Answer:
The answer is, t = 28.
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
1
8
t+
−5
2
=1
Step 2: Add 5/2 to both sides.
1
8
t+
−5
2
+
5
2
=1+
5
2
1
8
t=
7
2
Step 3: Multiply both sides by 8.
8*(
1
8
t)=8*(
7
2
)
t=28
Help me on this please thank you
Answer:
A. ∠ABC ≅ ∠DBE
Step-by-step explanation:
The whole proof is not shown, but in order to show the triangles similar, one would need to (a) show the sides are proportional, and (b) show the included angle is the same. The portion of the proof that is shown is on the way to showing side lengths are proportional. The missing part for showing triangle similarity is the congruence statement for angle B, as shown above.
__
Once the triangles are shown to be similar, additional work is needed to show DE║AC. At least one pair of corresponding "base" angles must be shown congruent, too.
Parabolas y=3x2 and y=−3x2+k intersect at points M and N that are in the first and the second quadrants respectively. Find k if length of the segment MN is 6.
Answer:
[tex]k=54[/tex]
Step-by-step explanation:
Find the coordinates of points M and N in terms of k. Solve the system of two equations:
[tex]\left\{\begin{array}{l}y=3x^2\\ \\y=-3x^2+k\end{array}\right.\Rightarrow \left\{\begin{array}{l}y=3x^2\\ \\y=-y+k\end{array}\right.\\ \\2y=k\\ \\y=\dfrac{k}{2}\\ \\\dfrac{k}{2}=3x^2\\ \\x^2=\dfrac{k}{6}\\ \\x=\pm\sqrt{\dfrac{k}{6}}[/tex]
Two points have the coordinates [tex]M\left(\sqrt{\dfrac{k}{6}},\dfrac{k}{2}\right)[/tex] and [tex]N\left(-\sqrt{\dfrac{k}{6}},\dfrac{k}{2}\right)[/tex]
Find the distance between M and N:
[tex]MN=\sqrt{\left(\sqrt{\dfrac{k}{6}}-\left(-\sqrt{\dfrac{k}{6}}\right)\right)^2+\left(\dfrac{k}{2}-\dfrac{k}{2}\right)^2}=\sqrt{4\dfrac{k}{6}}=\sqrt{\dfrac{2k}{3}}[/tex]
Since MN = 6, you have
[tex]\sqrt{\dfrac{2k}{3}}=6\\ \\\dfrac{2k}{3}=36\\ \\2k=108\\ \\k=54[/tex]
Write a quadratic function whose zeros are -5 and -6
Final answer:
A quadratic function with zeros at -5 and -6 can be written as f(x) = (x + 5)(x + 6), which expands to f(x) = x² + 11x + 30.
Explanation:
To write a quadratic function whose zeros are -5 and -6, you start by remembering that if α and β are the zeros of a quadratic function, the function can be written as f(x) = a(x - α)(x - β) where a is a nonzero coefficient. In this case, -5 and -6 are the zeros, so our function is f(x) = a(x + 5)(x + 6).
For simplicity, if we choose a to be 1, the quadratic function simplifies to
f(x) = (x + 5)(x + 6)
f(x) = x² + 11x + 30.
Therefore, the quadratic function with zeros at -5 and -6 is f(x) = x² + 11x + 30.
PLEASE HELP!!! 45 PTS AND BRAINLIEST!!!
1) Complete the work for each method below:
Method A: Given f(x) = 3x - 4 and g(x) = x+4/3
Show that these are inverse functions by finding f^-1 (x) and showing that it is the same as g(x)
Method B: Given f(x) = 3x - 4 and g(x) = x+4/3
Show that these are inverse functions by showing that when the output of one function is used for the input of the other function, the final output is equal to the original input value. (you may choose any initial input)
Method C: Given f(x) = 3x - 4 and g(x) = x+4/3
Verify that these are the inverse function by showing that f(g(x)) = x AND g(f(x)) = x
Answer:
See explanation!
Step-by-step explanation:
Let us first give some principle theory to aid our solution.
