Answer:
15 cm
Step-by-step explanation:
The area of an equilateral triangle is:
[tex]\frac{\sqrt{3} }{4}a^2[/tex], where a is the length of one side.
We can find the value of a (the length) by:
[tex]\frac{25\sqrt{3} }{4} = \frac{\sqrt{3} }{4}a^2[/tex]
[tex]a^2 = 25[/tex]
a = 5, so the side length of this triangle is 5 cm.
The perimeter of an equilateral triangle will be 3 times the length.
[tex]3\cdot5=15[/tex]
Hope this helped!
Graph the rational function
f (x)=- 3x + 1
-x+2
Answer:
Step-by-step explanation:
You must show that this is a rational function. As written, it is not such.
-3x + 1
f(x) = ------------
-x + 2
is a rational function; the horizontal line --------- indicates division.
If we let x grow large, the graph approaches the horizontal line y = 3, which we call "the horizontal asymptote." There is a vertical asymptote at x = 2, which we know because the denominator will be zero at that x value. The vertical intercept is
f(0) = 1/2, or (0, 1/2).
As x decreases towards negative infinity, the graph approaches the horizontal line (horizontal asymptote) y = 3.
Find the volume. Show work plz
Answer:
[tex]93\frac{1}{3}[/tex] [tex]yd^{3}[/tex]
Step-by-step explanation:
The volume of a pyramid is:
[tex]V=\frac{lwh}{3}[/tex] (basically saying that you multiply the length, width, and the height together and then you divide that by 3)
Now, let's do the first part.
8 × 5 × 7 = 280
Now, let's divide.
280 ÷ 3 = 93 1/3
That's your answer!
Hope that helps and maybe earns a brainliest!
Have a great day! :)
PLEASE HALP I GIVE OUT BRAINLIEST
Since there is two negative signs in the original equation, you need two negative signs in the equivalent one as well.
Because one of the negatives if before the fraction, it doesn't matter if the second negative is on the 13 or on the 12.
The answer is A.
A teacher took a group of 48 students to the movie theater. They have saved $353 in a fund for the students' tickets. How much money will they have left in the fund if the ticket for each student was $7
Answer:
$17
Step-by-step explanation:
If each ticket is $7 and there are 48 student multiply 7 and 48 to see how much the tickets were in total (336)
Now subtract 353 and 336 to see how much money is left (17)
Answer: -17?
Step-by-step explanation:
because 7*48= 336
then you would do 336-353= -17
which gave me the answer of -17
what would it be if the sum of six consecutive even numbers is 130 what would the 2nd number be in the sequence PLZ HELP
Answer:
[tex]\huge\boxed{Second\ Number = 42}[/tex]
Step-by-step explanation:
Let the consecutive even numbers be x,x+2,x+4, x+ 6, x+ 8 and x+10
So, the given condition is:
x+x+2+x+4+x+6+x+8+x+10 = 270
6x + 30 = 270
Subtracting both sides by 30
6x = 270 - 30
6x = 240
Dividing both sides by 6
x = 40
So,
First Number = x = 40
Second Number = x+2 = 40+2 = 42
Third Number = x+4 = 40+4 = 44
Fourth Number = x+6 = 40+6 = 46
Fifth Number = x+8 = 40+8 = 48
Sixth Number = x+10 = 40+10 = 50
Answer:
22 I think
Step-by-step explanation:
i need this quick!!! please hurry!! Solve the following proportion for X. X over 5 = 17 over 3 Round your answer to the nearest tenth.
Answer:
[tex]\huge\boxed{x = 28.3}[/tex]
Step-by-step explanation:
=> [tex]\frac{x}{5} = \frac{17}{3}[/tex]
Cross Multiplying
=> x * 3 = 5 * 17
=> 3x = 85
Dividing both sides by 3
=> x = 85/3
=> x = 28.3 (To nearest tenth)
Answer:
[tex]\Huge \boxed{x=28.3}[/tex]
Step-by-step explanation:
The proportion is given,
[tex]\displaystyle \frac{x}{5} =\frac{17}{3}[/tex]
We need the x variable isolated on one side, so we can find the value of x that makes the proportion true.
