Answer: 1) Each of the 126 cubes has a volume = (1/3)3 = 1/3 × 1/3 × 1/3 = 1/27 cubic feet.
2) It takes 126 cubes to fill the bin, so the bin has a volume of 126 × 1/27 = 126/27 cubic feet. (Don't do this division yet - leave it as an improper fraction)
3) The volume of the bin is also given by the formula Volume = Area of Base × Height. Plus we know the volume is 126/27 cubic feet and the height is 2 1/3 = 7/3 of a foot, so:
Step-by-step explanation: Volume = Area of Base × Height
126/27 = Area of Base × 7/3
126/27 × 3/7 = Area of Base
The area of the base of bin is 2 feet².
What is Volume of Cube?The formula of volume of the cube is given by: Volume = a³, where a is the length of its sides or edges.
Given:
Edge = 1/3 feet
Volume of 1 cube= l³= (1/3)³ = 1/27
Totals cubes= 126
So, Volume of 126 cube= 126 x 1/27 = 126/ 27
Then, Volume of Plastic Bin= Area of base x height
126 / 27 = Area of base x 7/3
Area of base = 126 /27 x 3 /7
Area of base = 2 ft²
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Laura won a charity raffle. Her prize will be randomly selected from the 9 prizes shown below. The prizes include 4 rings, 3 cameras, and 2 headsets. Find the odds against Laura winning a camera. Find the odds in favor of Laura winning a camera.
The odds in favor of Laura winning a camera 1/3.
What are the odds in favor?
The ratio of favorable outcomes to bad outcomes is known as the odds of the probability of a specific event.
The ratio of positive outcomes to unfavorable outcomes determines the odds in favor of a specific event.
Odds against are determined by dividing the number of unfavorable results by the number of favorable results.
9 prizes consist of 4 rings, 3 cameras, and 2 headsets.
Odds in favor = ( Number of favorable outcomes/ Number of unfavorable outcomes)
The odds in favor of Laura winning a camera = 3/9= 1/3
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Graph the equation of a line y= X/6 -3
Solution
To graph the line y = x/6 - 3,
Since the y-intercept is -3
This picture should be of help
The price p and the quantity x sold of a small flat-screen television set obeys the demand equation below.
a) Express the revenue R as a function of x. Use the formula R=px
b) How much should be charged for the television set if there are 70 television sets in stock?
c) How much should be charged for the television set if there are 1250 television sets in stock?
d) What is the revenue when there are 1250 sets in stock?
p= .14x +350
a. The revenue R as a function of x will be R = px.
b. The amount that charged for the television set if there are 70 television sets in stock is R / 70.
c. The amount that charged for the television set if there are 1250 television sets in stock is R / 1250
d. The revenue when there are 1250 sets in stock is 1250p
How to illustrate the information?1. From the information, the price p and the quantity x sold of a small flat-screen television is.
given. The revenue will be:
= Price × Quantity
= p × x.
= px
b. The amount that charged for the television set if there are 70 television sets in stock will be:
R = px
R = 70p
p = R / 70
c. The amount that should be charged for the television set if there are 1250 television sets in stock will be:
R = px
R = 1250p
p = R / 1250
d. The revenue when there are 1250 sets in stock will be:
= Price × Quantity
= p × 1250
= 1250p
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Select ALL the correct answers. Consider the graph given below. A diagonal curve declines from (negative 2, 10), (0, 6), (1, 4), (2, 2), (3, 0), (4, negative 2), (5, negative 4), (6, negative 6), (7, negative 8),and (8, negative 10) on an x y coordinate plane. Determine which sequences of transformations could be applied to the parent function, f(x) = x, to obtain the graph above. Reflect over the x-axis, vertically stretch by a factor of 2, and then shift up 6 units Shift right 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2 Shift left 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2 Shift left 2 units, reflect over the y-axis, and then vertically stretch by a factor of 6 Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2
The sequence of transformations needed to transform the parent function f(x) into the linear function g(x) = 6 - 2x is given as follows:
Reflect over the x-axis, vertically stretch by a factor of 2, and then shift up 6 units.Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units.Linear function and transformationA linear function is defined according to the following rule:
y = mx + b.
