Which of the following inequalities would have the solution set graphed below?
t - 2 ≤ 0
t - 3 ≤ 5
t + 2 ≤ 0
t + 3 ≤ 1
Answers
Answer:
t - 2 ≤ 0
Step-by-step explanation:
Given inequality
t- 2 ≤ 0
Add 2 on both sides of the inequality without changing the meaning
t - 2 + 2 ≤ 0 + 2
or
t ≤ 2
Looking at the number line given, we can see that all numbers to the left of 2 including 2 are part of the solution set
Hence the solution set graphed is t- 2 ≤ 0
Related Questions
The topic of this problem is "Scale Factors". This is the information: Solid 1 has: * A surface area of 128 cm^2* A volume of 15360 cm^3 Solid 2 has: * An unknown surface area. * A volume of 6480 cm^3 I need to find the surface area of solid 2.
Answers
Let the unknown surface area be x
The ratio of the surface area to volume in solid 1 must be equal to the ratio of the surface area to volume in solid 2.
[tex]\begin{gathered} \frac{128}{15360}=\frac{x}{6480} \\ \Rightarrow x=\frac{128}{15360}\times6480=54\text{ cm}^2 \end{gathered}[/tex]Hence, the surface area of solid 2 is 54 cm^2
Find the value of x.
Answers
Answer:
x = 82
Step-by-step explanation:
The sum of the interior angles of a polygon with n sides = (n-2) x 180°
This polygon has 7 sides so the sum of its interior angles
= (7-2) x 180°
= 5 x 180°
= 900°
Adding up the given angles we get
x + 160 + 2x + 125 + 110 + 112 + 147 = 900
3x + 654 = 900
3x = 900 - 654
3x = 246
x = 246/3 = 82
Answer:
x = 82
Step-by-step explanation:
Sum of interior angles of a polygon
[tex]S=(n-2) \times 180^{\circ}[/tex]
where n is the number of sides.
The given polygon has 7 sides:
n = 7To find the value of x, substitute the sum of the interior angles and the found value of n into the formula and solve for x:
[tex]\implies x+160+2x+125+110+112+145=(7-2)\times 180[/tex]
[tex]\implies x+2x+160+125+110+112+145=5\times 180[/tex]
[tex]\implies 3x+654=900[/tex]
[tex]\implies 3x+654-654=900-654[/tex]
[tex]\implies 3x=246[/tex]
[tex]\implies \dfrac{3x}{3}=\dfrac{246}{3}[/tex]
[tex]\implies x=82[/tex]
Therefore, the value of x is 82.
(8) Write the equation of the line that passes through the points (12, 4) and 1 (22,9).
Answers
Answer:
Step by step solution:
The
Use the Law of Sines to find the indicated angle 0. (Assume C = 67º. Round your answer to one decimal place.)
Answers
Answer
40.3º
Explanation
The Sine rule is used to solve angles and sides of triangle.
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the sine rule is given as
[tex]\frac{\text{ Sin A}}{a}=\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]For this triangle,
Angle A = ? (Isn't given)
Angle B = θ
Angle C = 67º
Side a = ? (Isn't given)
Side b = 56.3
Side c = 80.2
We are then told to find the Angle B, that is, θ
So, using the later parts of the Sine Rule
[tex]\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]Substituting the known variables, we have
[tex]\begin{gathered} \frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c} \\ \frac{\text{ Sin }\theta}{56.3}=\frac{\text{ Sin }67º}{80.2} \\ \text{ Sin }\theta=\frac{56.3\times\text{ Sin }67º}{80.2}=\frac{56.3\times0.9205}{80.2} \\ \text{ Sin }\theta\text{ = 0.6462} \\ \theta=Sin^{-1}(0.6462)=40.3º \end{gathered}[/tex]Hope this Helps!!!
