Answer:
Volume 25cm³
Pyramid height 3cm
Base area 25cm
Explanation:
V = A h/3 = 25·3/3 =
25cm³
I will give u brainliest if u actually help me explain this in ur own words :,(
When a complex number is in the denominator, why is it necessary to multiply by the conjugate?
Answer:
It just makes doing things (like adding and subtracting other numbers) easier if the denominator is a real number. Other than that we just do it out of tradition
This step is done to make the denominator go from a complex number in the form a+bi into a purely real number in the form a^2+b^2 (where 'a' and b are any real numbers).
This is because multiplying a+bi with its conjugate a-bi leads to the following steps
(a+bi)(a-bi)
(a)^2 - (bi)^2 ... difference of squares
a^2 - b^2*i^2
a^2 - b^2*(-1) .... recall that i^2 = -1
a^2 + b^2
----------------
So for example, if your denominator was 2+3i, then you'd multiply that by the conjugate 2-3i and you'd end up with the final denominator of 2^2+3^2 = 4+9 = 13. In this case, a = 2 and b = 3.
Note: make sure to multiply both top and bottom by a-bi (not just the denominator).
which line is parallel to y=3/4x+10
1. y=-3/4+1
2. y=4/3x+8
3. y=-4/3-10
4. y=3/4x-6
The answer would be number 4, y=3/4x-6.
This is because both of the equations share the same slope of 3/4x.
c)
Beth invests $2000 at a rate of 2% per year compound interest.
Calculate the minimum number of complete years it takes for the value
of Beth's investment to increase from $2000 to more than $2500.
Answer:
Step-by-step explanation:
We'll first find out how long it takes for the account to have 2500 in it, then we'll add a year (we'll check ourselves anyway, just to be sure!) This is an exponential growth problem of the form
[tex]A(t)=P(1+r)^t[/tex] since the compounding is only done once a year. Filling in:
[tex]2500=2000(1.02)^t[/tex] Begin by dividing both sides by 2000 to get
[tex]1.25=(1.02)^t[/tex] In order to get that t down from its current position in the equation, we will take the natural log of both sides. This allows us to pull the t down and put it out front like this:
ln(1.25) = t ln(1.02) Now divid both sides by ln(1.02) and you will see that
t = 11 years. At 11 years (rounded), the account will have
[tex]A(t)=2000(1.02)^{11}[/tex] = 2486.75 and after 12 years:
[tex]A(t)=2000(1.02)^{12[/tex] = 2536.48
t = 12 works!
The minimum number of complete years it would take the investment to increase to $2500 is 12 years.
Definition of compound interestCompound interest is when both the principal and the interest earned increases in value at the interest rate per period.
Formula for determining the number of yearsNumber of years = In(FV / PV) ÷ r
FV = future value PV = present value r = interest rate
In(2500 / 2000) ÷ 0.02
In (1.25) ÷ 0.02
= 11.2 years
= 12 years
To learn more about compound interest, please check: https://brainly.com/question/18760477
Can someone help me with this? i’m struggling urgent help please!!!!
Answer:
Similar by SAS
Step-by-step explanation:
If you multiply the two given sides by 3/2 you will get the sides for the large triangle
3/2 * 10 = 30 / 2 = 15
3/2 * 24 = 72 / 2 = 36
Therefore they are similar by SAS postulate for similarity. Notice that the right angle is between the legs of the triangle. That is the main qualification that allows you to use SAS for similarity.
Find the other two angles of both the triangles, if they were similar then the triangles are similar
The equation a + b = c could be true or false.
What is the value of x in the equation -5x+9=
- 3x + 9 = 1 / 8x - 3?
