kayla has 5 books in her backpack that weigh 25 pounds. How much would 2 books weigh
A 14 ounce energy drink contains 10 1/2 teaspoons of sugar.How much sugar is in one ounce of the drink?
A.3/4 teaspoon
B.1 1/3 teaspoons
C.1 1/2 teaspoons
D.3 1/2 teaspoons
fil in the balnk for what makes the equation true 10* =5
Answer:
1/2 or 0.5
Step-by-step explanation
1/2 of 10 = 5
We can write 1/2 as a decimal.
Do you need a decimal or fraction as the answer?
Still stuck? Get 1-on-1 help from an expert tutor now.
10 pounds of
strawberries cost
$20. 7 pounds of
strawberries cost
$14. What is the
cost per pound?
Find the area. PLEASE HELP!!!!
Answer:
623 mm²
Step-by-step explanation:
I am going to split this shape into a 15mm x 19mm rectangle and a 26mm x 13mm rectangle. (the 19mm comes from 32mm at the bottom minus 13mm at the top to find how long the first rectangle is)
Rectangle 1: 15mm • 19mm = 285mm²
Rectangle 2: 26mm • 13mm = 338mm²
Total Area: 285mm² + 338mm² = 623mm²
Triangle ABC is shown on the grid below.
Which value best represents the length of AB?
a 8 units
b 12 units
c 15 units
d 21 units
Answer:
15 units
Step-by-step explanation:
you have to use pythagoras to solve (c²=a²+b²)
AB is the longest side of the triangle which is c in the pythagoras
so counting the units for AC, you get 9 units, and CB you get 12 units
now solve for c in pythagoras
c²=9²+12²
c = 15 units
Use 3.14 as an approximation for π. Round your answer to the nearest tenth.
Answer:
7
Step-by-step explanation:
1.5 x 1.5 = 2.25
2.25 x 3.14 = 7.065
[tex]Area \: = \pi {r}^{2} = 3.14 \times {1.5cm}^{2} \\ = 7.065 \: \: {cm}^{2} [/tex]
= 7 cm^2
someone please give a step by step way on how to solve this problem
Answer:
10
Step-by-step explanation:
There are several ways to solve this problem which I’ll demonstrate these ways and see which method is way easier to understand.
First Method
This method is to convert the fractional expression to a single exponent expression using a law of exponent.
[tex]\displaystyle \large{\frac{m^a}{m^b} = m^{a-b}}[/tex]
In words, it means if both divisor (denominator) and dividend (numerator) have same values or are same, we can subtract the exponent from dividend (numerator) with divisor (denominator).
The dividend (numerator) exponent is unknown, let’s say it’s got ‘x’ as an exponent and this ‘x’ is what we are going to find since we don’t know its value.
Now we have the equation:
[tex]\displaystyle \large{\frac{m^x}{m^7} = m^3}[/tex]
Apply the exponent rules above.
[tex]\displaystyle \large{m^{x-7} = m^3}[/tex]
Solve an exponential equation - If both sides of equation have same base, we can solve the exponents.
Since LHS (Left-Handed Side) and RHS (Right-Handed Side) both have same base which is ‘m’ therefore, solve exponents.
[tex]\displaystyle \large{x-7=3}\\\displaystyle \large{x=7+3}\\\displaystyle \large{x=10}[/tex]
Therefore, the missing exponent is 10.
Additional Info
You can also use logarithm to solve an exponential equation.
[tex]\displaystyle \large{m^{x-7} = m^3}[/tex]
Take a logarithm of base ‘m’ both sides so we can apply other properties.
[tex]\displaystyle \large{\log_m m^{x-7} = \log_m m^3}[/tex]
From the property [tex]\displaystyle \large{\log_a b^n = n \log_a b}[/tex]
[tex]\displaystyle \large{(x-7) \log_m m = 3 \log_m m}[/tex]
From the property [tex]\displaystyle \large{\log_a a = 1}[/tex]
[tex]\displaystyle \large{(x-7)1 = 3 \cdot 1}\\\displaystyle \large{x-7=3}\\\displaystyle \large{x=10}[/tex]
______________________________
Second Method
This method is to isolate the term with missing exponent.
[tex]\displaystyle \large{\frac{m^x}{m^7} = m^3}[/tex]
Transport m^7 to multiply with m^3 via transportation property.
[tex]\displaystyle \large{m^x = m^3 \cdot m^7}[/tex]
We also have to apply another law of exponent as well.
