Lucas put 4 quarters and 3 nickels into coin bank. How much money did Lucas put into his coin bank?

Answer: X = 8 And Y = 5 "First Choice Letter A"

Step-by-step explanation: x + y = 13......x = 13 - y

2x - 3y = 1

2(13 - y) - 3y = 1

26 - 2y - 3y = 1

-2y - 3y = 1 - 26

-5y = -25

y = -25/-5

y = 5

x + y = 13

x + 5 = 13

x = 13 - 5

x = 8

so, x = 8 and y = 5

Answer:

9

Step-by-step explanation:

What you're going to do is

-take the area and divide it by the amount of sides (a square has 4)

36/4=9

Answer:

C. Black grapes cost more per pound than green grapes.

Step-by-step explanation:

Verify each statement

A. Three pounds of green grapes cost $6.00

The statement is False

Because

For x=3 pounds

y=1.5x

y=1.5(3)=$4.5

B. Black grapes cost less per pound than green grapes

The statement is False

Because

For x=1 pound

The green grapes cost ----> y=1.5(1)=$1.5

Observing the graph

For x=1 pound

The black grapes cost $2

C. Black grapes cost more per pound than green grapes.

The statement is True

D. Two pounds of black grapes cost $3.00.

The statement is False

Because

Observing the graph

Two pounds of black grapes cost $4

An equation is formed of two equal expressions. The third statement is true.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

A.) The cost of a pound of green grapes is,

Y = 1.5X = 1.5×3 = 4.5

Hence, the first statement is false.

B.) The cost of a pound of green grapes is $1.5, while the cost of a pound of black grapes is $2. Thus, the second statement is false.

C.) The cost of a pound of green grapes is $1.5, while the cost of a pound of black grapes is $2. Thus, the third statement is true.

D.) As per the graph, the cost of 2 pounds of grapes is $4. Thus, the fourth statement is wrong.

Hence, the third statement is true.

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Answer:

  650 kg/m³

Step-by-step explanation:

The density is the ratio of mass to volume. The volume is the product of the dimensions of the prism.

  density = (146.25 kg)/((1.5 m)(0.75 m)(0.2 m)) = 146.25/0.225 kg/m³

  = 650 kg/m³

Answer:

  650 kg/m³

Step-by-step explanation:

so the bike costs $129, but she already has $24 saved, then she'll be saving $3 per week so let's take a peek at a table of those savings

week 1..................... total amount......... 24 + 3(1)

week 2..................... total amount......... 24 + 3(2)

week 3..................... total amount......... 24 + 3(3)

week 4..................... total amount......... 24 + 3(4)

week 5..................... total amount......... 24 + 3(5)

week w..................... total amount......... 24 + 3(w)

[tex]\bf \stackrel{\textit{total savings}}{s(x)}=\stackrel{\textit{initial amount}}{24}+\stackrel{\textit{weekly savings}}{3w} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{cost of the bike}}{129}=24+3w\implies 105=3w\implies \cfrac{105}{3}=w\implies 35=w[/tex]

Answer:

24 + 3x = 129

35 weeks

Step-by-step explanation:

She already has 24 dollars saved, but will save 3 dollars every week. Use x to represent the number of weeks. In total she will save 129.

Solve for x using the equation:

24-24 + 3x = 129-24

3x = 105

3x/3 = 105/3

x= 35

Answer:

The measure of angle LMW is [tex]m\angle LMW=67\°[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of arc MW

we know that

The inscribed angle measures half that of the arc comprising

so

[tex]m\angle MLK=\frac{1}{2}[arc\ MW+arc\ WK][/tex]

substitute the given values

[tex]65\°=\frac{1}{2}[arc\ MW+68\°][/tex]

[tex]130\°=[arc\ MW+68\°][/tex]

[tex]arc\ MW=130\°-68\°=62\°[/tex]

step 2

Find the measure of arc LK

we know that

[tex]arc\ LM+arc\ MW+arc\ WK+arc\ LK=360\°[/tex] -----> by complete circle

substitute the given values

[tex]164\°+62\°+68\°+arc\ LK=360\°[/tex]

[tex]294\°+arc\ LK=360\°[/tex]

[tex]arc\ LK=360\°-294\°=66\°[/tex]

step 3

Find the measure of angle LMW

we know that

The inscribed angle measures half that of the arc comprising

so

[tex]m\angle LMW=\frac{1}{2}[arc\ LK+arc\ WK][/tex]

substitute the given values

[tex]m\angle LMW=\frac{1}{2}[66\°+68\°]=67\°[/tex]

Applying the inscribed angle theorem, the measure of angle LMW is found as: 67°.

According to the inscribed angle theorem, the measure of an inscribed angle is half the measure of the arc that is intercepted.

