Answer:
D x=15
Step-by-step explanation:
3(2x+5)=3x+4x
Distribute the 3
6x +15 = 3x+4x
Combine like terms
6x+15 = 7x
Subtract 6x from each side
6x+15 -6x = 7x-6x
15 =x
What is the simplified form of the following expression? 5sqrt 8-sqrt18-2sqrt2
Answer:
5 sqrt2.
Step-by-step explanation:
sqrt8 = sqrt4 * sqrt2 = 2 sqrt2
sqrt18 = sqrt9 * sqrt2 = 3 sqrt2
So simplifying:
5sqrt 8 - sqrt18 - 2 sqrt2
= 5*2sqrt2 - 3 sqrt 2 - 2 sqrt2
= 10 sqrt2 - 5 sqrt2
= 5 sqrt2 (answer).
For this case we must simplify the following expression:
[tex]5 \sqrt {8} - \sqrt {18} -2 \sqrt {2}[/tex]
Rewriting we have:
[tex]8 = 2 * 2 * 2 = 2 ^ 2 * 2\\18 = 9 * 2 = 3 ^ 2 * 2\\5 \sqrt {2 ^ 2 * 2} - \sqrt {3 ^ 2 * 2} -2 \sqrt {2} =[/tex]
We have that by definition of properties of roots and powers it is fulfilled:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]5 * 2 \sqrt {2} -3 \sqrt {2} -2 \sqrt {2} =\\10 \sqrt {2} -3 \sqrt {2} -2 \sqrt {2} =\\10 \sqrt {2} -5 \sqrt {2} =\\5 \sqrt {2}[/tex]
Answer:
[tex]5 \sqrt {2}[/tex]
What is the area of the polygon below?
A. 147 square units
B. 111 square units
C. 156 square units
D. 120 square units
Area of the given polygon is required.
The area of the polygon is A. [tex]147\ \text{square units}[/tex]
The polygon is a rectangle with one corner of the rectangle removed.
The removed area is a square.
The area of the complete rectangle is
[tex]13\times 12=156\ \text{square units}[/tex]
Area of the removed square
[tex]3\times 3=9\ \text{square units}[/tex]
The area of the polygon is
[tex]156-9=147\ \text{square units}[/tex]
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Plzzzz help me on this questions fast
This is Trigonometry
Answer:
x ≈ 20.42, y ≈ 11.71
Step-by-step explanation:
Using the cosine ratio on the right triangle on the right, that is
cos20° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{11}{y}[/tex]
Multiply both sides by y
y × cos20° = 11 ( divide both sides by cos20° )
y = [tex]\frac{11}{cos20}[/tex] ≈ 11.71
Using the sine ratio on the right triangle on the left, that is
sin35° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{x}[/tex] = [tex]\frac{11.71}{x}[/tex]
Multiply both sides by x
x × sin35° = 11.71 ( divide both sides by sin35° )
x = [tex]\frac{11.71}{sin35}[/tex] ≈ 20.42
Answer:
x = 20.41 units, y = 11.71 units to the nearest hundredth.
Step-by-step explanation:
Consider the small triangle:
cos 20 = 11/y
y = 11 / cos 20
= 11.706 units.
Now the larger triangle:
sin 35 = 11.706 / x
x = 11.706 / sin 35
x = 20.409 units.
Write the slope-intercept form of the equation that passes through the point (-2, 3) and is parallel to the line y = -6x - 9 y = 1/6x - 1 y = 6x - 9 y = -6x - 1 y = -6x - 9
Answer:
y = -6x - 9Step-by-step explanation:
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept
Parallel lines have the same slope.
===========================================
We have y= -6x - 9 → m = -6
Put the value of a slope and the coordinates of the point (-2, 3) to the equation of a line:
3 = -6(-2) + b
3 = 12 + b subtract 12 from both sides
-9 = b → b = -9
Finally:
y = -6x - 9
What square root of 9 is less than 2 squared
The square root of 9 is 3, but the negative square root of 9, which is -3, is less than 2 squared (4). Therefore, the answer to the question is -3.
