Answer:
They have to drive [tex]20\frac{1}{4}[/tex] miles more
Step-by-step explanation:
Given:
Total Distance of the road trip = [tex]32 \frac{3}{4}[/tex] miles
Distance travelled already = [tex]12 \frac{1}{2}[/tex] miles.
To Find:
How much farther do they have to drive = ?
Solution:
The distance they have to travel farther = Total distance - distance travelled
The distance they have to travel farther = [tex]32 \frac{3}{4} - 12 \frac{1}{2}[/tex]
=>[tex]\frac{128 + 3}{4} - \frac{24 +1}{2}[/tex]
=>[tex]\frac{131}{4} - \frac{25}{2}[/tex]
=>[tex]\frac{131- 50}{4}[/tex]
=>[tex]\frac{81}{4}[/tex]
=>[tex]20\frac{1}{4}[/tex]
Which property of multiplication is shown?
g • h = h • g
Commutative property of multiplication
My explanation is attached in the image provided.
Hardcover books cost $8 and paperbacks cost $3. John buys 15 books for $70. How many of each book type did he buy?
Answer:
10 paperback and 5 hardcover books
Step-by-step explanation:
Please see attached picture for full solution.
Let's check:
total cost= 10(3) + 5(8)= $70 ✓
You could also try to solve the question by assuming John bought all paperback books first instead of all hardcover books. The answer should be the same.
Can someone please help me with this question
Answer:
B, E
Step-by-step explanation:
It can be helpful to factor the first two terms:
f(x) = x^2(x -7) +36
This can make it easier to evaluate the function for different values of x.
The answer choices suggest you need to know whether f(5) and f(-14) match the values given here.
f(5) = 5^2(5 -7) +36 = -50 +36 = -14 . . . . matches choice B (and E)
f(-14) = (-14)^2(-14-7) +36 = -21(196) +36 . . . . does not match choice A (or D)
__
The one remaining answer choice we need to consider is C. If we look at f(0) for this equation, we find it is (-5)(-10) +14 = 64, which does not match f(0) = 36 for the function given in the problem statement.
The only true answer choices are B and E.
_____
The remainder theorem tells you that f(a) = the remainder from f(x)/(x -a).
Find the perimeter of the polygon
Answer:
The perimeter of the polygon is 48 cm.
Step-by-step explanation:
Given: [tex]\angle B \cong \angle D[/tex]
To find the perimeter of the polygon, we need to find the lengths of the AB, BC, CD and DA
Since, [tex]\angle B \cong \angle D[/tex] and to find the length, from circle theorem, "Two tangents from an external point to a circle are always equal in length".
From this statement we shall conclude,
The length of [tex]AB=5+6=11[/tex]
The length of [tex]BC=6+7=13[/tex]
The length of [tex]CD=7+6=13[/tex]
The length of [tex]DA=6+5=11[/tex]
Thus, the perimeter of the polygon is
[tex]\begin{aligned}\text {Perimeter} &=A B+B C+C D+D A \\&=11+13+13+11 \\&=48 \mathrm{cm}\end{aligned}[/tex]
Hence, the perimeter of the polygon is 48 cm.
Aaden is packing boxes into a carton that is 8 inches long, 8 inches wide, and 4 inches tall. The boxes are 2 inches long, 1 inch wide, and 1 inch tall. How many boxes will fit into the carton?
Answer:
first multiply length×width×height,of the carton
8×8×4=256
then multiply length×width×height for boxes
2×1×1=2
divide 256 by 2
256÷2=128
Given the two linear equations 4r - 5 = 17 and 12 - 2s = 2, what is the product of r and s?
