What is the graph of the solution to the following compound inequality?5x - 1 < 19 and -3- X+1s1
Answers
on5x - 1 < 19
To solve this inequality add 1 to both sides
[tex]\begin{gathered} 5x-1+1<19+1 \\ 5x<20 \end{gathered}[/tex]Now divide both sides by 5
[tex]\begin{gathered} \frac{5x}{5}<\frac{20}{5} \\ x<4 \end{gathered}[/tex]The solutions lie in the area left to the number 4
For the second inequality
[tex]-3-x+1\leq1[/tex]Add first we will add the like terms in the left side
[tex]\begin{gathered} (-3+1)-x\leq1 \\ -2-x\leq1 \end{gathered}[/tex]Now add 2 for both sides
[tex]\begin{gathered} -2+2-x\leq1+2 \\ -x\leq3 \end{gathered}[/tex]We need to divide both sides by -1, but we should reverse the sign of inequality
[tex]\begin{gathered} \frac{-x}{-1}\ge\frac{3}{-1} \\ x\ge-3 \end{gathered}[/tex]We reversed the sign of inequality when divides it by -ve number
Since 2 < 3
Then if we divide both sides by -1, then it will be
-2 < -3 which is wrong -2 greater than -3, then we should reverse the sign of inequality if we multiply or divide it by a negative number
Then the solutions of the 2nd inequality lie right to -3
Let us draw them
The red part is the solution to the 1st inequality
The blue par is the solution to the 2nd inequality
The area with the 2 colors is the area of the common solution of both inequalities
Related Questions
Write a quadratic equation in standard form with the given root(s) -7,3/4 and can you explain how you did it? i need it ASAP please and thank you
Answers
The equation of the quadratic equation is P(x) = x² + 23/4x - 21/4
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the quadratic equation?The given parameters are
Zeros = -7 and 3/4
The sum of multiplicities of the quadratic equation must be equal to the degree.
This means that the multiplicity of the zeros -7 and 3/4 is 1
The equation of the quadratic equation is then calculated as
P(x) = (x - zero)^ multiplicity
So, we have
P(x) = (x + 7)(x -3/4)
Expand
P(x) = x² + 7x - 3/4x - 21/4
This gives
P(x) = x² + 23/4x - 21/4
Hence, the equation is P(x) = x² + 23/4x - 21/4
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a jewelry company loses $450 as a result of a delivery delay.The 9 owners of the company must share the loss equally. Which integer was represents the change in profit for each owner A. $-50 B. $-35 C. $5 D. $50
Answers
We know that they lots of $450.
If they want to share the loss equally, we just have to divide the amount by 9 owners.
[tex]\frac{450}{9}=50[/tex]Therefore, the loss per owner is A. $-50.Remember that losses are represented by negative numbers.
Ravi built a large wooden storage box. The box was in the shape of a rectangular prism, as shown below. He covered all the sides of the box with special wallpaper that cost a total of $856. How much did the wallpaper cost per square foot?
Answers
The area, A, of a rectangle with dimensions l and b is given by:
A = l times b
Therefore the total area of the two opposite and congruent rectangular sides with
the dimension 6 by 5 is:
[tex]2\times6\times5=60ft^2[/tex]The total area of the two opposite and congruent rectangular sides with
the dimension 6 by 7 is:
[tex]\begin{gathered} 2\times6\times7=84ft^2 \\ The\text{ total area of the two opposite and congruent rectangular sides with the dimension} \\ 5\text{ by 7 is:} \\ 2\times5\times7=70ft^2 \\ \\ \text{Hence the total surface area = 60+84+70=214 square ft} \\ \\ \text{Therefore the cost per square foot = }\frac{856}{214}=4dollars\text{ per square foot} \end{gathered}[/tex]The following data set represents the ACT scores for students in Mrs. Smith's collegescience class.18 32 16 2319 21 28 2922 30 19 21What is the range for the ACT scores for the class?
Answers
The range is the difference between the greatest and the smallest number, so it is 32 - 16 = 16.
Solve the following quadratic equation by the square root method. If needed, write your answer as a fraction reduced to lowest term
Answers
Solution
Solve the following quadratic equation by the square root method.
[tex]\begin{gathered} y^2-10y+25=-49 \\ y^2-10y+25+49=0 \\ y^2-10y+74=0 \end{gathered}[/tex]Therefore the correct answer for y are
[tex]y=5+7i,\text{ 5-7i}[/tex]In the figure, ABCD and DEFG are squares.AC:FD=7:5, find CE
Answers
Given:
The ratio of the diagonals of the squares ABCD and DEFG is:
[tex]AC:FD=7:5[/tex]Required-the value of CE.