Considering two functions [tex]A(x)[/tex] and [tex]B(x)[/tex], in order to show that function
which is the inverse of [tex]y=ax[/tex].
Now let as solve our problem. We are given the following:
[tex]f(x)=3x-4\\g(x)=\frac{x+4}{3}[/tex]
Method A: Show that these are inverse functions by finding f^-1 (x) and showing that it is the same as g(x).
Let us take [tex][f(x)=y]=3x-4[/tex] and "exchanging" our variables we have
[tex]x=3y-4\\x+4=3y\\\\y=\frac{x+4}{3}[/tex]
which is exactly the same with our given function of [tex]g(x)=\frac{x+4}{3}[/tex], so proved!
Method B: Show that these are inverse functions by showing that when the output of one function is used for the input of the other function, the final output is equal to the original input value. (you may choose any initial input)
For this case we will use a simple input let us say [tex]x=1[/tex]. Thus taking the [tex]f(x)[/tex] function and plugging in we have:
[tex]f(x=1) = 3(1)-4\\f(1)=3-4\\f(1)=-1[/tex]
Now let us take the output of [tex]f(1)[/tex] which is [tex]-1[/tex] and use it the input to our second function of [tex]g(x)[/tex], so we have:
[tex]g(x=-1) = \frac{(-1)+4}{3}\\ \\g(-1)=\frac{3}{3}\\ \\g(-1)=1[/tex]
so the output of the second function is equal to the original input value of the first function, hence proved!
Method C: Verify that these are the inverse function by showing that f(g(x)) = x AND g(f(x)) = x.
Basically we are asked to prove that both [tex]f(g(x))=g(f(x))=x[/tex]
To do so, we just replace one function into the [tex]x[/tex] value of the other function as follow:
[tex]f(g(x))=3(\frac{x+4}{3} )-4\\\\f(g(x))=x+4-4\\\\f(g(x))=x[/tex]
Lets repeat now for the opposite as follow:
[tex]g(f(x))=\frac{(3x-4)+4}{3}\\ \\g(f(x))=\frac{3x}{3}\\ \\g(f(x))=x[/tex]
Hence proved!
Addie walked 2 1/2 miles in 45 minutes. Suzie covered 2 2/5 miles in 2/3 of an hour.
What was Addie's speed?
Addie's speed was [tex]3\frac{1}{3}\ mph[/tex]
Step-by-step explanation:
Given,
Distance walked by Addie = [tex]2\frac{1}{2}=\frac{5}{2}\ miles[/tex]
Time taken by Addie = 45 minutes
Converting the time into hours;
1 hour = 60 minutes
45 minutes = [tex]\frac{45}{60}=\frac{3}{4}\ hour[/tex]
Distance = Speed * Time
Speed = Distance/Time
Speed = [tex]\frac{5}{2} / \frac{3}{4}[/tex]
Speed = [tex]\frac{5}{2}*\frac{4}{3} = \frac{10}{3}\ mph[/tex]
Speed = [tex]3\frac{1}{3}\ mph[/tex]
Addie's speed was [tex]3\frac{1}{3}\ mph[/tex]
Keywords: speed, distance
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Answer fast I think is b
Answer:
b
Step-by-step explanation:
yes it b because it goes origion and it not a zero pair
Broccoli costs $1.50 per pound at the store. How much money does 32 ounces of the broccoli cost
Answer:No
Step-by-step explanation:
Which would be the best trend line for the given data set?
y=-3/2x+8
y=3/2x+5
y=2/3x+8
y=-2/3x+5
y=-2/3x+5
Step-by-step explanation:
From the scattered plot, it is evident that the line of best fit will have a negative slope from the way the plots are aligned.
