Answer:
The set of equations has an infinite number of solutions
Step-by-step explanation:
The system of linear equations represented by the following equations:
Line A: 4x + 4y = 16 and Line B: x + y = 4 are dependent.
This is because both equations represent the same line;
if we divide both sides of the equation of line A by 4, we would obtain
x + y = 4, which is basically the equation of line B
If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.
Christopher has six times as much money as Michael. If Michael earns $80 and Christopher earns $60, Christopher will then have three times as much money as Michael. How much money do Christopher and Michael have before and after earning $60 and $80, respectively?
Answer:
360 and 60.
Step-by-step explanation:
Let Christopher earns x amount of money and y be money earned by Michael.
Firstly, Christopher has six times as much money as Michael so,
x=6y........ (i)
If Michael earns $80 and Christopher earns $60, Christopher will then have three times as much money as Michael so,
x+60=3(y+80)
From (i),
6y +60= 3(y+80)
3(2y+20)=3(y+80)
2y+20=y+80
2y-y=80-20
y=60
Substituting value of y in equation (i),
x=6×60=360.
Therefore, Christopher earned 360 and Michael earned 60.
Final answer:
Initially, Michael has $60, and Christopher has $360. After Michael earns $80 and Christopher earns $60, Michael will have $140, and Christopher will have $420.
Explanation:
Let's denote Christopher's initial amount of money as C and Michael's initial amount of money as M.
According to the given information, Christopher has six times as much money as Michael: C = 6M.
When Michael earns $80, and Christopher earns $60, Christopher will then have three times as much money as Michael: C + $60 = 3(M + $80).
Now we can solve these two equations together:
C = 6M
C + $60 = 3(M + $80)
Substitute the expression from the first equation into the second equation:
6M + $60 = 3(M + $80)
6M + $60 = 3M + $240
Combine like terms:
6M - 3M = $240 - $60
3M = $180
Divide both sides by 3:
M = $60
Use the value of M to find C:
C = 6M = 6 × $60
C = $360
Now, adding their respective earnings:
Michael's new total: $60 + $80 = $140
Christopher's new total: $360 + $60 = $420
What is the opposite of -|-7| ?
Answer:
7
Step-by-step explanation:
-|-7|=
-1 (|-7) =
|-7| = absolute value of |-7| is 7 because an absolute number is always positive.
the minus symbol should be -1.
so the sum is -1(7) = -7
the opposite of -7 is 7
Answer:
Step-by-step explanation:
the opposite of -|-7| is : - (-|-7|) = 1+7l
An exam was given to a group of freshman and sophomore students. The results are below:
Freshman: 106 got A’s, 130 got B’s, and 149 got C’s.
Sophomore: 192 got A’s, 118 got B’s, and 168 got C’s.
If one student is chosen at random from those who took the exam, find the probability that:
b)The student was a freshman or received a C .
c) The student was a sophomore, given they got a
C.
d) The student got an A, given they are a freshman.
*round to 4 decimal places as needed*
A rectangular field is 400 meters long and 300 meters wide area in square kilometers
A rectangle is the shape with parallel opposite sides, combined with all the 90 degree angles. As the type of the parallelogram, it has the opposite parallel sides. In the rectangle, 1 set of parallel sides is longer than the other, making it look like an elongated square
The rectangle field is 400 meters long and 300 meters wide. What is the area in square kilometers?
1km=1000m
Secondly the area of the rectangle is defined as the product of the width or the height:
A= w∗h
We could now approach the problem in 2 ways, we convert the sides of the rectangle to kilometers 1st and we convert the area from square meters to the square kilometers.
Convert sides:Let w = width, h = height and A = area
w=300m=300/1000m=0.3km
h=400m=400/1000m=0.4km
A=0.3∗0.4km2=0.12km2
Convert area:Let's first calculate the area in square meters:
Am=300∗400=120000m2
We know from above that 1km=1000m
That gives 1km2=1000∗1000m2=1000000m2
So Ak=Am/1000000=0.12km2
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the area of the rectangular field is 0.12 square kilometers.