Explanation:The square root of 9 is 3. We denote the square root symbolically as √9 = 3. However, if we're looking for which square root of 9 is less than 2 squared (which is 4), we consider that every positive number has two square roots: one positive and one negative. The negative square root of 9 is -3, which is indeed less than 4. Therefore, the square root of 9 that is less than 2 squared is -3.
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1. Given the functions f(x)=3x-4 and g(x)=4x+10, find the value of x for which f(x) = g(x)
A. 2
B. -2
C. -6
D. -14
Answer:
answer is D
Step-by-step explanation:
3x-4=4x+10
3x=4x+14
-1x=14
x= -14
Answer:
-14
Step-by-step explanation:
It's multiple choice so we could plug in values of x and see which makes f(x)=g(x) true.
What I mean is would could plug in values of x to see which gives us
3x-4=4x+10 is true.
Or we could just solve it.
3x-4=4x+10
Subtract 3x on both sides:
-4=1x+10
-4=x+10
Subtract 10 on both sides:
-14=x
So x=-14 would make f(x)=g(x) hold.
Let's check it and see!
f(-14)=3(-14)-4=-42-4=-46.
g(-14)=4(-14)+10=-56+10=-46.
They have the same value of -46 so x=-14 is certainly going to make f(x)=g(x) be true.
Which is an equation of the line passing
through the point (10, 8) with a slope of 2/5?
Multiple choice:
(1): y=2/5x+4
(2):y=2/5x+8
(3):y=2/5x+12
(4):y=2/5x
The multiple choices are in fraction and please help
[tex]\bf (\stackrel{x_1}{10}~,~\stackrel{y_1}{8})~\hspace{10em} slope = m\implies \cfrac{2}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-8=\cfrac{2}{5}(x-10) \\\\\\ y-8=\cfrac{2}{5}x-4\implies y=\cfrac{2}{5}x+4[/tex]
The coordinates G(7, 3), H(9, 0), I(5, -1) form what type of polygon?
an obtuse triangle
Answer:
Is an acute triangle
Step-by-step explanation:
we have
[tex]G(7, 3),H(9, 0),I(5, -1)[/tex]
so
The polygon is a triangle
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Remember that
If applying the Pythagoras Theorem
[tex]c^{2}=a^{2}+b^{2}[/tex] -----> is a right triangle
[tex]c^{2}>a^{2}+b^{2}[/tex] -----> is an obtuse triangle
[tex]c^{2}<a^{2}+b^{2}[/tex] -----> is an acute triangle
where
c is the greater side
step 1
Find the distance GH
[tex]G(7, 3),H(9, 0),I(5, -1)[/tex]
substitute
[tex]d=\sqrt{(0-3)^{2}+(9-7)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(2)^{2}}[/tex]
[tex]GH=\sqrt{13}\ units[/tex]
step 2
Find the distance HI
[tex]G(7, 3),H(9, 0),I(5, -1)[/tex]
substitute
[tex]d=\sqrt{(-1-0)^{2}+(5-9)^{2}}[/tex]
[tex]d=\sqrt{(-1)^{2}+(-4)^{2}}[/tex]
[tex]HI=\sqrt{17}\ units[/tex]
step 3
Find the distance GI
[tex]G(7, 3),H(9, 0),I(5, -1)[/tex]
substitute
[tex]d=\sqrt{(-1-3)^{2}+(5-7)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(-2)^{2}}[/tex]
[tex]GI=\sqrt{20}\ units[/tex]
step 4
Let
[tex]c=GI=\sqrt{20}\ units[/tex]
[tex]a=HI=\sqrt{17}\ units[/tex]
[tex]b=GH=\sqrt{13}\ units[/tex]
Find [tex]c^{2}[/tex] ------> [tex]c^{2}=(\sqrt{20})^{2}=20[/tex]
Find [tex]a^{2}+b^{2}[/tex] ----> [tex](\sqrt{17})^{2}+(\sqrt{13})^{2}=30[/tex]
Compare
[tex]20 < 30[/tex]
therefore
Is an acute triangle
-36+(-9)+14+(-31)-(-66)
Answer:
4
Step-by-step explanation:
−36−9+14−31−(−66)
=−45+14−31−(−66)
=−31−31−(−66)
=−62−(−66)
=4
If a diameter intersects a chord of a circle at a right angle, what conclusion can be made?
