Answer:
D:Spring A is 3 m longer than spring B because 15 – 12 = 3.
Step-by-step explanation:
In this question, you should remember the Hooke's Law in physics.
The Hooke's Law simply explains that the extension that occurs on a spring is directly proportional to the load applied on it.
The mathematical expression for this law is
[tex]F=-kx[/tex]
where;
F= force applied on the spring
x = the extension on the spring
k= the spring constant which varies in spring.
The question will need you to calculate the extension on the springs A and B then compare the values obtained.
In spring A
Force, F=60N and spring constant ,k=4 N/m
To find the extension x apply the expression;
[tex]F=-kx\\\\60=-4*x\\\\60=-4x\\\\\frac{60}{-4} =\frac{-4x}{-4} \\\\\\-15=x[/tex]
Here the spring extension is 15 m
In spring B
Force, F=60N and spring constant , k=5N/m
To find the extension x apply the same expression
[tex]F=-kx\\\\60=-5*x\\\\60=-5x\\\\\\\frac{60}{-5} =\frac{-5x}{-5} \\\\\\-12=x[/tex]
Here the extension on the spring is 12 m
Compare
The extension on spring A is 3 m longer than that in spring B because when you subtract the value of spring B from that in spring A you get 3m
[tex]=15m-12m=3m[/tex]
Answer:
D)Spring A is 3 m longer than spring B because 15 – 12 = 3.
trust
Is it possible for two different numbers, when
squared, to give the same result? What does this
result tell you about solving an equation when the
variable is squared? How many solutions will an
equation like this have? Will there always be the
same number of solutions for any equation with a
squared variable? Explain.
Answer:
yes it is possible for two different numbers to eventually have the same result
Step-by-step explanation:
its basically like saying five times 2 which is 10 and 2 times 5 which is also 10 its different numbers but same outcome
Answer:
Yes. Squared variables usually have two solutions, unless they are 0 (1 solution) or negative (no solution).
Step-by-step explanation:
Solving the generic x² = c has two solutions when c>0, one solution when c=0, and no (real) solutions for c<0.
When c>0, the solutions are x = √c and x= -√c.
f(x)=3x^7, as x ---> - infinity the F(x) approaches what
Answer:
negative infinity
Step-by-step explanation:
f(x) = 3 x^7
As x approaches - infinity we do not care about the 3 since it is positive
f(-inf) = (- inf)^7
We can take the negative out since it is to a negative power
f(-inf) = - (inf)^7
inf raised to a power is still infinity
F(-inf) = - inf
It will approach negative infinity
Convert this decimal into its fractional
form, simplified completely.
0.625
Hello There!
Answer Attached In Image Below.
Have A Great Day!
Answer:
5/8
Step-by-step explanation:
0.625 as a fraction is equal to 5/8
When you place 625 over 1000 you get 5/8 when simplified:
625/1000 = 5/8
What is the solution to the following equation?
X+(-13) = -5
The answer is -65
X+(-13)=-5
x=13*-5
13 * -5= -65
x=65
An equation is formed when two equal expressions. The solution of the equation x+(-13) = -5 is 8.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of the equation x+(-13) = -5 is,
x + (-13) = -5
x - 13 = -5
x = -5 + 13
x = 8
Hence, The solution of the equation x+(-13) = -5 is 8.
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Simplify square root of 8y/share root of y
Answer:
[tex]2\sqrt{2}[/tex]
Step-by-step explanation:
We are required to simplify the following expression;
[tex]\frac{\sqrt{8y} }{\sqrt{y} }[/tex]
Using the properties of radicals;
[tex]\frac{\sqrt{a} }{\sqrt{b}}=\sqrt{\frac{a}{b} }[/tex]
The expression can be re-written as;
[tex]\sqrt{\frac{8y}{y}}=\sqrt{8}[/tex]
Now;
[tex]\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}\\ \\2\sqrt{2}[/tex]
What is the length of diameter EF?
3
6
9
Answer:
6
Step-by-step explanation:
You are given the radius, 3
The diameter is twice the radius, so 6.
Which of the following sets are continuous?
