Anna is saving to buy some souvenirs on a family vacation. She has already saved $125, and she saves another $2 from her allowance every day. Formulate and then graph the equation that models the total amount Anna saves, y, in terms of the number of days she adds to her savings, X.​

Answer:

B. 1 must be a root of the polynomial 3x^2+x-4

Step-by-step explanation:

Given polynomial

3x^2+x-4

Divided by factor x-1

Gives a remainder of 0

Remainder 0 represents that divisor (x-1) is a factor polynomial 3x^2+x-4

If x-1 is a factor of the polynomial, we can equate x-1 to 0

x-1=0

Solve for x to get one of the roots

x-1=0

Add 1 to both sides

x-1+1=0+1

x=1

B. 1 must be a root of the polynomial 3x^2+x-4

Answer:

I Think it is the 3rd equation

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

When squaring the number 5 (i.e [tex]5^2[/tex] ) the answer is 25. [tex]5^{2}[/tex] is the same thing as 5 times 5. Basically with the square root, you are going backwards, so you are therefore finding the base of it all.

We have a square that has area of 25 square units. The question is: what is the side length? That would be 5 since 5*5 = 25. You would use guess and check if you weren't familiar with square roots. A better option is to use the square root function on the calculator.

Note: the square root undoes the squaring operation

Answer:

D. The quotient of the coordinates will be a coefficient in the equation.

Step-by-step explanation:

Given a line through (0,0) and (4,7)

the slope of the line is m = (7-0) / (4-0) = 7/4

The equation of the line is

y = mx

Therefore

The quotient of the coordinates will be a coefficient in the equation.

Answer:

D

Step-by-step explanation:

Answer:

The answer is -(29+3a).

Step-by-step explanation:

=2(3-4a)+5(a-7)

= 6- 8a +5a -35

= 6-35-8a+5a

= -29-3a

= -(29+3a)

Hope it helps..

Answer:

Step-by-step explanation:

[tex]2(3 - 4a) + 5(a - 7)[/tex]

Distribute 2 through the parentheses

[tex] = 6 - 8a + 5(a - 7)[/tex]

Distribute 5 through the parentheses

[tex] = 6 - 8a + 5a - 35[/tex]

Calculate the difference

[tex] = - 29 - 8a + 5a[/tex]

Collect like terms

[tex] = - 29 - 3a[/tex]

Hope this helps...

Best regards!!

Answer:

The diameter is 1.

Step-by-step explanation:

The circumference is 3.14 units

C = pi * d

Using 3.14 for pi

3.14 = 3.14 d

Divide each side by 3.14

3.14/3.14 = 3.14 d/ 3.14

1 =d

Answer:

5x+2y=48 or 5x-12y=-8

The value of x is 5 and y is 4.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

The Equations are:

5x - 12y= -8...................(1)

and, 5 x + 2 y = 48 ..................(2)

Solving the Equation (1) and (2) we get

-12y -2y = -8 - 48

-14y = -56

y= -56 /(-14)

y = 4

and, 5x +2y= 48

5x + 8 = 48

5x= 40

x= 5

Learn more about Equation here:

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Answer: 197

Step-by-step explanation: square 28 + square 195 = x squared so then find the sqrt of that

Answer:

b)37.5

Step-by-step explanation:

the ratio 3:2 is the same as 1.5, so you  multiply 1.5 & 25 to get 37.5 units

The required measure of the perimeter of the ΔABC is 37.5 units. Option B is correct.

Given that,
ΔABC is similar to ΔMNO. The scale factor from ΔMNO to ΔABC is 3∕2. If the perimeter of ΔMNO is 25 units, what's the perimeter of ΔABC?

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
3/2ΔMNO =  ΔABC
The perimeter of the ΔABC = 3/2  The perimeter of the ΔMNO
The perimeter of the ΔABC  = 3 / 2 [25]
The perimeter of the ΔABC  = 37.5

Thus, the required measure of the perimeter of the ΔABC is 37.5 units. Option B is correct.

Learn more about Scale factors here:

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Answer:

B 2/5

Step-by-step explanation:

Used a calculator.

RQP=ONP

Since R is the midpoint of MQ, then MR and RQ are equal.