Selecting the line of best fit that will cut the y axis at +5, the points can be estimated as;
(5,1.5) and (3.5,2.5)
The slope can be found as;
m=Δy/Δx
m=2.5-1.5/3.5-5 =1.0/ -1.5 = -0.67
Finding the equation as;
m=Δy/Δx
-0.66 = y-2.5/x-3.5
-0.66(x-3.5) = y-2.5
-0.66x+2.3=y-2.5
-0.66x+2.3+2.5=y
-0.66x+4.7=y
⇒⇒ y= -0.66 x + 4.7
⇒⇒y= -2/3 x + 5
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Keywords: best trend line, data set
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A taxi service charges a flat fee of $1.25 and $0.75 per mile. If Henri has $14.00, which of the following shows the number of miles he can afford to ride in the taxi?
m less-than-or-equal-to 17
m greater-than-or-equal-to 17
m less-than-or-equal-to 20.3
m greater-than-or-equal-to 20.3
Answer:
Option A M<17 m is less than or equal to 17
Step-by-step explanation:
Answer:
A.
Step-by-step explanation:
Which equation has a slope of -5/2 and a y-intercept of -2
[tex]\bf \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \implies y = \stackrel{\stackrel{m}{\downarrow }}{-\cfrac{5}{2}}x\stackrel{\stackrel{b}{\downarrow }}{-2}[/tex]
12) Cost of a hat: $39.95
Markup: 10%
Discount: 50%
Tax: 4%
Answer:
22.77
Step-by-step explanation:
39.95 * 1.14 (tax + markup) * 0.5 (discount) = 22.77 (rounded)
Simplify the following expression.
-7x² - 5x-6x² +4 + 15x
Answer: -13x^2 + 10x + 4
Step-by-step explanation:
group all of the same variables together to simplify the equation.
-7 - 6 = -13 // the x^2 value
-5 + 15 = 10 // the x value
4 is the only number without an exponent so leave it alone.
Answer:
-13x²+10x+4
Step-by-step explanation:
You need to group all of the same variables together:
-7x² - 5x - 6x² + 4 + 15x
-7x²-6x²-5x+15x+4
-13x²+10x+4
Graph the equation y = -6x + 12
Answer:
The three points for the line y = -6x + 12 ...Red color line
point A( x₁ , y₁) ≡ ( 0 , 12) (blue color point on the graph)
point B( x₂ , y₂) ≡ (2 , 0) (green color point on the graph)
point C(x₃ , y₃ ) ≡ (1 , 6) (purple color point on the graph)
The Graph is attached below.
Step-by-step explanation:
Given:
[tex]y = -6x +12[/tex] ........... equation of a line
Let the points be point A, point B, and point C
To Find:
point A( x₁ , y₁) ≡ ?
point B( x₂ , y₂) ≡ ?
point C(x₃ , y₃ ) ≡ ?
Solution:
For Drawing a graph we require minimum two points but we will have here three points.
For point A( x₁ , y₁)
Put x = 0 in the given equation we get
y = 0 + 12
y = 12
∴ point A( x₁ , y₁) ≡ ( 0 , 12)
For point B( x₂ , y₂)
Put y= 0 in the given equation we get
0 = -6x + 12
6x = 12
[tex]x=\dfrac{12}{6}=2[/tex]
∴ point B( x₂ , y₂) ≡ (2 , 0)
For point C(x₃ , y₃ )
Put x = 1 in the given equation we get
y = -6 × 1 + 12
y = 6
∴ point C(x₃ , y₃ )≡ (1 , 6)
Therefore,
The three points for the line -2y = -x + 8 are
point A( x₁ , y₁) ≡ ( 0 , 12) (blue color point on the graph)
point B( x₂ , y₂) ≡ (2 , 0) (green color point on the graph)
point C(x₃ , y₃ ) ≡ (1 , 6) (purple color point on the graph)
The Graph is attached below..
What is the vertex of g (x)=-3x^2+18x+2
Answer:
vertex=?
Step-by-step explanation:
given data:
g(x)=-3x^2+18x+2
find values of a,b,c:from the given equation
a=-3,b=18,c=2
x-value of the vertex:x=-b/2a
x=-(18)/2(-3)
x=3
y-value of the vertex:
put value of x in the given equation
y=-3(3)^2+18(3)+2
y=-27+54+2
y=29
Write down the x and y values as an ordered pair.
x=3 y=29
(3,29)
How can you use equivalent fractions to know that 43/200 is between 1/5 and 1/4
The fraction 43/200 is evidently between 1/5 and 1/4 from equivalent fractions.
