Give that m/_ y=39, find the measures of angles a and b

Give That M/_ Y=39, Find The Measures Of Angles A And B

Answers

Answer 1

Answer:

  ∠a = 39°

  ∠b = 129°

Step-by-step explanation:

Vertical angles are congruent. An exterior angle of a triangle is equal to the sum of the remote interior angles.

Application

Angle y and angle 'a' are vertical angles, so congruent.

  ∠a = ∠y = 39°

The angle marked 'b' is an exterior angle to the triangle. Its remote interior angles are 'a' and the one marked 90°.

  ∠b = ∠a +90° = 39° +90°

  ∠b = 129°

Answer 2

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

Given:[tex]\longrightarrow\bold{m<a= \: 39}[/tex] ✓

[tex]\longrightarrow\bold{m<b= \: 141}[/tex]

In the given figure, angles a and y are vertically opposite angles. The measure of vertical angles is equal, therefore :-

[tex]\small\longrightarrow\sf{m<a = m<y}[/tex]

[tex]\small\longrightarrow\sf{m<a= \: 39^\circ}[/tex]

Next, angles a and 90° are the opposite interior angles to the exterior angle b. By the triangle theorem below :-

[tex]\small\longrightarrow\sf{m<b=m<a+90^\circ}[/tex]

[tex]\small\longrightarrow\sf{39^\circ+90^\circ}[/tex]

• [tex]\small\longrightarrow\sf{m<b= 129^\circ}[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

m<a= [tex]\large\sf{\boxed{\sf 39^\circ}}[/tex]

m<b = [tex]\large\sf{\boxed{\sf 129^\circ}}[/tex]


Related Questions

How many gold medals have been awarded for the 1500-meter race from 1896 - 2000 ?

Answers

Answer:

Hola disculpa no me acuerdo

Step-by-step explanation:

De verdad que me encantaria ayudar pero no me acuerdo :(

Answer:

6

Step-by-step explanation:

Patty pays $235 in advance on her account at the athletic club. Each time she uses the club, $6 is deducted from the account. Write an equation that represents the value remaining in her account after x visits to the club. Find the value remaining in the account after 5 visits.
a. V=235 - 6x; $1415
b. V= 6 - 235x; $205
c. V=235 - 6x; $1401
d. V=235 - 6x; $205

*show your work*

Answers

Answer:

205

Step-by-step explanation:

We start with 235, this will be our y-intercept.

6 Is deducted from our value every visit, making our slope -6.

Put the two into slope intercept form:

[tex]y=235-6x[/tex]

To find the value after 5 visits substitute x for 5:

[tex]y=235-6(5)[/tex]

Solve

[tex]y=235-6(5)\\y=235-30\\y=205[/tex]

Therefore you have 205 left in your account after 5 visits.

Calculate the following, and place the calculated solution on the appropriate line. In all cases, assume the companies that are the subject of the question are US companies using US GAAP.

a. Berful sells one product. It had one item in beginning inventory that cost $10,000, and purchased 4 more items during the accounting period. The cost changed with each purchase, as shown below:

Item Cost of Item
First $12,000
Second 14,000
Third 15,000
Fourth 16,000
If 3 items were sold during the year, calculate the cost of ending inventory using the following cost flow assumptions (Remember beginning inventory in your calculations!):
FIFO $_____________
LIFO $_____________
Weighted Average $_____________

b. Berful purchased a machine on the first day of the accounting period at a cost of $22,000. The machine is expected to have a life of 5 years or 20,000 units, and a salvage value of $2,000. Calculate the second year depreciation expense using the following depreciation methods (6,000 units produced in year 2):

Straight-line $_____________
Double-declining Balance $_____________
Units-of-production $_____________


c. Calculate the correct balance of cash to be included in the Cash account on the firm’s balance sheet by preparing a bank reconciliation of its checking account from the data given below:
Item Amount
Balance per Bank Statement $16,655.44
Balance per Books $12,091.94
Deposits in Transit $ 2,234.81
Outstanding Checks $ 6,808.16
Bank Service Charge $ 9.85
Correct balance of cash in this account $__________

d. Show the accounting entry required as a result of the above bank reconciliation in the space below:



e. If Berful uses the Allowance Method to determine its bad debt expenses, establishing its estimate as 1% of Net Sales, and Net Sales total $600,000, show the adjusting journal entry required if the Allowance for Bad Debts account has a debit balance of $2,000?

