Answer:
Sophia now has 39 cents.
Step-by-step explanation:
One quarter = 25 cents
Since Sophia had 64 cents until she spent 25 cents (1 quarter).
So we subtract 25 cents from 64 cents.
[tex] \: \: \: 64 \: cents \\ \frac{ - 25 \: cents}{ \: \: \: 39 \: cents} [/tex]
Therefore, Sophia now has 39 cents.
Solve : 4/x-3 + 2/x-2 = 6/x
Answer:
x = [tex]\frac{9}{4}[/tex] or 2.5
Step-by-step explanation:
[tex]\frac{4}{x-3} + \frac{2}{x-2} = \frac{6}{x}[/tex]
Finding L.C.M. of (x - 3) and (x - 2)
[tex]\frac{4(x-2) + 2(x-3) }{(x-3)(x-2)} = \frac{6}{x}[/tex]
[tex]\frac{(4x-8) + (2x-6)}{x^{2} - 3x-2x+6}=\frac{6}{x}[/tex]
[tex]\frac{4x-8 +2x-6}{x^{2} -5x +6} = \frac{6}{x}[/tex]
[tex]\frac{6x-14}{x^{2} -5x+6}= \frac{6}{x}[/tex]
Cross multiplying:
x (6x - 14) = 6 (x² - 5x +6)
6x² - 14x = 6x² - 30x + 36
Cancelling 6x² from both the sides:
- 14x = - 30x + 36
30x - 14x = 36
16x = 36
x = [tex]\frac{36}{16}[/tex]
∴ x = [tex]\frac{9}{4}[/tex] or 2.5
Can anyone answer this geometry question help pls!!
Please help me.
The coordinates for the vertices of quadrilateral ABCD are A(-3,2) B(-2,6) C(2,7) and D(1,3). Use this information to answer the questions below.
Slope of side AB:
A. 1/4
B. 4/1
C. -1/4
D. -4/1
Slope of side CD
A. 1/4
B. 4/1
C. -1/4
D. -4/1
Slope of side DA
A. 1/4
B. 4/1
C. -1/4
D. -4/1
Classify the quadrilateral
A. Square
B. Rectangule
C. Rhombus
D. Parallelogram
E. Trapezoid
A 64-ounce bottle of apple juice costs $1.35. What is the approximate unit price for this bottle of apple juice?
The approximate unit price for the juice is about $0.50
Step-by-step explanation:
To find the unit price of an item, you must divide the price ($1.35) by how many units the item has (64 ounces). So 64 divided by 1.35 would be 47, or 50 since it's asking for the approximate unit price. Convert it and you have your answer. $0.50. Hope this helps :) I apologize if it's not completely correct
Tomika heard that the diagonals of a rhombus are perpendicular to each other. Help her test her conjecture. Graph quadrilateral ABCD on a coordinate grid with A(1, 4), B(6, 6), C(4, 1), and D(–1, –1).
a. A rhombus has 4 sides that are equal length. Is ABCD a rhombus? Show how you know.
b. Write the equations of the lines on which the diagonals lie. That is, write the equations of lines AC and BD.
c. Compare the slopes of lines AC and BD. What do you notice?