The chord is bisected.
The diameter is bisected.
The diameter and the chord are congruent.
The diameter is twice as long as the chord.
Answer:
The chord is bisected.
Step-by-step explanation:
see the attached figure to better understand the problem
In the circle of the figure
The diameter is the segment DE
The chord is the segment AB
PA=PB=r ----> radius of the circle
Triangles PAC and PBC are congruent right triangles by SSS
Because
PA=PB
PC is a common side
AC=BC ----> Applying Pythagoras Theorem
therefore
The chord AB is bisected
Answer:
The chord is bisected
Step-by-step explanation:
I Need The Answer Plz I’m Failing Plz
Answer:
M<A is less than or equal to 90°
Step-by-step explanation:
If it is less than or equal to, then the first statement has to be false, that it is greater. This means the statement is negated because they can't work together.
What is the slope of a line perpendicular to this line? What is the slope of a line parallel to this line?
Consider the line7X-6Y=-5
Answer:
See below in bold.
Step-by-step explanation:
Convert the equation into slope-intercept form:
7x - 6y = -5
6y = 7x + 5
y = (7/6) x + 5/6
- so the slope is 7/6.
The slope of a line parallel to this has the same slope 7/6.
The slope of a line perpendicular to this has a slope of - 1 / 7/6
= -6/7.
Answer:
Step-by-step explanation:
calculate the slope of given line :
7X-6Y=-5
6y = 7x+5
y=7/6 x +5/6
the slope is : 7/6
the slope of a line parallel to this lineis 7/6 ( same slope )
the slope of a line perpendicular to this line is : a when : a× 7/6= - 1
so : a = -6/7
solve
[tex]tan(a) - 1 = 0[/tex]
[tex]\tan a-1=0\\\tan a =1\\\\a=\dfrac{\pi}{4}+k\pi, k\in\mathbb{Z}[/tex]
Which line has a slope of LaTeX: \frac{1}{2}12and goes through the point (2, 4)?
Answer:
[tex]y = \frac{1}{2}x+3[/tex]
Step-by-step explanation:
The standard form of a line with slope and point is:
y= mx+b
We know the slope is 1/2
So,
[tex]y=\frac{1}{2} x+b[/tex]
Putting the point to find the value of b
[tex]4=\frac{1}{2}(2) +b\\ 4=1+b\\4-1 =b\\b=3[/tex]
So the equation of line is:
[tex]y = \frac{1}{2}x+3[/tex]
..
I Need Help Answer Plz I Need It Badly!!!
Answer: Yes it is.
Step-by-step explanation: So we are already told that segment AC is congruent to segment DC. They both have a right angle, as indicated by the angle symbol, and they share side-length BC.
According to the Hypotenuse-Leg Theorem, two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles. AC and DC are hypotenuses and they are congruent. And BC, the shared side, is a corresponding congruent leg. And since they are both right triangles, we then know that the HL Theorem applies.
Please help! Will mark brainlyest!
Answer: The black hole is [tex]3.302\times10^{6}[/tex] times more masive than the sun.
Step-by-step explanation:
Given : The mass of black hole = [tex]6.57\times10^{36}\ kg[/tex]
The mass of Sum is approximately [tex]1.99\times10^{30}\ kg[/tex]
Now, the number of times the mass of black hole more massive than the mass of sun is given by :-
[tex]n=\dfrac{6.57\times10^{36}}{1.9\times10^{30}}[/tex]
i.e.[tex]n=\dfrac{6.57}{1.9}\times\dfrac{10^{36}}{10^{30}}[/tex]
Using the division law of exponent :-
[tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex]
[tex]=\approx3.302\times10^{36-30}}\\\\=3.302\times10^{6}[/tex]
Hence, the black hole is [tex]3.302\times10^{6}[/tex] times more masive than the sun.