Answers

a) The calculation of the cost of ending inventory using the following cost flow assumptions are as follows:

FIFO $31,000 ($15,000 + $16,000)

LIFO $22,000 ($10,000 + $12,000)

Weighted Average $26,800 ($13,400 x 2)

b) The calculation of the second-year depreciation expense using these depreciation methods is as follows:

Straight-line $4,000

Double-declining Balance $5,280

Units-of-production $6,000.

c) The correct balance of cash to be included in the Cash account on the firm’s balance sheet based on the bank reconciliation is $12,082.09.

d) The accounting entry required for the bank reconciliation is as follows:

Debit Bank Service Charges $9.85

Credit Cash Account $9.85

To record the bank service charge for the period.

e) The adjusting journal entry required is as follows:

Debit Bad Debt Expense $8,000

Credit Allowance for Bad Debts $8,000

To record the bad debt expense for the period.

Data and Calculations:

a) Berful Company:

Beginning inventory = $10,000

Purchases:

First $12,000

Second 14,000

Third 15,000

Fourth 16,000

The total cost of goods available for sale = $67,000

Weighted average cost = $13,400 ($67,000/5)

Total items available for sale = 5 items (1 + 4)

Sales = 3 items

Ending inventory = 2 items (5 - 3)

b) Cost of machine = $22,000

Estimated useful life = 5 years or 20,000 units

Salvage value = $2,000

Depreciable amount = $20,000 ($22,000 - $2,000)

Straight-line Method:

Annual depreciation for second year = $4,000 ($20,000/5)

Double-declining balance:

Depreciation rate = 40% (100/5 x 2)

For the first year = $8,800 ($22,000 x 40%)

Declined balance = $13,200 ($22,000 - $8,800)

For the second year = $5,280 ($13,200 x 40%)

Units-of-production Method:

Depreciation per unit = $1 ($20,000/20,000)

For the second year, Depreciation = $6,000 ($1 x 6,000)

c) Bank Reconciliation Statement:

Balance per Bank Statement $16,655.44

Add: Deposits in Transit          $ 2,234.81

Less: Outstanding Checks      $ 6,808.16

Balance as per Cash Book    $12,082.09

Cash Book Adjustment:

Balance per book   $12,091.94

Bank Service Charge   ($ 9.85)

The correct balance of cash in this account $12,082.09.

d) Transaction Analysis:

Bank Service Charges $9.85 Cash Account $9.85

e) Data and Calculations:

Allowance for Bad Debts = $2,000 Debit

Net Sales = $600,000

Estimated allowance for bad debt expenses = 1% of Net Sales

= $6,000 ($600,000 x 1%)

Bad Debt Expense $8,000 Allowance for Bad Debts $8,000 ($2,000 + $6,000)

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y+6=5(x-4)
wtirte the formula for f(x) in terms of x

Answers

The formula for f(x) in y + 6 = 5(x - 4) in terms of x is f(x) = 5(x - 4)- 6

What is a linear equation?

A linear equation is a equation that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

How to rewrite the formula?

A system of linear equations is a collection of at least two linear equations.

In this case, the linear function in the question is given as:

y + 6 = 5(x - 4)

Subtract 6 from both sides of the equation

y + 6 - 6 = 5(x - 4) - 6

Evaluate the difference in the above equation

y = 5(x - 4) - 6

Express the above equation as a function f(x)  i.e. we express y as a function of x

f(x) = 5(x - 4) - 6

Hence, the formula for f(x) in y + 6 = 5(x - 4) in terms of x is f(x) = 5(x - 4) - 6

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Using Figure A above name three obtuse angles.
O MOL, NOK, MOJ
O MOK, NOK, MOJ
O MOL, NOJ, MOJ

Answers

Obtuse angle means its degree is greater than 90° but smaller than 180°.

