Answer:
The answer is [tex]9[/tex]
Step-by-step explanation:
we have
[tex](243)^{\frac{2}{5}}[/tex]
we know that
[tex]a^{\frac{n}{m}}=\sqrt[m]{a^{n}}[/tex]
so
[tex](243)^{\frac{2}{5}}=\sqrt[5]{243^{2}}[/tex]
Remember that
[tex]243=3^{5}[/tex]
Substitute
[tex]\sqrt[5]{243^{2}}=\sqrt[5]{(3^{5})^{2}}\\ \\= \sqrt[5]{(3^{10})}\\ \\=3^{\frac{10}{5}}\\ \\= 3^{2} \\ \\=9[/tex]
The area of the base of a pyramid is 15 cm2.
If the height of the pyramid is 4 cm, what is the volume of the pyramid?
20 cm3 60 cm3 120 cm3 180 cm3
Devin started the work shown to solve for the unknown angle measures. 8x – 1 + 9x – 6 = 180 17x – 7 = 180 17x = 187 What are the measures of angles Q and R?
Answer:
[tex]m<R=87\°[/tex]
[tex]m<Q=93\°[/tex]
Step-by-step explanation:
we have that
[tex]m<R=(8x-1)\°[/tex]
[tex]m<Q=(9x-6)\°[/tex]
[tex]m<R+m<Q=180\°[/tex] ------> by supplementary angles
Substitute the values and solve for x
[tex]8x-1+9x-6=180\°[/tex]
[tex]17x-7=180\°[/tex]
[tex]17x=187\°[/tex]
[tex]x=11\°[/tex]
Find the value of angle R
[tex]m<R=(8*11-1)\°=87\°[/tex]
Find the value of angle Q
[tex]m<Q=(9*11-6)\°=93\°[/tex]
The measure of angle Q and R can be obtained by supplementary angle. The supplementary angle is defined as the addition of two angle is [tex]180^{\circ}[/tex].
The angle Q is [tex]93^{\circ}[/tex] and angle R is [tex]87^{\circ}[/tex].
Given:
The equation for unknown angle is,
[tex]8x -1 + 9x - 6 = 180[/tex]
The supplementary angle is,
[tex]\angle R+\angle Q=180^{\circ}[/tex]
Compare the above equation.
[tex]\angle R=(8x-1)^{\circ}\\\angle Q=(9x-6)^{\circ}[/tex]
Solve the given expression.
[tex]\begin{aligned}8x -1 + 9x -6 &= 180\\ 17x - 7 &= 180 \\17x &= 187 \\x&=11\\\end[/tex]
Calculate the Angle R.
[tex]\angle R=(8\times 11-1)\\\angle R=87^{\circ}[/tex]
Calculate the Angle Q.
[tex]\angle Q=(9\times 11-6)\\\angle Q=93^{\circ}[/tex]
Thus, the angle Q is [tex]93^{\circ}[/tex] and angle R is [tex]87^{\circ}[/tex].
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if the discriminant of an equation is zero, which of the following is true of the equation?
a. it has one real solution
b. it has two complex solutions
c. it has two real solutions
d. it has one complex solution
If the discriminant of an equation is zero, then the correct statement amongst given statement is:
a. It has one real solution
Step-by-step explanation:We have three cases of discriminant--
If the discriminant of the equation is strictly greater than zero then the equation has two real solutions.If the discriminant is equal to zero then it has one real solution.and if the discriminant is strictly less than zero then the equation has 0 real solutions i.e. both the solutions of the equation are complex.
Which are correct representations of the inequality 6x ≥ 3 + 4(2x – 1)? Check all that apply.
a blue print for a house has a scale of 1:35 in in a wall in the blue print is 3 inches what is the length in feet
Alana is writing a coordinate proof to show that the diagonals of a rectangle are congruent. she starts by assigning coordinates to a rectangle as shown. then she uses the coordinates to write and simplify expressions for the lengths of the diagonals.
The solution for the problem is:
d(S,P) = √(0-0)^2
+ √(b-0)^2
d(S,P) = √b^2
d(S,P) = b
so we know that, SP = b
d(P, Q) = √(a-0)^2 + √(b-b)^2
d(P, Q) = √a^2
d(P, Q) = a
so
PQ = a
SQ = c^2 = a^2 + b^2
SQ = √(a^2 + b^2)
Therefore, the answer is √(a^2 + b^2).
Proof of the congruence of the diagonals of a rectangle involves the distance formula stemming from the Pythagorean theorem and can be shown using specific coordinates. Comparing areas of squares uses the squares of the side lengths which simplifies to ratios.
Explanation:The lengths of the diagonals of a rectangle can be found using the distance formula, which is derived from the Pythagorean theorem. To prove the diagonals are congruent, coordinates are assigned to the vertices of the rectangle and the distance formula is applied to both diagonals. If the rectangle is placed with one corner at the origin and sides along the axes, then this process is further simplified as one can use the differences in x-coordinates and y-coordinates directly.