Answer:
A, C and D are continuous
Step-by-step explanation:
A is a set of any number x which 30 < x <=45
B is a set that contains only 3 and 7
C is a set of any number x which 60 <= x < 100
D is a set of any number x which -infinity < x < + infinity
E is a set that contains only even whole numbers
A continuous data set is a quantitative data set representing a scale of measurement that can consist of numbers other than whole number, like decimals and fractions.
Step by step If C(m)=0.50m + 30 represents the cost of renting a car, how many miles were driven if the cost is $130
Answer:
200 miles were driven
Step-by-step explanation:
We know that [tex]C (m) = 0.50m + 30[/tex] represents the cost of renting a car
Where m represents the number of miles driven
If we know that the cost was $ 130 then we can equal C(m) to 130 and solve for m.
[tex]C(m) =0.50m + 30=130[/tex]
[tex]0.50m + 30=130[/tex]
[tex]0.50m=130-30[/tex]
[tex]0.50m=100[/tex]
[tex]m=\frac{100}{0.50}[/tex]
[tex]m=200\ miles[/tex]
Two lines, A and B, are represented by the following equations: Line A: 4x + 4y = 16 Line B: x + y = 4 Which statement is true about the solution to the set of equations?
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.
Which equation represents a line that passes through (–9, –3) and has a slope of –6?
y – 9 = –6(x – 3)
y + 9 = –6(x + 3)
y – 3 = –6(x – 9)
y + 3 = –6(x + 9)
The answer is:
The last equation,
[tex]y+3=-6(x+9)[/tex]
Why?To find which of the given equations represents a line that passes through the point (-9,-3) and has a slope of -6, we need to find an equation that can be satisfied by evaluating the given point.
We can see that the only equation that can be satisfied evaluating the point (-9,-3) is the last equation:
[tex]y+3=-6(x+9)[/tex]
Evaluating the point, we have:
[tex]-3+3=-6*(-9+9)[/tex]
[tex]0=-6*(0)[/tex]
[tex]0=0[/tex]
We can see that the equation is satisfied!
Also, we can see that evaluating the point into the other equations, they will not be satisfied.
Let's prove that:
Evaluating:
First equation:
[tex]y-9=-6(x-3)\\-3-9=-6*(-9-3)\\-12=-6*(-12)=72[/tex]
The equation is not satisfied.
Second equation:
[tex]y+9=-6(x+3)\\-3+9=-6*(-9+3)\\6=-6*(-6)=36[/tex]
The equation is not satisfied.
Third equation:
[tex]y-3=-6(x-9)[/tex]
[tex]-3-3=-6(-9-9)[/tex]
[tex]-6=-6(-18)=108[/tex]
The equation is not satisfied.
Hence, the correct option is the last option, the equation that represents a line that passes through (–9, –3) and has a slope of –6 is the last equation:
[tex]y+3=-6(x+9)[/tex]
Have a nice day!
Note: I have attached a picture for better understanding.
Answer: D. y + 3 = –6(x + 9)
Step-by-step explanation:
10 In(100x) – 3 = 117
To solve the equation 10 ln(100x) - 3 = 117, first isolate the ln(100x) by adding 3 to both sides and then divide by 10. Exponentiate both sides with base e to remove the ln, and finally divide by 100 to solve for x.
Explanation:Solve the logarithmic equationWe are given the equation 10 ln(100x) – 3 = 117. To solve for x, follow these steps:
Add 3 to both sides of the equation to isolate the logarithmic expression.
10 ln(100x) = 120
Divide both sides by 10 to isolate ln(100x).ln(100x) = 12
To remove the natural log, we exponentiate both sides with base e.100x = e^12
Divide both sides by 100 to solve for x.x = (e^12) / 100
Now, by using a calculator we can find the value of e^12 and then divide it by 100 to find the value of x.
Final answer is: x = 1627.54
A factory is currently running at 85% of it's original capacity, and management is considering upgrading the equipment. The upgrade will take 6 months, during which time the factory will not run at all. Once complete, the factory's output will increase to 120% of the original capacity. After how long would the upgraded factory's production match the current 85% production, or how long will it take for the factory to make up for the loss of six months? If you get stuck, try letting the factory's original output be 100 units per month.