Answer:
a. The four sides of the quadrilateral ABCD are equal, therefore, ABCD is a rhombus
b. The equation of the diagonal line AC is y = 5 - x
The equation of the diagonal line BD is y = 5 - x
c. The diagonal lines AC and BD of the quadrilateral ABCD are perpendicular to each other
Step-by-step explanation:
The vertices of the given quadrilateral are;
A(1, 4), B(6, 6), C(4, 1) and D(-1, -1)
a. The length, l, of the sides of the given quadrilateral are given as follows;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
The length of side AB, with A = (1, 4) and B = (6, 6) gives;
[tex]l_{AB} = \sqrt{\left (6-4 \right )^{2}+\left (6-1 \right )^{2}} = \sqrt{29}[/tex]
The length of side BC, with B = (6, 6) and C = (4, 1) gives;
[tex]l_{BC} = \sqrt{\left (1-6 \right )^{2}+\left (4-6 \right )^{2}} = \sqrt{29}[/tex]
The length of side CD, with C = (4, 1) and D = (-1, -1) gives;
[tex]l_{CD} = \sqrt{\left (-1-1 \right )^{2}+\left (-1-4 \right )^{2}} = \sqrt{29}[/tex]
The length of side DA, with D = (-1, -1) and A = (1,4) gives;
[tex]l_{DA} = \sqrt{\left (4-(-1) \right )^{2}+\left (1-(-1) \right )^{2}} = \sqrt{29}[/tex]
Therefore, each of the lengths of the sides of the quadrilateral ABCD are equal to √(29), and the quadrilateral ABCD is a rhombus
b. The diagonals are AC and BD
The slope, m, of AC is given by the formula for the slope of a straight line as follows;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Therefore;
[tex]Slope, \, m_{AC} =\dfrac{1-4}{4-1} = -1[/tex]
The equation of the diagonal AC in point and slope form is given as follows;
y - 4 = -1×(x - 1)
y = -x + 1 + 4
The equation of the diagonal AC is y = 5 - x
[tex]Slope, \, m_{BD} =\dfrac{-1-6}{-1-6} = 1[/tex]
The equation of the diagonal BD in point and slope form is given as follows;
y - 6 = 1×(x - 6)
y = x - 6 + 6 = x
The equation of the diagonal BD is y = x
c. Comparing the lines AC and BD with equations, y = 5 - x and y = x, which are straight line equations of the form y = m·x + c, where m = the slope and c = the x intercept, we have;
The slope m for the diagonal AC = -1 and the slope m for the diagonal BD = 1, therefore, the slopes are opposite signs
The point of intersection of the two diagonals is given as follows;
5 - x = x
∴ x = 5/2 = 2.5
y = x = 2.5
The lines intersect at (2.5, 2.5), given that the slopes, m₁ = -1 and m₂ = 1 of the diagonals lines satisfy the condition for perpendicular lines m₁ = -1/m₂, therefore, the diagonals are perpendicular.
A scatter plot showed a positive correlation for 11 bowlers. As the number of strikes, s, a bowler made in a game increased, the number of points, p, the bowler scores also increased. The equation for the line of best fit for the data is p=25s+40. Estimate the number of strikes made by a bowler with 140 points.
Answer:
s = 4
Step-by-step explanation:
The equation for the line of best fit for the data is p=25s+40.
Where p is no. of points and s is no. fo strikes
We need to find the number of strikes made by a bowler with 140 points.
Put p = 140
p=25s+40
140 = 25s+40
Subtract 40 to both sides,
140-40 = 25s+40-40
100 = 25s
⇒ s = 4
So, there are 4 strikes made by a bowler with 140 points.
A sports team is ordering a new banner to hang over the entrance of their stadium. The banner will be a right triangle where one leg is 33 feet and the other leg is 56 feet. All three edges of the banner will be lined with a ribbon that costs $0.50 per foot. How much will the ribbon cost?
Answer:
The ribbon cost is $77
Step-by-step explanation:
Firstly, we need to get the 3rd side of the triangle
This represents the hypotenuse since we have 2 legs, we need the side connecting the legs
To get this, we use Pythagoras’ theorem
This states that the square of the hypotenuse equals the sum of the squares of the two other sides
Let the hypotenuse be marked x
Thus;
x^2 = 56^2 + 33^2
x^2 = 3136 + 1089
x^2 = 4225
x = square root of 4225
x = 65 feet
So the length of all the sides will be;
56 + 33 + 65 = 154 feet
So the cost of the ribbon will be;
154 feet. * 0.5
= $77
hi guys can you help me with this maths calculation
$36 - $17.85 =
Answer and Step-by-step explanation:
36 dollars minus 17.85 dollars equals $18.15, or 18 dollars and 15 cents.
All you have to do is subtract 36 by 17.85
36 - 17 = 19
100 - 85 = 15
1 is subtracted from 19 because of the decimal.
18.15
#teamtrees #WAP (Water And Plant)
HELP, I have to turn this in tomorrow ... is this correct??
Answer: yes
Step-by-step explanation:
here are two receipts from a meal in a restaurant one persons subtotal is $24.95 if the tax rate at the restaurant is 9.5% how much will their sale tax be?
Answer:
$24.95X.095=$2.37
Answer:
Step-by-step explanation: 3.27
Josue tosses a coin and spins the spinner at the right. What are all the possible outcomes?
Answer:
50 50 ?
Step-by-step explanation:
Evaluate the expression yz when x= 3, y=6 and z=12.
