Answer:
The number 1 is not necessary when expressing powers of one. For example, you needn't write "5" as [tex]5^{1}[/tex].
Step-by-step explanation:
The number 1 is written when it is part of a larger number, as it is significant. It is not necessary to write leading zeros. In scientific notation, trailing zeros are excluded, and the number is written in a form where only non-zero digits appear before the decimal.
Explanation:Understanding when to write the number 1 and when it's not needed depends on the context in mathematics, especially when dealing with significant figures and scientific notation. Generally, all non-zero numbers are considered significant (rule 1), which means that when a value like 1 is part of a larger number, it contributes to the meaning of that number. However, leading zeros do not count as significant (rule 3).
In the case of multiplication by units, like converting from kilograms to grams, we utilize the concept of multiplying by the number 1 to affect the units without changing the value. For example 0.7 kg can be multiplied by 1000/1 (1000 g / 1 kg) to convert to grams. This is because 1000/1 is equal to 1000, indicating multiplication by one does not change the value.
When expressing numbers in scientific notation, it's important to include the non-zero digits only before the decimal point, excluding any trailing zeros. Thus, 1,500,000 would be written as 1.5 x 106, with the power indicating the necessary number of decimal point movements to place it after the first significant digit.
At grocery store, the price of a watermelon is determined by how many pounds the watermelon weighs. The price of the watermelon that weighs 7.3 pounds is $4.38. Write an equation that can be used to determine the price, p. in dollars, of any watermelon based on the number of pounds, w, the watermelon weighs.
Determine the cost of a watermelon that weighs 8.5 pounds.
please help with this question
Answer:
7.3 divided by 4.38
Step-by-step explanation:
What is six lots of five
Answer:
6 lots of 5 means 6×5=30
Step-by-step explanation:
Answer:
Multiplication - When we multiply we find 'lots of'
6 lots of 5 = 30
6×5=30
The events committee buys 100 flowers for a school dance. The flowers are a
combination of carnations and roses. Each carnation costs $0.75, and each rose
costs $2.75. The committee spends a total of $139, not including tax.
How many of each type of flower does the committee buy?
0 61 carnations: 40 roses
48 carnations: 24 roses
54 carnations: 32 roses
68 carnations: 32 roses
Answer:
D) 68 carnations & 32 roses
Step-by-step explanation:
First of all, we need to identify the parts of the problem that we already know.
1) The events committee bought a total of 100 flowers.
2) The events committee spent a total of $139 on the carnations and roses, combined.
3) One carnation costs $0.75
4) One rose costs $2.75
We can create a formula to find the price of the flowers:
(x times $0.75) + (y times $2.75)= $139
If we calculate it out, the only option that fits the equation is 68 carnations and 32 roses.
ABCD is a rectangle. Two circles are drawn inside ABCD such that the circles are tangent at point G. E is the tangent point of the first circle and AB, and F is the tangent point of the second circle and BC, as shown. Find m∠EGF.
Answer:135 degrees
Step-by-step explanation: Pretend that the 2 circles are equal, and connect the lines that form the angle. You can draw a right triangle on the circle that is on the right, connecting 2 radii to form it. Then, because the two radii are of equal length, you know that it is a 45-45-90 triangle. Then draw a line that is from the top line and connect in to G. That line is perpendicular, so 45 degrees plus 90 degrees is 135 degrees. I hope this helps!
Please show work for both problems
Answer:
1) x = 25 2) x = 23; m∠CBD = 80 degrees
Step-by-step explanation:
1) 5x + 15 = 6x - 10 Set both equations equal to each other
- 5x - 5x Subtract 5x from both sides
15 = x - 10
+ 10 + 10 Add 10 to both sides
25 = x
2) 2x + 14 + x + 7 = 90 Set the equations equal to 90
3x + 21 = 90 Combine like terms
- 21 - 21 Subtract 21 on both sides
3x = 69 Divide both sides by 3
x = 23
Plug 23 into the equation
2(23) + 14 = 60
8m²n³-24m²n²+4m³n
how do I factor out the GCF
Answer:
[tex]8 {m}^{2} {n}^{3} - 24 {m}^{2} {n}^{2} + 4 {m}^{3}n = 4 {m}^{2} n(2 {n}^{2} - 6n + m)[/tex]
Step-by-step explanation:
The given expresion is
[tex]8 {m}^{2} {n}^{3} - 24 {m}^{2} {n}^{2} + 4 {m}^{3}n[/tex]
Observe that 4 is common to 8,-24, and 4
Observe also that, m²n is common to all the terms.
