5 Quick algebra 1 questions for 50 points!

Only answer if you know all 5, Tysm! :)

Answer:

is this tye required answer

Considering her change, it is found that she will donate $0.28 to the animal shelter.

The amount of change is given by the subtraction of the total paid and the price of the products.

In this problem, the price of the products bought is given by:

$15.74 + $3.98 = $19.72

She paid $20, hence the change is given by:

$20 - $19.72 = $0.28.

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One can determine the number of roots by seeing the degree of the given polynomial.

The number of roots can be determined by just seeing the highest power of the given equation.

1) for the equation  x-4=0

here, the highest power of the equation is one. So, it will have one root.

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtract multiplication, on,  and non-negative integer exponentiation of variables.

Let's check it by simplifying x-4=0  which implies x=4

Hence, the equation has only one root namely x = 4.

2) Consider a quadratic equation,

10t^2-t-3=0

here, the highest power of the equation is two. So, it will have two roots.

Let's check it by simplifying using the middle term splitting method,

10t^2+5t-6t-3=0

5t(2t+1)-3(2t+1)=0

(5t-3)(2t+1)=0

t=-3/5 or t=-1/2

Thus, the equation has two roots.

Hence, one can determine the number of roots by seeing the degree of the given polynomial.

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Answer: 12

Step-by-step explanation:

For this counting question, we need to figure out the possible choices for each selection.

For main protein, there are four options, so we can make four slots

_ _ _ _

For beans, there's three options, so we can make three slots
_ _ _

Doing some casework, we know that 4*3 = 12, which is the answer.

Answer:

12

Step-by-step explanation:

This is a special triangle with angle measure 45-45-90

The side lengths for this special right triangle is as follows:

The side length that sees angle measure 90 is represented by a[tex]\sqrt{2}[/tex]

The side lengths that see angle measures 45 is represented by a

We can see from the image hypotenuse (the side that sees angle 90)

is given as 12[tex]\sqrt{2}[/tex] that means a = 12

So the missing side lengths (both see angle measure 45) = 12

The value of (1+tanx)(1-tanx)+sec²x is 0 and the value of [tex]\frac{sec^{2}-4 }{sec+2}[/tex] is [tex]sec\theta \ -2[/tex].

Given that, (1+tanx)(1-tanx)+sec²x.

Now, (1-tan²x)+sec²x

=1-tan²x+sec²x

=1+sec²x-tan²x

=1-1=0

Now, evaluate [tex]\frac{sec^{2}-4 }{sec+2}[/tex]

[tex]=\frac{sec^{2} \theta \ -2^{2} }{sec\theta \ +2} =\frac{(sec \theta \ +2)(sec \theta \ -2)}{sec \theta \ +2}[/tex] (∵a²-b²=(a+b)(a-b))

[tex]=sec \theta \ -2[/tex]

Hence, the value of (1+tanx)(1-tanx)+sec²x is 0 and the value of [tex]\frac{sec^{2}-4 }{sec+2}[/tex] is [tex]sec\theta \ -2[/tex].

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Answer:

nth term: 0.5n² + 2.5n + 3

Explanation:

pattern 1 = 6 bowls

pattern 2 = 10 bowls

pattern 3 = 15 bowls

pattern 4 = 21 bowls

First difference:

Second difference:

This is not an arithmetic nor a geometric sequence.

Solve:

2a  = 2nd difference

2a = 1

a = 1/2 or 0.5

===================

3a + b = 1st difference

3a + b = 4

b = 4 - 3(1/2)

b = 2.5

====================

a + b + c = first term

1/2 + 2.5 + c = 6

c = 3

Quadratic nth term:

0.5n² + 2.5n + 3

Answer:

90 degrees

Step-by-step explanation:

the clock is a circle so the entire # of degrees is 360.

there are 12 sections on the clock so 360 /12 =30

so each section is 30 degrees.

if you go from 3:00 to 3:15, that is 3 sections.

so 3 times 30 is 90

Answer:

the median is 9

Explanation

Finding the median is easy, all you need to do is put the numbers in numeric order and the one that's in the middle of the numbers is the median

9 , 9 , 9 , 4 , 9 , 1 , 10  =   1, 4, 9, (9), 9, 9, 10

                                              (median)

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Given the Ages of students: 9,9,9,4,9,1,10. State the median

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\boxed{\begin{minipage}{7cm} Before finding the median, we\\ need to arrange \\ our data from least to greatest. \end{minipage}}[/tex]

Thus,

[tex]\bf{1,4,9,9,9,9,10}[/tex].