If rolling a number cube, identify the following events as disjointed or overlapping.
Event A: rolling a prime number
Event B: rolling a number larger than 4
Overlapping events ?
or
disjointed events ?
Answer:
Overlapping events
Step-by-step explanation:
Note that in the question, it specifically specifies that there is only a number cube (or 1 number cube). Note that the two events asked for us to solve is does not conflict at all.
Event A is asking for the probability of you rolling a prime number (1 , 3 , 5), while Event B is asking for the probability of you rolling a number larger than 4 (5 , 6). These two can occur at the same time, and both events can be confirmed by rolling the number 5.
~
Answer:
overlapping events
Step-by-step explanation:
Event A: Rolling a prime
The following are the prime numbers from 1 to 6 (inclusive):
2,3,5
Event B: Rolling a number larger than 4
The following are larger than 4 from 1 to 6 (inclusive):
5,6
Do you see any overlap?
The overlap is 5.
These are overlapping events.
The paragraph below comes from the rental agreement Susan signed when she opened her account at Super Video.
“All rentals are due back by midnight of the due date as printed on the transaction receipt. Any rental not received by midnight on the day it is due is subject to a late charge of $1.50 for each day it is late. Any rental not returned by the fifth day after the due date will be transferred to a sale. The Customer will then be required to pay the purchase price of the item in addition to five (5) days of late fees. The Customer will not be required to return the product once the total balance is paid.”
Susan went into her local Super Video to rent a movie last week. When she had made her choice, she approached the checkout counter where the clerk asked for her ID, scanned her movies and asked for $5.83. Susan gave her a $10 bill and the clerk gave her $4.17 as change as she said, “Thank you, have a good day!”.
Which of the following events invalidates the contract Susan signed with Super Video?
a.
Susan rented the wrong movie.
b.
The clerk gave Susan the wrong amount of change.
c.
The clerk asked Susan for her ID rather than her membership card.
d.
The clerk completed the transaction without giving Susan a receipt or otherwise informing her of the due date.
Answer:
option D
Step-by-step explanation:
As per the contract:
"All rentals are due back by midnight of the due date as printed on the transaction receipt. "
In given case clerk did not give any transaction receipt.
so option D is correct
The clerk completed the transaction without giving Susan a receipt or otherwise informing her of the due date !
Answer:
d
Step-by-step explanation:
i just did the test
Cinemark Theater has three categories for ticket prices. Adult tickets
sell for $6.50 after 3pm or $3.25 for a matinee (before 3pm), and Under 12
tickets sell for $3 at any time. The theater has a maximum capacity of 408
seats. What is the greatestamount that could be collected at:
a) an 8pm showing?
b) a 1pm showing?
c) Explain how much you think would be collected at a
matinee showing of a children's movie.â
High population density can cause increases in competition for resources, such as food and shelter. The table shows the number of zebras living in four different regions.
In which region is competition for resources most likely the greatest?
Region A
Region B
Region C
Region D
Answer:
The answer is Region C
Step-by-step explanation:
Region C has total population of Zebra as 16,400 divided by the area occupied in square km which is 625. This gives population density of approximately 26 zebras/km square
[tex] \frac{16400}{625} = 26.24[/tex]
If you follow the same procedure for other regions, you will discover that region C has the highest number of Zebras/square km which is 26.
I hope this helped?
The region that would have the greatest competition for resources is Region C.
What is population density?
Population density is the amount of organisms that live in a square feet of an area.
Population density = population / area
Population density in Region A = 1312 / 212 = 6.19Population density in Region B = 630 / 314 = 2Population density in Region C = 16400 / 625 = 26.24Population density in Region D = 17800 / 902 = 19.7To learn more about population density, please check:
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What is the probability of the spinner landing on 2? please respond fast
Solve. Use the basic percent equation. 0.95% of 250 is what?
