This is likely what Jeremy did
[tex]\frac{2\text{x}^2-10}{\text{x}-5}-\frac{\text{x}^2+15}{\text{x}-5}\\\\\frac{2\text{x}^2-10-\text{x}^2+15}{\text{x}-5}\\\\\frac{\text{x}^2+5}{\text{x}-5}\\\\[/tex]
The error happens in line 2
This is what his steps should be
[tex]\frac{2\text{x}^2-10}{\text{x}-5}-\frac{\text{x}^2+15}{\text{x}-5}\\\\\frac{2\text{x}^2-10-(\text{x}^2+15)}{\text{x}-5}\\\\\frac{2\text{x}^2-10-\text{x}^2-15}{\text{x}-5}\\\\\frac{\text{x}^2-25}{\text{x}-5}\\\\\frac{(\text{x}-5)(\text{x}+5)}{\text{x}-5}\\\\\text{x}+5[/tex]
On the 2nd step, we subtract all of (x^2+15) and not just the x^2 part. The negative distributes to each term in step 3. Then we combine like terms, factor and cancel out the (x-5) terms.
Therefore, [tex]\frac{2\text{x}^2-10}{\text{x}-5}-\frac{\text{x}^2+15}{\text{x}-5}=\text{x}+5[/tex] is an identity as long as [tex]\text{x} \ne 5[/tex] to avoid a division by zero error.
The line y = kx + 4 goes through the point (2, -2). Find the value of k.
k = -3 is the value in straight line.
What is straight line?
Simply put, a straight line is a line devoid of bends. A straight line is one that does not curve and reaches to infinity on both sides.
Different type
Horizontal Line Horizontal Lines.Crossing Lines.Lines that are parallel.On putting the values of the point in the equation of line, the value of X = 2 and Y = -8
When a line passes through a point, the point satisfies the equation of the line.
The line y = kx + 4 goes through the point (2, -2)
So, ( 2 , -2 ) must satisfy the equation of the line.
Put x = 2 y= - 2 in equation y = kx + 4
-2 = k * 2 + 4
- 2 = 2k + 4
-2 -4 = 2k
-6 =2k
k = -6/2
k = -3
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Find the sum of 2.53 x 1019 and 3.197 x 1017.
2.56197 x 1019
3.2223 x 1019
2.56197 x 1036
3.2223 x 1036
Taking into account the scientific notation, the result of the sum is 2.56197×10¹⁹.
Scientific notationScientific notation is a quick way to represent a number using powers of base ten.
The numbers are written as a product:
a×10ⁿ
where:
a is a real number greater than or equal to 1 and less than 10, to which a decimal point is added after the first digit if it is a non-integer number.n is an integer, which is called an exponent or an order of magnitude. Represents the number of times the comma is shifted. It is always an integer, positive if it is shifted to the left, negative if it is shifted to the right.Sum in scientific notationYou want to add the following two numbers in scientific notation:
2.53×10¹⁹3.197×10¹⁷When the numbers to be added do not have the same base 10 exponent, the base 10 power with the highest exponent must be found. In this case, the highest exponent is 19.
Then all the values are expressed as a function of the base 10 exponent with the highest exponent. In this case: 3.197×10¹⁷= 0.03197×10¹⁹
Taking the quantities to the same exponent, all you have to do is add what was previously called the number "a". In this case:
2.53×10¹⁹ + 0.03197×10¹⁹= (2.53 + 0.03197)×10¹⁹= 2.56197×10¹⁹
Finally, the result of the sum is 2.56197×10¹⁹.
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Bob invested his savings in two investment funds. The amount he invested in Fund A was $8000 less than the amount he invested in Fund B. Fund A
returned a 2% profit and Fund B returned a 7% profit. How much did he invest in Fund B, if the total profit from the two funds together was $1730?
a = amount invested at 2%
how much is 2% of "a"? (2/100) * "a", namely 0.02a.
b = amount invested at 7%
how much is 7% of "b"? (7/100) * "b", namely 0.07b.