Sean has $900 in a savings account that earns 5% annually. The interest is notcompounded. How much will he have in 1 year?Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), ris the interest rate expressed as a decimal, and t is the time in years.Submit
Answers
Answer:
The interest after one year is $45
Explanation:
Principal = $900
Rate = 5%
Time = 1 year
I = P x R x T / 100
I = 900 x 5 x 1 / 100
I = 4500/100
I = $45
Therefore, the interest after one year is $45
Stella bought 4 chicken wings for $7.60. What's the unit cost of one wing?
Answers
Answer:
$1.90 for each chicken wing
Step-by-step explanation:
7.6 / 4 = 1.9
Answer: $1.90
Step-by-step explanation:
divide 7.60 by 4. you get 1.9 :)
Solve: 1/4 (36x – 16) = 5x – 18
Answers
We must solve for x the following equation:
[tex]\frac{1}{4}(36x-16)=5x-18.[/tex]1) We multiply both sides by 4, and we get:
[tex]\begin{gathered} 36x-16=4\cdot(5x-18), \\ 36x-16=20x-72. \end{gathered}[/tex]2) We pass the -16 at the left side as +16 at the right side:
[tex]\begin{gathered} 36x=20x-72+16, \\ 36x=20x-56. \end{gathered}[/tex]3) We pass the -56 at the right side as +56 at the left side:
[tex]\begin{gathered} 36x-20x=-56, \\ 16x=-56. \end{gathered}[/tex]4) Finally, dividing both sides by 16, we get:
[tex]x=-\frac{56}{16}=-3.5.[/tex]Answerx = -3.5
PLEASE HELP IM SICK AND I DONT UNDERSTAND.DUE IN 30 MINS!!!!!!
Answers
Answer:
x = 11
Step-by-step explanation:
all angles in a triangle will add up to 180.
So we can start with the equation:
(19 + x) + (7 + 8x) + angle str = 180.
we are given the angle stv. This angle equals 125.
the angle of a straight line is 180. In order to find the angle next to another angle like angle stv and str are, all you have to do is subtract the angle from 180.
So to find str:
180 - 125 = 55
we already have one of our angles which is 55
so the equation is now:
(19 + x) + (7 + 8x) + 55 = 180
now do some simple simplification:
(19 + x) + (7 + 8x) + 55 = 180
______________ -55_-55
(19 + x) + (7 + 8x) = 125
26 + 9x = 125
-26_____-26
9x = 99
99/9 = 11
x = 11
Therefore, x = 11
Simplify the expression 6x4÷2+3^3
Answers
Answer:12+27= 39.
Step-by-step explanation: You would do 6x4 first due to PEMDAS. Then you would do 24 divided by 2 which is 12. Then, you add it to 3 to the power of 3, which is 39. The simplified equation would be be 12+27.
negative h over 4 equal 15 ?
Answers
7=- (1/5)x
[tex]\begin{gathered} 7=-\frac{1}{5}x \\ 7\cdot-5=x \\ -35=x \end{gathered}[/tex]The table shows the number of bottles collected for recycling. Round the number of bottles collected by each grade to the nearest ten, nearest hundred, and nearest thousand. Choose from the rounded numbers in the box to fill in the table. 2,000 2,200 2,220 2,230 2,300 2,600 2,660 2,670 2,700 3,000 Grade Nearest Ten Nearest Hundred Number of Bottles Collected 2,227 2,664 Nearest Thousand 3 4
Answers
Explanation
Step 1
[tex]2227[/tex]a)nearest ten
If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
so,In this case, the digit to the right (7) is 5 or above. So, we add 1 to the tens place (2). The digit(s) at the right (7) becomes 0, thus we get 2230 as answer.
