Answer:
3 months
Explanation:
Amount saved in Gina’s saving account= 250
Amount Gina puts in her account each month= 4% of 3100
=[tex]\frac{4}{100} \times 3100[/tex]
= 4 × 31
= 124
Hence total amount added in each month =124
Therefore money credited x months
= 250 + 124 x
Amount saved in Rodger’s account = 350
Amount Rodger puts in his account each month = 3% of 2900
=[tex]\frac{3}{100} \times 290[/tex]
=87
Hence total amount added in each month = 87
Therefore money credited x months
=350 + 87 x
Now to calculate the nearest month when Gina have more in her account than Rodger does
=Amount of money credited in x months in Gina’s account ≥ Amount of money credited in x months in Rodger’s account
=250+124 x ≥ 350+87 x
=37 x≥100
= x≥2.78
=3
Suppose a,b,and c are all negative numbers how do you find the distance between points (a,b) and (a,c)?
Answer:
Distance = |b - c|
Step-by-step explanation:
Suppose a, b, and c are all negative numbers.
We have to describe the way to find the distance between points (a,b) and (a.c).
Since the x-coordinates of the two points are the same and are a, therefore, the distance between the y-coordinates of the two points will give the distance between the two points.
Mathematically the distance d will be given by d = |b - c|, where |x| is the absolute value function of x. (Answer)
Find the value of x to the nearest tenth.
tan 34° = 20
Answer:
The value of x = 13.5.
Step-by-step explanation:
In this question x is missing.
So, the question would be:
tan 34° = x/20.
Now, to find the value of [tex]x[/tex]:
[tex]tan 34 = \frac{x}{20}[/tex]
[tex]\frac{x}{20} = tan 34[/tex]
Multiplying both sides by 20 we get:
[tex]x=tan 34\times 20[/tex]
On simplifying both sides we get:
[tex]x=13.49[/tex]
So, to get the value of [tex]x=13.49[/tex] to nearest tenth is 13.5. As we see in hundredth place it is 9 and 4 in tenth place, so after rounding to tenth place 4 will change to 5 so the value is 13.5.
Therefore, the value of x = 13.5.
Answer:13.5
Step-by-step explanation:
(Score for Question 3:_ of 16 points)
3. Mr. Sanchez's class sold fruit pies for $1.55 each and Mr. Kelly's class sold bottles of fruit juice for $1.40
each. Together, the classes sold 60 items and earned $88.20 for their school.
(a) Write and solve a system of equations that model the problem. Show all your work
(b) Which class earned more money?
(c) How much more money did that class earn?
Answer:
Answer:
a) Mr. Sanchez's class sold 28 fruit pies and Mr. Kelly's class sold 32 bottles of fruit juice.
b) Mr. Kelly's class
c) Mr. Kelly's classs earned $1.40 more than Mr. Sanchez's class.
Step-by-step explanation:
Let x be the number of fruit pies sold and y be the number of bottles of fruit juice sold.
Together, the classes sold 60 items, so
x + y = 60
Mr. Sanchez’s class sold fruit pies for $1.55 each, so x fruit pies cost $1.55x.
Mr. Kelly’s class sold bottles of fruit juice for $1.40 each, so y bottles of fruit juice cost $1.40y.
Together, the classes earned $88.20 for their school, so
1.55x + 1.40y = 88.20.
a) You get the system of two equations:
[tex]\left\{\begin{array}{l}x+y=60\\ \\1.55x+1.40y=88.20\end{array}\right.[/tex]
From the first equation:
[tex]x=60-y[/tex]
Substitute it into the second equation:
[tex]1.55(60-y)+1.4y=88.2\\ \\155(60-y)+140y=8,820\\ \\9,300-155y+140y=8,820\\ \\-15y=8,820-9,300\\ \\-15y=-480\\ \\15y=480\\ \\y=32\\ \\x=60-32=28[/tex]
Mr. Sanchez's class sold 28 fruit pies and Mr. Kelly's class sold 32 bottles of fruit juice.
b) Mr. Sanchez's calss earned:
[tex]\$1.55\cdot 28=\$43.40[/tex]
Mr. Kellyz's calss earned:
[tex]\$1.40\cdot 32=\$44.80[/tex]
Since [tex]\$44.80>\$43.40,[/tex] Mr. Kelly's class earned more.
c) Mr. Kelly's classs earned [tex]\$44.80-\$43.40=\$1.40[/tex] more than Mr. Sanchez's class.
