A right square pyramid is shown. The height of the pyramid is 6 units. The distance from the center of the base of the pyramid to vertex D is 2.5 units, as shown. Find the length of segment AD, in units.
Answers
Answer:
AD is 6.5 units
Step-by-step explanation:
Find the diagram attached.
From the diagram, you can see that the dotted triangle is a right angled triangle with side AD as the hypotenuse.
To get AD, we will use the pythagoras theorem as shown;
Hyp² = Opp² + Adj²
AD² = 6²+2.5²
AD² = 36 + 6.25
AD² = 42.25
AD = √42.25
AD = 6.5
Hence the measure of length segment AD is 6.5 units
Related Questions
Solve the puzzle. M + M + M = 30. M + N + N =20. N + Q + Q = 9. N + Q × M = ?Solve for M.
A. 8
B. 9
C. 10
Answers
Answer:
M=10
N=5
Q=2
Step-by-step explanation:
if you look at the equation it says
M+M+M=30
Since there's 3 M's you can combine it and make it into 3M=30.
you could then divide 30 by 3 in order to get M by itself and you would get M=10.
Hope this helped :)
a 40ft flag pole has a rope tied from the top to the ground. the rope makes a 25 degree angle with the ground, how long is the rope
Answers
Answer:
The rope is 94.65 feet.
Step-by-step explanation:
Find a formula for the function f(x) such that f′(x)=sin(x) and f(2)=5.
Answers
Answer: f(x) = -cos(x) + 4.584
Step-by-step explanation:
we know that f'(x) = sin(x)
if we integrate that, we get:
f(x) = -cos(x) + C
Where C is a constant of integration.
And we also want that:
f(2) = 5
with that relationship we can find the value of C.
f(2) = 5 = -cos(2) + C
(The calculation is done in radians)
5 = -(-0.416) + C
5 - 0.416 = C = 4.584
Then the function is:
f(x) = -cos(x) + 4.584
how many times does 67 117
Answers
please help me :((((
Answers
Answer:
b i think
Step-by-step explanation:
Answer:
its G
Step-by-step explanation:
the y intercept (where the line crosses y line) is (0,2)
can you simplify this?
[tex] \frac{a {}^{3} }{2} [/tex]
Answers
find slope of the line passes through (7, 3)and (9, 6
Answers
Answer:
slope = 3/2
Step-by-step explanation:
(y2-y1)/(x2-x1)
= (6-3)/(9-7)
= 3/2
Hope this helps! :3
plz mark as brainliest!
8. The table shows the linear relationship between the balance of a student's savings
account and the number of weeks he has been saving.
Savings Account
Week
1 3
8 13
Balance
53
88
(dollars)
123
0
6
32
39
74
Based on the table, what was the rate of change of the balance of the student's
savings account in dollars and cents per week?
Answers
Answer:
7 dollars
Step-by-step explanation:
y = x2+x-30
what are the factors
Answers
Answer:
2 and x are the factors of 2
Step-by-step explanation:
Solve the system of linear equations by multiplying.
7x-2y=22
3x+9y=39
Answers
Answer: The answer (4,3) or x=4 and y=3
What is the y intercept of the line 2x + 3y = -15?
Answers
Answer:
y intercept: (0,-5)
Step-by-step explanation:
i need help 5+(−4)+(−7)+2
can you guy help me for this questions
Answers
Answer:
-4
Step-by-step explanation:
first remove the parentheses
5-4-7+2
then calculate the sum or difference
-4
Read the image below please.
Answers
Answer:
30
Step-by-step explanation:
Plz help i will mark branliest
Writing Equations From Two Points & Point-Slope Form
Answers
Answer:
problem #2:
y - 4 = 2 ( x + 1) , y - 1 = -1/3x ( x - 2)
problem #3:
slope: 2/3 point: -2, 4
slope: -3 point: -5, -1
Step-by-step explanation:
good luck!
I NEED THE ANSWER I HAVE 15 MINUTES LEFT!!
