Answer:
x = 3.
Step-by-step explanation:
log4 (3x - 1) = log4 (x + 5) Since they are both logs to the base 4:
3x - 1 = x + 5
2x = 6
x = 3.
On solving the logarithmic equation, we find that x = 3.
What are logarithmic equations?A logarithmic equation is an equation that involves the logarithm of an expression containing a variable.
[tex]log_{4}(3x-1) = log_{4}(x+5)\\\\3x-1 = x+5\\\\3x-x=5+1\\\\ 2x=6\\\\x=3[/tex]
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3 6=-3(x+2) need help
Answer:
x = -14
Step-by-step explanation:
Hi there !
36 = - 3(x + 2)
36 = - 3x - 6
3x = - 36 - 6
3x = - 42
x = - 42/3
x = - 14
Good luck !
MAX POINTS ASAP MULTIPLE CHOICE WILL MARK BRAINLIEST ONLY CORRECT ANSWER
A conjecture and the two-column proof used to prove the conjecture are shown.
Given: the measure of angle C B D equals 90 degrees. Prove: triangle A B C is a right triangle. Ray B D extends down and perpendicular from point B on segment B C.
Drag an expression or phrase to each box to complete the proof.
Statement Reason
1. m∠CBD=90° Given
2. ∠ABC and ∠CBD are supplementary. Response area
3. Response area Definition of supplementary
4. m∠ABC+90°=180° Response area
5. Response area Subtraction Property of Equality
6. ∠ABC is a right angle. Definition of right angle
7. △ABC is a right triangle. Definition of right triangle
Answer:
I took the test
Step-by-step explanation: Linear pair postulate
m<abc + m<cbd =180°
subtraction property of equality
m<abc -90°
All expression and phrase are filled below.
Here,
We have to filled all expression and phrase.
What is right angled triangle?
A right-angled triangle is a triangle, which has one of its interior angles equal to 90 degree.
Now,
Given that;
⇒ m∠CBD = 90 degree ….(i)
We have to prove triangle ABC is right angled triangle.
We can see that the line extends down and perpendicular to the line segment BC at point B.
We can also see that ∠ABC and ∠CBD are supplementary angle.
Hence, We prove as;
Statement Reason
1) m∠CBD = 90 degree ( Given )
2) ∠ABC and ∠CBD are supplementary. ( Because ABD is a line and
∠ABC and ∠CBD are linear
pair)
3). ∠ABC+∠CBD = 180 degree ( Definition of supplementary)
4) ∠ABC+ 90 = 180 degree ( m∠CBD = 90 degree )
5) ∠ABC + 90 - 90 = 180° - 90° ( subtraction property of equality)
∠ABC = 180° – 90° (from (i))
∠ABC = 90 degree
6) ∠ABC is a right angle. ( Definition of right angle)
7) Δ ABC is a right triangle. ( Definition of right triangle)
Therefore, according to definition of right angled triangle,
The triangle ABC is a right angled triangle.
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A line passes through the point (-9,1) and has a slope of -2/3
Answer:
y - 1 = (-2/3)(x + 9)
Step-by-step explanation:
Here you are given a point on a line and the slope of the line. You'll need to apply the "point-slope" formula
y - k = m(x - h) (Memorize this)
Then m = slope = -2/3, h = -9 and k = 1.
Making the appropriate substitutions, we get:
y - 1 = (-2/3)(x + 9)
In a class of 40 students, every student take either Biology or Integrated Science, 30 students take Biology, 20 students take Integrated Science and 10 take both Integrated Science and Biology. Illustrate this information on a Venn diagram.
Answer
20 students will take biology, 10 take Integrated Science and 10 take both
Step-by-step explanation:
With Venn diagrams it's best you work from the inside out. With that in mind we know 10 students take both Biology and Integrated Science. In Biology there are 30 total students including the ones that also take both sciences. So we subtract the ones that take both and get 20 students taking only biology. After that there's 30 students total, subtract that from 40, the total number of students and you get 10, the amount of students who take Integrated Science
Ramon earns $1,865 each month and pays $53.50 on electricity. To the nearest tenth of a percent, what percent of Ramon's are spent on electricity each month?