A fraction which is equivalent to 1/5 with denominator, 200 is; 40/200.A fraction which is equivalent to 1/4 with denominator, 200 is; 50/200.Im essence, since 43 lies between, 40 and 50;
The fraction 43/200 in turn lies between fractions 1/5 and 1/4.
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Rearrange so x is independent variable. -4x-6=-5y+9
[tex]\text{Solve for x:}\\\\-4x-6=-5y+9\\\\\text{Add 6 to both sides}\\\\-4x=-5y+15\\\\\text{Divide both sides by -4}\\\\\boxed{x=\frac{5}{4}y-\frac{15}{4}}[/tex]
HELPP ITS DUE TOMORROW
x° = 10°
Solution:
In the given figure the angle L represents 90°.
The center ray splits 90° into two angles.
(3x + 6)° + (5x + 4)° = 90°
⇒ 3x° + 6° + 5x° + 4° = 90°
Combine like terms together.
⇒ 3x° + 5x°+ 6° + 4° = 90°
⇒ 8x°+ 10° = 90°
Subtract 10° on both sides of the equation.
⇒ 8x°+ 10° – 10° = 90° – 10°
⇒ 8x° = 90° – 10°
⇒ 8x° = 80°
Divide by 8 on both sides of the equation.
⇒ x° = 10°
Hence, the value of x° = 10°.
Find the required measurements of the following trapezoids.
a=8 cm
b= 16 cm
h=12 cm
Compute the area.
cm2
Answer:
Area of trapezoid = 144 cm²
Step-by-step explanation:
The length of parallel sides are,
a = 8 cm
b = 16 cm
h = 12 cm
Formula area of trapezoid:-
[tex]A=\dfrac{1}{2}(a+b)\times h[/tex]
[tex]A=\dfrac{1}{2}(8+16)\times 12[/tex]
[tex]A=144[/tex]
Hence, the area of trapezoid is 144 cm²
Answer:
Hence, the area of trapezoid is 12 cm²
Step-by-step explanation:
10x-7x=12 how to solve this
Answer:
x=4
Step-by-step explanation:
10x-7x=12
3x=12
divide both sides by 3
x=4
Answer: x = 4
Step-by-step explanation: To solve this equation, we can first combine our like terms on the left side of the equation which are the x's.
10x - 7x = 3x so we now have the equation 3x = 12.
Now to solve for x, we want to get x by itself on the left side of the equation. Since x is being multiplied by 3, to get x by itself, we need to divide by 3 on the left side of the equation. Since we divided by 3 on the left side, we must also divide by 3 on the right side.
On the left side, notice that the 4's cancel out so we're simply left with x. On the right side we have 12 divided by 3 which is 4 so x = 4.
Finally, remember to check your answer by substituting a 4 back into the original equation.
So we have 10(4) - 7(4) = 12 or 40 - 28 = 12 or 12 = 12.
Since this a true statement, we know our answer is correct.
Remember to show all your work when solving equations.
Which expression is equivalent to 8/15?
A. 8÷1/5
B. 8÷15
C. 15÷1/8
D. 15÷8
Answer:B
Step-by-step explanation:
a rectangular blue tile has a length of 4.25 inches and a width of 6.75 inches. a similar tile has a length of 12.75 inches.what is the width of the red tile.
Answer:
The width of the red tile would be [tex]2.25[/tex] inches.
Step-by-step explanation:
Given blue tile has a length of [tex]4.25[/tex] inches, and a width of [tex]6.75[/tex]inches.
Also, length of similar tile is [tex]12.75[/tex] inches.
Let us assume [tex]x[/tex] as the width of red tile.
It is given in the question that both tiles are similar.
So, their area will be the same.
Area of blue tile would be [tex]4.25\times 6.75=28.6875\ inch^2[/tex]
Area of red tile would be [tex]12.75\times x[/tex]
The area of blue tile would be equal to area of red tile.