[tex]\begin{gathered} 2227\Rightarrow2230 \\ \text{because the 7 is greater or equak than 5} \end{gathered}[/tex]b)Nearest hundred
Remember that the hundreds place is three moves from the left of the decimal point (if it exists). To round to the nearest hundred (nearest 100), we use the tens place to determine whether the hundreds place rounds up or stays the same,so
in this case: 27
[tex]\begin{gathered} 2227\Rightarrow2200 \\ \cdot\text{because 27is smaller than 50} \end{gathered}[/tex]c)nearest thousand
Remember that the thousand place is four moves from the left of the decimal point (if it exists). To round to the nearest thousand (nearest 10000), we use the hundreds place to determine whether the thousands place rounds up or stays the same
so,in this case:227
[tex]\begin{gathered} 2227\Rightarrow2000 \\ \text{because 227 is smaller than 500} \end{gathered}[/tex]Step 2
now, for :
[tex]2664[/tex]a) nearest ten
[tex]\begin{gathered} 2664\Rightarrow2660 \\ \text{because 4 is smaller than 5} \end{gathered}[/tex]b)nearest hundred
[tex]\begin{gathered} 2664\Rightarrow2700 \\ \text{because 64 is greater than 50} \end{gathered}[/tex]c)nearest thousand
[tex]\begin{gathered} 2664\Rightarrow3000 \\ \text{because 664 is greater than 500} \end{gathered}[/tex]I hope this helps you
Which model represents 3×15?
Answers
(3x10)(3x5)=45
May I please get help with this for I am confused on were I should put the triangle translation as I have tried multiple times but still could not get it right
Answers
Explanation
Labeled the given triangle as shown below:
The coordinates of triangle ABC are:
A(-4, -2)
B(0, -4)
C(2, 2)
The translation of the triangle 4 units to the left and 3 units down will be given as:
A(-4, -2) → A'(-8, -5)
B(0, -4) → B'(-4, -7)
C(2, 2) → C'(-2, -1)
So, the diagram of the triangle after a translation of 4 units to the left and 3 units down is shown below:
A man who weighs 200 lbs goes on a diet and loses 16%of his body weight. How much weight, in ounces, did he loses?
Answers
We know that the man loses 16% of his weight, to find how much was that we just have to multiply his total weight by 0.16, like this:
lost weight = 0.16 * total weight, by replacing 200 lbs for total weight, we get:
lost weight = 0.16 * 200 = 32
Now we need to express 32 lbs in ounces, we can do this by multiplying the weight in pounds by 16, since 1 pound is equivalent to 16 ounces, then we get:
lost weight in ounces = 32 * 16 = 512
Then, the man lost 512 ounces
help me please
thank you
Answers
Answer:
Domain: A, [tex][1, \infty)[/tex]
Range: A, [tex][-4, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
A metallurgist has one alloy containing 29% titanium and another containing 70% titanium. How many pounds of each alloy must he use to make 54 pounds of a third alloy containing 52% titanium? (Round to two decimal places if necessary.)
Answers
The weights of the first and second alloys to be used are 23.707 and 30.293 pounds.
The percentage of titanium in the first alloy is 29%.The percentage of titanium in the second alloy is 70%.Let the weight of the first alloy taken be "x".Let the weight of the second alloy taken be "y".The percentage of titanium in the third alloy is 52%.The weight of the third alloy is 54 pounds.The weights of the first and second alloys taken are equal to the weight of the third alloy.x + y = 54We also know that the third alloy is made using the first and second alloys.29x + 70y = 52*5429x + 70y = 2808We have a system of two equations in two variables.Upon solving, we get the values of "x" and "y".The value of "x" is 23.707.The value of "y" is 30.293.To learn more about equations, visit :
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let f(x) = 4x -8 and g(x) =1/x^2
find (f . g) (x), then choose the correct domain for (f . g) (x).
Answers
Multiplication of two real functions, (f . g) (x) is 4/x - 8/x² and the correct domain for (f . g) (x) is (-∞,0) U (0,∞)
Let f(x) and g(x) are two real functions.
f(x)= 4x -8
g(x)= 1/x²
then
(f . g)(x) = (4x -8 ) x (1/x²)
(f . g)(x) = 4/x - 8/x²
The set of all the initial elements in all the ordered pairs in a relation R is known as the domain of R.
domain for (f . g) (x).(f . g)(x) = 4/x - 8/x²we know that f(x) is undefined at x=0
so, domain will be
(-∞,0) U (0,∞)
Multiplication of two real functions, (f . g) (x) is 4/x - 8/x² and the correct domain for (f . g) (x) is (-∞,0) U (0,∞)
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A trade magazine routinely checks to drive-through service times of fast food restaurants and 95% confidence interval that results from examining 501 customers in one fast food chains drive-through has a lower bound of 166.2 seconds in an upper bound of 169.6 seconds what does this mean?