< MOK exists 180°

< NOJ exists 90°

What is Obtuse Angle?

An obtuse angle exists a kind of angle that is always larger than 90° but less than 180°. In other words, it lies between 90° and 180°.

It exists not equivalent to 90° and 180°.

Because if obtuse angle equal to 90 degree it exists "Right angle'

If obtuse angle equal to 180 degree it exists 'Straight Angle'.

Obtuse angle means its degree is greater than 90° but smaller than 180°.

< MOK exists 180°

< NOJ exists 90°

Therefore, the correct answer is option a) MOL, NOK, MOJ.

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Answer:

Step-by-step explanation:

using figure a above name two right angles

Consider the functions f(x) = (four-fifths) Superscript x and g(x) = (four-fifths) Superscript x + 6. What are the ranges of the two functions?

Answers

Let the two exponential functions be

[tex]$f(x) = (4/5)^x[/tex] and

[tex]$g(x) = (4/5)^{(x + 6)}.[/tex]

Both of these exist exponential functions with positive bases, we end that the range for both exists: {y| y > 0}.

Therefore, the ranges of the two functions exists {y| y > 0}.

How to find the ranges of the two functions?

Let the two exponential functions be

[tex]$f(x) = (4/5)^x[/tex] and

[tex]$g(x) = (4/5)^{(x + 6)}.[/tex]

Both of these exist exponential functions with positive bases, then neither of these can contain negative outcomes, while, as x increases, the outcome will also increase.

Then both the functions exist exponential growths, so the range for both of these exists the set of all real positive values, written in both cases as: {y| y > 0}.

Therefore, the ranges of the two functions exists {y| y > 0}.

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Need help with this question

Answers

Answer:

y=-1/2n+44

Step-by-step explanation:

The number of bean stalks, n, represents the x values

The yield, y, represents the y values

After reading the problem, we have two coordinates: (30,29) and (32, 28) Because this problem is asking for y=mn+b, we have to find the slope. How do we find the slope? We do so by using the slope formula y2-y1/x2-x1. Now let's input the coordinates into this formula.

1.) 28-29/32-30 = -1/2

Let's plug -1/2 into y=mn +b

2.) y=-1/2n+b

Now we have to find what b ( y intercept) equals. To find B, we plug a coordinate into x and y. Let's use (30,29)

3.) 29 = -1/2(30)+b

29 = -15 +b

44 = b

We have now found the linear relationship form for this problem: y=-1/2n +44

6) Evaluate 3/4x if X = -1/4

Answers

Answer: [tex]-\frac{3}{16}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}(-\frac{1}{4} )[/tex]

multiply the numberator and denominator:

3*-1 = -3

and

4*4 = 16 so,

[tex]-\frac{3}{16}[/tex]  is the answer

Answer: [tex]\Large\boxed{-\frac{3}{16} }[/tex]

Step-by-step explanation:

Given information

x = - 1/4

Given expression

[tex]\dfrac{3}{4} ~x[/tex]

Substitute values into the expression

[tex]=\dfrac{3}{4} \times(-\dfrac{1}{4} )[/tex]

[tex]=\dfrac{3\times1}{4\times4}[/tex]

[tex]\Large\boxed{=-\frac{3}{16} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Someone pls help with this<3

Answers

Answer: No

Step-by-step explanation:

The sum of exterior angles in a polygon is always equal to 360 degrees.

Bluff is at a hardware store trying to decide what brand of wood glue to buy for his carpentry project 11. Ounces of Orangutan wood glue cost $5.99

Answers

Answer:

yes

Step-by-step explanation:

yes

17, 18, 22, 31, 47, ? Continue the pattern

Answers

Answer:

17 +1^2=18

18+2^2=22

22+3^2=31

31+4^2=47

47+5^2=72

72+6^2=108

Step-by-step explanation:

If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x).

