Answer:
m = 60
Step-by-step explanation:
log is another way to write an exponent.
Example:
exponent form:
7^2 = 49
log form:
log_7 (49) = 2
In your question, we need to change to exponent form, from log form.
log_5 (2m+5)=3
5 is the base. 3 is the exponent.
Now it can be solved.
5^3 = 2m+5
125 = 2m + 5
120 = 2m
60 = m
Given circle O lies perfectly within square ABCD. If side BC = 6.84, then what is the area of the orange region?
What we get to know by looking at picture :
There are two figures: 1. square 2. circle inside it touching all square's wall.As O is center of circle (given) ∴ OP is radius of circleAs the sides are of square , therefore AB = BC = DC = AD[tex] \\ \\\\ [/tex]
To find :
Area of orange region[tex] \\ \\ \\ [/tex]
Given:
O is the center of the circle.ABCD is squareLength of BC is equal to 6.84.[tex] \\ \\ \\ [/tex]
Concept:
So as we can orange doesn't lies inside circle. And the wall of circle touches all four sides of circle. So first we have to find area of circle and then Area of square. And then we will subtract the ares. The result will be Area of orange part.
[tex] \\\\ \\ [/tex]
Solution:[tex] \\ \\\\ [/tex]
[tex] \red{ \textsf{ \textbf{Area of circle: }}}[/tex]
[tex] \\ [/tex]
To find area of circle we need radius of it i.e Length of OP.
As BC = AB
∴AB = 6.84
As O is the center of square ∴it's center of circle too
Therefore:
AB = 2 OP6.84 = 2 OPOP = 6.84/2OP = 684/2 × 10OP = 342/10OP = 3.42[tex] \\\\ [/tex]
Now Let's find area :
[tex] \\\\ [/tex]
[tex] \star \boxed{ \rm Area~of~circle = \pi {r}^{2} }[/tex]
here :
r is the radius of circle.[tex] \\ [/tex]
[tex]: \implies\sf Area~of~circle = \pi {r}^{2} \\ \\ \\ : \implies\sf Area~of~circle = \dfrac{22}{7} \times {3.42}^{2} \\ \\ \\ : \implies\sf Area~of~circle = \dfrac{22}{7} \times {3.42}^{2} \\ \\ \\ : \implies\sf Area~of~circle = \dfrac{22}{7} \times11.7\\\\\\: \implies\sf Area~of~circle = \dfrac{257.4}{7} \\ \\ \\ : \implies \boxed{ \orange{\tt{ Area~of~circle = 36.6 \{approx \}}}} \bf \dag[/tex]
[tex] \\ \\ [/tex]
[tex] \red{ \textsf{ \textbf{Area of square: }}}[/tex]
[tex] \\\\ [/tex]
[tex] \star \boxed{ \rm Area~of~square = {side}^{2} }[/tex]
[tex] \\ \\ [/tex]
[tex]: \implies\sf Area~of~square = {side}^{2} \\ \\ \\ : \implies\sf Area~of~square = {6.84}^{2} \\ \\ \\ : \implies\sf Area~of~square = {6.84} \times 6.84 \\ \\ \\ : \implies \boxed{\tt{ \orange{Area~of~square = 46.8 \{aprox \}}}}\bf\dag[/tex]
[tex] \\ \\ [/tex]
[tex] \red{ \textsf{ \textbf{Area of orange \: part: }}}[/tex]
[tex] \\ [/tex]
[tex] \star\sf \boxed{ \rm Area_{(orange \: part)} = Area_{(square)} - Area_{(circle)}}[/tex]
[tex] \\ \\ [/tex]
[tex]: \implies\sf Area_{(orange \: part)} = 46.8 - 36.6 \\ \\ \\ : \implies \boxed{ \blue{\tt{Area_{(orange \: part)} = 10.2}}}\bf\dag[/tex]
It takes Greg and Nikki a total of 40 minutes to paint a room if they work together. If Greg works alone, he takes 18 minutes longer to paint he room than Nikki takes if she works alone. When x represents the number of minutes it takes Nikki to paint the room working alone, the situation is represented by this equation: Which value is a solution of the rational equation that must be discarded because of the context
Using the together rate, it is found that the value that must be discarded is given by x = -9.
What is the together rate?It is the sum of each separate rate.