[tex]\fbox{The median is the number in the middle.}[/tex]

Thus,

[tex]\bf{9}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

            [tex]\bf{=9}[/tex]

[tex]\begin{tabular}{c | 1} Data Parameter & What to Do \\ \cline{1-2} \\ Mean & Add all the numbers and divide by how many there are \\ Median & Arrange the numbers from least to greatest and take the number \\ & in the middle. Take the mean of the 2 numbers in the middle \\ & if there's an even amount of numbers \\ Mode & The number that occurs the most \\ Range & The largest number minus the smallest number \\ Minimum & The smallest value \\ Maximum & The largest value \end{tabular}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]

1. x = a

2. y = b

3. It has an undefined slope.

4. You can either use, rise/run or change in y / change in x.

5. Rewrite the given equation in slope-intercept form, then determine the y-intercept, b, of the line.

Equation of a line with m as slope and b as y-intercept is given as: y = mx + b.

1. Vertical lines have undefined slope. This implies that, for a given point, (a, b), the equation that models the line would be expressed as x = a, where a is the x-intercept.

Vertical line equation is: x = a.

2. Horizontal lines have 0 as a slope value, therefore, given (a, b), the equation that models the line is: y = b.

3. Equation for a vertical line cannot be written in slope-intercept form because the slope for a vertical line is undefined.

4. Using the following, rise/run or change in y / change in x, the slope (m), can be calculated given the coordinates of two points on a line.

5. To find an equation in point-slope form, e.g. y - 3 = 6(x - 4), rewrite the equation in slope-intercept form:

y - 3 = 6x - 24

y = 6x - 24 + 3

y = 6x - 21

The y-intercept, b, is: -21.

Therefore, the coordinate of the y-intercept would be: (0, -21).

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Step-by-step explanation:

the answer is C) 8x^5y - 6x^4y^2

pls like and follow.

hope you understand as well

Answer:

5

Step-by-step explanation:

........................

Answer:

If Natalia's pasta recipe calls for two pounds of pasta for one quart of sauce.

Then she needs to cook 5 pounds of pasta if she has 2.5 quarts of sauce.

Step-by-step explanation:

Step 1 of 2

Given that Natalia's pasta recipe calls for two pounds of pasta for one quart of sauce.

If one quart of sauce calls for two pounds of pasta,

Then to find how much pasta is needed for 2.5  quarts of sauce we need to form a proportion.

Let the pounds of pasta needed be x .

[tex]$$\begin{aligned}\frac{\text { pasta }(\text { inPounds })}{\text { Sauce }(\text { inQuarts })} &=\frac{\text { pasta }(\text { inPounds })}{\text { Sauce(inQuarts })} \\\frac{2}{1} &=\frac{x}{2.5}\end{aligned}$$[/tex]

Multiplying both sides by 2.5 we get,

[tex]$$\begin{aligned}\frac{2}{1} \times 2.5 &=\frac{x}{2.5} \times 2.5 \\x &=2 \times 2.5 \\x &=5\end{aligned}$$[/tex]

Step 2 of 2

To check if the answer is reasonable, we substitute it back in the formed proportion

[tex]$\frac{2}{1}=\frac{x}{2.5}$$[/tex]

We found x=5 hence,

[tex]$$\begin{aligned}\frac{2}{1} &=\frac{5}{2.5} \\2 &=2\end{aligned}$$[/tex]

Here, LHS =RHS

Hence, our answer is correct.

By the vertex form of the parabola, the equation of the parabola shown in the diagram is equal to the quadratic equation y - 1 = (2/3) · (x - 3)².

Parabolae are represented mathematically by second order polynomials, which can be described either in standard form or in vertex form. In accordance to the picture, we have a parabola with a vertical axis of symmetry. The formula in vertex form is described by this expression:

y - k = C · (x - h)²

Where:

Please notice that vertices represent the absolute extreme of the parabola. We can determine the equation by knowing the vertex and another point. Let be (h, k) = (3, 1) and (x, y) = (0, 7), then we find that the vertex constant is:

7 - 1 = C · (0 - 3)²

6 = 9 · C

C = 2/3

By the vertex form of the parabola, the equation of the parabola shown in the diagram is equal to the quadratic equation y - 1 = (2/3) · (x - 3)².

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Answer:

[tex]\boxed{192~cupcakes}[/tex]

Step-by-step explanation:

dozen = 12

3 × 12 = 36 cupcakes

I.

36 cupcakes ----------------  90 minutes

                x    ----------------  60 minutes

[tex]x=\dfrac{36\cdot 60}{90 } ~ cupcakes\\\\x=24~cupcakes[/tex]

II.

