Step-by-step explanation:
General equation for directly proportional variables: y = kx, where k is a real constant
When x = 8, y = 26.
Hence y = 26/8 x or y = 13/4 x.
The equation will be ; y = [tex]\frac{26}{8}[/tex] × x .
It is given that y varies directly with x and y = 26 when x = 8.
We have to find out an equation that represents this relationship.
What will be the 8 times of a number x ?
The number will 8 x.
The direct variation relationship equation will be ;
y = k × x
where ; k = a constant
Given ;
at x = 8 ; y = 26
so the value of k = 26 / 8
and the required equation will be ;
y = ([tex]\frac{26}{8}[/tex]) × x
Thus , the equation will be ; y = [tex]\frac{26}{8}[/tex] × x .
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The perimeter of the rectangle and the triangle shown are the same. Write an equation to represent this situation, and solve for x. Then, find the perimeter of each shape.
Answer:
Step-by-step explanation:
Perimeter of a polygon = Sum of all sides of the polygon
Perimeter of the given rectangle = 2[(5x - 2) + (3x - 0.5)]
= 2[8x - 2.5]
= (16x - 5)
Perimeter of the given triangle = (2x + 3) + (2x + 3) + (10x - 5)
= 14x + 1
Since perimeter of the rectangle and triangle are same, equation will be
(16x - 5) = (14x + 1)
16x - 14x = 5 + 1
2x = 6
x = 3
Perimeter = (16x - 5)
= 48 - 5
= 43 units
Anybody can help ?? 6-3d=5(2-d)
Answer:
d = 4
Step-by-step explanation:
6-3d=10-d
-2d=4
divide d by -2
the answer is 4.
Answer:
6-3d=10-5d...Multiplying 5 with (2-d)
5d-3d=10-6....Taking - 5d to left and writing it +5d and Taking +6 to right and making it - 6
2d=4...Subtracting as required
d=4/2
d=2....Normal division
oceanside bike rental shop charges a 14 dollar fixed fee plus 7 dollars an hour for renting a bike. Tim paid 49 dollars to rent a bike. How many hours did he pay to have the bike checked out?
Answer:
5 hours
Step-by-step explanation:
49 - 14 = 35 and 35 ÷ 7 = 5
At a conference, there are 42 middle school math teachers and 14 middle school
science teachers. If the high school sends half as many math teachers, how many
science teachers should they send if they want to keep the ratios proportional?
4. Show your work:
Answer:
7 science teachers
Step-by-step explanation:
42 and 14 in a ratio 3:1
if 42/2 =21 maths teachers then 7 science teachers
Last one lol please help!!!
Answer:
(C) 50π
Step-by-step explanation:
For this problem, we need to find a way to relate the inner circle, to the square, to the outer circle.
Given that we know the area of a circle is πr^2, and our inner circle has a area of 25π, we can find the radius.
25π = πr^2
25 = r^2
5 = r
Note, that the diameter of the inner circle is parallel to the side of the square, meaning that the diameter of the inner circle is the length of the side of the square.
diameter = 2 * radius
d = 2 * 5 = 10.
Now that we know the value of the side of the square, we can find the length of the diagonal of the square, which is the diameter of the outer circle.
Using the properties of the 45-45-90 right triangle, we can say that the diagonal of the square is the length of the side times sqrt(2).
Outer_Diameter = 10 * sqrt(2)
Now to find the outer area, we need the formula for the area of a circle. Note that the diameter is twice the radius, so we will simply divide by 2.
A = πr^2
A = π * [ ( 10 * sqrt(2) ) / 2 ]^2
A = π * [ 5 * sqrt(2) ] ^2
A = π * 25 * 2
A = 50π
So the area of the outer circle is 50π.
Cheers.
A camping group began with 240 pounds of food and each day consumed about 12 pounds after how many days did they have 180 pounds left does anyone know step by step ?