[tex]\text{You're solving the equations:}\\\\4r - 5 = 17\\ 12 - 2s = 2\\\\\text{Solve for r:}\\\\4r-5=17\\\\\text{add 5 to both sides}\\\\4r=22\\\\\text{Divide both sides by 4}\\\\\boxed{r=5.5}\\\\\text{Solve for s:}\\\\12 - 2s = 2\\\\\text{Subtract 12 from both sides}\\\\-2s=-10\\\\\text{Divide both sides by -2}\\\\[/tex]
[tex]\boxed{s=5}[/tex]
An equation is formed when two equal expressions. The product of r and s is 27.5.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation 4r - 5 = 17 can be solved for r as shown below,
4r - 5 = 17
Add 5 on both the sides of the equation,
4r - 5 + 5 = 17 + 5
4r = 22
Divide both the sides of the equation by 4,
4r / 4 = 22 / 4
r = 11/2
r = 5.5
The given equation 12 - 2s = 2 can be solved for s as shown below,
12 - 2s = 2
Subtract 12 from both the sides of the equation,
12 - 2s - 12 = 2 - 12
-2s = -10
Divide both the sides of the equation by -2,
-2s/-2 = -10/-2
s = 5
Now, the product of r and s can be written as,
r × s
= 5.5 × 5
= 27.5
Hence, the product of r and s is 27.5.
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Ann works in a supermarket for $10.00 per hour. If her pay is increased $12.00, then what is her percent increase in pay
Answer: 20%
Step-by-step explanation:
Percentage increase = increase / original value x 100
Increase = $12.00 - $10.00 = $2
Therefore :
% increase = [tex]\frac{2}{10}[/tex] x 100
% increase = 20
Answer:
20%
Step-by-step explanation:
12.00 - 10.00 = 2.00
2 divided by 10 = 0.2
100 multiplied by 0.2 which gives you 20%
Antonio has $350 to spend on skis. Sales tax is 6%. Decide if each description of a price and discount, plus sales tax, represents a pair of skis that Antonio can purchase with the money he has .
Choose Yes or No for each description
a. 25% off $450 Yes or No
b. 20% off $385 Yes or No
c. $20 off $360 Yes or No
d. 15% off $380 Yes or No
e. $10 off $340 Yes or No
Answer:
False
Step-by-step explanation:
3/?= 2/1.25 can you answer this for me please
Answer:
3/15/8=2/1.25
Step-by-step explanation:
Answer:
see attached work shown
If a lb of beef cost $4.25, how much would 1 1/4 lb cost?
Step-by-step explanation:
$4.25×1 1/4=$4.25/1×5/4=$21.25/4=$5.25
Answer:it would cost 5.25
Step-by-step explanation:
Simplify this expression.
1 + 4.25n + 32p – 3 + (–2p) + 54n
A. 5.5n – 12p – 2
B. 9.5n + 1.5p – 2
C. 94n − 1.5p − 4
The correct expression to simplify is:
[tex]1+4.25n + 3/2p -3+(-2p)+5/4n[/tex]
Answer:
[tex]5.5n-1/2p-2[/tex]
Explanation:
1. Given expression:
[tex]1+4.25n + 3/2p -3+(-2p)+5/4n[/tex]
2. Group like terms:
[tex](1-3)+(4.25n+5/4n)+(3/2p-2p)[/tex]
3. Simplify:
1 - 3 = - 24.25n + 5/4n = 4.25n + 1.25n = 5.5n3/2p - 2p = 1.5p - 2p = - 0.5p = - 1/2p[tex]-2+5.5n-1/2p=5.5n-1/2p-2[/tex]
PLEASE HELP ASAP!!!!!! 30 POINTS!!!!
I JUST NEED SOMEONE TO HELP ME WITH THE TOP ONE!!! PLEASE!!!!!
Graph the following lines given the equation or y-intercept with an ordered pair, with a y-intercept of 3 and an ordered pair of (3, 4).
