Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Sparkles the Clown makes balloon animals for children at birthday parties. At Bridget's party, she made 2 balloon poodles and 4 balloon giraffes, which used a total of 22 balloons. For Erik's party, she used 15 balloons to make 1 balloon poodle and 3 balloon giraffes. How many balloons does each animal require? Each poodle requires balloons and each giraffe requires balloons

The solution of the given equation are; (x + 8)(x − 9)

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

We have been given the quadratic equation as;

x² − x − 72

Solving;

x² − (9-8)x − 72

x² − 9x +8x− 72

The factors are;

(x + 8)(x − 9)

Therefore, the solution of the given equation are; (x + 8)(x − 9)

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Answer:

4

Step-by-step explanation:

so when it says f(x)=-x+1

the x values are constant so what value is in f(x) the value of x goes right into -x+1

f(-3)=-x+1

f(-3)=-(-3)+1

f(-3)=4

Answer:

yea the anwser is 4

（>﹏<）

The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.

The graph is given in the question.

As per the given line, we take two points (0, 4) and (5, 8)

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = 0, y₁ = 4

x₂ = 5, y₂ = 8

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute values in the equation, we get

⇒ y - 4 = (8 - 4)/(5-0 )[x -0]

⇒ y - 4 = (4/5)x

⇒ y = (4/5)x + 4

The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.

So, the equation of the line would be y = (4/5)x + 4.

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If we write a quadratic in vertex form:

\(y=a(x-h)^2+k\)

Then:

\(\bold{a}\)   \(\longrightarrow\)    is the coefficient of \(x^2\)

\(\bold{h}\)   \(\longrightarrow\)    is the axis of symmetry.

\(\bold{k}\)   \(\longrightarrow\)    is the max/min value of the function.

Also:

If \(a > 0\) then the parabola will be of the form \(\cup\) and will have a minimum value.

\(a < 0\) then the parabola will be of the form \(\cap\) and will have a minimum value.

For the given functions:

\(a < 0\)

\(f(x)=-(x-1)^2+5\)        this has a maximum value of \(\bold{5}\)

\(a > 0\)

\(f(x)=(x+2)^2-3\)           this has a minimum value of \(\bold{-3}\)

Answer:

all 3

Step-by-step explanation:

Based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.

To determine whose purple paint will be redder based on the percent of red paint, we need to compare the ratios of red paint to the total paint used by Isaiah and Casho.

Isaiah's Ratio:

Isaiah mixes 3 cups of blue paint and 7 cups of red paint, making a total of 3 + 7 = 10 cups of paint.

To calculate the percent of red paint, we divide the amount of red paint (7 cups) by the total amount of paint (10 cups) and multiply by 100 to get the percentage:

Red paint percentage for Isaiah = (7 cups / 10 cups) * 100 = 70%

Casho's Ratio:

Casho mixes 4 cups of blue paint and 13 cups of red paint, making a total of 4 + 13 = 17 cups of paint.

To calculate the percent of red paint, we divide the amount of red paint (13 cups) by the total amount of paint (17 cups) and multiply by 100 to get the percentage:

Red paint percentage for Casho = (13 cups / 17 cups) * 100 = 76.47% (rounded to two decimal places)

Comparing the percentages, we can see that Casho's purple paint will be redder because Casho's paint has a higher percentage of red paint (76.47%) compared to Isaiah's paint (70%).

Therefore, based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.

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Answer:

he needs $279

Step-by-step explanation:

715-436= 279

Answer:

p = t X 10.25

Step-by-step explanation:

if she makes 10.25 an hour/time then when you multiply it you will get the total pay.

Answer:

One solution

x = 3

Step-by-step explanation:

3x + 5 + 6x - 7 = 25

combine like terms:

9x -2 = 25

add 2 to each side of the equation:

9x = 27

divide both sides by n9:

x = 3

Answer:

0.5a + 0.75p ≤ 23

Step-by-step explanation:

Cost of a apples: 0.5a

Cost of p pears: 0.75p

The total cost must be $23 or less.

