We have the sum of
[tex]\mleft(x^2-5x+1\mright)+(3x^2-3x+4)[/tex]we sum similar terms
[tex]4x^2-8x+5[/tex]then we subtract (4x^2-5) from the result of the sum above
[tex](4x^2-8x+5)-\mleft(4x^2-5\mright)=4x^2-8x+5-4x^2+10[/tex]then we sum similar terms, and we find the answer
[tex]-8x+10[/tex]is (-4 -4) a solution of y>-6x-1
Substitute -4 for x and -4 for y in the inequality to check the point is solution or not.
[tex]\begin{gathered} -4>-6\cdot(-4)-1 \\ -4>24-1 \\ -4>23 \end{gathered}[/tex]The inequality is false means point (-4,-4) is not a solution of inequality.
Answer: No point is not a solution of inequality.
The work of a student to solve a set of equations is shown below:Equation 1: m = 8 + 2n Equation 2: 4m = 4 + 4nStep 1: −4(m) = −4(8 + 2n)4m = 4 + 4nStep 2: −4m = −32 − 8n4m = 4 + 4nStep 3: −4m + 4m = −32 − 8n + 4nStep 4: 0 = −32 − 4nStep 5: n = − 8In which step did the student first make an error? (4 points)a. Step 1b. Step 2c. Step 3d. Step 4
Given:
m = 8 + 2n
4m = 4 + 4n
Let's follow the steps shown to find out the step with the error.
Step 1:
Multiply equation 1 by -4
-4(m) = -4(8 + 2n)
4m = 4 + 4n
Step 2:
-4m = -32 - 8n
4m = 4 + 4n
Step 3:
Use elimination method to simplify
-4m = -32 - 8n
4m = 4 + 4n
-4m + 4m = -32 + 4 -8n + 4n
This is where the student made the first error, because "4" was ommited.
This error led to subsequent errors in step 4 and 5
Step 4:
0 = -28 - 4n
Add 4n to both sides
0 + 4n = -28 - 4n + 4n
4n = -28
Step 5:
Divide both sides by 4
[tex]\begin{gathered} \frac{4n}{4}=\frac{-28}{4} \\ \\ n\text{ = -7} \end{gathered}[/tex]ANSWER:
The student first made an error in step 3.
Simplify.10(15 + n)50 + n0 150 + nO 150 + 10 n150 n
ANSWER
150 + 10n
EXPLANATION
We want to simplify:
10(15 + n)
To do this, we have to use the distributive property:
a(b + c) = a*b + a*c
Therefore:
10(15 + n) = (10 * 15) + (10 * n)
= 150 + 10n
That is the answer
A rectangular garden has a walkway around it. The area of the garden is 4(4.5x+3.5). The combined area of the garden and the walkway is 5.5(8x+6). Find the area of the walkway around the garden as the sum of two terms.
We can express the area of the walkway around the garden as the sum of two terms as given - A[W] = 26x + 19.
What is a Rectangle?Rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.
Given is a rectangular garden that has a walkway around it. The area of the garden is 4(4.5x + 3.5). The combined area of the garden and the walkway is 5.5(8x + 6).
The area of the walkway (A[W]) can be calculated by subtracting the area of garden (A[G]) from the combined area of the garden and the walkway (A[T]).
A[W] = A[T] - A[G]
A[W] = 5.5(8x + 6) - 4(4.5x + 3.5)
A[W] = 44x + 33 - 18x - 14
A[W] = 26x + 19
Therefore, we can express the area of the walkway around the garden as the sum of two terms as given - A[W] = 26x + 19.
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Question 9
1 pts
The price of gasoline has risen from $3.52/gallon last week to $4.31/gallon this week.
What is the percent change? Round answer to the tenths place.
Question 10
1 pts
Answer: 122.4% increase
Divide the new cost from the old
4.31 / 3.52 = 1.22443181818
Multiply by 100 to get a percent.
