The accompanying diagram show a cross-section of a rectangular pyramid. The cross sectional area is 36in and is 3 inches from the vertex of the pyramid. If the height of the pyramid is 5 inches, what is the area of the rectangular base?
The area of the rectangular base is the amount of space on the rectangular base
The area of the rectangular base is 60 square inches
How to determine the area of the rectangular base?The question is incomplete; as the diagram is not given.
So, I will apply the concept of similar shapes to determine the area of the rectangular base
To determine the area of the rectangular base, we make use of the following equivalent ratio:
Ratio = Height : Area
This gives
3 : 36 = 5 : Area
Express as fraction
36/3 = Area/5
Evaluate the quotient
12 = Area/5
Multiply both sides by 5
Area = 60
Hence, the area of the rectangular base is 60 square inches
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The graph of g(x)=3x^2+bx-24 has the same x-intercepts. what is the value of b?
(A) -6
(B) 14
(C) -2
(D) 1
The value of b so that 3 · x² + b · x - 24 has the same x-intercepts (only one x-intercept) is 12 √2.
How to determine a missing coefficient in a second order polynomial
Second order polynomials are represented graphically by parabolae and it may have two, one or no x-intercepts. The quantity of x-intercepts can be deducted from the discriminant of the quadratic formula, which is defined below:
For a · x² + b · x + c = 0, the discriminant is defined by:
d = b² - 4 · a · c (1)
There are three rules to determine the number of possible intercepts:
If d < 0, then there are no x-intercepts.If d = 0, then there is only one x-intercept.If d > 0, then there are two x-intercepts.Then, we have to find a value of b so that (1) has the following form:
b² - 4 · 3 · (-24) = 0
b² - 288 = 0
b = 12√ 2
The value of b so that 3 · x² + b · x - 24 has the same x-intercepts (only one x-intercept) is 12 √2. [tex]\blacksquare[/tex]
RemarkThe answer choices do not correspond with the given statement, the phrase "same x-intercepts" may lead to confusion and possible graph cannot be found. A possible corrected statement is shown below:
The graph of g(x) = 3 · x² + b · x - 24 has only one x-intercept. What is the value of b?
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Answer:
Step-by-step explanation:
What is the area of the figure shown delow?
Answer:
160mm2 is the correct answer
Step-by-step explanation:
What is the value of the unknown?
4x?+ ?= -2x?
Answer:
If the whole transaction is written separately from the beginning, an algebraic equation is obtained
Step-by-step explanation:
[tex]4x = s[/tex]
[tex] - 2x = w[/tex]
[tex]w \times s = - 8 {x}^{2} [/tex]
[tex]w = s = s \times s = 16 {x}^{2} [/tex]
[tex] - 8 {x}^{2} + 16 {x}^{2} = 8 {x}^{2} [/tex]
This is the way to get the answer
Problem
* Henry has many different screwdrivers. Each screwdriver is 6 inches long. He wants to make a line of
screwdrivers that is 1 yard long. How many screwdrivers will Henry need?
Answer:
Henry will need 6 screwdrivers.
Answer:
Henry will need 6 screwdrivers.
Step-by-step explanation:
[tex]1yard = 36inches\\\frac{36inches}{6inches/screwdriver} = 6screwdrivers[/tex]
If tanθ= 2/5 find cosθ using identities. This is in quad. 1.
Answer: 5/2
Step-by-step explanation:
The distance between the points (1,2) and (x,-1) is 5 units. Find the possible values of x
Answer:
-3,5
Step-by-step explanation:
[tex]d = \sqrt{(x _{2} - x _1) {}^{2} + (y _{2} - y _{1} {} ) {}^{2} } [/tex]
[tex]5 = \sqrt{(x - 1) {}^{2} + ( - 1 - 2) {}^{2} } [/tex]
[tex]5 = \sqrt{(x - 1) {}^{2} + ( - 3) {}^{2} } [/tex]
[tex]25 = (x - 1) {}^{2} + 9[/tex]
[tex]16 = (x - 1) {}^{2} [/tex]
[tex]4 = x - 1[/tex]
[tex]x = 5[/tex]
Or
[tex] - 4 = x - 1[/tex]
[tex]x = - 3[/tex]
Martin is an artist who molds plaster into unique shapes.
