Answer: The width of the rectangle is 5 cm and the length is 13 cm
Step-by-step explanation:
Let the width be x cm
Let the length be (x+8) cm
Area = 65cm²
[tex]\Rightarrow x(x+8)=65 \ [\because$ Area of rectangle $=$ length $\times$ width $]$ \\$\Rightarrow x^{2}+8 x-65=0 \Rightarrow x^{2}+13 x-5 x-65=0$ \\$\Rightarrow x(x+13)-5(x+13)=0 \Rightarrow(x+13)(x-5)=0$ \\$\Rightarrow x=-13$ or $x=5$ \\But width car't be negative. so $x=5$ \\[/tex]
Therefore:
Width = 5 cm
Length = 5 + 8 = 13 cm
Expand the logarithmic expression log3(2xy3z5). Question 9 options: A) 2(log3x + 3log3y + 5log3z) B) log32x + log3y3 + log3z5 C) log32 + log3x + 3log3y − 5log3z D) log32 + log3x + 3log3y + 5log3z
Answer: D
Step-by-step explanation:
[tex]\log _{3}\left(2 x y^{3} z^{5}\right) \\ =\log _{3} 2+\log _{3} x+\log _{3} y^{3}+\log _{3} z^{5}[/tex]
[tex]\left(\because \log _{c}(a \cdot b)=\log _{c} a+\log _{c} b\right)[/tex]
[tex]=\log _{3} 2+\log _{3} x+3 \log _{3} y+5 \log _{3}z \rightarrow \left(\because \log _{c} a^{b}=b \log _{c} a\right)[/tex]
Therefore, Option D is the correct answer
Which equation has the solution x = 2?
A. 2x - 3 = 19
B. 3 x + 2 = 8
C. 4x - 4 = -4
D. 5x + 1 = 10
Answer:
=> B. 3 x + 2 = 8
Step-by-step explanation:
=> 3x+2 = 8
=> 3(2) +2 = 8
=> 6+2 = 8
=> 8 = 8
Every day, the Lee Pet Store uses 1/3 of a bag of dog food to feed the dogs. How many days
will 1 1/3 bags of dog food last?
What are the prime factors of 700?
O A.2 x 2 x 25 x 7
OB. 350 x 2
OC. 2 x 2 x 2 x 5x5x7
OD 2 x 2 x 5x5x7
Answer:
b. 350x2
Step-by-step explanation:
the answer is 350x2 because if you do 350x2 you will get 700
The pendulum of a clock swings through an angle of 2.5 radians as its tip
travels through an arc of 50 centimeters. Find the length of the pendulum, in
centimeters.
r = 50/2.5 = 20 cm
------------------------
Clock pendulums swing 8 degrees or less, which is an included angle of ~0.28 radians
Geometry is so confusing to me, i don’t get how to figure out angles and measurements. I have read my instructors over and over again and I still don’t understand
Answer:
reference attached
Step-by-step explanation:
hope it helps you <3Answer:
It's ok. Math can be really difficult, but don't give up and you'll understand.
To begin, this is a transversal. A transversal is a set of parallel lines that have a third line intersecting them.
In the photo below, you can see the original angle given and it is 35°. On the same line directly across from it is an angle that is also 35°. This follows the rule of vertical angles, which are angles produced by the same two lines. It also states that they are congruent.
You'll also see that the angle next to the original angle is 145°. This follows the rule of supplementary angles, which states that two angles that are on the same straight line will equal 180° when added together.
The angle opposite to that is 145°, which can be proven by vertical angles.
Through a method called corresponding angles, we can see that the original angle is corresponding with the angle below it.
Then you would repeat the process for the top.
Hope this helps!
Select True or False for each statement.
Statement True False
In the ordered pair (3, 5), the number 5 is the y-coordinate.
True – In the ordered pair ( 3, 5 ) , the number 5 is the y-coordinate.
False – In the ordered pair ( 3, 5 ) , the number 5 is the y-coordinate.
The origin has coordinates (0, 0).