WHATS THE ANSWER
Answer:
0
Step-by-step explanation:
-5x+9=-3x+9
-5x-(-3x)+9=9
-5x+3x=9-9
-2x=0
x=0/-2
x=0
Lucas and Tony were trying to solve the equation: x^2=16x+25 Lucas said, "The x^2, squared term is isolated, so I"ll take the square root of both sides and solve." Tony said, "I'll solve using the quadratic formula with a=1,b=16, an c equals 25." Whose solution strategy would work? Choose 1 answer:
Answer:
Tony's solution strategy
Step-by-step explanation:
Given the equation that Lucas and Tony trying to solve expressed as: x^2=16x+25
This can be written in standard form as x^2 - 16x - 25 = 0
This can then be factorized using the general formula
x = -b±√b²-4ac/2a where a, b and c are constants
From the given expression;
a = 1, b = -16, c = -15
Hence the best strategy that would have worked based on the explanation is Tony's
Answer: Neither
Step-by-step explanation: got it right on khan
Find the center and raduis of the circle
Answer:
B
Step-by-step explanation:
Because the equation can be written in the form (x-p)^2+(y-q)^2. So it represents a circle with the radius r=3 and the center of (5,0).
Answer:
C
Step-by-step explanation:
The circle equation (x-a)²+(y-b)²=r² has a radius of r and a center of (a,b).
You can expand your equation from (x-5)²+y²=9 to (x-5)²+(y-0)²=3².
Using this information, you can see that a=5, b=0, and r=3.
Therefore the center is (5,0) and the radius is 3.
**This question involves circle equations, which you may want to revise. I'm always happy to help!
What is the inverse of the function f(x)=2x-10
Answer:
Last Option is correct
Step-by-step explanation:
[tex]f(x) = 2x - 10[/tex]
[tex]y=2x−10[/tex]
[tex]x=2y−10[/tex]
[tex]2y−10=x[/tex]
[tex]2y=x+10[/tex]
[tex]y = \frac{1}{2} x + 5[/tex]
[tex]h(x) = \frac{1}{2} x + 5[/tex]
Hope it is helpful...Write an equation of the line in point-slope form that passes through the given points.
(-1,3) and (-9,-2)
could someone please help
I will mark you brainliest
Which solutions make this inequality true? 3x>-30?*
X can be - 10
X can be -8
X can be o
X can be -12
x can be 3
Answer:
X can be -8, 0, and 3
Step-by-step explanation:
-8x3=-24
0x3=0
3x3=9
so -24, 0, and 9 are all bigger than -30 because -30 is a negative number.
-24>-30
0>-30
9>-30
Hope this helps!
for 1 trial, 3 spinners are spun where each spinner has 3 equal sections labeled 1, 2, and 3. What is the probability that at least two spinners land on 1?
Answer:
80/121
Step-by-step explanation:
For simplicity,
Probabilities of getting a red, a blue or a green in a single spin are, respectively, 4/11, 4/11 & 3/11.
Therefore, probabilities of getting 2 reds, 2 blues or 2 greens in 2 spins are, 16/121, 16/121 & 9/121 respectively.
Then, total probability of getting same colour both times would be 16/121 + 16/121 + 9/121 = 41/121.
Any other option would result in 2 different colours. Thus, the probability of getting two different colours in 2 spins = 1 - 41/121 = 80/121.
please look on the pic Above
Answer:
x = 2
Step-by-step explanation:
If a line is parallel to a side of a triangle and it intersects the other 2 sides then it divides those sides proportionally, that is
[tex]\frac{6x+2}{x +5}[/tex] = [tex]\frac{24-8}{8}[/tex] = [tex]\frac{16}{8}[/tex] = 2 ( multiply both sides by x + 5 )
6x + 2 = 2(x + 5)
6x + 2 = 2x + 10 ( subtract 2x from both sides )
4x + 2 = 10 ( subtract 2 from both sides )
4x = 8 ( divide both sides by 4 )
x = 2
What is the slope of the line through (-2,3) and (4,0)? 4 3 (-2,3) (4,0) x -3 -2 -1 2 2 3 4 -1 -2 -3 4 O A. 2 B. O c. -2 O D. - 1/2 PREVIOUS
Answer:
- 1/2
Step-by-step explanation:
y2 - y1 / x2 - x1
0 - 3 / 4 - (-2)
-3 / 6
= -1/2
Describe how to transform (^5 sq root x^7)^3 into an expression with a rational exponent. Make sure you respond with complete sentences.