[tex]\displaystyle \large{m^a \cdot m^b = m^{a+b}}[/tex]
Similar to the one with division (fraction), this one, when same bases multiply each other, we have to add both exponents while the other one subtracts exponents.
[tex]\displaystyle \large{m^x = m^{3+7}}\\\displaystyle \large{m^x = m^{10}}[/tex]
In the first method, we know that when solving an exponential equation, if two bases from left and right sides are same, we solve the exponent.
Therefore, [tex]\displaystyle \large{m^x = m^{10} \to \boxed{x=10}}[/tex]
______________________________
Summary
Laws of Exponent
[tex]\displaystyle \large{a^m \cdot a^n = a^{m+n}}\\\displaystyle \large{\frac{a^m}{a^n} = a^m \div a^n = a^{m-n}}\\[/tex]
For what I demonstrate in my explanation only.
Exponential Equation
When two bases from left side and right side are same, we can solve through exponents.
Examples:
[tex]\displaystyle \large{2^{x-3} = 2^{4}}\\\displaystyle \large{x-3=4}\\\displaystyle \large{x=4+3}\\\displaystyle \large{x=7}[/tex]
You can also substitute x-value in an equation to see if both sides are equal or not.
[tex]\displaystyle \large{2^{x-4} =2^3}[/tex]
Substitute x = 7 for check.
[tex]\displaystyle \large{2^{7-4} = 2^3}\\\displaystyle \large{2^3 = 2^3 \ \ \checkmark}[/tex]
Logarithm
This is not necessary used in this question. This is mostly used for converting to exponential and more advanced mathematics.
[tex]\displaystyle \large{\log_a b^n = n\log_a b}\\\displaystyle \large{\log_a a = 1}[/tex]
Only from what I demonstrate in my explanation.
______________________________
If you are still stuck or need clarification regarding my answer and explanation, you may ask in comment below.
Hope this helps! And wish you luck in your assignment.
Peyton invested \$1700$1700 in an account that pays 3.5% interest compounded annually. Assuming no deposits or withdrawals are made, find how much money Peyton would have in the account 15 years after her initial investment. Round to the nearest tenth (if necessary).
Based on the amount Peyton invested, and the interest rate, the amount in the account 15 years later would be $2,848.09.
How much would be in the account after 15 years?The amount in the account after 15 years would be:
= Amount x ( 1 + rate) ^ number of years
Solving gives:
= 1,700 x ( 1 + 3.5%)¹⁵
= $2,848.09
Find out more on future value at https://brainly.com/question/24978019.
Answer:
2848.1
Step-by-step explanation:
Given the function f(x)=3x^2+4x−4
find the following.
(a) the average rate of change of f on [−4,0].
(b) the average rate of change of f on [x,x+ℎ].
Answer:
(a) -8
(b) 6x +4 +3h
Step-by-step explanation:
Sometimes, it works well to find the general solution first, then use that to solve the specific problem. That's what we'll do here.
(b)The average rate of change on the interval [x, x+h] is defined as ...
m = (f(x+h) -f(x))/h
For the given f(x), this is ...
[tex]m=\dfrac{((3(x+h)^2+4(x+h)-4)-(3x^2+4x-4)}{h}\\\\m=\dfrac{3x^2 +6xh+3h^2+4x+4h-4-3x^2-4x+4}{h}\\\\m=\dfrac{6xh+3h^2+4h}{h}\\\\\boxed{m=6x+4+3h}\qquad\text{average rate of change on $[x,x+h]$}[/tex]
__
(a)Using the above result for the interval [-4. 0], we have x=-4 and h=4. The average rate of change on that interval is ...
m = 6(-4) +4 +3(4) = -24 +4 +12 = -8
The average rate of change on [-4, 0] is -8.
_____
Additional comment
In the above, we worked the generic problem first. That way, we only needed to expand f(x+h)-f(x) once. If you're not terribly comfortable with doing algebra on literal expressions, sometimes it is more comfortable to work the numerical problem--as this question would have you do. This lets you get an idea of the kinds of operations that are involved and the way terms combine.
We note that the average rate of change is the instantaneous rate of change (derivative of the function) at the midpoint of the interval. That derivative is the value of m when h=0: 6x+4. The midpoint of the interval [-4,0] is x=-2, and the derivative there is 6(-2)+4 = -8, as above.
hi can anyone help with this? 15 points.