Since R is the midpoint of MQ, then P must be the midpoint of NQ

The triangles are congruent and the trapezoid is three or those triangles.

RQR reflected is a triangle inside the trapezoid. The triangles at the left and right of the trapezoid are congruent.

Since all the triangles are the exact same, then they have the same height and same length.

So you connect them without like sliding a triangle up a little bit.

The 4 congruent triangles add up to be a parallelogram.

I don't know if this is what you learned in class or where ever you did learn it but this is my way (not where-I-learned-it-from's way).

Answer:

7 classmates

Step-by-step explanation:

The last person in the line is in position 35.

The Maria's leading classmate is in the position 35-23+1 = 13.

So, Maria's classmates are from position 13 to 19 (not including herself), and their number is 19-12 = 7 persons.

ANSWER.  Maria has 7 classmates  (not including herself).

Hope this helps.

Answer:

Step-by-step explanation:

We have a right triangle. Therefore, we can use the Pythagorean theorem:

The sum of the areas of the squares built on the legs is equal to the area of ​​the square built on the hypotenuse.

We have the area of the largest square (the square built on the hypotenuse).

A₃ = 36 u²

From the Pythagorean therem we have the equation:

A₃ = A₁ + A₂

We need the areas of the smaller squares (A₁ and A₂).

A₁ + A₂ = 36.

From the second picture, we have:

A) 6 and 30 → 6 + 30 = 3          CORRECT

B) 8 and 28 → 8 + 28 = 36       CORRECT

C) 4 and 16 → 4 + 16 = 20 ≠ 36  INCORRECT

Answer:

Mean

Step-by-step explanation:

The numbers have a very large range. So you should use the mean(or average) to get more accurate data.

Answer:

x = 1, y = 2, z = 4

Step-by-step explanation:

(x + 4y – z = 5

2(3x – 2y + 2z = 7 )

6x - 4y + 4z = 14

7x + 3z = 19

3(2x – z= -2)

6x - 3z = -6

13x = 13

x = 1

6(1) - 3z = -6

-3z = -12

z = 4

(1) + 4y - 4 = 5

4y = 8

y = 2

Answer:

The amount of nuts is 16 kg and cereal mixture is 44 kg to obtain 60 kg of a mix that will sell for $1.40 per kg

Step-by-step explanation:

Let

x=nuts at $2.50 per kg

y=cereal at $1 per kg

x+y=60 kg (1)

2.50x+y=1.40(60) (2)

From (1)

x=60-y

Substitute x=60-y into (2)

2.50x+y=1.40(60)

2.50(60-y)+y=84

150-2.5y+y=84

-1.5y=84-150

-1.5y=-66

Divide both sides by -1.5

y=44 kg

Substitute y=44 into (1)

x+y=60

x+44=60

x=60-44

=16

x=16 kg

Answer:

[tex]\sin C\approx0.85\\\\\cos C \approx0.52\\\\\tan C\approx1.63[/tex]

Step-by-step explanation:

According to the trigonometric ratios in aright triangle :

[tex]\sin x =\dfrac{\text{Side opposite to x}}{\text{Hypotenuse}}\\\\\cos x =\dfrac{\text{Side adjacent to x}}{\text{Hypotenuse}}\\\\\tan x=\dfrac{\sin x}{\cos x}[/tex]

Given:  ΔBCA ~ ΔSTR

Since , corresponding angles of two similar triangles are equal.

So, ∠C = ∠T                            ...(i)    [Middle letter]

In triangle STR

[tex]\sin T=\dfrac{\text{Side opposite to T}}{\text{Hypotenuse}}\\\\=\dfrac{26.4}{30.9}\approx0.85\\\\\cos x =\dfrac{\text{Side adjacent to T}}{\text{Hypotenuse}}\\\\=\dfrac{16.2}{30.9}\approx0.52\\\\\tan T=\dfrac{\sin T}{\cos T}\\\\=\dfrac{0.85}{0.52}\approx1.63[/tex]  ...(ii)

From (i) and (ii), we have

[tex]\sin C\approx0.85\\\\\cos C \approx0.52\\\\\tan C\approx1.63[/tex]