In which:
m is the slope of the function, which is by how much y changes by when x changes by 1.b is the intercept of the function, which is the value of y when x = 0.From the stated graph, we have that when x = 0 and y = 6, and when x increases by 1, y decays by 2, hence the function is defined as follows:
y = -2x + 6.
The parent function is:
f(x) = x.
Then, to generate the transformed function, we have that:
x -> -x, hence the function was reflected over any of the axis.-x -> -2x, hence there was a vertical stretch by a factor of 2.-2x -> -2x + 6, meaning that the function was shifted up 6 units.Using these three bullet points, the correct options were chosen.
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Answer:
Your welcome
Step-by-step explanation:
weiyr the coordinates of the two points on the line then find the slope
ANSWER:
two points are (3,4) and (3,0)
the slope is undefined or indeterminate
SOLUTION:
since the denominator of the slope (change in x) is 0, the slope, change in y over change in x is indeterminate
A 4 1/2 bag of raisians must be divided equally into 1/4 bag portions
Answer:
18 portions
Step-by-step explanation:
1/4 x 4 1/2 = 18
The adult daily dosage for a certain medicine is 90 mg (milligrams) of medicine for every pounds of body weight.
At this rate, find the daily dose for a man who weighs 175 pounds.
A daily dose of 15750 mg is required of a certain medicine for a man weighing 175 pounds
An adult daily dose of a certain medicine = 90 mg for every pound of body weight
Daily dose: The adult daily dose specifies the amount of drug dose in mg that must be taken within 24 hours as per the body weight of the person. The body weight of the person determines how much dose is required for the medicine to be effective in the body.
Weight of the man = 175 pounds
The daily dose for a man is given:
Weight of man*Daily dose per pound of body weight
= 175*90
= 15750
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What is the area of the triangle shown below?131310units2
SOLUTION
We want to find the area of the triangle in the image.
To do this, we will make use of the Heroes formula which states
[tex]\begin{gathered} A=\sqrt{s(s-a)(s-b)(s-c)} \\ where\text{ s =}\frac{a+b+c}{2} \\ a,b\text{ and c are the sides of the triangle } \end{gathered}[/tex]applying this, we have
[tex]\begin{gathered} s=\frac{13+13+10}{2} \\ s=\frac{36}{2} \\ s=18 \end{gathered}[/tex]The area A becomes
[tex]\begin{gathered} A=\sqrt{18(18-13)(18-13)(18-10)} \\ =\sqrt{18\times5\times5\times8} \\ =\sqrt{3,600} \\ =60\text{ units}^2 \end{gathered}[/tex]Hence the answer is 60 square units
Find the time (in years) for the investment to double. (Round your answer to two decimal places)
Solution
Step 1
Write the compound interest formula
[tex]\text{A = P\lparen1 + }\frac{r}{n})^{nt}[/tex]Step 2
n = 4 (quarterly)
[tex]\begin{gathered} \text{P = x} \\ \text{A = 2x} \\ r\text{ = 7}\frac{3}{4}\text{ = 7.75\% = 0.0775} \end{gathered}[/tex]Step 3:
Substitute in the formula to find t.
[tex]\begin{gathered} 2x\text{ = x\lparen 1 + }\frac{0.0775}{4})^{4t} \\ \text{2 = \lparen1 + 0.019375\rparen}^4t \\ \text{2 = 1.019375}^{4t} \\ Take\text{ natural logarithm of both sides} \\ In(2)\text{ = 4t In\lparen1.019375\rparen} \\ 4t\text{ = }\frac{ln(2)}{ln(1.019375)} \\ 4t\text{ = 36.12080351} \\ t\text{ = }\frac{36.12080351}{4} \\ t\text{ = 9.03 years} \end{gathered}[/tex]Final answer
t = 9.03
HELP PLEASE URGENT I ONLY HAVE 30MINS PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE
Using the properties of parallel lines we find the value of x is 9 and the value of y is 13.
In geometry, parallel lines are coplanar, straight lines that never intersect.
Any parallel planes in the same three-dimensional space are those that never intersect. Parallel curves are those that have a predetermined minimum separation between them and do not touch or intersect. If a line and a plane in three-dimensional Euclidean space do not intersect at a point, they are also said to be parallel. On the other hand, skew lines are two noncoplanar lines. A transversal is a line that crosses across two other lines in the same plane at two separate points. Transversals play a crucial role in establishing if two or more other lines in the Euclidean plane are parallel.15). In the given figure the two angles represented by 12x+1 and 15x -26 are equal. as they are alternate exterior angles.
