Answer:
x = 8
Step-by-step explanation:
Since P is at the midpoint of HR, then
HP = PR ← substitute values
7x + 2 = 58 ( subtract 2 from both sides )
7x = 56 ( divide both sides by 7 )
x = 8
9x + 2y = 30
6x + 4y = 12
1. Simplifying
9x + 2y = 30
Solving
9x + 2y = 30
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2y' to each side of the equation.
9x + 2y + -2y = 30 + -2y
Combine like terms: 2y + -2y = 0
9x + 0 = 30 + -2y
9x = 30 + -2y
Divide each side by '9'.
x = 3.333333333 + -0.2222222222y
Simplifying
x = 3.333333333 + -0.2222222222y
-------------------------------------------------------------------------------------------
2. Simplifying
6x + 4y = 12
Solving
6x + 4y = 12
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-4y' to each side of the equation.
6x + 4y + -4y = 12 + -4y
Combine like terms: 4y + -4y = 0
6x + 0 = 12 + -4y
6x = 12 + -4y
Divide each side by '6'.
x = 2 + -0.6666666667y
Simplifying
x = 2 + -0.6666666667y
Answer:
For graphing, your answer is...(4,-3)
Step-by-step explanation:
1.Subtract 9x on both sides...
2y=30-9x
6x+4y=12
2. Divide each term by 2, then simplify...
-Divide... 2y=30-9x by 2.
2y/2=30/2+-9x/2
6x+4y=12
3. Reduce expression by...cancelling your common factors...
Cancel...2 from 2y/2
6x+4y=12
Divide y by 1...
y=30/2+-9x/2
6x+4y=12
4.Simplify each term...
-Divide thirty by two.
y=15+-9x/2
6x+4y=12
-Move your negative in the front of your fraction.
y=15 - 9x/2
6x+4y=12
5. Subtract 6x from both sides of your equation...
y=15 - 9x/2
4y=12-6x
6. Divide each term by four...divide terms in 4y=12-6x by four...
y=15 - 9x/2
4y/4=12/4+-6x/4
-Reduce expression by cancelling common factors in 4y/4...
Divide y by one...
y=15 - 9x/2
y=12/4+-6x/2
7. Simplify each term...Divide twelve by four...
y=15 - 9x/2
y=3+-6x/4
-Reduce expression by cancelling all common factors...
Your factor is 2 our of -6x...
y=15 - 9x/2
y=3+2(-3x)/4
-Cancel the common factors.. two out of four...
y=15 - 9x/2
y=3+2(-3x)/2(2)
-Cancel common factors again...
y=15 - 9x/2
y=3+-3x/2
8. Move your negative over to the front of your fraction...
y= 15 - 9x/2
y=3 - 3x/2
You get... (4,-3)
I hope this helps you and I also do hope that this is what you are looking for! If not, then my bad! Good luck, mate!
how do you simplify a algebraic equasion
Final answer:
To simplify an algebraic equation, combine like terms, reduce fractions, and cancel factors; multiply or divide both sides by the same number if needed, and check your work by substituting values back into the original equation.
Explanation:
Simplifying Algebraic Equations
To simplify an algebraic equation, you need to eliminate terms wherever possible. This process may involve combining like terms, reducing fractions, and canceling out factors. Multiplication or division by the same number on both sides of the equation does not change the equation's equality, so apply these operations carefully to all terms. Often, you'll want to collect constants inside the parentheses to consolidate them into a single value, making the equation simpler. After simplifying, it's important to check your answer to ensure that it is reasonable, which may involve plugging the solution back into the original equation or assessing the steps you've taken to make sure no errors were made.
Let's consider an example:
Simplify the equation by dividing both sides by a common factor, if applicable.
Collect like terms together and simplify further.
Check the simplified equation by substituting numbers to see if both sides remain equal or by ensuring logical algebraic steps were taken.
Remember, solving for an unknown variable requires doing the same operation on both sides of the equation, thereby maintaining balance. Systematic simplification and attentive checking are your keys to mastering algebraic equations.
If the two spinners below are spun, what is the probability that the numbers will match
Answer:
Yes, you are correct :)
Answer:
1/4
Step-by-step explanation:
what is the coefficient of determination for this data set.....the answer is 0.91
The coefficient of determination for this data set would be 0.91
What is Correlation Coefficient ?A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables. In other words, it reflects how similar the measurements of two or more variables are across a dataset.
The correlation coefficient for this data set will be positive, since the dependent variable increases as the independent variable decreases.
Since the data appears to be fairly linear, the correlation coefficient will be close to 1 which means 0.91 is our best choice.