Multiply both sides of the equation by 5.
[tex]\displaystyle \frac{x}{5} \times (5)=\frac{17}{3} \times (5)[/tex]
Simplify the equation.
[tex]\displaystyle x=\frac{85}{3}[/tex]
[tex]x=28.33333333...[/tex]
The value of x that makes the proportion true is 28.3 (rounded to nearest tenth place).
Identifying Kinds of Context Clues
example
Match each sentence with the type of context clue it includes
Large herbivores, such as elephants and
giraffes, need to eat a lot.
synonym
Their service is expedient - I'm amazed
by how fast they are!
antonym
Jane is always very enthusiastic and
never negative or doubtful.
explanation
Carburetors, which feed fuel and air to
engines, are very important.
Answer:
Large herbivores, such as elephants and
giraffes, need to eat a lot. = Example
Their service is expedient - I'm amazed
by how fast they are! Example, explanation
Jane is always very enthusiastic and
never negative or doubtful. = antonym
Carburetors, which feed fuel and air to
engines, are very important. = explanation
Step-by-step explanation:
Answer:
Step-by-step explanation:
Please Answer For Brainliest!!!
Answer:
C
Step-by-step explanation:
They want to find out altogether and the total number so add it up!
Answer: 72,132,204
Step-by-step explanation:
i need the answer plz
Answer:
Step-by-step explanation:
The second answer choice correctly shows the result of multiplying functions m and n together.
Missing Portion on Spinner:
So theres a circle,
2/3 is covered,
1/6 is covered,
and 1/9 is covered
what fraction is the portion that isn't covered
============================================
Explanation:
The fractions 2/3, 1/6 and 1/9 have the denominators 3, 6 and 9. The LCM is 18, so the LCD of the fractions is 18.
2/3 = 12/18 after multiplying top and bottom by 6
1/6 = 3/18 after multiplying top and bottom by 3
1/9 = 2/18 after multiplying top and bottom by 2
--------
The three original fractions 2/3, 1/6, and 1/9 are equivalent to 12/18, 3/18, and 2/18 in that exact order.
With the fractions all having the same denominator, we can add the numerators to place over the common denominator
12/18 + 3/18 + 2/18 = (12+3+2)/18 = 17/18
--------
After combining all of the shaded areas, we have 17/18 of the circle shaded in with 1/18 of the circle not shaded in.
You subtract 17/18 from 1 to get 1/18
1 - (17/18) = 18/18 - 17/18 = (18-17)/18 = 1/18
You could think of it like having 18 slices of cake total, and 17 are eaten by guests, so 18-17 = 1 is left over out of the 18 overall. So 1/18 of the cake hasn't been eaten.
The required fraction is 1/18, that is not covered.
What is a fraction?A fraction is a numeral that represents a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
In the given spinner,
2/3 part is covered,
1/6 part is covered,
and 1/9 part is covered.
To determine the fraction of the portion that is not covered,
Let the not covered portion is x.
Since, Total value of circle = 1
2/3 + 1/6 + 1/9 + x = 1
(4 + 1)/6 + 1/9 + x = 1
5 / 6 + 1/9 + x = 1
(15 + 2) / 18 + x = 1
17/18 + x = 1
x = 1 - 17 / 18
x = 1 / 18
The portion of the circle that is not covered is 1/18.
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Find the distance between (4.9) and (5, 12)
Answer:
[tex]\sqrt{10}[/tex]
Step-by-step explanation:
[tex]\sqrt{(x_{2} - x_{1}) ^ {2} + (y_{2} - y_{1}) ^ {2}}[/tex]
[tex]\sqrt{(5-4) ^ {2} + (12 - 9) ^ {2}} = \sqrt{1^{2}+3^{2}} = \sqrt{10}[/tex]
An atom consists of electrons, protons, and neutrons. Each electron has a charge of -1, each proton has a charge of +1, and each neutron has no charge. If 3 electrons are removed from each of 4 atoms, what is the combined net change to the charge of the 4 atoms?