True – The origin has coordinates ( 0, 0 ) .
False – The origin has coordinates ( 0, 0 ) .
The horizontal axis in a coordinate plane is the y-axis.
The number 5 in the ordered pair (3, 5) is the y-coordinate (TRUE)
(0, 0) is the origin on a coordinate plane (TRUE)
y-axis is the horizontal axis on a coordinate plane (FALSE).
What is an Ordered Pair?An ordered pair is a set of numbers that represents the location of a point on a coordinate plane that has an x-axis (horizontal axis) and y-axis (vertical axis).
An ordered pair is given as (x, y). Therefore, the following statements given are matched as shown below:
The number 5 in the ordered pair (3, 5) is the y-coordinate (TRUE)(0, 0) is the origin on a coordinate plane (TRUE)y-axis is the horizontal axis on a coordinate plane (FALSE).Learn more about ordered pair on:
https://brainly.com/question/1528681
The diameter of a circle is 33 cm. Find its area to the nearest whole number.
Answer:
⇒855cm²
Step-by-step explanation:
→Solution,
Diameter(d)=33cm
Radius(r)=d/2=33cm/2=16.5cm
Now,
Area=πr²
Area=3.14×(16.5cm)²
Area=854.865cm²=855cm²
How many pounds are in 3 tons?
600 pounds
900 pounds
6,000 pounds
9,000 pounds
Answer:
6,000
Step-by-step explanation:
1 ton is 2,000 pounds, so 3 tons are 6,000 pounds because 2,000 x 3 = 6,000.
Have a great day!
Please help again,am very slow of mathematics,
please po!
Step-by-step explanation:
a) 7/10
b) 9/10
c) 4/10 = 2/5
d) 9/10
e) 2/10 = 1/5
I hope it helped you
MAX POINTS PLEASE HELP Will make Brainliest
What is the period and frequency of the function graphed and how would the equation be written??
Answer:
Period: 6, Frequency: 1/6, Equation: -4cos([tex]\frac{\pi }{3}x[/tex])-2
Step-by-step explanation:
Because the graph starts at x = 0 at a minimum/maximum, it's easiest to use cosine, so we don't have to shift the graph horizontally. cos(x)
If you take the max/min points and average them, you can use the distance between the average value and the max/min to get the total amplitude, A, which is 4.
Because this function starts at a minimum, but cosine starts at a maximum, we will flip it vertically by adding a negative coefficient to whatever the amplitude is.
We see that the same part of the graph recurres every 6 x-units, so the period is 6. The frequency of this is 1/(period), 1/6.
The coefficient of x in a sin/cos function is [tex]2\pi /Period[/tex], = [tex]\pi[/tex]/3.
The vertical shift (how much the average value of the function moved from 0 to its current position) is -2.
Put all that together, you get y = -4cos([tex]\frac{\pi }{3}x[/tex])-2
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
let's solve ~
Period :
Difference between two successive crest or trough is known as period, so here :
period = 9 - 3 = 6
Frequency
Now, we know that frequency = 1/period
So, frequency for given function is 1/6 hertz , or approximately 0.167 hertz
Amplitude (A) = 4 (flipped)b = 2π ÷ Period = 2π /6 = π/3 k = -2The required equation is ~
[tex]\qquad \sf \dashrightarrow \:y = a \cos(bx) + k[/tex]
[tex]\qquad \sf \dashrightarrow \:y = - 4 \cos( \frac{ \pi}{3} x) - 2[/tex]
giving brainliest to whoever gives me the answers (to a and b) :)
Answer:
a.) Graph is attached; blue is Petunia's and red is Billy's
b.) Number of Hours: 4 | Cost: 32 Pounds
kinda confusing problem given by my teacher:
What is the total discount percent as compared to the original price, if trousers are discounted by 12% and then a further 20% discount is given and new price is $281.6. (answer like this xx.x)
Answer:
Below
Step-by-step explanation:
281.6x20%= 56.32
281.6+56.31=337.91
337.91x12%=40.55
337.91+40.55=378.46
Using the three Indicated points on the given line and the concept of similar triangles, show and explain why the slope of the line is the same between any two of these three points. calculate the slope of the line
Answer:
it is the same because slope is a measure of steepness.