2.375 is 0.95% of 250
Equation: Y = P% multiplied by X
Y = 0.95% multiplied by 250
Converting percent to a decimal:
P = 0.95%÷100 = 0.0095
Y = 0.0095 × 250
Y = 2.375
Therefore, 2.375 is 0.95% of 250
is a common external tangent to circles W and Y. What is the distance between the two centers of the circles? Round to the nearest hundredth. (Hint: Draw segment connecting the centers of the two circles, and then draw a segment, , so that YS + SZ = YZ and .)
Answer:
[tex]WY=42.8\ units[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
In the right triangle WYS
Applying the Pythagoras Theorem
[tex]WY^{2}=WS^{2}+YS^{2}[/tex]
we have that
[tex]WS=XZ=42\ units[/tex]
[tex]YS=YZ-WX=19-11=8\ units[/tex]
substitute
[tex]WY^{2}=42^{2}+8^{2}[/tex]
[tex]WY^{2}=1,828[/tex]
[tex]WY=42.8\ units[/tex]
Which factors can be multiplied together to make the trinomial 5x2 + 8x – 4? Check all that apply.
(x + 1)
(2x + 1)
(x + 2)
(5x + 1)
(5x – 2)
Answer:
x+2
5x-2
Step-by-step explanation:
There is only 2 binomials that will multiply together that will give the given trinomial.
ax^2+bx+c
5x^2+8x-4
Goal: Find two numbers that multiply to be a*c and add up to be b.
We will use this goal to factor our trinomial.
a=5
b=8
c=-4
--------
a*c=-20
b=8
Can you think of two numbers that multiply to be -20 and add up to be 8? I hope you said 10 and -2.
So we are going to replace 8x with -2x+10x.
5x^2+8x-4
5x^2-2x+10x-4
We are going to pair the first terms together and the second two terms together like so:
(5x^2-2x)+(10x-4)
Now we are going to factor each pair.
x(5x-2)+2(5x-2)
(5x-2)(x+2)
So (x+2) is a factor of the given trinomial and (5x-2) is a factor of the given trinomial.
Answer
x+2 and 5x-2
Step-by-step explanation:
Solve step by step :
(2+2i)(5+3i)
Answer:
(2 + 2i)(5 + 3i) = 4 + 16iStep-by-step explanation:
Use FOIL: (a + b)(c + d) = ac + ad + bc + bd
and i² = -1
(2 + 2i)(5 + 3i) = (2)(5) + (2)(3i) + (2i)(5) + (2i)(3i)
= 10 + 6i + 10i + 6i² = 10 + 6i + 10i + 6(-1)
= 10 + 6i + 10i - 6 combine like terms
= (10 - 6) + (6i + 10i)
= 4 + 16i
Answer:
[tex]\displaystyle 4+16i[/tex]
Step-by-step explanation:
Distributive property: ⇒ A(B+C)=AB+AC
A=2, B=2, C=5, and D=3
[tex]\displaystyle (2*5-2*3)+(2*3+2*5)i[/tex]
Simplify and refine to find the answer.
[tex]\displaystyle2*3+2*5=2*3=6, 2*5=10, 10+6=16[/tex]
[tex]\displaystyle2*5-2*3=2*5=10-2*3=2*3=6, 10-6=4[/tex]
[tex]\displaystyle 4+16i[/tex] , which is our correct answer.
Given the equation A=250(1.1)t, you can determine that the interest is compounded annually and the interest rate is 10%. Suppose the interest rate were to change to being compounded quarterly. Rewrite the equation to find the new interest rate that would keep A and P the same.
What is the approximate new interest rate?
Convert your answer to a percentage, round it to the nearest tenth, and enter it in the space provided, like this: 42.53%
Final answer:
To find the new interest rate compounded quarterly, divide the annual interest rate by the number of compounding periods per year.
Explanation:
To rewrite the equation to find the new interest rate, we need to consider the compounding frequency. Currently, the interest is compounded annually. To find the new interest rate compounded quarterly, we need to divide the annual interest rate by the number of compounding periods per year.
So, for an interest rate of 10%, the quarterly interest rate would be 10% divided by 4, which is 2.5%.
Therefore, the approximate new interest rate, compounded quarterly, would be 2.5%.
The new interest rate when compounded quarterly that would keep the future value (A) and the present value (P) the same is approximately 9.38%.
