The weight of the smallest rectangular block is 1400 pounds.
What is density?The density refers to the heaviness of an object. It is the ratio of mass to volume.
Then we have
Density = Mass / Volume
A sculptor is planning to order a rectangular block of composite stone to sculpt a lion.
The sculptor anticipates that the lion will be 5 feet long, about 2 feet wide and at the tallest part of the lion's body, have a height of 3.5 feet.
The composite stone weighs 40 pounds per cubic foot.
To the nearest cubic foot, estimate the weight of the smallest rectangular block that the sculptor must purchase in order to create his statue.
Then the weight of the smallest rectangular block will be
Mass = density x volume
The volume will be
V = 5 x 2 x 3.5
V = 35 cubic feet
Then the weight will be
Mass = 40 x 35
Mass = 1400 pounds
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If f(x) = -3 and g(x) = 4x² + x − 4, find (ƒ+ g)(x).
Answer:
4x² + x - 7
Step-by-step explanation:
Given f(x) = -3 and g(x) = 4x² + x - 4, solve for (f + g)(x).
Step 1: Replace the function designators with the actual functions in f(x) and g(x); that gives us 4x² + x - 4 - 3.
Step 2: Simplify; that gives us the answer 4x² + x - 7.
Please mark me as Brainliest! Thanks :)The standard form of an absolute value function is f(x)-a|x-h|+k. Which of the following represents the vertex?
(-k.h)
(-h.k)
(k,b)
(h,k)
Answer:
(h, k )
Step-by-step explanation:
given the standard form of an absolute function
f(x) = a| x - h | + k , then
vertex = (h, k )
The standard form of an absolute value function is f(x) = a|x - h| + k, where (h,k) is the vertex of the absolute value function.
The correct option is (h,k).
What is a function?The term "function" refers to a relationship between a set of inputs and outputs. Just one output is connected to each input in a function, which connects inputs in that manner. Every function has a domain, co-domain, and range.
In general, the standard form of an absolute value function is given as:
f(x) = a |x - h| + k
where:
a is a non-negative constant that determines the shape and direction of the V-shaped graph of the absolute value function
h is the horizontal shift of the graph of the function from the origin (if h > 0, the graph shifts to the right; if h < 0, the graph shifts to the left)
k is the vertical shift of the graph of the function from the origin (if k > 0, the graph shifts up; if k < 0, the graph shifts down)
The vertex of the absolute value function is the point where the graph changes direction, that is, the point where the graph changes from sloping downwards to sloping upwards or vice versa.
Since the vertex is the point of the absolute value function where the graph changes direction, it lies at the center of the V-shaped graph. Thus, the vertex is located at the point (h,k).
Therefore, in the standard form f(x) = a |x - h| + k, (h,k) represents the coordinates of the vertex of the absolute value function.
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3 *(x-7)*(x+7)-(x-1)*(3x+2)=13
The value of x will be 158. The value of x is obtained by simplifying the equation.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Identity used;
(x+a)(x-a) = x² - a²
Given expression;
3(x-7)(x+7) - (x-1)(3x+2) = 13
Solving the equation step by step;
[tex]\rm 3(x^2 - 7^2 ) - [x(3x+2)-1(3x+2) ]= 13\\\\ 3x^ 2 -147 -[3x^2 +2x -3x-2] = 13 \\\\ 3x^2 -147 -[3x^2 -x-2] = 13\\\\ 3x^2-147-3x^2 +x+2 = 13 \\\\ x= 13+145 \\\\ x= 158[/tex]
Hence, the value of x will be 158.
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After covering 4/5 of the journey, James found that he has traveled 48 km. How much of the journey is still left?
Answer:
12 km
Step-by-step explanation:
Let the total distance to be traveled = x
[tex]\sf \dfrac{4}{5} \ of \ the \ journey = 48\\\\[/tex]
[tex]\sf \dfrac{4}{5}*x = 48\\\\[/tex]
[tex]x = 48*\dfrac{5}{4}[/tex]
= 12 * 5
x = 60 Km
Distance still to traveled = 60 - 48 = 12Km
What is the distance from -5 to 0?