Answer:

[tex]\sum_{n=10}^{15}(n+\frac{3}{n})=\sum_{n=10}^{15} n + \sum_{n=10}^{15} \frac{3}{n}[/tex]

Step-by-step explanation:

Given expression : [tex]\sum_{n=10}^{15}(n+\frac{3}{n})[/tex]

Solving further:

[tex]\sum_{n=10}^{15}(n+\frac{3}{n})[/tex]

[tex]\Rightarrow \sum_{n=10}^{15} n + \sum_{n=10}^{15} \frac{3}{n}[/tex]

So,[tex]\sum_{n=10}^{15}(n+\frac{3}{n})=\sum_{n=10}^{15} n + \sum_{n=10}^{15} \frac{3}{n}[/tex]

So, Option A is true

Hence the given expression is equivalent to Option A

Answer:

a

Step-by-step explanation:

edg 21 ^u^

Answer: D

Step-by-step explanation:

In every other solution, x gets canceled out, so it has no impact on the equation.  Thus, A, B, and C all have either infinite or no solution, because they have 6x on both sides of the equation.

Further proof:

6x-6=15x+15

Add(6)

6x=15x+21

Subtract(15x)

-9x=21

Divide(-9)

x = -2 3/9

Hope it helps <3

Answer:

d) 6x - 6 = 15x + 15

Step-by-step explanation:

Well let’s solve.

a)

6x - 15 = 6x + 15

Lets use the communicative property which is the moving of numbers.

We can start with -15, so we do +15,

6x = 6x + 30

Then we can do -6x

0 = 30

This is a false statement meaning there is no solution.

b)

6x - 6 = 6x + 15

We can start by doing +6

6x = 6x + 21

-6x

0 = 21

Again, this is a false statement meaning this has no solutions.

c)

6x + 15 = 6x + 15

So we do -15

6x = 6x

If this is the case then there is infinitely many solutions.

d)

6x - 6 = 15x + 15

So we can start by doing +5p6

6x = 15x + 21

Then we can do -15x

-9x = 21

then we can do 21 / -9 which is -2 1/3.

x = -2 1/3

So this has one solution.

Answer:

You can try substituting the 1's for different variables (E, D) in the formula , to get answers for each.

Answer:

Connect every other intersection of an arc and the circle with a segment.

Step-by-step explanation:

Connect every other intersection of an arc and the circle with a segment.

Answer:

a) Connect every other intersection of an arc and the circle with a segment.

b) Connect the intersections of the diameters and the circle with a segment.

c) Connect every intersection of an arc and the circle with a segment.

d) Connect the intersections of the perpendicular bisector and the circle with a segment

HOPE THIS HELPS :)

Answer:

35 red marbles

Step-by-step explanation:

So we can put the different color marbles in a ratio. So 7:2:11. If we add all of those up we get 20. We do 100/20 to get 5. Each number in the ratio is equivalent to 5 marbles. Then we do 7*5 to get 35. We can check our work by doing, (7*5) + (2*5) + (11*5) = 100. And it does equal 100 so the answer is correct.

Answer:

35 red marbles

Step-by-step explanation:

The total number of marbles the student recorded is 20

Now we have to make a ratio of red to the total number of marbles

That would be 7 : 20

After this, there will be a new ratio which is x : 100

Lastly we will solve for x making the equation 20x = 700, x = 35

Answer: 1/2, 2/10, and 3/15

Explanation: Let's find 3 fractions that are equivalent to 4/20.

To find 3 fractions that are equivalent to 4/20,

notice that 4/20 is not in lowest terms.

In this situation, let's first rewrite 4/20 so that it's in lowest terms.

To do this, we divide the numerator and denominator by the

greatest common factor of 4 and 20, which is 4, and we have 1/5.

Since 1/5 is equivalent to 4/20, we can use

1/5 to find more equivalent fractions.

If we multiply 1/5 by 2 in both the numerator and

denominator, we get the equivalent fraction 2/10.

If we multiply 1/5 by 3 in both the numerator and

denominator, we get the equivalent fraction 3/15.

So 4/20 is equivalent to 1/5, 2/10, and 3/15.

