The lines y = x and x = a enclose a triangle with the x- and y-axes.
a) Find the area of the triangle when a = 5

Answer:

5(x+4)=6

5 times a number and (+) 4 is equal to 6.

Answer:

Step-by-step explanation:

y=5x=10

Answer:

10.50x = 63

You'll divide 63 by 10.50 to get 6 weeks.

Answer:

Step-by-step explanation:

multiples of 4

12/3 = 4

16/4 = 4

4/1 = 4

24/6 = 4

36/9 = 4

The integer 4 can be represented as a fraction by placing it over 1. Therefore, the fraction that represents the integer 4 is 4/1 and it is already in its simplest form.

The integer 4 can be represented as a fraction simply by placing it over 1. Hence, the fraction equivalent of the integer 4 is 4/1. However, it's noteworthy to mention that a fraction can be simplified when the numerator and the denominator have a common factor, other than 1. In this case, there are no other common factors between 4 and 1, so it is already in its simplest form.

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I can save $2,128 in my academic year and my roommate can save $392 in their academic year.

Step-by-step explanation:

Total housing amount= rent + electricity= $1,025 + $60= $1,085 per month

My rent is 40% of $1,085 which equals $434 a month while my roommate’s rent would be 60% of $1,085 which equals $651 a month.

The scholarship gives me $700 a month for housing out of which I spend $434 and my roommate spends $651.

I save; $700 - $434 = $266 a month

My roommate saves; $700 - $651 = $49 a month.

An academic year lasts for 8 months so my savings= $266 x 8 = $2,128

My roommate’s savings= $49 x 8 = $392  

Answer:

$2,128

Step-by-step explanation:

Expenses is allocated based on the decided ratios. Expenses and Inflows

Expenses will be calculated for 8 Months time period.

Rent = 1,025 x 8 months = $8,200

Electricity Expense = $60 x 8 = $480

Total Expense = $8,200 + $480 = $8,680

Total Scholarship = $700 x 8 = $5,600

Out of Pocket Cost = $8,680 x 40% = $3,472

Saving is the difference between The scholarship received and the Expenses made from pocket.

Saving = $5,600 - $3,472 = $2,128

Answer:

Therefore [tex]m_{2}[/tex] = -3.

Step-by-step explanation:

i) let us say the slope of the line passing through (-2,7) and (4,9) is [tex]m_{1}[/tex].

ii) to find the slope of the line passing through two points ([tex]x_{1}[/tex], [tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) we use the formula m = [tex]\dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]. Therefore we can say that  [tex]m_{1}[/tex] = [tex]\dfrac{9 - 7}{4 - (-2)}[/tex] = [tex]\dfrac{1}{3}[/tex].

iii) let us say the slope of the perpendicular line to the line  passing through (-2,7) and (4,9) is [tex]m_{2}[/tex]

iv) from the formula for the slopes of a line and the line perpendicular to it which is given by [tex]m_{1}[/tex] × [tex]m_{2}[/tex] = -1, therefore [tex]m_{2}[/tex] = -1 ÷  [tex]m_{1}[/tex] = -3. Therefore [tex]m_{2}[/tex] = -3

ciro needs 3 cups of flour johanna needs 20 x 15 cups

So, I think I had this for my Imagine math, so I'll help you :D

Ciro (How many cups in 1 batch):; 15 / 5 = 15 divided by 5

Johanna (How many cups for 20 batches):; 15 x 4 = 15 multiplied by 4

I hope this helps :)

Answer:

Step-by-step explanation:

Tom and Dipak share $114 in the ratio 7:5

Total amount shared = $114

Ratio of Tom to Dipak = 7:5

Total ratio = 7+5 = 12

Dipak got = 5/12 × $114 = $ 47.5

Step-by-step explanation:

9.

Given that, the measure of [tex]\angle A[/tex] is [tex]45^\circ[/tex]. The measure of [tex]\angle B[/tex]is [tex]b^\circ[/tex]. The measure of[tex]\angle C[/tex] is [tex]3b^\circ[/tex] .

We know that the sum of all angles of triangle is [tex]180^\circ[/tex].

