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.
Is MNO=PQR? If so, name the congruence postulate that applies.
Given:
ME=PQ
NO=QR
MO=PR
A. Congruent - ASA
B. Congruent - SSS
C. Congruent - SAS
D. Might not be congruent
Answer:
B. Congruent - SSS
Step-by-step explanation:
Since, corresponding sides of both the triangles are congruent. Hence, both the triangles are congruent by SSS Postulate.
ΔMNO ≅ ΔPQR due to Congruent-SSS
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
Given:
In ΔMNO and ΔPQR
Side ME=Side PQ
Side NO=Side QR
Side MO=Side PR
MNO ≅PQR
Since, corresponding sides of both the triangles are congruent.
So, both the triangles are congruent by SSS Postulate.
Hence , ΔMNO ≅ ΔPQR
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Find the vertex of f(x)= x^2+ 6x + 36
Pls help soon
Answer:
vertex(-3,27)
Step-by-step explanation:
f(x)= x^2+ 6x + 36 ( a=1,b=6,c=36)
V(h,k)
h=-b/2a=-6/2=-3
k=f(-3)=3²+6(-3)+36
f(-3)=9-18+36=27
vertex(-3,27)
If 1 pound of grass seed costs 25x cents, represent in terms of x the cost of 7 pounds of seed? In polynomial simplest form
Answer:
175 cents
Step-by-step explanation:
25x=
25 • 7
25 • 7 = 175
Therefore the cost of 7 pounds of seed is 175 cents.
Suppose y varies jointly as x & z. If y = -180 when z = 15and x = -3,then find y when x = 7 and z = -5. 1 point
Answer:
y = - 140
Step-by-step explanation:
The statement
y varies jointly as x & z is written as
y = kxzto find y when x = 7 and z = -5 we must first find the relationship between the variables
when y = - 180
z = 15
x = - 3
- 180 = k(15)(-3)
-180 = - 45k
Divide both sides by - 45
k = 4
The formula for the variation is
y = 4xzwhen
x = 7
z = -5
y = 4(7)(-5)
y = 4(-35)
y = - 140Hope this helps you
a ladder 7.5m long is leaning against a wall if the foot of the ladder is 3m from the wall how far up the wall does the ladder reach to reach the nearest metres
Answer:
7 m
Step-by-step explanation:
Use the pythagorean theorem.
a^2+b^2=c^2
7.5 is your hypotenuse and 3 is one of your legs.
7.5^2 - 3^2 = 47.25
the sqrt of 47.25 is 6.873863542, therefore the nearest meter it reaches is 7.
-
What is the product?
(-3s +2)(4s-1)
Answer: -12s + -2
Step-by-step explanation: You need to combine the like terms so -3sx4s = -12s and 2+-1 = -2 so it’s -12s + -2 or -12s - 2
Answer:
-12s²+11s-2
Step-by-step explanation:
(-3s+2)(4s-1)
First you have to FOIL (First, inner, outter, last)
First: -3s × 4s
Inner: -3s × -1
Outter: 2 × 4s
Last: 2 × -1
Now you should have -12s² + 3s + 8s -2
----------------------
Next you combine your like terms
Finally you have your answer, -12s²+11s-2 .
if the first step of the equation -x + 6 = 5 - 3x is "subtract 5" then what should the next step be
Answer:
The next step is add x to each side
Step-by-step explanation:
-x + 6 = 5 - 3x
Subtract 5 from each side
-x + 6-5 = 5-5 - 3x
-x+1 = -3x
Add x to each side
-x+1 = -3x+x
1 = -2x
Answer:
Step-by-step explanation:
all you need to do is solve for x right? so in that case when you subtract 5 from both sides you get -x+1=-3x
then you will add x on each side
you should now have 1=-2x
divide each side by -2 and then you will have
-1/2=x
Desmond is 2 inches taller than Niki. If we let w represent Nikis height in inches, write an algebraic expression for Desmonds height. Enter your answer as an expression. Example: 3x^2+1
Answer:
w + 2
Step-by-step explanation:
Niki's height = w in
Desmond height = w + 2
Answer:
w+2
Step-by-step explanation:
Since Desmonds is 2 inches taller than Niki, w+2 would make the most sense.
