Answers
Answer:
the value of x is 12 and the measure of angle MNQ is 23
Related Questions
Q1.Simplify:
(I) {1³+2³}×(1/3) ²
(II) {5^-1×4^-1}²
(III) {(1/3) ^-1×(1/2)^-2}÷(1/4) ^-3
Give correct answer I will mark as brianlist. It wrong will deleated.
Answers
[tex]\textbf{(i)}\\\\\{1^3 +2^3 \} \times \left(\dfrac 13 \right)^2\\\\=(1+8) \left(\dfrac 19 \right)\\\\=9\left(\dfrac 19 \right)\\\\=1\\\\[/tex]
[tex]\textbf{(ii)}\\\\\{5^{-1}\times 4^{-1}\}^2\\\\=\left(5^{-1} \right)^2 \times \left(4^{-1} \right)^2~~~~~~~~~~~;[(ab)^m = a^mb^m]\\\\=5^{-2}\times 4^{-2}~~~~~~~~~~~~~~~~~~~~;[(a^m)^n = a^{mn}]\\\\=\dfrac 1{5^2} \times \dfrac 1{4^2}~~~~~~~~~~~~~~~~~~~~~~;\left[a^{-m} = \dfrac 1{a^m},~ a\neq 0 \right]\\\\=\dfrac{1}{400}\\\\=0.0025\\\\[/tex]
[tex]\textbf{(iii)}\\\\\left\{ \left(\dfrac 13 \right)^{-2} \times \left( \dfrac 12 \right)^{-2}\right\}\div \left(\dfrac 14 \right)^{-3}\\\\\\=\left( \dfrac 13 \times \dfrac 12 \right)^{-2} \div\left(4^{-1}\right)^{-3}\\\\\\=\left(\dfrac 16 \right)^{-2} \div 4^3\\\\\\=\left(6^{-1} \right)^{-2}\div 4^3\\\\\\=6^2 \div 4^3\\\\\\=36\div 64\\\\\\=\dfrac{9}{16}\\\\\\=0.5625[/tex]
Write the following as algebraic expressions. r decreased by 3
Answers
Answer:
r - 3
Step-by-step explanation:
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to write the verbal phrase "r decreased by 3" as an algebraic expression.
[tex]\triangle~\fbox{\bf{KEY:}}\star[/tex]
Think about it. "decreased by". If we decrease a number by another number, what happens to the first number?Here we decrease the variable "r" by 3.
Remember, variables always represent some number.
Let's think about it this way...
///\\\////\\\\////\\\///\\\///\\\///\\\///\\\///\\///\\///\\///\\///\//\\///\\\///\\\///\\\///\\///\\\///\
So we have a number r, and we decrease it by 3.
Now its value is less than the original value.
We subtracted 3 from the original value of r, and now its value is less than the original one.
Thus, "decreased by" is the same as "subtracted" in mathematics.
r decreased by 3 ⇒ [tex]\star\large\pmb{r-3}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
5. Find the value of the 11th term of the arithmetic sequence
-2, 5, 12, 19, 26, ...(11th term)
Answers
Answer:
-2, 5, 12, 19, 26, 33, 40, 47, 54, 61, 68, 75, 82, 89, 96, 103
could someone please help will give brainliest
Answers
Answer:
A - x = 4
Step-by-step explanation:
According to The Midsegment Trapezoid Theorem the length of the midsegment is the sum of both bases divided by 2.
So to find the value of x:
x + 3 + 4x 7 = 15*2 add like terms
5x + 10 = 30 subtract 10 from both sides
5x = 20 divide both sides by 5
x = 4
22+6[(14-5)÷3(17-14)]
I got 76 and every calculator I use says 76 but in the back of the book it says the answer is 28. Am I missing something or could it be a typo?