Hence, The coefficient of determination for this data set would be 0.91
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585,156.22 nearest thousand
The graph shows the relationship between the late fines the library charges and the number of days late
Answer:
[tex]y=0.25x[/tex]
Step-by-step explanation:
We are given that a graph which shows the relationship between the late fines the library charges and the number of days late.
From given graph we can see that
The graph passes through the points (2,0.5) and (10,2.5).
We have to find the equation for the relationship.
Slope formula:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
By using the formula
Slope of graph=[tex]m=\frac{2.5-0.5}{10-2}[/tex]
Slope of graph=m=[tex]\frac{2}{8}=\frac{1}{4}[/tex]
Point slope- form:[tex]y-y_1=m(x-x_1)[/tex]
We have [tex]y_1=2.5,x_1=10[/tex]
Substitute the values then we get
The equation of for the relationship
[tex]y-2.5=\frac{1}{4}(x-10)[/tex]
[tex]y-2.5=0.25x-2.5[/tex]
[tex]y=0.25x-2.5+2.5=0.25x[/tex]
Hence, the equation for the relationship is given by
[tex]y=0.25x[/tex]
Hannah and Francine have $120.hannah and Peter have $230.Peter has 6 times as much money as Francine.How much money does Hannah have?
Answer:
$98
Step-by-step explanation:
x+6(120-x)=230
x+720-6x=230
-5x=-490
x-98
x represented how much money Hannah had.
4x + 6 over 2 equals 3x - 15 over 3
Answer:
x = -8Step-by-step explanation:
[tex]\dfrac{4x+6}{2}=\dfrac{3x-15}{3}\qquad\text{cross multiply}\\\\3(4x+6)=2(3x-15)\qquad\text{use the distributive property}\\\\(3)(4x)+(3)(6)=(2)(3x)+(2)(-15)\\\\12x+18=6x-30\qquad\text{subtract 18 from both isdes}\\\\12x=6x-48\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\6x=-48\qquad\text{divide both sides by 6}\\\\x=-8[/tex]
x=-8
Given equation is (4x+6)/2=(3x-15)/3, we need to find x
What is cross multiplication method?Multiply the numerator of one fraction to the denominator of other and denominator of the first term to the numerator of another term is called Cross Multiplication Method.
Given, (4x+6)/2=(3x-15)/3
Apply cross multiplication method
3(4x+6)=2(3x-15)
12x+18=6x-30
12x-6x=-30-18
6x=-48
Divide both sides by 6
x=-8
Therefore value of x in (4x+6)/2=(3x-15)/3 is '-8'.
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What is the volume of this rectangular prism?
Answer:
The answer is B. 54 cm
Step-by-step explanation:
When you find the volume of a rectangle you have to multiply the length, width, and height. The length is 9, width 3, and height 2. When you multiply them together you'll get 54
The height of a triangle is twice it's base. If the area of the triangle is 40 cm squared, what is the measure of it's height
3.7 ft
7.2 ft
8.1 ft
what is the answer?
Answer:
if this question was a volume question, then the answer would be 215.784ft^3
why: length times width times height
if this is not what you needed ignore it. I am basing this off of the given number.s
Step-by-step explanation:
What is the solution set of 4x2 - 36 = 0?
4x^2 - 36 = 0
4x^2 = 36
x^2 = 36/4
x^2 = 9
sqrt{x^2} = sqrt{9}
x = - 3 and x = 3
Find the value that makes the ratios equal. 51/18=x/6
if g is the midpoint of FH and FH =6y-2 find y
Answer:8
Step-by-step explanation: trust me
The relationship between y and x, given that g is the midpoint of FH is y = (1/3)x + (1/3).
If g is the midpoint of FH, it means that FH is divided into two equal segments, FG and GH, such that FG = GH.
Given that FH = 6y - 2, set up an equation to represent this:
FH = FG + GH
Substituting the values we know:
6y - 2 = FG + GH
Since FG = GH then
6y - 2 = x + x
Now, combine like terms:
6y - 2 = 2x
To find the value of y, isolate it on one side of the equation:
6y = 2x + 2
Now, divide both sides by 6 to solve for y:
y = (2x + 2) / 6
y = (2/6)x + (2/6)
y = (1/3)x + (1/3)
So, y is equal to (1/3)x + (1/3).
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90 POINTS Determine the measures of L and M.
Hey!
------------------------------------------------
To Solve We Need:
By looking at the picture we can see that the measure of N is 48 degrees.
A triangle needs a total of 180 degrees to be a complete triangle.
