Answer:
3^x-8=8 then x=log_3(16)
3^(x-8)=8 then log_3(8)+8
Step-by-step explanation:
So if it is 3^x-8=8
then 3^x=16
and then convert to logarithmic form you write it as log_3(16)=x
_3 means the subscript (the base) is 3
So if it is 3^(x-8)=8
then the log form is log_3(8)=x-8
add 8 on both sides log_3(8)+8=x
The value of x that satisfies the given equation is 9.8929
Logarithmic equationFrom the question, we are to solve [tex]3^{x-8} =8[/tex] for x, using the change of base formula [tex]\log _{b} y = \frac{log _{} y}{log _{} b}[/tex]
From the given equation,
[tex]3^{x-8} =8[/tex]
Take [tex]log_3[/tex] of both sides,
That is,
[tex]\log _{3} 3^{x-8} = \log _{3} 8[/tex]
This becomes,
[tex](x-8)\log _{3} 3= \log _{3} 8[/tex]
Since [tex]\log _{x} x =1[/tex],
∴ [tex]\log _{3} 3 =1[/tex]
[tex](x-8)(1)= \log _{3} 8[/tex]
[tex]x-8= \log _{3} 8[/tex]
Using the change of base formula [tex]\log _{b} y = \frac{log _{} y}{log _{} b}[/tex]
[tex]\log _{3} 8=\frac{\log 8}{\log 3}[/tex]
Then,
[tex]x-8=\frac{\log 8}{\log 3}[/tex]
[tex]x-8=\frac{0.9031}{0.4771}[/tex]
x - 8 = 1.8929
x = 8 + 1.8929
x = 9.8929
Hence, the value of x that satisfies the given equation is 9.8929
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Which expression has a value of 1?
A; 4/8 x 8/16
B; 2/3 x 3/2
C; 8/4 x 4/4
D; 2/3 x 3/3
Please help me solve this problem
Answer:
Option B , D and E are correct.
Step-by-step explanation:
We set the denominator equal to zero to find the number to put in division box
So, if 3 is in the division box then the denominator will be
x-3 = 0 => x=3 is the root.
So, Option E is correct
2x^2-2x-12 ÷ x-3 = 2x+4 is correct.
because after division the result given is 2x+4 which is correct.
So, Option B is correct
x-3 is a factor of 2x^2-2x-12 because because when the term is divided we get the remainder 0.
So, Option D is correct
So, Option B,D and E are correct.
you read 4 1/2 pages in 12 minutes. at the same rate, how many pages could you read in an hour?
Answer:
22.5 pages
Step-by-step explanation:
First divide the page number by the minutes it takes to read them to find pages per minute-
4.5 / 12 = .375
Then take that number and multiply it by the minutes in an hour-
(.375) (60) = 22.5
22.5 pages in one hour.
Answer:
22 1/2 pages
Step-by-step explanation:
60/12 = 5
5(4.5) = 22 1/2
An angle is formed by
Answer:
2 lines meet at a shared point.
Step-by-step explanation:
Hope my answer has helped you!
Can someone help me with this
Answer:
No, because they look like they are different sizes. Or you could say the first answer
Hello There!
The answer is "C"
In this problem, you need dilation to map onto each-other.
Dilation is transformation hat changes the size of something
The graph represents this system of equations:
2x + y = 3
2x - 5y = 15
What is the solution to the system of equations
represented by the graph?
(0, -3)
(1,1)
(1.5,0)
(2.5, -2)
Answer:
(2.5, - 2)
Step-by-step explanation:
The solution to a system of equations given graphically is at the point of intersection of the 2 lines, that is
(2.5, - 2 ) ← point of intersection
Answer:
Option D is the correct answer.
Step-by-step explanation:
Refer the given figure showing the graph.
We can see the point of intersection is (2.5, -2).
Option D is the correct answer.
Alternatively:
2x + y = 3 ---------------------eqn 1
2x - 5y = 15 ---------------------eqn 2
eqn1 - eqn 2 gives
2x + y - ( 2x - 5y) = 3 - 15
6y = -12
y = -2
Substituting in eqn 1
2x - 2 = 3
x = 2.5
Point of intersection is (2.5, -2).
Option D is the correct answer.
which statement best describes a line in a slope-intercept form when the coeficient of the x-term is negative?
@ line slants down
b- line slants up
c-line is horizontal
d- line is vertical
Answer:
Option a: Line slants down.
