Expanded form of 3( 6 + 7) is [tex]3 \times 10+9 \times 1[/tex]
Solution:Need to use distributive property to write the expanded form of 3(6 + 7)
Let’s understand what is distributive property.
The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products together.
According to distributive property, for numbers a , b and c
[tex]a(b+c)=a \times b+b \times c[/tex] ----- eqn 1
3(6 + 7) can be rewritten as 3 ( 6 + 4 + 3 ) = 3 ( 10 + 3 )
Now in our case a = 3 , b = 10 and c = 3
On substituting the values of a , b and c in equation 1 we get
[tex]3(10+3)=3 \times 10+3 \times 3=3 \times 10+9 \times 1[/tex]
So expanded form of 3( 6 + 7) is [tex]3 \times 10+9 \times 1[/tex]
If 27 cards are in the whole set, how many are in 3/9 of the set
Answer: 9 cards
Step-by-step explanation:
x=27
3/9x = 1/3x = 27/3 = 9
Could someone help me with this?
Answer:
1. 18.74%
2. 33.34%
3. 45.5%
4. 20%
5. 33.11%
6. 16.38%
Step-by-step explanation:
1. For Shoes, the actual price is $79.99 and the selling price is $65.00.
The discount is [tex]\frac{79.99 - 65}{79.99} \times 100 = 18.74[/tex]%.
2. For 12 pack og golf balls, the actual price is $29.99 and the selling price is $19.99.
The discount is [tex]\frac{29.99 - 19.99}{29.99} \times 100 = 33.34[/tex]%.
3. For Exercise bike, the actual price is $1099 and the selling price is $599.
The discount is [tex]\frac{1099 - 599}{1099} \times 100 = 45.5[/tex]%.
4. For Basketball, the actual price is $49.99 and the selling price is $39.99.
The discount is [tex]\frac{49.99 - 39.99}{49.99} \times 100 = 20[/tex]%.
5. For Sports socks, the actual price is $14.95 and the selling price is $10.00.
The discount is [tex]\frac{14.95 - 10}{14.95} \times 100 = 33.11[/tex]%.
6. For Hockey sticks, the actual price is $299 and the selling price is $250.
The discount is [tex]\frac{299 - 250}{299} \times 100 = 16.38[/tex]%.
Kamille is attending a community college to obtain a two-year degree. the annual cost of tuition is $3,750. Kamille has obtained an annual scholarship of $1,250 and anual grants in the amount of $835. the remainder of kamille’s tuition and fees will be paid be paid for using student loans. At the end of the two-year degree, what will kamille’s student loan balance be ?
The balance of student loan will be $3330 at the end of two year degree.
Step-by-step explanation:
Annual cost of tuition = $3750
As it is two year degree, therefore, total cost of tuition;
Total cost of tuition = 3750*2 = $7500
Annual scholarship = $1250
Annual grant = $835
Total = 1250 + 835 = $2085
As this is one year amount, she will get same the next year.
Total amount received in 2 years = 2085*2 = $4170
Balance in student loans = Total cost of tuition - Total amount received as grant and scholarship
Balance in student loan = [tex]7500-4170 =\$3330[/tex]
The balance of student loan will be $3330 at the end of two year degree.
Keywords: multiplication, subtraction
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Answer:
The balance of student loan will be $3330 at the end of two year degree.
Step-by-step explanation:
What is the distance between the points (3,12) and (14,2)
Answer:
square root of 221
Step-by-step explanation:
d= sqrt (14-3)^2 + (2-12)^2
sqrt 121+100= sqaure root of 221
Answer:
Distance between the points (3, 12) and (14, 2) is 14.8661
Step-by-step explanation:
Distance between two points = √(xB−xA)^2+(yB−yA)^2
Solution :
Distance between two points = √(14−3)^2+(2−12)^2
= √11^2+(−10)^2
= √121+100
= √221 = 14.8661
x + y = 75
10x + y = 48
Can someone help me?
Final answer:
The system of linear equations x + y = 75 and 10x + y = 48 is solved using the elimination method, resulting in the solution x = 3 and y = 72.