Step-by-step explanation:
that a picture of what you need. Go through it and get back to me.
Turtle Chocolate Company is having a Valentine’s Day sale for its customers. Matt is trying to determine the combinations of dark chocolate candy and white chocolate candy he can buy. He wants to spend no more than $60.
If boxes of dark chocolate candy cost $12 each and boxes of white chocolate candy cost $10 each, which inequality represents all possible combinations of x boxes of dark chocolate candy and y boxes of white chocolate candy?
The inequality that represents all the possible combinations he can buy is $12x + $10y ≤ $60.
What do inequality signs mean?
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
What equation represents the total combinations he can buy?The inequality sign to use is ≤ less than or equal to. This is because he does not want to spend more than $60.
$12x + $10y ≤ $60.
To learn more about inequality, please check: https://brainly.com/question/5031619
a rectangular poster is 17 inches by 54 inches long. write and solve an equation to estimate the area of the rectangle poster. what is the actual area of the rectangular poster
It should be noted that the area of the rectangle given will be 918 inches².
How to calculate area of a rectangleFrom the information given, it was stated that a rectangular poster is 17 inches by 54 inches long.
The area of the rectangle will be:
Area = Length × Width
Area = 17 × 54
Area = 918 inches²
Learn more about area on:
https://brainly.com/question/25292087
The sum of the second and third terms of a geometric sequence is 280 and the sum of the fifth and the sixth terms is 4375. Determine the common ratio and the first term
Step-by-step explanation:
I'll do it on my laptop.......
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = - 6x - 8
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 10) and (x₂, y₂ ) = (- 1, - 2) ← 2 points on the line
m = [tex]\frac{-2-10}{-1-(-3)}[/tex] = [tex]\frac{-12}{-1+3}[/tex] = [tex]\frac{-12}{2}[/tex] = - 6
the line crosses the y- axis at (0, - 8 ) ⇒ c = - 8
y = - 6x - 8 ← equation of line
Please I need helppp!!
Answer:
1) c
2) b
Step-by-step explanation:
1) translated 6 units to the left will be negative = x-6
5 units up will be positive = y+5
2) when reflecting across the x-axis, the x-values of each original point will remain the same and the y-values will become opposite. For example one point is (-5, 3) which will be (-5, -3) as the opposite of 3 is -3 which is in the form (x,-y)
Write a quadratic function f whose zeros are -12 and 1.
Someone please help me out with this /: I can’t find the answer
PLEASE
Answer: x= -20/3 and y= 34/3
hope this helps :)
Step-by-step explanation:
what is the unit rate for 4 gallons
Answer:
completing the division operation: numerator divided by denominator.
Step-by-step explanation:
If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.
Graph this line using the slope and y-intercept: y = 1/8x + 4
(1/8 is a fraction)
Answer:
Two points, (0,4) & (8,5)
Step-by-step explanation:
In this equation, we can easily find the first point by looking at the +4 in this equation. This should automatically signal to you that the point is (0,4)
Now, we have to look at the 1/8x in the equation.
This 1/8 means that the slope is 1/8!
Now we use the slope and to rise/run to find our next point
We go up 1 from 4 (this is the rise) to get to 5 on the y-axis
Next, we go over 8 horizontally to get to 8 for your x-axis point.
So therefore, our next point is, (8,5)
You can use this rise/run system infinitely and is very useful
Can someone help me with number 5? Thanks:)
Answer:
Yes
Step-by-step explanation:
Domain : 0 ≤ x ≤ 8
Range : 0 ≤ y ≤ 56
In the data set {(0,−1);(−2,4);(−4,−8);(−1,5);(1,−3);(2,1);(3,−2);(−1,2)}, which point is a possible outlier?
(−4,−8)open paren negative 4 comma negative 8 close paren
(2,1)open paren 2 comma 1 close paren
(−1,5)open paren negative 1 comma 5 close paren
(3,−2)
From the coordinate points, we can see that the data point that differs significantly is (−4,−8)
What is an outlier?An outlier in statistics is a data point that differs significantly from other observations in the given data
This may be due to variability in the measurement or it may indicate an experimental error.
From the coordinate points, we can see that the data point that differs significantly is (−4,−8). This gives the possible outlier of the given coordinate
Learn more on outlier here: https://brainly.com/question/3631910
Answer:
It's would be -4,-8 Have a great day
In a bag containing 4 yellow balls and 3 blue balls. 2 balls are drawn in a succession without replacement. Find The values of random variables. B where B represents the number of blue balls drawn
The above pic is your answer mate.