1092 flowers are arranged into 26 vases with the same number of flowers in each vase. How many flowers would be needed to fill 130 such vases?
Answer:
5460
Step-by-step explanation:
can u help me.............
Answer:
2 should be your answer
Step-by-step explanation:
There is 2 horizontal and 2 vertical in total there are 2 lines of symmetry.
What equation represents this coordinate grid?
16 points will mark brainiest
Answer:
E=5
Step-by-step explanation:
Given,
[tex]32= 2^E[/tex]
We know [tex]32[/tex] can be written as [tex]2^5[/tex]
Substituting [tex]2^5[/tex] in place of [tex]32[/tex]
We get,
[tex]2^5 = 2^E[/tex]
Since the base is equal, now comparing the exponent.
Therefore [tex]E=5[/tex] is the missing exponent.
Answer:
E = 5 and [tex]32 = 2^5[/tex]
Step-by-step explanation:
Given:
[tex]32 = 2^E[/tex]
Now we know that E is denoted as an exponent term,
Exponent term indicates the value which can be to the power of a number.
Now 32 can be written as,
[tex]32 = 2\times 2\times2\times 2\times2[/tex]
Hence from above we can say that 2 can be multiplied 5 times to get the value as 32.
hence we can say that,
[tex]32 = 2^5[/tex]
Hence E=5
11. Find the values of x and y.
(1 pc
(14y+30)°
(3x)0
156°
x=8, y = 9
x = 10, y = 9
x = 8, y = 10
Answer:
Reasoning and Proof Unit Test
Step-by-step explanation:
1. 67
2. counterexample
3. If you join the gym, then it is free for the first three months.
Hypothesis: you join the gym
Conclusion: it is free for the first three months
4. Yes; two lines intersect at right angles if (and only if) they are perpendicular
5. An angle is obtuse if and only if its measure is greater than 180
6. Symmetric Property
7. 12
8. RT-ST
9. x=8, y=9
10. 7
11. Symmetric Property
12. invalid
13. A. is Substitution Property of Equality, B. is Supplementary Angles, C. is Subtraction Property of Equality
14. (A) 180, (B) 180, (C) transitive property, (D) 3, (E) 3
15. The value of x is 3.
a) Addition of line segments
b) Substitution rule
c) Simplification by addition of like terms
d) Collecting lie terms
e) Dividing both sides by 8
AB = 2x
BC = 6x + 8
AC = 32
AB + BC = AC (Addition rule)
Addition of the component segments of a line
2x + 6x + 8 = 32 (Substitution rule)
Substituting for AB, BC, and AC in the equation AB + BC = AC
8x + 8 = 32 (Simplification)
Simplifying 2x + 6x + 8 = 32 by adding like terms
8x = 24 (Collecting like terms)
8x = 32 - 8
8x = 24
x = 3 (Divide both sides by 8)
8x / 8 = 24/8
x = 3
16. If it is square it is a Quadrilateral.
17. 7y = 8x - 14
7(6) = 8x - 14
Collect like terms.
42 = 8x - 14.
8x = 42 + 14
8x = 56
x = 56/8
x = 7
These are all the correct answers as of 2022
A set of scales is used to show that two lemons and seven tomatoes are required
to balance one cabbage. If two lemons balance one tomato, how many tomatoes will balance one cabbage?