Therefore

[tex]45^\circ + b^\circ +3b^\circ =180^\circ[/tex]

⇔[tex]4b^\circ[/tex] = [tex]135^\circ[/tex]

10.

Given that , the measure of [tex]\angle X[/tex] and [tex]\angle Y[/tex]are same [tex]x^\circ[/tex]. The angle of [tex]\angle Z[/tex] is twice the measure of [tex]\angle Y[/tex].

∴[tex]\angle X[/tex]+[tex]\angle Y[/tex]+[tex]\angle Z[/tex]=[tex]180^\circ[/tex]

⇔[tex]x^\circ[/tex]+[tex]x^\circ[/tex]+2[tex]x^\circ[/tex]=[tex]180^\circ[/tex]

⇔4[tex]x^\circ[/tex]= [tex]180^\circ[/tex]

Answer:

600

Step-by-step explanation:

you round up 19 to 20 then you round up 28 to 30 and multiply 20 and 30

Answer:

20*30

= 600

About 600

C

Answer:

the first one would be m<EOF+m<FOB=180°,

and the second one would be 76ft

Step-by-step explanation:

supplementary angle means the angle that would make it equal 180°. if m<EOF is an acute angle then the angle that is supplementary to EOF would be obtuse, so FOB.

then for the second question, the midpoint splits the angle in HALF, so that means in order to find RT you multiply 38×2.

Answer: Answer is 40%

Step-by-step explanation: The total number of players in the game is 30 (that is boys and girls added together becomes 18 + 12= 30) altogether which is a hundred percent. The percentage of girls playing the game is calculated as;

12/30 × 100%

=2/5 × 100%

=200/5

=40%

Answer:

The values for the two equations are x=-3 and y=1

Therefore the solution is (-3,1)

Step-by-step explanation:

Given equations are [tex]y=2x+7\hfill (1)[/tex]

[tex]y=-2x+5\hfill (2)[/tex]

To solve the given equations by Substitution method :

We are using here to solve the given equations by Substitution method because equations (1) and (2) are equivalent ( it has same solution )

Therefore we can equate the two given equations  or substitute the y value equation (1) in (2) we get

2x+7=-2x-5

Subtracting with -(2x-5) on both sides we get

2x+7-(-2x-5)=-2x-5-(-2x-5)

2x+7+2x+5=-2x-5+2x+5

4x+12=0 ( adding the like terms )

4x=-12

[tex]x=-\frac{12}{4}[/tex]

Therefore x=-3

Now substitute the value x=-3 in equation (1) we get

y=2(-3)+7

y=-6+7

Therefore y=1

The values are x=-3 and y=1

The solution is (-3,1)

The 3 angles when added together make a straight line which is 180 degrees. To find x subtract the 2 known angles from 180.

The answer would be x = 180 - (67 + 52)

Answer:

x=14

y=10

Step-by-step explanation:

The median divide the data‘s set into two parts with the same frequency = 50%

then we must have 2+5+x+12+17 = 50 ⇔ 36+x=50 then x =50-36=14

also 20+y+9+7+4=50 ⇔ y=10

Answer:

50-6=14

Step-by-step explanation:

just do the math and then you will find the answer

Answer:

C. 560

Step-by-step explanation:

50% is one half, so there is another half of 280. 280*2=560

Answer:

C

Step-by-step explanation:

Answer:

She is not correct.

Step-by-step explanation:

If she originally purchases the teas for $100 and then she marks the price up 20%, the retail price would then be 100 + 0.20(100) = 100 + 20 = 120. The sales price would then be 120 - 0.2(120) = 120 - 24 = 96. This is less than the purchase price, so she is losing money, rather than gaining.

I hope this helps. If you download an app called Slader, it has the same math book you are using with the answers.

