Answer:
The answer is A and BStep-by-step explanation:
Because 4 to the power of -3 divided by 4 to the power of -1 switched (Like when there is a negative exponent you move the number or variable to the other side of the fraction) and scince both have a negative number you switch both. and 1-3 is -2 so you switch it to the bottem and put a 1 at the top.
^^Hope this helps!
The expressions equivalent to 4^-3 / 4^-1 are 1/4^2 and (4^-1)^-3.
Explanation:In the subject of mathematics, the given expression is 4^-3 / 4^-1. To simplify this expression, you need to understand two rules of exponents:
The rule a^-n = 1/a^n, which says that a negative exponent indicates the reciprocal of the positive exponent, andWhen you divide numbers with the same base, you should subtract the exponents.Applying these two rules, 4^-3 / 4^-1 = 4^-3 * 4^1 = 4^(1 - 3) = 1/4^2.
Another way to simplify the expression is to use the rules of exponents to rewrite each part independently. 4^-3 = 1/4^3 and 4^-1 = 1/4. Therefore, 4^-3 / 4^-1 = (1/4^3) / (1/4) = 4, which is equivalent to (4^-1)^-3.
Therefore, the equivalent expressions are (B) 1/4^2 and (D) (4^-1)^-3.
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What is the value of y in the equation 5x + 2y = 20, when x = 0.3?
2.5
2.8
9.25
10.75
Answer:
9.25
Step-by-step explanation:
An equation is formed of two equal expressions.The value of y in the equation 5x + 2y = 20, when x = 0.3 is 9.25. The correct option is C, 9.25.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The value of y in the equation 5x + 2y = 20, when x = 0.3 can be found by substituting the value in the equation.
5x + 2y = 20
Substitute the value of x,
5(0.3) + 2y = 20
1.5 + 2y = 20
Subtract 1.5 from both sides of the equation,
1.5 + 2y - 1.5 = 20 - 1.5
Divide both the sides of the equation by 2,
2y /2 = 18.5 /2
y = 9.25
Hence, the value of y in the equation 5x + 2y = 20, when x = 0.3 is 9.25.
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If two angles are congruent, then the angles are vertical angles.
Which diagram provides a counterexample for the statement?
A) A
B) B
C) C
D) D
Based on the , the counterexample to the statement "If two angles are congruent, then the angles are vertical angles" is:
B) Right Triangle with Two 45° Angles
Here's why:
The diagram shows a right triangle ABC.
Angles ∠ACB and ∠CAB are both 45 degrees, as indicated by the markings.
Therefore, ∠ACB and ∠CAB are congruent (they have the same measure).
However, these angles are not vertical angles. They are adjacent angles in the right triangle, sharing the vertex C but not formed by intersecting lines.
Therefore, diagram C provides a counterexample to the original statement. The other diagrams:
A) Doesn't show any congruent angles.
B) Shows vertical angles, but they are not marked as congruent.
D) Shows congruent corresponding angles in parallel lines, but not vertical angles.
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.
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
(please help!) Two buses leave the bus station at 8 am. If Bus #1 makes its route in a total of 60 minutes and Bus #2 makes its route in a total of 80 minutes, at what time will the two buses meet again?
Answer:
12 pm noon
Step-by-step explanation:
The least common multiple of the two times is 240 minutes, or 4 hours. The buses will meet at the station again at noon.
__
60 = 20×3
80 = 20×4
The least common multiple is 20×3×4 = 240 minutes. There are 60 minutes in an hour, so this is 240/60 = 4 hours. 4 hours after 8 am is 12 pm, noon.