[tex]28.6875=12.75\times x[/tex]
[tex]\frac{28.6875}{12.75}=x\\\\x=2.25[/tex]
So, the width of the red tile would be [tex]2.25[/tex] inches.
6 times the sum of a number and 5
Answer:
6(x+5)
Step-by-step explanation:
Answer: 6 x (x+5)
Step-by-step explanation: Since it is six times a number AND five, you want to do the addition equation first. To show this you place parentheses around a variable (x) plus 5. You add six in front of this because it comes first in the word problem.
Find the value of x. Round your answer to the nearest tenth.
A.) 52.6
B.) 52.9
C.) 6.2
D.) 6.5
Answer:
6.2
Step-by-step explanation:
sin 20 = x/18
solve for x
A bag contains 18
red gumballs and 6
yellow gumballs.
Without looking,
what is the
probability that you
will randomly
choose yellow
gumball?
Answer:
There are 24 gumballs, 6 of which are yellow.
P(yellow) = 6/24 = 1/4
Sally has $40,000 to invest some money at 9% interest and the rest at 11%. If her total annual income from these two investments is $4,300, how much does she invest at
a = amount invested at 9%
b = amount invested at 11%
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hfill \stackrel{\textit{9\% of "a"}}{\left( \cfrac{9}{100} \right)a\implies 0.09a}~\hfill \stackrel{\textit{11\% of "b"}}{\left( \cfrac{11}{100} \right)b\implies 0.11b}[/tex]
we know she has a total of $40,000 to invest, so, if she invested "a" amount in one, the other quantity must be the slack left from 40,000 and "a", namely b = 40000 - a.
we also know that the yield or earned interest from both amounts is 4300, thus
[tex]\bf \stackrel{\textit{yield of "a"}}{0.09a}~~+~~\stackrel{\textit{yield of "b"}}{0.11b}~~=~~\stackrel{\textit{annual income from both}}{4300} \\\\\\ \stackrel{\textit{yield of "a"}}{0.09a}~~+~~\stackrel{\textit{yield of "b"}}{0.11(40000-a)}~~=~~4300 \\\\\\ 0.09a+4400-0.11a = 4300\implies -0.02a+4400 = 4300 \\\\\\ 4400=4300+0.02a\implies 100=0.02a\implies \cfrac{100}{0.02}=a\implies \boxed{5000=a} \\\\\\ \stackrel{\textit{we know that}}{b = 40000-a}\implies \boxed{b = 35000}[/tex]
At Elmwood Middle School there are 4 teachers for every 68 students. There are 425 students enrolled at the school. How many teachers are needed?
The number of teachers required for the 425 students that enrolled at the school is 25.
What are ratio and proportion?A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.
At Elmwood Middle School there are 4 teachers for every 68 students.
There are 425 students enrolled at the school.
Let the number of teachers be x required for the 425 students will be
[tex]\rm \dfrac{x}{4} = \dfrac{425}{68}\\\\x \ = \dfrac{425*4}{68}\\\\x \ = 25[/tex]
The number of teachers required for the 425 students that enrolled at the school is 25.
More about the ratio and the proportion link is given below.
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Approximately 25 teachers are needed at Elmwood Middle School. So the correct option is c) 25.
To find out how many teachers are needed at Elmwood Middle School, we can set up a proportion using the given ratio of teachers to students.
Given:
- There are 4 teachers for every 68 students.
Let's set up the proportion:
[tex]\[\frac{\text{Number of teachers}}{\text{Number of students}} = \frac{4}{68}\][/tex]
We know there are 425 students enrolled at the school, so let's find out how many teachers are needed:
[tex]\[\text{Number of teachers} = \frac{4}{68} \times 425\][/tex]
[tex]\[\text{Number of teachers} = \frac{4 \times 425}{68}\][/tex]
[tex]\[\text{Number of teachers} = \frac{1700}{68}\][/tex]
[tex]\[\text{Number of teachers} \approx 25\][/tex]
So, approximately 25 teachers are needed at Elmwood Middle School.
Therefore, the answer is option C. 25.