Given:

Find m(MK):

m(MK) = 2(m∠MLK) (inscribed angle theorem)

Substitute

m(MK) = 2(65°)

m(MK) = 130°

Find m(LK):

m(LK) = 360° - m(LM) - m(MK) (full circle)

Substitute

m(LK) = 360° - 164° - 130°

m(LK) = 66°

Therefore:

m∠LMW = 1/2[m(LK) + m(WK) (inscribed angle theorem)

Substitute

m∠LMW = 1/2[66° + 68°]

m∠LMW = 1/2[134°]

m∠LMW = 67°

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Answer: -30

I really hope this helped you

To solve 3 3/5 x (-8 1/3), we convert the mixed numbers into improper fractions, multiply them, and simplify to get the answer -30.

The student is asking to perform multiplication between a mixed number and a mixed number with a negative sign. To compute 3 3/5 x (-8 1/3), we first convert the mixed numbers into improper fractions. The number 3 3/5 can be converted to 18/5 (since 3*5 + 3 = 18) and -8 1/3 can be converted to -25/3 (since -8*3 + 1 = -25). Multiplying these two improper fractions gives us (18/5) * (-25/3). To multiply fractions, we multiply the numerators together and the denominators together, giving us -450/15. Simplifying this fraction, we get the final answer, which is -30.

Answer:

The area of triangle ABC is [tex]25\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of triangle ABC is equal to the area of triangle ABO minus the area of triangle ACO

see the attached figure to better understand the problem

step 1

Find the area of triangle ABO

The area is equal to

[tex]A=\frac{1}{2}(AO)(BO)[/tex]

substitute values

[tex]A=\frac{1}{2}(10)(5+2)=35\ cm^{2}[/tex]

step 2

Find the area of triangle ACO

The area is equal to

[tex]A=\frac{1}{2}(AO)(CO)[/tex]

substitute values

[tex]A=\frac{1}{2}(10)(2)=10\ cm^{2}[/tex]

step 3

Find the area of triangle ABC

[tex]35\ cm^{2}-10\ cm^{2}=25\ cm^{2}[/tex]

i think this is the right one sorry if im wrong

Answer: The answers are:

row 1-  slope from P to Q = F/E

row 2- definition of slope

row 3- F´/E´ = F/E

I think that this is the correct picture was the correct one for your problem.

Answer:

-23

Step-by-step explanation:

Each term is 6 less than the past term. Hopw this helps!

There is no "standard" way to solve an exercise like this: you just have to eyeball the sequence and try to find/guess the pattern.

The most common (and easy!) examples are arithmetic or geometric sequence, where the difference or ratio between two consecutive terms is constant.

This is one of those cases: this is an arithmetic sequence, because you obtain every next term by subtracting 6 from the previous one:

[tex]a_1 = 7\\a_2 = a_1-6 = 7-6 = 1\\a_3 = a_2-6 = 1-6 = -5\\a_4 = a_3-6 = -5-6 = -11\\a_5 = a_4-6 = -11-6 = -17[/tex]

So, we can deduce

[tex]a_6 = a_5-6 = -17-6 = -23[/tex]

Answer:

[tex]x+y>0[/tex]

[tex]x-y\leq 0[/tex]

Step-by-step explanation:

Given that the sum of x and y is greater than 0.

So we can write inequality [tex]x+y>0[/tex].

When y is subtracted from x, the difference is less than or equal to 0.

So the next inequality is [tex]x-y\leq 0[/tex].

Hence required system of inequalities that can be used to  solve for x and y is :

[tex]x+y>0[/tex]

[tex]x-y\leq 0[/tex]

Answer:

100% sure its A

Step-by-step explanation:

I took the test

Answer:

A

Step-by-step explanation:

The degree of a polynomial is determined by the largest exponent in the terms of the polynomial. The leading coefficient is the coefficient of the term with the largest exponent.

Given

f(x) = 2x³ + 2x² - [tex]\frac{1}{x}[/tex]

The term - [tex]\frac{1}{x}[/tex] means that f(x) is not a polynomial

Since terms with division by a variable are not allowed.

