Given:
A square base pyramid whose base length is 10 in. and height of triangular surface is 4 in.
To find:
The surface area of the pyramid to the nearest whole number.
Solution:
A square base pyramid contains square base with edge 10 in. and 4 congruent triangles with base 10 in. and height 4 in.
Area of a square is
[tex]A_1=(edge)^2[/tex]
[tex]A_1=(10)^2[/tex]
[tex]A_1=100[/tex]
So, area of square base is 100 sq. in.
Area of a triangle is
[tex]A_2=\dfrac{1}{2}\times base\times height[/tex]
[tex]A_2=\dfrac{1}{2}\times 10\times 4[/tex]
[tex]A_2=20[/tex]
So, area of each triangular surface is 20 sq. in.
Now, the total surface area of the pyramid is
Total area = Area of square base + Area of 4 congruent triangles.
[tex]A=A_1+4\times A_2[/tex]
[tex]A=100+4\times 20[/tex]
[tex]A=100+80[/tex]
[tex]A=180[/tex]
Therefore, the area of the pyramid is 180 sq. in.
What is the equation of the line perpendicular to the line y = 2x + 3 with a y-intercept of -6
Answer:
y = -¹/₂ x - 6Step-by-step explanation:
Two lines are perpendicular if the product of theirs slopes is equal -1:
y=m₁x+b₁ ⊥ y=m₂x+b₂ ⇒ m₁×m₂ = -1
y = 2x + 3 ⇒ m₁=2
2×m₂ = -1 ⇒ m₂ = -¹/₂
The y-intercept is b=-6 so the equation in slope-intercept form:
y = -¹/₂ x - 6
What is the multiplayer for a 3% increase?
Answer:
3% = 0.03
verified with calculator
*WILL GIVE A BRAINIST*
GEOMETRY
What expression below is equivalent to 3a + 12?
3(a + 12)
В.
3(a + 4)
C.
15 + a
D.
15a
Answer:
B. 3(a + 4)
Step-by-step explanation:
Divide by a factor of 3:
3a/3 = a
12/3 = 4
Therefore, 3(a + 4) is equivalent to 3a + 12.
What is the measure of EFG in O0 below?
GE=60
EFG=360-60=300
:)
the equation of the line which has a gradient of 3 and passes through the point (-1,3)
Answer:
Call the line (d): y = ax + b
(d) intersects the vertical axis at the point where the intersection is 3 ⇒x = 0, y = 3 Instead of (d) we have: b = 3
(d) intersects the horizontal axis at the point where the coordinate is -1 ⇒x = −1, y = 0 Instead of (d) we have: −a + b = 0
Replace into b = 3 into -a + b = 0 we have: −a + 3 = 0⇔a = 3
So the equation for the line is y = 3x + 3
Step-by-step explanation:
7(n+4)= 21 what’s does n equal
Answer:
Step-by-step explanation:
here you go mate
step 1
7(n+4)= 21 equation/Question
step 2
7(n+4)= 21 simplify
7n+28=21
step 3
7n+28=21 subtract
7n=-7
step 4
[tex]\frac{7n}{7} =\frac{-7}{7}[/tex]Divide
answer
n=-1
Evaluate 7b-b when b=4
Thank you!!
Answer:
The correct answer is 24.
Step-by-step explanation:
Help with number 2 please
Answer:
3 in a half miles
Step-by-step explanation:
For the school play, the advance tickets cost 3, while tickets at the door cost 5. Thirty more tickets were sold at door than in advance, and was collected. How many of each kind of ticket were sold? Write your answer in a sentence.
Answer:
Number of tickets sold in advance = 310
Number of tickets sold at the door = 340
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
For the school play, the advance tickets cost $3, while tickets at the door cost $5. Thirty more tickets were sold at the door than in advance, and $2630 was collected. How many of each kind of ticket were sold?