We know that fund A is less than fund B by 8000, that is a = b - 8000.
we also know that the yielded amount in interest is $1730, so if we simply add their interest, that'd be 0.02a + 0.07b = 1730.
[tex]\boxed{a = b - 8000} \\\\\\ 0.02a~~ + ~~0.07b~~ = ~~1730\implies 0.02(\stackrel{a}{b-8000})~~ + ~~0.07b~~ = ~~1730 \\\\\\ 0.02b-160+0.07b=1730\implies 0.02b+0.07b=1890\implies 0.09b=1890 \\\\\\ b=\cfrac{1890}{0.09}\implies \blacksquare~~ b=21000 ~~\blacksquare[/tex]
HELP WITH NUMBER 5 FOR 20 POINTS
Answer:
5
Step-by-step explanation:
that is hte anwers
Select the correct answer form each drop-down menu.
Given: m/WOZ = 90°
Prove: m/WOX = 90°
X
W
N
Complete the proof.
Suppose m/WOX # 90°. By the
✓ZWOXis supplementary to ZWOZ. Therefore,
m/WOX + m/WOZ = 180°. By the assumption and the substitution property of equality. 90° +m/WOZ 180°. Using the
subtraction property of equality, the measure of angle WOZ
✓90°, which contradicts the given. Therefore, the
assumption is not true, and m/WOX = 90°.
4
Reset
Next. Answer?
The complete proof are;
Suppose m ∠WOX ≠ 90°. By the definition of linear pair of straight line ∠ WOX is supplementary to ∠WOZ.
Therefore, m ∠WOX + m ∠WOZ = 180°.
By the assumption and the substitution property of equality.
90° + m ∠WOZ = 180°.
Using the subtraction property of equality, the measure of angle WOZ is equal to 90°, which contradicts the given.
Therefore, the assumption is not true and m ∠WOX = 90°.
What are Supplementary angles?
The two angles are called supplementary angles when sum of both angles are 180 degree.
Given that;
m ∠WOZ = 90°
Now, The proof of m ∠WOX = 90° is given as;
Suppose m ∠WOX ≠ 90°.
By the definition of linear pair of straight line ∠ WOX is supplementary to ∠WOZ.
Therefore,
⇒ m ∠WOX + m ∠WOZ = 180°.
By the assumption and the substitution property of equality.
⇒ 90° + m ∠WOZ = 180°.
Using the subtraction property of equality, the measure of angle WOZ is equal to 90°, which contradicts the given assumption.
Therefore, The assumption is not true and m ∠WOX = 90°.
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Sara has a rectangular shaped backyard. The backyard is 22.5 feet wide and 35.75 feet long. What is the area of the rectangular backyard?
The area of the rectangular backyard is 804.37
How to calculate the area of the rectangle ?
The area of a rectangle can be calculated by multiplying the length and the width
Area= length × width
Length= 35.75 feet
Width= 22.5 feet
Area= 35.75 × 22.5
= 804.37
Hence the area of the rectangular backyard is 804.37
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You're going on a 1211-mile trip, and your car gets about 29 miles per gallon. Gas prices along your route average $3.10. Estimate the cost of gasoline for this trip by rounding the distance to 1200 miles, the mileage to 30 miles per gallon, and the cost of gas to $3.00 per gallon. Calculate the answer without using estimation and compare the two results. (Round your answers to the nearest cent.)
Using proportions, it is found that:
Without estimation, the cost is of $129.46.With estimation, the cost is of $120.For the estimation, the mileage was rounded up while the cost was rounded down, hence the estimated cost is less than the actual cost.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Without the estimate, the number of gallons used is:
1211/29 = 41.76 gallons.
Hence the cost is:
41.76 x 3.10 = $129.46.
With the estimate, the number of gallons used is:
1200/30 = 40 gallons.
Hence the cost is:
40 x 3 = $120.