Answer:
The net charge on the four atoms is 12
Step-by-step explanation:
The given parameters are;
The charge of each electron = -1
The charge of each proton = + 1
The charge of each neutron = neutral
Therefore, if 3 electrons are removed from each of the three atoms, we have;
The quantity of net negative charge removed from the four atoms = 3 × -1 × 4 = -12
Given that the at the four atoms add equal number of protons and electrons, we have;
Original charge on the four atoms = n×(-1) + n×(+1) = 0
Therefore;
The net charge on the four atoms after removal of the 12 electrons = Original charge - (-12)
The net charge on the four atoms = 0 - (-12) = +12
The net charge on the four atoms = +12.
Find f-l.
f(x) = 4log (x-7)
Answer:
f⁻¹(x) = [tex]2^{\dfrac{x}{4} }[/tex] + 7
Step-by-step explanation:
The inverse of a function reverses the operations performed by the function in the question such if f(x) = y, then we have, f⁻¹(y) = x, which reverses the operation of the first function.
The inverse of a function f(x) = 4·㏒₂(x - 7) is found as follows;
We have;
y = 4·㏒₂(x - 7)
We substitute x for y to get;
x = 4·㏒₂(y - 7) which gives;
x/4 = ㏒₂(y - 7)
[tex]2^{\dfrac{x}{4} }[/tex] = y - 7
y = [tex]2^{\dfrac{x}{4} }[/tex] + 7
Therefore;
f⁻¹(x) = [tex]2^{\dfrac{x}{4} }[/tex] + 7.
Identify each function as linear, quadratic, or exponential. ƒ(x) = 4x2 g(x) = 1 - x h(x) = 32x
Answer:
f(x) is quadratic. g(x) and h(x) are linear.
Step-by-step explanation:
So we have the three functions:
[tex]f(x)=4x^2\\g(x)=1-x\\h(x)=32x[/tex]
Linear functions are polynomials in which the highest degree is 1.
Quadratic functions are polynomials in which the highest degree is 2.
And exponential functions usually have a variable in the exponent (e.g. 2^x).
For f(x), the highest degree is 2. Thus, f(x) is a quadratic function.
For g(x), the highest degree is 1 and there are no variables in the exponent. Thus, g(x) is a linear function.
Similarly, for h(x), the highest degree is 1 and there are no variables in the exponents, so h(x) is also a linear function.
If you're good at angles of elevation pls help meeee
Adam notices that the angle of elevation to the top of a building is 22 degrees. He walks 120m towards the building and the angle of elevation is now 28 degrees. How tall is the building?
Answer:
202m
Step-by-step explanation:
Please see attached picture for full solution.
Let x meters be the height of the building.
Use the table shown in the image! 1. Which equation expresses “y” in terms of “x”? A. y=17x B. y=25x C. x=51y D. x=85y 2. What is the charge for renting a machine for 3.5 hours? A. $51.50 B. $59.50 C. $65.50 D. $86.50
Please include all work!
Answer: 1. A. y=17x
2. $59.50
Step-by-step explanation:
1. In the table , it can be seen that as x increases y increases with the proportionality constant k = [tex]\dfrac{y}{x}=\dfrac{51}{3}=\dfrac{85}{5}=\dfrac{119}{7}=17[/tex],.
Equation of direct variation between x and y : [tex]y=kx[/tex]
Put k= 17 , we get
[tex]y=17x[/tex] , which is the required equation.
So correct option is "A".
2. To find : The charge for renting a machine for 3.5 hours.
Put x= 3.5 in above equation , we get
[tex]y=17(3.5)=59.5[/tex]
Hence, the charge for renting a machine for 3.5 hours is $59.50.
So correct option is "B".
Yan has already finished Three-fifths of the 45 math problems he was assigned today. Each math problem took him 1 four-fifths of a minute to complete. If this pace continues, how much more time, to the nearest minute, will the rest of the problems take him to finish?