To calculate the area of a rectangular field in square kilometers, you need to multiply the length and width of the field and then convert the result from square meters to square kilometers. Given that the rectangular field is 400 meters long and 300 meters wide, the area in square meters is calculated as follows:
Area = length × width = 400 m × 300 m = 120,000 m2
Since 1 square kilometer (km2) is equal to 1,000,000 square meters (m2), you convert square meters to square kilometers by dividing by 1,000,000:
Area in square kilometers = Area in square meters / 1,000,000 = 120,000 m2 / 1,000,000 = 0.12 km2
Therefore, the area of the rectangular field is 0.12 square kilometers.
Which functions are even? check all the boxes that apply.
pls hurry!!
If a function is even, it gives the same result for positive and negative inputs such as 8 and -8.
From the choices, the even functions are D and A.
D because the absolute value thing makes any input positive, and A because any number raised to an even power gives a positive result.
A function assigns the value of each element of one set to the other specific element of another set. The correct options are A and D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A function is an even function if f of x is equal to f of −x for all the values of x.
A.)
f(x) = x⁴ - x²
f(-x) = (-x)⁴ - (-x)²
= x⁴ - x²
Since f(x) and f(-x) are equal, therefore, the given function is a function.
B.)
f(x) = x² - 3x + 2
f(-x) = (-x)² - 3(-x) + 2
= x² + 3x + 2
Since f(x) and f(-x) are not equal, therefore, the given function is a function.
C.)
f(-x) = √[(-x)- 2]
= √(-x- 2)
Since f(x) and f(-x) are not equal, therefore, the given function is a function.
D.)
f(x) = |x| = x
f(-x) = |-x| = x
Since f(x) and f(-x) are equal, therefore, the given function is a function.
Hence, the correct options are A and D.
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The graph of which function has an axis of symmetry at x = 3?
f(x) = x2 + 3x +1
f(x) = x2 -3x - 3
f(X) = x2 + 6x + 3
f(x) = x2 - 6x - 1
f(x) = x² - 6x - 1
To find the axis of symmetry, use the axis of symmetry formula: -b\2a, according to the Quadratic Equation y = Ax² + Bx + C. You understand?
Answer:
[tex]f(x) = x^2 - 6x -1[/tex]
Step-by-step explanation:
To find axis of symmetry we use formula
[tex]x=\frac{-b}{2a}[/tex]
[tex]f(x) = x^2 + 3x +1[/tex]
a=1, b=3
[tex]x=\frac{-3}{2}[/tex]
[tex]f(x) = x^2 -3x - 3[/tex]
a=1, b=-3
[tex]x=\frac{3}{2}[/tex]
[tex]f(x) = x^2 + 6x + 3[/tex]
a=1, b=6
[tex]x=\frac{-6}{2}=-3[/tex]
[tex]f(x) = x^2 - 6x -1[/tex]
a=1, b=-6
[tex]x=\frac{6}{2}=3[/tex]
James wants to build a wooden barrel to hold rain water to use for irrigation. He wants the height of the barrel in feet to be 4 less
than the area of the base in square feet. He also wants the area of the base in square feet to be equal to its perimeter in feet. He
also needs to place a pump inside the barrel to move the collected water. After the pump is put inside the barrel, he needs it to
still hold at least 90 cubic feet of water
The cost for the materials to build the barrel will be 58 per square foot. Since the barrel is meant to catch rain water, he will not
need a top. The cost of the pump is proportional to its volume. For each cubic foot of volume that the pump takes up the cost
will be 550 James can only afford to spend up to $1,100 on this project
If x represents the area of the base of the barrel in square feet and y represents the volume of the pump in cubic feet, then which
of the following systems of inequalities can be used to determine the dimensions of the barrel and the volume of the pump?
Answer:
Step-by-step explanation:
To create a system of inequalities, write an inequality to model each condition that must be satisfied in the given situation.
It is given that x represents the area of the base of the barrel in square feet and y represents the volume of the pump in cubic feet.