We know from the property of parallel lines that they are equal.
Therefore:
12x+1 = 15x -26
or, 12x-15x = -26-1
or, -3x = -27
or, x = 9
Therefore the angles are 12x + 1 = 109
Now,
109 + 4y-9 +28 =180
or, 4y = 180 - 128
or, y = 13.
Therefore as the line l and m are parallel the value of x is 9 and the value of y is 13 .
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Find the equation for the line through points (2,0) and (8,4) use y=Mx+b
Explanation:
To find the equation with the form y = mx + b, we can use the following equation:
[tex]y=m(x-x_1)+y_1[/tex]Where m is the slope and it is ca
On August 31, 2024, Shocker borrows $57,000 from a local bank. A note is signed with principal and 9% interest to be paid on August 31, 2025. Record the adjusting entry for interest for Shocker at its year-end of December 31.
(a)Dr Unearned Revenue $1,400
Cr Service Revenue $1,400
(b)Dr Advertising Expense $880
Cr Prepaid Advertising $880
(c)Dr Salaries Expense $7,800
Cr Salaries Payable $7,800
(d)Dr Interest Expense $1,360
Interest Payable $1,360
Journal entry preparation
(a) According to the information provided, Shocker gets a $4,200 payment from a client for services done over the following three months, which implies the journal entry will be:
Unearned Dr. $1,400 in revenue
($4,200 x 1/3)
$1,400 in Cr Service Revenue
(a) Based on the information provided, we were told that the firm pays a local radio station $2,640 for radio advertisements throughout the months of December, January, and February, which implies that the Journal entry would be entered as:
Dr. Advertising Cost $880
($2,640 x 1/3)
$880 in Cr Prepaid Advertising
(c) According to the information provided, the corporation Employee salaries for the month of December were $7,800, which will be paid on January 7, 2022, implying that the Journal entry would be:
Dr Salaries Cost $7,800
$7,800 in Cr Salaries
(d) According to the facts provided, Shocker borrows $68,000 from a local bank, which implies the Journal entry will be:
$1,360 in Dr. Interest Expense
($68,000 x 6% x 4/12)
$1,360 in payable interest
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Solve the equation for x, accurate to three decimal places: e4x − e2x = 12.x = 1.280x = 1.866x = 0.549x = 0.693
Given:
[tex]e^{4x}-e^{2x}=12[/tex]To Determine: The value of x
Solution
[tex]\begin{gathered} e^{4x}-e^{2x}=12 \\ (e^x)^4-(e^x)^2=12 \end{gathered}[/tex][tex]\begin{gathered} let:a=e^x \\ Therefore, \\ (e^x)^4-(e^x)^2=12 \\ a^4-a^2=12 \\ a^4-a^2-12=0 \end{gathered}[/tex]Solve the derived equation by factorizing completing
[tex]\begin{gathered} a^4-a^2-12=0 \\ a^4-4a^2+3a^2-12=0 \\ a^2(a^2-4)+3(a^2-4)=0 \\ (a^2-4)(a^2+3)=0 \\ a^2-4=0,or,a^2+3=0 \end{gathered}[/tex][tex]\begin{gathered} a^2-4=0 \\ a^2-2^2=0 \\ diiference\text{ of two square is expanded as} \\ a^2-b^2=(a-b)(a+b) \\ Therefore \\ a^2-2^2=0 \\ (a-2)(a+2)=0 \\ a-2=0,or,a+2=0 \\ a=2,a=-2 \end{gathered}[/tex][tex]\begin{gathered} Also,a^2+3=0 \\ a^2=-3(No\text{ solution because square root of a negative number is an imaginary number\rparen} \end{gathered}[/tex]Therefore
[tex]a=2,or,a=-2[/tex][tex]\begin{gathered} e^x=a \\ e^x=2,or,e^x=-2(no\text{ solution\rparen} \\ x=ln2 \\ x=0.693 \end{gathered}[/tex]Hence, the value of x is 0.693
Which property is shown -2x1/-2=1
Answer:
Multiplicative inverse
Step-by-step explanation:
Find the measures of the sides of the sides of triangle JKL then classify it by its sides if J(-7, -7), K(-9 1), L(-1, -1)
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ J(\stackrel{x_1}{-7}~,~\stackrel{y_1}{-7})\qquad K(\stackrel{x_2}{-9}~,~\stackrel{y_2}{1}) ~\hfill JK=\sqrt{(~~ -9- (-7)~~)^2 + (~~ 1- (-7)~~)^2} \\\\\\ ~\hfill JK=\sqrt{( -2)^2 + ( 8)^2} \implies \boxed{JK=\sqrt{ 68 }}[/tex]