PLEASE PLEASE HELPP PLEASEEEEEE I WILL MARK BRAINLIEST
Answer:
roughly 3%
Step-by-step explanation:
Answer:
about 34.9%
Step-by-step explanation:
I could be wrong on this, but by multiplying his profit per month by 12, and his electricity cost by 12, then you get his yearly profit and cost of electricity. Then, you divide the profit by electricity and wa la you get 34.9%.
PLZ mark me brainliest!!!! :)))))
Find the sum of (-236) and 573
Answer:
the answer is 337
Step-by-step explanation:
-236+573=337
Solve the differential equation y" + 3y' + 2y = P1 where, y" = d2y/dx2, y' = dy/dx, P1 = P1(x)) and the initial conditions are y(0) = 0, y'(0) = 0. The input function is given by P1() = { 0, < 0 1, 0 ≤ ≤ 1 0, > 1
Answer:
[tex]y(x) = 0[/tex]
Step-by-step explanation:
Let P(1) = 0, the differential equation becomes:
y" + 3y' + 2y = 0
Also let y' = my and y'' = m²y
Substitute
m²y+3my+2y = 0
(m²+3m+2)y = 0
The auxiliary equation is expressed as:
m²+3m+2 = 0
Factorize
m²+2m+m+2 = 0
m(m+2)+1(m+2) = 0
(m+1)(m+2) = 0
m+1 = 0 and m+2 = 0
m₁ = -1 and m₂ = -2
Since the value of m is real and distinct, the solution to the differential equation will be expressed as:
[tex]y = C_1e^{m_1x}+C_2e^{m_2x}\\[/tex]
[tex]y(x) = C_1e^{-x}+C_2e^{-2x}\\[/tex]
Given the initial condition y(0) = 0
[tex]y(0) = C_1e^{-0}+C_2e^{-2(0)}\\0 = C_1+C_2\\C_1+C_2 = 0 ................. 1[/tex]
If y'(0) = 0
[tex]y'(x) = -C_1e^{-x}-2C_2e^{-2x}\\y'(0) = -C_1e^{-0}-2C_2e^{-2(0)}\\0 = -C_1-2C_2\\C_1-2C_2 = 0...................... 2[/tex]
Solve eqn 1 and 2 simultaneously
From 1:
C₁ = -C₂ .......... 3
Substitute equation 3 into 2:
-C₂-2C₂ = 0
-3C₂ = 0
C₂ = 0
Substitute the constant into the differential equation.
[tex]y(x) = C_1e^{-x}+C_2e^{-2x}\\\\y(x) = 0[/tex]
What would 2300 divided by 330 times 3 epuals what ?
Answer: 23
Step-by-step explanation:
Simplify the expression:
4 + 7(-7 + -9k)
Answer:
-63k - 45
Step-by-step explanation:
combine like terms
The quotient of a number and twelve is the sum of eight and the number.
Answer: n/12=8+n
Answer:
Step-by-step explanation:
12(n/12 = 8 + n)
n = 96 + 12n
-11n = 96
n = -96/11
Answer:
-96/11 or -8 8/11
Step-by-step explanation:
For this, create an equation, x/12=x+8.
Any number without a denominator has a denominator of 1, so x/12=(x+8)/1.
Now, cross multiply to get 1*x=12(x+8).
Simplify that to x=12x+96.
Subtract 12x from both sides, and you have -11x=96.
Divide by -11, and x=-96/11.
What vocabulary words can you use to describe 36 and 27?
Answer:
Divisible by 3 and 9
Step-by-step explanation:
Answer
multiples of 3 and 9
Step-by-step explanation:
3*12=36
9*3=27
9*4=36
10 1/7 divide by 5 can you help me
Answer:
2.02857142857
Step-by-step explanation:
The length of a rectangle is 3m more than the width. The area is 70m². Find the dimensions of the rectangle.