Hence the GCF is:4m²n
We factor the GCF to get;
[tex]8 {m}^{2} {n}^{3} - 24 {m}^{2} {n}^{2} + 4 {m}^{3}n = 4 {m}^{2} n(2 {n}^{2} - 6n + m)[/tex]
i need help PLEASE!!!!
Answer:
The answer is 11
Step-by-step explanation:
write an equation in point-slope form for the line throught the given slope (8,3);m=6
Answer: [tex]y - 3 = 6 (x - 8 )[/tex]
Step-by-step explanation:
The equation of line in point slope form is given as :
[tex]y - y_{1} = m ( x - x_{1} )[/tex]
[tex]x_{1}[/tex] = 8
[tex]y_{1}[/tex] = 3
[tex]m = 6[/tex]
substituting into the formula , we have :
[tex]y - 3 = 6 (x - 8 )[/tex]
please help me out I will give Brainlyeist to who ever answers right!!!!
2. Find the area of the triangle.
A. 362.24mm B. 20.55 mm C. 181.12 mm D. 41.1 mm
Multiply the base and height (28.3*12.8=362.24)
Divide by 2: 181.12
So the answer is C
Hope this helped
what is the mathematical name of this shape please tell me ASAP. ( I will give brainliest )
Answer:
its a triangle
Step-by-step explanation:
3 sides
Answer:
the shape is known as a triangle
Find the 9th term in a geometric sequence whose common ration is 1/3 and first term is 6
Answer:
Therefore 9th term of the geometric sequence is [tex]\frac{2}{2187}[/tex]
Step-by-step explanation:
Given first term(a) = 6
and common ratio = [tex]\frac{1}{3}[/tex]
[tex]T_n= ar^{n-1}[/tex]
[tex]\therefore T_9=ar^{9-1}[/tex]
[tex]\Leftrightarrow T_9=a r^8[/tex]
[tex]\Leftrightarrow T_9=6\times ( \frac{1}{3}) ^8[/tex]
[tex]\Leftrightarrow T_9=\frac{2}{2187}[/tex]
Therefore 9th term of the geometric sequence is [tex]\frac{2}{2187}[/tex]
What is the solution to the system of equations? 3 x - 4 y = 16. 2 x + 3 y = 5.
Answer:
Step-by-step explanation:
Equation 1
3x - 4y = 16
multiplying equation by 3
it becomes
9x - 12y = 48 ------------(A)
equation 2
2x + 3y = 5
multiplying equation by 4
8x + 12y = 20 -------------(B)
Now comparing equation A & B
17x = 68
x = 4
putting the value of x in equation 2
2(4) + 3y = 5
8 + 3y = 5
3y = -3
y = -1
So, solution is (4 , -1)
Find the value of x
A. 18
B. 27
C. 50
D. 40
Answer:
the sum interior angles of a triangleis equal to 180
so (x + 13) +(x +23) + 90 = 180
2x + 36 + 90 = 180
2x = 180 - 126
2x = 54
x = 27
How do you convert decimal to percent like for example.( convert 1.37 to a percent) please show work thank you
answer: 137%
to convert from decimal to percent, you multiply the decimal by 100.
Answer: 137%
Step-by-step explanation:
100% is equal to 1. Therefore, 1.37 is equal to 137% if you move the decimal point correctly. Multiplying by 100 is also another way to do it.
what is the answer to
feet
=
8.5
meter?
Answer:
27.8871 feet
Step-by-step explanation:
1 meter ≅ 3.28084
You need to multiply the meters by 3.28084 to get the answer in feet.
So, 8.5 * 3.28084 ≅ 27.8871
The graph of the quadratic function y = x2 is shown below. If this parabola is reflected about the x-axis, what is the new equation of the quadratic function?
The graph of the quadratic function y = x2 is shown below. If this parabola is reflected about the x-axis, what is the new equation of the quadratic function?
Select one:
A. y=−x2−1
B. y=10x2
C. y=−x2
D. y=−(x−1)2
Answer:
Option C. [tex]y=-x^2[/tex]
Step-by-step explanation:
we know that
We can reflect the graph of any function f(x) about the x-axis by graphing y=-f(x)
so
The rule of the reflection of a function f(x) across the x-axis is
(x,f(x)) ------> (x,-f(x))
In this problem we have
[tex]f(x)=x^{2}[/tex]
Applying the rule of the reflection across the x-axis
[tex](x,x^2) ----> (x,-x^2)[/tex]
therefore
The new equation of the quadratic function is
[tex]y=-x^2[/tex]
Enter the value for x that makes the equation 1/2(4x-8)+3x=36 true
Answer:
the correct answer for x is 8
Step-by-step explanation:
since: 1/2 ((4) (8) - 8) + (3) (8) = 36
The correct value for x that makes the equation true is 8.