Answer:
Five days
Step-by-step explanation:
First, we have to find out how much food they ate:
240 - 180 = 60
Now, we have to find out the number of days they would take to eat 60 pounds of food. We can do that by dividing:
60/12 = 5
They took five days to have 180 pounds leftover.
If a biker is riding at 14 miles per hour, and he had been riding for 4 hours in the past 3 days, which unit of measure best fits the distance the biker has ridden
Answer: miles
because hes measuring in miles and i answered this same question today
I just need no. a please help me to prove this.
Answer: see proof below
Step-by-step explanation:
Given: A + B + C = π and cos A = cos B · cos C
scratchwork:
A + B + C = π
A = π - (B + C)
cos A = cos [π - (B + C)] Apply cos
= - cos (B + C) Simplify
= -(cos B · cos C - sin B · sin C) Sum Identity
= sin B · sin C - cos B · cos C Simplify
cos B · cos C = sin B · sin C - cos B · cos C Substitution
2cos B · cos C = sin B · sin C Addition
[tex]2=\dfrac{\sin B\cdot \sin C}{\cos B \cdot \cos C}[/tex] Division
2 = tan B · tan C
[tex]\text{Use the Sum Identity:}\quad \tan(B+C)=\dfrac{\tan B+\tan C}{1-\tan B\cdot \tan C}[/tex]
Proof LHS → RHS
Given: A + B + C = π
Subtraction: A = π - (B + C)
Apply tan: tan A = tan(π - (B + C))
Simplify: = - tan (B + C)
[tex]\text{Sum Identity:}\qquad \qquad \qquad =-\bigg(\dfrac{\tan B+\tan C}{1-\tan B\cdot \tan C}\bigg)[/tex]
Substitution: = -(tan B + tan C)/(1 - 2)
Simplify: = -(tan B + tan C)/-1
= tan B + tan C
LHS = RHS: tan B + tan C = tan B + tan C [tex]\checkmark[/tex]
The ratio of “D”s to “A”s in the school was 6 to 19. If there were 872 As in the school this term, how many Ds were there?
Answer:
The amount of D's there were is 275.4
Step-by-step explanation:
D : A
6 : 19
D : 872
Cross multiply 872 and 6
6*872 = 5232
Then divide the total by 19
5232/19 = 275.4 (simplified)
Which number is greater than -2
Simplify: [tex]\frac{1}{(x+3)(x+4)} +\frac{2}{(x+4)(x+5)}[/tex]
Answer:
[tex]\frac{3x+11}{(x+3)(x+4)(x+5)}[/tex]
Step-by-step explanation:
Before adding we require the fractions to have a common denominator.
Multiplying the numerator/ denominator of the first fraction by (x + 5)
Multiplying the numerator/ denominator of the second fraction by (x + 3)
= [tex]\frac{x+5}{(x+3)(x+4)(x+5)}[/tex] + [tex]\frac{2(x+3)}{(x+3)(x+4)(x+5)}[/tex]
Now add the numerators leaving the common denominator
= [tex]\frac{x+5+2x+6}{(x+3)(x+4)(x+5)}[/tex]
= [tex]\frac{3x+11}{(x+3)(x+4)(x+5)}[/tex]
A toy box is 3 feet wide, 4 feet long, and 2 feet tall. What is the volume of the toy box?
Answer:
24 cubic feet
Step-by-step explanation:
3 × 4 × 2 = 24
Step-by-step explanation:
The formula for volume is l×w×h, a d the ending unit will be cubed/to the third power.
So you would do 4ft×3ft×2ft, which equals 24ft³
How do you right coordinates?
Answer: You write the latitude first, followed by a comma, and then the longitude.
Step-by-step explanation:
. Denise has multiplied (2r – 3)(2r + 3) to get 4r2 – 9. After looking at her work, Hyder says her solution must be incorrect because multiplying two binomials will always produce a trinomial. Which student is correct? Explain the error to the incorrect student. HELP ME PLEASE NEED IT IN TIME THANKS.
Answer:
Answer:
The answer is 4r² – 9
Denise answer is correct.
