a would the compound inequality have infinite solutions if a = 4
x < 4 AND x > a.
if a = 4 and we use an "or" instead of the "and" we have:
x < 4 or x > 4.
This is:
"x is larger than 4 or smaller than 4."
Then the solution of this is all the real numbers except the value x = 4.
The set of solutions can be written as:
{xI x ∈ R \ [4]}
Where this reads:
"x belongs to the set of the reals minus the number 4".
Or we also could write it as:
x ∈ (-∞, 4) ∪ (4, ∞)
Where we have two open ends in the "4" side, so the value x = 4 does not belong to that set.
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Write an equation of a line in slope-intercept form with the given slope and y-intercept. slope: -6, y-intercept: -2
Answer:
Step-by-step explanation:
Hope this helps :)
Sophia is buying pretzel sticks by the pound. For every 5 pounds of pretzel sticks she buys, she pays $11. What is the cost, per pound, for the pretzel sticks?
Sophiya has to pay 2.2 dollars for per pound of pretzel sticks.
What is unitary method?Unitary method is a mathematical technique for first obtaining the value of a single unit then deriving the given units by multiplying it with the single unit.
The cost per pound of pretzel sticks can be obtained by the unitary method.
Given that 5 pounds of pretzels costs 11 dollars,
Now to obtain the cost of per pound of pretzel sticks we'll put the total cost at the numerator and the total weight of the pretzel sticks on the denominator.
∴ Per pound of pretzel costs (11/5) dollars which is,
= 2.2 dollars per pound of pretzel sticks.
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Taylor's work:
12x+3=3(4x)
Taylor's Check:3(4x)=12x
It should be noted that since Taylor got 3(4x) and the correct expression is 3(4x + 1), he is incorrect.
How to calculate the value?It should be noted that the expression given is illustrated as 12x+3=3(4x).
We need to solve this:
12x + 3
It should be noted that the common factor is 4.
Therefore, 12x + 3 = 3(4x + 1)
Therefore, since Taylor got 3(4x). He is incorrect.
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Taylor's work:
12x+3=3(4x)
Taylor's Check:3(4x)=12x
Is this correct?
If the length of a rectangle is four less than twice its width and the perimeter is 220 inches, what is the width of the rectangle?
Group of answer choices
38 inches
72 inches
55 inches
56 inches
Given the length and perimeter, the width of the rectangle is 38 inches.
Hence, option A) 38inches is the correct answer.
What is the width of the rectangle?The perimeter of a rectangle is expressed mathematically as;
P = 2( l + w )
Given the data in the question;
Let "x" represent the width of the rectangle.
Width w = xLength l = 2x - 4Perimeter P = 220 inchesTo determine the width of the rectangle, plug the given values into the formula above and solve for x.
P = 2( l + w )
220 = 2( (2x - 4) + x )
220 = 2( 2x - 4 + x )
220 = 2( 3x - 4 )
Apply distributive property
220 = 2( 3x - 4 )
220 = 2(3x) + 2(-4)
220 = 6x - 8
Collect like terms
220 + 8 = 6x
228 = 6x
6x = 228
x = 228/6
x = 38
Now, since "x" represent the width of the rectangle,
The width of the rectangle w = x = 38 inches.
Given the length and perimeter, the width of the rectangle is 38 inches.
Hence, option A) 38inches is the correct answer.
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Answer the question in photo
[ Brainliest + easy points ]
Answer:
Step-by-step explanation:
acute
Describe in words where the square root of 60 minus 11 would be plotted on a number line.
Between −3 and −4, but closer to −3
Between −3 and −4, but closer to −4
Between 7 and 8, but closer to 8
Between 7 and 8, but closer to 7
The square root of 60 minus 11 would be plotted on a number line in between −3 and 8, but closer to 8.
What is number line?
A straight line with numbers placed at equal intervals or segments along its length. Number line is a straight line with a "zero" point in the middle, with positive and negative numbers listed on either side of zero and going on indefinitely.
Given:
The square root of 60 minus 11 would be plotted on a number line.
According to given question we have
We know that the square root of 60
=
[tex]\sqrt{60} \\\\=7.74[/tex]
So, By the statement square root of 60 minus 11 we have,
=7.74-11
=-3.25
So, in the number line the points are lies in between −3 and 8, but
closer to 8.
Therefore, the square root of 60 minus 11 would be plotted on a number line in between −3 and 8, but closer to 8.