Step-by-step explanation:
(0,1) (2,4)
4-1/2-0=3/2
slope=3/2
Solve the system of equations by elimination. Show your work. i’ll give brainliest
Answer:
x = 5
y = 4
Step-by-step explanation:
multiply the second equation by -1 and add the first equation to eliminate "x"
[tex]4x+6y=44\\-4x-2y=-28[/tex]
_____________
[tex]4y=16[/tex]
[tex]y=16/4 =4[/tex]
Replace "y" in the first equation:
[tex]4x+6(4)=44[/tex]
[tex]4x+24=44[/tex]
[tex]4x=44-24[/tex]
[tex]x=20/4=5[/tex]
Hope this helps
Answer:
x = 5, y = 4.
Step-by-step explanation:
4x + 6y = 44 (A)
4x + 2y = 28 (B)
Subtract equations: (A) - (B).
0 + 4y = 16
y = 16/4
y = 4.
Now plug y = 4 into equation A:
4x + 6(4) = 44
4x = 44 - 24
4x = 20
x = 5.
Now check if these roots are correct by plugging them into equation B:
4x + 2y = 28
4(5) + 2(4) = 28 - check OK.
PLEASE AWNSER NEEDED NOW Find the volume of the figure. Round your answers to the nearest hundredth, if necessary
10.If Zoe paints the outside faces of
her shed and tho roof. what is the
total surface area that she paints?
CA
A. 130 p2
B. 155 p2
C. 180 02
D. 205 pp
Step-by-step explanation:
Area of one side of the shed
5*4=20
she painted 4 sides so 20*4 =80
Triangle that is part of the pyramid as the roof of the shed has a side of 5. Using the Pythagorean theorem,
[tex]{5}^{2} - {2.5}^{2} =18.75[/tex]
we need to find the square root of 18.75 to find the height of the triangle which is
[tex] \sqrt{18.75} = 4.330127019[/tex]
that is the height
(base x height) /2 is the formula for a right triangle. there are 2 of these right triangles per side of the roof. so we need to multiply the numbers by 8
[tex]\frac{2.5 \times 4.330127019}{2} \times 8[/tex]
this number gives us 43.30127019
we can finally add that number to 80 to get the total surface area Zoe painted which is 123.3012702
Which statement(s) are true?
No event can be impossible.
No event can be certain.
The more unlikely an event, the closer it is to impossible.
The more likely an event, the closer it is to certain.
Answer:
no event can be impossible
Answer: no event can be impossible
Step-by-step explanation:
Need help asap! Having trouble !
In a trapezoid, the segment at the midpoint is the average of the other two bases.
In other words: YZ = (QR + TS) / 2
5x + 1 = ( (2x + 7) + 19 ) / 2
2(5x + 1) = 2x + 26
10x + 2 = 2x + 26
8x = 24
x = 3
YZ = 5x + 1
YZ = 5(3) + 1
YZ = 15 + 1
YZ = 16
Hope this helps!
Find the surface area of the triangular prism.
A triangular prism. The base has sides of 17 meters, 17 meters, and 16 meters. The height of the prism is 10 meters. Apothem goes from the base vertex to the midpoint of the base edge, 16 meters, and measures 15 meters.
The surface area is
square meters.
All of the following have the same solution except _____. 50 = 5 m x - 6 = 4 = 2 b + 2 = 8
Answer: b+2=8
Step-by-step explanation:
can you please help me solve this logarithm function
Answer:
I think the solution is x=84 if this is correct can u mark me brainliest
Answer:
[tex]\boxed{\sf{x=84}}[/tex]Step-by-step explanation:
This problem can be solved by using the logarithm function.
Isolate the term of x from one side of the equation.
First, you divide by -6 from both sides.