If it were a square it would be 17.5meters on every side, but we are not solving for a square we are solving for a rectangle. The dimensions for this rectangle are 19 long 16 wide.
Answer:
304m?
Step-by-step explanation:
okay bye
bye
the ratio of students getting an A in math to students getting a B is 1:2. if 23 students received an A, how many received a B?
4*4*6*4*4*6 in exponential form
Answer:
4^4×6^2
Step-by-step explanation:
There are four 4's and two 6's
So in exponential form it is 4^4×6^2
could some one please help I'm not that good with math
Answer:
D and E
Step-by-step explanation:
It is acute because all angles are under 90 degrees. This means that it cannot be F, obtuse. It cannot be A because A scalene triangle is a triangle in which all three sides have different lengths. It cannot be B either because it has 3 sides of equal angles. It cannot be right because non of the angles are 90 degrees. It is equilateral.
Hope this helps.
The band boosters sell snickers bars for 75¢ each. Which of the following statements are true? Select all that apply.
A. If Tom spent $6.00 on snickers bars, he bought 9.
B. When the band boosters sell 10 snickers bars they make $7.50.
C. For every 4 snickers bars sold the band boosters earn $3.00.
D. If Tom bought 6 snickers bars, he paid $3.50. E. 75¢ is the unit price for a snickers bar.
Answer:
B, C, and E
Step-by-step explanation:
B because 0.75*10=7.5. C because 4*0.75=3. And E because 0.75 is how much each snickers bar is is that is the unit price
Find the inverse of the following functions algebraically
1. The center of circle S is (9,2), and the radius of the circle is 5 units. Which point is on the circle?
Answer:
Find the equation of the circle that is shifted 5 units to the left and 2 units down from the circle ... If one circular table has a radius of 4 feet and a center at C(-4, 6), find the center and ... The points (-5, 2) and (-5, 8) lie on a circle with a radius of 3.
Step-by-step explanation:
hope this helps
The equation p = 3.25b can be used to find the price, p, in dollars, of b pounds of blueberries at a particular supermarket. Each of the tables gives the prices of various pounds of blueberries at a different supermarket. Which of these tables represents blueberries that are more expensive than those represented by the equation? Select all that apply.
Answer:
Table C, Table D, Table E
Step-by-step explanation:
See attachment for tables
Given
[tex]p = 3.25b[/tex]
Required
Which of the tables is more expensive than the given function
To answer this question, we simply determine the equation of each table and then compare the equation with [tex]p = 3.25b[/tex]
Table A:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (1,2.75)[/tex]
[tex](b_2,p_2) = (4,11)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{11 - 2.75}{4 - 1}[/tex]
[tex]m = \frac{8.25}{3}[/tex]
[tex]m = 2.75[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 2.75 = 2.75(b-1)[/tex]
[tex]p - 2.75 = 2.75b-2.75[/tex]
[tex]p = 2.75b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]2.75 < 3.25[/tex]
Hence:
This equation is less expensive than [tex]p = 3.25b[/tex]
Table B:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (1.5,3.75)[/tex]
[tex](b_2,p_2) = (6,15)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{15 - 3.75}{6 - 1.5}[/tex]
[tex]m = \frac{11.25}{4.5}[/tex]
[tex]m = 2.5[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 3.75 = 2.5(b-1.5)[/tex]
[tex]p - 3.75 = 2.5b- 3.75[/tex]
[tex]p = 2.5b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]2.5 < 3.25[/tex]
Hence:
This equation is also less expensive than [tex]p = 3.25b[/tex]
Table C:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (2,7)[/tex]
[tex](b_2,p_2) = (4,14)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{14 - 7}{4 - 2}[/tex]