My work:
22+6[(14-5)÷3(17-14)]
22+6[(9)÷3(3)]
22+6 [(3)(3)]
22+6(9)
22+54 = 76
Answers
The simplification of the expression is 28. The mistake in your calculation occurred in step 3.
What is the process involved in simplifying expression involving brackets?TO simplify expressions involving brackets, we use a common method called BODMAS (Brackets, Of, Division, Multiplication, Addition, and Subtraction).
This means that we will first solve the expression in brackets first, followed by division, multiplication, addition, and subtraction as the case may be.
Now, from the given information, we have:
= 22+6[(14-5)÷3(17-14)]
solving parameters in the bracket first, we have:
= 22 + 6[(9) ÷3(3)]
= 22 + 6[(9) ÷9]
The above step is where you missed it from your calculation, you must first open all brackets within brackets before solving them.= 22 + 6[(9) ÷9]
= 22 + 6[ 1]
= 22 + 6
= 28
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The quadrilaterals JKLM and PQRS are similar.
Find the length x of QR.
K
Q
7
M
2
Z
3.6
S
1.8
A
X
3.6
R
Answers
Answer:
x = 6.3
Step-by-step explanation:
since the quadrilaterals are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{QR}{KL}[/tex] = [tex]\frac{RS}{LM}[/tex] ( substitute values )
[tex]\frac{x}{7}[/tex] = [tex]\frac{3.6}{4}[/tex] ( cross- multiply )
4x = 7 × 3.6 = 35.2 ( divide both sides by 4 )
x = 6.3
Suppose you have the following null and alternative hypothesis
Answers
A type I error takes place if a given null hypothesis is rejected but is said to be true in the population such as the forecast shows it is snowing outside but actually it is isn't.
What is type 11 error?A type II error is known to be a statistical term that tells the error that takes place when one fails not to accept a null hypothesis that is said to be really false. A type II error create a false negative.
It known is known also as an error of omission. Example is the forecast shows that It is not snowing but it is actually snowing.Note that:
Type I error is false positive.Type II error is false negative.The power of the test shows that:
The Power is the likelihood of rejecting the null hypothesis even if it is false.Power is the likelihood of making the right decision that is to reject the null hypothesis even if the null hypothesis is false.Power is the likelihood of not making a Type II error and others.See full question below
Suppose you have the following null and alternative hypothesis:
H o: it is snowing.
H a: It is not snowing
(A) in the context of this problem, describe a Type-1 error
(B) Describe Type II error
(C)Describe power of the test
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Make a table to help solve this problem. Cory, Srey, Molly, and Mao each visited a different city: Santa Clara, Seattle, Des Moines, and Pittsburgh. Cory and Molly visited cities with two words in their names. Mao and Cory visited cities whose names start with an S. Who visited Pittsburgh?
Answers
From the table we can say Srey visited Pittsburgh if the Cory, Srey, Molly, and Mao each visited a different city: Santa Clara, Seattle, Des Moines, and Pittsburgh.
What is reasoning?When making a choice or addressing an issue, reasoning is the ability to appraise things rationally by using logic based on new or existing information.
We have:
Cory, Srey, Molly, and Mao each visited a different city: Santa Clara, Seattle, Des Moines, and Pittsburgh. Cory and Molly visited cities with two words in their names.
Mao and Cory visited cities whose names start with an S.
The table can be make to show the information provided:
Cory - city with 2 words
Molly - city with 2 words
Mao - starting with an s
Cory - starting with an s
cities are : Seattle, Santa Clara,Pittsburgh,Des Moines
The table is:
Name City name
Cory Santa Clare
Molly Des Moines
Mao Seattle
Srey Pittsburgh
Thus, from the table we can say Srey visited Pittsburgh if the Cory, Srey, Molly, and Mao each visited a different city: Santa Clara, Seattle, Des Moines, and Pittsburgh.