Write an inequality to represent the amount of water that the barrel needs to hold after the pump is inserted. To find the volume of the barrel, multiply the area of the base by the height of the barrel. Then subtract the volume that will be taken up by the pump from that amount.
x(x-4) - y ≤ 90
To find the cost of the supplies for the barrel, find the surface area by multiplying the perimeter of the base by the height of the barrel and then adding the area of the base. Since there is no top, the area of the base only needs to be added once. Then, multiply the cost per square foot by the surface area.
To find the cost of the pump, multiply the cost per square foot of the pump by its volume.
Write an inequality representing the total cost. The cost must be less than or equal to $1,100.
8(x(x-4)+x) + 50y ≤ 1,100
Combining both of the inequalities gives the following system of inequalities.
x(x-4) - y ≤ 90
8(x(x-4)+x) + 50y ≤ 1,100
Answer:
The answer is
x(x-4) - y GREATER THAN OR EQUAL TO 90
8(x(x-4) + x) +50y LESS THAN OR EQUAL TO 1,100
Step-by-step explanation:
-5=c/7 solve equation
Answer:
c=−35
Step-by-step explanation:
Let's solve your equation step-by-step.
−5=
c
7
Step 1: Simplify both sides of the equation.
−5=
1
7
c
Step 2: Flip the equation.
1
7
c=−5
Step 3: Multiply both sides by 7.
7*(
1
7
c)=(7)*(−5)
[tex]\frac{c}{7} = -5[/tex]
***I switched the order of c/7 and -5. It means the same thing, but I just find it easier this way
To solve for c you must isolate this by bringing 7 to the other side. To do this you must multiply 7 to both sides. This will cancel 7 from the left side (the right side in the way the equation is written in the question) and bring it over to the right side
[tex]7(\frac{c}{7} ) = -5 * 7[/tex]
c = -35
Hope this helped!
~Just a girl in love with Shawn Mendes
Solve log_8 12 = x – 2 . Round your answer to four decimal places.
Step-by-step answer:
Let's attack the left side:
log_8 12 = log (base 8) 12 = log(12)/log(8) = 1.1949875 (approx.)
Next solve
log_8 12 = x-2
log(12)/log(8) = x-2
x = 2 + log(12)/log(8)
= 3.195 (to one thousandth)
For this case we have the following expression:
[tex]log_ {8} (12) = x-2[/tex]
We rewrite how:
[tex]x-2 = log_ {8} (12)[/tex]
We add 2 to both sides of the equation:
[tex]x = log_ {8} (12) +2[/tex]
We rewrite [tex]log_ {8} (12)[/tex] as[tex]log_ {8} (2 ^ 2 * 3):[/tex]
[tex]x = log_ {8} (2 ^ 2 * 3) +2[/tex]
We apply logarithm properties:
[tex]x = log_ {8} (2 ^ 2) + log_ {8} (3) +2[/tex]
We apply logarithm properties:
[tex]x = 2log_ {8} (2) + log_ {8} (3) +2[/tex]
The logarithmic base 8 of 2 is [tex]\frac {1} {3}:[/tex]
[tex]x = 2 (\frac {1} {3}) + log_ {8} (3) +2\\x = \frac {2} {3} + log_ {8} (3) +2[/tex]
We simplify:
[tex]x = \frac {2} {3} + 2 + log_ {8} (3)\\x = \frac {2 + 6} {3} + log_ {8} (3)\\x = \frac {8} {3} + log_ {8} (3)[/tex]
Decimal form:
3,195
Answer:
[tex]x = \frac {8} {3} + log_ {8} (3) = 3,195[/tex]
21. Which property is represented by the
equation below?
2/3 x 3/2=1
A. Multiplicative Inverse Property
B. Multiplicative Identity Property
C. Distributive Property
D. Commutative Property of
Multiplication
Answer:
A. Multiplicative Inverse Property
X=1
Step-by-step explanation:
First, you do is multiply fractions from left to right.
[tex]\frac{2*3}{3*2}x=1[/tex]
Then, you can cancel the fraction out.
Common factor term of 2.