solve for y: -2(5y-1)-y=-4(y-3)
Answer:
[tex]y = - \frac{10}{7} [/tex]Step-by-step explanation:
- 2(5y - 1) - y = - 4(y - 3)
Expand the terms in the bracket
That's
-10y + 2 - y = - 4y + 12
Group like terms
Send the constants to the right side of the equation and those with variables to the left side
That's
- 10y - y + 4y = 12 - 2
- 7y = 10
Divide both sides by - 7
We have the final answer as
[tex]y = - \frac{10}{7} [/tex]Hope this helps you
MATH QUESTION: When 8668/25 + 4141/9 - 5533/25 is computed and written as a mixed number in simplest form, what is the fractional part of that mixed number?
Answer:
23/45
Step-by-step explanation:
8668/25 + 4141/9 - 5533/25
= 26348/45
= 585(23/45)
=23/45
Which property can you apply to Hayley's expression to show that it is equivalent to Gretchens expression?
Answer: Distributive property of the multiplication.
Step-by-step explanation:
You did not post Gretchen's expression, but i gues that it is 3*(x + y)
I guess that it is the distributive property of the multiplication.
For 3 numbers, A, B and C, we have that:
A*(B + C) = A*B + A*C
here we have:
3*x + 3*y
We can do the inverse process to the distributive property, and get:
3*x + 3*y = 3*(x + y)
which i guess is Gretchen's expression.
Answer:
the other person is right it is Distributive property of the multiplication.
4x- 3y = -13 -x + 6y = -44
Answer:
3x and 9y and -31 is the correct answer if you are bloviating.
Step-by-step explanation:
bloviate the factors of x and y.
Which two complex numbers when subtracted from each other equal another complex number from the table? A -3 − 4i B -7 − 6i C 13 + i D -9 + 6i E 8 − 8i F -15 + 9i G 2 + 12i H 6 − 10i
Answer:
if you have a ti-84 plus, input ur problem into the calculator
Step-by-step explanation: you may use calculator for answers
Answer:
The difference of A and D equals the complex number in row H in the table (6 − 10i):
A − D
=
-3 − 4i − (-9 + 6i)
=
-3 − 4i + 9 − 6i
=
-3 + 9 − 4i − 6i
=
(-3 + 9) + (-4 − 6)i
= 6 − 10i
Step-by-step explanation:
Work out the value of angle x
======================================================
Explanation:
The given exterior angle 97 is adjacent to the interior angle 180-97 = 83. This is the base angle of the isosceles triangle. The other base angle is directly above it. The base angles are always opposite the congruent sides.
The missing interior angle (adjacent to the blue angle x) is unknown, so we'll call it angle y. This angle adds to the other two base angles (83 each) to get a sum of 180. Adding any three interior angles of a triangle always gets you 180
y+83+83 = 180
y+166 = 180
y = 180-166
y = 14
Angle x and y are supplementary. They form a 180 degree angle
x+y = 180
x = 180-y
x = 180-14
x = 166
As you can see, the base angles combine to form the exterior angle we're after. This is because of the remote interior angle theorem.
Counting from 1 to 46, how many 4s will you encounter? 8 10 11 12 14
Answer:
11
Step-by-step explanation:
4=1
14=2
24=3
34=4
40=5
41=6
42=7
43=8
44=9
45=10
46=11
You will encounter 11 4s.
Which of the following is most likely the next step in the series?
A.
B.
C.
D.
Answer:
C
Step-by-step explanation:
The amount of sides on the shape are increasing, like 4, 5, 6, so the best answer should be 7 sides for the next shape, however there is no shape that is 7, so C which has 8 sides is the next best answer.
Most likely the next step in the series is hectogon. Therefore, option A is the correct answer.