Answers
The confidence level of an interval is the probability that the mean of an distribution rest inside this interval.
Then, there is a 95% probability that the mean drive-through service time of this fast-food chain is between 166.2 seconds and 169.6 seconds.
Interpret the decay factor from the exponential function y = 900(0.65)3.
Answers
Answer:
0.65
Explanation:
If we have an exponential equation of the form
[tex]y=ab^x[/tex]where
a = inital amount
b = decay factor
Now in our case, the function we have is
[tex]y=900(0.65)^x[/tex]therefore,
the inital amount = 900
the decay factor = 0.65
Hence, the decay factor of the exponential function is 0.65.
What is the expression in simplest radical form?√432
Answers
ANSWER :
12√3
EXPLANATION :
From the problem, we have the radical expression :
[tex]\sqrt{432}[/tex]We need to factor 432 in which one of the factors is a perfect square.
Note that 432 is 3 x 144
and 144 is a perfect square.
Then :
[tex]\sqrt{432}=\sqrt{3\times144}[/tex]Extracting the root of 144 which is 12 since 12 x 12 = 144.
[tex]\sqrt{3\times144}=12\sqrt{3}[/tex]Can someone please help me? Im confused.
Answers
Answer:
12
Step-by-step explanation:
9/12 to y/16 (the ratio of the short side relative to the long side)
0.75 = y/16 (a ratio can be expressed as a decimal)
16(0.75) = y (multiply 16 to both sides, isolate y)
y = 12 (b/c three-quarters of 16 is 12)
Answer:
y = 12
Step-by-step explanation:
Δ RSQ and Δ ROP are similar ( AA postulate ) then the ratio of corresponding sides are in proportion, that is
[tex]\frac{SQ}{OP}[/tex] = [tex]\frac{RS}{RO}[/tex] ( substitute values )
[tex]\frac{y}{16}[/tex] = [tex]\frac{9}{12}[/tex] ( cross- multiply )
12y = 16 × 9 = 144 ( divide both sides by 12 )
y = 12
A rectangle has vertices at (0, 0), (3,0), and (0,6). What is the area of the rectangle? у 10- 9- 8 ? square units 7 6 DONE 5- 4 3- 2 1 х o i 2 3 4 5 6 ; 8 9 10
Answers
Shawn, this is the solution to the exercise:
Width of the rectangle = 3 units (from 0 to 3)
Length of the rectangle = 6 units (from 0 to 6)
In consequence, the area is:
• Area = Width * Length
,• Area = 3 * 6
,• Area = 18 units²
Which expression is equivalent to 8x3 − 27 when factored completely?
Answers
The given expression is
[tex]8x^3-27[/tex]To find the equivalent expression, we use the formula for the difference of perfect cubes.
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]But, we have to express the numbers 8 and 27 as cubic powers.
[tex]\begin{gathered} 8=2\cdot2\cdot2=2^3 \\ 27=3\cdot3\cdot3=3^3 \end{gathered}[/tex]Then, we know that a and b are
[tex]\begin{gathered} a=2x \\ b=3 \end{gathered}[/tex]So, the difference would be
[tex](2x)^3-(3)^3[/tex]Once we have the difference expressed in cubes, we apply the formula using the a and b values we determined before.
[tex](2x)^3-(3)^3=(2x-3)((2x)^2+(2x)(3)+(3)^2)_{}=(2x-3)(4x^2_{}+6x+9)[/tex]Therefore, the factors are
[tex](2x-3)(4x^2+6x+9)_{}[/tex]Need help with homework
Answers
We have an original function, this is:
[tex]y=x^2[/tex]In addition, we have a second function that is based on the original function but with a translation.