To solve the equation [tex]\( \frac{1}{2}(4x-8)+3x=36 \)[/tex], follow these steps:
1. Distribute the [tex]\( \frac{1}{2} \)[/tex] to both terms inside the parentheses:
[tex]\[ \frac{1}{2} \cdot 4x - \frac{1}{2} \cdot 8 + 3x = 36 \][/tex]
2. Simplify the equation by multiplying:
[tex]\[ 2x - 4 + 3x = 36 \][/tex]
3. Combine like terms:
[tex]\[ 5x - 4 = 36 \][/tex]
4. Add 4 to both sides of the equation to isolate the term with x:
[tex]\[ 5x = 36 + 4 \][/tex]
[tex]\[ 5x = 40 \][/tex]
5. Divide both sides by 5 to solve for x:
[tex]\[ x = \frac{40}{5} \][/tex]
[tex]\[ x = 8 \][/tex]
What is the measure of BC
Enter your answer in the box.
Answer:
Angle BDC is an inscribed angle.
The inscribed angle equals one half of the intercepted arc.
Therefore, the intercepted arc equals 130 degrees.
Step-by-step explanation:
The measure of BC should be 130 degrees.
Given information:The angle of d is 65 degrees:
Calculation of measure of BC:Since angle of D is 65
So, the BC should be doubled i.e. 130 degrees.
Learn more about the circle here: https://brainly.com/question/14337527
rked
Scon Given that f(x)= x2 - 18 and g(x) = 5x + 19. find (g- 1)(-6), if it exists.
Answer:
Step-by-step explanation:
Since g is a one-one function, its inverse exists.
Let (g^-1)(-6) = t
We have to find t
-5
(g^-1)(-6) = t inplies
-6 = g(t)
-6 = 5t + 19
5t = -25
t = -5
I need help solving these problems please!!
5 female giraffes have a mean weight of x kg
7 male giraffes have a mean weight of y kg
Write down an expression, in terms of x and y, for the mean weight of all the giraffes.
Step-by-step explanation:
Weight of all female giraffes = 5x kg
Weight of all male giraffes = 7y kg
Mean weight of all giraffes
[tex] = \frac{5x + 7y}{5 + 7} \\ \\ = \frac{5x + 7y}{12} \: kg[/tex]
The mean weight of all the giraffes, in terms of x and y, is calculated by adding the total weights of both female and male giraffes and then dividing by the total number of giraffes. The expression for the mean weight is (5x + 7y) / 12.
To find the mean weight of all the giraffes in terms of x and y, we must first calculate the total weight of female and male giraffes separately and then combine these totals to find the overall mean.
For the 5 female giraffes: Total weight = 5 × x = 5x kg
For the 7 male giraffes: Total weight = 7 × y = 7y kg
Then, we add these together to get the combined total weight: Combined total weight = 5x + 7y kg
Since there are 5 + 7 = 12 giraffes in total, we then divide the combined weight by the number of giraffes to find the overall mean weight.
Overall mean weight = (5x + 7y) / 12
Which equation results from adding the equations in this system?
Negative 2 x + y = 8. 5 x minus y = negative 5.
7 x = 13
7 x = 3
3 x = 3
3 x = 13
Answer:
The correct option is second one i.e 7x = 3
Therefore the results from adding the equation in this system is
[tex]7x=3[/tex]
Step-by-step explanation:
Given:
Equations as
[tex]2x+y=8[/tex] .......................1
[tex]5x-y=-5[/tex] .......................2
To Find :
Result when adding equation 1 and 2 = ?
Solution
On adding equation 1 and 2 the "y" term will get cancel and the like terms will combine that is add (2x and 5x ) and ( 8 and - 5) as shown below
2x + y = 8
5x - y = - 5
-------------------------------------------
7x + 0 = 3
---------------------------------------------
Therefore the results from adding the equation in this system is
[tex]7x=3[/tex]
Answer:
It's 3x=3
Step-by-step explanation:
I did it in edg! But its correct
The thomas family drinks 524.2 ounces of water each week. About how many ounces of water will they drink in 5 weeks?
Answer:
2621
Step-by-step explanation:
We know how much they drink in 1 week, now we need to know how many they drink in 5 weeks.
To do so, multiply how much they drink in 1 week by 5 to get the value for 5 weeks.