Explanation:
The student is given a system of two linear equations:
x + y = 7510x + y = 48To solve this system, we can use the method of elimination or substitution. Here, elimination appears to be the more straightforward method. We'll subtract the second equation from the first to eliminate the variable y, as they both have the same coefficient in y. Subtracting the second equation from the first gives us:
9x = 27
Solving for x, we find:
x = 27 / 9 = 3
Now that we have the value for x, we can substitute it back into either of the original equations to find the value for y. Substituting into the first equation:
3 + y = 75 => y = 75 - 3 => y = 72
So the solution to the system is x = 3 and y = 72. This method remains effective even with the advent of computer algebra methods and Mathcad.
A baby flower is 2 inches tall. It is growing at a rate of 3 inches every month. Write an equation that represents that situation.(algebra) helppppppppppppp!!!!!
The equation would be y = 3x+2
Here's an explanation:
Let y represent the length of the baby flower in total, and let x represent the number of months that have passed. Since the flower grows at a rate of 3 inches every month, then for x number of months, it would grow 3 times x, which is 3x. The problem also tell us that the flower is already 2 inches tall, which now makes it 3x+2. So the total length is equal to 3x + 2 inches, so the equation would be y=3x+2
m2 + 8m +7
m² + 5m + 6
m2 + 10m +9
m2 – 6m +8
m2 - 8m + 12
m2 + 11m + 24
How do I factor each trinomial ??
Answer:
m² + 8m + 7 = (m + 1) (m + 7)
m² – 6m + 8 = (m – 2) (m – 4)
Step-by-step explanation:
If a trinomial ax² + bx + c is "factorable", you can use the AC method.
1. Multiply a and c.
2. Find factors of ac that add up to b.
3. Divide the factors by a and reduce.
4. The numerators are the constants, the denominators are the coefficients.
For example:
m² + 8m + 7
a = 1, b = 8, c = 7
1. ac = 1×7 = 7
2. Factors of 7 that add up to 8 are 1 and 7.
3. Divide by 1: 1/1 and 7/1
4. The factors are (m + 1) and (m + 7).
Therefore, m² + 8m + 7 = (m + 1) (m + 7).
Let's try one with a negative coefficient:
m² – 6m + 8
a = 1, b = -6, c = 8
1. ac = 1×8 = 8
2. Factors of 8 that add up to -6 are -2 and -4.
3. Divide by 1: -2/1 and -4/1
4. The factors are (m – 2) and (m – 4)
Therefore, m² – 6m + 8 = (m – 2) (m – 4).
You can check your answers by distributing.
Solve the rational equation x divided by 6 equals x squared divided by quantity x minus 1 end quantity, and check for extraneous solutions.
Answer:
Solution: [tex]x=-\frac{1}{5}[/tex],[tex]x=0[/tex]
Step-by-step explanation:
Given:
The rational equation to solve is given as:
[tex]\frac{x}{6}=\frac{x^2}{x-1}[/tex]
Doing cross product, we get:
[tex]x\times (x-1)=6\times x^2\\x^2-x=6x^2\\\textrm{Bringing all variables to the right side, we get:}\\6x^2-x^2+x=0\\5x^2+x=0\\x(5x+1)=0\\x=0\ or\ 5x+1=0\\x=0\ or\ x=-\frac{1}{5}[/tex]
Now, for [tex]x=0[/tex], the rational equation is equal to 0. So, [tex]x=0[/tex] is a solution.
Also, [tex]x=-\frac{1}{5}[/tex] is also a solution.
So, no extraneous solution.
The distance it takes stop a car varies directly at the square of the sure of the car. If it takes 112 feet for a car traveling at 40mph to stop, what distance is required for a speed of 59 mph?
The distance required for a speed 59 mph is 243.67 feet
Step-by-step explanation:
The direct variation is a relation ship between two quantities, the
ratio between them is constant
If y varies directly with x, then y = k xx is the constant of variationTo find k substitute y and x by their initial values∵ The distance it takes stop a car varies directly at the square
of the speed of the car
∴ d = k v², where d is the distance in feet and v is the speed in mph
∵ it takes 112 feet for a car traveling at 40 mph to stop
∴ d = 112 feet , v = 40 mph ⇒ initial values
- Substitute these values in the rule above to find k
∵ 112 = k (40)²
∴ 112 = 1600 k
- Divide both sides by 1600
∴ k = 0.07
∴ d = 0.07 v² ⇒ equation of variation
∵ The speed v = 59 mph
- To find the distance required for this speed substitute v in
the equation of variation by 59
∵ d = 0.07 (59)²
∴ d = 243.67 feet
The distance required for a speed 59 mph is 243.67 feet
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Applying the direct variation formula between the speed and stopping distance of a car, we deduce that a car traveling at 59mph would require approximately 245 feet to stop.