Answer:
[tex]\boxed{\sf 18\ problems = 22\ minutes}[/tex]
Step-by-step explanation:
Yan has finished = [tex]\frac{3}{5} of \ 45 \ maths \ problems[/tex]
Yan has finished = [tex]\frac{3}{5} * 45[/tex]
=> 3 * 9
=> 27 problems
Yan has problem left:
=> 45 - 27
=> 18 problems
1 problem = [tex]1 \frac{4}{5}[/tex] of a minute
1 problem = 1.2 minutes
18 problems = 1.2 * 18
18 problems = 21.6 minutes
18 problems ≈ 22 minutes
Answer:
[tex]\boxed{\sf 32 \ minutes}[/tex]
Step-by-step explanation:
Yan finished 3/5 of 45 math problems.
[tex]\frac{3}{5} \times 45=27[/tex]
Yan finished 27 math problems.
[tex]\sf 1\frac{4}{5} \ of \ a \ minute= 108 \ seconds=1.8 \ minutes[/tex]
Yan has [tex]45-27=18[/tex] problems left.
1 problem = 1.8 minutes
18 problems = [tex]1.8* 18=32.4[/tex] minutes
32.4 minutes to nearest minute will be 32 minutes.
A, B, C and D lie on the circumierence of the circle.
Lengths AB and AD are equal.
Lengths BC and BD are equal.
Work out CBD.
Answer:
Step-by-step explanation:goofy
PLEASE HELP ME!! I WILL GIVE BRAINLIEST!!
Find the output, y, when the input, x, is -5.
Answer:
[tex]\boxed{y = -2}[/tex]
Step-by-step explanation:
Hey there!
To find y when x is -5 we go to -5 on the x-axis.
When at -5 find where the blue line is vertical to -5,
which is -2.
Hope this helps :)
During a certain 25-year period, the consumer price index (CPI) increased by 99%,but during the
next 25-year period, it increased by only 1%. Which of these conditions must have existed during the
second 25-year period?
A. Conflation
B. Deflation
C. Inflation
D. Stagnation
For the next 25-year period,(CPI) is increased by only 1% due to Inflation and Stagnation.
What is Stagnation ?
Stagnation is a situation of slow economic growth and relatively high unemployment (which basically means that aggregate production is reducing and some of the inputs of the economy, such capital or labor, are unemployed) , accompanied by rising prices, or inflation.
In terms of national accounting, it means a reduction in gross domestic product (GDP), with inflation (rise in all prices in the economy).
In terms of aggregate demand and supply models, stagnation is the result of a contraction of aggregate supply, which ceteris paribus, results in lower levels of production and higher prices.
Many theories have tried to explain this phenomena. Common interpretations link stagnation with and increase of the cost of production in the economy (that might be generated by an increase of gasoline for example), and its implications in the production (lower production because of higher costs), consequently unemployment and a rise of prices due to the increase of cost.
Here, During a certain 25-year period, the consumer price index (CPI) increased by 99% and during the next 25-year period, it increased by only 1% which shows slow economic growth which can be due to Inflation and Stagnation.
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Complete each congruency statement and name the rule used. If you cannot show the triangles are congruent from the given information, leave the triangle's name blank and write CNBD for "Cannot be determined" in place of the rule. GA ∩ TN = I ∆GIT ≅ ∆_____ by _____
Answer:
The correct answer is;
ΔGIT≅ ΔNIA by Side Angle Side (SAS) rule of congruency
Step-by-step explanation:
The given information are;
The point of intersection of GA ∩ TN = I
Segment TI is congruent to segment NI (Given)
Segment GI is congruent to segment IA (Given)
Angle ∠GIT is congruent to angle ∠AIN (Vertically opposite angles)
Therefore, we have;
Triangle, ΔGIT is congruent to triangle ΔNIA (Side Angle Side (SAS) rule of congruency)
Two triangles are said to be congruent by the Side Angle Side (SAS) rule of congruency, when two of the sides and the included angle (the angle in between the two sides) of one of the triangle are equal to two sides and the included angle of the other triangle.