Answer:

[tex]\large\boxed{\dfrac{7x^2}{6x-10}}[/tex]

Step-by-step explanation:

[tex]\dfrac{7x^2}{2x+6}\div\dfrac{3x-5}{x+3}=\dfrac{7x^2}{2(x+3)}\cdot\dfrac{x+3}{3x-5}\\\\\text{cancel}\ (x+3)\\\\=\dfrac{7x^2}{2}\cdot\dfrac{1}{3x-5}=\dfrac{(7x^2)(1)}{(2)(3x-5)}\\\\\text{use the distributive property}\ a(b-c)=ab-ac\\\\=\dfrac{7x^2}{6x-10}[/tex]

Answer:

a) 235.62in³

b) 904.78in³

Step-by-step explanation:

a) The formula to find the volume of a cylinder is:

[tex]V = \pi r^2h[/tex]

We are given that r = 5 and h = 3, so we can just plug in and solve:

[tex]V = \pi(5)^2(3) = 235.62in^3[/tex]

b) The formula to find the volume of a sphere is:

[tex]V = \frac{4}{3}\pi r^3[/tex]

We are given that the diameter is 12in, which means that the radius (r) must be 6in (half the diameter). Now, we can plug in and solve:

[tex]V = \frac{4}{3}\pi (6)^3 = 904.78in^3[/tex]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]g(x)=2^{x-1}+3[/tex]

This is a exponential function

The domain is the interval ----> (-∞,∞)

All real numbers

The range is the interval ----> (3,∞)

All real numbers greater than 3

The y-intercept of the function is the value of the function when the value of x is equal to zero

For x=0

[tex]g(0)=2^{0-1}+3[/tex]

[tex]g(0)=2^{-1}+3[/tex]

[tex]g(0)=\frac{1}{2} +3[/tex]

[tex]g(0)=3.5[/tex]

The y-intercept is the point (0,3.5)

using a graphing tool

The graph in the attached figure

Answer:

The first answer

Step-by-step explanation:

I took the test

Answer:

1/26

Step-by-step explanation:

There's only 1 four of spades and only 1 six of diamonds.  So the probability is:

P = P(4 of spades) + P(six of diamonds)

P = 1/52 + 1/52

P = 1/26

The probability of selecting the four of spades or the six of diamonds from a standard 52-card deck is 1/26. This is determined by adding the probabilities of each individual card being drawn since they are mutually exclusive events.

The question asks about the probability of selecting a specific card from a standard 52-card deck. To find the probability of selecting either the four of spades or the six of diamonds, we recognize that these are two distinct events. Since there is one four of spades and one six of diamonds in a deck, and there are 52 cards in total, the probability of drawing the four of spades is 1/52 and similarly the probability of drawing the six of diamonds is also 1/52. These events are mutually exclusive, meaning they cannot happen at the same time, so we can simply add the two probabilities together to find the total probability:

Probability(four of spades or six of diamonds) = Probability(four of spades) + Probability(six of diamonds) = 1/52 + 1/52 = 2/52.

Therefore, the probability is 2/52, which can be simplified to 1/26.

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ANSWER

D. 135 m^2

EXPLANATION

The area of a kite is half the product of the diagonals.

The first diagonal is

9m+6m=15m

Note that the vertical diagonal is the axis of symmetry of the kite.

This diagonal bisect the kite

Therefore the second diagonal is

2(9m)=18m

The area of the kite

[tex] = \frac{1}{2} \times 18 \times 15[/tex]

[tex] = 9 \times 15[/tex]

[tex] = 135 {m}^{2} [/tex]

Answer:

[tex]A_{T}=135 m^{2[/tex]

Step-by-step explanation:

Hello

To solve this problem we can divide the kite into simpler geometric figures to find its area, we have four triangles

the area of a triangle =(b*h)/2

b is the base and his the heigth

Step 1

triangle 1 (LEFT UP)

[tex]b=9\ m\\\ h= 9\ m\\A=\frac{9 m* 9m}{2}\\\\A_{1} =40.5\ m^{2}[/tex]

Step 2

triangle 2 (RIGHT UP)

[tex]b=9\ m\\\ h= 9\ m\\A=\frac{9 m* 9m}{2}\\\\A_{2} =40.5\ m^{2}[/tex]

Step 3

triangle 3 (LEFT DOWN)

[tex]b=9\ m\\\ h= 6\ m\\A=\frac{9 m* 6m}{2}\\\\A_{3} =27\ m^{2}[/tex]

Step 4

triangle 4 (RIGHT DOWN)

[tex]b=9\ m\\\ h= 6\ m\\A=\frac{9 m* 6m}{2}\\\\A_{4} =27\ m^{2}[/tex]

Step 5

Total Area

the total area is

[tex]A_{T}=A_{1}+A_{2}+A_{3}+A_{4}   \\A_{T}=(40.5+40.5+27+27)m^{2} \\A_{T}=135 m^{2}[/tex]

Have a great day

Answer:

Angle addition postulate and 2x=56

Step-by-step explanation:

The value of x is 28 degree.

Linear pair of angles are formed when two lines intersect each other at a single point.

Given:

m∠ELG = 124

as, m∠ELG and m∠ELD are in linear pair.