If we have a rectangle with vertices at coordinates (0,0), (a,0), (a,b), and (0,b), the diagonal lengths can be found by using the distance formula: the diagonal between (0,0) and (a,b) would have a length of √(a² + b²), and the diagonal between (a,0) and (0,b) would also have a length of √(a² + b²), proving that they are congruent. Additionally, when comparing areas using ratios, one simply needs to compare the squares of the lengths of respective sides, as the area of a square is the square of its side length.
Can someone please help me with both of these! Thank youuuu!!! ❤️
The product of two positive even numbers is 168. What are the numbers? A) 12 and 14 B) 16 and 18 C) −12 and −14 D) −16 and −18
The lighthouse on the beach casts a shadow that is 4848 feet long. Your friend is 5.55.5 feet tall and casts a shadow that is 2.22.2 feet long. What is the height of the lighthouse?
How many combinations are there to make $2.50 using one dollar bills, quarters, and dimes?
Final answer:
To make $2.50 using one dollar bills, quarters, and dimes, there are 7 different combinations.
Explanation:
To make $2.50 using one dollar bills, quarters, and dimes, we can use the concept of combinations. Let's break it down:
Start with the number of one dollar bills:0 one dollar bills: This gives us 0 dollars.1 one dollar bill: This gives us 1 dollar. We need to make $1.50 more with quarters and dimes.2 one dollar bills: This gives us 2 dollars. We need to make $0.50 more with quarters and dimes.Now let's consider the quarters and dimes:0 quarters and 25 dimes: This gives us $2.50.1 quarter and 20 dimes: This gives us $2.50.2 quarters and 15 dimes: This gives us $2.50.3 quarters and 10 dimes: This gives us $2.50.4 quarters and 5 dimes: This gives us $2.50.So, there are 7 different combinations to make $2.50 using one dollar bills, quarters, and dimes.
Determine the probability of getting a 4 when rolling a fair number cube. If Thelma rolls a fair number cube 600 times, how many times can she expect to get a 4?
A television commercial claims thta 9 out 10 dentists surveyed recommended bliss toothpaste. if 450 of the dentists surveyed recommended bliss, then how many did not recommend it?
in a tank that contains only golden platys, the probability of getting a female fish is 30%. If there are 18 female fishin the tank, how many total fish are in the tank?
Using probability concept in mathematics, the total number of fish in the tank would be 60, this is solved by the equation
[tex]X = (18*100)/30[/tex]Explanation:The student's question involves the concept of probability in mathematics. Given that the probability of finding a female golden platy is 30% and there are 18 female golden platys, we can formulate an equation to find the total number of fish. Let's say the total number of fish in the tank is X. Accordingly, we can write 30/100 * X = 18. Solving this equation would give X = 18 / (30/100), which simplifies to
[tex]X = (18*100)/30 = 60[/tex]golden platys in the tank.
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Multiply.
3⋅3/5
Enter your answer as an improper fraction, in simplified form, in the box.
Answer:
[tex]1\frac{4}{5}[/tex]
Step-by-step explanation:
3 times 3/5
[tex]3 \cdot \frac{3}{5}[/tex]
To multiply whole number by fraction , then we multiply 3 with the numerator
[tex]\frac{3 \cdot 3}{5}[/tex]
[tex]\frac{9}{5}[/tex]
Now write the fraction in mixed form
when we divide 9 by 5, the quotient is 1 and 4 is the remainder
[tex]\frac{9}{5}[/tex]
[tex]1\frac{4}{5}[/tex]
Use the graph to fill in the blank.
F(0)=_
Help please . Thank you
1. Estimate the area of the irregular shape. Explain your method and show your work.
Answer:
The estimated area of figure is 30 square units.
Step-by-step explanation:
We need to find the area of the irregular shape.
Draw a quadrilateral as shown below.
It is a trapezium with bases 5 units and 7 units, and height 5 units.
Area of a trapezoid is
[tex]Area=\frac{a+b}{2}\times h[/tex]
where, a, b are bases and h is height.
Substitute a=5,b=7 and h=5 in the above formula.
[tex]Area=\frac{5+7}{2}\times 5[/tex]
[tex]Area=6\times 5[/tex]
[tex]Area=30[/tex]
Therefore, the estimated area of figure is 30 square units.
What is the value of r? 5+r−2=9
The value of r in a solution of the expression 5 + r - 2 = 9 is,
⇒ r = -6
Given that,
A mathematical expression is,
⇒ 5 + r - 2 = 9
Now, simplify the expression by combining like terms as,
⇒ 5 + r - 2 = 9
⇒ 3 - r = 9
Add r on both sides,
⇒ 3 = 9 + r
Subtract 9 on both sides,
⇒ 3 - 9 = r
⇒ - 6 = r
Therefore, the solution of the expression is,
⇒ r = -6
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Which term describes a person's previous pattern of borrowing and repaying?
k/2 -6=28
solve for k
If a is a 3-digit integer and b is a 3-digit integer, is the units digit of the product of a and b greater than 5?
the three inside angles (A, B, C) of a right angled triangle are in the ratio 7:18:11. The smallest angle is 35 degrees. Work out the angle A, B,C
The three inside angles (A, B, C) of a right angled triangle are [tex]\rm \angle A = 35^\circ[/tex] which is the smallest angle, [tex]\rm \angle B = 90^\circ[/tex] which is the right angle and [tex]\rm \angle C = 55^\circ[/tex] which is the third angle of the triangle.