[tex]K(\stackrel{x_1}{-9}~,~\stackrel{y_1}{1})\qquad L(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill KL=\sqrt{(~~ -1- (-9)~~)^2 + (~~ -1- 1~~)^2} \\\\\\ ~\hfill KL=\sqrt{( 8)^2 + ( -2)^2} \implies \boxed{KL=\sqrt{ 68 }} \\\\\\ L(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad J(\stackrel{x_2}{-7}~,~\stackrel{y_2}{-7}) ~\hfill LJ=\sqrt{(~~ -7- (-1)~~)^2 + (~~ -7- (-1)~~)^2} \\\\\\ ~\hfill LJ=\sqrt{( -6)^2 + (-6)^2} \implies \boxed{LJ=\sqrt{ 72 }}[/tex]
well, let's notice, the triangle has two sides that are twins, JK and KL, that means is an isosceles, and isosceles triangle is a triangle with twin sides.
A political gathering in South America was attended by 8,475 people. Each of South America's 12 countries and 3 territories was equally represented. How many representatives attended from each country?
There were 707 representatives who attended political gatherings from each country in South America.
We have been given that a political gathering in South America was attended by 8,475 people.
Each of South America's 12 countries and 3 territories were equally represented.
The number of representatives attended from each country is the ratio of the total number of people in the gathering to the total number of countries.
The number of representatives :
⇒ total number of people in the gathering / total number of countries
The number of representatives = 8,475 / 12
The number of representatives = 706.25 ≈ 707
Hence, there were 707 representatives who attended political gatherings from each country.
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Factor p(x) into linear factor
The two other linear factors of the polynomial when it is given that k = -1 is a zero of the given polynomial are (x+1)(x-4)
In the above question, A cubic polynomial is given as follows
P(x) = [tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 7x - 4
K = -1
We need to find the, linear factors of the polynomial when it is given that k = -1 is a zero of the given polynomial
So, we got that ( x +1 ) is a one linear factor of P(x). As the highest degree of the polynomial is 3 so there will be three zeroes of the given polynomial. Therefore, We need to find others two
If we divide P(x) = [tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 7x - 4 by ( x + 1 ) by long division method we'll get, [tex]x^{2}[/tex] -3x - 4
Now we'll solve the quotient by squaring method, to get the other two
Let's say h(x) = [tex]x^{2}[/tex] -3x - 4
h(x) = [tex]x^{2}[/tex] -3x - 4
h(x) = [tex]x^{2}[/tex] -( 4 -1) x - 4
h(x) = [tex]x^{2}[/tex] -4x + x - 4
h(x) = x( x-4) + 1( x -4 )
h(x) = (x+1)(x-4)
Therefore, the two other linear factors of the polynomial when it is given that k = -1 is a zero of the given polynomial are (x+1)(x-4)
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Find the point-slope form of the equation given: g(5) = 10 and g(2) = 8
will give brainliest
Answer:
[tex]y -10=\cfrac{2}{3} (x -5 )[/tex]========================
Given Two points: (5, 10) and (2, 8)To findThe point-slope form of the equation representing this lineSolutionPoint-slope form is:
[tex]y -y_1=m(x - x_1)[/tex], where (x₁, y₁) is one of the points and m is the slopeFind the slope:
[tex]m=\cfrac{y_2-y_1}{x_2-x_1} =\cfrac{8-10}{2-5} =\cfrac{-2}{-3} =\cfrac{2}{3}[/tex]Use one of the points and the slope to determine the equation of the line:
[tex]y -y_1=m(x - x_1)[/tex], substitute the slope and [tex]y -10=\cfrac{2}{3} (x -5 )[/tex]Answer:
[tex]y-10=\frac{2}{3} (x-5)[/tex]
Step-by-step explanation:
Pre-SolvingWe are given: g(5)=10, and g(2)=8.