24 cupcakes ---------------------- 60 minutes = 1 hour

          y         ----------------------    8 hours

[tex]y=\dfrac{8\cdot 24 }{1} ~cupcakes\\\\\boxed{y=192~cupcakes}[/tex]

They will produce 192 cupcakes in 8 hours.

Answer:

The Three options are

1.  m∠5 + m∠6 = 180°  ...........Linear Pair

2. ∠ 2+ ∠ 3 = ∠ 6.................Exterior angle Property of Triangle

3. m∠2 + m∠3 + m∠5 = 180° .....Triangle Sum Property

Step-by-step explanation:

Consider Δ ABC with Exterior angles as

∠ 1 , ∠ 4 ,and ∠ 6

Exterior angle Property of Triangle:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

For Exterior ∠ 1 we have

∠ 1 = ∠ 5 + ∠ 3 .................Exterior angle Property of Triangle

Similarly,

For Exterior ∠ 4 we have

∠ 4 = ∠ 5 + ∠ 2.................Exterior angle Property of Triangle

Similarly,

For Exterior ∠ 6 we have

∠ 6 = ∠ 2 + ∠ 3.................Exterior angle Property of Triangle

Triangle Sum Property:

Ina triangle sum of the measures of angles is equal to 180°

∴ m∠2 + m∠3 + m∠5 = 180° .....Triangle Sum Property

Linear Pair:

The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

∴ m∠5 + m∠6 = 180°  ...........Linear Pair

Answer:

m∠5 + m∠6 =180°

m∠2 + m∠3 = m∠6

m∠2 + m∠3 + m∠5 = 180°

Step-by-step explanation:

got it correct on my test

Answer:

Angle CAE is congruent to angle    CBE  

Angle CBF is congruent to angle    CAF  

===================================================

Explanation:

Angle CAE is an inscribed angle that subtends the minor arc CE

Minor arc CE is the distance around the circle from C to E following the shorter path. All minor arcs are smaller than 180 degrees.

What other inscribed angle also subtends minor arc CE? That would be inscribed angle CBE

Notice that CAE and CBE both have "C" and "E" as the first and last items. The only change is the middle letter. This is a quick nonvisual way to determine inscribed angles.

Recall that if two inscribed angles subtend the same arc, then they are congruent. Therefore, angle CAE is congruent to angle CBE

-------------------

For similar reasoning, angles CBF and CAF are congruent inscribed angles that subtend minor arc CF.

For more information, check out the inscribed angle theorem. Also I recommend using GeoGebra as a handy tool.

Answer:

(2 + StartRoot 3 EndRoot) – (1 + StartRoot 3 EndRoot)i

Step-by-step explanation:

I'm 100% sure! ^^

Answer:

B: (2 + StartRoot 3 EndRoot) – (1 + StartRoot 3 EndRoot)i

Step-by-step explanation:

Took the quiz

Answer:

Raheem

Step-by-step explanation:

The 97% confidence interval for the proportion of adults is 0.801<P<0.851.

Given that 867 adults are randomly selected from 1050 who always wear seat belts.

A confidence interval refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.

Let's assume n=1050 and x=867

Find the sample proportion by dividing the given proportion with sample size as,

[tex]\begin{aligned}\hat{p}&=\frac{x}{n}\\\hat{p}&=\frac{867}{1050}\\ \hat{p}&=0.826 \end[/tex]

Find the α by subtracting the given confidence interval that is 97% from 1 as

α=1-(97÷100)

α=1-0.97

α=0.03

To find the critical value that is [tex]Z_{\frac{\alpha}{2}}[/tex] by dividing alpha with 2,

[tex]\begin{aligned}Z_{\frac{\alpha}{2}}&=Z_{\frac{0.03}{2}}\\ Z_{\frac{\alpha}{2}}&=Z_{0.015}\end[/tex]

From this table which is shown in the figure it says that the critical value is

[tex]Z_{crit}=\pm 2.17[/tex]

Use this formula to find the confidence interval [tex]P=\hat{p}\pm Z_{Crit}\times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]

Substitute the values in the formula,

[tex]\begin{aligned}P&=0.826\pm 2.17\times \sqrt{\frac{0.826(1-0.826)}{1050}}\\ P&=0.826\pm 2.17\times \sqrt{\frac{0.826\times 0.174}{1050}}\\ P&=0.826\pm 2.17\times 0.0116995\\ P&=0.826\pm 0.025\end{aligned}[/tex]

Hence, a 97% confidence interval for the proportion of adults who always wear seat belts is 0.801<P<0.851.