[tex]=\frac{3}{3}[/tex]
Divide the numbers.
[tex]\frac{3\div3=1}{3\div3=1}=1[/tex]
[tex]x*1=1[/tex]
X=1 is the correct answer.
Multiplicative Inverse Property is the correct answer.
prove that angle abc is a right angle with vertices a(-4,3), B(0,-1) and C(2,1)
Check the picture below.
clearly the angle at vertex C isn't the right angle, so let's check if AB ⟂ BC.
[tex]\bf A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad B(\stackrel{x_2}{0}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-3}{0-(-4)}\implies \cfrac{-4}{0+4}\implies \cfrac{-4}{4}\implies -1 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf B(\stackrel{x_1}{0}~,~\stackrel{y_1}{-1})\qquad C(\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-1)}{2-0}\implies \cfrac{1+1}{2}\implies \cfrac{2}{2}\implies 1 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-1\implies \cfrac{-1}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{1}{-1}}\qquad \stackrel{negative~reciprocal}{+\cfrac{1}{1}\implies 1}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{so is a right triangle}}{AB\perp BC}~\hfill[/tex]
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
–2.2, –11.8, –19.8
–3, –11.8, –25
–3, –9.6, –22.8
0, –6.6, –19.8
Answer:
–3, –9.6, –22.8
Step-by-step explanation:
Given rule is:
[tex]A(n) =-3+(n-1)(-2.2)[/tex]
So,
For first term:
[tex]A(1) =-3+(1-1)(-2.2)\\A(1) = -3 +0\\= 0[/tex]
For fourth term:
[tex]A(4) =-3+(4-1)(-2.2)\\=-3+(3)(-2.2)\\=-3+ (-6.6)\\=-3-6.6\\= -9.6[/tex]
For tenth term:
[tex]A(10) =-3+(10-1)(-2.2)\\=-3+(9)(-2.2)\\=-3+ (-19.8)\\=-3-19.8\\= -22.8[/tex]
The first, fourth and tenth terms are -3, -9.6 and -22.8 respectively.
So, third option is correct ..
what is the slope-intercept from of the equation y+5=4(x+8)?
Answer:
y=4x+27
Step-by-step explanation:
y+5=4(x+8)= (5-)y+5=4x+32(-5)
y=4x+27
Think about the system associated with the equation –x2 + x + 6 = 2x + 8.
Which graph represents the system?
Answer: see graph
Step-by-step explanation:
Set each equation equal to y, then graph each equation.
y = -x² + x + 6 (parabola)
y = 2x + 8 (line)
Notice that the system has NO SOLUTION because the parabola and the line never intersect.
The given equation represents the inconsistent system (It has no solution).
What is meant by an inconsistent system?The graphs of a system that does not have any point of intersection are said to be inconsistent system. Which means the system has no solution.
Graphing:The given system of equations as
[tex]y=-x^2+x+6[/tex] and [tex]y=2x+8[/tex]
So, plotting these equations in the graph,
We get a curve and a line that do not have any intersections.
So, the given system has no solution.
Therefore, the given system is an inconsistent system.
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If x varies directly with y and x = 6 when y = 15, find x when y= 20.
Answer:
8
Step-by-step explanation:
Varies directly think y=kx
Varies indirectly think y=k/x
We have first option so y=kx
x=6 and y=15 means we have 15=k(6)
So k=15/6 or reducing gives=5/2
So we just found our constant of proportionality, this number never changes. It stays the same no matter what x or y they give you...
So the equation is y=5/2 *x
Now what is x if y=20
Plug in 20=5/2 *x
So x=20*2/5=40/5=8
Classify the triangle.
scalene
equilateral
isosceles
Answer:
Scalene
Step-by-step explanation:
Note the definition of each triangle:
Equilateral: For a triangle to be an Equilateral, all sides must have the same measurements.
Isosceles: For a triangle to be an Isosceles, the two leg sides must be congruent. The base can vary, but cannot equal the leg sides.
Scalene: For a triangle to be an Scalene, none of the sides can be congruent.