The explation of the answer is now given as follows:
Let a represents number of tickets sold in advance. Therefore, we have:
a = number of tickets sold in advance at $3 each
a + 30 = number of tickets sold at the door at $5 each
The total amount collected can be represented by this equation:
3a + 5(a + 30) = 2630
Solving for a, wee have:
3a + 5a + 150 = 2630
8a = 2630 - 150
8a = 2,480
a = 2,480 / 8
a = 310
Therefore, this implies:
Number of tickets sold in advance = 310
Number of tickets sold at the door = a + 30 = 310 + 30 = 340
The multiplication property of equality could be used to solve which of the following equations?
OX+2)x-3) = 0
m+7=-12
OD-2) = 18
03+y=7
Answer:
I pretty sure its C. OD-2) = 18
Step-by-step explanation:
The line plots shows the weights of 9 grapefruits. What is the difference in the total weight of all the 1 1/2 lb grapefruits and the total weight of all the 1 1/4 lb grapefruits? A 1/4lb B 2 lb C 4 1/2lb D 7 lb
Answer:
The difference of weight is [tex]2[/tex] pounds.
Step-by-step explanation:
Given: The line plots shows the weights of [tex]9[/tex] grapefruits
To find: The difference in the total weight of all the [tex]1\frac{1}{2} lb[/tex] grapefruits and the total weight of all the [tex]1 \frac{1}{4}lb[/tex] grapefruits.
Firstly, we need to convert the given mixed fractions as following:
[tex]1\frac{1}{2} lb=\frac{2+1}{2}=\frac{3}{2}lb[/tex]
[tex]1\frac{1}{4} lb=\frac{4+1}{4}=\frac{5}{4}lb[/tex]
Now, we know that,
Point diagrams divide a sample into different classes, and allow to observe the frequencies of each class.
In this case, the different weights of the grapefruit constitute the classes. From a sample of 10 grapefruit, some will weigh others weigh.
We need to observe the dot diagram to know how many grapefruit we have of weight [tex]\frac{3}{2} lb[/tex] and how many grapefruit we have of weight [tex]\frac{5}{4} lb[/tex]. In other words, we need to know, in the diagram, how many points there are about class of [tex]\frac{3}{2} lb[/tex] and how many points there are about class of [tex]\frac{5}{4} lb[/tex].
Then, the total difference between all grapefruit of pounds and all grapefruit of pounds is calculated as follows:
[tex]x (1\frac{1}{2} ) - y (1\frac{1}{4} ) = Z[/tex]
Where
[tex]Z[/tex]: Weight difference
[tex]x[/tex]: Quantity of [tex]1\frac{1}{2} lb[/tex] grapefruit
[tex]y[/tex]: Quantity of [tex]1\frac{1}{4}lb[/tex] grapefruit
Suppose that of the [tex]10[/tex] total grapefruits, [tex]3[/tex] of them weigh [tex]1\frac{1}{2} lb[/tex] and [tex]2[/tex] of them weigh [tex]1 \frac{1}{4}[/tex] pounds. This is: [tex]x=3[/tex] and [tex]y=2[/tex]
Now,
[tex]3(\frac{3}{2} )-2(\frac{5}{4} )[/tex]
[tex]=\frac{9}{2} -\frac{5}{2}[/tex]
[tex]=\frac{4}{2}[/tex]
[tex]=2[/tex]
Hence, for this case, the difference of weight is [tex]2[/tex] pounds.
Please help me thanks please
Answer:
6
Step-by-step explanation:
Step-by-step explanation:
make it braintliest please
Solve for X
8(x— 4) = –64
X =
Answer:
8(x-4)=-64
8x-32=-64 +32
8x=-32 :8
x=-4
Step-by-step explanation:
prove me wrong
For what value of p would the statement 5p = 30 be true
Answer:
p = 6 is the answer
Step-by-step explanation:
is 315/8 rational or irrational
Answer:
315/8 GIVES 39.375. But 35.375 Is actually a rational number, because it is terminating after 3 decimal places.
Step-by-step explanation:
Answer:
315/8 is rational.
Step-by-step explanation:
It is rational because 315/8 = 39.375. But 35.375 Is actually a rational number because it is terminating after 3 decimal places.
1) Work out the size of angle x.