Line 1: y-intercept: 3 ordered pair: (3, 4)
Line 2: y=-2x+2
Answer:
Part 1) The graph in the attached figure N 1
Part 2) The graph in the attached figure N 2
Step-by-step explanation:
Part 1) we have
Line 1: y-intercept: 3 ordered pair: (3, 4)
we know that
To draw a line we need a minimum of two points
Remember that the y-intercept is the value of y when the value of x is equal to zero
so
In this problem we have
(0,3) and (3,4)
Plot the points on a coordinate plane and connect them to graph the line
see the attached figure N 1
Part 2) we have
Line 2: y=-2x+2
Find the intercepts of the line
Find the y-intercept (value of y when the value of x is equal to zero)
For x=0
[tex]y=-2(0)+2=2[/tex]
The y-intercept is the point (0,2)
Find the x-intercept (value of x when the value of y is equal to zero)
For y=0
[tex]0=-2x+2\\2x=2\\x=1[/tex]
The x-intercept is the point (1,0)
Plot the intercepts and connect them to graph the line
see the attached figure N 2
Answer:
Part 1) The graph in the attached figure N 1
Part 2) The graph in the attached figure N 2
Step-by-step explanation:
Part 1) we have
Line 1: y-intercept: 3 ordered pair: (3, 4)
we know that
To draw a line we need a minimum of two points
Remember that the y-intercept is the value of y when the value of x is equal to zero
so
In this problem we have
(0,3) and (3,4)
Plot the points on a coordinate plane and connect them to graph the line
see the attached figure N 1
Part 2) we have
Line 2: y=-2x+2
Find the intercepts of the line
Find the y-intercept (value of y when the value of x is equal to zero)
For x=0
The y-intercept is the point (0,2)
Find the x-intercept (value of x when the value of y is equal to zero)
For y=0
The x-intercept is the point (1,0)
Plot the intercepts and connect them to graph the line
see the attached figure N 2
Find the cosine of T.
Answer:
c o s t = x \displaystyle P: \text{cos}t=x P:cost=x.
Step-by-step explanation:
The cosine of t is equal to the x-coordinate of point P
How many points need to be removed from this graph so
that it will be a function?
1 point
2 points
3points
4 points
Answer:
OPtion 3 points
Step-by-step explanation:
See the attached figure.
As shown, we can notice that the coordinates of all the points are (-3,2), (-3,3), (1,4), (1,-4), (2,-2), (2,-4).
The figure will be a function if for each value of x there exist a unique value of y.
In the figure, for each value of x we have two values of y. So it is not a function. We need to remove any of ordered pairs that have same input values.
From (-3,2) and (-3,3), we need to remove one point.
From (1,4) and (1,-4), we need to remove one point.
From (2,-2) and (2,-4), we need to remove one point.
It means total we need to remove 3 points from this graph so that it will be a function.
So, the correct option is 3 points.
I need the answer please ;/
Answer:Q
Step-by-step explanation: EF is a segment. k is not uppercase. and MN is a line. So only Q could work.
9 goes into 300 how many times
Answer:
300/9 = 33.33 repeating
Step-by-step explanation:
9 can go into 300, 33 times with a remainder of 3.
How many gallons of 90% antifreeze must be mixed with 60 gallons of 15% antifreeze to get a mixture that is 80%?
390 gallons of 90 % antifreeze must be mixed with 60 gallons of 15% antifreeze to get a mixture that is 80%
Solution:
Let "x" be the gallons of 90 % antifreeze
60 gallons of 15 % antifreeze
Then, (x + 60) is the gallons present in final mixture that is 80 %
Therefore, x gallons of 90 % antifreeze is mixed with 60 gallons of 15 % antifreeze to get a mixture that is (x + 60) gallons of 80 %
Thus, a equation is framed:
90 % of x + 15 % of 60 = 80 % of (x + 60)
Solve the above equation for "x"
[tex]90 \% \times x + 15 \% \times 60 = 80 \% \times (x+60)\\\\\frac{90}{100} \times x + \frac{15}{100} \times 60 = \frac{80}{100} \times (x+60)\\\\0.9x + 0.15 \times 60 = 0.8(x + 60)\\\\0.9x + 9 = 0.8x + 48\\\\0.9x - 0.8x = 48 - 9\\\\0.1x = 39\\\\ x = 390[/tex]
Thus 390 gallons of 90 % antifreeze must be mixed
Kara spends $16 on tubes of paint and paint brushes. A tube of paint costs $3 and a paint brush costs $.50. Kara purchases twice as many brushes as tubes of paint. How many tubes of paint and how many brushes did she buy?
