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3 years ago

Question 1

Mathematics

1 answer:

Ahat [919]3 years ago

5 0

Answer: x = 22

Explanation:

1) Corresponding sides and correspoding angles of congruent triangles are equal.

2) When you name two congruent triangles the order of the vertices signal which sides and angles are congruents.

That triangle ABC is congruent to triangle DEF means that these are the corresponding parts, which are congruent to each other:

∠A and ∠D are congruent
∠B and ∠ E are congruent
∠C and ∠F are congruent
Segment AB and segment DE are congruent
Segment BC and segment EF are congruent
Segment AC and segment DF are congruent

In the figures, it is given that the segment DF measures (1/2)x - 1 and the corresponding segment AC measures 10 units.

Hence, you set this equation: (1/2)x - 1 = 10

Solving for x:

(1/2)x = 10 + 1
(1/2)x = 11
x = 2(11)
x = 22 ← answer

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Can someone please help me I'm confused as to what I'm supposed to do.

kobusy [5.1K]

I hope this helps you

(fog)(5)=f (g (5))=?

x= 5 g (5)=-4.5+3=-20+3=-17

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4 0

2 years ago

Is 0, 2, 4, 6, a arithmetic sequence

amid [387]

Yes, 0 + 2 = 2
2 + 2 = 4
4 + 2 = 6.
Since they're just ADDING 2, not MULTIPLYING by 2, it's arithmetic, not geometric.

6 0

2 years ago

Read 2 more answers

Angie paid $66.50 for 3.5 yards of fabric. What is the price of 1 yard of fabric?

tatyana61 [14]

Answer:

$19

Step-by-step explanation:

First you need to make a equation out of given information and this will be easiest to solve as an equation.

3.5 $66.50

1 x

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

3.5:1=66.50:x

3.5x=66.50/:3.5

x=19

On the right side you put one information(in this case number of yards) and on the left other information(cost) and you make proportion from up to down and solve for x.

3 0

2 years ago

At the end of the day of teaching the skill of cutting and sewing to make capes, Ms. Ironperson and Mr. Thoro decided to go to t

Thepotemich [5.8K]

Answer:

a) What is the cost of a chicken shawarma wrap?

$10.99

b) What is the cost of one order of spiced potatoes?

$4.99

c) If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?

3x + 2y = $42.95 .............Equation 1

5x + 4y = $74.91 ................Equation 2

Step-by-step explanation:

Let x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes,

Cost of a chicken sharwarma wrap = x

Cost of an order of spiced potatoes = y

Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.

3x + 2y = $42.95 .............Equation 1

Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.

5x + 4y = $74.91 ................Equation 2

Hence, the Equations needed to solve the question is:

3x + 2y = $42.95 .............Equation 1

5x + 4y = $74.91 ................Equation 2

We use Elimination method to solve for this.

Multiply Equation 1 by coefficient of x in Equation 2

Equation 2 by coefficient of x in Equation 1

3x + 2y = $42.95 .............Equation 1 × 5

5x + 4y = $74.91 ................Equation 2 × 3

15x + 10y = 214.75..............Equation 3

15x + 12y = 224.73..............Equation 4

Subtract Equation 3 from Equation 4

2y = 9.98

y = 9.98/2

y = 4.99

Therefore, y = Cost of an order of spiced potatoes = $4.99

Subtitute 4.99 for y in Equation 1

3x + 2y = $42.95 .............Equation 1

3x +2(4.99) = 42.95

3x + 9.98 = 42.95

3x = 42.95 - 9.98

3x = 32.97

x = 32.97/3

x = 10.99

x = Cost of a chicken sharwarma wrap = $10.99

Therefore,

The cost of a chicken sharwarma wrap = $10.99

The cost of an order of spiced potatoes = $4.99

4 0

3 years ago

A survey of 1060 randomly selected US teens ages 13 to 17 found that 605 of them say they have made a new friend online

NikAS [45]

Answer:

The 90% confidence interval for the proportion of all US teens who have made a new friend online is (0.55, 0.60).

Step-by-step explanation:

The complete question is:

A survey of 1060 randomly selected US teens ages 13-17 found that 605 of them say they have made a new friend online. Find and interpret a 90% confidence interval for the proportion, p, of all US teens who have made a new friend online.

Solution:

In a sample of 1060 randomly selected US teens ages 13 to 17, 605 said they have made a new friend online.

Compute the sample proportion of US teens ages 13 to 17 who said they have made a new friend online as follows:

$\hat p=\frac{605}{1060}=0.571$

The (1 - α)% confidence interval for population proportion is:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

The critical value of <em>z</em> for 90% confidence interval is:

$z_{\alpha/2}=z_{0.10/2}=z_{0.05}=1.645$

*use a z-table.

Compute the 90% confidence interval for the proportion of all US teens who have made a new friend online as follows:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

$=0.571\pm 1.645\sqrt{\frac{0.571(1-0.571)}{1060}}\\=0.571\pm 0.025\\=(0.546, 0.596)\\\approx (0.55, 0.60)$

Thus, the 90% confidence interval for the proportion of all US teens who have made a new friend online is (0.55, 0.60).

8 0

3 years ago