For the estimation, the mileage was rounded up while the cost was rounded down, hence the estimated cost is less than the actual cost.
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PLS HELP!! 25 POINTS + BRAINLIEST
Answer:
A. 5/4n - 3/8
Step-by-step explanation:
-5n/2 + 1/4 + 15/4n - 5/8
15/4n - 10/4n + 2/8 - 5/8
5/4n - 3/8
Bo kept track of his cookie sales. He
discovered that 3 out of 5 people who
came into his bakery for cookies bought
chocolate chip cookies.
If 400 customers bought cookies at Bo's
Bakery last month, how many of them
bought chocolate chip cookies?
Answer:240
Step-by-step explanation:
400/5 = 80
80 x 3 = 240
240/400 people bought choc chip
Evaluate the expressions when x = 3; y = 4 & z = -2
(x + y) * z, 2y + 3z + 4y - xz =
comma = separate
Answer:
Sub in the numbers given to x, y, z and use calculator to solve
The midpoint of AB is M(-6, 4). If the coordinates of A are (-7, 2), what are the
coordinates of B?
The coordinates of B is (-5, 6).
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space
What is section formula ?
The section formula helps in determining the coordinates of a point which facilitates division of the line joining two points in a ratio. This takes place either internally or externally.
P (x, y)= (c*m + a*n)/(m + n) , (d*m + b*n)/(m + n ).
Given:
let the coordinates of B (x, y)
M is midpoint M(-6,4) and coordinates of A are (-7, 2)
Using section formula
-6 = (x -7)/2
-12 = x -7
x = -5
and, 4 = y+2/2
8 = y+2
y = 6
Hence, the coordinates of B is (-5, 6)
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What is the answer at the A - B i don't know how to do this so I want answer or explanations The
Answer:
where is the question bro?
Step-by-step explanation:
HELP!!! Describe the distribution of points per game
Definition: n math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
Given,
Points scored per game by 35 NBA players during the 2017 basketball season.
Context: Points scored per game by 35 NBA players
Shape: dotted, no gaps
Outliers: none
Center: 14(Median)
Spread: Data varies from somewhere between (12-14) to somewhere between (24-26)
context is about the graph
shape is about the representation
outliers is whether any point is farther
center is the median
spread is till where the graph is extended with gaps in between
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Write the equation of the line with slope 35 that passes through point (0,−3).
Answer:
[tex]y = 35x - 3[/tex]
Step-by-step explanation:
Based on the given conditions
[tex]m = 35[/tex]
Substitute and calculate
Substitute:
[tex]m = 35 \\ x = 0 \\ y = - 3[/tex]
Into:
[tex]y = mx + b[/tex]
Therefore, the equation of the line is:
[tex]y = 35x - 3[/tex]
A plane climbs from an altitude of 6000 ft to a cruising altitude of 39,000 ft. The plane ascends at a rate of 6600 ft/min. How long will it take to reach cruising altitude?
The time taken to ascend from the initial height to the final height; Time taken = 5 minutes
What is the time taken?We are given;
Initial Height = 6000 ft
Final height = 6600 ft/min
Speed = 6600 ft/min
Now, the time taken to ascend from the initial height to the final height;
Time taken = (39000 - 6000)/6600
Time taken = 5 minutes
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8^6x8^9= ?
64^15
64^3
8^15
8^54
Answer:
[tex]8^{15[/tex]
Step-by-step explanation:
Hello!
Use exponent rule: [tex]a^b * a^c = a^{b + c}[/tex]
Use the rule to simplify the exponential expression.
Simplify[tex]8^6 * 8^9[/tex][tex]8^{6 + 9}[/tex][tex]8^{15[/tex]The simplified form is [tex]8^{15[/tex].
Which of these questions is most likely to result in response bias?
OA. "What do you think of this dress?"
OB. "What is your opinion of this dress?"
O C. "How do you like this beautiful dress?"
OD. "How do you feel about this dress?"