[tex]\Longrightarrow: \sf{\dfrac{-6\log _3(x-3)}{-6}=\dfrac{-24}{-6}}[/tex]
Solve.
Divide the numbers from left to right.
-24/-6=4
Rewrite the problem down.
[tex]\Longrightarrow: \sf{\log _3(x-3)=4}[/tex]
x-3=81
Add by 3 from both sides.
[tex]\Longrightarrow:\sf{x-3+3=81+3}[/tex]
Solve.
Add the numbers from left to right.
81+3=84
[tex]\Longrightarrow: \boxed{\sf{x=84}}[/tex]
Therefore, the solution is x=84, which is our answer.I hope this helps you! Let me know if my answer is wrong or not.
find the missing coordinates y+7x=1
(-1, )
(4, )
Answer:
(-1,8)
(4,-27)
Step-by-step explanation:
y+7x=1
Let x = -1 and find y
y+7(-1)=1
y -7 =1
Add 7 to each side
y-7+7 = 1+7
y = 8
(-1,8)
Let x = 4 and find y
y+7(4)=1
y +28 =1
Subtract 28 from each side
y+28-28 = 1-28
y = -27
(4,-27)
John and Monica completed the same task on different lines in an assembly plant. When John had completed 7/9 of the task, Monica had only completed 5/9 of the task. How much more of the task has John completed than Monica?
Answer:
2/9ths
Step-by-step explanation:
7/9 - 5/9 = 2/9
Hope this helps <3
Write an equation of the line in slope-intercept form: y-intercept of 2, x-intercept of 4
Answer:
[tex]\sf y=-\dfrac12x+2[/tex]
Step-by-step explanation:
y-intercept is when x = 0, so (0, 2)
x-intercept is when y = 0, so (4, 0)
[tex]\sf slope=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{0-2}{4-0}=-\dfrac12[/tex]
Slope-intercept form of linear equation: [tex]\sf y=mx+b[/tex]
(where m is the slope and b is the y-intercept)
Given:
[tex]\sf m=-\dfrac12[/tex]b = 2[tex]\sf \implies y=-\dfrac12x+2[/tex]
In ΔGHI, the measure of ∠I=90°, IH = 11, HG = 61, and GI = 60. What is the value of the sine of ∠G to the nearest hundredth?
Answer: 0.18
Step-by-step explanation:
Using the sin rule:
11/sin(∠G) = 61/90
sin(∠G) = 11/61
sin(∠G) = 0.18°
Therefore, the value of angle G is 0.18 degrees
18. Cancellation refers to the procedure for
A. reducing fractions to make multiplying easier.
B. inverting the divisor in a division problem.
C. changing a mixed number to an improper fraction.
D. finding the lowest common denominator for a group of fractions.
The correct option regarding the operation of cancellation in a fraction is given by:
A. reducing fractions to make multiplying easier.
What is an example of cancellation in a fraction?It happens when two fractions are multiplying each other, and terms are simplified to make the multiplication easier. For example:
[tex]\frac{2}{3} \times \frac{6}{4} = \frac{6}{3} \times \frac{2}{4} = 2 \times \frac{1}{2} = 1[/tex]
The terms 2 and 4, and 3 and 6, were canceled. Hence option A is correct.
More can be learned about cancellation in a fraction at https://brainly.com/question/571030
Apply the distributive property to factor out the greatest common factor.
{25p + 50q} =
Answer:
25(p+25q)
Step-by-step explanation:
50 and 25 have 25 in common so you divide that out of the equation
ABC is circumscribed about H, with the points of tangency D,E, and F.
Find the solutions to the equation below.
Check all that apply.
x^2 - 25 = 0
A. x = 1
B. x = 5
C. x = -1
D. x = -5
E. x = 3
F. x = -3
Answer:
B and D
Step-by-step explanation:
x² - 25 = 0
Add 25 to both sides:
⇒ x² -25 + 25 = 0 + 25
⇒ x² = 25
Square root both sides:
⇒ √x² = √25
⇒ x = ±5
Therefore:
x = 5, x = -5
So B and D are the solutions
