{gathered} \Delta BEC\cong\Delta\text{ECF}\ldots\text{..} \\ \text{parallel lines cut by a transverse form congruent alternate interior angle.} \end{gathered}[/tex]Step 4: is correct
[tex]<\text{BEC}\congStep 5: is correct [tex]<\text{BEC}\congStep 6 : is not correct , because corresponding parts of the congruent triangle are not congruent.
Step 7: is correct , because its a rhombus.
Find the length of arc CD. Use 3.14for tt. Round to the nearest tenth.h 7.9 cm66.40D[? ]cm
For this problem we know that the radius is 7.9cm and the angle between C and D is 66.4ª. We also want to find the arclenght so we can use the following formula:
[tex]AL=\frac{x}{360}\cdot2\pi r[/tex]Where x is the angle and r the radius r=7.9cm. So then replacing into the function we got:
[tex]AL=\frac{66.4}{360}\cdot2\pi(7.9cm)=9.16\operatorname{cm}[/tex]And if we round to the nearest tenth we got 9.2 cm
A squirrel is perched in a tree 50 feet above sea level. Directly below the squirrel, a bird is flying 17 feet above sea level. Directly below the bird is a trout, swimming 23 feet below seal level.how far apart are the squirrel and bird?
Solution
We can do the following operation_
17-50 = -33 ft
And that represent the distance between te heron and the squirrel
And since the actual height is -23 ft
Then the answer would be given by:
17 -(-23) = 40 ft
The distance from the squirrel and the bird is 40 ft
#24Graph the function and tell wether or not it has a point of discontinuity at x = 0. If there is a discontinuity, tell wether it is removable or non removable.
We have the function:
g(x) = x/(x - 2)
Notice that if x = 2 the denominator equals zero and then we have a vertical asymptote at x = 2. Furthermore, if x = 0, g(0) = 0.
The graph of g(x) is shown below:
As you can notice, there is no a discontinuity at x = 0.
Use the quadratic formula to solve for X 5x^2 +2x=2
Given:
[tex]5x^2+2x=2[/tex]To solve for x using the quadratic formula, we simplify the given equation first:
[tex]\begin{gathered} 5x^2+2x=2 \\ 5x^2+2x-2=0 \end{gathered}[/tex]Next, we use the quadratic formula of the form ax^2+bx+c=0:
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where:
a=5
b=2
c=-2
We plug in what we know:
[tex]\begin{gathered} x_{1,2}=\frac{-2\pm\sqrt[]{2^2^{}-4(5)(-2)}}{2(5)} \\ \text{Simplify} \\ x_{1,2}=\frac{-2\pm\sqrt[]{44}}{10} \\ x_{1,2}=\frac{-2\pm2\sqrt[]{11}}{10} \end{gathered}[/tex]We separate the solutions:
[tex]x_1=\frac{-2+2\sqrt[]{11}}{10}=\frac{-1+\sqrt[]{11}}{5}=0.46[/tex][tex]x_2=\frac{-2-2\sqrt[]{11}}{10}=-\frac{1+\sqrt[]{11}}{5}=-0.86[/tex]Therefore,
[tex]x=0.46,-0.86[/tex]find the are and perimeter
L: Length
W: Width
The perimeter of a rectangle is:
[tex]P=2W+2L[/tex][tex]\begin{gathered} P=2(3ft)+2(5ft) \\ P=6ft+10ft \\ P=16ft \end{gathered}[/tex]The area of a rectangle is:
[tex]A=W\cdot L[/tex][tex]\begin{gathered} A=3ft\cdot5ft \\ A=15ft^2 \end{gathered}[/tex]Use a graph to predict the value of jewelry in 7 years.
Solution:
Given that the initial cost price of the jewelry is $2,200.
The rate at which it decreases each year is 12%.
Thus, the exponential decay function is;
[tex]\begin{gathered} y(t)=2200(1-0.12)^t \\ \\ \text{ Where }t\text{ is the time in years.} \end{gathered}[/tex]The graph of the function is;
From the graph;
CORRECT OPTION:
[tex]\approx899.09[/tex]Marco states that 7.696696669...... is a rational numberbecause it is a repeating decimal. Is he correct? Justifyyour answer.Yes he is correct because it keeps going and going and it will go on forever and ever so that is my guess
The answer is NO, Marco is wrong.