Step-by-step explanation:
One of the methods of solving the given equation [(2r – 3)(2r + 3)] is the FOIL method
Using the FOIL method (Used for multiplying binomials)
F stands for first
O stands for outer
I stands for inner
L stands for last
In this method, it means we will first multiply the first terms followed by multiplying the outer term, then multiplying the inner terms and finally, the last terms.
So, for the equation (2r – 3)(2r + 3)
First : (2r)(2r) = 4r²
Outer : (2r)(+3) = 6r
Inner : (–3)(2r) = – 6r
Last : (–3)(+3) = – 9
Adding the results we get
4r² + 6r – 6r – 9 (+6r and – 6r cancels out)
= 4r² – 9
∴ (2r – 3)(2r + 3) = 4r² – 9
Hence, Denise answer is correct
21(2−x)+12x=44
What does X=
Answer:
x= -2/9
Step-by-step explanation:
42-21x+12x=44
-21x+12x=44-42
-9x=2
x= -2/9
the perimiter of a parallelogram is 72 meters the width of the paralleogram is 4 meters less than its length. find the length and width of the parallelogram.
Answer:
length = 20 m
width = 16m
Step-by-step explanation:
-8+9·2÷-3 math please answer quick please
Answer:
Exact form: [tex]-11.06[/tex]
Decimal form: [tex]-11.066667[/tex]
Step-by-step explanation:
[tex]-8+9.2[/tex] ÷ [tex]-3[/tex]
Let's simplify. We will have to change [tex]9.2[/tex] and [tex]-3[/tex] a draction
[tex]-8+\frac{9.2}{-3}[/tex]
This equals
Exact form: [tex]-11.06[/tex]
Decimal form: [tex]-11.066667[/tex]
Hope this helps!
About how many ants would it take to wrap around the earth
Answer:
Ten billion
Step-by-step explanation:
There would around 16×10⁻¹⁰ ants to wrap around the earth.
What is circumference?Circumference is the distance around a circle., basically it is the perimeter of the circle.
Given that, an average sized ant is about 4×10⁻³ meter long the circumference of the earth is about 4×10⁻⁷ meters, we are asked to find the number of ants that would it take to wrap around earth,
To find the same, we will multiply the size of ants to the circumference of the earth,
So, 4×10⁻³ × 4×10⁻⁷
= 16×10⁻¹⁰
Hence, there would around 16×10⁻¹⁰ ants to wrap around the earth.
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Solve for n nn. ( 3 3 ) 2 = n 6 (3 3 ) 2 =n 6 left parenthesis, 3, cubed, right parenthesis, squared, equals, n, start superscript, 6, end superscript n = n=n, equals
Answer:
3Step-by-step explanation:
given the expression (3³)² = n⁶, we are to find the value of n.
To do that we will apply one of the laws of indices shown
[tex](a^m)^n = a^{mn}[/tex]
Applying the law to the question
(3³)² = n⁶
[tex]3^{3*2} = n^6\\\\[/tex]
[tex]3^6 = n^6\\\\[/tex]
Since the power of both values at both sides are equal, they will cancel out to give;
[tex]3 = n[/tex]
Hence the value of n is 3
its 2
N=2
and i know this since i got it wrong and it showed me the correct answer :)
2 i hopeMulti-Step: <ABD and <BDE are supplementary. Find the measures of both angles.
28. m<ABD = (12x - 12)° , m<BDE = (3x + 48)°
Answer:
get it helps me with lI do not know the answer
Step-by-step explanation:
sorry
Write an equation in point-slope form for a line that passes through the given set of points.
(-2, - 4) and (1, 8)
First off, we need the slope
[tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{8-(-4)}{1-(-2)}[/tex]
That leaves you with
12/3 = 4
point-slope form: y-y1 = m ( x - x1)
So...
y - (-4) = 4 ( x - (-2))
y + 4 = 4 (x + 2)
y + 4 = 4x + 8
Now subtract 4 from both sides of the equation
y = 4x +4
5. Find the base of the triangle if its area is 48 sq. in and its height is 16 in. 10 points none of the options 9 in O 12 in 6 in
Answer:
The answer is 6 inStep-by-step explanation:
Area of a triangle is given by
[tex] A = \frac{1}{2} bh[/tex]
where b is the base
h is the height
From the question
A = 48 sq. in
h = 16 in.
