The solution set for the given equations is x = 4.
What is a set?
A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is a mathematical model for a collection of various things.
Here,
we put the value of x in the given equation and justify our answer
when we x=4, we get
5x−5=15
5(4) - 5 = 15
20 - 5 = 15
15 = 15
Hence, the solution set for the given equations is x = 4.
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How do you solve #4 - #9?
4. There is no enough information.
5. ΔPEF ≅ ΔREF are congruent by SAS.
6. ΔKMO ≅ ΔOLK are congruent by SSS.
7. No enough information.
8. ΔPAN ≅ ΔKLC are congruent by SSS.
9. ΔABC ≅ ΔDEF are congruent by SSS.
What is the SSS and SAS Theorems?The SSS and SAS are theorems of triangle congruence that can be used to prove that two triangles are congruent. To prove that two triangles are congruent by SSS, both triangles must have three pairs of corresponding lengths that are congruent, while SAS is used when the two triangles have two pairs of congruent sides that are corresponding, and a pair of congruent included angles.
4. There is no enough information to prove triangles HNJ and RDF are congruent by neither SAS nor SSS.
5. Triangles PEF and REF are congruent by SAS.
6. Triangles KMO and OLK are congruent by SSS.
7. No enough information.
8. Triangles PAN and KLC are congruent by SSS.
9. Triangles ABC and DEF are congruent by SSS.
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simplify (4i+1)^2
show all work
The simplified answer is 8i-15.
What do you mean by iota?
Iota is a mathematical concept that is represented by the symbol i and has the value of [tex]i^{2}=-1[/tex] , or i =[tex]\sqrt{-1}[/tex] . It is an imaginary unit number that is denoted by i. You could have run into instances when the discriminant is negative while attempting to solve quadratic equations.
According to the given question,
We have: [tex](4i+1)^{2}[/tex]
Now, we will solving this by formula,
[tex](a+b)^{2}=a^{2} +b^{2}+2ab[/tex]
Putting the values in it,
[tex](4i+1)^{2}=(4i)^{2}+1^{2}+2(4i)(1)\\=16i^{2} +1+8i\\ =16(-1)+8i+1\\=8i-16+1\\=8i-15[/tex]
Therefore, the required answer is 8i-15.
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Keilantra read 16 1/2 pages in 3/4 of an hour. If she continues reading at the same rate, how many pages will she read in an hour?
Answer: Around 40 pages
Step-by-step explanation: Im not sure if this is the answer but from what I can do this would be the answer
Answer:
she will read 22 pages :)
Step-by-step explanation:
Convert 3/4 of an hour into minutes - 60 x 3/4 = 45so kellantra is reading 16.5 pages every 45 minutes kellantra has 15 minutes left before an hour has passed, so divide 16.5 by 3 to work how how much she reads in 1/4 of an hour 16.5/3 = 5.5 pages per 1/4 houradd your values: 16.5 + 5.5 = 22 pages!The points (4, -3) and (x, 3) lie on the same straight line.
If the slope of the line is 2, what is the value of x ?
answer:
(1,3)
step-by-step explanation:
desmos.
The value of x will be equal to 7 for the given slope of 2 for the line.
What is the slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
Given that the points (4, -3) and (x, 3) lie on the same straight line. The slope of the line is 2.
The slope of the line is calculated by the formula,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
2 = ( 3 + 3 ) / ( x - 4)
2(x-4) = 6
2x - 8 = 6
2x = 8 + 6
2x = 14
x = 14 / 2
x = 7
Therefore, the value of x will be equal to 7 for the given slope of 2 for the line.
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Graph this system of equations on the coordinate plane:
y=4/3x+4
3y=-2x-6
The graph the system of linear equations on a coordinate plane is added as an attachment
How to graph the system of linear equations on a coordinate plane?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
y=4/3x+4
3y=-2x-6
Rewrite the equations in the system of equations as follows:
So, we have the following representation
y = 4/3x + 4
3y = -2x - 6
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (-3, 0)
This means that the solution to the system of equations is (-3, 0)
See attachment for the graph of the system of equations
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some pennies are arranged in rows. the number of pennies in each row is the same as the number of rows. after 10 pennies are removed, the remaining pennies can be arranged into 2 fewer rows, but with 1 additional penny in each row. how many pennies were there originally?