Will mark as brainliest if right
3/5p+1/5(40-p)=0 what value makes p true
The value of p that makes the equation true is -20
Step-by-step explanation:
To solve an equation of one variable
Simplify the equation if necessaryUse the mathematics operations to put the variable in one side and the numerical term in the other sideDivide both sides by the coefficient of the variable to find its value∵ The equation is [tex]\frac{3}{5}p+\frac{1}{5}(40 - p)=0[/tex]
- Simplify the left hand side
∵ [tex]\frac{1}{5}(40-p)=\frac{1}{5}(40)-\frac{1}{5}(p)[/tex]
∴ [tex]\frac{1}{5}(40-p)=8-\frac{1}{5}p[/tex]
- Substitute [tex]\frac{1}{5}(40-p)[/tex] in the equation by [tex]8-\frac{1}{5}p[/tex]
∴ [tex]\frac{3}{5}p+8-\frac{1}{5}p=0[/tex]
- Add the like terms
∴ [tex](\frac{3}{5}p-\frac{1}{5}p)+8=0[/tex]
∴ [tex]\frac{2}{5}p+8=0[/tex]
- Subtract 8 from both sides
∴ [tex]\frac{2}{5}p=-8[/tex]
- Divide both sides by [tex]\frac{2}{5}[/tex]
∴ p = -20
To check the answer substitute p by -20 in the equation, the left hand side is equal to the right hand side, then the answer is right
∵ left hand side = [tex]\frac{3}{5}(-20)+\frac{1}{5}(40-(-20))[/tex]
∴ left hand side = [tex]\frac{-60}{5}+\frac{1}{5}(40+20)[/tex]
∴ left hand side = [tex]\frac{-60}{5}+\frac{60}{5}[/tex]
∴ left hand side = 0
∵ Right hand side = 0
∴ Left hand side = Right hand side
∴ The value of p makes the equation true
The value of p that makes the equation true is -20
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Answer:
-20
Step-by-step explanation:
{-2x+y=0
5x+3y=-11
Solve the substitution
[tex]\bf \begin{cases} -2x+y=0\\ \boxed{y} = 2x\\[-0.5em] \hrulefill\\ 5x+3y=-11 \end{cases}\qquad \qquad \implies \stackrel{\textit{substituting on the 2nd equation}}{5x+3\left( \boxed{2x} \right)=-11} \\\\\\ 5x+6x=-11\implies 11x=-11\implies x = \cfrac{-11}{11}\implies \blacktriangleright x = -1 \blacktriangleleft \\\\\\ \stackrel{\textit{we know that}}{y = 2x}\implies \blacktriangleright y = -2 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (-1~~,~~-2)~\hfill[/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.
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
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
Please help me I really need help i beg of u due today
Answer:
The volume of the observatory is 497.43 [tex]feet^{3}[/tex]
Step-by-step explanation:
i) The diameter of the floor is 10 feet. The floor is circular and has a radius,
r = [tex]\frac{10}{2}[/tex] = 5 feet.
Therefore the area of the circular floor of the observatory
= [tex]\pi r^{2}[/tex] = 3.14159 × [tex]5^{2}[/tex] = 78.54 [tex]feet^{2}[/tex]
ii) The observatory is made up of two parts
a) 3 foot tall cylinder
∴ volume of cylinder = [tex]\pi r^{2}[/tex] × h
= 78.54 × 3
= 235.62 [tex]feet^{3}[/tex]
b) hemisphere = [tex]\frac{1}{2}[/tex] × [tex]\frac{4}{3} \pi r^{3}[/tex] = 0.6667 × 78.54 × 5 = 261.81 [tex]feet^{3}[/tex]
c) Therefore the total volume of the observatory is = a) + b)
= 235.62 + 261.81 = 497.43 [tex]feet^{3}[/tex]
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)
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:
Anyone? Can help !!!
Answer:
C.g(x) = 5x²
Step-by-step explanation:
To find the equation for the function g(x), use the format for a quadratic equation. Without any up/down and left/right shifts, the form is y = ax².
Substituting "x" and "y" into the equation tells you if a point is on the graph.
"a" tells you the vertical stretch (greater than 1) or compression (greater than 0, less than 1).
In f(x) = x², a = 1 even though it's not written.
Use the point (1, 5) on g(x) and substitute it into the form for a quadratic function. Remember points are (x, y), so x = 1 and y = 5.
g(x) = ax²
y = ax² In function notation, g(x) replaces the "y". Switch it back to "y".
5 = a(1)² Substitute x = 1 and y = 5
5 = a(1) Solve the exponent first. (1)² = 1
5 = a When you multiply "a" by 1, the answer is just "a".
a = 5 Solved for "a". Put variable on left side for standard formatting.
With the quadratic form, substitute "a" into g(x).
y = ax²
g(x) = 5x²
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:
Mrs. Smith has 50 students in her math class. If 40% of the students completed the homework, how many students did not complete the homework?
Answer:
30 students
Step-by-step explanation:
check the photo
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:
At what rate per annum will Rs.4500 amount to Rs.5715 in 3 years?
Answer:
5715x3=
Rs.17145
Step-by-step explanation:
The interest rate required for Rs.4500 to amount to Rs.5715 in 3 years is 9% per annum. This is obtained using the simple interest formula. Therefore, the annual rate is 9%.