0.5a + 0.75p ≤ 23

The solution of the system is then given by:

x = t[1 -1 1 0.5 0.5 0.33] + s[0 -2 1 1 -2 1]

This is the general solution of the system in the form of a sum of scalar multiples of fixed column vectors.

The system of linear equations can be written in matrix form as:

[1 0 1 2 1 3 | 1]

[2 1 2 4 0 10| 5]

[3 1 3 6 6 15| 8]

where the augmented matrix is [A | B].

To solve the system using the method of specifying appropriate free variables, we first convert the coefficient matrix into reduced row echelon form using Gaussian elimination.

In reduced row echelon form, the first non-zero element of each row (known as the leading entry) is 1, and the leading entries of lower rows are to the right of the leading entries of higher rows.

Applying Gaussian elimination to the coefficient matrix, we get:

[1 0 1 2 1 3 | 1]

[0 1 0 2 -2 7| 0]

[0 0 0 0 0 0| 0]

We can see that there are two non-zero rows, indicating that the system has two independent equations.

We can choose two of the variables to be free variables, and express the other variables in terms of the free ones.

Let's choose x1 and x3 as the free variables.

We can find x2 as follows:

x2 = -x1 - 2x3 + 7

And we can find x4, x5 and x6 as follows:

x4 = (1 - x1 - x3)/2

x5 = 1 - x1 - 2x3 + 2x4

x6 = (1 - x1 - x3 - 2x4)/3

So the general solution of the system can be expressed as a sum of scalar multiples of fixed column vectors:

x1 = t

x2 = -t - 2s + 7

x3 = s

x4 = (1 - t - s)/2

x5 = 1 - t - 2s + (1 - t - s)/2

x6 = (1 - t - s)/3

where t and s are scalars.

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\(1\frac{3}{4}\) feet as a multiplication expression using the unit, 1 foot, as a factor is \(1\frac{3}{4}\)×1.

The given fraction is \(1\frac{3}{4}\).

\(1\frac{3}{4}\) feet can be written as a multiplication expression as follows: 1 foot × 1 3/4. This is because \(1\frac{3}{4}\) is the same as 1 + 3/4.

Furthermore, 3/4 can be written as 0.75, which is the same as 0.75 × 1 foot.

Therefore, the multiplication expression is 1 foot × \(1\frac{3}{4}\) = 1 foot × (1 + 0.75) = 1 foot × 1 + 1 foot × 0.75 = 1 foot + 1.75 feet.

Therefore, \(1\frac{3}{4}\) feet as a multiplication expression using the unit, 1 foot, as a factor is \(1\frac{3}{4}\)×1.

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Step-by-step explanation:

1ft=12in

1¾ft=x

x=12×7/4=21in

1¾ft=1¾×1 ft

The salesperson's gross earnings for a week, based on the informations, equals to $1,195.

An employees' gross pay is what they earn before taxes, benefits, and other payroll deductions are deducted from their pay. It is opposite of net pay, also known as take-home pay which is the amount left over after all withholdings are deducted.

Data

Weekly base salary of $600 on a quota of $4500.

On the next $2000, she receives a commission of 11 %.

On any additional sales, the commission rate is 15%.

Gross earning is computed as:

= Base salary + (First sales *11%) + (Additional sales*15%)

= $600 + ($2,000*11%) + ($2,500 * 15%)

= $1,195

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Answer:

1

Step-by-step explanation:

Answer:

Following are the response to the given choice.

Step-by-step explanation:

Please find the complete question in the attached file.

Subjective opinion = Question of opinion.

Therefore this requires only just opinion and we don't have to do any actual calculations.

Does this seem like a great number of girls, a little number of girls, or a decent number of girls to you but if 1,300 babies were born, 5 of whom were females?

This is a small number of beautiful gals, in my honest opinion. We anticipate boys and girls to be produced about the very same frequency, thus I expect some half of them to be females if there are 1 300 newborns. You should have roughly 650 girls if 50% of the infants are girls, but now we only have five. That appears to me to be considerably low. which is your own opinion.