0, because 151=0
O 5, because 1-51=5
O5, because 1-51=-5
O-5, because 1-51 = -5
7 of 23 QUESTIONS
SUBMIT
Answer:
distance between -5 to 0 = 5 units
Solve the compound inequality for x and identify the graph of its solution.
x+7>3 and x-5≤-1
O A. Solution: x<-4 or x ≥ 4
-5-4-3 -2 -1 0 1 2 3 4 5
OB. Solution: x>-4 and x≤ 4
-5-4-3 -2 -1 0 1 2 3 4 5
O C. Solution: x>-4 and x≤ 4
-5 -4 -3 -2 -1 0 1 2 3 4 5
OD. Solution: x²-4 and x < 4
Answer:
C is the answers for the question
Step-by-step explanation:
please mark me as brainlest
The perimeter of a triangle is 84 cm and it's area is 336cm².If one of it's sides is 30 cm find the length of other two sides.
Answer:
26,28
Step-by-step explanation:
We can make a system of equations based on the information given
first we can make one for the perimeter
and one for the area using herons formula
(x and y are the two unknown sides)
[tex]84=30+x+y[/tex]
[tex]336=\sqrt{42(12)(42-x)(42-y)}[/tex]
Now solve for x and y or you can find it by graphing
x and y = 26 and 28, the order does not matter since they are both unkown
so the two sides are 26 and 28
Helppppppppp plssssss
Solve equation
-15+n=-9
Mary is running a marathon which is a total of 26 miles. She is running at a pace of 7.5 miles per hour and
has already run 8 miles. If she stays at the same pace, how much time in hours does she have left? (Round your answer to the nearest tenth)
===================================================
Explanation:
She has already ran 8 miles, so she has 26-8 = 18 miles left to go.
She runs at a pace of 7.5 mph, which means she has 18/(7.5) = 2.4 hours left to go.
I used the equation distance = rate*time, and solved for time to get time = distance/rate.
--------------------
Another approach:
Here's how you can use algebra.
x = time she has left in hours
7.5x = distance covered in those x hours
7.5x+8 = total distance
7.5x+8 = 26
7.5x = 26-8
7.5x = 18
x = 18/(7.5)
x = 2.4
Point T is located at (6, –2) and point S is located at (1, 13). What are the coordinates of the point that is `\frac{4}{5}` of the way from T to S?
The coordinates of the point that is 4/5 of the way from T to S is (2,10)
How to determine the coordinates of the point?The given parameters are:
T = (6,-2)
S = (1,13)
Location = 4/5
The location 4/5 means
Ratio, m : n = 4 : 1
The coordinate is then calculated as:
[tex](x,y) = \frac{1}{m +n} * (mx_2 + nx_1,my_2 + ny_1)[/tex]
This gives
[tex](x,y) = \frac{1}{4 +1} * (4 * 1 + 1 * 6 , 4 * 13 + 1 * -2)[/tex]
Evaluate
[tex](x,y) = \frac{1}{5} * (10 , 50)[/tex]
This gives
(x,y) = (2,10)
Hence, the coordinates of the point that is 4/5 of the way from T to S is (2,10)
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select the most appropriate measurement for each of the following
Answer:The following what
Step-by-step explanation:
what is the following and there is no questions.
Squares are cut out of the corners of a piece of 18*18 graph paper so that the sides can be folded to make an open box. What is the largest possible number of cubic units in the volume of the box if we require that the length of each edge is a whole number?
Answer:
432 mm²
Step-by-step explanation:
We need to cut out 3x3 squares from corners and make an open box. It's height will be 3mm(see the plan). So volume will be:
V = 12 * 12 * 3 = 432mm²
Timothy has a savings account that he started five years ago to begin saving for college. The
savings account has an interest rate of 3% and has earned $225 in interest since he began the
account. How much money did Timothy start the account with when he originally opened the
savings account?
A. $1500.00
B. $33.75
C. $7500.00
D. $3375.00
of $18
Answer:
A. $1500.00
Step-by-step explanation:
Assuming this is a simple interest savings account.
Simple interest formula
I = Prt
where:
I = total interestP = principal amountr = interest rate (in decimal form)t = time (in years)Given:
I = $225r = 3% = 0.03t = 5 yearsSubstitute the given values into the formula and solve for P:
⇒ I = Prt
⇒ 225 = P(0.03 ×5)
⇒ 225 = P(0.15)
⇒ P = 225 ÷ 0.15
⇒ P = 1500
Therefore, Timothy started the account with $1500.00.