------------------------------------------------
Solution:
180 - 48 = 132 degrees
132 / 2 = 66 degrees
------------------------------------------------
Answer:
L and M measure 66 degrees!
------------------------------------------------
Hope This Helped! Good Luck!
Answer:
La and M 66 degrees !
Step-by-step explanation:
What is the slope of the line represented by the equation y = –y equals negative StartFraction one-half EndFraction x plus StartFraction one-fourth EndFraction.x + StartFraction one-fourth EndFraction.?
Answer:
Slope:
[tex]m = -\displaystyle\frac{1}{2}[/tex]
Step-by-step explanation:
We are given the equation:
[tex]y = -\displaystyle\frac{1}{2}x + \displaystyle\frac{1}{4}[/tex]
Comparing this equation to the slope-intercept form:
[tex]y = mx + c[/tex]
where m is the slope of line and c is the y-intercept that is the value of y when x is zero.
on comparing, we get:
[tex]m = -\displaystyle\frac{1}{2}\\c = \displaystyle\frac{1}{4}[/tex]
The slope of the given line is
[tex]m = -\displaystyle\frac{1}{2}[/tex]
The slope of the given line is -1/2
How to find the slope of an equationThe standard equation of a line is expressed as y = mx +b
where
m is the slope
b is the y-intercept
Given the equation y = -1/2x + 1/4
Compare the equations
mx = -1/2 x
m = -1/2
Hence the slope of the given line is -1/2
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Evaluate A 2-B 2 for A = 4 and B = -5.
Answer:
- 9
Step-by-step explanation:
Given
A² - B² ← substitute A = 4 and B = - 5 into the expression
= 4² - (- 5)²
= 16 - 25
= - 9
it takes 4/5 of an hour to paint 2/5 of a room, how long does it take to paint one room?
Answer:
120 mins
or
2hrs
Step-by-step explanation:60 min=1 hr
60 min/5=12 min
12(4)=48 min
24 min=1/5 of room
24(5)=120 min
120 min=2 hrs
It would take 2 hours to paint one room.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Time taken to paint 2/5 of the room = 4/5 hour
To find the time taken to paint one room,
Use ratio property,
2/5 room takes = 4/5 hour
1 room takes = 4/5 x 5/2 hours
= 4 / 2 hours
= 2 hours.
The one room takes 2 hours to paint.
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Help! I need help with this math problem. Only need to to D! (Will mark brainliest if you do all of them, though. :])
Answer:
Answer to D: 3/5
Step-by-step explanation:
There are 5 songs.
And 3 of them have the word "Mama" in the title.
Make 5 the total amount of songs and 3 songs are how many times the word "Mama" appears once in each song.
A trust fund worth $25,000 is invested in two different portfolios, this year, one portfolio is expected to earn 5.25% interest and the other is expected to earn 4%. Plans are for the total interest on the fund to be $1,150 in one year. How much money should be invested at each rate
Answer:
The amount of money that should be invested at the rate of 5.25% is $12,000 and the amount money that should be invested at the rate of 4% is $13,000
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
Let
x ------> the amount of money that should be invested at the rate of 5.25%
25,000-x -----> the amount money that should be invested at the rate of 4%
in this problem we have
[tex]t=1\ year\\ P_1=\$x\\P_2=\$(25,000-x)\\r_1=0.0525\\r_2=0.04\\I=\$1,150[/tex]
substitute in the formula above
[tex]I=P_1(r_1t)+P_2(r_2t)[/tex]
[tex]1,150=x(0.0525*1)+(25,000-x)(0.04*1)[/tex]
Solve for x
[tex]1,150=0.0525x+1,000-0.04x[/tex]
[tex]0.0525x-0.04x=1,150-1,000[/tex]
[tex]0.0125x=150[/tex]
[tex]x=\$12,000[/tex]
[tex]|$25,000-x=\$13,000[/tex]
therefore
The amount of money that should be invested at the rate of 5.25% is $12,000 and the amount money that should be invested at the rate of 4% is $13,000
Answer:
Step-by-step explanation:
Let x be the investment at 5.25% and y at 4%
Then we have
[tex]x+y =25000\\5.25x+4y = 115000[/tex]
We have to solve this system to get x and y
Multiply I equation by 4
[tex]100000=4x+4y\\115000=5.25x+4y\\-----------------------------\\15000 = 1.25x\\x = 12000\\y =25000-12000 = 13000[/tex]
12000 should be invested in 5.25% and 13000 in 4% interest.