As you can see in the above image, the function in the red line is moved 6 units to the right.
Let's remember one of the rules of function translation.
y = f(x) Original function
y = f(x-c) Where it is translated horizontally, "c" units to the right.
Since in this case, we have 6 units of translation to the right the equation of the function shown in red is:
[tex]y=(x-6)^2[/tex]
el ancho de un rectángulo es el doble de su largo si el perímetro es de 78 pies cuál es el largo y el ancho?
Answers
The width of the rectangle is twice its length.
So lets assume the width to be------ 2x feet
Then the length will be ------ x feet
The perimeter is given as ---- 78 feet
The formula for perimeter of a rectangle is ; 2[ l+w ] where l is length and w is width
Use the assumed measurements in the equation for perimeter as;
2[ l+w ] =78
2{x +2x] =78
2x +4x =78
6x = 78
x=13 feet
Length = x = 13 feet
Width = 2x = 2*13 = 26 feet
For his long distance phone service, Bill pays an $8 monthly fee plus 6 cents per minute. Last month, Bill's long distance bill was $13.64. For how many minutes was Bill billed?
Answers
The long distance bill is
Monthly fixed $8
Monthly variable $0.06 per minute
If the cost is c and minutes m, we can write cost as:
[tex]c=8+0.06m[/tex]Given, last month's cost, c, to be $13.64, we want to find the minutes.
We put 13.64 into 'c' of the formula found and find m.
Shown below:
[tex]\begin{gathered} 13.64=8+0.06m \\ 13.64-8=0.06m \\ 5.64=0.06m \\ m=\frac{5.64}{0.06} \\ m=94 \end{gathered}[/tex]Ansswe
Write an equivalent exponential expression to the expression 2^6 x 8^6.A 10^6B 16^6C 16^12D 16^36
Answers
so the answer is B
In the past 2 months, your bank account has decreased by $80.00 The account decreased by the same amount each month What was the change
each month?
Answers
Answer:
$40.00
Step-by-step explanation:
In the first month your money went down by $40 then the second month another $40, so in total $80 has been lost
The circumference of a wheel is 150 cm what would be the diameter
Answers
With a circumference of 150cm, the diameter of the wheel will be
47.77 cm
by using the formula d = C/π
Explanation:The circumference of a circle is the length of one complete lap around it. It is the outer measurement, Diameter is the length of the line segment that divides a circle in half. while the diameter is the inner measurement.Circumference is calculated as,
C = dπ
is the formula for calculating circumference with diameter.
As a result, to calculate the diameter from the circumference, divide the circumference value by π, where π = 22/7 or 3.142.
⇒ d= C/π
here given C= 150 cm
by substituting the values ,
d = 150/3.14
= 47.77 cm
∴ the value of diameter of the wheel with a circumference of 150cm will be 47.77 cm
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I know how to do everything except the #1 step
Answers
Answer:
[tex]A^{\doubleprime}(-6,-21),B^{\doubleprime}(6,-15)\text{ and C}^{\doubleprime}(-3,-12)[/tex]Explanation:
Given the coordinates A, B and C as follows:
[tex]A(-3,4),B(1,2)\text{ and C(-2,1)}[/tex]If a point is reflected across the x-axis, we have the transformation rule:
[tex](x,y)\to(x,-y)[/tex]Thus, the image of A are:
[tex]A(-3,-4),B(1,-2)\text{ and C(-2,-1)}[/tex]Next, a translation by <1,-3>:
[tex]\begin{gathered} A(-3+1,-4-3),B(1+1,-2-3)\text{ and C(-2+1,-1-3)} \\ A(-2,-7),B(2,-5)\text{ and C}(-1,-4) \end{gathered}[/tex]Finally, a dilation by K=3 gives the final image required:
[tex]A^{\doubleprime}(-6,-21),B^{\doubleprime}(6,-15)\text{ and C}^{\doubleprime}(-3,-12)[/tex]