Step-by-step explanation:
It is important to remember that the equation of the line in Slope-Intercept form is the following:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
The slope of a line can be positive (The line slopes upwards to the right), negative (The line slopes downwards to the right), zero (Horizontal line), or undefined (Vertical line).
Therefore, the statement that best describes a line in a slope-intercept form when the coeficient of the x-term (The slope) is negative is: "Line slants down".
Find the radius of a circle with the given circumference.
12 x
in.
=
6 inches
6pi
inches
12 inches
24 pi inches
Answer:
12x=2pi*r
Step-by-step explanation:
2*22/7*r=12x
r=12x*7/44
r=21x/11
The radius of a circle is calculated by dividing the given circumference by 2π. When given circumferences of 6 inches, 6π inches, 12 inches, and 24π inches, the corresponding radii are approximately 0.955 inches, 3 inches, 1.91 inches, and 12 inches, respectively.
To find the radius of a circle given its circumference, we use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius. Since we are given the circumference, we can rearrange this formula to solve for the radius as follows: r = C / (2π).
Given the possible circumferences provided, we can calculate the radius for each.
For 6 inches: r = 6 / (2π) = 6 / (2 * 3.14) = 6 / 6.28 = approximately 0.955 inches
For 6π inches: r = 6π / (2π) = 6 / 2 = 3 inches
For 12 inches: r = 12 / (2π) = 12 / (2 * 3.14) = 12 / 6.28 = approximately 1.91 inches
For 24π inches: r = 24π / (2π) = 24 / 2 = 12 inches
The value of the square root of 13 is between
Answer:
the square root of thirteen is 3.6
Step-by-step explanation:
if you put the 13 with the square root box and press the = button you will get the square root of 13 is 3.6
Given the function f(x)=0.5|x-4| -3, for what values of x is f(x)=7
Answer:
x = -16 or x = 24Step-by-step explanation:
[tex]f(x)=0.5|x-4|-3\\\\f(x)=7\Rightarrow0.5|x-4|-3=7\qquad\text{add 3 to both sides}\\\\0.5|x-4|=10\qquad\text{multiply both sides by 2}\\\\|x-4|=20\iff x-4=\pm20\\\\x-4=-20\qquad\text{add 4 to both sides}\\x=-16\\\\x-4=20\qquad\text{add 4 to both sides}\\x=24[/tex]
Will needs 8 hours of sleep every night, Brad needs 9 hours, and Nick needs 10. One Saturday, they all have to get up at 6 a.m. to go fishing. On Friday evening, who will be the first to bed?
Answer: Nick
Step-by-step explanation:
Nick is the one who will go to bed first because he needs the most sleep. Nick needs 10 hours of sleep, then it would be Brad who needs 9 , then Will who needs 8
Nick will be the first to bed on Friday evening out of Will, Brad, and Nick.
On Friday evening, Nick would be the first to bed among Will, Brad, and Nick. Nick needs 10 hours of sleep every night, so to wake up at 6 a.m. on Saturday, he would have to go to bed earlier than Will and Brad who need 8 and 9 hours of sleep, respectively.
What is the value of x?
Answer:
x = 2
Step-by-step explanation:
Given 2 secants intersecting a circle from an external point, then
The product of the external part and the entire part of one secant is equal to the product of the external part and the entire part of the other secant, that is
(x + 1)(x + 1 + 11) = (x + 4)(x + 4 + 1)
(x + 1)(x + 12) = (x + 4)(x + 5) ← expand both sides
x² + 13x + 12 = x² + 9x + 20
Subtract x² + 9x from both sides
4x + 12 = 20 ( subtract 12 from both sides )
4x = 8 ( divide both sides by 4 )
x = 2
A sphere with a radius of 5 cm is enlarged by a scale factor of 2. What is the approximate volume of the new sphere in cubic inches?
To find the volume of the new sphere, calculate the volume of the original sphere and then multiply it by the scale factor cubed. Convert the volume from cubic centimeters to cubic inches using the conversion factor: 1 cm³ = 0.0610237 in³. The approximate volume of the new sphere in cubic inches is 255.3 in³.
To find the volume of the new sphere, we need to first find the volume of the original sphere and then multiply it by the scale factor cubed. The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius.
Given that the radius of the original sphere is 5 cm, we can calculate its volume using the formula:
V1 = (4/3)π(5 cm)³ ≈ 523.6 cm³.
Next, we can calculate the volume of the new sphere by multiplying the volume of the original sphere by the scale factor cubed:
V2 = V1 × (2)³ = 523.6 cm³ × 8 ≈ 4188.8 cm³.
