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3 years ago

Cassie’s age is 3 less than twice Kara’s age. The sum of their ages is 42.

Mathematics

2 answers:

rodikova [14]3 years ago

8 0

Answer:

the first blank is 2 the next is 3 and the last is 42

kiruha [24]3 years ago

5 0

Kara: 30 Cassie:12

Step-by-step explanation:

N+2n-3=42

3n-3=42

3n=42+3

3n=45/3

n=15

Karas age: 2n= 30

Cassies age n-3= 12

A: Kara is old 30 years,Cassie is 12

I hope I helped

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Peter attends 6 dance lessons each week all year long a year has 52 weeks peter missed 5 dance lessons while sick how many dance

viktelen [127]

6 lessons per week multiplied by the number of weeks in a year
6 x 52 = 312
total - 5 missed
312 - 5 = 307 dance lessons

5 0

3 years ago

A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh

aleksklad [387]

The spider's movement is an illustration of a parabola.

The equation of a parabola is: $\mathbf{y = -\frac{1}{160}(x - 40) + 10}$
The focus of a parabola is: (40,-30)
The axis of symmetry is: $\mathbf{x = 40}$
The directrix is: $\mathbf{y = 50}$

<u>(a) The equation</u>

The spider passes through the origin.

So, we have:

$\mathbf{(x,y) = (0,0)}$

The spider jumps to a maximum height of 10mm, midway 80mm.

So, the vertex is:

$\mathbf{(h,k) = (40,10)}$

The equation of a parabola is:

$\mathbf{y = a(x - h)^2 + k}$

So, we have:

$\mathbf{0 = a(0 - 40)^2 + 10}$

Subtract 10 from both sides

$\mathbf{a(0 - 40)^2 =- 10}$

$\mathbf{1600a =- 10}$

Solve for a

$\mathbf{a =- \frac{1}{160}}$

Substitute $\mathbf{a =- \frac{1}{160}}$ and $\mathbf{(h,k) = (40,10)}$ in $\mathbf{(h,k) = (40,10)}$

$\mathbf{y = -\frac{1}{160}(x - 40) + 10}$

<u>(b) The focus, directrix and the axis of symmetry</u>

The focus of a parabola is:

$\mathbf{Focus= (h, k + p)}$

Where:

$\mathbf{p = \frac{1}{4a}}$

So, we have:

$\mathbf{p = \frac{1}{4 \times -1/160}}$

$\mathbf{p = -\frac{160}{4}}$

$\mathbf{p = -40}$

So, we have:

$\mathbf{Focus = (40,10-40)}$

$\mathbf{Focus = (40,-30)}$

The axis of symmetry is:

$\mathbf{x = h}$

So, we have:

$\mathbf{x = 40}$

The directrix is:

$\mathbf{y = k - p}$

$\mathbf{y = 10 + 40}$

$\mathbf{y = 50}$

Read more about parabolas at:

brainly.com/question/25237745

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3 years ago

Can somebody please solve this and explain it with steps?

Rina8888 [55]

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In this case, it will be
lat sa = (2 × l × h) + (2 × w × h)
lat sa = (2 × 11 × 4) + (2 × 8 × 4)
lat sa = 88 + 64
lat sa = 152

The lateral surface area is 152 squares unit

5 0

3 years ago

Please help will give 30 points

swat32

2.) 8/12 + 8/4= 2 2/3

3.) 2/8 + 6/10= 17/20

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Hoped this helped!

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3 years ago

Drag the tiles to correct boxes to complete the pairs.

Natasha_Volkova [10]

Answer:

Step-by-step explanation:

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4 years ago

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