The number that when added to 43, would give the result of 112 can be found to be 69.
How to find the number ?To find the number that, when added to 43, equals 112, you can use algebraic reasoning.
Let's represent the unknown number with the variable "x". The equation can be set up as:
43 + x = 112
To solve for "x," we need to isolate it on one side of the equation.
First, subtract 43 from both sides of the equation:
43 + x - 43 = 112 - 43
The 43 on the left side cancels out:
x = 112 - 43
Simplifying the right side of the equation:
x = 69
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To solve the equation 43 + x = 112, subtract 43 from both sides to isolate 'x'. The value of 'x' is 69.
Explanation:To find the number that, when added to 43, equals 112, we can use algebra. Let's use the variable 'x' to represent the unknown number. So, the equation is 43 + x = 112.
To isolate 'x', we need to move 43 to the other side of the equation.
By subtracting 43 from both sides, we get x = 112 - 43. Evaluating the subtraction, we find that x = 69.
The length of a rectangle is 5 inches longer than the width. The perimeter of the rectangle is 40 inches. What is the width of the rectangle, in inches?
Answer:
W = 7.5 in
Step-by-step explanation:
We'll use the formula for the perimeter of a rectangle: P = 2W + 2L.
Here, L = W + 5, so P = 2W + 2L becomes:
P = 2W + 2(W + 5), and this equals 40 in.
Thus we have the equation in W (the desired variable) as follows:
2W + 2(W + 5) = 40 in, or 4W + 10 = 40.
Then 4W = 30, and W = 7.5 in.
Based on the perimeter of this rectangle, the width is 7.5 inches.
The perimeter of a rectangle is calculated by:
= Length + Width + Length + Width
Assuming the width is denoted by x, the length would be:
Length = 5 + Width
Length = 5 + x
The perimeter is given so we can solve for the width:
Length + Width + Length + Width = Perimeter
5 + x + x + 5 + x + x = 40
10 + 4x = 40
4x = 40 - 10
x = 30/4
x = 7.5 inches
In conclusion, the width is 7.5 inches.
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Write standard form
5+0.5+0.03+0.006
Answer:
5.5360
Step-by-step explanation:
I added
5+0.5= 5.5
5.5+0.03=5.53
5.53+0.006=
5.5360
What is the slope of the line - 4x + y = -1?
-4 is the slope........
Answer:
4
Step-by-step explanation:
To find slope, we will rewrite this equation into slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept,
- 4x + y = -1
+ 4x +4x
y= -1 + 4x
y=4x - 1
98 POINTS The total cost of a boat rental includes the price per hour plus the cost of one full tank of gas. The table below represents the boat rental fees.
No. of Hours 2 4 6 8
Rental Fee $79 $125$171 $217
What is the cost for a full tank of gas?
A.
$23
B.
$33
C.
$46
D.
$217
PLZ ANSWER BRAINLISET AND ALOT OF POINT
the correct answer is b.33
Answer:
b
Step-by-step explanation:
Identify the nonlinear equation. A) y = x B) y = 3x - 7 C) y = x2 D) y = 3 E) y = 1 3
ANSWER
C)
[tex]y = {x}^{2} [/tex]
EXPLANATION
A linear function is a function whose graph is a straight line.
The graph of y=x is a straight line.
The graph of y=3x -7 is also a straight line.
The graph of y=x² is a parabola.
This graph is not a straight line .
It is a non-linear function.
y=3 and y=13 are also straight lines.
The correct choice is C.
ABCD is a rectangle Ac=3x+4 and BD=5x-50 what is the value of x
what is the measure of MN
Answer:
C
Because of the markings showing equal length lines 7x + 4 is double 4x or 48 is three times the length of 4x
Either solve 7x + 4 = 8x
4 = x
Or solve 48 = 12x
4 = x
Substitute back in to 7x + 4 ......MN = 7 x 4 + 4 = 32
BRAINLIEST PLZ !!!! :)Three friends went to the peach orchards in the country. There they can pick as many peaches as they want, but the owner gets p amount of peaches from each person who picks peaches. The three friends pick these amounts:
2p, 4p + 3, and 3p + 2.
After giving the owner his peaches, what did the three friends take home?
Answer:
The three friends took 6p + 5 peaches home
Explanation:
We are given that the three friends picked 2p, 4p+3 and 3p+2 peaches
This means that:
Total picked = 2p + 4p + 3 + 3p + 2 = 9p+5 peaches
Now, we know that the owner will take p peaches from each of the three friends
This means that:
Amount taken by owner = 3p peaches
Finally, to get the amount that the three friends will take home, we subtract the amount that the owner will take from the total amount they picked
This means that:
Number of peaches they took home = total picked - amount taken by owner
Number of peaches they took home = 9p + 5 - 3p
Number of peaches they took home = 6p + 5 peaches
Hope this helps :)
If ED = 2x + 4 and DF= 4x-6. Find DG
Answer:
x=5, Now you just have to insert x into the equation for DG
Step-by-step explanation:
2x+4=4x-6
-2x -2x
4=2x-6
+6 +6
10=2x
÷2 ÷2
5=x
What is the simplified form of the product x^2+8x+15/x-4•x^2-16/2x+6
Final result :
(x + 5) • (x + 4)
———————
2
Step by step solution :
Step 1 :
x2 - 16
Simplify ———————
2x + 6
Step 2 :
Pulling out like terms :
2.1 Pull out like factors :
2x + 6 = 2 • (x + 3)
Trying to factor as a Difference of Squares :
2.2 Factoring: x2 - 16
Theory : 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 : 16 is the square of 4
Check : x2 is the square of x1
Factorization is : (x + 4) • (x - 4)
Polynomial Long Division :
2.3 Polynomial Long Division
Dividing : x + 4
("Dividend")
By : x + 3 ("Divisor")
dividend x + 4
- divisor * x0 x + 3
remainder 1
Quotient : 1
Remainder : 1
Equation at the end of step 2 :
(((x2)+8x)+15) (x+4)•(x-4)
——————————————•———————————
(x-4) 2•(x+3)
Step 3 :
x2 + 8x + 15
Simplify ————————————
x - 4
Trying to factor by splitting the middle term
3.1 Factoring x2 + 8x + 15
The first term is, x2 its coefficient is 1 .
The middle term is, +8x its coefficient is 8 .
The last term, "the constant", is +15
Step-1 : Multiply the coefficient of the first term by the constant 1 • 15 = 15
Step-2 : Find two factors of 15 whose sum equals the coefficient of the middle term, which is 8 .
-15 + -1 = -16
-5 + -3 = -8
-3 + -5 = -8
-1 + -15 = -16
1 + 15 = 16
3 + 5 = 8 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 5
x2 + 3x + 5x + 15
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+3)
Add up the last 2 terms, pulling out common factors :
5 • (x+3)
Step-5 : Add up the four terms of step 4 :
(x+5) • (x+3)
Which is the desired factorization
Equation at the end of step 3 :
(x + 5) • (x + 3) (x + 4) • (x - 4)
————————————————— • —————————————————
x - 4 2 • (x + 3)
Step 4 :
Canceling Out :
4.1 Cancel out (x+3) which appears on both sides of the fraction line.
Canceling Out :
4.2 Cancel out (x-4) which appears on both sides of the fraction line.
Final result :
(x + 5) • (x + 4)
——————---
2
PLEASE HELP!!!!!!!!!!!
What is x
A: 35
2:135
3: 45
4:55
the sum of all interior angles in a polygon is
180(n - 2)
n = number of sides in the polygon
this polygon has 5 sides, so is a PENTAgon, so the sum of all its sides is
180(5 - 2) => 180(3) => 540
so then
[tex]\bf 90+148+(3x+10)+(x)+112=540\implies 360+4x=540 \\\\\\ 4x=180\implies x=\cfrac{180}{4}\implies x=45[/tex]
Gary is testing a river water sample in his lab. Initially, there are 64 bacteria in the river water sample. The number of bacteria after 3 hours can be calculated using the expression shown below.
64(1.12)3
The 3 is a exponent.
Use the given expression to complete the statements.
The quantity that represents the initial number of bacteria is ........
..
The quantity that represents the rate at which the number of bacteria is increasing is .........
which means the growth rate percentage for the bacteria is %.......l.l
The answers are:
- The quantity that represents the initial number of bacteria is 64.
- The quantity that represents the rate at which the number of bacteria is increasing is (1+0.12) or 1.12 which means the growth rate percentage for the bacteria is 0.12 or (0.12*100), it will be 12%.
Why?To solve the problem, and complete the statements, we need to remember the form of the exponential growth.
The exponential growth formula is given by the following formula:
[tex]P(t)=StartAmount(1+PercentageRate)^{t}[/tex]
Where,
Start Amount, is the starting population or amount.
(1+Percentage Rate), is the increasing rate
Percentage Rate, is the growth rate percentage.
t, is the time elapsed.
Now, we are given the following expression:
[tex]P(3)=64(1.12)^{3}[/tex]
Which can be rewrited as:
[tex]P(3)=64(1+0.12)^{3}[/tex]
So, we have that:
- The quantity that represents the initial number of bacteria is 64.
- The quantity that represents the rate at which the number of bacteria is increasing is (1+0.12) or 1.12 which means the growth rate percentage for the bacteria is 0.12 or (0.12*100), it will be 12%.
Have a nice day!
Answer:
b
Step-by-step explanation:
Can someone help me please
Answer:
w/5 ≥ 25
Step-by-step explanation:
Quotient means division
w/5
is at least means great than or equal to
w/5 ≥ 25
Determine the equation of the line given by the graph. A) y = 2x + 4 B) y = 4x + 2 C) y = 1 2 x − 2 D) y = −2x + 4
Answer:
the answer is a. y=2x+4
Answer: A y = 2x + 4
for USATestprep
Find the solutions to the system of equations. Select all that apply.
Y=x^2-4
Y=-2x-5
A. (-2,0)
B. (-5,0)
C. (2,0)
D. (-1,-3)
Answer:
D. (-1, -3)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=x^2-4&(1)\\y=-2x-5&(2)\end{array}\right\\\\\text{Put (1) to (2):}\\\\x^2-4=-2x-5\qquad\text{add}\ 2x\ \text{and 5 to both sides}\\\\x^2+2x+1=0\\\\x^2+x+x+1=0\\\\x(x+1)+1(x+1)=0\\\\(x+1)(x+1)=0\\\\(x+1)^2=0\iff x+1=0\qquad\text{subtract 1 from both sides}\\\\x=-1\\\\\text{put the value of}\ x\ \text{to}\ (2):\\\\y=-2(-1)-5\\\\y=2-5\\\\y=-3[/tex]
Answer: Hello there!
The system of equation given is:
y = x^2-4
y = -2x-5
And we want to solve this system:
the first step we can do is replace y in the first equation by the given in the second equation:
y = x^2-4 = -2x - 5
now we can solve it for x:
x^2-4 +2x + 5 = 0
x^2 +2x + 1 = 0
and now we can use the cuadratic equation forumla:
this is, if we have a function of the form:
ax^2 + bx + c = 0
the solutions are:
[tex]x = \frac{-b +/- \sqrt{b^2 -4ac} }{2a}[/tex]
in our equation we have a=1, b = 2 and c= 1
we replace it in the formula given, and we obtain:
[tex]x = \frac{-2 +/- \sqrt{2^2 -4*(1)} }{2} = \frac{-2 +/- \sqrt{4 - 4} }{2} = -2/2 = -1[/tex]
Now we got the value of x, and we could replace it in one of the equations and get the value of y:
y = -2x-5
y = -2*(-1) - 5 = 2 -5 = -3
then the pair is (-1, -3)
and the correct option is D.
HELP SUPER DUPER FAST PLS I REALLY NEED IT THANK YOU!!!!!!!!!
D. x < -2
(Divide 4 by -2 to isolate x)
9) Craig earns the same amount
of money each month. His
telephone bill is 1/20 of his
monthly earnings, and he pays a
total of $720 each year for his
telephone service. How much
does Craig earn each month, in
dollars?
Answer:
Craig earns $1,200 each month
Explanation:
We are given that Craig pays a total of $720 each year for his telephone service
We also know that a year has 12 months
This means that:
Craig pays [tex]\frac{720}{12}= 60[/tex] dollars each month for his telephone services
We are given that the monthly phone bill is [tex]\frac{1}{20}[/tex] of his monthly earnings
Assume that his monthly payment is x
We have:
[tex]\frac{1}{20}x = PhoneBill\\ \\ \frac{1}{20}x = 60\\ \\ x=60*20 = 1200[/tex] dollars
Hope this helps :)
Craig earns about $1200 each month and pays a total of $720 each year for his telephone service.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount earned each month
Hence:
(1/20)x * 12 months = 720
x = 1200
Craig earns about $1200 each month and pays a total of $720 each year for his telephone service.
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Find f(1\3) if f(n) = 3n.
Answer:
f(1/3) = 1
Step-by-step explanation:
Given
f(n)=3n
We have to find f(1/3).
In order to find the value of the given function at a point, we put the value in the function where the variable is used.
i.e. to find f(2) for f(x); x will be replaced by 2 in the function. Similarly to find f(1/3), we will replace n by 1/3 in the function.
So to find
f(1/3)=3* 1/3
=1
So, the value of f(1/3) is 1 ..
Help me find the range of this function please
Answer:
{-2, -14, -26, -50}
Step-by-step explanation:
The range of the function is the function evaluated at each point of the given domain. So to find the range of the function we need to find the value of the function for each point in the domain:
- For x = -8
[tex]f(x)=-2x-18[/tex]
[tex]f(-8)=-2(-8)-18[/tex]
[tex]f(-8)=16-18[/tex]
[tex]f(-8)=-2[/tex]
The first value of the range of the function is -2
- For x = -2
[tex]f(x)=-2x-18[/tex]
[tex]f(-2)=-2(-2)-18[/tex]
[tex]f(-2)=4-18[/tex]
[tex]f(-2)=-14[/tex]
The second value of the range is -14
- For x = 4
[tex]f(x)=-2x-18[/tex]
[tex]f(4)=-2(4)-18[/tex]
[tex]f(4)=-8-18[/tex]
[tex]f(4)=-26[/tex]
Th third values of the range is -26
- For x = 16
[tex]f(x)=-2x-18[/tex]
[tex]f(16)=-2(16)-18[/tex]
[tex]f(16)=-32-18[/tex]
[tex]f(16)=-50[/tex]
The fourth and last value of the range is -50
Now we can put all the values of the range together
The range of the function is {-2, -14, -26, -50}
Samantha is buying an ice-cream sundae. There are 3 sizes of sundaes, 11 different ice cream flavors, and 4 different toppings. How many ways can Samantha choose a sundae
Answer: 132
Step-by-step explanation:
There are three different things to choose from: size, flavors, and toppings
3 kinds of sizes x 11 kinds of flavors x 4 kinds of toppings
= 3x11x4
= 12x11
= 132
Solve 4(t+1)=6t-1
A) 1 1/2
B) 2 1/2
C) 1
D) 0
Answer:
answer is B...2 1/2
Step-by-step explanation:
4(t+1)=6t-1
4t+4=6t -1
4t-6t+4=6t-6t-1
-2t+4=-1
-2t+4-4=-1-4
-2t=-5
Divide by -2 for -2t and -5
-2t/-2=-5/-2
t=5/2= 2 1/2
Answer is b) 2 1/2
A box without a top is made from a rectangular piece of cardboard, with dimensions 25 inches by 20 inches, by cutting out square corners with side length x inches.
PLEASE HELP
Which expression represents the volume of the box in terms of x?
(2x−25)(2x−20)x
(25−2x)(20−2x)x
(25−x)(20−x)x
(25−2x)(20−2x)4x
Answer:
i think its A if it isnt im sorry
Step-by-step explanation:
Answer:
The second option :: V = [tex](25-2x)(20-2x)x[/tex] is correct.
Step-by-step explanation:
The vertical side was 25 inches before cutting out the corners.
The horizontal side was 20 inches before cutting out the corners.
So now, if you fold all of the corner up, you get a box that has a height of "x".
The sides are now missing a length of x from each end.
So the longer edges of the box are now [tex](25-2x)[/tex] inches
The shorter edges of the box are now [tex](20-2x)[/tex] inches
The volume of a box is given by V = length x width x height
So, here the volume becomes:
V = [tex](25-2x)(20-2x)x[/tex] cubic inches.
Convert the following measurements. a. 2 cubic yards to cubic feet b. 135 cubic feet to cubic yards c. 6,912 cubic feet to cubic inches d. 279,936 cubic inches to cubic feet
Answer:
[tex]a.\ 54ft^3\\b.\ 5yd^3\\c.\ 11,943,936in^3\\d.\ 162ft^3[/tex]
Step-by-step explanation:
a. Remember that:
[tex]1yd^3=27ft^3[/tex]
Then, 2 cubic yards to cubic feet is:
[tex](2yd^3)(\frac{27ft^3}{1yd^3})=54ft^3[/tex]
b. 135 cubic feet to cubic yards is:
[tex](135ft^3)(\frac{1yd^3}{27ft^3})=5yd^3[/tex]
c. Remember that:
[tex]1ft^3=1,728in^3[/tex]
Then, 6,912 cubic feet to cubic inches:
[tex](6,912ft^3)(\frac{1,728in^3}{1ft^3})=11,943,936in^3[/tex]
d. 279,936 cubic inches to cubic feet is:
[tex](279,936in^3)(\frac{ft^3}{1,728in^3})=162ft^3[/tex]
Answer:
A 54ft3
B 5yd3
C 11,943,936in3
D 162ft3
Step-by-step explanation:
I need help with my math
Answer:
28.26
Step-by-step explanation:
π r² = A
A = (3.14) (3²)
A = 3.14 · 9 = 28.26
Hello There!
WHAT WE KNOW
Pi = 3.14
R = 3
HOW TO SOLVE
A = 3.14*9
Answer 28.26
Plz help god blees if you do it all i will give u BRAINLIEST
IF YOU DO ONE THAT WILL NOT BE HELPING AND I WILL REPORT YOU!!!!!!!!!! 3 to dooooo
Answer:
1st pic: Answer is 3
2nd pic: Answer is 5
3rd pic: Answer 4
Step-by-step explanation:
PLEASE HELP ME PLEASE
±1/2. The equation [tex]4x^{2} =1[/tex] has two possible solutions +1/2 and -1/2.
The problem is a quadratic equations and it can be solved using the equation [tex]x=-b±\frac{\sqrt{b^{2} -4ac} }{2a}[/tex].
Ordering the quadratic equation given in the problem, we obtain [tex]4x^{2} -1=0[/tex] where a = 4, b = 0, and c = -1
Substituting the values
[tex]x=±\frac{\sqrt{-4(4)(-1)} }{2(4)}=±\frac{\sqrt{16}}{8} =±\frac{4}{8} \\x=±\frac{1}{2}[/tex]
The answer is:
The correct option is the second option,
[tex]4x^{2}=+-\frac{1}{2}[/tex]
Why?We are given the expression:
[tex]4x^{2}[/tex]
Now, solving we have:
Applying square root to both sides of the equation in order to isolate x:
[tex]4x^{2}=1\\\\\sqrt{4x^{2} } =+-\sqrt{1}\\\\2x=+-1\\\\x=+-\frac{1}{2}[/tex]
Hence, the correct option is the second option,
[tex]4x^{2}=+-\frac{1}{2}[/tex]
Have a nice day!