Substitute the values into the above formula and solve for the base
That's
[tex]48 = \frac{1}{2} 16b \\ 48 = 8b \\ \frac{8b}{8} = \frac{48}{8} [/tex]
We have the final answer as
6 inHope this helps you
A student Is asked to find the sum of 297 +613. Which expression can the student use to find
the answer?
Answer:
The student can used
297+613 = x
Step-by-step explanation:
It is because the sum is unknown , and we can imagine it as "x". This, we formed a equation.
To solve the equation X - 62 = 123, you would ?
Evaluate f(x)=12 for the function f(x)=5(x-3)+17
Answer:
x = 5
Step-by-step explanation:
We are given the function;
f(x) = 5(x-3) + 17
And f(x) = 12
Thus;
5(x-3) + 17 = 12
Expanding the bracket gives;
5x - 15 + 17 = 12
5x + 2 = 12
5x = 12 - 2
5x = 10
x = 10/2
x = 5
Thus,for f(x) = 12, x has to be 5
A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building. What are the dimensions of this rectangular room in the actual building? Group of answer choices
======================================================
The blueprints say that 1 inch represents 10 feet. This means we can form the equation below
1 inch = 10 feet
Of course 10 feet is much larger than 1 inch, so they cannot be actually equal to one another, but it helps tie together the two quantities. And it also allows us to multiply both sides by 3 to get
3 inches = 30 feet
So 3 inches on paper means we have 30 feet in real life.
Similarly,
1 inch = 10 feet
5.5 inches = 55 feet (multiply both sides by 5.5)
The 3 inch by 5.5 inch rectangle on paper corresponds to a 30 feet by 55 feet rectangle in real life.
----------------
In short, you multiply each given dimension by 10
3 inches goes to 3*30 = 30 feet
5.5 inches goes to 5.5*10 = 55 feet
Donalita ate 5 out of every 7 candies in a jar. If she ate 25 candies, what fraction represents the number of candies she ate over the total number of candies?
Answer:
25/35
Step-by-step explanation:
5 times 7 equals 35 and that means that this is the denominator because that is our total amount.
5 times 5 equals 25 and that makes it the numerator because that is what is being taken out of 5 jars
Hopefully this helps you :)
What rewrite 4/6 : 1/3 as a unit rate
Answer:
unit rate is 2
Step-by-step explanation:
Notice that if we multiply both '1' and '3' in 1/3 by 2, we get:
4/6 : 2/6,
which reduces to 4/2, or 2, which is the desired unit rate.
Answer:
The answer is 2:1
Step-by-step explanation:
what is a unit rate?
A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
When writing a unit rate the denominator is always 1
If you want to obtain a unit rate you divide both quantities by the second one.
I need help because I don’t know what they are asking
Answer:
16x -2
Step-by-step explanation:
You know how to compute the perimeter of a rectangle of length L and width W:
P = 2(L+W)
Here, you're asked to use the given algebraic expressions for length and width and simplify the result of putting those in the perimeter formula.
P = 2((5x-2) +(3x+1))
P = 2(8x -1)
P = 16x -2 . . . the perimeter of the rectangle
It is 60 Celsius on the crust of a volcano. What is this number in Kelvin?
Answer:
333.15 Kelvin (K)
Step-by-step explanation:
When you convert from Celsius to Kelvin, you add 273.15
60 C + 273.15 = 333.15 K
So, that is the answer. Hope this helps!
Answer:
333.15 Kelvin (333 rounded)
Step-by-step explanation:
You must add 273.15.
60 + 273.15 = 333.15.
The answer is 333.15 (333 rounded.)