Answer:
22
Step-by-step explanation:
please help me with this math problem
Answer:
[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{\boxed{4}}{8}-\dfrac{1}{8}=\dfrac{\boxed{3}}{\boxed{8}}[/tex]
Step-by-step explanation:
When adding or subtracting fractions that have different denominators, first rewrite the fractions as equivalent fractions with the same denominator. To do this, find the lowest common multiple (LCM) of the denominators.
The given subtraction is:
[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}[/tex]
The LCM of the denominators 2 and 8 is 8. Therefore, we need to rewrite the first fraction as an equivalent fraction with 8 as its denominator. To do this, multiply its numerator and denominator by 4:
[tex]\implies \sf \dfrac{1}{2} \times\dfrac{4}{4}=\dfrac{4}{8}[/tex]
Therefore:
[tex]\implies \sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{4}{8}-\dfrac{1}{8}[/tex]
To subtract fractions with the same denominator, simply subtract the numerators. (The denominator stays the same).
[tex]\implies \sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{4}{8}-\dfrac{1}{8}=\dfrac{4-1}{8}=\dfrac{3}{8}[/tex]
Final solution
[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{\boxed{4}}{8}-\dfrac{1}{8}=\dfrac{\boxed{3}}{\boxed{8}}[/tex]
If ΔLMN is similar to ΔPQR, what is the length of PR?
If ΔLMN is similar to ΔPQR then length of PR = 15 by corresponding sides of similar triangles property.
What is the relation between corresponding sides of two similar triangles?
Two figures are said to be similar if they have same shape but size may vary.If two triangles are similar then their :-Corresponding angles are congruent. Corresponding sides are in the same ratio.ΔLMN is similar to ΔPQR
Corresponding angles are equal - ∠L = ∠P, ∠M = ∠Q, ∠N = ∠R.Corresponding sides are in same ratio - [tex]\frac{LM}{PQ} = \frac{LN}{PR} = \frac{MN}{QR}[/tex]According to the given data:
ΔLMN is similar to ΔPQR, therefore their corresponding sides are in same ratio,
LM/PQ = 8/6
LN/PR = 20/(2x - 1)
Substituting the values and solving for 2x -1 which is given length of PR
[tex]\frac{8}{6} = \frac{20}{2x -1} \\\\8(2x -1) = (20)(6)\\\\PR = 2x - 1 = \frac{120}{8} \\\\[/tex]Therefore, length of PR = 15.
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question 6 what if we use a p-value cutoff of 10%? do we reject, fail to reject, or are we unable to tell using our confidence interval? assign cutoff ten percent to the number corresponding to the correct answer. reject the null / data is consistent with the alternative hypothesis fail to reject the null / data is consistent with the null hypothesis unable to tell using our staff confidence interval
0.10 > 0.05 is value of p - value of the data .
What does P stand for?
The likelihood, for a particular statistical model, that the statistical summary would be equal to or more extreme than the actual observed findings when the null hypothesis is true is known as the P value.The p-value is the likelihood that, assuming the null hypothesis is true, a result will be at least as dramatic as the one that was actually seen in the biological, clinical, or epidemiological investigation.If we use 10% p - value cutoff = 0.10
then as 0.10 > 0.05
reject the null / data is consistent with the alternative hypothesis .
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A city doubles its size every 83 years. If the population is currently 88,200, what will the
population be in 249 years?
people
Answer:
264,600
Step-by-step explanation:
249 ÷ 83 = 3
88,200 ×3 = 264,600
Look at the figure. Which step should be take. Next to construct a line through point R that is perpendicular to ST?
Extend the compass from point T to little more than the midpoint of ST in such a way the arc drawn touches the point R. Similar is to be done from point S. Draw a line through the cut made by the 2 arcs at R.
at intel, the sizes of processor chips have a mean of 1 cm with a standard deviation of 0.2 cm. multiple random samples, each consisting of 35 processor chips, are taken. the sample mean and standard deviation for each sample are recorded to form a sampling distribution. what is the mean and standard deviation of this sampling distribution?
The mean and standard deviation of this sampling distribution is 1 cm and 0.033 cm, respectively.
The sample mean is the arithmetic mean of all the samples of processor chips. The mean of the sample group is known as the sample mean.
Let X denote the multiple random samples of 35 processor chips and each of which represents the size of the processor chips.