Answers

Answer:

-40x

Step-by-step explanation:

f(x) =-3x-5

g(x) =4x-2

(f+g)(x) =?

now,

f(g(x))

=f(4x-2)

=-3×4x-2-5

=-10×4x

=-40x

please help!!!
maths functions

Answers

Answer:

Point A:  (2, 10)

Point B:  (-3, 0)

Point C:  (-5, -4)

Point D:  (-5, -32)

Step-by-step explanation:

Part (a)

Points A and B are the points of intersection between the two graphs.

Therefore, to find the x-values of the points of intersection, substitute one equation into the other and solve for x:

[tex]\implies 2x+6=-2x^2+18[/tex]

[tex]\implies 2x^2+2x-12=0[/tex]

[tex]\implies 2(x^2+x-6)=0[/tex]

[tex]\implies x^2+x-6=0[/tex]

[tex]\implies x^2+3x-2x-6=0[/tex]

[tex]\implies x(x+3)-2(x+3)=0[/tex]

[tex]\implies (x-2)(x+3)=0[/tex]

[tex]\implies x=2, -3[/tex]

From inspection of the graph:

The x-value of point A is positive ⇒ x = 2The x-value of point B is negative ⇒ x = -3

To find the y-values, substitute the found x-values into either of the equations:

[tex]\begin{aligned} \textsf{Point A}: \quad 2x+6 & =y\\2(2)+6 & =10\\ \implies & (2, 10)\end{aligned}[/tex]

[tex]\begin{aligned} \textsf{Point B}: \quad -2x^2+18 & =y\\-2(-3)^2+18 & =0\\ \implies & (-3,0)\end{aligned}[/tex]

Therefore, point A is (2, 10) and point B is (-3, 0).

Part (b)

If the distance between points C and D is 28 units, the y-value of point D will be 28 less than the y-value of point C.  The x-values of the two points are the same.

Therefore:

[tex]\textsf{Equation 1}: \quad y=2x+6[/tex]

[tex]\textsf{Equation 2}: \quad y-28=-2x^2+18[/tex]

As the x-values are the same, substitute the first equation into the second equation and solve for x to find the x-value of points C and D:

[tex]\implies 2x+6-28=-2x^2+18[/tex]

[tex]\implies 2x^2+2x-40=0[/tex]

[tex]\implies 2(x^2+x-20)=0[/tex]

[tex]\implies x^2+x-20=0[/tex]

[tex]\implies x^2+5x-4x-20=0[/tex]

[tex]\implies x(x+5)-4(x+5)=0[/tex]

[tex]\implies (x-4)(x+5)=0[/tex]

[tex]\implies x=4,-5[/tex]

From inspection of the given graph, the x-value of points C and D is negative, therefore x = -5.

To find the y-value of points C and D, substitute the found value of x into the two original equations of the lines:

[tex]\begin{aligned} \textsf{Point C}: \quad 2x+6 & =y\\2(-5)+6 & =-4\\ \implies & (-5,-4)\end{aligned}[/tex]

[tex]\begin{aligned} \textsf{Point D}: \quad -2x^2+18 & = y \\ -2(-5)^2+18 & =-32\\ \implies & (-5, -32)\end{aligned}[/tex]

Therefore, point C is (-5, -4) and point D is (-5, -32).

Answer:

a) A = (2, 10) and B = (-3, 0)

b) C = (-5, -4) and D = (-5, -32)

Explanation:

a) To determine the coordinates of A and B, find the intersection points of  the line "y = 2x + 6" and curve "y = -2x² + 18".

Solve the equation's simultaneously:

y = y

⇒ 2x + 6 =  -2x² + 18

⇒ 2x² + 2x + 6 - 18 = 0

⇒ 2x² + 2x - 12= 0

⇒ 2x² + 6x - 4x - 12 = 0

⇒ 2x(x + 3) - 4(x + 3) = 0

⇒ (2x - 4)(x + 3) = 0

⇒ 2x - 4 = 0, x + 3 = 0

⇒ x = 2, x = -3

Then find value of y at this x points,

at x = 2, y = 2(2) + 6 = 10

at x = -3, y = 2(-3) + 6 = 0

Intersection points: A(2, 10) and B(-3, 0)

b) Given that CD = 28 units. Also stated parallel to y axis so x coordinates for both will be same but differ in y coordinate.