Answer:
8 tomatoes are required to balance 1 cabbage
Step-by-step explanation:
Given :
Two lemons and seven tomatoes are required to balance one cabbage:
2 Lemons + 7 tomatoes = 1 cabbage (equation 1)
two lemons balance one tomato
2 lemons = 1 tomato
put in equation 1:
1 tomato + 7 tomatoes = 1 cabbage
8 tomatoes = 1 cabbage
8 tomatoes required to balance one cabbage
Rewriting the expression 15x+9 as 9+ 15x is an example of the ———— property of ———-?
Rewriting the expression 15x+9 as 9+ 15x is an example of the commutative property of addition
Solution:The commutative property of addition states that when two numbers are being added, their order can be changed without affecting the sum.
To “commute” means to move around or travel.
According to the commutative property of addition, changing the order of the numbers we are adding, does not change the sum
When two numbers are added, the sum is the same regardless of the order of the addends. For example 4 + 2 = 2 + 4
For addition, the rule is a + b = b + a
Here in the problem 15x + 9 is equivalent to 9 + 15x
Hence, rewriting the expression 15x+9 as 9+ 15x is an example of the commutative property of addition
The process of rewriting 15x + 9 as 9 + 15x uses the Commutative property of addition. This asserts that changing the order of addition doesn't affect the sum.
Explanation:Rewriting the expression 15x+9 as 9+15x is an example of the Commutative property of addition. The Commutative property states that the order in which you add or multiply numbers does not affect the sum or product. So in your case, 15x + 9 = 9 + 15x because of the Commutative property of addition. This is true for addition of ordinary numbers as well, for instance 2 + 3 will yield the same result as 3 + 2.
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if 2 is the square root of four what is the squre root of 81
5)
→ A down payment of $400 is what percent of the cost of $2500?
This needs to be shown full work on elementary math class ASAP!
Answer:
The percent of down payment of the cost $2500 is 16% .
Step-by-step explanation:
Given:
Down payment = $400.
Cost = $2500.
Now, to find the percent of down payment of the cost.
According to question:
$400 / $2500 × 100.
⇒[tex]\frac{400}{2500} \times 100[/tex]
⇒[tex]0.16\times 100[/tex]
⇒[tex]16[/tex].
Therefore, the percent of down payment of the cost $2500 is 16%.
16% is the answer to your question.
An item was listed price of $60. If the sales tax rate is 6%, how much is the sales tax (in dollars)
Select the equation of the line that passes through the point (3,5) and is
perpendicular to the line x = 4, (2 points)
O 1) y = 5
O2) x = 5
O3) y = 4
O 4) x=3
The equation of the line that passes through the point (3 , 5) and is
perpendicular to the line x = 4 is y = 5 ⇒ answer 1
Step-by-step explanation:
Let us revise some notes about the horizontal and vertical lines
The horizontal line is a line parallel to x-axisThe equation of a horizontal line passes through point (a , b) is y = b, because the y-coordinates of all points on the line are equalThe vertical line is a line parallel to y-axisThe equation of a vertical line passes through point (a , b) is x = a, because the x-coordinates of all points on the line are equalThe horizontal line and the vertical line are perpendicular∵ The equation of the given line is x = 4
- From the 4th note above the given line is a vertical line
∴ The given line is a vertical line
- The perpendicular line to a vertical line is a horizontal line
∴ The perpendicular line to the given line is horizontal
∵ The perpendicular line passes through the point (3 , 5)
∵ The equation of the horizontal line is y = b, where b the
y-coordinate of any point lies on the line
∵ The point (3 , 5) lies on the line
- The y-coordinate of the point is 5
∴ b = 5
∴ The equation of the perpendicular line is y = 5
The equation of the line that passes through the point (3 , 5) and is
perpendicular to the line x = 4 is y = 5
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How to solve 5-2x=-4x-7
Answer:
x=-6
Step-by-step explanation:
Use Substitution
so 5-2x=-4x-7
I'ma move that -4x to the other side by making it a positive
5+2x=-7
than I'ma move that 5 to the other side by making it a negative
2x=-12
to isolate the x you dived by both sides by the 2
x=-6
I doubled checked and it's -6
Answer:
Pull out like terms: 12 + 2x = 2 • (x + 6)
Solve: x+6 = 0
Then you get; X=-6
I hope this is right and hopefully it helped you
Translate this sentence into a equation
The sum of 21 and Vanessa's savings is 68
whats the unit rate of 122 and 4?