How much plaster can Martin fit into the mold shown?
Step-by-step explanation:
the volume of this object is the sum of the volume of the 2 blocks.
the large block is a cube of 4×4×4 = 64 ft³
the small block is 1×1×2 = 2 ft³
so, in total, he can fit 64+2 = 66 ft³ of plaster into the mold.
Your gross pay is $1,878.96, net income is $1,196.34, and fixed expenses are $1,338.54. What is your discretionary income?
$142.20
You have a deficit of $142.20.
You have a deficit of $540.42.
Answer:
You have a deficit of $142.20
Step-by-step explanation:
Given
Gross pay = $1,878.96Net income = $1,196.34Fixed expenses = $1,338.54Solving
discretionary income = net income - fixed expenses= 1196.34 - 1338.54= -142.20Deficit of $142.20What is 1 + 1 x 3 Whoever answers it to
Answer:
It equals 4
Step-by-step explanation:
1 + 1 x 3=4
Answer:
I think it equals 4
Step-by-step explanation:
1 + 1 x 3=4
Estimate f(4.04) for f as in the figure
Answer:
2.013 to 3 DP's.
Step-by-step explanation:
f(4.04) will be very close to the tangent line.
Equation of tangent line
is y - 4 = m(x - 10)
m = (4-2) / (10-4) = 1/3
y - 4 = 1/3(x - 10)
y = 1/3x - 10/3 + 4
y = 1/3x + 2/3
So the require estimate of f(4.04)
= 1/3(4.04) + 2/3
= 2.013333
6. Roughly what percent of the US
flag is red?
Answer:
about 14 percent but the exact is 14 3
Which pair shows equivalent expressions?
2x + 10 = -2(x-5)
-2(x+5) = 2x-10
-2x-10 = -2(x+5)
-2(x-5) = -2x-10
Answer:
The 3rd equation, -2x-10 = -2(x+5)
Step-by-step explanation:
Equivalent expressions means both sides of the equal sign equal the same thing
To find which ones are equivalent expressions, we must solve/simplify both sides of each equation to see if they're actually equal to each other
We will use PEMDAS for this
1. 2x + 10 = -2(x - 5)
Start with Parentheses, and distribute the -2 to what's inside said parentheses
2x + 10 = -2x + 10
Not equal
2. -2(x+5) = 2x-10
Once again, start with Parentheses, and distribute the -2 to what's inside said parentheses
-2x - 10 = 2x - 10
Not equal
3. -2x-10 = -2(x+5)
Once again, start with Parentheses, and distribute the -2 to what's inside said parentheses
-2x - 10 = -2x - 10
Equal
4. -2(x-5) = -2x-10
Once again, start with Parentheses, and distribute the -2 to what's inside said parentheses
-2x + 10 = -2x - 10
Not equal
After plotting the data where x=the side of a polygon, and f(x) = the area of the polygon, Jack used technology and
determined the appropriate model to approximate the area of the polygon, F(x) = x^2 + 3x + 2. Use the model Jack
created to predict the area of a polygon that has a side length of 3.
10
18
19
020
Answer: 19
Step-by-step explanation:
As per the model created by Jack; f(x) determines the area and x represents length so f(3) = 9+9+1
Therefore, f(3) = 19
A school's principal wanted to give a special 'Good Luck' pencil for each student in the fifth grade. If there are 105 kids in the fifth grade, and there are 12 pencils in each box, how many boxes will he need to buy?
Solve: 101x-99y=103
-99x+101y=-97
Answer:
[tex]x=2; y=1[/tex]
Step-by-step explanation:
Let's remember that if we replace one equation in a system with a linear combination of the equations (ie adding or subtracting them together, after multiplying them with some nice numbers) we are left with an equivalent system. So let's add and subtract them together, and use the new equations to work with.
[tex]I+II: 2x+2y=6\\I-II:200x-200y=200[/tex]
Better, now let's simplify the expression and let's use the new system
[tex]x+y=3\\x-y=1[/tex]
Done. At this point you can use whatever method you like to solve the system to get to the final solution. Adding and subtracting works great, and you get [tex]x=2, y=1[/tex] which, if you check by replacing in the original, is indeed a valid solution.