[tex]m = \frac{7}{2}[/tex]
[tex]m = 3.5[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 7 = 3.5(b - 2)[/tex]
[tex]p - 7 = 3.5b - 7[/tex]
[tex]p = 3.5b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]3.5 > 3.25[/tex]
Hence:
This equation is more expensive than [tex]p = 3.25b[/tex]
Table D:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (2.5,10)[/tex]
[tex](b_2,p_2) = (5,20)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{20 - 10}{5 - 2.5}[/tex]
[tex]m = \frac{10}{2.5}[/tex]
[tex]m = 4[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 10 = 4(b - 2.5)[/tex]
[tex]p - 10 = 4b - 10[/tex]
[tex]p = 4b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]4 > 3.25[/tex]
Hence:
This equation is more expensive than [tex]p = 3.25b[/tex]
Table E:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (6, 22.5)[/tex]
[tex](b_2,p_2) = (12,45)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{45 - 22.5}{12 - 6}[/tex]
[tex]m = \frac{22.5}{6}[/tex]
[tex]m = 3.75[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 22.5 = 3.75(b - 6)[/tex]
[tex]p - 22.5 = 3.75b - 22.5[/tex]
[tex]p = 3.75b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]3.75>3.25[/tex]
Hence:
This equation is more expensive than [tex]p = 3.25b[/tex]
Table F:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (7, 21)[/tex]
[tex](b_2,p_2) = (14,42)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{42 - 21}{14 - 7}[/tex]
[tex]m = \frac{21}{7}[/tex]
[tex]m = 3[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p -21 =3(b -7)[/tex]
[tex]p -21 =3b -21[/tex]
[tex]p = 3b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]3 < 3.25[/tex]
Hence:
This equation is less expensive than [tex]p = 3.25b[/tex]
Rewrite the equation 4x^2 - 3x + 9 = 2x+1 in Standard form pls
Answer:
[tex]4x^2-5x+8=0[/tex]
Step-by-step explanation:
[tex]4x^2-3x+9=2x+1[/tex]
We need to get the equation in standard form:
[tex]ax^2+bx+c=0[/tex]
Subtract [tex]2x[/tex] from both sides of the equation:
[tex]4x^2-5x+9=1[/tex]
Subtract [tex]1[/tex] from both sides of the equation:
[tex]4x^2-5x+8=0[/tex]
|x-3|+2<6
help please
A set of 4 consecutive even integers adds up to 68.
Answer:X=14,/ integers are-14,16,18,20
Step-by-step explanation:
Solve the word problems using either the percent equation or the percent
proportion. Make sure to answer in a complete sentence. Round to the whole
number if necessary.
Tyler and Ilan scored 48% of their team’s points in the math
competition. If they scored 84 points, what was the team’s total score?
Answer:
Tyler and llan scored 24 points.
Explanation:
Another way to state this problem is what is 48% of 50.
"Percent" or "%" means "out of 100" or "per 100", Therefore 48% can be written as
48
100
.
When dealing with percents the word "of" means "times" or "to multiply".
Finally, lets call the number we are looking for "n".
Putting this altogether we can write this equation and solve for n
while keeping the equation balanced:
n=48,100 × 50
n = 24,001,00
n= 24
Step-by-step explanation:
manny's cleaning supply store receives a mixture of 80% detergent and 20% water in 15 gallon buckets. manny would like a mixture of 60% detergent and 40% water in each 5 gallon bucket. how many gallons of pure water does manny add to each 5 gallon bucket? express your answer as a decimal to the nearest hundredth
Answer:
1.25
Thanks,
SunshineMadison101
What is the value of the expression 5(X+3) when X=-3?
Answer:
0
Step-by-step explanation:
5(x+3) replace x with -3
5(-3+3)
5(0)
0
I need help on this plz
Answer:
b
Step-by-step explanation:
Simplify 2x+3y^2-2(x-Y)
y^2, 2y^2, 4y^2, or 5y^2
Answer:
3y^2+2y
Step-by-step explanation:
simplify 5(b – 4) + 12
Answer: 5b-8
Step-by-step explanation:
PLEASEEE SOMEONE HELP I WILL MARK BRAINLIEST please do step by step explanation!