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During a math game, a team kept track of their answers. The following diagram describes the number of answers they got right to the number they got wrong
Answers
the amount of wrong answers is 2
so that would give us a ratio of 2:10
we can simplify this answer
this gives us 1:5
1 being wrong and 5 being right
flip these and the answer is
5:1
A runner runs a distance of 350 metres in a time of 50 seconds.
What is his average speed?
Answers
Answer:
7
Step-by-step explanation:
350÷50=7
................
1/4 of the players on every team are girls. Write 3 fractions equivalent to 1/4
Answers
Answer:
2/8, 3/12 and 4/16
Step-by-step explaination:
All these fractions are equivalent to 1/4 as the numerator is a multiple of 1, the denominator is a multiple of 4, and the numerators are all a quarter of their respective denominators.
Given (x – 1)2 = 50, select the values of x.
Answers
Answer:
[tex]x= 1 +5\sqrt 2,~~ x=1-5\sqrt 2[/tex]
Step-by-step explanation:
[tex]~~~~~~(x-1)^2 = 50\\\\\implies x -1 = \pm\sqrt{50}\\\\\implies x = \pm\sqrt{25 \times 2} +1\\\\\implies x= 1 \pm 5\sqrt 2[/tex]
A triangle has a base length of 2ac2 and a height 6 centimeters more than the base length. Find the area of the triangle if a = 4 and c = 2.
Answers
The area of the triangle is 608 cm².
What is area?Area is the region bounded by a plane shape.
To calculate the area of the triangle, we use the formula below.
Formula:
A = bh/2............................ Equation 1Where:
A = Area of the triangleb = Base of the triangleh = Height of the triangleFrom the question,
Given:
b = 2ac²If
a = 4, c = 2b = (2×4×2²) = 32 cmh = (32+6) = 38 cmSubstitute these values into equation 1
A = (32×38)/2A = 608 cm²Hence, the area is 608 cm².
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Write down the first three and last two terms of the binomial expansion of:
a) (3x+(2/x))^15
b) (2x-(3/x))^20
Answers
Answer:
a) [tex](3x)^{15} + 15(3x)^{14}(\frac{2}{x}) + 105(3x)^{13}(\frac{2}{x})^2 + ... + 15(3x)(\frac{2}{x})^{14} + (\frac{2}{x})^{15}[/tex]
b) [tex](2x)^{20} + 20(2x)^{19}(-\frac{3}{x}) + 190(2x)^{18}(-\frac{3}{x})^2 + ... + 20(2x)(-\frac{3}{x})^{19} + (-\frac{3}{x})^{20}[/tex]
Step-by-step explanation:
The binomial expansion formula is:
[tex](a + b)^n = a^n + \binom{n}{1}a^{n-1} b + \binom{n}{2}a^{n-2}b^2 + ... + \binom{n}{r}a^{n-r}b^{r} + ... + b^n[/tex]
The (n r) in front of each term is the binomial coefficient. This can be calculated on a calculator using the nCr button (in this case, you'd put 15C1 for (n 1), 15C2 for (n 2), etc). This can be calculated without a calculator using this formula:
[tex]\binom{n}{r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}[/tex]
In a), a = 3x, b = 2/x and n = 15.
You can plug these into the formula above to get:
[tex](3x)^{15} + 15(3x)^{14}(\frac{2}{x}) + 105(3x)^{13}(\frac{2}{x})^2 + ... + 15(3x)(\frac{2}{x})^{14} + (\frac{2}{x})^{15}[/tex]
Here's how to do this without the formula:
Start with the a^nIn the second term, you subtract 1 from a's power (in this case, 15 to 14) and add 1 to b's power (0 to 1). Then you multiply it by nCr.This keeps going until you get to b^n. To check you've done it correctly, the powers of a and b in each term should add up to n. For example, in term 3 above, a's power is 13 and b's power is 2. These add to make 15.Remember, a's power goes down by 1 each time, and b's power goes up by 1 each time. There is no b in the first term because b^0 = 1.You could 'simplify' this by expanding the brackets, but this gives you massive numbers so it's probably best to leave it like this.