Finally, to convert the volume from cubic centimeters to cubic inches, we need to use the conversion factor: 1 cm³ = 0.0610237 in³. Therefore, the approximate volume of the new sphere in cubic inches is:
V2 ≈ 4188.8 cm³ × 0.0610237 in³/cm³ ≈ 255.3 in³.
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given sin28.4=.4756, cos28.4=.8796, and tan28.4=.5407 find the cot of 61.6
Answer:
The cotangent of 61.6° is .5407.
Step-by-step explanation:
Refer to the sketch attached.
61.6° + 28.4° = 90°. In other words, 61.6° is the complementary angle of 28.4°.
Consider a right triangle OAB with a 61.6° angle [tex]\rm O\hat{A}B[/tex]. The other acute angle [tex]\rm O\hat{B}A[/tex] will be 28.4°.
[tex]\displaystyle \tan{61.6\textdegree{}}=\tan{\rm O\hat{A}B} = \frac{\text{Opposite of }\rm O\hat{A}B}{\text{Adjacent of }\rm O\hat{A}B} = \frac{a}{b}[/tex].
The cotangent of an angle is the reciprocal of its tangent.
[tex]\displaystyle \cot{61.6^{\circ}}=\frac{1}{\tan{\rm O\hat{B}A}} = \frac{\text{Adjacent of }\rm O\hat{B}A}{\text{Opposite of }\rm O\hat{B}A} = \frac{a}{b} = \tan{\rm O\hat{A}B} = \tan{28.4^{\circ}}[/tex].
In other words,
[tex]\cot{61.6^{\circ}} = \tan{28.4^{\circ}} \approx 0.5407[/tex].
Use the properties of exponents to rewrite the expression
(-5uv)(-5uv)(-5uv)(-5uv)
[tex]\bf (-5u)(-5u)(-5u)(-5u)\implies (-5u)^1(-5u)^1(-5u)^1(-5u)^1 \\\\\\ (-5u)^{1+1+1+1}\implies (-5u)^4\implies (-5)^4u^4\implies 625u^4[/tex]
Maria practices the piano 5/6 of an hour every day how many hours does she practice in 4 days
Answer:
20/6 or 3.33 or 3 1/3 or 3 hours and 20 mins
Step-by-step explanation:
5/6 * 4 = (5*4)/6 = 20/6
Answer:
she will have praticed 3 hours and 20 min
Step-by-step explanation:
Find the 11th term of this sequence -10, 20, -40
Answer:
Step-by-step explanation:
the nth term of the geometric sequence is : An =A1 × r^(n-1)
A1 = -10
r= -40/20=20/-10=-2
n =11
A11 = -10× (-2)^(11-1)
A11 = -10× (-2)^(10)
A11 = - 10240
Answer:
-10,240.
Step-by-step explanation:
This is a geometric sequence with common ratio 20/-10 = -40/20 = -2.
The nth term = a1r^(n-1) where a1 = the first term and r = the common ratio, so the 11th term = -10 * (-2)^ (11-1)
= -10 * 1024
= -10,240.
Which point lies on a sphere?
J
B
S
Answer:
Point B lies on a sphere.Step-by-step explanation:
Remember, a sphere is defined as a three-dimensional object where all points on its surface are equidistant form its center.
According to its definition, all point on the boundaries can be called a point on the sphere.
So, among the options, only point B is on the sphere, because J and S are inside.
Therefore, the right answer is Point B.
Find the value of x in each of the following exercises:
Check the picture below.
let's notice those two corresponding angles of 90° - 2x, and also recall that the sum of all interior angles in a triangle is 180°.
[tex]\bf 60+3x+(90-2x)=180\implies x+150=180\implies x=30[/tex]
What are the roots of the polynomial ?
Answer:
B and E
Step-by-step explanation:
By looking at the discriminant, which is [tex]b^2-4ac[/tex], you get that [tex]5^2-4*1*7=25-28=-3[/tex]. Therefore, the only two answers with a -3 inside the square root are B and E.
Answer:
B & E
Step-by-step explanation:
see attached
Please explain now thanks
Answer:
24x - 20
Step-by-step explanation:
4(6x-5)
= 4(6x) - 4(5).............. (Distributive property)
= 24x - 20 (Ans)
Hello There!
The answer would be (24x-20)
We use order of operations so first we would multiply 4 by 6 and get 24x
then, we would multiply 4 by -5 and get -20
Your answer would be 24x - 20
Knowing that sin 30° = 1/2 , what is a?
Answer:
14! Hope you ace your test!!