The number 7.696696669.... has not a repeating decimal there is no a number that is repeating, like 0.6969696969... in the last number the 69 is repeating, in the Marco's number the decimal number change every time.
1. 9c-3c=48A) c=9B) c=3C) c=4D) C=8
To solve this equation, we need to subtract both, 9c - 3c:
[tex]9c\text{ - 3c = 6c = 48}[/tex]Dividing by 6 at both sides of the equation
[tex]\frac{6c}{c}\text{ = }\frac{48}{6}[/tex]Then
[tex]c\text{ = 8}[/tex]Then the answer C = 8. (Option D)
There are 73 students in a classroom, and the desired ratio of students to computers is 6 to 1. How many computers are needed to achieve the desired ration?
Answer: 12
Explanation:
Given:
Total number of students in a classroom = 73
Ratio of students to computers = 6:1
To find the number of computers needed to achieve the desired ration, we use the ratio:
[tex]\begin{gathered} \frac{\text{Total number of students}}{\text{Total number of computers}}=\frac{6}{1} \\ We\text{ plug in what we know} \\ \frac{\text{7}3}{\text{Total number of computers}}=\frac{6}{1} \\ \text{Simplify and rearrange} \\ \text{Total number of computers = 73(}\frac{1}{6}) \\ \text{Calculate} \\ T\text{otal number of computers = }12.16\text{ =12} \\ \end{gathered}[/tex]Therefore, the number of computers needed is 12.
Find the slope and y-intercept of the graph of the linear equation. Give the y intercept in point form in the space provided. Use the equation editor to enter the slope if there are fractions. 5x - y = -5
The general equation of a line is:
y = mx + b
Here, y refers to how far up and x refers to how far along.
m is slop, that is the change in y to the change in x
and b is y intercept or the point where the value of x is zero.
So,
The given equation is:
5x - y = -5
The simplest step is to map the given equation with the standard equation (y = mx + b).
So,
- y = -5 -5x
Multiplying both sides by -1, we get
y = 5 + 5x
or
y = 5x + 5
Now, if we map this form with the standard equation (y = mx + b), we get
m = 5 and b = 5
Therefore, the slope (m) is equal to 5.
Also, y-intercept (b) is equal to 5.
Does the following table show a proportional relationship? 8 h 3 9 6 36 9 81 O Yes No
Proportional relationships are relationships between two variables where their ratios are equivalent.
From the table given;
g:h are respectively;
[tex]\begin{gathered} 3\colon9=1\colon3 \\ 6\colon36=1\colon6 \\ 9\colon81=1\colon2 \end{gathered}[/tex]Since the ratios above are not equivalent, their relationship is not proportional.
Hence, the correct option is B
What is the y intercept of this equation10x+5y=30Write answer in (x,y)
The y intercept of a straight line is the point on the y axis where the line cuts the y axis.
Given equation of lineis
[tex]10x+5y=30[/tex]Putting x=0 in the above equation, we have,
[tex]\begin{gathered} 5y=30 \\ y=6 \end{gathered}[/tex]So, the y intercept is
[tex](0,6)[/tex]Harry fills up his Jeep with gasoline and notes that the odometer reading is 23,529.6 miles. The next time he fills up his Jeep, he pays for 10 gallons of gasoline he notes his odometer reading is 23,640.6 miles. How many miles per gallon did he get? (Round the answer to the nearest 10th if necessary.)
Answer:
11.1 miles per gallon
Explanation:
Given;
Odometer reading when the jeep is filled up with gasoline = 23,529.6 miles
Odometer reading when the jeep is filled up with 10 gallons of gasoline =23,640.6 miles
We can now go ahead and determine how many miles per gallon Harry got as seen below;
[tex]\begin{gathered} \frac{(Reading\text{ when j}eep\text{ is filled with 10 gallons }-Reading\text{ when j}eep\text{ is filled up)}}{\text{Gallo of gasoline}} \\ =\frac{23640.6-23529.6}{10}=\frac{111}{10}=11.1\text{miles per gallon} \end{gathered}[/tex]So Harry got 11.1 miles per gallon