On a high school varsity baseball team, 5 players are sophomores, 11 are juniors, and 13 are seniors. The team selects 4 honorary co-captains by drawing names from a hat. What's the probability that all 4 co-captains come from the same class?
Answers
Answer:
The probability is 0.0442
Step-by-step explanation:
If they all come from the same class, what it means is that we select 4 sophomores or , 4 juniors or 4 seniors
When we have or, it means we are to add each possible probability scenarios
The total number from which we want to select from is;
5 + 11 + 13 = 29
So the probability will be;
5C4/29C4 or 11C4/29C4 or 13C4/29C4
= 5C4/29C4 + 11C4/29C4 + 13C4/29C4
=0.0442
In the supermarket, there were 434 boxes of cereal, 285 gallons of milk, and 176 cans of orange juice. About how many
breakfast items were there? Use rounding to the nearest hundred to estimate the total number of breakfast items.
Answers
Answer:
900
Step-by-step explanation:
434+285+176 is 895,895 to the nearest hundred is 900
6.Zena needs a salesperson. Sales person anyway is offering his services for an initial $50 in addition to $5 per hour. Sales person B is offering her services for $15 per hour. How many hours will two sales people charge the same amount of money?
Answers
Answer:
5 hours (when salespersons A and B will both charge $75)
7t=x, for t
Show your work!
Answers
Answer:
.
Step-by-step explanation:
Answer:
[tex]t=\frac{x}{7}[/tex]
Step-by-step explanation:
You need to isolate the variable t. Use inverse operations for this.
7t can be seen as 7×t, and the opposite of multiplication is division. Divide both sides by 7:
[tex]\frac{7t}{7}=\frac{x}{7}\\\\t=\frac{x}{7}[/tex]
The common term 7 on the left side cancels out.
:Done
Find the discriminant and state the number and type of solutions.
-3.02 - 6x + 5 = 8
Answers
x = 1.00(3)
y = -2x+3 write in standard form
Answers
Answer:
y + 2x - 3 = 0
Step-by-step explanation:
You should learn the topic.
Answer:
2x+y-3=0
Step-by-step explanation:
The standard form is a representation of equations that start from the variable term towards the constant term, generally leaving the RHS empty.
Here,
[tex]y=-2x+3\\y+2x=3\\y+2x-3=0\\2x+y-3=0[/tex]
A circular clock has a circumference of 48.5 meters. What the measurement of the radius, in meters, of the clock?
Answers
Answer:
The radius of the clock is 7.72 meters
Step-by-step explanation:
Here, we want to calculate the radius of a clock which has a circumference of 48.5 m
Mathematically;
Circumference C = 2 * pi * r
48.5 = 2 * 22/7 * r
7 * 48.5 = 44r
r = (7 * 48.5)/44
r = 7.72 meters
What is the distance from QR?
Q
6n + 3
s
4n + 11
R
Answers
Answer:
The distance of QR is 54 units
Step-by-step explanation:
In the isosceles triangle, The height drawn from the vertex angle to the base bisects the base
In ΔPQR
∵ PQ = PR
∴ Δ PQR is an isosceles triangle
∵ P is the vertex angle
∵ QR is the base
∵ PS ⊥ QR
→ By using the fact above
∴ PS bisects QR
∴ S is the midpoint of QR
→ That means S divided QR into 2 equal parts QS and SR
∵ QS = SR
∵ QS = 6n + 3
∵ SR = 4n + 11
→ Equate them to find n
∴ 6n + 3 = 4n + 11
→ Subtract 4 n from both sides
∵ 6n - 4n + 3 = 4n - 4n + 11
∴ 2n + 3 = 11
→ Subtract 3 from both sides
∵ 2n + 3 - 3 = 11 - 3
∴ 2n = 8
→ Divide both sides by 2
∴ n = 4
→ Find the length of QS by substitute x in its expression by 4
∵ QS = 6(4) + 3 = 24 + 3
∴ QS = 27
∵ QS = SR
∴ SR = 27
∵ QR = QS + SR
∴ QR = 27 + 27
∴ QR = 54 units
∴ The distance of QR is 54 units
Triangle CAT is an isosceles triangle with base angles C and T each represent by (3x + 11) degrees, while angle A is represented by (9x + 8) degrees. Find the measure of angle C.