2) Give reasons for your answer.
(15 points if correct)
Answer:
x= 75°
because 180°-105°=75°
Hi I need help please 10 points for answering questions 3 and 4 correctly please it’s due tomorrow
Answer:
3. 150% 4. 8.3%
Step-by-step explanation:
Percent error formula is the difference between the actual and estimated divided by actual times 100.
3. (5-2) / 2 x 100= 150%
4. (24-22)/ 24 x 100 = 8.3%
A line has this equation: y = x + 4 Write an equation for the perpendicular line that goes through (2, 5).
Answer:
y = -x + 7
Step-by-step explanation:
y = x + 4 slope: 1
slope of perpendicular line: -1
for (2,5) y interception (b) = y - mx = 5 - (-1)*2 = 7
equation: y = -x + 7
check: -x+7 = -2+7 =5
solve (−8x−12)+(9x+4)=
If LN = 12x + 16, what is the length of Line segment L N in units?
Answer:
Step-by-step explanation:
16 units 40 units 48 units 64 units.
Answer:
64 units
Step-by-step explanation:
Given M lies on LN, so LN = LM + MN --------------(1)
LN = 12x + 16
LM = 10x + 8
MN = 5x - 4
Substituting the values in equation 1, we get:
12x + 16 = (10x + 8) + (5x - 4)
12x + 16 = 15x + 4
15x - 12x = 16 -4
3x=12
Therefore x=4
LN= 12(4) + 16 = 64 units
Can I get some help thank u sm
Answer:
11Step-by-step explanation:
The sum of interior angles is equal to exterior angle
Given the following
Interior angles = 5x + 10 and 58
Exterior angle 11x+2
According to the postulate:
5x + 10 + 58 = 11x + 2
5x + 68 = 11x + 2
Collect like terms
5x -11x = 2 - 68
-6x = -66
x = -66/-6
x = 11
The value of x is 11
Select the correct answer. For what value of x is sin x = cos 19º, where 0°< x < 90°? OA. 38° ° O B. 71° OC. 26° O D. 19°
Answer:
x = 71°
Option B is correct answer.
Step-by-step explanation:
We need to find for what value of x is [tex]sin\: x = cos 19^{\circ}[/tex], where 0°< x < 90°?
Solving:
[tex]sin\: x = cos\: 19^{\circ}\\Finding \:cos\: 19^{\circ}=0.94551\\Putting\:value:\\sin\:x=0.94551\\Now\:taking\:sin\:inverse\\x=sin^{-1}(0.94551)\\x=71^{\circ}[/tex]
So, we get x = 71°
Option B is correct answer.
Hey guys please help me! Very appreciate it
Answer:
30.9
Step-by-step explanation:
.
I need help with this
Answer:
The order is from top to bottom just an FYI :)
First blank: 1
Second blank: 7
Third blank: 4
Step-by-step explanation:
I did the division, got the answer as 1.1, so the first blank is 1. The second blank should be 7 and the third blank should be 4 so that the numbers subtract to 0.
Helpppp meeeeee pleaseeeee
Answer:
x+3=5 is the answer you're looking for.
Answer:
x+3=5
Step-by-step explanation:
which equation represents this graph?
Answer:
It would be the 1st answer, y= 3/2x + 2.
Step-by-step explanation:
The intersection on the Y axis determins the "+2". To find the slope, it is always x/y. It rises 3, and runs 2. Hope this helps
I need help with homework
Answer:
C
Step-by-step explanation:
Point C is on the x-axis.
Answer:
c
Step-by-step explanation:
the x axis is labeled
x axis is always horizontal (think the horizon)
y axis is always vertical
Rena has posters that measure 8 inches wide by 10 inches tall. If she uses a poster maker which creates similar posters, what is the area of the poster if the height of the poster is 35 inches?
Answer:
B . 980 just trust me
Step-by-step explanation:
You set up proportions
Greatest common factor of 4 and 19?
Answer:
The greatest common factor of 4 and 19 is 1
Step-by-step explanation:
Answer:
Greatest common factor of 4 and 19 is 1