Divide: 1,485 ÷ 0.09
1,485 ÷ 0.09
Answer:
16500
Step-by-step explanation:
Someone please help!!
Answer:
I believe the answer would be option D
Step-by-step explanation:
the distance formula is
[tex] \sqrt{(x - x1)^{2} + (y - y1)^{2} } [/tex]
So, substituting the values of the coordinates, you will get the answer of D
I need help with a question
Answer:
y = 3
x = -15
Step-by-step explanation:
When substituting, we want to get rid of one of the variables. (It's easiest ot find the variable in terms of other variable)
so, we know that...
x + 5y = 0
- 5y - 5y
x = -5y
We can plug this x-value into the second equation to find our y-value:
3y + 2x = -21
3y + 2(-5y) = -21
3y - 10y = -21
-7y = -21
÷ -7 ÷ -7
y = 3
So, if x = -5y,
x = -5y
x = -5(3)
x = -15
(we can test these values in one of the original equations):
x + 5y = 0
(-15) + 5(3)= 0
-15 + 15 = 0
{true}
so, y = 3 ; and x = -15
hope this helps!! :)
Convert scientific notation to decimal format.
9.8*10^-9
Answer:
- 9,800,000,000
Step-by-step explanation:
9.8 * [tex]10^{-9}[/tex]
Simplify 10 with exponent
[tex]{10}^{-9}[/tex] = -10 with 9 zeroes
Rewrite
[tex]{10}^{-9}[/tex] = -1,000,000,000
Place back into expression
9.8 * -1,000,000,000
Simplify by multiplying
- 9,800,000,000
Let me know if you have any questions!
How many solutions does the following system of equations have?
Answer:
1
Step-by-step explanation:
Solutions to a systems of equations are when the (x, y) of two equations are equal with both equations remaining true or in other words when both equations intersect. So by looking at the graph, both equations seem to be linear so there should only be 0, 1, or infinitely many solutions. Since they do have one intersection there is only 1.
Answer:
The system of equations only has 1 solution.
Explanation:
This can be seen by looking at the graph and seeing where the lines were to intersect. For example, if the lines were parallel and never intersected, then there would be 0 solutions. On the other hand, if the lines were essentially the same and overlapped at every point, then there would be infinitely many solutions.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Answer:
Hey there : y= 3x - 3
Answer:
y = [tex]\frac{3}{2}[/tex] x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line
m = [tex]\frac{3-0}{0-(-2)}[/tex] = [tex]\frac{3}{0+2}[/tex] = [tex]\frac{3}{2}[/tex]
the line crosses the y- axis at (0, 3 ) ⇒ c = 3
y = [tex]\frac{3}{2}[/tex] x + 3 ← equation of line
if(√14/√7-2)-(√14/√7+2)=a√7+b√2 find the values of a and b where a and b are rational numbers
Answer:
a = 4/3 and b = 0============================
Given expression:[tex]\dfrac{\sqrt{14} }{\sqrt{7}-2} -\dfrac{\sqrt{14} }{\sqrt{7}+2}[/tex]
Simplify it in steps:Step 1Bring both fractions into common denominator:
[tex]\dfrac{\sqrt{14} (\sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} - \dfrac{\sqrt{14} (\sqrt{7}-2)}{(\sqrt{7}-2)(\sqrt{7}+2)}[/tex]
Step 2Simplify:
[tex]\dfrac{\sqrt{14} ((\sqrt{7}+2) - (\sqrt{7}-2))}{(\sqrt{7}-2)(\sqrt{7}+2)} =[/tex]
[tex]\dfrac{\sqrt{14} (\sqrt{7}+2 - \sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} =[/tex]
[tex]\dfrac{4\sqrt{14} }{(\sqrt{7}-2)(\sqrt{7}+2)} =[/tex]
[tex]\dfrac{4\sqrt{14} }{(\sqrt{7})^2-2^2} =[/tex]
[tex]\dfrac{4\sqrt{14} }{7-4} =[/tex]
[tex]\dfrac{4}{3} \sqrt{14} }[/tex]
Step 3Compare the result with given expression to get:
a = 4/3 and b = 0It’s 12 points thank you
The value of y when x is equal to zero will be 330.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The given function is;
y = 330 + 25x
We have to find the value of y when x is equal to zero.