Let 'x' be the sample mean of all the random samples X which represents the size of the processor chips.
The mean of the size of processor chips= μ =1 cm
The mean of the sampling distribution x of sample means is equal to the mean of the sizes of the processor chips μ
Mean of sampling distribution x = mean of the size of the processor chips μ
⇒ x = μ
x = 1 cm
The mean of this sampling distribution is 1 cm.
The standard deviation is the amount of variation among the set of values. It is the measure of the dispersion of values in the data set.
The size of the processor chips has a standard deviation of 0.2 cm so σ = 0.2 cm
Let 'x' be the standard deviation of random samples X of the size of processor chips.
Number of random multiple samples of processor chips, n =35
The standard deviation of this sampling distribution can be calculated by using the below formula;
x = σ/[tex]\sqrt{n}[/tex]
Substituting the value of \sigma as "0.2" cm and the value of "n" as 35 in the above formula, we get;
x = 0.2/√35
x = 0.033 cm
The standard deviation of this sampling distribution is 0.033 cm.
The mean of this sampling distribution is 1cm and the standard deviation of this sampling distribution is 0.033 cm.
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Give the domain and range of the relationship. List items from least to greatest. Do not include duplicates. Determine whether or not the relationship is a function.
Answer:
Domain: {2, 3, 4, 5} Range: {12, 13, 14}
Step-by-step explanation:
The relationship is a function even though two different inputs have the same output.
What is the slope of the secant line that intersects the graph of f(x) = √4x+1 at x = = 0 and x = 6?
=
Solve for w.
63 =
3
Simplify your answer as much as possible.
W =
Answer:
That doesn't even make any sense you can't simplify or solve for anything if there isn't the right equation???????
Step-by-step explanation:
PLS HELP !! ITS DUE tommorow!!
In the given square, the values of f and g are equal that is 4√3cm.
What is a square?A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.So, the values of f and g are:
From the given diagram we know that ABCD is a square.So, all sides are the same.The area of ABCD is 48cm².
Now, calculate for sides as follows:The formula for the area of the square: A = s²Then,
A = s²48 = s²s = √48s = √2×2×2×2×3s = 2×2√3s = 4√3Since f and g are 2 sides of the square, their values are 4√3cm.
Therefore, in the given square, the values of f and g are equal that is 4√3cm.
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The temperature at the end of the day was 87 degrees. The temperature had decreased twice during the day, once by 9 degrees and another time by 7 degrees.
Which expression shows what the temperature was at the start of the day?
71+9+771+9+7
87−9−7
87+9+7
87+9−7
The temperature at the end of the day was 87 degrees. The temperature had decreased twice during the day, once by 9 degrees and another time by 7 degrees.
Which expression shows what the temperature was at the start of the day?
71+9+771+9+7
87−9−7
87+9+7
87+9−7
find the area of a rhombus whose diagonals are the lengths 36cm and 22.5 cm
Answer:
area of rhombus=1/2*36*22.5
=405cm^2
Step-by-step explanation:
A right triangle has a hypotenuse of length 10 centimeters. If one angle is 40°, find the length of each leg.
If a right triangle has a hypotenuse of length 10 centimeters. If one angle is 40 degrees, the length of the each legs are 6.43 centimeter and 7.66 centimeter
The hypotenuse of the right triangle = 10 centimeter
The measure of angle = 40 degree
Here we have to use the trigonometric functions
sin θ = Opposite side / Hypotenuse
Substitute the values in the equation
sin 40 = Opposite side / 10
Opposite side = 10 × sin 40
= 6.43 centimeter
Similarly
cos θ = Adjacent side / Hypotenuse
Substitute the values in the equation
cos 40 = Adjacent side / 10
Adjacent side = 10 × cos40
= 7.66 centimeter
Hence, if a right triangle has a hypotenuse of length 10 centimeters. If one angle is 40 degrees, the length of the each legs are 6.43 centimeter and 7.66 centimeter
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Three consecutive even integers have the property that when the product of the first two is taken, the result is four less than the square of the third one. What are the integers?
The three consecutive even integers are -2, 0 and 2.
How to calculate the value?Let the three consecutive even integers be x, x+2 and x+4.