Explanation:
Given that the ratio of the diagonals of the squares ABCD and DEFG is:
[tex]AC:FD=7:5[/tex]So, the sides will be in the same ratio.
[tex]AD:GD=7:5[/tex]Let the sides of the two triangles ABCD and DEFG be 7x and 5x.
Given that
[tex]AG=3cm[/tex]So, we can write AG as:
[tex]\begin{gathered} AG=AD-GD \\ 3=7x-5x \\ \\ 2x=3....(1) \end{gathered}[/tex]Now, we have to find CE, so we can write CE as:
[tex]\begin{gathered} CE=CD+DE \\ \\ CE=7x+5x \\ \\ CE=12x \\ \\ CE=6(2x) \\ \\ CE=6\times3 \\ \\ CE=18cm \end{gathered}[/tex]Final answer: The value of CE is 18 cm.
what is written on the back of a deposit slip?
Answers
Some banks merely need one to write "for deposit only" on the back of your check along with the account number, routing information, and sort code.
Some banks will need one to enclose a deposit slip with the check.
What is a Deposit Slip?A deposit slip is a form that a bank gives a depositor to complete and is intended to list the things involved in the deposit transaction in categories. The categories include the item's nature and, if it's a check, the source, such as a state if the bank is out of town. Along with the deposit (cash and checks), the teller retains the deposit slip and issues a receipt to the depositor. It is quite convenient to pay for them because they are filled out in a store rather than a bank. They serve as a vehicle for moving money as well.To learn more about Deposit slip, refer to:
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7. Write the equation of the line in slope-intercept form given the following:Point (-5, -3), slope =3/5
Answers
start by writing in the form
[tex]y=mx+b[/tex]where you already have the slope and you must find b, which is the y-intercept
[tex]y=\frac{3}{5}x+b[/tex]use the point given (-5,-3) to find b
[tex]\begin{gathered} -3=\frac{3}{5}(-5)+b \\ -3=-3+b \\ -3+3=b \\ b=0 \end{gathered}[/tex]Expressions: Tutorial
Simplify this expression:
4(126) + 76 - 10.
Type the correct answer in the box.
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(0) 101
0
Vo 4
X
=
A
VI
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a B
A
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لا
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sin
cos tan
CSC sec cot
Answers
The simplified form of expression 4(126) + 76 - 10 is 6 (100 - 5).
What is a expressions?A mathematical expression is a sentence that contains a minimum of two numbers or variables and at least one mathematical operation. Let's learn how to write expressions.
A number is 6 more than half of another number, and that other number is called x. In a mathematical expression, this statement is represented as x/2 + 6. Complex puzzles can be solved using mathematical expressions.
We have been asked to simply the expression
4(126) + 76 - 10
= 4(60 + 66) + 66
= 4(60) + 4(66) + 66
= 4(60) + 5(66)
= 4(60) + 5( 60 + 6)
= 4(60) + 5(60) +5(6)
= 60(4+5) + 6(5)
= 60(9) + 6(5)
= 6(90 + 5)
= 6(95)
= 6 (100 - 5) simplified form
= 600 - 30
= 570
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Seven less than n is 11
Answers
MATHEMATICALLY THIS CAN BE WRITTEN AS:
[tex]n - 7 = 11 \\ n = 11 + 7 \\ n = 18[/tex]
THAT NUMBER n IS 18
HOPE THIS HELPS
Which statement does NOT represent an expression? A (8 + x) - 7 B 4 + x = 12 C x2 = 24 D 5
Answers
Answer
The statement that does not represent an expression are 4 + x = 12 and x^2 = 24 which are option B and C respectively
Explanation:
An expression is a set of term combined using the operators +, - /
From the option given
8+ x - 7 this can be further expressed as
8 + x - 7
x + 8 - 7
x - 1
The only expression in the option are x - 1, and 5
4 + X = 12 is an equation. This is because it is a combination of two expressions that are equal to each other
x^2 = 24 is also an equation
Therefore, the statement that does not represent an expression are 4 + x = 12 and x^2 = 24 which are option B and C respectively
this is precents
60% of 90
please leave a sloution
Answers
To calculate the 60% of 90, we need to understand what means 60% in terms of fractions. Converting a percentage into a fraction has a simple method: Dividing the percentage by 100. So 60% in fraction form is just
[tex]\frac{60}{100}=\frac{3}{5}[/tex]Now, to solve the problem, we only need to multiply our number 90 by this fraction; it gives us
[tex]90\cdot\frac{3}{5}=\frac{270}{5}=54[/tex]Thus the 60% of 90 is 54.