So, 124 + 2x =180

2x =56

x -28

Hence, the value of x is 28 degree

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ANSWER

The coordinates of the image are (2,2)

EXPLANATION

The mapping for a reflection across the line y=k is :

[tex](x,y)\to (x,2k-y)[/tex]

We want to find the image of the point (2,-4) after a reflection in the line y=-1.

In this case k=-1.

[tex](2, - 4)\to (2,2( - 1)- - 4)[/tex]

This simplifies to,

[tex](2, - 4)\to (2, - 2 + 4)[/tex]

[tex](2, - 4)\to (2, 2)[/tex]

Hence the image is (2,2)

Answer:

5

Step-by-step explanation:

total sum of the 6 numbers

= 4 ×6

= 24

sum of numbers without the two 2s

= 24 - 2(2)

= 20

average of other 4 numbers

= 20 ÷ 4

= 5

The average of the other four numbers is 5.

How to find the average?

The average of six numbers is 4. If the of two of those numbers is 2.

The total sum of the 6 numbers

= 4 ×6

= 24

The sum of numbers without the two 2s

= 24 - 2(2)

= 20

The average of other 4 numbers

= 20 ÷ 4

= 5

Hence, The average of the other four numbers is 5.

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I do not see an illustration.

Answer:

The numbers are 44 and 46

Step-by-step explanation:

Let

x, x+2 ----> the two consecutive positive even integers

we know that

[tex](x+x+2)^{2} =4,048+x^{2} +(x+2)^{2} \\ \\(2x+2)^{2} =4,048+x^{2} +x^{2}+4x+4\\ \\4x^{2}+8x+4=2x^{2}+4x+4,052\\ \\2x^{2} +4x-4,048=0[/tex]

Solve the quadratic equation using a graphing calculator

The solution is x=44

see the attached figure

x+2=44+2=46

therefore

The numbers are 44 and 46

The answers are:

First box: 7 times the cube of the sum of x and 8

Second box: 8 added to the cube of 7x.

Third box: 8 added to 7 and x cubed.

Fourth box: the cube of the sum of 7x and 8.

We are given the expression and we need to macth to the correct verbal description, so we have:

First box:

[tex]7(x+8)x^{3}[/tex]

It's 7 times the cube of the sum of x and 8

Second box:

[tex](7x)^{3}+8[/tex]

We have that "7x" is cubed and then, added to 8, so,  it's 8 added to the cube of 7x.

Third box:

[tex]7x^{3}+8[/tex]

We have "7" times "x" cubed and added to 8, so it's 8 added to 7 and x cubed.

Fourth box:

[tex](7x+8)x^{3}[/tex]

We have "7x" added to 8, and the expression is cubed, so, it's the cube of the sum of 7x and 8.

Have a nice day!

Answer:

False

Step-by-step explanation:

12 × 15 = 180

12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 = 180

Answer:

180.

Step-by-step explanation:

Something wrong there. Mine says 180.

12 * 15 = 12*10 + 12*5

= 120 + 60

= 180.

Check the picture below.

The answer is a=8 btw

Answer:

6 : 11

Step-by-step explanation:

the ratio 6 : 11 applies to all linear measure in the similar polygons

Both side lengths and perimeter are linear, hence

ratio of both is 6 : 11

Answer:

Degree: 5

Y-intercept: 12

Step-by-step explanation:

The given expression is

[tex]f(x)=-(x+1)^2(2x-3)(x+2)^2[/tex]

Since the factors are multiplying, we can analyse the degree of each factor and add them to find the degree of the polynomial.

The degree of the factor [tex]-(x+1)^2[/tex] is 2.

The degree of [tex](2x-3)[/tex] is 1

The degree of [tex](x+2)^2[/tex] is 2

Therefore the degree of the polynomial is 2+1+2=5

To find the y-intercept, we put x=0.

[tex]f(0)=-(0+1)^2(2(0)-3)(0+2)^2[/tex]

[tex]f(0)=-(-3)(4)=12[/tex]

The y-intercept is 12

Answer:

4

Step-by-step explanation:

An angle of depression is measured from the horizontal downwards

From the given diagram this is represented by angle 4

Answer: The mean

Step-by-step explanation: a) The mean:

To find the mean, we just simply need to add the hours spent by the students playing games and divide by the number of hours.

Mean =  = 2.85

b) The median:

We will arrange the number of hours for in ascending order and the middle value will be the median.

Median = 3

c) The mode:

Mode is the number which occurs most frequently. So in this case Mode = 2, 3.

d)Percentage of the students play video games for more than 4 hours in a month  =  = 45%

Answer:

Downwards.

Step-by-step explanation:

The coefficient of x^2 is negative (-3) so it opens downwards. All values of x will be 0 or negative.