Can someone help me!
Answer:
Top left.
Step-by-step explanation:
How many square meters are there in a floor that is 9 meters long by 12 meters wide?
99
108
109
117
Answer:
108
9×12
Step-by-step explanation:
please mark me as brainlest
Given g(x)
-2 – 2, find g(-3).
Answer:
The calculation of the function given shows that since g(x) = -2x² - 9, the value of g(3) will be -27.
How to calculate the function?From the complete function, it should be noted that the value of g(x) = -2x² - 9.
Therefore, the value of g(3) will be calculated thus:
= -2(3)² - 9
= -2(9) - 9.
= -18 - 9
= -27
In conclusion, g(3) is -27.
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Answer:
A
Step-by-step explanation:
If y is a function of x, then the equation for y would be y=Ix(+or-or*or%) to nI
For this specific event, the proper equation would be y=Ix-0.5I
Breaking down this equation, y equals the absolute value of x-0.5.
So if x was 2, it would go as y=I2-0.5I where y equals 1.5.
Martina is ordering an ice cream dessert. She must order a size and a flavor of ice cream. There are 4 sizes and 2 flavors to choose from. How many different
cream desserts could she order?
Answer: 8.
Step-by-step explanation: There are 4 sizes, so let's say that the sizes are small, medium, large, and extra large. There are 2 flavors, so let's say that the flavors are chocolate and vanilla. The possible combinations are below:
Small chocolateMedium chocolateLarge chocolateExtra large chocolateSmall vanillaMedium vanillaLarge vanillaExtra large vanillaAs you can see, there are 8 possible combinations that she can choose from as far as 4 sizes and 2 flavors go.
Have a great day! :)
A ball follows a path described by the function h(x) = -3x^2 +12x +14 where h(x) is the height of the ball after x seconds. After how many seconds will the ball be at its
highest point?
A. 1 second
B. 2 seconds
C. 3 seconds
D. 4 seconds
Answer:
3
Step-by-step explanation:
2. Find the length of AD if the length of AB is 14 units, the length of BC is 5 units, and the length of CD is 8 units,
Answer: sqrt(285)
Step-by-step explanation:
The field trip to the science museum will cost $22 per student. If Mrs. Robertson has 24 students, how much money will she collect in all?
Answer:
528
Step-by-step explanation:
22x24=528
Answer:528$
Step-by-step explanation: you have to do 22 dollars times 24 students which would be 528
least to greatest 52, 63, 55, 56, 62, 54, 59, 60, 53, 61, 88
Answer:
52, 53, 54, 55, 56, 59, 60, 61, 62, 88
Step-by-step explanation:
You need to start from 52 to 88 (least to greatest) and then you will get answer.
Ted needs 2500 metres of lighting cable for a job. What is this length in kilometres?
Answer:
2.5km
Step-by-step explanation:
1000m=1km
We have 2500m
2500m=2.5km
9
Emily drives 186 miles in 3 hours.
(a) What is her average speed?
Answer:
Her average speed would be 62 mph.
Step-by-step explanation:
Step 1. Do 186 divided by 3
Step 2. The answer you would get is 62
Step 3. Label to get 62 miles per hour (mph)
I hope that this helps! :)
Step-by-step explanation:
Displacement = 186 miles
Time taken = 3hours
Average speed = ?
Now,
[tex]average \: speed = \frac{total \: distnce}{total \: time \: } \\ = \frac{186}{3} \\ [/tex]
= 62 miles per hour
20.
19. Make Sense and Persevere Use the Distributive
Property to expand 7(7x - 3y) - 6.
HELP PLEASE
Answer:
49x-21y-6
Step-by-step explanation:
7(7x) 7(-3y) -6
49x-21y-6=0
Can the sides of a triangle have lengths 2, 6, and 7?
Answer:
Yes
Step-by-step explanation:
The third largest side is 7 and the other two sides added are bigger than seven.
2 + 6 = 8
Is this answer accurate?
can someone help me answer this question?
check picture uploaded to see steps
children = 201
adults = 277