Step-by-step explanation:
The value of the side 'a' will be 14 units.
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The value of a is calculated as:-
Sin 30 = P / H
Sin 30 = 7 / a
1 / 2 = 7 / a
a = 7 x 2
a = 14 units
Therefore the value of the side 'a' will be 14 units.
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25 Points ! Write a paragraph proof.
Given: ∠T and ∠V are right angles.
Prove: ∆TUW ∆VWU
Answer:
Δ TUW ≅ ΔVWU ⇒ by AAS case
Step-by-step explanation:
* Lets revise the cases of congruent for triangles
- SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ
- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and
including angle in the 2nd Δ
- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ
≅ 2 angles and the side whose joining them in the 2nd Δ
- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles
and one side in the 2ndΔ
- HL ⇒ hypotenuse leg of the first right angle triangle ≅ hypotenuse
leg of the 2nd right angle Δ
* Lets solve the problem
- There are two triangles TUW and VWU
- ∠T and ∠V are right angles
- LINE TW is parallel to line VU
∵ TW // VU and UW is a transversal
∴ m∠VUW = m∠TWU ⇒ alternate angles (Z shape)
- Now we have in the two triangles two pairs of angle equal each
other and one common side, so we can use the case AAS
- In Δ TUW and ΔVWU
∵ m∠T = m∠V ⇒ given (right angles)
∵ m∠TWU = m∠VUW ⇒ proved
∵ UW = WU ⇒ (common side in the 2 Δ)
∴ Δ TUW ≅ ΔVWU ⇒ by AAS case
Answer:
Step-by-step explanation:
Given ∠T and ∠V are right angles.
TW ║ UV
To prove ⇒ ΔTUW ≅ ΔVWU
Proof ⇒ In ΔTUW and ΔVUW,
∠T ≅ ∠ V ≅ 90° (given)
Side UW ≅ UW ( Common in both the triangles )
TW ║ UV
and UW is a transverse.
So ∠TWU ≅ ∠WUV [alternate interior angles]
Since Angle = Angle = side are equal
Therefore, ΔTUW ≅ ΔVWU
Does this graph show a function? explain how you know
Answer:
C
Step-by-step explanation:
The vertical line test is basically just drawing a vertical line and seeing if the line intersects the graph more than once. If it does, then it is not a function, if it doesn't than it is a function.
Answer:
C
Step-by-step explanation:
what is the measure or angle C?
•25 degrees
•30 degrees
•60 degrees
•75 degrees
Answer:
25
Step-by-step explanation:
look B=C
so,
A+B+C=180 Sum of all <s of Tri
x+5+3x+3x=180
7x=175
x=175÷7
x=25
Answer: A or 25
Step-by-step explanation:
did the exam on edge 2020
Factor the trinomial below. x^2-3x-40
Answer:
(x-8) (x+5)
Step-by-step explanation:
x^2-3x-40
What 2 numbers multiply to -40 and add to -3
-8 *5 = -40
-8+5 = -3
(x-8) (x+5)
The equation below describes a circle. What are the coordinates of the center of the circle? (X-6)^2+(y+5)^2=15^2
Answer:
Step-by-step explanation:
6,-5 ON APEXXXXX
Answer: (6, -5)
Step-by-step explanation:
The general equation of a circle is given by :-
[tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is center and r is radius of the circle.
Given : The equation of a circle : [tex](x-6)^2+(y+5)^2=15^2[/tex]
[tex]\Rightarrow\ (x-6)^2+(y-(-5))^2=15^2[/tex]
Comparing to the general equation of circle , we get
[tex](h,k)=(6, -5)[/tex]
Hence, the coordinates of the center of the circle = (6, -5)
NEED HELP ASAP 10 POINT QUESTION
Answer:
The original price of the car can be written in percentage which is 100%. Because the price increased by 6%, therefore, the new price should be represented as:
100% + 6% = 106% = 1.06 (remember: not 0.06, that is how much the price increased, not 0.94 either, because the price increased, not decreased).
So the answer for the first question should be:
(a) new price = 1.06 × original price
from that, we can appy the answer above for the second question:
(b) new price: $33390
Find the surface area of a cylinder with a radius 19.3 ft and height 14.7 ft use a calcutor round to the nearest tenth
Helpppppppp meeeeee pleaseeeee
Answer:
C
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) - g(x) = [tex]4^{x}[/tex] - 8 - (5x + 6)
= [tex]4^{x}[/tex] - 8 - 5x - 6 ← collect like terms
= [tex]4^{x}[/tex] - 5x - 14 → C