Answers
Answer:
Angle C = 41°
Step-by-step explanation:
Given:
Angle C = (3x + 11) degree
Angle T = (3x + 11) degree
Angle A = (9x + 8) degree
Find:
Angle C
Computation:
Using angle sum property
(3x + 11) + (3x + 11) + (9x + 8) = 180
15x + 30 = 180
x = 10
So,
Angle C = (3x + 11) degree
Angle C = 3(10) + 11
Angle C = 41°
Emily's car broke down the weekend before she started a new job. She borrowed $880 from her parents, at an annual interest rate of 3%, to quickly pay for the car repairs. If Emily paid her parents a total of $893.20 in six months, how much simple interest did she pay?
Answers
Answer:
$13.2Step-by-step explanation:
Step one:
given data
principal=$880
rate= 3%
final amount = $893.2
time t= 6 months =0.5 years
Step two:
Required
Simple interest
SI=PRT/100
SI=880*3*0.5/100
SI=1320/100
SI=13.2
She paid Simple interest of $13.2
Devin has 48 gingerbread cookies and 60 candy canes that he will put in gift bags for his friends and family. What is the greatest number of gift bags he can make if each bag will have the same number of cookies and the same number of candy canes? Also, identify the number of cookies and candy canes each bag will have.
Answers
Answer:
12 is the largest one number of gift bags he can make. Each will have 4 gingerbread cookies and 5 candy canes
Step-by-step explanation:
How do cells maintain homeostasis? Describe one way a cell will maintain stable internal conditions.
Answers
Answer:
One way that a cell maintains homeostasis is by controlling the movement of substances across the cell membrane. Cells are suspended in a fluid environment.
PLEASE HELP!!!!!!!!
find the missing value
y=-4x-1
( ,11)?
Answers
You would make -1 positive and add it to 11. This gives you 12. Then divide 12 and -4 which gives you -3.
6. Triangle CDE with vertices C(-2,-2), D(1,-4), and E(-3,-4):
a) dilation with scale factor of 4 centered (-1.-3)
b) reflection in the line y = -x
Answers
The coordinates of C'D'E' after dilation with the scale factor are; C'(3, 1), D'(-9, -7), E'(7, -7)
How to work with transformation of objects?
We are given the vertices of Triangle CDE as;
C(-2,-2), D(1,-4), and E(-3,-4).
Now when we dilate an object by a scale factor of 4, it means we multiply each coordinate by 4 if it is about the origin.
However, we are told that it is centered about the point (-1.-3).
Thus;
Point C is 1 unit vertically above point (-1.-3) and as such C' will be (1 * 4) = 4 units above the center point.
Point C is 1 unit horizontally to the right of point (-1.-3) and as such C' will be (1 * 4) = 4 units to the right of the center point. Thus, C' is (3, 1)
Point D is 1 unit vertically below point (-1.-3) and as such D' will be (1 * 4) = 4 units below the center point.
Point D is 2 unit horizontally to the left of point (-1.-3) and as such D' will be (2 * 4) = 8 units to the right of the center point. Thus, C' is (-9, -7)
Point E is 1 unit vertically below point (-1.-3) and as such D' will be (1 * 4) = 4 units below the center point.
Point D is 2 unit horizontally to the right of point (-1.-3) and as such D' will be (2 * 4) = 8 units to the right of the center point. Thus, C' is (7, -7)
B) Reflection in the line y = -x gives;
C'(2, -2), D(-1, 4), and E(3, 4)
Read more about Objects Transformation at; https://brainly.com/question/3457976
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$5,000 is invested in two different accounts yielding 2% and 2.5% interest. The interest earned on the two accounts is $120. How much money was invested at 2% interest?
$1,000
$3,000
$4,000
$5,000
Answers
Answer:
1000
Step-by-step explanation:
i am beyond confused
Answers
Your answer would be B