Answer:

c

Step-by-step explanation:

there are two answers there divisible by three

(12 and 6) so the probability of it landing on one of them is 2/8 as there are 8 numbers altogether. 2/8 is equal to 1/4 so that's the answer

Answer:

4n(7+3-6)

Step-by-step explanation:

 28n              12n .               24n  

14 .   2 .        6 .  2              12 .   2

7 . 2 . 2 n .   3 . 2 . 2  n .     6 . 2

7                     3                     3 . 2 . 2 . 2  n

                                                  3x2=6

2x2xn=4n

GCF=4n

Answer:

16n

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\text{Domain:}\ x>0\\\\\log_83+\dfrac{1}{2}\log_825=\log_8x\qquad\text{use}\ n\log_ab=\log_ab^n\\\\\log_83+\log_825^\frac{1}{2}=\log_8x\qquad\text{use}\ a^\frac{1}{2}=\sqrt{a}\\\\\log_83+\log_8\sqrt{25}=\log_8x\\\\\log_83+\log_85=\log_8x\qquad\text{use}\ \log_ab+\log_ac=\log_a(bc)\\\\\log_8(3\cdot5)=\log_8x\\\\\log_815=\log_8x\iff15=x\to x=15\in D[/tex]

Answer:

Your answer would be x = 15

I hope his helped and have a wonderful day!

~Real

Answer:

59,778

Step-by-step explanation:

The product of 729 and 82 is calculated through standard multiplication, resulting in a final product of 59,778.

The student is asking to calculate the product of two numbers, 729 and 82. To find the product, we can use basic multiplication skills. Here is the step-by-step calculation:

First, set up the multiplication:

Next, multiply 2 by each digit of 729 and write the result below the line.

Then, multiply 8 by each digit of 729, remember to shift one place to the left.

Now, add both results to get the final

product

.

The final product of 729 multiplied by 82 is 59,778.

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Answer:

an equation for how much your phone costs per month=

.15x+10

Answer:

[tex]A=189\ mm^2[/tex]

Step-by-step explanation:

Surface Areas

Is the sum of all the lateral areas of a given solid. We need to compute the total surface area of the given prism. It has 5 sides, two of them are equal (top and bottom areas) and the rest are rectangles.

Computing the top and bottom areas. They form a right triangle whose legs are 4.5 mm and 6 mm. The area of both triangles is

[tex]\displaystyle A_t=2*\frac{b.h}{2}=b.h=(4.5)(6)=27 mm^2[/tex]

The front area is a rectangle of dimensions 7.7 mm and 9 mm, thus

[tex]A_f=b.h=(7.5)(9)=67.5 \ mm^2[/tex]

The back left area is another rectangle of 4.5 mm by 9 mm

[tex]A_l=b.h=(4.5)(9)=40.5 \ mm^2[/tex]

Finally, the back right area is a rectangle of 6 mm by 9 mm

[tex]A_r=b.h=(6)(9)=54 \ mm^2[/tex]

Thus, the total surface area of the prism is

[tex]A=A_t+A_f+A_l+A_r=27+67.5+40.5+54=189\ mm^2[/tex]

[tex]\boxed{A=189\ mm^2}[/tex]

Answer:

18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

List your factors first to find the answer

36: 1-36, 2-18, 3-12, 4-9, 6-6

90: 1-90, 2-45, 3-30, 5-18, 6-15, 9-10

Now find in the factors which would be the greatest/largest. The largest factor shared between 36 and 90 is 18.

Answer:

- 11 m elevation.

Step-by-step explanation:

The driver starts at an elevation of 5 m and he drives to get a change in elevation by - 16 m.

There is no doubt that the driver drives down to the negative elevation.

So, the driver first reaches the zero elevation then drives towards negative elevation.

Now, the final elevation of the driver will be at (5 - 16) m = - 11 m. (Answer)

Answer:

Explanation:

The vertices of the figure 1 are:

The vertices of figure 2 are:

By simple inspection, you can tell that if you rotate the figure 1 90º clockwise and then reflect the image across the x-axys you obtain the figure 2.

You can prove that analitically.

1. Rotation 90º clockwise

A 90º clockwise reotation is the same that a 270º counterclockwise rotation and the mathematical rule for this is:

Applying that rule to the vertices of figure 1, you obtain:

2. Reflection across the x-axis.

A reflection across the x-axis keeps the same x-coordinate and changes the sign of the y-coordinate. The rule is:

Applying that rule to the previous points yields to:

Which are the coordinates of the figure 2. Thus, you have proved that the sequence of transformations 90° clockwise rotation around the origin, then a reflection across the x-axis (first choice) maps the figure 1 to figure 2.