The complete question is:
At Elmwood Middle School there are 4 teachers for every 68 students. There are 425 students enrolled at the school. How many teachers are needed? A. 17 B. 21 C. 25 D. 28
what is the solution of y= -5x + 1 and y= 3x - 2
Answer:
x=3/8, y=-7/8. (3/8, -7/8).
Step-by-step explanation:
y=-5x+1
y=3x-2
----------
-5x+1=3x-2
-5x-3x+1=-2
-8x+1=-2
-8x=-2-1
-8x=-3
8x=3
x=3/8
y=3(3/8)-2=9/8-2=9/8-16/8=-7/8
Y=3/4x
5/2x+2y=5
Show work
Answer:
x = 5/4
y = 15/16
Step-by-step explanation:
We are given y = 3/4x
and 5/2x +2y = 5
Substituting the value y=3/4 x in second equation we get
5/2x + 2(3/4)x = 5
8/2x = 5
4x = 5
and so , x = 5/4
substituting value of x in y = 3/4x we get,
y = 3/4 (5/4)
So, y = 15/16
which are the required values of x and y on solving the two given equations.
The solution to the equation is (5/4, 15/16)
Given the system of equations
Y=3/4x 5/2x+2y=5Substitute equation 1 into 2 to have:
5/2x + 2(3/4x) = 5
5/2x + 3/2x = 5
8/2x = 5
4xx = 5
x = 5/4
Snce y = 3/4x
y = 3/4(5/4)
y = 15/16
Hence the solution to the equation is (5/4, 15/16)
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What expression is equivalent to 5(3-2n)+12n ?
Break it down please
Answer: Order if operations
Step-by-step explanation:
15-10n+12n
15+12n
The diagram shows triangle ABC.
ADB is a straight line.
The size of angle DCB: The size of angle ACD=2:1
Work out the size of angle BDC.
=======================================================
Explanation:
Check out figure 1 which is one of the attached images below.
In this diagram, I have angle A as 75 degrees and angle B as 51 degrees.
Angle C is therefore, C = 180-A-B = 180-75-51 = 54 degrees.
----------
Point D is somewhere between A and B such that it is on segment AB.
Figure 2 (also attached as an image) shows segment CD forming two angles DCB and ACD.
These are the blue and red angles respectively, such that the blue angle is twice as large as the red angle.
blue angle = 2*(red angle)
This is what it means when it says the ratio of the two angles is 2:1.
I have 2x as the blue angle and x as the red angle. We don't know what x is yet, but we do know that the x and 2x combine back to angle C = 54 degrees.
So,
(angle DCB) + (angle ACD) = angle C
(2x) + (x) = 54
3x = 54
x = 54/3
x = 18
Since x = 18, this means 2*x = 2*18 = 36
Therefore,
angle DCB = 2x = 36 degrees
angle ACD = x = 18 degrees
--------
Focus solely on triangle DCB. We found angle DCB = 36 degrees and we know that angle DBC = 51
The remaining angle y = angle BDC is...
(angle BDC)+(angle DCB)+(angle DBC) = 180
(y)+(36)+(51) = 180
y+87 = 180
y+87-87 = 180-87
y = 93
angle BDC = 93 degrees
Figure 3 shows the angles we found (basically I replaced x, 2x and y with their respective numbers).
The size of angle BDC is 0 degrees.
To find the size of angle BDC, you can use the fact that the sum of the angles in a triangle is always 180 degrees. Since angle ACD is 1 part and angle DCB is 2 parts, we can express their sizes as:
Angle ACD = x degrees
Angle DCB = 2x degrees
Now, you know that the sum of the angles in triangle ABC is 180 degrees. So, you can write the equation:
x (angle ACD) + 2x (angle DCB) + 180 degrees (angle BDA) = 180 degrees
Now, simplify and solve for x:
x + 2x + 180 = 180
Combine like terms:
3x + 180 = 180
Now, subtract 180 from both sides of the equation:
3x = 0
Finally, divide by 3:
x = 0
Now that you know the value of x, you can find the size of angle BDC (2x):
Angle BDC = 2x = 2(0) = 0 degrees
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