Answer: 30.5
Step-by-step explanation:
30.5 times 4 equals 122
Write in point-slope form an equation of the line that
passes through the given point and has the given slope.
1. (1, 5); m = 2
2. (-2, 4); m = -3
3. (4, 2); m
= 3
4. (-1, 5); m = -2
5. (2, -4); m = -3
6. (-5, 1); m = 2
Answer:
6. [tex]\displaystyle y - 1 = 2(x + 5)[/tex]
5. [tex]\displaystyle y + 4 = -3(x - 2)[/tex]
4. [tex]\displaystyle y - 5 = -2(x + 1)[/tex]
3. [tex]\displaystyle y - 2 = 3(x - 4)[/tex]
2. [tex]\displaystyle y - 4 = -3(x + 2)[/tex]
1. [tex]\displaystyle y - 5 = 2(x - 1)[/tex]
Step-by-step explanation:
In the Point-Slope Formula [y - y₁ = m(x - x₁)], all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT SIGNS.
I am joyous to assist you anytime.
To complete her holiday wrapping, Bella needs identical strips of ribbon measuring 3.5 feet each. She has 85 feet of ribbon in total. About how many pieces of ribbon can she cut from this long strip? PLS ANSWER ASAP
Bella can cut 24 pieces of ribbon from this long strip
Solution:
Given that Bella has 85 feet of ribbons in total
She needs identical strips of ribbon measuring 3.5 feet each
To find: Number of peices of ribbon can she cut from long strip
Number of peices of ribbon can she cut from long strip can be calculated by dividing the total feet of ribbon she has by length of identical strips she needs
Mathematically written as:
[tex]\text { Number of Strip that can be cut }=\frac{\text { Total length of ribbon }}{\text { Length of each piece }}[/tex]
[tex]\begin{array}{l}{\text { Number of Strip that can be cut }=\frac{85}{3.5}} \\\\ {\text { Number of Strip that can be cut }=24.28 \approx 24}\end{array}[/tex]
Hence , the number of strip can be 24 each of size 3.5 feet
What value of x will make the equation 5x-2/11 = -7 a true statement
Answer:
X=-15
Step-by-step explanation:
Multiply both sides by 11
5x-2=-77
add 2 to both sides
5x=-75
Divide both sides by 5
x=-15
The value of x equal to -15 will make the given equation a true statement.
What is an equation?It is a mathematical statement that shows that two mathematical expressions are equal.
The given equation is
(5x-2) / 11 = -7
Multiply both sides by 11
i.e. 5x-2 = -77
Then add 2 to both sides
i.e. 5x = -75
Divide both sides by 5
i.e x = -15
Hence, the value of x that will make the equation 5x-2/11 = -7 a true statement is -15.
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32. Which value of x will make the equation below true?
3x = 243
A). 3
B). 5
C). 8
D). 9
The quadratic function g(x) = a.ca + bx+c has the complex roots (-7+ 4i) and (-7 – 4i). You may assume that a=1. What is the value of b? What is the value of c?