Answer:
15 months needed
The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function? The domain is all real numbers. The range is {y|y < 16}. The domain is all real numbers. The range is {y|y ≤ 16}. The domain is {x|–5 < x < 3}. The range is {y|y < 16}. The domain is {x|–5 ≤ x ≤ 3}. The range is {y|y ≤ 16}.
Answer:
The domain is all real numbers. The range is {y|y ≤ 16}
Step-by-step explanation:
we have
[tex]f(x)=-x^{2}-2x+15[/tex]
This is a the equation of a vertical parabola open downward
The vertex is a maximum
The vertex is the point (-1,16)
see the attached figure
therefore
The domain of the function is all real numbers ----> interval (-∞,∞)
Te range of the function is
[tex]y\leq 16[/tex]
All real numbers less than or equal to 16 ----> interval (-∞,16]
Answer:b
Step-by-step explanation:
Find the indicated term of the given geometric sequence.
a = 14, r = –2, n = 11
Answer:
-14336
Step-by-step explanation:
We are given the first term (a) = 14, the common ratio (r) = -2 and the number of term (n) = 11 that we are to find for a geometric sequence.
We know that the formula of nth term for a geometric sequence is given by:
[tex]n^{th}term = ar^{n-1}[/tex]
Substituting the given values in the above formula to find the 11th term:
11th term = [tex] 14 \times 2^{11-1}[/tex] = -14336
Miriam has a jar of one dollar bills, dimes, and pennies in her closet. If she has a total of 963 cents, which combination
would be less money than she has?
A.9 one dollar bills, 50 dimes, and 1 penny.
B.900 one dollar bills, 3 dimes, and 8 pennies
C.9 one dollar bills, 5 dimes, and 6 pennies
D.900 one dollar bills, 60 dimes, and 2 pennies
The combination that represents less money than Miriam has (963 cents) is option C, which has a total of 956 cents.
Explanation:First, let's remember the conversion of dollars, dimes, and pennies into cents. One dollar is equivalent to 100 cents, a dime is equal to 10 cents and a penny is one cent. So to solve the problem, we convert all the options into cents and find out which combination is less than 963 cents.
1. Option A: (9*100 cents) + (50*10 cents) + (1*1 cent) = 900 + 500 + 1 = 1401 cents
2. Option B: (900*100 cents) + (3*10 cents) + (8*1 cent) = 90000 + 30 + 8 = 90038 cents
3. Option C: (9*100 cents) + (5*10 cents) + (6*1 cent) = 900 + 50 + 6 = 956 cents
4. Option D: (900*100 cents) + (60*10 cents) + (2*1 cent) = 90000 + 600 + 2 = 90602 cents
Among all the options, option C is the only combination that is less than 963 cents.
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help me help me plsss
60 points
-75 = -8b - 7b
To solve for "b" you must isolate it, meaning that "b" must be the only thing on the right side of the equation.
First you must combine like terms. Like terms are numbers that have matching variables OR are numbers with out variables. In this case the like terms are -8b and -7b, since they both have the variables "b" attached.
-8b + (-7b) = -15b
so...
-75 = -15b
Next, to completely isolate b, divide -15 to both sides. Since -15 is being multiplied by b, division (the opposite of multiplication) will cancel -15 out (in this case it will make -15 one) from the right side and bring it over to the left side.
-75/-15 = -15b/-15
5 = 1b
b = 5
Check:
-75 = -8(5) - 7(5)
-75 = -40 - 35
-75 = -75
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
8b is the answer to this question.
Step-by-step explanation:
Use the quadratic function to predict f(x) if x equals 8.
f(x) = 25x2 − 28x + 585
Answer:
1961
Step-by-step explanation:
replace x with 8
25(8)^2-28(8)+585
25(64)-28(8)+585
1600-224+585
1961
f(8) = 1961.
The quadratic function given is: f(x) = 25x2 - 28x + 585
To predict f(x) when x = 8:
Substitute x = 8 into the function:
f(8) = 25(8)2 - 28(8) + 585
f(8) = 25(64) - 224 + 585
f(8) = 1600 - 224 + 585
f(8) = 1961
Therefore, f(8) equals 1961.
