Answer:
The surface area is 55 cm².
Step-by-step explanation:
The formula to compute the surface area of the triangular pyramid is:
[tex]SA=(0.50\times \text{Base Perimeter}\times h)+\text{Base Area}[/tex]
Here h is the slant height.
Compute the Base perimeter as follows:
Perimeter of the equilateral triangle = 3 × side
= 3 × 4
= 12 cm
Compute the Base area as follows:
Area of the equilateral triangle = 0.50 × side × height
= 0.50 × 4 × 3.50
= 7 cm²
Compute the surface area as follows:
[tex]SA=(0.50\times \text{Base Perimeter}\times h)+\text{Base Area}[/tex]
[tex]=(0.50\times 12\times 8)+7\\=48+7\\=55\ \text{cm}^{2}[/tex]
Thus, the surface area is 55 cm².
Find the remainder when x^3-ax^2 +6x -a is divided by x-a
Answer:
When x^3 - ax^2 + 6x -a is divided by x-a
Remainder = 5a
5^-4 over 5^3
simplify
A. 5^7
B. 5^-1
C. 1/5
D. 1/5^7
Answer:
D is the correct answer.
Darnell goes to the movies with his friends. The receipt on his phone
shows the cost of the tickets after a discount. What is the price of a ticket before the discount?
answer
8(+ - 0.75)=62.00
the price of the tickets before is 8.50
Step-by-step explanation:
8(+-.075)=62.00
+-0.75+0.23
+=8.50
resolver la siguiente ecuación por eliminación o sustitución: a-8b= -9 a-2b= -7
Answer: Solution: [tex]a=\dfrac{-19}{3}[/tex] and [tex]b=\dfrac{1}{3}[/tex] .
Step-by-step explanation:
The given pair of equations:
[tex]a-8b= -9\ ...(i)\\\\ a-2b= -7\ ...(ii)[/tex]
Eliminate equation (i) from (ii) , we get
[tex]-2b-(-8b)=-7-(-9)\\\\\Rightarrow\ -2b+8b=-7+9\\\\\Rightarrow\ 6b=2\\\\\Rightarrow\ b=\dfrac{1}{3}[/tex]
Put value of b in (ii) , we get
[tex]a-2\times\dfrac{1}{3}=-7\\\\\Rightarrow\ a=-7+\dfrac{2}{3}\\\\\Rightarrow\ a=\dfrac{-21+2}{3}\\\\\Rightarrow\ a=\dfrac{-19}{3}[/tex]
Solution: [tex]a=\dfrac{-19}{3}[/tex] and [tex]b=\dfrac{1}{3}[/tex] .
Suppose the radius of a circle is 2. What is its circumference?
Answer:
12.57
Step-by-step explanation:
The formula to solve the circumference of a circle is:
2 x PI x R (radius)
=> 2 x PI x 2
=> 4 PI or 12.57
Line R: 2x + 2y = 18 Line M: x + y = 9 Which statement is true about the solution to the set of equations?
Answer:
Step-by-step explanation:
2x + 2y = 18
-2x -2y = -18
0 = 0
infinite solution of equations
What Is the answer to it?
Answer:
2(x + 10)
Step-by-step explanation:
The sum of x and 10 is x + 10
The product of 2 and x + 10 means multiply them, thus
2 × (x + 10)
= 2(x + 10) ← parenthesis indicates x and 10 are added before being multiplied by 2
Which of the following is true? Tangent is positive in Quadrant I. Sine is negative in Quadrant II. Cosine is positive in Quadrant III. Sine is positive in Quadrant IV.
Answer:
A
Step-by-step explanation:
I had this question and got it right the user above explains it in detail
4(3−y)=6−2(1−3y) Enter your answer in the box. y=
Answer:
12-4y=4-12y
8y=-8
y=-1
Answer:
y= 0.8
Step-by-step explanation
4(3−y) = 6−2(1−3y)
12−4y = 6−2(1−3y)
12−4y = 6−2+6y
12−4y = 4+6y
12 = 4+10y
8 = 10y
0.8 = y
This is correct i just took the test. I hope this helps :)
Ajay is researching how the population of his hometown has changed over time. Specifically, he learns his hometown had a population of 20{,}00020,00020, comma, 000 in 199019901990, and that the population has since increased by about 8\%8%8, percent every 333 years.
Ajay predicts that his town can only support a population of 50{,}00050,00050, comma, 000. Ajay is relieved to see that population has not exceeded 50{,}00050,00050, comma, 000 ttt years after 199019901990.
Write an inequality in terms of ttt that models the situation.
Answer:
Could you Write the question more clearly?
Step-by-step explanation:
Place the two large triangles around the square to form a triangle, a parallelogram ,and a trapezoid .Please answer it step by step
Answer:
Step-by-step explanation:
he blood platelet counts of a group of women have a bell-shaped distribution with a mean of 247.3 and a standard deviation of 60.7. (All units are 1000 cells/μL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 65.2 and 429.4
Answer:
The approximate percentage of women with platelet counts within 3 standard deviations of the mean is 99.7%.