[tex]2x + 6 = -2x^2 + 18 + 28[/tex]

[tex]-2x^2 + 18 + 28-2x - 6 = 0[/tex]

[tex]-2x^2-2x+40=0[/tex]

[tex]-2x^2-10x+8x+40=0[/tex]

[tex]-2(x+5)+8(x+5)=0[/tex]

[tex](-2x+8)(x+5)=0[/tex]

[tex]x = -5, 4[/tex]

[tex]\leftrightarrow \sf C(-5, y_2), \ D(-5, y_2)[/tex]

Find y value for Point C : 2x + 6 = 2(-5) + 6 = -4

Find y value for Point D :  -2x² + 18 =  -2(-5)² + 18 = -32

[tex]\sf \rightarrow Point \ C = (-5, -4)\\ \\\rightarrow Point \ D = (-5, -32)[/tex]

I'll give you 25 points! I just need help!

Find the surface area of the composite figure.
2 cm
5 cm
4 cm
4 cm
3 cm
3 cm
5 cm
5 cm
If you'd like,
SA = [ ? ] cm2
you can use a
calculator.

Answers

Answer:

add sum of all the angle given

WILL GIVE BRAINLIEST

Directions: Factor the following trinomials containing negative numbers. Follow the rules for operations with signed numbers to identify the correct binomial factors.

1. x2 + 6x - 7

2. x2 - 5x + 6

3. x2 - 6x - 7

4. x2 + 5x - 6

5. x2 + x - 12

6. x2 - 2x - 8

7. x2 - 4x - 5

8. x2 + 2x - 3

9. x2 - 16

10. x2 - x - 12

11. x2 -9x + 18

12. x2 -5x - 14

13. x2 - 7x + 10

14. x2 -11x + 24

15. x2 - x - 30

Answers

Factorization refers to the process by which the terms that are common in an expression are obtained.

What is factorization?

Factorization refers to the process by which the terms that are common in an expression are obtained.

Given the trinomials, the correct binomial factors are;

1) (x−1)(x+7)

2) (x−2)(x−3)

3) (x+1)(x−7)

4) (x−1)(x+6)

5) (x−3)(x+4)

6) (x+2)(x−4)

7) (x+1)(x−5)

8) (x−1)(x+3)

9) (x+4)(x−4)

10) (x+3)(x−4)

11) (x−3)(x−6)

12) (x+2)(x−7)

13) (x−2)(x−5)

14) (x−3)(x−8)

15) (x+5)(x−6)

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(questions in image)
A. Which plane contains line b?
B. Name 3 Collinear Points
C. Name the plane containing point W
D. Name two points not coplanar with points T and Q
E. At which line do the planes M and N intersect

Answers

Answer:

1. Plane N

2. Points P, Q, R

3. Plane CRW …

4. Points K and H

5. Line a

How to make 3 dimensional object be 4 dimensional object

Answers

In order to make a 3-dimensional object into a 4-dimensional object, it's important to draw the 4-dimensional shape in a way that gives the illusion of the 3-dimensional object.

How to illustrate the information?

It should be noted that shapes play an important part in geometry.

Here, to make a 3-dimensional object into a 4-dimensional object, it's important to draw the 4-dimensional shape in a way that gives the illusion of the 3-dimensional object.

Also, it should be noted that a 4D tesseract can be used to project the image.

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How many lines can you draw using 3 non-collinear points A, B and C on a plane?​

Answers

Answer:3 lines could be used

Step-by-step explanation:

You need 2 points to draw a line. The order doesn't really matter. Line AB is the same as line BA. The problem is to select 2 points out of 3 to draw different lines. If we do the same to the others, we get the following pairs of points to draw lines.

AB , AC

BA , BC

CA , CB

which is only 3 lines

What is the length of S?

Answers

Answer:

S = √( 1009)

Step-by-step explanation:

S = √( h² + 1/2)²)

S = √(28² + 15²)

S = √( 1009)

Hope this helps u!

find all the zeros in y=x^2+2x-24

Answers

Answer:

x = 4 and x = 6

Step-by-step explanation:

divide the sum of 36 and the product of 18 and 6 by 12

Answers

Answer:

12

Step-by-step explanation:

Here is what you have defined:

(36+ (18 x 6) ÷ 12

(36 + 108) / 12

144/12

12

Find the x - and y -intercepts of the graph of the function f(x)=−4|x−3|+12 .