Name the property: 3x(4x5)=(3x4)x5
Answer:
Commutative Property because it only switched the numbers around.
The property represented by the equation 3x(4x5)=(3x4)x5 is the Associative Property of Multiplication, which indicates that numbers' grouping does not influence the outcome of multiplication.
Explanation:The property represented by the equation 3x(4x5)=(3x4)x5 is called the Associative Property of Multiplication. This property states that the way in which numbers are grouped when being multiplied does not change the product. In your equation, whether you multiply 4 and 5 first (in the expression 3x(4x5)) or 3 and 4 first (in the expression (3x4)x5), the result is the same.
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Graph g(x), where f(x)=2x-5 and g(x)=f(x+1)
Answer:
Graph g(x) = 2x - 3
Step-by-step explanation:
Plug in (x+1) to f(x) = 2x - 5:
g(x) = 2(x+1) - 5 = 2x + 2 - 5
g(x) = 2x - 3
Answer:
Refer the attached figure.
Step-by-step explanation:
Given : Functions [tex]f(x)=2x-5[/tex] and [tex]g(x)=f(x+1)[/tex]
To find : Graph g(x)?
Solution :
First we find the function g(x),
As [tex]g(x)=f(x+1)[/tex]
Finding f(x+1) by substituting x=x+1 in f(x)
[tex]f(x+1)=2(x+1)-5[/tex]
[tex]f(x+1)=2x+2-5[/tex]
[tex]f(x+1)=2x-3[/tex]
Substitute in g(x),
[tex]g(x)=2x-3[/tex]
Now, To plot the g(x) we find the x-intercept and y-intercept
x-intercept, g(x)=0
[tex]2x-3=0[/tex]
[tex]x=\frac{3}{2}[/tex]
y-intercept, x=0
[tex]g(x)=2(0)-3[/tex]
[tex]g(x)=-3[/tex]
Plotting these two points draw the graph,
Refer the attached figure below.
the number 3.453 has two 3s.Why does each 3 have a different value
Hello There!
They're in different places the 3 in the ones place couldn't equal as much as the three in the thousands place. It all depends on where the numbers are in relation to the decimal.
The perimeter of the scalene triangle is 60 cm. The length of the longest side is 4 times that of the shortest side.
Which statements about the possible measures of the sides are reasonable? Check all that apply.
The value of x can equal 40.
The longest side can equal 30 cm.
The shortest side can equal 7 cm.
The value of x can equal 25.
The shortest side can equal 5.
Answer:
Only option C: The shortest side can equal 7 cm.
Step-by-step explanation:
Let the length of the shortest side be x cm, then the length of the longest side is 4x cm. Let the length of the middle side be y cm. Note that
[tex]x<y<4x[/tex]
The perimeter is
[tex]x+y+4x=60\\ \\5x+y=60[/tex]
A. The value x cannot be 40 cm, because then y is negative
B. If the longest side is 30 cm long, then
[tex]4x=30\\ \\x=7.5\\ \\y=60-5\cdot 7.5=22.5[/tex]
But
[tex]x+y=7.5+22.5=30\ cm[/tex]
This means that such triangle does not exist
C. If x=7 cm, then 4x=28 cm,
[tex]y=60-5\cdot 7=25\ cm[/tex]
Since,
[tex]7+25=32>28\\ \\7+28=35>25\\ \\25+28=53>7,[/tex]
such triangle exists and this option is possible
D. If x=25 cm, then y is negative
E. If x=5 cm, then 4x=20 cm and
[tex]y=60-5\cdot 5=35\ cm[/tex]
But this triangle does not exist, because [tex]5+20<35[/tex]
The longest side of this scalene triangle with a perimeter of 60 cm can equal 30 cm or the shortest side can equal 7 cm.
Further ExplanationWe can use the variables x, y and z to represent the shortest (x), medium (y) and longest (z) sides. The perimeter of a triangle is found by adding together all of the sides; this gives us the equation
x + y + z = 60
We know that the longest side, z, is equal to 4 times the length of the shortest side, x. This means that z = 4x; we can now write our equation as
x + y + 4x = 60
Combining like terms, we have
5x + y = 60
1. Checking all of the possible options, we first determine if x can equal 40:
5(40) + y = 60200 + y = 60This would give us a negative side length, which is impossible.