Applying this to b):
a = 2x, b = -3/x, n = 20
[tex](2x)^{20} + 20(2x)^{19}(-\frac{3}{x}) + 190(2x)^{18}(-\frac{3}{x})^2 + ... + 20(2x)(-\frac{3}{x})^{19} + (-\frac{3}{x})^{20}[/tex]
write an equation to estimate the difference of 18/20 - 5/8
Answers
Answer:
0.275
Step-by-step explanation:
What additional information would prove that DEFG
an isosceles trapezoid?
A- DE≈GF
B-DE≈DG
C-EF≈DG
D-EF≈GF
Answers
For the trapezoid to be proven to be an isosceles trapezoid, the additional information needed is: A. DE ≅ GF
What is an Isosceles Trapezoid?An isosceles trapezoid is a type of trapezoid whose opposite non-parallel sides have the same side length and base angles that are congruent.
In essence, for trapezoid DEFG to be proven to be an isosceles trapezoid, DE must be congruent to GF.
The additional information needed is therefore: A. DE ≅ GF
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Look at the dot plots below. Compare the shapes of the distributions of the results from the two experiments.
Answers
The shape of experiment 1 is roughly bell shaped. This indicates that it is normally distributed. The shape of experiment 2 is asymmetrical. This indicates that it is not normally distributed.
What is a dot plot?
A dot plot is a graph that is used to represent the frequency of a data set using dots. The dots represents the frequency of a number. The results from experiment 1 is more spread out over the numbers compared to experiment 2 which is concentrated around the center.
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Please HELP!! Need to finish before the end of the day!
Answers
Answer & Step-by-step explanation:
I have attached two ways you can find the number of green Jolos, by adding and/or subtracting from the other known values. Both ways will give the answer of C. 280 Jolos
find the vertical height of a cone if the radius is 4 cm and the curved surface area is 60 cm
Answers
Answer:
2.65 cm
Step-by-step explanation:
Applied Formula :
Curved Surface Area = πrlSolving :
60 = 3.14 x 4 x ll x 12.56 = 60l = 4.8 cmh² = l² - r²h² = (4.8)² - (4)²h = √23.04 - 16h = √7.04h = 2.65 cmWhat is the volume, in cubic centimeters, of a rectangular prism with a height of 8 centimeters, a width of 6 centimeters, and a length of 6 centimeters?
Answers
Answer:
288
Step-by-step explanation:
area of the base times the height. base is 6*6=36. Then 36*8 is 288
Work out the perimeter of a circle with radius 3cm.
Give your answer in terms of [tex]\pi[/tex]
Answers
Answer:
6π cm
Step-by-step explanation:
For a circle, the perimeter is equal to the circumference. The formula for the circumference of a circle is ...
C = 2πr
where r is the radius of the circle.
__
using the formulaSubstituting the given value of radius into the formula gives ...
C = 2π(3 cm)
C = 6π cm
The perimeter of the circle is 6π cm.
what is a good approximating for 4pi^3
Answers
Answer: 123.84
Step-by-step explanation: You can set pi as 3.14. Then, you get 123.836576. Round to the nearest hundredth to get 123.84.
Metal A has a density of 12.7 g/cm3.
55 g of metal A is combined with metal B to create an alloy with mass 90 g and density 10.7 g/cm3.
What is the density of metal B?
Round your answer to 2 decimal places.