Explanation:In this problem, we use the relation that the distance it takes to stop a car varies directly with the square of the speed- this is an example of a direct variation. Given the initial condition we can establish an equation to relate the speed and the stopping distance: D = kV² where D represents the stopping distance, V is the speed, and k is a constant of variation.
First, we utilize the given information (D=112 feet and V=40 mph) to determine the constant k: 112 = k(40²), yielding k = 112/(40²) = 0.07. This factor remains constant for the car irrespective of its speed.
With the constant k determined, we then substitute V=59 and the constant k into our original equation to calculate the distance required to stop at this speed: D = 0.07*(59²), resulting in D approximately equal to 245 feet. Therefore, a car traveling at 59 mph would require approximately 245 feet to stop.
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James paid $37.50 for 5 movie tickets.
What is the unit rate representing the cost of 1 movie ticket?
Answer: $7.50 per ticket
Step-by-step explanation: To solve this problem, we can rewrite the given statement using fractions.
All my work will be attached in the image provided.
to find out what will go in the blank, notice that we have a 1 in the denominator of our second fraction so we want to find a fraction that is equivalent to 37.50/5 that has a 1 in the denominator.
If we divide the numerator and the denominator of 37.50/5 by 5, we get the equivalent fraction 7.50/1 or $7.50 for 1 movie ticket.
This means that the unit rate for $37.50 for 5 movie tickets is $7.50 per ticket.
Answer:187.50 cents
Step-by-step explanation:37.50*5=187.5 so it would be 187.50 cents
a hockey season ticket holder pays $99.26 for her tickets plus $4.50 for a program each game. A second person pays $18.68 for a ticket to evey game, but doesn't buy programs. In how many games will they have paid the same amount
Answer:
7 games
Step-by-step explanation:
First Person:
Fixed Cost of 99.26
Variable Cost of 4.50 per game (program cost)
Second Person:
No Fixed Cost
Variable cost of 18.68 per game (ticket cost)
Now, we let the number of games be "x", so we can write 2 equations for each person. Then we equate and find at what number of games, the amount paid by both person would be same. Shown below:
First Person Equation:
99.26 + 4.50x
Second Person Equation:
18.68x
Now, equate and solve for x:
99.26 + 4.50x = 18.68x
99.26 = 18.68x - 4.50x
99.26 = 14.18x
x = 99.26/14.18
x = 7
So, the answer is 7 games
Wnting equadions
1 Scott works on Cars. He charges 35$
for each car Plus $7 per hour. Write
an equation that represents this Scenario
if Kylie's Car bill was $63
Good evening ,
Answer:
35+7x = 63
Step-by-step explanation:
35+7x = 63
then 7x = 63 - 35
then 7x = 28
then x = 28/7
then x = 4.
:)
A box of cereal weighs 600 grams. How much is this weight in pounds. Explain or show your reasoning.
To convert grams to pounds, divide the weight in grams by 453.6. In this case, the weight of the box of cereal is 600 grams, which is approximately 1.32 pounds.
Explanation:To convert grams to pounds, divide the weight in grams by 453.6. In this case, the weight of the box of cereal is 600 grams. So, 600 grams ÷ 453.6 = 1.3228 pounds. Therefore, the weight of the box of cereal is approximately 1.32 pounds.
solve the system using elimination 3x+2y=17 and 2x+5y=26
Answer:
3x + 2y = 17
2x + 5 y = 26
Step-by-step explanation:
3x + 2y = 17 }
2x + 5 y = 26}
x - 3y = - 9
x = -9 + 3y
=> 2 (-9+3y)+5y=26
-18+6y+5y=26
-18+11y=26
11y=26+18
11y=44
y= 4
3x + 8=17
3x = 17 - 8
3x = 9
x = 9 : 3
x = 3
Final answer:
By using the elimination method to solve the system of equations, we found that the solution is x = 3 and y = 4 after eliminating y, solving for x, and then substituting x back into one of the original equations to solve for y.
Explanation:
Elimination Method: Solving the System of Equations
To solve the system of equations using the elimination method, we will manipulate the equations to eliminate one variable and solve for the other. The two equations given are:
3x + 2y = 17
2x + 5y = 26
We want to eliminate one of the variables. To do this we find a common multiple for the coefficients of either x or y and then subtract or add the equations. Let's eliminate y by multiplying the first equation by 5 and the second equation by 2, which will give us equations with the same coefficient for y but opposite signs:
5(3x + 2y) = 5(17)
2(2x + 5y) = 2(26)
Now, our two new equations are:
15x + 10y = 85
4x + 10y = 52
Subtract the second new equation from the first:
(15x + 10y) - (4x + 10y) = 85 - 52
11x = 33
Solving for x:
x = 33 / 11
x = 3
Now that we have the value for x, substitute it back into one of the original equations to find y. Let's use the first original equation:
3(3) + 2y = 17
9 + 2y = 17
2y = 17 - 9
2y = 8
y = 8 / 2
y = 4
The solution to the system of equations is x = 3, y = 4.
If mr. Brown and his son together had 220 dollars, and mr. Brown had 10 times as much as his son how much money did each have?
Answer:
the son had $20 and the father had $200
Step-by-step explanation:
20 x 10 = 200
200 + 20 = 220
Cant be 22, Ah, 20!
Because 20 Times 10 is 200, and you add the 20 and you get 220!
This pair of figures is similar. Find the missing side. Help ASAP!!
Answer:
The missing side “x” is 2.
Step-by-step explanation:
From the given figure, we came to know that these are “similar triangles” where the ratio of the one “corresponding side” of a triangle is equal to the other two “corresponding sides” of a triangle.
Let the triangles be ∆ABC and ∆DEF
[tex]\Delta A B C \sim \Delta D E F[/tex]
From similarity of triangle rule the sides,
[tex]\frac{A B}{D E}=\frac{B C}{E F}[/tex]
Given that,
AB = x, DE = 8, BC = 4 and EF = 16
[tex]\text { Substitute the values in } \frac{A B}{D E}=\frac{B C}{E F} \text { to find }^{u} \mathrm{x}^{\prime \prime}[/tex]
[tex]\frac{x}{8}=\frac{4}{16}[/tex]
[tex]\frac{x}{8}=\frac{1}{4}[/tex]
[tex]x=\frac{8}{4}[/tex]
x = 2
Therefore, we found the missing side x = 2
suppose x varies directly with x if y=16 and x=-8what is the value of x when y=-14
The value of x when y = -14 is 7
Step-by-step explanation:
Direct variation is a relationship between two variables that can
be expressed by an equation in which one variable is equal to a
constant times the other
If y varies directly with x, then
y ∝ xy = k x, is the equation of variation where k is the constant of variation∵ y varies directly with x
∴ y ∝ x
∴ y = k x
To find k substitute x and y by their initial values
∵ y = 16 and x = -8
- Substitute y by 16 and x by -8 in the equation above
∴ 16 = k(-8)
- Divide both sides by -8
∴ -2 = k
∴ The value of k is -2
- Substitute the value of k in the equation above
∴ y = -2 x ⇒ equation of variation
∵ y = -14
- To find x substitute y by -14 in the equation of variation
∵ -14 = -2 x
- Divide both sides by -2
∴ 7 = x
∴ The value of x is 7
The value of x when y = -14 is 7
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Help!
What is the area of triangle with a base of 5 1/2 cm and a height of 3 1/2 cm?
Answer:19.25
Step-by-step explanation:
Answer:
9⅝cm²
Step-by-step explanation:
So the formula is
A=1/2bh
A=1/2(5 1/2)(3 1/2)
Turn to improper so it'll be easier
A=1/2(11/2)(7/2)
A=11/4(7/2)
A=77/8
a=9 5/8 cm²
your welcome
A hospital has a large tank with a dimension shown. The tank does not have a cover. What is the surface area of the fish tank.
Answer:
Surface area of the fish tank [tex]332\ square\ feet[/tex]
Step-by-step explanation:
We have to find the surface area of the hospital tank.
As mentioned it does not have a cover.
The tank is in cuboid shape as it has different length [tex](l)[/tex],width [tex](w)[/tex] and height [tex](h)[/tex].
Surface area of a cuboid [tex]=2(lw+wh+hl)[/tex]
But here we have to subtract the surface area of the cover,that is [tex](lw)[/tex].
So the equation for the surface area of the cuboid can be re-framed as [tex]2(wh+hl)+(lw)[/tex]
Plugging the values of [tex]h=8\ ft[/tex] and [tex]l=12\ ft[/tex] and [tex]w=5\ ft[/tex]
Now
Surface area of the tank:
[tex]2(wh+hl)+(lw)[/tex]
[tex]2(5\times 8+8\times 12)+(12\times 5)[/tex]
[tex]2(40+96)+(60)[/tex]
[tex]2(136)+60[/tex]
[tex](272+60)=332\ ft^{2}[/tex]
So the surface area of the fish tank in the hospital is [tex]332\ ( ft)^{2}[/tex]
A box of laundry detergent contains 35 cups. It takes 1 1/4 cups per load of laundry.
Part A. Write an equation to represent how many loads x you can wash with one box.
Part B. How many loads can you wash with one box.?
Part C. How many loads can you wash with 3 boxes.?
Answer:
I don't know nan molla
Step-by-step explanation:
For example, Kino had a good opportunity to barely have a better life and he could have done anything to save his family but instead of doing that he refused to take the 1500 pesos.
Bri and Ali are the owners of Forever Nails. Bris work day is 7 hours and Mables work day is 5 hours. Bri and Ali each work 35 hours per week. On Monday, Bri has 13 clients in 7 hours and Ali has 11 clients in 5 hours. They each earn 14.25 per client. Assuming that for the rest of the week Bri and Ali have the same number of clients per workday as they did on Monday, what will be the difference between their weekly earnings?
Answer:
The difference between their weekly earning is $(1097.25 - 926.25) = $171.
Step-by-step explanation:
In 7 hours Bri has 13 clients and he earns $14.25 per client.
So, in 35 hours working in a week, Bri will get [tex]\frac{13 \times 35}{7} = 65[/tex] clients and he earns $(14.25 × 65) =$926.25 from his clients.
Again, in 5 hours Ali has 11 clients and he earns $14.25 per client.
So, in 35 hours working in a week, Bri will get [tex]\frac{11 \times 35}{5} = 77[/tex] clients and he earns $(14.25 × 77) =$1097.25 from his clients.
Therefore, the difference between their weekly earning is $(1097.25 - 926.25) = $171. (Answer)
$(1097.25 - 926.25) = $171 in 7 hours bri has 13 clients and he earns $14.25 per client in 5 hours ali has 11 clients and he earns $14.25 per client. the difference between their weekly earnings is 1097.25 - 926.25 = $171.
Select the graph of the solution. Click until the correct graph appears. |x| = 2
Graph of |x| = 2 is two vertical lines symmetric about the y-axis, intersecting x-axis at (2, 0) and (-2, 0).
The equation |x| = 2 represents two parallel vertical lines symmetrically positioned about the y-axis. These lines intersect the x-axis at points (2, 0) and (-2, 0), indicating the absolute value of x being equal to 2. The graph exhibits symmetry with respect to the y-axis, forming a V-shape.
It conveys that any value of x, whether positive or negative, yielding an absolute value of 2 satisfies the equation. The graph emphasizes the notion that the distance of x from the origin is fixed at 2 units, illustrating a clear geometric representation of the absolute value function.
What is the equation of the line that is parallel to y=6x−1 and passes through the point (−3,4)?
The equation will be in slope-intercept form.
Answer:
y=6x+22
Step-by-step explanation:
we know that the slope of a parrallel line is the same as the other line. so that gives us y=6x +b. to find b, x needs to equal 0, so to do that we must add 3 to x. we also need to add 3×6 to the y value of 4 to find the y intercept. therefore, the y intercept is 22
The slope of the given line is 6. The line parallel to this passing through the point (-3,4) would also have a slope of 6. Solving for y-intercept, we get the equation of the line as y = 6x + 22.
Explanation:To find the equation of a line that is parallel to the given line and passes through a particular point, we need to use the fact that parallel lines have the same slope.