In this problem, the rates are given as follows:
Together: [tex]\frac{1}{40}[/tex].Nikki's: [tex]\frac{1}{x}[/tex].Greg's: [tex]\frac{1}{x + 18}[/tex].Hence:
[tex]\frac{1}{x} + \frac{1}{x + 18} = \frac{1}{40}[/tex]
[tex]\frac{x + 18 + x}{x(x + 18)} = \frac{1}{40}[/tex]
[tex]x^2 + 18x = 80x + 720[/tex]
[tex]x^2 - 72x - 720 = 0[/tex]
Then, we have a quadratic function, with coefficients a = 1, b = -72, c = -720, so:
[tex]\Delta = (-72)^2 - 4(1)(-720) = 8064[/tex]
[tex]x_1 = \frac{72 + \sqrt{8064}}{2} = 80.9[/tex]
[tex]x_2 = \frac{72 - \sqrt{8064}}{2} = -9[/tex]
They cannot have a negative rate, hence the value that must be discarded is given by x = -9.
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Answer:
X = -10
Step-by-step explanation:
PLATO
5. M's class is having a give-away
here 3 of her lucky students will
ceive 500 classroom credits. She
ll pull names out of a hat and select
winners. Once a student wins, they
e not eligible to win again. There
e 75 total students in the class,
cluding you and your 2 best friends.
The probability that both I and my best friend get the 100 classroom credits is 0.06%.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Since Mr Q's class is having a give-away where his students can receive 100 classroom credits, he will pull names out of a hat and select two winners, and once a student wins, they are not eligible to win a second time, if there are 40 total people in the class, including me and my best friend, to determine what is the probability that both I and my best friend get the 100 classroom credits, the following calculation must be performed:
I = 1/40 = 0.025
my best friend = 1/39 = 0.02564
0.02564 x 0.025 = X
0.0006410 = X
X x 100 = 0.064
Therefore, the probability that both I and my best friends get the 100 classroom credits is 0.06%.
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3. The FFA had a fundraiser by selling hot dogs for $1.50 and drinks for $2.00. Their total sales were $400.
a) Write an equation to calculate the total of $400 based on the hot dog and drink sales.
b) Graph the relationship between hot dog sales.
The equation that represents the total of $400 based on the hot dog and drink sales is $400= $1.50H + $2.00D
Using equation for expressionsThe amount sold for each hot dog = $1.50
The total number of hot dogs sold = H × $1.50
The amount sold for each drink = $2.00
The total number of drinks sold = D× $2.00
The total sales made was = $400
Therefore the equation that represents the total of $400 based on the hot dog and drink sales is;
$400= $1.50H + $2.00D
The relationship that exists between the hot dog sales is that the cost is the drinks is higher than the cost of the hot dog.
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I have 25% off coupon. The items in my cart come to a total of $178.99. What will be my bill after my discount?
Good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
No he is wrong
If he is referring to table only then correct else wrong
Always 2^x can't have less intercept.
After some while it will cross 5(x)².
You can observe it from graphs
Need some help, thanks in advance!
Answer: = 3 acres per day
Showing Work
This is a fraction equal to
3 acres ÷ 1 days
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 1
3 acres ÷ 1
__________
1 days ÷ 1
=
3 acres
_____
1 day
=
3 acres
______
day
= 3 acres per day
Q5. the population of an island has decreased by 40% over 50 years.
the population in 2018 was 360
what was the population in 1968?
Answer:
The population was 600 in 1968
Step-by-step explanation:
The population of an island decreased by 40% over 50 years, so the population in 1968 will be equal to 600.
What is the Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.
As per the data provided by the question,
The current population in 2018 = is 360
which is 40% less than the population in 1968.
So, 60% of the total population will be equal to 360.
Let the total population is x.
60% × x = 360
x = (360 × 100)/60
x = 600
Therefore, the population at that time was 600.
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Can someone help me to solve this question? Prove that the quadrilateral ABCD whose vertices are A(-2,-1), B(-2,-3), C( 5,6), and D(5,-1)is a trapezium.Find the area of trapezium ABCD. Also Can you tell how to find the height of trapezium with vertices without knowing the area? Thank you.
If the height of the trapezium is 7 units. Then the area of the trapezium will be 31.5 square units.
What is a trapezium?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezium, one pair of opposite sides are parallel.
The quadrilateral ABCD whose vertices are A(-2,-1), B(-2,-3), C( 5,6), and D(5,-1).
The lines AB and CD are parallel to the y-axis. Then the quadrilateral ABCD is a trapezium.
The height of the trapezium will be 7 units.
The area of the trapezium will be
Area = 1/2 (2 + 7) x 7
Area = 0.5 x 9 x 7
Area = 31.5 square units.
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Find pi using circumference of 78.5 and the radius is 5. Explain how you found pi.
Answer:
Pi is normally 3.14 but in this case it is 15.7
Step-by-step explanation:
78.5 divided by 5 = 15.7
5 x 3.14 = 15.7
Find the value of x.