Step-by-step explanation:
We are given that the blood platelet counts of a group of women have a bell-shaped distribution with a mean of 247.3 and a standard deviation of 60.7.
Let X = the blood platelet counts of a group of women
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 247.3
[tex]\sigma[/tex] = standard deviation = 60.7
Now, according to the empirical rule;
68% of the data values lie within one standard deviation of the mean.95% of the data values lie within two standard deviations of the mean.99.7% of the data values lie within three standard deviations of the mean.Since it is stated that we have to calculate the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 65.2 and 429.4, i.e;
z-score for 65.2 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{65.2-247.3}{60.7}[/tex] = -3
z-score for 429.4 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{429.4-247.3}{60.7}[/tex] = 3
So, it means that the approximate percentage of women with platelet counts within 3 standard deviations of the mean is 99.7%.
The table shows the steps for solving the given inequality 4-3(x-5)>6x-17
Step-by-step explanation:
(=) 1 ( x-5 ) > 6x-17
(=) x-5 > 6x -17
(=) -5x > -12
=> x < 12/5
What is the percent change from 75 to 14?
Answer:
the change is -81.33% (the 3 is repeating)
find the value of x
3+x/4=5
Step-by-step explanation:
it think it will help you
Answer:
the value of x = 8
Step-by-step explanation:
3+x/4 = 5
x/4 = 5 - 3
= 2
X = 2 ×4
=8
solve each equation type the answers in the boxes below a( 3x equals 12 B( -3x equals 9 c( 3 x equals 1/2 D( 1/2 x equals 12
Answer:
a) x = 4
b) x = -3
c) x = 1/6
d) x = 24
Step-by-step explanation:
Basic solve for x techniques
a) 3x = 4
Divide both sides by 4. This applies to all the questions.
How do you simplify the square root of 64a^6
Answer:
it's (2a)^6
Step-by-step explanation:
so first you need to write 64a^6 in exponential form simplifying it to 2^6a^6
then multiply the bases which gives you (2a)^6
sorry if I didn't explain it very well but I hope I helped!
Answer:
[tex]\sqrt{64a^{6} } = 8a^{3}[/tex]
8*8 = 64
a^3*a63 = a^6
Step-by-step explanation:
Find the area of triangle ABC to the nearest tenth if AB = 11 ft, ∠BCA = 67 , and ∠CAB = 28 .
Answer:
30.7
Step-by-step explanation:
Assuming the angled are degrees and not radian.
side BC= (11÷sin67)•sin28= 5.6
angle ABC= 180-67-28=85°
A= 11•5.6•sin85÷2≈30.68
Which of the following images shows a scale copy of the trapezoid using a scale factor of 1/2
PLEASE HELP
Answer:
1
Step-by-step explanation:
split the shape to triangle and a rectangle
the rectangle at the original trapezoid has 2 squares in width and 3 squares for height multiply those numbers by 1/2 you will get 1 square for width and 1.5 squares for the height which is showen in option 1
What is the perimeter of a square which has the same area as a circle with circumfrence of 4π
Answer:
Perimeter square = 8 sqrt(pi)
Step-by-step explanation:
The perimeter of a square is 4*s
The area of a circle is Area = pi * r^2
The circumference of a circle is C = 2*pi * r
C = 4 pi
4pi = 2*pi * r
r = 2
So the area of the circle is pi * r^2 = pi * 2^2 = 4pi
The square has the same area
Area = 4*pi
Square = 4*pi
s^2 = 4*pi
s = sqrt(4*pi)
s = 2*sqrt(pi)
The perimeter = 4 * 2 * sqrt(pi)
The perimeter = 8 * sqrt(pi)
What is the scale factor of abc to def
Answer:
[tex]\large \boxed{\mathrm{B. \ 6}}[/tex]
Step-by-step explanation:
Length AB is similar to length DE.
Scale factor = DE/AB
Scale factor = 12/2
Scale factor = 6
The required Scale factor would be 6 to transform triangle ΔABC to triangle ΔDEF which is the correct option (B).
What is a scale image?Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.
Length AB is similar to length DE.
Here triangle ΔABC is dilated to form triangle ΔDEF
Length of the side DE = 12
Length of the side AB = 2
As we know scale factor is the ratio of sides in the original image and the image after dilation.
Scale factor = DE/AB
Substitute the values of the length of the side DE and AB,
Scale factor = 12/2
Apply the division operation, and we get
Scale factor = 6
Therefore, the required Scale factor would be 6 to transform triangle ΔABC to triangle ΔDEF.
Learn more about the Scale images here:
brainly.com/question/13194929
#SPJ5
Algebra!! In the triangle to the below, the measure of ∠A equals the measure of ∠B. Find the value of x.
Answer:
x=21
Step-by-step explanation:
45=2x+3
Subtract 3 from both sides of the equation.
42=2x
Divide 2 from both sides of the equation.
21=x
Hope this helps!
Answer:
x=21°
Step-by-step explanation:
Angle A = Angle B
Angle A = 45°
2x+3 =45°
To work out what x is, you would have to do inverse operations.
45-3=42°
2x=42°
42÷2=21° (We divide by 2 because, in algebra, whenever a number is next to a letter, it means times, so then we have to do the opposite and divide).