The value of b is 14
The value of c is 65
Step-by-step explanation:
The quadratic equation ax² - bx + c = 0, where a = 1 has two roots
Their sum = bTheir product = c∵ The quadratic function is g(x) = ax² + bx + c
∵ a = 1
∴ g(x) = x² + bx + c
∵ g(x) has two complex roots (-7 + 4i) and (-7 - 4i)
∴ g(x) = 0
∴ x² + bx + c = 0
∵ The general form of the quadratic equation is x² - bx + c = 0,
with sum of roots b and product of roots c
- Compare them
∴ x² - (-b) + c = 0
∵ -b = the sum of the two roots
∴ -b = (-7 + 4i) + (-7 - 4i)
- Add like terms
∴ -b = (-7 + -7) + (4i + -4i)
∴ -b = -14 + 0
∴ -b = -14
- Multiply both sides by -1
∴ b = 14
The value of b is 14
∵ c is the product of the two roots
∴ c = (-7 + 4i)(-7 - 4i)
- Remember (a + b)(a - b) = a² - b²
∵ (-7 + 4i)(-7 - 4i) = (-7)² - (4i)²
∵ (-7)² = 49
∵ (4i)² = 16i²
∵ i² = -1
∴ (4i)² = -16
∴ (-7)² - (4i)² = 49 - (-16) = 49 + 16 = 65
∴ (-7 + 4i)(-7 - 4i) = 65
∴ c = 65
The value of c is 65
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Eric wants to buy a video game that cost $24 but he only wants to spend 40% of your savings. How much must Eric saying in order to buy the game
Answer:
$14.4
Step-by-step explanation:
I don't really understand the question, but this is what I think it is
Eric needs to have $60 in savings if he wants to spend only 40% of it on a $24 video game.
Explanation:To determine how much Eric must have in savings to spend only 40% on a $24 video game, we set up a simple equation where 40% of his total savings (S) equals the price of the game ($24). The equation is 0.40 × S = $24. Solving this equation for S (total savings), we divide both sides by 0.40:
× S = $24
÷ 0.40 ÷ 0.40
S = $24 ÷ 0.40
S = $60
Therefore, Eric must have a total of $60 in savings to spend only 40% on the video game.
James and Lin got married and got new jobs. Lin earns $3100 more per year than James. Together they earn $81,980. How much does each of them earn per year?
Answer:
The earning to James per year is $ 39,440
The earning of Lin per year is $ 42,540 .
Step-by-step explanation:
Given as :
The total earning of James and Lin together = $ 81,980 per year
The earning of Lin is $ 3100 more per year than James
Let The earning of James = $ J
And The earning of Lin = $ J + $ 3100
So, According to question
The total earning of James and Lin together = $ 81,980 per year
Or, The earning of Lin + The earning of James = $ 81,980 per year
Or, $ J + $ 3100 + $ J = $ 81,980 per year
or, 2 $ J = $ 81,980 - $ 3100
Or, 2 $ J = $ 78880
∴ J = [tex]\frac{78880}{2}[/tex]
I.e The earning to James per year = $ 39,440
And The earning of Lin per year = $ 34,440 + $ 3100 = $ 42,540
Hence, The earning to James per year is $ 39,440
And The earning of Lin per year is $ 42,540 . answer
The value of the expression 4 square root of 81^3 is ______.
Choices:
9
27
350
1.4
2.3
Answer:27
Step-by-step explanation:
Nathan hit 19 homeruns. He scored 3 fewer homeruns than twice the number of homeruns hit by jason. Write and solve an equation to show how many homeruns Jason hit
Jason hit 11 homeruns.
Step-by-step explanation:
Homeruns hit by Nathan = 19
Let,
Homeruns hit by Nathan = x
Homerun hit by Jason = y
According to given statement;
x = 2y - 3 Eqn 1
We know that Nathan hit 19 homeruns, therefore, putting x=19 in Eqn 1
[tex]19=2y-3\\19+3=2y\\22=2y\\2y=22[/tex]
Dividing both sides by 2;
[tex]\frac{2y}{2}=\frac{22}{2}\\y=11[/tex]
Jason hit 11 homeruns.
Keywords: linear equations, addition
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Decide whether the pair of lines is parallel, perpendicular, or neither.