Therefore, the correct answer is ΔGIT≅ ΔNIA by Side Angle Side (SAS) rule of congruency
Answer:
△GIT≅△AIN
By Rule: SAS
if
[tex] \sqrt{5} x = \sqrt{3} x + \sqrt{7} [/tex]
find the value of x in the form
[tex] \sqrt{ \frac{a}{b} } [/tex]
Answer:
[tex]$x=\sqrt{\frac{7(4+\sqrt{15})}{2}} $[/tex]
Step-by-step explanation:
From the way it is written, the [tex]x[/tex] is outside the square root. I will rewrite it as:
[tex]x\sqrt{5} =x\sqrt{3} +\sqrt{7}[/tex]
[tex]x\sqrt{5}-x\sqrt{3}=\sqrt{7}[/tex]
[tex]x(\sqrt{5} - \sqrt{3} )=\sqrt{7}[/tex]
[tex]$x= \frac{\sqrt{7} }{\sqrt{5} - \sqrt{3}} \implies \frac{\sqrt{7}(\sqrt{5} + \sqrt{3}) }{2} $[/tex]
[tex]$x=\frac{1}{2} \sqrt{7} (\sqrt{5} + \sqrt{3} )$[/tex]
[tex]$x=\frac{\sqrt{35}}{2} +\frac{ \sqrt{21}}{2} $[/tex]
[tex]$x=\frac{\sqrt{35}+\sqrt{21}}{2} $[/tex]
Multiply denominator and numerator by 3
[tex]$x=\frac{3\sqrt{35}+3 \sqrt{21}}{6} $[/tex]
Factor [tex]\sqrt{3}[/tex]
[tex]\sqrt{3} (\sqrt{105}+3 \sqrt{7})[/tex]
[tex]$x=\frac{\sqrt{3} (\sqrt{105}+3 \sqrt{7})}{6} $[/tex]
Divide denominator and numerator by [tex]\sqrt{3}[/tex]
[tex]$x=\frac{\sqrt{105}+3 \sqrt{7}}{2\sqrt{3} } $[/tex]
Let's rewrite it again
[tex]$x=\frac{\sqrt{ (\sqrt{105}+3 \sqrt{7})^2}}{\sqrt{12} } $[/tex]
[tex]$x=\sqrt{ \frac{1}{12} \cdot (\sqrt{105}+3 \sqrt{7})^2}$[/tex]
It is already in the form [tex]$\sqrt{\frac{a}{b} } $[/tex]
Expanding the perfect square, we have
[tex]63+42\sqrt{15}+105[/tex]
[tex]$\frac{63}{12} +\frac{42\sqrt{15}}{12} +\frac{105}{12} $[/tex]
[tex]$\frac{21}{4} +\frac{7\sqrt{15}}{2} +\frac{35}{4} $[/tex]
Factor [tex]$\frac{7}{2} $[/tex]
[tex]$\frac{7}{2} (4+\sqrt{15} )$[/tex]
Therefore,
[tex]$x=\sqrt{\frac{7}{2} \left(4+\sqrt{15} \right)} $[/tex]
[tex]$x=\sqrt{\frac{7(4+\sqrt{15})}{2}} $[/tex]
Choose the correct description of the graph of the compound inequality 3x + 1 > 10 and 4x less than or equal to 20 (1 point) A number line with an open circle on 3, a closed circle on 5, and shading in between A number line with an open circle on 3, shading to the left, and a closed circle on 5, shading to the right A number line with a closed circle on 3, shading to the left, and an open circle on 5, and shading to the right A number line with a closed circle on 3, an open circle on 5, and shading in between
Answer:
A number line with an open circle on 3, a closed circle on 5, and shading in between
Step-by-step explanation:
The solution to the first inequality is ...
3x +1 > 10
3x > 9 . . . . . subtract 1
x > 3 . . . . . . divide by 3
__
The solution to the second inequality is ...