524.2*5=2621
Is 1/8 -10(3/4-3/8x) + 5/8x equivalent to -1/8(59 -35X)
Yes, The expression [tex]\frac{1}{8} -10(\frac{3}{4}-\frac{3}{8}x)+\frac{5}{8} x[/tex] is equivalent to [tex]-\frac{1}{8} (59-35x)[/tex]
Explanation:
The given expression is [tex]\frac{1}{8} -10(\frac{3}{4}-\frac{3}{8}x)+\frac{5}{8} x[/tex]
Solving, we get,
[tex]\frac{1}{8} -\frac{30}{4}+\frac{30}{8}x+\frac{5}{8} x[/tex]
Adding the similar terms, we have,
[tex](\frac{1}{8} -\frac{30}{4})+(\frac{30}{8}x+\frac{5}{8} x)\\[/tex]
[tex]\frac{1-60}{8} +\frac{35}{8}x[/tex]
Adding, we get,
[tex]-\frac{59}{8} +\frac{35}{8}x[/tex]
Taking out the common term [tex]-\frac{1}{8}[/tex] , we have,
[tex]-\frac{1}{8} (59-35x)[/tex]
Thus, the expression [tex]\frac{1}{8} -10(\frac{3}{4}-\frac{3}{8}x)+\frac{5}{8} x[/tex] is equivalent to [tex]-\frac{1}{8} (59-35x)[/tex]
A box measures 1/4ft. long, 1/6ft. wide, and 1/3ft. high. Find the volume of the
box in inches
Answer:
24 cubic inches
Step-by-step explanation:
1 ft = 12 inches
convert all dimensions to inches
1/4 ft = 1/4 * 12= 3 inches
1/6 ft = 1/6 * 12 = 2 inches
1/3 ft = 1/3 * 12 = 4 inches
Volume of a box = L*W*H
= 3 * 2 * 4
= 24 cubic inches
Therefore 1/72 ft will be 1/72 * 12
= 1/6 inches
PLEASE HELP GET 20 PTS HELLLLLLP !!!!!
ALSO GET NAMED BRAINLIEST AND GET A THANK U AND A FOLLOW
1.
Given the data presented in the bar graph, which sport represents 20% of the favorite sport for those surveyed?
Baseball
Tennis
Basketball
Soccer
Answer:
Baseball
Step-by-step explanation:
There are 30 people in total who voted in survey
9 Soccer
7 Basketball
5 Tennis
3 Hockey
6 Baseball
If 30 represents 100% of them then we divide 30 by 100 then multiply by 20
30 ÷ 100 × 20 = 6 is the number of people likes baseball as their favourite.
Fill in the blanks to make the solution correct.
3 3/4-_* _/8=2
When graphed, which function would appear to be shifted 5 units up from the graph of f(x)=x^2+3?
Answer:
f(x)=x^2+8
Step-by-step explanation:
To move a function upwards, you need to shift the function up the y axis. The function intersects the y axis at 3, so you need to add 5 to 3 to shift the graph up 5 units. I hope this helps you!
What is the value of x? Enter your answer in the box. 68mm 57mm 129.2mm
Question:
What is the value of x? Enter your answer in the box. 68mm 57mm 129.2mm
The image of the triangle is attached below:
Answer:
The value of x is 98mm
Explanation:
It is given that VT = 57, TK = 129.2, YK = 68 and VK = x
Now, we need to find the value of x.
We shall determine the value of x, using angle bisector theorem,
[tex]\frac{YK}{TK} =\frac{YV}{VT}[/tex]
Let us substitute the values, we get,
[tex]\frac{68}{129.2}=\frac{x-68}{57}[/tex]
Switch sides, we have,
[tex]\frac{x-68}{57}=\frac{68}{129.2}[/tex]
Multiply both sides by 57,
[tex]\frac{57(x-68)}{57}=\frac{68 *57}{129.2}[/tex]
Simplifying, we get,
[tex]x-68=30[/tex]
Adding both sides by 68, we have,
[tex]x=98[/tex]
Thus, the value of x is 98mm
What is the next fraction in this sequence? Simplify your answer.
2/3 1/3 1/6 1/12
Answer:
1/24
Step-by-step explanation:
As you go fraction to the next fraction you divide by 2.
2/3 divided by 2 = 1/3
1/3 divided by 2 = 1/6
the rule is "divide by 2"
Final answer:
The next fraction in the sequence is 1/24, found by continuing the pattern of halving each successive fraction.
Explanation:
To determine the next fraction in the sequence 2/3, 1/3, 1/6, 1/12, we observe a pattern. The second fraction is half of the first, the third is half of the second, and the fourth is half of the third. By continuing this pattern, to find the next fraction, we need to take half of the last fraction in the sequence.
To solve the more difficult problem, multiply the numerator and denominator by a skillfully chosen factor: 1/2. For the fraction 1/12, we multiply both the numerator (1) and the denominator (12) by 1/2 to get our next fraction:
Numerator: 1 imes 1/2 = 1/2Denominator: 12 imes 1/2 = 6Therefore, the next fraction in the sequence is 1/2 divided by 6 which simplifies to 1/24.