The value inside the parentheses is the x value, and the value that it (g(x)) is equal to is the y value.
So, as points, the values are (5, 10), and (2, 8).
The equation wants to be written in point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.
Solving SlopeWe first want to find the slope of the line.
The slope (m) can be found with two points using the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.
We can label the values of the points we were given.
[tex]x_1=5\\y_1=10\\x_2=2\\y_2=8[/tex]
Now, substitute these values into the formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{8-10}{2-5}[/tex]
Subtract.
[tex]m=\frac{-2}{-3}[/tex]
Simplify.
[tex]m=\frac{2}{3}[/tex]
The slope is 2/3.
Since we now have the value of the slope, as well as [tex](x_1, y_1)[/tex], we can plug these values into the formula for point-slope form.
Point-Slope FormRecall that [tex]x_1=5[/tex] and [tex]y_1=10[/tex]; plug these in for [tex]x_1[/tex] and [tex]y_1[/tex] respectively.
[tex]y-10=m(x-5)[/tex]
We also just found the slope, which is 2/3. Plug that in for m.
[tex]y-10=\frac{2}{3} (x-5)[/tex]
Topics: Point-slope form, functions
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1. AI = 400 ft2. Calculate the distance MI for the length of the zipline cable. 3. Calculate the angle at which our zipliners will be descending toward the island . Safety regulations state that the angle at which a zipline cable meets the launching point cannot be smaller than 68 degrees . Please determine if we are in compliance with these regulations
2. The Pythagorean theorem states:
[tex]c^2=a^2+b^2[/tex]where a and b are the legs and c is the hypotenuse of a right triangle.
Applying this theorem to triangle AMI (where AI and MA are the legs and MI is the hypotenuse), we get:
[tex]\begin{gathered} MI^2=AI^2+MA^2 \\ MI^2=400^2+100^2 \\ MI^2=160000+10000 \\ MI^2=170000 \\ MI=\sqrt[]{170000} \\ MI\approx412.31\text{ ft} \end{gathered}[/tex]3. By definition:
[tex]\tan (angle)=\frac{\text{opposite}}{\text{adjacent}}[/tex]Applying this definition to triangle AMI, considering the angle M, we get:
[tex]\begin{gathered} \tan (\angle M)=\frac{AI}{MA} \\ \tan (\angle M)=\frac{400}{100} \\ \tan (\angle M)=4 \\ \angle M=\arctan (4) \\ \angle M\approx76\text{ \degree} \end{gathered}[/tex]This angle is greater than 68°, then it satisfies the regulation.
patterns in proportional relationships, need help with the graph and the process table, i need to find a algebraic rule that represents the relationship between the number of pizzas, x, and the total cost, y.
Since the cost of each medium pizza is $7, then
Assume that the number of pizzas is x and the total cost is y, then
Multiply x by x to find y
The algebraic rule is
[tex]y=7x[/tex]a) Let us complete the table
x: Process: y
0 0 x 7 = 0 0
1 1 x 7 = 7 7
2 2 x 7 = 14 14
3 3 x 7 = 21 21
4 4 x 7 = 28 28
a) We need to find the cost of 10 pizzas, then
Substitute x by 10 in the algebraic rule
[tex]\begin{gathered} y=7(10) \\ y=70 \end{gathered}[/tex]The cost of the 10 pizzas is $70
b) If you have exactly $84, then substitute y by 84 to find x
[tex]\begin{gathered} y=84 \\ 84=7x \end{gathered}[/tex]Divide both sides by 7 to find x
[tex]\begin{gathered} \frac{84}{7}=\frac{7x}{7} \\ 12=x \end{gathered}[/tex]You can buy 12 pizzas buy $84
c) If you buy 0 pizza, then the cost of it is
[tex]\begin{gathered} x=0 \\ y=7(0) \\ y=0 \end{gathered}[/tex]Since zero multiplied by any number give zero
The cost of zero pizza is zero
Because 0 x $7 = $0
Which angle is congruent
Answer:
they can be acute, obtuse, exterior, or interior angles
Step-by-step explanation:
Congruent angles are two or more angles that are identical to each other. the measure of these angles is equal to each other. The type of angles does not make any difference in the congruence of angles, which means they can be acute, obtuse, exterior, or interior angles.