3x - 6y = -13 and
18x + 9y = 5
A) Parallel
B) Perpendicular
C) Neither
The lines are: B) Perpendicular
Step-by-step explanation:
we have to convert both lines in slope-intercept form to find slopes
So,
[tex]3x - 6y = -13\\-6y = -3x-13\\\frac{-6y}{-6} = \frac{-3x-13}{-6}\\\frac{-6y}{-6} = \frac{-3x}{-6}+\frac{-13}{-6}\\y = \frac{1}{2} +\frac{13}{6}[/tex]
Let m1 be the slope of first line
[tex]m_1 = \frac{1}{2}[/tex]
For the second line:
[tex]18x + 9y = 5\\9y = -18x+5\\\frac{9y}{9} = \frac{-18x+5}{9}\\\frac{9y}{9} = \frac{-18}{9}x+\frac{5}{9}\\y = -2x+\frac{5}{9}[/tex]
Let m2 be the slope of line 2
So,
If the lines are parallel, their slopes are equal
If the lines are perpendicular, product of their slopes is -1
We can see that
[tex]\frac{1}{2} * -2 = -1[/tex]
Hence,
The lines are: B) Perpendicular
Keywords: Slopes, Parallel lines
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The lines given by the equations 3x - 6y = -13 and 18x + 9y = 5 are neither parallel nor perpendicular because their slopes, 1/2 and -2 respectively, are neither equal nor negative reciprocals of each other.
Explanation:To decide whether the pair of lines given by the equations 3x - 6y = -13 and 18x + 9y = 5 is parallel, perpendicular, or neither, we need to find the slope of each line. First, we convert the equations into the slope-intercept form, which is y = mx + b where m is the slope.
For the first equation, 3x - 6y = -13, we solve for y:
-6y = -3x - 13y = (1/2)x + 13/6The slope of this line is 1/2.
For the second equation, 18x + 9y = 5, we also solve for y:
9y = -18x + 5 y = -2x + 5/9The slope of this line is -2.
Since the slopes of the two lines are neither equal (which would make them parallel) nor negative reciprocals of each other (which would make them perpendicular), the lines are neither parallel nor perpendicular.
Solve for x -1/2(x+5)=-10
Answer:
-15
Step-by-step explanation:
x-1/2(x+5)=-10
x-1/2x-5/2=-10
2/2x-1/2x-5/2=-10
1/2x-5/2=-10
1/2x=-10+5/2
1/2x=-20/2+5/2
1/2x=-15/2
x=(-15/2)/(1/2)
x=(-15/2)(2/1)
x=-15/1
x=-15
Jessie estimated the weight of his cat to be 12 pounds. The actual weight of the cat is 15 pounds.
What is the percent error?
Round your answer to the nearest whole percent.
Answer:
20%
Step-by-step explanation:
% of error is given by the following formula:
% Error = [tex]\frac{|\textrm {Approx Value - Exact Value}|}{\textrm {Exact Value}} \times 100[/tex]
Now, Jessie estimated the weight of his cat to be 12 pounds i.e. Approximate value is 12 pounds.
Again, The actual weight of the cat is 15 pounds i.e. the exact value is 15 pounds.
Therefore, the % error = [tex]\frac{|12 - 15|}{15} \times 100 = \frac{3}{15} \times 100 = 20[/tex]% (Answer)
Answer:
20%
Step-by-step explanation:
Jessie thinks to greatly of his cat
and I took the test
Ashley solved the equation for m using the following steps.
-4.5 + m = 17
-4.5 -4.5
m = 12.5
What was Ashley’s error?
Ashley should have subtracted 17 to both sides.
Ashley should have added 4.5 to both sides.
Ashley should have added 17 to both sides.
Ashley’s work does not have an error.
Answer:
Ashley should have added 4.5 to both sides.
Step-by-step explanation:
Given expression:
[tex]-4.5+m=17[/tex]
Ashley's solution:
Subtracted 4.5 to both sides and got,
[tex]m=12.5[/tex]
Correct solution:
Adding 4.5 to both sides.
[tex]-4.5+m=17[/tex]
[tex]+4.5[/tex] [tex]+4.5[/tex]
∴ [tex]m=21.5[/tex]
Error made by Ashley was subtracting 4.5 both sides. Instead he should have added 4.5 both sides.