To find the annual interest rate at which Rs.4500 amounts to Rs.5715 in 3 years, we use the formula for simple interest:
Final Amount (A) = Principal (P) + Interest (I)
Given:
Principal (P) = Rs.4500Final Amount (A) = Rs.5715Time (T) = 3 yearsFirst, we calculate the interest:
Interest (I) = A - P = Rs.5715 - Rs.4500 = Rs.1215Next, we use the simple interest formula:
I = P × R × TRearranging for the rate (R), we get:
R = I / (P ×T)Substitute the known values:
R = 1215 / (4500 × 3) = 1215 / 13500 ≈ 0.09Converting to a percentage:
R ≈ 9% per annumTherefore, the rate per annum required for Rs.4500 to grow to Rs.5715 in 3 years is 9%.
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.
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
Ben wants to play a carnival game that costs $2. In his pocket he has 5
red tickets worth 35 cents each, and 15 blue tickets worth 10 cents each.
Which of the following systems of inequalities correctly represents the
constraints on the variables in this problem? Let rrepresent the red
tickets and b represent the blue tickets.
Answer:
R=$1.75 B=$1.50
Step-by-step explanation:
35r+10b=X
b is 10
r is 5
X=3.25$
Answer:
Step-by-step explanation:
R=$1.75 B=$1.50
35r+10b=X
b is 10
r is 5
X=3.25$
Try the numbers 22, 23, 24, 25 in the equation 4/3 = 32/d to test whether any of them is a solution. a. 23 is a solution. c. 24 is a solution. b. 25 is a solution. d. 22 is a solution.
Answer:
c. 24 is a solution
Step-by-step explanation:
Given equation:
[tex]\frac{4}{3}=\frac{32}{d}[/tex]
To test the numbers 22, 23, 24, 25 for the solution.
Solution:
In order to test the given number for the solution, we will plugin each number in the unknown variable [tex]d[/tex] and see if it satisfies the equation.
1) [tex]d=22[/tex]
[tex]\frac{4}{3}=\frac{32}{22}[/tex]
Reducing fraction to simplest form by dividing the numerator and denominator by their G.C.F.
[tex]\frac{4}{3}=\frac{32\div 2}{22\div 2}[/tex]
[tex]\frac{4}{3}=\frac{16}{11}[/tex]
The above statement can never be true and hence 22 is not a solution.
2) [tex]d=23[/tex]
[tex]\frac{4}{3}=\frac{32}{23}[/tex]
The fractions can no further be reduced.
The statement can never be true and hence 23 is not a solution.
3) [tex]d=24[/tex]
[tex]\frac{4}{3}=\frac{32}{24}[/tex]
Reducing fraction to simplest form by dividing the numerator and denominator by their G.C.F.
[tex]\frac{4}{3}=\frac{32\div 8}{24\div 8}[/tex]
[tex]\frac{4}{3}=\frac{4}{3}[/tex]
The above statement is always true and hence 24 is a solution.
4) [tex]d=25[/tex]
[tex]\frac{4}{3}=\frac{32}{25}[/tex]
The fractions can no further be reduced.
The statement can never be true and hence 25 is not a solution.
Four pounds of sugar costs $2.40 at the grocery store. What is the unit rate for the cost of sugar in relation to its weight?
A.$0.60 per pound
B. not enough information
C.$1.67 per pound
D.$2.40 per pound
Answer:
c
Step-by-step explanation:
solve this equation 4/2.40
please help me. i don’t know how the answer is 1/12 so can you guys please explain step by step on why the answer is 1/12.
Answer:
see explanation
Step-by-step explanation:
P(head) = [tex]\frac{1}{2}[/tex]
P(4) = [tex]\frac{1}{6}[/tex]
P(head and 4 ) = P(head) × P(4) = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{12}[/tex]
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:
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]
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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A circle has a circumference of 20. It has an arc of length 4. What is the central angle of the arc,in degrees
Answer:
Step-by-step explanation: 72.1°
The circumference of the circle is given to be = 20
The first thing to do here is to calculate the radius of the circle from the circumference given,
Formula for circumference = 2πr or πd, where d is the diameter.
Make r the subject of the formula by equating it to 20
2πr = 20,
r = 20/2π, π = ²²/₇ or 3.142
r = 10/22/7
= ( 10 x 7 )/22
= 70/22
= 3.18.
Now since the radius is known, we could now calculate the central angle of the arc.
Arc length = 2πr∅°/360°, reducing this to lowest term now becomes
= πr∅°/180°
Therefore equate the formula to 4 and solve for ∅°, since the arc length is 4
πr∅°/180° = 4
Multiply through by 180°
πr∅° = 4 x 180°
πr∅°= 720
Divide through by πr to get ∅°
∅° = 720/πr
= 720/3.142 x 3.18
= 720/9.99
= 72.07
= 72.1°
The angle substended by the arc length 4 is 72.1°