So, x=21°
Hope this helps :)
Please answer this question now
Answer:
1306.24 cm².
Step-by-step explanation:
From the diagram given above, we obtained the following information:
Radius (r) = 13 cm
Pi (π) = 3.14
Slant height (l) = 19 cm
Surface Area (SA) =.?
The surface area of the cone can be obtained as follow:
SA = πr² + πrl
SA = πr ( r + l)
SA = 3.14 × 13 ( 13 + 19)
SA = 40.82 (32)
SA= 1306.24 cm²
Therefore, the surface area of the cone is 1306.24 cm².
Members of a soccer team raised $1946.50 to go to a tournament. They rented a bus for $974.50 and budgeted $60.75 per player for meals. Write and solve an equation which can be used to determine pp, the number of players the team can bring to the tournament.
Answer:
16 players can be brought to the tournament. The equation is written within my step-by-step explanation.
Step-by-step explanation:
Variable p = number of players
Set up an equation:
974.50 + 60.75p = 1946.50
Isolate variable p:
60.75p = 972
Divide:
p = 16
Check your work:
974.50 + 60.75(16) = 1946.50
974.50 + 972 = 1946.50
1946.50 = 1946.50
Correct!
Answer:
Step-by-step explanation:
is the value of x=3 find the value of 4x³-2x²+3x
Answer:
99
Step-by-step explanation:
4x³-2x²+3x
4×3³-2×3²+3×3
4(27)-2(9)+9
108-18+9
99
99
=(4)(27)−2(32)+(3)(3)
=108−2(32)+(3)(3)
=108−(2)(9)+(3)(3)
=108−18+(3)(3)
=90+(3)(3)
=90+9
=99
the volume of a cube is 125cm cubed. The area of a square is 64cm squared. How does the length of one edge of the cube compare to the length of one side of the square? Explain
Answer:
One edge of the cube is 5 cm, one edge of the square is 8 cm, so the edge of the cube is 3 cm shorter than the edge of the square.
Step-by-step explanation:
The volume of the cube is found by the formula
V = s³,
where s is the side length (called the edge in this problem)
Since V = 125 cm³, we can take the cube root of 125 to find the edge length.
The cube root of 125 is 5, ( 5³ = 125)
So the edge of the cube is 5 cm
The are of a square is found by the formula
A = s² ,
where s is the side length (called the edge in this problem)
Since A = 64 cm², we can take the square root of 64 to find the edge length.
The square root of 64 is 8 (8² = 84)
So the edge of the square is 8cm
Comparing the two edges tells us that the edge of the cube is 3cm shorter than the edge of the square.
On a survey, 6 students reported how many minutes it takes them to travel to school. Here are their responses.
Find the mean travel time for these students.
4, 11, 14, 9, 4, 8
A certain box has a width that is 2 inches more than its length and a height that is 5 inches less than its length. If each of the two smallest faces of the box has an area of 36 square inches, what is the volume if the box?
Answer:
V = 396 cubic inches
Step-by-step explanation:
width = w; length = l; height = h; volume = V; area of smallest face = a
base units are inches
w = 2 + l
h = l - 5
Height is smallest and length is second smallest (h = l -, l = l, w = l +), so a is for h and l.
a = h × l = (l - 5) × l
36 = l^2 - 5l ==> l^2 - 5l - 36 = 0
Factor ==> (l - 9) × (l + 4) = 0
l = 9 and l = -4
Since length cannot be negative, 9 is the only Real answer.
l = 9
h = l - 5 = 9 - 5 = 4
w = 2 + l = 2 + 9 = 11
Volume of rectangular prism/box is length times width times height.
V = l × w × h = 9 × 11 × 4 = 396
The volume of the box with the given dimensions is;
Volume = 396 in³
Let us denote the properties of the box as follows;
Length of box = l
Width of box = w
Height of box = h
Area of the smallest face of box = a
We are told that the width is 2 inches more than the length. Thus;
w = 2 + l
We are told that the height is 5 inches less than its length. Thus;
h = l - 5
Since length is smaller than width but bigger than height, the height and length are the 2 smallest faces
Thus,
a = h × l
plugging in the relevant values gives;
a = (l - 5) × l
a = l² - 5l
We are told that the area of the two smallest faces is 36 in². Thus;
l² - 5l = 36
l² - 5l - 36 = 0
Using online quadratic equation solver, we have; l = 9 inches
Plugging in 9 for h in; h = l - 5
h = 9 - 5
h = 4
Also, plugging in 9 for l into; w = 2 + l, we have;
w = 2 + 9
w = 11
Volume of box is given by;
Volume = length × width × height
Volume = 9 × 11 × 4
Volume = 396 in³
Read more at;https://brainly.com/question/13973603
ans of this
fast to get 10 pts
Answer:
2.equivalent sets is answer.31. Which inequality is represented by
this graph?
Answer:
A. x/5 - 6 > -4
Step-by-step explanation:
The graph shows that x > 10. We need to solve each of the inequalities. After we do, we see that A is the answer.
A. x/5 - 6 > -4
x/5 > 2
x > 10