Answers

The x and y-intercept(s) of the graph of the function f(x)=−4|x−3|+12 are: ( 0, 0 ), ( 6, 0 ) and ( 0, 0 ) respectively.

What are the x and y -intercepts of the graph of the function f(x)=−4|x−3|+12 ?

Given the function;

f(x) = −4| x-3 | + 12

First, we find the x-intercepts by simply substituting 0 for y and solve for x.

f(x) = −4| x-3 | + 12

y = −4| x-3 | + 12

0 = −4| x-3 | + 12

−4| x-3 | + 12 = 0

−4| x-3 | = -12

Divide both sides by -4

| x-3 | = 3

We remove the absolute value sign

x - 3 = ±3

x = 3±3

x = 3-3, 3+3

x = 0, 3

Hence, x-intercepts are: ( 0, 0 ), ( 6, 0 )

Next, we find the y-intercept by substituting 0 for x and solve for y.

f(x) = −4| x-3 | + 12

y = −4| 0-3 | + 12

y = −4| -3 | + 12

We remove the absolute value sign

y = −4(3) + 12

y = −12 + 12

y = 0

Hence, y-intercept is: ( 0, 0 ).

The x and y-intercept(s) of the graph of the function f(x)=−4|x−3|+12 are: ( 0, 0 ), ( 6, 0 ) and ( 0, 0 ) respectively.

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What is the simplest form of the expression below?

-2x²(3x²-2x-6)

Answers

Answer:

   

Solution Given:

To find the simplest form we need to open bracket

-2x²(3x²-2x-6)

-2x²*3x²-2x²*(-2x) -2x²*(-6)\

[tex]-6x^{4}+4x^{3}+12x^2[/tex] is  a required answer.

75. [-/1 Points]
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TANAPCALCBR10 8.6.003.
Evaluate the double integral for the function f(x, y) and the given region R. (Give your answer correct to 3 decimal places.)
f(x, y) = 8xy³; R is the rectangle defined by -2 ≤ x ≤ 0 and -1 ≤ y ≤ 2
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Answers

The value of the double integral for the function f(x, y) and the given region R is -60.

We can use the double integral to translate our understanding of volumes under surfaces in a three-dimensional coordinate system from areas under curves in a two-dimensional coordinate system. Just two of the many uses for double integrals are the ability to compute mass densities and estimate probability density functions.

We may get the volume under the area enclosed by the region using the double integral. By evaluating integrals with respect to only one variable while holding the other variable constant, we can compute double integrals.

Given function is: f(x, y) = 8xy³; R is the rectangle defined by -2 ≤ x ≤ 0 and -1 ≤ y ≤ 2.

Firstly integrate w.r.t y and apply the limits, similarly integrate w.r.t x and apply the corresponding limits.

The value of this double integral is calculated to be -60.

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The lateral edges of a prism are

Answers

Step-by-step explanation:

in a survey of 100 people ,65 read Kantipur ,45 read Gorkhapatra, 40 read himalayan times dream,25 read Kantipur as well as Gorkhapatra ,20 read kantipur as well as himalaya times,15 read gorkhapatra,as well as himalaya times and 5 read all three news papers.

1)draw a Venn diagram to illustrate the above information.

2find how many people do not read all three news paper ?

The lateral edges are congruent and parallel. The correct option is D.

A prism is a 3-dimensional object that has two bases that are similar and congruent to each other and are connected to each other with straight lines. A few examples of the prism are given in the image below.

Lateral edges are the edges that connect the two bases of the prism.

Since the lateral edges are straight lines and connect the similar vertices of the bases. Therefore, the lateral edges are always congruent and parallel.

Hence, the correct option is D.

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The given question is incomplete. Probably the complete question is:

The lateral edges of a prism are

A. congruent, only

B. congruent and perpendicular

C. perpendicular, only

D. congruent and parallel

If AC=24, what is AB?
Write an equation and solve for x first.