= 122.443181818%
= 122.4
5 out of 8 students said football is their fav sport what is the decimal equivilant of students who chose football
(with explaining)
Answer:
0.625
Step-by-step explanation:
another way to write 5 out of 8 is 5/8 or 5 divided by 8
because 5 of the group of 8 chose football
so we do 5÷8=0.625
If a gallon of paint weighs twelve pounds and seven ounces, what is the weight of a gallon of paint inkilograms? (Round to the nearest tenth.)Plan: Set up a plan or formula for solving the problem. (4 points)
Let:
Wlboz = Weight in lb + oz
Wkg = Weight in kg
The weight in kg is given by:
[tex]\begin{gathered} Wkg=12lb+7oz=12lb+0.4375lb=12.4375lb \\ Wkg=12.4375lb\times\frac{0.453592}{1lb}\approx5.6kg \end{gathered}[/tex]Answer:
5.6kg
The slopes are different, and the y-intercepts are different. The slopes are different, and the y-intercepts are the same. The slopes are the same, and the y-intercepts are different. The slopes are the same, and the y-intercepts are the same.
Answer:
The slopes are the same and the y-intercepts are different.
Explanation:
Given:
[tex]\begin{gathered} x+2y=8 \\ 2x+4y=12 \end{gathered}[/tex]Recall that the slope-intercept equation of a line is generally given as;
[tex]y=mx+b[/tex]where;
m = slope of the line
b = y-intercept of the line
Let's go ahead and rewrite the first equation in slope-intercept form as seen below;
[tex]\begin{gathered} x+2y=8 \\ 2y=-x+8 \\ y=-\frac{1}{2}x+\frac{8}{2} \\ y=-\frac{1}{2}x+4 \end{gathered}[/tex]We can see from the above that the slope(m) of the first equation is -1/2 and the y-intercept(b) is 4.
Let's go ahead and rewrite the second equation in slope-intercept form as seen below;
[tex]\begin{gathered} 2x+4y=12 \\ 4y=-2x+12 \\ y=-\frac{2}{4}x+\frac{12}{4} \\ y=-\frac{1}{2}x+3 \end{gathered}[/tex]We can see from the above that the slope(m) of the second equation is -1/2 and the y-intercept(b) is 3.
We can see from the above that, for the two equations, the slopes are the same, and the y-intercepts are different.
What are the solutions to the equation x² + 9 = 0
To determine the solution of the given equation, isolate the variable x by subtracting 9 on both sides of the equation,
[tex]x^2+9-9=0-9[/tex][tex]x^2=-9[/tex]Get the square root on both sides of the equation.
[tex]\sqrt{x^2}=\sqrt{-9}[/tex][tex]x=\pm\sqrt{-9}[/tex]As we can see, the value of x is a negative number under the radical sign. However, a negative number under a radical sign is not considered a real number.
Hence, the solution to this equation is an imaginary number +3i and -3i.
Use exponential notation to simplify the given expressionsPresent your answer using only positive integer exponentsAswer the first one
We will use the next rule
[tex]\sqrt[n]{x^m}=x^{\frac{m}{n}}[/tex]Then
[tex]\sqrt[7]{x^6}\ast\sqrt[5]{x}=x^{\frac{6}{7}}\ast x^{\frac{1}{5}}=x^{\frac{6}{7}+\frac{1}{5}}[/tex][tex]x^{37/35}[/tex]The table below shows that 1 day equals 24 hours. Notice that 12 hours is one-half of that. Use the table to help you determine how many days are equal to 30 hours. 1 day 24 hours 12 hours 12 hours (3 points) a 1 and 1 over 4. days b 1 and 1 over 2. days c 1 and 3 over 4. days d 2 days
54 hours is equivalent to 2 and 1 over 4 days. Because 1 day has 24 hours so we have to divide 54/24 to get the numeral of days which is equal to 2.25 days and .25 is equivalent to 1/4 of a day i.e., 2 1/4 days.
How is math operated in time?Time math entails learning how to tell time and converting it into seconds, minutes, hours, days, weeks, months, and years. Finding time math solutions can involve adding and subtracting to determine the amount of time elapsed or multiplying or dividing to convert time units. Time can be defined in mathematics as an ongoing and continuous sequence of events that occur in succession, from the past to the present to the future. Time is used to quantify, measure, compare, and even sequence events. Atomic clocks provide the most accurate measurement of time intervals the duration between two events. These clocks emit electromagnetic radiation, such as microwaves, at a precise frequency that causes the clock's atoms to jump from one energy level to another.
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Need help with this please
Answer:225
Step-by-step explanation:
27 . 24
648
648-423 = 225 hope this helped
have a good day ^^
Mrs. Sullivan's 5th grade class
scooped 494 seeds out of a
pumpkin and roasted them. The
seeds were divided evenly
among the 26 students in the
class. How many seeds did each
student receive?
Answer: = 19
Step-by-step explanation:
For this worded question, you have to take out the values.. the question is essentially asking how many seeds each student received. There are 494 seeds, and 26 students. This is a division question.