Given :
[tex]\rm \angle A :\angle B:\angle C = 7:18:11[/tex]Smallest angle = [tex]35^\circ[/tex]To solve this kind of problems first let x be in degree. So, angle A, angle B and angle C beecomes:
[tex]\rm \angle A = 7x[/tex] ----- (1)
[tex]\rm \angle B = 18x[/tex] ----- (2)
[tex]\rm \angle C = 11x[/tex] ----- (3)
From the properties of triangle, the sum of interior angles of a triangle is [tex]180^\circ[/tex].
[tex]\rm \angle A +\angle B+\angle C = 180^\circ[/tex] --- (4)
Now, put the values of [tex]\rm \angle A,\;\angle B,\;and \; \angle C[/tex] in equation (4).
[tex]7x+18x+11x=180^\circ[/tex]
[tex]36x = 180^\circ[/tex]
[tex]x = 5[/tex]
Now, put the value of x in equation (1), (2) and (3).
[tex]\rm \angle A = 7\times 5 = 35^\circ[/tex]
[tex]\rm \angle B = 18\times5 = 90^\circ[/tex]
[tex]\rm \angle C = 11\times5=55^\circ[/tex]
The three inside angles (A, B, C) of a right angled triangle are [tex]\rm \angle A = 35^\circ[/tex] which is the smallest angle, [tex]\rm \angle B = 90^\circ[/tex] which is the right angle and [tex]\rm \angle C = 55^\circ[/tex] which is the third angle of the triangle.
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jeunesse earned $725 dollars by working 5 days in a week. What is the average amount that she earned per day?
If all marbles in a bag are red, and all red marbles weigh 3oz, then all 3oz marbles are red. true or false?
In triangle abc, the measure of angle b is 20 more than three times the measure of angle
a. the measure of angle c is 55 more than the measure of angle
a. find the measure of each angle
Dylan is 6 years younger than Briana. Briana's age can be represented by x. Write an expression representing Dylan's age.
Answer:
x - 6
Step-by-step explanation:
usatestprep
k-12
At the fast food restaurant, four cheeseburgers and five small fries have a total of 2,310 calories. Three cheeseburgers and two small fries have a total of 1,330 calories. How many calories does each item contain? Create two equations to model this situation using X and Y for your variables. Use a comma to separate your equations.
A cheeseburger contains 290 calories and a small fries contains 230 calories.
Explanation:Let X be the number of calories in a cheeseburger, and Y be the number of calories in a small fries.
From the given information, we can create two equations:
4X + 5Y = 23103X + 2Y = 1330To solve this system of equations, we can use substitution or elimination. Let's use elimination:
Multiply equation 1 by 3 and equation 2 by 4 to eliminate the X term:12X + 15Y = 693012X + 8Y = 5320Subtract the second equation from the first equation:12X + 15Y - 12X - 8Y = 6930 - 53207Y = 1610Divide both sides by 7:Y = 230Substitute the value of Y into either equation and solve for X:3X + 2(230) = 13303X + 460 = 13303X = 870X = 290Therefore, a cheeseburger contains 290 calories and a small fries contains 230 calories.
The following sequence is arithmetic. 18, 11, 4, -3, -10, -17….
True
False
I can't study this because keystones makes you take the quiz before giving instructions.
The statement "The following sequence is arithmetic. 18, 11, 4, -3, -10, -17 is True.
To determine if a sequence is arithmetic, one must check if there is a common difference between consecutive terms. The common difference (d) can be found by subtracting any term in the sequence from the term immediately following it.
Let's calculate the common difference for the given sequence:
- For the first two terms: (11 - 18 = -7)
- For the next two terms: (4 - 11 = -7)
- For the following two terms: (-3 - 4 = -7)
- And for the last two terms provided: (-10 - (-3) = -10 + 3 = -7)
Since the difference between each pair of consecutive terms is constant and equal to \(-7\), this confirms that the sequence is indeed arithmetic. Therefore, the statement is True.
Which of the following is being constructed in the image?
Answer:
C) A line perpendicular to a given line through a point not on a line.
Step-by-step explanation:
In the given construction we draw a perpendicular line from a point which is not on line.
Please see the attachment for construction and naming of point.
We are given a line s and point P which is not on line. Through point P we draw an arc on line which cut at two points A and B Now we open an compass and mark an arc through point A. Using same arc we cut the arc A through point B at point C.Now we join PC. Such that PC ⊥ to line sThus, C is correct option. " a line perpendicular to a given line through a point not on a line".
The equation for line r can be written as y =-1 5 x – 1 .Line s includes the point (10, 4)and is parallel to line r. What is the equation of line s?