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Elodia [21]
3 years ago
12

Kat has 19 coins, all quarters and dimes, that are worth a total of $4. The system of equations that can be used to the number o

f quarters,q, and the number of dimes,d, she has shown
Mathematics
1 answer:
Luden [163]3 years ago
7 0
<span>q + d=19 0.25q + 0.1d=4 
</span><span> (d) -0.1(q + d=19) 0.25q + 0.1d=4 Opposites cancel -0.1q -0.1 d=1.9 0.25q + 0.1d=4</span>
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Given the following equation of the hyperbola, what are the x-values of the vertices? x^2/4 - y^2/49 = 1 is it 2 and -2?
Jet001 [13]

Answer:

  yes, ±2

Step-by-step explanation:

The x-intercepts are found by setting y=0 and solving for x:

  x^2/4 = 1

  x^2 = 4

  x = ±√4

  x = ±2

The x-values of interest are -2 and +2.

3 0
3 years ago
Erik and Caleb were trying to solve the equation: 0=(3x+2)(x-4) Erik said, "The right-hand side is factored, so I'll use the zer
Mumz [18]

Answer:

C) Both

Step-by-step explanation:

The given equation is:

0=(3x+2)(x-4)

To solve the given equation, we can use the Zero Product Property according to which if the product <em>A.B = 0</em>, then either A = 0 OR B = 0.

Using this property:

(3x+2) = 0 \Rightarrow \bold{x = -\frac{2}{3}}\\(x-4) = 0 \Rightarrow \bold{x = 4}

So, Erik's solution strategy would work.

Now, let us discuss about Caleb's solution strategy:

Multiply (3x+2)(x-4) i.e. 3x^2-12x+2x-8 = 3x^2-10x-8

So, the equation becomes:

0=3x^2-10x-8

Comparing this equation to standard quadratic equation:

ax^2+bx+c=0

a = 3, b = -10, c = -8

So, this can be solved using the quadratic formula.

x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

x=\dfrac{-(-10)\pm\sqrt{(-10)^2-4\times3 \times (-8)}}{2\times 3}\\x=\dfrac{-(-10)\pm\sqrt{196}}{6}\\x=\dfrac{10\pm14}{6} \\\Rightarrow x= 4, -\dfrac{2}{3}

The answer is same from both the approaches.

So, the correct answer is:

C) Both

3 0
3 years ago
Can somebody please help me fill in the blanks for this !!
cupoosta [38]

Answer:it has four side

Step-by-step explanation:

idito

3 0
3 years ago
The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.1. This distribution
cluponka [151]

Answer:

Step-by-step explanation:

Hello!

The definition of the Central Limi Theorem states that:

Be a population with probability function f(X;μ,δ²) from which a random sample of size n is selected. Then the distribution of the sample mean tends to the normal distribution with mean μ and variance δ²/n when the sample size tends to infinity.

As a rule, a sample of size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation.

X[bar]≈N(μ;σ²/n)

If the variable of interest is X: the number of accidents per week at a hazardous intersection.

There is no information about the distribution of this variable, but a sample of n= 52 weeks was taken, and since the sample is large enough you can approximate the distribution of the sample mean to normal. With population mean μ= 2.2 and standard deviation σ/√n= 1.1/√52= 0.15

I hope it helps!

5 0
3 years ago
91 more than the square root of a number
Genrish500 [490]

Answer:

Step-by-step explanation:

y = x 2 + 91

Explanation:

Let the number be  x

, then  Square of the number is  x ^2

91 more than the square of a number" will be  x^ 2  +  91

So, we can write it as an algebraic expression with two variables as :

y = x ^2  +  91

3 0
3 years ago
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