494 ÷ 26 = 19.
(In tests you should be permitted to use a calculator if you bring one.. so no need to memorise how to divide large numbers, although you can always use long division to work our division related questions.)
To learn about long division learning from this link :
https://www.khanacademy.org/math/arithmetic-home/multiply-divide/mult-digit-div-2/v/division-2
After 5 years, Amanda's account earned $1500 in interest. If the interest rate (in decimal form) is 0.1, how much did Amanda initially
invest?
Amanda's starting capitalization is $3000.
Simple interest: What is it?Simple interest tells us how much interest will be charged on a loan.
Simple Interest = Principal x Interest Rate x Time" is the written formula.
Principal, rate of interest, and period make up the basic interest formula.
Rate (in decimal) Equals 0.1, as stated.
5 years is time.
$5000 with simple interest
As a result, 1500 = p (0.1). (5)
1500/0.5 equals the principal value
Principal is 3000.
Consequently, the first outlay is $3000.
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Solve the system of equations for x, y, and z.
x+2y+z=13
4x+6y=16
3x-6y = -30
By solving equations, the values of x, y, and z are 10.8, 10.4, and -18.6.
What are equations?A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. The meanings of the word equation and its cognates in other languages can vary slightly. For instance, in French, an equation is defined as having one or more variables, whereas, in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign. Based on the degree, there are three different types of equations. Equations that are linear, quadratic, and cubic.So, the values of x, y, and z are:
Take equation (3) and solve for 'x'":
3x-6y = -303x = -30 + 6yx = (-30 + 6y)/3Now, substitute x = (-30 + 6y)/3 in equation (2):
4x+6y=164[(-30 + 6y)/3]+6y=16(-120 + 24y)/12 + 6y = 16-120 + 24y + 6y = 19230y = 192 + 1030y = 312y = 312/30y = 10.4Put y = 10.4 in equation (3) as follows:
3x-6y = -303x-6(10.4) = -303x - 62.4 = -303x = -30 + 62.43x = 32.4x = 32.4/3x = 10.8Now, put x = 10.8 and y = 10.4 in equation (1):
x+2y+z=1310.8 + 2(10.4) + z = 1310.8 + 20.8 + z = 1331.6 + z = 13z = 13 - 31.6z = -18.6Therefore, by solving equations, the values of x, y, and z are 10.8, 10.4, and -18.6.
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Line I is parallel to line m. If the measure of <6 is 75^ what is the measure of <3
Solution:
Given;
[tex]m\angle6=75^o[/tex]Thus;
[tex]\begin{gathered} m\operatorname{\angle}8+m\operatorname{\angle}6=180^o.............\text{ Sum of angles on a straight line} \\ \\ m\operatorname{\angle}8=180^o-75^o \\ \\ m\operatorname{\angle}8=105^o \\ \end{gathered}[/tex]Then;
[tex]m\operatorname{\angle}8=m\operatorname{\angle}3...........\text{ Corresponding angles are equal}[/tex]Thus;
[tex]m\operatorname{\angle}3=105^o[/tex]Please help, picture attached
The measures of the unknown angles are as follows:
∠1 = 27∠2 = 97°∠3 = 56°∠4 = 27°∠5 = 56°How to find the measures of angles?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles etc.
The parallel lines are line m and line l . The parallel lines m and l are cut by two transversals.
Therefore, the measures of the unknown angles are as follows:
∠1 = 27°(vertically opposite angles)
∠1 = ∠4(alternate angles)
∠4 = 27°
Alternate angles are congruent. Vertically opposite angles are congruent.
Therefore,
∠1 + ∠2 = 124
27 + ∠2 = 124
∠2 = 124 - 27
∠2 = 97°
∠3 = 180 - ∠2 - ∠1 (sum of angles on a straight line)
∠3 = 180 - 97 - 27
∠3 = 56°
∠5 = 180 - ∠4 - ∠2
∠5 = 180 - 97 - 27
∠5 = 56°
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Select the new equation formed after collecting all variables on one side of the equal sign. (There is more than 1 correct answer.)
1/2(6x + 8) = x − 8
A. 4 = -2x - 8
B. 2x + 8 = 8
C. 3x = x -12
D. 8 = -2x - 8
E. 2x + 4 = -8
F. 3x + 12 = x
The equivalent equations to 1/2(6x + 8) = x − 8 include:
A. 4 = -2x - 8
E. 2x + 4 = -8
What is an equation?It should be noted that an equation shows the relationship between the variables. This usually illustrated by having and equal to sign.
In this case, 1/2(6x + 8) = x − 8 will be:
3x + 4 = x - 8
Collect like terms
3x - x = -8 - 4.
2x = -12
Divide
x = -12/2
x = -6
Therefore, 4 = -2x - 8
2x = -8 - 4
2x = -12
x = -12/2 = -6
Therefore, A is correct.
E. 2x + 4 = -8
2x = -8 - 4
2x = -12
x = -12/2
x = -6
E is also correct.
The correct options are A and E.
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During summer vacation, you charge $12 per hour for golf lessons and a registration fee of $50. If you make$98 one day, how many hours did you spend teaching lessons? Let g represent golf lessons, write an equationfor the situation.
Solution:
The question indicates a linear equation showing the relationship between the fee charged on golf lessons and the hour spent.
The linear equation can be represented by;
[tex]\begin{gathered} y=r+g \\ \text{where y is the total f}ee\text{ charged} \\ r\text{ is the registration fe}e \\ g\text{ is the golf lesson fe}e \end{gathered}[/tex]Given:
[tex]\begin{gathered} r=\text{ \$50} \\ g=12t,\text{ where t is the number of hours for the golf lesson} \\ y=\text{ \$98} \end{gathered}[/tex]From the above,
The equation can be re-written as;
[tex]y=50+12t[/tex]Hence, substituting the total amount made for the day into the equation to get the number of hours used teaching the lessons;
[tex]\begin{gathered} 98=50+12t \\ \text{Collecting the like terms to get t,} \\ 98-50=12t \\ 48=12t \\ \text{Dividing both sides by 12;} \\ t=\frac{48}{12} \\ t=4\text{hours} \end{gathered}[/tex]Therefore, 4 hours was spent teaching the lessons for the day $98 was made.
Watch help video The hypotenuse of a right triangle measures 20 cm and one of its legs measures 11 em. Find the measure of the other leg. If necessary, round to the nearest tenth oo Answer
We use pythagoras theorem
[tex]\text{hypothenus}^2=opposite^2+adjacent^2[/tex]Let y represent the other leg
[tex]\begin{gathered} 20^2=11^2+y^2 \\ 400=121+y^2 \\ y^2=400-121 \\ y^2=279 \\ y=\sqrt[]{279} \\ y=3\sqrt[]{31}\text{ cm} \\ y=16.70\text{ cm} \\ \end{gathered}[/tex]The measure of the other leg is 16.70 cm
Express the relation below as a table. I’m confused some help would be nice
STEP-BY-STEP EXPLANATION
Given information
The following ordered pairs were provided in the question given
(11, -3)
(-20, 3)
(-17, 2)
Recall that, the general form of writing ordered pairs is (x, y)
Where,
x = input
y = output
For the above-ordered pairs
(11, -3) can be expressed as
x = 11 , and y = -3
(-20, 3)
x = -20, and y = 3
(-17, 2)
x = -17, and y = 2
The next step is to write the above-ordered pairs as a table
BRAINLIEST (statistics) (please help fast)
Data were collected from a typing class with 10 students. The class had an average of 56 words per minute (WPM) with a standard deviation of 7 WPM. The teacher realized that the data from one student who typed 70 WPM was not entered. If this student’s results were included in the data set, what effect would it have on the standard deviation?
The standard deviation would be noticeably larger.
The standard deviation would be noticeably smaller.
The standard deviation would be about the same, perhaps a little larger.
The standard deviation would be about the same, perhaps a little smaller.
Answer: The STandard deviation would be noticably A is the answer
Step-by-step explanation:
2 What is the slope of a line that is parallel to the following: y= 3x -4
Parallel lines are defined by the same slope and will never intersect. They continue without touching eachother assuming them on the same plane.
Lines are represented by the following expression:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Then, for a parallel line to:
[tex]y=3x-4[/tex]The slope would be 3.
Tyler wants to crate a scale drawing of his bedroom. His bedroom is a rectangle with length 5m and width 4m. He decides on a scale of 1 to 80.
The scale drawing with length 0.0625m and width 0.05m.
What is scale factor?To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilised. It is employed to change the size of an object.
When both the original dimensions and the new dimensions are known, the scale factor may be determined. When employing the scale factor, there are two terms that must be understood. When a figure's size is increased, we refer to this as scaling up, and when its size is decreased, we refer to this as scaling down.
Given:
length= 5m
width= 4m
and,
The scaled dimension = (Actual dimension) x (scale factor) ...(i)
scale factor =1/50
(1) The actual width = 4 m.
So, the width of the door on the scale drawing= 4x (1/80)= 0.05 m
(2)The actual length = 5 m.
So, the length of the door on the scale drawing= 5 x (1/80)= 0.0625 m
Hence, the scale drawing with length 0.0625m and width 0.05m.
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Given ƒ(x) = − ½ (9 – 2x)
What is the value of f (15) ?
Answer: h of 15= -1/2(-21)= 10.5
Step-by-step explanation:
h(15)= -1/2(9-2(15))
h(15)=-1/2(9-30)
h(15)=-1/2(-21)
h(15)= 10.5
Hello! This is my first time using brainly tutor! Can anybody help me out with this question? Read the instructions carefully please!
The graph of the function of the problem is a line. The general equation of a line is:
[tex]y=m\cdot x+b.[/tex]Where m is the slope of the line and b is its y-intercept.
Now, the general equation of an inverse variation is:
[tex]y=\frac{k}{x}.[/tex]Comparing the equation of a line, and the equation of an inverse variation, we conclude that the relationship shown is NOT an inverse variation.
Answers
0. N
,1. n/a
the company for ocean has already cleared the Earth oceans of 125 million pounds of trash they are committed to picking up exactly 550 pounds of trash per day . write an equation to represent P pounds of trash removed as a function of number of the days passed? how many years have passed if the the company for ocean has a total of 125,602,250 pounds cleared from the ocean ?
1. pounds of trash cleared, P = 550D+125,000,000
2. 125,602,250=550D+ 125,000,000
550d=602250, therefore D= 602250/550 = 1095 days=1095/365= 3 years
Lynn paid a coeal of $2,780 for 261 tickets to the heater. Student tickets cost $10 and adult tickets cost urs. how many student tickets and how many acuit tickets did Lynn buy?
Answer:
245 students and 16 adults
Step-by-step explanation:
I need help in math can you please help me 0
Answer:
We will use the following identities:
[tex]\begin{gathered} \csc (x)=\frac{1}{\sin (x)} \\ \cot (x)=\frac{\cos (x)}{\sin (x)} \end{gathered}[/tex]So, replacing the identities on the left side, we get:
[tex]\frac{1+\csc^2(x)}{\cot^2(x)+1}=\frac{1+(\frac{1}{\sin(x)})^2}{(\frac{\cos (x)}{\sin (x)})^2+1}[/tex]Then, solving the power and adding the expressions, we get:
[tex]\frac{1+csc^2(x)}{\cot^2(x)+1}=\frac{1+\frac{1}{\sin^2(x)}}{\frac{\cos^2(x)}{\sin^2(x)}+1}[/tex][tex]\frac{1+csc^2(x)}{\cot^2(x)+1}=\frac{\frac{\sin^2(x)+1}{\sin^2(x)}}{\frac{\cos ^2(x)+\sin ^2(x)}{\sin ^2(x)}}[/tex]Dividing the expression and simplifying, we get:
[tex]\frac{1+csc^2(x)}{\cot^2(x)+1}=\frac{\sin ^2(x)+1}{\cos ^2(x)+\sin ^2(x)}[/tex]Finally, we know that cos²(x) + sin²(x) = 1, so we can rewrite the expression as:
[tex]\begin{gathered} \frac{1+\csc^2(x)}{\cot^2(x)+1}=\frac{\sin ^2(x)+1}{1} \\ \frac{1+\csc^2(x)}{\cot^2(x)+1}=\sin ^2(x)+1 \end{gathered}[/tex]Question 3 Cindy and Pam read their tavorite books, Cindy read for 4 hours and Pam read for 7 hours How much longer did Pam read than Cindy? A 23 hours 12 B 3 hours 31 hours D 12 5 12 hours Illuminate Education, Inc.
Let:
tc = Time that cindy read
tp = Time that pam read
How much longer did Pam read than Cindy? we need to find the difference, so:
[tex]\begin{gathered} tc=4\frac{3}{4}=\frac{19}{4} \\ tp=7\frac{2}{3}=\frac{23}{3} \\ so\colon \\ d=tp-tc=\frac{23}{3}-\frac{19}{4}=\frac{35}{12}=2\frac{11}{12} \end{gathered}[/tex]