What is the pattern?A pattern in mathematics is an arrangement of numbers, shapes, colours and other elements that repeat. This arrangement can be related to any event or object. When a group of numbers is organised in a certain way, it is referred to as a pattern. Patterns can also be referred to as a series.
The given series has square, pentagon and hexagon.
We know that, square has 4 sides, pentagon has 5 sides and hexagon has 6 sides.
So, the next figure in the series must have 7 sides.
Thus, 7 sided figure is called has hectogon and septagon.
Therefore, option A is the correct answer.
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Please Help! Three times the quantity of a number increased by 7 is equal to the same number decreased by 15
The equation is written as 3x + 7 = x - 15. And the solution of the equation will be negative 11.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Multiple times the amount of a number expanded by 7 is equivalent to a similar number diminished by 15.
Let the number be 'x'.
The three times the number plus 7. Then the expression is given as,
⇒ 3x + 7
The number 'x' is decreased by 15. Then the expression is given as,
⇒ x - 15
Both expressions are equal to each other. Then we have
3x + 7 = x - 15
3x - x = - 15 - 7
2x = - 22
x = - 11
The equation is written as 3x + 7 = x - 15. And the solution of the equation will be negative 11.
More about the solution of the equation link is given below.
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Use the diagram to complete the statement. Triangle J K L is shown. Angle K J L is a right angle. Angle J K L is 52 degrees and angle K L J is 38 degrees. Given △JKL, sin(38°) equals cos(38°). cos(52°). tan(38°). tan(52°).
Answer:
[tex]\bold{sin(38^\circ)=cos(52^\circ)}[/tex]
Step-by-step explanation:
Given that [tex]\triangle KJL[/tex] is a right angled triangle.
[tex]\angle JKL = 52^\circ\\\angle KLJ = 38^\circ[/tex]
and
[tex]\angle KJL = 90^\circ[/tex]
Kindly refer to the attached image of [tex]\triangle KJL[/tex] in which all the given angles are shown.
To find:
sin(38°) = ?
a) cos(38°)
b) cos(52°)
c) tan(38°)
d) tan(52°)
Solution:
Let us use the trigonometric identities in the given [tex]\triangle KJL[/tex].
We have to find the value of sin(38°).
We know that sine trigonometric identity is given as:
[tex]sin\theta =\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]sin(\angle JLK) = \dfrac{JK}{KL}\\OR\\sin(38^\circ) = \dfrac{JK}{KL}[/tex]....... (1)
Now, let us find out the values of trigonometric functions given in options one by one:
[tex]cos\theta =\dfrac{Base}{Hypotenuse}[/tex]
[tex]cos(\angle JLK) = \dfrac{JL}{KL}\\OR\\cos(38^\circ) = \dfrac{JL}{KL}[/tex]....... (2)
By (1) and (2):
sin(38°) [tex]\neq[/tex] cos(38°).
[tex]cos(\angle JKL) = \dfrac{JK}{KL}\\OR\\cos(52^\circ) = \dfrac{JK}{KL}[/tex] ...... (3)
Comparing equations (1) and (3):
we get the both are same.
[tex]\therefore \bold{sin(38^\circ)=cos(52^\circ)}[/tex]
Answer:
B in EDG
Step-by-step explanation:
A truck costs $8,000 with a residual value of $1,000. It has an estimated useful life of 7 years. If the truck was bought on July 9 what would be the book value at the end of year 1?
Answer:
$7520.55
Step-by-step explanation:
Cost of truck = $8000
Residual value = $1000
Estimated useful life = 7 years
Depreciation = (cost of asset - salvage value) / useful life
Depreciation = (8000 - 1000) / 7
Depreciation = 7000 / 7
Depreciation = $1000
Truck was purchased on July 9, Therefore, Depreciation by the end of year one will be;
Number of days between July 9 and year end = 175 days
Daily Depreciation = $1000 / 365 = $2.739
Total Depreciation by year end = (daily Depreciation * 175 days) = $479.45.
Book value at the end of year 1 = (8000 - 479.45)
= $7520.55
Answer:
The answer is "$7,500".
Step-by-step explanation:
Formula:
In the month of July-December the depreciation:
[tex]\frac{\text{Cost-Residual}}{\text{Useful life}}\times \frac{6}{12} \\[/tex]
Cost-Residual= costs -residual value
Given:
Cost-Residual = $8, 000 - $ 1,00
= $7,000
Useful life= 7 years
Put the value in the above-given formula:
[tex]=\frac{7 000}{7}\times \frac{6}{12}\\\\= 1 000\times \frac{1}{2}\\\\= 5 00\\[/tex]
Therefore, the book value on point at the end of one year is:
= $8,000 -$ 500
= $7,500
solve the equation: sin(2x)= sin x
Answer:
Below
Step-by-step explanation:
sin(2x) = 2 ×cos(x)× sin(x)
● sin(x) = 2 × cos(x) × sin(x)
● 2 × cos(x) = 1
● cos (x) = 1/2
So we can deduce that:
● x = Pi/3 + 2*k*Pi
● or x = -Pi/3 + 2*k*Pi
K is an integer
The Solution of x:
x = π/3 + 2πn, where n is an integer.
x = 2π/3 + 2πn, where n is an integer.
In degrees:
x = 60° + 360°n, where n is an integer.
x = 120° + 360°n, where n is an integer.
To solve the equation sin(2x) = sin(x), we can use the properties of trigonometric functions.
First, let's simplify the equation using the double angle identity for sine:
sin(2x) = 2sin(x)cos(x).
Now we can rewrite the equation as:
2sin(x)cos(x) = sin(x).
2cos(x) = 1.
Dividing both sides of the equation by cos(x), we get:
2 = 1/cos(x).
Now, we can find the value of cos(x) by taking the reciprocal of both sides:
cos(x) = 1/2.
From the unit circle or trigonometric values,
we know that cos(x) = 1/2 corresponds to angles of π/3 or 2π/3 (in radians) or 60° or 120° .
So, the solutions for x are:
x = π/3 + 2πn, where n is an integer.
or
x = 2π/3 + 2πn, where n is an integer.
In degrees:
x = 60° + 360°n, where n is an integer.
or
x = 120° + 360°n, where n is an integer.
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Without attempting to solve, how many solutions does this system of equations have? y=2x+1 −3y=6x+6 1. One Solution 2. No Solution 3. An infinite number of solutions 4. Cannot be determined without solving
Answer:
1. One Solution
Step-by-step explanation:
y=2x+1
−3y=6x+6
Divide the second equation by -3
−3y/-3=6x/-3+6/-3
y = -2x-2
The slopes are different so we know that the lines are not parallel
The will intersect at a point
There will be one solution
I need this answer ASAP pls someone help ASAP work shown
Worth 10 pts
Answer:
5c² + 4c - 4
Step-by-step explanation:
Subtract the shaded area from the area of the outer rectangle, that is
(2c + 3)(3c - 2) - (c + 2)(c - 1) ← expand both pairs of factors using FOIL
= 6c² + 5c - 6 - (c² + c - 2) ← distribute parenthesis by - 1
= 6c² + 5c - 6 - c² - c + 2 ← collect like terms
= 5c² + 4c - 4
Bart opens a bank account and deposits $10 each week. If he has $90 in his account, how many weeks has he been depositing money?
The number of weeks Bart has been depositing money is 9 weeks according to investment and time.
The number of weeks of money depositing will be given by the formula -
Number of weeks = total amount deposited each week/total number of weeks × 100
Keep the values in formula to find the number of weeks of money deposit
Number of weeks = 90/10
Perform division that will include cancelling zeroes
Number of weeks = 9
Hence, Bart deposited the money for 9 weeks.
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The value of y varies directly with x, where LaTeX: y=50y = 50 when LaTeX: x=40x = 40. Find the value of x when y is 10.
Group of answer choices
LaTeX: x=8 x = 8 x = 8 x = 8 x = 8 x = 8 x = 8 x = 8
LaTeX: x=12.5 x = 12.5 x = 12.5 x = 12.5 x = 12.5 x = 12.5 x = 12.5 x = 12.5
LaTeX: x=1.25 x = 1.25 x = 1.25 x = 1.25 x = 1.25 x = 1.25 x = 1.25 x = 1.25
LaTeX: x=0
Answer:
x= 8
Step-by-step explanation:
The equation of direct variation is
y = kx
When y = 50 when x = 40
50 = k* 40
Divide each side by 40
50/40 = k
5/4 = k
The equation is
y = 5/4x
Let y = 10
10 = 5/4x
Multiply each side by 4/5
4/5 * 10 = 5/4 x * 4/5
8 = x
Find the LCM of
[tex]14 {a}^{3} {b}^{2} [/tex]
and
[tex]20 {a}^{4} {b}^{2} [/tex]
Answer:
Hi,
I hope you are searching for this answer.
The lcm of an expression is calculated by taking the common factor and multiply the common factor with the remaining one, alright.
or, simply the lcm of an expression is calculated by the product of common factors and the factors which are not common.
Hope it helps...
Please answer this question now
Answer:
113 degrees
Step-by-step explanation:
Measure of arc ADCB = 58+108+60 = 226 degrees
Measure of angle B = 226/2 = 113 degrees
Answer:50
Step-by-step explanation:
The mean of 5 numbers is 11. The numbers are in the ratio 1 : 1 : 2 : 3 : 4. Find the numbers.
Answer:
5, 5, 10, 15, 20
Step-by-step explanation:
Since the mean of the 5 numbers is 11, we know that the sum of the 5 numbers is 5 * 11 = 55. If we call the numbers x, x, 2x, 3x and 4x respectively based off of the ratio, we can write:
x + x + 2x + 3x + 4x = 55
11x = 55
x = 5 so 2x = 2 * 5 = 10, 3x = 3 * 5 = 15 and 4x = 4 * 5 = 20, therefore, the numbers are 5, 5, 10, 15, and 20.
Given that
Numbers are in ratio 1:1:2:3:4 Mean of these numbers is 11 .To Find.
We have to find these five numbers.Solution .
→ Let's assume these numbers as
→ x , x , 2x , 3x and 4x
→ Mean of any observations is = Sum of observations/ Number of observations.
→ Sum of observations = x+x+2x+3x+4x
→ 11x
→ Number of observations = 5
→ Mean = 11
→ 11 = 11x/5
→ 11 (5) = 11x
→ 11(5)/11 = x
→ value of x = 5
Putting the value of x for finding all numbers .
→ 1st number = x → 5
→ 2nd number = x → 5
→ 3rd number = 2x → 10
→ 4th number = 3x → 15
→ 5th number = 4x → 20
Help me with this please
Answer:
Hey there!
Point n is either -3+5 or -3-5.
Thus, the two possible values are 2 or -8.
Let me know if this helps :)
A dealer bought 3 gross buttons at $.38 a dozen. He sold the buttons at 5 cents each. How much was his profit per gross?(12 dozen equals one gross)
Answer:
$2.64
Step-by-step explanation:
Selling them at 5 cents each ($0.05), he could sell 1 dozen buttons for
12 * $0.05 = $0.60
As he bought them at $0.38 per dozen, the profit per dozen would be
$0.60 - $0.38 = $0.22
As 12 dozen is 1 gross, the profit per gross would be
12 * $0.22 = $2.64
3 x 12 = 36
.5 x 36 = 18.0
36 divided by .38 is about 94.7
18 - 94.7 = -76.7
ANSWER:
about -76.7
(I may have done this wrong
Does The TI-Nspire works just like the TI-84 ?
Answer:
TI-Nspire models automatically detect most points of interest such as x and y-intercepts, maximum values, and minimum values when you are in trace mode. TI-84 Plus models require you to use a series of left and right bounds and guesses to find those same values.