Note that these are just 3 possible answers.

There are many other fractions that are also equivalent to 4/20.

Answer:

Color, favorite pet, genre of music

Step-by-step explanation:

Categorical variables are simply statistical variables which are non - numeric, usually employed in characterization and groupings based on a certain number of fixed attributes, categories. In the options atated above, the categorical variables fall under a heading with a limited and fixed attributes such as color, pet and genre of music. However, options such as number of siblings and profit are purely numeric variables which can take up any numeric digits and allow for direct numeric computation. They are called quantitative variables.

Answer:

colors, genre of music, favorite pet

Answer:

[tex]\boxed{ \mathrm{y = \ negative \ 3 x + 3}}[/tex]

Step-by-step explanation:

The coordinates are (-6,0) and (-8,6)

Finding slope of the line

Slope = [tex]\frac{rise}{run} = \frac{y2-y1}{x2-x1}[/tex]

Slope = [tex]\frac{6-0}{-8+6}[/tex]

Slope =[tex]\frac{6}{-2}[/tex]

Slope = -3

Parallel lines have equal slopes.

So, the line which is parallel to this line is y = negative 3 x + 3

Answer:

[tex]\boxed{ \mathrm{y = \ negative \ 3 x + 3}}[/tex]

Step-by-step explanation:

The coordinates are given (-6, 0) and (-8, 6)

Find slope of the line.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{6-0}{-8--6}[/tex]

[tex]m=\frac{6}{-2}[/tex]

[tex]m=-3[/tex]

Parralel lines have same slope.

y = mx + b

m = -3

The QUESTION is not well presented

Name the sets of numbers to which the given number belongs.

[tex]\sqrt{25}[/tex]

N represents Natural Numbers

W represents Whole Numbers

Z represents Integers

QR represents Rational Numbers

IR represents Irrational Numbers

Answer:

a. N, W, Z, QR

Step-by-step explanation:

Given

[tex]\sqrt{25}[/tex]

Required

Select the set of number belongs to;

First, the expression needs to be evaluated

[tex]Expression = \sqrt{25}[/tex]

[tex]Expression = \±5[/tex]

Comparing the result of the expression to the given categories;

[tex]\±5[/tex] is a natural number

[tex]\±5[/tex] is a whole number

[tex]\±5[/tex] is an integer

[tex]\±5[/tex]  is rational because it can be expressed as ratios

Since [tex]\±5[/tex] is rational, it can't be irrational;

Hence, the correct option is A.

Answer:

  see the attached

Step-by-step explanation:

Step 1.

The sample size is the number of numbers. There are 10 of them.

  n = 10

The mean is the sum of the numbers (1240) divided by the number of them (10).

  [tex]\overline{x}=\dfrac{1240}{10}=124[/tex]

__

Step 2.

It is convenient to let a spreadsheet (or calculator) do the math. Enter the numbers and the formulas shown in the table, and let the spreadsheet do the rest.

  [tex]\sum{(x-\overline{x})^2}=1494[/tex]

The formulas for the sample variance and sample standard deviation are given. Fill in the numbers you have so far and do the indicated calculation.

  [tex]s^2=\dfrac{\sum{(x-\overline{x})^2}}{n-1}=\dfrac{1494}{9}=166\\\\s=\sqrt{166}\approx 12.88[/tex]

Answer:

x=25°

Step-by-step explanation:

sin (x+22)=cos(2x-7)=sin (90-(2x-7))

x+22=90-(2x-7)

x+22=90-2x+7

x+2x=97-22

3x=75

x=75/3=25°

Answer:

x = 25

Step-by-step explanation:

Recall the trig identity sin(x) = cos(90 - x)

In other words, sin(x + 22) = cos(90 -(x+22)) = cos(68 - x)

Now, set them equal to each other:

cos(68 - x) = cos(2x - 7)

We can ignore the cosine:

68 - x = 2x - 7

3x = 75

x = 25

Answer:

80 lamps

Step-by-step explanation:

number of lamp bases*no. of lampshades*no. of lightbulbs= total number of lamp choices

5*(3*3)*2

=5*9*2

=40*2

=80

hope it helps :)