Since the product of the first two is taken, the result is four less than the square of the third one. This will be:
x(x + 2) = (x + 4)² - 4
x² + 2x = x² + 8x + 16 - 4
x² + 2x = x² + 8x + 12
Collect like terms
x² - x² + 2x - 8x - 12
-6x - 12 = 0
-6x = 12.
Divide
x = -12/6
x = -2
x + 2 = -2 + 2 = 0
x + 4 = -2 + 4 = 2
They're -2, 0, and 2.
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Let the function f be defined as p (x) = -5 (-3x + 4) and function g be
defined as m (x)= 5x - 2 (5x - 6). What value of x satisfies the
equations m (x)= p (x)?
If the functions are equal. Then the value of the variable 'x' will be 1.6.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Let the capability f be characterized as p(x) = - 5(- 3x + 4) and work g be characterized as m(x) = 5x - 2(5x - 6).
If the functions are equal. Then the value of the variable 'x' will be given as,
m(x) = p(x)
- 5(- 3x + 4) = 5x - 2(5x - 6)
15x - 20 = 5x - 10x + 12
15x - 20 = - 5x + 12
20x = 32
x = 1.6
If the functions are equal. Then the value of the variable 'x' will be 1.6.
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a person's blood glucose level and diabetes are closely related, let x be a measurement in milligrams of glucose per deciliter of blood, after 12-hour fast, the variable x will have a Distribution that is approximately normal with a mean of 85 and standard deviation of 25. this is only true for adults under 50. Use this information to answer the question that follow:
what percentage of people have a blood glucose level between 100 and 125?
The percentage of people that have a blood glucose level between 100 and 125 is 21.945%
How to determine the percentage between 100 and 125?From the question, the given parameters about the distribution are
Mean value of the set of data = 85
Standard deviation value of the set of data = 25
The actual data values = 100 and 125
The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
For x = 100, we have:
Substitute the given parameters in the above equation
z = (100 - 85)/25 = 0.6
For x = 125, we have:
Substitute the given parameters in the above equation
z = (125 - 85)/25 = 1.6
The percentage between 100 and 125 is then calculated as:
P(100 < x < 125) = P(z < 1.6) - P(z < 0.6)
From the z table of probabilities, we have;
P(100 < x < 125) = 0.9452 - 0.72575
This gives
P(100 < x < 125) = 0.21945
Express as percentage
P(100 < x < 125) = 21.945%
Hence, the percentage is 21.945%
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five whole numbers are written in order
4 6 x y 10
median and mean of the five numbers are the same.
Workout the values of x and y
The values of x and y if the mean and median are equal are:
x = 7
y = 8.
What is the Mean and Median of a Data Set?The mean is the total sum of the values in a data set divided by the number of values of the data set.
The median of a data set is the center value when the data distribution is ordered.
Given the ordered data set as, 4, 6, x, y, and 10.
The center value is x. Therefore, the median of the data set is x.
The mean of the data = (4 + 6 + x + y + 10)/5
The mean of the data = (20 + x + y)/5
The mean and the median are equal, therefore:
(20 + x + y)/5 = x
20 + x + y = 5x
20 + y = 5x - x
20 + y = 4x
The value of x cannot be less than 6, if x = 7, we woud have:
20 + y = 4(7)
20 + y = 28
y = 28 - 20
y = 8
The values of x = 7, y = 8.
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a passenger train traveled 240 miles in the same amount of time it took a freight train to travel miles. the rate of the freight train was miles per hour slower than the rate of the passenger train. find the rate of the passenger train.
The rate of the passenger train is 60mph.
We know that,
Speed = Distance / Time
Time = Distance / Speed
s = speed of passenger train
speed of freight train = (s - 20)
T = 240 / s
T = 160 / (s-20)
240 / s = 160 / (s-20)
240(s - 20)/s(s - 20) = 160s/s(s - 20)
240(s - 20)/s(s - 20) - 160s/s(s - 20) = 0
240(s - 20) - 160s = 0s(s - 20)
240s - 4800 - 160s = 0
80s - 4800 = 0
80s = 4800
Hence the speed of the freight train is 40mph, while the speed of the passenger train is 60mph.
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The endpoints of AB¯¯¯¯¯¯¯¯ are given. Find the coordinates of the midpoint M. Then find AB. Round your answers to the nearest tenth, if necessary.
A(−5, 1), B(4,−5)
The coordinates of the midpoint M for the line segment AB are (-1/2, -2).