An object is dropped from a height of 144 feet off the ground. The height
h
of the object after
t
seconds can be found using the function
h
(
t
)
=
144
−
16
t
2
When will the height be 128 feet?
seconds
When will the object reach the ground?
seconds
Answer:
The height will reach 128 feet after 1 second.
The object will reach the ground after 3 seconds.
Step-by-step explanation:
Plug in the height into the equation: h(t)=144-16t^2
Solve for t.
Ex:
128=144-16t^2, subtract 144 on both sides
-16=-16t^2, divide -16 on both sides
1=t^2, find the square root of both sides
1=t
Find the area of the figure (Please respond I need help)
Answer: 32 unit squared
Step-by-step explanation:
To find the area you multiply the amount of unit squares on one side of the shape and multiply it by the amount of unit squares at the top of the shape.
Answer:
to find the area of a shape you want to use the formula A=wl which is area is equal to width multiplied by length.
for this exact problem you want to count the squares on one short side and one long side. when you get the two numbers you multiply them
answer is: 4x8=32hope this helped!
Solve 3 < 2x + 1 ≤9 I’m so confused
Answer:
1 < x ≤4
Step-by-step explanation:
3 < 2x + 1 ≤9
Solve for x
Subtract 1 from all sides
3-1 < 2x + 1-1 ≤9-1
2 < 2x ≤8
Divide by 2
2/2 < 2x/2 ≤8/2
1 < x ≤4
Evaluate the expression |2x – 5| for x = –3 and for x = 3.
Answer:
9 and 1 respectively
Step-by-step explanation:
|2(-3)-5| = |-9| = 9
|2(2)-5| = |1| = 1
the vertical lines represents absolute value, this just mean that any negative values are then turned into their positive counterparts.
The grocery store is having a sale on frozen vegetables. 4 bags are being sold for
$11.96. At this rate, what is the cost of:
9 bags
Answer: $98.67
Step-by-step explanation:
Answer:
$26.91
Step-by-step explanation:
11.96 divided 4 = 2.99
2.99 x 9 = $26.91
please hellppp!!!!!!!!!
Answer:
C
Step-by-step explanation:
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
That's the value of x, but you need to evaluate the expression x + 26 for
X = 28.5.
The answer to the expression is 54.6
How to solve variable related problems?1. Switch the positions of the variables in the equation. Starting with "solving for x" (or any other variable) in one of the equations, this "substitution" approach begins. [2] Say your equations are, respectively, 4x + 2y = 8 and 5x + 3y = 9.
2. To "solve for x," divide both sides of the equation.
3. Reconnect this to the other equation. Don't use the equation you just employed; rather, return to the other one.
When a particular variable's value is given to you
we just have to substitute that value in the required equation.
For instance in this question
x= 28.5
And the given equation is x + 26
Therefore the answer is 28.5 + 26 = 54.6 .
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1. There is a two digit number where the difference in the units digit and the tens digit is 5. If the digits are reversed, the
new number is the sum of twice the original number and seven. Find the number.
Answer:
38
Step-by-step explanation:
Let x = the ones digit, and let y = the tens digit.
The number looks like yx.
The value of the original number is
10y + x
"the difference in the units digit and the tens digit is 5."
x - y = 5 Equation 1
When you reverse the digits, you have xy.
The value of the new number is
10x + y
"If the digits are reversed, the new number is the sum of twice the original number and seven."
10x + y = 2(10y + x) + 7 Equation 2
We have a system of 2 equations.
x - y = 5
10x + y = 2(10y + x) + 7
Simplify the second equation.
10x + y = 2(10y + x) + 7
10x + y = 20y + 2x + 7
8x - 19y = 7
x - y = 5
8x - 19y = 7
Solve the first equation for x. Substitute that value for x in the second equation.
x = 5 + y
8(5 + y) - 19y = 7
40 + 8y - 19y = 7
-11y = -33
y = 3
x = 5 + y
x = 5 + 3
x = 8
The digits are:
ones digit: 8
tens digit: 3
The number is 38.