~
Answer:
scalene
Step-by-step explanation:
an scalene triangle has sides of all different lengths
What value of c makes the polynomial below a perfect square?
x^2+14x+c
c=
A) 196
B) 49
C) 7
D) 28
Answer:
The value for c is B. 49
Mr. Shaw graphs the function f(x) = –5x + 2 for his class. The line contains the point (-2, 12). What is the point-slope form of the equation of the line he graphed?
Answer:
y - 12 = - 5(x + 2)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Given f(x) = - 5x + 2 ← in slope- intercept form with slope m = - 5
using m = - 5 and (a, b) = (- 2, 12), then
y - 12 = - 5(x - (- 2)), that is
y - 12 = - 5(x + 2) ← on point- slope form
Answer:
a y – 12 = –5(x + 2)
Step-by-step explanation:
Working out diameter and radius from circumference. How.
Answer:
d = 28 cm
r = 14 cm
Step-by-step explanation:
Circumference = Pi × Diameter
( Divide both sides by Pi )
Circumference ÷ Pi = Diameter
28 ÷ π = Diameter
Diameter = 28
Radius = Half the diameter
28 ÷ 2 = 14
somebody pleaseeeee helppppppp quick!!!!!!!!!!
Mia surveys a random sample of 260 students from her middle school to learn what type of school lunch is preferred. The table below shows the result of the survey:
Lunch Type Sandwich Hot Dog Salad
Number of students 122 15 123
Which of the following inferences can be made based on the data?
A sandwich is the most preferred lunch.
Sandwiches and salads are almost equally preferred.
A hot dog is two times more popular than sandwich.
A salad is almost two times more popular than a hot dog.
Answer:
the answer is the second one
Answer:
The correct answer is "Sandwiches and salads are almost equally preferred."
Step-by-step explanation:
From the survey, we get
122 students prefers Sandwich
15 students prefers Hot Dog
123 students prefers Salad
We are going to analyse every option
A sandwich is the most preferred lunch. FALSE
Most preferred lunch is Salad (123) , sandwich is 122
Sandwiches and salads are almost equally preferred. TRUE
A hot dog is two times more popular than sandwich. FALSE
No, hot dog is 15 , and sandwich is 122, sandwich is more popular than hot dog
A salad is almost two times more popular than a hot dog. FALSE
No, hot dog is just 15 , and salad 123 more than 8 times hot dog
0.2 is 1/10 of 2 true or false
Answer:
true
Step-by-step explanation:
1/10=0.1
0.1*2=0.2
By property of fraction, 0.2 is 1/10 of 2 is true.
What is property of fraction ?By the property of fraction we know that 1/x times of a is a/x where a and x are two non-zero real numbers.
Given statement is 1/10 of 2
Thus we have, 1/10*2 = 2/10
And, 2/10 = 0.2 .
Therefore, by property of fraction, 0.2 is 1/10 of 2 is true.
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2 Points
Each exterior angle of a regular polygon measures 24°. How many sides
does the polygon have?
O A. 15
O B. 24
O C. 16
O D. 18
SUBMIT
The number of the sides of the polygon will be 15. Then the correct option is A.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
Each exterior angle of a regular polygon measures 24°.
Then the number of the sides of the polygon will be
Let n be the number of the sides. Then we have
360° / n = 24°
n = 360° / 24°
n = 15
Then the number of the sides of the polygon will be 15.
Then the correct option is A.
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The power of (-7)4 is negative. True False
Answer:
i believe its positive
Step-by-step explanation:
Answer:
false
Step-by-step explanation:
KLMN and PQRS are similar trapezoids. which side of PQRS corresponds to LM
Answer:
QR
Step-by-step explanation:
KLMN is in the same spot as PQRS
Answer:
QR corresponds to LM
Step-by-step explanation:
Two figures are said to be similar if they have same shape but not necessarily same size.
Two polygons are said to be similar if their corresponding angles are equal and corresponding sides are proportional .
A trapezoid is a polygon in which a pair of sides is parallel .
Here, two trapezoids are given i.e KLMN, PQRS.