2. Let the longest side be 30 cm. This means that the shortest side is 1/4 of that; 30÷4 = 7.5. Using 7.5 for x,
5(7.5)+y = 6037.5 + y = 6037.5 + y - 37.5 = 60-37.5y = 22.5This is within the range of acceptable side lengths, since it is between the smallest (7.5) and the largest (30).
3. Let the shortest side be 7 cm. This means x = 7:
5(7)+y = 6035+y = 6035+y-35 = 60-35y = 25This is between the longest side, 7 cm, and the longest side, 4(7) = 28 cm. This is acceptable.
4. Let the value of x be 25:
5(25)+y = 60125+y = 60This will give us a negative value for the medium side, which is impossible.
5. Let the shortest side be 5 cm. This means x = 5:
5(5)+y = 6025+y = 6025+y-25 = 60-25y = 35This means the medium value, 35, would be greater than the longest side, 20; this is incorrect.
This means the correct options are that the longest side can be 30 cm and the shortest side can be 7 cm.
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Keywords: perimeter of scalene triangle, finding side lengths of scalene triangles, finding perimeter
Which of the following is the conjugate of the expression below when x> -3?
7- square root of x+3
Answer:
[tex]7+\sqrt{x+3}[/tex]
Step-by-step explanation:
The conjugate of a radical expression is obtained by changing the sign of the middle term.
The conjugate of [tex]a+\sqrt{b}[/tex] is simply [tex]a-\sqrt{b}[/tex]
Therefore, to obtain the conjugate of the given expression we simply shall be changing the negative sign to positive;
The conjugate of [tex]7-\sqrt{x+3}[/tex] is simply;
[tex]7+\sqrt{x+3}[/tex]
What is the square root of 16x^
36?
Note that [tex]\sqrt[2]{x}=x^{\frac{1}{2}}[/tex]
[tex]\sqrt[2]{16x^{36}}=\sqrt[2]{4^2x^{18\cdot2}}[/tex]
[tex]4^{2\cdot\frac{1}{2}}x^{18\cdot2\cdot\frac{1}{2}}=4^{\frac{2}{2}}x^{\frac{18\cdot2}{2}}[/tex]
[tex]\boxed{4x^{18}}[/tex]
Hope this helps.
r3t40
WILL MARK BRAINLIEST
Answer:
The correct answer is second option
3π in²
Step-by-step explanation:
Points to remember
Area of circle = πr²
Where r is the radius of the circle
To find the area of outer ring
Here radius of large circle = 1 + 1 = 2 in and
radius of small circle = 1 in
Area of outer ring = Area of large circle - area of small circle
= π2² - π1²
= 4π - π
= 3π in²
The correct answer is second option
3π in²
Answer:
3pi
Step-by-step explanation:
To find the area of the outer ring, we must first find the areas of the two circles. The red circle has a diameter of 2 which means the radius is 1. So the area of the red circle is pi.
Finding the area of the whole target, the radius is 2. So the total area is 4 pi.
So the area of the outer ring is 3pi
Which of the following is a solid consisting of a disc, a point not in the same
plane as the disc, and all the points between them?
A. Cone
B. Pyramid
C. Prism
D. Cube
Answer:
Cone
Step-by-step explanation:
Answer:
The answer is cone.
Step-by-step explanation:
Which of the following is a solid consisting of a disc, a point not in the same plane as the disc, and all the points between them?
The correct answer is a cone.
A cone is a solid consisting of a disc, a point not in the same plane as the disc, and all the points between them.
The disc specification is ruled out in cube and pyramid The point is ruled out in prism.
So, the answer is cone.
Point R divides PO in the ratio 1:3. If the x-coordinate of R is -1 and the x-coordinate of P is-3, what is the x-coordinate of Q?