The Speed of onward and return journey will be "20 mph and 10 mph".

Let,

According to the question,

Time taken,

Return Journey travel time,

then,

→ \(\frac{40}{S} -\frac{40}{S+10} =2\)

S = 10, -20 (negative)

→ \(t_1 = \frac{40}{20}\)

      \(= 2 \ hr\)

→ \(t_2 = \frac{40}{10}\)

      \(= 4 \ hr\)

hence,

→ The speed for onward journey will be:

= \(\frac{40}{2}\)

= \(20 \ mph\)

→ The speed for return journey will be:

= \(\frac{40}{4}\)  

= \(10 \ mph\)

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The right response is 400%. In other words, Johnny moves at four times the pace of Jane.

We must compare the speeds of Johnny and Jane in relation to one another in order to get their ratio. According to the issue, Jane moves at a pace that is 1/4 that of Johnny. In other words, Jane moves at a speed that is one-fourth that of Johnny.

We may compare the speeds as a fraction to figure out the ratio:

Johnny's speed divided by Jane's speed equals 4/1.

This indicates that Johnny is moving at a speed that is four times that of Jane. We can express Johnny's speed as 400% of Jane's speed in percentage terms.

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so correlation coefficient = σ^XY/σ^Xσ^Y = 1.225 / 1.36 = 0.9

Step-by-step explanation:                                                                          

a) We need to find the conditional p m f of X when Y = 1.

So, when Y = 1, there are only two X values: X =1 and X =2.

X can have any of the following values: 0, 1, 2, or 3                                                                                                        

so P(0) = 0/ 0.2 = 0          

P(1) = 0.1/(0.1+0.1) = 0.5

P(2) = 0.1/( 0.1+ 0.1) = 0.5

P(3) = 0/ 0.2 = 0

b)  The correlation coefficient of X and Y isρXY              

ρ^XY=(X,Y)=(X,Y)/σ^Xσ^Y=σ^XY/σ^Xσ^Y

We will calculate σ^X first by μ^x

f x(x) = 0.2; x = 0

= 0.2; x =1

= 0.2 ; x = 2

= 0.4 ; x = 3

μ^x = 0.2 * 0 + 0.2 * 1 + 0.2 * 2 + 0.4 * 3 = 1.8

σ^X^ 2 = 0.2 * 1.82 + 0.2 * 0.82 + 0.2 * 0.22 + 0.4 * 1.22 = 1.36

σ^X = 1.166

We will calculate σ^y first by μ^y

f^ x (X) = 0.2; y = 0

= 0.2; y =1

= 0.2 ; y= 2

= 0.4 ; y = 3

μ^y = 0.2 * 0 + 0.2 * 1 + 0.2 * 2 + 0.4 * 3 = 1.8

σ^y^ 2 = 0.2 * 1.82 + 0.2 * 0.82 + 0.2 * 0.22 + 0.4 * 1.22 = 1.36

σ^y = 1.166

Now we will calculate σ^XY

σ^2^XY = 0.4 * ( 3 - 1.8)* ( 3-1.8) + 0.2 *( 0 -1.8) * ( 0 - 1.8) + 0.1 * ( 1- 1.8) * ( 1- 1.8) + 0.1 * ( 2 -1.8) * ( 1 -1.8) + 0.1 * ( 1 - 1.8) * ( 2 - 1.8) + 0.1 * ( 2 - 1.8) * ( 2 - 1.8) = 1.26

σ^XY = 1.225        

so correlation coefficient = σ^XY/σ^Xσ^Y = 1.225 / 1.36 = 0.9

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Answer:

t = 8°

Step-by-step explanation:

We know that the sum of all the angles in a triangle is equal to 180°

Let's set up our equation => 18t + 36 = 180

Subtract 36 from both sides

18t = 144

t = 8

Thus, we have our answer

Answer:

35°

Step-by-step explanation:

Answer:

a) 0.15

b) 0.45

c) 0.16

Step-by-step explanation:

a)

The total probability will add up to 1, so the probability of getting a rat = 1 - 0.35 - 0.4 - 0.1 = 0.15

b)

Probability of cat: 0.35

Probability of hamster: 0.1

Probability of cat or hamster: 0.35+0.1 = 0.45

c)

The probability for getting card out of deck 1: 0.4

The probability for getting card out of deck 1: 0.4

Probability of both: 0.4*0.4 = 0.16

Answer:

The standard form of the equation of a circle with center at (h, k) and radius r is:

(x - h)^2 + (y - k)^2 = r^2

We are given that the center of the circle is (4, -1), so h = 4 and k = -1. We also know that the circle passes through the point (-4, 1), which means that the distance from the center of the circle to (-4, 1) is the radius of the circle.

The distance between two points (x1, y1) and (x2, y2) is given by the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

So the radius of the circle is:

r = sqrt((-4 - 4)^2 + (1 - (-1))^2) = sqrt(100) = 10

Now we can substitute the values of h, k, and r into the standard form equation of a circle:

(x - 4)^2 + (y + 1)^2 = 10^2

Expanding the equation gives:

x^2 - 8x + 16 + y^2 + 2y + 1 = 100

Simplifying and putting the equation in standard form, we get:

x^2 + y^2 - 8x + 2y - 83 = 0

Therefore, the equation in standard form of the circle with center at (4, −1) and that passes through the point (−4, 1) is:

x^2 + y^2 - 8x + 2y - 83 = 0

Answer: C

Step-by-step explanation: I took the test!!

The required distance that the ladder foot away from the base of the wall is √133  meters. Option C is correct.

In a right-angled triangle, its side, such as hypotenuse, perpendicular, and base is Pythagorean triplets.

Here,
Let the base length be x,
According to the question, a 13-meter ladder reach, the foot of the ladder is 6 meters.
So, applying the Pythagoras theorem,
13² = 6² + x²
x = √169 - 36
x = √133

Thus, the required distance that the ladder foot away from the base of the wall is √133  meters.

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Answer:

100k each without tax + interest

Step-by-step explanation:

Answer:

Volume = 105 cm³

Step-by-step explanation:

Volume of a cuboid = l × b × h (l = length. b = breadth. h = height)

Volume = 7 × 5 × 3

Volume = 35 × 3

Volume = 105 cm³

This question is incomplete, the complete question is;

Find an equation of the tangent plane to the surface z=1y²−1x² at the point (-4, 3, -7).

z = .....................

Note: Your answer should be an expression of x and y; e.g. 3x - 4y + 6.

Answer:

Z = 8x + 6y + 7

Step-by-step explanation:

Given that z = 1y² - 1x²

with points (-4, 3, -7)

so

Z = y² - x²

Equation of tangent plane to the surface Z = f(x,y) at the points ( x₀,y₀,z₀) is

Z - Z₀ = fx (x₀,y₀)(x-x₀) + fy (x₀y₀)(y-y₀)

therefore

Z = f(x,y) = y² - x²

fx = -2x, fx (-4, 3, -7) = -2(-4) = 8

fy = -2y, fy ( -4, 3, -7 ) = 6

Z + 7 = 8(x+4) + 6(y-3)

Z + 7 = 8x + 32 + 6y - 18

Z + 7 = 8x + 32 + 6y - 18

Z + 7 = 8x + 6y + 14

Z = 8x + 6y + 14 - 7

Z = 8x + 6y + 7

Answer:

83°

Step-by-step explanation:

Fund the diagram attached. The sum of the ange in the triangle given is 180°, hence;

2x+1+x+15+x = 180

Collect like terms

2x+x+x+1+15 = 180

4x+16 = 180

4x = 180-16

4x = 164

x= 164/4

x =41

Out of the angles the largest angle is 2X+1

Get the largest angle;

2x+1 = 2(41)+1

=82 +1

= 83°

Hence the measure of the largest angle is 83°