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A culture of 10 bacteria is started, and the number of bacteria will double every hour. In about how many hours will there be 3,000,000 bacteria?
Time required to form 3,000,000 bacteria from 10 if it will double every hour = 18.2years.
In basic terms exponential growth:The phrase exponential refers to a high number expressed in smaller terms, or something that grows at an ever-increasing rate. 25 is shown as 5x5 as an example of an exponential. The erosion that is occurring on the Holderness coast in eastern England is an example of exponential erosion.
According to the given data:Using the formula of exponential growth:
y = a*b^t
a = reflects the initial bacterial population
t = represents the doubling.
the information given
a = 10
t = 1 hour
After 1 hour, the number of bacteria multiplies by 2, so:
y = 2 × 10 = 20
So that:
20 = 10 × b^1
Dividing through by 10 gives:
2 = b
solving this we get an equation:
y = 10(2)^t
Solving for 3,000,000 bacteria.
Substituting the value in the formula:
3000000 = 10(2)^t
3000000/10 = (2)^t
300000 = (2)^t
Applying the log of both sides, it gives:
Log 300000 = tlog2
5.477 = 0.301t
t = 5.477/0.301
t = 18.2 years
Time required to form 3,000,000 bacteria from 10 if it will double every hour = 18.2years.
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Use this method to write each equation in logarithmic form. Show your work.
6⁸=a+1
The equation 6 ⁸ = a + 1 in the logarithm form will be given as log ₆ ( a + 1 ) = 8 .
Logarithms are another form of exponents.
For example, we know that 2 raised to which power is equal to 8,
this is expressed by the exponential form as follows 2³ = 8 is equal to log ₂ 8 = 3
Both equations describe the same relationship between the numbers 2, 3, 8 where 2 is the base and 3 is the exponent
The difference is that while the exponential form isolates the power 8,the logarithmic form isolates 3
So by writing given equation in logarithmic form we get -log₆ ( a + 1 ) = 8.
Therefore, the equation 6 ⁸ = a + 1 in the logarithm form will be given as log ₆ ( a + 1 ) = 8 .
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The price of Stock A at 9 A.M. was $14.56. Since then, the price has been increasing at the rate of $0.12 each hour.At noon the price of Stock B was $15.06. It begins to decrease at the rate of $0.07 each hour.If the two rates continue, in how many hours will the prices of the two stocks be the same?
Please help Savvas Realize- 2-2Solve Equations with Variables on Both Sides Practice & PS
Answer:
2 hours
Explanation:
Stock A:
9AM $14.56 +$0.12/hr
10AM $14.68 +1hr
11AM $14.80 +2hrs
12PM $14.92 +3hrs
Stock B:
12 PM (Noon) $15.06 -$0.07/hr
1PM $14.99 +1hr
2PM $14.92 {+2HR}
Brian received a gift card of $50 for a pizza restaurant. The restaurant charges $8 per pizza. Rita received a gift card of $70 for a different pizza restaurant. The restaurant charges $12 per pizza. - Let x be the number of pizzas purchased.
Answer: X = - 5
Step-by-step explanation:
Pls help fast thank you
The time taken to hit the ground is 13 seconds.
How to calculate the value?It should be noted that the function that was given based on the information is:
h(t) = 16t²
where h = height
t = time
Therefore, when the height is 2704ft, the time will be:
h(t) = 16t²
2704 = 16t²
t² = (2704 / 16)
t² = 169
t = ✓169
t = 13
The time taken is 13 seconds.
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Rebecca collected data and told you that her sample mean was 56 and her sample median was 64. She then draws a histogram based on her data and asks you to guess the shape of it without looking. What would the most likely shape be for her histogram?.
Rebeeca’s histogram most likely shape will be Skewed to the left.
The histogram shows a symmetrical data distribution. A distribution is symmetrical if a vertical line can be drawn at any point in the histogram such that the shapes to the left and right of the vertical line are mirror copies of each other.
The mean and the median both reflect the skewing, but the mean reflects it more so. This is because the mean and median are measures of central tendency. Because in Rebecca’s data the mean is smaller compared to the median, it makes the histogram skewed to the left. If the median were to be smaller than the mean, it would be skewed to the right.
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Students in a school are split into teams. the purple team has 51 students, the green team has 42 students, and the gray team has 48 students. what is the constant of proportionality for the ratio of green team students to gray team students?
The constant of proportionality for the ratio of green team students to gray team students is 7/8.
Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other.
It can be expressed in different ways:
1) Use the ":" to separate the values : a : b
2) Use the word "to" : a to b
3) Write it in fraction: a / b
The ratio that relates two given values is called the constant of proportionality, a/b.
If the green team has 42 students, and the gray team has 48 students, then the ratio of green team students to gray team students can be written as:
42 : 48 or 42 to 48 or 42/48
To simplify the ratio, divide both numbers in the ratio by the same number until they cannot be divided any more.
Divide both number by 6.
42 : 48 = 7 : 8 or 7/8
Hence the constant of proportionality is 7/8.
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What is (11-3) divided by 2+1 step by step
The result of the expression described by the word phrase as in the task content is; 8/3 = 2.667.
What is the result of the evaluation described by the word phrase?It follows from the task content that the expression described by the word phrase be evaluated.
First, (11-3) = 8 and
Also, (2+1) = 3.
Ultimately, when (11-3) is divided by (2+1); we have; 8/3 = 2.667.
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1.44 make-up exam: in a class of 20 students, 19 of them took an exam in class and 1 student took a make-up exam the following day. the professor graded the first batch of 19 exams and found an average score of 79 points with a standard deviation of 7.3 points. the student who took the make-up the following day scored 60 points on the exam.
a) Since the new score is less than the average score, it will decrease the average.
What a standard deviation means?The degree of data dispersion from the mean is indicated by the standard deviation. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.Think about the following data: 2, 1, 3, 2, 4. The average and the total square of the observations' departures from the mean will be 2.4 and 5.2, respectively. There will be a standard deviation of (5.2/5) = 1.01.Statistics experts have established that measures that are within plus or minus 2 SD of the true value are more accurate than those that fall outside of this range. For data points that frequently fall outside of the 2SD range, the majority of QC programs mandate that remedial action be taken.a) Since the new score is less than the average score, it will decrease the average.
b) Sum of 27 scores = 27*79
Hence,
New average = (79*27 + 63)/28 = 78.43
c) Since the variability would increase in the overall data, the standard deviation increases.
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Arrange the steps to show how to solve for x.
Arranged steps after solving equation [tex]\frac{-8}{3} x+4(x+\frac{9}{4} )= \frac{-2}{3} (x+\frac{12}{8} )+3[/tex] are
[tex]\frac{-8}{3} x+4x+9= \frac{-2}{3} x-1 +3[/tex][tex]\frac{-8}{3} x+4x= \frac{-2}{3} x-7[/tex][tex]\frac{-8}{3} x+4x+\frac{2}{3} x =-7[/tex][tex]2x=-7[/tex][tex]x=\frac{-7}{2}[/tex]What is an equation and how to solve it?An equation is an formula which equates two mathematical expressions.
We can solve equations by adding or subtracting same number from both sides or by diving both sides by same number (positive or negative)
[tex]\frac{-8}{3} x+4(x+\frac{9}{4} )= \frac{-2}{3} (x+\frac{12}{8} )+3\\[/tex]
After Opening brackets, we get:
[tex]\frac{-8}{3} x+4x+4(\frac{9}{4} )= \frac{-2}{3} x-\frac{2}{3} *\frac{12}{8} +3[/tex]
[tex]\frac{-8}{3} x+4x+9= \frac{-2}{3} x-1 +3[/tex]
Subtracting 9 from both sides, we get:
[tex]\frac{-8}{3} x+4x+9-9= \frac{-2}{3} x-1 +3-9\\\frac{-8}{3} x+4x= \frac{-2}{3} x-7[/tex]
Moving all terms of x on to one side:
[tex]\frac{-8}{3} x+4x+\frac{2}{3} x =-7\\\\\\frac{-8x+12x+2x}{y} =-7\\\\\frac{6x}{3}= -7\\ 2x=-7[/tex]
Dividing both sides by 2 , we get
[tex]x=\frac{-7}{2}[/tex]
On solving the given equation we got x =-7/2
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Christopher records his test scores in his World Cultures and Geography class for the past year. The information he records is below.
87, 90, 77, 68, 65, 62, 75, 83, 98, 100.
What is the mean of Christopher's test score throughout the year rounded to the nearest tenth?