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What would be included to prove both triangles are congruent by the AAS theorem is: B. AB ≅ QN because they are both opposite a right angle.

The AAS congruence theorem states that two triangle are congruent if both have two pairs of corresponding congruent angles and a pair of non-included corresponding congruent sides.

In the image given, since AB and QN both lie opposite a right triangle, then they are congruent to each other.

Therefore, to prove both triangles are congruent by AAS theorem, what would be included is: B. AB ≅ QN because they are both opposite a right angle.

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Answer:

AngleA ≅ AngleQ because of the third angle theorem

Step-by-step explanation:

right on edge

Answer:

22x^2-9x+32

Step-by-step explanation:

(21x² - 6x +14) + (x²-3x+18)

To add, we need to combine like terms

21x^2+x^2     -6x-3x    +14+18

22x^2-9x+32

Answer:

22x² - 9x + 32

Step-by-step explanation:

(21x² - 6x +14) + (x²-3x+18)

Get rid of the parenthesis:

21x² - 6x + 14 + x² - 3x + 18

Group like terms:

22x² - 9x + 32

The true options include the following:

This is defined as a pictorial representation of data or variables in an organized manner.

Function f(x) = (x + 4)(x – 6)

Graph intersects the x-axis at points (-4,0) and (6,0).

x-coordinate of vertex = -4+6/2 = 1

y-coordinate of vertex = (1+4) (1-6) = 5(-5) = -25

The vertex is at the point (1,-25).

The graph is positive for all x< -4 or x>6.

The graph is negative for –4 < x < 6.

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Answer:

Inversión en una circunferencia es una transformación que conserva la magnitud de los ángulos pero cada ángulo se transforma en un ángulo de signo opuesto . El sentido o dirección de cada ángulo se invierte. La inversión en una circunferencia es una transformación anti-conforme(como la reflexión en una recta).

Step-by-step explanation:

El sentido o dirección de cada ángulo se invierte. La inversión en una circunferencia es una transformación anti-conforme(como la reflexión en una recta).

Answer:

inversion transformations are a natural extension of Poincaré transformations to include all conformal one-to-one transformations on coordinate space-time.

The sum of the unknown angle and 33 degrees are supplementary. The measure of x is 147 degrees

The sum of the unknown angle and 33 degrees are supplementary to have:

x + 33 = 180

Subtract 33 from both sides

x + 33 - 33 = 180 - 33

x = 180 - 33

x = 147degrees

Hence the measure of x is 147 degrees

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Answer:

Step-by-step explanation:

x + 33° = 180°

reason :( they are cointerior angle )

x = 180° - 33°

x = 147°

Answer:

117 bags

Step-by-step explanation:

Day 1: 3 bags

Day 2: 3 × 3 = 9 bags

Day 3: 9 × 3 = 27 bags

Day 4: 27 × 3 = 81 bags

Total: 9 + 27 + 81 = 117 bags

Answer:

81 bags of cement in the last 3 days.

Step-by-step explanation:

On the first day he used 3 bags.

The second day he used twice that amount so that would be 3²=9

The third day he used twice the amount he used the second day. So that would be 9²=81.

He used 81 bags of cement in the last 3 days.

Hope this helps!

If not, I am sorry.

Answer:

1/4

Step-by-step explanation:

The ratio of the areas is the square of the ratio of the lengths of sides.

(1/2)² = 1/4

Answer: 1/4

Answer: 11

Step-by-step explanation:

By the secant-secant theorem,

[tex]5(5+7)=(JK)(15)\\\\60=(JK)(15)\\\\JK=4\\\\\implies IJ=15-4=11[/tex]

ΔFGH is congruent to ΔFJH They are not congruent because only one pair of corresponding sides is congruent.

The correct option is (C)

Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.

Given:

ΔFGH and ΔFJH share common side FH. Sides FG and GH are congruent.

As, per the information, it can be seen that the triangles are not congruent as one pair of corresponding side is not congruent.

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Answer: C

Step-by-step explanation: edge

Answer: one

Step-by-step explanation:

     When a system of equations is graphed the solutions are the point of intersections. Here, we only have one point of intersection since these are both linear equations. That means there is only one solution.

Serena should focus on a certain amount and track her spending. Option B

From the information given, Serena wants to reduce debt and to do this she needs to pay attention on how she borrows and the possible way to pay her debts.

Some possible ways to reduce debts include;

Thus, Serena should focus on a certain amount and track her spending. Option B

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