By theorem we have that if two sides of a triangle are equal, then the angles opposite to those sides are equal, with this or with knowing that the angle between the known sides are equal we conclude that both triangles are equal [the latter solution is using congruency SAS for the triangles, where S is side and A angle.]
w/2 + 4 is greater than 5
Answer:
I say w is equal to 4, because:
4 divided by 2 = 2
2 + 4 = 6
6 > 5
Step-by-step explanation:
Hope it helps! =D
Please show and explain this please
The graph of the function (E) f(x) = (x + 10)(x - 3)²(x + 1) matches the given graph.
What is a graph of a function?Defining a function's graph: The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We could also say that the graph of f is the graph of y = f(x). As a result, the graph of an equation is a particular instance of the graph of a function. We merely select a value for x, then determine the value of y that corresponds. Equations that have been solved for y are graphed as functions! In this instance, the graph of f(x) is the graph of y = x² - 3. Making points for the graph is simple.So, the function with which the given graph matches:
The graph of the option (E) f(x) = (x + 10)(x - 3)²(x + 1) is:(Refer to the graph attached below)We can easily see that coordinates of the given graph and the graph of equation (E) match.Therefore, the graph of the function (E) f(x) = (x + 10)(x - 3)²(x + 1) matches the given graph.
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find the distance from line y= -3x + 4 to line y = -3x - 1
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
74.52
Step-by-step explanation:
[tex]P(10)=0.018(10)^3-0.294(10)^2+3.074(10)+55.180 \\ \\ =74.52[/tex]
A school is organising a fun runThe fun run involves a 5
1
2
mile run around the field, then a 5
4
7
mile run back to the school. Find the total distance of the fun run.Give your answer as a mixed number in its simplest form.
In mixed fraction the total distance of the fun run is 11 1/14
A school is organising a fun run. The fun run involves a 5 1/2
mile run around the field, then a 5 4/7 mile run back to the school.
The total distance is equal to summation of run around the field and run back to school.
total distance = 5 1/2 + 5 4/7
= 11/2 + 39/7
The L. C. M of 2 and 7 is 14
= [tex]\frac{11.7}{2.7} + \frac{39.2}{7.2}[/tex]
(77 + 78)/14
155/14
Upon dividing 155 by 14, the quotient is 11 and the the remainder is 1
In mixed fraction it is 11 1/14
So in mixed fraction the total distance of the fun run is 11 1/14
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find the 12th term of the series; 0.008, 0.04, 0.2
Answer
12th term = 390,625
Explanation
On close observation, we can see that the given series is in geometric progression.
Geometric progression has a general formula of
aₙ = a (rⁿ⁻¹)
where
aₙ = nth term
a = First term
r = Common ratio
n = number or position of the term
For this question, we need to compute the common ratio
Common Ratio = (Next term) ÷ (Current term)
= (Second term) ÷ (First term)
= (Third term) ÷ (Second term)
For this question,
Common Ratio = 0.04 ÷ 0.008 = 5
OR
0.2 ÷ 0.04 = 5
And we can see that the first term is 0.008
So, the 12th term will have the formula
aₙ = a (rⁿ⁻¹)
a = 0.008
n = 12
r = 5
a₁₂ = 0.008 (5¹²⁻¹)
= 0.008 (5¹¹)
= 0.008 (48,828,125)
= 390,625
Hope this Helps!!!
Estimate [tex] \sqrt[3]{20} [/tex] between two integers.
Answer
∛20 is between 2 and 3.
Explanation
The question asks us to find the cube root of 20.
∛20
The key to doing this without the calculator is to take the cube of numbers and the one that has 20 in between them is the answer.
1³ = 1
2³ = 8
3³ = 27
We can see that 20 is between 8 and 27.
So,the cube root of 20 has to be betwen 2 and 3.
The other way to do this with the calculator is to actually find the cube root of 20
∛20 = 2.71
Which is between 2 and 3.
Hope this Helps!!!
what is 4 divided by 1 over2
Answer:
4/1÷2 =4×1/2
Step-by-step explanation:
You have to invert and then multiply
so the answer will be 2
1/2(4×5)-2³= what's the awnser
Explanation:
[tex]\frac{1}{2}(4\times5)-2^3=[/tex]First we have to solve the products, divisions and powers in each term. The terms are separated by + or - signs. In this expression there are two terms.
In the first term there's a product inside a parenthesis. This means that we have to solve that first:
[tex]=\frac{1}{2}\cdot20-2^3[/tex]Now we can solve the multiplication in the first term:
[tex]=10-2^3[/tex]Solve the power in the second term:
[tex]=10-8[/tex]And do the substraction:
[tex]=2[/tex]Answer:
1/2(4x5) - 2³ = 2
what is the ratio of 12
Answer:
12.:1 Is the great answer of this question
find X and Y X - 3 y + 3 15 12
To solve this problem we have to remember that diagonals of a parallelogram bisect each other. This means that they intersect in the midle point of each other. From this we can conclude that
[tex]\begin{gathered} x-3=15 \\ \text{and} \\ y+3=12 \end{gathered}[/tex]Once we have our equations we can solve them. Let's find x
[tex]\begin{gathered} x-3=15 \\ x=15+3 \\ x=18 \end{gathered}[/tex]Now, let's find y
[tex]\begin{gathered} y+3=12 \\ y=12-3 \\ y=9 \end{gathered}[/tex]Then x=18 and y=9,
K
A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the mean salary.
Salary ($) Employees
5,001-10,000
10,001-15,000
17
15
15,001-20,000
20,001-25,000
25,001-30,000
OA. $7,376.62
B. $17,625
C. $15,862.50
D. $19,387.50
16
13
19
The mean salary of the employees is $17625.5.
The total number of employees in the company is 80.
The total salary for the first interval is [(5001+10000)/2]*17 = 127508.5.
The total salary for the second interval is [(10001+15000)/2]*15 = 187507.5.
The total salary for the third interval is [(15001+20000)/2]*16 = 280008.
The total salary for the fourth interval is [(20001+25000)/2]*13 = 292506.5.
The total salary for the fifth interval is [(25001+30000)/2]*19 = 522509.5.
In math, a mean is the average of a data collection, which is calculated by adding all of the numbers together and then dividing the total of the numbers by the number of numbers. The mean salary is the sum of all salaries divided by the total number of employees.
M = (127508.5 + 187507.5 + 280008 + 292506.5 + 522509.5)/80
M = 17625.5
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6. The National Institute of Health is studying the relationship between number of
smoked per day and the birth weight of babies born to mothers who
smoke cigarettes. A sample of the 6 points is selected are listed below.
cigarettes
No. of Cigarettes per day (X) 22 13 29 11 28 6
Birth weight (Y)
6.1 7.9 5.8 7.4 6.3 8.2
Compute Pearson's sample correlation coefficient.
Compute the equation of the least squares regression line.
ŷ
=
What is the predicted baby weight born for a mother smoke 40 cigarettes per day.
Using the calculator for the line of best-fit, the measures are given as follows:
Correlation Coefficient: -0.9405.Regression Line: y = -0.1x + 8.77.Baby weight for the mother that smokes 40 cigarettes a day: 4.77 grams.How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) given in the problem in the calculator. These points are given on a table or in a scatter plot in the problem.
From the given table, the points in this problem are as follows:
(22, 6.1), (13, 7.9), (29, 5.8), (11, 7.4), (28, 6.3), (6, 8.2).
Hence:
The correlation coefficient is of -0.9405.The regression line is of: y = -0.1x + 8.77.Hence, for a mother that smokes 40 cigarettes on a day, the predicted weight is of:
y = -0.1(40) + 8.77 = 4.77 grams.
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any whole number is a proper subset or rational number
Answer:
The natural numbers, whole numbers, and integers are all subsets of rational numbers
Step-by-step explanation:
hope it helps
have a good day
Can somebody Answer this?
Garry needs 18.4 oz of glue and 9.2 oz of glitter to make 4 bottles.
What is direct proportion?In direct proportion between two or more than two quantities if one quantity is multiplied or divided by some constant k other quantities will also be multiplied or divided by the same constant k.
Given, Making 1 bottle of glitter glue Garyy requires 4.6 oz of glue and 2.3 oz of glitter.
∴ 4 bottles of glitter glue require (4.6×4) = 18.4 oz of glue and (2.3×4) = 9.2 oz of glitter.
As the no. of bottles is multiplied by 4 thus material requirements will also be multiplied by a factor of 4.
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Alan mose lawn in the summer to make money he knows that on an average he can mow 1/2 of a lawn in 1/4 hours calculate his average mowing rate in lawns per hour
Answer:
2 Lawns Mowed per hour
Step-by-step explanation:
This question requires the concept of: Conversion.
ConversionThe concept of Conversion is about converting to a certain unit value.
Example: 24 Sour Plums per 2 baskets = 12 Sour Plums per basket.
Application:For this question, we are asked to convert the unit from 0.25 hours to 1 hour.
(Note: 1/4 hours = 0.25 hours)
0.25 hours = 0.5 Lawn Mowed
(0.25 ÷ 0.25) hours = (0.5 ÷ 0.25) Lawn Mowed
1 hour = 2 Lawns Mowed per hour.
Note: You can use fractions to solve the problem, it will give you the same result.
Solve the equation for y in terms of x. In other words, algebraicallyrearrange the equation so that the y variable is by itself one side of theequation. Type your answer in the form y = mx + b. If you have a valuethat is not an integer then type it rounded to the nearest hundredth. Donot put spaces between your characters.4.2 + 2y = 8y = ?4x+2y=8
Given:
[tex]4x+2y=8[/tex]Solve the equation for y,
[tex]\begin{gathered} 4x+2y=8 \\ Subtract\text{ -4 from both sides} \\ 4x+2y-4x=8-4x \\ 2y=8-4x \\ \text{Divide by 2 on both side} \\ \frac{2y}{2}=\frac{8-4x}{2} \\ y=\frac{8}{2}-\frac{4x}{2} \\ y=4-2x \\ \text{ express the equation in the form y=mx+b} \\ y=-2x+4 \end{gathered}[/tex]Answer: y = -2x +4
Which of these shows the result of using the first equation to substitute fory in the second equation, then combining like terms? y- 3x 3x+ 2y= 18 OA. 3y 18 B. 9x= 18 OC. 6x= 18 OD. 3x= 18 m
In the accompanying diagram of BCD m
Given:
m∠C = 70°
m∠CDE = 130°
Question 1:
To find ∠CDB, let's use the exterior angle theorem.
The exterior angle theorem states that the sum of 2 opposite interior angles is equal to the exterior angle.
Thus,
m∠C + m∠B = 130
70 + m∠B = 130
Subtract 70 from both sides:
70 - 70 + m∠B = 130 -70
m∠B = 60°
Now, use the triangle angle sum theorem to find ∠CDB.
The triangle angle sum theorem states that the sum of interior angles in a triangle is 180°
∠CDB = 180 - 70 - 60 = 50°
∠CDB = 50°
Question 2:
∠CBA = ∠C + ∠CDB
∠CBA = 70 + 50 = 120°
∠CBA = 120°
ANSWER:
∠CDB = 50°
∠CBA = 120°
Write an explicit equation for the arithmetic sequence defined byt(n+1)= t(n)-4t(2) = 10
We need to find the explicit equation for the sequence:
[tex]\begin{gathered} t\mleft(n+1\mright)=t\mleft(n\mright)-4 \\ \\ t(2)=10 \end{gathered}[/tex]First, we can complete the given table. Notice that when we subtract 4 from the n-th term, we obtain the next term (n+1).
Then, to find a previous term, we can add 4. Thus. we obtain:
n t(n)
0 14+4 = 18
1 10+4 = 14
2 10
3 10-4 = 6
4 6-4 = 2
5 2-4 = -2
Now, observing the above relations, we need to write an expression for t(n) in terms of n:
n t(n)
0 18 = 18 - 0*4
1 14 = 18 - 1*4
2 10 = 18 - 2*4
3 6 = 18 - 3*4
4 2 = 18 - 4*4
5 -2 = 18 - 5*4
...
n 18 - n*4
Therefore, an explicit equation for the sequence is:
[tex]t(n)=18-4n[/tex]8. Use the point-slope formula to write an equationof a line in slope-intercept form using the points(1/2,5) and (5/2,9)
We have the next two points:
- (1/2,5)
- (5/2,9)
And we must use the point-slope formula to write an equation of a line in slope-intercept
First, we need to calculate the slope of the line using the point-slope formula
[tex]\begin{gathered} y_2-y_1=m(x_2-x_1) \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Where (x1, y1) and (x2, y2) are the two points
Now, replacing the points
[tex]m=\frac{9-5}{\frac{5}{2}-\frac{1}{2}}=\frac{4}{\frac{4}{2}}=\frac{4}{2}=2[/tex]Now, we must replace the slope and one of the two points in the point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]Replacing m = 2 and (1/2, 5)
[tex]y-5=2(x-\frac{1}{2})[/tex]Finally, we must simplify to obtain the slope-intercept form
[tex]\begin{gathered} y-5=2x-1 \\ y=2x-1+5 \\ y=2x+4 \end{gathered}[/tex]ANSWER:
y = 2x + 4
a Fill in the blank. If necessary, use the slash mark (/) for a fraction bar. If cosg = then tang =
We can use a right triangle and the below trigonometric ratios.
[tex]\begin{gathered} \cos(\theta)=\frac{\text{ Adjacent leg}}{\text{ Hypotenuse}} \\ \tan(\theta)=\frac{\text{ Opposite leg}}{\text{ Adjacent leg}} \end{gathered}[/tex]In this case, we have:
[tex]\cos(\theta)=\frac{3}{5}=\frac{\text{Adjacent leg}}{\text{Hypotenuse}}[/tex]As we can see, we need to know the value of the opposite leg. Since it is a right triangle, we can use the Pythagorean theorem formula.
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{ Where} \\ a\text{ and }b\text{ are the legs} \\ c\text{ is the hypotenuse} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} a=3 \\ b=? \\ c=5 \\ a^{2}+b^{2}=c^{2} \\ 3^2+b^2=5^2 \\ 9+b^2=25 \\ \text{ Subtract 9 from both sides} \\ 9+b^2-9=25-9 \\ b^2=16 \\ $$\text{ Apply square root to both sides of the equation}$$ \\ \sqrt{b^2}=\sqrt{16} \\ b=4 \end{gathered}[/tex]Finally, we have:
Then, we can find the value of tan(θ):
[tex]\begin{gathered} \tan(\theta)=\frac{\text{Opposite leg}}{\text{Adjacentleg}} \\ \tan(\theta)=\frac{4}{3} \end{gathered}[/tex]Answer[tex]\tan(\theta)=\frac{4}{3}[/tex]Winston is making a model of a statute using a scale where 2 inches equals 6 feet. If the actual height of
the statue is 20 feet, how tall is the model, in inches?
Answer:
6 2/3 inches
Step-by-step explanation:
2 inches / 6 feet * 20 feet = 6 2/3 inches
Length is 3x − 4, area is 6x4 − 8x3 + 9x2 − 3x − 12
The width of the given rectangle is 2x²-3x+3.
Given that, area of rectangle = [tex]6x^4-8x^3+9x^2-3x-12[/tex] and the length of rectangle = 3x-4.
What is the area of a rectangle?The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units. The formula to find the area of a rectangle = Length × Width.
Now, (3x-4) × width = [tex]6x^4-8x^3+9x^2-3x-12[/tex]
⇒ Width = [tex]\frac{6x^4-8x^3+9x^2-3x-12}{3x-4}[/tex]
3x-4|[tex]6x^4-8x^3+9x^2-3x-12[/tex]|2x³-3x+3
[tex]6x^4[/tex] - 8x³
_________________
0+9x²-3x-12
(-) 9x²+12x
_________________
0+9x-12
(-) 9x(+)12
_________________
0
So, width = 2x²-3x+3
Therefore, the width of the given rectangle is 2x²-3x+3.
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5. Evaluate the following V16
ach function is a transformation of the parent sine function. Based on the period, which graph represents each transformed function?
Given the functions:
• f(x) = sin(-x)
,• f(x) = sin(2x)
,• f(x) = sin(1/2x)
Given that each function is a transformation of the parent sine function, let's select the graph which represents each transformed function.
We have the parent sine function:
f(x) = sin(x).
• For function A.
f(x) = sin(-x)
The graph of this transformed function will be:
• For function B.
f(x) = sin(2x)
The period of this function will be:
[tex]T=\frac{2\pi}{B}=\frac{2\pi}{2}=\pi[/tex]Therefore, the graph which represents this function is:
• Function C.
f(x) = sin(1/2x)
The period of this function will be:
[tex]T=\frac{2\pi}{B}=\frac{2\pi}{\frac{1}{2}}=4\pi[/tex]Therefore, the graph of this function will be:
ANSWER:
A tank has two inlet pipes and one outlet pipe. The inlet pipes can fill the tank in 4 hoursand 10 hours. The outlet pipe can drain the tank in 2 hours. One day the outlet pipe was leftopen as the empty tank was being filled. Will the tank ever be full? If so, how long will ittake to fill the tank? If not, explain why not.
The two inlet pipes can fill the tank in 4 hours and 10 hours.
The work done by the inlet pipes per hour is calculated to be:
[tex]\Rightarrow\frac{1}{4}+\frac{1}{10}=\frac{7}{20}\text{ units per hour}[/tex]The outlet pipe drains the tank in 2 hours. The work done will be:
[tex]\Rightarrow\frac{1}{2}\text{ units per hour}[/tex]Therefore, if both inlet pipes and the outlet pipes are opened at the same time, the work done by the pipes combined will be:
[tex]\Rightarrow\frac{7}{20}-\frac{1}{2}=-\frac{3}{20}\text{ units per hour}[/tex]Since the work done to fill the tank is negative, it means that the tank will never get full as it empties faster than it fills up.
40 POINTSSSSS!!!!!!!!!! PLS HELP NO LOOKING IT UP!A polygon is shown on the graph: What effect will a translation 3 units down and 2 units left have on the polygon? Be sure to address how it could impact the angles, side lengths, and congruency between the original pre-image and the image.
we know that
A translation is a rigid transformation
In a translation the preimage and the image are congruent
that means -----> the angles and side lengths of the image and the preimage are congruent (are equal)
The only difference between the image and the preimage is the location
Remember that
If two figures are congruent, then their corresponding angles and their corresponding sides are equal
State the null and alternative hypotheses for the claimA report from five years ago said that the average income of accountants was $51,497; but nowadays it's more than that.
ANSWER and EXPLANATION
We want to state the null and alternative hypotheses for the claim given.
A null hypothesis is a statement about a population parameter such that the likelihood can be tested to either accept or reject the alternative hypothesis.
An alternative hypothesis on the other hand is a statement that directly contradicts the null hypothesis.
Therefore, going by that, we see that the null hypothesis is:
[tex]\mu=\$51,497[/tex]and the alternative hypothesis is:
[tex]\mu>\$51,497[/tex]The length of a rectangle is six times its width.
If the perimeter of the rectangle is 84 m, find its area.
The area when the length of a rectangle is six times its width is 216m².
How to calculate the value?Let the width = w
Let the length = 6 × w = 6w
Therefore the perimeter will be:
= 2(Length + Width) = 84
2(w + 6w) = 84
2 × 7w = 84
14w = 84
Divide
w = 84 / 14
w = 6
Width = 6m
Length = 6w = 6 × 6 = 36m
The area will be:
= Length × Width
= 36m × 6m
= 216m²
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