Simplify 6^4 x 6^3 divided by
6^-1
Answer:
6^6
Step-by-step explanation:
6^4 x 6^3 / 6^-1
exponent rule add exponents 4+3=7 so 6^7
exponent rule subtract exponents 7-(-1) so
Answer= 6^8
Answer:
1644624
At least that's what i got on my calculator
a printer that sells for $190 is on sale for 20% off what is the sale price of the printer to work please
Hey!
---------------------------------------------------
Solution:
20% = 0.2 (percentage as decimal)
190 x 0.2 = 38 (discount)
190 - 38 = 152 (sale price)
---------------------------------------------------
Answer:
The sale price of the printer is $152.
---------------------------------------------------
Hope This Helped! Good Luck!
Andy ran the 100-meter dash in 13.4 seconds. Below is a table showing Andy's heart rate during the race. What parent function does Andy's data best represent? Time (in seconds) Heart Rate 0 61.1 5 85.6 9 105.2 11 115 13.5 122.3 A. a linear function B. a cubic function C. a square root function D. an absolute value function
4. Mimi has 15 cousins. All but 3 of her cousins live in Texas what percent of her cousins live in Texas?
Write a proportion and solve Show your work
It’s Not sure on the right answer
Answer:
20%
Step-by-step explanation:
15= 100%
3/15 = 1/5
100% divided by 5 is 20%
proportion: 1/5
Mimi has 15 cousins, and after subtracting the 3 who do not live in Texas, 12 of her cousins live there. By setting up a proportion, we calculate that 80% of Mimi's cousins live in Texas.
Mimi has 15 cousins, and all but 3 live in Texas. To find the percentage of her cousins that live in Texas, we first need to calculate the number of cousins who live in Texas. We do this by subtracting the 3 that do not live in Texas from the total number of cousins, which is 15.
Number of cousins living in Texas = Total cousins - Cousins not living in Texas
Number of cousins living in Texas = 15 - 3 = 12
Next, we set up a proportion to find the percentage. The proportion is based on the number of cousins in Texas over the total number of cousins:
Proportion = (Number of cousins in Texas / Total number of cousins) ×100%
Percentage = (12 / 15)× 100%
Percentage = 0.80 × 100%
Percentage = 80%
Therefore, 80% of Mimi's cousins live in Texas.
A human heart beats approximately 60 times per minute. If a man lives to the age of 90, how many times will his heart in his lifetime.
Answer:
90 Years = 47,304,000 Minutes = 47304000 Minutes.
Step-by-step explanation:
During a drought the water level of a lake changes -3 1/5 feet per day. Write and solve an equation to find how long it takes for the water level to change -16 feet
Answer:
-3.2x=-16
Step-by-step explanation:
The diameter of a basketball is 9.47 inches. What is the length of 12 basketballs lined up next to each other?
A) 112.92 inches B) 21.47 inches
B) 116.88 inches C) 108 inches
Answer:
B) 116.88 inches
Step-by-step explanation:
we know that
To find out the length of 12 basketballs lined up next to each other, multiply the diameter of one basketball by 12
[tex]12(9.47)=113.64\ in[/tex]
therefore
The logical answer between the options is 116.88 inches, because the length cannot be less than 113.64 in
Unit 4 HomeWUIR
The following table shows the times for
athletes running a 100-meter race.
100-Meter Race
Time
Runner
(seconds)
Mary
0.34
Rhea
0.394
Lindsay
0.402
Mei
0.334
Brooke
0.35
If the first three places receive ribbons, which
runners received ribbons for the race?
1st Place Ribbon:
2nd Place Ribbon:
3rd Place Ribbon:
Answer:
1st Place: Mei
2nd Place: Mary
3rd Place: Brooke
Hi i just need help on this quick question, ty :)
A deck is being built around a rectangular swimming pool. The swimming pool is 35 ft x 20 ft and the deck has a uniform width of 7 ft. What is the area of the deck only?
A. 700 ft^2
B. 877 ft^2
C. 966 ft^2
D. 1134 ft^2
Answer: C. 966
Step-by-step explanation: First find the ft. of the entire area, the deck, and pool. Then get the area of the pool
Entire area: (35+7+7) * (20+7+7)= 1666
Pool: 35*20=700
Then subtract the ft. of the entire area by the pool
1666-700= 966
What is 1,000,000 written as a power of ten?
10–6
10–7
107
106
Answer:
10^6 aka D
Step-by-step explanation:
We know this because we start off with 1. we take the decimal and swipe it 6 places to the right filling the gaps with zero. As shown in the problem itself.
Answer:
10^6
Step-by-step explanation:
10^6 is 10 × 10 × 10 × 10 × 10 × 10, and that is 1,000,000.