4x ≤ 20
x ≤ 5 . . . . . divide by 4
__
The solution set is then ...
3 < x ≤ 5
This is represented by a graph with an open circle at 3, a closed circle at 5, and shading between.
How many units away is 1 from -6 on a number line?
Answer:
7 units
Step-by-step explanation:
(number line:)
<- -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ->
←there are 7 units from 1 to -6 (you don't count the 0)
(I'm not sure if you understood my explanation, but I do am sure about the answer, so if there is something you didn't understand let me know, and which part are you confused about so I can help you out!)
Answer:
[tex]\huge\boxed{\sf 7\ units}[/tex]
Step-by-step explanation:
To find that how much far they are from each other, we can subtract both of them.
=> 1 - (-6)
=> 1 + 6
=> 7 units
So, they are 7 units apart from each other.
Which equation could you use to solve for x in the proportion StartFraction 4 over 5 EndFraction = StartFraction 9 over x EndFraction?
Answer:
x = 9x5 / 4
x = 45/4
(either one)
Step-by-step explanation:
[tex]\frac{4}{5}[/tex] = [tex]\frac{9}{x}[/tex]
Multiple known diagonals and divide by number opposite to unknown number (x).
Hope that helped!!! k
Answer:
(b) 4 x = 4 5 is the needed expression to solve for the value of x.
Step-by-step explanation:
Here, the given proportion is simplified as:
4/5=9/x
Now, to simplify any proportion of the form the simplest way is cross multiplication.
So, cross multiplying a/b=c/d -> ad=bc
Similarly cross multiplying 4/5=9/x, we get:
4 (x) = (9) (5)
can somewon plz help me
Answer:
1253 in^3
Step-by-step explanation:
The volume of the smaller container is (7 in)(5 in)(5 in) = 175 in^3.
The volume of the larger one is (11 in)(14 in)(7 in) = 1078 in^3
The total volume is the sum of these two volumes: 1253 in^3
Answer:
1253 in^3
Step-by-step explanation:
Volume of small one is 7*5*5 = 175
Volume of the large one is 11*14*7 = 1078
To find the total volume we add them up. We get 1253 and since we are talking about volume it is 1253 inches cubed
(will give brainliest) find the value of x
Answer:
x = 180 - [(180 - 3x) + (180 - 2x)]
Step-by-step explanation:
Start off by finding the angles of the triangle
Angle F = 180 - 3x
The angle across from I (which I will call I) = 180 - 2x
Angle G = 180 - (F + I)
Now that we know what G is, we know what x is because the Alternate Exterior Angles Theorem states that if a pair of parallel lines are cut by a transversal, then the alternate exterior angles are congruent. So pretty much X = G
Therefore x = 180 - (F + I) or otherwise said as:
x = 180 - [(180 - 3x) + (180 - 2x)]
I hope this is helpful :)
A fair coin is flipped 32 times. Let X be the number of heads. What normal distribution best approximates X?
Answer:
you can land on heads a possibility of 16 times
Step-by-step explanation:
6.01 what is the value of the expression 2 + 3² • (4 - 1)
Answer:
29
Step-by-step explanation:
using pemdas, you first need to solve 3² which is 9. Then you do what's in the parenthesis (4-1) which is 3. you'll first multiply 9 and 3 (27) add the 2 and there's your answer, 29.
In which of the following cases would the quantity 'q' decrease proportionally when the quantity 'p' is increased?
a) P = 3 x q
b) p-3=q
c) p=3/q
d) 1/p=3/q
Please give me the correct answer along with the explanation and I shall mark you as the brainliest. Please answer ASAP, it's urgent
Answer:
c) p = 3/q
Step-by-step explanation:
If 3 is divided by a smaller number "q", then it would result in a larger number "p".
Example:
1. Substitute 3 for "q"
3/3 = 1
q = 3
p = 1
2. Substitute 1 for "q"
3/1 = 3
q = 1
p = 3
When "q" decreased, "p" increased.
Step-by-step explanation:
c) p=3/q
i can confirm after 10.30