Answer:
[tex]x^{\frac{21}{5}}[/tex]
Step-by-step explanation:
[tex]5^{th} \ root \ of \ x^7 = (x^ 7)^{\frac{1}{5}}[/tex]
[tex]Using \ the \ rule : \sqrt[n]{x} =x^{\frac{1}{n}} \\\\(x^a)^b = x^{ab}[/tex]
[tex](x^7)^{\frac{1}{5}} = x^{\frac{7}{5}}[/tex]
[tex]( x^{\frac{7}{5}})^3 = x^{\frac{21}{5}}[/tex]
What value of x makes this equation true?
12x - 15 = 6 - 3x
Answer:
7/5
Step-by-step explanation:
Isolate x
12x-15=6-3x
12x-15+15=6-3x+15 (add fifteen, addition property of equality)
12x=6-3x+15
12x=21-3x (combine like terms)
12x+3x=21-3x+3x (add 3x, addition property of equality)
15x=21 (combine like terms)
15x/15=21/15 (divide by 15, division property of equality)
x=7/5 (simplify)
Please help with math
Answer:
easy that thing needs help
x = 8 × Cos( 72 )
x = 8 × Cos( 90 - 18 )
x = 8 × Sin( 18 )
x = 8 × 0.309
x = 2.472
x = 2.470
x = 2.500
x = 2.5
If this net were to be folded into a cube, which number would be opposite of the number 1?
Answer:
4
Step-by-step explanation:
When you fold it to make it a cube, the number opposite to 1 is 4
Math/Trigonometry!!!!!!!!!!!!!!!!!!!!!!! 22 pts.
Answer:
Approximately 1,320 feet.
Step-by-step explanation:
Let one person be x miles from the skycraper, then the other one will be 5 - x miles away from it.
So we have the 2 equations:
tan 4 = h/x
tan 10 = h/(5 - x) where h is the height of the skyscraper
From the first equation:
h = x tan 4
Substituting in the second equation:
tan 10 = x tan 4 / (5 - x)
5 tan 10 - x tan 10 = x tan 4
x tan 10 + x tan 4 = 5 tan 10
x = 5 tan 10 / ( tan 10 + tan 4)
= 3.58 miles
h = 3.58 * tan 4
= 0.25 miles
= 1320 feet approx.
A man received a monthly salary of $3500 together with a commission of 5% on all sales over $5000 per month. Calculate his gross salary in a month in which his sales amounted to $40,000.
Answer:
$5500
Step-by-step explanation:
3500 + 0.05 * 40,000 = 5500
His gross salary in a month in which his sales amounted to $40,000 would be; 5500 dollars.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
It is given that man received a monthly salary of $3500 together with a commission of 5% on all sales over $5000 per month.
Let the x represents his gross salary in a month in which his sales amounted to $40,000.
Therefore,
x = 3500 + 0.05 (40,000)
x = 3500 + 2000
x = 5500
Hence, his gross salary in a month in which his sales amounted to $40,000 would be; 5500 dollars.
Learn more about multiplications;
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can someone help me figure this one out please?
Answer:
Linear equations
Step-by-step explanation:
An easy and simple equation. F(t) = -15t +300
Find the distance between the points (4, 3) and (0, 6).
Answer:
5
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√(0 - 4)² + (6 - 3)²
√(-4)² + (3)²
√(16) + (9)
√25
= 5
Help ASAP (Math) will give brainiest and points!!