A 73.2
B 78.3
C 80.5
D 89.4
The mean of Christopher's test score throughout the year is 80.5
How to calculate the mean ?Christopher scores during the World Cultures and Geography class for the past year are
87, 90, 77, 68, 65, 62, 75, 83, 98, 100
The mean can be calculated as follows
87+ 90+77+ 68+ 65+62+75+83+98+100/10
= 805/10
= 80.5
Hence the the mean of Christopher's test score throughout the year is 80.5
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1. A car rental company charges a processing fee of $20 to rent a minivan and $34 per day the minivan is rented. this situation can be represented by y=34 x+20, where x is the number of days and y is the total cost to rent the minivan. write this relationship in function notation, as a function c(d), where c(d) represents the cost of renting a minivan for d days.
2. Select the ordered pair that would represent this function C, given d=10.
A. (360,10)
B. (c(10)10)
C. (20,C(34))
D. (10,c(10))
Answer:
Best answer choice seems to be C.
Step-by-step explanation:
simplify 8/18 = ?/? please helpp
Answer:4/9
Step-by-step explanation:
Find the GCD
8/2
18/2
Answer:
4/9
Step-by-step explanation:
Let's simplify the value,
→ 8/18
→ (8 ÷ 2)/(18 ÷ 2)
→ 4/9
Thus, the value is 4/9.
3. What is the ratio of the sides for triangle XYC?
Answer:
Option 4
Step-by-step explanation:
This is the ratio of the lengths of the sides of a 45-45-90 triangle.
Given: 2q - r = 4p, 2r = q, r = 2p; prove: q = r
give the statement and reason using properties of equality.
Solving the problem as per a linear equation, it can be proved that q = r.
A linear equation is an algebraic equation in the form of y = mx+ b. The highest power of a variable in a linear equation is always 1. Such equations always form a straight line on the graph.
From equation 1 we can write,
2q - r = 4p.................(1)
or, 2q - 4p = r ( side switched ) ................(2)
Now, 2p = r
or, 4p = 2r and we know 2r = q
Hence, we can write 4p = q ...............(3)
If we put equation (3) in (1)
we will get, 2q - q = r
or, q = r
q = r is proved.
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I’m stuck please help.
Answer:
Step-by-step explanation:
PS =5 because PS's line is parallel to 5 the line.
So now all that is left is the angle one
m∠Q =105° we can come to this conclusion because 105° is parallel to m∠Q
If you are still confused please, let me know! :)
can y’all please help me figure out what this problem is g=6x, for x
Answer:
x=g/6
Step-by-step explanation:
because if u do the inverse of multiplication which is division on both sides it gives u that and solves for x
.Two angles form a linear pair. The measure of one
angle is 1/3 the measure of the other angle.
Answer:
45o and 135o
Step-by-step explanation:
The sum of angles of a linear pair is always equal to 180°.
So if the first angle is x,
then the second angle is 3x
x + 3x = 180
4x = 180
x = 45
then 3x = 135
what operation will you use to solve the x - 3 = 12
Answer: addition
Step-by-step explanation: add three to both sides to eliminate the 3 on the X side and isolate the X
Answer:
X=9
In order to find X u must subtract 3 from 12
12-3=9
so X=9
Refelection about what you've learn about factors and so be it 150 words
Answer:
the throwing back by a body or surface of light, heat, or sound without absorbing it.
"the reflection of light" The reflection factor of a body is the ratio of the light reflected by the body to the incident light.
Find 65% of 300 kilometers.
Answer: 195
Step-by-step explanation:
65%=65/100
300 * 65/100=
300 * 6.5/10=
300 * 13/20=
3900/20=
390/2=195
EXAMINAR: Mr Shiwarira
QUESTION 1
1.1
1.2
1.3
1.3.1
1.3.2
INFORMAL TEST
Add (6a + 4b-7c) and (12a-10b + 15c)
Subtract (3x + 8y - 10z) from (7x - 12y + 18z)
Simplify the following:
25a³ x 4a²
24a³b ÷ 4a²b
Addition of algebraic terms
(6a+4b-7c) + (12a-10b+15c)
⇒ simplify each term
⇒6a+4b-7c+12a-10b+15c
⇒18a-6b+8c
subtraction of algebraic terms
(7x-12y+18z) -(3x+18y-10z)
⇒ 7x-12y+18z-3x-18y+10z
⇒4x-30y+28z
: A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 25 is the square of 5
Check : 4 is the square of 2
Check : a2 is the square of a1
Factorization is : (5a + 2) • (5a - 2)
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Help please just look at the pic ig
Answer:
0.00037
Step-by-step explanation:
pls help ty i’m so bad at math
Answer:
pls rate as brainliest is you really want to appreciate it