Answer:
The x-coordinate of Q is 5
Step-by-step explanation:
* Lets revise the division of the line segment
- If point (x , y) divides a line segment internally whose endpoints are
(x1 , y1) and (x2 , y2) at the ratio m1 : m2 from (x1 , y1), then:
# [tex]x=\frac{m_{2}x_{1}+m_{1}x_{2}}{m_{1}+m_{2}}[/tex]
# [tex]y=\frac{m_{2}y_{1}+m_{1}y_{2}}{m_{1}+m_{2}}[/tex]
* Lets solve the problem
∵ Point R divides PQ in the ratio 1 : 3
∴ R is (x , y)
∴ P is (x1 , y1) and Q is (x2 , y2)
∴ m1 = 1 and m2 = 3
∵ x-coordinate of R is -1 and the x-coordinate of P is -3
∴ x = -1
∴ x1 = -3
- Use the rule above
∵ [tex]-1=\frac{(3)(-3)+(1)(x_{2})}{1+3}=\frac{-9+x_{2}}{4}[/tex]
- By cross multiplication
∴ (-1) (4) = -9 + x2
∴ -4 = -9 + x2 ⇒ add 9 to both sides
∴ 5 = x2
* The x-coordinate of Q is 5
the x-coordinate of point O is -2.5.
The question deals with dividing a line segment in a given ratio and finding the coordinates of a point. We are told that point R divides line segment PO in the ratio 1:3, the x-coordinate of R is -1, and the x-coordinate of P is -3. We are asked to find the x-coordinate of point Q, presumably typo for O.
Using the section formula, which states that the coordinates of a point dividing a line segment in the ratio m:n can be calculated using the formula (mx2 + nx1) / (m + n) for x-coordinate, here we have m = 1, n = 3, x1 (P's x-coordinate) = -3, and R's x-coordinate = -1. So, we can calculate the x-coordinate of point O (Q seems to be a typo in the question) as follows:
(1×(-1) + 3×(-3)) / (1 + 3) = (-1 - 9) / 4 = -10 / 4 = -2.5
Therefore, the x-coordinate of point O is -2.5.
What is the domain of the function y= x + 6 - 7
Answer:
x is in the element of all real numbers.
Step-by-step explanation:
Simplify the equation.
[tex]y=x+6-7[/tex]
[tex]y=x-1[/tex]
This means that the equation [tex]y=x[/tex] has just been moved down one.
Since the equation can be any number on the x axis, the domain is all real numbers.
Answer: X is all numbers I think.
Step-by-step explanation:
A rectangular field is 3 times as long as it is wide,
and it has an area of 192 square yards. How many
yards long is it?
It is 24 yards long.
Let the width = x
Given that the rectangular field is 3 times as long as it is wide.
So, the length = 3x.
So area = Length * width = [tex](3x)*(x) = 3x^2[/tex].
Given: it has an area of 192 square yards.
So,
[tex]3x^2=192\\x^2=64\\x=\sqrt{64}\\x=8[/tex]
So length = 3x = 3(8) = 24.
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42 base x +53base x = 125base x. what
is the value of x
Answer:
x = 7Step-by-step explanation:
The largest number is 5. Therefore x ≥ 6.
Convert numbers from x system to decimal system:
[tex]42_x=4x+2\\\\53_x=5x+3\\\\125_x=1x^2+2x+5[/tex]
Solve the equation for x:
[tex]42_x+53_x=125_x\Rightarrow4x+2+5x+3=x^2+2x+5\qquad\text{combine like terms}\\\\(4x+5x)+(2+3)=x^2+2x+5\\\\9x+5=x^2+2x+5\qquad\text{subtract 5 from both sides}\\\\9x=x^2+2x\qquad\text{subtract}\ 9x\ \text{from both sides}\\\\0=x^2-7x\\\\x^2-7x=0\qquad\text{distributive}\\\\x(x-7)=0\iff x=0\ \vee\ x-7=0\\\\x=0<7\qquad\bold{it's\ not\ a\ solution}\\\\x-7=0\qquad\text{add 7 to both sides}\\\\x=7\qquad\bold{it's\ a\ solution}[/tex]
URGENT please help me with this !!!
Answer:
480 mm³
Step-by-step explanation:
The volume (V) of a pyramid is
V = [tex]\frac{1}{3}[/tex] area of base × height, hence
V = [tex]\frac{1}{3}[/tex] × 96 × 15 = 32 × 15 = 480