Answer:
[tex]2.17 \times 10^{-1}[/tex]
Step-by-step explanation:
[tex](7 \times 10 ^{-6}) + 0.26 - (5 \times 10^{-2}) = \frac{7}{10^3} + \frac{26}{10^2}-\frac{5}{10^2}[/tex]
[tex]= \frac{7 + (26 \times 10) - ( 5 \times 10)}{10^3}\\\\=\frac{7 + 260 - 50 }{10^3}\\\\=\frac{217}{10^3}\\\\= 2.17 \times 10^2 \times 10^{-3}\\\\= 2.17 \times 10^{-1}[/tex]
What is a cofunction? Give examples and explain the purpose.
Please help i need help its very URGENT
Answer:
AB = 19.05
∠A = 45°
∠C = 45°
Step-by-step explanation:
To find a missing side length, Use Pythagorean Theorem
Pythagorean Theorem: [tex]a^{2} +b^2=c^2[/tex]
Then fill in the dimensions given in the triangle
In this case, we're looking for b^2 so...
[tex]11^2+b^2=22^2[/tex]
[tex]121+b^2=484[/tex]
[tex]b^2=484-121[/tex]
b^2 = 363
[tex]\sqrt{363} =19.05[/tex]
so the answer is approximately 19
Now in this case we already know the measure of B by the 90° angle.
so if the total is 180, then 180 - 90 = 90 then divided by 2 for the 2 missing angles = 45°
so the answer is 45°
Answer:
AB=11SR3 or about 19.1. Angle A is 30 degrees. Angle C is 60 degrees. SR(square root).
Step-by-step explanation:
Pythagorean Theorm for AB and Trigonometry for A and C. Hope it helps.
（4tan30°)(5sin60°)-6cos60°
Answer:
7
Step-by-step explanation:
Using exact values
(4tan30°)(5sin60°) - 6cos60°
= 20tan30°sin60° - 6cos60°
= 20 × [tex]\frac{1}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] - 6 × [tex]\frac{1}{2}[/tex]
= [tex]\frac{20}{2}[/tex] - 3
= 10 - 3
= 7
Answer:
6.804
Step-by-step explanation:
Given data:
（4tan30°)(5sin60°)-6cos60°
Now it can be calculated as:
4(0.57)×5(0.86)-6(0.5)
2.28×4.3-3
9.804-3
6.804
Answer will be 6.804
Slope of (-16,3) (-5,-6)
Find the measure of m∠K
Answer:
<k = 20
Step-by-step explanation:
Inscribed Angle = 1/2Intercepted Arc
<K = 1/2 (40)
<k = 20
Tomas bikes 3 3/4 miles each morning and 2 1/2 miles each afternoon
Answer:
6 1/4
Step-by-step explanation:
1/2 = 2/4
2/4 + 3/4 = 5/4 which is 1 1/4 simplified.
Then add the whole numbers, 2 + 3 = 5
5 + 1 1/4 = 6 1/4
Tomas rides 6 1/4 miles everyday.
En el numeral 87.684 la cifra de las decimas es la cifra de las centésimas es la cifra de las milésimas es la parte entera de la expresión decimas es en la parte entera, la cifra de unidades es , mientras que la cifra de la decena es
Answer:
La cifra de las decimas es 6, la cifra de las centésimas es 8, la cifra de las milésimas es 4, y en la parte entera, la cifra de unidades es 7, mientras que la cifra de la decena es 8.
Step-by-step explanation:
Para responder la pregunta, se debe descomponer el número en cuestión:
87.684
8 = Indica la cantidad de decenas del número, es decir, 8 decenas (80).
7 = Indica las unidades dentro de la decena, es decir, 7 unidades más que 80.
.6 = Indica la cantidad de decenas del entero.
.08 = Indica la cantidad de centésimas del entero.
.004 = Indica la cantidad de milésimas del entero.
Así, la cifra de las decimas es 6, la cifra de las centésimas es 8, la cifra de las milésimas es 4, y en la parte entera, la cifra de unidades es 7, mientras que la cifra de la decena es 8.