Given the equation y=6x-1, we can observe that the slope of this line is 6. As such, the line parallel to this one will also have a slope of 6.
Given the point (-3,4), the equation of the line parallel to the given line and passing through the indicated point in the form y=mx+c, where m is the slope and c is the y-intercept, can be found by substituting the x and y values from the point and the known slope m=6 into the equation to solve for c.
4 = 6*(-3) + c.
After solving, c = 22.
Therefore, our desired equation of the line is y = 6x + 22.
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Write the equation of a line that is perpendicular to y =3x-2 and that passes through the point(-9,5)
Answer:
y = -1/3x + 8
Step-by-step explanation:
If two lines are perpendicular, the signs of the slope must be opposite and the slopes are reciprocals.
(basically if one is say -2/3, the other is 3/2. just flip it upside down)
So this slope is 3, so the new slope should be -1/3
The equation is now y = -1/3x + b
To find b, substitute (-9,5) in the equation
y = -1/3x + b
5 = -1/3(9) + b
5 = -3 + b
8 = b
So the equation is y = -1/3x + b
Answer:
y = -1/3x + 2
Step-by-step explanation:
I dont know who verified the other guy but he is wrong
what is the perimeter of an equilateral triangle whose height is 2√3
Answer:
12
Step-by-step explanation:
The perimeter of an equilateral triangle is 12 unit.
Let us consider that, each side of equilateral triangle is a . Because in equilateral triangle each sides are equal in length.
Apply Pythagoras theorem,
[tex](2\sqrt{3} )^{2}+(\frac{a}{2} )^{2}=a^{2} \\\\12+\frac{a^{2} }{4} =a^{2}\\\\a^{2}-\frac{a^{2} }{4} =12\\\\\frac{3}{4}a^{2}=12\\\\a^{2}=16\\\\a=4[/tex]
The perimeter of an equilateral triangle = [tex]3*a[/tex]
= [tex]3*4=12unit[/tex]
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I need help with question 10 (math work is about adding fractions with putting them in simplest form)
Answer: The answer is equivalent fractions.
Step-by-step explanation:
I hope this helped you! :D
Let f(x) = 3/4 x
Let g(x) = (3/4)x – 6
Which statement describes the graph of g(x) with respect to the graph of f(x)?
g(x) is translated 6 units right from
f(x).
g(x) is translated 6 units left from
f(x).
g(x) is translated 6 units down from
f(x)
g(x) is translated 6 units up from
f(x)
Answer:
g(x) is translated six units down from f(x).
Step-by-step explanation:
f(x ± k) is for a horizontal translation. So that rules out the first two.
f(x) ± k is a vertical translation. In this case, a negative number means it's moving down and a positive means it's moving up. Because we have a negative (in other words subtracting) we move line on the graph down.
The best description of the graph of g (x) with respect to the graph of
f (x) will be;
''g (x) is translated 6 units down from f (x)''
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The functions are,
⇒ f (x) = 3/4 x
And, g(x) = (3/4)x - 6
Now,
Since, We know that;
The function f (x) after the translation 'a' unit down, so we get the new function,
⇒ g (x) = f (x) - a
Here, The function g (x) is translation of f (x).
Thus, The best description of the graph of g (x) with respect to the graph of f (x) will be;
''g (x) is translated 6 units down from f (x)''
Therefore, The best description of the graph of g (x) with respect to the graph of f (x) will be;
''g (x) is translated 6 units down from f (x)''.
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What are the factors of the polynomial: x^3+5x^2-17x-21
Answer: (x-3)(x+1)(x+7)
Step-by-step explanation:
Answer:D on edge :) (x+7)(x-3)(x+1)
Step-by-step explanation:did the test
Belle the cat naps 56 hours per week during daylight hours how many hours each day does bell nap? Write a division sentence with a blank for the missing number and solve
Answer: Its 8 hours a day.
56/7=8hours
order of operations with integers:
Please include steps:
- 5 x 6 -7
Answer:
-37
Step-by-step explanation:
-5(6) - 7
= -30-7
= -37
Hope this helps!
Answer:
-37.
Step-by-step explanation:
The order of operations is given by PEDMAS.
ParenthesesExponentsDivideMultiplyAddSubtract.
- 5 x 6 - 7:
Multiplication is done before Subtraction:
= -30 - 7
= -37.