Answer: 72
Step-by-step explanation:
y=6, z=12
yz=6 x 12=72
A model house has a scale of 3 cm : 6 m.
If the model house is 9 cm wide, then how
wide is the real house?
Ricardo bought a bicycle that was discounted 20% off the original price. If the original price was $110.00, what was the price of the bicycle after the discount was applied?
Answer:
88$
Step-by-step explanation:
I WILL GIVE YOU BRAINLIEST FOR THE CORRECT ANSWERS
1. 25x^(2)-35x+7y-y^(2)
2. a^2+8a+16b-4b^2
3. 9a^2-4b^2-3a+2b
Factor completely
8> -1; Subtract 8 from both sides.
Answer:
0 > -9
Step-by-step explanation:
8 > -1
-8 -8
0 > -9
Find the measure of the indicated angle. Round to the nearest tenth of a
degree.
pls help with this asap
Help me please I'm so stuck lol 15 pts.!!
Answer:
r = 0.1
Step-by-step explanation:
Constant proportionality or slope(rate of change) is found by Y divided by X.
1.4(y) ÷ 14(x) = 0.1(slope)
1.6(y) ÷ 16(x) = 0.1(slope)
2.1(y) ÷ 21(x) = 0.1(slope)
Check Work:
14 x 0.1 = 1.4
16 x 0.1 = 1.6
21 x 0.1 = 2.1
Answer:
1/10.
Step-by-step explanation:
The proportionality equation is given to you: [tex]y = rx[/tex]
Next, plug in the given [tex]x[/tex] and [tex]y[/tex] variables into the equation:
When: [tex]x = 14[/tex] & [tex]y = 1.4[/tex]
[tex]1.4 = r(14)\\1.4 = 14r\\(1.4)/14 = (14r)/14\\1.4/14 = r\\r = 0.1[/tex]
When: [tex]x = 16[/tex] & [tex]y = 1.6[/tex]
[tex]1.6 = r(16)\\1.6 = 16r\\(1.6)/16 = (16r)/16\\r = 1.6/16\\r = 0.1[/tex]
When: [tex]x = 21[/tex] & [tex]y = 2.1[/tex]
[tex]2.1 = r(21)\\[/tex]
[tex]21r = 2.1\\(21r)/21 = (2.1)/21\\r = 2.1/21\\r = 0.1[/tex]
r = 0.1 in all of the given, ∴ 0.1 is your answer. Change the decimal into a fraction:
0.1 = 1/10
1/10 is your answer.
~
help solve for x please!
x to the third power= -8
Answer:
X = 2
Step-by-step explanation:
2 x 2 x 2 = 8
Hope this helps. Pls give brainliest.
Answer:
2 :)
Step-by-step explanation:
(-2/10)^4 power
HELP MEE PLS
Answer:
1/625
Step-by-step explanation:
simply
(-1/5)^4
1/625
Answer:
The answer is 1/625
Step-by-step explanation:
hope this helps
Find the median of the
data. 7,5, 12, 8, 2,9,4
Answer:
7
Step-by-step explanation:
First, put them in numerical order: 2, 4, 5, 7, 8, 9, 12
Then cross out one from each side until you get to the middle
The median of the given data set 7,5, 12, 8, 2,9,4 is 7.
What are the mode and median?Mode is the highest frequency number while the median is the middle value of a data set after writing either increasing or decreasing manner.
For example;
Set { 1,2,2,3,4,5,6} here mode is 2 and median is 3.
Given the data set,
7,5, 12, 8, 2,9,4
If we write it in increasing order then,
2, 4, 5, 7, 8, 9, 12
Now median is middle value so here 7 is in between 3 - 3 from left and right.
Hence "The median of the given data set 7,5, 12, 8, 2,9,4 is 7".
To learn more about mode and median,
https://brainly.com/question/300591
#SPJ2
Which equation describes a line with a slope of -1/2 that contains the point (-5, 2)?
A. x + 2y = 1
B. x - 2y = -1
C. x - 2y = 1
D. x + 2y = -1
Answer:
The equation x + 2y = -1 describes a line with a slope of -1/2 that contains the point (-5, 2) ⇒ D
Step-by-step explanation:
The slope of the linear equation of the form ax + by = c is m = [tex]\frac{-a}{b}[/tex] , where a and b are integersLet us use this rule to solve the question
The slope of the line is [tex]-\frac{1}{2}[/tex] and the line contains the point (-5, 2)
We want to find which equation has the same slope and contains the point
A.