Answer: 3(4) + .5(8) = 16
Step-by-step explanation:Replace b with 2p in the 1st equation
3p + .50(2p) = 16
3p + 1P = 16
4p = 16
p = 16/4
p = 4 tubes of pain
then
b = 2(4)
b = 8 brushes
Kara bought 4 tubes of paint and 8 brushes, given the total cost of $16, the price per tube of paint is $3, and the price per brush is $.50.
Explanation:The question is asking how many tubes of paint and brushes Kara bought if she spent a total of $16, each tube of paint costs $3, each brush costs $0.50, and the number of brushes is twice the number of tubes of paint. To solve this problem, we can denote the number of paint tubes as x and the number of brushes as 2x.
So we set up the equation considering the total amount spent: $3x + $0.50(2x) = $16. This simplifies to:
$3x + $1x = $16 $4x = $16 x = 4
So, she bought 4 tubes of paint and 2 times that number of brushes, which is 8 brushes.
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A 100-gram sample of a radioactive isotope decays at a rate of 6% every week. How much of the sample will be left one year from now?
4 grams sample will be left after 1 year
Step-by-step explanation:
The decay function for percentage decay is given by:
[tex]y =a (1-r)^x[/tex]
Here,
a is the initial value
r is the rate
x is the number of time periods
Given
Initial value = 100 grams
Rate = 6% = 0.06
Time = 1 year = 52 weeks
Putting the values in the formula
[tex]y = 100 (1-0.06)^{52}\\y = 100(0.94)^{52}\\y = 4.00\ grams[/tex]
Hence,
4 grams sample will be left after 1 year
Keywords: Decay, percentage
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The handford high school basketball team scored 79, 68, 86, 91 and 72 points in their first five games. What was the average number of points scored in these five games?
Answer: 79.2 points
Step-by-step explanation: The word "average" is the same as the word "mean" so to find the average of the points scored in their first 5 games, we want to add up all the points and divide them by the number of games they played which is 5 games.
Let's begin by adding the numbers.
79 + 68 + 86 + 91 + 72
Adding these numbers, we get a sum of 396.
This will be divided by how many games they played which is 5.
396 ÷ 5 = 79.2
This means that the average number of points scored is 79.2 points which could round down to 79 points but don't round unless the problem asks.
What is the arc length of the semicircle
Answer:
The arc length of the semicircle is half the circumference of the full circle
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=11 \end{cases}\implies C=2\pi (11)\implies C=22\pi \\\\\\ \stackrel{~\hfill \textit{a semicircle has half of that}}{C=\cfrac{22\pi }{2}\implies C=11\pi \implies C\approx 34.56}[/tex]
. If the perimeter of a rectangle is 18x + 4 what is the length of the missing side?
2X-3
Answer:
Step-by-step explanation:
Let the length b y
Width = 2x - 3
Perimeter = 18x + 4
And
Perimeter = 2(l + w)
18x + 4 = 2(y + 2x - 3)
Dividing through by 2
9x + 2 = y + 2x - 3
Making y as subject
y = 9x - 2x + 2 + 3
y = 7x + 5
The missing side is 7x + 5
7x+14=7(x+2)
[tex]7x + 14 = 7(x + 2)[/tex]
Answer:
The equation has infinitely many solutionsx ∈ REach real number is the solution of this equation.Step-by-step explanation:
[tex]7x+14=7(x+2)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\7x+14=(7)(x)+(7)(2)\\\\7x+14=7x+14\qquad\text{subtract}\ 7x\ \text{from both sides}\\\\7x-7x+14=7x-7x+14\\\\14=14\qquad\bold{TRUE}\\\\\bold{CONCLUSION}\\\text{The equation has infinitely many solutions}[/tex]
I need help solving these problems--Images down below.
On the long word problem, I was given hints:
X=Less than 5 weeks
Y=Less than 200
- Use substitution instead of graphing.
Answer:
all work is pictured and shown
John’s dog weighed 7 pounds when he got him. The dogs weight tripled each year for two years. How many ounces did John’s dog now weigh?