Answers

Answer:

AB = 6

Step-by-step explanation:

from the diagram

AB + BC = AC , that is

x + 3x = 24

4x = 24 ( divide both sides by 4 )

x = 6

then

AB = x = 6

The length of AB calculated is 6 units

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

AC = 24

Here, from the number line the data given are :

AB = x

BC = 3x

CD = 4x-13

Now calculating length AB or x by adding AB and BC and equating to 24 :

AC = AB+BC

24 = x+3x

4x = 24

x = 24/4

x = 6

Therefore, the length of AB calculated is 6 units

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Find the distance of PQ
P(0,4) and Q(10,-6)

Answers

Answer:

PQ ≈ 14.14 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = P (0, 4 ) and (x₂, y₂ ) = Q (10, - 6 )

PQ = [tex]\sqrt{(10-0)^2+(-6-4)^2}[/tex]

     = [tex]\sqrt{10^2+(-10)^2}[/tex]

     = [tex]\sqrt{100+100}[/tex]

     = [tex]\sqrt{200}[/tex]

     ≈ 14.14 units ( to 2 dec. places )

Answer:

[tex]PQ=10\sqrt{2}\:\: \sf units[/tex]

Step-by-step explanation:

Distance between two points formula

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}[/tex]

Define the variables:

Let (x₁, y₁) = (0, 4)Let (x₂, y₂) = (10, -6)d = PQ

Substitute the defined variables into the distance formula and solve for PQ:

[tex]\implies PQ=\sqrt{(10-0)^2+(-6-4)^2}[/tex]

[tex]\implies PQ=\sqrt{10^2+(-10)^2}[/tex]

[tex]\implies PQ=\sqrt{100+100}[/tex]

[tex]\implies PQ=\sqrt{200}[/tex]

[tex]\implies PQ=\sqrt{100 \cdot 2}[/tex]

[tex]\implies PQ=\sqrt{100}\sqrt{2}[/tex]

[tex]\implies PQ=10\sqrt{2}\: \sf units[/tex]

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A 5 -ounce container of Greek yogurt contains 150 calories. Find the unit rate of calories per ounce.

Answers

Answer:

30calories

Step-by-step explanation:

Answer:

30 calories per ounce

Step-by-step explanation:

The answer given by rachelwang2022 is correct.

I am just adding to the explanation

Since there are 150 calories in a 5-ounce container, you can determine the number of calories per ounce by simply dividing 150 by 5.

150/5 = 30 calories per ounce

What is the slope - intercept equation for this line? ​

Answers

Answer:

y = -2x - 1

Step-by-step explanation:

the ? mark part or the first [] is the slope

the slope is rise / run

the "rise" is 2 down

the "run" is 1 left

so

-2 / 1 is the slope

the y intercept is -1 as the line touches the y axis at -1

so

y = -2x - 1

is your answer

There are 40 students in Mrs. Rusczyk's first grade class. if there are three times as many students with blond hair as with blue eyes, 3 students with blond hair and blue eyes, and 15 students with neither blond hair nor blue eyes, how many students have blue eyes?

Answers

by solving a system of equations, we conclude that there are 7 students with blue eyes in the class.

How many students have blue eyes?

We know that there are 40 students in the first-grade class, and we also know that:

Let's define the variables.

B = number of students with blue eyes.H = number of students with blond hair.

We know that:

H = 3*B

We also know that there are 3 students that have both blue eyes and blond hair.

And there are 15 students with none of these traits, so:

40 - 15 = 25

There are 25 students that have blue eyes, blond hair, or both.

Because we know that 3 students have both traits, we can write:

B + H - 3  =25

(Where we subtract 3 because we don't want to add these students twice).

Then we created a system of two equations:

H = 3*B

B + H - 3  =25

Replacing the first equation into the second one, we get:

B + (3*B) - 3 = 25

4*B = 25 + 3 = 28

B = 28/4 = 7

Then, by solving that system of equations, we conclude that there are 7 students with blue eyes in the class.

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