∵ x + 2y = 1
∴ a = 1 and b = 2
→ Use the rule above to find m
∴ m = [tex]\frac{-1}{2}[/tex]
∴ The line has the same slope
→ Let us find if the line contains the point (-5, 2), by substituting x by -5
and y by 2 in the left side of the equation if the answer equals
the right side, then the line contains it
∵ L.S = -5 + 2(2) = -5 + 4 = -1
∵ R.S = 1
∴ L.S ≠ R.S
∴ The line does not contain the point (-5, 2)
B.
∵ x - 2y = -1
∴ a = 1 and b = -2
→ Use the rule above to find m
∴ m = [tex]\frac{-1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
∴ The line does not have the same slope
C.
∵ x - 2y = 1
∴ a = 1 and b = -2
→ Use the rule above to find m
∴ m = [tex]\frac{-1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
∴ The line does not have the same slope
D.
∵ x + 2y = -1
∴ a = 1 and b = 2
→ Use the rule above to find m
∴ m = [tex]\frac{-1}{2}[/tex]
∴ The line has the same slope
→ Substitute x by -5 and y by 2 in the left side
∵ L.S = -5 + 2(2) = -5 + 4 = -1
∵ R.S = -1
∴ L.S = R.S
∴ The line contains the point (-5, 2)
The equation x + 2y = -1 describes a line with a slope of -1/2 that contains the point (-5, 2)
A store sells a 1/1/4 pound package of turkey for $9 whats the unit price of the turkey in the package
Answer:
$7.20
Step-by-step explanation:
The first step is to convert 1 1/4 to decimal form. 1/4=0.25, which when added to the 1 gives a total weight of 1.25 pounds. Dividing this by the price to find the unit price, you get 9/1.25=$7.20 per pound of turkey. Hope this helps!
Chef Rita is cooking for a Sunday brunch. She knows that 22 pancakes can feed 8 people. She is wondering how many people (p)(p)left parenthesis, p, right parenthesis she can feed with 55 pancakes. She assumes each person eats the same quantity of pancakes.
How many people can Rita feed with 55 pancakes?
Answer:we can solve the problem by setting a simple proportion.
We know that 22 pancakes can feed 8 people, so we have to find the number x which corresponds to the number of people that can be feeded with 55 pancakes:
Solving the proportion, we find
So, 55 pancakes can feed 20 people.
Step-by-step explanation:
Anyone? If you know it can you please help mee if you maybe know it please comment thanks I appreciate you all <:)
Answer:
Answer is 159
Step-by-step explanation:
Use PEMDAS
First, solve paranthesis
10² + 8² - 5
Then from left to right, solve the exponents
100 + 8² - 5
100 + 64 - 5
Then, add
164 - 5
Subtract
159
Answer:
=159
Step-by-step explanation:
10^2 + (3+5)^2 - 5
10^2 = 10 x 10 = 100
100+ (3+5) (3+5) - 5
100+(8)(8)-5
100+64-5
164-5
=159
Hope this helps! :)
Please help me ASAP!
Answer:
A and B are parallel to D and C
or
A and D to B and C
basically do a line and expand them if they touch they are not parralelogram but if they don't they are
I need help please!!
Answer:
y=-2x+5
Step-by-step explanation:
thats the equation because you use the formula, y=mx+b. b is the y intercept (the verticle straight line) and m is the slope. hope this helped!!
What’s the answer? True or false
Answer:
True because it is true thank U
5) The sides of a quadrilateral are in the ratio 1:2:3:6. The perimeter is 138 cm.
Answer:
The first side is 11.5cm, the second is 11.5cm×2 = 23cm, the third is 11.5cm × 3 = 34.5cm,
and the fourth side is 11.5cm × 6 = 69cm.
Step-by-step explanation:
A quadrilateral is a 4 sided shape, while perimeter is the addition of all the sides of the quadrilateral. Since the sides of the quadrilateral is not stade, assume the sides of the quadrilateral is x, therefore 1:2:3:6 = x:2x:3x:6x. The total ratio is x+2x+3x+6x=12x, therefore 12x= 138 , x = 11.5cm, Therefore the first side is 11.5cm, the second is 11.5cm×2 = 23cm, the third is 11.5cm × 3 = 34.5cm, and the fourth is 11.5cm × 6 = 69cm.