the radius of the circle x^2+y^2 +px+6y-3=0 is 4. find the possible values of p
Here, the given equation is,
x^2+y^2+px+6y-3=0
By copairing it with x^2+y^2+2gx+2fy+c=0, we get,
2g=p or, g=p/2
2f=6 or, f=3
c=-3
now the radius is,
r^2=g^2+f^2-c
or, 4^2=(p/2)^2 +3^2 -(-3)
or, 16= p^2/4 +9+3
or, 16-9-3=p^2/4
or p^2/4=4
or, p^2=4×4
or p^2=4^2
or p=4
therefore the rewuired value of p is 4.
Answer:
Possible values are 4 and -4.
Step-by-step explanation:
First complete the square on the x and y terms:
x^2 + y^2 + px + 6y - 3 = 0
(x + 0.5p)^2 - 0.25p^2 + (y + 3)^2 - 9 - 3 = 0
(x + 0.5p)^2 + (y + 3)^2 = 12 + 0.25p^2
This is the standard form of the equation of the circle where the right side = radius^2 so we can write:
12 + 0.25p^2 = 4^2
0.25p^2 = 16 - 12 = 4
Taking square roots:-
0.5p = +/- 2
p = 2 / 0.5 , -2 / 0.5
p = 4, -4.
At a particular restaurant, each slider has 250 calories and each chicken wing has 60 calories. A combination meal with sliders and chicken wings has a total of 12 sliders and chicken wings altogether and contains 1100 calories. Determine the number of sliders in the combination meal and the number of chicken wings in the combination meal.
Final answer:
To find the number of sliders and chicken wings in the combination meal, set up a system of equations and solve. There are 2 sliders and 10 chicken wings in the combination meal.
Explanation:
In order to find the number of sliders and chicken wings in the combination meal, we can set up a system of equations. Let's assume that the number of sliders is 's' and the number of chicken wings is 'c'. We know that each slider has 250 calories and each chicken wing has 60 calories. The total number of sliders and chicken wings in the combination meal is 12, so we have the equation s + c = 12.
We also know that the total number of calories in the combination meal is 1100. Since each slider has 250 calories and each chicken wing has 60 calories, we can write the equation 250s + 60c = 1100.
Now we can solve this system of equations to find the values of 's' and 'c'.
Multiplying the first equation by 60, we get 60s + 60c = 720. Subtracting this equation from the second equation, we get 250s - 60s = 1100 - 720, which simplifies to 190s = 380. Dividing both sides by 190, we find that s = 2.
Substituting this value back into the first equation, we have 2 + c = 12. Solving for 'c', we find that c = 10.
Therefore, there are 2 sliders and 10 chicken wings in the combination meal.
The surface area of a regular pyramid with a square base which has a slant height of five units and base side lengths of nine units is:
Answer:
171 sq units.
Step-by-step explanation:
Since you don't specify you want a the side surface area only, we'll calculate both.
First, the base...
We have a square with a side of 9 units.
Area of the base is then 9 x 9 = 81 sq units.
For the sides, we have 4 triangles with a base of 9 and a height of 5 units.
The area of a triangle is calculated with A = (b * h)/2
So, each of the sides of the pyramid has an area of:
A = (9 * 5) / 2 = 22.5 sq units
There are four sides, so total lateral area: 4 * 22.5 = 90 sq units.
Total area: 81 + 90 = 171 sq units.
Consider the function represented by the equation y - x - 4 = 0. What is the equation written in function notation, with x as
the independent variable?
O
f(x) = x + 4
O f(x) = -y + 4
O f(x) = -X-4
O f(x) = y-4
Answer:
f(x) = x + 4
Step-by-step explanation:
Given
y - x - 4 = 0 ( add x to both sides )
y - 4 = x ( add 4 to both sides )
y = x + 4 ( let y = f(x) )
f(x) = x + 4