Answers
Using the given information, the density of metal B is 8.58 g/cm³
Calculating densityFrom the question, we are to determine the density of metal B
From the given information,
55 g of metal A is combined with metal B to create an alloy with mass 90 g
∴ Mass of metal B in the alloy = 90 g - 55 g = 35 g
Now, we will determine the volume of metal A in the alloy
Using the formula,
Density = Mass / Volume
∴ Volume = Mass / Density
Volume of metal A in the alloy = 55/12.7
Volume of metal A in the alloy = 4.33 cm³
Then, we will determine the volume of the alloy
Volume of the alloy = 90/10.7
Volume of the alloy = 8.41 cm³
∴ Volume of metal B in the alloy = 8.41 cm³- 4.33 cm³
Volume of metal B in the alloy = 4.08 cm³
Now, for the density of metal B
Density = mass / volume
Density of metal B = 35 / 4.08
Density of metal B = 8.58 g/cm³
Hence, the density of metal B is 8.58 g/cm³.
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Layne says the probability of the high school team winning the football game is 75%.
abdul says the probability is 3 5 .
who thinks the event is more likely, layne or abdul? explain.
Answers
The person who thinks the event is more likely is Layne. This is because she has a higher probability value than Abdul.
Who thinks the event is more likely?Probability determines the chances that an event would happen. The probability the event occurs with certainty is 1 and the probability that the event would not occur with certainty is 0. The closer the event is to 1, the more likely the event would happen
Layne's probability that the event would happen = 75%
Abdul's probability that the event would happen = 3/5 x 100 = 60%
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did I solve this problem right?
Answers
Step-by-step explanation:
¿qué es eso?¿es esto importante? :)
Which table represents a function?
Answers
Answer:
The one on the top left
Step-by-step explanation:
What makes a function, a function is that the x coordinate (x,y), cannot be repeated in the tables. The y coordinate can though.
nich
2. What quantity should be added to both sides of
this equation to complete the square?
x² - 8x = 5
Answers
Answer:
[tex]16[/tex]
Step-by-step explanation:
[tex]~~~~~~x^2 -8x = 5 \\\\\implies x^2 -2\cdot 4 \cdot x+ 4^2 = 5+ 4^2~~~~~~~~~~~~;[\text{Add}~ 4^2 = 16 ~ \text{to both sides }]\\\\\implies (x-4)^2 = 21[/tex]
need help with this ASAP: methods for solving right triangles.
Answers
Explanation:
1) sin(37º)=x/10.3————>trigonometric ratio (sine)
2)7²+10²=c²—————-> pythagorean theorem
3) using sine—————> sin(51º)=9/x
using tangent —————> tan(51º)=9/x and x = 7.3 (rounded)
4)using pythagorean theorem————> 6²+7²=c²
angle b is tanx=6/7 where x = 40.6 degrees, angle a is tanx=7/6 where x = 49.4
Answers:
1)x= 6.2
2)x= 12.2
3)x= 11.6 (rounded)
4)x= 9.2
credit to genan for question 3 and 4
ur welcome :)
correct me if im wrong
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Line segment AB has endpoints A(1,8) and B(7,−4). What are the coordinates of the point located 5/6 of the way from A to B?
O (-4, 11 1/3)
O (3, -2 1/3)
O (6, -2)
O (12, -14)
Answers
The coordinate of the point is (6,-2)
How to determine the coordinate of the point?The given parameters are:
A = (1,8)
B = (7,-4)
The location of the point (i.e 5/6) means that the ratio is:
m :n = 5 : (6 - 5)
m : n = 5 : 1
The coordinate of the point is then calculated as:
[tex](x,y) = \frac{1}{m + n}* (mx_2 + nx_1,my_2 + ny_1)[/tex]
So, we have:
[tex](x,y) = \frac{1}{5 + 1}* (5 * 7 + 1 * 1 , 5 * -4 + 1 * 8)[/tex]
Evaluate
[tex](x,y) = \frac{1}{6}* (36 , -12)[/tex]
Evaluate the product
(x,y) = (6,-2)
Hence, the coordinate of the point is (6,-2)
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What is the measure of USQ⌢
Answers
Explanation: Arc URS is a semi-circle, equaling to 180.
Angle UPT is 47, vertical to Angle QPR.
So just add 180 + 47. = 227