8:5 = 1/x:1
Answer:x=61
Step-by-step explanation
856−5x3{131}=2
8(x−9)+5(5−18)+1(15−6x)=2
8x−72−65+15−6x=2
2x=122
x=61
sorry if i'm wrong
in a group of 70 people, 37 like tea, 52 like milk and each people likes at least one of the two drinks.
1)how many people like both tea and milk ?
2) how many people like tea only ?
3)how many people like milk only ?
4)show the above information in a Venn diagram.
Step-by-step explanation:
got the answer see in the image :)
About 2% of the students at a college with a population of 9,000 students have significant vision impairments. A polling organization took a random sample of 800 of these students. is the 10% conditon met?
Yes, 10(800) = 8,000, which is less than the total population
Yes, 10% of 800 = 80, which is less than the total population
No, 10(9,000) = 90,000, which is more than the sample
No, 10% of 9000 = 900, which is more than the sample
Answer:
total population: 9,000
10% of 9,000= 900 students
they only surveyed 800 students so Yes the 10(800)=8,000 which is less then 9,000 or Option A
HELP HELP HELP PLEASE PLEASE
Answer:
Fourth one
Step-by-step explanation:
You can find the x coordinate of the vertex (which is the axis of symmetry)
by calculating x = - b/ 2a
( when equation is arranged into y = a x^2 + bx + c form )
first one - -2/4 = 1/2
second one -2/ -4 = 1/2
third one - -2 / 4 = 1/2
fourth one - 2 / 4 = - 1/2 BINGO !
help with practice problem
Answer:
i think the answer is r=0.5 or r=−3/2−x^2
Step-by-step explanation:
-4r^2-4r=6
step 1. -4r(-4r)= 16r
16r-4r=6
step 2. 16r-4r=12r
12r=6
step 3. /12 on both sides
r= 0.5
Complete the square and graph: 9y²−x − 18y +10=0
Answer:
See below ~
Step-by-step explanation:
Completing the square :
9y² - x - 18y + 10 = 09y² - 18y + 9 - 9 - x + 10 = 0(3y - 3)² - x + 1 = 0Graph :
Answer:
x = 9(y - 1)² + 1
see attached for graph
Step-by-step explanation:
Completing the squareGiven equation:
9y² - x - 18y + 10 = 0
As there is a y² in the equation, this implies it is a sideways parabola.
To complete the square for a sideways parabola, collect the y variable terms on the left and everything else on the right:
⇒ 9y² - 18y = x - 10
Factor out the leading coefficient from the left side:
⇒ 9(y² - 2y) = x - 10
Take the coefficient of y, half it, then square it: (-2 ÷ 2)² = 1
Add this inside the parentheses, and add the distributed value of this to the right side:
⇒ 9(y² - 2y + 1) = x - 10 + 9
Factor the parentheses and simplify the right side:
⇒ 9(y - 1)² = x - 1
Add 1 to both sides to make x the subject:
⇒ x = 9(y - 1)² + 1
Graphing the parabolaConic form of a sideways parabola with a horizontal axis of symmetry:
x = a(y - k)² + h
(where (h, k) is the vertex and y = k is the axis of symmetry)
If a > 0, the parabola opens to the right, and if a < 0, the parabola opens to the left.
Therefore, for x = 9(y - 1)² + 1
vertex = (1, 1)axis of symmetry: y = 1a > 0 ⇒ the parabola opens to the rightTo find the x-intercept, set y = 0 and solve for x:
⇒ x = 9(0 - 1)² + 1
⇒ x = 9(-1)² + 1
⇒ x = 9(1) + 1
⇒ x = 10
Therefore, the y-intercept is (10, 0)
As the axis of symmetry is y = 1, the other value of y when x = 10 is y = 2
Plot the vertex and points. Add an axis of symmetry to help draw the curve. Draw the parabola opening to the right.
**graph attached**
A card is drawn from a standard deck of 52 playing cards. What is the probability of drawing a club or a red king?
Answer:
1/2
Step-by-step explanation:
number of required outcome ÷number of possible outcomes
1/2
find the zeros for 3x2-8=-2x
Answer:
Here is the answer ..hope it helps:)
What is the value of x?
Enter your answer as a decimal to the nearest tenth in the box.
ft
B
29
27 ft
C
Answer:
23.6 ft
Step-by-step explanation:
In the right triangle, an acute angle, the hypotenuse, and an adjacent side are marked. We went to know the length of the adjacent side. The trig relation involved is ...
Cos = Adjacent/Hypotenuse
__
Filling in the given information, this relation tells us ...
cos(29°) = x/(27 ft)
Solving for x, we get ...
x = (27 ft)cos(29°) ≈ 23.614 ft
The value of x is about 23.6 ft.