As KLMN and PQRS are similar, so their angles are equal i.e
[tex]\angle K=\angle P\,,\,\angle L=\angle Q\,,\,\angle M=\angle R\,,\,\angle N=\angle S[/tex]
Also, corresponding sides are proportional i.e
[tex]\frac{KL}{PQ}=\frac{LM}{QR}=\frac{MN}{RS}=\frac{KN}{PS}[/tex]
Therefore, side QR corresponds to LM.
Use the function to find f(-2)
Answer:
f(-2) = 1/9
Step-by-step explanation:
Plug in -2 to x in the equation:
f(x) = 3^x
f(-2) = 3^(-2)
Solve. Note that if there is a negative in the power, you must flip the "fraction" and set it over 1. The answer itself does not become negative:
f(-2) = 1/(3^2)
f(-2) = 1/(9)
f(-2) = 1/9 is your answer.
~
[tex]\frac{1}{9}[/tex]
Step-by-step explanation:Substitute the -2 into the equation. [tex]f(-2)=3^{-2}[/tex]Begin to simplify the exponent. [tex]x^{-y}=\frac{1}{x^y}[/tex], so you get [tex]f(-2)=\frac{1}{3^2}[/tex]Finish simplifying the exponent. 3 times 3 is 9. [tex]f(-2)=\frac{1}{9}[/tex]Given a cone with a volume of 288, and height 7 in., find the base radius of the cone. Use 3.14 for pi. Round your answer to the
tenths place.
Answer:
The radius of the base is [tex]r=6.3\ in[/tex]
Step-by-step explanation:
we know that
The volume of a cone is equal to
[tex]V=\frac{1}{3}\pi r^{2} h[/tex]
we have
[tex]V=288\ in^{3}[/tex]
[tex]h=7\ in[/tex]
[tex]\pi=3.14[/tex]
substitute and solve for r
[tex]288=\frac{1}{3}(3.14)r^{2} (7)[/tex]
[tex]864=(3.14)r^{2} (7)[/tex]
[tex]r^{2}=864/[(3.14)(7)][/tex]
[tex]r=6.3\ in[/tex]
Help again Please ..thank you whoever helps I’ll mark u Brainliest :)
Answer:
2
Step-by-step explanation:
The median is the middle. The middle of 5 numbers is the third number. the list goes through 12235 so the median is 2
How many positive integers less than 60 have an even number of positive divisors?
Answer:
There are 52 such numbers that have even divisors.
Step-by-step explanation:
All the numbers between 2 and 59 have an EVEN number of positive divisors.
Except the Perfect Squares..
or 4, 9, 16, 25, 36 and 49, which have 3 divisors each.
So:
59 - 2 + 1 =58
Now subtract 58 from 6 (perfect squares)
58- 6=52
Therefore,it means that there are 52 such numbers that have EVEN divisors....
Answer:
52
Step-by-step explanation:
The average value of the function F (T) =(t-4)^2 on [0,9] is
Answer:
7
Step-by-step explanation:
Average value of a function F(t) on interval [a,b]
is [tex] \frac{1}{b-a} \int_a^b F(x)dx[/tex]
So let's plug it in!
a=0
b=9
F(x)=(x-4)^2
To integrate (x-4)^2 just use power rule for integration.
So this what we get
[tex] \frac{1}{9-0} \frac{(x-4)^3}{3}|_0^9 [/tex]
[tex] \frac{1}{9-0} [\frac{(9-4)^3}{3}-\frac{(0-4)^3}{3}] [/tex]
[tex] \frac{1}{9} [\frac{5^3}{3}-\frac{(-4)^3}{3}] [/tex]
[tex] \frac{1}{9} \cdot \frac{125+64}{3} [/tex]
[tex] \frac{1}{9} \cdot \frac{189}{3} [/tex]
7
What is the product of (3) (-16) (-7)(-14),
OA.
7
0
B. -
OC -
OD.
help
Answer:
(3)(-16)(-7)(-14) = (-48)(-7)(-14) = (+336)(-14) = - 4704;
Step-by-step explanation: