From the given information, the measure of DEF is 81°
Calculating the measure of anglesFrom the question, we are to determine the measure of DEF
From the given information,
DEF and RST are complementary angles. This means they sum up to 90°
Thus,
(3(-5 + 2x)) + (x - 7) = 90
(3(-5 + 2x)) + (x - 7) = 90
(-15 + 6x) + (x - 7 ) = 90
-15 + 6x + x - 7 = 90
6x + x = 90 + 15 + 7
7x = 112
x = 112/7
x = 16
Then, substitute the value of x to determine the measure of DEF
(3(-5 + 2x))
= (3(-5 + 2(16)))
= (3(-5 + 32))
= (3(27))
= 81°
Hence, the measure of DEF is 81°
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Simplify the expression.
[tex]\huge\boxed{4x}[/tex]
Start by simplifying the power.
[tex](5x)^3=5^3x^3=125x^3[/tex]
[tex]\dfrac{500x^4}{125x^3}[/tex]
Cancel out the common factor of [tex]125[/tex].
[tex]\dfrac{4x^4}{x^3}[/tex]
Finally, cancel out the common factor of [tex]x^3[/tex].
[tex]\boxed{4x}[/tex]
In a recent year, 27.2% of all registered doctors were female. If there were 55,900 female registered doctors that year, what was the total number of registere doctors? Round your answer to the nearest whole number. In a recent year , 27.2 % of all registered doctors were female . If there were 55,900 female registered doctors that year , what was the total number of registere doctors ? Round your answer to the nearest whole number .
it's B why they need me to write something long the answer is ez B
Step-by-step explanation:
it f common sense
For a normally distributed data set with a mean of 830 and a standard deviation of 96.7, calculate the z-score for a
data point of 915.
Round this however your teacher instructs.
=================================================
Work Shown:
mu = 830 = mean
sigma = 96.7 = standard deviation
x = 915 = given raw score we want to convert
z = (x - mu)/sigma
z = (915 - 830)/(96.7)
z = (85)/(96.7)
z = 0.8790072 approximately
Find the non-extraneous solutions of the square root of the quantity x plus 6 minus 5 equals quantity x plus 1
The non-extraneous solutions are -6 and -5.
How to find non-extraneous solutions?By checking these solution values in the original equation.
[tex](x+6)^{1/2}-5=x+1\\(x+6)^{1/2}=x+6\\((x+6)^{1/2})^2=(x+6)^2\\x+6=x^2+12x+36\\0=x^2+11x+30\\(-11+(11^2-4(1)(30))^{1/2})/2\\(-11+((1)^{1/2})/2\\(-11+1)/2=-5\\(-11-1)/2=-6\\((-6)+6)^{1/2}-5=(-6)+1\\(0^{1/2})-5=-5[/tex]
Thus, -6 is non-extraneous.
[tex]((-5)+6)^{1/2}-5=(-5)+1\\(1^{1/2})-5=-4\\1-5=-4\\-4=-4[/tex]
Thus, -5 is non-extraneous.
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One of the tables shows a proportional relationship.
Use the points from this table to graph the line representing the proportional
relationship.
Line
10-
9
8-
7
5
4
3
2
-2-
3 7 4
-3-
Undo
1 2
3
4
Redo
$
6
x Reset
7 8 9 10
X
y
x
y
X
y
X
y
2
1
2
1
0
2
1
3
2
4
3
2
2
2
4
5
6
3
4
6
4
5
3
7
27
6
4
8
4
5
8
9
6
Answer:
See attached
Step-by-step explanation:
The graph of a proportional linear relationship is a line that passes through the origin (0, 0).
From inspection of the given tables, the linear equations for each table of points is:
Table 1: y = x + 1Table 2: y = x/2Table 3: y = x + 2Table 4: y = 2x + 1The only equation for which y = 0 when x = 0 is y = x/2 → Table 2.
Given points from Table 2:
(2, 1)(4, 2)(6, 3)(8, 4)To graph the line, plot the given points and draw a line through them (see attached).
find the quotient: -10/9 divided by -5/7
Answer:
70/45
Step-by-step explanation:
(-10/9) divided by (-5/7) = (-10/9) / (-5/7)
dividing two fractions is the same as multiplying the top fraction by the reciprocal of the bottom one
top fraction = -10/9
bottom fraction = -5/7
reciprocal just means switching the numerator and denominator
reciprocal of bottom fraction = 7 / -5 = -7/5
thus,
(-10/9) / (-5/7) = (-10/9) * reciprocal of (-5/7) = (-10/9) * (-7/5) = 70/45
note that to multiply two fractions, you just multiply the numerators to get your new numerator and do the same thing with the denominators
Which expression is a non-real complex number?
-4 +√7
3
1 + √²
5-√15
27
28
The expression that represents a complex number is the one in the second option.
[tex]\frac{2}{3} + \sqrt{-\frac{27}{28} }= \frac{2}{3} + \sqrt{\frac{27}{28} } i\\[/tex]
Which expression is a non-real complex number?Remember that the complex number i is given by:
[tex]i = \sqrt{-1}[/tex]
So we have complex numbers when we have negative arguments inside of square roots.
In this particular case, the only option with a negative argument on a square root is on the second option:
[tex]\frac{2}{3} + \sqrt{-\frac{27}{28} } \\\\\frac{2}{3} + \sqrt{-1} *\sqrt{\frac{27}{28} } \\\\\frac{2}{3} + \sqrt{\frac{27}{28} } i\\[/tex]
We conclude that the correct option is the second one.
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Answer:
(2)/(3)+\sqrt(-(27)/(28))
Step-by-step explanation:
Plato/Edmentum
Desperately need help. pls
By applying the concept of composition between two functions and utilizing the information given in the two tables, we find the following results: f ° g (0) = - 2, f ° g (x) = 1.
How to find the value of composition between two functions
Compositions are binary operators between two functions: f - Former function, g - Latter function.
f ° g (x)
Where the input of the former function is the output of the latter function. By a brief observation, we find the following relationships in accordance with the two tables:
Case I
f(x):
0 → 1
g(x):
1 → - 2
Case II
f(x):
1 → 0
g(x):
0 → 1
By applying the concept of composition between two functions and utilizing the information given in the two tables, we find the following results: f ° g (0) = - 2, f ° g (x) = 1.
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The cost of 25 apples is $18.50. What is the cost of one apple
Answer:
0. 74$Step-by-step explanation:
$18. 50÷25=0. 74$
6) Simplify the following:
axaxbxb
The simplified expression of axaxbxb is a^2b^2
How to simplify the expression?The expression is given as;
axaxbxb
Rewrite properly as:
a * a * b * b
Evaluate the product
a^2b^2
Hence, the simplified expression of axaxbxb is a^2b^2
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Peter analyzed a set of data with explanatory and response variables x and y. He concluded the mean and standard deviation for x as 7.8 and 3.70, respectively. He also concluded the mean and standard deviation for y as 12.2 and 4.15, respectively. The correlation was found to be 0.964. Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place.
The y-intercept is 3.78.
We have given that,
[tex]\overline{x}=7.8 ,S_x=3.70,\\\overline{y}= 12.2,S_y=4.15\\r=0.964[/tex]
What is the formula of the slope?[tex]Slope=r \times\frac{S_y}{S_x} \\\\Slope=0.964\times \frac{4.15}{3.70}\\ Slope=1.08=\overline{y}-slope\:\times \overline{x}\ intercept\\=\overline{y}-slope\:\times \overline{x}\\=12.2-1.08(7.8)\\=3.78[/tex]
Therefore the y-intercept is 3.78.
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Question 5 3 pts A corral for cattle is in the shape of a circle with a radius of 17.8 m; find the total area of the corral. Round your answer to the nearest whole number. Do not type the units in the space below.
Step-by-step explanation:
the area of s circle is
pi×r²
r being the radius.
so, in our case
pi×17.8² = pi×316.84 = 995.3822164... ≈ 995 m²
Identify the type of sequence and write the recursive rule −1,−2,−4,−8,
Identify the segments that are parallel, if any angle ABC equals angle HCB
Answer: A. DC||AB
Step-by-step explanation:
Line DC is parallel to AB so the correct answer is option B.
What is the similarity?
If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
In the given image we can see that the two angles ABC and HCB are congruent to each other. So the line DC is parallel to AB.
Therefore Line DC is parallel to AB so the correct answer is option B.
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Dont Really need explanation Simply answer Just I didn’t understand Maybe I can get help
Based on the calculations, Tart & Sweet's total profit from April to June is equal to -2 dollars.
What is a bar chart?A bar chart can be defined as a type of chart that is used for the graphical representation of a data set, especially by using rectangular bars or vertical columns.
In order to determine Tart & Sweet's total profit, we would simply add the amount of money (in dollars) generated from April to June as follows:
April = -8.May = 2.June = 4.Total profit = -8 + 2 + 4
Total profit = -$2.
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look at this system of exquations. y=2x-1 4x +y=2 which shows a correct step using substitution to solve the system of equations?
The solution to the system of equations is x = 0.5, y = 0
How to solve the system of equations?The system of equations is given as:
y = 2x-1
4x + y=2
Substitute y = 2x-1 in 4x + y=2
4x + 2x-1 =2
Evaluate the like terms
6x = 3
Divide by 6
x = 0.5
Substitute x = 0.5 in y = 2x-1
y = 2 * 0.5 - 1
Evaluate
y = 0
Hence, the solution to the system of equations is x = 0.5, y = 0
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Find the value of x.
x = 2
x = 3
x = 33
x = 52
If f(x) = 8- 10x and g(x) = 5x + 4, what is the value of (fg) (-2)?
O -196
O -168
O 22
O 78
In isosceles ∆ABC, points M and N belong to base
BC
so that BM = CN. Prove:
∆BAM ≅ ∆CAN
∆AMN is an isosceles triangle.
From the statements and reasons given below as regards the Isosceles Triangle, we have been able to prove that; ∆BAM ≅ ∆CAN
How to prove an Isosceles Triangle?Isosceles Triangle means that two sides of the triangle are equal and also 2 angles are equal.
Now, we are told that triangle ABC is an Isosceles and as such, AB and AC are congruent.
We are given that BM and NC are congruent. Now, due to the fact that Triangle AMN is an isosceles triangle, it means that the sides AM and AN are congruent to each other.
Thus, from the proofs above and from the definition of the isosceles Triangle, we can say that triangles BAM and CAN are congruent.
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Answer & Step-by-step explanation:
To prove ∆BAM ≅ ∆CAN:
1. Given that ∆ABC is an isosceles triangle with base BC, and BM = CN, we know that AB = AC.
2. Using the Side-Angle-Side (SAS) congruence criterion, we can show that ∆ABM and ∆ACN are congruent.
3. Therefore, corresponding angles ∠BAM and ∠CAN are congruent.
4. Similarly, ∠BMA and ∠CNA are congruent.
5. By showing that corresponding angles in ∆ABM and ∆ACN are congruent, we can conclude that ∆BAM ≅ ∆CAN.
To prove ∆AMN is an isosceles triangle:
1. From the given information, we know that BM = CN.
2. By proving ∆BAM ≅ ∆CAN, we have shown that ∠BAM ≅ ∠CAN.
3. Since ∠BAM and ∠CAN are congruent, we can conclude that ∠BAN ≅ ∠CAM using the Transitive Property of Congruence.
4. By establishing that ∠BAN ≅ ∠CAM, we can conclude that ∆AMN is an isosceles triangle because it has two congruent angles.
Please help me with this on the picture
Answer:
5, 7
Step-by-step explanation:
The mode of the numbers is 5, which means that 5 should be the most common card (highest frequency). Therefore the cards should have at least one more 5 among them.
Considering that 5 is one of the hidden cards and x is the other,
• Using the equation for the mean:
[tex]mean = \frac{sum \space\ \space\ of \space\ \space\ numbers}{number \space\ \space\ of \space\ \space\ numbers}[/tex]
[tex]6 = \frac{4+5+ 9 + 5 + x}{5}[/tex]
⇒ [tex]30=23 + x[/tex]
⇒ [tex]x = 7[/tex]
This means 5 and 7 are the hidden cards.
Select the expression that is modeled on the number line. A number line from zero to one partitioned into sixths. There are four hops beginning at one sixth and ending at five sixths.
The answer to the question that is modeled here is one sixth plus four sixths.
How to solve for the expression
We have the following fractions
1/6 and 5/6
We are to find the fraction which when added to 1/6 would give us 5/6. Hence we have
1/6 + 4/6 = 5/6
Hence the correct answer to the question here is option a.
complete questionPLS HELP 1HOUR LEFT Select the expression that is modeled on the number line. A number line from zero to one partitioned into sixths. There are four hops beginning at one sixth and ending at five sixths one sixth plus five sixths
one sixth plus four sixths
five sixths minus one sixth
five sixths minus four sixths
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Solve for t in this equation and show steps please d = vt + 1/2(a)(t^2)
Solve the following equation for m.
F=mv^2 / r
Answer:
Step-by-step explanation:
F = [tex]\frac{mv^2}{r}[/tex]
mv² = Fr
m = [tex]\frac{Fr}{v^2}[/tex]
can someone please help with part III?? don’t use my work it’s prob wrong lol :)
Answer: formula
AB= (-1- -3)+((3-1)
(-1+3 )^2+(3-1)^2
2^2+2^2
Sq rt of 8 is 2.83
length of AB is 2
BC= (-3- -1)^2 + (5-3)^2
-3+1 =-2^2+2^2=4+4=8
Sq rt of 8 is 2.828= 2.83
Step-by-step explanation:
why is the derivative of a constant zero
A constant function is exactly that - constant - meaning it exhibits no change whatsoever with respect to any change in its input. If [tex]f(x) = 1[/tex], then it doesn't matter what value of [tex]x[/tex] I give you, the value of [tex]f(x)[/tex] will always be nothing other than 1.
That the derivative of such a function is zero follows immediately from the definition of the derivative. If [tex]c\in\Bbb R[/tex] and [tex]f(x) = c[/tex], then
[tex]f'(x) = \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \lim_{h\to0} \frac{1 - 1}h = \lim_{h\to0}\frac0h = 0[/tex]
Melissa's mother asked her to buy a gallon of milk at the store. The store only had quarts of milk. How many quarts of milk does Melissa need to buy?
Answer:
4 quarts of milk
Step-by-step explanation:
4 quarts = 1 gallon
so, melissa needs to buy 4 quarts
From a group of 13 women and 12 men, a researcher wants to randomly select 8 women and 8 men for a study. In how many ways can the study group be selected?
The total number of ways the study can be selected is: 637065
Given,
Total number of women in a group= 13
Total number of men in a group = 12
Number of women chosen = 8
Number of men chosen = 8
∴ the total number of ways the study group can be selected = 13C₈ and 12C₈.
This in the form of combination factor = nCr
∴ nCr = n!/(n₋r)! r!
13C₈ = 13!/(13 ₋ 8)! 8!
= 13!/5!.8!
= 1287
12C₈ = 12!/(12₋8)! 8!
= 12!/5! 8!
= 495
Now multiply both the combinations of men and women
= 1287 × 495
= 637065
Hence the total number of ways the study group is selected is 637065
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Find f(2) and f(a + h) when f(x) = 3x2 + 2x + 4.
Step-by-step explanation:
[tex]f(x) = 3 {x}^{2} + 2x + 4[/tex]
[tex] \: [/tex]
[tex]f(2) = 3. {2}^{2} + 2.2 + 4[/tex]
[tex]f(2) = 3.4 + 4 + 4[/tex]
[tex]f(2) = 12 + 8[/tex]
[tex]f(2) = 20 \\ [/tex]
[tex] \: [/tex]
[tex]f(a + h) = 3 {(a + h)}^{2} + 2.(a + h) + 4[/tex]
[tex]f(a + h) = 3( {a}^{2} + 2ah + {h}^{2} ) + 2a + 2h[/tex]
[tex]f(a + h) = 3 {a}^{2} + 6ah + 3 {h}^{2} + 2a + 2h + 4[/tex]
[tex]f(a + h) = 3 {a}^{2} + 3 {h}^{2} + 6ah + 2a + 2h + 4[/tex]
Find the value of x and y using the diagram below.
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
x = 2 , y = 3Step-by-step explanation:
As the given figure is a rectangle, therefore the opposite sides should be equal. So -
3x + y = 12 – y...(eqn (i) )
and
y – x = x – 1...(eqn (ii) )
Solving eqn (ii) we get -
→ y – x = x – 1
→ y = x + x – 1
→ y = 2x – 1...eqn(iii)
Solving eqn (i) we get -
→ 3x + y = 12 – y
→ 3x = 12 – y – y
→ 3x = 12 – 2y
Substituting the value of eqn (iii)
→ 3x = 12 – 2(2x– 1)
→ 3x = 12 – 4x + 2
→ 3x + 4x = 14
→ 7x = 14
→ x = 14/7
→ x = 2
Hope it helps you!!Answer:
x = 2; y = 3
Step-by-step explanation:
Since the quadrilateral has 4 right angles, it is a rectangle.
In a rectangle, opposite sides are congruent.
3x + y = 12 - y
x - 1 = y - x
We have a system of two equation is 2 variables.
Let's simplify both equations.
3x + 2y = 12
2x - y = 1
Rewrite the first equation. Multiply both sides of the second equation by 2. Add the equations.
3x + 2y = 12
(+) 4x - 2y = 2
-------------------------
7x = 14
Divide both sides by 2.
x = 2
Substitute 2 for x in the second original equation and solve for y.
x - 1 = y - x
2 - 1 = y - 2
1 = y - 2
y = 3
Answer: x = 2; y = 3
A student's grade on the Fundamentals of Engineering exam has a z-score of 0.5. Make an observation about the student's grade.
The observation about the student's grade with the z score illustrated is that it's a half standard deviation above the mean of the total test score.
What is z score?It should be noted that the z score is a numerical measurement which describes the relationship of a value to the mean value of the group.
In this case, the observation about the student's grade with the z score illustrated is that it's a half standard deviation above the mean of the total test score.
This is illustrated as the z score is 0.5.
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