Rebecca can do 150 jumping jacks in two minutes and Marcus can do 625 jumping jacks in eight minutes. who can do more jumping jacks per minute and by how much?
Answer:
Marcus can do more jumping jacks per minute.
Step-by-step explanation:
By 3 more jumping jacks.
Answer:
ryan can do the most
Step-by-step explanation:
by 3
What is the value of x?
Enter your answer as a decimal in the box.
Answer:
[tex]x = 22.5[/tex]
Explanation:
Given Sides:
HB = 6HD = 6+15 = 21HM = 9HT = 9 + x-----------------------------
using all these sides, create similarities equation:
[tex]\frac{HB}{HD} = \frac{HM}{HT}[/tex]
[tex]\frac{6}{21} = \frac{9}{9+x}[/tex]
[tex]6(9+x) = 9(21)[/tex]
[tex]54 + 6x = 189[/tex]
[tex]6x = 189 - 54[/tex]
[tex]6x = 135[/tex]
[tex]x = \frac{135}{6}[/tex]
[tex]x = 22.5[/tex]
Which relationship is proportional?
A. Bob scored 24 points in 4 games and Joe scored 48 points in 10 games.
B. At one store it costs $18 for 3 necklaces and at another it's $30 for 5 necklaces
C. Casey worked 4 hours for $32 and Allie worked 7 hours for $28.
Somebody please help me I am struggling very much
Answer:
B
Step-by-step explanation:
We will divide 18 by 3 and 30 by 5, and if the results are the same, then this relationship is proportional.
18/3 = 6
30/5 = 6
The two answers are the same, so this relationship is proportional.
list the sides of the triangle from smallest to largest.
Tiffany took her friends out to dinner. The total cost of the dinner was $29.53. If she wanted to leave a 20% tip, how much money would she need to leave total?
Answer:
$35.436
Step-by-step explanation:
Hope this helps! :)
Answer:
$35.436
Step-by-step explanation:
Hope you like bro !!!!!!!!!!!
PLS MARK ME THE BRAINLIEST
The factory pays 7 cents per kWh for energy. Find the cost for each bulb type at 0 hours of
and at 10,000 hours of use. Show your work. (4 points: 1 point for each of the four costs)
Cost at 0 hours ($)
Cost at 10,000 hours ($)
CFL bulb
$
LED bulb
$
Answer:
$46.27¢
Step-by-step explanation:
Good thing I was a teacher
Ben and Landon took turns driving on a 820 mile road trip. Ben averaged 60 miles per hour and Landon averaged 56 miles per hour. The trip took them 14 hours. How many hours did Landon drive?
Answer:
See below!
Explanation:
distance = speed * timespeed = distance/timetime = distance/speedequation for distance:
Lets Ben hours be x and Landon hours be y,
60x + 56y = 820 .........equation 1
equation for time:
[tex]\frac{60x}{60}+ \frac{56x}{56} =14[/tex]
x + y = 14 .........equation 2
Make x the subject:
60x + 56y = 820
x = (820 - 56y)/60 ..........equation 3
x + y = 14
x = 14 - y ........equation 4
Solve equation 3 and 4 simultaneously:
14 - y = (820 - 56y)/6060(14 - y) = 820 - 56y840 - 60y = 820 -56y840 - 820 = -56y + 60y20 = 4yy = 5[ Therefore Landon drove 5 hours ]
Extra's further investigated:
if y = 5
x = 14 - yx = 14 - 5x = 9[ Therefore Ben drove 9 hours ]
Answer:
Landon drove 5 hours (and Ben drove 9 hours)
Step-by-step explanation:
Let B = number of miles Ben drove
Let L = number of miles Landon drove
Given The trip took them 14 hours
⇒ B + L = 14
Given, Ben averaged 60 miles per hour and Landon averaged 56 miles per hour. Ben and Landon took turns driving on a 820 mile road trip:
⇒ 60B + 56L = 820
Rewrite B + L = 14 to make B the subject, substitute into 60B + 56L = 820, and solve for L:
⇒ B = 14 - L
⇒ 60(14 - L) + 56L = 820
⇒ 840 - 60L + 56L = 820
⇒ 20 = 4L
⇒ L = 5
Therefore, Landon drove for 5 hours