Answer: C
Step-by-step explanation:
Options A, B and D are all unbiased since there is nothing in the question taht could nudge you into a specific thought, but in option C, they specifically call it beautiful to put it in your mind and you will be more likely to call the dress beautiful compared to anything else.
2. Consider the graph of y = f(x) below.
YA
F
14
/2 -1 0
-1+
+
1 2
(a) Find all values for which f(x) is discontinuous.
(b) For each point in (a), describe where the 3-part definition fails.
(c) Classify each discontinuity as jump, removable, or infinite.
Answer:
Step-by-step explanation:
31
Question 5 (1 point)
Match the expressions that are equivalent.
Column A
1/32
32
2
1/2
64
1/64
Column B
a. (2^3)(2^2)
b. 2^(-2) x 2^(-3)
C. (2^3) x (2^-3)
d. (2^2)^3
e. 2^2/2^3
f. 2^3/2^2
It should be noted that the correct matching of the expressions illustrated will be:
a. (2^3)(2^2) = 32
b. 2^(-2) x 2^(-3) = 1/32
C. (2^3) x (2^-3) = 1
d. (2^2)^3 = 64
e. 2^2/2^3 = 1/2
f. 2^3/2^2 = 2
How to illustrate the information?It should be noted that (2^3)(2^2) will be:
= 2³ × 2²
= 8 × 4
= 32
b. 2^(-2) x 2^(-3) will be illustrated as:
= 1/4 × 1/8
= 1/32
C. (2^3) x (2^-3)
= 8 × 1/8
= 1
d. (2^2)^3
= 4³
= 64
e. 2^2/2^3
= 4 / 8
= 1/2
f. 2^3/2^2
= 2³ / 2²
= 8 / 4
= 2
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A party planner purchased roses to decorate tables for an event. There were 15 tables and 5 roses were placed on each table. If the roses were $1.98 each, how much did the party planner spend on roses?
A. $148.50
B. $29.70
C. $9.90
D. $75.00
Answer: 148.50
Step-by-step explanation:
15*5=75
75*$1.98=$148.50
Trey Invested his savings in two Investment funds. The $12,000 that he invested in Fund A returned a 1% profit. The amount that he invested in Fund B returned a 6% profit. How much did he invest in Fund B, if both funds together returned a 3% profit?
The amount Trey invested in Fund B is $8,000.
Profit is a residual income, It is the gain amount from any kind of business activity. In short, if the selling price (SP) of the product is more than the cost price (CP) of a product, then it is considered as a gain or profit. while return is a total revenue. Profits may be negative, whereas returns, such as wages and interest are always positive.
amount invested in Fund A = $12,000 (given)
profit returned by Fund A = 1% of $12,000 (given)
= 1/100*$12,000
= $120
Let amount invested in Fund B = x (assumption)
profit returned by Fund B = 6% of x (given)
= 6/100*x
= $ 6x/100
Given that both funds A and B together returned a 3% profit, So the equation we get is
120+6x/100 = 3% of (12,000+x)
(12,000+6x)/100 = 3/100* (12,000+x)
12,000+6x = 3(12,000+x)
12,000+6x = 36,000+3x
6x-3x = 36,000-12,000 (bringing like terms on same side)
3x = 24,000
x = 24,000/3
x = $8,000
Therefore, we can conclude that the amount Trey invested in Fund B is $8,000
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Find x for this equation
Show clear algebraic fraction
Answer:
x = [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
[tex]\frac{2}{5x-2}[/tex] = [tex]\frac{3}{6x+1}[/tex] ( cross- multiply )
3(5x - 2) = (2(6x + 1) ← distribute parenthesis on both sides )
15x - 6 = 12x + 2 ( subtract 12x from both sides )
3x - 6 = 2 ( add 6 to both sides )
3x = 8 ( divide both sides by 3 )
x = [tex]\frac{8}{3}[/tex]
The average donut weighs approximately 50 g, and has approximately
11,000 mg of sugar. How much sugar is in three donuts? Answer in g.