Describe the meaning of mid point of line segment?The halfway of such a line segment is its center. It is equally from both endpoints and serves as the segment and endpoint centroid. It cuts the portion in half.As per the stated values;
Th end points of the line segment AB are given as;
A(−5, 1) = (x1, y1)
B(4,−5) = (x2, y2)
The formula for the evaluation of the coordinates of the mid point is-
Mid point - M(x, y)
x = (x1 + x2)/ 2
x = (-5 + 4) /2
x = -1/2
y = (y1 + y2)/2
y = (1 - 5)/2
y = -2
Thus, the coordinates of the midpoint M for the line segment AB are (-1/2, -2).
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help pls!!! I WILL BRAINIEST!!!!
The average daily profit of an electronics store is $27,235. The company estimates that 15% is lost each day to returns, with a margin of error of ±3%. What is the maximum the company can expect for returned items?
The maximum the company can expect for returned items is $4190.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, The average daily profit of an electronics store is $27,235.
The company estimates that 15% is lost each day to returns.
∴ The amount of return is (15/100)×27135.
= 0.15×27125.
= $4068.
Now this has an error of ± 3%, therefore the maximum the company can expect for returned items is {(100 + 3)/100}×100
= 1.03×4068.
= $4190.
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what is the probability that a couple will have at least four sons if they plan to have 5 children and if the probability of having a son equals the probability of having a daughter? (enter your probability as a fraction.)
0.1875 is the probability of having a daughter .
Describe probability using an example?
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. The most basic illustration is a coin toss. There are only two outcomes that can occur when you flip a coin: either heads or tails.Let X = No. of sons
n = 5 and p = 0.5, because probability of having son and daughter is same.
X follows Binomial distribution with parameter n and p. Then its pmf is,
P(X= x) = \binom{n}{x}p^xq^{(n-x)} \ \ \ \ \ x = 0,1,----5
Now,
P(X= 5) = \binom{5}{5}(0.5)^5 (0.5)^{(5-5)} \\ \\ \\ P(X= 5) = 0.03125
Probability of haveing at least four sons
P(X\ge4) = P(X=4) +P(X=5) \\\\ P(X\ge4) = 0.15625 + 0.03125 \\\\ P(X\ge4) = 0.1875
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24. The height of an object varies directly with the length of its shadow. If a tree 8 feet tall casts a shadow 10 feet long, how long will be the shadow of a tree that is 12 feet tall?
Answer:
15 feet
Step-by-step explanation:
Given an 8' object casts a 10' shadow, you want to know the length of the shadow of a 12' object.
ProportionThe shadow length is proportional to the object length:
shadow/object = 10'/8' = s/12'
Multiplying by 12', we have ...
s = (12')(10/8) = 15'
The shadow of a tree 12 feet tall will be 15 feet long.
Higher Order Thinking You use a garden hose to fill a
vading pool. If the water level rises 11 centimeters every
minutes and you record the data point of (10, y), what is
he value of y? Use slope to justify your answer
The value of y = 110.
What is slope intercept form?
The graph of the linear equation y = mx + c is a line with m as slope, m and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.
Rise of the water = 11
run = 1 min
slope m = 11/1 = 11.
The slope intercept form is
y = mx +b
after substituting the values, we get
m = 11,
x = 10and y = ?
y = 10 (11)
y = 110.
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N is an integer. Work out:
a. the smallest possible value of N if N >= 6.5
b. the largest possible of N if N < -3
c. the possible values of N if N >= -2 and N <2.
According to the integer N,
a) The smallest possible value of N is 6.5 if N >= 6.5
b) The largest possible value of N is -2 if N < - 3
c) The possible value of N is {-2, -1, 0, 1} if N >= -2 and N < 2.
Integer
Integer refers a collection of whole numbers and negative numbers.
Given,
Here we have the integer N.
And we need to find the following:
a. the smallest possible value of N if N >= 6.5
b. the largest possible of N if N < -3
c. the possible values of N if N >= -2 and N <2.
Part a). smallest possible value of N if N >= 6.5
Here the smallest number is 6.5 because other value are greater than this one.
Part b). the largest possible of N if N < -3
The largest possible number is -2, because the other values on N are less than -2.
Part c). the possible values of N if N >= -2 and N <2.
Here the possible values between these are {-2, -1, 0, 1}.
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