So,
Put x = 0
y = 330 + 25x
y = 330 + 25(0)
y = 330
Hence, the value of y when x is equal to zero will be 330.
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Teresa is factoring this polynomial by grouping. Which common factors should be used in the next step of factoring?
10x3+3x2−20x−6
(10x3+3x2)+(−20x−6)
x2 and −2x
2x2 and −2x
x2 and −2
2x2 and −2
Answer: [tex]x^2[/tex] and [tex]-2[/tex]
Step-by-step explanation:
original :
[tex](10x^3+3x^2)+(-20x-6)[/tex]
factored :
[tex]x^2(10x+3)+-2(10x+3)[/tex]
Answer :
[tex]x^2[/tex] and [tex]-2[/tex]
Y=-5x +6 Y= 3x -2 Find the solution to the system of equations
X = _____
Y= _____
Answer:
x=1, y=1. (1, 1).
Step-by-step explanation:
y=-5x+6
y=3x-2
------------
-5x+6=3x-2
-5x-3x+6=-2
-8x+6=-2
-8x=-2-6
-8x=-8
8x=8
x=8/8=1
y=3(1)-2=3-2=1
It’s 12 points if you help me thank you :)
Based on the calculations, Celine would earn a total of $65.00 assuming she delivered 10 packages.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variable.
Given the following function:
y = 20.00 + 0.45(x)
In this exercise, you're required to determine Celine's weekly earnings based on the number of packages she delivered. However, the number of packages delivered by Celine wasn't shown, thus, we would assume a value for the purpose of an explanation:
Assuming x = 10 packages.
Substituting the value of x into the function, we have:
y = 20.00 + 0.45(10)
y = 20.00 + 45
y = $65.00.
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En una tienda comercial anuncia descuentos sucecivos del 30% y 20% en todos los electrodomésticos, ¿Que descuento único equivale?
Answer:
0
Step-by-step explanation:
square root of 342354456
Answer:
18502.8229198
Answer:
18502.82292
Step-by-step explanation:
calculator
Given ST|UV and SU || TV, find the measure of each angle below.
Find the angle of STU
Find the angle of TVW
Answer: [tex]\angle STU=34^{\circ}, \angle TVW=116^{\circ}[/tex]
Step-by-step explanation:
By the alternate interior angles theorem,
[tex]3x+4=2x+14\\\\x+4=14\\\\x=10\\\\\implies \angle STU=3(10)+4=\boxed{34^{\circ}}[/tex]
By the alternate interior angles theorem, [tex]\angle UTV=82^{\circ}[/tex], and we also know that [tex]\angle TUV=34^{\circ}[/tex].
Thus, by the exterior angle theorem,
[tex]\angle TVW=82+34=\boxed{116^{\circ}}[/tex]
A portion of John Locke's time card is shown below. How many hours did he work for the week?
PLS PLS HELP IVE BEEN STUCK ON THIS FOR A VERY LONG TIME AND PLS IF YOU DONT KNOW THE ANSWER DONT ANSWER!!!!!
Answer:
40
Step-by-step explanation:
it's 8+8+8+7+9 so it's gonna be 40
Lindsey is a member of the swim team at a local university. She has been working hard to perfect her dive for an upcoming swim meet. Lindsey's dive can be modeled by the quadratic equation y = – 16x2 + 33x + 45, where x is time in seconds, and y is Lindsey's height in the air in feet.
1. At what time will Lindsey be 30 feet in the air?
2. How high is the diving board? Explain your thinking.
Answer:
1. [tex]x = 2.45s[/tex]
2. The diving board is 45 ft high.
Step-by-step explanation:
• When Lindsey is 30 feet in the air, y = 30.
[tex]30 = -16x^2 + 33x +45\\\\-16x^2 + 33x +15 = 0\\\\16x^2 - 33x -15 = 0\\[/tex]
Using quadratic formula, solve for x:
[tex]x = \frac{33 + \sqrt[]{(-33)^2 - 4(16)(-15)} }{2(16)}[/tex]
[tex]x = 2.45s[/tex]
• If we calculate the height of Lindsey in the air when she is standing on the diving board, we can find the height of the diving board above the ground.
When she is standing on the board, x = 0 as no time has passed after jumping.
[tex]y = -16(0)^2 + 33(0) +45\\\\y = 45 ft[/tex]