What is m<1?
Please someone help me! Thank you
Answers
Answer:
108°
Step-by-step explanation:
[tex]m\angle 3=72^{\circ}[/tex] (corresponding angles)
[tex]m\angle 1=108^{\circ}[/tex] (linear pair)
Write the following comparison as a ratio reduced to lowest terms 2 nickels to 27 dimes
Answers
The ratio of 2 nickels to 27 dimes is 27.
What is ratio?A ratio in mathematics demonstrates how many times one number is contained in another. For instance, the ratio of oranges to lemons in a dish of fruit is eight to six if there are eight oranges and six lemons present. Similarly, the ratio of oranges to the total amount of fruit is 8:14 while that of lemons to oranges is 6:8. A ratio is an ordered pair of numbers a and b, expressed as a / b, where b is not equal to 0. A percentage is an equation in which two ratios are made equal to one another. For instance, you could express the ratio as 1: 3 (one boy to three females), meaning that one in four of the population is male.
Nickel is equivalent to 0.05 dollars.
2 nickels are equivalent to (0.05 × 2) = 0.01 dollars.
1 dime is equal to 0.1 dollars.
27 dimes are equivalent to (27 × 0.01) = 0.27dollars.
Therefore, to compare 27 nickels to 2 dimes as a ratio reduced to lowest term will be 0.27 : 0.01
= 27
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Subjects in a marketing study were shown a movie and at the end of the movie were given a test to measure their recall. The scores are listed below. 10, 22, 97, 49, 61, 85, 35, 57, 31, 26, 27, 40, 86, 88, 28, 61, 87, 62, 92, 58, 101, 210 Construct a box-plot for the test scores. Are there any outliers?
Answers
One observation (210) given a test at the end of the movie to measure their recall is an outlier because it is above the fence above, as can be seen.
Data should first be arranged as follows in ascending order:
10, 22, 26, 27, 28, 31, 35, 40, 49, 57, 58, 61, 61, 62, 86, 86, 87, 88, 92, 97, 101, 210
There are n = 22 observations. Here n is even. Hence median is the mean of the middle two observations.
Median = (11 + 12) th observation /2 = (58 + 61)/2 = 59.5
We now divide the ordered data equally into two halves. Therefore, there are 11 observations in the lower section and 11 observations in the upper part.
The first quartile now corresponds to the median of the lower half.
Q1 = [(11 + 1)/2] the observation = 6th observation = 31
The third quartile represents the upper half part's median.
Q3 = [(11 + 1)/2] the observation = 6th observation = 87
IQR = Q3 - Q1 = 87 - 31 = 56
Lower fence = Q1 - 1.5 × IQR = 31 - 1.5 × 56 = -53
Upper fence = Q3 + 1.5 × IQR = 87 + 1.5 × 56 = 171
One observation (210) is an outlier since it is above the upper fence, as can be seen.
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the sum of 3 and w is greater than or equal to -22.
Answers
1) Let's write the inequality and solve it
w+3≥-22 Subtracting 3 from both sides
w ≥ -22 -3
w ≥ -25
2) Now let's write the solution as an interval. Considering that the solution is a set for all values greater than or equal to -25 for w. Including the -25 (closed) up to infinite (open).
[tex]S=\lbrack-25,\infty)[/tex]sarah knows how important it is to budget her monthly expenses she earns 3,120 every month and her monthly expenses total $2,130. Determine how much money Sarah spends on her monthly Rent. Rent=49%, School Loan=23%, Car Insurance=3%, Car=20%, Phone=5%?
Answers
The rent represents 49% of her expenses.
Her total expenses are $2130, then she spends $2130*49% = $1043.7 on her rent.
Make sure to show your work when answering the question. The insurance company pays the full cost of 3,900 prescriptions claims out of 4,500 prescriptions claims submitted. What is the rate of the claims paid expressed as a percent? Round to two decimal places.
Answers
The rate of the claims paid expressed as a percent is 86.67%.
Out of the 4,500 prescription claim submissions, it has been stated that the insurance company covers 3,900 prescription claims in full.
We must determine what percentage of 4,500 is 3,900 in order to solve the presented problem.
Percent of the claims paid = 3,900 / 4,500 x 100
Percent of the claims paid = 0.8666666 × 100
Percent of the claims paid 86.66666%
Percent of the claims paid = 86.67%
As a result, 86.67% would be the rate of claims paid represented as a percentage.
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Select the correct answer. Jessica is 5 years older than her sister Jenna. Jenna tells her sister that in 5 years, she will be as old as Jessica was 5 years ago. If Jenna’s age is x, which equation represents the situation? How many solutions does the equation have? A. x + 5 = (5 − x) − 5, which has one solution B. x + 5 = (x + 5) − 5, which has infinitely many solutions C. x + 5 = (x + 5) − 5, which has no solution D. x + 5 = (5 − x) − 5, which has infinitely many solutions E. (x + 5) + 5 = (x + 5) + 5, which has infinitely many solutions
Answers
Write the equation of the line with the given information. Through (-1, -1) parallel to h(x)=-1+10
Answers
The equation of a line that passes through (-1, -1) and parallel to h(x) = -1x + 10 is y = -x -2
How to find equation of a line?The line passes through (-1, -1) and it is parallel to h(x) = -1x + 10
When lines are parallel, the slopes are the same.
Therefore, the equation of a line that passes through (-1, -1) and parallel to h(x) = -1x + 10 can be calculated as follows:
Hence,
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the y-intercept using (-1, -1)
y = -x + b
-1 = -(-1) + b
b = -1 - 1
b = -2
Therefore, the equation of the lines is y = -x -2
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which of the following are not an example of a rigid transformation
Answers
When we talk of rigid transformation, we refer to transformation that occurs, and the size of the shape is not affected. Of the three options, dilation is the only sort of transformation that affects the size of the object.
DILATION
how do I solve this problem?
Answers
The complete table describing the probability distribution of X is:
x | P(x)
0 0.027
1 0.189
2 0.441
3 0.343
The values of the random variable X are given and the corresponding probabilities are to be found.
The probability distribution is binomial.
That is, P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ, where p is the probability of success of X in n trials.
So here values of x are given.
From the table, it is clear that p = 0.7
and 1-p = 0.3
Number of trials, n = maximum number of x = 3
Now consider each x.
When x = 2,
P(X = 2) = P( getting 2 tails out of 3 flips)
= P(TTH or THT or HTT)
= P(TTH) +P(THT) +P(HTT) [since each of them are independent events]
= ³C₂ p²(1-p)³⁻²
= 3 (0.7)²(0.3)
= 0.441
When x = 3,
P(X = 3) = P( getting 3 tails out of 3 flips)
= P(TTT)
= ³C₃ p³(1-p)³⁻³
= 1 (0.7)³(0.3)⁰
= 0.343
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What ordered lair is closest to a local minimum of the function, f(x)?A. (-1, -3)B. (0, -2)C. (1, 4)D. (2, 1)
Answers
We have the following function given:
x f(y)
-2 -8
-1 -3
0 -2
1 4
2 1
3 3
And we can see that the minimum of the function is for the lowest f(y) value on this case -8
And the closest pair to this local minimum is:
A. (-1,3)
Written Assignment #5
3.) Your stats test has five multiple choice questions, each having four possible answers with one correct
answer per question. If you completely guess (which you would never do), what is the probability (in
decimal form) that each of the following will happen? Show your work.
a.) get all of the questions correct
b.) get none of the questions correct
c.) get at least one of the questions incorrect
d.) get the first three questions correct and the last two incorrect
Answers
The probability of doing all questions correct is 1/3.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.So, the probability to get all questions correct:
Probability formula: P(E) = Favourable outcomes/Total outcomes
The number of questions is 5.The options for each question are 4. Possible answers are 1.Then,
Favourable events = 1 × 5 = 5Total events = 3 × 5 = 15Now, find the probability by putting the values as follows:
P(E) = Favourable outcomes/Total outcomesP(E) = 5/15P(E) = 1/3Therefore, the probability of doing all questions correct is 1/3.
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The correct question is given below:
Your stats test has five multiple-choice questions, each having four possible answers with one correct answer per question. If you completely guess (which you would never do), what is the probability (in decimal form) that each of the following will happen? Show your work.
A) Get all of the questions correct
Write a function rule for the table. X f(x) 3 5 9 101
Answers
Based on the data of the table, you can notice that the following function f(x):
f(x) = x + 4
represents the relation in between the values of the columns of the table.
For instance, you have:
f(3) = 3 + 4 = 7
f(4) = 4 + 4 = 8
f(5) = 5 + 4 = 9
f(6) = 6 + 4 = 10
Which expression is equivalent to -4(2 - 6x) - 2.5x ?
Answers
Rewriting the expression, we have:
[tex]\begin{gathered} -4\mleft(2-6x\mright)-2.5x \\ =-8+24x-2.5x \\ =21.5x-8 \end{gathered}[/tex]So an equivalent expression is 21.5x - 8.
Find the distance between the points (0,–1) and (0,–11).Question 4 options:1191012
Answers
We are given the following points:
[tex](0,-1);(0,-11)[/tex]We can use the formula for the euclidean distance:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where:
[tex]\begin{gathered} (x_1,y_1)=(0,-1) \\ (x_2,y_2)=(0,-11) \end{gathered}[/tex]Replacing the values:
[tex]d=\sqrt[]{(0-0)^2+(-11-(-1))^2}[/tex]Solving we get:
[tex]d=\sqrt[]{(-11+1)^2}[/tex]Solving the square root
[tex]d=-11+1=10[/tex]Therefore, the distance is 10.
water stations will be placed every 400 metets of a 5 kilometer racehow many water staions are neeedded
Answers
13 water stations will be placed every 400 meters of a 5 kilometer.
Given: Water stations will be placed ; every 400 meters
Also the total distance = 5 km = 5000 meters
Thus if a water station is supposed to be kept at every 400 meter distance then that means we can find out this distance by using unitary method
this means by using unitary method we get;
Number of water stations needed is = 5000 divided by 400
12.5 = 13 water stations would be required.
Thus 13 water stations will be placed every 400 meters of a 5 kilometer.
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BUILD PERSEVERANCE Point
C
(
6
,
9
)
is located on the segment between point
A
(
4
,
8
)
and point B. The ratio of AC to CB is 1:3. What are the coordinates of point B?
Answers
The co ordinates of the point B is (12, 12)
Given,
The co ordinates:
Point C = (6, 9)
Point A = (4, 8)
Point B = (x, y)
AC : CB(m : n) = 1 : 3
We have to find the co ordinates of point B.
Lets use the formula to find the coordinates of point C.
C = 1 / (m + n) × (mx₂ + nx₁, my₂ + ny₁)
Where,
C = (6, 9)
m = 1
n = 3
x₁ = 4
x₂ = x
y₁ = 8
y₂ = y
So,
(6, 9) = 1 / (1 + 3) × ((1 × x) + (3 × 4), (1 × y) + (3 × 8))
(6, 9) = 1/4 × (x + 12, y + 24)
(6 × 4, 9 × 4) = (x + 12, y + 24)
(24, 36) = (x + 12, y + 24)
Lets evaluate:
x + 12 = 24 and y + 24 = 36
Solve for x,
x + 12 = 24
Add -12 to both sides
x + 12 - 12 = 24 - 12
We get,
x = 12
Now solve for y,
y + 24 = 36
Add -24 to both sides
y + 24 - 24 = 36 - 24
We get,
y = 12
That is, the co ordinates of the point B is (12, 12)
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O GRAPHS AND FUNCTIONSFinding a difference quotient for a linear or quadratic function
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given difference quotient formula
[tex]\frac{f(x+h)-f(x)}{h}[/tex]STEP 2: Write the given function f(x)
[tex]f(x)=-2x^2-4x+7[/tex]STEP 3: Get f(x+h)
[tex]\begin{gathered} f(x)=-2x^2-4x+7,\text{ we n}eed\text{ to get }f(x+h) \\ f(x+h)=-2(x+h)^2-4(x+h)+7 \\ -2(x+h)^2-4(x+h)+7=-2(x^2+2xh+h^2)-4x-4h+7 \\ \Rightarrow-2x^2-4xh-2h^2-4x-4h+7 \\ \Rightarrow-2x^2-2h^2-4xh-4x-4h+7 \end{gathered}[/tex]STEP 4: Rewrite the expression by substitution
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}\Rightarrow\frac{-2x^2-2h^2-4xh-4x-4h+7-(-2x^2-4x+7)}{h} \\ \Rightarrow\frac{-2x^2-2h^2-4xh-4x-4h+7+2x^2+4x-7_{}}{h} \\ Re-\text{arrange the expression} \\ \frac{-2x^2+2x^2-2h^2-4xh-4x+4x-4h+7-7}{h} \\ \Rightarrow\frac{-2h^2-4xh-4h}{h} \\ \Rightarrow\frac{-h(2h)}{h}-\frac{(4x)h}{h}-\frac{h(4)}{h} \\ \Rightarrow-2h-4x-4 \end{gathered}[/tex]Hence, the result of the simplification is:
[tex]-2h-4x-4[/tex]