Answer:

First choice: 90° clockwise rotation around the origin, then a reflection across the x-axis.

Step-by-step explanation:

Final answer:

To factor the trinomials x^2 - 2x - 1 and x^2 - 3x + 1, you can use the quadratic formula or factoring by grouping.

Explanation:

To factor the trinomials x^2 - 2x - 1 and x^2 - 3x + 1, we can use the quadratic formula or factoring by grouping.

a) For x^2 - 2x - 1, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac))/(2a)

Plugging in the values, we have:

x = (-(-2) ± sqrt((-2)^2 - 4(1)(-1)))/(2(1))

x = (2 ± sqrt(4 + 4))/(2)

x = (2 ± sqrt(8))/(2)

x = (2 ± 2sqrt(2))/(2)

x = 1 ± sqrt(2)

Therefore, the factored form is: x^2 - 2x - 1 = (x - (1 + sqrt(2)))(x - (1 - sqrt(2)))

b) For x^2 - 3x + 1, we can also use the quadratic formula:

x = (3 ± sqrt(3^2 - 4(1)(1)))/(2(1))

x = (3 ± sqrt(5))/(2)

Therefore, the factored form is: x^2 - 3x + 1 = (x - (3 + sqrt(5))/(2))(x - (3 - sqrt(5))/(2))

a) x^2 - 2x - 1 = (x - 1)(x + 1)

b) x^2 - 3x + 1 = (x - 1)^2

a) x^2 - 2x - 1:

This trinomial is in the form ax^2 + bx + c. To factor it, we need to find two numbers that:

Multiply to ac (in this case, 1 * -1 = -1).

Add up to b (in this case, -2).

These two numbers are -1 and 1.

So, we can rewrite the trinomial as:

(x - 1)(x + 1)

Therefore, the factored form of x^2 - 2x - 1 is (x - 1)(x + 1).

b) x^2 - 3x + 1:

This trinomial is also in the form ax^2 + bx + c. To factor it, we need to find two numbers that:

Multiply to ac (in this case, 1 * 1 = 1).

Add up to b (in this case, -3).

These two numbers are -1 and -1.

So, we can rewrite the trinomial as:

(x - 1)(x - 1)

However, it is common practice to simplify repeated factors, so the fully factored form of x^2 - 3x + 1 is (x - 1)^2.

Answer:

fraction > -18/5

dec> -3.6

Step-by-step explanation:

Answer:

See image attached.

Step-by-step explanation:

Final answer:

The initial setup for the equation based on the coin values and the total amount led to an incorrect result with a negative number of nickels. This suggests there was an error in the calculations or assumptions, and the equation should be revisited and the numbers checked to find the correct number of each type of coin.

Explanation:

Let's call the number of nickels Sarah has n. According to the problem, Sarah has 10 more dimes than nickels, which means she has n+10 dimes. It is also given that she has twice as many quarters as dimes, making it 2(n+10) quarters. In terms of their values, nickels are worth 5 cents, dimes are worth 10 cents, and quarters are worth 25 cents. The total value of Sarah’s coins is $9.25, which is equivalent to 925 cents.

To find the number of each coin, we can set up the following equation:

5n + 10(n+10) + 25(2(n+10)) = 925

Simplifying the equation:

5n + 10n + 100 + 50n + 1000 = 925

65n + 1100 = 925

65n = 925 – 1100

65n = -175

n = -175 / 65

n = -2.6923

This result is not possible since we cannot have a negative number of coins. It seems there was an error in the calculations or assumptions. It is important to check the equation and numbers we're using to ensure they properly represent the coin values and the total amount.

Answer: $1.50

Step-by-step explanation: To find 5% of $30, first write 5% as a decimal by moving the decimal point 2 places to the left to get .05. Next, "of $30" means times 30 so we multiply .05 times 30 which gives us 1.5.

Finally, remember that we want to write our answer in terms of dollars so 1.5 dollars is the same thing as $1.50.

So 5% of $30 is $1.50.