In figure MNL, the value of x is:
Answer:
x=6
Step-by-step explanation:
Those are scalene triangles, if 9 is the base, then the other two sides will be congruent, so x=6.
find the selling price of a $36 item after a 50% markup
Answer:
$54
Step-by-step explanation:
36 divided by 2= 18
$36+$18=$54
Part B: Your cell phone and tablet use the same account. The cell phone costs $0.10 for
each minute of use and the tablet costs $0.15 for every minute of use. Each month, you
want to only spend up to $450 and use less than 5,000 minutes on both of the devices.
Now, create a system of inequalities using the above information (use x and y as the
variables).
please help me ill mark you brainliest
The inequalities are x + y < 5000 and 0.10x + 0.15y ≤ $450 which shows each month, you want to only spend up to $450 and use less than 5,000 minutes on both of the devices.c
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.
Let's suppose the total minutes for cell phone is x
and total minutes for tablet is y
Then total minutes will be:
x + y < 5000 (less than 5,000 minutes on both of the devices)
And total cost:
0.10x + 0.15y ≤ $450
Thus, the inequalities are x + y < 5000 and 0.10x + 0.15y ≤ $450 which shows each month, you want to only spend up to $450 and use less than 5,000 minutes on both of the devices.
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Please awnser my other question
Answer:
S = (-6, -1)
T = (-7, 4)
U = (-6, 9)
V = (-4, 4)
in fgh, m f=60 degrees g= 68 degrees. which side of fgh is the shortest
Answer:
h=52 and h is the shortest
Step-by-step explanation:
180-f-g=h step 1. -f from 180
180-60=120 step 2. -g from 120
120-68= 52
h=52 degrees
Trina is trying to decide which lunch combination to order at a sandwich shop: 4, 5, 6, or
7. Each combination comes with the choice of an apple, an orange, or a pear. How many
possible outcomes are there for a lunch combination and a piece of fruit?
apple
orange
pear
apple
5
orange
pear
apple
orange
pear
apple
orange
pear
Type the answer in the box.
10
What fraction is equivalent to the decimal number 0.90?(theres a line above the 0.90)
A. 10 over 11
B. 9 over 10
C 1 over 9
D 1 over 90
Answer:
B
Step-by-step explanation:
The number is in the tenths spot so you do 0.90 times 10 which gives you 9/10.
-3(x + 9) = 15
Enter value for x
Answer:
x = -14
Step-by-step explanation:
-3(x + 9) = 15Divide each side by -3.
-3(x + 9)/-3 = 15/-3x + 9 = -5Subtract 9 from each side.
x + 9 - 9 = -5 - 9x = -14Answer:
x = -14
Step-by-step explanation:
-3(x + 9) = 15
-3 × x + -3 × 9 = 15-3x + (-27) = 15+27 on both sides-3x = 42[tex] \frac{ - 3x}{ - 3} = \frac{42}{ - 3} [/tex]x = -14A triangle has sides with lengths of 17 feet, 31 feet, and 36 feet. Is it a right triangle?
yes
no
I WILL GIVE BRAINLIEST! Draw the line of reflection that reflects ABC onto ABC prime
Answer:
put the line on y= -2
Step-by-step explanation:
The figure ABC is reflected along the line y = -2 and the new coordinated will be A(-2, -4), B (3, 0), and C (-2, -7).
What is reflection?Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point.
Given:
The coordinates of the figure of ABC is given as A(-2, 0), C(-2, 3), and B(3, -4),
The new coordinates of A'B'C' are A(-2, -4), B(3, 0), and C(-2, -7),
If the given figure is reflected as y = -x,
Then, the coordination will change like (-y, -x),
Thus, the new coordinates of ABC will be A(-2, -4), B (3, 0), and C (-2, -7).
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Does anybody understand this? Been struggling with it for awhile. Use the rectangle to find the measure of the following angles. BAC=25
Answer:
∠CBA =90°; ∠CAD =65°; ∠ACD =25°; ∠CBD = 65°
∠BWA = 130°; ∠AWD = 50°
Step-by-step explanation:
The diagonals of a rectangle divide the figure into two pairs of congruent isosceles triangles. The figure is symmetrical about both the vertical and horizontal centerlines. Each corner angle of the rectangle is 90°. Of course, the sum of angles in any of the triangles is 180°.
__
The above descriptions tell you ...
∠ABD =∠ACD =∠BAC =∠BDC = 25°
∠CBA =∠BCD =∠CDA =∠DAB = 90°
∠CAD =∠CBD =∠ACB =∠ADB = 90° -25° = 65°
∠BWA =∠CWD = 180° -25° -25° = 130°
∠AWD = ∠BWC = 180° -65° -65° = 50°