Answer:
Step-by-step explanation:
1st year- 7*3=21
2nd year- 21*3=63
how many days in one week?
Answer:
7 , Monday, Tuesday, Wednesday, Thursday, Friday, then you have you r weekend Saturday, Sunday, then you restart the week . :)
Step-by-step explanation:
Answer:
7 days in 1 week
Step-by-step explanation:
Count the days. (Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday)
-4 times a number plus 29
Answer:
-4x + 29
Step-by-step explanation:
solve the equation 1/3m+6m-9/3m=3m-3/4m
The correct answer is option B, as the solution of the equation:
[tex]\frac{1}{3 m}+\frac{6 m-9}{3 m}=\frac{3 m-3}{4 m}[/tex] is [tex]\frac{23}{15}[/tex]
Solving this type of equation containing the fractions involves the mathematical operations like finding a common denominator, combining the fractions, eliminating the fraction denominators, cancelling common terms, distributing, adding/subtracting to both sides, simplifying, and dividing both sides by the same factor.
The Steps of calculation are as follows:
Let's verify the answer:
We had the equation:
[tex]\[\frac{1}{3m} + \frac{6m - 9}{3m} = \frac{3m - 3}{4m}\][/tex]
And we simplified it to:
[tex]\[\frac{6m - 8}{3m} = \frac{3m - 3}{4m}\][/tex]
Next, we cross multiplied:
[tex]\[4m(6m - 8) = 3m(3m - 3)\][/tex]
[tex]\[24m^2 - 32m = 9m^2 - 9m\][/tex]
We then brought all terms to one side:
[tex]\[24m^2 - 9m^2 - 32m + 9m = 0\][/tex]
[tex]\[15m^2 - 23m = 0\][/tex]
Factoring out m:
[tex]\[m(15m - 23) = 0\][/tex]
So, either m = 0 or 15m - 23 = 0.
If 15m - 23 = 0, then [tex]\(m = \frac{23}{15}\)[/tex].
Therefore, the correct answer is: b. [tex]\frac{23}{15}$[/tex].
The total weight of a fully loaded coal truck is 4 tons. The ratio of the weight of the truck to the weight of the coal is 7:5. What is the weight of the truck and the coal?
Answer:
Step-by-step explanation:
total weight is 4 tons.
ratio of weight of truck to weight of coal is 7:5....added = 12
so 7/12 of the total weight is the truck's
and 5/12 of the total weight is the coal
7/12 of 4 tons = 7/12 * 4 = 28/12 = 2 1/3 tons <== weight of truck
5/12 of 4 tons = 5/12 * 4 = 20/12 = 1 2/3 tons <== weight of coal
You roll a number cube two times. How many outcomes are possible? Please explain work.
The total number of possible outcomes when rolling a six-sided number cube twice is 36. This is calculated by multiplying the 6 possible outcomes from the first roll with the 6 possible outcomes from the second roll.
When you roll a six-sided number cube two times, you create a series of possible outcomes that can be categorised by understanding that each roll is independent of the other. On the first roll, you have 6 possible outcomes (1, 2, 3, 4, 5, or 6), and for the second roll, regardless of what the first number was, you again have 6 possible outcomes. To find the total number of outcomes possible when rolling a cube twice, you multiply the number of outcomes for each event. So, we calculate the total outcomes with 6 (for the first roll) times 6 (for the second roll), which equals 36 possible outcomes.
This means that rolling two dice can lead to one of thirty-six different combinations, where the first number of the pair corresponds to the result of the first roll and the second number to the result of the second. For instance, if you first roll a 4 and then a 3, one possible outcome is (4,3).
It is important to note that when calculating probabilities for specific sums of the two dice, such as the probability of rolling a seven, the outcomes are not all equally likely. If we consider the sum of the dice, rolling a two is less likely than rolling a seven because there's only one combination (1,1) for a sum of two, while there are six combinations (1,6; 2,5; 3,4; 4,3; 5,2; 6,1) for a sum of seven.