To find the new interest rate when the interest is compounded quarterly instead of annually, we need to use the compound interest formula and equate the two expressions for A.
Given:
[tex]A = 250(1.1)^_t[/tex] (interest compounded annually)
[tex]A = P(1 + r/m)^_(mt)[/tex] (compound interest formula)
Where:
A = Future value
P = Present value (250)
r = Annual interest rate
m = Number of times interest is compounded per year
t = Time in years
Step 1: Equate the two expressions for A.
[tex]250(1.1)^t = 250(1 + r/m)^_{(mt)}[/tex]
Step 2: Substitute m = 4 (interest compounded quarterly).
[tex](1.1)^t = (1 + r/4)^_{(4t)}[/tex]
Step 3: Solve for r.
[tex](1 + r/4)^4 = 1.1[/tex]
[tex]1 + r/4 = (1.1)^_{(1/4)}[/tex]
[tex]r/4 = (1.1)^_(1/4)} -1[/tex]
[tex]r= 4((1.1)^_(1/4)} -1)[/tex]
r ≈ 0.0938 or 9.38%
How does the graph of g(x) = (x - 3)^3 + 4 compare to the parent function f(x) = x^3?
Answer:
The graph of g(x) is equal to the graph of f(x) shifted 3 units to the right and 4 units above.
Step-by-step explanation:
we know that
[tex]f(x)=x^{3}[/tex] ----> the turning point is the point (0,0)
[tex]g(x)=(x-3)^{3}+4[/tex] ----> the turning point is the point (3,4)
The rule of the translation of f(x) to g(x) is equal to
(x,y) ------> (x+3,y+4)
That means-----> The translation is 3 units at right and 4 units up
therefore
The graph of g(x) is equal to the graph of f(x) shifted 3 units to the right and 4 units above.
210 donuts can be made in 10 hours how many can be made in 3 hours
Answer:
63 donuts
Step-by-step explanation:
210 donuts -> 10 hours
x donuts -> 3 hours
This is already setup for a proportion:
[tex]\frac{210}{x}=\frac{10}{3}[/tex]
Cross multiply:
[tex]3(210)=10x[/tex]
Simplify:
[tex]630=10x[/tex]
Divide both sides by 10:
[tex]\frac{630}{10}=x[/tex]
Simplify:
[tex]63=x[/tex]
63 donuts can be made in hours.
The division is one of the four fundamental arithmetic operations. The number of donuts that can be made in 3 hours time period is 63 donuts.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that 210 donuts can be made in 10 hours. Therefore, the number of donuts that can be made per hour are:
Number of donuts per hour = 210 donuts / 10 hour
= 21 donuts / hour
Now, the number of donuts that can be made in 3 hours are,
Number of donuts = 21 donuts / hour × 3 donuts
= 63 donuts
Hence, the number of donuts that can be made in 3 hours time period is 63 donuts.
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13. Pizza Perfection sold 93 pizzas on Monday, 67 pizzas on Tuesday, 78 pizzas on Wednesday, 44 pizzas on Thursday, and 123 pizzas on Friday. On average, how many pizzas did they sell per day?
A. 83
B. 63
C. 81
D. 82
Add all of the number of pizzas together
93+67+78+44+123
160+245
405
Divide by 5 because there are 5 numbers
405/5=81
81 pizzas
Answer: 81 pizzas -C.
Which expression is equivalent to -32 to 3/5 power
Answer:
8
Step-by-step explanation:
We are given the following expression and we are to find the simplest form of this expression:
[tex] - 3 2 ^ { \frac { 3 } { 5 } } [/tex]
First of all, we will factor the coefficient:
[tex] 3 2 = 2 ^ 5 [/tex]
Rewriting it as:
[tex] - ( 2 ^ 5 ) ^ { \frac { 3 } { 5 } }[/tex]
Applying the exponent rule [tex](a^b)^c = a^{bc}[/tex] to get:
[tex]-2^{5.\frac{3}{5}}=-2^3[/tex]
[tex]-2^3=-8[/tex]