Answer:
33 g
Step-by-step explanation:
the weight of the donut is a distractor number. if each donut has 11,000 mg of sugar, then 11,000 x 3 = 33,000 mg. In order to convert mg into g, we move the decimal over to the left 3 times.
33000. (0 times)
3300.0 (1 time)
330.00 (2 times)
33.000 (3 times)
Find the difference between the largest and the smallest of the four numbers below.
10,743.93
234.018
324.1
23.107
Answer:
10720.823
Step-by-step explanation:
largest number is 10743.93 and the smallest number is 23.107. subtracting 23.107 from 10773.93 to get 10743.93
Sixty-one percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 8 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual?
The unusual outcomes for the binomial distribution are given as follows:
0 or 1 employee making judgements.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In the binomial distribution, a measure is considered unusual if it is more than 2.5 standard deviations from the mean.
For this problem, the parameters are given as follows:
n = 8, p = 0.61.
Hence the mean and the standard deviation are given by:
E(X) = np = 8 x 0.61 = 4.88.[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{8(0.61)(0.39)} = 1.38[/tex]The bounds of usual outcomes are:
4.88 - 2.5 x 1.38 = 1.43.4.88 + 2.5 x 1.38 = 8.33.Hence outcomes of less than 1 employee making judgements would be unusual.
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An herbalist has 50 oz of herbs costing $4 per ounce. How many ounces of herbs costing $1 per ounce should be mixed with these 50 oz of herbs to produce a mixture costing $2.50 per ounce?
The ounces of herbs costing $1 per ounce that should be mixed with these 50 oz of herbs to produce a mixture costing $2.50 per ounce?
is 50 ounces.
How to illustrate the information?Let x = the amount of herb that costs $1 per ounce.
Based on the information,the total weight will be:
x + 50 = y.
At $2.50, the cost of the mixture will be:
1x + 4(50) = 2.50y
x + 200 = 2.50y
x + 200 = 2.50(x + 50)
x + 200 = 2.50x + 125
Collect like terms
2.5x - x = 200 - 125
1.5x = 75
Divide
x = 75/1.5
x = 5.
Therefore, the correct option is 50
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how to factorise 3x + 6
Answer:
it is 3(x+2)
Answer:
3(x+2)
Step-by-step explanation:
You first find the common factor.
3x+6
3(x+2) solution.
What is the length of the line segment that joins
points (4, -1) and (7,5)?
A. 5 B. √13
C. √29 D. √45
Answer:
5 is the answer to that question
Answer:
D. √45
Step-by-step explanation:
(4, -1) (7, 5)
(x₁, y₁) (x₂, y₂)
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(7 - 4)² + (5 - (-1))²
d = √(3)² + (6)²
d = √9 + 36
d = √45
I hope this helps!
Convert the following ratios into percentages.
2:3
Answer:
66%
Step-by-step explanation:
Answer:
66 %
Step-by-step explanation:
It is 66 % because to convert you have to follow these steps
Step 1: Identify the ratio.
Step 2: Express the ratio a:b in the form of a fraction a/b.
Step 3: Multiply the fraction by 100.
Step 4: Simplify and write the answer with the percent symbol (%).
If a// b and m 1 = 90° then m 2 =
Slope m2=90°
The slope of a line, also known as the gradient is defined as the value of the steepness or the direction of a line in a coordinate plane. Slope can be calculated using different methods, given the equation of a line or the coordinates of points lying on the straight line.
given that, since slope is a measure of the angle of a line from the horizontal, and since parallel lines must have the same angle, then parallel lines have the same slope — and lines with the same slope are parallel.
so we can conclude since m1=90° the m2 is also = 90°
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Answer:
M2 slope = 90°
Step-by-step explanation:
The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of approaches.
Given that parallel lines must have the same angle from the horizontal and that slope is a measurement of that angle, parallel lines must therefore have the same slope, therefore lines with the same slope are parallel.
We can then deduce that if m1=90°, m2 must also be 90°.
